LMFDB - Embedded newform 770.2.n.c.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	770.631
Dual form			770.2.n.c.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +1.00000 q^{10} +(3.30902 - 0.224514i) q^{11} -1.61803 q^{12} +(0.618034 + 0.449028i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.500000 + 1.53884i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.809017 + 2.48990i) q^{19} +(0.809017 + 0.587785i) q^{20} -1.61803 q^{21} +(2.80902 + 1.76336i) q^{22} +0.472136 q^{23} +(-1.30902 - 0.951057i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.236068 + 0.726543i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(1.23607 + 3.80423i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(-3.61803 - 2.62866i) q^{31} -1.00000 q^{32} +(-1.30902 + 5.20431i) q^{33} -0.618034 q^{34} +(0.809017 + 0.587785i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(-1.14590 - 3.52671i) q^{37} +(-2.11803 + 1.53884i) q^{38} +(-1.00000 + 0.726543i) q^{39} +(0.309017 + 0.951057i) q^{40} +(1.97214 - 6.06961i) q^{41} +(-1.30902 - 0.951057i) q^{42} -2.38197 q^{43} +(1.23607 + 3.07768i) q^{44} +0.381966 q^{45} +(0.381966 + 0.277515i) q^{46} +(-3.47214 + 10.6861i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-0.309017 - 0.951057i) q^{51} +(-0.236068 + 0.726543i) q^{52} +(-2.00000 - 1.45309i) q^{53} -5.47214 q^{54} +(2.54508 - 2.12663i) q^{55} -1.00000 q^{56} +(-3.42705 - 2.48990i) q^{57} +(-1.23607 + 3.80423i) q^{58} +(-0.427051 - 1.31433i) q^{59} +(-1.30902 + 0.951057i) q^{60} +(6.47214 - 4.70228i) q^{61} +(-1.38197 - 4.25325i) q^{62} +(-0.118034 + 0.363271i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.763932 q^{65} +(-4.11803 + 3.44095i) q^{66} +5.09017 q^{67} +(-0.500000 - 0.363271i) q^{68} +(-0.236068 + 0.726543i) q^{69} +(0.309017 + 0.951057i) q^{70} +(5.23607 - 3.80423i) q^{71} +(-0.309017 + 0.224514i) q^{72} +(-3.50000 - 10.7719i) q^{73} +(1.14590 - 3.52671i) q^{74} +(1.30902 + 0.951057i) q^{75} -2.61803 q^{76} +(1.23607 + 3.07768i) q^{77} -1.23607 q^{78} +(9.47214 + 6.88191i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(5.16312 - 3.75123i) q^{82} +(0.0729490 - 0.0530006i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(-0.190983 + 0.587785i) q^{85} +(-1.92705 - 1.40008i) q^{86} -6.47214 q^{87} +(-0.809017 + 3.21644i) q^{88} +3.14590 q^{89} +(0.309017 + 0.224514i) q^{90} +(-0.236068 + 0.726543i) q^{91} +(0.145898 + 0.449028i) q^{92} +(5.85410 - 4.25325i) q^{93} +(-9.09017 + 6.60440i) q^{94} +(0.809017 + 2.48990i) q^{95} +(0.500000 - 1.53884i) q^{96} +(-11.1631 - 8.11048i) q^{97} -1.00000 q^{98} +(1.07295 + 0.673542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + 11 q^{11} - 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 4 q^{18} - q^{19} + q^{20} - 2 q^{21} + 9 q^{22} - 16 q^{23} - 3 q^{24} - q^{25} - 8 q^{26} - 11 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 10 q^{31} - 4 q^{32} - 3 q^{33} + 2 q^{34} + q^{35} + 4 q^{36} - 18 q^{37} - 4 q^{38} - 4 q^{39} - q^{40} - 10 q^{41} - 3 q^{42} - 14 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 2 q^{48} - q^{49} + q^{50} + q^{51} + 8 q^{52} - 8 q^{53} - 4 q^{54} - q^{55} - 4 q^{56} - 7 q^{57} + 4 q^{58} + 5 q^{59} - 3 q^{60} + 8 q^{61} - 10 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} - 12 q^{66} - 2 q^{67} - 2 q^{68} + 8 q^{69} - q^{70} + 12 q^{71} + q^{72} - 14 q^{73} + 18 q^{74} + 3 q^{75} - 6 q^{76} - 4 q^{77} + 4 q^{78} + 20 q^{79} + q^{80} - 14 q^{81} + 5 q^{82} + 7 q^{83} - 2 q^{84} - 3 q^{85} - q^{86} - 8 q^{87} - q^{88} + 26 q^{89} - q^{90} + 8 q^{91} + 14 q^{92} + 10 q^{93} - 14 q^{94} + q^{95} + 2 q^{96} - 29 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + 11 * q^11 - 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 2 * q^17 - 4 * q^18 - q^19 + q^20 - 2 * q^21 + 9 * q^22 - 16 * q^23 - 3 * q^24 - q^25 - 8 * q^26 - 11 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 10 * q^31 - 4 * q^32 - 3 * q^33 + 2 * q^34 + q^35 + 4 * q^36 - 18 * q^37 - 4 * q^38 - 4 * q^39 - q^40 - 10 * q^41 - 3 * q^42 - 14 * q^43 - 4 * q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 2 * q^48 - q^49 + q^50 + q^51 + 8 * q^52 - 8 * q^53 - 4 * q^54 - q^55 - 4 * q^56 - 7 * q^57 + 4 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 10 * q^62 + 4 * q^63 - q^64 + 12 * q^65 - 12 * q^66 - 2 * q^67 - 2 * q^68 + 8 * q^69 - q^70 + 12 * q^71 + q^72 - 14 * q^73 + 18 * q^74 + 3 * q^75 - 6 * q^76 - 4 * q^77 + 4 * q^78 + 20 * q^79 + q^80 - 14 * q^81 + 5 * q^82 + 7 * q^83 - 2 * q^84 - 3 * q^85 - q^86 - 8 * q^87 - q^88 + 26 * q^89 - q^90 + 8 * q^91 + 14 * q^92 + 10 * q^93 - 14 * q^94 + q^95 + 2 * q^96 - 29 * q^97 - 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$	1.00000			0.316228
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$	−1.61803			−0.467086
$13$	0.618034	+	0.449028i	0.171412	+	0.124538i	0.670184	−	0.742195i	$-0.266215\pi$
$13$	0.618034	+	0.449028i	0.171412	+	0.124538i	−0.498772	+	0.866733i	$0.666215\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	0.500000	+	1.53884i	0.129099	+	0.397327i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	−0.646766	−	0.762688i	$-0.723879\pi$
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	0.525498	+	0.850795i	$0.323879\pi$
$18$	0.118034	+	0.363271i	0.0278209	+	0.0856239i
$19$	−0.809017	+	2.48990i	−0.185601	+	0.571222i	−0.999958	−	0.00914245i	$-0.997090\pi$
$19$	−0.809017	+	2.48990i	−0.185601	+	0.571222i	0.814357	+	0.580364i	$0.197090\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	−1.61803			−0.353084
$22$	2.80902	+	1.76336i	0.598884	+	0.375949i
$23$	0.472136			0.0984472			0.0492236	−	0.998788i	$-0.484325\pi$
$23$	0.472136			0.0984472			0.0492236	+	0.998788i	$0.484325\pi$
$24$	−1.30902	−	0.951057i	−0.267202	−	0.194134i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.236068	+	0.726543i	0.0462967	+	0.142487i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	1.23607	+	3.80423i	0.229532	+	0.706427i	0.997800	+	0.0662984i	$0.0211189\pi$
$29$	1.23607	+	3.80423i	0.229532	+	0.706427i	−0.768268	+	0.640129i	$0.778881\pi$
$30$	−0.500000	+	1.53884i	−0.0912871	+	0.280953i
$31$	−3.61803	−	2.62866i	−0.649818	−	0.472120i	0.213391	−	0.976967i	$-0.431549\pi$
$31$	−3.61803	−	2.62866i	−0.649818	−	0.472120i	−0.863209	+	0.504846i	$0.831549\pi$
$32$	−1.00000			−0.176777
$33$	−1.30902	+	5.20431i	−0.227871	+	0.905954i
$34$	−0.618034			−0.105992
$35$	0.809017	+	0.587785i	0.136749	+	0.0993538i
$36$	−0.118034	+	0.363271i	−0.0196723	+	0.0605452i
$37$	−1.14590	−	3.52671i	−0.188384	−	0.579788i	0.811606	−	0.584206i	$-0.198594\pi$
$37$	−1.14590	−	3.52671i	−0.188384	−	0.579788i	−0.999990	+	0.00441771i	$0.998594\pi$
$38$	−2.11803	+	1.53884i	−0.343590	+	0.249633i
$39$	−1.00000	+	0.726543i	−0.160128	+	0.116340i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	1.97214	−	6.06961i	0.307996	−	0.947914i	−0.670546	−	0.741868i	$-0.733940\pi$
$41$	1.97214	−	6.06961i	0.307996	−	0.947914i	0.978542	−	0.206046i	$-0.0660597\pi$
$42$	−1.30902	−	0.951057i	−0.201986	−	0.146751i
$43$	−2.38197			−0.363246			−0.181623	−	0.983368i	$-0.558135\pi$
$43$	−2.38197			−0.363246			−0.181623	+	0.983368i	$0.558135\pi$
$44$	1.23607	+	3.07768i	0.186344	+	0.463978i
$45$	0.381966			0.0569401
$46$	0.381966	+	0.277515i	0.0563178	+	0.0409173i
$47$	−3.47214	+	10.6861i	−0.506463	+	1.55873i	0.291834	+	0.956469i	$0.405735\pi$
$47$	−3.47214	+	10.6861i	−0.506463	+	1.55873i	−0.798297	+	0.602264i	$0.794265\pi$
$48$	−0.500000	−	1.53884i	−0.0721688	−	0.222113i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$	−0.309017	−	0.951057i	−0.0432710	−	0.133175i
$52$	−0.236068	+	0.726543i	−0.0327367	+	0.100753i
$53$	−2.00000	−	1.45309i	−0.274721	−	0.199597i	0.441891	−	0.897069i	$-0.354308\pi$
$53$	−2.00000	−	1.45309i	−0.274721	−	0.199597i	−0.716612	+	0.697472i	$0.754308\pi$
$54$	−5.47214			−0.744663
$55$	2.54508	−	2.12663i	0.343179	−	0.286754i
$56$	−1.00000			−0.133631
$57$	−3.42705	−	2.48990i	−0.453924	−	0.329795i
$58$	−1.23607	+	3.80423i	−0.162304	+	0.499519i
$59$	−0.427051	−	1.31433i	−0.0555973	−	0.171111i	0.919402	−	0.393320i	$-0.128673\pi$
$59$	−0.427051	−	1.31433i	−0.0555973	−	0.171111i	−0.974999	+	0.222209i	$0.928673\pi$
$60$	−1.30902	+	0.951057i	−0.168993	+	0.122781i
$61$	6.47214	−	4.70228i	0.828672	−	0.602066i	−0.0905112	−	0.995895i	$-0.528850\pi$
$61$	6.47214	−	4.70228i	0.828672	−	0.602066i	0.919183	+	0.393830i	$0.128850\pi$
$62$	−1.38197	−	4.25325i	−0.175510	−	0.540164i
$63$	−0.118034	+	0.363271i	−0.0148709	+	0.0457679i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.763932			0.0947541
$66$	−4.11803	+	3.44095i	−0.506895	+	0.423552i
$67$	5.09017			0.621863			0.310932	−	0.950432i	$-0.399359\pi$
$67$	5.09017			0.621863			0.310932	+	0.950432i	$0.399359\pi$
$68$	−0.500000	−	0.363271i	−0.0606339	−	0.0440531i
$69$	−0.236068	+	0.726543i	−0.0284192	+	0.0874654i
$70$	0.309017	+	0.951057i	0.0369346	+	0.113673i
$71$	5.23607	−	3.80423i	0.621407	−	0.451479i	−0.232006	−	0.972714i	$-0.574529\pi$
$71$	5.23607	−	3.80423i	0.621407	−	0.451479i	0.853413	+	0.521236i	$0.174529\pi$
$72$	−0.309017	+	0.224514i	−0.0364180	+	0.0264592i
$73$	−3.50000	−	10.7719i	−0.409644	−	1.26075i	−0.916955	−	0.398991i	$-0.869360\pi$
$73$	−3.50000	−	10.7719i	−0.409644	−	1.26075i	0.507311	−	0.861763i	$-0.330640\pi$
$74$	1.14590	−	3.52671i	0.133208	−	0.409972i
$75$	1.30902	+	0.951057i	0.151152	+	0.109819i
$76$	−2.61803			−0.300309
$77$	1.23607	+	3.07768i	0.140863	+	0.350735i
$78$	−1.23607			−0.139957
$79$	9.47214	+	6.88191i	1.06570	+	0.774275i	0.975134	−	0.221615i	$-0.0711329\pi$
$79$	9.47214	+	6.88191i	1.06570	+	0.774275i	0.0905644	+	0.995891i	$0.471133\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	5.16312	−	3.75123i	0.570171	−	0.414254i
$83$	0.0729490	−	0.0530006i	0.00800719	−	0.00581757i	−0.583774	−	0.811916i	$-0.698425\pi$
$83$	0.0729490	−	0.0530006i	0.00800719	−	0.00581757i	0.591782	+	0.806098i	$0.298425\pi$
$84$	−0.500000	−	1.53884i	−0.0545545	−	0.167901i
$85$	−0.190983	+	0.587785i	−0.0207150	+	0.0637543i
$86$	−1.92705	−	1.40008i	−0.207799	−	0.150975i
$87$	−6.47214			−0.693886
$88$	−0.809017	+	3.21644i	−0.0862415	+	0.342874i
$89$	3.14590			0.333465			0.166732	−	0.986002i	$-0.446678\pi$
$89$	3.14590			0.333465			0.166732	+	0.986002i	$0.446678\pi$
$90$	0.309017	+	0.224514i	0.0325733	+	0.0236659i
$91$	−0.236068	+	0.726543i	−0.0247466	+	0.0761624i
$92$	0.145898	+	0.449028i	0.0152109	+	0.0468144i
$93$	5.85410	−	4.25325i	0.607042	−	0.441042i
$94$	−9.09017	+	6.60440i	−0.937579	+	0.681191i
$95$	0.809017	+	2.48990i	0.0830034	+	0.255458i
$96$	0.500000	−	1.53884i	0.0510310	−	0.157057i
$97$	−11.1631	−	8.11048i	−1.13344	−	0.823495i	−0.147251	−	0.989099i	$-0.547042\pi$
$97$	−11.1631	−	8.11048i	−1.13344	−	0.823495i	−0.986192	+	0.165605i	$0.947042\pi$
$98$	−1.00000			−0.101015
$99$	1.07295	+	0.673542i	0.107835	+	0.0676935i
$100$	1.00000			0.100000
$101$	−10.3262	−	7.50245i	−1.02750	−	0.746522i	−0.0596925	−	0.998217i	$-0.519012\pi$
$101$	−10.3262	−	7.50245i	−1.02750	−	0.746522i	−0.967807	+	0.251695i	$0.919012\pi$
$102$	0.309017	−	0.951057i	0.0305972	−	0.0941686i
$103$	4.23607	+	13.0373i	0.417392	+	1.28460i	0.910094	+	0.414403i	$0.136009\pi$
$103$	4.23607	+	13.0373i	0.417392	+	1.28460i	−0.492701	+	0.870198i	$0.663991\pi$
$104$	−0.618034	+	0.449028i	−0.0606032	+	0.0440308i
$105$	−1.30902	+	0.951057i	−0.127747	+	0.0928136i
$106$	−0.763932	−	2.35114i	−0.0741996	−	0.228363i
$107$	2.50000	−	7.69421i	0.241684	−	0.743827i	−0.754480	−	0.656323i	$-0.772111\pi$
$107$	2.50000	−	7.69421i	0.241684	−	0.743827i	0.996164	−	0.0875042i	$-0.0278891\pi$
$108$	−4.42705	−	3.21644i	−0.425993	−	0.309502i
$109$	10.1803			0.975100			0.487550	−	0.873095i	$-0.337891\pi$
$109$	10.1803			0.975100			0.487550	+	0.873095i	$0.337891\pi$
$110$	3.30902	−	0.224514i	0.315502	−	0.0214066i
$111$	6.00000			0.569495
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	−3.33688	+	10.2699i	−0.313907	+	0.966108i	0.662294	+	0.749244i	$0.269583\pi$
$113$	−3.33688	+	10.2699i	−0.313907	+	0.966108i	−0.976202	+	0.216864i	$0.930417\pi$
$114$	−1.30902	−	4.02874i	−0.122601	−	0.377326i
$115$	0.381966	−	0.277515i	0.0356185	−	0.0258784i
$116$	−3.23607	+	2.35114i	−0.300461	+	0.218298i
$117$	0.0901699	+	0.277515i	0.00833621	+	0.0256562i
$118$	0.427051	−	1.31433i	0.0393132	−	0.120994i
$119$	−0.500000	−	0.363271i	−0.0458349	−	0.0333010i
$120$	−1.61803			−0.147706
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$	8.00000			0.724286
$123$	8.35410	+	6.06961i	0.753264	+	0.547278i
$124$	1.38197	−	4.25325i	0.124104	−	0.381953i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−0.309017	+	0.224514i	−0.0275294	+	0.0200013i
$127$	6.61803	−	4.80828i	0.587256	−	0.426666i	−0.254077	−	0.967184i	$-0.581772\pi$
$127$	6.61803	−	4.80828i	0.587256	−	0.426666i	0.841333	+	0.540518i	$0.181772\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	1.19098	−	3.66547i	0.104860	−	0.322727i
$130$	0.618034	+	0.449028i	0.0542052	+	0.0393824i
$131$	8.14590			0.711710			0.355855	−	0.934541i	$-0.384190\pi$
$131$	8.14590			0.711710			0.355855	+	0.934541i	$0.384190\pi$
$132$	−5.35410	+	0.363271i	−0.466015	+	0.0316187i
$133$	−2.61803			−0.227012
$134$	4.11803	+	2.99193i	0.355744	+	0.258463i
$135$	−1.69098	+	5.20431i	−0.145537	+	0.447916i
$136$	−0.190983	−	0.587785i	−0.0163767	−	0.0504022i
$137$	10.3992	−	7.55545i	0.888462	−	0.645506i	−0.0470142	−	0.998894i	$-0.514971\pi$
$137$	10.3992	−	7.55545i	0.888462	−	0.645506i	0.935477	+	0.353388i	$0.114971\pi$
$138$	−0.618034	+	0.449028i	−0.0526105	+	0.0382238i
$139$	−0.472136	−	1.45309i	−0.0400460	−	0.123249i	0.929035	−	0.369992i	$-0.120640\pi$
$139$	−0.472136	−	1.45309i	−0.0400460	−	0.123249i	−0.969081	+	0.246743i	$0.920640\pi$
$140$	−0.309017	+	0.951057i	−0.0261167	+	0.0803789i
$141$	−14.7082	−	10.6861i	−1.23865	−	0.899935i
$142$	6.47214			0.543130
$143$	2.14590	+	1.34708i	0.179449	+	0.112649i
$144$	−0.381966			−0.0318305
$145$	3.23607	+	2.35114i	0.268741	+	0.195252i
$146$	3.50000	−	10.7719i	0.289662	−	0.891488i
$147$	−0.500000	−	1.53884i	−0.0412393	−	0.126922i
$148$	3.00000	−	2.17963i	0.246598	−	0.179164i
$149$	6.23607	−	4.53077i	0.510879	−	0.371175i	−0.302278	−	0.953220i	$-0.597747\pi$
$149$	6.23607	−	4.53077i	0.510879	−	0.371175i	0.813157	+	0.582045i	$0.197747\pi$
$150$	0.500000	+	1.53884i	0.0408248	+	0.125646i
$151$	6.23607	−	19.1926i	0.507484	−	1.56188i	−0.289070	−	0.957308i	$-0.593346\pi$
$151$	6.23607	−	19.1926i	0.507484	−	1.56188i	0.796554	−	0.604567i	$-0.206654\pi$
$152$	−2.11803	−	1.53884i	−0.171795	−	0.124817i
$153$	−0.236068			−0.0190850
$154$	−0.809017	+	3.21644i	−0.0651924	+	0.259188i
$155$	−4.47214			−0.359211
$156$	−1.00000	−	0.726543i	−0.0800641	−	0.0581700i
$157$	−1.90983	+	5.87785i	−0.152421	+	0.469104i	−0.997890	−	0.0649201i	$-0.979321\pi$
$157$	−1.90983	+	5.87785i	−0.152421	+	0.469104i	0.845469	+	0.534024i	$0.179321\pi$
$158$	3.61803	+	11.1352i	0.287835	+	0.885866i
$159$	3.23607	−	2.35114i	0.256637	−	0.186458i
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	0.145898	+	0.449028i	0.0114984	+	0.0353884i
$162$	2.38197	−	7.33094i	0.187145	−	0.575973i
$163$	18.2984	+	13.2945i	1.43324	+	1.04131i	0.989402	+	0.145202i	$0.0463832\pi$
$163$	18.2984	+	13.2945i	1.43324	+	1.04131i	0.443837	+	0.896107i	$0.353617\pi$
$164$	6.38197			0.498348
$165$	2.00000	+	4.97980i	0.155700	+	0.387677i
$166$	0.0901699			0.00699854
$167$	−8.09017	−	5.87785i	−0.626036	−	0.454842i	0.228989	−	0.973429i	$-0.426458\pi$
$167$	−8.09017	−	5.87785i	−0.626036	−	0.454842i	−0.855025	+	0.518587i	$0.826458\pi$
$168$	0.500000	−	1.53884i	0.0385758	−	0.118724i
$169$	−3.83688	−	11.8087i	−0.295145	−	0.908362i
$170$	−0.500000	+	0.363271i	−0.0383482	+	0.0278616i
$171$	−0.809017	+	0.587785i	−0.0618671	+	0.0449491i
$172$	−0.736068	−	2.26538i	−0.0561247	−	0.172734i
$173$	1.47214	−	4.53077i	0.111924	−	0.344468i	−0.879369	−	0.476141i	$-0.842035\pi$
$173$	1.47214	−	4.53077i	0.111924	−	0.344468i	0.991293	+	0.131673i	$0.0420350\pi$
$174$	−5.23607	−	3.80423i	−0.396945	−	0.288398i
$175$	1.00000			0.0755929
$176$	−2.54508	+	2.12663i	−0.191843	+	0.160301i
$177$	2.23607			0.168073
$178$	2.54508	+	1.84911i	0.190762	+	0.138597i
$179$	−2.51722	+	7.74721i	−0.188146	+	0.579054i	−0.999988	−	0.00482295i	$-0.998465\pi$
$179$	−2.51722	+	7.74721i	−0.188146	+	0.579054i	0.811842	+	0.583877i	$0.198465\pi$
$180$	0.118034	+	0.363271i	0.00879773	+	0.0270766i
$181$	18.7082	−	13.5923i	1.39057	−	1.01031i	0.394767	−	0.918781i	$-0.370825\pi$
$181$	18.7082	−	13.5923i	1.39057	−	1.01031i	0.995803	−	0.0915270i	$-0.0291748\pi$
$182$	−0.618034	+	0.449028i	−0.0458117	+	0.0332842i
$183$	4.00000	+	12.3107i	0.295689	+	0.910036i
$184$	−0.145898	+	0.449028i	−0.0107557	+	0.0331028i
$185$	−3.00000	−	2.17963i	−0.220564	−	0.160249i
$186$	7.23607			0.530574
$187$	−1.57295	+	1.31433i	−0.115025	+	0.0961132i
$188$	−11.2361			−0.819474
$189$	−4.42705	−	3.21644i	−0.322021	−	0.233962i
$190$	−0.809017	+	2.48990i	−0.0586923	+	0.180636i
$191$	−0.618034	−	1.90211i	−0.0447194	−	0.137632i	0.926204	−	0.377023i	$-0.123052\pi$
$191$	−0.618034	−	1.90211i	−0.0447194	−	0.137632i	−0.970923	+	0.239391i	$0.923052\pi$
$192$	1.30902	−	0.951057i	0.0944702	−	0.0686366i
$193$	2.85410	−	2.07363i	0.205443	−	0.149263i	−0.480307	−	0.877101i	$-0.659475\pi$
$193$	2.85410	−	2.07363i	0.205443	−	0.149263i	0.685749	+	0.727838i	$0.259475\pi$
$194$	−4.26393	−	13.1230i	−0.306132	−	0.942179i
$195$	−0.381966	+	1.17557i	−0.0273532	+	0.0841844i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−5.41641			−0.385903			−0.192952	−	0.981208i	$-0.561806\pi$
$197$	−5.41641			−0.385903			−0.192952	+	0.981208i	$0.561806\pi$
$198$	0.472136	+	1.17557i	0.0335532	+	0.0835442i
$199$	3.23607			0.229399			0.114699	−	0.993400i	$-0.463410\pi$
$199$	3.23607			0.229399			0.114699	+	0.993400i	$0.463410\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	−2.54508	+	7.83297i	−0.179516	+	0.552495i
$202$	−3.94427	−	12.1392i	−0.277518	−	0.854113i
$203$	−3.23607	+	2.35114i	−0.227127	+	0.165018i
$204$	0.809017	−	0.587785i	0.0566425	−	0.0411532i
$205$	−1.97214	−	6.06961i	−0.137740	−	0.423920i
$206$	−4.23607	+	13.0373i	−0.295141	+	0.908350i
$207$	0.145898	+	0.106001i	0.0101406	+	0.00736759i
$208$	−0.763932			−0.0529692
$209$	−2.11803	+	8.42075i	−0.146507	+	0.582476i
$210$	−1.61803			−0.111655
$211$	−22.7254	−	16.5110i	−1.56448	−	1.13666i	−0.932210	−	0.361917i	$-0.882122\pi$
$211$	−22.7254	−	16.5110i	−1.56448	−	1.13666i	−0.632273	−	0.774746i	$-0.717878\pi$
$212$	0.763932	−	2.35114i	0.0524671	−	0.161477i
$213$	3.23607	+	9.95959i	0.221732	+	0.682420i
$214$	6.54508	−	4.75528i	0.447413	−	0.325064i
$215$	−1.92705	+	1.40008i	−0.131424	+	0.0954850i
$216$	−1.69098	−	5.20431i	−0.115057	−	0.354108i
$217$	1.38197	−	4.25325i	0.0938140	−	0.288730i
$218$	8.23607	+	5.98385i	0.557817	+	0.405278i
$219$	18.3262			1.23837
$220$	2.80902	+	1.76336i	0.189384	+	0.118885i
$221$	−0.472136			−0.0317593
$222$	4.85410	+	3.52671i	0.325786	+	0.236697i
$223$	−7.09017	+	21.8213i	−0.474793	+	1.46126i	0.371444	+	0.928455i	$0.378863\pi$
$223$	−7.09017	+	21.8213i	−0.474793	+	1.46126i	−0.846237	+	0.532807i	$0.821137\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	0.309017	−	0.224514i	0.0206011	−	0.0149676i
$226$	−8.73607	+	6.34712i	−0.581115	+	0.422204i
$227$	−3.57295	−	10.9964i	−0.237145	−	0.729857i	−0.996830	−	0.0795655i	$-0.974647\pi$
$227$	−3.57295	−	10.9964i	−0.237145	−	0.729857i	0.759685	−	0.650292i	$-0.225353\pi$
$228$	1.30902	−	4.02874i	0.0866918	−	0.266810i
$229$	−6.23607	−	4.53077i	−0.412091	−	0.299402i	0.362357	−	0.932039i	$-0.381972\pi$
$229$	−6.23607	−	4.53077i	−0.412091	−	0.299402i	−0.774448	+	0.632638i	$0.781972\pi$
$230$	0.472136			0.0311317
$231$	−5.35410	+	0.363271i	−0.352274	+	0.0239015i
$232$	−4.00000			−0.262613
$233$	−15.6353	−	11.3597i	−1.02430	−	0.744197i	−0.0571398	−	0.998366i	$-0.518198\pi$
$233$	−15.6353	−	11.3597i	−1.02430	−	0.744197i	−0.967160	+	0.254169i	$0.918198\pi$
$234$	−0.0901699	+	0.277515i	−0.00589459	+	0.0181417i
$235$	3.47214	+	10.6861i	0.226497	+	0.697087i
$236$	1.11803	−	0.812299i	0.0727778	−	0.0528762i
$237$	−15.3262	+	11.1352i	−0.995546	+	0.723307i
$238$	−0.190983	−	0.587785i	−0.0123796	−	0.0381005i
$239$	1.32624	−	4.08174i	0.0857872	−	0.264026i	−0.898956	−	0.438038i	$-0.855673\pi$
$239$	1.32624	−	4.08174i	0.0857872	−	0.264026i	0.984743	+	0.174013i	$0.0556734\pi$
$240$	−1.30902	−	0.951057i	−0.0844967	−	0.0613904i
$241$	−13.8541			−0.892421			−0.446211	−	0.894928i	$-0.647227\pi$
$241$	−13.8541			−0.892421			−0.446211	+	0.894928i	$0.647227\pi$
$242$	9.69098	+	5.20431i	0.622960	+	0.334546i
$243$	−3.94427			−0.253025
$244$	6.47214	+	4.70228i	0.414336	+	0.301033i
$245$	−0.309017	+	0.951057i	−0.0197424	+	0.0607608i
$246$	3.19098	+	9.82084i	0.203450	+	0.626154i
$247$	−1.61803	+	1.17557i	−0.102953	+	0.0747998i
$248$	3.61803	−	2.62866i	0.229745	−	0.166920i
$249$	0.0450850	+	0.138757i	0.00285714	+	0.00879339i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−14.4721	−	10.5146i	−0.913473	−	0.663677i	0.0284177	−	0.999596i	$-0.490953\pi$
$251$	−14.4721	−	10.5146i	−0.913473	−	0.663677i	−0.941891	+	0.335919i	$0.890953\pi$
$252$	−0.381966			−0.0240616
$253$	1.56231	−	0.106001i	0.0982213	−	0.00666423i
$254$	8.18034			0.513280
$255$	−0.809017	−	0.587785i	−0.0506626	−	0.0368085i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.68034	−	5.17155i	−0.104817	−	0.322593i	0.884871	−	0.465837i	$-0.154247\pi$
$257$	−1.68034	−	5.17155i	−0.104817	−	0.322593i	−0.989687	+	0.143244i	$0.954247\pi$
$258$	3.11803	−	2.26538i	0.194120	−	0.141037i
$259$	3.00000	−	2.17963i	0.186411	−	0.135435i
$260$	0.236068	+	0.726543i	0.0146403	+	0.0450583i
$261$	−0.472136	+	1.45309i	−0.0292245	+	0.0899437i
$262$	6.59017	+	4.78804i	0.407142	+	0.295806i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$	−4.54508	−	2.85317i	−0.279731	−	0.175600i
$265$	−2.47214			−0.151862
$266$	−2.11803	−	1.53884i	−0.129865	−	0.0943524i
$267$	−1.57295	+	4.84104i	−0.0962629	+	0.296267i
$268$	1.57295	+	4.84104i	0.0960832	+	0.295714i
$269$	−11.3262	+	8.22899i	−0.690573	+	0.501731i	−0.876848	−	0.480767i	$-0.840358\pi$
$269$	−11.3262	+	8.22899i	−0.690573	+	0.501731i	0.186275	+	0.982498i	$0.440358\pi$
$270$	−4.42705	+	3.21644i	−0.269422	+	0.195746i
$271$	1.94427	+	5.98385i	0.118106	+	0.363493i	0.992582	−	0.121575i	$-0.0387946\pi$
$271$	1.94427	+	5.98385i	0.118106	+	0.363493i	−0.874476	+	0.485069i	$0.838795\pi$
$272$	0.190983	−	0.587785i	0.0115800	−	0.0356397i
$273$	−1.00000	−	0.726543i	−0.0605228	−	0.0439724i
$274$	12.8541			0.776545
$275$	0.809017	−	3.21644i	0.0487856	−	0.193959i
$276$	−0.763932			−0.0459833
$277$	13.8541	+	10.0656i	0.832412	+	0.604783i	0.920241	−	0.391353i	$-0.127993\pi$
$277$	13.8541	+	10.0656i	0.832412	+	0.604783i	−0.0878285	+	0.996136i	$0.527993\pi$
$278$	0.472136	−	1.45309i	0.0283168	−	0.0871503i
$279$	−0.527864	−	1.62460i	−0.0316024	−	0.0972622i
$280$	−0.809017	+	0.587785i	−0.0483480	+	0.0351269i
$281$	−14.3992	+	10.4616i	−0.858983	+	0.624088i	−0.927608	−	0.373555i	$-0.878139\pi$
$281$	−14.3992	+	10.4616i	−0.858983	+	0.624088i	0.0686248	+	0.997643i	$0.478139\pi$
$282$	−5.61803	−	17.2905i	−0.334549	−	1.02964i
$283$	3.05573	−	9.40456i	0.181644	−	0.559043i	−0.818230	−	0.574891i	$-0.805045\pi$
$283$	3.05573	−	9.40456i	0.181644	−	0.559043i	0.999874	+	0.0158474i	$0.00504458\pi$
$284$	5.23607	+	3.80423i	0.310703	+	0.225739i
$285$	−4.23607			−0.250923
$286$	0.944272	+	2.35114i	0.0558360	+	0.139026i
$287$	6.38197			0.376716
$288$	−0.309017	−	0.224514i	−0.0182090	−	0.0132296i
$289$	−5.13525	+	15.8047i	−0.302074	+	0.929688i
$290$	1.23607	+	3.80423i	0.0725844	+	0.223392i
$291$	18.0623	−	13.1230i	1.05883	−	0.769286i
$292$	9.16312	−	6.65740i	0.536231	−	0.389595i
$293$	4.85410	+	14.9394i	0.283580	+	0.872768i	0.986821	+	0.161817i	$0.0517354\pi$
$293$	4.85410	+	14.9394i	0.283580	+	0.872768i	−0.703241	+	0.710951i	$0.748265\pi$
$294$	0.500000	−	1.53884i	0.0291606	−	0.0897471i
$295$	−1.11803	−	0.812299i	−0.0650945	−	0.0472939i
$296$	3.70820			0.215535
$297$	−13.9271	+	11.6372i	−0.808129	+	0.675258i
$298$	7.70820			0.446524
$299$	0.291796	+	0.212002i	0.0168750	+	0.0122604i
$300$	−0.500000	+	1.53884i	−0.0288675	+	0.0888451i
$301$	−0.736068	−	2.26538i	−0.0424263	−	0.130575i
$302$	16.3262	−	11.8617i	0.939469	−	0.682564i
$303$	16.7082	−	12.1392i	0.959861	−	0.697380i
$304$	−0.809017	−	2.48990i	−0.0464003	−	0.142805i
$305$	2.47214	−	7.60845i	0.141554	−	0.435659i
$306$	−0.190983	−	0.138757i	−0.0109178	−	0.00793223i
$307$	−3.50658			−0.200131			−0.100065	−	0.994981i	$-0.531905\pi$
$307$	−3.50658			−0.200131			−0.100065	+	0.994981i	$0.531905\pi$
$308$	−2.54508	+	2.12663i	−0.145020	+	0.121176i
$309$	−22.1803			−1.26180
$310$	−3.61803	−	2.62866i	−0.205491	−	0.149298i
$311$	−0.381966	+	1.17557i	−0.0216593	+	0.0666605i	−0.961302	−	0.275497i	$-0.911158\pi$
$311$	−0.381966	+	1.17557i	−0.0216593	+	0.0666605i	0.939643	+	0.342157i	$0.111158\pi$
$312$	−0.381966	−	1.17557i	−0.0216246	−	0.0665536i
$313$	9.97214	−	7.24518i	0.563658	−	0.409522i	−0.269138	−	0.963102i	$-0.586739\pi$
$313$	9.97214	−	7.24518i	0.563658	−	0.409522i	0.832796	+	0.553580i	$0.186739\pi$
$314$	−5.00000	+	3.63271i	−0.282166	+	0.205006i
$315$	0.118034	+	0.363271i	0.00665046	+	0.0204680i
$316$	−3.61803	+	11.1352i	−0.203530	+	0.626402i
$317$	−14.4721	−	10.5146i	−0.812836	−	0.590560i	0.101815	−	0.994803i	$-0.467535\pi$
$317$	−14.4721	−	10.5146i	−0.812836	−	0.590560i	−0.914651	+	0.404243i	$0.867535\pi$
$318$	4.00000			0.224309
$319$	4.94427	+	12.3107i	0.276826	+	0.689269i
$320$	−1.00000			−0.0559017
$321$	10.5902	+	7.69421i	0.591086	+	0.429449i
$322$	−0.145898	+	0.449028i	−0.00813058	+	0.0250234i
$323$	−0.500000	−	1.53884i	−0.0278207	−	0.0856234i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$	0.618034	−	0.449028i	0.0342824	−	0.0249076i
$326$	6.98936	+	21.5110i	0.387105	+	1.19139i
$327$	−5.09017	+	15.6659i	−0.281487	+	0.866328i
$328$	5.16312	+	3.75123i	0.285086	+	0.207127i
$329$	−11.2361			−0.619464
$330$	−1.30902	+	5.20431i	−0.0720590	+	0.286488i
$331$	−3.32624			−0.182827			−0.0914133	−	0.995813i	$-0.529138\pi$
$331$	−3.32624			−0.182827			−0.0914133	+	0.995813i	$0.529138\pi$
$332$	0.0729490	+	0.0530006i	0.00400360	+	0.00290878i
$333$	0.437694	−	1.34708i	0.0239855	−	0.0738197i
$334$	−3.09017	−	9.51057i	−0.169087	−	0.520395i
$335$	4.11803	−	2.99193i	0.224992	−	0.163466i
$336$	1.30902	−	0.951057i	0.0714127	−	0.0518844i
$337$	−0.392609	−	1.20833i	−0.0213868	−	0.0658217i	0.939794	−	0.341743i	$-0.111017\pi$
$337$	−0.392609	−	1.20833i	−0.0213868	−	0.0658217i	−0.961180	+	0.275921i	$0.911017\pi$
$338$	3.83688	−	11.8087i	0.208699	−	0.642309i
$339$	−14.1353	−	10.2699i	−0.767722	−	0.557782i
$340$	−0.618034			−0.0335176
$341$	−12.5623	−	7.88597i	−0.680287	−	0.427049i
$342$	−1.00000			−0.0540738
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	0.736068	−	2.26538i	0.0396861	−	0.122141i
$345$	0.236068	+	0.726543i	0.0127095	+	0.0391157i
$346$	3.85410	−	2.80017i	0.207198	−	0.150538i
$347$	−1.64590	+	1.19581i	−0.0883564	+	0.0641947i	−0.631086	−	0.775713i	$-0.717391\pi$
$347$	−1.64590	+	1.19581i	−0.0883564	+	0.0641947i	0.542730	+	0.839907i	$0.317391\pi$
$348$	−2.00000	−	6.15537i	−0.107211	−	0.329962i
$349$	0.472136	−	1.45309i	0.0252729	−	0.0777819i	−0.937625	−	0.347649i	$-0.886980\pi$
$349$	0.472136	−	1.45309i	0.0252729	−	0.0777819i	0.962897	+	0.269868i	$0.0869799\pi$
$350$	0.809017	+	0.587785i	0.0432438	+	0.0314184i
$351$	−4.18034			−0.223130
$352$	−3.30902	+	0.224514i	−0.176371	+	0.0119666i
$353$	−12.0344			−0.640529			−0.320264	−	0.947328i	$-0.603772\pi$
$353$	−12.0344			−0.640529			−0.320264	+	0.947328i	$0.603772\pi$
$354$	1.80902	+	1.31433i	0.0961482	+	0.0698557i
$355$	2.00000	−	6.15537i	0.106149	−	0.326693i
$356$	0.972136	+	2.99193i	0.0515231	+	0.158572i
$357$	0.809017	−	0.587785i	0.0428177	−	0.0311089i
$358$	−6.59017	+	4.78804i	−0.348301	+	0.253056i
$359$	3.79837	+	11.6902i	0.200471	+	0.616985i	0.999869	+	0.0161837i	$0.00515164\pi$
$359$	3.79837	+	11.6902i	0.200471	+	0.616985i	−0.799399	+	0.600801i	$0.794848\pi$
$360$	−0.118034	+	0.363271i	−0.00622094	+	0.0191461i
$361$	9.82624	+	7.13918i	0.517170	+	0.375746i
$362$	23.1246			1.21540
$363$	−3.16312	+	17.5150i	−0.166021	+	0.919301i
$364$	−0.763932			−0.0400409
$365$	−9.16312	−	6.65740i	−0.479620	−	0.348464i
$366$	−4.00000	+	12.3107i	−0.209083	+	0.643492i
$367$	8.94427	+	27.5276i	0.466887	+	1.43693i	0.856594	+	0.515992i	$0.172577\pi$
$367$	8.94427	+	27.5276i	0.466887	+	1.43693i	−0.389706	+	0.920939i	$0.627423\pi$
$368$	−0.381966	+	0.277515i	−0.0199114	+	0.0144664i
$369$	1.97214	−	1.43284i	0.102665	−	0.0745907i
$370$	−1.14590	−	3.52671i	−0.0595724	−	0.183345i
$371$	0.763932	−	2.35114i	0.0396614	−	0.122065i
$372$	5.85410	+	4.25325i	0.303521	+	0.220521i
$373$	12.9443			0.670229			0.335114	−	0.942177i	$-0.391225\pi$
$373$	12.9443			0.670229			0.335114	+	0.942177i	$0.391225\pi$
$374$	−2.04508	+	0.138757i	−0.105749	+	0.00717497i
$375$	1.61803			0.0835549
$376$	−9.09017	−	6.60440i	−0.468790	−	0.340596i
$377$	−0.944272	+	2.90617i	−0.0486325	+	0.149675i
$378$	−1.69098	−	5.20431i	−0.0869748	−	0.267681i
$379$	13.6353	−	9.90659i	0.700396	−	0.508867i	−0.179665	−	0.983728i	$-0.557501\pi$
$379$	13.6353	−	9.90659i	0.700396	−	0.508867i	0.880061	+	0.474860i	$0.157501\pi$
$380$	−2.11803	+	1.53884i	−0.108653	+	0.0789409i
$381$	4.09017	+	12.5882i	0.209546	+	0.644916i
$382$	0.618034	−	1.90211i	0.0316214	−	0.0973206i
$383$	−3.47214	−	2.52265i	−0.177418	−	0.128902i	0.495532	−	0.868590i	$-0.334973\pi$
$383$	−3.47214	−	2.52265i	−0.177418	−	0.128902i	−0.672950	+	0.739688i	$0.734973\pi$
$384$	1.61803			0.0825700
$385$	2.80902	+	1.76336i	0.143161	+	0.0898689i
$386$	3.52786			0.179564
$387$	−0.736068	−	0.534785i	−0.0374164	−	0.0271846i
$388$	4.26393	−	13.1230i	0.216468	−	0.666221i
$389$	2.47214	+	7.60845i	0.125342	+	0.385764i	0.993963	−	0.109713i	$-0.0349933\pi$
$389$	2.47214	+	7.60845i	0.125342	+	0.385764i	−0.868621	+	0.495477i	$0.834993\pi$
$390$	−1.00000	+	0.726543i	−0.0506370	+	0.0367899i
$391$	−0.236068	+	0.171513i	−0.0119385	+	0.00867381i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	−4.07295	+	12.5352i	−0.205453	+	0.632320i
$394$	−4.38197	−	3.18368i	−0.220760	−	0.160392i
$395$	11.7082			0.589104
$396$	−0.309017	+	1.22857i	−0.0155287	+	0.0617380i
$397$	32.5410			1.63319			0.816593	−	0.577213i	$-0.195860\pi$
$397$	32.5410			1.63319			0.816593	+	0.577213i	$0.195860\pi$
$398$	2.61803	+	1.90211i	0.131230	+	0.0953443i
$399$	1.30902	−	4.02874i	0.0655328	−	0.201689i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−22.2533	+	16.1680i	−1.11128	+	0.807389i	−0.982864	−	0.184331i	$-0.940988\pi$
$401$	−22.2533	+	16.1680i	−1.11128	+	0.807389i	−0.128412	+	0.991721i	$0.540988\pi$
$402$	−6.66312	+	4.84104i	−0.332326	+	0.241449i
$403$	−1.05573	−	3.24920i	−0.0525896	−	0.161854i
$404$	3.94427	−	12.1392i	0.196235	−	0.603949i
$405$	−6.23607	−	4.53077i	−0.309873	−	0.225136i
$406$	−4.00000			−0.198517
$407$	−4.58359	−	11.4127i	−0.227200	−	0.565705i
$408$	1.00000			0.0495074
$409$	−25.3262	−	18.4006i	−1.25230	−	0.909851i	−0.253949	−	0.967218i	$-0.581729\pi$
$409$	−25.3262	−	18.4006i	−1.25230	−	0.909851i	−0.998353	+	0.0573671i	$0.981729\pi$
$410$	1.97214	−	6.06961i	0.0973969	−	0.299757i
$411$	6.42705	+	19.7804i	0.317023	+	0.975697i
$412$	−11.0902	+	8.05748i	−0.546373	+	0.396964i
$413$	1.11803	−	0.812299i	0.0550149	−	0.0399706i
$414$	0.0557281	+	0.171513i	0.00273889	+	0.00842942i
$415$	0.0278640	−	0.0857567i	0.00136779	−	0.00420963i
$416$	−0.618034	−	0.449028i	−0.0303016	−	0.0220154i
$417$	2.47214			0.121061
$418$	−6.66312	+	5.56758i	−0.325904	+	0.272319i
$419$	−14.7426			−0.720225			−0.360113	−	0.932909i	$-0.617262\pi$
$419$	−14.7426			−0.720225			−0.360113	+	0.932909i	$0.617262\pi$
$420$	−1.30902	−	0.951057i	−0.0638735	−	0.0464068i
$421$	2.61803	−	8.05748i	0.127595	−	0.392698i	−0.866770	−	0.498708i	$-0.833808\pi$
$421$	2.61803	−	8.05748i	0.127595	−	0.392698i	0.994365	+	0.106011i	$0.0338078\pi$
$422$	−8.68034	−	26.7153i	−0.422552	−	1.30048i
$423$	−3.47214	+	2.52265i	−0.168821	+	0.122656i
$424$	2.00000	−	1.45309i	0.0971286	−	0.0705680i
$425$	0.190983	+	0.587785i	0.00926404	+	0.0285118i
$426$	−3.23607	+	9.95959i	−0.156788	+	0.482544i
$427$	6.47214	+	4.70228i	0.313209	+	0.227559i
$428$	8.09017			0.391053
$429$	−3.14590	+	2.62866i	−0.151885	+	0.126913i
$430$	−2.38197			−0.114869
$431$	−15.9443	−	11.5842i	−0.768009	−	0.557991i	0.133348	−	0.991069i	$-0.457427\pi$
$431$	−15.9443	−	11.5842i	−0.768009	−	0.557991i	−0.901356	+	0.433078i	$0.857427\pi$
$432$	1.69098	−	5.20431i	0.0813575	−	0.250393i
$433$	0.371323	+	1.14281i	0.0178446	+	0.0549202i	0.959582	−	0.281428i	$-0.0908081\pi$
$433$	0.371323	+	1.14281i	0.0178446	+	0.0549202i	−0.941738	+	0.336348i	$0.890808\pi$
$434$	3.61803	−	2.62866i	0.173671	−	0.126180i
$435$	−5.23607	+	3.80423i	−0.251050	+	0.182399i
$436$	3.14590	+	9.68208i	0.150661	+	0.463687i
$437$	−0.381966	+	1.17557i	−0.0182719	+	0.0562352i
$438$	14.8262	+	10.7719i	0.708425	+	0.514701i
$439$	24.3607			1.16267			0.581336	−	0.813664i	$-0.302530\pi$
$439$	24.3607			1.16267			0.581336	+	0.813664i	$0.302530\pi$
$440$	1.23607	+	3.07768i	0.0589272	+	0.146723i
$441$	−0.381966			−0.0181889
$442$	−0.381966	−	0.277515i	−0.0181683	−	0.0132000i
$443$	−8.15248	+	25.0907i	−0.387336	+	1.19210i	0.547436	+	0.836848i	$0.315604\pi$
$443$	−8.15248	+	25.0907i	−0.387336	+	1.19210i	−0.934772	+	0.355249i	$0.884396\pi$
$444$	1.85410	+	5.70634i	0.0879918	+	0.270811i
$445$	2.54508	−	1.84911i	0.120649	−	0.0876563i
$446$	−18.5623	+	13.4863i	−0.878951	+	0.638595i
$447$	3.85410	+	11.8617i	0.182293	+	0.561039i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−22.4443	−	16.3067i	−1.05921	−	0.769562i	−0.0852685	−	0.996358i	$-0.527175\pi$
$449$	−22.4443	−	16.3067i	−1.05921	−	0.769562i	−0.973942	+	0.226796i	$0.927175\pi$
$450$	0.381966			0.0180061
$451$	5.16312	−	20.5272i	0.243122	−	0.966589i
$452$	−10.7984			−0.507913
$453$	26.4164	+	19.1926i	1.24115	+	0.901749i
$454$	3.57295	−	10.9964i	0.167687	−	0.516087i
$455$	0.236068	+	0.726543i	0.0110670	+	0.0340608i
$456$	3.42705	−	2.48990i	0.160486	−	0.116600i
$457$	4.39919	−	3.19620i	0.205785	−	0.149512i	−0.480119	−	0.877203i	$-0.659407\pi$
$457$	4.39919	−	3.19620i	0.205785	−	0.149512i	0.685905	+	0.727691i	$0.259407\pi$
$458$	−2.38197	−	7.33094i	−0.111302	−	0.342552i
$459$	1.04508	−	3.21644i	0.0487804	−	0.150131i
$460$	0.381966	+	0.277515i	0.0178093	+	0.0129392i
$461$	39.1246			1.82221			0.911107	−	0.412169i	$-0.135229\pi$
$461$	39.1246			1.82221			0.911107	+	0.412169i	$0.135229\pi$
$462$	−4.54508	−	2.85317i	−0.211456	−	0.132741i
$463$	−30.6525			−1.42454			−0.712271	−	0.701905i	$-0.752333\pi$
$463$	−30.6525			−1.42454			−0.712271	+	0.701905i	$0.752333\pi$
$464$	−3.23607	−	2.35114i	−0.150231	−	0.109149i
$465$	2.23607	−	6.88191i	0.103695	−	0.319141i
$466$	−5.97214	−	18.3803i	−0.276654	−	0.851453i
$467$	0.763932	−	0.555029i	0.0353506	−	0.0256837i	−0.569970	−	0.821666i	$-0.693045\pi$
$467$	0.763932	−	0.555029i	0.0353506	−	0.0256837i	0.605320	+	0.795982i	$0.293045\pi$
$468$	−0.236068	+	0.171513i	−0.0109122	+	0.00792821i
$469$	1.57295	+	4.84104i	0.0726320	+	0.223538i
$470$	−3.47214	+	10.6861i	−0.160158	+	0.492915i
$471$	−8.09017	−	5.87785i	−0.372775	−	0.270837i
$472$	1.38197			0.0636101
$473$	−7.88197	+	0.534785i	−0.362413	+	0.0245894i
$474$	−18.9443			−0.870139
$475$	2.11803	+	1.53884i	0.0971821	+	0.0706069i
$476$	0.190983	−	0.587785i	0.00875369	−	0.0269411i
$477$	−0.291796	−	0.898056i	−0.0133604	−	0.0411192i
$478$	3.47214	−	2.52265i	0.158812	−	0.115384i
$479$	−18.7082	+	13.5923i	−0.854800	+	0.621048i	−0.926465	−	0.376380i	$-0.877169\pi$
$479$	−18.7082	+	13.5923i	−0.854800	+	0.621048i	0.0716656	+	0.997429i	$0.477169\pi$
$480$	−0.500000	−	1.53884i	−0.0228218	−	0.0702382i
$481$	0.875388	−	2.69417i	0.0399143	−	0.122843i
$482$	−11.2082	−	8.14324i	−0.510520	−	0.370914i
$483$	−0.763932			−0.0347601
$484$	4.78115	+	9.90659i	0.217325	+	0.450300i
$485$	−13.7984			−0.626552
$486$	−3.19098	−	2.31838i	−0.144746	−	0.105164i
$487$	−10.4377	+	32.1239i	−0.472977	+	1.45567i	0.375690	+	0.926746i	$0.377406\pi$
$487$	−10.4377	+	32.1239i	−0.472977	+	1.45567i	−0.848667	+	0.528928i	$0.822594\pi$
$488$	2.47214	+	7.60845i	0.111908	+	0.344418i
$489$	−29.6074	+	21.5110i	−1.33889	+	0.972762i
$490$	−0.809017	+	0.587785i	−0.0365477	+	0.0265534i
$491$	8.31966	+	25.6053i	0.375461	+	1.15555i	0.943167	+	0.332319i	$0.107831\pi$
$491$	8.31966	+	25.6053i	0.375461	+	1.15555i	−0.567706	+	0.823231i	$0.692169\pi$
$492$	−3.19098	+	9.82084i	−0.143861	+	0.442757i
$493$	−2.00000	−	1.45309i	−0.0900755	−	0.0654437i
$494$	−2.00000			−0.0899843
$495$	1.26393	−	0.0857567i	0.0568095	−	0.00385448i
$496$	4.47214			0.200805
$497$	5.23607	+	3.80423i	0.234870	+	0.170643i
$498$	−0.0450850	+	0.138757i	−0.00202031	+	0.00621786i
$499$	−0.500000	−	1.53884i	−0.0223831	−	0.0688880i	0.939241	−	0.343258i	$-0.111531\pi$
$499$	−0.500000	−	1.53884i	−0.0223831	−	0.0688880i	−0.961624	+	0.274370i	$0.911531\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	13.0902	−	9.51057i	0.584826	−	0.424901i
$502$	−5.52786	−	17.0130i	−0.246721	−	0.759328i
$503$	−3.79837	+	11.6902i	−0.169361	+	0.521240i	−0.999331	−	0.0365680i	$-0.988357\pi$
$503$	−3.79837	+	11.6902i	−0.169361	+	0.521240i	0.829970	+	0.557808i	$0.188357\pi$
$504$	−0.309017	−	0.224514i	−0.0137647	−	0.0100006i
$505$	−12.7639			−0.567988
$506$	1.32624	+	0.832544i	0.0589585	+	0.0370111i
$507$	20.0902			0.892236
$508$	6.61803	+	4.80828i	0.293628	+	0.213333i
$509$	1.79837	−	5.53483i	0.0797115	−	0.245327i	−0.903257	−	0.429099i	$-0.858831\pi$
$509$	1.79837	−	5.53483i	0.0797115	−	0.245327i	0.982969	+	0.183773i	$0.0588310\pi$
$510$	−0.309017	−	0.951057i	−0.0136835	−	0.0421135i
$511$	9.16312	−	6.65740i	0.405353	−	0.294506i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−4.42705	−	13.6251i	−0.195459	−	0.601561i
$514$	1.68034	−	5.17155i	0.0741166	−	0.228107i
$515$	11.0902	+	8.05748i	0.488691	+	0.355055i
$516$	3.85410			0.169667
$517$	−9.09017	+	36.1401i	−0.399785	+	1.58944i
$518$	3.70820			0.162929
$519$	6.23607	+	4.53077i	0.273733	+	0.198879i
$520$	−0.236068	+	0.726543i	−0.0103523	+	0.0318610i
$521$	11.6074	+	35.7239i	0.508529	+	1.56509i	0.794756	+	0.606929i	$0.207599\pi$
$521$	11.6074	+	35.7239i	0.508529	+	1.56509i	−0.286227	+	0.958162i	$0.592401\pi$
$522$	−1.23607	+	0.898056i	−0.0541012	+	0.0393068i
$523$	29.0623	−	21.1150i	1.27081	−	0.923295i	0.271572	−	0.962418i	$-0.412457\pi$
$523$	29.0623	−	21.1150i	1.27081	−	0.923295i	0.999234	+	0.0391237i	$0.0124566\pi$
$524$	2.51722	+	7.74721i	0.109965	+	0.338438i
$525$	−0.500000	+	1.53884i	−0.0218218	+	0.0671606i
$526$	−9.70820	−	7.05342i	−0.423298	−	0.307544i
$527$	2.76393			0.120399
$528$	−2.00000	−	4.97980i	−0.0870388	−	0.216718i
$529$	−22.7771			−0.990308
$530$	−2.00000	−	1.45309i	−0.0868744	−	0.0631180i
$531$	0.163119	−	0.502029i	0.00707876	−	0.0217862i
$532$	−0.809017	−	2.48990i	−0.0350753	−	0.107951i
$533$	3.94427	−	2.86568i	0.170845	−	0.124126i
$534$	−4.11803	+	2.99193i	−0.178205	+	0.129473i
$535$	−2.50000	−	7.69421i	−0.108084	−	0.332650i
$536$	−1.57295	+	4.84104i	−0.0679410	+	0.209101i
$537$	−10.6631	−	7.74721i	−0.460148	−	0.334317i
$538$	−14.0000			−0.603583
$539$	−2.54508	+	2.12663i	−0.109625	+	0.0916003i
$540$	−5.47214			−0.235483
$541$	−14.4164	−	10.4741i	−0.619810	−	0.450318i	0.233045	−	0.972466i	$-0.425131\pi$
$541$	−14.4164	−	10.4741i	−0.619810	−	0.450318i	−0.852855	+	0.522148i	$0.825131\pi$
$542$	−1.94427	+	5.98385i	−0.0835136	+	0.257029i
$543$	11.5623	+	35.5851i	0.496186	+	1.52710i
$544$	0.500000	−	0.363271i	0.0214373	−	0.0155751i
$545$	8.23607	−	5.98385i	0.352794	−	0.256320i
$546$	−0.381966	−	1.17557i	−0.0163466	−	0.0503098i
$547$	8.31559	−	25.5928i	0.355549	−	1.09427i	−0.600141	−	0.799894i	$-0.704889\pi$
$547$	8.31559	−	25.5928i	0.355549	−	1.09427i	0.955690	−	0.294374i	$-0.0951110\pi$
$548$	10.3992	+	7.55545i	0.444231	+	0.322753i
$549$	3.05573			0.130415
$550$	2.54508	−	2.12663i	0.108523	−	0.0906797i
$551$	−10.4721			−0.446128
$552$	−0.618034	−	0.449028i	−0.0263053	−	0.0191119i
$553$	−3.61803	+	11.1352i	−0.153854	+	0.473515i
$554$	5.29180	+	16.2865i	0.224827	+	0.691946i
$555$	4.85410	−	3.52671i	0.206045	−	0.149701i
$556$	1.23607	−	0.898056i	0.0524210	−	0.0380861i
$557$	1.34752	+	4.14725i	0.0570964	+	0.175725i	0.975537	−	0.219833i	$-0.0705513\pi$
$557$	1.34752	+	4.14725i	0.0570964	+	0.175725i	−0.918441	+	0.395558i	$0.870551\pi$
$558$	0.527864	−	1.62460i	0.0223463	−	0.0687747i
$559$	−1.47214	−	1.06957i	−0.0622647	−	0.0452380i
$560$	−1.00000			−0.0422577
$561$	−1.23607	−	3.07768i	−0.0521868	−	0.129940i
$562$	−17.7984			−0.750779
$563$	−35.3435	−	25.6785i	−1.48955	−	1.08222i	−0.974320	−	0.225169i	$-0.927707\pi$
$563$	−35.3435	−	25.6785i	−1.48955	−	1.08222i	−0.515229	−	0.857052i	$-0.672293\pi$
$564$	5.61803	−	17.2905i	0.236562	−	0.728063i
$565$	3.33688	+	10.2699i	0.140384	+	0.432056i
$566$	8.00000	−	5.81234i	0.336265	−	0.244311i
$567$	6.23607	−	4.53077i	0.261890	−	0.190274i
$568$	2.00000	+	6.15537i	0.0839181	+	0.258273i
$569$	−6.01064	+	18.4989i	−0.251979	+	0.775512i	0.742431	+	0.669923i	$0.233673\pi$
$569$	−6.01064	+	18.4989i	−0.251979	+	0.775512i	−0.994410	+	0.105589i	$0.966327\pi$
$570$	−3.42705	−	2.48990i	−0.143543	−	0.104290i
$571$	26.8328			1.12292			0.561459	−	0.827504i	$-0.310240\pi$
$571$	26.8328			1.12292			0.561459	+	0.827504i	$0.310240\pi$
$572$	−0.618034	+	2.45714i	−0.0258413	+	0.102738i
$573$	3.23607			0.135189
$574$	5.16312	+	3.75123i	0.215504	+	0.156573i
$575$	0.145898	−	0.449028i	0.00608437	−	0.0187258i
$576$	−0.118034	−	0.363271i	−0.00491808	−	0.0151363i
$577$	−19.6803	+	14.2986i	−0.819303	+	0.595259i	−0.916513	−	0.400005i	$-0.869008\pi$
$577$	−19.6803	+	14.2986i	−0.819303	+	0.595259i	0.0972096	+	0.995264i	$0.469008\pi$
$578$	−13.4443	+	9.76784i	−0.559208	+	0.406288i
$579$	1.76393	+	5.42882i	0.0733065	+	0.225614i
$580$	−1.23607	+	3.80423i	−0.0513249	+	0.157962i
$581$	0.0729490	+	0.0530006i	0.00302644	+	0.00219883i
$582$	22.3262			0.925452
$583$	−6.94427	−	4.35926i	−0.287602	−	0.180542i
$584$	11.3262			0.468683
$585$	0.236068	+	0.171513i	0.00976021	+	0.00709121i
$586$	−4.85410	+	14.9394i	−0.200521	+	0.617141i
$587$	−3.28115	−	10.0984i	−0.135428	−	0.416804i	0.860229	−	0.509909i	$-0.170321\pi$
$587$	−3.28115	−	10.0984i	−0.135428	−	0.416804i	−0.995656	+	0.0931050i	$0.970321\pi$
$588$	1.30902	−	0.951057i	0.0539830	−	0.0392209i
$589$	9.47214	−	6.88191i	0.390293	−	0.283564i
$590$	−0.427051	−	1.31433i	−0.0175814	−	0.0541100i
$591$	2.70820	−	8.33499i	0.111401	−	0.342856i
$592$	3.00000	+	2.17963i	0.123299	+	0.0895821i
$593$	−12.6180			−0.518161			−0.259080	−	0.965856i	$-0.583419\pi$
$593$	−12.6180			−0.518161			−0.259080	+	0.965856i	$0.583419\pi$
$594$	−18.1074	+	1.22857i	−0.742955	+	0.0504089i
$595$	−0.618034			−0.0253369
$596$	6.23607	+	4.53077i	0.255439	+	0.185588i
$597$	−1.61803	+	4.97980i	−0.0662217	+	0.203810i
$598$	0.111456	+	0.343027i	0.00455778	+	0.0140274i
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	−0.908951	−	0.416904i	$-0.863115\pi$
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	0.115618	+	0.993294i	$0.463115\pi$
$600$	−1.30902	+	0.951057i	−0.0534404	+	0.0388267i
$601$	2.02786	+	6.24112i	0.0827183	+	0.254581i	0.983859	−	0.178946i	$-0.0572688\pi$
$601$	2.02786	+	6.24112i	0.0827183	+	0.254581i	−0.901141	+	0.433527i	$0.857269\pi$
$602$	0.736068	−	2.26538i	0.0299999	−	0.0923302i
$603$	1.57295	+	1.14281i	0.0640554	+	0.0465390i
$604$	20.1803			0.821126
$605$	7.94427	−	7.60845i	0.322981	−	0.309328i
$606$	20.6525			0.838949
$607$	27.5066	+	19.9847i	1.11646	+	0.811154i	0.983668	−	0.179990i	$-0.0576067\pi$
$607$	27.5066	+	19.9847i	1.11646	+	0.811154i	0.132789	+	0.991144i	$0.457607\pi$
$608$	0.809017	−	2.48990i	0.0328100	−	0.100979i
$609$	−2.00000	−	6.15537i	−0.0810441	−	0.249428i
$610$	6.47214	−	4.70228i	0.262049	−	0.190390i
$611$	−6.94427	+	5.04531i	−0.280935	+	0.204111i
$612$	−0.0729490	−	0.224514i	−0.00294879	−	0.00907544i
$613$	14.8541	−	45.7162i	0.599952	−	1.84646i	0.0716033	−	0.997433i	$-0.477188\pi$
$613$	14.8541	−	45.7162i	0.599952	−	1.84646i	0.528348	−	0.849028i	$-0.322812\pi$
$614$	−2.83688	−	2.06111i	−0.114487	−	0.0831798i
$615$	10.3262			0.416394
$616$	−3.30902	+	0.224514i	−0.133324	+	0.00904593i
$617$	13.2016			0.531477			0.265739	−	0.964045i	$-0.414384\pi$
$617$	13.2016			0.531477			0.265739	+	0.964045i	$0.414384\pi$
$618$	−17.9443	−	13.0373i	−0.721824	−	0.524436i
$619$	6.31559	−	19.4374i	0.253845	−	0.781255i	−0.740210	−	0.672376i	$-0.765274\pi$
$619$	6.31559	−	19.4374i	0.253845	−	0.781255i	0.994055	−	0.108879i	$-0.0347262\pi$
$620$	−1.38197	−	4.25325i	−0.0555011	−	0.170815i
$621$	−2.09017	+	1.51860i	−0.0838756	+	0.0609392i
$622$	−1.00000	+	0.726543i	−0.0400963	+	0.0291317i
$623$	0.972136	+	2.99193i	0.0389478	+	0.119869i
$624$	0.381966	−	1.17557i	0.0152909	−	0.0470605i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	12.3262			0.492656
$627$	−11.8992	−	7.46969i	−0.475208	−	0.298311i
$628$	−6.18034			−0.246622
$629$	1.85410	+	1.34708i	0.0739279	+	0.0537118i
$630$	−0.118034	+	0.363271i	−0.00470259	+	0.0144731i
$631$	−6.41641	−	19.7477i	−0.255433	−	0.786142i	−0.993744	−	0.111682i	$-0.964376\pi$
$631$	−6.41641	−	19.7477i	−0.255433	−	0.786142i	0.738311	−	0.674461i	$-0.235624\pi$
$632$	−9.47214	+	6.88191i	−0.376781	+	0.273748i
$633$	36.7705	−	26.7153i	1.46150	−	1.06184i
$634$	−5.52786	−	17.0130i	−0.219540	−	0.675673i
$635$	2.52786	−	7.77997i	0.100315	−	0.308739i
$636$	3.23607	+	2.35114i	0.128318	+	0.0932288i
$637$	−0.763932			−0.0302681
$638$	−3.23607	+	12.8658i	−0.128117	+	0.509360i
$639$	2.47214			0.0977962
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	7.62461	−	23.4661i	0.301154	−	0.926857i	−0.679930	−	0.733277i	$-0.737990\pi$
$641$	7.62461	−	23.4661i	0.301154	−	0.926857i	0.981084	−	0.193580i	$-0.0620100\pi$
$642$	4.04508	+	12.4495i	0.159647	+	0.491342i
$643$	−5.30902	+	3.85723i	−0.209367	+	0.152114i	−0.687527	−	0.726158i	$-0.741304\pi$
$643$	−5.30902	+	3.85723i	−0.209367	+	0.152114i	0.478160	+	0.878273i	$0.341304\pi$
$644$	−0.381966	+	0.277515i	−0.0150516	+	0.0109356i
$645$	−1.19098	−	3.66547i	−0.0468949	−	0.144328i
$646$	0.500000	−	1.53884i	0.0196722	−	0.0605449i
$647$	6.38197	+	4.63677i	0.250901	+	0.182290i	0.706126	−	0.708086i	$-0.250441\pi$
$647$	6.38197	+	4.63677i	0.250901	+	0.182290i	−0.455225	+	0.890376i	$0.650441\pi$
$648$	7.70820			0.302807
$649$	−1.70820	−	4.25325i	−0.0670529	−	0.166955i
$650$	0.763932			0.0299639
$651$	5.85410	+	4.25325i	0.229440	+	0.166698i
$652$	−6.98936	+	21.5110i	−0.273724	+	0.842437i
$653$	−1.85410	−	5.70634i	−0.0725566	−	0.223306i	0.908201	−	0.418533i	$-0.137456\pi$
$653$	−1.85410	−	5.70634i	−0.0725566	−	0.223306i	−0.980758	+	0.195227i	$0.937456\pi$
$654$	−13.3262	+	9.68208i	−0.521097	+	0.378599i
$655$	6.59017	−	4.78804i	0.257499	−	0.187084i
$656$	1.97214	+	6.06961i	0.0769990	+	0.236978i
$657$	1.33688	−	4.11450i	0.0521567	−	0.160522i
$658$	−9.09017	−	6.60440i	−0.354372	−	0.257466i
$659$	21.0902			0.821556			0.410778	−	0.911735i	$-0.365257\pi$
$659$	21.0902			0.821556			0.410778	+	0.911735i	$0.365257\pi$
$660$	−4.11803	+	3.44095i	−0.160294	+	0.133939i
$661$	37.7771			1.46936			0.734679	−	0.678415i	$-0.237333\pi$
$661$	37.7771			1.46936			0.734679	+	0.678415i	$0.237333\pi$
$662$	−2.69098	−	1.95511i	−0.104588	−	0.0759876i
$663$	0.236068	−	0.726543i	0.00916812	−	0.0282166i
$664$	0.0278640	+	0.0857567i	0.00108133	+	0.00332801i
$665$	−2.11803	+	1.53884i	−0.0821338	+	0.0596737i
$666$	1.14590	−	0.832544i	0.0444026	−	0.0322604i
$667$	0.583592	+	1.79611i	0.0225968	+	0.0695457i
$668$	3.09017	−	9.51057i	0.119562	−	0.367975i
$669$	−30.0344	−	21.8213i	−1.16120	−	0.843660i
$670$	5.09017			0.196650
$671$	20.3607	−	17.0130i	0.786015	−	0.656780i
$672$	1.61803			0.0624170
$673$	−11.2082	−	8.14324i	−0.432045	−	0.313899i	0.350421	−	0.936592i	$-0.386038\pi$
$673$	−11.2082	−	8.14324i	−0.432045	−	0.313899i	−0.782466	+	0.622693i	$0.786038\pi$
$674$	0.392609	−	1.20833i	0.0151227	−	0.0465430i
$675$	1.69098	+	5.20431i	0.0650860	+	0.200314i
$676$	10.0451	−	7.29818i	0.386349	−	0.280699i
$677$	8.85410	−	6.43288i	0.340291	−	0.247236i	−0.404494	−	0.914541i	$-0.632552\pi$
$677$	8.85410	−	6.43288i	0.340291	−	0.247236i	0.744785	+	0.667305i	$0.232552\pi$
$678$	−5.39919	−	16.6170i	−0.207355	−	0.638172i
$679$	4.26393	−	13.1230i	0.163635	−	0.503616i
$680$	−0.500000	−	0.363271i	−0.0191741	−	0.0139308i
$681$	18.7082			0.716900
$682$	−5.52786	−	13.7638i	−0.211673	−	0.527044i
$683$	−45.3050			−1.73355			−0.866773	−	0.498703i	$-0.833810\pi$
$683$	−45.3050			−1.73355			−0.866773	+	0.498703i	$0.833810\pi$
$684$	−0.809017	−	0.587785i	−0.0309335	−	0.0224745i
$685$	3.97214	−	12.2250i	0.151768	−	0.467092i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	10.0902	−	7.33094i	0.384964	−	0.279693i
$688$	1.92705	−	1.40008i	0.0734681	−	0.0533777i
$689$	−0.583592	−	1.79611i	−0.0222331	−	0.0684264i
$690$	−0.236068	+	0.726543i	−0.00898695	+	0.0276590i
$691$	2.59017	+	1.88187i	0.0985347	+	0.0715897i	0.635962	−	0.771721i	$-0.280604\pi$
$691$	2.59017	+	1.88187i	0.0985347	+	0.0715897i	−0.537427	+	0.843310i	$0.680604\pi$
$692$	4.76393			0.181098
$693$	−0.309017	+	1.22857i	−0.0117386	+	0.0466696i
$694$	−2.03444			−0.0772264
$695$	−1.23607	−	0.898056i	−0.0468867	−	0.0340652i
$696$	2.00000	−	6.15537i	0.0758098	−	0.233319i
$697$	1.21885	+	3.75123i	0.0461671	+	0.142088i
$698$	1.23607	−	0.898056i	0.0467859	−	0.0339919i
$699$	25.2984	−	18.3803i	0.956872	−	0.695208i
$700$	0.309017	+	0.951057i	0.0116797	+	0.0359466i
$701$	−1.29180	+	3.97574i	−0.0487905	+	0.150162i	−0.972484	−	0.232972i	$-0.925155\pi$
$701$	−1.29180	+	3.97574i	−0.0487905	+	0.150162i	0.923693	+	0.383133i	$0.125155\pi$
$702$	−3.38197	−	2.45714i	−0.127644	−	0.0927389i
$703$	9.70820			0.366152
$704$	−2.80902	−	1.76336i	−0.105869	−	0.0664590i
$705$	−18.1803			−0.684711
$706$	−9.73607	−	7.07367i	−0.366422	−	0.266221i
$707$	3.94427	−	12.1392i	0.148340	−	0.456542i
$708$	0.690983	+	2.12663i	0.0259687	+	0.0799235i
$709$	−26.5066	+	19.2582i	−0.995475	+	0.723255i	−0.961113	−	0.276154i	$-0.910940\pi$
$709$	−26.5066	+	19.2582i	−0.995475	+	0.723255i	−0.0343621	+	0.999409i	$0.510940\pi$
$710$	5.23607	−	3.80423i	0.196506	−	0.142770i
$711$	1.38197	+	4.25325i	0.0518278	+	0.159509i
$712$	−0.972136	+	2.99193i	−0.0364323	+	0.112127i
$713$	−1.70820	−	1.24108i	−0.0639727	−	0.0464789i
$714$	1.00000			0.0374241
$715$	2.52786	−	0.171513i	0.0945368	−	0.00641424i
$716$	−8.14590			−0.304427
$717$	5.61803	+	4.08174i	0.209809	+	0.152435i
$718$	−3.79837	+	11.6902i	−0.141754	+	0.436274i
$719$	1.74265	+	5.36331i	0.0649897	+	0.200018i	0.978279	−	0.207295i	$-0.0664659\pi$
$719$	1.74265	+	5.36331i	0.0649897	+	0.200018i	−0.913289	+	0.407313i	$0.866466\pi$
$720$	−0.309017	+	0.224514i	−0.0115164	+	0.00836714i
$721$	−11.0902	+	8.05748i	−0.413020	+	0.300076i
$722$	3.75329	+	11.5514i	0.139683	+	0.429900i
$723$	6.92705	−	21.3193i	0.257620	−	0.792872i
$724$	18.7082	+	13.5923i	0.695285	+	0.505154i
$725$	4.00000			0.148556
$726$	−12.8541	+	12.3107i	−0.477060	+	0.456894i
$727$	−25.3050			−0.938509			−0.469254	−	0.883063i	$-0.655477\pi$
$727$	−25.3050			−0.938509			−0.469254	+	0.883063i	$0.655477\pi$
$728$	−0.618034	−	0.449028i	−0.0229059	−	0.0166421i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	−3.50000	−	10.7719i	−0.129541	−	0.398686i
$731$	1.19098	−	0.865300i	0.0440501	−	0.0320043i
$732$	−10.4721	+	7.60845i	−0.387061	+	0.281216i
$733$	−5.94427	−	18.2946i	−0.219557	−	0.675726i	−0.998799	−	0.0490028i	$-0.984396\pi$
$733$	−5.94427	−	18.2946i	−0.219557	−	0.675726i	0.779242	−	0.626723i	$-0.215604\pi$
$734$	−8.94427	+	27.5276i	−0.330139	+	1.01606i
$735$	−1.30902	−	0.951057i	−0.0482838	−	0.0350802i
$736$	−0.472136			−0.0174032
$737$	16.8435	−	1.14281i	0.620437	−	0.0420961i
$738$	2.43769			0.0897328
$739$	21.8262	+	15.8577i	0.802891	+	0.583335i	0.911761	−	0.410721i	$-0.134723\pi$
$739$	21.8262	+	15.8577i	0.802891	+	0.583335i	−0.108870	+	0.994056i	$0.534723\pi$
$740$	1.14590	−	3.52671i	0.0421240	−	0.129644i
$741$	−1.00000	−	3.07768i	−0.0367359	−	0.113062i
$742$	2.00000	−	1.45309i	0.0734223	−	0.0533444i
$743$	17.7984	−	12.9313i	0.652959	−	0.474402i	−0.211319	−	0.977417i	$-0.567776\pi$
$743$	17.7984	−	12.9313i	0.652959	−	0.474402i	0.864278	+	0.503015i	$0.167776\pi$
$744$	2.23607	+	6.88191i	0.0819782	+	0.252303i
$745$	2.38197	−	7.33094i	0.0872685	−	0.268585i
$746$	10.4721	+	7.60845i	0.383412	+	0.278565i
$747$	0.0344419			0.00126016
$748$	−1.73607	−	1.08981i	−0.0634769	−	0.0398475i
$749$	8.09017			0.295608
$750$	1.30902	+	0.951057i	0.0477985	+	0.0347277i
$751$	−15.2705	+	46.9978i	−0.557229	+	1.71497i	0.132755	+	0.991149i	$0.457618\pi$
$751$	−15.2705	+	46.9978i	−0.557229	+	1.71497i	−0.689984	+	0.723825i	$0.742382\pi$
$752$	−3.47214	−	10.6861i	−0.126616	−	0.389683i
$753$	23.4164	−	17.0130i	0.853341	−	0.619989i
$754$	−2.47214	+	1.79611i	−0.0900299	+	0.0654105i
$755$	−6.23607	−	19.1926i	−0.226954	−	0.698492i
$756$	1.69098	−	5.20431i	0.0615005	−	0.189279i
$757$	−21.0902	−	15.3229i	−0.766535	−	0.556920i	0.134373	−	0.990931i	$-0.457098\pi$
$757$	−21.0902	−	15.3229i	−0.766535	−	0.556920i	−0.900908	+	0.434010i	$0.857098\pi$
$758$	16.8541			0.612169
$759$	−0.618034	+	2.45714i	−0.0224332	+	0.0891886i
$760$	−2.61803			−0.0949661
$761$	−5.44427	−	3.95550i	−0.197355	−	0.143387i	0.484719	−	0.874670i	$-0.338922\pi$
$761$	−5.44427	−	3.95550i	−0.197355	−	0.143387i	−0.682074	+	0.731283i	$0.738922\pi$
$762$	−4.09017	+	12.5882i	−0.148171	+	0.456024i
$763$	3.14590	+	9.68208i	0.113889	+	0.350515i
$764$	1.61803	−	1.17557i	0.0585384	−	0.0425306i
$765$	−0.190983	+	0.138757i	−0.00690501	+	0.00501678i
$766$	−1.32624	−	4.08174i	−0.0479189	−	0.147479i
$767$	0.326238	−	1.00406i	0.0117798	−	0.0362544i
$768$	1.30902	+	0.951057i	0.0472351	+	0.0343183i
$769$	25.4164			0.916539			0.458270	−	0.888813i	$-0.348469\pi$
$769$	25.4164			0.916539			0.458270	+	0.888813i	$0.348469\pi$
$770$	1.23607	+	3.07768i	0.0445448	+	0.110912i
$771$	8.79837			0.316866
$772$	2.85410	+	2.07363i	0.102721	+	0.0746314i
$773$	11.2361	−	34.5811i	0.404133	−	1.24379i	−0.517484	−	0.855693i	$-0.673131\pi$
$773$	11.2361	−	34.5811i	0.404133	−	1.24379i	0.921617	−	0.388101i	$-0.126869\pi$
$774$	−0.281153	−	0.865300i	−0.0101058	−	0.0311026i
$775$	−3.61803	+	2.62866i	−0.129964	+	0.0944241i
$776$	11.1631	−	8.11048i	0.400733	−	0.291149i
$777$	1.85410	+	5.70634i	0.0665155	+	0.204714i
$778$	−2.47214	+	7.60845i	−0.0886304	+	0.272776i
$779$	13.5172	+	9.82084i	0.484305	+	0.351868i
$780$	−1.23607			−0.0442583
$781$	16.4721	−	13.7638i	0.589419	−	0.492508i
$782$	−0.291796			−0.0104346
$783$	−17.7082	−	12.8658i	−0.632840	−	0.459785i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	1.90983	+	5.87785i	0.0681648	+	0.209790i
$786$	−10.6631	+	7.74721i	−0.380341	+	0.276334i
$787$	−11.3541	+	8.24924i	−0.404730	+	0.294054i	−0.771465	−	0.636272i	$-0.780476\pi$
$787$	−11.3541	+	8.24924i	−0.404730	+	0.294054i	0.366735	+	0.930326i	$0.380476\pi$
$788$	−1.67376	−	5.15131i	−0.0596253	−	0.183508i
$789$	6.00000	−	18.4661i	0.213606	−	0.657411i
$790$	9.47214	+	6.88191i	0.337003	+	0.244847i
$791$	−10.7984			−0.383946
$792$	−0.972136	+	0.812299i	−0.0345433	+	0.0288638i
$793$	6.11146			0.217024
$794$	26.3262	+	19.1271i	0.934283	+	0.678796i
$795$	1.23607	−	3.80423i	0.0438388	−	0.134922i
$796$	1.00000	+	3.07768i	0.0354441	+	0.109086i
$797$	−27.8885	+	20.2622i	−0.987863	+	0.717724i	−0.959452	−	0.281872i	$-0.909045\pi$
$797$	−27.8885	+	20.2622i	−0.987863	+	0.717724i	−0.0284109	+	0.999596i	$0.509045\pi$
$798$	3.42705	−	2.48990i	0.121316	−	0.0881414i
$799$	−2.14590	−	6.60440i	−0.0759164	−	0.233647i
$800$	−0.309017	+	0.951057i	−0.0109254	+	0.0336249i
$801$	0.972136	+	0.706298i	0.0343487	+	0.0249558i
$802$	−27.5066			−0.971291
$803$	−14.0000	−	34.8586i	−0.494049	−	1.23013i
$804$	−8.23607			−0.290464
$805$	0.381966	+	0.277515i	0.0134625	+	0.00978110i
$806$	1.05573	−	3.24920i	0.0371864	−	0.114448i
$807$	−7.00000	−	21.5438i	−0.246412	−	0.758377i
$808$	10.3262	−	7.50245i	0.363276	−	0.263935i
$809$	−21.3885	+	15.5397i	−0.751981	+	0.546346i	−0.896440	−	0.443164i	$-0.853856\pi$
$809$	−21.3885	+	15.5397i	−0.751981	+	0.546346i	0.144459	+	0.989511i	$0.453856\pi$
$810$	−2.38197	−	7.33094i	−0.0836938	−	0.257583i
$811$	15.3885	−	47.3611i	0.540365	−	1.66307i	−0.191398	−	0.981513i	$-0.561302\pi$
$811$	15.3885	−	47.3611i	0.540365	−	1.66307i	0.731763	−	0.681559i	$-0.238698\pi$
$812$	−3.23607	−	2.35114i	−0.113564	−	0.0825089i
$813$	−10.1803			−0.357040
$814$	3.00000	−	11.9272i	0.105150	−	0.418049i
$815$	22.6180			0.792275
$816$	0.809017	+	0.587785i	0.0283213	+	0.0205766i
$817$	1.92705	−	5.93085i	0.0674190	−	0.207494i
$818$	−9.67376	−	29.7728i	−0.338235	−	1.04098i
$819$	−0.236068	+	0.171513i	−0.00824888	+	0.00599316i
$820$	5.16312	−	3.75123i	0.180304	−	0.130998i
$821$	15.2918	+	47.0633i	0.533687	+	1.64252i	0.746468	+	0.665421i	$0.231748\pi$
$821$	15.2918	+	47.0633i	0.533687	+	1.64252i	−0.212781	+	0.977100i	$0.568252\pi$
$822$	−6.42705	+	19.7804i	−0.224169	+	0.689922i
$823$	−41.6525	−	30.2623i	−1.45191	−	1.05488i	−0.985379	−	0.170374i	$-0.945502\pi$
$823$	−41.6525	−	30.2623i	−1.45191	−	1.05488i	−0.466535	−	0.884503i	$-0.654498\pi$
$824$	−13.7082			−0.477548
$825$	4.54508	+	2.85317i	0.158240	+	0.0993346i
$826$	1.38197			0.0480847
$827$	−20.8262	−	15.1311i	−0.724199	−	0.526162i	0.163524	−	0.986539i	$-0.447714\pi$
$827$	−20.8262	−	15.1311i	−0.724199	−	0.526162i	−0.887723	+	0.460378i	$0.847714\pi$
$828$	−0.0557281	+	0.171513i	−0.00193669	+	0.00596050i
$829$	0.909830	+	2.80017i	0.0315997	+	0.0972539i	0.965612	−	0.259986i	$-0.0837179\pi$
$829$	0.909830	+	2.80017i	0.0315997	+	0.0972539i	−0.934013	+	0.357240i	$0.883718\pi$
$830$	0.0729490	−	0.0530006i	0.00253210	−	0.00183968i
$831$	−22.4164	+	16.2865i	−0.777617	+	0.564972i
$832$	−0.236068	−	0.726543i	−0.00818418	−	0.0251883i
$833$	0.190983	−	0.587785i	0.00661717	−	0.0203656i
$834$	2.00000	+	1.45309i	0.0692543	+	0.0503162i
$835$	−10.0000			−0.346064
$836$	−8.66312	+	0.587785i	−0.299620	+	0.0203290i
$837$	24.4721			0.845881
$838$	−11.9271	−	8.66551i	−0.412013	−	0.299345i
$839$	−3.29180	+	10.1311i	−0.113645	+	0.349765i	−0.991662	−	0.128865i	$-0.958866\pi$
$839$	−3.29180	+	10.1311i	−0.113645	+	0.349765i	0.878017	+	0.478630i	$0.158866\pi$
$840$	−0.500000	−	1.53884i	−0.0172516	−	0.0530951i
$841$	10.5172	−	7.64121i	0.362663	−	0.263490i
$842$	6.85410	−	4.97980i	0.236208	−	0.171615i
$843$	−8.89919	−	27.3889i	−0.306504	−	0.943323i
$844$	8.68034	−	26.7153i	0.298790	−	0.919580i
$845$	−10.0451	−	7.29818i	−0.345561	−	0.251065i
$846$	−4.29180			−0.147555
$847$	4.78115	+	9.90659i	0.164282	+	0.340395i
$848$	2.47214			0.0848935
$849$	12.9443	+	9.40456i	0.444246	+	0.322764i
$850$	−0.190983	+	0.587785i	−0.00655066	+	0.0201609i
$851$	−0.541020	−	1.66509i	−0.0185459	−	0.0570785i
$852$	−8.47214	+	6.15537i	−0.290251	+	0.210879i
$853$	29.3607	−	21.3318i	1.00529	−	0.730386i	0.0420745	−	0.999114i	$-0.486603\pi$
$853$	29.3607	−	21.3318i	1.00529	−	0.730386i	0.963216	+	0.268728i	$0.0866033\pi$
$854$	2.47214	+	7.60845i	0.0845948	+	0.260356i
$855$	−0.309017	+	0.951057i	−0.0105682	+	0.0325254i
$856$	6.54508	+	4.75528i	0.223706	+	0.162532i
$857$	47.6869			1.62895			0.814477	−	0.580196i	$-0.197024\pi$
$857$	47.6869			1.62895			0.814477	+	0.580196i	$0.197024\pi$
$858$	−4.09017	+	0.277515i	−0.139636	+	0.00947419i
$859$	43.8541			1.49628			0.748141	−	0.663539i	$-0.230947\pi$
$859$	43.8541			1.49628			0.748141	+	0.663539i	$0.230947\pi$
$860$	−1.92705	−	1.40008i	−0.0657119	−	0.0477425i
$861$	−3.19098	+	9.82084i	−0.108748	+	0.334693i
$862$	−6.09017	−	18.7436i	−0.207432	−	0.638410i
$863$	−32.5623	+	23.6579i	−1.10843	+	0.805324i	−0.982416	−	0.186704i	$-0.940220\pi$
$863$	−32.5623	+	23.6579i	−1.10843	+	0.805324i	−0.126018	+	0.992028i	$0.540220\pi$
$864$	4.42705	−	3.21644i	0.150611	−	0.109426i
$865$	−1.47214	−	4.53077i	−0.0500541	−	0.154051i
$866$	−0.371323	+	1.14281i	−0.0126181	+	0.0388344i
$867$	−21.7533	−	15.8047i	−0.738780	−	0.536755i
$868$	4.47214			0.151794
$869$	32.8885	+	20.6457i	1.11567	+	0.700358i
$870$	−6.47214			−0.219426
$871$	3.14590	+	2.28563i	0.106595	+	0.0774456i
$872$	−3.14590	+	9.68208i	−0.106534	+	0.327877i
$873$	−1.62868	−	5.01255i	−0.0551224	−	0.169649i
$874$	−1.00000	+	0.726543i	−0.0338255	+	0.0245757i
$875$	0.809017	−	0.587785i	0.0273498	−	0.0198708i
$876$	5.66312	+	17.4293i	0.191339	+	0.588881i
$877$	−6.52786	+	20.0907i	−0.220430	+	0.678415i	0.778293	+	0.627901i	$0.216086\pi$
$877$	−6.52786	+	20.0907i	−0.220430	+	0.678415i	−0.998723	+	0.0505135i	$0.983914\pi$
$878$	19.7082	+	14.3188i	0.665120	+	0.483238i
$879$	−25.4164			−0.857274
$880$	−0.809017	+	3.21644i	−0.0272720	+	0.108426i
$881$	34.3394			1.15692			0.578462	−	0.815709i	$-0.303653\pi$
$881$	34.3394			1.15692			0.578462	+	0.815709i	$0.303653\pi$
$882$	−0.309017	−	0.224514i	−0.0104051	−	0.00755978i
$883$	10.6246	−	32.6992i	0.357547	−	1.10042i	−0.596971	−	0.802262i	$-0.703629\pi$
$883$	10.6246	−	32.6992i	0.357547	−	1.10042i	0.954518	−	0.298153i	$-0.0963706\pi$
$884$	−0.145898	−	0.449028i	−0.00490708	−	0.0151024i
$885$	1.80902	−	1.31433i	0.0608094	−	0.0441806i
$886$	−21.3435	+	15.5069i	−0.717048	+	0.520966i
$887$	−6.79837	−	20.9232i	−0.228267	−	0.702534i	−0.997944	−	0.0640996i	$-0.979582\pi$
$887$	−6.79837	−	20.9232i	−0.228267	−	0.702534i	0.769676	−	0.638434i	$-0.220418\pi$
$888$	−1.85410	+	5.70634i	−0.0622196	+	0.191492i
$889$	6.61803	+	4.80828i	0.221962	+	0.161265i
$890$	3.14590			0.105451
$891$	−9.52786	−	23.7234i	−0.319195	−	0.794764i
$892$	−22.9443			−0.768231
$893$	−23.7984	−	17.2905i	−0.796382	−	0.578606i
$894$	−3.85410	+	11.8617i	−0.128900	+	0.396715i
$895$	2.51722	+	7.74721i	0.0841414	+	0.258961i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−0.472136	+	0.343027i	−0.0157642	+	0.0114533i
$898$	−8.57295	−	26.3848i	−0.286083	−	0.880473i
$899$	5.52786	−	17.0130i	0.184365	−	0.567416i
$900$	0.309017	+	0.224514i	0.0103006	+	0.00748380i
$901$	1.52786			0.0509005
$902$	16.2426	−	13.5721i	0.540821	−	0.451900i
$903$	3.85410			0.128256
$904$	−8.73607	−	6.34712i	−0.290557	−	0.211102i
$905$	7.14590	−	21.9928i	0.237538	−	0.731066i
$906$	10.0902	+	31.0543i	0.335223	+	1.03171i
$907$	−16.8262	+	12.2250i	−0.558706	+	0.405924i	−0.830985	−	0.556295i	$-0.812223\pi$
$907$	−16.8262	+	12.2250i	−0.558706	+	0.405924i	0.272279	+	0.962218i	$0.412223\pi$
$908$	9.35410	−	6.79615i	0.310427	−	0.225538i
$909$	−1.50658	−	4.63677i	−0.0499700	−	0.153792i
$910$	−0.236068	+	0.726543i	−0.00782558	+	0.0240847i
$911$	21.0902	+	15.3229i	0.698749	+	0.507671i	0.879524	−	0.475854i	$-0.157861\pi$
$911$	21.0902	+	15.3229i	0.698749	+	0.507671i	−0.180776	+	0.983524i	$0.557861\pi$
$912$	4.23607			0.140270
$913$	0.229490	−	0.191758i	0.00759502	−	0.00634626i
$914$	5.43769			0.179863
$915$	10.4721	+	7.60845i	0.346198	+	0.251528i
$916$	2.38197	−	7.33094i	0.0787024	−	0.242221i
$917$	2.51722	+	7.74721i	0.0831260	+	0.255835i
$918$	2.73607	−	1.98787i	0.0903037	−	0.0656095i
$919$	17.1803	−	12.4822i	0.566727	−	0.411751i	−0.267188	−	0.963645i	$-0.586094\pi$
$919$	17.1803	−	12.4822i	0.566727	−	0.411751i	0.833915	+	0.551893i	$0.186094\pi$
$920$	0.145898	+	0.449028i	0.00481012	+	0.0148040i
$921$	1.75329	−	5.39607i	0.0577728	−	0.177806i
$922$	31.6525	+	22.9969i	1.04242	+	0.757362i
$923$	4.94427			0.162743
$924$	−2.00000	−	4.97980i	−0.0657952	−	0.163823i
$925$	−3.70820			−0.121925
$926$	−24.7984	−	18.0171i	−0.814925	−	0.592078i
$927$	−1.61803	+	4.97980i	−0.0531432	+	0.163558i
$928$	−1.23607	−	3.80423i	−0.0405759	−	0.124880i
$929$	−15.9164	+	11.5639i	−0.522200	+	0.379401i	−0.817432	−	0.576025i	$-0.804603\pi$
$929$	−15.9164	+	11.5639i	−0.522200	+	0.379401i	0.295232	+	0.955426i	$0.404603\pi$
$930$	5.85410	−	4.25325i	0.191964	−	0.139470i
$931$	−0.809017	−	2.48990i	−0.0265145	−	0.0816031i
$932$	5.97214	−	18.3803i	0.195624	−	0.602068i
$933$	−1.61803	−	1.17557i	−0.0529721	−	0.0384865i
$934$	0.944272			0.0308975
$935$	−0.500000	+	1.98787i	−0.0163517	+	0.0650103i
$936$	−0.291796			−0.00953765
$937$	22.9721	+	16.6902i	0.750467	+	0.545246i	0.895972	−	0.444111i	$-0.146481\pi$
$937$	22.9721	+	16.6902i	0.750467	+	0.545246i	−0.145505	+	0.989358i	$0.546481\pi$
$938$	−1.57295	+	4.84104i	−0.0513586	+	0.158066i
$939$	6.16312	+	18.9681i	0.201126	+	0.619002i
$940$	−9.09017	+	6.60440i	−0.296489	+	0.215412i
$941$	−43.5066	+	31.6094i	−1.41827	+	1.03044i	−0.426220	+	0.904619i	$0.640155\pi$
$941$	−43.5066	+	31.6094i	−1.41827	+	1.03044i	−0.992053	+	0.125817i	$0.959845\pi$
$942$	−3.09017	−	9.51057i	−0.100683	−	0.309871i
$943$	0.931116	−	2.86568i	0.0303213	−	0.0933194i
$944$	1.11803	+	0.812299i	0.0363889	+	0.0264381i
$945$	−5.47214			−0.178009
$946$	−6.69098	−	4.20025i	−0.217543	−	0.136562i
$947$	51.3394			1.66831			0.834153	−	0.551533i	$-0.185957\pi$
$947$	51.3394			1.66831			0.834153	+	0.551533i	$0.185957\pi$
$948$	−15.3262	−	11.1352i	−0.497773	−	0.361653i
$949$	2.67376	−	8.22899i	0.0867940	−	0.267124i
$950$	0.809017	+	2.48990i	0.0262480	+	0.0807830i
$951$	23.4164	−	17.0130i	0.759329	−	0.551685i
$952$	0.500000	−	0.363271i	0.0162051	−	0.0117737i
$953$	8.38854	+	25.8173i	0.271732	+	0.836304i	0.990066	+	0.140606i	$0.0449049\pi$
$953$	8.38854	+	25.8173i	0.271732	+	0.836304i	−0.718334	+	0.695698i	$0.755095\pi$
$954$	0.291796	−	0.898056i	0.00944725	−	0.0290756i
$955$	−1.61803	−	1.17557i	−0.0523584	−	0.0380406i
$956$	4.29180			0.138807
$957$	−21.4164	+	1.45309i	−0.692294	+	0.0469716i
$958$	−23.1246			−0.747122
$959$	10.3992	+	7.55545i	0.335807	+	0.243978i
$960$	0.500000	−	1.53884i	0.0161374	−	0.0496659i
$961$	−3.39919	−	10.4616i	−0.109651	−	0.337472i
$962$	2.29180	−	1.66509i	0.0738905	−	0.0536846i
$963$	2.50000	−	1.81636i	0.0805614	−	0.0585313i
$964$	−4.28115	−	13.1760i	−0.137887	−	0.424371i
$965$	1.09017	−	3.35520i	0.0350938	−	0.108008i
$966$	−0.618034	−	0.449028i	−0.0198849	−	0.0144472i
$967$	−26.0000			−0.836104			−0.418052	−	0.908423i	$-0.637287\pi$
$967$	−26.0000			−0.836104			−0.418052	+	0.908423i	$0.637287\pi$
$968$	−1.95492	+	10.8249i	−0.0628333	+	0.347925i
$969$	2.61803			0.0841034
$970$	−11.1631	−	8.11048i	−0.358426	−	0.260412i
$971$	−6.58359	+	20.2622i	−0.211278	+	0.650245i	0.788119	+	0.615522i	$0.211055\pi$
$971$	−6.58359	+	20.2622i	−0.211278	+	0.650245i	−0.999397	+	0.0347230i	$0.988945\pi$
$972$	−1.21885	−	3.75123i	−0.0390945	−	0.120321i
$973$	1.23607	−	0.898056i	0.0396265	−	0.0287904i
$974$	−27.3262	+	19.8537i	−0.875589	+	0.636153i
$975$	0.381966	+	1.17557i	0.0122327	+	0.0376484i
$976$	−2.47214	+	7.60845i	−0.0791311	+	0.243541i
$977$	−25.5066	−	18.5316i	−0.816028	−	0.592879i	0.0995442	−	0.995033i	$-0.468262\pi$
$977$	−25.5066	−	18.5316i	−0.816028	−	0.592879i	−0.915572	+	0.402154i	$0.868262\pi$
$978$	−36.5967			−1.17023
$979$	10.4098	−	0.706298i	0.332700	−	0.0225734i
$980$	−1.00000			−0.0319438
$981$	3.14590	+	2.28563i	0.100441	+	0.0729745i
$982$	−8.31966	+	25.6053i	−0.265491	+	0.817097i
$983$	9.65248	+	29.7073i	0.307866	+	0.947515i	0.978592	+	0.205809i	$0.0659827\pi$
$983$	9.65248	+	29.7073i	0.307866	+	0.947515i	−0.670726	+	0.741705i	$0.734017\pi$
$984$	−8.35410	+	6.06961i	−0.266319	+	0.193492i
$985$	−4.38197	+	3.18368i	−0.139621	+	0.101441i
$986$	−0.763932	−	2.35114i	−0.0243286	−	0.0748756i
$987$	5.61803	−	17.2905i	0.178824	−	0.550364i
$988$	−1.61803	−	1.17557i	−0.0514765	−	0.0373999i
$989$	−1.12461			−0.0357606
$990$	1.07295	+	0.673542i	0.0341006	+	0.0214066i
$991$	−61.2361			−1.94523			−0.972614	−	0.232427i	$-0.925333\pi$
$991$	−61.2361			−1.94523			−0.972614	+	0.232427i	$0.925333\pi$
$992$	3.61803	+	2.62866i	0.114873	+	0.0834599i
$993$	1.66312	−	5.11855i	0.0527775	−	0.162432i
$994$	2.00000	+	6.15537i	0.0634361	+	0.195236i
$995$	2.61803	−	1.90211i	0.0829973	−	0.0603010i
$996$	−0.118034	+	0.0857567i	−0.00374005	+	0.00271731i
$997$	3.97871	+	12.2452i	0.126007	+	0.387810i	0.994083	−	0.108621i	$-0.0346435\pi$
$997$	3.97871	+	12.2452i	0.126007	+	0.387810i	−0.868076	+	0.496431i	$0.834644\pi$
$998$	0.500000	−	1.53884i	0.0158272	−	0.0487112i
$999$	16.4164	+	11.9272i	0.519392	+	0.377360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.c.631.1	yes	4
11.3	even	5	inner	770.2.n.c.421.1	✓	4
11.5	even	5		8470.2.a.bk.1.1		2
11.6	odd	10		8470.2.a.bx.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.c.421.1	✓	4	11.3	even	5	inner
770.2.n.c.631.1	yes	4	1.1	even	1	trivial
8470.2.a.bk.1.1		2	11.5	even	5
8470.2.a.bx.1.1		2	11.6	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +1.00000 q^{10} +(3.30902 - 0.224514i) q^{11} -1.61803 q^{12} +(0.618034 + 0.449028i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.500000 + 1.53884i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.809017 + 2.48990i) q^{19} +(0.809017 + 0.587785i) q^{20} -1.61803 q^{21} +(2.80902 + 1.76336i) q^{22} +0.472136 q^{23} +(-1.30902 - 0.951057i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.236068 + 0.726543i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(1.23607 + 3.80423i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(-3.61803 - 2.62866i) q^{31} -1.00000 q^{32} +(-1.30902 + 5.20431i) q^{33} -0.618034 q^{34} +(0.809017 + 0.587785i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(-1.14590 - 3.52671i) q^{37} +(-2.11803 + 1.53884i) q^{38} +(-1.00000 + 0.726543i) q^{39} +(0.309017 + 0.951057i) q^{40} +(1.97214 - 6.06961i) q^{41} +(-1.30902 - 0.951057i) q^{42} -2.38197 q^{43} +(1.23607 + 3.07768i) q^{44} +0.381966 q^{45} +(0.381966 + 0.277515i) q^{46} +(-3.47214 + 10.6861i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-0.309017 - 0.951057i) q^{51} +(-0.236068 + 0.726543i) q^{52} +(-2.00000 - 1.45309i) q^{53} -5.47214 q^{54} +(2.54508 - 2.12663i) q^{55} -1.00000 q^{56} +(-3.42705 - 2.48990i) q^{57} +(-1.23607 + 3.80423i) q^{58} +(-0.427051 - 1.31433i) q^{59} +(-1.30902 + 0.951057i) q^{60} +(6.47214 - 4.70228i) q^{61} +(-1.38197 - 4.25325i) q^{62} +(-0.118034 + 0.363271i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.763932 q^{65} +(-4.11803 + 3.44095i) q^{66} +5.09017 q^{67} +(-0.500000 - 0.363271i) q^{68} +(-0.236068 + 0.726543i) q^{69} +(0.309017 + 0.951057i) q^{70} +(5.23607 - 3.80423i) q^{71} +(-0.309017 + 0.224514i) q^{72} +(-3.50000 - 10.7719i) q^{73} +(1.14590 - 3.52671i) q^{74} +(1.30902 + 0.951057i) q^{75} -2.61803 q^{76} +(1.23607 + 3.07768i) q^{77} -1.23607 q^{78} +(9.47214 + 6.88191i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(5.16312 - 3.75123i) q^{82} +(0.0729490 - 0.0530006i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(-0.190983 + 0.587785i) q^{85} +(-1.92705 - 1.40008i) q^{86} -6.47214 q^{87} +(-0.809017 + 3.21644i) q^{88} +3.14590 q^{89} +(0.309017 + 0.224514i) q^{90} +(-0.236068 + 0.726543i) q^{91} +(0.145898 + 0.449028i) q^{92} +(5.85410 - 4.25325i) q^{93} +(-9.09017 + 6.60440i) q^{94} +(0.809017 + 2.48990i) q^{95} +(0.500000 - 1.53884i) q^{96} +(-11.1631 - 8.11048i) q^{97} -1.00000 q^{98} +(1.07295 + 0.673542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + 11 q^{11} - 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 4 q^{18} - q^{19} + q^{20} - 2 q^{21} + 9 q^{22} - 16 q^{23} - 3 q^{24} - q^{25} - 8 q^{26} - 11 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 10 q^{31} - 4 q^{32} - 3 q^{33} + 2 q^{34} + q^{35} + 4 q^{36} - 18 q^{37} - 4 q^{38} - 4 q^{39} - q^{40} - 10 q^{41} - 3 q^{42} - 14 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 2 q^{48} - q^{49} + q^{50} + q^{51} + 8 q^{52} - 8 q^{53} - 4 q^{54} - q^{55} - 4 q^{56} - 7 q^{57} + 4 q^{58} + 5 q^{59} - 3 q^{60} + 8 q^{61} - 10 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} - 12 q^{66} - 2 q^{67} - 2 q^{68} + 8 q^{69} - q^{70} + 12 q^{71} + q^{72} - 14 q^{73} + 18 q^{74} + 3 q^{75} - 6 q^{76} - 4 q^{77} + 4 q^{78} + 20 q^{79} + q^{80} - 14 q^{81} + 5 q^{82} + 7 q^{83} - 2 q^{84} - 3 q^{85} - q^{86} - 8 q^{87} - q^{88} + 26 q^{89} - q^{90} + 8 q^{91} + 14 q^{92} + 10 q^{93} - 14 q^{94} + q^{95} + 2 q^{96} - 29 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + 11 * q^11 - 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 2 * q^17 - 4 * q^18 - q^19 + q^20 - 2 * q^21 + 9 * q^22 - 16 * q^23 - 3 * q^24 - q^25 - 8 * q^26 - 11 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 10 * q^31 - 4 * q^32 - 3 * q^33 + 2 * q^34 + q^35 + 4 * q^36 - 18 * q^37 - 4 * q^38 - 4 * q^39 - q^40 - 10 * q^41 - 3 * q^42 - 14 * q^43 - 4 * q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 2 * q^48 - q^49 + q^50 + q^51 + 8 * q^52 - 8 * q^53 - 4 * q^54 - q^55 - 4 * q^56 - 7 * q^57 + 4 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 10 * q^62 + 4 * q^63 - q^64 + 12 * q^65 - 12 * q^66 - 2 * q^67 - 2 * q^68 + 8 * q^69 - q^70 + 12 * q^71 + q^72 - 14 * q^73 + 18 * q^74 + 3 * q^75 - 6 * q^76 - 4 * q^77 + 4 * q^78 + 20 * q^79 + q^80 - 14 * q^81 + 5 * q^82 + 7 * q^83 - 2 * q^84 - 3 * q^85 - q^86 - 8 * q^87 - q^88 + 26 * q^89 - q^90 + 8 * q^91 + 14 * q^92 + 10 * q^93 - 14 * q^94 + q^95 + 2 * q^96 - 29 * q^97 - 4 * q^98 + 11 * q^99

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