LMFDB - Embedded newform 71.2.c.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(5,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("71.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.c (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:	$0.566937854351$
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} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + \cdots + 961 $ x^20 - 6x^19 + 28x^18 - 91x^17 + 268x^16 - 604x^15 + 1278x^14 - 1990x^13 + 3162x^12 - 4046x^11 + 6406x^10 - 8426x^9 + 12709x^8 - 13621x^7 + 17787x^6 - 13514x^5 + 9316x^4 - 1639x^3 - 228x^2 + 620*x + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.4
Root			$-0.363618 - 0.264184i$ of defining polynomial
Character	$\chi$	$=$	71.25
Dual form			71.2.c.a.54.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.363618 - 0.264184i) q^{2} +(-2.65787 + 1.93106i) q^{3} +(-0.555609 + 1.70999i) q^{4} +(0.225736 + 0.694745i) q^{5} +(-0.456296 + 1.40433i) q^{6} +(1.83483 - 1.33308i) q^{7} +(0.527502 + 1.62348i) q^{8} +(2.40825 - 7.41182i) q^{9} +O(q^{10})$	\(q+(0.363618 - 0.264184i) q^{2} +(-2.65787 + 1.93106i) q^{3} +(-0.555609 + 1.70999i) q^{4} +(0.225736 + 0.694745i) q^{5} +(-0.456296 + 1.40433i) q^{6} +(1.83483 - 1.33308i) q^{7} +(0.527502 + 1.62348i) q^{8} +(2.40825 - 7.41182i) q^{9} +(0.265622 + 0.192986i) q^{10} +(-2.07849 + 1.51011i) q^{11} +(-1.82535 - 5.61784i) q^{12} +(3.29842 + 2.39644i) q^{13} +(0.314998 - 0.969464i) q^{14} +(-1.94157 - 1.41063i) q^{15} +(-2.28850 - 1.66269i) q^{16} +(3.62333 + 2.63250i) q^{17} +(-1.08240 - 3.33129i) q^{18} +(0.776610 - 0.564240i) q^{19} -1.31343 q^{20} +(-2.30248 + 7.08630i) q^{21} +(-0.356829 + 1.09821i) q^{22} -3.09861 q^{23} +(-4.53707 - 3.29637i) q^{24} +(3.61337 - 2.62527i) q^{25} +1.83247 q^{26} +(4.86618 + 14.9766i) q^{27} +(1.26010 + 3.87820i) q^{28} +(-2.99308 - 9.21175i) q^{29} -1.07866 q^{30} +(4.51529 - 3.28055i) q^{31} -4.68546 q^{32} +(2.60824 - 8.02734i) q^{33} +2.01297 q^{34} +(1.34034 + 0.973812i) q^{35} +(11.3361 + 8.23615i) q^{36} -1.47354 q^{37} +(0.133326 - 0.410336i) q^{38} -13.3944 q^{39} +(-1.00883 + 0.732958i) q^{40} -5.12171 q^{41} +(1.03486 + 3.18499i) q^{42} +(2.48485 + 7.64758i) q^{43} +(-1.42744 - 4.39322i) q^{44} +5.69295 q^{45} +(-1.12671 + 0.818603i) q^{46} +(1.00670 + 0.731409i) q^{47} +9.29328 q^{48} +(-0.573632 + 1.76546i) q^{49} +(0.620333 - 1.90919i) q^{50} -14.7138 q^{51} +(-5.93052 + 4.30877i) q^{52} +(-0.352578 - 1.08512i) q^{53} +(5.72601 + 4.16019i) q^{54} +(-1.51833 - 1.10313i) q^{55} +(3.13211 + 2.27561i) q^{56} +(-0.974550 + 2.99936i) q^{57} +(-3.52193 - 2.55883i) q^{58} +(-0.636148 - 1.95786i) q^{59} +(3.49092 - 2.53630i) q^{60} +(0.513734 + 0.373249i) q^{61} +(0.775173 - 2.38574i) q^{62} +(-5.46183 - 16.8098i) q^{63} +(2.87328 - 2.08756i) q^{64} +(-0.920343 + 2.83252i) q^{65} +(-1.17229 - 3.60794i) q^{66} +(4.05686 - 12.4857i) q^{67} +(-6.51470 + 4.73321i) q^{68} +(8.23570 - 5.98358i) q^{69} +0.744636 q^{70} +(5.05972 - 6.73789i) q^{71} +13.3033 q^{72} +(5.60875 - 4.07499i) q^{73} +(-0.535806 + 0.389286i) q^{74} +(-4.53433 + 13.9552i) q^{75} +(0.533353 + 1.64149i) q^{76} +(-1.80057 + 5.54157i) q^{77} +(-4.87046 + 3.53859i) q^{78} +(-1.57062 - 4.83387i) q^{79} +(0.638549 - 1.96525i) q^{80} +(-22.9397 - 16.6667i) q^{81} +(-1.86235 + 1.35307i) q^{82} +(-0.182535 - 0.561785i) q^{83} +(-10.8382 - 7.87443i) q^{84} +(-1.01100 + 3.11154i) q^{85} +(2.92391 + 2.12434i) q^{86} +(25.7436 + 18.7038i) q^{87} +(-3.54804 - 2.57780i) q^{88} +(2.46898 + 7.59875i) q^{89} +(2.07006 - 1.50399i) q^{90} +9.24667 q^{91} +(1.72161 - 5.29859i) q^{92} +(-5.66613 + 17.4386i) q^{93} +0.559280 q^{94} +(0.567312 + 0.412177i) q^{95} +(12.4533 - 9.04788i) q^{96} -17.3772 q^{97} +(0.257823 + 0.793497i) q^{98} +(6.18715 + 19.0421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.363618	−	0.264184i	0.257117	−	0.186806i	−0.451758	−	0.892140i	$-0.649203\pi$
$2$	0.363618	−	0.264184i	0.257117	−	0.186806i	0.708875	+	0.705334i	$0.249203\pi$
$3$	−2.65787	+	1.93106i	−1.53452	+	1.11490i	−0.580865	+	0.814000i	$0.697286\pi$
$3$	−2.65787	+	1.93106i	−1.53452	+	1.11490i	−0.953657	+	0.300896i	$0.902714\pi$
$4$	−0.555609	+	1.70999i	−0.277805	+	0.854994i
$5$	0.225736	+	0.694745i	0.100952	+	0.310699i	0.988759	−	0.149517i	$-0.0477719\pi$
$5$	0.225736	+	0.694745i	0.100952	+	0.310699i	−0.887807	+	0.460216i	$0.847772\pi$
$6$	−0.456296	+	1.40433i	−0.186282	+	0.573317i
$7$	1.83483	−	1.33308i	0.693499	−	0.503857i	−0.184309	−	0.982868i	$-0.559005\pi$
$7$	1.83483	−	1.33308i	0.693499	−	0.503857i	0.877809	+	0.479012i	$0.159005\pi$
$8$	0.527502	+	1.62348i	0.186500	+	0.573988i
$9$	2.40825	−	7.41182i	0.802749	−	2.47061i
$10$	0.265622	+	0.192986i	0.0839971	+	0.0610275i
$11$	−2.07849	+	1.51011i	−0.626687	+	0.455315i	−0.855251	−	0.518214i	$-0.826597\pi$
$11$	−2.07849	+	1.51011i	−0.626687	+	0.455315i	0.228564	+	0.973529i	$0.426597\pi$
$12$	−1.82535	−	5.61784i	−0.526932	−	1.62173i
$13$	3.29842	+	2.39644i	0.914817	+	0.664653i	0.942228	−	0.334971i	$-0.108727\pi$
$13$	3.29842	+	2.39644i	0.914817	+	0.664653i	−0.0274117	+	0.999624i	$0.508727\pi$
$14$	0.314998	−	0.969464i	0.0841867	−	0.259100i
$15$	−1.94157	−	1.41063i	−0.501311	−	0.364224i
$16$	−2.28850	−	1.66269i	−0.572125	−	0.415673i
$17$	3.62333	+	2.63250i	0.878786	+	0.638475i	0.932930	−	0.360058i	$-0.117243\pi$
$17$	3.62333	+	2.63250i	0.878786	+	0.638475i	−0.0541443	+	0.998533i	$0.517243\pi$
$18$	−1.08240	−	3.33129i	−0.255125	−	0.785193i
$19$	0.776610	−	0.564240i	0.178167	−	0.129446i	−0.495128	−	0.868820i	$-0.664879\pi$
$19$	0.776610	−	0.564240i	0.178167	−	0.129446i	0.673294	+	0.739375i	$0.264879\pi$
$20$	−1.31343			−0.293691
$21$	−2.30248	+	7.08630i	−0.502442	+	1.54636i
$22$	−0.356829	+	1.09821i	−0.0760761	+	0.234138i
$23$	−3.09861			−0.646104			−0.323052	−	0.946381i	$-0.604709\pi$
$23$	−3.09861			−0.646104			−0.323052	+	0.946381i	$0.604709\pi$
$24$	−4.53707	−	3.29637i	−0.926125	−	0.672869i
$25$	3.61337	−	2.62527i	0.722674	−	0.525054i
$26$	1.83247			0.359376
$27$	4.86618	+	14.9766i	0.936498	+	2.88224i
$28$	1.26010	+	3.87820i	0.238137	+	0.732911i
$29$	−2.99308	−	9.21175i	−0.555801	−	1.71058i	−0.693820	−	0.720149i	$-0.744074\pi$
$29$	−2.99308	−	9.21175i	−0.555801	−	1.71058i	0.138019	−	0.990430i	$-0.455926\pi$
$30$	−1.07866			−0.196935
$31$	4.51529	−	3.28055i	0.810971	−	0.589205i	−0.103141	−	0.994667i	$-0.532889\pi$
$31$	4.51529	−	3.28055i	0.810971	−	0.589205i	0.914112	+	0.405462i	$0.132889\pi$
$32$	−4.68546			−0.828280
$33$	2.60824	−	8.02734i	0.454037	−	1.39738i
$34$	2.01297			0.345222
$35$	1.34034	+	0.973812i	0.226558	+	0.164604i
$36$	11.3361	+	8.23615i	1.88935	+	1.37269i
$37$	−1.47354			−0.242249			−0.121124	−	0.992637i	$-0.538650\pi$
$37$	−1.47354			−0.242249			−0.121124	+	0.992637i	$0.538650\pi$
$38$	0.133326	−	0.410336i	0.0216284	−	0.0665653i
$39$	−13.3944			−2.14483
$40$	−1.00883	+	0.732958i	−0.159510	+	0.115891i
$41$	−5.12171			−0.799877			−0.399938	−	0.916542i	$-0.630968\pi$
$41$	−5.12171			−0.799877			−0.399938	+	0.916542i	$0.630968\pi$
$42$	1.03486	+	3.18499i	0.159683	+	0.491454i
$43$	2.48485	+	7.64758i	0.378936	+	1.16625i	0.940785	+	0.339005i	$0.110090\pi$
$43$	2.48485	+	7.64758i	0.378936	+	1.16625i	−0.561848	+	0.827240i	$0.689910\pi$
$44$	−1.42744	−	4.39322i	−0.215195	−	0.662302i
$45$	5.69295			0.848655
$46$	−1.12671	+	0.818603i	−0.166124	+	0.120696i
$47$	1.00670	+	0.731409i	0.146842	+	0.106687i	0.658781	−	0.752335i	$-0.271073\pi$
$47$	1.00670	+	0.731409i	0.146842	+	0.106687i	−0.511939	+	0.859022i	$0.671073\pi$
$48$	9.29328			1.34137
$49$	−0.573632	+	1.76546i	−0.0819475	+	0.252208i
$50$	0.620333	−	1.90919i	0.0877284	−	0.270000i
$51$	−14.7138			−2.06035
$52$	−5.93052	+	4.30877i	−0.822415	+	0.597520i
$53$	−0.352578	−	1.08512i	−0.0484303	−	0.149053i	0.923917	−	0.382593i	$-0.124969\pi$
$53$	−0.352578	−	1.08512i	−0.0484303	−	0.149053i	−0.972347	+	0.233540i	$0.924969\pi$
$54$	5.72601	+	4.16019i	0.779211	+	0.566130i
$55$	−1.51833	−	1.10313i	−0.204732	−	0.148746i
$56$	3.13211	+	2.27561i	0.418545	+	0.304091i
$57$	−0.974550	+	2.99936i	−0.129082	+	0.397274i
$58$	−3.52193	−	2.55883i	−0.462452	−	0.335991i
$59$	−0.636148	−	1.95786i	−0.0828195	−	0.254892i	0.901069	−	0.433676i	$-0.142784\pi$
$59$	−0.636148	−	1.95786i	−0.0828195	−	0.254892i	−0.983888	+	0.178784i	$0.942784\pi$
$60$	3.49092	−	2.53630i	0.450676	−	0.327435i
$61$	0.513734	+	0.373249i	0.0657768	+	0.0477897i	0.620188	−	0.784453i	$-0.287056\pi$
$61$	0.513734	+	0.373249i	0.0657768	+	0.0477897i	−0.554411	+	0.832243i	$0.687056\pi$
$62$	0.775173	−	2.38574i	0.0984471	−	0.302989i
$63$	−5.46183	−	16.8098i	−0.688126	−	2.11783i
$64$	2.87328	−	2.08756i	0.359160	−	0.260945i
$65$	−0.920343	+	2.83252i	−0.114154	+	0.351331i
$66$	−1.17229	−	3.60794i	−0.144299	−	0.444107i
$67$	4.05686	−	12.4857i	0.495625	−	1.52538i	−0.320356	−	0.947297i	$-0.603803\pi$
$67$	4.05686	−	12.4857i	0.495625	−	1.52538i	0.815981	−	0.578079i	$-0.196197\pi$
$68$	−6.51470	+	4.73321i	−0.790023	+	0.573986i
$69$	8.23570	−	5.98358i	0.991462	−	0.720339i
$70$	0.744636			0.0890011
$71$	5.05972	−	6.73789i	0.600479	−	0.799641i
$71$	5.05972	−	6.73789i	0.600479	−	0.799641i
$72$	13.3033			1.56781
$73$	5.60875	−	4.07499i	0.656454	−	0.476942i	−0.209009	−	0.977914i	$-0.567024\pi$
$73$	5.60875	−	4.07499i	0.656454	−	0.476942i	0.865464	+	0.500972i	$0.167024\pi$
$74$	−0.535806	+	0.389286i	−0.0622862	+	0.0452536i
$75$	−4.53433	+	13.9552i	−0.523580	+	1.61141i
$76$	0.533353	+	1.64149i	0.0611798	+	0.188292i
$77$	−1.80057	+	5.54157i	−0.205194	+	0.631521i
$78$	−4.87046	+	3.53859i	−0.551471	+	0.400667i
$79$	−1.57062	−	4.83387i	−0.176708	−	0.543853i	0.822999	−	0.568043i	$-0.192299\pi$
$79$	−1.57062	−	4.83387i	−0.176708	−	0.543853i	−0.999707	+	0.0241902i	$0.992299\pi$
$80$	0.638549	−	1.96525i	0.0713920	−	0.219722i
$81$	−22.9397	−	16.6667i	−2.54885	−	1.85185i
$82$	−1.86235	+	1.35307i	−0.205662	+	0.149422i
$83$	−0.182535	−	0.561785i	−0.0200358	−	0.0616639i	0.940539	−	0.339687i	$-0.110321\pi$
$83$	−0.182535	−	0.561785i	−0.0200358	−	0.0616639i	−0.960575	+	0.278023i	$0.910321\pi$
$84$	−10.8382	−	7.87443i	−1.18255	−	0.859171i
$85$	−1.01100	+	3.11154i	−0.109658	+	0.337494i
$86$	2.92391	+	2.12434i	0.315293	+	0.229074i
$87$	25.7436	+	18.7038i	2.76000	+	2.00526i
$88$	−3.54804	−	2.57780i	−0.378222	−	0.274795i
$89$	2.46898	+	7.59875i	0.261712	+	0.805466i	0.992433	+	0.122790i	$0.0391841\pi$
$89$	2.46898	+	7.59875i	0.261712	+	0.805466i	−0.730721	+	0.682676i	$0.760816\pi$
$90$	2.07006	−	1.50399i	0.218204	−	0.158534i
$91$	9.24667			0.969314
$92$	1.72161	−	5.29859i	0.179491	−	0.552416i
$93$	−5.66613	+	17.4386i	−0.587551	+	1.80830i
$94$	0.559280			0.0576854
$95$	0.567312	+	0.412177i	0.0582050	+	0.0422884i
$96$	12.4533	−	9.04788i	1.27101	−	0.923446i
$97$	−17.3772			−1.76439			−0.882196	−	0.470883i	$-0.843935\pi$
$97$	−17.3772			−1.76439			−0.882196	+	0.470883i	$0.843935\pi$
$98$	0.257823	+	0.793497i	0.0260440	+	0.0801553i
$99$	6.18715	+	19.0421i	0.621832	+	1.91380i
$100$	2.48156	+	7.63745i	0.248156	+	0.763745i
$101$	0.0564087			0.00561288			0.00280644	−	0.999996i	$-0.499107\pi$
$101$	0.0564087			0.00561288			0.00280644	+	0.999996i	$0.499107\pi$
$102$	−5.35022	+	3.88716i	−0.529750	+	0.384886i
$103$	−5.75075			−0.566638			−0.283319	−	0.959026i	$-0.591436\pi$
$103$	−5.75075			−0.566638			−0.283319	+	0.959026i	$0.591436\pi$
$104$	−2.15066	+	6.61906i	−0.210890	+	0.649052i
$105$	−5.44293			−0.531175
$106$	−0.414876	−	0.301425i	−0.0402963	−	0.0292770i
$107$	−5.18650	−	3.76821i	−0.501398	−	0.364287i	0.308153	−	0.951337i	$-0.400289\pi$
$107$	−5.18650	−	3.76821i	−0.501398	−	0.364287i	−0.809551	+	0.587050i	$0.800289\pi$
$108$	−28.3135			−2.72447
$109$	0.876714	−	2.69825i	0.0839740	−	0.258445i	−0.900250	−	0.435374i	$-0.856616\pi$
$109$	0.876714	−	2.69825i	0.0839740	−	0.258445i	0.984224	+	0.176929i	$0.0566162\pi$
$110$	−0.843522			−0.0804267
$111$	3.91648	−	2.84549i	0.371736	−	0.270082i
$112$	−6.41550			−0.606208
$113$	4.37937	+	13.4783i	0.411977	+	1.26793i	0.914927	+	0.403618i	$0.132248\pi$
$113$	4.37937	+	13.4783i	0.411977	+	1.26793i	−0.502951	+	0.864315i	$0.667752\pi$
$114$	0.438018	+	1.34808i	0.0410241	+	0.126259i
$115$	−0.699468	−	2.15274i	−0.0652258	−	0.200744i
$116$	17.4150			1.61694
$117$	25.7054	−	18.6761i	2.37647	−	1.72660i
$118$	−0.748551	−	0.543854i	−0.0689097	−	0.0500659i
$119$	10.1575			0.931137
$120$	1.26596	−	3.89622i	0.115566	−	0.355674i
$121$	−1.35951	+	4.18414i	−0.123592	+	0.380377i
$122$	0.285409			0.0258397
$123$	13.6128	−	9.89031i	1.22743	−	0.891779i
$124$	3.10097	+	9.54381i	0.278475	+	0.857059i
$125$	5.59449	+	4.06463i	0.500386	+	0.363552i
$126$	−6.42690	−	4.66941i	−0.572554	−	0.415985i
$127$	−3.98072	−	2.89216i	−0.353232	−	0.256638i	0.396992	−	0.917822i	$-0.370054\pi$
$127$	−3.98072	−	2.89216i	−0.353232	−	0.256638i	−0.750224	+	0.661184i	$0.770054\pi$
$128$	3.38905	−	10.4304i	0.299553	−	0.921928i
$129$	−21.3723	−	15.5279i	−1.88173	−	1.36716i
$130$	0.413654	+	1.27310i	0.0362799	+	0.111658i
$131$	0.245964	−	0.178703i	0.0214900	−	0.0156134i	−0.576988	−	0.816752i	$-0.695772\pi$
$131$	0.245964	−	0.178703i	0.0214900	−	0.0156134i	0.598478	+	0.801139i	$0.295772\pi$
$132$	12.2775	+	8.92013i	1.06862	+	0.776398i
$133$	0.672768	−	2.07057i	0.0583364	−	0.179541i
$134$	−1.82338	−	5.61180i	−0.157516	−	0.484786i
$135$	−9.30643	+	6.76151i	−0.800970	+	0.581938i
$136$	−2.36251	+	7.27106i	−0.202584	+	0.623488i
$137$	1.70940	+	5.26099i	0.146044	+	0.449476i	0.997144	−	0.0755272i	$-0.0240640\pi$
$137$	1.70940	+	5.26099i	0.146044	+	0.449476i	−0.851100	+	0.525004i	$0.824064\pi$
$138$	1.41388	−	4.35148i	0.120358	−	0.370423i
$139$	−5.31087	+	3.85858i	−0.450462	+	0.327280i	−0.789778	−	0.613392i	$-0.789804\pi$
$139$	−5.31087	+	3.85858i	−0.450462	+	0.327280i	0.339316	+	0.940672i	$0.389804\pi$
$140$	−2.40991	+	1.75090i	−0.203675	+	0.147978i
$141$	−4.08806			−0.344277
$142$	0.0597639	−	3.78672i	0.00501528	−	0.317774i
$143$	−10.4746			−0.875930
$144$	−17.8348	+	12.9578i	−1.48624	+	1.07981i
$145$	5.72417	−	4.15885i	0.475366	−	0.345374i
$146$	0.962894	−	2.96348i	0.0796897	−	0.245260i
$147$	−1.88456	−	5.80008i	−0.155436	−	0.478382i
$148$	0.818713	−	2.51974i	0.0672978	−	0.207121i
$149$	−11.0073	+	7.99727i	−0.901753	+	0.655162i	−0.938916	−	0.344147i	$-0.888168\pi$
$149$	−11.0073	+	7.99727i	−0.901753	+	0.655162i	0.0371623	+	0.999309i	$0.488168\pi$
$150$	2.03799	+	6.27228i	0.166401	+	0.512129i
$151$	−2.52027	+	7.75659i	−0.205097	+	0.631222i	0.794613	+	0.607116i	$0.207674\pi$
$151$	−2.52027	+	7.75659i	−0.205097	+	0.631222i	−0.999709	+	0.0241058i	$0.992326\pi$
$152$	1.32570	+	0.963176i	0.107528	+	0.0781239i
$153$	28.2375	−	20.5157i	2.28287	−	1.65860i
$154$	0.809277	+	2.49070i	0.0652134	+	0.200706i
$155$	3.29841	+	2.39644i	0.264935	+	0.192486i
$156$	7.44207	−	22.9043i	0.595842	−	1.83381i
$157$	1.87228	+	1.36029i	0.149425	+	0.108563i	0.659986	−	0.751278i	$-0.270562\pi$
$157$	1.87228	+	1.36029i	0.149425	+	0.108563i	−0.510561	+	0.859841i	$0.670562\pi$
$158$	−1.84814	−	1.34275i	−0.147030	−	0.106823i
$159$	3.03254	+	2.20327i	0.240496	+	0.174730i
$160$	−1.05768	−	3.25520i	−0.0836168	−	0.257346i
$161$	−5.68541	+	4.13069i	−0.448073	+	0.325544i
$162$	−12.7443			−1.00129
$163$	4.12163	−	12.6851i	0.322831	−	0.993571i	−0.649580	−	0.760294i	$-0.725055\pi$
$163$	4.12163	−	12.6851i	0.322831	−	0.993571i	0.972410	−	0.233277i	$-0.0749449\pi$
$164$	2.84567	−	8.75807i	0.222209	−	0.683890i
$165$	6.16573			0.480002
$166$	−0.214787	−	0.156052i	−0.0166707	−	0.0121120i
$167$	−7.99281	+	5.80712i	−0.618503	+	0.449368i	−0.852398	−	0.522893i	$-0.824853\pi$
$167$	−7.99281	+	5.80712i	−0.618503	+	0.449368i	0.233896	+	0.972262i	$0.424853\pi$
$168$	−12.7191			−0.981297
$169$	1.11941	+	3.44520i	0.0861087	+	0.265015i
$170$	0.454401	+	1.39850i	0.0348509	+	0.107260i
$171$	−2.31178	−	7.11493i	−0.176786	−	0.544092i
$172$	−14.4579			−1.10240
$173$	18.1188	−	13.1641i	1.37755	−	1.00085i	0.380445	−	0.924803i	$-0.375771\pi$
$173$	18.1188	−	13.1641i	1.37755	−	1.00085i	0.997104	−	0.0760449i	$-0.0242292\pi$
$174$	14.3021			1.08424
$175$	3.13022	−	9.63382i	0.236622	−	0.728248i
$176$	7.26746			0.547805
$177$	5.47154	+	3.97531i	0.411266	+	0.298803i
$178$	2.90524	+	2.11078i	0.217757	+	0.158210i
$179$	2.29114			0.171248			0.0856240	−	0.996328i	$-0.472712\pi$
$179$	2.29114			0.171248			0.0856240	+	0.996328i	$0.472712\pi$
$180$	−3.16306	+	9.73489i	−0.235760	+	0.725596i
$181$	−22.7961			−1.69442			−0.847210	−	0.531257i	$-0.821720\pi$
$181$	−22.7961			−1.69442			−0.847210	+	0.531257i	$0.821720\pi$
$182$	3.36226	−	2.44282i	0.249227	−	0.181074i
$183$	−2.08620			−0.154217
$184$	−1.63452	−	5.03054i	−0.120498	−	0.370856i
$185$	−0.332632	−	1.02373i	−0.0244556	−	0.0752665i
$186$	2.54668	+	7.83788i	0.186732	+	0.574701i
$187$	−11.5064			−0.841431
$188$	−1.81003	+	1.31507i	−0.132010	+	0.0959110i
$189$	28.8936	+	20.9924i	2.10170	+	1.52697i
$190$	0.315175			0.0228652
$191$	5.70899	−	17.5705i	0.413088	−	1.27136i	−0.500861	−	0.865528i	$-0.666983\pi$
$191$	5.70899	−	17.5705i	0.413088	−	1.27136i	0.913950	−	0.405828i	$-0.133017\pi$
$192$	−3.60561	+	11.0969i	−0.260213	+	0.800852i
$193$	−1.72722			−0.124328			−0.0621642	−	0.998066i	$-0.519800\pi$
$193$	−1.72722			−0.124328			−0.0621642	+	0.998066i	$0.519800\pi$
$194$	−6.31868	+	4.59079i	−0.453655	+	0.329599i
$195$	−3.02361	−	9.30571i	−0.216525	−	0.666396i
$196$	−2.70020	−	1.96181i	−0.192871	−	0.140129i
$197$	5.29147	+	3.84448i	0.377002	+	0.273908i	0.760108	−	0.649796i	$-0.225146\pi$
$197$	5.29147	+	3.84448i	0.377002	+	0.273908i	−0.383107	+	0.923704i	$0.625146\pi$
$198$	7.28037	+	5.28950i	0.517394	+	0.375908i
$199$	−0.932003	+	2.86841i	−0.0660679	+	0.203336i	−0.978641	−	0.205578i	$-0.934093\pi$
$199$	−0.932003	+	2.86841i	−0.0660679	+	0.203336i	0.912573	+	0.408914i	$0.134093\pi$
$200$	6.16814	+	4.48142i	0.436153	+	0.316884i
$201$	13.3280	+	41.0195i	0.940088	+	2.89329i
$202$	0.0205112	−	0.0149023i	0.00144317	−	0.00104852i
$203$	−17.7718	−	12.9119i	−1.24733	−	0.906241i
$204$	8.17514	−	25.1605i	0.572374	−	1.76159i
$205$	−1.15616	−	3.55828i	−0.0807494	−	0.248521i
$206$	−2.09108	+	1.51926i	−0.145692	+	0.105852i
$207$	−7.46221	+	22.9663i	−0.518660	+	1.59627i
$208$	−3.56388	−	10.9685i	−0.247111	−	0.760529i
$209$	−0.762109	+	2.34553i	−0.0527162	+	0.162244i
$210$	−1.97915	+	1.43793i	−0.136574	+	0.0992269i
$211$	−8.99394	+	6.53448i	−0.619169	+	0.449852i	−0.852631	−	0.522513i	$-0.824994\pi$
$211$	−8.99394	+	6.53448i	−0.619169	+	0.449852i	0.233462	+	0.972366i	$0.424994\pi$
$212$	2.05144			0.140894
$213$	−0.436845	+	27.6791i	−0.0299321	+	1.89654i
$214$	−2.88141			−0.196969
$215$	−4.75220	+	3.45267i	−0.324097	+	0.235470i
$216$	−21.7473	+	15.8003i	−1.47972	+	1.07508i
$217$	3.91154	−	12.0385i	0.265533	−	0.817226i
$218$	−0.394045	−	1.21275i	−0.0266881	−	0.0821375i
$219$	−7.03829	+	21.6616i	−0.475603	+	1.46376i
$220$	2.72994	−	1.98342i	0.184052	−	0.133722i
$221$	5.64261	+	17.3662i	0.379563	+	1.16818i
$222$	0.672370	−	2.06934i	0.0451265	−	0.138885i
$223$	11.9563	+	8.68680i	0.800656	+	0.581711i	0.911107	−	0.412171i	$-0.135229\pi$
$223$	11.9563	+	8.68680i	0.800656	+	0.581711i	−0.110450	+	0.993882i	$0.535229\pi$
$224$	−8.59700	+	6.24609i	−0.574411	+	0.417334i
$225$	−10.7561	−	33.1040i	−0.717075	−	2.20693i
$226$	5.15317	+	3.74400i	0.342784	+	0.249047i
$227$	−0.748566	+	2.30385i	−0.0496841	+	0.152912i	−0.972820	−	0.231561i	$-0.925617\pi$
$227$	−0.748566	+	2.30385i	−0.0496841	+	0.152912i	0.923136	+	0.384473i	$0.125617\pi$
$228$	−4.58740	−	3.33294i	−0.303808	−	0.220729i
$229$	−2.92946	−	2.12838i	−0.193584	−	0.140647i	0.486771	−	0.873530i	$-0.338175\pi$
$229$	−2.92946	−	2.12838i	−0.193584	−	0.140647i	−0.680355	+	0.732882i	$0.738175\pi$
$230$	−0.823059	−	0.597988i	−0.0542709	−	0.0394301i
$231$	−5.91541	−	18.2058i	−0.389206	−	1.19785i
$232$	13.3763	−	9.71842i	0.878195	−	0.638046i
$233$	−17.2262			−1.12853			−0.564264	−	0.825594i	$-0.690840\pi$
$233$	−17.2262			−1.12853			−0.564264	+	0.825594i	$0.690840\pi$
$234$	4.41303	−	13.5819i	0.288489	−	0.887877i
$235$	−0.280894	+	0.864504i	−0.0183235	+	0.0563940i
$236$	3.70137			0.240939
$237$	13.5090	+	9.81484i	0.877502	+	0.637543i
$238$	3.69345	−	2.68345i	0.239411	−	0.173942i
$239$	7.85457			0.508070			0.254035	−	0.967195i	$-0.418242\pi$
$239$	7.85457			0.508070			0.254035	+	0.967195i	$0.418242\pi$
$240$	2.09783	+	6.45646i	0.135414	+	0.416763i
$241$	−6.33864	−	19.5083i	−0.408308	−	1.25664i	−0.918102	−	0.396345i	$-0.870278\pi$
$241$	−6.33864	−	19.5083i	−0.408308	−	1.25664i	0.509794	−	0.860297i	$-0.329722\pi$
$242$	0.611041	+	1.88059i	0.0392792	+	0.120889i
$243$	45.9130			2.94532
$244$	−0.923687	+	0.671098i	−0.0591330	+	0.0429626i
$245$	−1.35603			−0.0866338
$246$	2.33701	−	7.19259i	0.149003	−	0.458583i
$247$	3.91376			0.249026
$248$	7.70775	+	5.60001i	0.489443	+	0.355601i
$249$	1.56999	+	1.14067i	0.0994942	+	0.0722867i
$250$	3.10807			0.196571
$251$	5.09540	−	15.6820i	0.321619	−	0.989840i	−0.651325	−	0.758799i	$-0.725787\pi$
$251$	5.09540	−	15.6820i	0.321619	−	0.989840i	0.972944	−	0.231042i	$-0.0742134\pi$
$252$	31.7792			2.00190
$253$	6.44041	−	4.67923i	0.404905	−	0.294181i
$254$	−2.21153			−0.138764
$255$	−3.32145	−	10.2224i	−0.207997	−	0.640149i
$256$	0.671760	+	2.06746i	0.0419850	+	0.129216i
$257$	−6.03703	−	18.5801i	−0.376580	−	1.15899i	−0.942407	−	0.334469i	$-0.891443\pi$
$257$	−6.03703	−	18.5801i	−0.376580	−	1.15899i	0.565827	−	0.824524i	$-0.308557\pi$
$258$	−11.8736			−0.739217
$259$	−2.70369	+	1.96435i	−0.167999	+	0.122059i
$260$	−4.33223	−	3.14755i	−0.268674	−	0.195203i
$261$	−75.4839			−4.67233
$262$	0.0422264	−	0.129959i	0.00260875	−	0.00802892i
$263$	1.05077	−	3.23395i	0.0647935	−	0.199414i	−0.913419	−	0.407021i	$-0.866568\pi$
$263$	1.05077	−	3.23395i	0.0647935	−	0.199414i	0.978212	+	0.207607i	$0.0665676\pi$
$264$	14.4081			0.886758
$265$	0.674294	−	0.489903i	0.0414215	−	0.0300945i
$266$	−0.302380	−	0.930630i	−0.0185401	−	0.0570606i
$267$	−21.2359	−	15.4288i	−1.29961	−	0.944224i
$268$	19.0964	+	13.8744i	1.16650	+	0.847513i
$269$	−12.5637	−	9.12810i	−0.766025	−	0.556550i	0.134727	−	0.990883i	$-0.456984\pi$
$269$	−12.5637	−	9.12810i	−0.766025	−	0.556550i	−0.900752	+	0.434333i	$0.856984\pi$
$270$	−1.59770	+	4.91722i	−0.0972330	+	0.299252i
$271$	21.1802	+	15.3883i	1.28661	+	0.934775i	0.999731	−	0.0231924i	$-0.00738303\pi$
$271$	21.1802	+	15.3883i	1.28661	+	0.934775i	0.286877	+	0.957968i	$0.407383\pi$
$272$	−3.91494	−	12.0490i	−0.237378	−	0.730575i
$273$	−24.5765	+	17.8558i	−1.48743	+	1.08068i
$274$	2.01144	+	1.46139i	0.121515	+	0.0882860i
$275$	−3.54590	+	10.9132i	−0.213826	+	0.658089i
$276$	5.65603	+	17.4075i	0.340453	+	1.04781i
$277$	−2.25686	+	1.63970i	−0.135602	+	0.0985203i	−0.653518	−	0.756911i	$-0.726708\pi$
$277$	−2.25686	+	1.63970i	−0.135602	+	0.0985203i	0.517917	+	0.855431i	$0.326708\pi$
$278$	−0.911756	+	2.80610i	−0.0546835	+	0.168298i
$279$	−13.4409	−	41.3669i	−0.804688	−	2.47657i
$280$	−0.873937	+	2.68970i	−0.0522277	+	0.160740i
$281$	19.8791	−	14.4430i	1.18589	−	0.861596i	0.193062	−	0.981187i	$-0.438158\pi$
$281$	19.8791	−	14.4430i	1.18589	−	0.861596i	0.992823	+	0.119591i	$0.0381582\pi$
$282$	−1.48649	+	1.08000i	−0.0885195	+	0.0643132i
$283$	8.23875			0.489743			0.244871	−	0.969556i	$-0.421254\pi$
$283$	8.23875			0.489743			0.244871	+	0.969556i	$0.421254\pi$
$284$	8.71049	+	12.3957i	0.516873	+	0.735550i
$285$	−2.30378			−0.136464
$286$	−3.80876	+	2.76722i	−0.225216	+	0.163629i
$287$	−9.39745	+	6.82764i	−0.554714	+	0.403023i
$288$	−11.2837	+	34.7278i	−0.664901	+	2.04635i
$289$	0.945144	+	2.90885i	0.0555967	+	0.171109i
$290$	0.982709	−	3.02447i	0.0577066	−	0.177603i
$291$	46.1864	−	33.5564i	2.70750	−	1.96711i
$292$	3.85192	+	11.8550i	0.225417	+	0.693762i
$293$	−6.46877	+	19.9088i	−0.377910	+	1.16309i	0.563585	+	0.826058i	$0.309422\pi$
$293$	−6.46877	+	19.9088i	−0.377910	+	1.16309i	−0.941495	+	0.337028i	$0.890578\pi$
$294$	−2.21755	−	1.61114i	−0.129330	−	0.0939637i
$295$	1.21661	−	0.883922i	0.0708340	−	0.0514639i
$296$	−0.777295	−	2.39227i	−0.0451794	−	0.139048i
$297$	−32.7306	−	23.7801i	−1.89922	−	1.37986i
$298$	−1.88970	+	5.81591i	−0.109468	+	0.336906i
$299$	−10.2205	−	7.42563i	−0.591067	−	0.429435i
$300$	−21.3440	−	15.5073i	−1.23230	−	0.895315i
$301$	14.7541	+	10.7195i	0.850412	+	0.617861i
$302$	1.13275	+	3.48625i	0.0651825	+	0.200611i
$303$	−0.149927	+	0.108928i	−0.00861309	+	0.00625777i
$304$	−2.71543			−0.155741
$305$	−0.143345	+	0.441170i	−0.00820789	+	0.0252613i
$306$	4.84773	−	14.9198i	0.277126	−	0.852907i
$307$	−29.9248			−1.70790			−0.853949	−	0.520356i	$-0.825799\pi$
$307$	−29.9248			−1.70790			−0.853949	+	0.520356i	$0.825799\pi$
$308$	−8.47562	−	6.15790i	−0.482943	−	0.350879i
$309$	15.2848	−	11.1050i	0.869519	−	0.631743i
$310$	1.83246			0.104077
$311$	3.96297	+	12.1968i	0.224719	+	0.691615i	0.998320	+	0.0579417i	$0.0184538\pi$
$311$	3.96297	+	12.1968i	0.224719	+	0.691615i	−0.773601	+	0.633674i	$0.781546\pi$
$312$	−7.06559	−	21.7456i	−0.400010	−	1.23110i
$313$	1.34997	+	4.15477i	0.0763047	+	0.234842i	0.981932	−	0.189232i	$-0.0605998\pi$
$313$	1.34997	+	4.15477i	0.0763047	+	0.234842i	−0.905628	+	0.424074i	$0.860600\pi$
$314$	1.04016			0.0586999
$315$	10.4456	−	7.58916i	0.588542	−	0.427601i
$316$	9.13851			0.514081
$317$	−8.33234	+	25.6443i	−0.467991	+	1.44033i	0.387191	+	0.922000i	$0.373445\pi$
$317$	−8.33234	+	25.6443i	−0.467991	+	1.44033i	−0.855182	+	0.518328i	$0.826555\pi$
$318$	1.68475			0.0944763
$319$	20.1318	+	14.6266i	1.12716	+	0.818933i
$320$	2.09893	+	1.52496i	0.117333	+	0.0852478i
$321$	21.0617			1.17555
$322$	−0.976055	+	3.00399i	−0.0543934	+	0.167406i
$323$	4.29928			0.239218
$324$	41.2453	−	29.9664i	2.29140	−	1.66480i
$325$	18.2097			1.01009
$326$	−1.85249	−	5.70139i	−0.102600	−	0.315771i
$327$	2.88028	+	8.86458i	0.159280	+	0.490212i
$328$	−2.70171	−	8.31501i	−0.149177	−	0.459120i
$329$	2.82214			0.155590
$330$	2.24197	−	1.62889i	0.123416	−	0.0896673i
$331$	11.2746	+	8.19145i	0.619706	+	0.450243i	0.852819	−	0.522207i	$-0.174891\pi$
$331$	11.2746	+	8.19145i	0.619706	+	0.450243i	−0.233113	+	0.972450i	$0.574891\pi$
$332$	1.06206			0.0582883
$333$	−3.54865	+	10.9216i	−0.194465	+	0.598501i
$334$	−1.37218	+	4.22315i	−0.0750826	+	0.231080i
$335$	9.59019			0.523968
$336$	17.0516	−	12.3887i	0.930239	−	0.675858i
$337$	−1.36084	−	4.18823i	−0.0741295	−	0.228147i	0.907126	−	0.420860i	$-0.138272\pi$
$337$	−1.36084	−	4.18823i	−0.0741295	−	0.228147i	−0.981255	+	0.192713i	$0.938272\pi$
$338$	1.31721	+	0.957006i	0.0716465	+	0.0520543i
$339$	−37.6672	−	27.3668i	−2.04580	−	1.48636i
$340$	−4.75897	−	3.45760i	−0.258092	−	0.187515i
$341$	−4.43098	+	13.6372i	−0.239951	+	0.738494i
$342$	−2.72026	−	1.97638i	−0.147095	−	0.106870i
$343$	6.20687	+	19.1028i	0.335139	+	1.03145i
$344$	−11.1050	+	8.06823i	−0.598739	+	0.435010i
$345$	6.01616	+	4.37100i	0.323899	+	0.235327i
$346$	3.11059	−	9.57341i	0.167226	−	0.514670i
$347$	−3.82483	−	11.7716i	−0.205328	−	0.631934i	−0.999700	−	0.0245021i	$-0.992200\pi$
$347$	−3.82483	−	11.7716i	−0.205328	−	0.631934i	0.794372	−	0.607431i	$-0.207800\pi$
$348$	−46.2867	+	33.6293i	−2.48123	+	1.80272i
$349$	4.23583	−	13.0365i	0.226739	−	0.697830i	−0.771372	−	0.636385i	$-0.780429\pi$
$349$	4.23583	−	13.0365i	0.226739	−	0.697830i	0.998110	−	0.0614451i	$-0.0195709\pi$
$350$	−1.40690	−	4.32999i	−0.0752018	−	0.231447i
$351$	−19.8398	+	61.0605i	−1.05897	+	3.25917i
$352$	9.73866	−	7.07555i	0.519072	−	0.377128i
$353$	1.53449	−	1.11487i	0.0816727	−	0.0593387i	−0.546200	−	0.837655i	$-0.683926\pi$
$353$	1.53449	−	1.11487i	0.0816727	−	0.0593387i	0.627872	+	0.778316i	$0.283926\pi$
$354$	3.03977			0.161562
$355$	5.82328	+	1.99423i	0.309068	+	0.105843i
$356$	−14.3656			−0.761374
$357$	−26.9973	+	19.6147i	−1.42885	+	1.03812i
$358$	0.833100	−	0.605283i	0.0440307	−	0.0319902i
$359$	8.95797	−	27.5698i	0.472784	−	1.45508i	−0.376140	−	0.926563i	$-0.622749\pi$
$359$	8.95797	−	27.5698i	0.472784	−	1.45508i	0.848923	−	0.528516i	$-0.177251\pi$
$360$	3.00304	+	9.24242i	0.158274	+	0.487118i
$361$	−5.58657	+	17.1937i	−0.294030	+	0.904931i
$362$	−8.28908	+	6.02237i	−0.435664	+	0.316529i
$363$	−4.46641	−	13.7462i	−0.234426	−	0.721488i
$364$	−5.13753	+	15.8117i	−0.269280	+	0.828758i
$365$	4.09718	+	2.97678i	0.214456	+	0.155812i
$366$	−0.758581	+	0.551141i	−0.0396517	+	0.0288086i
$367$	6.23562	+	19.1913i	0.325497	+	1.00178i	0.971216	+	0.238201i	$0.0765577\pi$
$367$	6.23562	+	19.1913i	0.325497	+	1.00178i	−0.645719	+	0.763575i	$0.723442\pi$
$368$	7.09116	+	5.15203i	0.369652	+	0.268568i
$369$	−12.3343	+	37.9612i	−0.642100	+	1.97618i
$370$	−0.391405	−	0.284373i	−0.0203482	−	0.0147838i
$371$	−2.09347	−	1.52100i	−0.108688	−	0.0789662i
$372$	−26.6716	−	19.3781i	−1.38286	−	1.00471i
$373$	3.42445	+	10.5394i	0.177311	+	0.545708i	0.999731	−	0.0231724i	$-0.00737665\pi$
$373$	3.42445	+	10.5394i	0.177311	+	0.545708i	−0.822420	+	0.568881i	$0.807377\pi$
$374$	−4.18393	+	3.03981i	−0.216346	+	0.157185i
$375$	−22.7185			−1.17318
$376$	−0.656395	+	2.02018i	−0.0338510	+	0.104183i
$377$	12.2030	−	37.5569i	0.628486	−	1.93428i
$378$	16.0521			0.825630
$379$	7.81168	+	5.67552i	0.401259	+	0.291532i	0.770054	−	0.637979i	$-0.220229\pi$
$379$	7.81168	+	5.67552i	0.401259	+	0.291532i	−0.368795	+	0.929511i	$0.620229\pi$
$380$	−1.02002	+	0.741089i	−0.0523260	+	0.0380170i
$381$	16.1652			0.828167
$382$	−2.56595	−	7.89717i	−0.131285	−	0.404054i
$383$	4.03412	+	12.4157i	0.206134	+	0.634414i	0.999665	+	0.0258849i	$0.00824033\pi$
$383$	4.03412	+	12.4157i	0.206134	+	0.634414i	−0.793531	+	0.608530i	$0.791760\pi$
$384$	11.1341	+	34.2672i	0.568183	+	1.74869i
$385$	−4.25643			−0.216928
$386$	−0.628050	+	0.456305i	−0.0319669	+	0.0232253i
$387$	62.6666			3.18552
$388$	9.65495	−	29.7149i	0.490156	−	1.50854i
$389$	23.5287			1.19295			0.596476	−	0.802631i	$-0.296567\pi$
$389$	23.5287			1.19295			0.596476	+	0.802631i	$0.296567\pi$
$390$	−3.55786	−	2.58494i	−0.180159	−	0.130893i
$391$	−11.2273	−	8.15709i	−0.567787	−	0.412522i
$392$	−3.16878			−0.160048
$393$	−0.308654	+	0.949940i	−0.0155695	+	0.0479181i
$394$	2.93973			0.148101
$395$	3.00376	−	2.18236i	0.151136	−	0.109806i
$396$	−35.9994			−1.80904
$397$	−5.96060	−	18.3449i	−0.299154	−	0.920702i	−0.981794	−	0.189947i	$-0.939168\pi$
$397$	−5.96060	−	18.3449i	−0.299154	−	0.920702i	0.682640	−	0.730755i	$-0.260832\pi$
$398$	0.418895	+	1.28923i	0.0209973	+	0.0646231i
$399$	2.21025	+	6.80245i	0.110651	+	0.340548i
$400$	−12.6342			−0.631710
$401$	−25.0550	+	18.2035i	−1.25118	+	0.909039i	−0.998290	−	0.0584547i	$-0.981383\pi$
$401$	−25.0550	+	18.2035i	−1.25118	+	0.909039i	−0.252895	+	0.967494i	$0.581383\pi$
$402$	15.6830	+	11.3944i	0.782198	+	0.568300i
$403$	22.7550			1.13351
$404$	−0.0313412	+	0.0964583i	−0.00155928	+	0.00479898i
$405$	6.40075	−	19.6995i	0.318056	−	0.978876i
$406$	−9.87326			−0.490002
$407$	3.06273	−	2.22521i	0.151814	−	0.110299i
$408$	−7.76157	−	23.8877i	−0.384255	−	1.18262i
$409$	−16.1631	−	11.7432i	−0.799213	−	0.580662i	0.111470	−	0.993768i	$-0.464444\pi$
$409$	−16.1631	−	11.7432i	−0.799213	−	0.580662i	−0.910683	+	0.413105i	$0.864444\pi$
$410$	−1.36044	−	0.988418i	−0.0671873	−	0.0488145i
$411$	−14.7026	−	10.6821i	−0.725226	−	0.526908i
$412$	3.19517	−	9.83372i	0.157415	−	0.484473i
$413$	−3.77721	−	2.74430i	−0.185864	−	0.135038i
$414$	3.35394	+	10.3224i	0.164837	+	0.507317i
$415$	0.349092	−	0.253630i	0.0171363	−	0.0124502i
$416$	−15.4546	−	11.2284i	−0.757724	−	0.550519i
$417$	6.66449	−	20.5112i	0.326361	−	1.00444i
$418$	0.342535	+	1.05422i	0.0167539	+	0.0515633i
$419$	16.3199	−	11.8571i	0.797279	−	0.579257i	−0.112836	−	0.993614i	$-0.535993\pi$
$419$	16.3199	−	11.8571i	0.797279	−	0.579257i	0.910115	+	0.414357i	$0.135993\pi$
$420$	3.02414	−	9.30734i	0.147563	−	0.454152i
$421$	2.03302	+	6.25699i	0.0990832	+	0.304947i	0.988296	−	0.152546i	$-0.0487474\pi$
$421$	2.03302	+	6.25699i	0.0990832	+	0.304947i	−0.889213	+	0.457493i	$0.848747\pi$
$422$	−1.54406	+	4.75211i	−0.0751634	+	0.231329i
$423$	7.84545	−	5.70005i	0.381459	−	0.277146i
$424$	1.57569	−	1.14481i	0.0765224	−	0.0555968i
$425$	20.0034			0.970309
$426$	7.15352	+	10.1800i	0.346589	+	0.493223i
$427$	1.44018			0.0696953
$428$	9.32527	−	6.77521i	0.450754	−	0.327492i
$429$	27.8401	−	20.2270i	1.34413	−	0.976571i
$430$	−0.815844	+	2.51091i	−0.0393435	+	0.121087i
$431$	−9.46207	−	29.1213i	−0.455772	−	1.40272i	−0.870226	−	0.492652i	$-0.836028\pi$
$431$	−9.46207	−	29.1213i	−0.455772	−	1.40272i	0.414454	−	0.910070i	$-0.363972\pi$
$432$	13.7652	−	42.3649i	0.662277	−	2.03828i
$433$	−20.0668	+	14.5794i	−0.964348	+	0.700640i	−0.954156	−	0.299309i	$-0.903244\pi$
$433$	−20.0668	+	14.5794i	−0.964348	+	0.700640i	−0.0101912	+	0.999948i	$0.503244\pi$
$434$	−1.75807	−	5.41078i	−0.0843900	−	0.259726i
$435$	−7.18312	+	22.1074i	−0.344404	+	1.05997i
$436$	4.12687	+	2.99834i	0.197641	+	0.143595i
$437$	−2.40641	+	1.74836i	−0.115114	+	0.0836354i
$438$	3.16340	+	9.73596i	0.151153	+	0.465202i
$439$	−18.0415	−	13.1079i	−0.861072	−	0.625606i	0.0671040	−	0.997746i	$-0.478624\pi$
$439$	−18.0415	−	13.1079i	−0.861072	−	0.625606i	−0.928177	+	0.372140i	$0.878624\pi$
$440$	0.989994	−	3.04689i	0.0471961	−	0.145255i
$441$	11.7038	+	8.50332i	0.557325	+	0.404920i
$442$	6.63962	+	4.82397i	0.315815	+	0.229453i
$443$	−29.9407	−	21.7532i	−1.42252	−	1.03352i	−0.991348	−	0.131257i	$-0.958099\pi$
$443$	−29.9407	−	21.7532i	−1.42252	−	1.03352i	−0.431177	−	0.902268i	$-0.641901\pi$
$444$	2.68972	+	8.27812i	0.127649	+	0.392862i
$445$	−4.72186	+	3.43063i	−0.223837	+	0.162627i
$446$	6.64246			0.314529
$447$	13.8128	−	42.5114i	0.653323	−	2.01072i
$448$	2.48909	−	7.66062i	0.117598	−	0.361930i
$449$	11.9725			0.565018			0.282509	−	0.959265i	$-0.408833\pi$
$449$	11.9725			0.565018			0.282509	+	0.959265i	$0.408833\pi$
$450$	−12.6567	−	9.19560i	−0.596641	−	0.433485i
$451$	10.6454	−	7.73434i	0.501272	−	0.364196i
$452$	−25.4810			−1.19852
$453$	−8.27986	−	25.4828i	−0.389022	−	1.19729i
$454$	0.336448	+	1.03548i	0.0157903	+	0.0485975i
$455$	2.08731	+	6.42408i	0.0978546	+	0.301165i
$456$	−5.38348			−0.252105
$457$	−22.7150	+	16.5034i	−1.06256	+	0.771996i	−0.974561	−	0.224124i	$-0.928048\pi$
$457$	−22.7150	+	16.5034i	−1.06256	+	0.771996i	−0.0880011	+	0.996120i	$0.528048\pi$
$458$	−1.62749			−0.0760476
$459$	−21.7941	+	67.0753i	−1.01726	+	3.13080i
$460$	4.06980			0.189755
$461$	30.9909	+	22.5162i	1.44339	+	1.04868i	0.987321	+	0.158739i	$0.0507427\pi$
$461$	30.9909	+	22.5162i	1.44339	+	1.04868i	0.456068	+	0.889945i	$0.349257\pi$
$462$	−6.96063	−	5.05719i	−0.323838	−	0.235282i
$463$	35.6500			1.65679			0.828397	−	0.560141i	$-0.189253\pi$
$463$	35.6500			1.65679			0.828397	+	0.560141i	$0.189253\pi$
$464$	−8.46664	+	26.0576i	−0.393054	+	1.20970i
$465$	−13.3944			−0.621151
$466$	−6.26377	+	4.55090i	−0.290164	+	0.210816i
$467$	−13.2200			−0.611747			−0.305873	−	0.952072i	$-0.598948\pi$
$467$	−13.2200			−0.611747			−0.305873	+	0.952072i	$0.598948\pi$
$468$	17.6537	+	54.3325i	0.816043	+	2.51152i
$469$	−9.20084	−	28.3173i	−0.424855	−	1.30757i
$470$	0.126250	+	0.388557i	0.00582347	+	0.0179228i
$471$	−7.60309			−0.350332
$472$	2.84299	−	2.06555i	0.130859	−	0.0950748i
$473$	−16.7134	−	12.1430i	−0.768483	−	0.558336i
$474$	7.50503			0.344718
$475$	1.32490	−	4.07762i	0.0607906	−	0.187094i
$476$	−5.64360	+	17.3692i	−0.258674	+	0.796117i
$477$	−8.89183			−0.407129
$478$	2.85606	−	2.07505i	0.130633	−	0.0949107i
$479$	11.1634	+	34.3575i	0.510070	+	1.56983i	0.792078	+	0.610421i	$0.209000\pi$
$479$	11.1634	+	34.3575i	0.510070	+	1.56983i	−0.282008	+	0.959412i	$0.591000\pi$
$480$	9.09714	+	6.60946i	0.415226	+	0.301679i
$481$	−4.86035	−	3.53125i	−0.221613	−	0.161011i
$482$	−7.45863	−	5.41901i	−0.339731	−	0.246829i
$483$	7.13448	−	21.9577i	0.324630	−	0.999109i
$484$	−6.39948	−	4.64950i	−0.290886	−	0.211341i
$485$	−3.92267	−	12.0727i	−0.178119	−	0.548195i
$486$	16.6948	−	12.1295i	0.757291	−	0.550204i
$487$	−4.17813	−	3.03559i	−0.189329	−	0.137556i	0.489083	−	0.872237i	$-0.337332\pi$
$487$	−4.17813	−	3.03559i	−0.189329	−	0.137556i	−0.678412	+	0.734682i	$0.737332\pi$
$488$	−0.334969	+	1.03093i	−0.0151633	+	0.0466679i
$489$	13.5408	+	41.6743i	0.612337	+	1.88458i
$490$	−0.493078	+	0.358242i	−0.0222750	+	0.0161837i
$491$	−6.15202	+	18.9340i	−0.277637	+	0.854477i	0.710873	+	0.703320i	$0.248300\pi$
$491$	−6.15202	+	18.9340i	−0.277637	+	0.854477i	−0.988510	+	0.151157i	$0.951700\pi$
$492$	9.34890	+	28.7729i	0.421481	+	1.29718i
$493$	13.4050	−	41.2564i	0.603732	−	1.85810i
$494$	1.42311	−	1.03395i	0.0640289	−	0.0465197i
$495$	−11.8327	+	8.59698i	−0.531841	+	0.386405i
$496$	−15.7878			−0.708893
$497$	0.301570	−	19.1079i	0.0135273	−	0.857105i
$498$	0.872223			0.0390852
$499$	−22.2388	+	16.1575i	−0.995547	+	0.723307i	−0.961129	−	0.276101i	$-0.910958\pi$
$499$	−22.2388	+	16.1575i	−0.995547	+	0.723307i	−0.0344178	+	0.999408i	$0.510958\pi$
$500$	−10.0588	+	7.30816i	−0.449844	+	0.326831i
$501$	10.0300	−	30.8691i	0.448107	−	1.37913i
$502$	−2.29016	−	7.04839i	−0.102215	−	0.314585i
$503$	−8.91411	+	27.4348i	−0.397460	+	1.22326i	0.529568	+	0.848267i	$0.322354\pi$
$503$	−8.91411	+	27.4348i	−0.397460	+	1.22326i	−0.927029	+	0.374990i	$0.877646\pi$
$504$	24.4093	−	17.7344i	1.08728	−	0.789952i
$505$	0.0127335	+	0.0391897i	0.000566633	+	0.00174392i
$506$	1.10567	−	3.40291i	0.0491531	−	0.151278i
$507$	−9.62813	−	6.99524i	−0.427600	−	0.310670i
$508$	7.15729	−	5.20008i	0.317554	−	0.230716i
$509$	−6.99223	−	21.5199i	−0.309925	−	0.953852i	−0.977793	−	0.209572i	$-0.932793\pi$
$509$	−6.99223	−	21.5199i	−0.309925	−	0.953852i	0.667868	−	0.744280i	$-0.267207\pi$
$510$	−3.90832	−	2.83956i	−0.173063	−	0.125738i
$511$	4.85879	−	14.9538i	0.214940	−	0.661518i
$512$	18.5358	+	13.4670i	0.819172	+	0.595163i
$513$	12.2295	+	8.88527i	0.539947	+	0.392294i
$514$	−7.10373	−	5.16117i	−0.313332	−	0.227649i
$515$	−1.29815	−	3.99531i	−0.0572035	−	0.176054i
$516$	38.4272	−	27.9190i	1.69166	−	1.22906i
$517$	−3.19692			−0.140600
$518$	−0.464162	+	1.42854i	−0.0203941	+	0.0627666i
$519$	−22.7369	+	69.9770i	−0.998039	+	3.07165i
$520$	−5.08404			−0.222950
$521$	35.4981	+	25.7909i	1.55520	+	1.12992i	0.939811	+	0.341695i	$0.111001\pi$
$521$	35.4981	+	25.7909i	1.55520	+	1.12992i	0.615389	+	0.788224i	$0.288999\pi$
$522$	−27.4473	+	19.9416i	−1.20134	+	0.872822i
$523$	0.784135			0.0342878			0.0171439	−	0.999853i	$-0.494543\pi$
$523$	0.784135			0.0342878			0.0171439	+	0.999853i	$0.494543\pi$
$524$	0.168921	+	0.519884i	0.00737934	+	0.0227113i
$525$	10.2837	+	31.6501i	0.448819	+	1.38132i
$526$	−0.472277	−	1.45352i	−0.0205923	−	0.0633765i
$527$	24.9964			1.08886
$528$	−19.3160	+	14.0339i	−0.840619	+	0.610746i
$529$	−13.3986			−0.582549
$530$	0.115761	−	0.356275i	0.00502833	−	0.0154756i
$531$	−16.0433			−0.696222
$532$	3.16685	+	2.30085i	0.137300	+	0.0997545i
$533$	−16.8935	−	12.2739i	−0.731740	−	0.531641i
$534$	−11.7978			−0.510540
$535$	1.44717	−	4.45392i	0.0625664	−	0.192560i
$536$	22.4104			0.967982
$537$	−6.08956	+	4.42432i	−0.262784	+	0.190924i
$538$	−6.97990			−0.300925
$539$	−1.47375	−	4.53573i	−0.0634788	−	0.195368i
$540$	−6.39138	−	19.6706i	−0.275041	−	0.846490i
$541$	−2.37612	−	7.31293i	−0.102157	−	0.314407i	0.886896	−	0.461970i	$-0.152857\pi$
$541$	−2.37612	−	7.31293i	−0.102157	−	0.314407i	−0.989053	+	0.147563i	$0.952857\pi$
$542$	11.7669			0.505430
$543$	60.5891	−	44.0205i	2.60013	−	1.88910i
$544$	−16.9769	−	12.3345i	−0.727881	−	0.528836i
$545$	2.07250			0.0887762
$546$	−4.21922	+	12.9854i	−0.180566	+	0.555724i
$547$	−7.09389	+	21.8327i	−0.303313	+	0.933501i	0.676989	+	0.735994i	$0.263285\pi$
$547$	−7.09389	+	21.8327i	−0.303313	+	0.933501i	−0.980301	+	0.197507i	$0.936715\pi$
$548$	−9.94598			−0.424871
$549$	4.00365	−	2.90883i	0.170872	−	0.124146i
$550$	1.59373	+	4.90500i	0.0679569	+	0.209150i
$551$	−7.52209	−	5.46512i	−0.320452	−	0.232822i
$552$	14.0586	+	10.2142i	0.598374	+	0.434744i
$553$	−9.32574	−	6.77555i	−0.396571	−	0.288126i
$554$	−0.387451	+	1.19245i	−0.0164612	+	0.0506625i
$555$	2.86098	+	2.07862i	0.121442	+	0.0882327i
$556$	−3.64735	−	11.2254i	−0.154682	−	0.476063i
$557$	13.6703	−	9.93208i	0.579231	−	0.420836i	−0.259216	−	0.965819i	$-0.583464\pi$
$557$	13.6703	−	9.93208i	0.579231	−	0.420836i	0.838447	+	0.544984i	$0.183464\pi$
$558$	−15.8159	−	11.4909i	−0.669538	−	0.486448i
$559$	−10.1309	+	31.1797i	−0.428492	+	1.31876i
$560$	−1.44821	−	4.45713i	−0.0611981	−	0.188348i
$561$	30.5825	−	22.2195i	1.29119	−	0.938107i
$562$	3.41278	−	10.5035i	0.143959	−	0.443062i
$563$	5.11418	+	15.7398i	0.215537	+	0.663354i	0.999115	+	0.0420611i	$0.0133924\pi$
$563$	5.11418	+	15.7398i	0.215537	+	0.663354i	−0.783578	+	0.621293i	$0.786608\pi$
$564$	2.27137	−	6.99055i	0.0956418	−	0.294355i
$565$	−8.37541	+	6.08509i	−0.352356	+	0.256002i
$566$	2.99576	−	2.17654i	0.125921	−	0.0914870i
$567$	−64.3083			−2.70069
$568$	13.6079	+	4.66013i	0.570974	+	0.195535i
$569$	45.8270			1.92117			0.960584	−	0.277989i	$-0.0896680\pi$
$569$	45.8270			1.92117			0.960584	+	0.277989i	$0.0896680\pi$
$570$	−0.837696	+	0.608621i	−0.0350872	+	0.0254923i
$571$	−4.50382	+	3.27222i	−0.188479	+	0.136938i	−0.678023	−	0.735040i	$-0.737163\pi$
$571$	−4.50382	+	3.27222i	−0.188479	+	0.136938i	0.489544	+	0.871978i	$0.337163\pi$
$572$	5.81978	−	17.9115i	0.243337	−	0.748916i
$573$	18.7558	+	57.7244i	0.783535	+	2.41147i
$574$	−1.61333	+	4.96531i	−0.0673390	+	0.207248i
$575$	−11.1964	+	8.13468i	−0.466923	+	0.339239i
$576$	−8.55306	−	26.3236i	−0.356377	−	1.09682i
$577$	−6.31000	+	19.4202i	−0.262689	+	0.808473i	0.729528	+	0.683951i	$0.239740\pi$
$577$	−6.31000	+	19.4202i	−0.262689	+	0.808473i	−0.992217	+	0.124522i	$0.960260\pi$
$578$	1.11214	+	0.808020i	0.0462591	+	0.0336092i
$579$	4.59074	−	3.33537i	0.190785	−	0.138613i
$580$	3.93119	+	12.0990i	0.163234	+	0.502382i
$581$	−1.08382	−	0.787444i	−0.0449646	−	0.0326687i
$582$	7.92916	−	24.4034i	0.328674	−	1.01156i
$583$	2.37148	+	1.72298i	0.0982167	+	0.0713586i
$584$	9.57431	+	6.95614i	0.396188	+	0.287847i
$585$	18.7777	+	13.6428i	0.776364	+	0.564062i
$586$	2.90743	+	8.94816i	0.120105	+	0.369645i
$587$	−13.7989	+	10.0255i	−0.569543	+	0.413798i	−0.834939	−	0.550342i	$-0.814497\pi$
$587$	−13.7989	+	10.0255i	−0.569543	+	0.413798i	0.265396	+	0.964140i	$0.414497\pi$
$588$	10.9651			0.452195
$589$	1.65560	−	5.09542i	0.0682180	−	0.209953i
$590$	0.208865	−	0.642820i	0.00859883	−	0.0264645i
$591$	−21.4880			−0.883896
$592$	3.37220	+	2.45004i	0.138596	+	0.100696i
$593$	−15.2378	+	11.0709i	−0.625743	+	0.454629i	−0.854923	−	0.518755i	$-0.826396\pi$
$593$	−15.2378	+	11.0709i	−0.625743	+	0.454629i	0.229180	+	0.973384i	$0.426396\pi$
$594$	−18.1838			−0.746088
$595$	2.29292	+	7.05687i	0.0940005	+	0.289304i
$596$	−7.55949	−	23.2657i	−0.309649	−	0.953001i
$597$	−3.06192	−	9.42361i	−0.125316	−	0.385683i
$598$	−5.67809			−0.232195
$599$	−2.69813	+	1.96031i	−0.110243	+	0.0800959i	−0.641541	−	0.767089i	$-0.721704\pi$
$599$	−2.69813	+	1.96031i	−0.110243	+	0.0800959i	0.531298	+	0.847185i	$0.321704\pi$
$600$	−25.0480			−1.02258
$601$	0.000229126	0	0.000705177i	9.34624e−6	0	2.87648e-5i	−0.951052	−	0.309031i	$-0.899995\pi$
$601$	0.000229126	0	0.000705177i	9.34624e−6	0	2.87648e-5i	0.951061	+	0.309003i	$0.0999952\pi$
$602$	8.19677			0.334076
$603$	−82.7722	−	60.1375i	−3.37074	−	2.44899i
$604$	−11.8634	−	8.61926i	−0.482715	−	0.350713i
$605$	−3.21380			−0.130660
$606$	−0.0257391	+	0.0792167i	−0.00104558	+	0.00321796i
$607$	−21.1986			−0.860427			−0.430213	−	0.902727i	$-0.641562\pi$
$607$	−21.1986			−0.860427			−0.430213	+	0.902727i	$0.641562\pi$
$608$	−3.63878	+	2.64373i	−0.147572	+	0.107217i
$609$	72.1687			2.92442
$610$	0.0644272	+	0.198287i	0.00260858	+	0.00802839i
$611$	1.56773	+	4.82499i	0.0634237	+	0.195198i
$612$	19.3927	+	59.6845i	0.783902	+	2.41260i
$613$	−9.97369			−0.402834			−0.201417	−	0.979506i	$-0.564555\pi$
$613$	−9.97369			−0.402834			−0.201417	+	0.979506i	$0.564555\pi$
$614$	−10.8812	+	7.90565i	−0.439130	+	0.319046i
$615$	9.94415	+	7.22485i	0.400987	+	0.291334i
$616$	−9.94645			−0.400754
$617$	12.0623	−	37.1240i	0.485611	−	1.49456i	−0.345483	−	0.938425i	$-0.612285\pi$
$617$	12.0623	−	37.1240i	0.485611	−	1.49456i	0.831094	−	0.556132i	$-0.187715\pi$
$618$	2.62404	−	8.07597i	0.105555	−	0.324863i
$619$	22.5283			0.905490			0.452745	−	0.891640i	$-0.350445\pi$
$619$	22.5283			0.905490			0.452745	+	0.891640i	$0.350445\pi$
$620$	−5.93051	+	4.30877i	−0.238175	+	0.173044i
$621$	−15.0784	−	46.4065i	−0.605075	−	1.86223i
$622$	4.66320	+	3.38801i	0.186977	+	0.135847i
$623$	14.6599	+	10.6510i	0.587336	+	0.426725i
$624$	30.6531	+	22.2708i	1.22711	+	0.891546i
$625$	5.33992	−	16.4346i	0.213597	−	0.657384i
$626$	1.58850	+	1.15411i	0.0634891	+	0.0461275i
$627$	−2.50376	−	7.70580i	−0.0999907	−	0.307740i
$628$	−3.36635	+	2.44579i	−0.134332	+	0.0975978i
$629$	−5.33912	−	3.87910i	−0.212885	−	0.154670i
$630$	1.79327	−	5.51911i	0.0714455	−	0.219887i
$631$	−5.32298	−	16.3825i	−0.211905	−	0.652176i	−0.999359	−	0.0358024i	$-0.988601\pi$
$631$	−5.32298	−	16.3825i	−0.211905	−	0.652176i	0.787454	−	0.616373i	$-0.211399\pi$
$632$	7.01920	−	5.09975i	0.279209	−	0.202857i
$633$	11.2863	−	34.7356i	0.448590	−	1.38062i
$634$	3.74503	+	11.5260i	0.148734	+	0.457756i
$635$	1.11072	−	3.41845i	0.0440777	−	0.135657i
$636$	−5.45247	+	3.96145i	−0.216204	+	0.157082i
$637$	−6.12290	+	4.44854i	−0.242598	+	0.176258i
$638$	11.1844			0.442795
$639$	−37.7550	−	53.7283i	−1.49356	−	2.12546i
$640$	8.01151			0.316683
$641$	18.7836	−	13.6471i	0.741907	−	0.539027i	−0.151401	−	0.988472i	$-0.548378\pi$
$641$	18.7836	−	13.6471i	0.741907	−	0.539027i	0.893308	+	0.449445i	$0.148378\pi$
$642$	7.65841	−	5.56416i	0.302253	−	0.219600i
$643$	−8.28043	+	25.4846i	−0.326548	+	1.00501i	0.644188	+	0.764867i	$0.277195\pi$
$643$	−8.28043	+	25.4846i	−0.326548	+	1.00501i	−0.970737	+	0.240146i	$0.922805\pi$
$644$	−3.90457	−	12.0170i	−0.153862	−	0.473537i
$645$	5.96342	−	18.3535i	0.234809	−	0.722669i
$646$	1.56329	−	1.13580i	0.0615070	−	0.0446875i
$647$	2.94502	+	9.06383i	0.115781	+	0.356336i	0.992109	−	0.125378i	$-0.0400144\pi$
$647$	2.94502	+	9.06383i	0.115781	+	0.356336i	−0.876328	+	0.481714i	$0.840014\pi$
$648$	14.9573	−	46.0339i	0.587579	−	1.80838i
$649$	4.27881	+	3.10874i	0.167958	+	0.122029i
$650$	6.62138	−	4.81072i	0.259712	−	0.188692i
$651$	12.8506	+	39.5502i	0.503656	+	1.55009i
$652$	19.4013	+	14.0959i	0.759813	+	0.552037i
$653$	−7.32786	+	22.5528i	−0.286761	+	0.882561i	0.699104	+	0.715020i	$0.253583\pi$
$653$	−7.32786	+	22.5528i	−0.286761	+	0.882561i	−0.985865	+	0.167541i	$0.946417\pi$
$654$	3.38920	+	2.46240i	0.132528	+	0.0962874i
$655$	0.179676	+	0.130542i	0.00702052	+	0.00510071i
$656$	11.7210	+	8.51582i	0.457629	+	0.332487i
$657$	−16.6959	−	51.3846i	−0.651368	−	2.00471i
$658$	1.02618	−	0.745565i	0.0400047	−	0.0290651i
$659$	−7.40211			−0.288345			−0.144173	−	0.989553i	$-0.546052\pi$
$659$	−7.40211			−0.288345			−0.144173	+	0.989553i	$0.546052\pi$
$660$	−3.42574	+	10.5433i	−0.133347	+	0.410399i
$661$	4.39521	−	13.5271i	0.170954	−	0.526142i	−0.828472	−	0.560031i	$-0.810789\pi$
$661$	4.39521	−	13.5271i	0.170954	−	0.526142i	0.999426	+	0.0338890i	$0.0107893\pi$
$662$	6.26369			0.243445
$663$	−48.5324	−	35.2608i	−1.88484	−	1.36942i
$664$	0.815760	−	0.592685i	0.0316576	−	0.0230006i
$665$	1.59038			0.0616724
$666$	1.59496	+	4.90880i	0.0618036	+	0.190212i
$667$	9.27437	+	28.5436i	0.359105	+	1.10521i
$668$	−5.48923	−	16.8941i	−0.212385	−	0.653653i
$669$	−48.5531			−1.87717
$670$	3.48717	−	2.53357i	0.134721	−	0.0978805i
$671$	−1.63143			−0.0629808
$672$	10.7882	−	33.2026i	0.416163	−	1.28082i
$673$	2.71475			0.104646			0.0523230	−	0.998630i	$-0.483337\pi$
$673$	2.71475			0.104646			0.0523230	+	0.998630i	$0.483337\pi$
$674$	−1.60129	−	1.16340i	−0.0616793	−	0.0448126i
$675$	56.9009	+	41.3409i	2.19012	+	1.59121i
$676$	−6.51321			−0.250508
$677$	−12.6553	+	38.9491i	−0.486384	+	1.49694i	0.343582	+	0.939123i	$0.388360\pi$
$677$	−12.6553	+	38.9491i	−0.486384	+	1.49694i	−0.829966	+	0.557814i	$0.811640\pi$
$678$	−20.9263			−0.803671
$679$	−31.8842	+	23.1652i	−1.22360	+	0.889000i
$680$	−5.58483			−0.214169
$681$	−2.45927	−	7.56886i	−0.0942395	−	0.290039i
$682$	1.99154	+	6.12932i	0.0762598	+	0.234704i
$683$	−6.39662	−	19.6868i	−0.244760	−	0.753293i	−0.995676	−	0.0928953i	$-0.970388\pi$
$683$	−6.39662	−	19.6868i	−0.244760	−	0.753293i	0.750916	−	0.660397i	$-0.229612\pi$
$684$	13.4509			0.514308
$685$	−3.26917	+	2.37519i	−0.124909	+	0.0907514i
$686$	7.30358	+	5.30636i	0.278852	+	0.202598i
$687$	11.8962			0.453867
$688$	7.02900	−	21.6330i	0.267978	−	0.824751i
$689$	1.43748	−	4.42412i	0.0547638	−	0.168546i
$690$	3.34233			0.127240
$691$	−32.5099	+	23.6198i	−1.23673	+	0.898540i	−0.997376	−	0.0723914i	$-0.976937\pi$
$691$	−32.5099	+	23.6198i	−1.23673	+	0.898540i	−0.239358	+	0.970931i	$0.576937\pi$
$692$	12.4435	+	38.2971i	0.473030	+	1.45584i
$693$	36.7369	+	26.6909i	1.39552	+	1.01391i
$694$	−4.50065	−	3.26991i	−0.170842	−	0.124124i
$695$	−3.87958	−	2.81868i	−0.147161	−	0.106919i
$696$	−16.7856	+	51.6606i	−0.636255	+	1.95819i
$697$	−18.5576	−	13.4829i	−0.702920	−	0.510701i
$698$	−1.90382	−	5.85936i	−0.0720607	−	0.221780i
$699$	45.7851	−	33.2648i	1.73175	−	1.25819i
$700$	14.7345	+	10.7053i	0.556914	+	0.404621i
$701$	8.14331	−	25.0625i	0.307569	−	0.946599i	−0.671138	−	0.741333i	$-0.734194\pi$
$701$	8.14331	−	25.0625i	0.307569	−	0.946599i	0.978706	−	0.205266i	$-0.0658060\pi$
$702$	8.91712	+	27.4441i	0.336555	+	1.03581i
$703$	−1.14437	+	0.831431i	−0.0431606	+	0.0313580i
$704$	−2.81963	+	8.67793i	−0.106269	+	0.327062i
$705$	−0.922825	−	2.84016i	−0.0347556	−	0.106967i
$706$	0.263437	−	0.810776i	0.00991459	−	0.0305140i
$707$	0.103500	−	0.0751973i	0.00389253	−	0.00282809i
$708$	−9.83777	+	7.14756i	−0.369726	+	0.268622i
$709$	45.0059			1.69023			0.845116	−	0.534582i	$-0.179531\pi$
$709$	45.0059			1.69023			0.845116	+	0.534582i	$0.179531\pi$
$710$	2.64429	−	0.813279i	0.0992386	−	0.0305218i
$711$	−39.6102			−1.48550
$712$	−11.0341	+	8.01671i	−0.413519	+	0.300439i
$713$	−13.9911	+	10.1651i	−0.523972	+	0.380688i
$714$	−4.63483	+	14.2645i	−0.173454	+	0.533837i
$715$	−2.36450	−	7.27718i	−0.0884272	−	0.272151i
$716$	−1.27298	+	3.91783i	−0.0475734	+	0.146416i
$717$	−20.8764	+	15.1676i	−0.779644	+	0.566445i
$718$	−4.02622	−	12.3914i	−0.150257	−	0.462444i
$719$	11.8703	−	36.5331i	0.442689	−	1.36246i	−0.442310	−	0.896862i	$-0.645841\pi$
$719$	11.8703	−	36.5331i	0.442689	−	1.36246i	0.884999	−	0.465593i	$-0.154159\pi$
$720$	−13.0283	−	9.46563i	−0.485537	−	0.352763i
$721$	−10.5516	+	7.66621i	−0.392963	+	0.285505i
$722$	2.51092	+	7.72782i	0.0934468	+	0.287600i
$723$	54.5190	+	39.6103i	2.02758	+	1.47312i
$724$	12.6657	−	38.9811i	0.470718	−	1.44872i
$725$	−34.9984	−	25.4278i	−1.29981	−	0.944366i
$726$	−5.25559	−	3.81841i	−0.195053	−	0.141715i
$727$	31.9769	+	23.2326i	1.18596	+	0.861650i	0.992831	−	0.119524i	$-0.0381369\pi$
$727$	31.9769	+	23.2326i	1.18596	+	0.861650i	0.193128	+	0.981174i	$0.438137\pi$
$728$	4.87764	+	15.0118i	0.180777	+	0.556375i
$729$	−53.2118	+	38.6606i	−1.97081	+	1.43187i
$730$	2.27623			0.0842469
$731$	−11.1288	+	34.2511i	−0.411615	+	1.26682i
$732$	1.15911	−	3.56738i	0.0428420	−	0.131854i
$733$	18.0526			0.666789			0.333394	−	0.942787i	$-0.391806\pi$
$733$	18.0526			0.666789			0.333394	+	0.942787i	$0.391806\pi$
$734$	7.33741	+	5.33094i	0.270829	+	0.196769i
$735$	3.60416	−	2.61857i	0.132941	−	0.0965876i
$736$	14.5184			0.535155
$737$	10.4227	+	32.0777i	0.383925	+	1.18160i
$738$	5.54375	+	17.0619i	0.204068	+	0.628058i
$739$	−5.98770	−	18.4282i	−0.220261	−	0.677894i	−0.998738	−	0.0502209i	$-0.984007\pi$
$739$	−5.98770	−	18.4282i	−0.220261	−	0.677894i	0.778477	−	0.627673i	$-0.215993\pi$
$740$	1.93539			0.0711463
$741$	−10.4023	+	7.55768i	−0.382136	+	0.277638i
$742$	−1.16305			−0.0426968
$743$	12.6313	−	38.8751i	0.463397	−	1.42619i	−0.397591	−	0.917563i	$-0.630154\pi$
$743$	12.6313	−	38.8751i	0.463397	−	1.42619i	0.860988	−	0.508626i	$-0.169846\pi$
$744$	−31.3001			−1.14752
$745$	−8.04081	−	5.84199i	−0.294593	−	0.214034i
$746$	4.02953	+	2.92762i	0.147531	+	0.107188i
$747$	−4.60344			−0.168431
$748$	6.39306	−	19.6758i	0.233753	−	0.719419i
$749$	−14.5397			−0.531268
$750$	−8.26084	+	6.00185i	−0.301643	+	0.219157i
$751$	−22.6269			−0.825668			−0.412834	−	0.910806i	$-0.635461\pi$
$751$	−22.6269			−0.825668			−0.412834	+	0.910806i	$0.635461\pi$
$752$	−1.08772	−	3.34766i	−0.0396651	−	0.122077i
$753$	16.7399	+	51.5203i	0.610038	+	1.87750i
$754$	−5.48471	−	16.8802i	−0.199741	−	0.614741i
$755$	−5.95777			−0.216825
$756$	−51.9503	+	37.7441i	−1.88941	+	1.37274i
$757$	−20.3208	−	14.7639i	−0.738570	−	0.536603i	0.153693	−	0.988119i	$-0.450883\pi$
$757$	−20.3208	−	14.7639i	−0.738570	−	0.536603i	−0.892263	+	0.451516i	$0.850883\pi$
$758$	4.33985			0.157630
$759$	−8.08192	+	24.8736i	−0.293355	+	0.902854i
$760$	−0.369904	+	1.13845i	−0.0134178	+	0.0412958i
$761$	−19.4566			−0.705299			−0.352650	−	0.935755i	$-0.614719\pi$
$761$	−19.4566			−0.705299			−0.352650	+	0.935755i	$0.614719\pi$
$762$	5.87795	−	4.27058i	0.212936	−	0.154707i
$763$	−1.98836	−	6.11955i	−0.0719835	−	0.221543i
$764$	26.8734	+	19.5246i	0.972244	+	0.706376i
$765$	20.6274	+	14.9867i	0.745786	+	0.541845i
$766$	4.74692	+	3.44884i	0.171513	+	0.124612i
$767$	2.59362	−	7.98235i	0.0936502	−	0.288226i
$768$	−5.77784	−	4.19784i	−0.208490	−	0.151477i
$769$	−6.87052	−	21.1453i	−0.247757	−	0.762519i	−0.995171	−	0.0981594i	$-0.968705\pi$
$769$	−6.87052	−	21.1453i	−0.247757	−	0.762519i	0.747413	−	0.664359i	$-0.231295\pi$
$770$	−1.54772	+	1.12448i	−0.0557758	+	0.0405235i
$771$	51.9248	+	37.7256i	1.87003	+	1.35865i
$772$	0.959662	−	2.95354i	0.0345390	−	0.106300i
$773$	−10.9379	−	33.6634i	−0.393409	−	1.21079i	−0.930193	−	0.367070i	$-0.880361\pi$
$773$	−10.9379	−	33.6634i	−0.393409	−	1.21079i	0.536784	−	0.843720i	$-0.319639\pi$
$774$	22.7867	−	16.5555i	0.819052	−	0.595076i
$775$	7.70310	−	23.7077i	0.276704	−	0.851606i
$776$	−9.16652	−	28.2117i	−0.329059	−	1.01274i
$777$	3.39280	−	10.4420i	0.121716	−	0.374603i
$778$	8.55546	−	6.21591i	0.306728	−	0.222851i
$779$	−3.97757	+	2.88988i	−0.142511	+	0.103541i
$780$	17.5926			0.629916
$781$	−0.341618	+	21.6453i	−0.0122240	+	0.774531i
$782$	−6.23741			−0.223049
$783$	123.396	−	89.6521i	4.40980	−	3.20390i
$784$	4.24817	−	3.08648i	0.151720	−	0.110231i
$785$	−0.522415	+	1.60783i	−0.0186458	+	0.0573858i
$786$	0.138727	+	0.426957i	0.00494822	+	0.0152290i
$787$	1.79329	−	5.51919i	0.0639240	−	0.196738i	−0.913994	−	0.405729i	$-0.867018\pi$
$787$	1.79329	−	5.51919i	0.0639240	−	0.196738i	0.977918	+	0.208991i	$0.0670178\pi$
$788$	−9.51401	+	6.91233i	−0.338923	+	0.246242i
$789$	3.45211	+	10.6245i	0.122899	+	0.378243i
$790$	0.515677	−	1.58709i	0.0183470	−	0.0564662i
$791$	26.0030	+	18.8923i	0.924562	+	0.671734i
$792$	−27.6508	+	20.0895i	−0.982527	+	0.713848i
$793$	0.800038	+	2.46226i	0.0284102	+	0.0874376i
$794$	−7.01380	−	5.09582i	−0.248910	−	0.180844i
$795$	−0.846155	+	2.60420i	−0.0300100	+	0.0923614i
$796$	−4.38712	−	3.18743i	−0.155497	−	0.112975i
$797$	−21.1175	−	15.3428i	−0.748020	−	0.543468i	0.147193	−	0.989108i	$-0.452976\pi$
$797$	−21.1175	−	15.3428i	−0.748020	−	0.543468i	−0.895212	+	0.445640i	$0.852976\pi$
$798$	2.60079	+	1.88958i	0.0920668	+	0.0668904i
$799$	1.72216	+	5.30027i	0.0609257	+	0.187510i
$800$	−16.9303	+	12.3006i	−0.598577	+	0.434891i
$801$	62.2665			2.20008
$802$	−4.30136	+	13.2382i	−0.151886	+	0.467458i
$803$	−5.50402	+	16.9396i	−0.194233	+	0.597787i
$804$	−77.5481			−2.73491
$805$	−4.15318	−	3.01746i	−0.146380	−	0.106352i
$806$	8.27412	−	6.01150i	0.291444	−	0.211746i
$807$	51.0197			1.79598
$808$	0.0297557	+	0.0915786i	0.00104680	+	0.00322173i
$809$	−7.60272	−	23.3988i	−0.267297	−	0.822657i	−0.991155	−	0.132708i	$-0.957633\pi$
$809$	−7.60272	−	23.3988i	−0.267297	−	0.822657i	0.723858	−	0.689949i	$-0.242367\pi$
$810$	−2.87686	−	8.85407i	−0.101083	−	0.311100i
$811$	−46.7235			−1.64068			−0.820342	−	0.571874i	$-0.806217\pi$
$811$	−46.7235			−1.64068			−0.820342	+	0.571874i	$0.806217\pi$
$812$	31.9534	−	23.2155i	1.12135	−	0.814705i
$813$	−86.0101			−3.01650
$814$	0.525802	−	1.61825i	0.0184293	−	0.0567197i
$815$	9.74328			0.341292
$816$	33.6726	+	24.4646i	1.17878	+	0.856431i
$817$	6.24484	+	4.53714i	0.218479	+	0.158734i
$818$	−8.97955			−0.313963
$819$	22.2683	−	68.5347i	0.778116	−	2.39480i
$820$	6.72699			0.234917
$821$	−12.7220	+	9.24309i	−0.444002	+	0.322586i	−0.787223	−	0.616668i	$-0.788482\pi$
$821$	−12.7220	+	9.24309i	−0.444002	+	0.322586i	0.343221	+	0.939255i	$0.388482\pi$
$822$	−8.16817			−0.284898
$823$	6.77207	+	20.8423i	0.236060	+	0.726517i	0.996979	+	0.0776705i	$0.0247482\pi$
$823$	6.77207	+	20.8423i	0.236060	+	0.726517i	−0.760919	+	0.648846i	$0.775252\pi$
$824$	−3.03353	−	9.33625i	−0.105678	−	0.325244i
$825$	−11.6494	−	35.8531i	−0.405579	−	1.24825i
$826$	−2.09846			−0.0730149
$827$	−33.4314	+	24.2894i	−1.16252	+	0.844623i	−0.990095	−	0.140398i	$-0.955162\pi$
$827$	−33.4314	+	24.2894i	−1.16252	+	0.844623i	−0.172429	+	0.985022i	$0.555162\pi$
$828$	−35.1261	−	25.5206i	−1.22072	−	0.886902i
$829$	1.73938			0.0604111			0.0302056	−	0.999544i	$-0.490384\pi$
$829$	1.73938			0.0604111			0.0302056	+	0.999544i	$0.490384\pi$
$830$	0.0599312	−	0.184449i	0.00208024	−	0.00640232i
$831$	2.83208	−	8.71624i	0.0982437	−	0.302363i
$832$	14.4800			0.502004
$833$	−6.72603	+	4.88674i	−0.233043	+	0.169316i
$834$	−2.99540	−	9.21889i	−0.103722	−	0.319224i
$835$	−5.83873	−	4.24209i	−0.202058	−	0.146804i
$836$	−3.58740	−	2.60640i	−0.124073	−	0.0901441i
$837$	71.1037	+	51.6599i	2.45770	+	1.78563i
$838$	2.80175	−	8.62291i	0.0967850	−	0.297873i
$839$	38.6686	+	28.0944i	1.33499	+	0.969926i	0.999612	+	0.0278420i	$0.00886354\pi$
$839$	38.6686	+	28.0944i	1.33499	+	0.969926i	0.335377	+	0.942084i	$0.391136\pi$
$840$	−2.87115	−	8.83650i	−0.0990642	−	0.304888i
$841$	−52.4362	+	38.0972i	−1.80815	+	1.31370i
$842$	2.39224	+	1.73806i	0.0824420	+	0.0598976i
$843$	−24.9458	+	76.7751i	−0.859177	+	2.64428i
$844$	−6.17678	−	19.0102i	−0.212613	−	0.654357i
$845$	−2.14084	+	1.55541i	−0.0736472	+	0.0535078i
$846$	1.34689	−	4.14529i	0.0463069	−	0.142518i
$847$	3.08333	+	9.48951i	0.105944	+	0.326063i
$848$	−0.997351	+	3.06953i	−0.0342492	+	0.105408i
$849$	−21.8975	+	15.9095i	−0.751521	+	0.546012i
$850$	7.27361	−	5.28459i	0.249483	−	0.181260i
$851$	4.56593			0.156518
$852$	−47.0882	−	16.1257i	−1.61321	−	0.552458i
$853$	12.2841			0.420599			0.210300	−	0.977637i	$-0.432556\pi$
$853$	12.2841			0.420599			0.210300	+	0.977637i	$0.432556\pi$
$854$	0.523677	−	0.380473i	0.0179198	−	0.0130195i
$855$	4.42121	−	3.21219i	0.151202	−	0.109855i
$856$	3.38174	−	10.4079i	0.115586	−	0.355736i
$857$	−1.65383	−	5.08996i	−0.0564937	−	0.173870i	0.918828	−	0.394658i	$-0.129137\pi$
$857$	−1.65383	−	5.08996i	−0.0564937	−	0.173870i	−0.975322	+	0.220788i	$0.929137\pi$
$858$	4.77952	−	14.7098i	0.163170	−	0.502186i
$859$	4.62131	−	3.35758i	0.157677	−	0.114559i	−0.506149	−	0.862446i	$-0.668931\pi$
$859$	4.62131	−	3.35758i	0.157677	−	0.114559i	0.663826	+	0.747887i	$0.268931\pi$
$860$	−3.26367	−	10.0445i	−0.111290	−	0.342516i
$861$	11.7926	−	36.2940i	0.401892	−	1.23690i
$862$	−11.1340	−	8.08929i	−0.379224	−	0.275522i
$863$	−15.4662	+	11.2369i	−0.526477	+	0.382508i	−0.819038	−	0.573739i	$-0.805492\pi$
$863$	−15.4662	+	11.2369i	−0.526477	+	0.382508i	0.292561	+	0.956247i	$0.405492\pi$
$864$	−22.8003	−	70.1721i	−0.775682	−	2.38730i
$865$	13.2358	+	9.61635i	0.450030	+	0.326966i
$866$	−3.44501	+	10.6026i	−0.117066	+	0.360292i
$867$	−8.12923	−	5.90623i	−0.276083	−	0.200586i
$868$	18.4124	+	13.3774i	0.624957	+	0.454058i
$869$	10.5642	+	7.67532i	0.358365	+	0.260368i
$870$	3.22850	+	9.93631i	0.109456	+	0.336872i
$871$	43.3026	−	31.4612i	1.46725	−	1.06602i
$872$	4.84303			0.164006
$873$	−41.8487	+	128.797i	−1.41636	+	4.35912i
$874$	−0.413126	+	1.27147i	−0.0139742	+	0.0430081i
$875$	15.6834			0.530195
$876$	−33.1306	−	24.0708i	−1.11938	−	0.813276i
$877$	44.0680	−	32.0173i	1.48807	−	1.08115i	0.513227	−	0.858253i	$-0.328450\pi$
$877$	44.0680	−	32.0173i	1.48807	−	1.08115i	0.974843	−	0.222894i	$-0.0715503\pi$
$878$	−10.0231			−0.338263
$879$	−21.2519	−	65.4067i	−0.716809	−	2.20611i
$880$	1.64053	+	5.04903i	0.0553022	+	0.170203i
$881$	−4.15658	−	12.7926i	−0.140039	−	0.430994i	0.856301	−	0.516477i	$-0.172757\pi$
$881$	−4.15658	−	12.7926i	−0.140039	−	0.430994i	−0.996340	+	0.0854825i	$0.972757\pi$
$882$	6.50216			0.218939
$883$	32.6844	−	23.7466i	1.09992	−	0.799137i	0.118871	−	0.992910i	$-0.462072\pi$
$883$	32.6844	−	23.7466i	1.09992	−	0.799137i	0.981046	+	0.193773i	$0.0620724\pi$
$884$	−32.8311			−1.10423
$885$	−1.52670	+	4.69870i	−0.0513194	+	0.157945i
$886$	−16.6338			−0.558824
$887$	1.08656	+	0.789431i	0.0364831	+	0.0265065i	0.605877	−	0.795558i	$-0.292822\pi$
$887$	1.08656	+	0.789431i	0.0364831	+	0.0265065i	−0.569394	+	0.822065i	$0.692822\pi$
$888$	6.68555	+	4.85734i	0.224353	+	0.163002i
$889$	−11.1594			−0.374275
$890$	−0.810635	+	2.49488i	−0.0271725	+	0.0836285i
$891$	72.8482			2.44051
$892$	−21.4974	+	15.6188i	−0.719785	+	0.522955i
$893$	1.19450			0.0399725
$894$	−6.20826	−	19.1070i	−0.207635	−	0.639035i
$895$	0.517194	+	1.59176i	0.0172879	+	0.0532066i
$896$	−7.68626	−	23.6559i	−0.256780	−	0.790288i
$897$	41.5041			1.38578
$898$	4.35343	−	3.16295i	0.145276	−	0.105549i
$899$	−43.7342	−	31.7748i	−1.45862	−	1.05975i
$900$	62.5836			2.08612
$901$	1.57908	−	4.85991i	0.0526068	−	0.161907i
$902$	1.82757	−	5.62469i	0.0608515	−	0.187282i
$903$	−59.9144			−1.99383
$904$	−19.5717	+	14.2197i	−0.650945	+	0.472939i
$905$	−5.14591	−	15.8375i	−0.171056	−	0.526455i
$906$	−9.74285	−	7.07860i	−0.323685	−	0.235171i
$907$	−3.50918	−	2.54957i	−0.116520	−	0.0846570i	0.527999	−	0.849245i	$-0.322942\pi$
$907$	−3.50918	−	2.54957i	−0.116520	−	0.0846570i	−0.644519	+	0.764588i	$0.722942\pi$
$908$	−3.52365	−	2.56008i	−0.116936	−	0.0849593i
$909$	0.135846	−	0.418091i	0.00450573	−	0.0138672i
$910$	2.45612	+	1.78448i	0.0814196	+	0.0591548i
$911$	−12.1769	−	37.4766i	−0.403438	−	1.24165i	−0.922193	−	0.386731i	$-0.873604\pi$
$911$	−12.1769	−	37.4766i	−0.403438	−	1.24165i	0.518755	−	0.854923i	$-0.326396\pi$
$912$	7.21726	−	5.24365i	0.238987	−	0.173635i
$913$	1.22775	+	0.892014i	0.0406327	+	0.0295213i
$914$	−3.89964	+	12.0019i	−0.128989	+	0.396986i
$915$	−0.470932	−	1.44938i	−0.0155685	−	0.0479150i
$916$	5.26714	−	3.82680i	0.174031	−	0.126441i
$917$	0.213075	−	0.655778i	0.00703637	−	0.0216557i
$918$	9.79549	+	30.1474i	0.323299	+	0.995013i
$919$	−2.21503	+	6.81717i	−0.0730671	+	0.224878i	−0.980920	−	0.194411i	$-0.937720\pi$
$919$	−2.21503	+	6.81717i	−0.0730671	+	0.224878i	0.907853	+	0.419289i	$0.137720\pi$
$920$	3.12597	−	2.27115i	0.103060	−	0.0748776i
$921$	79.5362	−	57.7865i	2.62081	−	1.90413i
$922$	17.2173			0.567020
$923$	32.8361	−	10.0991i	1.08081	−	0.332414i
$924$	34.4183			1.13228
$925$	−5.32445	+	3.86844i	−0.175067	+	0.127194i
$926$	12.9630	−	9.41815i	0.425990	−	0.309500i
$927$	−13.8492	+	42.6235i	−0.454868	+	1.39994i
$928$	14.0239	+	43.1613i	0.460358	+	1.41684i
$929$	−9.30043	+	28.6238i	−0.305137	+	0.939116i	0.674489	+	0.738285i	$0.264364\pi$
$929$	−9.30043	+	28.6238i	−0.305137	+	0.939116i	−0.979626	+	0.200831i	$0.935636\pi$
$930$	−4.87045	+	3.53859i	−0.159708	+	0.116035i
$931$	0.550654	+	1.69474i	0.0180470	+	0.0555429i
$932$	9.57105	−	29.4567i	0.313510	−	0.964886i
$933$	−34.0857	−	24.7647i	−1.11592	−	0.810760i
$934$	−4.80701	+	3.49250i	−0.157290	+	0.114278i
$935$	−2.59741	−	7.99401i	−0.0849444	−	0.261432i
$936$	43.8799	+	31.8806i	1.43426	+	1.04205i
$937$	7.15158	−	22.0103i	0.233632	−	0.719045i	−0.763668	−	0.645609i	$-0.776603\pi$
$937$	7.15158	−	22.0103i	0.233632	−	0.719045i	0.997300	−	0.0734362i	$-0.0233965\pi$
$938$	−10.8266	−	7.86596i	−0.353500	−	0.256833i
$939$	−11.6111	−	8.43598i	−0.378915	−	0.275298i
$940$	−1.32222	−	0.960652i	−0.0431262	−	0.0313330i
$941$	9.86942	+	30.3749i	0.321734	+	0.990195i	0.972893	+	0.231254i	$0.0742829\pi$
$941$	9.86942	+	30.3749i	0.321734	+	0.990195i	−0.651160	+	0.758941i	$0.725717\pi$
$942$	−2.76462	+	2.00862i	−0.0900763	+	0.0654442i
$943$	15.8702			0.516804
$944$	−1.79950	+	5.53829i	−0.0585687	+	0.180256i
$945$	−8.06204	+	24.8124i	−0.262258	+	0.807148i
$946$	−9.28528			−0.301891
$947$	13.6764	+	9.93652i	0.444425	+	0.322894i	0.787391	−	0.616454i	$-0.211431\pi$
$947$	13.6764	+	9.93652i	0.444425	+	0.322894i	−0.342966	+	0.939348i	$0.611431\pi$
$948$	−24.2890	+	17.6470i	−0.788869	+	0.573147i
$949$	28.2655			0.917537
$950$	−0.595485	−	1.83271i	−0.0193201	−	0.0594611i
$951$	−27.3743	−	84.2495i	−0.887673	−	2.73198i
$952$	5.35810	+	16.4905i	0.173657	+	0.534462i
$953$	34.9649			1.13263			0.566313	−	0.824191i	$-0.308370\pi$
$953$	34.9649			1.13263			0.566313	+	0.824191i	$0.308370\pi$
$954$	−3.23323	+	2.34908i	−0.104680	+	0.0760542i
$955$	13.4957			0.436711
$956$	−4.36407	+	13.4312i	−0.141144	+	0.434397i
$957$	−81.7525			−2.64268
$958$	13.1359	+	9.54380i	0.424402	+	0.308346i
$959$	10.1498	+	7.37423i	0.327753	+	0.238126i
$960$	−8.52345			−0.275093
$961$	0.0463258	−	0.142576i	0.00149438	−	0.00459923i
$962$	−2.70021			−0.0870584
$963$	−40.4197	+	29.3666i	−1.30251	+	0.946327i
$964$	36.8808			1.18785
$965$	−0.389897	−	1.19998i	−0.0125512	−	0.0386287i
$966$	−3.20664	−	9.86902i	−0.103172	−	0.317531i
$967$	15.8692	+	48.8405i	0.510320	+	1.57060i	0.791639	+	0.610990i	$0.209228\pi$
$967$	15.8692	+	48.8405i	0.510320	+	1.57060i	−0.281318	+	0.959615i	$0.590772\pi$
$968$	−7.51003			−0.241382
$969$	−11.4269	+	8.30214i	−0.367085	+	0.266703i
$970$	−4.61578	−	3.35356i	−0.148204	−	0.107676i
$971$	−1.99502			−0.0640232			−0.0320116	−	0.999487i	$-0.510191\pi$
$971$	−1.99502			−0.0640232			−0.0320116	+	0.999487i	$0.510191\pi$
$972$	−25.5097	+	78.5107i	−0.818223	+	2.51823i
$973$	−4.60074	+	14.1596i	−0.147493	+	0.453937i
$974$	−2.32120			−0.0743760
$975$	−48.3991	+	35.1640i	−1.55001	+	1.12615i
$976$	−0.555080	−	1.70836i	−0.0177677	−	0.0546833i
$977$	30.3015	+	22.0153i	0.969429	+	0.704332i	0.955321	−	0.295569i	$-0.0955092\pi$
$977$	30.3015	+	22.0153i	0.969429	+	0.704332i	0.0141079	+	0.999900i	$0.495509\pi$
$978$	15.9334	+	11.5763i	0.509493	+	0.370168i
$979$	−16.6067	−	12.0655i	−0.530752	−	0.385614i
$980$	0.753424	−	2.31880i	0.0240672	−	0.0740714i
$981$	−17.8876	−	12.9961i	−0.571107	−	0.414934i
$982$	2.76506	+	8.50999i	0.0882368	+	0.271565i
$983$	−17.4393	+	12.6704i	−0.556227	+	0.404123i	−0.830076	−	0.557650i	$-0.811703\pi$
$983$	−17.4393	+	12.6704i	−0.556227	+	0.404123i	0.273849	+	0.961773i	$0.411703\pi$
$984$	23.2375	+	16.8831i	0.740786	+	0.538212i
$985$	−1.47646	+	4.54406i	−0.0470438	+	0.144786i
$986$	−6.02498	−	18.5430i	−0.191874	−	0.590529i
$987$	−7.50089	+	5.44971i	−0.238756	+	0.173466i
$988$	−2.17452	+	6.69248i	−0.0691806	+	0.212916i
$989$	−7.69958	−	23.6969i	−0.244832	−	0.753516i
$990$	−2.03141	+	6.25203i	−0.0645624	+	0.198703i
$991$	−25.0973	+	18.2343i	−0.797242	+	0.579230i	−0.910104	−	0.414380i	$-0.863998\pi$
$991$	−25.0973	+	18.2343i	−0.797242	+	0.579230i	0.112861	+	0.993611i	$0.463998\pi$
$992$	−21.1562	+	15.3709i	−0.671711	+	0.488027i
$993$	−45.7845			−1.45293
$994$	−4.93834	−	7.02764i	−0.156635	−	0.222903i
$995$	−2.20320			−0.0698461
$996$	−2.82283	+	2.05090i	−0.0894447	+	0.0649854i
$997$	3.78054	−	2.74672i	0.119731	−	0.0869896i	−0.526308	−	0.850294i	$-0.676424\pi$
$997$	3.78054	−	2.74672i	0.119731	−	0.0869896i	0.646039	+	0.763304i	$0.276424\pi$
$998$	−3.81790	+	11.7503i	−0.120853	+	0.371949i
$999$	−7.17052	−	22.0686i	−0.226865	−	0.698219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.c.a.25.4	✓	20
3.2	odd	2		639.2.f.c.451.2		20
71.14	odd	10		5041.2.a.j.1.5		10
71.54	even	5	inner	71.2.c.a.54.4	yes	20
71.57	even	5		5041.2.a.i.1.5		10
213.125	odd	10		639.2.f.c.622.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.c.a.25.4	✓	20	1.1	even	1	trivial
71.2.c.a.54.4	yes	20	71.54	even	5	inner
639.2.f.c.451.2		20	3.2	odd	2
639.2.f.c.622.2		20	213.125	odd	10
5041.2.a.i.1.5		10	71.57	even	5
5041.2.a.j.1.5		10	71.14	odd	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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.363618 - 0.264184i) q^{2} +(-2.65787 + 1.93106i) q^{3} +(-0.555609 + 1.70999i) q^{4} +(0.225736 + 0.694745i) q^{5} +(-0.456296 + 1.40433i) q^{6} +(1.83483 - 1.33308i) q^{7} +(0.527502 + 1.62348i) q^{8} +(2.40825 - 7.41182i) q^{9} +O(q^{10})\)	\(q+(0.363618 - 0.264184i) q^{2} +(-2.65787 + 1.93106i) q^{3} +(-0.555609 + 1.70999i) q^{4} +(0.225736 + 0.694745i) q^{5} +(-0.456296 + 1.40433i) q^{6} +(1.83483 - 1.33308i) q^{7} +(0.527502 + 1.62348i) q^{8} +(2.40825 - 7.41182i) q^{9} +(0.265622 + 0.192986i) q^{10} +(-2.07849 + 1.51011i) q^{11} +(-1.82535 - 5.61784i) q^{12} +(3.29842 + 2.39644i) q^{13} +(0.314998 - 0.969464i) q^{14} +(-1.94157 - 1.41063i) q^{15} +(-2.28850 - 1.66269i) q^{16} +(3.62333 + 2.63250i) q^{17} +(-1.08240 - 3.33129i) q^{18} +(0.776610 - 0.564240i) q^{19} -1.31343 q^{20} +(-2.30248 + 7.08630i) q^{21} +(-0.356829 + 1.09821i) q^{22} -3.09861 q^{23} +(-4.53707 - 3.29637i) q^{24} +(3.61337 - 2.62527i) q^{25} +1.83247 q^{26} +(4.86618 + 14.9766i) q^{27} +(1.26010 + 3.87820i) q^{28} +(-2.99308 - 9.21175i) q^{29} -1.07866 q^{30} +(4.51529 - 3.28055i) q^{31} -4.68546 q^{32} +(2.60824 - 8.02734i) q^{33} +2.01297 q^{34} +(1.34034 + 0.973812i) q^{35} +(11.3361 + 8.23615i) q^{36} -1.47354 q^{37} +(0.133326 - 0.410336i) q^{38} -13.3944 q^{39} +(-1.00883 + 0.732958i) q^{40} -5.12171 q^{41} +(1.03486 + 3.18499i) q^{42} +(2.48485 + 7.64758i) q^{43} +(-1.42744 - 4.39322i) q^{44} +5.69295 q^{45} +(-1.12671 + 0.818603i) q^{46} +(1.00670 + 0.731409i) q^{47} +9.29328 q^{48} +(-0.573632 + 1.76546i) q^{49} +(0.620333 - 1.90919i) q^{50} -14.7138 q^{51} +(-5.93052 + 4.30877i) q^{52} +(-0.352578 - 1.08512i) q^{53} +(5.72601 + 4.16019i) q^{54} +(-1.51833 - 1.10313i) q^{55} +(3.13211 + 2.27561i) q^{56} +(-0.974550 + 2.99936i) q^{57} +(-3.52193 - 2.55883i) q^{58} +(-0.636148 - 1.95786i) q^{59} +(3.49092 - 2.53630i) q^{60} +(0.513734 + 0.373249i) q^{61} +(0.775173 - 2.38574i) q^{62} +(-5.46183 - 16.8098i) q^{63} +(2.87328 - 2.08756i) q^{64} +(-0.920343 + 2.83252i) q^{65} +(-1.17229 - 3.60794i) q^{66} +(4.05686 - 12.4857i) q^{67} +(-6.51470 + 4.73321i) q^{68} +(8.23570 - 5.98358i) q^{69} +0.744636 q^{70} +(5.05972 - 6.73789i) q^{71} +13.3033 q^{72} +(5.60875 - 4.07499i) q^{73} +(-0.535806 + 0.389286i) q^{74} +(-4.53433 + 13.9552i) q^{75} +(0.533353 + 1.64149i) q^{76} +(-1.80057 + 5.54157i) q^{77} +(-4.87046 + 3.53859i) q^{78} +(-1.57062 - 4.83387i) q^{79} +(0.638549 - 1.96525i) q^{80} +(-22.9397 - 16.6667i) q^{81} +(-1.86235 + 1.35307i) q^{82} +(-0.182535 - 0.561785i) q^{83} +(-10.8382 - 7.87443i) q^{84} +(-1.01100 + 3.11154i) q^{85} +(2.92391 + 2.12434i) q^{86} +(25.7436 + 18.7038i) q^{87} +(-3.54804 - 2.57780i) q^{88} +(2.46898 + 7.59875i) q^{89} +(2.07006 - 1.50399i) q^{90} +9.24667 q^{91} +(1.72161 - 5.29859i) q^{92} +(-5.66613 + 17.4386i) q^{93} +0.559280 q^{94} +(0.567312 + 0.412177i) q^{95} +(12.4533 - 9.04788i) q^{96} -17.3772 q^{97} +(0.257823 + 0.793497i) q^{98} +(6.18715 + 19.0421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

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