LMFDB - Embedded newform 62.2.d.b.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(33,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("62.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.d (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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1903140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + x^{5} + 29x^{4} + 43x^{3} + 194x^{2} + 209x + 361 $ x^8 - 3x^7 + 6x^6 + x^5 + 29x^4 + 43x^3 + 194x^2 + 209x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.2
Root			$-1.37168 + 0.996583i$ of defining polynomial
Character	$\chi$	$=$	62.35
Dual form			62.2.d.b.39.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.523934 - 1.61250i) q^{3} +(-0.809017 + 0.587785i) q^{4} -0.429835 q^{5} -1.69549 q^{6} +(-0.500000 + 0.363271i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.101388 + 0.0736626i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.523934 - 1.61250i) q^{3} +(-0.809017 + 0.587785i) q^{4} -0.429835 q^{5} -1.69549 q^{6} +(-0.500000 + 0.363271i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.101388 + 0.0736626i) q^{9} +(0.132826 + 0.408797i) q^{10} +(2.64197 - 1.91950i) q^{11} +(0.523934 + 1.61250i) q^{12} +(-1.77479 + 5.46226i) q^{13} +(0.500000 + 0.363271i) q^{14} +(-0.225205 + 0.693111i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.347744 - 0.252651i) q^{17} +(0.0387267 - 0.119189i) q^{18} +(1.48057 + 4.55673i) q^{19} +(0.347744 - 0.252651i) q^{20} +(0.323809 + 0.996583i) q^{21} +(-2.64197 - 1.91950i) q^{22} +(-6.68520 - 4.85708i) q^{23} +(1.37168 - 0.996583i) q^{24} -4.81524 q^{25} +5.74336 q^{26} +(4.28694 - 3.11464i) q^{27} +(0.190983 - 0.587785i) q^{28} +(0.221276 + 0.681017i) q^{29} +0.728780 q^{30} +(3.64011 - 4.21302i) q^{31} -1.00000 q^{32} +(-1.71099 - 5.26588i) q^{33} +(-0.132826 + 0.408797i) q^{34} +(0.214917 - 0.156147i) q^{35} -0.125322 q^{36} -7.66590 q^{37} +(3.87618 - 2.81621i) q^{38} +(7.87804 + 5.72373i) q^{39} +(-0.347744 - 0.252651i) q^{40} +(-1.63283 - 5.02532i) q^{41} +(0.847744 - 0.615922i) q^{42} +(-1.16590 - 3.58828i) q^{43} +(-1.00914 + 3.10582i) q^{44} +(-0.0435801 - 0.0316628i) q^{45} +(-2.55352 + 7.85892i) q^{46} +(-1.50000 + 4.61653i) q^{47} +(-1.37168 - 0.996583i) q^{48} +(-2.04508 + 6.29412i) q^{49} +(1.48799 + 4.57957i) q^{50} +(-0.589595 + 0.428366i) q^{51} +(-1.77479 - 5.46226i) q^{52} +(7.82717 + 5.68677i) q^{53} +(-4.28694 - 3.11464i) q^{54} +(-1.13561 + 0.825069i) q^{55} -0.618034 q^{56} +8.12346 q^{57} +(0.579307 - 0.420891i) q^{58} +(-1.21770 + 3.74770i) q^{59} +(-0.225205 - 0.693111i) q^{60} +7.62704 q^{61} +(-5.13168 - 2.16006i) q^{62} -0.0774535 q^{63} +(0.309017 + 0.951057i) q^{64} +(0.762869 - 2.34787i) q^{65} +(-4.47942 + 3.25449i) q^{66} +1.79123 q^{67} +0.429835 q^{68} +(-11.3347 + 8.23512i) q^{69} +(-0.214917 - 0.156147i) q^{70} +(-9.12890 - 6.63253i) q^{71} +(0.0387267 + 0.119189i) q^{72} +(12.5393 - 9.11034i) q^{73} +(2.36889 + 7.29071i) q^{74} +(-2.52287 + 7.76460i) q^{75} +(-3.87618 - 2.81621i) q^{76} +(-0.623684 + 1.91950i) q^{77} +(3.00914 - 9.26119i) q^{78} +(1.09410 + 0.794910i) q^{79} +(-0.132826 + 0.408797i) q^{80} +(-2.66012 - 8.18701i) q^{81} +(-4.27479 + 3.10582i) q^{82} +(-0.354102 - 1.08981i) q^{83} +(-0.847744 - 0.615922i) q^{84} +(0.149472 + 0.108598i) q^{85} +(-3.05237 + 2.21768i) q^{86} +1.21408 q^{87} +3.26565 q^{88} +(5.66577 - 4.11642i) q^{89} +(-0.0166461 + 0.0512314i) q^{90} +(-1.09688 - 3.37586i) q^{91} +8.26336 q^{92} +(-4.88634 - 8.07705i) q^{93} +4.85410 q^{94} +(-0.636401 - 1.95864i) q^{95} +(-0.523934 + 1.61250i) q^{96} +(7.43156 - 5.39934i) q^{97} +6.61803 q^{98} +0.409259 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9} - 5 q^{10} + 6 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} - 23 q^{15} - 2 q^{16} + 5 q^{17} - 3 q^{18} - 2 q^{19} - 5 q^{20} + q^{21} - 6 q^{22} - 15 q^{23} - 3 q^{24} + 16 q^{25} + 18 q^{26} + 37 q^{27} + 6 q^{28} - 19 q^{29} - 2 q^{30} + 13 q^{31} - 8 q^{32} + 30 q^{33} + 5 q^{34} + 18 q^{36} - 40 q^{37} - 3 q^{38} + 30 q^{39} + 5 q^{40} - 7 q^{41} - q^{42} + 12 q^{43} + q^{44} - 31 q^{45} - 20 q^{46} - 12 q^{47} + 3 q^{48} + 6 q^{49} + 19 q^{50} - 22 q^{51} + 7 q^{52} + 9 q^{53} - 37 q^{54} - 13 q^{55} + 4 q^{56} + 28 q^{57} - q^{58} - 18 q^{59} - 23 q^{60} + 12 q^{61} - 3 q^{62} + 6 q^{63} - 2 q^{64} - 16 q^{65} + 10 q^{66} - 26 q^{67} - 50 q^{69} - 25 q^{71} - 3 q^{72} + 35 q^{73} - 5 q^{74} + 26 q^{75} + 3 q^{76} - 8 q^{77} + 15 q^{78} + 6 q^{79} + 5 q^{80} + 43 q^{81} - 13 q^{82} + 24 q^{83} + q^{84} - q^{85} + 8 q^{86} + 8 q^{87} + 14 q^{88} - 7 q^{89} - 4 q^{90} - 16 q^{91} - 10 q^{92} + 3 q^{93} + 12 q^{94} + 30 q^{95} + 2 q^{96} + 26 q^{97} + 44 q^{98} - 46 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9 - 5 * q^10 + 6 * q^11 - 2 * q^12 + 7 * q^13 + 4 * q^14 - 23 * q^15 - 2 * q^16 + 5 * q^17 - 3 * q^18 - 2 * q^19 - 5 * q^20 + q^21 - 6 * q^22 - 15 * q^23 - 3 * q^24 + 16 * q^25 + 18 * q^26 + 37 * q^27 + 6 * q^28 - 19 * q^29 - 2 * q^30 + 13 * q^31 - 8 * q^32 + 30 * q^33 + 5 * q^34 + 18 * q^36 - 40 * q^37 - 3 * q^38 + 30 * q^39 + 5 * q^40 - 7 * q^41 - q^42 + 12 * q^43 + q^44 - 31 * q^45 - 20 * q^46 - 12 * q^47 + 3 * q^48 + 6 * q^49 + 19 * q^50 - 22 * q^51 + 7 * q^52 + 9 * q^53 - 37 * q^54 - 13 * q^55 + 4 * q^56 + 28 * q^57 - q^58 - 18 * q^59 - 23 * q^60 + 12 * q^61 - 3 * q^62 + 6 * q^63 - 2 * q^64 - 16 * q^65 + 10 * q^66 - 26 * q^67 - 50 * q^69 - 25 * q^71 - 3 * q^72 + 35 * q^73 - 5 * q^74 + 26 * q^75 + 3 * q^76 - 8 * q^77 + 15 * q^78 + 6 * q^79 + 5 * q^80 + 43 * q^81 - 13 * q^82 + 24 * q^83 + q^84 - q^85 + 8 * q^86 + 8 * q^87 + 14 * q^88 - 7 * q^89 - 4 * q^90 - 16 * q^91 - 10 * q^92 + 3 * q^93 + 12 * q^94 + 30 * q^95 + 2 * q^96 + 26 * q^97 + 44 * q^98 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.523934	−	1.61250i	0.302494	−	0.930980i	−0.678107	−	0.734963i	$-0.737199\pi$
$3$	0.523934	−	1.61250i	0.302494	−	0.930980i	0.980601	−	0.196017i	$-0.0628006\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.429835			−0.192228			−0.0961140	−	0.995370i	$-0.530641\pi$
$5$	−0.429835			−0.192228			−0.0961140	+	0.995370i	$0.530641\pi$
$6$	−1.69549			−0.692180
$7$	−0.500000	+	0.363271i	−0.188982	+	0.137304i	−0.678253	−	0.734828i	$-0.737263\pi$
$7$	−0.500000	+	0.363271i	−0.188982	+	0.137304i	0.489271	+	0.872132i	$0.337263\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.101388	+	0.0736626i	0.0337960	+	0.0245542i
$10$	0.132826	+	0.408797i	0.0420034	+	0.129273i
$11$	2.64197	−	1.91950i	0.796583	−	0.578752i	−0.113326	−	0.993558i	$-0.536151\pi$
$11$	2.64197	−	1.91950i	0.796583	−	0.578752i	0.909910	+	0.414806i	$0.136151\pi$
$12$	0.523934	+	1.61250i	0.151247	+	0.465490i
$13$	−1.77479	+	5.46226i	−0.492239	+	1.51496i	0.328976	+	0.944338i	$0.393297\pi$
$13$	−1.77479	+	5.46226i	−0.492239	+	1.51496i	−0.821215	+	0.570619i	$0.806703\pi$
$14$	0.500000	+	0.363271i	0.133631	+	0.0970883i
$15$	−0.225205	+	0.693111i	−0.0581478	+	0.178960i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.347744	−	0.252651i	−0.0843402	−	0.0612768i	0.544816	−	0.838556i	$-0.316599\pi$
$17$	−0.347744	−	0.252651i	−0.0843402	−	0.0612768i	−0.629156	+	0.777279i	$0.716599\pi$
$18$	0.0387267	−	0.119189i	0.00912798	−	0.0280930i
$19$	1.48057	+	4.55673i	0.339666	+	1.04538i	0.964378	+	0.264529i	$0.0852165\pi$
$19$	1.48057	+	4.55673i	0.339666	+	1.04538i	−0.624712	+	0.780856i	$0.714783\pi$
$20$	0.347744	−	0.252651i	0.0777579	−	0.0564944i
$21$	0.323809	+	0.996583i	0.0706610	+	0.217472i
$22$	−2.64197	−	1.91950i	−0.563270	−	0.409239i
$23$	−6.68520	−	4.85708i	−1.39396	−	1.01277i	−0.995418	−	0.0956218i	$-0.969516\pi$
$23$	−6.68520	−	4.85708i	−1.39396	−	1.01277i	−0.398543	−	0.917150i	$-0.630484\pi$
$24$	1.37168	−	0.996583i	0.279993	−	0.203427i
$25$	−4.81524			−0.963048
$26$	5.74336			1.12636
$27$	4.28694	−	3.11464i	0.825021	−	0.599413i
$28$	0.190983	−	0.587785i	0.0360924	−	0.111081i
$29$	0.221276	+	0.681017i	0.0410899	+	0.126462i	0.969497	−	0.245102i	$-0.0788216\pi$
$29$	0.221276	+	0.681017i	0.0410899	+	0.126462i	−0.928407	+	0.371564i	$0.878822\pi$
$30$	0.728780			0.133056
$31$	3.64011	−	4.21302i	0.653784	−	0.756681i
$31$	3.64011	−	4.21302i	0.653784	−	0.756681i
$32$	−1.00000			−0.176777
$33$	−1.71099	−	5.26588i	−0.297845	−	0.916672i
$34$	−0.132826	+	0.408797i	−0.0227795	+	0.0701082i
$35$	0.214917	−	0.156147i	0.0363277	−	0.0263936i
$36$	−0.125322			−0.0208871
$37$	−7.66590			−1.26027			−0.630133	−	0.776487i	$-0.717000\pi$
$37$	−7.66590			−1.26027			−0.630133	+	0.776487i	$0.717000\pi$
$38$	3.87618	−	2.81621i	0.628800	−	0.456850i
$39$	7.87804	+	5.72373i	1.26150	+	0.916530i
$40$	−0.347744	−	0.252651i	−0.0549831	−	0.0399476i
$41$	−1.63283	−	5.02532i	−0.255005	−	0.784824i	−0.993829	−	0.110925i	$-0.964619\pi$
$41$	−1.63283	−	5.02532i	−0.255005	−	0.784824i	0.738824	−	0.673898i	$-0.235381\pi$
$42$	0.847744	−	0.615922i	0.130810	−	0.0950388i
$43$	−1.16590	−	3.58828i	−0.177799	−	0.547208i	0.821952	−	0.569557i	$-0.192885\pi$
$43$	−1.16590	−	3.58828i	−0.177799	−	0.547208i	−0.999750	+	0.0223496i	$0.992885\pi$
$44$	−1.00914	+	3.10582i	−0.152134	+	0.468220i
$45$	−0.0435801	−	0.0316628i	−0.00649653	−	0.00472001i
$46$	−2.55352	+	7.85892i	−0.376496	+	1.15874i
$47$	−1.50000	+	4.61653i	−0.218797	+	0.673389i	0.780065	+	0.625699i	$0.215186\pi$
$47$	−1.50000	+	4.61653i	−0.218797	+	0.673389i	−0.998862	+	0.0476905i	$0.984814\pi$
$48$	−1.37168	−	0.996583i	−0.197985	−	0.143844i
$49$	−2.04508	+	6.29412i	−0.292155	+	0.899161i
$50$	1.48799	+	4.57957i	0.210434	+	0.647649i
$51$	−0.589595	+	0.428366i	−0.0825598	+	0.0599832i
$52$	−1.77479	−	5.46226i	−0.246120	−	0.757479i
$53$	7.82717	+	5.68677i	1.07514	+	0.781138i	0.976830	−	0.214017i	$-0.0686549\pi$
$53$	7.82717	+	5.68677i	1.07514	+	0.781138i	0.0983144	+	0.995155i	$0.468655\pi$
$54$	−4.28694	−	3.11464i	−0.583378	−	0.423849i
$55$	−1.13561	+	0.825069i	−0.153126	+	0.111252i
$56$	−0.618034			−0.0825883
$57$	8.12346			1.07598
$58$	0.579307	−	0.420891i	0.0760668	−	0.0552657i
$59$	−1.21770	+	3.74770i	−0.158531	+	0.487909i	−0.998502	−	0.0547234i	$-0.982572\pi$
$59$	−1.21770	+	3.74770i	−0.158531	+	0.487909i	0.839970	+	0.542632i	$0.182572\pi$
$60$	−0.225205	−	0.693111i	−0.0290739	−	0.0894802i
$61$	7.62704			0.976543			0.488271	−	0.872692i	$-0.337628\pi$
$61$	7.62704			0.976543			0.488271	+	0.872692i	$0.337628\pi$
$62$	−5.13168	−	2.16006i	−0.651724	−	0.274328i
$63$	−0.0774535			−0.00975822
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.762869	−	2.34787i	0.0946222	−	0.291217i
$66$	−4.47942	+	3.25449i	−0.551379	+	0.400600i
$67$	1.79123			0.218833			0.109416	−	0.993996i	$-0.465102\pi$
$67$	1.79123			0.218833			0.109416	+	0.993996i	$0.465102\pi$
$68$	0.429835			0.0521251
$69$	−11.3347	+	8.23512i	−1.36453	+	0.991392i
$70$	−0.214917	−	0.156147i	−0.0256875	−	0.0186631i
$71$	−9.12890	−	6.63253i	−1.08340	−	0.787137i	−0.105128	−	0.994459i	$-0.533525\pi$
$71$	−9.12890	−	6.63253i	−1.08340	−	0.787137i	−0.978273	+	0.207322i	$0.933525\pi$
$72$	0.0387267	+	0.119189i	0.00456399	+	0.0140465i
$73$	12.5393	−	9.11034i	1.46761	−	1.06628i	0.486318	−	0.873782i	$-0.338340\pi$
$73$	12.5393	−	9.11034i	1.46761	−	1.06628i	0.981297	−	0.192502i	$-0.0616602\pi$
$74$	2.36889	+	7.29071i	0.275378	+	0.847527i
$75$	−2.52287	+	7.76460i	−0.291316	+	0.896579i
$76$	−3.87618	−	2.81621i	−0.444629	−	0.323042i
$77$	−0.623684	+	1.91950i	−0.0710754	+	0.218748i
$78$	3.00914	−	9.26119i	0.340718	−	1.04862i
$79$	1.09410	+	0.794910i	0.123096	+	0.0894343i	0.647630	−	0.761955i	$-0.275760\pi$
$79$	1.09410	+	0.794910i	0.123096	+	0.0894343i	−0.524534	+	0.851390i	$0.675760\pi$
$80$	−0.132826	+	0.408797i	−0.0148504	+	0.0457049i
$81$	−2.66012	−	8.18701i	−0.295569	−	0.909667i
$82$	−4.27479	+	3.10582i	−0.472072	+	0.342980i
$83$	−0.354102	−	1.08981i	−0.0388677	−	0.119623i	0.929740	−	0.368217i	$-0.120032\pi$
$83$	−0.354102	−	1.08981i	−0.0388677	−	0.119623i	−0.968608	+	0.248594i	$0.920032\pi$
$84$	−0.847744	−	0.615922i	−0.0924964	−	0.0672026i
$85$	0.149472	+	0.108598i	0.0162126	+	0.0117791i
$86$	−3.05237	+	2.21768i	−0.329146	+	0.239138i
$87$	1.21408			0.130163
$88$	3.26565			0.348120
$89$	5.66577	−	4.11642i	0.600570	−	0.436340i	−0.245511	−	0.969394i	$-0.578956\pi$
$89$	5.66577	−	4.11642i	0.600570	−	0.436340i	0.846081	+	0.533054i	$0.178956\pi$
$90$	−0.0166461	+	0.0512314i	−0.00175465	+	0.00540027i
$91$	−1.09688	−	3.37586i	−0.114985	−	0.353886i
$92$	8.26336			0.861515
$93$	−4.88634	−	8.07705i	−0.506690	−	0.837551i
$94$	4.85410			0.500662
$95$	−0.636401	−	1.95864i	−0.0652933	−	0.200952i
$96$	−0.523934	+	1.61250i	−0.0534738	+	0.164576i
$97$	7.43156	−	5.39934i	0.754560	−	0.548220i	−0.142677	−	0.989769i	$-0.545571\pi$
$97$	7.43156	−	5.39934i	0.754560	−	0.548220i	0.897237	+	0.441549i	$0.145571\pi$
$98$	6.61803			0.668522
$99$	0.409259			0.0411321
$100$	3.89561	−	2.83033i	0.389561	−	0.283033i
$101$	10.2914	+	7.47717i	1.02404	+	0.744006i	0.967106	−	0.254372i	$-0.0818688\pi$
$101$	10.2914	+	7.47717i	1.02404	+	0.744006i	0.0569302	+	0.998378i	$0.481869\pi$
$102$	0.589595	+	0.428366i	0.0583786	+	0.0424145i
$103$	−1.49258	−	4.59368i	−0.147068	−	0.452629i	0.850203	−	0.526455i	$-0.176479\pi$
$103$	−1.49258	−	4.59368i	−0.147068	−	0.452629i	−0.997271	+	0.0738258i	$0.976479\pi$
$104$	−4.64647	+	3.37586i	−0.455624	+	0.331030i
$105$	−0.139185	−	0.428366i	−0.0135830	−	0.0418042i
$106$	2.98971	−	9.20139i	0.290387	−	0.893718i
$107$	−9.66462	−	7.02176i	−0.934314	−	0.678819i	0.0127309	−	0.999919i	$-0.495948\pi$
$107$	−9.66462	−	7.02176i	−0.934314	−	0.678819i	−0.947045	+	0.321100i	$0.895948\pi$
$108$	−1.63746	+	5.03960i	−0.157565	+	0.484935i
$109$	0.340455	−	1.04781i	0.0326097	−	0.100362i	−0.933427	−	0.358768i	$-0.883197\pi$
$109$	0.340455	−	1.04781i	0.0326097	−	0.100362i	0.966037	+	0.258405i	$0.0831970\pi$
$110$	1.13561	+	0.825069i	0.108276	+	0.0786673i
$111$	−4.01643	+	12.3613i	−0.381223	+	1.17328i
$112$	0.190983	+	0.587785i	0.0180462	+	0.0555405i
$113$	−13.7079	+	9.95934i	−1.28953	+	0.936896i	−0.999796	−	0.0202123i	$-0.993566\pi$
$113$	−13.7079	+	9.95934i	−1.28953	+	0.936896i	−0.289731	+	0.957108i	$0.593566\pi$
$114$	−2.51029	−	7.72587i	−0.235110	−	0.723594i
$115$	2.87353	+	2.08774i	0.267958	+	0.194683i
$116$	−0.579307	−	0.420891i	−0.0537873	−	0.0390788i
$117$	−0.582307	+	0.423071i	−0.0538343	+	0.0391129i
$118$	3.94056			0.362758
$119$	0.265653			0.0243523
$120$	−0.589595	+	0.428366i	−0.0538224	+	0.0391043i
$121$	−0.103679	+	0.319092i	−0.00942539	+	0.0290084i
$122$	−2.35689	−	7.25375i	−0.213382	−	0.656724i
$123$	−8.95885			−0.807792
$124$	−0.468562	+	5.54801i	−0.0420781	+	0.498226i
$125$	4.21893			0.377353
$126$	0.0239344	+	0.0736626i	0.00213225	+	0.00656239i
$127$	−3.77201	+	11.6091i	−0.334712	+	1.03014i	0.632152	+	0.774844i	$0.282172\pi$
$127$	−3.77201	+	11.6091i	−0.334712	+	1.03014i	−0.966864	+	0.255293i	$0.917828\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−6.39697			−0.563222
$130$	−2.46869			−0.216519
$131$	−13.3260	+	9.68192i	−1.16430	+	0.845913i	−0.990316	−	0.138835i	$-0.955664\pi$
$131$	−13.3260	+	9.68192i	−1.16430	+	0.845913i	−0.173984	+	0.984748i	$0.555664\pi$
$132$	4.47942	+	3.25449i	0.389884	+	0.283267i
$133$	−2.39561	−	1.74051i	−0.207726	−	0.150922i
$134$	−0.553519	−	1.70356i	−0.0478168	−	0.147165i
$135$	−1.84267	+	1.33878i	−0.158592	+	0.115224i
$136$	−0.132826	−	0.408797i	−0.0113898	−	0.0350541i
$137$	5.45478	−	16.7881i	0.466033	−	1.43430i	−0.391645	−	0.920117i	$-0.628094\pi$
$137$	5.45478	−	16.7881i	0.466033	−	1.43430i	0.857678	−	0.514187i	$-0.171906\pi$
$138$	11.3347	+	8.23512i	0.964871	+	0.701020i
$139$	−0.0552905	+	0.170167i	−0.00468968	+	0.0144333i	−0.953374	−	0.301791i	$-0.902415\pi$
$139$	−0.0552905	+	0.170167i	−0.00468968	+	0.0144333i	0.948684	+	0.316225i	$0.102415\pi$
$140$	−0.0820912	+	0.252651i	−0.00693797	+	0.0213529i
$141$	6.65827	+	4.83751i	0.560727	+	0.407392i
$142$	−3.48693	+	10.7317i	−0.292617	+	0.900581i
$143$	5.79586	+	17.8378i	0.484674	+	1.49167i
$144$	0.101388	−	0.0736626i	0.00844899	−	0.00613855i
$145$	−0.0951120	−	0.292725i	−0.00789862	−	0.0243095i
$146$	−12.5393	−	9.11034i	−1.03776	−	0.753977i
$147$	9.07781	+	6.59542i	0.748725	+	0.543981i
$148$	6.20185	−	4.50590i	0.509789	−	0.370383i
$149$	−8.79467			−0.720487			−0.360244	−	0.932858i	$-0.617306\pi$
$149$	−8.79467			−0.720487			−0.360244	+	0.932858i	$0.617306\pi$
$150$	8.16418			0.666603
$151$	17.9946	−	13.0738i	1.46438	−	1.06393i	0.482182	−	0.876071i	$-0.339844\pi$
$151$	17.9946	−	13.0738i	1.46438	−	1.06393i	0.982195	−	0.187862i	$-0.0601557\pi$
$152$	−1.48057	+	4.55673i	−0.120090	+	0.369599i
$153$	−0.0166461	−	0.0512314i	−0.00134576	−	0.00414182i
$154$	2.01828			0.162638
$155$	−1.56465	+	1.81090i	−0.125676	+	0.145455i
$156$	−9.73779			−0.779647
$157$	3.63168	+	11.1772i	0.289840	+	0.892035i	0.984906	+	0.173089i	$0.0553749\pi$
$157$	3.63168	+	11.1772i	0.289840	+	0.892035i	−0.695066	+	0.718945i	$0.744625\pi$
$158$	0.417909	−	1.28619i	0.0332470	−	0.102324i
$159$	13.2709	−	9.64185i	1.05245	−	0.764648i
$160$	0.429835			0.0339814
$161$	5.10704			0.402491
$162$	−6.96428	+	5.05985i	−0.547166	+	0.397539i
$163$	−4.84660	−	3.52126i	−0.379615	−	0.275806i	0.381572	−	0.924339i	$-0.375383\pi$
$163$	−4.84660	−	3.52126i	−0.379615	−	0.275806i	−0.761187	+	0.648533i	$0.775383\pi$
$164$	4.27479	+	3.10582i	0.333805	+	0.242524i
$165$	0.735442	+	2.26346i	0.0572541	+	0.176210i
$166$	−0.927051	+	0.673542i	−0.0719531	+	0.0522770i
$167$	−2.69270	−	8.28729i	−0.208368	−	0.641290i	−0.999558	−	0.0297201i	$-0.990538\pi$
$167$	−2.69270	−	8.28729i	−0.208368	−	0.641290i	0.791191	−	0.611570i	$-0.209462\pi$
$168$	−0.323809	+	0.996583i	−0.0249824	+	0.0768880i
$169$	−16.1691	−	11.7476i	−1.24378	−	0.903658i
$170$	0.0570934	−	0.175715i	0.00437886	−	0.0134768i
$171$	−0.185548	+	0.571059i	−0.0141892	+	0.0436700i
$172$	3.05237	+	2.21768i	0.232741	+	0.169096i
$173$	5.13446	−	15.8023i	0.390366	−	1.20142i	−0.542146	−	0.840284i	$-0.682388\pi$
$173$	5.13446	−	15.8023i	0.390366	−	1.20142i	0.932512	−	0.361139i	$-0.117612\pi$
$174$	−0.375170	−	1.15465i	−0.0284416	−	0.0875342i
$175$	2.40762	−	1.74924i	0.181999	−	0.132230i
$176$	−1.00914	−	3.10582i	−0.0760670	−	0.234110i
$177$	5.40519	+	3.92710i	0.406279	+	0.295179i
$178$	−5.66577	−	4.11642i	−0.424667	−	0.308539i
$179$	−0.668553	+	0.485733i	−0.0499700	+	0.0363054i	−0.612490	−	0.790478i	$-0.709832\pi$
$179$	−0.668553	+	0.485733i	−0.0499700	+	0.0363054i	0.562520	+	0.826784i	$0.309832\pi$
$180$	0.0538679			0.00401508
$181$	−12.7729			−0.949405			−0.474703	−	0.880146i	$-0.657444\pi$
$181$	−12.7729			−0.949405			−0.474703	+	0.880146i	$0.657444\pi$
$182$	−2.87168	+	2.08640i	−0.212863	+	0.154654i
$183$	3.99607	−	12.2986i	0.295398	−	0.909142i
$184$	−2.55352	−	7.85892i	−0.188248	−	0.579368i
$185$	3.29507			0.242259
$186$	−6.17177	+	7.14313i	−0.452536	+	0.523760i
$187$	−1.40369			−0.102648
$188$	−1.50000	−	4.61653i	−0.109399	−	0.336695i
$189$	−1.01201	+	3.11464i	−0.0736128	+	0.226557i
$190$	−1.66612	+	1.21051i	−0.120873	+	0.0878193i
$191$	3.90568			0.282605			0.141302	−	0.989966i	$-0.454871\pi$
$191$	3.90568			0.282605			0.141302	+	0.989966i	$0.454871\pi$
$192$	1.69549			0.122361
$193$	1.92241	−	1.39672i	0.138378	−	0.100538i	−0.516443	−	0.856322i	$-0.672744\pi$
$193$	1.92241	−	1.39672i	0.138378	−	0.100538i	0.654821	+	0.755784i	$0.272744\pi$
$194$	−7.43156	−	5.39934i	−0.533555	−	0.387650i
$195$	−3.38625	−	2.46026i	−0.242495	−	0.176183i
$196$	−2.04508	−	6.29412i	−0.146077	−	0.449580i
$197$	8.57781	−	6.23215i	0.611144	−	0.444022i	−0.238673	−	0.971100i	$-0.576712\pi$
$197$	8.57781	−	6.23215i	0.611144	−	0.444022i	0.849817	+	0.527078i	$0.176712\pi$
$198$	−0.126468	−	0.389229i	−0.00898769	−	0.0276613i
$199$	−1.47956	+	4.55361i	−0.104883	+	0.322797i	−0.989703	−	0.143136i	$-0.954281\pi$
$199$	−1.47956	+	4.55361i	−0.104883	+	0.322797i	0.884820	+	0.465933i	$0.154281\pi$
$200$	−3.89561	−	2.83033i	−0.275461	−	0.200134i
$201$	0.938485	−	2.88836i	0.0661956	−	0.203729i
$202$	3.93098	−	12.0983i	0.276583	−	0.851234i
$203$	−0.358032	−	0.260125i	−0.0251289	−	0.0182572i
$204$	0.225205	−	0.693111i	0.0157675	−	0.0485275i
$205$	0.701846	+	2.16006i	0.0490190	+	0.150865i
$206$	−3.90762	+	2.83905i	−0.272257	+	0.197806i
$207$	−0.320013	−	0.984899i	−0.0222424	−	0.0684552i
$208$	4.64647	+	3.37586i	0.322175	+	0.234074i
$209$	12.6583	+	9.19677i	0.875591	+	0.636154i
$210$	−0.364390	+	0.264745i	−0.0251453	+	0.0182691i
$211$	27.1392			1.86834			0.934169	−	0.356830i	$-0.116142\pi$
$211$	27.1392			1.86834			0.934169	+	0.356830i	$0.116142\pi$
$212$	−9.67491			−0.664476
$213$	−15.4779	+	11.2454i	−1.06053	+	0.770520i
$214$	−3.69156	+	11.3614i	−0.252350	+	0.776653i
$215$	0.501146	+	1.54237i	0.0341779	+	0.105189i
$216$	5.29894			0.360548
$217$	−0.289587	+	3.42886i	−0.0196584	+	0.232766i
$218$	−1.10174			−0.0746190
$219$	−8.12068	−	24.9929i	−0.548745	−	1.68886i
$220$	0.433764	−	1.33499i	0.0292444	−	0.0900050i
$221$	1.99722	−	1.45106i	0.134347	−	0.0976090i
$222$	12.9974			0.872331
$223$	−6.05016			−0.405149			−0.202574	−	0.979267i	$-0.564931\pi$
$223$	−6.05016			−0.405149			−0.202574	+	0.979267i	$0.564931\pi$
$224$	0.500000	−	0.363271i	0.0334077	−	0.0242721i
$225$	−0.488207	−	0.354703i	−0.0325471	−	0.0236469i
$226$	13.7079	+	9.95934i	0.911833	+	0.662485i
$227$	8.05873	+	24.8022i	0.534877	+	1.64618i	0.743915	+	0.668274i	$0.232967\pi$
$227$	8.05873	+	24.8022i	0.534877	+	1.64618i	−0.209038	+	0.977907i	$0.567033\pi$
$228$	−6.57202	+	4.77485i	−0.435243	+	0.316222i
$229$	4.89769	+	15.0735i	0.323648	+	0.996087i	0.972047	+	0.234786i	$0.0754390\pi$
$229$	4.89769	+	15.0735i	0.323648	+	0.996087i	−0.648399	+	0.761301i	$0.724561\pi$
$230$	1.09759	−	3.37804i	0.0723730	−	0.222741i
$231$	2.76844	+	2.01139i	0.182150	+	0.132340i
$232$	−0.221276	+	0.681017i	−0.0145275	+	0.0447109i
$233$	−7.78672	+	23.9651i	−0.510125	+	1.57000i	0.281855	+	0.959457i	$0.409050\pi$
$233$	−7.78672	+	23.9651i	−0.510125	+	1.57000i	−0.791980	+	0.610547i	$0.790950\pi$
$234$	0.582307	+	0.423071i	0.0380666	+	0.0276570i
$235$	0.644752	−	1.98434i	0.0420590	−	0.129444i
$236$	−1.21770	−	3.74770i	−0.0792656	−	0.243954i
$237$	1.85503	−	1.34776i	0.120497	−	0.0875464i
$238$	−0.0820912	−	0.252651i	−0.00532118	−	0.0163769i
$239$	−2.65226	−	1.92698i	−0.171560	−	0.124646i	0.498692	−	0.866779i	$-0.333814\pi$
$239$	−2.65226	−	1.92698i	−0.171560	−	0.124646i	−0.670252	+	0.742134i	$0.733814\pi$
$240$	0.589595	+	0.428366i	0.0380582	+	0.0276509i
$241$	−6.18035	+	4.49028i	−0.398111	+	0.289245i	−0.768771	−	0.639524i	$-0.779131\pi$
$241$	−6.18035	+	4.49028i	−0.398111	+	0.289245i	0.370660	+	0.928769i	$0.379131\pi$
$242$	0.335513			0.0215676
$243$	1.30152			0.0834928
$244$	−6.17041	+	4.48306i	−0.395020	+	0.286999i
$245$	0.879049	−	2.70543i	0.0561604	−	0.172844i
$246$	2.76844	+	8.52037i	0.176509	+	0.543239i
$247$	−27.5177			−1.75091
$248$	5.42127	−	1.26880i	0.344251	−	0.0805690i
$249$	−1.94286			−0.123123
$250$	−1.30372	−	4.01244i	−0.0824546	−	0.253769i
$251$	4.27206	−	13.1481i	0.269650	−	0.829898i	−0.720935	−	0.693002i	$-0.756288\pi$
$251$	4.27206	−	13.1481i	0.269650	−	0.829898i	0.990585	−	0.136895i	$-0.0437125\pi$
$252$	0.0626612	−	0.0455260i	0.00394728	−	0.00286787i
$253$	−26.9853			−1.69655
$254$	12.2065			0.765903
$255$	0.253429	−	0.184127i	0.0158703	−	0.0115305i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.18798	+	2.31621i	0.198861	+	0.144481i	0.682760	−	0.730643i	$-0.260780\pi$
$257$	3.18798	+	2.31621i	0.198861	+	0.144481i	−0.483899	+	0.875124i	$0.660780\pi$
$258$	1.97677	+	6.08388i	0.123069	+	0.378766i
$259$	3.83295	−	2.78480i	0.238168	−	0.173039i
$260$	0.762869	+	2.34787i	0.0473111	+	0.145609i
$261$	−0.0277308	+	0.0853466i	−0.00171649	+	0.00528282i
$262$	13.3260	+	9.68192i	0.823284	+	0.598151i
$263$	0.583729	−	1.79653i	0.0359943	−	0.110779i	−0.931445	−	0.363882i	$-0.881451\pi$
$263$	0.583729	−	1.79653i	0.0359943	−	0.110779i	0.967439	+	0.253103i	$0.0814511\pi$
$264$	1.71099	−	5.26588i	0.105304	−	0.324092i
$265$	−3.36439	−	2.44437i	−0.206673	−	0.150157i
$266$	−0.915043	+	2.81621i	−0.0561049	+	0.172673i
$267$	−3.66926	−	11.2928i	−0.224555	−	0.691109i
$268$	−1.44913	+	1.05286i	−0.0885198	+	0.0643134i
$269$	−3.05516	−	9.40281i	−0.186276	−	0.573299i	0.813692	−	0.581297i	$-0.197454\pi$
$269$	−3.05516	−	9.40281i	−0.186276	−	0.573299i	−0.999968	+	0.00799727i	$0.997454\pi$
$270$	1.84267	+	1.33878i	0.112142	+	0.0814757i
$271$	6.16333	+	4.47792i	0.374396	+	0.272015i	0.759031	−	0.651054i	$-0.225673\pi$
$271$	6.16333	+	4.47792i	0.374396	+	0.272015i	−0.384636	+	0.923069i	$0.625673\pi$
$272$	−0.347744	+	0.252651i	−0.0210851	+	0.0153192i
$273$	−6.01828			−0.364243
$274$	−17.6520			−1.06640
$275$	−12.7217	+	9.24287i	−0.767148	+	0.557366i
$276$	4.32946	−	13.3247i	0.260603	−	0.802053i
$277$	−1.25271	−	3.85546i	−0.0752683	−	0.231652i	0.906343	−	0.422543i	$-0.138862\pi$
$277$	−1.25271	−	3.85546i	−0.0752683	−	0.231652i	−0.981611	+	0.190891i	$0.938862\pi$
$278$	0.178924			0.0107311
$279$	0.679406	−	0.159009i	0.0406750	−	0.00951963i
$280$	0.265653			0.0158758
$281$	7.44171	+	22.9032i	0.443935	+	1.36629i	0.883647	+	0.468153i	$0.155080\pi$
$281$	7.44171	+	22.9032i	0.443935	+	1.36629i	−0.439712	+	0.898139i	$0.644920\pi$
$282$	2.54323	−	7.82726i	0.151447	−	0.466107i
$283$	−17.3792	+	12.6267i	−1.03309	+	0.750581i	−0.968924	−	0.247359i	$-0.920437\pi$
$283$	−17.3792	+	12.6267i	−1.03309	+	0.750581i	−0.0641618	+	0.997940i	$0.520437\pi$
$284$	11.2839			0.669578
$285$	−3.49175			−0.206833
$286$	15.1738	−	11.0244i	0.897244	−	0.651886i
$287$	2.64197	+	1.91950i	0.155950	+	0.113305i
$288$	−0.101388	−	0.0736626i	−0.00597434	−	0.00434061i
$289$	−5.19620	−	15.9922i	−0.305659	−	0.940720i
$290$	−0.249006	+	0.180914i	−0.0146222	+	0.0106236i
$291$	−4.81281	−	14.8123i	−0.282132	−	0.868313i
$292$	−4.78959	+	14.7408i	−0.280289	+	0.862642i
$293$	19.2400	+	13.9787i	1.12401	+	0.816643i	0.984813	−	0.173621i	$-0.0555468\pi$
$293$	19.2400	+	13.9787i	1.12401	+	0.816643i	0.139200	+	0.990264i	$0.455547\pi$
$294$	3.46742	−	10.6716i	0.202224	−	0.622381i
$295$	0.523411	−	1.61089i	0.0304741	−	0.0937898i
$296$	−6.20185	−	4.50590i	−0.360475	−	0.261900i
$297$	5.34739	−	16.4576i	0.310287	−	0.954965i
$298$	2.71770	+	8.36422i	0.157432	+	0.484527i
$299$	38.3955	−	27.8960i	2.22047	−	1.61326i
$300$	−2.52287	−	7.76460i	−0.145658	−	0.448289i
$301$	1.88647	+	1.37060i	0.108734	+	0.0790001i
$302$	−17.9946	−	13.0738i	−1.03547	−	0.752314i
$303$	17.4490	−	12.6774i	1.00242	−	0.728300i
$304$	4.79123			0.274796
$305$	−3.27837			−0.187719
$306$	−0.0435801	+	0.0316628i	−0.00249131	+	0.00181004i
$307$	1.80208	−	5.54624i	0.102850	−	0.316541i	−0.886370	−	0.462978i	$-0.846781\pi$
$307$	1.80208	−	5.54624i	0.102850	−	0.316541i	0.989220	+	0.146438i	$0.0467807\pi$
$308$	−0.623684	−	1.91950i	−0.0355377	−	0.109374i
$309$	−8.18935			−0.465876
$310$	2.20578	+	0.928469i	0.125280	+	0.0527335i
$311$	−19.6909			−1.11657			−0.558284	−	0.829650i	$-0.688540\pi$
$311$	−19.6909			−1.11657			−0.558284	+	0.829650i	$0.688540\pi$
$312$	3.00914	+	9.26119i	0.170359	+	0.524311i
$313$	−9.83923	+	30.2820i	−0.556146	+	1.71164i	0.136752	+	0.990605i	$0.456334\pi$
$313$	−9.83923	+	30.2820i	−0.556146	+	1.71164i	−0.692898	+	0.721036i	$0.743666\pi$
$314$	9.50786	−	6.90787i	0.536560	−	0.389833i
$315$	0.0332922			0.00187580
$316$	−1.35238			−0.0760774
$317$	19.2452	−	13.9825i	1.08092	−	0.785334i	0.103076	−	0.994673i	$-0.467131\pi$
$317$	19.2452	−	13.9825i	1.08092	−	0.785334i	0.977843	+	0.209340i	$0.0671314\pi$
$318$	−13.2709	−	9.64185i	−0.744193	−	0.540688i
$319$	1.89182	+	1.37448i	0.105921	+	0.0769564i
$320$	−0.132826	−	0.408797i	−0.00742521	−	0.0228525i
$321$	−16.3862	+	11.9053i	−0.914591	+	0.664489i
$322$	−1.57816	−	4.85708i	−0.0879475	−	0.270675i
$323$	0.636401	−	1.95864i	0.0354103	−	0.108982i
$324$	6.96428	+	5.05985i	0.386905	+	0.281103i
$325$	8.54607	−	26.3021i	0.474050	−	1.45898i
$326$	−1.85124	+	5.69752i	−0.102530	+	0.315556i
$327$	−1.51123	−	1.09797i	−0.0835711	−	0.0607180i
$328$	1.63283	−	5.02532i	0.0901577	−	0.277477i
$329$	−0.927051	−	2.85317i	−0.0511100	−	0.157300i
$330$	1.92541	−	1.39889i	0.105990	−	0.0770066i
$331$	8.35233	+	25.7058i	0.459086	+	1.41292i	0.866271	+	0.499575i	$0.166510\pi$
$331$	8.35233	+	25.7058i	0.459086	+	1.41292i	−0.407185	+	0.913346i	$0.633490\pi$
$332$	0.927051	+	0.673542i	0.0508785	+	0.0369654i
$333$	−0.777230	−	0.564690i	−0.0425919	−	0.0309448i
$334$	−7.04959	+	5.12183i	−0.385736	+	0.280254i
$335$	−0.769931			−0.0420658
$336$	1.04787			0.0571659
$337$	−7.25086	+	5.26806i	−0.394980	+	0.286969i	−0.767493	−	0.641057i	$-0.778496\pi$
$337$	−7.25086	+	5.26806i	−0.394980	+	0.286969i	0.372513	+	0.928027i	$0.378496\pi$
$338$	−6.17606	+	19.0080i	−0.335933	+	1.03390i
$339$	8.87746	+	27.3220i	0.482158	+	1.48393i
$340$	−0.184758			−0.0100199
$341$	1.53016	−	18.1179i	0.0828628	−	0.981138i
$342$	0.600447			0.0324685
$343$	−2.60081	−	8.00448i	−0.140431	−	0.432201i
$344$	1.16590	−	3.58828i	0.0628613	−	0.193467i
$345$	4.87204	−	3.53974i	0.262302	−	0.190573i
$346$	−16.6155			−0.893254
$347$	4.69778			0.252190			0.126095	−	0.992018i	$-0.459756\pi$
$347$	4.69778			0.252190			0.126095	+	0.992018i	$0.459756\pi$
$348$	−0.982208	+	0.713616i	−0.0526519	+	0.0382538i
$349$	−14.0532	−	10.2102i	−0.752249	−	0.546541i	0.144274	−	0.989538i	$-0.453915\pi$
$349$	−14.0532	−	10.2102i	−0.752249	−	0.546541i	−0.896523	+	0.442997i	$0.853915\pi$
$350$	−2.40762	−	1.74924i	−0.128693	−	0.0935008i
$351$	9.40454	+	28.9442i	0.501977	+	1.54493i
$352$	−2.64197	+	1.91950i	−0.140817	+	0.102310i
$353$	−0.188688	−	0.580721i	−0.0100428	−	0.0309087i	0.945910	−	0.324431i	$-0.105173\pi$
$353$	−0.188688	−	0.580721i	−0.0100428	−	0.0309087i	−0.955952	+	0.293522i	$0.905173\pi$
$354$	2.06460	−	6.35418i	0.109732	−	0.337721i
$355$	3.92392	+	2.85089i	0.208260	+	0.151310i
$356$	−2.16413	+	6.66051i	−0.114699	+	0.353006i
$357$	0.139185	−	0.428366i	0.00736643	−	0.0226715i
$358$	0.668553	+	0.485733i	0.0353341	+	0.0256718i
$359$	4.76565	−	14.6672i	0.251522	−	0.774104i	−0.742974	−	0.669321i	$-0.766585\pi$
$359$	4.76565	−	14.6672i	0.251522	−	0.774104i	0.994495	−	0.104783i	$-0.0334148\pi$
$360$	−0.0166461	−	0.0512314i	−0.000877326	−	0.00270013i
$361$	−3.20034	+	2.32518i	−0.168439	+	0.122378i
$362$	3.94706	+	12.1478i	0.207453	+	0.638474i
$363$	0.460216	+	0.334367i	0.0241551	+	0.0175497i
$364$	2.87168	+	2.08640i	0.150517	+	0.109357i
$365$	−5.38983	+	3.91594i	−0.282117	+	0.204970i
$366$	−12.9316			−0.675943
$367$	−15.4481			−0.806385			−0.403193	−	0.915115i	$-0.632100\pi$
$367$	−15.4481			−0.806385			−0.403193	+	0.915115i	$0.632100\pi$
$368$	−6.68520	+	4.85708i	−0.348490	+	0.253193i
$369$	0.204630	−	0.629785i	0.0106526	−	0.0327853i
$370$	−1.01823	−	3.13380i	−0.0529354	−	0.162919i
$371$	−5.97942			−0.310436
$372$	8.70070	+	3.66235i	0.451110	+	0.189884i
$373$	27.9325			1.44629			0.723146	−	0.690695i	$-0.242695\pi$
$373$	27.9325			1.44629			0.723146	+	0.690695i	$0.242695\pi$
$374$	0.433764	+	1.33499i	0.0224294	+	0.0690307i
$375$	2.21044	−	6.80305i	0.114147	−	0.351308i
$376$	−3.92705	+	2.85317i	−0.202522	+	0.147141i
$377$	−4.11261			−0.211810
$378$	3.27493			0.168444
$379$	25.1985	−	18.3078i	1.29436	−	0.940407i	0.294476	−	0.955659i	$-0.404855\pi$
$379$	25.1985	−	18.3078i	1.29436	−	0.940407i	0.999884	+	0.0152517i	$0.00485495\pi$
$380$	1.66612	+	1.21051i	0.0854701	+	0.0620976i
$381$	16.7434	+	12.1648i	0.857789	+	0.623220i
$382$	−1.20692	−	3.71452i	−0.0617515	−	0.190051i
$383$	−5.65226	+	4.10660i	−0.288817	+	0.209838i	−0.722754	−	0.691105i	$-0.757124\pi$
$383$	−5.65226	+	4.10660i	−0.288817	+	0.209838i	0.433937	+	0.900943i	$0.357124\pi$
$384$	−0.523934	−	1.61250i	−0.0267369	−	0.0822878i
$385$	0.268081	−	0.825069i	0.0136627	−	0.0420494i
$386$	−1.92241	−	1.39672i	−0.0978483	−	0.0710909i
$387$	0.146114	−	0.449692i	0.00742737	−	0.0228591i
$388$	−2.83860	+	8.73632i	−0.144108	+	0.443519i
$389$	−20.8395	−	15.1408i	−1.05661	−	0.767669i	−0.0831489	−	0.996537i	$-0.526498\pi$
$389$	−20.8395	−	15.1408i	−1.05661	−	0.767669i	−0.973458	+	0.228868i	$0.926498\pi$
$390$	−1.29343	+	3.98078i	−0.0654956	+	0.201575i
$391$	1.09759	+	3.37804i	0.0555076	+	0.170835i
$392$	−5.35410	+	3.88998i	−0.270423	+	0.196474i
$393$	8.63018	+	26.5610i	0.435335	+	1.33982i
$394$	−8.57781	−	6.23215i	−0.432144	−	0.313971i
$395$	−0.470282	−	0.341680i	−0.0236625	−	0.0171918i
$396$	−0.331098	+	0.240557i	−0.0166383	+	0.0120884i
$397$	−17.0622			−0.856326			−0.428163	−	0.903701i	$-0.640839\pi$
$397$	−17.0622			−0.856326			−0.428163	+	0.903701i	$0.640839\pi$
$398$	4.78795			0.239998
$399$	−4.06173	+	2.95102i	−0.203341	+	0.147736i
$400$	−1.48799	+	4.57957i	−0.0743996	+	0.228978i
$401$	1.85803	+	5.71843i	0.0927857	+	0.285565i	0.986670	−	0.162732i	$-0.0520307\pi$
$401$	1.85803	+	5.71843i	0.0927857	+	0.285565i	−0.893885	+	0.448297i	$0.852031\pi$
$402$	−3.03700			−0.151472
$403$	16.5522	+	27.3605i	0.824522	+	1.36292i
$404$	−12.7209			−0.632889
$405$	1.14341	+	3.51906i	0.0568166	+	0.174864i
$406$	−0.136756	+	0.420891i	−0.00678708	+	0.0208885i
$407$	−20.2531	+	14.7147i	−1.00391	+	0.729382i
$408$	−0.728780			−0.0360800
$409$	−1.83750			−0.0908585			−0.0454293	−	0.998968i	$-0.514466\pi$
$409$	−1.83750			−0.0908585			−0.0454293	+	0.998968i	$0.514466\pi$
$410$	1.83746	−	1.33499i	0.0907455	−	0.0659304i
$411$	−24.2129	−	17.5917i	−1.19434	−	0.867736i
$412$	3.90762	+	2.83905i	0.192515	+	0.139870i
$413$	−0.752581	−	2.31621i	−0.0370321	−	0.113973i
$414$	−0.837805	+	0.608701i	−0.0411759	+	0.0299160i
$415$	0.152205	+	0.468440i	0.00747147	+	0.0229948i
$416$	1.77479	−	5.46226i	0.0870165	−	0.267809i
$417$	0.245426	+	0.178312i	0.0120186	+	0.00873199i
$418$	4.83503	−	14.8807i	0.236489	−	0.727838i
$419$	−4.19027	+	12.8963i	−0.204708	+	0.630027i	0.795017	+	0.606587i	$0.207462\pi$
$419$	−4.19027	+	12.8963i	−0.204708	+	0.630027i	−0.999725	+	0.0234402i	$0.992538\pi$
$420$	0.364390	+	0.264745i	0.0177804	+	0.0129182i
$421$	2.49872	−	7.69027i	0.121780	−	0.374801i	−0.871521	−	0.490359i	$-0.836866\pi$
$421$	2.49872	−	7.69027i	0.121780	−	0.374801i	0.993301	+	0.115558i	$0.0368656\pi$
$422$	−8.38647	−	25.8109i	−0.408247	−	1.25646i
$423$	−0.492147	+	0.357566i	−0.0239290	+	0.0173854i
$424$	2.98971	+	9.20139i	0.145193	+	0.446859i
$425$	1.67447	+	1.21657i	0.0812237	+	0.0590125i
$426$	15.4779	+	11.2454i	0.749908	+	0.544840i
$427$	−3.81352	+	2.77069i	−0.184549	+	0.134083i
$428$	11.9461			0.577438
$429$	31.8002			1.53533
$430$	1.31202	−	0.953236i	0.0632711	−	0.0459691i
$431$	0.383029	−	1.17884i	0.0184499	−	0.0567829i	−0.941408	−	0.337271i	$-0.890496\pi$
$431$	0.383029	−	1.17884i	0.0184499	−	0.0567829i	0.959858	+	0.280488i	$0.0904962\pi$
$432$	−1.63746	−	5.03960i	−0.0787825	−	0.242468i
$433$	24.7871			1.19119			0.595595	−	0.803285i	$-0.296916\pi$
$433$	24.7871			1.19119			0.595595	+	0.803285i	$0.296916\pi$
$434$	3.35053	−	0.784163i	0.160830	−	0.0376410i
$435$	−0.521852			−0.0250209
$436$	0.340455	+	1.04781i	0.0163049	+	0.0501812i
$437$	12.2345	−	37.6539i	0.585255	−	1.80123i
$438$	−21.2602	+	15.4465i	−1.01585	+	0.738060i
$439$	5.12718			0.244707			0.122354	−	0.992487i	$-0.460956\pi$
$439$	5.12718			0.244707			0.122354	+	0.992487i	$0.460956\pi$
$440$	−1.40369			−0.0669184
$441$	−0.670989	+	0.487502i	−0.0319518	+	0.0232144i
$442$	−1.99722	−	1.45106i	−0.0949979	−	0.0690200i
$443$	−10.0842	−	7.32658i	−0.479113	−	0.348096i	0.321869	−	0.946784i	$-0.395689\pi$
$443$	−10.0842	−	7.32658i	−0.479113	−	0.348096i	−0.800982	+	0.598688i	$0.795689\pi$
$444$	−4.01643	−	12.3613i	−0.190611	−	0.586641i
$445$	−2.43535	+	1.76938i	−0.115446	+	0.0838768i
$446$	1.86960	+	5.75404i	0.0885282	+	0.272462i
$447$	−4.60783	+	14.1814i	−0.217943	+	0.670759i
$448$	−0.500000	−	0.363271i	−0.0236228	−	0.0171630i
$449$	−0.160253	+	0.493207i	−0.00756279	+	0.0232759i	−0.954767	−	0.297356i	$-0.903895\pi$
$449$	−0.160253	+	0.493207i	−0.00756279	+	0.0232759i	0.947204	+	0.320632i	$0.103895\pi$
$450$	−0.186479	+	0.573922i	−0.00879068	+	0.0270549i
$451$	−13.9600	−	10.1425i	−0.657350	−	0.477593i
$452$	5.23593	−	16.1146i	0.246278	−	0.757965i
$453$	−11.6536	−	35.8662i	−0.547535	−	1.68514i
$454$	21.0980	−	15.3286i	0.990180	−	0.719408i
$455$	0.471479	+	1.45106i	0.0221033	+	0.0680269i
$456$	6.57202	+	4.77485i	0.307763	+	0.223603i
$457$	18.1025	+	13.1523i	0.846801	+	0.615237i	0.924262	−	0.381758i	$-0.124681\pi$
$457$	18.1025	+	13.1523i	0.846801	+	0.615237i	−0.0774611	+	0.996995i	$0.524681\pi$
$458$	12.8223	−	9.31596i	0.599147	−	0.435306i
$459$	−2.27767			−0.106313
$460$	−3.55188			−0.165607
$461$	−13.7514	+	9.99100i	−0.640468	+	0.465327i	−0.860011	−	0.510275i	$-0.829543\pi$
$461$	−13.7514	+	9.99100i	−0.640468	+	0.465327i	0.219543	+	0.975603i	$0.429543\pi$
$462$	1.05745	−	3.25449i	0.0491970	−	0.151413i
$463$	−1.86355	−	5.73541i	−0.0866064	−	0.266547i	0.898369	−	0.439241i	$-0.144753\pi$
$463$	−1.86355	−	5.73541i	−0.0866064	−	0.266547i	−0.984975	+	0.172694i	$0.944753\pi$
$464$	0.716063			0.0332424
$465$	2.10032	+	3.47180i	0.0973999	+	0.161001i
$466$	25.1984			1.16729
$467$	7.21377	+	22.2017i	0.333814	+	1.02737i	0.967304	+	0.253622i	$0.0816218\pi$
$467$	7.21377	+	22.2017i	0.333814	+	1.02737i	−0.633490	+	0.773751i	$0.718378\pi$
$468$	0.222421	−	0.684543i	0.0102814	−	0.0316430i
$469$	−0.895613	+	0.650701i	−0.0413555	+	0.0300466i
$470$	−2.08646			−0.0962413
$471$	19.9260			0.918141
$472$	−3.18798	+	2.31621i	−0.146739	+	0.106612i
$473$	−9.96799	−	7.24217i	−0.458329	−	0.332995i
$474$	−1.85503	−	1.34776i	−0.0852044	−	0.0619047i
$475$	−7.12930	−	21.9417i	−0.327115	−	1.00676i
$476$	−0.214917	+	0.156147i	−0.00985072	+	0.00715697i
$477$	0.374678	+	1.15314i	0.0171553	+	0.0527986i
$478$	−1.01307	+	3.11791i	−0.0463368	+	0.142610i
$479$	−5.07931	−	3.69033i	−0.232079	−	0.168616i	0.465668	−	0.884960i	$-0.345814\pi$
$479$	−5.07931	−	3.69033i	−0.232079	−	0.168616i	−0.697747	+	0.716344i	$0.745814\pi$
$480$	0.225205	−	0.693111i	0.0102792	−	0.0316360i
$481$	13.6054	−	41.8731i	0.620353	−	1.90925i
$482$	6.18035	+	4.49028i	0.281507	+	0.204527i
$483$	2.67575	−	8.23512i	0.121751	−	0.374711i
$484$	−0.103679	−	0.319092i	−0.00471270	−	0.0145042i
$485$	−3.19434	+	2.32083i	−0.145048	+	0.105383i
$486$	−0.402193	−	1.23782i	−0.0182438	−	0.0561488i
$487$	−20.6396	−	14.9956i	−0.935271	−	0.679514i	0.0120069	−	0.999928i	$-0.496178\pi$
$487$	−20.6396	−	14.9956i	−0.935271	−	0.679514i	−0.947278	+	0.320414i	$0.896178\pi$
$488$	6.17041	+	4.48306i	0.279321	+	0.202939i
$489$	−8.21735	+	5.97025i	−0.371601	+	0.269984i
$490$	−2.84466			−0.128509
$491$	−42.8298			−1.93288			−0.966442	−	0.256887i	$-0.917303\pi$
$491$	−42.8298			−1.93288			−0.966442	+	0.256887i	$0.917303\pi$
$492$	7.24786	−	5.26588i	0.326759	−	0.237404i
$493$	0.0951120	−	0.292725i	0.00428363	−	0.0131837i
$494$	8.50344	+	26.1709i	0.382588	+	1.17748i
$495$	−0.175914			−0.00790674
$496$	−2.88197	−	4.76385i	−0.129404	−	0.213903i
$497$	6.97386			0.312820
$498$	0.600375	+	1.84777i	0.0269035	+	0.0828004i
$499$	0.394955	−	1.21555i	0.0176806	−	0.0544154i	−0.941827	−	0.336098i	$-0.890893\pi$
$499$	0.394955	−	1.21555i	0.0176806	−	0.0544154i	0.959508	+	0.281683i	$0.0908926\pi$
$500$	−3.41319	+	2.47983i	−0.152642	+	0.110901i
$501$	−14.7741			−0.660058
$502$	−13.8247			−0.617026
$503$	−9.41248	+	6.83857i	−0.419682	+	0.304917i	−0.777510	−	0.628871i	$-0.783517\pi$
$503$	−9.41248	+	6.83857i	−0.419682	+	0.304917i	0.357828	+	0.933788i	$0.383517\pi$
$504$	−0.0626612	−	0.0455260i	−0.00279115	−	0.00202789i
$505$	−4.42362	−	3.21395i	−0.196849	−	0.143019i
$506$	8.33891	+	25.6645i	0.370710	+	1.14093i
$507$	−27.4146	+	19.9178i	−1.21752	+	0.884582i
$508$	−3.77201	−	11.6091i	−0.167356	−	0.515069i
$509$	4.21178	−	12.9625i	0.186684	−	0.574554i	−0.813290	−	0.581859i	$-0.802325\pi$
$509$	4.21178	−	12.9625i	0.186684	−	0.574554i	0.999973	+	0.00730559i	$0.00232546\pi$
$510$	−0.253429	−	0.184127i	−0.0112220	−	0.00815326i
$511$	−2.96013	+	9.11034i	−0.130948	+	0.403018i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	20.5397	+	14.9229i	0.906849	+	0.658864i
$514$	1.21770	−	3.74770i	0.0537105	−	0.165304i
$515$	0.641562	+	1.97453i	0.0282706	+	0.0870080i
$516$	5.17526	−	3.76005i	0.227828	−	0.165527i
$517$	4.89848	+	15.0760i	0.215435	+	0.663040i
$518$	−3.83295	−	2.78480i	−0.168410	−	0.122357i
$519$	−22.7911	−	16.5587i	−1.00042	−	0.726846i
$520$	1.99722	−	1.45106i	0.0875837	−	0.0636333i
$521$	−19.9628			−0.874587			−0.437294	−	0.899319i	$-0.644063\pi$
$521$	−19.9628			−0.874587			−0.437294	+	0.899319i	$0.644063\pi$
$522$	0.0897387			0.00392776
$523$	10.5480	−	7.66354i	0.461230	−	0.335103i	−0.332784	−	0.943003i	$-0.607988\pi$
$523$	10.5480	−	7.66354i	0.461230	−	0.335103i	0.794013	+	0.607900i	$0.207988\pi$
$524$	5.09009	−	15.6657i	0.222362	−	0.684358i
$525$	−1.55922	−	4.79879i	−0.0680499	−	0.209436i
$526$	−1.88899			−0.0823638
$527$	−2.33025	+	0.545375i	−0.101507	+	0.0237569i
$528$	−5.53687			−0.240961
$529$	13.9933	+	43.0668i	0.608403	+	1.87247i
$530$	−1.28508	+	3.95508i	−0.0558204	+	0.171798i
$531$	−0.399526	+	0.290272i	−0.0173379	+	0.0125967i
$532$	2.96114			0.128382
$533$	30.3475			1.31450
$534$	−9.60624	+	6.97934i	−0.415703	+	0.302026i
$535$	4.15419	+	3.01820i	0.179601	+	0.130488i
$536$	1.44913	+	1.05286i	0.0625930	+	0.0454764i
$537$	0.432968	+	1.33254i	0.0186839	+	0.0575032i
$538$	−7.99851	+	5.81125i	−0.344840	+	0.250541i
$539$	6.67854	+	20.5544i	0.287665	+	0.885342i
$540$	0.703839	−	2.16619i	0.0302884	−	0.0932182i
$541$	5.10960	+	3.71234i	0.219679	+	0.159606i	0.692182	−	0.721723i	$-0.256650\pi$
$541$	5.10960	+	3.71234i	0.219679	+	0.159606i	−0.472503	+	0.881329i	$0.656650\pi$
$542$	2.35418	−	7.24543i	0.101121	−	0.311218i
$543$	−6.69218	+	20.5964i	−0.287189	+	0.883877i
$544$	0.347744	+	0.252651i	0.0149094	+	0.0108323i
$545$	−0.146340	+	0.450387i	−0.00626850	+	0.0192925i
$546$	1.85975	+	5.72373i	0.0795900	+	0.244953i
$547$	−5.77466	+	4.19554i	−0.246907	+	0.179388i	−0.704355	−	0.709848i	$-0.748764\pi$
$547$	−5.77466	+	4.19554i	−0.246907	+	0.179388i	0.457448	+	0.889236i	$0.348764\pi$
$548$	5.45478	+	16.7881i	0.233017	+	0.717152i
$549$	0.773290	+	0.561828i	0.0330032	+	0.0239782i
$550$	12.7217	+	9.24287i	0.542456	+	0.394117i
$551$	−2.77559	+	2.01659i	−0.118244	+	0.0859094i
$552$	−14.0104			−0.596323
$553$	−0.835818			−0.0355426
$554$	−3.27965	+	2.38280i	−0.139339	+	0.101236i
$555$	1.72640	−	5.31332i	0.0732817	−	0.225538i
$556$	−0.0552905	−	0.170167i	−0.00234484	−	0.00721667i
$557$	2.98330			0.126406			0.0632032	−	0.998001i	$-0.479868\pi$
$557$	2.98330			0.126406			0.0632032	+	0.998001i	$0.479868\pi$
$558$	−0.361175	−	0.597017i	−0.0152897	−	0.0252737i
$559$	21.6693			0.916516
$560$	−0.0820912	−	0.252651i	−0.00346898	−	0.0106764i
$561$	−0.735442	+	2.26346i	−0.0310504	+	0.0955633i
$562$	19.4826	−	14.1550i	0.821826	−	0.597092i
$563$	41.8614			1.76425			0.882125	−	0.471016i	$-0.156113\pi$
$563$	41.8614			1.76425			0.882125	+	0.471016i	$0.156113\pi$
$564$	−8.23007			−0.346548
$565$	5.89211	−	4.28087i	0.247883	−	0.180098i
$566$	17.3792	+	12.6267i	0.730502	+	0.530741i
$567$	4.30416	+	3.12716i	0.180758	+	0.131328i
$568$	−3.48693	−	10.7317i	−0.146308	−	0.450291i
$569$	−35.0657	+	25.4767i	−1.47003	+	1.06804i	−0.489424	+	0.872046i	$0.662793\pi$
$569$	−35.0657	+	25.4767i	−1.47003	+	1.06804i	−0.980605	+	0.195993i	$0.937207\pi$
$570$	1.07901	+	3.32085i	0.0451947	+	0.139095i
$571$	−2.62532	+	8.07990i	−0.109866	+	0.338133i	−0.990842	−	0.135029i	$-0.956887\pi$
$571$	−2.62532	+	8.07990i	−0.109866	+	0.338133i	0.880976	+	0.473162i	$0.156887\pi$
$572$	−15.1738	−	11.0244i	−0.634447	−	0.460953i
$573$	2.04632	−	6.29792i	0.0854862	−	0.263100i
$574$	1.00914	−	3.10582i	0.0421208	−	0.129634i
$575$	32.1909	+	23.3880i	1.34245	+	0.975348i
$576$	−0.0387267	+	0.119189i	−0.00161361	+	0.00496619i
$577$	−11.0216	−	33.9211i	−0.458837	−	1.41216i	−0.866571	−	0.499054i	$-0.833681\pi$
$577$	−11.0216	−	33.9211i	−0.458837	−	1.41216i	0.407734	−	0.913101i	$-0.366319\pi$
$578$	−13.6038	+	9.88375i	−0.565844	+	0.411110i
$579$	−1.24499	−	3.83169i	−0.0517400	−	0.159239i
$580$	0.249006	+	0.180914i	0.0103394	+	0.00751204i
$581$	0.572949	+	0.416272i	0.0237699	+	0.0172699i
$582$	−12.6001	+	9.15451i	−0.522291	+	0.379467i
$583$	31.5949			1.30853
$584$	15.4994			0.641371
$585$	0.250296	−	0.181851i	0.0103485	−	0.00751859i
$586$	7.34903	−	22.6180i	0.303585	−	0.934340i
$587$	0.993997	+	3.05921i	0.0410266	+	0.126267i	0.969472	−	0.245202i	$-0.0788542\pi$
$587$	0.993997	+	3.05921i	0.0410266	+	0.126267i	−0.928445	+	0.371469i	$0.878854\pi$
$588$	−11.2208			−0.462738
$589$	24.5870	+	10.3493i	1.01309	+	0.426437i
$590$	−1.69379			−0.0697323
$591$	−5.55515	−	17.0970i	−0.228508	−	0.703276i
$592$	−2.36889	+	7.29071i	−0.0973610	+	0.299646i
$593$	−19.1349	+	13.9023i	−0.785776	+	0.570900i	−0.906707	−	0.421761i	$-0.861412\pi$
$593$	−19.1349	+	13.9023i	−0.785776	+	0.570900i	0.120931	+	0.992661i	$0.461412\pi$
$594$	−17.3045			−0.710013
$595$	−0.114187			−0.00468120
$596$	7.11503	−	5.16938i	0.291443	−	0.211746i
$597$	6.56752	+	4.77159i	0.268791	+	0.195288i
$598$	−38.3955	−	27.8960i	−1.57011	−	1.14075i
$599$	−10.1165	−	31.1355i	−0.413350	−	1.27216i	−0.913718	−	0.406349i	$-0.866802\pi$
$599$	−10.1165	−	31.1355i	−0.413350	−	1.27216i	0.500368	−	0.865813i	$-0.333198\pi$
$600$	−6.60496	+	4.79879i	−0.269646	+	0.195910i
$601$	−6.86134	−	21.1170i	−0.279880	−	0.861382i	−0.987887	−	0.155176i	$-0.950405\pi$
$601$	−6.86134	−	21.1170i	−0.279880	−	0.861382i	0.708007	−	0.706205i	$-0.249595\pi$
$602$	0.720568	−	2.21768i	0.0293681	−	0.0903858i
$603$	0.181609	+	0.131946i	0.00739567	+	0.00537327i
$604$	−6.87332	+	21.1539i	−0.279671	+	0.860740i
$605$	0.0445650	−	0.137157i	0.00181182	−	0.00557622i
$606$	−17.4490	−	12.6774i	−0.708818	−	0.514986i
$607$	−12.5814	+	38.7215i	−0.510663	+	1.57166i	0.280375	+	0.959891i	$0.409541\pi$
$607$	−12.5814	+	38.7215i	−0.510663	+	1.57166i	−0.791037	+	0.611768i	$0.790459\pi$
$608$	−1.48057	−	4.55673i	−0.0600450	−	0.184800i
$609$	−0.607038	+	0.441039i	−0.0245984	+	0.0178718i
$610$	1.01307	+	3.11791i	0.0410181	+	0.126241i
$611$	−22.5545	−	16.3868i	−0.912456	−	0.662938i
$612$	0.0435801	+	0.0316628i	0.00176162	+	0.00127989i
$613$	16.6893	−	12.1255i	0.674076	−	0.489745i	−0.197311	−	0.980341i	$-0.563221\pi$
$613$	16.6893	−	12.1255i	0.674076	−	0.489745i	0.871387	+	0.490596i	$0.163221\pi$
$614$	−5.83167			−0.235347
$615$	3.85083			0.155280
$616$	−1.63283	+	1.18632i	−0.0657884	+	0.0477981i
$617$	−8.60668	+	26.4886i	−0.346492	+	1.06639i	0.614288	+	0.789082i	$0.289443\pi$
$617$	−8.60668	+	26.4886i	−0.346492	+	1.06639i	−0.960780	+	0.277311i	$0.910557\pi$
$618$	2.53065	+	7.78853i	0.101798	+	0.313301i
$619$	−19.3524			−0.777838			−0.388919	−	0.921272i	$-0.627151\pi$
$619$	−19.3524			−0.777838			−0.388919	+	0.921272i	$0.627151\pi$
$620$	0.201404	−	2.38473i	0.00808858	−	0.0957730i
$621$	−43.7871			−1.75712
$622$	6.08482	+	18.7272i	0.243979	+	0.750891i
$623$	−1.33751	+	4.11642i	−0.0535861	+	0.164921i
$624$	7.87804	−	5.72373i	0.315374	−	0.229133i
$625$	22.2628			0.890511
$626$	31.8404			1.27260
$627$	21.4619	−	15.5930i	0.857107	−	0.622725i
$628$	−9.50786	−	6.90787i	−0.379405	−	0.275654i
$629$	2.66577	+	1.93679i	0.106291	+	0.0772251i
$630$	−0.0102879	−	0.0316628i	−0.000409878	−	0.00126147i
$631$	28.9209	−	21.0123i	1.15132	−	0.836485i	0.162667	−	0.986681i	$-0.447990\pi$
$631$	28.9209	−	21.0123i	1.15132	−	0.836485i	0.988656	+	0.150196i	$0.0479904\pi$
$632$	0.417909	+	1.28619i	0.0166235	+	0.0511619i
$633$	14.2192	−	43.7621i	0.565161	−	1.73939i
$634$	−19.2452	−	13.9825i	−0.764325	−	0.555315i
$635$	1.62134	−	4.98998i	0.0643410	−	0.198021i
$636$	−5.06902	+	15.6008i	−0.201000	+	0.618613i
$637$	−30.7505	−	22.3416i	−1.21838	−	0.885205i
$638$	0.722610	−	2.22396i	0.0286084	−	0.0880476i
$639$	−0.436990	−	1.34492i	−0.0172871	−	0.0532041i
$640$	−0.347744	+	0.252651i	−0.0137458	+	0.00998689i
$641$	−4.03488	−	12.4181i	−0.159368	−	0.490485i	0.839209	−	0.543809i	$-0.183018\pi$
$641$	−4.03488	−	12.4181i	−0.159368	−	0.490485i	−0.998577	+	0.0533241i	$0.983018\pi$
$642$	16.3862	+	11.9053i	0.646714	+	0.469865i
$643$	−7.12519	−	5.17675i	−0.280990	−	0.204151i	0.438359	−	0.898800i	$-0.355560\pi$
$643$	−7.12519	−	5.17675i	−0.280990	−	0.204151i	−0.719349	+	0.694649i	$0.755560\pi$
$644$	−4.13168	+	3.00184i	−0.162811	+	0.118289i
$645$	2.74964			0.108267
$646$	−2.05944			−0.0810274
$647$	30.4324	−	22.1104i	1.19642	−	0.869250i	0.202492	−	0.979284i	$-0.435096\pi$
$647$	30.4324	−	22.1104i	1.19642	−	0.869250i	0.993928	+	0.110034i	$0.0350961\pi$
$648$	2.66012	−	8.18701i	0.104499	−	0.321616i
$649$	3.97659	+	12.2387i	0.156095	+	0.480410i
$650$	−27.6557			−1.08474
$651$	5.37733	+	2.26346i	0.210754	+	0.0887119i
$652$	5.99072			0.234615
$653$	−7.16184	−	22.0419i	−0.280264	−	0.862565i	−0.987778	−	0.155866i	$-0.950183\pi$
$653$	−7.16184	−	22.0419i	−0.280264	−	0.862565i	0.707514	−	0.706700i	$-0.249817\pi$
$654$	−0.577238	+	1.77656i	−0.0225718	+	0.0694688i
$655$	5.72799	−	4.16163i	0.223811	−	0.162608i
$656$	−5.28394			−0.206303
$657$	1.94242			0.0757812
$658$	−2.42705	+	1.76336i	−0.0946163	+	0.0687428i
$659$	−11.4989	−	8.35441i	−0.447932	−	0.325441i	0.340847	−	0.940119i	$-0.389286\pi$
$659$	−11.4989	−	8.35441i	−0.447932	−	0.325441i	−0.788779	+	0.614677i	$0.789286\pi$
$660$	−1.92541	−	1.39889i	−0.0749466	−	0.0544519i
$661$	0.182384	+	0.561321i	0.00709392	+	0.0218329i	0.954541	−	0.298080i	$-0.0963463\pi$
$661$	0.182384	+	0.561321i	0.00709392	+	0.0218329i	−0.947447	+	0.319913i	$0.896346\pi$
$662$	21.8667	−	15.8871i	0.849873	−	0.617469i
$663$	−1.29343	−	3.98078i	−0.0502328	−	0.154601i
$664$	0.354102	−	1.08981i	0.0137418	−	0.0422930i
$665$	1.02972	+	0.748134i	0.0399307	+	0.0290114i
$666$	−0.296875	+	0.913688i	−0.0115037	+	0.0354047i
$667$	1.82848	−	5.62749i	0.0707991	−	0.217897i
$668$	7.04959	+	5.12183i	0.272757	+	0.198169i
$669$	−3.16989	+	9.75591i	−0.122555	+	0.377185i
$670$	0.237922	+	0.732248i	0.00919172	+	0.0282892i
$671$	20.1504	−	14.6401i	0.777898	−	0.565176i
$672$	−0.323809	−	0.996583i	−0.0124912	−	0.0384440i
$673$	0.278868	+	0.202609i	0.0107496	+	0.00781002i	0.593147	−	0.805094i	$-0.297885\pi$
$673$	0.278868	+	0.202609i	0.0107496	+	0.00781002i	−0.582397	+	0.812904i	$0.697885\pi$
$674$	7.25086	+	5.26806i	0.279293	+	0.202918i
$675$	−20.6426	+	14.9978i	−0.794535	+	0.577264i
$676$	19.9861			0.768698
$677$	24.3744			0.936783			0.468392	−	0.883521i	$-0.344834\pi$
$677$	24.3744			0.936783			0.468392	+	0.883521i	$0.344834\pi$
$678$	23.2415	−	16.8859i	0.892584	−	0.648500i
$679$	−1.75435	+	5.39934i	−0.0673259	+	0.207208i
$680$	0.0570934	+	0.175715i	0.00218943	+	0.00673838i
$681$	44.2159			1.69436
$682$	−17.7040	+	4.14347i	−0.677920	+	0.158662i
$683$	−1.73654			−0.0664467			−0.0332234	−	0.999448i	$-0.510577\pi$
$683$	−1.73654			−0.0664467			−0.0332234	+	0.999448i	$0.510577\pi$
$684$	−0.185548	−	0.571059i	−0.00709462	−	0.0218350i
$685$	−2.34466	+	7.21611i	−0.0895847	+	0.275713i
$686$	−6.80902	+	4.94704i	−0.259969	+	0.188879i
$687$	26.8722			1.02524
$688$	−3.77294			−0.143842
$689$	−44.9542	+	32.6611i	−1.71262	+	1.24429i
$690$	−4.87204	−	3.53974i	−0.185475	−	0.134756i
$691$	12.8277	+	9.31990i	0.487990	+	0.354546i	0.804411	−	0.594073i	$-0.202481\pi$
$691$	12.8277	+	9.31990i	0.487990	+	0.354546i	−0.316421	+	0.948619i	$0.602481\pi$
$692$	5.13446	+	15.8023i	0.195183	+	0.600712i
$693$	−0.204630	+	0.148672i	−0.00777324	+	0.00564759i
$694$	−1.45169	−	4.46785i	−0.0551055	−	0.169597i
$695$	0.0237658	−	0.0731435i	0.000901487	−	0.00277449i
$696$	0.982208	+	0.713616i	0.0372305	+	0.0270495i
$697$	−0.701846	+	2.16006i	−0.0265843	+	0.0818181i
$698$	−5.36783	+	16.5205i	−0.203175	+	0.625310i
$699$	34.5640	+	25.1122i	1.30733	+	0.949832i
$700$	−0.919629	+	2.83033i	−0.0347587	+	0.106976i
$701$	6.03559	+	18.5756i	0.227961	+	0.701592i	0.997978	+	0.0635680i	$0.0202480\pi$
$701$	6.03559	+	18.5756i	0.227961	+	0.701592i	−0.770016	+	0.638024i	$0.779752\pi$
$702$	24.6214	−	17.8885i	0.929275	−	0.675158i
$703$	−11.3499	−	34.9314i	−0.428070	−	1.31746i
$704$	2.64197	+	1.91950i	0.0995729	+	0.0723440i
$705$	−2.86195	−	2.07933i	−0.107787	−	0.0783122i
$706$	−0.493991	+	0.358905i	−0.0185916	+	0.0135076i
$707$	−7.86196			−0.295679
$708$	−6.68118			−0.251094
$709$	−30.2335	+	21.9659i	−1.13544	+	0.824948i	−0.986478	−	0.163895i	$-0.947594\pi$
$709$	−30.2335	+	21.9659i	−1.13544	+	0.824948i	−0.148965	+	0.988842i	$0.547594\pi$
$710$	1.49880	−	4.61284i	0.0562491	−	0.173117i
$711$	0.0523733	+	0.161188i	0.00196415	+	0.00604504i
$712$	7.00328			0.262459
$713$	−44.7979	+	10.4846i	−1.67769	+	0.392650i
$714$	−0.450411			−0.0168562
$715$	−2.49126	−	7.66732i	−0.0931680	−	0.286742i
$716$	0.255365	−	0.785932i	0.00954343	−	0.0293716i
$717$	−4.49687	+	3.26717i	−0.167939	+	0.122015i
$718$	−15.4220			−0.575543
$719$	−21.3156			−0.794940			−0.397470	−	0.917615i	$-0.630112\pi$
$719$	−21.3156			−0.794940			−0.397470	+	0.917615i	$0.630112\pi$
$720$	−0.0435801	+	0.0316628i	−0.00162413	+	0.00118000i
$721$	2.41504	+	1.75463i	0.0899409	+	0.0653459i
$722$	3.20034	+	2.32518i	0.119104	+	0.0865344i
$723$	4.00251	+	12.3185i	0.148855	+	0.458128i
$724$	10.3335	−	7.50775i	0.384042	−	0.279023i
$725$	−1.06550	−	3.27926i	−0.0395715	−	0.121789i
$726$	0.175787	−	0.541017i	0.00652407	−	0.0200790i
$727$	14.8730	+	10.8058i	0.551608	+	0.400767i	0.828378	−	0.560170i	$-0.189264\pi$
$727$	14.8730	+	10.8058i	0.551608	+	0.400767i	−0.276770	+	0.960936i	$0.589264\pi$
$728$	1.09688	−	3.37586i	0.0406532	−	0.125118i
$729$	8.66227	−	26.6597i	0.320825	−	0.987397i
$730$	5.38983	+	3.91594i	0.199487	+	0.144935i
$731$	−0.501146	+	1.54237i	−0.0185355	+	0.0570465i
$732$	3.99607	+	12.2986i	0.147699	+	0.454571i
$733$	−31.9315	+	23.1996i	−1.17942	+	0.856896i	−0.992106	−	0.125405i	$-0.959977\pi$
$733$	−31.9315	+	23.1996i	−1.17942	+	0.856896i	−0.187310	+	0.982301i	$0.559977\pi$
$734$	4.77373	+	14.6920i	0.176202	+	0.542293i
$735$	−3.90196	−	2.83494i	−0.143926	−	0.104568i
$736$	6.68520	+	4.85708i	0.246420	+	0.179034i
$737$	4.73236	−	3.43826i	0.174319	−	0.126650i
$738$	−0.662195			−0.0243757
$739$	−29.5292			−1.08625			−0.543124	−	0.839652i	$-0.682759\pi$
$739$	−29.5292			−1.08625			−0.543124	+	0.839652i	$0.682759\pi$
$740$	−2.66577	+	1.93679i	−0.0979956	+	0.0711980i
$741$	−14.4175	+	44.3724i	−0.529639	+	1.63006i
$742$	1.84774	+	5.68677i	0.0678328	+	0.208768i
$743$	25.3664			0.930603			0.465302	−	0.885152i	$-0.345946\pi$
$743$	25.3664			0.930603			0.465302	+	0.885152i	$0.345946\pi$
$744$	0.794440	−	9.40659i	0.0291256	−	0.344862i
$745$	3.78025			0.138498
$746$	−8.63163	−	26.5654i	−0.316026	−	0.972629i
$747$	0.0443769	−	0.136578i	0.00162367	−	0.00499713i
$748$	1.13561	−	0.825069i	0.0415220	−	0.0301675i
$749$	7.38312			0.269773
$750$	−7.15315			−0.261196
$751$	7.88996	−	5.73239i	0.287909	−	0.209178i	−0.434451	−	0.900696i	$-0.643058\pi$
$751$	7.88996	−	5.73239i	0.287909	−	0.209178i	0.722360	+	0.691518i	$0.243058\pi$
$752$	3.92705	+	2.85317i	0.143205	+	0.104044i
$753$	−18.9630	−	13.7774i	−0.691051	−	0.502078i
$754$	1.27087	+	3.91132i	0.0462822	+	0.142442i
$755$	−7.73470	+	5.61959i	−0.281494	+	0.204518i
$756$	−1.01201	−	3.11464i	−0.0368064	−	0.113278i
$757$	−10.2506	+	31.5482i	−0.372566	+	1.14664i	0.572540	+	0.819877i	$0.305958\pi$
$757$	−10.2506	+	31.5482i	−0.372566	+	1.14664i	−0.945106	+	0.326764i	$0.894042\pi$
$758$	−25.1985	−	18.3078i	−0.915250	−	0.664968i
$759$	−14.1385	+	43.5139i	−0.513195	+	1.57945i
$760$	0.636401	−	1.95864i	0.0230847	−	0.0710473i
$761$	−3.66269	−	2.66110i	−0.132772	−	0.0964647i	0.519417	−	0.854521i	$-0.326149\pi$
$761$	−3.66269	−	2.66110i	−0.132772	−	0.0964647i	−0.652189	+	0.758056i	$0.726149\pi$
$762$	6.39540	−	19.6830i	0.231681	−	0.713040i
$763$	0.210413	+	0.647585i	0.00761746	+	0.0234441i
$764$	−3.15976	+	2.29570i	−0.114316	+	0.0830555i
$765$	0.00715507	+	0.0220211i	0.000258692	+	0.000796173i
$766$	5.65226	+	4.10660i	0.204224	+	0.148378i
$767$	−18.3097	−	13.3028i	−0.661126	−	0.480336i
$768$	−1.37168	+	0.996583i	−0.0494962	+	0.0359611i
$769$	35.9407			1.29606			0.648028	−	0.761617i	$-0.275594\pi$
$769$	35.9407			1.29606			0.648028	+	0.761617i	$0.275594\pi$
$770$	−0.867529			−0.0312636
$771$	5.40519	−	3.92710i	0.194663	−	0.141431i
$772$	−0.734297	+	2.25993i	−0.0264279	+	0.0813367i
$773$	−8.01933	−	24.6810i	−0.288435	−	0.887712i	−0.985348	−	0.170556i	$-0.945444\pi$
$773$	−8.01933	−	24.6810i	−0.288435	−	0.887712i	0.696913	−	0.717156i	$-0.254556\pi$
$774$	−0.472834			−0.0169957
$775$	−17.5280	+	20.2867i	−0.629626	+	0.728721i
$776$	9.18591			0.329755
$777$	−2.48229	−	7.63970i	−0.0890517	−	0.274073i
$778$	−7.95999	+	24.4983i	−0.285380	+	0.878308i
$779$	20.4815	−	14.8807i	0.733826	−	0.533156i
$780$	4.18564			0.149870
$781$	−36.8494			−1.31858
$782$	2.87353	−	2.08774i	0.102757	−	0.0746575i
$783$	3.06972	+	2.23028i	0.109703	+	0.0797037i
$784$	5.35410	+	3.88998i	0.191218	+	0.138928i
$785$	−1.56102	−	4.80433i	−0.0557153	−	0.171474i
$786$	22.5941	−	16.4156i	0.805905	−	0.585524i
$787$	0.207331	+	0.638100i	0.00739056	+	0.0227458i	0.954684	−	0.297622i	$-0.0961935\pi$
$787$	0.207331	+	0.638100i	0.00739056	+	0.0227458i	−0.947293	+	0.320368i	$0.896194\pi$
$788$	−3.27643	+	10.0838i	−0.116718	+	0.359221i
$789$	−2.59108	−	1.88253i	−0.0922450	−	0.0670199i
$790$	−0.179632	+	0.552850i	−0.00639101	+	0.0196695i
$791$	3.23599	−	9.95934i	0.115058	−	0.354113i
$792$	0.331098	+	0.240557i	0.0117650	+	0.00854780i
$793$	−13.5364	+	41.6609i	−0.480693	+	1.47942i
$794$	5.27250	+	16.2271i	0.187114	+	0.575878i
$795$	−5.70428	+	4.14440i	−0.202310	+	0.146987i
$796$	−1.47956	−	4.55361i	−0.0524415	−	0.161398i
$797$	38.4732	+	27.9524i	1.36279	+	0.990124i	0.998262	+	0.0589313i	$0.0187693\pi$
$797$	38.4732	+	27.9524i	1.36279	+	0.990124i	0.364527	+	0.931193i	$0.381231\pi$
$798$	4.06173	+	2.95102i	0.143784	+	0.104465i
$799$	1.68798	−	1.22639i	0.0597166	−	0.0433866i
$800$	4.81524			0.170245
$801$	0.877667			0.0310108
$802$	4.86439	−	3.53419i	0.171768	−	0.124796i
$803$	15.6411	−	48.1384i	0.551963	−	1.69877i
$804$	0.938485	+	2.88836i	0.0330978	+	0.101865i
$805$	−2.19518			−0.0773700
$806$	20.9065	−	24.1969i	0.736399	−	0.852299i
$807$	−16.7628			−0.590077
$808$	3.93098	+	12.0983i	0.138291	+	0.425617i
$809$	10.2890	−	31.6663i	0.361742	−	1.11333i	−0.590254	−	0.807218i	$-0.700972\pi$
$809$	10.2890	−	31.6663i	0.361742	−	1.11333i	0.951996	−	0.306111i	$-0.0990278\pi$
$810$	2.99349	−	2.17490i	0.105181	−	0.0764182i
$811$	−28.0446			−0.984779			−0.492390	−	0.870375i	$-0.663876\pi$
$811$	−28.0446			−0.984779			−0.492390	+	0.870375i	$0.663876\pi$
$812$	0.442551			0.0155305
$813$	10.4499	−	7.59227i	0.366492	−	0.266272i
$814$	20.2531	+	14.7147i	0.709870	+	0.515751i
$815$	2.08324	+	1.51356i	0.0729726	+	0.0530177i
$816$	0.225205	+	0.693111i	0.00788376	+	0.0242637i
$817$	14.6246	−	10.6254i	0.511650	−	0.371736i
$818$	0.567819	+	1.74757i	0.0198533	+	0.0611022i
$819$	0.137464	−	0.423071i	0.00480338	−	0.0147833i
$820$	−1.83746	−	1.33499i	−0.0641667	−	0.0466199i
$821$	−3.96949	+	12.2168i	−0.138536	+	0.426371i	−0.996123	−	0.0879682i	$-0.971963\pi$
$821$	−3.96949	+	12.2168i	−0.138536	+	0.426371i	0.857587	+	0.514339i	$0.171963\pi$
$822$	−9.24851	+	28.4640i	−0.322579	+	0.992796i
$823$	−25.2479	−	18.3436i	−0.880085	−	0.639419i	0.0531891	−	0.998584i	$-0.483061\pi$
$823$	−25.2479	−	18.3436i	−0.880085	−	0.639419i	−0.933274	+	0.359165i	$0.883061\pi$
$824$	1.49258	−	4.59368i	0.0519964	−	0.160029i
$825$	8.23882	+	25.3565i	0.286839	+	0.882799i
$826$	−1.97028	+	1.43149i	−0.0685549	+	0.0498080i
$827$	−12.0223	−	37.0008i	−0.418056	−	1.28665i	−0.909488	−	0.415729i	$-0.863526\pi$
$827$	−12.0223	−	37.0008i	−0.418056	−	1.28665i	0.491432	−	0.870916i	$-0.336474\pi$
$828$	0.837805	+	0.608701i	0.0291157	+	0.0211538i
$829$	−6.01258	−	4.36840i	−0.208826	−	0.151721i	0.478457	−	0.878111i	$-0.341196\pi$
$829$	−6.01258	−	4.36840i	−0.208826	−	0.151721i	−0.687282	+	0.726391i	$0.741196\pi$
$830$	0.398479	−	0.289512i	0.0138314	−	0.0100491i
$831$	−6.87328			−0.238432
$832$	−5.74336			−0.199115
$833$	2.30138	−	1.67205i	0.0797381	−	0.0579331i
$834$	0.0937443	−	0.288515i	0.00324610	−	0.00999047i
$835$	1.15742	+	3.56217i	0.0400541	+	0.123274i
$836$	−15.6465			−0.541145
$837$	2.48288	−	29.3986i	0.0858210	−	1.01616i
$838$	13.5600			0.468423
$839$	−11.3967	−	35.0754i	−0.393457	−	1.21094i	−0.930157	−	0.367163i	$-0.880329\pi$
$839$	−11.3967	−	35.0754i	−0.393457	−	1.21094i	0.536700	−	0.843773i	$-0.319671\pi$
$840$	0.139185	−	0.428366i	0.00480232	−	0.0147800i
$841$	23.0467	−	16.7444i	0.794713	−	0.577393i
$842$	−8.08603			−0.278663
$843$	40.8305			1.40628
$844$	−21.9561	+	15.9520i	−0.755759	+	0.549091i
$845$	6.95006	+	5.04951i	0.239089	+	0.173708i
$846$	0.492147	+	0.357566i	0.0169204	+	0.0122934i
$847$	−0.0640773	−	0.197210i	−0.00220172	−	0.00677621i
$848$	7.82717	−	5.68677i	0.268786	−	0.195284i
$849$	11.2551	+	34.6396i	0.386274	+	1.18883i
$850$	0.639591	−	1.96846i	0.0219378	−	0.0675175i
$851$	51.2481	+	37.2339i	1.75676	+	1.27636i
$852$	5.91204	−	18.1954i	0.202543	−	0.623364i
$853$	7.74455	−	23.8353i	0.265168	−	0.816105i	−0.726486	−	0.687181i	$-0.758848\pi$
$853$	7.74455	−	23.8353i	0.265168	−	0.816105i	0.991655	−	0.128923i	$-0.0411521\pi$
$854$	3.81352	+	2.77069i	0.130496	+	0.0948109i
$855$	0.0797552	−	0.245461i	0.00272757	−	0.00839460i
$856$	−3.69156	−	11.3614i	−0.126175	−	0.388326i
$857$	−12.6100	+	9.16167i	−0.430748	+	0.312957i	−0.781948	−	0.623344i	$-0.785774\pi$
$857$	−12.6100	+	9.16167i	−0.430748	+	0.312957i	0.351200	+	0.936300i	$0.385774\pi$
$858$	−9.82681	−	30.2438i	−0.335482	−	1.03251i
$859$	−32.5714	−	23.6645i	−1.11132	−	0.807424i	−0.128452	−	0.991716i	$-0.541001\pi$
$859$	−32.5714	−	23.6645i	−1.11132	−	0.807424i	−0.982872	+	0.184292i	$0.941001\pi$
$860$	−1.31202	−	0.953236i	−0.0447394	−	0.0325051i
$861$	4.47942	−	3.25449i	0.152658	−	0.110913i
$862$	−1.23951			−0.0422178
$863$	7.13079			0.242735			0.121367	−	0.992608i	$-0.461272\pi$
$863$	7.13079			0.242735			0.121367	+	0.992608i	$0.461272\pi$
$864$	−4.28694	+	3.11464i	−0.145845	+	0.105962i
$865$	−2.20697	+	6.79236i	−0.0750393	+	0.230947i
$866$	−7.65963	−	23.5739i	−0.260285	−	0.801074i
$867$	−28.5100			−0.968251
$868$	−1.78115	−	2.94422i	−0.0604563	−	0.0999334i
$869$	4.41641			0.149816
$870$	0.161261	+	0.496311i	0.00546727	+	0.0168265i
$871$	−3.17906	+	9.78413i	−0.107718	+	0.331523i
$872$	0.891324	−	0.647585i	0.0301840	−	0.0219300i
$873$	1.15120			0.0389622
$874$	−39.5916			−1.33921
$875$	−2.10947	+	1.53262i	−0.0713130	+	0.0518119i
$876$	21.2602	+	15.4465i	0.718317	+	0.521888i
$877$	31.3830	+	22.8011i	1.05973	+	0.769939i	0.974038	−	0.226383i	$-0.0726900\pi$
$877$	31.3830	+	22.8011i	1.05973	+	0.769939i	0.0856917	+	0.996322i	$0.472690\pi$
$878$	−1.58439	−	4.87624i	−0.0534705	−	0.164565i
$879$	32.6212	−	23.7007i	1.10029	−	0.799404i
$880$	0.433764	+	1.33499i	0.0146222	+	0.0450025i
$881$	1.01034	−	3.10950i	0.0340392	−	0.104762i	−0.932593	−	0.360929i	$-0.882460\pi$
$881$	1.01034	−	3.10950i	0.0340392	−	0.104762i	0.966633	+	0.256167i	$0.0824597\pi$
$882$	0.670989	+	0.487502i	0.0225934	+	0.0164150i
$883$	4.85959	−	14.9563i	0.163538	−	0.503319i	−0.835387	−	0.549662i	$-0.814757\pi$
$883$	4.85959	−	14.9563i	0.163538	−	0.503319i	0.998926	+	0.0463429i	$0.0147567\pi$
$884$	−0.762869	+	2.34787i	−0.0256580	+	0.0789674i
$885$	−2.32334	−	1.68800i	−0.0780981	−	0.0567416i
$886$	−3.85181	+	11.8547i	−0.129404	+	0.398265i
$887$	8.57802	+	26.4004i	0.288022	+	0.886440i	0.985477	+	0.169811i	$0.0543158\pi$
$887$	8.57802	+	26.4004i	0.288022	+	0.886440i	−0.697455	+	0.716629i	$0.745684\pi$
$888$	−10.5152	+	7.63970i	−0.352865	+	0.256372i
$889$	−2.33123	−	7.17479i	−0.0781870	−	0.240635i
$890$	2.43535	+	1.76938i	0.0816330	+	0.0593098i
$891$	−22.7429	−	16.5237i	−0.761917	−	0.553565i
$892$	4.89468	−	3.55619i	0.163886	−	0.119070i
$893$	−23.2571			−0.778269
$894$	14.9112			0.498707
$895$	0.287368	−	0.208785i	0.00960564	−	0.00697891i
$896$	−0.190983	+	0.587785i	−0.00638029	+	0.0196365i
$897$	−24.8656	−	76.5285i	−0.830239	−	2.55521i
$898$	0.518589			0.0173055
$899$	3.67461	+	1.54674i	0.122555	+	0.0515866i
$900$	0.603457			0.0201152
$901$	−1.28508	−	3.95508i	−0.0428123	−	0.131763i
$902$	−5.33224	+	16.4110i	−0.177544	+	0.546425i
$903$	3.19849	−	2.32384i	0.106439	−	0.0773324i
$904$	−16.9438			−0.563544
$905$	5.49026			0.182502
$906$	−30.5096	+	22.1665i	−1.01361	+	0.736433i
$907$	37.5610	+	27.2897i	1.24719	+	0.906139i	0.998056	−	0.0623287i	$-0.0198527\pi$
$907$	37.5610	+	27.2897i	1.24719	+	0.906139i	0.249138	+	0.968468i	$0.419853\pi$
$908$	−21.0980	−	15.3286i	−0.700163	−	0.508698i
$909$	0.492640	+	1.51619i	0.0163398	+	0.0502888i
$910$	1.23435	−	0.896806i	0.0409182	−	0.0297288i
$911$	4.91592	+	15.1297i	0.162872	+	0.501268i	0.998873	−	0.0474596i	$-0.0151125\pi$
$911$	4.91592	+	15.1297i	0.162872	+	0.501268i	−0.836001	+	0.548727i	$0.815113\pi$
$912$	2.51029	−	7.72587i	0.0831239	−	0.255829i
$913$	−3.02743	−	2.19955i	−0.100193	−	0.0727946i
$914$	6.91455	−	21.2808i	0.228713	−	0.703907i
$915$	−1.71765	+	5.28638i	−0.0567838	+	0.174762i
$916$	−12.8223	−	9.31596i	−0.423661	−	0.307808i
$917$	3.14585	−	9.68192i	0.103885	−	0.319725i
$918$	0.703839	+	2.16619i	0.0232302	+	0.0714951i
$919$	−32.9984	+	23.9747i	−1.08852	+	0.790853i	−0.979148	−	0.203148i	$-0.934883\pi$
$919$	−32.9984	+	23.9747i	−1.08852	+	0.790853i	−0.109368	+	0.994001i	$0.534883\pi$
$920$	1.09759	+	3.37804i	0.0361865	+	0.111371i
$921$	−7.99917	−	5.81174i	−0.263582	−	0.191503i
$922$	13.7514	+	9.99100i	0.452879	+	0.329036i
$923$	52.4305	−	38.0930i	1.72577	−	1.25385i
$924$	−3.42198			−0.112575
$925$	36.9132			1.21370
$926$	−4.87883	+	3.54468i	−0.160328	+	0.116485i
$927$	0.187053	−	0.575691i	0.00614364	−	0.0189082i
$928$	−0.221276	−	0.681017i	−0.00726373	−	0.0223555i
$929$	−15.9210			−0.522350			−0.261175	−	0.965291i	$-0.584110\pi$
$929$	−15.9210			−0.522350			−0.261175	+	0.965291i	$0.584110\pi$
$930$	2.65284	−	3.07037i	0.0869901	−	0.100681i
$931$	−31.7085			−1.03920
$932$	−7.78672	−	23.9651i	−0.255063	−	0.785002i
$933$	−10.3167	+	31.7517i	−0.337755	+	1.03950i
$934$	18.8859	−	13.7214i	0.617966	−	0.448978i
$935$	0.603356			0.0197318
$936$	−0.719771			−0.0235264
$937$	11.8533	−	8.61193i	0.387231	−	0.281339i	−0.377089	−	0.926177i	$-0.623075\pi$
$937$	11.8533	−	8.61193i	0.387231	−	0.281339i	0.764320	+	0.644837i	$0.223075\pi$
$938$	0.895613	+	0.650701i	0.0292428	+	0.0212461i
$939$	43.6748	+	31.7316i	1.42527	+	1.03552i
$940$	0.644752	+	1.98434i	0.0210295	+	0.0647222i
$941$	−8.43605	+	6.12915i	−0.275007	+	0.199805i	−0.716737	−	0.697344i	$-0.754365\pi$
$941$	−8.43605	+	6.12915i	−0.275007	+	0.199805i	0.441729	+	0.897148i	$0.354365\pi$
$942$	−6.15747	−	18.9507i	−0.200621	−	0.617448i
$943$	−13.4926	+	41.5261i	−0.439381	+	1.35227i
$944$	3.18798	+	2.31621i	0.103760	+	0.0753861i
$945$	0.434997	−	1.33878i	0.0141504	−	0.0435506i
$946$	−3.80743	+	11.7181i	−0.123790	+	0.380988i
$947$	27.7428	+	20.1563i	0.901519	+	0.654992i	0.938856	−	0.344311i	$-0.111887\pi$
$947$	27.7428	+	20.1563i	0.901519	+	0.654992i	−0.0373364	+	0.999303i	$0.511887\pi$
$948$	−0.708559	+	2.18072i	−0.0230129	+	0.0708265i
$949$	27.5083	+	84.6619i	0.892957	+	2.74824i
$950$	−18.6648	+	13.5607i	−0.605565	+	0.439968i
$951$	−12.4636	−	38.3589i	−0.404159	−	1.24387i
$952$	0.214917	+	0.156147i	0.00696551	+	0.00506074i
$953$	−10.6361	−	7.72754i	−0.344536	−	0.250320i	0.402037	−	0.915623i	$-0.368302\pi$
$953$	−10.6361	−	7.72754i	−0.344536	−	0.250320i	−0.746573	+	0.665304i	$0.768302\pi$
$954$	0.980919	−	0.712679i	0.0317584	−	0.0230738i
$955$	−1.67880			−0.0543246
$956$	3.27837			0.106030
$957$	3.20755	−	2.33042i	0.103685	−	0.0753318i
$958$	−1.94012	+	5.97108i	−0.0626825	+	0.192917i
$959$	3.37124	+	10.3756i	0.108863	+	0.335046i
$960$	−0.728780			−0.0235213
$961$	−4.49913	−	30.6718i	−0.145133	−	0.989412i
$962$	−44.0280			−1.41952
$963$	−0.462635	−	1.42384i	−0.0149082	−	0.0458827i
$964$	2.36068	−	7.26543i	0.0760325	−	0.234004i
$965$	−0.826320	+	0.600357i	−0.0266002	+	0.0193262i
$966$	−8.65892			−0.278596
$967$	−51.6789			−1.66188			−0.830941	−	0.556361i	$-0.812197\pi$
$967$	−51.6789			−1.66188			−0.830941	+	0.556361i	$0.812197\pi$
$968$	−0.271436	+	0.197210i	−0.00872428	+	0.00633856i
$969$	−2.82488	−	2.05240i	−0.0907483	−	0.0659325i
$970$	3.19434	+	2.32083i	0.102564	+	0.0745172i
$971$	10.0626	+	30.9695i	0.322925	+	0.993860i	0.972369	+	0.233450i	$0.0750016\pi$
$971$	10.0626	+	30.9695i	0.322925	+	0.993860i	−0.649444	+	0.760409i	$0.724998\pi$
$972$	−1.05295	+	0.765016i	−0.0337735	+	0.0245379i
$973$	−0.0341714	−	0.105169i	−0.00109548	−	0.00337155i
$974$	−7.88364	+	24.2633i	−0.252608	+	0.777447i
$975$	−37.9347	−	27.5611i	−1.21488	−	0.882663i
$976$	2.35689	−	7.25375i	0.0754421	−	0.232187i
$977$	6.84152	−	21.0560i	0.218880	−	0.673642i	−0.779976	−	0.625810i	$-0.784769\pi$
$977$	6.84152	−	21.0560i	0.218880	−	0.673642i	0.998855	−	0.0478326i	$-0.0152314\pi$
$978$	8.21735	+	5.97025i	0.262762	+	0.190908i
$979$	7.06730	−	21.7509i	0.225872	−	0.695162i
$980$	0.879049	+	2.70543i	0.0280802	+	0.0864219i
$981$	0.111703	−	0.0811568i	0.00356639	−	0.00259114i
$982$	13.2351	+	40.7336i	0.422350	+	1.29986i
$983$	35.5822	+	25.8520i	1.13490	+	0.824550i	0.986400	−	0.164363i	$-0.0525570\pi$
$983$	35.5822	+	25.8520i	1.13490	+	0.824550i	0.148495	+	0.988913i	$0.452557\pi$
$984$	−7.24786	−	5.26588i	−0.231053	−	0.167870i
$985$	−3.68704	+	2.67879i	−0.117479	+	0.0853535i
$986$	−0.307789			−0.00980200
$987$	−5.08646			−0.161904
$988$	22.2623	−	16.1745i	0.708258	−	0.514580i
$989$	−9.63428	+	29.6513i	−0.306352	+	0.942855i
$990$	0.0543604	+	0.167304i	0.00172769	+	0.00531727i
$991$	50.5029			1.60428			0.802138	−	0.597138i	$-0.203696\pi$
$991$	50.5029			1.60428			0.802138	+	0.597138i	$0.203696\pi$
$992$	−3.64011	+	4.21302i	−0.115574	+	0.133764i
$993$	45.8268			1.45427
$994$	−2.15504	−	6.63253i	−0.0683537	−	0.210371i
$995$	0.635965	−	1.95730i	0.0201615	−	0.0620506i
$996$	1.57180	−	1.14198i	0.0498045	−	0.0361851i
$997$	−4.40283			−0.139439			−0.0697195	−	0.997567i	$-0.522210\pi$
$997$	−4.40283			−0.139439			−0.0697195	+	0.997567i	$0.522210\pi$
$998$	−1.27810			−0.0404576
$999$	−32.8632	+	23.8765i	−1.03975	+	0.755420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.d.b.35.2	✓	8
3.2	odd	2		558.2.i.g.469.2		8
4.3	odd	2		496.2.n.d.97.1		8
31.8	even	5	inner	62.2.d.b.39.2	yes	8
31.15	odd	10		1922.2.a.l.1.2		4
31.16	even	5		1922.2.a.i.1.3		4
93.8	odd	10		558.2.i.g.163.2		8
124.39	odd	10		496.2.n.d.225.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.b.35.2	✓	8	1.1	even	1	trivial
62.2.d.b.39.2	yes	8	31.8	even	5	inner
496.2.n.d.97.1		8	4.3	odd	2
496.2.n.d.225.1		8	124.39	odd	10
558.2.i.g.163.2		8	93.8	odd	10
558.2.i.g.469.2		8	3.2	odd	2
1922.2.a.i.1.3		4	31.16	even	5
1922.2.a.l.1.2		4	31.15	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.523934 - 1.61250i) q^{3} +(-0.809017 + 0.587785i) q^{4} -0.429835 q^{5} -1.69549 q^{6} +(-0.500000 + 0.363271i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.101388 + 0.0736626i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.523934 - 1.61250i) q^{3} +(-0.809017 + 0.587785i) q^{4} -0.429835 q^{5} -1.69549 q^{6} +(-0.500000 + 0.363271i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.101388 + 0.0736626i) q^{9} +(0.132826 + 0.408797i) q^{10} +(2.64197 - 1.91950i) q^{11} +(0.523934 + 1.61250i) q^{12} +(-1.77479 + 5.46226i) q^{13} +(0.500000 + 0.363271i) q^{14} +(-0.225205 + 0.693111i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.347744 - 0.252651i) q^{17} +(0.0387267 - 0.119189i) q^{18} +(1.48057 + 4.55673i) q^{19} +(0.347744 - 0.252651i) q^{20} +(0.323809 + 0.996583i) q^{21} +(-2.64197 - 1.91950i) q^{22} +(-6.68520 - 4.85708i) q^{23} +(1.37168 - 0.996583i) q^{24} -4.81524 q^{25} +5.74336 q^{26} +(4.28694 - 3.11464i) q^{27} +(0.190983 - 0.587785i) q^{28} +(0.221276 + 0.681017i) q^{29} +0.728780 q^{30} +(3.64011 - 4.21302i) q^{31} -1.00000 q^{32} +(-1.71099 - 5.26588i) q^{33} +(-0.132826 + 0.408797i) q^{34} +(0.214917 - 0.156147i) q^{35} -0.125322 q^{36} -7.66590 q^{37} +(3.87618 - 2.81621i) q^{38} +(7.87804 + 5.72373i) q^{39} +(-0.347744 - 0.252651i) q^{40} +(-1.63283 - 5.02532i) q^{41} +(0.847744 - 0.615922i) q^{42} +(-1.16590 - 3.58828i) q^{43} +(-1.00914 + 3.10582i) q^{44} +(-0.0435801 - 0.0316628i) q^{45} +(-2.55352 + 7.85892i) q^{46} +(-1.50000 + 4.61653i) q^{47} +(-1.37168 - 0.996583i) q^{48} +(-2.04508 + 6.29412i) q^{49} +(1.48799 + 4.57957i) q^{50} +(-0.589595 + 0.428366i) q^{51} +(-1.77479 - 5.46226i) q^{52} +(7.82717 + 5.68677i) q^{53} +(-4.28694 - 3.11464i) q^{54} +(-1.13561 + 0.825069i) q^{55} -0.618034 q^{56} +8.12346 q^{57} +(0.579307 - 0.420891i) q^{58} +(-1.21770 + 3.74770i) q^{59} +(-0.225205 - 0.693111i) q^{60} +7.62704 q^{61} +(-5.13168 - 2.16006i) q^{62} -0.0774535 q^{63} +(0.309017 + 0.951057i) q^{64} +(0.762869 - 2.34787i) q^{65} +(-4.47942 + 3.25449i) q^{66} +1.79123 q^{67} +0.429835 q^{68} +(-11.3347 + 8.23512i) q^{69} +(-0.214917 - 0.156147i) q^{70} +(-9.12890 - 6.63253i) q^{71} +(0.0387267 + 0.119189i) q^{72} +(12.5393 - 9.11034i) q^{73} +(2.36889 + 7.29071i) q^{74} +(-2.52287 + 7.76460i) q^{75} +(-3.87618 - 2.81621i) q^{76} +(-0.623684 + 1.91950i) q^{77} +(3.00914 - 9.26119i) q^{78} +(1.09410 + 0.794910i) q^{79} +(-0.132826 + 0.408797i) q^{80} +(-2.66012 - 8.18701i) q^{81} +(-4.27479 + 3.10582i) q^{82} +(-0.354102 - 1.08981i) q^{83} +(-0.847744 - 0.615922i) q^{84} +(0.149472 + 0.108598i) q^{85} +(-3.05237 + 2.21768i) q^{86} +1.21408 q^{87} +3.26565 q^{88} +(5.66577 - 4.11642i) q^{89} +(-0.0166461 + 0.0512314i) q^{90} +(-1.09688 - 3.37586i) q^{91} +8.26336 q^{92} +(-4.88634 - 8.07705i) q^{93} +4.85410 q^{94} +(-0.636401 - 1.95864i) q^{95} +(-0.523934 + 1.61250i) q^{96} +(7.43156 - 5.39934i) q^{97} +6.61803 q^{98} +0.409259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9} - 5 q^{10} + 6 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} - 23 q^{15} - 2 q^{16} + 5 q^{17} - 3 q^{18} - 2 q^{19} - 5 q^{20} + q^{21} - 6 q^{22} - 15 q^{23} - 3 q^{24} + 16 q^{25} + 18 q^{26} + 37 q^{27} + 6 q^{28} - 19 q^{29} - 2 q^{30} + 13 q^{31} - 8 q^{32} + 30 q^{33} + 5 q^{34} + 18 q^{36} - 40 q^{37} - 3 q^{38} + 30 q^{39} + 5 q^{40} - 7 q^{41} - q^{42} + 12 q^{43} + q^{44} - 31 q^{45} - 20 q^{46} - 12 q^{47} + 3 q^{48} + 6 q^{49} + 19 q^{50} - 22 q^{51} + 7 q^{52} + 9 q^{53} - 37 q^{54} - 13 q^{55} + 4 q^{56} + 28 q^{57} - q^{58} - 18 q^{59} - 23 q^{60} + 12 q^{61} - 3 q^{62} + 6 q^{63} - 2 q^{64} - 16 q^{65} + 10 q^{66} - 26 q^{67} - 50 q^{69} - 25 q^{71} - 3 q^{72} + 35 q^{73} - 5 q^{74} + 26 q^{75} + 3 q^{76} - 8 q^{77} + 15 q^{78} + 6 q^{79} + 5 q^{80} + 43 q^{81} - 13 q^{82} + 24 q^{83} + q^{84} - q^{85} + 8 q^{86} + 8 q^{87} + 14 q^{88} - 7 q^{89} - 4 q^{90} - 16 q^{91} - 10 q^{92} + 3 q^{93} + 12 q^{94} + 30 q^{95} + 2 q^{96} + 26 q^{97} + 44 q^{98} - 46 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9 - 5 * q^10 + 6 * q^11 - 2 * q^12 + 7 * q^13 + 4 * q^14 - 23 * q^15 - 2 * q^16 + 5 * q^17 - 3 * q^18 - 2 * q^19 - 5 * q^20 + q^21 - 6 * q^22 - 15 * q^23 - 3 * q^24 + 16 * q^25 + 18 * q^26 + 37 * q^27 + 6 * q^28 - 19 * q^29 - 2 * q^30 + 13 * q^31 - 8 * q^32 + 30 * q^33 + 5 * q^34 + 18 * q^36 - 40 * q^37 - 3 * q^38 + 30 * q^39 + 5 * q^40 - 7 * q^41 - q^42 + 12 * q^43 + q^44 - 31 * q^45 - 20 * q^46 - 12 * q^47 + 3 * q^48 + 6 * q^49 + 19 * q^50 - 22 * q^51 + 7 * q^52 + 9 * q^53 - 37 * q^54 - 13 * q^55 + 4 * q^56 + 28 * q^57 - q^58 - 18 * q^59 - 23 * q^60 + 12 * q^61 - 3 * q^62 + 6 * q^63 - 2 * q^64 - 16 * q^65 + 10 * q^66 - 26 * q^67 - 50 * q^69 - 25 * q^71 - 3 * q^72 + 35 * q^73 - 5 * q^74 + 26 * q^75 + 3 * q^76 - 8 * q^77 + 15 * q^78 + 6 * q^79 + 5 * q^80 + 43 * q^81 - 13 * q^82 + 24 * q^83 + q^84 - q^85 + 8 * q^86 + 8 * q^87 + 14 * q^88 - 7 * q^89 - 4 * q^90 - 16 * q^91 - 10 * q^92 + 3 * q^93 + 12 * q^94 + 30 * q^95 + 2 * q^96 + 26 * q^97 + 44 * q^98 - 46 * q^99

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