LMFDB - Embedded newform 231.2.j.g.169.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [231,2,Mod(64,231)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(231, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("231.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$231 = 3 \cdot 7 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	231.j (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121$ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{4}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.4
Root			$-1.07866 + 0.783695i$ of defining polynomial
Character	$\chi$	$=$	231.169
Dual form			231.2.j.g.190.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07866 + 0.783695i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.0686960 - 0.211425i) q^{4} +(0.706442 - 0.513260i) q^{5} +(1.07866 - 0.783695i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.915619 - 2.81798i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.16425 q^{10} +(1.79514 + 2.78881i) q^{11} -0.222305 q^{12} +(-0.0319918 - 0.0232434i) q^{13} +(0.412013 - 1.26805i) q^{14} +(-0.269837 - 0.830472i) q^{15} +(2.83639 - 2.06076i) q^{16} +(-1.65552 + 1.20280i) q^{17} +(-0.412013 - 1.26805i) q^{18} +(-1.75961 + 5.41551i) q^{19} +(-0.157046 - 0.114100i) q^{20} -1.00000 q^{21} +(-0.249220 + 4.41504i) q^{22} +5.97870 q^{23} +(-2.39712 - 1.74161i) q^{24} +(-1.30946 + 4.03011i) q^{25} +(-0.0162926 - 0.0501436i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.179849 + 0.130668i) q^{28} +(-1.44389 - 4.44385i) q^{29} +(0.359774 - 1.10727i) q^{30} +(-6.05057 - 4.39599i) q^{31} -1.25149 q^{32} +(3.20705 - 0.845493i) q^{33} -2.72838 q^{34} +(-0.706442 - 0.513260i) q^{35} +(-0.0686960 + 0.211425i) q^{36} +(3.57546 + 11.0041i) q^{37} +(-6.14214 + 4.46252i) q^{38} +(-0.0319918 + 0.0232434i) q^{39} +(-0.799528 - 2.46069i) q^{40} +(-1.90009 + 5.84788i) q^{41} +(-1.07866 - 0.783695i) q^{42} -1.79689 q^{43} +(0.466304 - 0.571118i) q^{44} -0.873210 q^{45} +(6.44901 + 4.68548i) q^{46} +(1.86885 - 5.75173i) q^{47} +(-1.08340 - 3.33438i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-4.57084 + 3.32091i) q^{50} +(0.632351 + 1.94618i) q^{51} +(-0.00271652 + 0.00836058i) q^{52} +(0.100643 + 0.0731211i) q^{53} -1.33330 q^{54} +(2.69955 + 1.04876i) q^{55} -2.96300 q^{56} +(4.60671 + 3.34697i) q^{57} +(1.92515 - 5.92499i) q^{58} +(-4.43316 - 13.6439i) q^{59} +(-0.157046 + 0.114100i) q^{60} +(-6.11572 + 4.44333i) q^{61} +(-3.08141 - 9.48360i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-7.02272 - 5.10230i) q^{64} -0.0345302 q^{65} +(4.12193 + 1.60134i) q^{66} +4.85938 q^{67} +(0.368030 + 0.267389i) q^{68} +(1.84752 - 5.68608i) q^{69} +(-0.359774 - 1.10727i) q^{70} +(9.10168 - 6.61275i) q^{71} +(-2.39712 + 1.74161i) q^{72} +(0.189413 + 0.582954i) q^{73} +(-4.76718 + 14.6719i) q^{74} +(3.42821 + 2.49074i) q^{75} +1.26585 q^{76} +(2.09759 - 2.56907i) q^{77} -0.0527241 q^{78} +(0.125581 + 0.0912401i) q^{79} +(0.946040 - 2.91161i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-6.63251 + 4.81880i) q^{82} +(-7.21319 + 5.24069i) q^{83} +(0.0686960 + 0.211425i) q^{84} +(-0.552176 + 1.69942i) q^{85} +(-1.93824 - 1.40822i) q^{86} -4.67254 q^{87} +(9.50249 - 2.50520i) q^{88} +5.17689 q^{89} +(-0.941901 - 0.684331i) q^{90} +(-0.0122198 + 0.0376086i) q^{91} +(-0.410713 - 1.26404i) q^{92} +(-6.05057 + 4.39599i) q^{93} +(6.52347 - 4.73958i) q^{94} +(1.53651 + 4.72888i) q^{95} +(-0.386732 + 1.19024i) q^{96} +(-6.42539 - 4.66832i) q^{97} -1.33330 q^{98} +(0.186920 - 3.31135i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25}+ \cdots - q^{99}+O(q^{100})$ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$ .

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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

)

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

$2$	1.07866	+	0.783695i	0.762731	+	0.554156i	0.899747	−	0.436412i	$-0.143751\pi$
$2$	1.07866	+	0.783695i	0.762731	+	0.554156i	−0.137016	+	0.990569i	$0.543751\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.0686960	−	0.211425i	−0.0343480	−	0.105712i
$5$	0.706442	−	0.513260i	0.315931	−	0.229537i	−0.418507	−	0.908214i	$-0.637446\pi$
$5$	0.706442	−	0.513260i	0.315931	−	0.229537i	0.734437	+	0.678677i	$0.237446\pi$
$6$	1.07866	−	0.783695i	0.440363	−	0.319942i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.915619	−	2.81798i	0.323720	−	0.996308i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.16425			0.368169
$11$	1.79514	+	2.78881i	0.541256	+	0.840858i
$11$	1.79514	+	2.78881i	0.541256	+	0.840858i
$12$	−0.222305			−0.0641739
$13$	−0.0319918	−	0.0232434i	−0.00887292	−	0.00644656i	0.583340	−	0.812228i	$-0.301746\pi$
$13$	−0.0319918	−	0.0232434i	−0.00887292	−	0.00644656i	−0.592213	+	0.805782i	$0.701746\pi$
$14$	0.412013	−	1.26805i	0.110115	−	0.338900i
$15$	−0.269837	−	0.830472i	−0.0696716	−	0.214427i
$16$	2.83639	−	2.06076i	0.709097	−	0.515189i
$17$	−1.65552	+	1.20280i	−0.401522	+	0.291723i	−0.770161	−	0.637850i	$-0.779824\pi$
$17$	−1.65552	+	1.20280i	−0.401522	+	0.291723i	0.368639	+	0.929573i	$0.379824\pi$
$18$	−0.412013	−	1.26805i	−0.0971124	−	0.298881i
$19$	−1.75961	+	5.41551i	−0.403681	+	1.24240i	0.518310	+	0.855193i	$0.326561\pi$
$19$	−1.75961	+	5.41551i	−0.403681	+	1.24240i	−0.921991	+	0.387211i	$0.873439\pi$
$20$	−0.157046	−	0.114100i	−0.0351165	−	0.0255136i
$21$	−1.00000			−0.218218
$22$	−0.249220	+	4.41504i	−0.0531340	+	0.941289i
$23$	5.97870			1.24665			0.623323	−	0.781965i	$-0.285782\pi$
$23$	5.97870			1.24665			0.623323	+	0.781965i	$0.285782\pi$
$24$	−2.39712	−	1.74161i	−0.489310	−	0.355505i
$25$	−1.30946	+	4.03011i	−0.261892	+	0.806021i
$26$	−0.0162926	−	0.0501436i	−0.00319525	−	0.00983397i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.179849	+	0.130668i	−0.0339882	+	0.0246939i
$29$	−1.44389	−	4.44385i	−0.268124	−	0.825202i	−0.990957	−	0.134179i	$-0.957160\pi$
$29$	−1.44389	−	4.44385i	−0.268124	−	0.825202i	0.722833	−	0.691023i	$-0.242840\pi$
$30$	0.359774	−	1.10727i	0.0656855	−	0.202159i
$31$	−6.05057	−	4.39599i	−1.08671	−	0.789544i	−0.107872	−	0.994165i	$-0.534404\pi$
$31$	−6.05057	−	4.39599i	−1.08671	−	0.789544i	−0.978841	+	0.204621i	$0.934404\pi$
$32$	−1.25149			−0.221234
$33$	3.20705	−	0.845493i	0.558275	−	0.147181i
$34$	−2.72838			−0.467913
$35$	−0.706442	−	0.513260i	−0.119411	−	0.0867568i
$36$	−0.0686960	+	0.211425i	−0.0114493	+	0.0352374i
$37$	3.57546	+	11.0041i	0.587803	+	1.80907i	0.587711	+	0.809071i	$0.300029\pi$
$37$	3.57546	+	11.0041i	0.587803	+	1.80907i	9.16819e−5		1.00000i	$0.499971\pi$
$38$	−6.14214	+	4.46252i	−0.996386	+	0.723917i
$39$	−0.0319918	+	0.0232434i	−0.00512278	+	0.00372192i
$40$	−0.799528	−	2.46069i	−0.126416	−	0.389070i
$41$	−1.90009	+	5.84788i	−0.296744	+	0.913285i	0.685886	+	0.727709i	$0.259415\pi$
$41$	−1.90009	+	5.84788i	−0.296744	+	0.913285i	−0.982630	+	0.185576i	$0.940585\pi$
$42$	−1.07866	−	0.783695i	−0.166442	−	0.120927i
$43$	−1.79689			−0.274024			−0.137012	−	0.990569i	$-0.543750\pi$
$43$	−1.79689			−0.274024			−0.137012	+	0.990569i	$0.543750\pi$
$44$	0.466304	−	0.571118i	0.0702979	−	0.0860992i
$45$	−0.873210			−0.130171
$46$	6.44901	+	4.68548i	0.950855	+	0.690837i
$47$	1.86885	−	5.75173i	0.272600	−	0.838977i	−0.717244	−	0.696822i	$-0.754597\pi$
$47$	1.86885	−	5.75173i	0.272600	−	0.838977i	0.989844	−	0.142155i	$-0.0454031\pi$
$48$	−1.08340	−	3.33438i	−0.156376	−	0.481276i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−4.57084	+	3.32091i	−0.646415	+	0.469648i
$51$	0.632351	+	1.94618i	0.0885469	+	0.272519i
$52$	−0.00271652	+	0.00836058i	−0.000376713	+	0.00115940i
$53$	0.100643	+	0.0731211i	0.0138243	+	0.0100440i	0.594676	−	0.803965i	$-0.297280\pi$
$53$	0.100643	+	0.0731211i	0.0138243	+	0.0100440i	−0.580852	+	0.814009i	$0.697280\pi$
$54$	−1.33330			−0.181439
$55$	2.69955	+	1.04876i	0.364007	+	0.141414i
$56$	−2.96300			−0.395948
$57$	4.60671	+	3.34697i	0.610174	+	0.443317i
$58$	1.92515	−	5.92499i	0.252784	−	0.777990i
$59$	−4.43316	−	13.6439i	−0.577148	−	1.77628i	−0.628747	−	0.777610i	$-0.716432\pi$
$59$	−4.43316	−	13.6439i	−0.577148	−	1.77628i	0.0515991	−	0.998668i	$-0.483568\pi$
$60$	−0.157046	+	0.114100i	−0.0202745	+	0.0147303i
$61$	−6.11572	+	4.44333i	−0.783037	+	0.568910i	−0.905889	−	0.423515i	$-0.860796\pi$
$61$	−6.11572	+	4.44333i	−0.783037	+	0.568910i	0.122852	+	0.992425i	$0.460796\pi$
$62$	−3.08141	−	9.48360i	−0.391339	−	1.20442i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−7.02272	−	5.10230i	−0.877840	−	0.637788i
$65$	−0.0345302			−0.00428295
$66$	4.12193	+	1.60134i	0.507375	+	0.197112i
$67$	4.85938			0.593668			0.296834	−	0.954929i	$-0.404069\pi$
$67$	4.85938			0.593668			0.296834	+	0.954929i	$0.404069\pi$
$68$	0.368030	+	0.267389i	0.0446301	+	0.0324257i
$69$	1.84752	−	5.68608i	0.222415	−	0.684524i
$70$	−0.359774	−	1.10727i	−0.0430012	−	0.132344i
$71$	9.10168	−	6.61275i	1.08017	−	0.784790i	0.102458	−	0.994737i	$-0.467329\pi$
$71$	9.10168	−	6.61275i	1.08017	−	0.784790i	0.977713	+	0.209948i	$0.0673294\pi$
$72$	−2.39712	+	1.74161i	−0.282503	+	0.205251i
$73$	0.189413	+	0.582954i	0.0221692	+	0.0682296i	0.961529	−	0.274703i	$-0.0885796\pi$
$73$	0.189413	+	0.582954i	0.0221692	+	0.0682296i	−0.939360	+	0.342933i	$0.888580\pi$
$74$	−4.76718	+	14.6719i	−0.554173	+	1.70557i
$75$	3.42821	+	2.49074i	0.395856	+	0.287606i
$76$	1.26585			0.145203
$77$	2.09759	−	2.56907i	0.239042	−	0.292773i
$78$	−0.0527241			−0.00596983
$79$	0.125581	+	0.0912401i	0.0141290	+	0.0102653i	0.594827	−	0.803853i	$-0.297220\pi$
$79$	0.125581	+	0.0912401i	0.0141290	+	0.0102653i	−0.580698	+	0.814119i	$0.697220\pi$
$80$	0.946040	−	2.91161i	0.105771	−	0.325528i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−6.63251	+	4.81880i	−0.732439	+	0.532148i
$83$	−7.21319	+	5.24069i	−0.791750	+	0.575240i	−0.908482	−	0.417923i	$-0.862758\pi$
$83$	−7.21319	+	5.24069i	−0.791750	+	0.575240i	0.116732	+	0.993163i	$0.462758\pi$
$84$	0.0686960	+	0.211425i	0.00749535	+	0.0230683i
$85$	−0.552176	+	1.69942i	−0.0598919	+	0.184328i
$86$	−1.93824	−	1.40822i	−0.209006	−	0.151852i
$87$	−4.67254			−0.500949
$88$	9.50249	−	2.50520i	1.01297	−	0.267055i
$89$	5.17689			0.548749			0.274374	−	0.961623i	$-0.411529\pi$
$89$	5.17689			0.548749			0.274374	+	0.961623i	$0.411529\pi$
$90$	−0.941901	−	0.684331i	−0.0992851	−	0.0721348i
$91$	−0.0122198	+	0.0376086i	−0.00128098	+	0.00394245i
$92$	−0.410713	−	1.26404i	−0.0428198	−	0.131786i
$93$	−6.05057	+	4.39599i	−0.627414	+	0.455843i
$94$	6.52347	−	4.73958i	0.672845	−	0.488850i
$95$	1.53651	+	4.72888i	0.157642	+	0.485173i
$96$	−0.386732	+	1.19024i	−0.0394706	+	0.121478i
$97$	−6.42539	−	4.66832i	−0.652399	−	0.473996i	0.211688	−	0.977337i	$-0.432104\pi$
$97$	−6.42539	−	4.66832i	−0.652399	−	0.473996i	−0.864088	+	0.503341i	$0.832104\pi$
$98$	−1.33330			−0.134684
$99$	0.186920	−	3.31135i	0.0187861	−	0.332804i
$100$	0.942018			0.0942018
$101$	7.35849	+	5.34626i	0.732198	+	0.531973i	0.890258	−	0.455457i	$-0.150524\pi$
$101$	7.35849	+	5.34626i	0.732198	+	0.531973i	−0.158060	+	0.987429i	$0.550524\pi$
$102$	−0.843115	+	2.59484i	−0.0834808	+	0.256928i
$103$	1.06225	+	3.26926i	0.104666	+	0.322130i	0.989652	−	0.143489i	$-0.0458320\pi$
$103$	1.06225	+	3.26926i	0.104666	+	0.322130i	−0.884986	+	0.465618i	$0.845832\pi$
$104$	−0.0947918	+	0.0688703i	−0.00929510	+	0.00675328i
$105$	−0.706442	+	0.513260i	−0.0689417	+	0.0500891i
$106$	0.0512548	+	0.157746i	0.00497831	+	0.0153217i
$107$	1.01716	−	3.13050i	0.0983328	−	0.302637i	−0.889775	−	0.456399i	$-0.849139\pi$
$107$	1.01716	−	3.13050i	0.0983328	−	0.302637i	0.988108	+	0.153762i	$0.0491389\pi$
$108$	0.179849	+	0.130668i	0.0173059	+	0.0125735i
$109$	9.99510			0.957357			0.478678	−	0.877990i	$-0.341116\pi$
$109$	9.99510			0.957357			0.478678	+	0.877990i	$0.341116\pi$
$110$	2.09000	+	3.24688i	0.199274	+	0.309578i
$111$	11.5704			1.09822
$112$	−2.83639	−	2.06076i	−0.268014	−	0.194723i
$113$	1.36048	−	4.18713i	0.127983	−	0.393892i	−0.866449	−	0.499265i	$-0.833603\pi$
$113$	1.36048	−	4.18713i	0.127983	−	0.393892i	0.994433	+	0.105372i	$0.0336035\pi$
$114$	2.34609	+	7.22051i	0.219731	+	0.676263i
$115$	4.22361	−	3.06863i	0.393853	−	0.286151i
$116$	−0.840349	+	0.610549i	−0.0780245	+	0.0566881i
$117$	0.0122198	+	0.0376086i	0.00112972	+	0.00347692i
$118$	5.91074	−	18.1914i	0.544127	−	1.67465i
$119$	1.65552	+	1.20280i	0.151761	+	0.110261i
$120$	−2.58733			−0.236190
$121$	−4.55492	+	10.0126i	−0.414084	+	0.910239i
$122$	−10.0790			−0.912512
$123$	4.97450	+	3.61419i	0.448536	+	0.325880i
$124$	−0.513771	+	1.58123i	−0.0461380	+	0.141998i
$125$	2.49262	+	7.67149i	0.222947	+	0.686159i
$126$	−1.07866	+	0.783695i	−0.0960950	+	0.0698171i
$127$	−10.5029	+	7.63082i	−0.931984	+	0.677126i	−0.946478	−	0.322769i	$-0.895386\pi$
$127$	−10.5029	+	7.63082i	−0.931984	+	0.677126i	0.0144941	+	0.999895i	$0.495386\pi$
$128$	−2.80304	−	8.62687i	−0.247756	−	0.762515i
$129$	−0.555270	+	1.70895i	−0.0488888	+	0.150464i
$130$	−0.0372465	−	0.0270612i	−0.00326674	−	0.00237342i
$131$	18.1255			1.58363			0.791817	−	0.610758i	$-0.209135\pi$
$131$	18.1255			1.58363			0.791817	+	0.610758i	$0.209135\pi$
$132$	−0.399069	−	0.619966i	−0.0347345	−	0.0539611i
$133$	5.69421			0.493750
$134$	5.24164	+	3.80827i	0.452809	+	0.328985i
$135$	−0.269837	+	0.830472i	−0.0232239	+	0.0714757i
$136$	1.87366	+	5.76653i	0.160665	+	0.494476i
$137$	−4.21254	+	3.06059i	−0.359902	+	0.261484i	−0.753011	−	0.658008i	$-0.771399\pi$
$137$	−4.21254	+	3.06059i	−0.359902	+	0.261484i	0.393109	+	0.919492i	$0.371399\pi$
$138$	6.44901	−	4.68548i	0.548976	−	0.398855i
$139$	−5.60812	−	17.2600i	−0.475674	−	1.46397i	−0.845046	−	0.534693i	$-0.820427\pi$
$139$	−5.60812	−	17.2600i	−0.475674	−	1.46397i	0.369372	−	0.929282i	$-0.379573\pi$
$140$	−0.0599861	+	0.184618i	−0.00506975	+	0.0156031i
$141$	−4.89272	−	3.55477i	−0.412041	−	0.299365i
$142$	15.0000			1.25878
$143$	0.00739155	−	0.130944i	0.000618113	−	0.0109501i
$144$	−3.50597			−0.292164
$145$	−3.30088	−	2.39823i	−0.274123	−	0.199162i
$146$	−0.252545	+	0.777254i	−0.0209008	+	0.0643260i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	2.08093	−	1.51188i	0.171051	−	0.124276i
$149$	−8.93925	+	6.49475i	−0.732332	+	0.532070i	−0.890300	−	0.455374i	$-0.849506\pi$
$149$	−8.93925	+	6.49475i	−0.732332	+	0.532070i	0.157968	+	0.987444i	$0.449506\pi$
$150$	1.74591	+	5.37335i	0.142553	+	0.438732i
$151$	4.92308	−	15.1517i	0.400634	−	1.23303i	−0.523852	−	0.851810i	$-0.675505\pi$
$151$	4.92308	−	15.1517i	0.400634	−	1.23303i	0.924486	−	0.381216i	$-0.124495\pi$
$152$	13.6497	+	9.91709i	1.10714	+	0.804382i
$153$	2.04633			0.165436
$154$	4.27596	−	1.12730i	0.344567	−	0.0908403i
$155$	−6.53066			−0.524555
$156$	0.00711193	+	0.00516712i	0.000569410	+	0.000413701i
$157$	4.94536	−	15.2203i	0.394683	−	1.21471i	−0.534526	−	0.845152i	$-0.679510\pi$
$157$	4.94536	−	15.2203i	0.394683	−	1.21471i	0.929208	−	0.369556i	$-0.120490\pi$
$158$	0.0639555	+	0.196835i	0.00508803	+	0.0156593i
$159$	0.100643	−	0.0731211i	0.00798147	−	0.00579888i
$160$	−0.884105	+	0.642340i	−0.0698947	+	0.0507814i
$161$	−1.84752	−	5.68608i	−0.145605	−	0.448126i
$162$	−0.412013	+	1.26805i	−0.0323708	+	0.0996271i
$163$	−17.8012	−	12.9333i	−1.39429	−	1.01301i	−0.995379	−	0.0960257i	$-0.969387\pi$
$163$	−17.8012	−	12.9333i	−1.39429	−	1.01301i	−0.398915	−	0.916988i	$-0.630613\pi$
$164$	1.36691			0.106738
$165$	1.83163	−	2.24334i	0.142593	−	0.174644i
$166$	−11.8877			−0.922665
$167$	3.81938	+	2.77494i	0.295553	+	0.214731i	0.725673	−	0.688040i	$-0.241529\pi$
$167$	3.81938	+	2.77494i	0.295553	+	0.214731i	−0.430120	+	0.902772i	$0.641529\pi$
$168$	−0.915619	+	2.81798i	−0.0706415	+	0.217412i
$169$	−4.01674	−	12.3622i	−0.308980	−	0.950942i
$170$	−1.92744	+	1.40037i	−0.147828	+	0.107403i
$171$	4.60671	−	3.34697i	0.352284	−	0.255949i
$172$	0.123439	+	0.379907i	0.00941216	+	0.0289677i
$173$	−2.92816	+	9.01194i	−0.222624	+	0.685165i	0.775900	+	0.630855i	$0.217296\pi$
$173$	−2.92816	+	9.01194i	−0.222624	+	0.685165i	−0.998524	+	0.0543100i	$0.982704\pi$
$174$	−5.04010	−	3.66185i	−0.382089	−	0.277604i
$175$	4.23750			0.320325
$176$	10.8388	+	4.21080i	0.817004	+	0.317401i
$177$	−14.3460			−1.07831
$178$	5.58412	+	4.05710i	0.418548	+	0.304093i
$179$	5.47531	−	16.8513i	0.409244	−	1.25952i	−0.508055	−	0.861324i	$-0.669636\pi$
$179$	5.47531	−	16.8513i	0.409244	−	1.25952i	0.917299	−	0.398199i	$-0.130364\pi$
$180$	0.0599861	+	0.184618i	0.00447110	+	0.0137606i
$181$	−13.1661	+	9.56574i	−0.978629	+	0.711016i	−0.957402	−	0.288759i	$-0.906757\pi$
$181$	−13.1661	+	9.56574i	−0.978629	+	0.711016i	−0.0212275	+	0.999775i	$0.506757\pi$
$182$	−0.0426547	+	0.0309905i	−0.00316178	+	0.00229717i
$183$	2.33600	+	7.18946i	0.172682	+	0.531460i
$184$	5.47421	−	16.8479i	0.403564	−	1.24204i
$185$	8.17385	+	5.93865i	0.600953	+	0.436618i
$186$	−9.97165			−0.731157
$187$	−6.32628	−	2.45772i	−0.462623	−	0.179726i
$188$	−1.34444			−0.0980534
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$	−2.04863	+	6.30503i	−0.148623	+	0.457415i
$191$	1.99194	+	6.13055i	0.144131	+	0.443591i	0.996898	−	0.0787007i	$-0.0250772\pi$
$191$	1.99194	+	6.13055i	0.144131	+	0.443591i	−0.852767	+	0.522292i	$0.825077\pi$
$192$	−7.02272	+	5.10230i	−0.506821	+	0.368227i
$193$	1.46492	−	1.06433i	0.105447	−	0.0766120i	−0.533812	−	0.845603i	$-0.679241\pi$
$193$	1.46492	−	1.06433i	0.105447	−	0.0766120i	0.639259	+	0.768991i	$0.279241\pi$
$194$	−3.27230	−	10.0711i	−0.234937	−	0.723062i
$195$	−0.0106704	+	0.0328402i	−0.000764126	+	0.00235174i
$196$	0.179849	+	0.130668i	0.0128463	+	0.00933340i
$197$	−6.85772			−0.488592			−0.244296	−	0.969701i	$-0.578557\pi$
$197$	−6.85772			−0.488592			−0.244296	+	0.969701i	$0.578557\pi$
$198$	2.79672	−	3.42535i	0.198754	−	0.243429i
$199$	−5.07400			−0.359687			−0.179843	−	0.983695i	$-0.557559\pi$
$199$	−5.07400			−0.359687			−0.179843	+	0.983695i	$0.557559\pi$
$200$	10.1578	+	7.38008i	0.718265	+	0.521850i
$201$	1.50163	−	4.62154i	0.105917	−	0.325979i
$202$	3.74751	+	11.5336i	0.263674	+	0.811504i
$203$	−3.78016	+	2.74645i	−0.265315	+	0.192763i
$204$	0.368030	−	0.267389i	0.0257672	−	0.0187210i
$205$	1.65918	+	5.10643i	0.115882	+	0.356648i
$206$	−1.41630	+	4.35891i	−0.0986780	+	0.303700i
$207$	−4.83687	−	3.51419i	−0.336186	−	0.244253i
$208$	−0.138640			−0.00961296
$209$	−18.2616	+	4.81441i	−1.26318	+	0.333020i
$210$	−1.16425			−0.0803411
$211$	−6.55861	−	4.76511i	−0.451513	−	0.328044i	0.338680	−	0.940902i	$-0.390020\pi$
$211$	−6.55861	−	4.76511i	−0.451513	−	0.328044i	−0.790193	+	0.612858i	$0.790020\pi$
$212$	0.00854585	−	0.0263014i	0.000586932	−	0.00180639i
$213$	−3.47653	−	10.6997i	−0.238208	−	0.733129i
$214$	3.55054	−	2.57962i	0.242710	−	0.176339i
$215$	−1.26940	+	0.922274i	−0.0865724	+	0.0628985i
$216$	0.915619	+	2.81798i	0.0623000	+	0.191740i
$217$	−2.31111	+	7.11287i	−0.156888	+	0.482853i
$218$	10.7814	+	7.83311i	0.730205	+	0.530525i
$219$	0.612954			0.0414196
$220$	0.0362847	−	0.642797i	0.00244631	−	0.0433373i
$221$	0.0809201			0.00544328
$222$	12.4806	+	9.06771i	0.837645	+	0.608585i
$223$	−5.00761	+	15.4119i	−0.335335	+	1.03205i	0.631222	+	0.775602i	$0.282554\pi$
$223$	−5.00761	+	15.4119i	−0.335335	+	1.03205i	−0.966557	+	0.256452i	$0.917446\pi$
$224$	0.386732	+	1.19024i	0.0258396	+	0.0795261i
$225$	3.42821	−	2.49074i	0.228547	−	0.166049i
$226$	4.74894	−	3.45031i	0.315895	−	0.229511i
$227$	7.31572	+	22.5155i	0.485561	+	1.49440i	0.831166	+	0.556024i	$0.187674\pi$
$227$	7.31572	+	22.5155i	0.485561	+	1.49440i	−0.345605	+	0.938380i	$0.612326\pi$
$228$	0.391169	−	1.20390i	0.0259058	−	0.0797299i
$229$	−8.21697	−	5.96998i	−0.542993	−	0.394507i	0.282203	−	0.959355i	$-0.408935\pi$
$229$	−8.21697	−	5.96998i	−0.542993	−	0.394507i	−0.825195	+	0.564848i	$0.808935\pi$
$230$	6.96073			0.458977
$231$	−1.79514	−	2.78881i	−0.118112	−	0.183490i
$232$	−13.8448			−0.908952
$233$	−19.0247	−	13.8223i	−1.24635	−	0.905527i	−0.248346	−	0.968671i	$-0.579887\pi$
$233$	−19.0247	−	13.8223i	−1.24635	−	0.905527i	−0.998004	+	0.0631448i	$0.979887\pi$
$234$	−0.0162926	+	0.0501436i	−0.00106508	+	0.00327799i
$235$	−1.63190	−	5.02247i	−0.106453	−	0.327630i
$236$	−2.58011	+	1.87456i	−0.167951	+	0.122023i
$237$	0.125581	−	0.0912401i	0.00815738	−	0.00592668i
$238$	0.843115	+	2.59484i	0.0546510	+	0.168199i
$239$	2.41823	−	7.44253i	0.156422	−	0.481417i	−0.841880	−	0.539664i	$-0.818551\pi$
$239$	2.41823	−	7.44253i	0.156422	−	0.481417i	0.998302	+	0.0582470i	$0.0185511\pi$
$240$	−2.47677	−	1.79948i	−0.159875	−	0.116156i
$241$	−6.86139			−0.441981			−0.220991	−	0.975276i	$-0.570929\pi$
$241$	−6.86139			−0.441981			−0.220991	+	0.975276i	$0.570929\pi$
$242$	−12.7601	+	7.23059i	−0.820249	+	0.464800i
$243$	1.00000			0.0641500
$244$	1.35955	+	0.987774i	0.0870366	+	0.0632358i
$245$	−0.269837	+	0.830472i	−0.0172392	+	0.0530569i
$246$	2.53340	+	7.79699i	0.161523	+	0.497118i
$247$	0.182168	−	0.132353i	0.0115911	−	0.00842140i
$248$	−17.9279	+	13.0253i	−1.13842	+	0.827110i
$249$	2.75519	+	8.47961i	0.174603	+	0.537373i
$250$	−3.32341	+	10.2284i	−0.210191	+	0.646902i
$251$	2.07682	+	1.50890i	0.131088	+	0.0952407i	0.651397	−	0.758737i	$-0.274183\pi$
$251$	2.07682	+	1.50890i	0.131088	+	0.0952407i	−0.520309	+	0.853978i	$0.674183\pi$
$252$	0.222305			0.0140039
$253$	10.7326	+	16.6735i	0.674755	+	1.04825i
$254$	−17.3094			−1.08609
$255$	1.44561	+	1.05030i	0.0905279	+	0.0657724i
$256$	−1.62758	+	5.00918i	−0.101724	+	0.313074i
$257$	−6.05411	−	18.6326i	−0.377645	−	1.16227i	−0.941677	−	0.336519i	$-0.890750\pi$
$257$	−6.05411	−	18.6326i	−0.377645	−	1.16227i	0.564032	−	0.825753i	$-0.309250\pi$
$258$	−1.93824	+	1.40822i	−0.120670	+	0.0876717i
$259$	9.36069	−	6.80094i	0.581645	−	0.422590i
$260$	0.00237209	+	0.00730054i	0.000147111	+	0.000452760i
$261$	−1.44389	+	4.44385i	−0.0893748	+	0.275067i
$262$	19.5514	+	14.2049i	1.20789	+	0.877581i
$263$	−26.5306			−1.63595			−0.817974	−	0.575255i	$-0.804903\pi$
$263$	−26.5306			−1.63595			−0.817974	+	0.575255i	$0.804903\pi$
$264$	0.553844	−	9.81155i	0.0340867	−	0.603859i
$265$	0.108628			0.00667298
$266$	6.14214	+	4.46252i	0.376599	+	0.273615i
$267$	1.59975	−	4.92351i	0.0979028	−	0.301314i
$268$	−0.333820	−	1.02739i	−0.0203913	−	0.0627580i
$269$	13.8542	−	10.0657i	0.844708	−	0.613716i	−0.0789736	−	0.996877i	$-0.525164\pi$
$269$	13.8542	−	10.0657i	0.844708	−	0.613716i	0.923682	+	0.383160i	$0.125164\pi$
$270$	−0.941901	+	0.684331i	−0.0573223	+	0.0416471i
$271$	1.63641	+	5.03635i	0.0994049	+	0.305937i	0.988377	−	0.152025i	$-0.0485795\pi$
$271$	1.63641	+	5.03635i	0.0994049	+	0.305937i	−0.888972	+	0.457962i	$0.848580\pi$
$272$	−2.21700	+	6.82324i	−0.134426	+	0.413720i
$273$	0.0319918	+	0.0232434i	0.00193623	+	0.00140675i
$274$	−6.94249			−0.419411
$275$	−13.5899	+	3.58278i	−0.819500	+	0.216050i
$276$	−1.32910			−0.0800021
$277$	−1.98213	−	1.44010i	−0.119094	−	0.0865272i	0.526644	−	0.850086i	$-0.323450\pi$
$277$	−1.98213	−	1.44010i	−0.119094	−	0.0865272i	−0.645738	+	0.763559i	$0.723450\pi$
$278$	7.47731	−	23.0128i	0.448459	−	1.38022i
$279$	2.31111	+	7.11287i	0.138363	+	0.425836i
$280$	−2.09319	+	1.52079i	−0.125092	+	0.0908847i
$281$	−0.244117	+	0.177362i	−0.0145628	+	0.0105805i	−0.595043	−	0.803694i	$-0.702865\pi$
$281$	−0.244117	+	0.177362i	−0.0145628	+	0.0105805i	0.580480	+	0.814274i	$0.302865\pi$
$282$	−2.49174	−	7.66880i	−0.148381	−	0.456670i
$283$	7.41931	−	22.8343i	0.441032	−	1.35736i	−0.445745	−	0.895160i	$-0.647061\pi$
$283$	7.41931	−	22.8343i	0.441032	−	1.35736i	0.886777	−	0.462198i	$-0.152939\pi$
$284$	−2.02335	−	1.47005i	−0.120064	−	0.0872313i
$285$	4.97224			0.294530
$286$	0.110593	−	0.135452i	0.00653952	−	0.00800945i
$287$	6.14882			0.362954
$288$	1.01248	+	0.735607i	0.0596608	+	0.0433461i
$289$	−3.95929	+	12.1854i	−0.232899	+	0.716791i
$290$	−1.68106	−	5.17377i	−0.0987151	−	0.303814i
$291$	−6.42539	+	4.66832i	−0.376663	+	0.273662i
$292$	0.110239	−	0.0800933i	0.00645124	−	0.00468710i
$293$	−0.606919	−	1.86791i	−0.0354566	−	0.109124i	0.931762	−	0.363070i	$-0.118271\pi$
$293$	−0.606919	−	1.86791i	−0.0354566	−	0.109124i	−0.967218	+	0.253946i	$0.918271\pi$
$294$	−0.412013	+	1.26805i	−0.0240291	+	0.0739539i
$295$	−10.1346	−	7.36323i	−0.590060	−	0.428704i
$296$	34.2833			1.99268
$297$	−3.09152	−	1.20104i	−0.179388	−	0.0696912i
$298$	−14.7324			−0.853422
$299$	−0.191269	−	0.138965i	−0.0110614	−	0.00803657i
$300$	0.291100	−	0.895912i	0.0168066	−	0.0517255i
$301$	0.555270	+	1.70895i	0.0320053	+	0.0985020i
$302$	17.1846	−	12.4854i	0.988865	−	0.718453i
$303$	7.35849	−	5.34626i	0.422734	−	0.307135i
$304$	6.16913	+	18.9866i	0.353824	+	1.08896i
$305$	−2.03982	+	6.27791i	−0.116800	+	0.359472i
$306$	2.20730	+	1.60370i	0.126183	+	0.0916774i
$307$	20.0180			1.14249			0.571243	−	0.820781i	$-0.306462\pi$
$307$	20.0180			1.14249			0.571243	+	0.820781i	$0.306462\pi$
$308$	−0.687261	−	0.266996i	−0.0391603	−	0.0152135i
$309$	3.43750			0.195553
$310$	−7.04439	−	5.11805i	−0.400095	−	0.290686i
$311$	5.47087	−	16.8376i	0.310225	−	0.954773i	−0.667451	−	0.744654i	$-0.732615\pi$
$311$	5.47087	−	16.8376i	0.310225	−	0.954773i	0.977676	−	0.210119i	$-0.0673853\pi$
$312$	0.0362072	+	0.111434i	0.00204983	+	0.00630873i
$313$	−22.9207	+	16.6529i	−1.29555	+	0.941276i	−0.999902	−	0.0140197i	$-0.995537\pi$
$313$	−22.9207	+	16.6529i	−1.29555	+	0.941276i	−0.295653	+	0.955295i	$0.595537\pi$
$314$	17.2624	−	12.5419i	0.974175	−	0.707780i
$315$	0.269837	+	0.830472i	0.0152036	+	0.0467918i
$316$	0.0106635	−	0.0328188i	0.000599867	−	0.00184620i
$317$	17.7623	+	12.9051i	0.997631	+	0.724821i	0.961579	−	0.274529i	$-0.0885219\pi$
$317$	17.7623	+	12.9051i	0.997631	+	0.724821i	0.0360518	+	0.999350i	$0.488522\pi$
$318$	0.165864			0.00930120
$319$	9.80105	−	12.0041i	0.548753	−	0.672100i
$320$	−7.57995			−0.423732
$321$	−2.66297	−	1.93476i	−0.148632	−	0.107988i
$322$	2.46330	−	7.58127i	0.137275	−	0.422488i
$323$	−3.60074	−	11.0819i	−0.200350	−	0.616615i
$324$	0.179849	−	0.130668i	0.00999158	−	0.00725931i
$325$	0.135565	−	0.0984939i	0.00751981	−	0.00546346i
$326$	−9.06570	−	27.9014i	−0.502103	−	1.54531i
$327$	3.08865	−	9.50590i	0.170803	−	0.525678i
$328$	14.7395	+	10.7089i	0.813851	+	0.591297i
$329$	−6.04773			−0.333422
$330$	3.73381	−	0.984369i	0.205540	−	0.0541877i
$331$	23.1465			1.27225			0.636123	−	0.771587i	$-0.280537\pi$
$331$	23.1465			1.27225			0.636123	+	0.771587i	$0.280537\pi$
$332$	1.60353	+	1.16503i	0.0880050	+	0.0639394i
$333$	3.57546	−	11.0041i	0.195934	−	0.603024i
$334$	1.94512	+	5.98646i	0.106432	+	0.327565i
$335$	3.43287	−	2.49413i	0.187558	−	0.136269i
$336$	−2.83639	+	2.06076i	−0.154738	+	0.112424i
$337$	10.8190	+	33.2975i	0.589349	+	1.81383i	0.581054	+	0.813865i	$0.302640\pi$
$337$	10.8190	+	33.2975i	0.589349	+	1.81383i	0.00829520	+	0.999966i	$0.497360\pi$
$338$	5.35553	−	16.4826i	0.291302	−	0.896536i
$339$	−3.56179	−	2.58779i	−0.193450	−	0.140550i
$340$	0.397232			0.0215429
$341$	1.39796	−	24.7653i	0.0757035	−	1.34112i
$342$	7.59210			0.410534
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−1.64527	+	5.06362i	−0.0887069	+	0.273012i
$345$	−1.61327	−	4.96515i	−0.0868558	−	0.267315i
$346$	−10.2211	+	7.42608i	−0.549491	+	0.399228i
$347$	3.04157	−	2.20983i	0.163280	−	0.118630i	−0.503145	−	0.864202i	$-0.667824\pi$
$347$	3.04157	−	2.20983i	0.163280	−	0.118630i	0.666425	+	0.745572i	$0.267824\pi$
$348$	0.320985	+	0.987890i	0.0172066	+	0.0529564i
$349$	−3.76196	+	11.5781i	−0.201373	+	0.619764i	0.798469	+	0.602035i	$0.205643\pi$
$349$	−3.76196	+	11.5781i	−0.201373	+	0.619764i	−0.999843	+	0.0177282i	$0.994357\pi$
$350$	4.57084	+	3.32091i	0.244322	+	0.177510i
$351$	0.0395440			0.00211070
$352$	−2.24660	−	3.49017i	−0.119744	−	0.186027i
$353$	−5.79059			−0.308202			−0.154101	−	0.988055i	$-0.549248\pi$
$353$	−5.79059			−0.308202			−0.154101	+	0.988055i	$0.549248\pi$
$354$	−15.4745	−	11.2429i	−0.822461	−	0.597553i
$355$	3.03574	−	9.34306i	0.161121	−	0.495878i
$356$	−0.355631	−	1.09452i	−0.0188484	−	0.0580095i
$357$	1.65552	−	1.20280i	0.0876192	−	0.0636591i
$358$	19.1123	−	13.8859i	1.01012	−	0.733892i
$359$	1.78020	+	5.47890i	0.0939555	+	0.289165i	0.986980	−	0.160843i	$-0.0514212\pi$
$359$	1.78020	+	5.47890i	0.0939555	+	0.289165i	−0.893025	+	0.450008i	$0.851421\pi$
$360$	−0.799528	+	2.46069i	−0.0421388	+	0.129690i
$361$	−10.8602	−	7.89042i	−0.571591	−	0.415285i
$362$	−21.6984			−1.14044
$363$	8.11503	+	7.42606i	0.425928	+	0.389767i
$364$	0.00879083			0.000460765
$365$	0.433017	+	0.314605i	0.0226651	+	0.0164672i
$366$	−3.11459	+	9.58572i	−0.162802	+	0.501054i
$367$	4.40597	+	13.5602i	0.229990	+	0.707836i	0.997747	+	0.0670949i	$0.0213730\pi$
$367$	4.40597	+	13.5602i	0.229990	+	0.707836i	−0.767757	+	0.640742i	$0.778627\pi$
$368$	16.9579	−	12.3207i	0.883993	−	0.642259i
$369$	4.97450	−	3.61419i	0.258962	−	0.188147i
$370$	4.16275	+	12.8116i	0.216411	+	0.666044i
$371$	0.0384420	−	0.118312i	0.00199581	−	0.00614247i
$372$	1.34507	+	0.977251i	0.0697387	+	0.0506681i
$373$	32.2223			1.66841			0.834203	−	0.551458i	$-0.185928\pi$
$373$	32.2223			1.66841			0.834203	+	0.551458i	$0.185928\pi$
$374$	−4.89783	−	7.60893i	−0.253261	−	0.393448i
$375$	8.06628			0.416541
$376$	−14.4971	−	10.5328i	−0.747633	−	0.543187i
$377$	−0.0570974	+	0.175728i	−0.00294066	+	0.00905043i
$378$	0.412013	+	1.26805i	0.0211917	+	0.0652212i
$379$	23.1196	−	16.7973i	1.18757	−	0.862822i	0.194567	−	0.980889i	$-0.437670\pi$
$379$	23.1196	−	16.7973i	1.18757	−	0.862822i	0.993006	+	0.118068i	$0.0376699\pi$
$380$	0.894250	−	0.649711i	0.0458741	−	0.0333295i
$381$	4.01176	+	12.3469i	0.205529	+	0.632552i
$382$	−2.65585	+	8.17388i	−0.135885	+	0.418212i
$383$	16.3108	+	11.8505i	0.833444	+	0.605533i	0.920532	−	0.390668i	$-0.127756\pi$
$383$	16.3108	+	11.8505i	0.833444	+	0.605533i	−0.0870873	+	0.996201i	$0.527756\pi$
$384$	−9.07082			−0.462894
$385$	0.163220	−	2.89151i	0.00831847	−	0.147365i
$386$	2.41427			0.122883
$387$	1.45372	+	1.05619i	0.0738966	+	0.0536890i
$388$	−0.545599	+	1.67918i	−0.0276986	+	0.0852474i
$389$	−5.11755	−	15.7502i	−0.259470	−	0.798567i	−0.992916	−	0.118819i	$-0.962089\pi$
$389$	−5.11755	−	15.7502i	−0.259470	−	0.798567i	0.733446	−	0.679748i	$-0.237911\pi$
$390$	−0.0372465	+	0.0270612i	−0.00188605	+	0.00137030i
$391$	−9.89784	+	7.19120i	−0.500555	+	0.363675i
$392$	0.915619	+	2.81798i	0.0462457	+	0.142330i
$393$	5.60110	−	17.2384i	0.282538	−	0.869562i
$394$	−7.39718	−	5.37436i	−0.372664	−	0.270757i
$395$	0.135546			0.00682005
$396$	−0.712942	+	0.187957i	−0.0358267	+	0.00944521i
$397$	30.9920			1.55545			0.777723	−	0.628607i	$-0.216375\pi$
$397$	30.9920			1.55545			0.777723	+	0.628607i	$0.216375\pi$
$398$	−5.47315	−	3.97647i	−0.274344	−	0.199323i
$399$	1.75961	−	5.41551i	0.0880905	−	0.271115i
$400$	4.59093	+	14.1294i	0.229547	+	0.706472i
$401$	−2.81752	+	2.04705i	−0.140700	+	0.102225i	−0.655909	−	0.754840i	$-0.727714\pi$
$401$	−2.81752	+	2.04705i	−0.140700	+	0.102225i	0.515209	+	0.857065i	$0.327714\pi$
$402$	5.24164	−	3.80827i	0.261429	−	0.189939i
$403$	0.0913906	+	0.281271i	0.00455249	+	0.0140111i
$404$	0.624831	−	1.92303i	0.0310865	−	0.0956745i
$405$	0.706442	+	0.513260i	0.0351034	+	0.0255041i
$406$	−6.22991			−0.309185
$407$	−24.2700	+	29.7253i	−1.20302	+	1.47343i
$408$	6.06329			0.300177
$409$	21.5104	+	15.6282i	1.06362	+	0.772765i	0.974755	−	0.223279i	$-0.0716760\pi$
$409$	21.5104	+	15.6282i	1.06362	+	0.772765i	0.0888652	+	0.996044i	$0.471676\pi$
$410$	−2.21219	+	6.80841i	−0.109252	+	0.336244i
$411$	1.60905	+	4.95214i	0.0793684	+	0.244271i
$412$	0.618229	−	0.449170i	0.0304580	−	0.0221290i
$413$	−11.6062	+	8.43236i	−0.571101	+	0.414929i
$414$	−2.46330	−	7.58127i	−0.121065	−	0.372599i
$415$	−2.40586	+	7.40448i	−0.118099	+	0.363472i
$416$	0.0400374	+	0.0290889i	0.00196299	+	0.00142620i
$417$	−18.1482			−0.888723
$418$	−23.4711	−	9.11838i	−1.14801	−	0.445995i
$419$	29.1491			1.42402			0.712012	−	0.702167i	$-0.247784\pi$
$419$	29.1491			1.42402			0.712012	+	0.702167i	$0.247784\pi$
$420$	0.157046	+	0.114100i	0.00766304	+	0.00556752i
$421$	−6.17753	+	19.0125i	−0.301074	+	0.926611i	0.680039	+	0.733176i	$0.261963\pi$
$421$	−6.17753	+	19.0125i	−0.301074	+	0.926611i	−0.981113	+	0.193435i	$0.938037\pi$
$422$	−3.34014	−	10.2799i	−0.162596	−	0.500418i
$423$	−4.89272	+	3.55477i	−0.237892	+	0.172839i
$424$	0.298204	−	0.216658i	0.0144821	−	0.0105218i
$425$	−2.67959	−	8.24693i	−0.129979	−	0.400035i
$426$	4.63527	−	14.2659i	0.224579	−	0.691184i
$427$	6.11572	+	4.44333i	0.295960	+	0.215028i
$428$	−0.731740			−0.0353700
$429$	−0.122251	−	0.0474938i	−0.00590234	−	0.00229302i
$430$	−2.09204			−0.100887
$431$	−13.6954	−	9.95033i	−0.659687	−	0.479290i	0.206870	−	0.978368i	$-0.433672\pi$
$431$	−13.6954	−	9.95033i	−0.659687	−	0.479290i	−0.866557	+	0.499078i	$0.833672\pi$
$432$	−1.08340	+	3.33438i	−0.0521253	+	0.160425i
$433$	−2.64255	−	8.13294i	−0.126993	−	0.390844i	0.867266	−	0.497845i	$-0.165875\pi$
$433$	−2.64255	−	8.13294i	−0.126993	−	0.390844i	−0.994259	+	0.107001i	$0.965875\pi$
$434$	−8.06723	+	5.86119i	−0.387240	+	0.281346i
$435$	−3.30088	+	2.39823i	−0.158265	+	0.114986i
$436$	−0.686623	−	2.11321i	−0.0328833	−	0.101204i
$437$	−10.5202	+	32.3777i	−0.503248	+	1.54884i
$438$	0.661172	+	0.480370i	0.0315920	+	0.0229529i
$439$	−33.9408			−1.61990			−0.809952	−	0.586496i	$-0.800507\pi$
$439$	−33.9408			−1.61990			−0.809952	+	0.586496i	$0.800507\pi$
$440$	5.42714	−	6.64703i	0.258729	−	0.316885i
$441$	1.00000			0.0476190
$442$	0.0872857	+	0.0634167i	0.00415176	+	0.00301643i
$443$	−10.8651	+	33.4393i	−0.516216	+	1.58875i	0.264844	+	0.964291i	$0.414680\pi$
$443$	−10.8651	+	33.4393i	−0.516216	+	1.58875i	−0.781059	+	0.624457i	$0.785320\pi$
$444$	−0.794844	−	2.44628i	−0.0377216	−	0.116095i
$445$	3.65717	−	2.65709i	0.173366	−	0.125958i
$446$	−17.4797	+	12.6998i	−0.827689	+	0.601352i
$447$	3.41449	+	10.5087i	0.161500	+	0.497045i
$448$	−2.68244	+	8.25570i	−0.126733	+	0.390045i
$449$	1.55978	+	1.13325i	0.0736107	+	0.0534813i	0.623982	−	0.781439i	$-0.285514\pi$
$449$	1.55978	+	1.13325i	0.0736107	+	0.0534813i	−0.550371	+	0.834920i	$0.685514\pi$
$450$	5.64987			0.266338
$451$	−19.7196	+	5.19879i	−0.928558	+	0.244801i
$452$	−0.978723			−0.0460352
$453$	−12.8888	−	9.36425i	−0.605568	−	0.439971i
$454$	−9.75407	+	30.0199i	−0.457781	+	1.40891i
$455$	0.0106704	+	0.0328402i	0.000500238	+	0.00153957i
$456$	13.6497	−	9.91709i	0.639206	−	0.464410i
$457$	6.19032	−	4.49753i	0.289571	−	0.210386i	−0.433510	−	0.901149i	$-0.642725\pi$
$457$	6.19032	−	4.49753i	0.289571	−	0.210386i	0.723081	+	0.690763i	$0.242725\pi$
$458$	−4.18471	−	12.8792i	−0.195539	−	0.601806i
$459$	0.632351	−	1.94618i	0.0295156	−	0.0908397i
$460$	−0.938929	−	0.682172i	−0.0437778	−	0.0318064i
$461$	40.7525			1.89803			0.949017	−	0.315224i	$-0.102080\pi$
$461$	40.7525			1.89803			0.949017	+	0.315224i	$0.102080\pi$
$462$	0.249220	−	4.41504i	0.0115948	−	0.205406i
$463$	−8.37407			−0.389176			−0.194588	−	0.980885i	$-0.562337\pi$
$463$	−8.37407			−0.389176			−0.194588	+	0.980885i	$0.562337\pi$
$464$	−13.2531	−	9.62897i	−0.615262	−	0.447014i
$465$	−2.01809	+	6.21103i	−0.0935865	+	0.288030i
$466$	−9.68883	−	29.8192i	−0.448827	−	1.38135i
$467$	−7.68254	+	5.58169i	−0.355505	+	0.258290i	−0.751175	−	0.660103i	$-0.770513\pi$
$467$	−7.68254	+	5.58169i	−0.355505	+	0.258290i	0.395670	+	0.918393i	$0.370513\pi$
$468$	0.00711193	−	0.00516712i	0.000328749	−	0.000238850i
$469$	−1.50163	−	4.62154i	−0.0693389	−	0.213403i
$470$	2.17582	−	6.69648i	0.100363	−	0.308885i
$471$	−12.9471	−	9.40663i	−0.596572	−	0.433435i
$472$	−42.5072			−1.95655
$473$	−3.22568	−	5.01119i	−0.148317	−	0.230415i
$474$	0.206964			0.00950619
$475$	−19.5209	−	14.1828i	−0.895683	−	0.650751i
$476$	0.140575	−	0.432645i	0.00644323	−	0.0198302i
$477$	−0.0384420	−	0.118312i	−0.00176014	−	0.00541715i
$478$	8.44113	−	6.13284i	0.386088	−	0.280510i
$479$	29.3659	−	21.3356i	1.34176	−	0.974849i	0.342387	−	0.939559i	$-0.388765\pi$
$479$	29.3659	−	21.3356i	1.34176	−	0.974849i	0.999377	−	0.0352896i	$-0.0112354\pi$
$480$	0.337698	+	1.03933i	0.0154137	+	0.0474386i
$481$	0.141388	−	0.435148i	0.00644675	−	0.0198410i
$482$	−7.40114	−	5.37724i	−0.337113	−	0.244927i
$483$	−5.97870			−0.272040
$484$	2.42982	+	0.275194i	0.110446	+	0.0125088i
$485$	−6.93523			−0.314912
$486$	1.07866	+	0.783695i	0.0489292	+	0.0355491i
$487$	1.65861	−	5.10466i	0.0751586	−	0.231314i	−0.906419	−	0.422381i	$-0.861195\pi$
$487$	1.65861	−	5.10466i	0.0751586	−	0.231314i	0.981577	+	0.191066i	$0.0611945\pi$
$488$	6.92157	+	21.3024i	0.313325	+	0.964314i
$489$	−17.8012	+	12.9333i	−0.804996	+	0.584864i
$490$	−0.941901	+	0.684331i	−0.0425507	+	0.0309149i
$491$	7.12636	+	21.9327i	0.321608	+	0.989808i	0.972948	+	0.231022i	$0.0742071\pi$
$491$	7.12636	+	21.9327i	0.321608	+	0.989808i	−0.651340	+	0.758786i	$0.725793\pi$
$492$	0.422400	−	1.30001i	0.0190432	−	0.0586091i
$493$	7.73547	+	5.62014i	0.348388	+	0.253119i
$494$	0.300222			0.0135076
$495$	−1.56754	−	2.43522i	−0.0704556	−	0.109455i
$496$	−26.2208			−1.17735
$497$	−9.10168	−	6.61275i	−0.408266	−	0.296623i
$498$	−3.67350	+	11.3059i	−0.164614	+	0.506629i
$499$	10.2406	+	31.5172i	0.458431	+	1.41090i	0.867060	+	0.498204i	$0.166007\pi$
$499$	10.2406	+	31.5172i	0.458431	+	1.41090i	−0.408629	+	0.912700i	$0.633993\pi$
$500$	1.45071	−	1.05400i	0.0648777	−	0.0471364i
$501$	3.81938	−	2.77494i	0.170637	−	0.123975i
$502$	1.05767	+	3.25518i	0.0472063	+	0.145286i
$503$	−5.59684	+	17.2253i	−0.249551	+	0.768038i	0.745304	+	0.666725i	$0.232304\pi$
$503$	−5.59684	+	17.2253i	−0.249551	+	0.768038i	−0.994855	+	0.101313i	$0.967696\pi$
$504$	2.39712	+	1.74161i	0.106776	+	0.0775775i
$505$	7.94237			0.353431
$506$	−1.49001	+	26.3962i	−0.0662392	+	1.17345i
$507$	−12.9984			−0.577281
$508$	2.33485	+	1.69637i	0.103592	+	0.0752642i
$509$	−4.81817	+	14.8288i	−0.213562	+	0.657275i	0.785691	+	0.618619i	$0.212308\pi$
$509$	−4.81817	+	14.8288i	−0.213562	+	0.657275i	−0.999253	+	0.0386557i	$0.987692\pi$
$510$	0.736217	+	2.26584i	0.0326002	+	0.100333i
$511$	0.495890	−	0.360286i	0.0219369	−	0.0159381i
$512$	−20.3582	+	14.7911i	−0.899713	+	0.653680i
$513$	−1.75961	−	5.41551i	−0.0776885	−	0.239101i
$514$	8.07196	−	24.8429i	0.356039	−	1.09577i
$515$	2.42840	+	1.76433i	0.107008	+	0.0777458i
$516$	0.399458			0.0175852
$517$	19.3953	−	5.11332i	0.853006	−	0.224883i
$518$	15.4269			0.677819
$519$	7.66602	+	5.56969i	0.336501	+	0.244482i
$520$	−0.0316165	+	0.0973057i	−0.00138648	+	0.00426714i
$521$	−4.78023	−	14.7120i	−0.209426	−	0.644546i	−0.999503	−	0.0315383i	$-0.989959\pi$
$521$	−4.78023	−	14.7120i	−0.209426	−	0.644546i	0.790077	−	0.613008i	$-0.210041\pi$
$522$	−5.04010	+	3.66185i	−0.220599	+	0.160275i
$523$	14.0335	−	10.1959i	0.613643	−	0.445837i	−0.237053	−	0.971497i	$-0.576181\pi$
$523$	14.0335	−	10.1959i	0.613643	−	0.445837i	0.850695	+	0.525659i	$0.176181\pi$
$524$	−1.24515	−	3.83218i	−0.0543947	−	0.167410i
$525$	1.30946	−	4.03011i	0.0571495	−	0.175888i
$526$	−28.6176	−	20.7919i	−1.24779	−	0.906571i
$527$	15.3043			0.666667
$528$	7.35407	−	9.00709i	0.320045	−	0.391983i
$529$	12.7449			0.554126
$530$	0.117173	+	0.0851315i	0.00508969	+	0.00369788i
$531$	−4.43316	+	13.6439i	−0.192383	+	0.592093i
$532$	−0.391169	−	1.20390i	−0.0169593	−	0.0521955i
$533$	0.196712	−	0.142919i	0.00852053	−	0.00619053i
$534$	5.58412	−	4.05710i	0.241649	−	0.175568i
$535$	−0.888197	−	2.73359i	−0.0384001	−	0.118183i
$536$	4.44934	−	13.6937i	0.192182	−	0.591476i
$537$	−14.3345	−	10.4147i	−0.618581	−	0.449426i
$538$	22.8325			0.984380
$539$	−3.09152	−	1.20104i	−0.133161	−	0.0517323i
$540$	0.194119			0.00835355
$541$	−24.5088	−	17.8067i	−1.05372	−	0.765569i	−0.0808002	−	0.996730i	$-0.525748\pi$
$541$	−24.5088	−	17.8067i	−1.05372	−	0.765569i	−0.972916	+	0.231161i	$0.925748\pi$
$542$	−2.18183	+	6.71498i	−0.0937176	+	0.288433i
$543$	5.02901	+	15.4777i	0.215815	+	0.664211i
$544$	2.07186	−	1.50530i	0.0888304	−	0.0645390i
$545$	7.06096	−	5.13009i	0.302458	−	0.219749i
$546$	0.0162926	+	0.0501436i	0.000697261	+	0.00214595i
$547$	−9.40927	+	28.9588i	−0.402311	+	1.23819i	0.520808	+	0.853674i	$0.325631\pi$
$547$	−9.40927	+	28.9588i	−0.402311	+	1.23819i	−0.923119	+	0.384513i	$0.874369\pi$
$548$	0.936469	+	0.680384i	0.0400040	+	0.0290646i
$549$	7.55944			0.322629
$550$	−17.4667	−	6.78570i	−0.744783	−	0.289343i
$551$	26.6064			1.13347
$552$	−14.3317	−	10.4126i	−0.609997	−	0.443188i
$553$	0.0479677	−	0.147630i	0.00203980	−	0.00627785i
$554$	−1.00945	−	3.10677i	−0.0428874	−	0.131994i
$555$	8.17385	−	5.93865i	0.346961	−	0.252082i
$556$	−3.26393	+	2.37139i	−0.138422	+	0.100569i
$557$	2.21706	+	6.82341i	0.0939399	+	0.289117i	0.986976	−	0.160868i	$-0.0514293\pi$
$557$	2.21706	+	6.82341i	0.0939399	+	0.289117i	−0.893036	+	0.449985i	$0.851429\pi$
$558$	−3.08141	+	9.48360i	−0.130446	+	0.401473i
$559$	0.0574858	+	0.0417659i	0.00243139	+	0.00176651i
$560$	−3.06145			−0.129370
$561$	−4.29236	+	5.25717i	−0.181223	+	0.221958i
$562$	−0.402318			−0.0169708
$563$	−7.29219	−	5.29809i	−0.307329	−	0.223288i	0.423421	−	0.905933i	$-0.360829\pi$
$563$	−7.29219	−	5.29809i	−0.307329	−	0.223288i	−0.730750	+	0.682646i	$0.760829\pi$
$564$	−0.415455	+	1.27864i	−0.0174938	+	0.0538404i
$565$	−1.18799	−	3.65625i	−0.0499790	−	0.153820i
$566$	25.8981	−	18.8161i	1.08858	−	0.790898i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	−10.3010	−	31.7031i	−0.432219	−	1.33023i
$569$	2.30526	−	7.09487i	0.0966417	−	0.297433i	−0.891036	−	0.453932i	$-0.850021\pi$
$569$	2.30526	−	7.09487i	0.0966417	−	0.297433i	0.987678	+	0.156499i	$0.0500209\pi$
$570$	5.36338	+	3.89672i	0.224647	+	0.163216i
$571$	−37.5921			−1.57318			−0.786590	−	0.617475i	$-0.788156\pi$
$571$	−37.5921			−1.57318			−0.786590	+	0.617475i	$0.788156\pi$
$572$	−0.0281926	+	0.00743259i	−0.00117879	+	0.000310772i
$573$	6.44604			0.269287
$574$	6.63251	+	4.81880i	0.276836	+	0.201133i
$575$	−7.82888	+	24.0948i	−0.326487	+	1.00482i
$576$	2.68244	+	8.25570i	0.111768	+	0.343987i
$577$	9.80773	−	7.12573i	0.408301	−	0.296648i	−0.364613	−	0.931159i	$-0.618799\pi$
$577$	9.80773	−	7.12573i	0.408301	−	0.296648i	0.772914	+	0.634511i	$0.218799\pi$
$578$	−13.8204	+	10.0411i	−0.574854	+	0.417656i
$579$	−0.559550	−	1.72212i	−0.0232541	−	0.0715688i
$580$	−0.280287	+	0.862635i	−0.0116383	+	0.0358190i
$581$	7.21319	+	5.24069i	0.299253	+	0.217420i
$582$	−10.5894			−0.438944
$583$	−0.0232530	+	0.411936i	−0.000963041	+	0.0170606i
$584$	1.81619			0.0751543
$585$	0.0279356	+	0.0202964i	0.00115499	+	0.000839152i
$586$	0.809207	−	2.49048i	0.0334280	−	0.102881i
$587$	−0.395768	−	1.21805i	−0.0163351	−	0.0502743i	0.942557	−	0.334046i	$-0.108414\pi$
$587$	−0.395768	−	1.21805i	−0.0163351	−	0.0502743i	−0.958892	+	0.283772i	$0.908414\pi$
$588$	0.179849	−	0.130668i	0.00741683	−	0.00538864i
$589$	34.4532	−	25.0317i	1.41962	−	1.03141i
$590$	−5.16132	−	15.8849i	−0.212488	−	0.653971i
$591$	−2.11915	+	6.52208i	−0.0871703	+	0.268283i
$592$	32.8183	+	23.8439i	1.34882	+	0.979978i
$593$	−24.7324			−1.01564			−0.507819	−	0.861464i	$-0.669548\pi$
$593$	−24.7324			−1.01564			−0.507819	+	0.861464i	$0.669548\pi$
$594$	−2.39347	−	3.71833i	−0.0982052	−	0.152565i
$595$	1.78688			0.0732548
$596$	1.98724	+	1.44381i	0.0814005	+	0.0591409i
$597$	−1.56795	+	4.82567i	−0.0641721	+	0.197501i
$598$	−0.0974089	−	0.299794i	−0.00398335	−	0.0122595i
$599$	22.5718	−	16.3994i	0.922260	−	0.670061i	−0.0218257	−	0.999762i	$-0.506948\pi$
$599$	22.5718	−	16.3994i	0.922260	−	0.670061i	0.944085	+	0.329701i	$0.106948\pi$
$600$	10.1578	−	7.38008i	0.414691	−	0.301290i
$601$	−10.6381	−	32.7407i	−0.433936	−	1.33552i	−0.894173	−	0.447722i	$-0.852235\pi$
$601$	−10.6381	−	32.7407i	−0.433936	−	1.33552i	0.460236	−	0.887797i	$-0.347765\pi$
$602$	−0.740343	+	2.27854i	−0.0301741	+	0.0928665i
$603$	−3.93132	−	2.85627i	−0.160096	−	0.116316i
$604$	−3.54163			−0.144107
$605$	1.92130	+	9.41120i	0.0781118	+	0.382620i
$606$	12.1272			0.492633
$607$	21.3777	+	15.5318i	0.867693	+	0.630416i	0.929967	−	0.367643i	$-0.119835\pi$
$607$	21.3777	+	15.5318i	0.867693	+	0.630416i	−0.0622737	+	0.998059i	$0.519835\pi$
$608$	2.20213	−	6.77746i	0.0893082	−	0.274862i
$609$	1.44389	+	4.44385i	0.0585095	+	0.180074i
$610$	−7.12025	+	5.17316i	−0.288290	+	0.209455i
$611$	−0.193478	+	0.140570i	−0.00782727	+	0.00568684i
$612$	−0.140575	−	0.432645i	−0.00568240	−	0.0174886i
$613$	−12.2373	+	37.6625i	−0.494260	+	1.52118i	0.323847	+	0.946109i	$0.395024\pi$
$613$	−12.2373	+	37.6625i	−0.494260	+	1.52118i	−0.818107	+	0.575066i	$0.804976\pi$
$614$	21.5927	+	15.6880i	0.871409	+	0.633115i
$615$	5.36922			0.216508
$616$	−5.31902	−	8.26326i	−0.214309	−	0.332936i
$617$	17.0640			0.686971			0.343486	−	0.939158i	$-0.388392\pi$
$617$	17.0640			0.686971			0.343486	+	0.939158i	$0.388392\pi$
$618$	3.70791	+	2.69395i	0.149154	+	0.108367i
$619$	9.04822	−	27.8476i	0.363679	−	1.11929i	−0.587126	−	0.809496i	$-0.699741\pi$
$619$	9.04822	−	27.8476i	0.363679	−	1.11929i	0.950804	−	0.309792i	$-0.100259\pi$
$620$	0.448630	+	1.38074i	0.0180174	+	0.0554520i
$621$	−4.83687	+	3.51419i	−0.194097	+	0.141020i
$622$	19.0968	−	13.8746i	0.765711	−	0.556322i
$623$	−1.59975	−	4.92351i	−0.0640925	−	0.197256i
$624$	−0.0428422	+	0.131855i	−0.00171506	+	0.00527841i
$625$	−11.4427	−	8.31361i	−0.457708	−	0.332544i
$626$	−37.7745			−1.50977
$627$	−1.06436	+	18.8555i	−0.0425064	+	0.753017i
$628$	−3.55766			−0.141966
$629$	−19.1551	−	13.9170i	−0.763763	−	0.554906i
$630$	−0.359774	+	1.10727i	−0.0143337	+	0.0441147i
$631$	−12.4517	−	38.3223i	−0.495693	−	1.52559i	−0.815875	−	0.578229i	$-0.803744\pi$
$631$	−12.4517	−	38.3223i	−0.495693	−	1.52559i	0.320182	−	0.947356i	$-0.396256\pi$
$632$	0.372098	−	0.270345i	0.0148012	−	0.0107537i
$633$	−6.55861	+	4.76511i	−0.260681	+	0.189396i
$634$	9.04592	+	27.8405i	0.359259	+	1.10569i
$635$	−3.50311	+	10.7815i	−0.139017	+	0.427849i
$636$	−0.0223733	−	0.0162552i	−0.000887161	−	0.000644560i
$637$	0.0395440			0.00156679
$638$	19.9796	−	5.26734i	0.791000	−	0.208536i
$639$	−11.2503			−0.445055
$640$	−6.40801	−	4.65569i	−0.253299	−	0.184032i
$641$	−3.88039	+	11.9426i	−0.153266	+	0.471705i	−0.997981	−	0.0635114i	$-0.979770\pi$
$641$	−3.88039	+	11.9426i	−0.153266	+	0.471705i	0.844715	+	0.535217i	$0.179770\pi$
$642$	−1.35618	−	4.17391i	−0.0535243	−	0.164731i
$643$	3.34694	−	2.43170i	0.131991	−	0.0958968i	−0.519831	−	0.854269i	$-0.674005\pi$
$643$	3.34694	−	2.43170i	0.131991	−	0.0958968i	0.651822	+	0.758372i	$0.274005\pi$
$644$	−1.07526	+	0.781223i	−0.0423712	+	0.0307845i
$645$	0.484868	+	1.49227i	0.0190917	+	0.0587581i
$646$	4.80087	−	14.7756i	0.188888	−	0.581337i
$647$	30.4262	+	22.1059i	1.19618	+	0.869073i	0.993903	−	0.110256i	$-0.0351670\pi$
$647$	30.4262	+	22.1059i	1.19618	+	0.869073i	0.202273	+	0.979329i	$0.435167\pi$
$648$	2.96300			0.116398
$649$	30.0920	−	36.8559i	1.18121	−	1.44672i
$650$	0.223419			0.00876320
$651$	6.05057	+	4.39599i	0.237140	+	0.172293i
$652$	−1.51155	+	4.65207i	−0.0591968	+	0.182189i
$653$	1.86070	+	5.72666i	0.0728150	+	0.224102i	0.980840	−	0.194814i	$-0.0624103\pi$
$653$	1.86070	+	5.72666i	0.0728150	+	0.224102i	−0.908025	+	0.418916i	$0.862410\pi$
$654$	10.7814	−	7.83311i	0.421584	−	0.306299i
$655$	12.8046	−	9.30311i	0.500319	−	0.363503i
$656$	6.66166	+	20.5025i	0.260094	+	0.800488i
$657$	0.189413	−	0.582954i	0.00738972	−	0.0227432i
$658$	−6.52347	−	4.73958i	−0.254311	−	0.184768i
$659$	−38.6192			−1.50439			−0.752195	−	0.658940i	$-0.771005\pi$
$659$	−38.6192			−1.50439			−0.752195	+	0.658940i	$0.771005\pi$
$660$	−0.600123	−	0.233144i	−0.0233598	−	0.00907511i
$661$	43.0833			1.67575			0.837874	−	0.545864i	$-0.183798\pi$
$661$	43.0833			1.67575			0.837874	+	0.545864i	$0.183798\pi$
$662$	24.9673	+	18.1398i	0.970382	+	0.705024i
$663$	0.0250057	−	0.0769596i	0.000971141	−	0.00298886i
$664$	8.16364	+	25.1251i	0.316811	+	0.975044i
$665$	4.02263	−	2.92261i	0.155991	−	0.113334i
$666$	12.4806	−	9.06771i	0.483614	−	0.351366i
$667$	−8.63261	−	26.5685i	−0.334256	−	1.02873i
$668$	0.324315	−	0.998138i	0.0125481	−	0.0386191i
$669$	13.1101	+	9.52505i	0.506866	+	0.368260i
$670$	5.65755			0.218570
$671$	−23.3702	−	9.07916i	−0.902196	−	0.350497i
$672$	1.25149			0.0482773
$673$	17.0032	+	12.3535i	0.655425	+	0.476194i	0.865115	−	0.501574i	$-0.167246\pi$
$673$	17.0032	+	12.3535i	0.655425	+	0.476194i	−0.209690	+	0.977768i	$0.567246\pi$
$674$	−14.4250	+	44.3956i	−0.555631	+	1.71006i
$675$	−1.30946	−	4.03011i	−0.0504012	−	0.155119i
$676$	−2.33775	+	1.69847i	−0.0899134	+	0.0653259i
$677$	19.3263	−	14.0414i	0.742770	−	0.539654i	−0.150807	−	0.988563i	$-0.548187\pi$
$677$	19.3263	−	14.0414i	0.742770	−	0.539654i	0.893578	+	0.448909i	$0.148187\pi$
$678$	−1.81393	−	5.58271i	−0.0696637	−	0.214403i
$679$	−2.45428	+	7.55350i	−0.0941866	+	0.289877i
$680$	4.28336	+	3.11204i	0.164259	+	0.119341i
$681$	23.6742			0.907196
$682$	20.9164	−	25.6179i	0.800930	−	0.980960i
$683$	−13.5672			−0.519134			−0.259567	−	0.965725i	$-0.583580\pi$
$683$	−13.5672			−0.519134			−0.259567	+	0.965725i	$0.583580\pi$
$684$	−1.02409	−	0.744048i	−0.0391572	−	0.0284494i
$685$	−1.40504	+	4.32426i	−0.0536837	+	0.165221i
$686$	0.412013	+	1.26805i	0.0157307	+	0.0484142i
$687$	−8.21697	+	5.96998i	−0.313497	+	0.227769i
$688$	−5.09669	+	3.70296i	−0.194309	+	0.141174i
$689$	−0.00152015	−	0.00467855i	−5.79132e−5	−	0.000178238i
$690$	2.15098	−	6.62004i	0.0818865	−	0.252021i
$691$	3.97366	+	2.88703i	0.151165	+	0.109828i	0.660797	−	0.750565i	$-0.270218\pi$
$691$	3.97366	+	2.88703i	0.151165	+	0.109828i	−0.509632	+	0.860393i	$0.670218\pi$
$692$	2.10650			0.0800771
$693$	−3.20705	+	0.845493i	−0.121826	+	0.0321176i
$694$	5.01266			0.190278
$695$	−12.8207	−	9.31477i	−0.486316	−	0.353329i
$696$	−4.27826	+	13.1671i	−0.162167	+	0.499099i
$697$	−3.88821	−	11.9667i	−0.147277	−	0.453271i
$698$	−13.1316	+	9.54069i	−0.497040	+	0.361120i
$699$	−19.0247	+	13.8223i	−0.719581	+	0.522806i
$700$	−0.291100	−	0.895912i	−0.0110025	−	0.0338623i
$701$	11.4102	−	35.1170i	0.430958	−	1.32635i	−0.466215	−	0.884672i	$-0.654383\pi$
$701$	11.4102	−	35.1170i	0.430958	−	1.32635i	0.897173	−	0.441680i	$-0.145617\pi$
$702$	0.0426547	+	0.0309905i	0.00160990	+	0.00116966i
$703$	−65.8845			−2.48488
$704$	1.62257	−	28.7444i	0.0611528	−	1.08334i
$705$	−5.28094			−0.198892
$706$	−6.24610	−	4.53806i	−0.235075	−	0.170792i
$707$	2.81069	−	8.65043i	0.105707	−	0.325333i
$708$	0.985513	+	3.03310i	0.0370378	+	0.113991i
$709$	−0.395914	+	0.287648i	−0.0148688	+	0.0108028i	−0.595195	−	0.803581i	$-0.702925\pi$
$709$	−0.395914	+	0.287648i	−0.0148688	+	0.0108028i	0.580326	+	0.814384i	$0.302925\pi$
$710$	10.5967	−	7.69892i	0.397685	−	0.288935i
$711$	−0.0479677	−	0.147630i	−0.00179893	−	0.00553654i
$712$	4.74005	−	14.5884i	0.177641	−	0.546723i
$713$	−36.1745	−	26.2823i	−1.35475	−	0.984281i
$714$	2.72838			0.102107
$715$	−0.0619867	−	0.0962983i	−0.00231817	−	0.00360135i
$716$	−3.93890			−0.147204
$717$	−6.33100	−	4.59974i	−0.236435	−	0.171780i
$718$	−2.37355	+	7.30503i	−0.0885800	+	0.272621i
$719$	3.13317	+	9.64292i	0.116848	+	0.359620i	0.992328	−	0.123634i	$-0.0394548\pi$
$719$	3.13317	+	9.64292i	0.116848	+	0.359620i	−0.875480	+	0.483254i	$0.839455\pi$
$720$	−2.47677	+	1.79948i	−0.0923036	+	0.0670625i
$721$	2.78100	−	2.02051i	0.103570	−	0.0752478i
$722$	−5.53086	−	17.0222i	−0.205837	−	0.633502i
$723$	−2.12029	+	6.52557i	−0.0788543	+	0.242689i
$724$	2.92689	+	2.12651i	0.108777	+	0.0790312i
$725$	19.7999			0.735350
$726$	2.93362	+	14.3699i	0.108877	+	0.533318i
$727$	−10.5834			−0.392516			−0.196258	−	0.980552i	$-0.562879\pi$
$727$	−10.5834			−0.392516			−0.196258	+	0.980552i	$0.562879\pi$
$728$	0.0947918	+	0.0688703i	0.00351322	+	0.00255250i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.220525	+	0.678707i	0.00816200	+	0.0251201i
$731$	2.97479	−	2.16131i	0.110026	−	0.0799389i
$732$	1.35955	−	0.987774i	0.0502506	−	0.0365092i
$733$	3.88595	+	11.9597i	0.143531	+	0.441742i	0.996819	−	0.0796971i	$-0.0253953\pi$
$733$	3.88595	+	11.9597i	0.143531	+	0.441742i	−0.853288	+	0.521439i	$0.825395\pi$
$734$	−5.87450	+	18.0798i	−0.216832	+	0.667339i
$735$	0.706442	+	0.513260i	0.0260575	+	0.0189319i
$736$	−7.48229			−0.275801
$737$	8.72328	+	13.5519i	0.321326	+	0.499190i
$738$	8.19824			0.301781
$739$	1.13052	+	0.821374i	0.0415870	+	0.0302147i	0.608385	−	0.793642i	$-0.291818\pi$
$739$	1.13052	+	0.821374i	0.0415870	+	0.0302147i	−0.566798	+	0.823857i	$0.691818\pi$
$740$	0.694066	−	2.13611i	0.0255144	−	0.0785251i
$741$	−0.0695819	−	0.214151i	−0.00255615	−	0.00786704i
$742$	0.134187	−	0.0974925i	0.00492616	−	0.00357906i
$743$	−19.5111	+	14.1756i	−0.715791	+	0.520053i	−0.885037	−	0.465521i	$-0.845867\pi$
$743$	−19.5111	+	14.1756i	−0.715791	+	0.520053i	0.169245	+	0.985574i	$0.445867\pi$
$744$	6.84783	+	21.0755i	0.251054	+	0.772664i
$745$	−2.98157	+	9.17632i	−0.109236	+	0.336194i
$746$	34.7570	+	25.2524i	1.27254	+	0.924557i
$747$	8.91599			0.326219
$748$	−0.0850315	+	1.50637i	−0.00310906	+	0.0550782i
$749$	−3.29161			−0.120273
$750$	8.70081	+	6.32151i	0.317709	+	0.230829i
$751$	−5.94079	+	18.2839i	−0.216783	+	0.667188i	0.782240	+	0.622978i	$0.214077\pi$
$751$	−5.94079	+	18.2839i	−0.216783	+	0.667188i	−0.999022	+	0.0442106i	$0.985923\pi$
$752$	−6.55214	−	20.1654i	−0.238932	−	0.735357i
$753$	2.07682	−	1.50890i	0.0756834	−	0.0549872i
$754$	−0.199306	+	0.144804i	−0.00725829	+	0.00527346i
$755$	−4.29888	−	13.2306i	−0.156452	−	0.481511i
$756$	0.0686960	−	0.211425i	0.00249845	−	0.00768944i
$757$	34.3682	+	24.9699i	1.24913	+	0.907548i	0.998171	−	0.0604493i	$-0.0192533\pi$
$757$	34.3682	+	24.9699i	1.24913	+	0.907548i	0.250961	+	0.967997i	$0.419253\pi$
$758$	38.1023			1.38394
$759$	19.1740	−	5.05495i	0.695971	−	0.183483i
$760$	14.7328			0.534414
$761$	−11.8940	−	8.64149i	−0.431157	−	0.313254i	0.350954	−	0.936393i	$-0.385857\pi$
$761$	−11.8940	−	8.64149i	−0.431157	−	0.313254i	−0.782111	+	0.623139i	$0.785857\pi$
$762$	−5.34889	+	16.4622i	−0.193770	+	0.596362i
$763$	−3.08865	−	9.50590i	−0.111817	−	0.344137i
$764$	1.15931	−	0.842289i	0.0419424	−	0.0304729i
$765$	1.44561	−	1.05030i	0.0522663	−	0.0379737i
$766$	8.30672	+	25.5654i	0.300134	+	0.923717i
$767$	−0.175305	+	0.539533i	−0.00632989	+	0.0194814i
$768$	4.26106	+	3.09584i	0.153758	+	0.111712i
$769$	−45.4931			−1.64052			−0.820262	−	0.571988i	$-0.806172\pi$
$769$	−45.4931			−1.64052			−0.820262	+	0.571988i	$0.806172\pi$
$770$	2.44212	−	2.99105i	0.0880080	−	0.107790i
$771$	−19.5915			−0.705571
$772$	−0.325659	−	0.236605i	−0.0117207	−	0.00851562i
$773$	1.87073	−	5.75752i	0.0672855	−	0.207084i	−0.911761	−	0.410722i	$-0.865277\pi$
$773$	1.87073	−	5.75752i	0.0672855	−	0.207084i	0.979046	+	0.203638i	$0.0652767\pi$
$774$	0.740343	+	2.27854i	0.0266111	+	0.0819005i
$775$	25.6393	−	18.6280i	0.920991	−	0.669139i
$776$	−19.0385	+	13.8322i	−0.683441	+	0.496549i
$777$	−3.57546	−	11.0041i	−0.128269	−	0.394772i
$778$	6.82325	−	20.9998i	0.244625	−	0.752879i
$779$	−28.3258	−	20.5799i	−1.01488	−	0.737352i
$780$	0.00767624			0.000274854
$781$	34.7805	+	13.5120i	1.24455	+	0.483497i
$782$	−16.3122			−0.583322
$783$	3.78016	+	2.74645i	0.135092	+	0.0981501i
$784$	−1.08340	+	3.33438i	−0.0386930	+	0.119085i
$785$	−4.31834	−	13.2905i	−0.154128	−	0.474358i
$786$	19.5514	−	14.2049i	0.697374	−	0.506672i
$787$	−44.3042	+	32.1889i	−1.57928	+	1.14741i	−0.661756	+	0.749720i	$0.730188\pi$
$787$	−44.3042	+	32.1889i	−1.57928	+	1.14741i	−0.917520	+	0.397691i	$0.869812\pi$
$788$	0.471098	+	1.44989i	0.0167822	+	0.0516502i
$789$	−8.19841	+	25.2321i	−0.291871	+	0.898287i
$790$	0.146208	+	0.106227i	0.00520186	+	0.00377937i
$791$	−4.40261			−0.156539
$792$	−9.16020	−	3.55867i	−0.325493	−	0.126452i
$793$	0.298931			0.0106153
$794$	33.4300	+	24.2883i	1.18639	+	0.861960i
$795$	0.0335680	−	0.103312i	0.00119053	−	0.00366409i
$796$	0.348564	+	1.07277i	0.0123545	+	0.0380233i
$797$	35.0241	−	25.4465i	1.24062	−	0.901361i	0.242978	−	0.970032i	$-0.421876\pi$
$797$	35.0241	−	25.4465i	1.24062	−	0.901361i	0.997639	+	0.0686704i	$0.0218757\pi$
$798$	6.14214	−	4.46252i	0.217429	−	0.157972i
$799$	3.82429	+	11.7700i	0.135294	+	0.416391i
$800$	1.63878	−	5.04364i	0.0579395	−	0.178319i
$801$	−4.18819	−	3.04290i	−0.147982	−	0.107515i
$802$	−4.64342			−0.163965
$803$	−1.28572	+	1.57472i	−0.0453722	+	0.0555708i
$804$	−1.08026			−0.0380980
$805$	−4.22361	−	3.06863i	−0.148863	−	0.108155i
$806$	−0.121851	+	0.375020i	−0.00429203	+	0.0132095i
$807$	−5.29185	−	16.2866i	−0.186282	−	0.573317i
$808$	21.8033	−	15.8410i	0.767036	−	0.557284i
$809$	12.5538	−	9.12083i	0.441366	−	0.320671i	−0.344811	−	0.938672i	$-0.612057\pi$
$809$	12.5538	−	9.12083i	0.441366	−	0.320671i	0.786178	+	0.618001i	$0.212057\pi$
$810$	0.359774	+	1.10727i	0.0126412	+	0.0389055i
$811$	12.8063	−	39.4138i	0.449691	−	1.38401i	−0.427566	−	0.903984i	$-0.640629\pi$
$811$	12.8063	−	39.4138i	0.449691	−	1.38401i	0.877257	−	0.480022i	$-0.159371\pi$
$812$	0.840349	+	0.610549i	0.0294905	+	0.0214261i
$813$	5.29554			0.185723
$814$	−49.4748	+	13.0433i	−1.73409	+	0.457169i
$815$	−19.2136			−0.673024
$816$	5.80419	+	4.21699i	0.203187	+	0.147624i
$817$	3.16182	−	9.73109i	0.110618	−	0.340448i
$818$	10.9547	+	33.7152i	0.383023	+	1.17882i
$819$	0.0319918	−	0.0232434i	0.00111788	−	0.000812190i
$820$	0.965645	−	0.701582i	0.0337218	−	0.0245003i
$821$	−12.3892	−	38.1299i	−0.432385	−	1.33074i	−0.895743	−	0.444572i	$-0.853356\pi$
$821$	−12.3892	−	38.1299i	−0.432385	−	1.33074i	0.463359	−	0.886171i	$-0.346644\pi$
$822$	−2.14535	+	6.60270i	−0.0748275	+	0.230296i
$823$	−3.42241	−	2.48653i	−0.119298	−	0.0866749i	0.526537	−	0.850152i	$-0.323490\pi$
$823$	−3.42241	−	2.48653i	−0.119298	−	0.0866749i	−0.645834	+	0.763478i	$0.723490\pi$
$824$	10.1853			0.354823
$825$	−0.792073	+	14.0319i	−0.0275764	+	0.488527i
$826$	−19.1275			−0.665532
$827$	−38.5811	−	28.0308i	−1.34160	−	0.974727i	−0.999384	−	0.0351040i	$-0.988824\pi$
$827$	−38.5811	−	28.0308i	−1.34160	−	0.974727i	−0.342212	−	0.939623i	$-0.611176\pi$
$828$	−0.410713	+	1.26404i	−0.0142733	+	0.0439286i
$829$	1.44782	+	4.45592i	0.0502847	+	0.154761i	0.973046	−	0.230612i	$-0.0740729\pi$
$829$	1.44782	+	4.45592i	0.0502847	+	0.154761i	−0.922761	+	0.385373i	$0.874073\pi$
$830$	−8.39798	+	6.10149i	−0.291498	+	0.211786i
$831$	−1.98213	+	1.44010i	−0.0687592	+	0.0499565i
$832$	0.106074	+	0.326463i	0.00367747	+	0.0113181i
$833$	0.632351	−	1.94618i	0.0219097	−	0.0674310i
$834$	−19.5759	−	14.2227i	−0.677857	−	0.492492i
$835$	4.12244			0.142663
$836$	2.27238	+	3.53022i	0.0785920	+	0.122095i
$837$	7.47891			0.258509
$838$	31.4420	+	22.8440i	1.08615	+	0.789132i
$839$	−2.14367	+	6.59755i	−0.0740078	+	0.227773i	−0.981217	−	0.192907i	$-0.938208\pi$
$839$	−2.14367	+	6.59755i	−0.0740078	+	0.227773i	0.907209	+	0.420680i	$0.138208\pi$
$840$	0.799528	+	2.46069i	0.0275863	+	0.0849020i
$841$	5.79854	−	4.21288i	0.199949	−	0.145272i
$842$	−21.5635	+	15.6668i	−0.743126	+	0.539913i
$843$	0.0932445	+	0.286977i	0.00321151	+	0.00988401i
$844$	−0.556911	+	1.71399i	−0.0191697	+	0.0589981i
$845$	−9.18264	−	6.67158i	−0.315893	−	0.229509i
$846$	−8.06345			−0.277227
$847$	10.9301	+	1.23791i	0.375563	+	0.0425352i
$848$	0.436146			0.0149773
$849$	−19.4240	−	14.1124i	−0.666630	−	0.484335i
$850$	3.57270	−	10.9957i	0.122543	−	0.377148i
$851$	21.3766	+	65.7905i	0.732782	+	2.25527i
$852$	−2.02335	+	1.47005i	−0.0693188	+	0.0503630i
$853$	5.04732	−	3.66709i	0.172817	−	0.125559i	−0.498015	−	0.867169i	$-0.665937\pi$
$853$	5.04732	−	3.66709i	0.172817	−	0.125559i	0.670831	+	0.741610i	$0.265937\pi$
$854$	3.11459	+	9.58572i	0.106579	+	0.328017i
$855$	1.53651	−	4.72888i	0.0525474	−	0.161724i
$856$	−7.89038	−	5.73270i	−0.269688	−	0.195939i
$857$	26.5684			0.907559			0.453779	−	0.891114i	$-0.350075\pi$
$857$	26.5684			0.907559			0.453779	+	0.891114i	$0.350075\pi$
$858$	−0.0946474	−	0.147038i	−0.00323121	−	0.00501978i
$859$	44.6475			1.52335			0.761677	−	0.647957i	$-0.224377\pi$
$859$	44.6475			1.52335			0.761677	+	0.647957i	$0.224377\pi$
$860$	0.282194	+	0.205026i	0.00962274	+	0.00699133i
$861$	1.90009	−	5.84788i	0.0647549	−	0.199295i
$862$	−6.97477	−	21.4661i	−0.237561	−	0.731139i
$863$	17.1761	−	12.4792i	0.584682	−	0.424796i	−0.255727	−	0.966749i	$-0.582315\pi$
$863$	17.1761	−	12.4792i	0.584682	−	0.424796i	0.840409	+	0.541953i	$0.182315\pi$
$864$	1.01248	−	0.735607i	0.0344452	−	0.0250259i
$865$	2.55690	+	7.86932i	0.0869371	+	0.267565i
$866$	3.52332	−	10.8437i	0.119727	−	0.368483i
$867$	10.3656	+	7.53102i	0.352033	+	0.255767i
$868$	1.66260			0.0564323
$869$	−0.0290150	+	0.514011i	−0.000984265	+	0.0174366i
$870$	−5.44002			−0.184434
$871$	−0.155460	−	0.112948i	−0.00526757	−	0.00382711i
$872$	9.15170	−	28.1660i	0.309916	−	0.953822i
$873$	2.45428	+	7.55350i	0.0830648	+	0.255647i
$874$	−36.7220	+	26.6801i	−1.24214	+	0.902468i
$875$	6.52576	−	4.74124i	0.220611	−	0.160283i
$876$	−0.0421075	−	0.129594i	−0.00142268	−	0.00437856i
$877$	2.97741	−	9.16354i	0.100540	−	0.309431i	−0.888118	−	0.459616i	$-0.847987\pi$
$877$	2.97741	−	9.16354i	0.100540	−	0.309431i	0.988658	+	0.150185i	$0.0479870\pi$
$878$	−36.6107	−	26.5992i	−1.23555	−	0.897680i
$879$	−1.96403			−0.0662452
$880$	9.81821	−	2.58844i	0.330972	−	0.0872561i
$881$	−38.9952			−1.31378			−0.656891	−	0.753985i	$-0.728129\pi$
$881$	−38.9952			−1.31378			−0.656891	+	0.753985i	$0.728129\pi$
$882$	1.07866	+	0.783695i	0.0363205	+	0.0263884i
$883$	4.58283	−	14.1045i	0.154225	−	0.474654i	−0.843857	−	0.536568i	$-0.819720\pi$
$883$	4.58283	−	14.1045i	0.154225	−	0.474654i	0.998081	+	0.0619139i	$0.0197204\pi$
$884$	−0.00555889	−	0.0171085i	−0.000186966	−	0.000575421i
$885$	−10.1346	+	7.36323i	−0.340671	+	0.247512i
$886$	−37.9260	+	27.5548i	−1.27415	+	0.925723i
$887$	−5.44150	−	16.7472i	−0.182708	−	0.562316i	0.817194	−	0.576363i	$-0.195529\pi$
$887$	−5.44150	−	16.7472i	−0.182708	−	0.562316i	−0.999901	+	0.0140468i	$0.995529\pi$
$888$	10.5941	−	32.6053i	0.355515	−	1.09416i
$889$	10.5029	+	7.63082i	0.352257	+	0.255929i
$890$	6.02721			0.202032
$891$	−2.09759	+	2.56907i	−0.0702718	+	0.0860672i
$892$	3.60245			0.120619
$893$	27.8601	+	20.2416i	0.932304	+	0.677358i
$894$	−4.55255	+	14.0113i	−0.152260	+	0.468608i
$895$	−4.78110	−	14.7147i	−0.159814	−	0.491858i
$896$	−7.33845	+	5.33170i	−0.245160	+	0.178119i
$897$	−0.191269	+	0.138965i	−0.00638630	+	0.00463992i
$898$	0.794360	+	2.44479i	0.0265081	+	0.0815837i
$899$	−10.7988	+	33.2351i	−0.360159	+	1.10845i
$900$	−0.762109	−	0.553704i	−0.0254036	−	0.0184568i
$901$	−0.254566			−0.00848081
$902$	−25.3450	−	9.84638i	−0.843898	−	0.327848i
$903$	1.79689			0.0597968
$904$	−10.5536	−	7.66764i	−0.351007	−	0.255022i
$905$	−4.39138	+	13.5153i	−0.145974	+	0.449263i
$906$	−6.56395	−	20.2018i	−0.218073	−	0.671159i
$907$	−37.2249	+	27.0455i	−1.23603	+	0.898031i	−0.997328	−	0.0730605i	$-0.976723\pi$
$907$	−37.2249	+	27.0455i	−1.23603	+	0.898031i	−0.238706	+	0.971092i	$0.576723\pi$
$908$	4.25776	−	3.09345i	0.141299	−	0.102660i
$909$	−2.81069	−	8.65043i	−0.0932249	−	0.286917i
$910$	−0.0142269	+	0.0437859i	−0.000471618	+	0.00145149i
$911$	−15.7758	−	11.4618i	−0.522677	−	0.379747i	0.294934	−	0.955517i	$-0.404702\pi$
$911$	−15.7758	−	11.4618i	−0.522677	−	0.379747i	−0.817611	+	0.575770i	$0.804702\pi$
$912$	19.9637			0.661065
$913$	−27.5640	−	10.7084i	−0.912235	−	0.354397i
$914$	10.2020			0.337451
$915$	5.34031	+	3.87996i	0.176545	+	0.128268i
$916$	−0.697727	+	2.14738i	−0.0230536	+	0.0709515i
$917$	−5.60110	−	17.2384i	−0.184965	−	0.569262i
$918$	2.20730	−	1.60370i	0.0728519	−	0.0529300i
$919$	−9.49601	+	6.89925i	−0.313244	+	0.227585i	−0.733287	−	0.679919i	$-0.762015\pi$
$919$	−9.49601	+	6.89925i	−0.313244	+	0.227585i	0.420043	+	0.907504i	$0.362015\pi$
$920$	−4.78014	−	14.7118i	−0.157597	−	0.485032i
$921$	6.18589	−	19.0382i	0.203832	−	0.627330i
$922$	43.9583	+	31.9376i	1.44769	+	1.05181i
$923$	−0.444882			−0.0146435
$924$	−0.466304	+	0.571118i	−0.0153403	+	0.0187884i
$925$	−49.0298			−1.61209
$926$	−9.03281	−	6.56272i	−0.296837	−	0.215664i
$927$	1.06225	−	3.26926i	0.0348887	−	0.107377i
$928$	1.80702	+	5.56143i	0.0593183	+	0.182563i
$929$	−28.8740	+	20.9782i	−0.947326	+	0.688273i	−0.950173	−	0.311723i	$-0.899094\pi$
$929$	−28.8740	+	20.9782i	−0.947326	+	0.688273i	0.00284654	+	0.999996i	$0.499094\pi$
$930$	−7.04439	+	5.11805i	−0.230995	+	0.167827i
$931$	−1.75961	−	5.41551i	−0.0576688	−	0.177486i
$932$	−1.61544	+	4.97183i	−0.0529156	+	0.162858i
$933$	−14.3229	−	10.4062i	−0.468911	−	0.340684i
$934$	−12.6612			−0.414288
$935$	−5.73060	+	1.51079i	−0.187411	+	0.0494082i
$936$	0.117169			0.00382979
$937$	−28.6021	−	20.7806i	−0.934390	−	0.678874i	0.0126738	−	0.999920i	$-0.495966\pi$
$937$	−28.6021	−	20.7806i	−0.934390	−	0.678874i	−0.947064	+	0.321046i	$0.895966\pi$
$938$	2.00213	−	6.16191i	0.0653718	−	0.201194i
$939$	8.75493	+	26.9449i	0.285706	+	0.879314i
$940$	−0.949769	+	0.690048i	−0.0309781	+	0.0225069i
$941$	24.7099	−	17.9528i	0.805520	−	0.585245i	−0.107008	−	0.994258i	$-0.534127\pi$
$941$	24.7099	−	17.9528i	0.805520	−	0.585245i	0.912528	+	0.409014i	$0.134127\pi$
$942$	−6.59366	−	20.2932i	−0.214833	−	0.661188i
$943$	−11.3601	+	34.9627i	−0.369935	+	1.13854i
$944$	−40.6908	−	29.5636i	−1.32437	−	0.962214i
$945$	0.873210			0.0284055
$946$	0.447822	−	7.93334i	0.0145600	−	0.257935i
$947$	38.9527			1.26579			0.632897	−	0.774236i	$-0.281866\pi$
$947$	38.9527			1.26579			0.632897	+	0.774236i	$0.281866\pi$
$948$	−0.0279173	−	0.0202831i	−0.000906713	−	0.000658765i
$949$	0.00749016	−	0.0230523i	0.000243141	−	0.000748311i
$950$	−9.94155	−	30.5970i	−0.322547	−	0.992696i
$951$	17.7623	−	12.9051i	0.575982	−	0.418476i
$952$	4.90530	−	3.56391i	0.158982	−	0.115507i
$953$	10.9035	+	33.5576i	0.353200	+	1.08704i	0.957046	+	0.289937i	$0.0936342\pi$
$953$	10.9035	+	33.5576i	0.353200	+	1.08704i	−0.603846	+	0.797101i	$0.706366\pi$
$954$	0.0512548	−	0.157746i	0.00165944	−	0.00510722i
$955$	4.55376	+	3.30850i	0.147356	+	0.107060i
$956$	−1.73966			−0.0562645
$957$	−8.38788	−	13.0308i	−0.271142	−	0.421227i
$958$	48.3966			1.56362
$959$	4.21254	+	3.06059i	0.136030	+	0.0988316i
$960$	−2.34233	+	7.20896i	−0.0755985	+	0.232668i
$961$	7.70506	+	23.7137i	0.248550	+	0.764959i
$962$	0.493534	−	0.358573i	0.0159122	−	0.0115609i
$963$	−2.66297	+	1.93476i	−0.0858129	+	0.0623467i
$964$	0.471350	+	1.45067i	0.0151812	+	0.0467228i
$965$	0.488605	−	1.50377i	0.0157288	−	0.0484081i
$966$	−6.44901	−	4.68548i	−0.207494	−	0.150753i
$967$	31.4791			1.01230			0.506150	−	0.862445i	$-0.331068\pi$
$967$	31.4791			1.01230			0.506150	+	0.862445i	$0.331068\pi$
$968$	24.0449	+	22.0034i	0.772831	+	0.707217i
$969$	−11.6522			−0.374324
$970$	−7.48078	−	5.43511i	−0.240193	−	0.174511i
$971$	−10.6540	+	32.7896i	−0.341903	+	1.05227i	0.621318	+	0.783559i	$0.286598\pi$
$971$	−10.6540	+	32.7896i	−0.341903	+	1.05227i	−0.963221	+	0.268711i	$0.913402\pi$
$972$	−0.0686960	−	0.211425i	−0.00220343	−	0.00678145i
$973$	−14.6822	+	10.6673i	−0.470691	+	0.341977i
$974$	5.78958	−	4.20638i	0.185510	−	0.134781i
$975$	−0.0517813	−	0.159367i	−0.00165833	−	0.00510381i
$976$	−8.18993	+	25.2060i	−0.262153	+	0.806825i
$977$	−4.46523	−	3.24418i	−0.142855	−	0.103790i	0.514062	−	0.857753i	$-0.328140\pi$
$977$	−4.46523	−	3.24418i	−0.142855	−	0.103790i	−0.656918	+	0.753962i	$0.728140\pi$
$978$	−29.3372			−0.938101
$979$	9.29325	+	14.4373i	0.297014	+	0.461420i
$980$	0.194119			0.00620090
$981$	−8.08620	−	5.87497i	−0.258173	−	0.187573i
$982$	−9.50159	+	29.2429i	−0.303208	+	0.933178i
$983$	−10.1999	−	31.3921i	−0.325327	−	1.00125i	−0.971293	−	0.237887i	$-0.923545\pi$
$983$	−10.1999	−	31.3921i	−0.325327	−	1.00125i	0.645966	−	0.763366i	$-0.276455\pi$
$984$	14.7395	−	10.7089i	0.469877	−	0.341386i
$985$	−4.84458	+	3.51980i	−0.154361	+	0.112150i
$986$	3.93949	+	12.1245i	0.125459	+	0.386123i
$987$	−1.86885	+	5.75173i	−0.0594862	+	0.183080i
$988$	−0.0404968	−	0.0294226i	−0.00128837	−	0.000936059i
$989$	−10.7431			−0.341610
$990$	0.217622	−	3.85525i	0.00691648	−	0.122528i
$991$	−40.9399			−1.30050			−0.650249	−	0.759721i	$-0.725335\pi$
$991$	−40.9399			−1.30050			−0.650249	+	0.759721i	$0.725335\pi$
$992$	7.57222	+	5.50154i	0.240418	+	0.174674i
$993$	7.15266	−	22.0136i	0.226983	−	0.698581i
$994$	−4.63527	−	14.2659i	−0.147022	−	0.452486i
$995$	−3.58449	+	2.60428i	−0.113636	+	0.0825614i
$996$	1.60353	−	1.16503i	0.0508097	−	0.0369154i
$997$	−11.7054	−	36.0256i	−0.370714	−	1.14094i	−0.946325	−	0.323217i	$-0.895236\pi$
$997$	−11.7054	−	36.0256i	−0.370714	−	1.14094i	0.575611	−	0.817724i	$-0.304764\pi$
$998$	−13.6538	+	42.0220i	−0.432202	+	1.33018i
$999$	−9.36069	−	6.80094i	−0.296159	−	0.215172i

Display

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p

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a_n

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a_n

instead) (See

a_n

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.169.4	✓	20
3.2	odd	2		693.2.m.j.631.2		20
11.3	even	5	inner	231.2.j.g.190.4	yes	20
11.5	even	5		2541.2.a.bq.1.4		10
11.6	odd	10		2541.2.a.br.1.7		10
33.5	odd	10		7623.2.a.cx.1.7		10
33.14	odd	10		693.2.m.j.190.2		20
33.17	even	10		7623.2.a.cy.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.4	✓	20	1.1	even	1	trivial
231.2.j.g.190.4	yes	20	11.3	even	5	inner
693.2.m.j.190.2		20	33.14	odd	10
693.2.m.j.631.2		20	3.2	odd	2
2541.2.a.bq.1.4		10	11.5	even	5
2541.2.a.br.1.7		10	11.6	odd	10
7623.2.a.cx.1.7		10	33.5	odd	10
7623.2.a.cy.1.4		10	33.17	even	10

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Classical	Maass
Hilbert	Bianchi

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

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	231.2.j.g.169.4

Level	$231$
Weight	$2$
Character	231.169
Analytic conductor	$1.845$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$