LMFDB - Embedded newform 825.2.n.b.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.b.526.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.500000 - 1.53884i) q^{6} +(4.23607 - 3.07768i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.500000 - 1.53884i) q^{6} +(4.23607 - 3.07768i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.23607 - 3.07768i) q^{11} -0.618034 q^{12} +(1.00000 + 3.07768i) q^{13} +(-6.85410 - 4.97980i) q^{14} +(-1.50000 + 4.61653i) q^{16} +(0.618034 - 1.90211i) q^{17} +(1.30902 - 0.951057i) q^{18} +(-4.04508 - 2.93893i) q^{19} +5.23607 q^{21} +(-4.11803 + 3.44095i) q^{22} +4.61803 q^{23} +(-0.690983 - 2.12663i) q^{24} +(4.23607 - 3.07768i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.00000 + 3.07768i) q^{28} +(-0.690983 + 0.502029i) q^{29} +(2.16312 + 6.65740i) q^{31} +3.38197 q^{32} +(0.809017 - 3.21644i) q^{33} -3.23607 q^{34} +(-0.500000 - 0.363271i) q^{36} +(-1.19098 + 0.865300i) q^{37} +(-2.50000 + 7.69421i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(-9.28115 - 6.74315i) q^{41} +(-2.61803 - 8.05748i) q^{42} +9.09017 q^{43} +(1.73607 + 1.08981i) q^{44} +(-2.30902 - 7.10642i) q^{46} +(4.92705 + 3.57971i) q^{47} +(-3.92705 + 2.85317i) q^{48} +(6.30902 - 19.4172i) q^{49} +(1.61803 - 1.17557i) q^{51} +(-1.61803 - 1.17557i) q^{52} +(-1.66312 - 5.11855i) q^{53} +1.61803 q^{54} -11.7082 q^{56} +(-1.54508 - 4.75528i) q^{57} +(1.11803 + 0.812299i) q^{58} +(-5.42705 + 3.94298i) q^{59} +(2.16312 - 6.65740i) q^{61} +(9.16312 - 6.65740i) q^{62} +(4.23607 + 3.07768i) q^{63} +(1.30902 + 4.02874i) q^{64} +(-5.35410 + 0.363271i) q^{66} -11.6180 q^{67} +(0.381966 + 1.17557i) q^{68} +(3.73607 + 2.71441i) q^{69} +(-2.47214 + 7.60845i) q^{71} +(0.690983 - 2.12663i) q^{72} +(3.66312 - 2.66141i) q^{73} +(1.92705 + 1.40008i) q^{74} +3.09017 q^{76} +(-14.7082 - 9.23305i) q^{77} +5.23607 q^{78} +(0.954915 + 2.93893i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-5.73607 + 17.6538i) q^{82} +(2.38197 - 7.33094i) q^{83} +(-2.61803 + 1.90211i) q^{84} +(-4.54508 - 13.9883i) q^{86} -0.854102 q^{87} +(-1.80902 + 7.19218i) q^{88} +4.14590 q^{89} +(13.7082 + 9.95959i) q^{91} +(-2.30902 + 1.67760i) q^{92} +(-2.16312 + 6.65740i) q^{93} +(3.04508 - 9.37181i) q^{94} +(2.73607 + 1.98787i) q^{96} +(0.781153 + 2.40414i) q^{97} -33.0344 q^{98} +(2.54508 - 2.12663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 4 q^{13} - 14 q^{14} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 5 q^{19} + 12 q^{21} - 12 q^{22} + 14 q^{23} - 5 q^{24} + 8 q^{26} + q^{27} - 4 q^{28} - 5 q^{29} - 7 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 2 q^{36} - 7 q^{37} - 10 q^{38} - 4 q^{39} - 17 q^{41} - 6 q^{42} + 14 q^{43} - 2 q^{44} - 7 q^{46} + 13 q^{47} - 9 q^{48} + 23 q^{49} + 2 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} - 20 q^{56} + 5 q^{57} - 15 q^{59} - 7 q^{61} + 21 q^{62} + 8 q^{63} + 3 q^{64} - 8 q^{66} - 42 q^{67} + 6 q^{68} + 6 q^{69} + 8 q^{71} + 5 q^{72} - q^{73} + q^{74} - 10 q^{76} - 32 q^{77} + 12 q^{78} + 15 q^{79} - q^{81} - 14 q^{82} + 14 q^{83} - 6 q^{84} - 7 q^{86} + 10 q^{87} - 5 q^{88} + 30 q^{89} + 28 q^{91} - 7 q^{92} + 7 q^{93} + q^{94} + 2 q^{96} - 17 q^{97} - 74 q^{98} - q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9 + 4 * q^11 + 2 * q^12 + 4 * q^13 - 14 * q^14 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 5 * q^19 + 12 * q^21 - 12 * q^22 + 14 * q^23 - 5 * q^24 + 8 * q^26 + q^27 - 4 * q^28 - 5 * q^29 - 7 * q^31 + 18 * q^32 + q^33 - 4 * q^34 - 2 * q^36 - 7 * q^37 - 10 * q^38 - 4 * q^39 - 17 * q^41 - 6 * q^42 + 14 * q^43 - 2 * q^44 - 7 * q^46 + 13 * q^47 - 9 * q^48 + 23 * q^49 + 2 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 - 20 * q^56 + 5 * q^57 - 15 * q^59 - 7 * q^61 + 21 * q^62 + 8 * q^63 + 3 * q^64 - 8 * q^66 - 42 * q^67 + 6 * q^68 + 6 * q^69 + 8 * q^71 + 5 * q^72 - q^73 + q^74 - 10 * q^76 - 32 * q^77 + 12 * q^78 + 15 * q^79 - q^81 - 14 * q^82 + 14 * q^83 - 6 * q^84 - 7 * q^86 + 10 * q^87 - 5 * q^88 + 30 * q^89 + 28 * q^91 - 7 * q^92 + 7 * q^93 + q^94 + 2 * q^96 - 17 * q^97 - 74 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	−0.956844	−	0.290604i	$-0.906144\pi$
$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	0.603290	−	0.797522i	$-0.293856\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$		0			0
$5$		0			0
$6$	0.500000	−	1.53884i	0.204124	−	0.628230i
$7$	4.23607	−	3.07768i	1.60108	−	1.16326i	0.715683	−	0.698425i	$-0.246115\pi$
$7$	4.23607	−	3.07768i	1.60108	−	1.16326i	0.885400	−	0.464830i	$-0.153885\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$12$	−0.618034			−0.178411
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	0.988588	+	0.150644i	$0.0481349\pi$
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	−0.711238	+	0.702951i	$0.751865\pi$
$14$	−6.85410	−	4.97980i	−1.83184	−	1.33091i
$15$		0			0
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	0.618034	−	1.90211i	0.149895	−	0.461330i	−0.847713	−	0.530456i	$-0.822021\pi$
$17$	0.618034	−	1.90211i	0.149895	−	0.461330i	0.997608	+	0.0691254i	$0.0220209\pi$
$18$	1.30902	−	0.951057i	0.308538	−	0.224166i
$19$	−4.04508	−	2.93893i	−0.928006	−	0.674236i	0.0174977	−	0.999847i	$-0.494430\pi$
$19$	−4.04508	−	2.93893i	−0.928006	−	0.674236i	−0.945504	+	0.325611i	$0.894430\pi$
$20$		0			0
$21$	5.23607			1.14260
$22$	−4.11803	+	3.44095i	−0.877968	+	0.733614i
$23$	4.61803			0.962927			0.481463	−	0.876466i	$-0.340105\pi$
$23$	4.61803			0.962927			0.481463	+	0.876466i	$0.340105\pi$
$24$	−0.690983	−	2.12663i	−0.141046	−	0.434096i
$25$		0			0
$26$	4.23607	−	3.07768i	0.830761	−	0.603583i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−1.00000	+	3.07768i	−0.188982	+	0.581628i
$29$	−0.690983	+	0.502029i	−0.128312	+	0.0932244i	−0.650090	−	0.759857i	$-0.725269\pi$
$29$	−0.690983	+	0.502029i	−0.128312	+	0.0932244i	0.521778	+	0.853081i	$0.325269\pi$
$30$		0			0
$31$	2.16312	+	6.65740i	0.388508	+	1.19570i	0.933904	+	0.357525i	$0.116379\pi$
$31$	2.16312	+	6.65740i	0.388508	+	1.19570i	−0.545396	+	0.838179i	$0.683621\pi$
$32$	3.38197			0.597853
$33$	0.809017	−	3.21644i	0.140832	−	0.559910i
$34$	−3.23607			−0.554981
$35$		0			0
$36$	−0.500000	−	0.363271i	−0.0833333	−	0.0605452i
$37$	−1.19098	+	0.865300i	−0.195796	+	0.142254i	−0.681364	−	0.731945i	$-0.738613\pi$
$37$	−1.19098	+	0.865300i	−0.195796	+	0.142254i	0.485568	+	0.874199i	$0.338613\pi$
$38$	−2.50000	+	7.69421i	−0.405554	+	1.24817i
$39$	−1.00000	+	3.07768i	−0.160128	+	0.492824i
$40$		0			0
$41$	−9.28115	−	6.74315i	−1.44947	−	1.05310i	−0.985954	−	0.167016i	$-0.946587\pi$
$41$	−9.28115	−	6.74315i	−1.44947	−	1.05310i	−0.463518	−	0.886087i	$-0.653413\pi$
$42$	−2.61803	−	8.05748i	−0.403971	−	1.24330i
$43$	9.09017			1.38624			0.693119	−	0.720823i	$-0.256236\pi$
$43$	9.09017			1.38624			0.693119	+	0.720823i	$0.256236\pi$
$44$	1.73607	+	1.08981i	0.261722	+	0.164296i
$45$		0			0
$46$	−2.30902	−	7.10642i	−0.340446	−	1.04778i
$47$	4.92705	+	3.57971i	0.718684	+	0.522155i	0.885964	−	0.463755i	$-0.153498\pi$
$47$	4.92705	+	3.57971i	0.718684	+	0.522155i	−0.167279	+	0.985910i	$0.553498\pi$
$48$	−3.92705	+	2.85317i	−0.566821	+	0.411820i
$49$	6.30902	−	19.4172i	0.901288	−	2.77388i
$50$		0			0
$51$	1.61803	−	1.17557i	0.226570	−	0.164613i
$52$	−1.61803	−	1.17557i	−0.224381	−	0.163022i
$53$	−1.66312	−	5.11855i	−0.228447	−	0.703087i	−0.997923	−	0.0644122i	$-0.979483\pi$
$53$	−1.66312	−	5.11855i	−0.228447	−	0.703087i	0.769476	−	0.638675i	$-0.220517\pi$
$54$	1.61803			0.220187
$55$		0			0
$56$	−11.7082			−1.56457
$57$	−1.54508	−	4.75528i	−0.204652	−	0.629853i
$58$	1.11803	+	0.812299i	0.146805	+	0.106660i
$59$	−5.42705	+	3.94298i	−0.706542	+	0.513333i	−0.882056	−	0.471144i	$-0.843841\pi$
$59$	−5.42705	+	3.94298i	−0.706542	+	0.513333i	0.175514	+	0.984477i	$0.443841\pi$
$60$		0			0
$61$	2.16312	−	6.65740i	0.276959	−	0.852392i	−0.711735	−	0.702448i	$-0.752090\pi$
$61$	2.16312	−	6.65740i	0.276959	−	0.852392i	0.988694	−	0.149945i	$-0.0479095\pi$
$62$	9.16312	−	6.65740i	1.16372	−	0.845490i
$63$	4.23607	+	3.07768i	0.533694	+	0.387752i
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$		0			0
$66$	−5.35410	+	0.363271i	−0.659044	+	0.0447156i
$67$	−11.6180			−1.41937			−0.709684	−	0.704520i	$-0.751162\pi$
$67$	−11.6180			−1.41937			−0.709684	+	0.704520i	$0.751162\pi$
$68$	0.381966	+	1.17557i	0.0463202	+	0.142559i
$69$	3.73607	+	2.71441i	0.449770	+	0.326777i
$70$		0			0
$71$	−2.47214	+	7.60845i	−0.293389	+	0.902957i	0.690369	+	0.723457i	$0.257448\pi$
$71$	−2.47214	+	7.60845i	−0.293389	+	0.902957i	−0.983758	+	0.179500i	$0.942552\pi$
$72$	0.690983	−	2.12663i	0.0814331	−	0.250625i
$73$	3.66312	−	2.66141i	0.428736	−	0.311495i	−0.352408	−	0.935847i	$-0.614637\pi$
$73$	3.66312	−	2.66141i	0.428736	−	0.311495i	0.781143	+	0.624352i	$0.214637\pi$
$74$	1.92705	+	1.40008i	0.224015	+	0.162757i
$75$		0			0
$76$	3.09017			0.354467
$77$	−14.7082	−	9.23305i	−1.67616	−	1.05220i
$78$	5.23607			0.592868
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	0.990295	−	0.138985i	$-0.0443839\pi$
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	−0.882858	+	0.469640i	$0.844384\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−5.73607	+	17.6538i	−0.633443	+	1.94954i
$83$	2.38197	−	7.33094i	0.261455	−	0.804675i	−0.731034	−	0.682341i	$-0.760962\pi$
$83$	2.38197	−	7.33094i	0.261455	−	0.804675i	0.992489	−	0.122334i	$-0.0390380\pi$
$84$	−2.61803	+	1.90211i	−0.285651	+	0.207538i
$85$		0			0
$86$	−4.54508	−	13.9883i	−0.490109	−	1.50840i
$87$	−0.854102			−0.0915693
$88$	−1.80902	+	7.19218i	−0.192842	+	0.766689i
$89$	4.14590			0.439464			0.219732	−	0.975560i	$-0.429482\pi$
$89$	4.14590			0.439464			0.219732	+	0.975560i	$0.429482\pi$
$90$		0			0
$91$	13.7082	+	9.95959i	1.43701	+	1.04405i
$92$	−2.30902	+	1.67760i	−0.240732	+	0.174902i
$93$	−2.16312	+	6.65740i	−0.224305	+	0.690340i
$94$	3.04508	−	9.37181i	0.314077	−	0.966628i
$95$		0			0
$96$	2.73607	+	1.98787i	0.279249	+	0.202886i
$97$	0.781153	+	2.40414i	0.0793141	+	0.244104i	0.982849	−	0.184410i	$-0.0590374\pi$
$97$	0.781153	+	2.40414i	0.0793141	+	0.244104i	−0.903535	+	0.428514i	$0.859037\pi$
$98$	−33.0344			−3.33698
$99$	2.54508	−	2.12663i	0.255791	−	0.213734i
$100$		0			0
$101$	6.04508	+	18.6049i	0.601508	+	1.85125i	0.519213	+	0.854645i	$0.326225\pi$
$101$	6.04508	+	18.6049i	0.601508	+	1.85125i	0.0822950	+	0.996608i	$0.473775\pi$
$102$	−2.61803	−	1.90211i	−0.259224	−	0.188337i
$103$	−3.73607	+	2.71441i	−0.368126	+	0.267459i	−0.756433	−	0.654071i	$-0.773060\pi$
$103$	−3.73607	+	2.71441i	−0.368126	+	0.267459i	0.388308	+	0.921530i	$0.373060\pi$
$104$	2.23607	−	6.88191i	0.219265	−	0.674827i
$105$		0			0
$106$	−7.04508	+	5.11855i	−0.684279	+	0.497158i
$107$	3.11803	+	2.26538i	0.301432	+	0.219003i	0.728211	−	0.685353i	$-0.240352\pi$
$107$	3.11803	+	2.26538i	0.301432	+	0.219003i	−0.426780	+	0.904356i	$0.640352\pi$
$108$	−0.190983	−	0.587785i	−0.0183773	−	0.0565597i
$109$	10.8541			1.03963			0.519817	−	0.854278i	$-0.326000\pi$
$109$	10.8541			1.03963			0.519817	+	0.854278i	$0.326000\pi$
$110$		0			0
$111$	−1.47214			−0.139729
$112$	7.85410	+	24.1724i	0.742143	+	2.28408i
$113$	2.80902	+	2.04087i	0.264250	+	0.191989i	0.712019	−	0.702161i	$-0.247781\pi$
$113$	2.80902	+	2.04087i	0.264250	+	0.191989i	−0.447769	+	0.894150i	$0.647781\pi$
$114$	−6.54508	+	4.75528i	−0.613003	+	0.445373i
$115$		0			0
$116$	0.163119	−	0.502029i	0.0151452	−	0.0466122i
$117$	−2.61803	+	1.90211i	−0.242037	+	0.175850i
$118$	8.78115	+	6.37988i	0.808371	+	0.587316i
$119$	−3.23607	−	9.95959i	−0.296650	−	0.912994i
$120$		0			0
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$	−11.3262			−1.02543
$123$	−3.54508	−	10.9106i	−0.319650	−	0.983780i
$124$	−3.50000	−	2.54290i	−0.314309	−	0.228359i
$125$		0			0
$126$	2.61803	−	8.05748i	0.233233	−	0.717817i
$127$	−0.600813	+	1.84911i	−0.0533135	+	0.164082i	−0.974168	−	0.225824i	$-0.927493\pi$
$127$	−0.600813	+	1.84911i	−0.0533135	+	0.164082i	0.920855	+	0.389906i	$0.127493\pi$
$128$	11.0172	−	8.00448i	0.973794	−	0.707503i
$129$	7.35410	+	5.34307i	0.647493	+	0.470431i
$130$		0			0
$131$	−9.18034			−0.802090			−0.401045	−	0.916058i	$-0.631353\pi$
$131$	−9.18034			−0.802090			−0.401045	+	0.916058i	$0.631353\pi$
$132$	0.763932	+	1.90211i	0.0664917	+	0.165558i
$133$	−26.1803			−2.27012
$134$	5.80902	+	17.8783i	0.501823	+	1.54445i
$135$		0			0
$136$	−3.61803	+	2.62866i	−0.310244	+	0.225405i
$137$	1.63525	−	5.03280i	0.139709	−	0.429981i	−0.856584	−	0.516008i	$-0.827417\pi$
$137$	1.63525	−	5.03280i	0.139709	−	0.429981i	0.996293	+	0.0860276i	$0.0274173\pi$
$138$	2.30902	−	7.10642i	0.196557	−	0.604939i
$139$	0.954915	−	0.693786i	0.0809948	−	0.0588462i	−0.546551	−	0.837426i	$-0.684060\pi$
$139$	0.954915	−	0.693786i	0.0809948	−	0.0588462i	0.627546	+	0.778580i	$0.284060\pi$
$140$		0			0
$141$	1.88197	+	5.79210i	0.158490	+	0.487782i
$142$	12.9443			1.08626
$143$	8.23607	−	6.88191i	0.688735	−	0.575494i
$144$	−4.85410			−0.404508
$145$		0			0
$146$	−5.92705	−	4.30625i	−0.490526	−	0.356388i
$147$	16.5172	−	12.0005i	1.36232	−	0.989782i
$148$	0.281153	−	0.865300i	0.0231106	−	0.0711272i
$149$	−6.21885	+	19.1396i	−0.509468	+	1.56798i	0.283660	+	0.958925i	$0.408451\pi$
$149$	−6.21885	+	19.1396i	−0.509468	+	1.56798i	−0.793127	+	0.609056i	$0.791549\pi$
$150$		0			0
$151$	12.3262	+	8.95554i	1.00310	+	0.728791i	0.962750	−	0.270395i	$-0.0871542\pi$
$151$	12.3262	+	8.95554i	1.00310	+	0.728791i	0.0403454	+	0.999186i	$0.487154\pi$
$152$	3.45492	+	10.6331i	0.280231	+	0.862461i
$153$	2.00000			0.161690
$154$	−6.85410	+	27.2501i	−0.552319	+	2.19588i
$155$		0			0
$156$	−0.618034	−	1.90211i	−0.0494823	−	0.152291i
$157$	−9.97214	−	7.24518i	−0.795863	−	0.578228i	0.113835	−	0.993500i	$-0.463687\pi$
$157$	−9.97214	−	7.24518i	−0.795863	−	0.578228i	−0.909698	+	0.415271i	$0.863687\pi$
$158$	4.04508	−	2.93893i	0.321810	−	0.233808i
$159$	1.66312	−	5.11855i	0.131894	−	0.405928i
$160$		0			0
$161$	19.5623	−	14.2128i	1.54173	−	1.12013i
$162$	1.30902	+	0.951057i	0.102846	+	0.0747221i
$163$	−2.02786	−	6.24112i	−0.158835	−	0.488843i	0.839695	−	0.543059i	$-0.182734\pi$
$163$	−2.02786	−	6.24112i	−0.158835	−	0.488843i	−0.998529	+	0.0542163i	$0.982734\pi$
$164$	7.09017			0.553649
$165$		0			0
$166$	−12.4721			−0.968025
$167$	2.79180	+	8.59226i	0.216036	+	0.664889i	0.999078	+	0.0429216i	$0.0136666\pi$
$167$	2.79180	+	8.59226i	0.216036	+	0.664889i	−0.783043	+	0.621968i	$0.786333\pi$
$168$	−9.47214	−	6.88191i	−0.730791	−	0.530951i
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$		0			0
$171$	1.54508	−	4.75528i	0.118156	−	0.363646i
$172$	−4.54508	+	3.30220i	−0.346559	+	0.251790i
$173$	13.3992	+	9.73508i	1.01872	+	0.740144i	0.966020	−	0.258466i	$-0.0832170\pi$
$173$	13.3992	+	9.73508i	1.01872	+	0.740144i	0.0527010	+	0.998610i	$0.483217\pi$
$174$	0.427051	+	1.31433i	0.0323747	+	0.0996389i
$175$		0			0
$176$	16.0623	−	1.08981i	1.21074	−	0.0821478i
$177$	−6.70820			−0.504219
$178$	−2.07295	−	6.37988i	−0.155374	−	0.478192i
$179$	8.51722	+	6.18812i	0.636607	+	0.462522i	0.858683	−	0.512507i	$-0.171283\pi$
$179$	8.51722	+	6.18812i	0.636607	+	0.462522i	−0.222076	+	0.975029i	$0.571283\pi$
$180$		0			0
$181$	−0.236068	+	0.726543i	−0.0175468	+	0.0540035i	−0.959447	−	0.281891i	$-0.909038\pi$
$181$	−0.236068	+	0.726543i	−0.0175468	+	0.0540035i	0.941900	+	0.335894i	$0.109038\pi$
$182$	8.47214	−	26.0746i	0.627996	−	1.93277i
$183$	5.66312	−	4.11450i	0.418630	−	0.304152i
$184$	−8.35410	−	6.06961i	−0.615873	−	0.447458i
$185$		0			0
$186$	11.3262			0.830480
$187$	−6.61803	+	0.449028i	−0.483959	+	0.0328362i
$188$	−3.76393			−0.274513
$189$	1.61803	+	4.97980i	0.117695	+	0.362227i
$190$		0			0
$191$	13.2812	−	9.64932i	0.960991	−	0.698200i	0.00760993	−	0.999971i	$-0.497578\pi$
$191$	13.2812	−	9.64932i	0.960991	−	0.698200i	0.953381	+	0.301771i	$0.0975777\pi$
$192$	−1.30902	+	4.02874i	−0.0944702	+	0.290749i
$193$	2.48278	−	7.64121i	0.178714	−	0.550026i	−0.821069	−	0.570829i	$-0.806622\pi$
$193$	2.48278	−	7.64121i	0.178714	−	0.550026i	0.999784	+	0.0208024i	$0.00662208\pi$
$194$	3.30902	−	2.40414i	0.237574	−	0.172607i
$195$		0			0
$196$	3.89919	+	12.0005i	0.278513	+	0.857176i
$197$	9.76393			0.695651			0.347826	−	0.937559i	$-0.386920\pi$
$197$	9.76393			0.695651			0.347826	+	0.937559i	$0.386920\pi$
$198$	−4.54508	−	2.85317i	−0.323005	−	0.202766i
$199$	−4.79837			−0.340148			−0.170074	−	0.985431i	$-0.554401\pi$
$199$	−4.79837			−0.340148			−0.170074	+	0.985431i	$0.554401\pi$
$200$		0			0
$201$	−9.39919	−	6.82891i	−0.662968	−	0.481674i
$202$	25.6074	−	18.6049i	1.80173	−	1.30903i
$203$	−1.38197	+	4.25325i	−0.0969950	+	0.298520i
$204$	−0.381966	+	1.17557i	−0.0267430	+	0.0823064i
$205$		0			0
$206$	6.04508	+	4.39201i	0.421181	+	0.306006i
$207$	1.42705	+	4.39201i	0.0991869	+	0.305266i
$208$	−15.7082			−1.08917
$209$	−4.04508	+	16.0822i	−0.279804	+	1.11243i
$210$		0			0
$211$	0.881966	+	2.71441i	0.0607170	+	0.186868i	0.976814	−	0.214088i	$-0.0686780\pi$
$211$	0.881966	+	2.71441i	0.0607170	+	0.186868i	−0.916097	+	0.400956i	$0.868678\pi$
$212$	2.69098	+	1.95511i	0.184817	+	0.134278i
$213$	−6.47214	+	4.70228i	−0.443463	+	0.322195i
$214$	1.92705	−	5.93085i	0.131730	−	0.405425i
$215$		0			0
$216$	1.80902	−	1.31433i	0.123088	−	0.0894287i
$217$	29.6525	+	21.5438i	2.01294	+	1.46249i
$218$	−5.42705	−	16.7027i	−0.367566	−	1.13125i
$219$	4.52786			0.305965
$220$		0			0
$221$	6.47214			0.435363
$222$	0.736068	+	2.26538i	0.0494016	+	0.152043i
$223$	17.0172	+	12.3637i	1.13956	+	0.827937i	0.987058	−	0.160367i	$-0.0512676\pi$
$223$	17.0172	+	12.3637i	1.13956	+	0.827937i	0.152500	+	0.988303i	$0.451268\pi$
$224$	14.3262	−	10.4086i	0.957212	−	0.695455i
$225$		0			0
$226$	1.73607	−	5.34307i	0.115482	−	0.355416i
$227$	−6.51722	+	4.73504i	−0.432563	+	0.314276i	−0.782673	−	0.622433i	$-0.786144\pi$
$227$	−6.51722	+	4.73504i	−0.432563	+	0.314276i	0.350110	+	0.936709i	$0.386144\pi$
$228$	2.50000	+	1.81636i	0.165567	+	0.120291i
$229$	2.13525	+	6.57164i	0.141102	+	0.434266i	0.996489	−	0.0837225i	$-0.0266809\pi$
$229$	2.13525	+	6.57164i	0.141102	+	0.434266i	−0.855387	+	0.517989i	$0.826681\pi$
$230$		0			0
$231$	−6.47214	−	16.1150i	−0.425835	−	1.06029i
$232$	1.90983			0.125386
$233$	3.17376	+	9.76784i	0.207920	+	0.639912i	0.999581	+	0.0289512i	$0.00921676\pi$
$233$	3.17376	+	9.76784i	0.207920	+	0.639912i	−0.791661	+	0.610961i	$0.790783\pi$
$234$	4.23607	+	3.07768i	0.276920	+	0.201194i
$235$		0			0
$236$	1.28115	−	3.94298i	0.0833960	−	0.256666i
$237$	−0.954915	+	2.93893i	−0.0620284	+	0.190904i
$238$	−13.7082	+	9.95959i	−0.888571	+	0.645585i
$239$	−17.8262	−	12.9515i	−1.15308	−	0.837764i	−0.164196	−	0.986428i	$-0.552503\pi$
$239$	−17.8262	−	12.9515i	−1.15308	−	0.837764i	−0.988888	+	0.148664i	$0.952503\pi$
$240$		0			0
$241$	0.618034			0.0398111			0.0199055	−	0.999802i	$-0.493663\pi$
$241$	0.618034			0.0398111			0.0199055	+	0.999802i	$0.493663\pi$
$242$	15.6803	+	8.42075i	1.00797	+	0.541306i
$243$	−1.00000			−0.0641500
$244$	1.33688	+	4.11450i	0.0855850	+	0.263404i
$245$		0			0
$246$	−15.0172	+	10.9106i	−0.957463	+	0.695638i
$247$	5.00000	−	15.3884i	0.318142	−	0.979142i
$248$	4.83688	−	14.8864i	0.307142	−	0.945287i
$249$	6.23607	−	4.53077i	0.395195	−	0.287126i
$250$		0			0
$251$	5.09017	+	15.6659i	0.321289	+	0.988825i	0.973088	+	0.230433i	$0.0740144\pi$
$251$	5.09017	+	15.6659i	0.321289	+	0.988825i	−0.651799	+	0.758391i	$0.725986\pi$
$252$	−3.23607			−0.203853
$253$	−5.70820	−	14.2128i	−0.358872	−	0.893554i
$254$	3.14590			0.197391
$255$		0			0
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	−7.73607	+	5.62058i	−0.482563	+	0.350602i	−0.802317	−	0.596898i	$-0.796400\pi$
$257$	−7.73607	+	5.62058i	−0.482563	+	0.350602i	0.319754	+	0.947500i	$0.396400\pi$
$258$	4.54508	−	13.9883i	0.282965	−	0.870876i
$259$	−2.38197	+	7.33094i	−0.148008	+	0.455522i
$260$		0			0
$261$	−0.690983	−	0.502029i	−0.0427708	−	0.0310748i
$262$	4.59017	+	14.1271i	0.283582	+	0.872775i
$263$	24.2148			1.49315			0.746574	−	0.665303i	$-0.231698\pi$
$263$	24.2148			1.49315			0.746574	+	0.665303i	$0.231698\pi$
$264$	−5.69098	+	4.75528i	−0.350256	+	0.292667i
$265$		0			0
$266$	13.0902	+	40.2874i	0.802610	+	2.47018i
$267$	3.35410	+	2.43690i	0.205268	+	0.149136i
$268$	5.80902	−	4.22050i	0.354842	−	0.257808i
$269$	0.263932	−	0.812299i	0.0160922	−	0.0495268i	−0.942688	−	0.333676i	$-0.891711\pi$
$269$	0.263932	−	0.812299i	0.0160922	−	0.0495268i	0.958780	+	0.284149i	$0.0917110\pi$
$270$		0			0
$271$	−14.8713	+	10.8046i	−0.903369	+	0.656336i	−0.939329	−	0.343018i	$-0.888551\pi$
$271$	−14.8713	+	10.8046i	−0.903369	+	0.656336i	0.0359605	+	0.999353i	$0.488551\pi$
$272$	7.85410	+	5.70634i	0.476225	+	0.345998i
$273$	5.23607	+	16.1150i	0.316901	+	0.975322i
$274$	−8.56231			−0.517268
$275$		0			0
$276$	−2.85410			−0.171797
$277$	7.00000	+	21.5438i	0.420589	+	1.29444i	0.907155	+	0.420797i	$0.138249\pi$
$277$	7.00000	+	21.5438i	0.420589	+	1.29444i	−0.486566	+	0.873644i	$0.661751\pi$
$278$	−1.54508	−	1.12257i	−0.0926680	−	0.0673273i
$279$	−5.66312	+	4.11450i	−0.339042	+	0.246328i
$280$		0			0
$281$	−0.336881	+	1.03681i	−0.0200966	+	0.0618511i	−0.960602	−	0.277928i	$-0.910352\pi$
$281$	−0.336881	+	1.03681i	−0.0200966	+	0.0618511i	0.940505	+	0.339779i	$0.110352\pi$
$282$	7.97214	−	5.79210i	0.474734	−	0.344914i
$283$	12.9721	+	9.42481i	0.771113	+	0.560247i	0.902299	−	0.431111i	$-0.141878\pi$
$283$	12.9721	+	9.42481i	0.771113	+	0.560247i	−0.131185	+	0.991358i	$0.541878\pi$
$284$	−1.52786	−	4.70228i	−0.0906621	−	0.279029i
$285$		0			0
$286$	−14.7082	−	9.23305i	−0.869714	−	0.545962i
$287$	−60.0689			−3.54575
$288$	1.04508	+	3.21644i	0.0615822	+	0.189531i
$289$	10.5172	+	7.64121i	0.618660	+	0.449483i
$290$		0			0
$291$	−0.781153	+	2.40414i	−0.0457920	+	0.140933i
$292$	−0.864745	+	2.66141i	−0.0506054	+	0.155747i
$293$	−20.6074	+	14.9721i	−1.20390	+	0.874682i	−0.994662	−	0.103183i	$-0.967097\pi$
$293$	−20.6074	+	14.9721i	−1.20390	+	0.874682i	−0.209234	+	0.977866i	$0.567097\pi$
$294$	−26.7254	−	19.4172i	−1.55866	−	1.13243i
$295$		0			0
$296$	3.29180			0.191332
$297$	3.30902	−	0.224514i	0.192009	−	0.0130276i
$298$	32.5623			1.88628
$299$	4.61803	+	14.2128i	0.267068	+	0.821950i
$300$		0			0
$301$	38.5066	−	27.9767i	2.21948	−	1.61255i
$302$	7.61803	−	23.4459i	0.438369	−	1.34916i
$303$	−6.04508	+	18.6049i	−0.347281	+	1.06882i
$304$	19.6353	−	14.2658i	1.12616	−	0.818202i
$305$		0			0
$306$	−1.00000	−	3.07768i	−0.0571662	−	0.175939i
$307$	−28.1246			−1.60516			−0.802578	−	0.596547i	$-0.796539\pi$
$307$	−28.1246			−1.60516			−0.802578	+	0.596547i	$0.796539\pi$
$308$	10.7082	−	0.726543i	0.610157	−	0.0413986i
$309$	−4.61803			−0.262711
$310$		0			0
$311$	−10.1353	−	7.36369i	−0.574718	−	0.417557i	0.262098	−	0.965041i	$-0.415586\pi$
$311$	−10.1353	−	7.36369i	−0.574718	−	0.417557i	−0.836816	+	0.547484i	$0.815586\pi$
$312$	5.85410	−	4.25325i	0.331423	−	0.240793i
$313$	−2.61803	+	8.05748i	−0.147980	+	0.455436i	−0.997382	−	0.0723104i	$-0.976963\pi$
$313$	−2.61803	+	8.05748i	−0.147980	+	0.455436i	0.849402	+	0.527746i	$0.176963\pi$
$314$	−6.16312	+	18.9681i	−0.347805	+	1.07043i
$315$		0			0
$316$	−1.54508	−	1.12257i	−0.0869178	−	0.0631495i
$317$	1.10739	+	3.40820i	0.0621973	+	0.191424i	0.977327	−	0.211736i	$-0.0679118\pi$
$317$	1.10739	+	3.40820i	0.0621973	+	0.191424i	−0.915130	+	0.403160i	$0.867912\pi$
$318$	−8.70820			−0.488332
$319$	2.39919	+	1.50609i	0.134329	+	0.0843246i
$320$		0			0
$321$	1.19098	+	3.66547i	0.0664742	+	0.204587i
$322$	−31.6525	−	22.9969i	−1.76392	−	1.28157i
$323$	−8.09017	+	5.87785i	−0.450149	+	0.327052i
$324$	0.190983	−	0.587785i	0.0106102	−	0.0326547i
$325$		0			0
$326$	−8.59017	+	6.24112i	−0.475766	+	0.345664i
$327$	8.78115	+	6.37988i	0.485599	+	0.352808i
$328$	7.92705	+	24.3970i	0.437698	+	1.34710i
$329$	31.8885			1.75807
$330$		0			0
$331$	−27.5967			−1.51685			−0.758427	−	0.651758i	$-0.774032\pi$
$331$	−27.5967			−1.51685			−0.758427	+	0.651758i	$0.774032\pi$
$332$	1.47214	+	4.53077i	0.0807940	+	0.248658i
$333$	−1.19098	−	0.865300i	−0.0652655	−	0.0474181i
$334$	11.8262	−	8.59226i	0.647103	−	0.470148i
$335$		0			0
$336$	−7.85410	+	24.1724i	−0.428476	+	1.31871i
$337$	23.3435	−	16.9600i	1.27160	−	0.923871i	0.272334	−	0.962203i	$-0.412204\pi$
$337$	23.3435	−	16.9600i	1.27160	−	0.923871i	0.999265	+	0.0383318i	$0.0122044\pi$
$338$	−3.30902	−	2.40414i	−0.179987	−	0.130768i
$339$	1.07295	+	3.30220i	0.0582746	+	0.179351i
$340$		0			0
$341$	17.8156	−	14.8864i	0.964769	−	0.806143i
$342$	−8.09017			−0.437466
$343$	−21.7082	−	66.8110i	−1.17213	−	3.60745i
$344$	−16.4443	−	11.9475i	−0.886616	−	0.644164i
$345$		0			0
$346$	8.28115	−	25.4868i	0.445198	−	1.37018i
$347$	8.70820	−	26.8011i	0.467481	−	1.43876i	−0.388355	−	0.921510i	$-0.626956\pi$
$347$	8.70820	−	26.8011i	0.467481	−	1.43876i	0.855835	−	0.517248i	$-0.173044\pi$
$348$	0.427051	−	0.310271i	0.0228923	−	0.0166323i
$349$	−26.0795	−	18.9479i	−1.39601	−	1.01426i	−0.995176	−	0.0981041i	$-0.968722\pi$
$349$	−26.0795	−	18.9479i	−1.39601	−	1.01426i	−0.400829	−	0.916153i	$-0.631278\pi$
$350$		0			0
$351$	−3.23607			−0.172729
$352$	−4.18034	−	10.4086i	−0.222813	−	0.554781i
$353$	17.8328			0.949145			0.474573	−	0.880216i	$-0.342603\pi$
$353$	17.8328			0.949145			0.474573	+	0.880216i	$0.342603\pi$
$354$	3.35410	+	10.3229i	0.178269	+	0.548654i
$355$		0			0
$356$	−2.07295	+	1.50609i	−0.109866	+	0.0798224i
$357$	3.23607	−	9.95959i	0.171271	−	0.527118i
$358$	5.26393	−	16.2007i	0.278207	−	0.856234i
$359$	−2.66312	+	1.93487i	−0.140554	+	0.102118i	−0.655840	−	0.754900i	$-0.727686\pi$
$359$	−2.66312	+	1.93487i	−0.140554	+	0.102118i	0.515286	+	0.857018i	$0.327686\pi$
$360$		0			0
$361$	1.85410	+	5.70634i	0.0975843	+	0.300334i
$362$	1.23607			0.0649663
$363$	−10.8992	+	1.48584i	−0.572059	+	0.0779864i
$364$	−10.4721			−0.548889
$365$		0			0
$366$	−9.16312	−	6.65740i	−0.478964	−	0.347988i
$367$	−17.8992	+	13.0045i	−0.934330	+	0.678830i	−0.947049	−	0.321089i	$-0.895951\pi$
$367$	−17.8992	+	13.0045i	−0.934330	+	0.678830i	0.0127192	+	0.999919i	$0.495951\pi$
$368$	−6.92705	+	21.3193i	−0.361097	+	1.11134i
$369$	3.54508	−	10.9106i	0.184550	−	0.567986i
$370$		0			0
$371$	−22.7984	−	16.5640i	−1.18363	−	0.859959i
$372$	−1.33688	−	4.11450i	−0.0693141	−	0.213327i
$373$	−32.7426			−1.69535			−0.847675	−	0.530516i	$-0.821998\pi$
$373$	−32.7426			−1.69535			−0.847675	+	0.530516i	$0.821998\pi$
$374$	4.00000	+	9.95959i	0.206835	+	0.514998i
$375$		0			0
$376$	−4.20820	−	12.9515i	−0.217022	−	0.667924i
$377$	−2.23607	−	1.62460i	−0.115163	−	0.0836711i
$378$	6.85410	−	4.97980i	0.352537	−	0.256133i
$379$	−1.54508	+	4.75528i	−0.0793657	+	0.244262i	−0.982865	−	0.184327i	$-0.940989\pi$
$379$	−1.54508	+	4.75528i	−0.0793657	+	0.244262i	0.903499	+	0.428590i	$0.140989\pi$
$380$		0			0
$381$	−1.57295	+	1.14281i	−0.0805846	+	0.0585482i
$382$	−21.4894	−	15.6129i	−1.09949	−	0.798827i
$383$	4.12868	+	12.7068i	0.210966	+	0.649285i	0.999415	+	0.0341862i	$0.0108839\pi$
$383$	4.12868	+	12.7068i	0.210966	+	0.649285i	−0.788450	+	0.615099i	$0.789116\pi$
$384$	13.6180			0.694942
$385$		0			0
$386$	−13.0000			−0.661683
$387$	2.80902	+	8.64527i	0.142790	+	0.439464i
$388$	−1.26393	−	0.918300i	−0.0641664	−	0.0466196i
$389$	17.0344	−	12.3762i	0.863680	−	0.627501i	−0.0652033	−	0.997872i	$-0.520770\pi$
$389$	17.0344	−	12.3762i	0.863680	−	0.627501i	0.928884	+	0.370371i	$0.120770\pi$
$390$		0			0
$391$	2.85410	−	8.78402i	0.144338	−	0.444227i
$392$	−36.9336	+	26.8339i	−1.86543	+	1.35531i
$393$	−7.42705	−	5.39607i	−0.374645	−	0.272196i
$394$	−4.88197	−	15.0251i	−0.245950	−	0.756956i
$395$		0			0
$396$	−0.500000	+	1.98787i	−0.0251259	+	0.0998942i
$397$	2.72949			0.136989			0.0684946	−	0.997651i	$-0.478180\pi$
$397$	2.72949			0.136989			0.0684946	+	0.997651i	$0.478180\pi$
$398$	2.39919	+	7.38394i	0.120260	+	0.370123i
$399$	−21.1803	−	15.3884i	−1.06034	−	0.770384i
$400$		0			0
$401$	−9.54508	+	29.3768i	−0.476659	+	1.46700i	0.367049	+	0.930202i	$0.380368\pi$
$401$	−9.54508	+	29.3768i	−0.476659	+	1.46700i	−0.843707	+	0.536803i	$0.819632\pi$
$402$	−5.80902	+	17.8783i	−0.289727	+	0.891689i
$403$	−18.3262	+	13.3148i	−0.912895	+	0.663257i
$404$	−9.78115	−	7.10642i	−0.486631	−	0.353558i
$405$		0			0
$406$	7.23607			0.359120
$407$	4.13525	+	2.59590i	0.204977	+	0.128674i
$408$	−4.47214			−0.221404
$409$	−8.12868	−	25.0175i	−0.401937	−	1.23704i	−0.923426	−	0.383777i	$-0.874623\pi$
$409$	−8.12868	−	25.0175i	−0.401937	−	1.23704i	0.521488	−	0.853258i	$-0.325377\pi$
$410$		0			0
$411$	4.28115	−	3.11044i	0.211174	−	0.153427i
$412$	0.881966	−	2.71441i	0.0434513	−	0.133729i
$413$	−10.8541	+	33.4055i	−0.534095	+	1.64378i
$414$	6.04508	−	4.39201i	0.297100	−	0.215856i
$415$		0			0
$416$	3.38197	+	10.4086i	0.165815	+	0.510325i
$417$	1.18034			0.0578015
$418$	26.7705	−	1.81636i	1.30939	−	0.0888409i
$419$	−24.5967			−1.20163			−0.600815	−	0.799388i	$-0.705157\pi$
$419$	−24.5967			−1.20163			−0.600815	+	0.799388i	$0.705157\pi$
$420$		0			0
$421$	3.11803	+	2.26538i	0.151964	+	0.110408i	0.661169	−	0.750237i	$-0.270061\pi$
$421$	3.11803	+	2.26538i	0.151964	+	0.110408i	−0.509205	+	0.860645i	$0.670061\pi$
$422$	3.73607	−	2.71441i	0.181869	−	0.132136i
$423$	−1.88197	+	5.79210i	−0.0915043	+	0.281621i
$424$	−3.71885	+	11.4454i	−0.180603	+	0.555839i
$425$		0			0
$426$	10.4721	+	7.60845i	0.507377	+	0.368631i
$427$	−11.3262	−	34.8586i	−0.548115	−	1.68692i
$428$	−2.38197			−0.115137
$429$	10.7082	−	0.726543i	0.516997	−	0.0350778i
$430$		0			0
$431$	−4.90983	−	15.1109i	−0.236498	−	0.727867i	−0.996919	−	0.0784361i	$-0.975007\pi$
$431$	−4.90983	−	15.1109i	−0.236498	−	0.727867i	0.760421	−	0.649431i	$-0.224993\pi$
$432$	−3.92705	−	2.85317i	−0.188940	−	0.137273i
$433$	0.836881	−	0.608030i	0.0402179	−	0.0292200i	−0.567495	−	0.823377i	$-0.692087\pi$
$433$	0.836881	−	0.608030i	0.0402179	−	0.0292200i	0.607713	+	0.794157i	$0.292087\pi$
$434$	18.3262	−	56.4024i	0.879688	−	2.70740i
$435$		0			0
$436$	−5.42705	+	3.94298i	−0.259909	+	0.188835i
$437$	−18.6803	−	13.5721i	−0.893602	−	0.649240i
$438$	−2.26393	−	6.96767i	−0.108175	−	0.332928i
$439$	25.3262			1.20876			0.604378	−	0.796698i	$-0.293422\pi$
$439$	25.3262			1.20876			0.604378	+	0.796698i	$0.293422\pi$
$440$		0			0
$441$	20.4164			0.972210
$442$	−3.23607	−	9.95959i	−0.153924	−	0.473730i
$443$	6.69098	+	4.86128i	0.317898	+	0.230967i	0.735278	−	0.677766i	$-0.237052\pi$
$443$	6.69098	+	4.86128i	0.317898	+	0.230967i	−0.417380	+	0.908732i	$0.637052\pi$
$444$	0.736068	−	0.534785i	0.0349322	−	0.0253798i
$445$		0			0
$446$	10.5172	−	32.3687i	0.498005	−	1.53270i
$447$	−16.2812	+	11.8290i	−0.770072	+	0.559490i
$448$	17.9443	+	13.0373i	0.847787	+	0.615953i
$449$	−10.5902	−	32.5932i	−0.499781	−	1.53817i	−0.809371	−	0.587298i	$-0.800192\pi$
$449$	−10.5902	−	32.5932i	−0.499781	−	1.53817i	0.309590	−	0.950870i	$-0.399808\pi$
$450$		0			0
$451$	−9.28115	+	36.8994i	−0.437032	+	1.73753i
$452$	−2.14590			−0.100935
$453$	4.70820	+	14.4904i	0.221211	+	0.680817i
$454$	10.5451	+	7.66145i	0.494905	+	0.359570i
$455$		0			0
$456$	−3.45492	+	10.6331i	−0.161791	+	0.497942i
$457$	−2.30902	+	7.10642i	−0.108011	+	0.332424i	−0.990425	−	0.138049i	$-0.955917\pi$
$457$	−2.30902	+	7.10642i	−0.108011	+	0.332424i	0.882414	+	0.470473i	$0.155917\pi$
$458$	9.04508	−	6.57164i	0.422649	−	0.307073i
$459$	1.61803	+	1.17557i	0.0755234	+	0.0548709i
$460$		0			0
$461$	8.05573			0.375193			0.187596	−	0.982246i	$-0.439930\pi$
$461$	8.05573			0.375193			0.187596	+	0.982246i	$0.439930\pi$
$462$	−21.5623	+	18.0171i	−1.00317	+	0.838230i
$463$	0.270510			0.0125717			0.00628583	−	0.999980i	$-0.497999\pi$
$463$	0.270510			0.0125717			0.00628583	+	0.999980i	$0.497999\pi$
$464$	−1.28115	−	3.94298i	−0.0594760	−	0.183048i
$465$		0			0
$466$	13.4443	−	9.76784i	0.622794	−	0.452486i
$467$	−9.54508	+	29.3768i	−0.441694	+	1.35939i	0.444375	+	0.895841i	$0.353426\pi$
$467$	−9.54508	+	29.3768i	−0.441694	+	1.35939i	−0.886069	+	0.463553i	$0.846574\pi$
$468$	0.618034	−	1.90211i	0.0285686	−	0.0879252i
$469$	−49.2148	+	35.7566i	−2.27253	+	1.65109i
$470$		0			0
$471$	−3.80902	−	11.7229i	−0.175510	−	0.540165i
$472$	15.0000			0.690431
$473$	−11.2361	−	27.9767i	−0.516635	−	1.28637i
$474$	5.00000			0.229658
$475$		0			0
$476$	5.23607	+	3.80423i	0.239995	+	0.174366i
$477$	4.35410	−	3.16344i	0.199361	−	0.144844i
$478$	−11.0172	+	33.9075i	−0.503916	+	1.55089i
$479$	2.03444	−	6.26137i	0.0929560	−	0.286089i	−0.893760	−	0.448546i	$-0.851942\pi$
$479$	2.03444	−	6.26137i	0.0929560	−	0.286089i	0.986716	+	0.162457i	$0.0519419\pi$
$480$		0			0
$481$	−3.85410	−	2.80017i	−0.175732	−	0.127677i
$482$	−0.309017	−	0.951057i	−0.0140753	−	0.0433194i
$483$	24.1803			1.10024
$484$	1.20820	−	6.69015i	0.0549184	−	0.304098i
$485$		0			0
$486$	0.500000	+	1.53884i	0.0226805	+	0.0698033i
$487$	−6.61803	−	4.80828i	−0.299892	−	0.217884i	0.427655	−	0.903942i	$-0.359340\pi$
$487$	−6.61803	−	4.80828i	−0.299892	−	0.217884i	−0.727547	+	0.686058i	$0.759340\pi$
$488$	−12.6631	+	9.20029i	−0.573232	+	0.416478i
$489$	2.02786	−	6.24112i	0.0917032	−	0.282233i
$490$		0			0
$491$	−5.82624	+	4.23301i	−0.262934	+	0.191033i	−0.711440	−	0.702747i	$-0.751957\pi$
$491$	−5.82624	+	4.23301i	−0.262934	+	0.191033i	0.448505	+	0.893780i	$0.351957\pi$
$492$	5.73607	+	4.16750i	0.258602	+	0.187885i
$493$	0.527864	+	1.62460i	0.0237738	+	0.0731682i
$494$	−26.1803			−1.17791
$495$		0			0
$496$	−33.9787			−1.52569
$497$	12.9443	+	39.8384i	0.580630	+	1.78700i
$498$	−10.0902	−	7.33094i	−0.452151	−	0.328507i
$499$	−9.04508	+	6.57164i	−0.404914	+	0.294187i	−0.771539	−	0.636182i	$-0.780513\pi$
$499$	−9.04508	+	6.57164i	−0.404914	+	0.294187i	0.366626	+	0.930368i	$0.380513\pi$
$500$		0			0
$501$	−2.79180	+	8.59226i	−0.124728	+	0.383874i
$502$	21.5623	−	15.6659i	0.962373	−	0.699205i
$503$	−11.2361	−	8.16348i	−0.500992	−	0.363992i	0.308404	−	0.951255i	$-0.400205\pi$
$503$	−11.2361	−	8.16348i	−0.500992	−	0.363992i	−0.809396	+	0.587264i	$0.800205\pi$
$504$	−3.61803	−	11.1352i	−0.161160	−	0.496000i
$505$		0			0
$506$	−19.0172	+	15.8904i	−0.845419	+	0.706416i
$507$	2.52786			0.112266
$508$	−0.371323	−	1.14281i	−0.0164748	−	0.0507042i
$509$	−7.66312	−	5.56758i	−0.339662	−	0.246779i	0.404857	−	0.914380i	$-0.367321\pi$
$509$	−7.66312	−	5.56758i	−0.339662	−	0.246779i	−0.744519	+	0.667601i	$0.767321\pi$
$510$		0			0
$511$	7.32624	−	22.5478i	0.324094	−	0.997458i
$512$	1.63525	−	5.03280i	0.0722687	−	0.222420i
$513$	4.04508	−	2.93893i	0.178595	−	0.129757i
$514$	12.5172	+	9.09429i	0.552111	+	0.401132i
$515$		0			0
$516$	−5.61803			−0.247320
$517$	4.92705	−	19.5887i	0.216691	−	0.861509i
$518$	12.4721			0.547994
$519$	5.11803	+	15.7517i	0.224657	+	0.691422i
$520$		0			0
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.970412	−	0.241453i	$-0.922376\pi$
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.0702381	+	0.997530i	$0.522376\pi$
$522$	−0.427051	+	1.31433i	−0.0186915	+	0.0575266i
$523$	1.16312	−	3.57971i	0.0508596	−	0.156530i	−0.922401	−	0.386234i	$-0.873776\pi$
$523$	1.16312	−	3.57971i	0.0508596	−	0.156530i	0.973261	+	0.229704i	$0.0737758\pi$
$524$	4.59017	−	3.33495i	0.200523	−	0.145688i
$525$		0			0
$526$	−12.1074	−	37.2627i	−0.527907	−	1.62473i
$527$	14.0000			0.609850
$528$	13.6353	+	8.55951i	0.593398	+	0.372505i
$529$	−1.67376			−0.0727723
$530$		0			0
$531$	−5.42705	−	3.94298i	−0.235514	−	0.171111i
$532$	13.0902	−	9.51057i	0.567531	−	0.412335i
$533$	11.4721	−	35.3076i	0.496913	−	1.52934i
$534$	2.07295	−	6.37988i	0.0897053	−	0.276084i
$535$		0			0
$536$	21.0172	+	15.2699i	0.907806	+	0.659559i
$537$	3.25329	+	10.0126i	0.140390	+	0.432075i
$538$	−1.38197			−0.0595808
$539$	−67.5582	+	4.58377i	−2.90994	+	0.197437i
$540$		0			0
$541$	−0.500000	−	1.53884i	−0.0214967	−	0.0661600i	0.939733	−	0.341910i	$-0.111074\pi$
$541$	−0.500000	−	1.53884i	−0.0214967	−	0.0661600i	−0.961229	+	0.275750i	$0.911074\pi$
$542$	24.0623	+	17.4823i	1.03356	+	0.750929i
$543$	−0.618034	+	0.449028i	−0.0265224	+	0.0192696i
$544$	2.09017	−	6.43288i	0.0896153	−	0.275808i
$545$		0			0
$546$	22.1803	−	16.1150i	0.949231	−	0.689657i
$547$	−15.6631	−	11.3799i	−0.669707	−	0.486570i	0.200220	−	0.979751i	$-0.435834\pi$
$547$	−15.6631	−	11.3799i	−0.669707	−	0.486570i	−0.869927	+	0.493181i	$0.835834\pi$
$548$	1.01064	+	3.11044i	0.0431725	+	0.132871i
$549$	7.00000			0.298753
$550$		0			0
$551$	4.27051			0.181930
$552$	−3.19098	−	9.82084i	−0.135817	−	0.418003i
$553$	13.0902	+	9.51057i	0.556651	+	0.404430i
$554$	29.6525	−	21.5438i	1.25981	−	0.915308i
$555$		0			0
$556$	−0.225425	+	0.693786i	−0.00956014	+	0.0294231i
$557$	34.2984	−	24.9192i	1.45327	−	1.05586i	0.468215	−	0.883615i	$-0.344897\pi$
$557$	34.2984	−	24.9192i	1.45327	−	1.05586i	0.985054	−	0.172247i	$-0.0551027\pi$
$558$	9.16312	+	6.65740i	0.387906	+	0.281830i
$559$	9.09017	+	27.9767i	0.384473	+	1.18329i
$560$		0			0
$561$	−5.61803	−	3.52671i	−0.237194	−	0.148898i
$562$	1.76393			0.0744070
$563$	6.38854	+	19.6619i	0.269245	+	0.828651i	0.990685	+	0.136174i	$0.0434806\pi$
$563$	6.38854	+	19.6619i	0.269245	+	0.828651i	−0.721440	+	0.692477i	$0.756519\pi$
$564$	−3.04508	−	2.21238i	−0.128221	−	0.0931582i
$565$		0			0
$566$	8.01722	−	24.6745i	0.336989	−	1.03715i
$567$	−1.61803	+	4.97980i	−0.0679510	+	0.209132i
$568$	14.4721	−	10.5146i	0.607237	−	0.441184i
$569$	18.2533	+	13.2618i	0.765218	+	0.555963i	0.900506	−	0.434843i	$-0.143196\pi$
$569$	18.2533	+	13.2618i	0.765218	+	0.555963i	−0.135289	+	0.990806i	$0.543196\pi$
$570$		0			0
$571$	−11.0902			−0.464109			−0.232055	−	0.972703i	$-0.574545\pi$
$571$	−11.0902			−0.464109			−0.232055	+	0.972703i	$0.574545\pi$
$572$	−1.61803	+	6.43288i	−0.0676534	+	0.268972i
$573$	16.4164			0.685805
$574$	30.0344	+	92.4365i	1.25361	+	3.85823i
$575$		0			0
$576$	−3.42705	+	2.48990i	−0.142794	+	0.103746i
$577$	9.27458	−	28.5442i	0.386106	−	1.18831i	−0.549569	−	0.835448i	$-0.685208\pi$
$577$	9.27458	−	28.5442i	0.386106	−	1.18831i	0.935675	−	0.352863i	$-0.114792\pi$
$578$	6.50000	−	20.0049i	0.270364	−	0.832096i
$579$	6.50000	−	4.72253i	0.270131	−	0.196262i
$580$		0			0
$581$	−12.4721	−	38.3853i	−0.517431	−	1.59249i
$582$	4.09017			0.169543
$583$	−13.6976	+	11.4454i	−0.567295	+	0.474021i
$584$	−10.1246			−0.418959
$585$		0			0
$586$	33.3435	+	24.2254i	1.37741	+	1.00074i
$587$	17.4894	−	12.7068i	0.721863	−	0.524464i	−0.165116	−	0.986274i	$-0.552800\pi$
$587$	17.4894	−	12.7068i	0.721863	−	0.524464i	0.886979	+	0.461810i	$0.152800\pi$
$588$	−3.89919	+	12.0005i	−0.160800	+	0.494891i
$589$	10.8156	−	33.2870i	0.445649	−	1.37157i
$590$		0			0
$591$	7.89919	+	5.73910i	0.324929	+	0.236075i
$592$	−2.20820	−	6.79615i	−0.0907566	−	0.279320i
$593$	3.11146			0.127772			0.0638861	−	0.997957i	$-0.479651\pi$
$593$	3.11146			0.127772			0.0638861	+	0.997957i	$0.479651\pi$
$594$	−2.00000	−	4.97980i	−0.0820610	−	0.204324i
$595$		0			0
$596$	−3.84346	−	11.8290i	−0.157434	−	0.484533i
$597$	−3.88197	−	2.82041i	−0.158878	−	0.115432i
$598$	19.5623	−	14.2128i	0.799962	−	0.581207i
$599$	−5.48936	+	16.8945i	−0.224289	+	0.690291i	0.774074	+	0.633095i	$0.218216\pi$
$599$	−5.48936	+	16.8945i	−0.224289	+	0.690291i	−0.998363	+	0.0571955i	$0.981784\pi$
$600$		0			0
$601$	8.38197	−	6.08985i	0.341908	−	0.248410i	−0.403559	−	0.914954i	$-0.632227\pi$
$601$	8.38197	−	6.08985i	0.341908	−	0.248410i	0.745466	+	0.666543i	$0.232227\pi$
$602$	−62.3050	−	45.2672i	−2.53936	−	1.84495i
$603$	−3.59017	−	11.0494i	−0.146203	−	0.449967i
$604$	−9.41641			−0.383148
$605$		0			0
$606$	31.6525			1.28579
$607$	−10.1976	−	31.3849i	−0.413906	−	1.27387i	−0.913226	−	0.407454i	$-0.866417\pi$
$607$	−10.1976	−	31.3849i	−0.413906	−	1.27387i	0.499319	−	0.866418i	$-0.333583\pi$
$608$	−13.6803	−	9.93935i	−0.554811	−	0.403094i
$609$	−3.61803	+	2.62866i	−0.146610	+	0.106518i
$610$		0			0
$611$	−6.09017	+	18.7436i	−0.246382	+	0.758286i
$612$	−1.00000	+	0.726543i	−0.0404226	+	0.0293687i
$613$	−3.04508	−	2.21238i	−0.122990	−	0.0893573i	0.524590	−	0.851355i	$-0.324219\pi$
$613$	−3.04508	−	2.21238i	−0.122990	−	0.0893573i	−0.647580	+	0.761998i	$0.724219\pi$
$614$	14.0623	+	43.2793i	0.567508	+	1.74661i
$615$		0			0
$616$	14.4721	+	36.0341i	0.583099	+	1.45186i
$617$	42.2492			1.70089			0.850445	−	0.526064i	$-0.176333\pi$
$617$	42.2492			1.70089			0.850445	+	0.526064i	$0.176333\pi$
$618$	2.30902	+	7.10642i	0.0928823	+	0.285862i
$619$	−34.6976	−	25.2093i	−1.39461	−	1.01325i	−0.995341	−	0.0964126i	$-0.969263\pi$
$619$	−34.6976	−	25.2093i	−1.39461	−	1.01325i	−0.399271	−	0.916833i	$-0.630737\pi$
$620$		0			0
$621$	−1.42705	+	4.39201i	−0.0572656	+	0.176245i
$622$	−6.26393	+	19.2784i	−0.251161	+	0.772993i
$623$	17.5623	−	12.7598i	0.703619	−	0.511209i
$624$	−12.7082	−	9.23305i	−0.508735	−	0.369618i
$625$		0			0
$626$	13.7082			0.547890
$627$	−12.7254	+	10.6331i	−0.508205	+	0.424647i
$628$	7.61803			0.303993
$629$	0.909830	+	2.80017i	0.0362773	+	0.111650i
$630$		0			0
$631$	32.0623	−	23.2946i	1.27638	−	0.927345i	0.276943	−	0.960886i	$-0.410679\pi$
$631$	32.0623	−	23.2946i	1.27638	−	0.927345i	0.999437	+	0.0335418i	$0.0106787\pi$
$632$	2.13525	−	6.57164i	0.0849359	−	0.261406i
$633$	−0.881966	+	2.71441i	−0.0350550	+	0.107888i
$634$	4.69098	−	3.40820i	0.186303	−	0.135357i
$635$		0			0
$636$	1.02786	+	3.16344i	0.0407575	+	0.125439i
$637$	66.0689			2.61774
$638$	1.11803	−	4.44501i	0.0442634	−	0.175980i
$639$	−8.00000			−0.316475
$640$		0			0
$641$	−3.42705	−	2.48990i	−0.135360	−	0.0983451i	0.518045	−	0.855354i	$-0.326660\pi$
$641$	−3.42705	−	2.48990i	−0.135360	−	0.0983451i	−0.653405	+	0.757009i	$0.726660\pi$
$642$	5.04508	−	3.66547i	0.199114	−	0.144665i
$643$	−4.22542	+	13.0045i	−0.166634	+	0.512848i	−0.999153	−	0.0411490i	$-0.986898\pi$
$643$	−4.22542	+	13.0045i	−0.166634	+	0.512848i	0.832519	+	0.553997i	$0.186898\pi$
$644$	−4.61803	+	14.2128i	−0.181976	+	0.560065i
$645$		0			0
$646$	13.0902	+	9.51057i	0.515026	+	0.374188i
$647$	9.76393	+	30.0503i	0.383860	+	1.18140i	0.937304	+	0.348513i	$0.113313\pi$
$647$	9.76393	+	30.0503i	0.383860	+	1.18140i	−0.553444	+	0.832886i	$0.686687\pi$
$648$	2.23607			0.0878410
$649$	18.8435	+	11.8290i	0.739670	+	0.464327i
$650$		0			0
$651$	11.3262	+	34.8586i	0.443910	+	1.36622i
$652$	3.28115	+	2.38390i	0.128500	+	0.0933606i
$653$	−35.2426	+	25.6053i	−1.37915	+	1.00201i	−0.382192	+	0.924083i	$0.624831\pi$
$653$	−35.2426	+	25.6053i	−1.37915	+	1.00201i	−0.996959	+	0.0779293i	$0.975169\pi$
$654$	5.42705	−	16.7027i	0.212214	−	0.653129i
$655$		0			0
$656$	45.0517	−	32.7319i	1.75897	−	1.27797i
$657$	3.66312	+	2.66141i	0.142912	+	0.103832i
$658$	−15.9443	−	49.0714i	−0.621572	−	1.91300i
$659$	42.0344			1.63743			0.818715	−	0.574201i	$-0.194687\pi$
$659$	42.0344			1.63743			0.818715	+	0.574201i	$0.194687\pi$
$660$		0			0
$661$	15.0902			0.586940			0.293470	−	0.955968i	$-0.405190\pi$
$661$	15.0902			0.586940			0.293470	+	0.955968i	$0.405190\pi$
$662$	13.7984	+	42.4670i	0.536289	+	1.65053i
$663$	5.23607	+	3.80423i	0.203352	+	0.147744i
$664$	−13.9443	+	10.1311i	−0.541143	+	0.393163i
$665$		0			0
$666$	−0.736068	+	2.26538i	−0.0285221	+	0.0877819i
$667$	−3.19098	+	2.31838i	−0.123555	+	0.0897682i
$668$	−4.51722	−	3.28195i	−0.174777	−	0.126983i
$669$	6.50000	+	20.0049i	0.251305	+	0.773436i
$670$		0			0
$671$	−23.1631	+	1.57160i	−0.894202	+	0.0606709i
$672$	17.7082			0.683109
$673$	−10.9098	−	33.5770i	−0.420543	−	1.29430i	−0.907198	−	0.420704i	$-0.861783\pi$
$673$	−10.9098	−	33.5770i	−0.420543	−	1.29430i	0.486655	−	0.873594i	$-0.338217\pi$
$674$	−37.7705	−	27.4419i	−1.45487	−	1.05702i
$675$		0			0
$676$	−0.482779	+	1.48584i	−0.0185684	+	0.0571477i
$677$	1.83688	−	5.65334i	0.0705971	−	0.217275i	−0.909533	−	0.415632i	$-0.863560\pi$
$677$	1.83688	−	5.65334i	0.0705971	−	0.217275i	0.980130	+	0.198357i	$0.0635604\pi$
$678$	4.54508	−	3.30220i	0.174553	−	0.126820i
$679$	10.7082	+	7.77997i	0.410943	+	0.298568i
$680$		0			0
$681$	−8.05573			−0.308696
$682$	−31.8156	−	19.9722i	−1.21828	−	0.764775i
$683$	−15.7082			−0.601058			−0.300529	−	0.953773i	$-0.597163\pi$
$683$	−15.7082			−0.601058			−0.300529	+	0.953773i	$0.597163\pi$
$684$	0.954915	+	2.93893i	0.0365121	+	0.112373i
$685$		0			0
$686$	−91.9574	+	66.8110i	−3.51095	+	2.55086i
$687$	−2.13525	+	6.57164i	−0.0814651	+	0.250724i
$688$	−13.6353	+	41.9650i	−0.519839	+	1.59990i
$689$	14.0902	−	10.2371i	0.536793	−	0.390003i
$690$		0			0
$691$	−9.05573	−	27.8707i	−0.344496	−	1.06025i	−0.961853	−	0.273567i	$-0.911797\pi$
$691$	−9.05573	−	27.8707i	−0.344496	−	1.06025i	0.617357	−	0.786683i	$-0.288203\pi$
$692$	−10.2361			−0.389117
$693$	4.23607	−	16.8415i	0.160915	−	0.639756i
$694$	−45.5967			−1.73083
$695$		0			0
$696$	1.54508	+	1.12257i	0.0585663	+	0.0425509i
$697$	−18.5623	+	13.4863i	−0.703097	+	0.510830i
$698$	−16.1180	+	49.6062i	−0.610077	+	1.87762i
$699$	−3.17376	+	9.76784i	−0.120043	+	0.369453i
$700$		0			0
$701$	−32.6976	−	23.7562i	−1.23497	−	0.897258i	−0.237717	−	0.971334i	$-0.576399\pi$
$701$	−32.6976	−	23.7562i	−1.23497	−	0.897258i	−0.997253	+	0.0740763i	$0.976399\pi$
$702$	1.61803	+	4.97980i	0.0610688	+	0.187950i
$703$	7.36068			0.277613
$704$	10.7812	−	9.00854i	0.406330	−	0.339522i
$705$		0			0
$706$	−8.91641	−	27.4419i	−0.335573	−	1.03279i
$707$	82.8673	+	60.2066i	3.11654	+	2.26430i
$708$	3.35410	−	2.43690i	0.126055	−	0.0915842i
$709$	5.81559	−	17.8986i	0.218409	−	0.672195i	−0.780485	−	0.625175i	$-0.785028\pi$
$709$	5.81559	−	17.8986i	0.218409	−	0.672195i	0.998894	−	0.0470197i	$-0.0149724\pi$
$710$		0			0
$711$	−2.50000	+	1.81636i	−0.0937573	+	0.0681187i
$712$	−7.50000	−	5.44907i	−0.281074	−	0.204212i
$713$	9.98936	+	30.7441i	0.374104	+	1.15137i
$714$	−16.9443			−0.634123
$715$		0			0
$716$	−6.50658			−0.243162
$717$	−6.80902	−	20.9560i	−0.254287	−	0.782616i
$718$	4.30902	+	3.13068i	0.160811	+	0.116836i
$719$	−21.7705	+	15.8172i	−0.811903	+	0.589882i	−0.914382	−	0.404853i	$-0.867323\pi$
$719$	−21.7705	+	15.8172i	−0.811903	+	0.589882i	0.102479	+	0.994735i	$0.467323\pi$
$720$		0			0
$721$	−7.47214	+	22.9969i	−0.278277	+	0.856448i
$722$	7.85410	−	5.70634i	0.292299	−	0.212368i
$723$	0.500000	+	0.363271i	0.0185952	+	0.0135102i
$724$	−0.145898	−	0.449028i	−0.00542226	−	0.0166880i
$725$		0			0
$726$	7.73607	+	16.0292i	0.287112	+	0.594900i
$727$	21.6738			0.803835			0.401918	−	0.915676i	$-0.368344\pi$
$727$	21.6738			0.803835			0.401918	+	0.915676i	$0.368344\pi$
$728$	−11.7082	−	36.0341i	−0.433935	−	1.33551i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	5.61803	−	17.2905i	0.207790	−	0.639513i
$732$	−1.33688	+	4.11450i	−0.0494125	+	0.152076i
$733$	3.92705	−	2.85317i	0.145049	−	0.105384i	−0.512894	−	0.858452i	$-0.671427\pi$
$733$	3.92705	−	2.85317i	0.145049	−	0.105384i	0.657943	+	0.753068i	$0.271427\pi$
$734$	28.9615	+	21.0418i	1.06899	+	0.776665i
$735$		0			0
$736$	15.6180			0.575688
$737$	14.3607	+	35.7566i	0.528982	+	1.31711i
$738$	−18.5623			−0.683288
$739$	−6.18034	−	19.0211i	−0.227347	−	0.699704i	−0.998045	−	0.0625022i	$-0.980092\pi$
$739$	−6.18034	−	19.0211i	−0.227347	−	0.699704i	0.770697	−	0.637201i	$-0.219908\pi$
$740$		0			0
$741$	13.0902	−	9.51057i	0.480879	−	0.349379i
$742$	−14.0902	+	43.3651i	−0.517266	+	1.59198i
$743$	9.78115	−	30.1033i	0.358836	−	1.10438i	−0.594916	−	0.803788i	$-0.702815\pi$
$743$	9.78115	−	30.1033i	0.358836	−	1.10438i	0.953752	−	0.300595i	$-0.0971852\pi$
$744$	12.6631	−	9.20029i	0.464252	−	0.337299i
$745$		0			0
$746$	16.3713	+	50.3858i	0.599397	+	1.84475i
$747$	7.70820			0.282028
$748$	3.14590	−	2.62866i	0.115025	−	0.0961132i
$749$	20.1803			0.737374
$750$		0			0
$751$	8.18034	+	5.94336i	0.298505	+	0.216876i	0.726948	−	0.686692i	$-0.240938\pi$
$751$	8.18034	+	5.94336i	0.298505	+	0.216876i	−0.428444	+	0.903569i	$0.640938\pi$
$752$	−23.9164	+	17.3763i	−0.872142	+	0.633648i
$753$	−5.09017	+	15.6659i	−0.185496	+	0.570898i
$754$	−1.38197	+	4.25325i	−0.0503282	+	0.154894i
$755$		0			0
$756$	−2.61803	−	1.90211i	−0.0952170	−	0.0691792i
$757$	−0.562306	−	1.73060i	−0.0204374	−	0.0628997i	0.940318	−	0.340298i	$-0.110528\pi$
$757$	−0.562306	−	1.73060i	−0.0204374	−	0.0628997i	−0.960755	+	0.277398i	$0.910528\pi$
$758$	8.09017			0.293848
$759$	3.73607	−	14.8536i	0.135611	−	0.539153i
$760$		0			0
$761$	3.07953	+	9.47781i	0.111633	+	0.343570i	0.991230	−	0.132149i	$-0.0421878\pi$
$761$	3.07953	+	9.47781i	0.111633	+	0.343570i	−0.879597	+	0.475719i	$0.842188\pi$
$762$	2.54508	+	1.84911i	0.0921987	+	0.0669863i
$763$	45.9787	−	33.4055i	1.66454	−	1.20936i
$764$	−3.13525	+	9.64932i	−0.113430	+	0.349100i
$765$		0			0
$766$	17.4894	−	12.7068i	0.631916	−	0.459114i
$767$	−17.5623	−	12.7598i	−0.634138	−	0.460728i
$768$	−4.19098	−	12.8985i	−0.151229	−	0.465435i
$769$	17.2361			0.621549			0.310774	−	0.950484i	$-0.399412\pi$
$769$	17.2361			0.621549			0.310774	+	0.950484i	$0.399412\pi$
$770$		0			0
$771$	−9.56231			−0.344378
$772$	1.53444	+	4.72253i	0.0552258	+	0.169967i
$773$	−22.2533	−	16.1680i	−0.800395	−	0.581521i	0.110635	−	0.993861i	$-0.464712\pi$
$773$	−22.2533	−	16.1680i	−0.800395	−	0.581521i	−0.911030	+	0.412340i	$0.864712\pi$
$774$	11.8992	−	8.64527i	0.427707	−	0.310748i
$775$		0			0
$776$	1.74671	−	5.37582i	0.0627033	−	0.192981i
$777$	−6.23607	+	4.53077i	−0.223718	+	0.162540i
$778$	−27.5623	−	20.0252i	−0.988157	−	0.717938i
$779$	17.7254	+	54.5532i	0.635079	+	1.95457i
$780$		0			0
$781$	26.4721	−	1.79611i	0.947247	−	0.0642699i
$782$	−14.9443			−0.534406
$783$	−0.263932	−	0.812299i	−0.00943216	−	0.0290292i
$784$	80.1763	+	58.2515i	2.86344	+	2.08041i
$785$		0			0
$786$	−4.59017	+	14.1271i	−0.163726	+	0.503897i
$787$	−10.1353	+	31.1931i	−0.361283	+	1.11191i	0.590993	+	0.806676i	$0.298736\pi$
$787$	−10.1353	+	31.1931i	−0.361283	+	1.11191i	−0.952276	+	0.305238i	$0.901264\pi$
$788$	−4.88197	+	3.54696i	−0.173913	+	0.126355i
$789$	19.5902	+	14.2331i	0.697429	+	0.506711i
$790$		0			0
$791$	18.1803			0.646418
$792$	−7.39919	+	0.502029i	−0.262919	+	0.0178388i
$793$	22.6525			0.804413
$794$	−1.36475	−	4.20025i	−0.0484330	−	0.149061i
$795$		0			0
$796$	2.39919	−	1.74311i	0.0850369	−	0.0617829i
$797$	4.72542	−	14.5434i	0.167383	−	0.515152i	−0.831821	−	0.555044i	$-0.812701\pi$
$797$	4.72542	−	14.5434i	0.167383	−	0.515152i	0.999204	+	0.0398919i	$0.0127013\pi$
$798$	−13.0902	+	40.2874i	−0.463387	+	1.42616i
$799$	9.85410	−	7.15942i	0.348613	−	0.253282i
$800$		0			0
$801$	1.28115	+	3.94298i	0.0452673	+	0.139318i
$802$	49.9787			1.76481
$803$	−12.7188	−	7.98424i	−0.448838	−	0.281758i
$804$	7.18034			0.253231
$805$		0			0
$806$	29.6525	+	21.5438i	1.04446	+	0.758847i
$807$	0.690983	−	0.502029i	0.0243238	−	0.0176722i
$808$	13.5172	−	41.6017i	0.475534	−	1.46354i
$809$	9.16970	−	28.2214i	0.322389	−	0.992212i	−0.650216	−	0.759750i	$-0.725322\pi$
$809$	9.16970	−	28.2214i	0.322389	−	0.992212i	0.972605	−	0.232463i	$-0.0746784\pi$
$810$		0			0
$811$	−35.2984	−	25.6458i	−1.23949	−	0.900545i	−0.241929	−	0.970294i	$-0.577780\pi$
$811$	−35.2984	−	25.6458i	−1.23949	−	0.900545i	−0.997565	+	0.0697492i	$0.977780\pi$
$812$	−0.854102	−	2.62866i	−0.0299731	−	0.0922477i
$813$	−18.3820			−0.644684
$814$	1.92705	−	7.66145i	0.0675431	−	0.268534i
$815$		0			0
$816$	3.00000	+	9.23305i	0.105021	+	0.323221i
$817$	−36.7705	−	26.7153i	−1.28644	−	0.934651i
$818$	−34.4336	+	25.0175i	−1.20394	+	0.874716i
$819$	−5.23607	+	16.1150i	−0.182963	+	0.563102i
$820$		0			0
$821$	−16.8435	+	12.2375i	−0.587841	+	0.427091i	−0.841542	−	0.540191i	$-0.818352\pi$
$821$	−16.8435	+	12.2375i	−0.587841	+	0.427091i	0.253702	+	0.967283i	$0.418352\pi$
$822$	−6.92705	−	5.03280i	−0.241609	−	0.175539i
$823$	5.10739	+	15.7189i	0.178032	+	0.547928i	0.999759	−	0.0219545i	$-0.00698889\pi$
$823$	5.10739	+	15.7189i	0.178032	+	0.547928i	−0.821727	+	0.569882i	$0.806989\pi$
$824$	10.3262			0.359732
$825$		0			0
$826$	56.8328			1.97747
$827$	−15.8885	−	48.8999i	−0.552499	−	1.70042i	−0.702459	−	0.711724i	$-0.747914\pi$
$827$	−15.8885	−	48.8999i	−0.552499	−	1.70042i	0.149960	−	0.988692i	$-0.452086\pi$
$828$	−2.30902	−	1.67760i	−0.0802439	−	0.0583006i
$829$	26.6074	−	19.3314i	0.924113	−	0.671407i	−0.0204314	−	0.999791i	$-0.506504\pi$
$829$	26.6074	−	19.3314i	0.924113	−	0.671407i	0.944544	+	0.328384i	$0.106504\pi$
$830$		0			0
$831$	−7.00000	+	21.5438i	−0.242827	+	0.747346i
$832$	−11.0902	+	8.05748i	−0.384482	+	0.279343i
$833$	−33.0344	−	24.0009i	−1.14458	−	0.831583i
$834$	−0.590170	−	1.81636i	−0.0204359	−	0.0628953i
$835$		0			0
$836$	−3.81966	−	9.51057i	−0.132106	−	0.328930i
$837$	−7.00000			−0.241955
$838$	12.2984	+	37.8505i	0.424840	+	1.30752i
$839$	−29.3713	−	21.3395i	−1.01401	−	0.736722i	−0.0489642	−	0.998801i	$-0.515592\pi$
$839$	−29.3713	−	21.3395i	−1.01401	−	0.736722i	−0.965047	+	0.262079i	$0.915592\pi$
$840$		0			0
$841$	−8.73607	+	26.8869i	−0.301244	+	0.927133i
$842$	1.92705	−	5.93085i	0.0664106	−	0.204391i
$843$	−0.881966	+	0.640786i	−0.0303765	+	0.0220698i
$844$	−1.42705	−	1.03681i	−0.0491211	−	0.0356886i
$845$		0			0
$846$	9.85410			0.338791
$847$	−10.2361	+	56.6799i	−0.351715	+	1.94754i
$848$	26.1246			0.897123
$849$	4.95492	+	15.2497i	0.170052	+	0.523367i
$850$		0			0
$851$	−5.50000	+	3.99598i	−0.188538	+	0.136981i
$852$	1.52786	−	4.70228i	0.0523438	−	0.161098i
$853$	7.21885	−	22.2173i	0.247169	−	0.760707i	−0.748104	−	0.663582i	$-0.769035\pi$
$853$	7.21885	−	22.2173i	0.247169	−	0.760707i	0.995272	−	0.0971248i	$-0.0309646\pi$
$854$	−47.9787	+	34.8586i	−1.64180	+	1.19284i
$855$		0			0
$856$	−2.66312	−	8.19624i	−0.0910235	−	0.280142i
$857$	−41.0132			−1.40098			−0.700491	−	0.713661i	$-0.747036\pi$
$857$	−41.0132			−1.40098			−0.700491	+	0.713661i	$0.747036\pi$
$858$	−6.47214	−	16.1150i	−0.220955	−	0.550156i
$859$	−39.2705			−1.33989			−0.669946	−	0.742410i	$-0.733683\pi$
$859$	−39.2705			−1.33989			−0.669946	+	0.742410i	$0.733683\pi$
$860$		0			0
$861$	−48.5967	−	35.3076i	−1.65617	−	1.20328i
$862$	−20.7984	+	15.1109i	−0.708395	+	0.514679i
$863$	7.11803	−	21.9071i	0.242301	−	0.745725i	−0.753768	−	0.657141i	$-0.771766\pi$
$863$	7.11803	−	21.9071i	0.242301	−	0.745725i	0.996069	−	0.0885842i	$-0.0282342\pi$
$864$	−1.04508	+	3.21644i	−0.0355545	+	0.109426i
$865$		0			0
$866$	−1.35410	−	0.983813i	−0.0460143	−	0.0334313i
$867$	4.01722	+	12.3637i	0.136432	+	0.419894i
$868$	−22.6525			−0.768875
$869$	7.86475	−	6.57164i	0.266793	−	0.222928i
$870$		0			0
$871$	−11.6180	−	35.7566i	−0.393662	−	1.21157i
$872$	−19.6353	−	14.2658i	−0.664934	−	0.483103i
$873$	−2.04508	+	1.48584i	−0.0692156	+	0.0502881i
$874$	−11.5451	+	35.5321i	−0.390518	+	1.20189i
$875$		0			0
$876$	−2.26393	+	1.64484i	−0.0764912	+	0.0555741i
$877$	−6.09017	−	4.42477i	−0.205650	−	0.149414i	0.480193	−	0.877163i	$-0.340567\pi$
$877$	−6.09017	−	4.42477i	−0.205650	−	0.149414i	−0.685844	+	0.727749i	$0.740567\pi$
$878$	−12.6631	−	38.9731i	−0.427360	−	1.31528i
$879$	−25.4721			−0.859154
$880$		0			0
$881$	−17.1459			−0.577660			−0.288830	−	0.957380i	$-0.593266\pi$
$881$	−17.1459			−0.577660			−0.288830	+	0.957380i	$0.593266\pi$
$882$	−10.2082	−	31.4176i	−0.343728	−	1.05789i
$883$	−18.7984	−	13.6578i	−0.632616	−	0.459622i	0.224690	−	0.974430i	$-0.427863\pi$
$883$	−18.7984	−	13.6578i	−0.632616	−	0.459622i	−0.857305	+	0.514808i	$0.827863\pi$
$884$	−3.23607	+	2.35114i	−0.108841	+	0.0790774i
$885$		0			0
$886$	4.13525	−	12.7270i	0.138927	−	0.427572i
$887$	−0.135255	+	0.0982684i	−0.00454142	+	0.00329953i	−0.590054	−	0.807364i	$-0.700893\pi$
$887$	−0.135255	+	0.0982684i	−0.00454142	+	0.00329953i	0.585512	+	0.810664i	$0.300893\pi$
$888$	2.66312	+	1.93487i	0.0893684	+	0.0649300i
$889$	3.14590	+	9.68208i	0.105510	+	0.324726i
$890$		0			0
$891$	2.80902	+	1.76336i	0.0941056	+	0.0590746i
$892$	−13.0000			−0.435272
$893$	−9.40983	−	28.9605i	−0.314888	−	0.969125i
$894$	26.3435	+	19.1396i	0.881057	+	0.640125i
$895$		0			0
$896$	22.0344	−	67.8150i	0.736119	−	2.26554i
$897$	−4.61803	+	14.2128i	−0.154192	+	0.474553i
$898$	−44.8607	+	32.5932i	−1.49702	+	1.08765i
$899$	−4.83688	−	3.51420i	−0.161319	−	0.117205i
$900$		0			0
$901$	−10.7639			−0.358599
$902$	61.4230	−	4.16750i	2.04516	−	0.138762i
$903$	47.5967			1.58392
$904$	−2.39919	−	7.38394i	−0.0797958	−	0.245586i
$905$		0			0
$906$	19.9443	−	14.4904i	0.662604	−	0.481410i
$907$	13.8713	−	42.6915i	0.460590	−	1.41755i	−0.403856	−	0.914823i	$-0.632330\pi$
$907$	13.8713	−	42.6915i	0.460590	−	1.41755i	0.864445	−	0.502727i	$-0.167670\pi$
$908$	1.53851	−	4.73504i	0.0510572	−	0.157138i
$909$	−15.8262	+	11.4984i	−0.524923	+	0.381379i
$910$		0			0
$911$	16.3475	+	50.3125i	0.541618	+	1.66693i	0.728899	+	0.684621i	$0.240032\pi$
$911$	16.3475	+	50.3125i	0.541618	+	1.66693i	−0.187281	+	0.982306i	$0.559968\pi$
$912$	24.2705			0.803677
$913$	−25.5066	+	1.73060i	−0.844145	+	0.0572745i
$914$	12.0902			0.399907
$915$		0			0
$916$	−3.45492	−	2.51014i	−0.114154	−	0.0829374i
$917$	−38.8885	+	28.2542i	−1.28421	+	0.933035i
$918$	1.00000	−	3.07768i	0.0330049	−	0.101579i
$919$	−6.87132	+	21.1478i	−0.226664	+	0.697600i	0.771454	+	0.636285i	$0.219530\pi$
$919$	−6.87132	+	21.1478i	−0.226664	+	0.697600i	−0.998118	+	0.0613155i	$0.980470\pi$
$920$		0			0
$921$	−22.7533	−	16.5312i	−0.749746	−	0.544723i
$922$	−4.02786	−	12.3965i	−0.132651	−	0.408257i
$923$	−25.8885			−0.852132
$924$	9.09017	+	5.70634i	0.299045	+	0.187725i
$925$		0			0
$926$	−0.135255	−	0.416272i	−0.00444475	−	0.0136795i
$927$	−3.73607	−	2.71441i	−0.122709	−	0.0891530i
$928$	−2.33688	+	1.69784i	−0.0767119	+	0.0557344i
$929$	−3.35410	+	10.3229i	−0.110045	+	0.338682i	−0.990881	−	0.134738i	$-0.956981\pi$
$929$	−3.35410	+	10.3229i	−0.110045	+	0.338682i	0.880837	+	0.473420i	$0.156981\pi$
$930$		0			0
$931$	−82.5861	+	60.0023i	−2.70665	+	1.96650i
$932$	−5.13525	−	3.73098i	−0.168211	−	0.122212i
$933$	−3.87132	−	11.9147i	−0.126741	−	0.390070i
$934$	49.9787			1.63535
$935$		0			0
$936$	7.23607			0.236518
$937$	5.31559	+	16.3597i	0.173653	+	0.534449i	0.999569	−	0.0293438i	$-0.00934176\pi$
$937$	5.31559	+	16.3597i	0.173653	+	0.534449i	−0.825916	+	0.563793i	$0.809342\pi$
$938$	79.6312	+	57.8554i	2.60005	+	1.88905i
$939$	−6.85410	+	4.97980i	−0.223675	+	0.162510i
$940$		0			0
$941$	−3.00000	+	9.23305i	−0.0977972	+	0.300989i	−0.987973	−	0.154629i	$-0.950582\pi$
$941$	−3.00000	+	9.23305i	−0.0977972	+	0.300989i	0.890175	+	0.455618i	$0.150582\pi$
$942$	−16.1353	+	11.7229i	−0.525715	+	0.381954i
$943$	−42.8607	−	31.1401i	−1.39574	−	1.01406i
$944$	−10.0623	−	30.9686i	−0.327500	−	1.00794i
$945$		0			0
$946$	−37.4336	+	31.2789i	−1.21707	+	1.01696i
$947$	4.56231			0.148255			0.0741275	−	0.997249i	$-0.476383\pi$
$947$	4.56231			0.148255			0.0741275	+	0.997249i	$0.476383\pi$
$948$	−0.590170	−	1.81636i	−0.0191678	−	0.0589925i
$949$	11.8541	+	8.61251i	0.384800	+	0.279574i
$950$		0			0
$951$	−1.10739	+	3.40820i	−0.0359096	+	0.110518i
$952$	−7.23607	+	22.2703i	−0.234522	+	0.721785i
$953$	−39.7148	+	28.8545i	−1.28649	+	0.934688i	−0.999728	−	0.0233143i	$-0.992578\pi$
$953$	−39.7148	+	28.8545i	−1.28649	+	0.934688i	−0.286760	+	0.958003i	$0.592578\pi$
$954$	−7.04508	−	5.11855i	−0.228093	−	0.165719i
$955$		0			0
$956$	13.6180			0.440439
$957$	1.05573	+	2.62866i	0.0341268	+	0.0849724i
$958$	−10.6525			−0.344166
$959$	−8.56231	−	26.3521i	−0.276491	−	0.850953i
$960$		0			0
$961$	−14.5623	+	10.5801i	−0.469752	+	0.341295i
$962$	−2.38197	+	7.33094i	−0.0767977	+	0.236359i
$963$	−1.19098	+	3.66547i	−0.0383789	+	0.118118i
$964$	−0.309017	+	0.224514i	−0.00995277	+	0.00723111i
$965$		0			0
$966$	−12.0902	−	37.2097i	−0.388995	−	1.19720i
$967$	−32.6738			−1.05072			−0.525359	−	0.850881i	$-0.676069\pi$
$967$	−32.6738			−1.05072			−0.525359	+	0.850881i	$0.676069\pi$
$968$	24.3713	−	3.32244i	0.783324	−	0.106787i
$969$	−10.0000			−0.321246
$970$		0			0
$971$	25.5172	+	18.5393i	0.818887	+	0.594956i	0.916393	−	0.400279i	$-0.131087\pi$
$971$	25.5172	+	18.5393i	0.818887	+	0.594956i	−0.0975068	+	0.995235i	$0.531087\pi$
$972$	0.500000	−	0.363271i	0.0160375	−	0.0116519i
$973$	1.90983	−	5.87785i	0.0612263	−	0.188435i
$974$	−4.09017	+	12.5882i	−0.131057	+	0.403354i
$975$		0			0
$976$	27.4894	+	19.9722i	0.879913	+	0.639294i
$977$	−14.2426	−	43.8344i	−0.455663	−	1.40239i	−0.870356	−	0.492424i	$-0.836111\pi$
$977$	−14.2426	−	43.8344i	−0.455663	−	1.40239i	0.414693	−	0.909961i	$-0.363889\pi$
$978$	−10.6180			−0.339527
$979$	−5.12461	−	12.7598i	−0.163783	−	0.407804i
$980$		0			0
$981$	3.35410	+	10.3229i	0.107088	+	0.329584i
$982$	9.42705	+	6.84915i	0.300829	+	0.218565i
$983$	15.3713	−	11.1679i	0.490269	−	0.356201i	−0.315019	−	0.949085i	$-0.602011\pi$
$983$	15.3713	−	11.1679i	0.490269	−	0.356201i	0.805288	+	0.592884i	$0.202011\pi$
$984$	−7.92705	+	24.3970i	−0.252705	+	0.777746i
$985$		0			0
$986$	2.23607	−	1.62460i	0.0712109	−	0.0517378i
$987$	25.7984	+	18.7436i	0.821171	+	0.596616i
$988$	3.09017	+	9.51057i	0.0983114	+	0.302571i
$989$	41.9787			1.33485
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	7.31559	+	22.5151i	0.232270	+	0.714855i
$993$	−22.3262	−	16.2210i	−0.708502	−	0.514757i
$994$	54.8328	−	39.8384i	1.73919	−	1.26360i
$995$		0			0
$996$	−1.47214	+	4.53077i	−0.0466464	+	0.143563i
$997$	9.13525	−	6.63715i	0.289316	−	0.210201i	−0.433654	−	0.901079i	$-0.642776\pi$
$997$	9.13525	−	6.63715i	0.289316	−	0.210201i	0.722971	+	0.690879i	$0.242776\pi$
$998$	14.6353	+	10.6331i	0.463271	+	0.336586i
$999$	−0.454915	−	1.40008i	−0.0143929	−	0.0442967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.b.676.1	yes	4
5.2	odd	4		825.2.bx.c.49.2		8
5.3	odd	4		825.2.bx.c.49.1		8
5.4	even	2		825.2.n.d.676.1	yes	4
11.3	even	5		9075.2.a.z.1.1		2
11.8	odd	10		9075.2.a.bt.1.2		2
11.9	even	5	inner	825.2.n.b.526.1	✓	4
55.9	even	10		825.2.n.d.526.1	yes	4
55.14	even	10		9075.2.a.by.1.2		2
55.19	odd	10		9075.2.a.bc.1.1		2
55.42	odd	20		825.2.bx.c.724.1		8
55.53	odd	20		825.2.bx.c.724.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.b.526.1	✓	4	11.9	even	5	inner
825.2.n.b.676.1	yes	4	1.1	even	1	trivial
825.2.n.d.526.1	yes	4	55.9	even	10
825.2.n.d.676.1	yes	4	5.4	even	2
825.2.bx.c.49.1		8	5.3	odd	4
825.2.bx.c.49.2		8	5.2	odd	4
825.2.bx.c.724.1		8	55.42	odd	20
825.2.bx.c.724.2		8	55.53	odd	20
9075.2.a.z.1.1		2	11.3	even	5
9075.2.a.bc.1.1		2	55.19	odd	10
9075.2.a.bt.1.2		2	11.8	odd	10
9075.2.a.by.1.2		2	55.14	even	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.500000 - 1.53884i) q^{6} +(4.23607 - 3.07768i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.500000 - 1.53884i) q^{6} +(4.23607 - 3.07768i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.23607 - 3.07768i) q^{11} -0.618034 q^{12} +(1.00000 + 3.07768i) q^{13} +(-6.85410 - 4.97980i) q^{14} +(-1.50000 + 4.61653i) q^{16} +(0.618034 - 1.90211i) q^{17} +(1.30902 - 0.951057i) q^{18} +(-4.04508 - 2.93893i) q^{19} +5.23607 q^{21} +(-4.11803 + 3.44095i) q^{22} +4.61803 q^{23} +(-0.690983 - 2.12663i) q^{24} +(4.23607 - 3.07768i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.00000 + 3.07768i) q^{28} +(-0.690983 + 0.502029i) q^{29} +(2.16312 + 6.65740i) q^{31} +3.38197 q^{32} +(0.809017 - 3.21644i) q^{33} -3.23607 q^{34} +(-0.500000 - 0.363271i) q^{36} +(-1.19098 + 0.865300i) q^{37} +(-2.50000 + 7.69421i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(-9.28115 - 6.74315i) q^{41} +(-2.61803 - 8.05748i) q^{42} +9.09017 q^{43} +(1.73607 + 1.08981i) q^{44} +(-2.30902 - 7.10642i) q^{46} +(4.92705 + 3.57971i) q^{47} +(-3.92705 + 2.85317i) q^{48} +(6.30902 - 19.4172i) q^{49} +(1.61803 - 1.17557i) q^{51} +(-1.61803 - 1.17557i) q^{52} +(-1.66312 - 5.11855i) q^{53} +1.61803 q^{54} -11.7082 q^{56} +(-1.54508 - 4.75528i) q^{57} +(1.11803 + 0.812299i) q^{58} +(-5.42705 + 3.94298i) q^{59} +(2.16312 - 6.65740i) q^{61} +(9.16312 - 6.65740i) q^{62} +(4.23607 + 3.07768i) q^{63} +(1.30902 + 4.02874i) q^{64} +(-5.35410 + 0.363271i) q^{66} -11.6180 q^{67} +(0.381966 + 1.17557i) q^{68} +(3.73607 + 2.71441i) q^{69} +(-2.47214 + 7.60845i) q^{71} +(0.690983 - 2.12663i) q^{72} +(3.66312 - 2.66141i) q^{73} +(1.92705 + 1.40008i) q^{74} +3.09017 q^{76} +(-14.7082 - 9.23305i) q^{77} +5.23607 q^{78} +(0.954915 + 2.93893i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-5.73607 + 17.6538i) q^{82} +(2.38197 - 7.33094i) q^{83} +(-2.61803 + 1.90211i) q^{84} +(-4.54508 - 13.9883i) q^{86} -0.854102 q^{87} +(-1.80902 + 7.19218i) q^{88} +4.14590 q^{89} +(13.7082 + 9.95959i) q^{91} +(-2.30902 + 1.67760i) q^{92} +(-2.16312 + 6.65740i) q^{93} +(3.04508 - 9.37181i) q^{94} +(2.73607 + 1.98787i) q^{96} +(0.781153 + 2.40414i) q^{97} -33.0344 q^{98} +(2.54508 - 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 4 q^{13} - 14 q^{14} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 5 q^{19} + 12 q^{21} - 12 q^{22} + 14 q^{23} - 5 q^{24} + 8 q^{26} + q^{27} - 4 q^{28} - 5 q^{29} - 7 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 2 q^{36} - 7 q^{37} - 10 q^{38} - 4 q^{39} - 17 q^{41} - 6 q^{42} + 14 q^{43} - 2 q^{44} - 7 q^{46} + 13 q^{47} - 9 q^{48} + 23 q^{49} + 2 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} - 20 q^{56} + 5 q^{57} - 15 q^{59} - 7 q^{61} + 21 q^{62} + 8 q^{63} + 3 q^{64} - 8 q^{66} - 42 q^{67} + 6 q^{68} + 6 q^{69} + 8 q^{71} + 5 q^{72} - q^{73} + q^{74} - 10 q^{76} - 32 q^{77} + 12 q^{78} + 15 q^{79} - q^{81} - 14 q^{82} + 14 q^{83} - 6 q^{84} - 7 q^{86} + 10 q^{87} - 5 q^{88} + 30 q^{89} + 28 q^{91} - 7 q^{92} + 7 q^{93} + q^{94} + 2 q^{96} - 17 q^{97} - 74 q^{98} - q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9 + 4 * q^11 + 2 * q^12 + 4 * q^13 - 14 * q^14 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 5 * q^19 + 12 * q^21 - 12 * q^22 + 14 * q^23 - 5 * q^24 + 8 * q^26 + q^27 - 4 * q^28 - 5 * q^29 - 7 * q^31 + 18 * q^32 + q^33 - 4 * q^34 - 2 * q^36 - 7 * q^37 - 10 * q^38 - 4 * q^39 - 17 * q^41 - 6 * q^42 + 14 * q^43 - 2 * q^44 - 7 * q^46 + 13 * q^47 - 9 * q^48 + 23 * q^49 + 2 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 - 20 * q^56 + 5 * q^57 - 15 * q^59 - 7 * q^61 + 21 * q^62 + 8 * q^63 + 3 * q^64 - 8 * q^66 - 42 * q^67 + 6 * q^68 + 6 * q^69 + 8 * q^71 + 5 * q^72 - q^73 + q^74 - 10 * q^76 - 32 * q^77 + 12 * q^78 + 15 * q^79 - q^81 - 14 * q^82 + 14 * q^83 - 6 * q^84 - 7 * q^86 + 10 * q^87 - 5 * q^88 + 30 * q^89 + 28 * q^91 - 7 * q^92 + 7 * q^93 + q^94 + 2 * q^96 - 17 * q^97 - 74 * q^98 - q^99

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