LMFDB - Embedded newform 770.2.n.k.421.2

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 18 x^{14} - 35 x^{13} + 89 x^{12} - 185 x^{11} + 837 x^{10} - 1660 x^{9} + 4196 x^{8} + \cdots + 25 $ x^16 - 5x^15 + 18x^14 - 35x^13 + 89x^12 - 185x^11 + 837x^10 - 1660x^9 + 4196x^8 - 8420x^7 + 13485x^6 - 14630x^5 + 11615x^4 - 5200x^3 + 1425x^2 - 225*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$0.347506 - 1.06951i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.k.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.347506 - 1.06951i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.909784 + 0.660997i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.40395 - 1.02003i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.347506 - 1.06951i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.909784 + 0.660997i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.40395 - 1.02003i) q^{9} -1.00000 q^{10} +(-2.21655 + 2.46717i) q^{11} -1.12455 q^{12} +(-5.71931 + 4.15532i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.347506 - 1.06951i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.78688 - 2.02478i) q^{17} +(-0.536261 + 1.65044i) q^{18} +(1.06183 + 3.26798i) q^{19} +(0.809017 - 0.587785i) q^{20} +1.12455 q^{21} +(0.343063 - 3.29883i) q^{22} +3.63913 q^{23} +(0.909784 - 0.660997i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.18458 - 6.72345i) q^{26} +(-4.30817 - 3.13007i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.68628 + 8.26751i) q^{29} +(0.347506 + 1.06951i) q^{30} +(3.65793 - 2.65764i) q^{31} +1.00000 q^{32} +(3.40894 + 1.51328i) q^{33} +3.44477 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.536261 - 1.65044i) q^{36} +(-0.241211 + 0.742372i) q^{37} +(-2.77991 - 2.01972i) q^{38} +(6.43167 + 4.67288i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-1.55091 - 4.77322i) q^{41} +(-0.909784 + 0.660997i) q^{42} -5.39500 q^{43} +(1.66146 + 2.87046i) q^{44} +1.73538 q^{45} +(-2.94412 + 2.13903i) q^{46} +(3.03694 + 9.34674i) q^{47} +(-0.347506 + 1.06951i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.19708 + 3.68423i) q^{51} +(2.18458 + 6.72345i) q^{52} +(-9.19999 + 6.68419i) q^{53} +5.32519 q^{54} +(-3.24339 + 0.693123i) q^{55} -1.00000 q^{56} +(3.12616 - 2.27129i) q^{57} +(-2.68628 - 8.26751i) q^{58} +(-3.25231 + 10.0096i) q^{59} +(-0.909784 - 0.660997i) q^{60} +(-0.369102 - 0.268168i) q^{61} +(-1.39720 + 4.30015i) q^{62} +(0.536261 + 1.65044i) q^{63} +(-0.809017 + 0.587785i) q^{64} -7.06945 q^{65} +(-3.64737 + 0.779455i) q^{66} +10.4937 q^{67} +(-2.78688 + 2.02478i) q^{68} +(-1.26462 - 3.89211i) q^{69} +(0.309017 - 0.951057i) q^{70} +(5.51245 + 4.00503i) q^{71} +(1.40395 + 1.02003i) q^{72} +(-4.67084 + 14.3754i) q^{73} +(-0.241211 - 0.742372i) q^{74} +(0.909784 - 0.660997i) q^{75} +3.43616 q^{76} +(-1.66146 - 2.87046i) q^{77} -7.94999 q^{78} +(13.1358 - 9.54373i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-0.241755 + 0.744045i) q^{81} +(4.06034 + 2.95001i) q^{82} +(-5.98951 - 4.35163i) q^{83} +(0.347506 - 1.06951i) q^{84} +(-1.06449 - 3.27617i) q^{85} +(4.36464 - 3.17110i) q^{86} +9.77573 q^{87} +(-3.03137 - 1.34567i) q^{88} -4.97143 q^{89} +(-1.40395 + 1.02003i) q^{90} +(-2.18458 - 6.72345i) q^{91} +(1.12455 - 3.46102i) q^{92} +(-4.11354 - 2.98866i) q^{93} +(-7.95082 - 5.77661i) q^{94} +(-1.06183 + 3.26798i) q^{95} +(-0.347506 - 1.06951i) q^{96} +(-2.33800 + 1.69866i) q^{97} +1.00000 q^{98} +(-0.595344 + 5.72472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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
$3$	−0.347506	−	1.06951i	−0.200633	−	0.617485i	−0.999865	−	0.0164615i	$-0.994760\pi$
$3$	−0.347506	−	1.06951i	−0.200633	−	0.617485i	0.799232	−	0.601023i	$-0.205240\pi$
$4$	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
$6$	0.909784	+	0.660997i	0.371418	+	0.269851i
$7$	−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
$9$	1.40395	−	1.02003i	0.467983	−	0.340010i
$10$	−1.00000			−0.316228
$11$	−2.21655	+	2.46717i	−0.668315	+	0.743878i
$11$	−2.21655	+	2.46717i	−0.668315	+	0.743878i
$12$	−1.12455			−0.324631
$13$	−5.71931	+	4.15532i	−1.58625	+	1.15248i	−0.677195	+	0.735804i	$0.736805\pi$
$13$	−5.71931	+	4.15532i	−1.58625	+	1.15248i	−0.909056	+	0.416675i	$0.863195\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	0.347506	−	1.06951i	0.0897258	−	0.276148i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.78688	−	2.02478i	−0.675917	−	0.491082i	0.196084	−	0.980587i	$-0.437178\pi$
$17$	−2.78688	−	2.02478i	−0.675917	−	0.491082i	−0.872001	+	0.489505i	$0.837178\pi$
$18$	−0.536261	+	1.65044i	−0.126398	+	0.389013i
$19$	1.06183	+	3.26798i	0.243601	+	0.749726i	0.995863	+	0.0908627i	$0.0289624\pi$
$19$	1.06183	+	3.26798i	0.243601	+	0.749726i	−0.752263	+	0.658863i	$0.771038\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	1.12455			0.245398
$22$	0.343063	−	3.29883i	0.0731413	−	0.703314i
$23$	3.63913			0.758812			0.379406	−	0.925230i	$-0.376128\pi$
$23$	3.63913			0.758812			0.379406	+	0.925230i	$0.376128\pi$
$24$	0.909784	−	0.660997i	0.185709	−	0.134925i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	2.18458	−	6.72345i	0.428432	−	1.31858i
$27$	−4.30817	−	3.13007i	−0.829108	−	0.602382i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	−2.68628	+	8.26751i	−0.498829	+	1.53524i	0.312073	+	0.950058i	$0.398977\pi$
$29$	−2.68628	+	8.26751i	−0.498829	+	1.53524i	−0.810903	+	0.585181i	$0.801023\pi$
$30$	0.347506	+	1.06951i	0.0634457	+	0.195266i
$31$	3.65793	−	2.65764i	0.656983	−	0.477326i	−0.208660	−	0.977988i	$-0.566910\pi$
$31$	3.65793	−	2.65764i	0.656983	−	0.477326i	0.865643	+	0.500662i	$0.166910\pi$
$32$	1.00000			0.176777
$33$	3.40894	+	1.51328i	0.593420	+	0.263428i
$34$	3.44477			0.590773
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	−0.536261	−	1.65044i	−0.0893768	−	0.275074i
$37$	−0.241211	+	0.742372i	−0.0396549	+	0.122045i	−0.968924	−	0.247358i	$-0.920438\pi$
$37$	−0.241211	+	0.742372i	−0.0396549	+	0.122045i	0.929269	+	0.369403i	$0.120438\pi$
$38$	−2.77991	−	2.01972i	−0.450961	−	0.327642i
$39$	6.43167	+	4.67288i	1.02989	+	0.748260i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	−1.55091	−	4.77322i	−0.242212	−	0.745451i	−0.996083	−	0.0884286i	$-0.971815\pi$
$41$	−1.55091	−	4.77322i	−0.242212	−	0.745451i	0.753871	−	0.657023i	$-0.228185\pi$
$42$	−0.909784	+	0.660997i	−0.140383	+	0.101994i
$43$	−5.39500			−0.822729			−0.411365	−	0.911471i	$-0.634948\pi$
$43$	−5.39500			−0.822729			−0.411365	+	0.911471i	$0.634948\pi$
$44$	1.66146	+	2.87046i	0.250475	+	0.432738i
$45$	1.73538			0.258695
$46$	−2.94412	+	2.13903i	−0.434087	+	0.315383i
$47$	3.03694	+	9.34674i	0.442983	+	1.36336i	0.884680	+	0.466198i	$0.154377\pi$
$47$	3.03694	+	9.34674i	0.442983	+	1.36336i	−0.441697	+	0.897164i	$0.645623\pi$
$48$	−0.347506	+	1.06951i	−0.0501582	+	0.154371i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−1.19708	+	3.68423i	−0.167625	+	0.515896i
$52$	2.18458	+	6.72345i	0.302947	+	0.932375i
$53$	−9.19999	+	6.68419i	−1.26372	+	0.918144i	−0.998934	−	0.0461646i	$-0.985300\pi$
$53$	−9.19999	+	6.68419i	−1.26372	+	0.918144i	−0.264782	+	0.964308i	$0.585300\pi$
$54$	5.32519			0.724667
$55$	−3.24339	+	0.693123i	−0.437339	+	0.0934607i
$56$	−1.00000			−0.133631
$57$	3.12616	−	2.27129i	0.414070	−	0.300839i
$58$	−2.68628	−	8.26751i	−0.352726	−	1.08558i
$59$	−3.25231	+	10.0096i	−0.423415	+	1.30314i	0.481089	+	0.876671i	$0.340241\pi$
$59$	−3.25231	+	10.0096i	−0.423415	+	1.30314i	−0.904504	+	0.426465i	$0.859759\pi$
$60$	−0.909784	−	0.660997i	−0.117453	−	0.0853343i
$61$	−0.369102	−	0.268168i	−0.0472586	−	0.0343354i	0.563905	−	0.825840i	$-0.309298\pi$
$61$	−0.369102	−	0.268168i	−0.0472586	−	0.0343354i	−0.611164	+	0.791504i	$0.709298\pi$
$62$	−1.39720	+	4.30015i	−0.177445	+	0.546120i
$63$	0.536261	+	1.65044i	0.0675625	+	0.207936i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−7.06945			−0.876858
$66$	−3.64737	+	0.779455i	−0.448960	+	0.0959443i
$67$	10.4937			1.28201			0.641006	−	0.767536i	$-0.278517\pi$
$67$	10.4937			1.28201			0.641006	+	0.767536i	$0.278517\pi$
$68$	−2.78688	+	2.02478i	−0.337958	+	0.245541i
$69$	−1.26462	−	3.89211i	−0.152243	−	0.468555i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	5.51245	+	4.00503i	0.654207	+	0.475309i	0.864702	−	0.502286i	$-0.167507\pi$
$71$	5.51245	+	4.00503i	0.654207	+	0.475309i	−0.210494	+	0.977595i	$0.567507\pi$
$72$	1.40395	+	1.02003i	0.165457	+	0.120212i
$73$	−4.67084	+	14.3754i	−0.546680	+	1.68251i	0.170282	+	0.985395i	$0.445532\pi$
$73$	−4.67084	+	14.3754i	−0.546680	+	1.68251i	−0.716962	+	0.697112i	$0.754468\pi$
$74$	−0.241211	−	0.742372i	−0.0280402	−	0.0862990i
$75$	0.909784	−	0.660997i	0.105053	−	0.0763253i
$76$	3.43616			0.394154
$77$	−1.66146	−	2.87046i	−0.189341	−	0.327119i
$78$	−7.94999			−0.900159
$79$	13.1358	−	9.54373i	1.47790	−	1.07375i	0.499668	−	0.866217i	$-0.333455\pi$
$79$	13.1358	−	9.54373i	1.47790	−	1.07375i	0.978227	−	0.207537i	$-0.0665447\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	−0.241755	+	0.744045i	−0.0268616	+	0.0826716i
$82$	4.06034	+	2.95001i	0.448390	+	0.325774i
$83$	−5.98951	−	4.35163i	−0.657434	−	0.477654i	0.208361	−	0.978052i	$-0.433187\pi$
$83$	−5.98951	−	4.35163i	−0.657434	−	0.477654i	−0.865795	+	0.500398i	$0.833187\pi$
$84$	0.347506	−	1.06951i	0.0379161	−	0.116694i
$85$	−1.06449	−	3.27617i	−0.115460	−	0.355350i
$86$	4.36464	−	3.17110i	0.470652	−	0.341948i
$87$	9.77573			1.04807
$88$	−3.03137	−	1.34567i	−0.323145	−	0.143449i
$89$	−4.97143			−0.526970			−0.263485	−	0.964663i	$-0.584872\pi$
$89$	−4.97143			−0.526970			−0.263485	+	0.964663i	$0.584872\pi$
$90$	−1.40395	+	1.02003i	−0.147989	+	0.107521i
$91$	−2.18458	−	6.72345i	−0.229006	−	0.704809i
$92$	1.12455	−	3.46102i	0.117243	−	0.360837i
$93$	−4.11354	−	2.98866i	−0.426554	−	0.309910i
$94$	−7.95082	−	5.77661i	−0.820064	−	0.595811i
$95$	−1.06183	+	3.26798i	−0.108942	+	0.335288i
$96$	−0.347506	−	1.06951i	−0.0354672	−	0.109157i
$97$	−2.33800	+	1.69866i	−0.237388	+	0.172472i	−0.700119	−	0.714026i	$-0.746870\pi$
$97$	−2.33800	+	1.69866i	−0.237388	+	0.172472i	0.462731	+	0.886499i	$0.346870\pi$
$98$	1.00000			0.101015
$99$	−0.595344	+	5.72472i	−0.0598343	+	0.575356i
$100$	1.00000			0.100000
$101$	−9.89152	+	7.18661i	−0.984243	+	0.715094i	−0.958653	−	0.284578i	$-0.908146\pi$
$101$	−9.89152	+	7.18661i	−0.984243	+	0.715094i	−0.0255899	+	0.999673i	$0.508146\pi$
$102$	−1.19708	−	3.68423i	−0.118529	−	0.364793i
$103$	1.14532	−	3.52493i	0.112852	−	0.347322i	−0.878641	−	0.477483i	$-0.841549\pi$
$103$	1.14532	−	3.52493i	0.112852	−	0.347322i	0.991493	+	0.130161i	$0.0415493\pi$
$104$	−5.71931	−	4.15532i	−0.560824	−	0.407463i
$105$	0.909784	+	0.660997i	0.0887858	+	0.0645067i
$106$	3.51408	−	10.8152i	0.341318	−	1.05047i
$107$	−0.881029	−	2.71153i	−0.0851723	−	0.262133i	0.899396	−	0.437135i	$-0.144007\pi$
$107$	−0.881029	−	2.71153i	−0.0851723	−	0.262133i	−0.984568	+	0.175002i	$0.944007\pi$
$108$	−4.30817	+	3.13007i	−0.414554	+	0.301191i
$109$	9.80121			0.938786			0.469393	−	0.882989i	$-0.344473\pi$
$109$	9.80121			0.938786			0.469393	+	0.882989i	$0.344473\pi$
$110$	2.21655	−	2.46717i	0.211340	−	0.235235i
$111$	0.877800			0.0833171
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	3.33837	+	10.2745i	0.314048	+	0.966539i	0.976145	+	0.217121i	$0.0696667\pi$
$113$	3.33837	+	10.2745i	0.314048	+	0.966539i	−0.662097	+	0.749418i	$0.730333\pi$
$114$	−1.19409	+	3.67502i	−0.111836	+	0.344197i
$115$	2.94412	+	2.13903i	0.274541	+	0.199466i
$116$	7.03277	+	5.10961i	0.652976	+	0.474415i
$117$	−3.79107	+	11.6677i	−0.350485	+	1.07868i
$118$	−3.25231	−	10.0096i	−0.299399	−	0.921457i
$119$	2.78688	−	2.02478i	0.255473	−	0.185612i
$120$	1.12455			0.102657
$121$	−1.17381	−	10.9372i	−0.106710	−	0.994290i
$122$	0.456235			0.0413055
$123$	−4.56608	+	3.31745i	−0.411709	+	0.299124i
$124$	−1.39720	−	4.30015i	−0.125473	−	0.386165i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−1.40395	−	1.02003i	−0.125074	−	0.0908714i
$127$	−17.2005	−	12.4969i	−1.52630	−	1.10892i	−0.958254	−	0.285919i	$-0.907701\pi$
$127$	−17.2005	−	12.4969i	−1.52630	−	1.10892i	−0.568042	−	0.822999i	$-0.692299\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	1.87480	+	5.77003i	0.165067	+	0.508023i
$130$	5.71931	−	4.15532i	0.501616	−	0.364446i
$131$	10.2637			0.896747			0.448373	−	0.893846i	$-0.352003\pi$
$131$	10.2637			0.896747			0.448373	+	0.893846i	$0.352003\pi$
$132$	2.49263	−	2.77446i	0.216956	−	0.241486i
$133$	−3.43616			−0.297953
$134$	−8.48960	+	6.16805i	−0.733389	+	0.532839i
$135$	−1.64557	−	5.06456i	−0.141628	−	0.435888i
$136$	1.06449	−	3.27617i	0.0912794	−	0.280929i
$137$	0.615590	+	0.447252i	0.0525934	+	0.0382113i	0.613771	−	0.789484i	$-0.289652\pi$
$137$	0.615590	+	0.447252i	0.0525934	+	0.0382113i	−0.561178	+	0.827695i	$0.689652\pi$
$138$	3.31083	+	2.40546i	0.281836	+	0.204766i
$139$	5.45036	−	16.7745i	0.462294	−	1.42279i	−0.400061	−	0.916489i	$-0.631011\pi$
$139$	5.45036	−	16.7745i	0.462294	−	1.42279i	0.862355	−	0.506305i	$-0.168989\pi$
$140$	0.309017	+	0.951057i	0.0261167	+	0.0803789i
$141$	8.94113	−	6.49611i	0.752979	−	0.547071i
$142$	−6.81376			−0.571798
$143$	2.42527	−	23.3210i	0.202811	−	1.95020i
$144$	−1.73538			−0.144615
$145$	−7.03277	+	5.10961i	−0.584040	+	0.424330i
$146$	−4.67084	−	14.3754i	−0.386561	−	1.18971i
$147$	−0.347506	+	1.06951i	−0.0286618	+	0.0882121i
$148$	0.631499	+	0.458811i	0.0519089	+	0.0377140i
$149$	−0.629561	−	0.457403i	−0.0515756	−	0.0374719i	0.561699	−	0.827342i	$-0.310148\pi$
$149$	−0.629561	−	0.457403i	−0.0515756	−	0.0374719i	−0.613274	+	0.789870i	$0.710148\pi$
$150$	−0.347506	+	1.06951i	−0.0283738	+	0.0873255i
$151$	4.14558	+	12.7588i	0.337362	+	1.03829i	0.965547	+	0.260230i	$0.0837983\pi$
$151$	4.14558	+	12.7588i	0.337362	+	1.03829i	−0.628184	+	0.778064i	$0.716202\pi$
$152$	−2.77991	+	2.01972i	−0.225480	+	0.163821i
$153$	−5.97797			−0.483290
$154$	3.03137	+	1.34567i	0.244274	+	0.108437i
$155$	4.52145			0.363171
$156$	6.43167	−	4.67288i	0.514946	−	0.374130i
$157$	−7.42757	−	22.8597i	−0.592785	−	1.82440i	−0.565458	−	0.824777i	$-0.691300\pi$
$157$	−7.42757	−	22.8597i	−0.592785	−	1.82440i	−0.0273272	−	0.999627i	$-0.508700\pi$
$158$	−5.01744	+	15.4421i	−0.399166	+	1.22851i
$159$	10.3459	+	7.51673i	0.820483	+	0.596116i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	−1.12455	+	3.46102i	−0.0886273	+	0.272767i
$162$	−0.241755	−	0.744045i	−0.0189940	−	0.0584577i
$163$	−0.732477	+	0.532176i	−0.0573720	+	0.0416832i	−0.616102	−	0.787667i	$-0.711289\pi$
$163$	−0.732477	+	0.532176i	−0.0573720	+	0.0416832i	0.558730	+	0.829350i	$0.311289\pi$
$164$	−5.01886			−0.391907
$165$	1.86840	+	3.22799i	0.145455	+	0.251299i
$166$	7.40344			0.574618
$167$	2.94548	−	2.14002i	0.227928	−	0.165600i	−0.467960	−	0.883750i	$-0.655011\pi$
$167$	2.94548	−	2.14002i	0.227928	−	0.165600i	0.695888	+	0.718150i	$0.255011\pi$
$168$	0.347506	+	1.06951i	0.0268107	+	0.0825149i
$169$	11.4266	−	35.1674i	0.878967	−	2.70518i
$170$	2.78688	+	2.02478i	0.213744	+	0.155294i
$171$	4.82419	+	3.50498i	0.368915	+	0.268033i
$172$	−1.66715	+	5.13095i	−0.127119	+	0.391231i
$173$	−0.982471	−	3.02373i	−0.0746959	−	0.229890i	0.906737	−	0.421697i	$-0.138565\pi$
$173$	−0.982471	−	3.02373i	−0.0746959	−	0.229890i	−0.981433	+	0.191807i	$0.938565\pi$
$174$	−7.90873	+	5.74603i	−0.599559	+	0.435605i
$175$	−1.00000			−0.0755929
$176$	3.24339	−	0.693123i	0.244480	−	0.0522461i
$177$	11.8356			0.889618
$178$	4.02197	−	2.92213i	0.301459	−	0.219023i
$179$	1.38482	+	4.26203i	0.103506	+	0.318559i	0.989377	−	0.145373i	$-0.0464381\pi$
$179$	1.38482	+	4.26203i	0.103506	+	0.318559i	−0.885871	+	0.463932i	$0.846438\pi$
$180$	0.536261	−	1.65044i	0.0399705	−	0.123017i
$181$	7.30491	+	5.30733i	0.542970	+	0.394491i	0.825187	−	0.564860i	$-0.191070\pi$
$181$	7.30491	+	5.30733i	0.542970	+	0.394491i	−0.282217	+	0.959351i	$0.591070\pi$
$182$	5.71931	+	4.15532i	0.423943	+	0.308013i
$183$	−0.158545	+	0.487950i	−0.0117199	+	0.0360703i
$184$	1.12455	+	3.46102i	0.0829033	+	0.255150i
$185$	−0.631499	+	0.458811i	−0.0464288	+	0.0337325i
$186$	5.08461			0.372822
$187$	11.1727	−	2.38765i	0.817031	−	0.174602i
$188$	9.82775			0.716762
$189$	4.30817	−	3.13007i	0.313373	−	0.227679i
$190$	−1.06183	−	3.26798i	−0.0770333	−	0.237084i
$191$	0.898838	−	2.76634i	0.0650377	−	0.200165i	−0.913257	−	0.407384i	$-0.866441\pi$
$191$	0.898838	−	2.76634i	0.0650377	−	0.200165i	0.978295	+	0.207219i	$0.0664411\pi$
$192$	0.909784	+	0.660997i	0.0656580	+	0.0477033i
$193$	6.28865	+	4.56897i	0.452667	+	0.328882i	0.790648	−	0.612271i	$-0.209744\pi$
$193$	6.28865	+	4.56897i	0.452667	+	0.328882i	−0.337981	+	0.941153i	$0.609744\pi$
$194$	0.893036	−	2.74848i	0.0641163	−	0.197330i
$195$	2.45668	+	7.56089i	0.175927	+	0.541446i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	26.2257			1.86851			0.934254	−	0.356609i	$-0.116067\pi$
$197$	26.2257			1.86851			0.934254	+	0.356609i	$0.116067\pi$
$198$	−2.88326	−	4.98133i	−0.204905	−	0.354008i
$199$	5.64963			0.400491			0.200246	−	0.979746i	$-0.435826\pi$
$199$	5.64963			0.400491			0.200246	+	0.979746i	$0.435826\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	−3.64663	−	11.2232i	−0.257214	−	0.791623i
$202$	3.77822	−	11.6282i	0.265835	−	0.818156i
$203$	−7.03277	−	5.10961i	−0.493604	−	0.358624i
$204$	3.13399	+	2.27698i	0.219423	+	0.159421i
$205$	1.55091	−	4.77322i	0.108320	−	0.333376i
$206$	1.14532	+	3.52493i	0.0797983	+	0.245594i
$207$	5.10916	−	3.71202i	0.355111	−	0.258003i
$208$	7.06945			0.490178
$209$	−10.4162	−	4.62393i	−0.720507	−	0.319844i
$210$	−1.12455			−0.0776016
$211$	−6.01078	+	4.36709i	−0.413799	+	0.300643i	−0.775138	−	0.631792i	$-0.782320\pi$
$211$	−6.01078	+	4.36709i	−0.413799	+	0.300643i	0.361339	+	0.932435i	$0.382320\pi$
$212$	3.51408	+	10.8152i	0.241348	+	0.742794i
$213$	2.36783	−	7.28742i	0.162241	−	0.499326i
$214$	2.30656	+	1.67582i	0.157673	+	0.114556i
$215$	−4.36464	−	3.17110i	−0.297666	−	0.216267i
$216$	1.64557	−	5.06456i	0.111967	−	0.344599i
$217$	1.39720	+	4.30015i	0.0948483	+	0.291913i
$218$	−7.92934	+	5.76101i	−0.537043	+	0.390185i
$219$	16.9978			1.14860
$220$	−0.343063	+	3.29883i	−0.0231293	+	0.222407i
$221$	24.3526			1.63814
$222$	−0.710155	+	0.515958i	−0.0476625	+	0.0346288i
$223$	0.467132	+	1.43769i	0.0312815	+	0.0962745i	0.965478	−	0.260484i	$-0.0838820\pi$
$223$	0.467132	+	1.43769i	0.0312815	+	0.0962745i	−0.934197	+	0.356758i	$0.883882\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	1.40395	+	1.02003i	0.0935966	+	0.0680019i
$226$	−8.73997	−	6.34996i	−0.581374	−	0.422393i
$227$	4.28167	−	13.1776i	0.284185	−	0.874630i	−0.702457	−	0.711726i	$-0.747914\pi$
$227$	4.28167	−	13.1776i	0.284185	−	0.874630i	0.986642	−	0.162904i	$-0.0520862\pi$
$228$	−1.19409	−	3.67502i	−0.0790803	−	0.243384i
$229$	−16.6223	+	12.0768i	−1.09844	+	0.798060i	−0.980804	−	0.194998i	$-0.937530\pi$
$229$	−16.6223	+	12.0768i	−1.09844	+	0.798060i	−0.117631	+	0.993057i	$0.537530\pi$
$230$	−3.63913			−0.239957
$231$	−2.49263	+	2.77446i	−0.164003	+	0.182546i
$232$	−8.69298			−0.570722
$233$	−13.1340	+	9.54242i	−0.860438	+	0.625145i	−0.928004	−	0.372570i	$-0.878477\pi$
$233$	−13.1340	+	9.54242i	−0.860438	+	0.625145i	0.0675664	+	0.997715i	$0.478477\pi$
$234$	−3.79107	−	11.6677i	−0.247830	−	0.762743i
$235$	−3.03694	+	9.34674i	−0.198108	+	0.609714i
$236$	8.51466	+	6.18626i	0.554257	+	0.402691i
$237$	−14.7719	−	10.7324i	−0.959541	−	0.697147i
$238$	−1.06449	+	3.27617i	−0.0690008	+	0.212363i
$239$	−0.121419	−	0.373690i	−0.00785397	−	0.0241720i	0.947053	−	0.321078i	$-0.104045\pi$
$239$	−0.121419	−	0.373690i	−0.00785397	−	0.0241720i	−0.954907	+	0.296906i	$0.904045\pi$
$240$	−0.909784	+	0.660997i	−0.0587263	+	0.0426671i
$241$	−3.32681			−0.214298			−0.107149	−	0.994243i	$-0.534172\pi$
$241$	−3.32681			−0.214298			−0.107149	+	0.994243i	$0.534172\pi$
$242$	7.37835	+	8.15843i	0.474299	+	0.524443i
$243$	−15.0958			−0.968395
$244$	−0.369102	+	0.268168i	−0.0236293	+	0.0171677i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	1.74409	−	5.36774i	0.111199	−	0.342235i
$247$	−19.6524	−	14.2783i	−1.25045	−	0.908509i
$248$	3.65793	+	2.65764i	0.232279	+	0.168760i
$249$	−2.57274	+	7.91809i	−0.163041	+	0.501789i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−13.9762	+	10.1543i	−0.882169	+	0.640934i	−0.933825	−	0.357731i	$-0.883550\pi$
$251$	−13.9762	+	10.1543i	−0.882169	+	0.640934i	0.0516551	+	0.998665i	$0.483550\pi$
$252$	1.73538			0.109318
$253$	−8.06632	+	8.97835i	−0.507126	+	0.564464i
$254$	21.2610			1.33403
$255$	−3.13399	+	2.27698i	−0.196258	+	0.142590i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.138608	+	0.426591i	−0.00864613	+	0.0266100i	−0.955287	−	0.295682i	$-0.904453\pi$
$257$	−0.138608	+	0.426591i	−0.00864613	+	0.0266100i	0.946640	+	0.322292i	$0.104453\pi$
$258$	−4.90828	−	3.56607i	−0.305576	−	0.222014i
$259$	−0.631499	−	0.458811i	−0.0392395	−	0.0285091i
$260$	−2.18458	+	6.72345i	−0.135482	+	0.416971i
$261$	4.66171	+	14.3473i	0.288552	+	0.888073i
$262$	−8.30354	+	6.03287i	−0.512994	+	0.372712i
$263$	26.1440			1.61211			0.806053	−	0.591843i	$-0.201600\pi$
$263$	26.1440			1.61211			0.806053	+	0.591843i	$0.201600\pi$
$264$	−0.385793	+	3.70972i	−0.0237439	+	0.228317i
$265$	−11.3718			−0.698565
$266$	2.77991	−	2.01972i	0.170447	−	0.123837i
$267$	1.72760	+	5.31701i	0.105728	+	0.325396i
$268$	3.24274	−	9.98012i	0.198082	−	0.609633i
$269$	−11.4570	−	8.32403i	−0.698549	−	0.507525i	0.180911	−	0.983500i	$-0.442096\pi$
$269$	−11.4570	−	8.32403i	−0.698549	−	0.507525i	−0.879459	+	0.475974i	$0.842096\pi$
$270$	4.30817	+	3.13007i	0.262187	+	0.190490i
$271$	−0.288687	+	0.888488i	−0.0175365	+	0.0539718i	−0.959442	−	0.281907i	$-0.909033\pi$
$271$	−0.288687	+	0.888488i	−0.0175365	+	0.0539718i	0.941905	+	0.335878i	$0.109033\pi$
$272$	1.06449	+	3.27617i	0.0645443	+	0.198647i
$273$	−6.43167	+	4.67288i	−0.389263	+	0.282816i
$274$	−0.760911			−0.0459683
$275$	−3.03137	−	1.34567i	−0.182798	−	0.0811469i
$276$	−4.09241			−0.246334
$277$	20.4882	−	14.8856i	1.23102	−	0.894388i	0.234053	−	0.972224i	$-0.424801\pi$
$277$	20.4882	−	14.8856i	1.23102	−	0.894388i	0.996966	+	0.0778361i	$0.0248011\pi$
$278$	5.45036	+	16.7745i	0.326891	+	1.00607i
$279$	2.42467	−	7.46238i	0.145161	−	0.446761i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	−22.4728	−	16.3274i	−1.34061	−	0.974013i	−0.999421	−	0.0340199i	$-0.989169\pi$
$281$	−22.4728	−	16.3274i	−1.34061	−	0.974013i	−0.341193	−	0.939993i	$-0.610831\pi$
$282$	−3.41521	+	10.5109i	−0.203373	+	0.625916i
$283$	−6.03056	−	18.5601i	−0.358479	−	1.10329i	−0.953964	−	0.299920i	$-0.903040\pi$
$283$	−6.03056	−	18.5601i	−0.358479	−	1.10329i	0.595485	−	0.803366i	$-0.296960\pi$
$284$	5.51245	−	4.00503i	0.327104	−	0.237655i
$285$	3.86415			0.228892
$286$	11.7456	+	20.2926i	0.694534	+	1.19993i
$287$	5.01886			0.296254
$288$	1.40395	−	1.02003i	0.0827285	−	0.0601058i
$289$	−1.58636	−	4.88231i	−0.0933153	−	0.287195i
$290$	2.68628	−	8.26751i	0.157744	−	0.485485i
$291$	2.62921	+	1.91023i	0.154127	+	0.111980i
$292$	12.2284	+	8.88446i	0.715613	+	0.519923i
$293$	−4.12553	+	12.6971i	−0.241016	+	0.741772i	0.755250	+	0.655437i	$0.227515\pi$
$293$	−4.12553	+	12.6971i	−0.241016	+	0.741772i	−0.996266	+	0.0863347i	$0.972485\pi$
$294$	−0.347506	−	1.06951i	−0.0202670	−	0.0623754i
$295$	−8.51466	+	6.18626i	−0.495743	+	0.360178i
$296$	−0.780576			−0.0453701
$297$	17.2717	−	3.69101i	1.00220	−	0.214174i
$298$	0.778180			0.0450788
$299$	−20.8133	+	15.1218i	−1.20367	+	0.874515i
$300$	−0.347506	−	1.06951i	−0.0200633	−	0.0617485i
$301$	1.66715	−	5.13095i	0.0960926	−	0.295743i
$302$	−10.8533	−	7.88536i	−0.624535	−	0.453751i
$303$	11.1235	+	8.08173i	0.639031	+	0.464283i
$304$	1.06183	−	3.26798i	0.0609002	−	0.187431i
$305$	−0.140984	−	0.433905i	−0.00807274	−	0.0248453i
$306$	4.83628	−	3.51376i	0.276472	−	0.200869i
$307$	25.7848			1.47162			0.735809	−	0.677189i	$-0.236802\pi$
$307$	25.7848			1.47162			0.735809	+	0.677189i	$0.236802\pi$
$308$	−3.24339	+	0.693123i	−0.184809	+	0.0394944i
$309$	−4.16798			−0.237108
$310$	−3.65793	+	2.65764i	−0.207756	+	0.150944i
$311$	1.58074	+	4.86503i	0.0896358	+	0.275871i	0.985819	−	0.167814i	$-0.0536709\pi$
$311$	1.58074	+	4.86503i	0.0896358	+	0.275871i	−0.896183	+	0.443685i	$0.853671\pi$
$312$	−2.45668	+	7.56089i	−0.139082	+	0.428051i
$313$	−13.3949	−	9.73200i	−0.757127	−	0.550085i	0.140901	−	0.990024i	$-0.455000\pi$
$313$	−13.3949	−	9.73200i	−0.757127	−	0.550085i	−0.898028	+	0.439939i	$0.855000\pi$
$314$	19.4456	+	14.1281i	1.09738	+	0.797294i
$315$	−0.536261	+	1.65044i	−0.0302149	+	0.0929919i
$316$	−5.01744	−	15.4421i	−0.282253	−	0.868685i
$317$	−12.4184	+	9.02252i	−0.697488	+	0.506755i	−0.879113	−	0.476613i	$-0.841864\pi$
$317$	−12.4184	+	9.02252i	−0.697488	+	0.506755i	0.181625	+	0.983368i	$0.441864\pi$
$318$	−12.7882			−0.717128
$319$	−14.4431	−	24.9529i	−0.808656	−	1.39709i
$320$	−1.00000			−0.0559017
$321$	−2.59386	+	1.88455i	−0.144775	+	0.105185i
$322$	−1.12455	−	3.46102i	−0.0626690	−	0.192875i
$323$	3.65776	−	11.2574i	0.203523	−	0.626380i
$324$	0.632922	+	0.459845i	0.0351623	+	0.0255469i
$325$	−5.71931	−	4.15532i	−0.317250	−	0.230496i
$326$	0.279781	−	0.861078i	0.0154957	−	0.0476907i
$327$	−3.40598	−	10.4825i	−0.188351	−	0.579686i
$328$	4.06034	−	2.95001i	0.224195	−	0.162887i
$329$	−9.82775			−0.541821
$330$	−3.40894	−	1.51328i	−0.187656	−	0.0833032i
$331$	−6.59151			−0.362302			−0.181151	−	0.983455i	$-0.557982\pi$
$331$	−6.59151			−0.362302			−0.181151	+	0.983455i	$0.557982\pi$
$332$	−5.98951	+	4.35163i	−0.328717	+	0.238827i
$333$	0.418593	+	1.28830i	0.0229387	+	0.0705981i
$334$	−1.12507	+	3.46262i	−0.0615613	+	0.189466i
$335$	8.48960	+	6.16805i	0.463836	+	0.336997i
$336$	−0.909784	−	0.660997i	−0.0496328	−	0.0360603i
$337$	−5.91912	+	18.2172i	−0.322435	+	0.992352i	0.650150	+	0.759806i	$0.274706\pi$
$337$	−5.91912	+	18.2172i	−0.322435	+	0.992352i	−0.972585	+	0.232547i	$0.925294\pi$
$338$	11.4266	+	35.1674i	0.621524	+	1.91285i
$339$	9.82858	−	7.14088i	0.533815	−	0.387839i
$340$	−3.44477			−0.186819
$341$	−1.55114	+	14.9155i	−0.0839990	+	0.807720i
$342$	−5.96303			−0.322444
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−1.66715	−	5.13095i	−0.0898864	−	0.276642i
$345$	1.26462	−	3.89211i	0.0680850	−	0.209544i
$346$	2.57214	+	1.86877i	0.138279	+	0.100466i
$347$	7.28330	+	5.29163i	0.390988	+	0.284069i	0.765860	−	0.643007i	$-0.222313\pi$
$347$	7.28330	+	5.29163i	0.390988	+	0.284069i	−0.374872	+	0.927076i	$0.622313\pi$
$348$	3.02087	−	9.29727i	0.161935	−	0.498386i
$349$	−2.07932	−	6.39948i	−0.111303	−	0.342556i	0.879855	−	0.475243i	$-0.157640\pi$
$349$	−2.07932	−	6.39948i	−0.111303	−	0.342556i	−0.991158	+	0.132686i	$0.957640\pi$
$350$	0.809017	−	0.587785i	0.0432438	−	0.0314184i
$351$	37.6462			2.00940
$352$	−2.21655	+	2.46717i	−0.118143	+	0.131500i
$353$	−29.9182			−1.59238			−0.796192	−	0.605044i	$-0.793156\pi$
$353$	−29.9182			−1.59238			−0.796192	+	0.605044i	$0.793156\pi$
$354$	−9.57520	+	6.95679i	−0.508916	+	0.369749i
$355$	2.10557	+	6.48027i	0.111752	+	0.343937i
$356$	−1.53626	+	4.72811i	−0.0814214	+	0.250589i
$357$	−3.13399	−	2.27698i	−0.165869	−	0.120511i
$358$	−3.62550	−	2.63408i	−0.191614	−	0.139216i
$359$	−7.28112	+	22.4090i	−0.384283	+	1.18270i	0.552717	+	0.833369i	$0.313591\pi$
$359$	−7.28112	+	22.4090i	−0.384283	+	1.18270i	−0.936999	+	0.349331i	$0.886409\pi$
$360$	0.536261	+	1.65044i	0.0282634	+	0.0869859i
$361$	5.81912	−	4.22784i	0.306269	−	0.222518i
$362$	−9.02937			−0.474573
$363$	−11.2896	+	5.05615i	−0.592549	+	0.265379i
$364$	−7.06945			−0.370540
$365$	−12.2284	+	8.88446i	−0.640064	+	0.465034i
$366$	−0.158545	−	0.487950i	−0.00828725	−	0.0255055i
$367$	−3.14266	+	9.67211i	−0.164045	+	0.504880i	−0.998965	−	0.0454926i	$-0.985514\pi$
$367$	−3.14266	+	9.67211i	−0.164045	+	0.504880i	0.834919	+	0.550372i	$0.185514\pi$
$368$	−2.94412	−	2.13903i	−0.153473	−	0.111505i
$369$	−7.04622	−	5.11938i	−0.366812	−	0.266504i
$370$	0.241211	−	0.742372i	0.0125400	−	0.0385941i
$371$	−3.51408	−	10.8152i	−0.182442	−	0.561499i
$372$	−4.11354	+	2.98866i	−0.213277	+	0.154955i
$373$	10.7767			0.557996			0.278998	−	0.960292i	$-0.409998\pi$
$373$	10.7767			0.557996			0.278998	+	0.960292i	$0.409998\pi$
$374$	−7.63550	+	8.49881i	−0.394822	+	0.439463i
$375$	1.12455			0.0580717
$376$	−7.95082	+	5.77661i	−0.410032	+	0.297906i
$377$	−18.9905	−	58.4468i	−0.978062	−	3.01016i
$378$	−1.64557	+	5.06456i	−0.0846392	+	0.260493i
$379$	4.36825	+	3.17372i	0.224382	+	0.163023i	0.694297	−	0.719689i	$-0.255715\pi$
$379$	4.36825	+	3.17372i	0.224382	+	0.163023i	−0.469915	+	0.882712i	$0.655715\pi$
$380$	2.77991	+	2.01972i	0.142606	+	0.103610i
$381$	−7.38832	+	22.7389i	−0.378515	+	1.16495i
$382$	0.898838	+	2.76634i	0.0459886	+	0.141538i
$383$	−5.80474	+	4.21739i	−0.296608	+	0.215498i	−0.726129	−	0.687559i	$-0.758682\pi$
$383$	−5.80474	+	4.21739i	−0.296608	+	0.215498i	0.429521	+	0.903057i	$0.358682\pi$
$384$	−1.12455			−0.0573872
$385$	0.343063	−	3.29883i	0.0174841	−	0.168124i
$386$	−7.77320			−0.395646
$387$	−7.57430	+	5.50305i	−0.385023	+	0.279736i
$388$	0.893036	+	2.74848i	0.0453370	+	0.139533i
$389$	5.11076	−	15.7293i	0.259126	−	0.797507i	−0.733863	−	0.679298i	$-0.762285\pi$
$389$	5.11076	−	15.7293i	0.259126	−	0.797507i	0.992989	−	0.118210i	$-0.0377154\pi$
$390$	−6.43167	−	4.67288i	−0.325680	−	0.236621i
$391$	−10.1418	−	7.36846i	−0.512894	−	0.372639i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−3.56672	−	10.9772i	−0.179917	−	0.553728i
$394$	−21.2171	+	15.4151i	−1.06890	+	0.776602i
$395$	16.2368			0.816960
$396$	5.26056	+	2.33524i	0.264353	+	0.117350i
$397$	16.7413			0.840221			0.420111	−	0.907473i	$-0.361991\pi$
$397$	16.7413			0.840221			0.420111	+	0.907473i	$0.361991\pi$
$398$	−4.57064	+	3.32077i	−0.229106	+	0.166455i
$399$	1.19409	+	3.67502i	0.0597791	+	0.183981i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	16.4564	+	11.9563i	0.821793	+	0.597067i	0.917225	−	0.398369i	$-0.130424\pi$
$401$	16.4564	+	11.9563i	0.821793	+	0.597067i	−0.0954328	+	0.995436i	$0.530424\pi$
$402$	9.54701	+	6.93631i	0.476162	+	0.345952i
$403$	−9.87746	+	30.3997i	−0.492032	+	1.51432i
$404$	3.77822	+	11.6282i	0.187974	+	0.578523i
$405$	−0.632922	+	0.459845i	−0.0314502	+	0.0228499i
$406$	8.69298			0.431425
$407$	−1.29690	−	2.24061i	−0.0642848	−	0.111063i
$408$	−3.87383			−0.191783
$409$	0.358871	−	0.260735i	0.0177450	−	0.0128925i	−0.578877	−	0.815415i	$-0.696509\pi$
$409$	0.358871	−	0.260735i	0.0177450	−	0.0128925i	0.596622	+	0.802522i	$0.296509\pi$
$410$	1.55091	+	4.77322i	0.0765941	+	0.235732i
$411$	0.264421	−	0.813805i	0.0130429	−	0.0401421i
$412$	−2.99849	−	2.17853i	−0.147725	−	0.107328i
$413$	−8.51466	−	6.18626i	−0.418979	−	0.304406i
$414$	−1.95153	+	6.00618i	−0.0959123	+	0.295188i
$415$	−2.28779	−	7.04109i	−0.112303	−	0.345634i
$416$	−5.71931	+	4.15532i	−0.280412	+	0.203731i
$417$	−19.8346			−0.971305
$418$	11.1448	−	2.38168i	0.545110	−	0.116492i
$419$	−18.6545			−0.911330			−0.455665	−	0.890151i	$-0.650599\pi$
$419$	−18.6545			−0.911330			−0.455665	+	0.890151i	$0.650599\pi$
$420$	0.909784	−	0.660997i	0.0443929	−	0.0322533i
$421$	3.79213	+	11.6710i	0.184817	+	0.568808i	0.999945	−	0.0104723i	$-0.00333350\pi$
$421$	3.79213	+	11.6710i	0.184817	+	0.568808i	−0.815128	+	0.579281i	$0.803333\pi$
$422$	2.29591	−	7.06609i	0.111763	−	0.343972i
$423$	13.7977	+	10.0246i	0.670865	+	0.487412i
$424$	−9.19999	−	6.68419i	−0.446791	−	0.324613i
$425$	1.06449	−	3.27617i	0.0516354	−	0.158918i
$426$	2.36783	+	7.28742i	0.114722	+	0.353077i
$427$	0.369102	−	0.268168i	0.0178621	−	0.0129776i
$428$	−2.85107			−0.137812
$429$	−25.7849	+	5.51032i	−1.24491	+	0.266041i
$430$	5.39500			0.260170
$431$	−17.7818	+	12.9192i	−0.856520	+	0.622298i	−0.926936	−	0.375220i	$-0.877567\pi$
$431$	−17.7818	+	12.9192i	−0.856520	+	0.622298i	0.0704163	+	0.997518i	$0.477567\pi$
$432$	1.64557	+	5.06456i	0.0791727	+	0.243669i
$433$	6.87085	−	21.1463i	0.330192	−	1.01623i	−0.638850	−	0.769331i	$-0.720590\pi$
$433$	6.87085	−	21.1463i	0.330192	−	1.01623i	0.969042	−	0.246896i	$-0.0794104\pi$
$434$	−3.65793	−	2.65764i	−0.175586	−	0.127571i
$435$	7.90873	+	5.74603i	0.379195	+	0.275501i
$436$	3.02874	−	9.32150i	0.145050	−	0.446419i
$437$	3.86415	+	11.8926i	0.184847	+	0.568901i
$438$	−13.7515	+	9.99106i	−0.657072	+	0.477391i
$439$	−11.0302			−0.526444			−0.263222	−	0.964735i	$-0.584785\pi$
$439$	−11.0302			−0.526444			−0.263222	+	0.964735i	$0.584785\pi$
$440$	−1.66146	−	2.87046i	−0.0792071	−	0.136844i
$441$	−1.73538			−0.0826370
$442$	−19.7017	+	14.3141i	−0.937114	+	0.680853i
$443$	9.53943	+	29.3593i	0.453232	+	1.39490i	0.873199	+	0.487365i	$0.162042\pi$
$443$	9.53943	+	29.3593i	0.453232	+	1.39490i	−0.419967	+	0.907540i	$0.637958\pi$
$444$	0.271255	−	0.834838i	0.0128732	−	0.0396196i
$445$	−4.02197	−	2.92213i	−0.190660	−	0.138522i
$446$	−1.22297	−	0.888538i	−0.0579092	−	0.0420735i
$447$	−0.270423	+	0.832275i	−0.0127905	+	0.0393653i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	11.3224	−	8.22619i	0.534336	−	0.388218i	−0.287641	−	0.957738i	$-0.592871\pi$
$449$	11.3224	−	8.22619i	0.534336	−	0.388218i	0.821977	+	0.569521i	$0.192871\pi$
$450$	−1.73538			−0.0818065
$451$	15.2140	+	6.75372i	0.716399	+	0.318020i
$452$	10.8032			0.508140
$453$	12.2051	−	8.86751i	0.573445	−	0.416632i
$454$	4.28167	+	13.1776i	0.200949	+	0.618457i
$455$	2.18458	−	6.72345i	0.102415	−	0.315200i
$456$	3.12616	+	2.27129i	0.146396	+	0.106363i
$457$	5.71598	+	4.15290i	0.267382	+	0.194264i	0.713395	−	0.700762i	$-0.247157\pi$
$457$	5.71598	+	4.15290i	0.267382	+	0.194264i	−0.446013	+	0.895026i	$0.647157\pi$
$458$	6.34917	−	19.5407i	0.296677	−	0.913078i
$459$	5.66862	+	17.4462i	0.264589	+	0.814320i
$460$	2.94412	−	2.13903i	0.137270	−	0.0997328i
$461$	10.6011			0.493744			0.246872	−	0.969048i	$-0.420597\pi$
$461$	10.6011			0.493744			0.246872	+	0.969048i	$0.420597\pi$
$462$	0.385793	−	3.70972i	0.0179487	−	0.172592i
$463$	4.59137			0.213379			0.106690	−	0.994292i	$-0.465975\pi$
$463$	4.59137			0.213379			0.106690	+	0.994292i	$0.465975\pi$
$464$	7.03277	−	5.10961i	0.326488	−	0.237207i
$465$	−1.57123	−	4.83575i	−0.0728641	−	0.224253i
$466$	5.01675	−	15.4400i	0.232396	−	0.715242i
$467$	25.0219	+	18.1795i	1.15787	+	0.841245i	0.989508	−	0.144479i	$-0.0461507\pi$
$467$	25.0219	+	18.1795i	1.15787	+	0.841245i	0.168367	+	0.985724i	$0.446151\pi$
$468$	9.92516	+	7.21105i	0.458790	+	0.333331i
$469$	−3.24274	+	9.98012i	−0.149736	+	0.460839i
$470$	−3.03694	−	9.34674i	−0.140084	−	0.431133i
$471$	−21.8677	+	15.8878i	−1.00761	+	0.732071i
$472$	−10.5247			−0.484438
$473$	11.9583	−	13.3103i	0.549842	−	0.612010i
$474$	18.2591			0.838670
$475$	−2.77991	+	2.01972i	−0.127551	+	0.0926712i
$476$	−1.06449	−	3.27617i	−0.0487909	−	0.150163i
$477$	−6.09826	+	18.7685i	−0.279220	+	0.859352i
$478$	0.317880	+	0.230953i	0.0145395	+	0.0105636i
$479$	−2.43807	−	1.77136i	−0.111398	−	0.0809357i	0.530691	−	0.847565i	$-0.321932\pi$
$479$	−2.43807	−	1.77136i	−0.111398	−	0.0809357i	−0.642090	+	0.766629i	$0.721932\pi$
$480$	0.347506	−	1.06951i	0.0158614	−	0.0488165i
$481$	−1.70523	−	5.24816i	−0.0777519	−	0.239296i
$482$	2.69144	−	1.95545i	0.122592	−	0.0890682i
$483$	4.09241			0.186211
$484$	−10.7646	−	2.26342i	−0.489301	−	0.102883i
$485$	−2.88993			−0.131225
$486$	12.2128	−	8.87308i	0.553982	−	0.402491i
$487$	0.928754	+	2.85841i	0.0420858	+	0.129527i	0.969892	−	0.243536i	$-0.0783075\pi$
$487$	0.928754	+	2.85841i	0.0420858	+	0.129527i	−0.927806	+	0.373063i	$0.878307\pi$
$488$	0.140984	−	0.433905i	0.00638206	−	0.0196420i
$489$	0.823710	+	0.598461i	0.0372495	+	0.0270633i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	10.7143	−	32.9753i	0.483531	−	1.48815i	−0.350567	−	0.936538i	$-0.614011\pi$
$491$	10.7143	−	32.9753i	0.483531	−	1.48815i	0.834098	−	0.551617i	$-0.185989\pi$
$492$	1.74409	+	5.36774i	0.0786295	+	0.241997i
$493$	24.2263	−	17.6014i	1.09110	−	0.792728i
$494$	24.2918			1.09294
$495$	−3.84655	+	4.28146i	−0.172890	+	0.192437i
$496$	−4.52145			−0.203019
$497$	−5.51245	+	4.00503i	−0.247267	+	0.179650i
$498$	−2.57274	−	7.91809i	−0.115287	−	0.354818i
$499$	−1.62301	+	4.99510i	−0.0726558	+	0.223611i	−0.980790	−	0.195069i	$-0.937507\pi$
$499$	−1.62301	+	4.99510i	−0.0726558	+	0.223611i	0.908134	+	0.418680i	$0.137507\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−3.31236	−	2.40657i	−0.147985	−	0.107518i
$502$	5.33843	−	16.4300i	0.238266	−	0.733307i
$503$	10.3992	+	32.0054i	0.463677	+	1.42705i	0.860639	+	0.509215i	$0.170064\pi$
$503$	10.3992	+	32.0054i	0.463677	+	1.42705i	−0.396962	+	0.917835i	$0.629936\pi$
$504$	−1.40395	+	1.02003i	−0.0625369	+	0.0454357i
$505$	−12.2266			−0.544076
$506$	1.24845	−	12.0049i	0.0555005	−	0.533683i
$507$	−41.5828			−1.84676
$508$	−17.2005	+	12.4969i	−0.763148	+	0.554459i
$509$	−6.23081	−	19.1765i	−0.276176	−	0.849982i	−0.988906	−	0.148543i	$-0.952542\pi$
$509$	−6.23081	−	19.1765i	−0.276176	−	0.849982i	0.712730	−	0.701438i	$-0.247458\pi$
$510$	1.19708	−	3.68423i	0.0530076	−	0.163141i
$511$	−12.2284	−	8.88446i	−0.540953	−	0.393025i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	5.65445	−	17.4026i	0.249650	−	0.768344i
$514$	−0.138608	−	0.426591i	−0.00611373	−	0.0188161i
$515$	2.99849	−	2.17853i	0.132129	−	0.0959975i
$516$	6.06697			0.267083
$517$	−29.7915	−	13.2249i	−1.31023	−	0.581630i
$518$	0.780576			0.0342965
$519$	−2.89251	+	2.10153i	−0.126967	+	0.0922471i
$520$	−2.18458	−	6.72345i	−0.0958002	−	0.294843i
$521$	−10.5375	+	32.4312i	−0.461658	+	1.42084i	0.401479	+	0.915868i	$0.368496\pi$
$521$	−10.5375	+	32.4312i	−0.461658	+	1.42084i	−0.863137	+	0.504970i	$0.831504\pi$
$522$	−12.2045	−	8.86709i	−0.534177	−	0.388102i
$523$	30.3943	+	22.0828i	1.32905	+	0.965612i	0.999771	+	0.0213788i	$0.00680559\pi$
$523$	30.3943	+	22.0828i	1.32905	+	0.965612i	0.329279	+	0.944233i	$0.393194\pi$
$524$	3.17167	−	9.76139i	0.138555	−	0.426428i
$525$	0.347506	+	1.06951i	0.0151664	+	0.0466775i
$526$	−21.1509	+	15.3670i	−0.922224	+	0.670035i
$527$	−15.5753			−0.678472
$528$	−1.86840	−	3.22799i	−0.0813119	−	0.140480i
$529$	−9.75670			−0.424204
$530$	9.19999	−	6.68419i	0.399622	−	0.290342i
$531$	5.64398	+	17.3704i	0.244928	+	0.753811i
$532$	−1.06183	+	3.26798i	−0.0460362	+	0.141685i
$533$	28.7044	+	20.8550i	1.24333	+	0.903329i
$534$	−4.52292	−	3.28610i	−0.195726	−	0.142203i
$535$	0.881029	−	2.71153i	0.0380902	−	0.117230i
$536$	3.24274	+	9.98012i	0.140065	+	0.431075i
$537$	4.07708	−	2.96217i	0.175939	−	0.127827i
$538$	14.1617			0.610554
$539$	3.24339	−	0.693123i	0.139703	−	0.0298549i
$540$	−5.32519			−0.229160
$541$	18.3195	−	13.3099i	0.787616	−	0.572236i	−0.119639	−	0.992817i	$-0.538174\pi$
$541$	18.3195	−	13.3099i	0.787616	−	0.572236i	0.907255	+	0.420581i	$0.138174\pi$
$542$	−0.288687	−	0.888488i	−0.0124002	−	0.0381638i
$543$	3.13776	−	9.65705i	0.134654	−	0.414424i
$544$	−2.78688	−	2.02478i	−0.119486	−	0.0868119i
$545$	7.92934	+	5.76101i	0.339656	+	0.246774i
$546$	2.45668	−	7.56089i	0.105136	−	0.323576i
$547$	7.52934	+	23.1729i	0.321931	+	0.990803i	0.972807	+	0.231619i	$0.0744021\pi$
$547$	7.52934	+	23.1729i	0.321931	+	0.990803i	−0.650875	+	0.759185i	$0.725598\pi$
$548$	0.615590	−	0.447252i	0.0262967	−	0.0191057i
$549$	−0.791739			−0.0337906
$550$	3.24339	−	0.693123i	0.138299	−	0.0295549i
$551$	−29.8704			−1.27252
$552$	3.31083	−	2.40546i	0.140918	−	0.102383i
$553$	5.01744	+	15.4421i	0.213363	+	0.656664i
$554$	−7.82581	+	24.0854i	−0.332487	+	1.02329i
$555$	0.710155	+	0.515958i	0.0301444	+	0.0219012i
$556$	−14.2692	−	10.3672i	−0.605150	−	0.439667i
$557$	7.77197	−	23.9197i	0.329309	−	1.01351i	−0.640149	−	0.768251i	$-0.721127\pi$
$557$	7.77197	−	23.9197i	0.329309	−	1.01351i	0.969458	−	0.245258i	$-0.0788727\pi$
$558$	2.42467	+	7.46238i	0.102645	+	0.315908i
$559$	30.8556	−	22.4179i	1.30505	−	0.948178i
$560$	1.00000			0.0422577
$561$	−6.43622	−	11.1197i	−0.271738	−	0.469473i
$562$	27.7779			1.17174
$563$	16.3399	−	11.8716i	0.688645	−	0.500330i	−0.187570	−	0.982251i	$-0.560061\pi$
$563$	16.3399	−	11.8716i	0.688645	−	0.500330i	0.876214	+	0.481922i	$0.160061\pi$
$564$	−3.41521	−	10.5109i	−0.143806	−	0.442590i
$565$	−3.33837	+	10.2745i	−0.140446	+	0.432250i
$566$	15.7882	+	11.4708i	0.663628	+	0.482154i
$567$	−0.632922	−	0.459845i	−0.0265802	−	0.0193117i
$568$	−2.10557	+	6.48027i	−0.0883477	+	0.271906i
$569$	8.00175	+	24.6269i	0.335451	+	1.03241i	0.966500	+	0.256668i	$0.0826248\pi$
$569$	8.00175	+	24.6269i	0.335451	+	1.03241i	−0.631049	+	0.775743i	$0.717375\pi$
$570$	−3.12616	+	2.27129i	−0.130940	+	0.0951338i
$571$	22.4564			0.939771			0.469885	−	0.882727i	$-0.344295\pi$
$571$	22.4564			0.939771			0.469885	+	0.882727i	$0.344295\pi$
$572$	−21.4301	−	9.51314i	−0.896037	−	0.397764i
$573$	−3.27099			−0.136648
$574$	−4.06034	+	2.95001i	−0.169475	+	0.123131i
$575$	1.12455	+	3.46102i	0.0468972	+	0.144335i
$576$	−0.536261	+	1.65044i	−0.0223442	+	0.0687684i
$577$	27.3915	+	19.9011i	1.14032	+	0.828493i	0.987164	−	0.159709i	$-0.0510555\pi$
$577$	27.3915	+	19.9011i	1.14032	+	0.828493i	0.153159	+	0.988202i	$0.451055\pi$
$578$	4.15315	+	3.01744i	0.172748	+	0.125509i
$579$	2.70124	−	8.31356i	0.112260	−	0.345500i
$580$	2.68628	+	8.26751i	0.111542	+	0.343290i
$581$	5.98951	−	4.35163i	0.248487	−	0.180536i
$582$	−3.24988			−0.134712
$583$	3.90125	−	37.5137i	0.161573	−	1.55366i
$584$	−15.1151			−0.625469
$585$	−9.92516	+	7.21105i	−0.410355	+	0.298140i
$586$	−4.12553	−	12.6971i	−0.170424	−	0.524512i
$587$	8.82383	−	27.1570i	0.364198	−	1.12089i	−0.586283	−	0.810106i	$-0.699409\pi$
$587$	8.82383	−	27.1570i	0.364198	−	1.12089i	0.950481	−	0.310781i	$-0.100591\pi$
$588$	0.909784	+	0.660997i	0.0375188	+	0.0272590i
$589$	12.5692	+	9.13206i	0.517905	+	0.376280i
$590$	3.25231	−	10.0096i	0.133895	−	0.412088i
$591$	−9.11362	−	28.0488i	−0.374884	−	1.15377i
$592$	0.631499	−	0.458811i	0.0259545	−	0.0188570i
$593$	34.9417			1.43488			0.717442	−	0.696618i	$-0.245313\pi$
$593$	34.9417			1.43488			0.717442	+	0.696618i	$0.245313\pi$
$594$	−11.8036	+	13.1381i	−0.484306	+	0.539064i
$595$	3.44477			0.141222
$596$	−0.629561	+	0.457403i	−0.0257878	+	0.0187359i
$597$	−1.96328	−	6.04236i	−0.0803518	−	0.247297i
$598$	7.94999	−	24.4675i	0.325099	−	1.00055i
$599$	25.1312	+	18.2589i	1.02683	+	0.746039i	0.967673	−	0.252210i	$-0.0811573\pi$
$599$	25.1312	+	18.2589i	1.02683	+	0.746039i	0.0591616	+	0.998248i	$0.481157\pi$
$600$	0.909784	+	0.660997i	0.0371418	+	0.0269851i
$601$	−13.3681	+	41.1429i	−0.545298	+	1.67825i	0.174983	+	0.984571i	$0.444013\pi$
$601$	−13.3681	+	41.1429i	−0.545298	+	1.67825i	−0.720281	+	0.693683i	$0.755987\pi$
$602$	1.66715	+	5.13095i	0.0679478	+	0.209122i
$603$	14.7326	−	10.7039i	0.599960	−	0.435896i
$604$	13.4154			0.545864
$605$	5.47909	−	9.53832i	0.222757	−	0.387788i
$606$	−13.7495			−0.558534
$607$	26.7795	−	19.4565i	1.08695	−	0.789714i	0.108067	−	0.994144i	$-0.465534\pi$
$607$	26.7795	−	19.4565i	1.08695	−	0.789714i	0.978881	+	0.204430i	$0.0655340\pi$
$608$	1.06183	+	3.26798i	0.0430629	+	0.132534i
$609$	−3.02087	+	9.29727i	−0.122412	+	0.376744i
$610$	0.369102	+	0.268168i	0.0149445	+	0.0108578i
$611$	−56.2079	−	40.8374i	−2.27393	−	1.65211i
$612$	−1.84730	+	5.68539i	−0.0746725	+	0.229818i
$613$	−5.26159	−	16.1935i	−0.212514	−	0.654049i	−0.999321	−	0.0368507i	$-0.988267\pi$
$613$	−5.26159	−	16.1935i	−0.212514	−	0.654049i	0.786807	−	0.617199i	$-0.211733\pi$
$614$	−20.8604	+	15.1559i	−0.841856	+	0.611644i
$615$	−5.64398			−0.227587
$616$	2.21655	−	2.46717i	0.0893074	−	0.0994049i
$617$	3.82168			0.153855			0.0769276	−	0.997037i	$-0.475489\pi$
$617$	3.82168			0.153855			0.0769276	+	0.997037i	$0.475489\pi$
$618$	3.37196	−	2.44987i	0.135640	−	0.0985484i
$619$	−8.79419	−	27.0657i	−0.353468	−	1.08786i	−0.956892	−	0.290443i	$-0.906197\pi$
$619$	−8.79419	−	27.0657i	−0.353468	−	1.08786i	0.603424	−	0.797421i	$-0.293803\pi$
$620$	1.39720	−	4.30015i	0.0561130	−	0.172698i
$621$	−15.6780	−	11.3907i	−0.629137	−	0.457095i
$622$	−4.13844	−	3.00676i	−0.165936	−	0.120560i
$623$	1.53626	−	4.72811i	0.0615488	−	0.189428i
$624$	−2.45668	−	7.56089i	−0.0983459	−	0.302678i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	16.5571			0.661753
$627$	−1.32565	+	12.7472i	−0.0529412	+	0.509073i
$628$	−24.0361			−0.959146
$629$	2.17537	−	1.58050i	0.0867376	−	0.0630186i
$630$	−0.536261	−	1.65044i	−0.0213652	−	0.0657552i
$631$	2.75267	−	8.47185i	0.109582	−	0.337259i	−0.881196	−	0.472750i	$-0.843261\pi$
$631$	2.75267	−	8.47185i	0.109582	−	0.337259i	0.990779	+	0.135491i	$0.0432612\pi$
$632$	13.1358	+	9.54373i	0.522515	+	0.379629i
$633$	6.75945	+	4.91103i	0.268664	+	0.195196i
$634$	4.74342	−	14.5987i	0.188385	−	0.579790i
$635$	−6.57000	−	20.2204i	−0.260722	−	0.802421i
$636$	10.3459	−	7.51673i	0.410241	−	0.298058i
$637$	7.06945			0.280102
$638$	26.3516	+	11.6979i	1.04327	+	0.463123i
$639$	11.8244			0.467768
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	8.72200	+	26.8436i	0.344498	+	1.06026i	0.961852	+	0.273571i	$0.0882049\pi$
$641$	8.72200	+	26.8436i	0.344498	+	1.06026i	−0.617353	+	0.786686i	$0.711795\pi$
$642$	0.990765	−	3.04926i	0.0391024	−	0.120345i
$643$	−22.4478	−	16.3093i	−0.885255	−	0.643175i	0.0493818	−	0.998780i	$-0.484275\pi$
$643$	−22.4478	−	16.3093i	−0.885255	−	0.643175i	−0.934636	+	0.355605i	$0.884275\pi$
$644$	2.94412	+	2.13903i	0.116015	+	0.0842896i
$645$	−1.87480	+	5.77003i	−0.0738200	+	0.227195i
$646$	3.65776	+	11.2574i	0.143913	+	0.442918i
$647$	−21.0894	+	15.3223i	−0.829110	+	0.602383i	−0.919307	−	0.393540i	$-0.871250\pi$
$647$	−21.0894	+	15.3223i	−0.829110	+	0.602383i	0.0901976	+	0.995924i	$0.471250\pi$
$648$	−0.782335			−0.0307330
$649$	−17.4864	−	30.2107i	−0.686401	−	1.18587i
$650$	7.06945			0.277287
$651$	4.11354	−	2.98866i	0.161222	−	0.117135i
$652$	0.279781	+	0.861078i	0.0109571	+	0.0337224i
$653$	3.35513	−	10.3260i	0.131296	−	0.404088i	−0.863699	−	0.504008i	$-0.831858\pi$
$653$	3.35513	−	10.3260i	0.131296	−	0.404088i	0.994996	+	0.0999191i	$0.0318584\pi$
$654$	8.91698	+	6.47857i	0.348682	+	0.253332i
$655$	8.30354	+	6.03287i	0.324446	+	0.235724i
$656$	−1.55091	+	4.77322i	−0.0605530	+	0.186363i
$657$	8.10566	+	24.9467i	0.316232	+	0.973262i
$658$	7.95082	−	5.77661i	0.309955	−	0.225196i
$659$	−8.76914			−0.341597			−0.170799	−	0.985306i	$-0.554635\pi$
$659$	−8.76914			−0.341597			−0.170799	+	0.985306i	$0.554635\pi$
$660$	3.64737	−	0.779455i	0.141974	−	0.0303402i
$661$	−18.7665			−0.729934			−0.364967	−	0.931020i	$-0.618920\pi$
$661$	−18.7665			−0.729934			−0.364967	+	0.931020i	$0.618920\pi$
$662$	5.33265	−	3.87439i	0.207259	−	0.150583i
$663$	−8.46270	−	26.0455i	−0.328664	−	1.01152i
$664$	2.28779	−	7.04109i	0.0887834	−	0.273247i
$665$	−2.77991	−	2.01972i	−0.107800	−	0.0783215i
$666$	−1.09589	−	0.796210i	−0.0424649	−	0.0308525i
$667$	−9.77573	+	30.0866i	−0.378518	+	1.16496i
$668$	−1.12507	−	3.46262i	−0.0435304	−	0.133973i
$669$	1.37529	−	0.999210i	0.0531720	−	0.0386317i
$670$	−10.4937			−0.405408
$671$	1.47975	−	0.316227i	0.0571250	−	0.0122078i
$672$	1.12455			0.0433806
$673$	−10.5371	+	7.65567i	−0.406176	+	0.295104i	−0.772052	−	0.635559i	$-0.780770\pi$
$673$	−10.5371	+	7.65567i	−0.406176	+	0.295104i	0.365876	+	0.930664i	$0.380770\pi$
$674$	−5.91912	−	18.2172i	−0.227996	−	0.701699i
$675$	1.64557	−	5.06456i	0.0633382	−	0.194935i
$676$	−29.9152	−	21.7346i	−1.15058	−	0.835948i
$677$	8.15524	+	5.92513i	0.313431	+	0.227721i	0.733367	−	0.679832i	$-0.237948\pi$
$677$	8.15524	+	5.92513i	0.313431	+	0.227721i	−0.419936	+	0.907554i	$0.637948\pi$
$678$	−3.75418	+	11.5542i	−0.144178	+	0.443736i
$679$	−0.893036	−	2.74848i	−0.0342716	−	0.105477i
$680$	2.78688	−	2.02478i	0.106872	−	0.0776469i
$681$	−15.5816			−0.597087
$682$	−7.51221	−	12.9786i	−0.287657	−	0.496977i
$683$	−8.98900			−0.343955			−0.171977	−	0.985101i	$-0.555016\pi$
$683$	−8.98900			−0.343955			−0.171977	+	0.985101i	$0.555016\pi$
$684$	4.82419	−	3.50498i	0.184458	−	0.134016i
$685$	0.235134	+	0.723669i	0.00898402	+	0.0276500i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	18.6927	+	13.5811i	0.713172	+	0.518150i
$688$	4.36464	+	3.17110i	0.166400	+	0.120897i
$689$	24.8427	−	76.4578i	0.946430	−	2.91281i
$690$	1.26462	+	3.89211i	0.0481434	+	0.148170i
$691$	−36.8731	+	26.7899i	−1.40272	+	1.01914i	−0.408390	+	0.912808i	$0.633910\pi$
$691$	−36.8731	+	26.7899i	−1.40272	+	1.01914i	−0.994331	+	0.106329i	$0.966090\pi$
$692$	−3.17934			−0.120860
$693$	−5.26056	−	2.33524i	−0.199832	−	0.0887085i
$694$	−9.00265			−0.341736
$695$	14.2692	−	10.3672i	0.541263	−	0.393250i
$696$	3.02087	+	9.29727i	0.114506	+	0.352412i
$697$	−5.34254	+	16.4426i	−0.202363	+	0.622809i
$698$	5.44372	+	3.95509i	0.206048	+	0.149703i
$699$	14.7699	+	10.7310i	0.558649	+	0.405883i
$700$	−0.309017	+	0.951057i	−0.0116797	+	0.0359466i
$701$	3.67718	+	11.3172i	0.138885	+	0.427445i	0.996174	−	0.0873909i	$-0.0278529\pi$
$701$	3.67718	+	11.3172i	0.138885	+	0.427445i	−0.857289	+	0.514836i	$0.827853\pi$
$702$	−30.4564	+	22.1279i	−1.14950	+	0.835163i
$703$	−2.68218			−0.101160
$704$	0.343063	−	3.29883i	0.0129297	−	0.124329i
$705$	11.0518			0.416236
$706$	24.2043	−	17.5855i	0.910941	−	0.661838i
$707$	−3.77822	−	11.6282i	−0.142095	−	0.437323i
$708$	3.65740	−	11.2563i	0.137453	−	0.423038i
$709$	41.4256	+	30.0974i	1.55577	+	1.13033i	0.939373	+	0.342897i	$0.111408\pi$
$709$	41.4256	+	30.0974i	1.55577	+	1.13033i	0.616397	+	0.787436i	$0.288592\pi$
$710$	−5.51245	−	4.00503i	−0.206879	−	0.150306i
$711$	8.70715	−	26.7978i	0.326543	−	1.00500i
$712$	−1.53626	−	4.72811i	−0.0575736	−	0.177193i
$713$	13.3117	−	9.67151i	0.498527	−	0.362201i
$714$	3.87383			0.144974
$715$	15.6698	−	17.4415i	0.586017	−	0.652276i
$716$	4.48137			0.167477
$717$	−0.357473	+	0.259720i	−0.0133501	+	0.00969941i
$718$	−7.28112	−	22.4090i	−0.271729	−	0.836295i
$719$	−8.61102	+	26.5020i	−0.321137	+	0.988357i	0.652018	+	0.758204i	$0.273923\pi$
$719$	−8.61102	+	26.5020i	−0.321137	+	0.988357i	−0.973154	+	0.230154i	$0.926077\pi$
$720$	−1.40395	−	1.02003i	−0.0523221	−	0.0380142i
$721$	2.99849	+	2.17853i	0.111670	+	0.0811327i
$722$	−2.22271	+	6.84078i	−0.0827205	+	0.254588i
$723$	1.15609	+	3.55807i	0.0429953	+	0.132326i
$724$	7.30491	−	5.30733i	0.271485	−	0.197245i
$725$	−8.69298			−0.322849
$726$	6.16153	−	10.7264i	0.228676	−	0.398093i
$727$	41.3933			1.53519			0.767597	−	0.640933i	$-0.221453\pi$
$727$	41.3933			1.53519			0.767597	+	0.640933i	$0.221453\pi$
$728$	5.71931	−	4.15532i	0.211972	−	0.154006i
$729$	5.97115	+	18.3773i	0.221154	+	0.680641i
$730$	4.67084	−	14.3754i	0.172875	−	0.532056i
$731$	15.0352	+	10.9237i	0.556096	+	0.404028i
$732$	0.415075	+	0.301570i	0.0153416	+	0.0111463i
$733$	−1.80755	+	5.56306i	−0.0667633	+	0.205476i	−0.978873	−	0.204470i	$-0.934453\pi$
$733$	−1.80755	+	5.56306i	−0.0667633	+	0.205476i	0.912109	+	0.409947i	$0.134453\pi$
$734$	−3.14266	−	9.67211i	−0.115998	−	0.357004i
$735$	−0.909784	+	0.660997i	−0.0335579	+	0.0243812i
$736$	3.63913			0.134140
$737$	−23.2598	+	25.8897i	−0.856788	+	0.953661i
$738$	8.70961			0.320605
$739$	−39.2795	+	28.5382i	−1.44492	+	1.04979i	−0.457933	+	0.888987i	$0.651410\pi$
$739$	−39.2795	+	28.5382i	−1.44492	+	1.04979i	−0.986986	+	0.160808i	$0.948590\pi$
$740$	0.241211	+	0.742372i	0.00886710	+	0.0272901i
$741$	−8.44154	+	25.9804i	−0.310108	+	0.954413i
$742$	9.19999	+	6.68419i	0.337742	+	0.245384i
$743$	−27.3921	−	19.9015i	−1.00492	−	0.730115i	−0.0417807	−	0.999127i	$-0.513303\pi$
$743$	−27.3921	−	19.9015i	−1.00492	−	0.730115i	−0.963137	+	0.269011i	$0.913303\pi$
$744$	1.57123	−	4.83575i	0.0576041	−	0.177287i
$745$	−0.240471	−	0.740093i	−0.00881017	−	0.0271149i
$746$	−8.71852	+	6.33438i	−0.319208	+	0.231918i
$747$	−12.8478			−0.470075
$748$	1.18177	−	11.3637i	0.0432099	−	0.415499i
$749$	2.85107			0.104176
$750$	−0.909784	+	0.660997i	−0.0332206	+	0.0241362i
$751$	10.7866	+	33.1976i	0.393608	+	1.21140i	0.930041	+	0.367457i	$0.119771\pi$
$751$	10.7866	+	33.1976i	0.393608	+	1.21140i	−0.536433	+	0.843943i	$0.680229\pi$
$752$	3.03694	−	9.34674i	0.110746	−	0.340841i
$753$	15.7170	+	11.4191i	0.572759	+	0.416134i
$754$	49.7178	+	36.1221i	1.81062	+	1.31549i
$755$	−4.14558	+	12.7588i	−0.150873	+	0.464339i
$756$	−1.64557	−	5.06456i	−0.0598490	−	0.184196i
$757$	15.1572	−	11.0124i	0.550899	−	0.400251i	−0.277218	−	0.960807i	$-0.589412\pi$
$757$	15.1572	−	11.0124i	0.550899	−	0.400251i	0.828117	+	0.560556i	$0.189412\pi$
$758$	−5.39945			−0.196117
$759$	12.4056	+	5.50702i	0.450294	+	0.199892i
$760$	−3.43616			−0.124643
$761$	21.5708	−	15.6721i	0.781940	−	0.568113i	−0.123620	−	0.992330i	$-0.539451\pi$
$761$	21.5708	−	15.6721i	0.781940	−	0.568113i	0.905561	+	0.424217i	$0.139451\pi$
$762$	−7.38832	−	22.7389i	−0.267651	−	0.823744i
$763$	−3.02874	+	9.32150i	−0.109648	+	0.337461i
$764$	−2.35319	−	1.70969i	−0.0851354	−	0.0618545i
$765$	−4.83628	−	3.51376i	−0.174856	−	0.127040i
$766$	2.21721	−	6.82388i	0.0801111	−	0.246557i
$767$	−22.9921	−	70.7623i	−0.830195	−	2.55508i
$768$	0.909784	−	0.660997i	0.0328290	−	0.0238517i
$769$	−38.2777			−1.38033			−0.690165	−	0.723652i	$-0.742462\pi$
$769$	−38.2777			−1.38033			−0.690165	+	0.723652i	$0.742462\pi$
$770$	1.66146	+	2.87046i	0.0598749	+	0.103444i
$771$	0.504413			0.0181660
$772$	6.28865	−	4.56897i	0.226334	−	0.164441i
$773$	2.32453	+	7.15415i	0.0836074	+	0.257317i	0.984118	−	0.177518i	$-0.0568068\pi$
$773$	2.32453	+	7.15415i	0.0836074	+	0.257317i	−0.900510	+	0.434835i	$0.856807\pi$
$774$	2.89313	−	8.90412i	0.103991	−	0.320052i
$775$	3.65793	+	2.65764i	0.131397	+	0.0954652i
$776$	−2.33800	−	1.69866i	−0.0839293	−	0.0609782i
$777$	−0.271255	+	0.834838i	−0.00973123	+	0.0299496i
$778$	5.11076	+	15.7293i	0.183230	+	0.563923i
$779$	13.9520	−	10.1367i	0.499881	−	0.363185i
$780$	7.94999			0.284655
$781$	−22.0997	+	4.72278i	−0.790789	+	0.168994i
$782$	12.5360			0.448286
$783$	37.4508	−	27.2096i	1.33838	−	0.972392i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	7.42757	−	22.8597i	0.265101	−	0.815898i
$786$	9.33778	+	6.78430i	0.333068	+	0.241988i
$787$	−0.174130	−	0.126513i	−0.00620706	−	0.00450969i	0.584677	−	0.811266i	$-0.301221\pi$
$787$	−0.174130	−	0.126513i	−0.00620706	−	0.00450969i	−0.590884	+	0.806756i	$0.701221\pi$
$788$	8.10420	−	24.9422i	0.288700	−	0.888528i
$789$	−9.08520	−	27.9614i	−0.323442	−	0.995451i
$790$	−13.1358	+	9.54373i	−0.467352	+	0.339551i
$791$	−10.8032			−0.384118
$792$	−5.62851	+	1.20283i	−0.200000	+	0.0427407i
$793$	3.22533			0.114535
$794$	−13.5440	+	9.84028i	−0.480658	+	0.349219i
$795$	3.95178	+	12.1623i	0.140155	+	0.431353i
$796$	1.74583	−	5.37311i	0.0618793	−	0.190445i
$797$	−22.8660	−	16.6131i	−0.809955	−	0.588467i	0.103862	−	0.994592i	$-0.466880\pi$
$797$	−22.8660	−	16.6131i	−0.809955	−	0.588467i	−0.913818	+	0.406125i	$0.866880\pi$
$798$	−3.12616	−	2.27129i	−0.110665	−	0.0804027i
$799$	10.4616	−	32.1974i	0.370103	−	1.13906i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	−6.97963	+	5.07100i	−0.246613	+	0.179175i
$802$	−20.3412			−0.718273
$803$	−25.1132	−	43.3874i	−0.886227	−	1.53111i
$804$	−11.8008			−0.416181
$805$	−2.94412	+	2.13903i	−0.103767	+	0.0753909i
$806$	−9.87746	−	30.3997i	−0.347919	−	1.07078i
$807$	−4.92128	+	15.1461i	−0.173237	+	0.533169i
$808$	−9.89152	−	7.18661i	−0.347982	−	0.252824i
$809$	3.70358	+	2.69081i	0.130211	+	0.0946038i	0.650984	−	0.759091i	$-0.274356\pi$
$809$	3.70358	+	2.69081i	0.130211	+	0.0946038i	−0.520773	+	0.853695i	$0.674356\pi$
$810$	0.241755	−	0.744045i	0.00849440	−	0.0261431i
$811$	13.7289	+	42.2533i	0.482088	+	1.48371i	0.836154	+	0.548494i	$0.184799\pi$
$811$	13.7289	+	42.2533i	0.482088	+	1.48371i	−0.354066	+	0.935220i	$0.615201\pi$
$812$	−7.03277	+	5.10961i	−0.246802	+	0.179312i
$813$	1.05057			0.0368451
$814$	2.36621	+	1.05040i	0.0829357	+	0.0368164i
$815$	−0.905391			−0.0317145
$816$	3.13399	−	2.27698i	0.109712	−	0.0797103i
$817$	−5.72857	−	17.6307i	−0.200417	−	0.616821i
$818$	−0.137077	+	0.421878i	−0.00479277	+	0.0147506i
$819$	−9.92516	−	7.21105i	−0.346813	−	0.251974i
$820$	−4.06034	−	2.95001i	−0.141793	−	0.103019i
$821$	15.9233	−	49.0068i	0.555726	−	1.71035i	−0.138291	−	0.990392i	$-0.544161\pi$
$821$	15.9233	−	49.0068i	0.555726	−	1.71035i	0.694017	−	0.719958i	$-0.255839\pi$
$822$	0.264421	+	0.813805i	0.00922276	+	0.0283847i
$823$	−2.43589	+	1.76978i	−0.0849099	+	0.0616906i	−0.629430	−	0.777057i	$-0.716712\pi$
$823$	−2.43589	+	1.76978i	−0.0849099	+	0.0616906i	0.544520	+	0.838748i	$0.316712\pi$
$824$	3.70633			0.129116
$825$	−0.385793	+	3.70972i	−0.0134316	+	0.129156i
$826$	10.5247			0.366201
$827$	14.2048	−	10.3204i	0.493949	−	0.358875i	−0.312752	−	0.949835i	$-0.601251\pi$
$827$	14.2048	−	10.3204i	0.493949	−	0.358875i	0.806701	+	0.590960i	$0.201251\pi$
$828$	−1.95153	−	6.00618i	−0.0678202	−	0.208729i
$829$	−16.9889	+	52.2865i	−0.590049	+	1.81598i	−0.0120791	+	0.999927i	$0.503845\pi$
$829$	−16.9889	+	52.2865i	−0.590049	+	1.81598i	−0.577970	+	0.816058i	$0.696155\pi$
$830$	5.98951	+	4.35163i	0.207899	+	0.151047i
$831$	−23.0401	−	16.7396i	−0.799254	−	0.580692i
$832$	2.18458	−	6.72345i	0.0757367	−	0.233094i
$833$	1.06449	+	3.27617i	0.0368825	+	0.113513i
$834$	16.0465	−	11.6585i	0.555646	−	0.403700i
$835$	3.64082			0.125996
$836$	−7.61641	+	8.47757i	−0.263419	+	0.293203i
$837$	−24.0776			−0.832242
$838$	15.0918	−	10.9648i	0.521337	−	0.378773i
$839$	2.51632	+	7.74445i	0.0868732	+	0.267368i	0.985051	−	0.172265i	$-0.0551085\pi$
$839$	2.51632	+	7.74445i	0.0868732	+	0.267368i	−0.898177	+	0.439633i	$0.855109\pi$
$840$	−0.347506	+	1.06951i	−0.0119901	+	0.0369018i
$841$	−37.6742	−	27.3719i	−1.29911	−	0.943859i
$842$	−9.92792	−	7.21306i	−0.342139	−	0.248578i
$843$	−9.65300	+	29.7089i	−0.332467	+	1.02323i
$844$	2.29591	+	7.06609i	0.0790286	+	0.243225i
$845$	29.9152	−	21.7346i	1.02911	−	0.747694i
$846$	−17.0549			−0.586358
$847$	10.7646	+	2.26342i	0.369877	+	0.0777720i
$848$	11.3718			0.390510
$849$	−17.7547	+	12.8995i	−0.609340	+	0.442711i
$850$	1.06449	+	3.27617i	0.0365118	+	0.112372i
$851$	−0.877800	+	2.70159i	−0.0300906	+	0.0926094i
$852$	−6.19905	−	4.50387i	−0.212376	−	0.154300i
$853$	14.9235	+	10.8425i	0.510969	+	0.371241i	0.813191	−	0.581997i	$-0.197728\pi$
$853$	14.9235	+	10.8425i	0.510969	+	0.371241i	−0.302222	+	0.953238i	$0.597728\pi$
$854$	−0.140984	+	0.433905i	−0.00482438	+	0.0148479i
$855$	1.84268	+	5.67118i	0.0630182	+	0.193950i
$856$	2.30656	−	1.67582i	0.0788367	−	0.0572782i
$857$	36.0108			1.23011			0.615054	−	0.788485i	$-0.289134\pi$
$857$	36.0108			1.23011			0.615054	+	0.788485i	$0.289134\pi$
$858$	17.6215	−	19.6139i	0.601590	−	0.669609i
$859$	25.6553			0.875349			0.437674	−	0.899134i	$-0.355802\pi$
$859$	25.6553			0.875349			0.437674	+	0.899134i	$0.355802\pi$
$860$	−4.36464	+	3.17110i	−0.148833	+	0.108134i
$861$	−1.74409	−	5.36774i	−0.0594383	−	0.182932i
$862$	6.79205	−	20.9038i	0.231338	−	0.711985i
$863$	−12.5009	−	9.08242i	−0.425535	−	0.309169i	0.354326	−	0.935122i	$-0.384710\pi$
$863$	−12.5009	−	9.08242i	−0.425535	−	0.309169i	−0.779861	+	0.625953i	$0.784710\pi$
$864$	−4.30817	−	3.13007i	−0.146567	−	0.106487i
$865$	0.982471	−	3.02373i	0.0334050	−	0.102810i
$866$	6.87085	+	21.1463i	0.233481	+	0.718581i
$867$	−4.67044	+	3.39327i	−0.158616	+	0.115242i
$868$	4.52145			0.153468
$869$	−5.57024	+	53.5624i	−0.188957	+	1.81698i
$870$	−9.77573			−0.331428
$871$	−60.0168	+	43.6048i	−2.03359	+	1.47749i
$872$	3.02874	+	9.32150i	0.102566	+	0.315666i
$873$	−1.54975	+	4.76965i	−0.0524512	+	0.161428i
$874$	−10.1165	−	7.35004i	−0.342195	−	0.248619i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	5.25261	−	16.1659i	0.177469	−	0.546194i
$877$	8.62760	+	26.5530i	0.291333	+	0.896632i	0.984428	+	0.175786i	$0.0562466\pi$
$877$	8.62760	+	26.5530i	0.291333	+	0.896632i	−0.693095	+	0.720846i	$0.743753\pi$
$878$	8.92365	−	6.48341i	0.301159	−	0.218804i
$879$	15.0134			0.506388
$880$	3.03137	+	1.34567i	0.102187	+	0.0453625i
$881$	23.1798			0.780946			0.390473	−	0.920614i	$-0.372311\pi$
$881$	23.1798			0.780946			0.390473	+	0.920614i	$0.372311\pi$
$882$	1.40395	−	1.02003i	0.0472734	−	0.0343462i
$883$	7.56807	+	23.2921i	0.254686	+	0.783843i	0.993891	+	0.110363i	$0.0352012\pi$
$883$	7.56807	+	23.2921i	0.254686	+	0.783843i	−0.739205	+	0.673480i	$0.764799\pi$
$884$	7.52538	−	23.1607i	0.253106	−	0.778980i
$885$	9.57520	+	6.95679i	0.321867	+	0.233850i
$886$	−24.9745	−	18.1451i	−0.839036	−	0.609596i
$887$	−6.98948	+	21.5114i	−0.234684	+	0.722283i	0.762479	+	0.647013i	$0.223982\pi$
$887$	−6.98948	+	21.5114i	−0.234684	+	0.722283i	−0.997163	+	0.0752700i	$0.976018\pi$
$888$	0.271255	+	0.834838i	0.00910273	+	0.0280153i
$889$	17.2005	−	12.4969i	0.576886	−	0.419132i
$890$	4.97143			0.166643
$891$	−1.29982	−	2.24566i	−0.0435456	−	0.0752325i
$892$	1.51167			0.0506145
$893$	−27.3203	+	19.8493i	−0.914237	+	0.664232i
$894$	−0.270423	−	0.832275i	−0.00904428	−	0.0278354i
$895$	−1.38482	+	4.26203i	−0.0462894	+	0.142464i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	23.4057	+	17.0053i	0.781494	+	0.567789i
$898$	−4.32476	+	13.3102i	−0.144319	+	0.444169i
$899$	12.1459	+	37.3811i	0.405087	+	1.24673i
$900$	1.40395	−	1.02003i	0.0467983	−	0.0340010i
$901$	39.1733			1.30505
$902$	−16.2781	+	3.47869i	−0.542002	+	0.115828i
$903$	−6.06697			−0.201896
$904$	−8.73997	+	6.34996i	−0.290687	+	0.211197i
$905$	2.79023	+	8.58744i	0.0927504	+	0.285456i
$906$	−4.66193	+	14.3479i	−0.154882	+	0.476678i
$907$	−23.5638	−	17.1201i	−0.782422	−	0.568463i	0.123283	−	0.992372i	$-0.460658\pi$
$907$	−23.5638	−	17.1201i	−0.782422	−	0.568463i	−0.905705	+	0.423909i	$0.860658\pi$
$908$	−11.2096	−	8.14422i	−0.372002	−	0.270276i
$909$	−6.55664	+	20.1793i	−0.217470	+	0.669304i
$910$	2.18458	+	6.72345i	0.0724182	+	0.222880i
$911$	0.632220	−	0.459335i	0.0209464	−	0.0152184i	−0.577263	−	0.816558i	$-0.695879\pi$
$911$	0.632220	−	0.459335i	0.0209464	−	0.0152184i	0.598209	+	0.801340i	$0.295879\pi$
$912$	−3.86415			−0.127955
$913$	24.0122	−	5.13150i	0.794689	−	0.169828i
$914$	−7.06533			−0.233700
$915$	−0.415075	+	0.301570i	−0.0137220	+	0.00996958i
$916$	6.34917	+	19.5407i	0.209782	+	0.645644i
$917$	−3.17167	+	9.76139i	−0.104738	+	0.322350i
$918$	−14.8406	−	10.7824i	−0.489814	−	0.355871i
$919$	−0.730013	−	0.530386i	−0.0240809	−	0.0174958i	0.575680	−	0.817675i	$-0.304738\pi$
$919$	−0.730013	−	0.530386i	−0.0240809	−	0.0174958i	−0.599761	+	0.800179i	$0.704738\pi$
$920$	−1.12455	+	3.46102i	−0.0370755	+	0.114107i
$921$	−8.96040	−	27.5773i	−0.295255	−	0.908702i
$922$	−8.57649	+	6.23119i	−0.282452	+	0.205213i
$923$	−48.1696			−1.58552
$924$	1.86840	+	3.22799i	0.0614660	+	0.106193i
$925$	−0.780576			−0.0256652
$926$	−3.71450	+	2.69874i	−0.122066	+	0.0886861i
$927$	−1.98756	−	6.11709i	−0.0652801	−	0.200912i
$928$	−2.68628	+	8.26751i	−0.0881814	+	0.271394i
$929$	−46.0934	−	33.4888i	−1.51227	−	1.09873i	−0.965155	−	0.261677i	$-0.915724\pi$
$929$	−46.0934	−	33.4888i	−1.51227	−	1.09873i	−0.547119	−	0.837055i	$-0.684276\pi$
$930$	4.11354	+	2.98866i	0.134888	+	0.0980020i
$931$	1.06183	−	3.26798i	0.0348001	−	0.107104i
$932$	5.01675	+	15.4400i	0.164329	+	0.505753i
$933$	4.65391	−	3.38126i	0.152362	−	0.110698i
$934$	−30.9287			−1.01202
$935$	10.4424	+	4.63552i	0.341501	+	0.151598i
$936$	−12.2682			−0.400998
$937$	−28.8890	+	20.9891i	−0.943763	+	0.685684i	−0.949324	−	0.314301i	$-0.898230\pi$
$937$	−28.8890	+	20.9891i	−0.943763	+	0.685684i	0.00556052	+	0.999985i	$0.498230\pi$
$938$	−3.24274	−	9.98012i	−0.105879	−	0.325862i
$939$	−5.75369	+	17.7080i	−0.187765	+	0.577880i
$940$	7.95082	+	5.77661i	0.259327	+	0.188412i
$941$	−7.47201	−	5.42873i	−0.243581	−	0.176972i	0.459296	−	0.888283i	$-0.348102\pi$
$941$	−7.47201	−	5.42873i	−0.243581	−	0.176972i	−0.702877	+	0.711311i	$0.748102\pi$
$942$	8.35271	−	25.7070i	0.272146	−	0.837579i
$943$	−5.64398	−	17.3704i	−0.183793	−	0.565658i
$944$	8.51466	−	6.18626i	0.277128	−	0.201346i
$945$	5.32519			0.173228
$946$	−1.85082	+	17.7972i	−0.0601755	+	0.578637i
$947$	−26.7339			−0.868736			−0.434368	−	0.900735i	$-0.643028\pi$
$947$	−26.7339			−0.868736			−0.434368	+	0.900735i	$0.643028\pi$
$948$	−14.7719	+	10.7324i	−0.479771	+	0.348574i
$949$	−33.0203	−	101.626i	−1.07188	−	3.29892i
$950$	1.06183	−	3.26798i	0.0344503	−	0.106027i
$951$	13.9652	+	10.1463i	0.452853	+	0.329017i
$952$	2.78688	+	2.02478i	0.0903232	+	0.0656236i
$953$	−12.7197	+	39.1473i	−0.412033	+	1.26811i	0.502845	+	0.864376i	$0.332287\pi$
$953$	−12.7197	+	39.1473i	−0.412033	+	1.26811i	−0.914878	+	0.403730i	$0.867713\pi$
$954$	−6.09826	−	18.7685i	−0.197439	−	0.607653i
$955$	2.35319	−	1.70969i	0.0761474	−	0.0553243i
$956$	−0.392921			−0.0127080
$957$	−21.6684	+	24.1183i	−0.700440	+	0.779635i
$958$	3.01362			0.0973658
$959$	−0.615590	+	0.447252i	−0.0198784	+	0.0144425i
$960$	0.347506	+	1.06951i	0.0112157	+	0.0345184i
$961$	−3.26215	+	10.0399i	−0.105231	+	0.323866i
$962$	4.46435	+	3.24354i	0.143937	+	0.104576i
$963$	−4.00276	−	2.90817i	−0.128987	−	0.0937146i
$964$	−1.02804	+	3.16398i	−0.0331109	+	0.101905i
$965$	2.40205	+	7.39276i	0.0773248	+	0.237981i
$966$	−3.31083	+	2.40546i	−0.106524	+	0.0773943i
$967$	31.2558			1.00512			0.502559	−	0.864543i	$-0.332392\pi$
$967$	31.2558			1.00512			0.502559	+	0.864543i	$0.332392\pi$
$968$	10.0392	−	4.49614i	0.322671	−	0.144511i
$969$	−13.3111			−0.427614
$970$	2.33800	−	1.69866i	0.0750686	−	0.0545405i
$971$	−3.17989	−	9.78669i	−0.102047	−	0.314070i	0.886979	−	0.461810i	$-0.152800\pi$
$971$	−3.17989	−	9.78669i	−0.102047	−	0.314070i	−0.989026	+	0.147741i	$0.952800\pi$
$972$	−4.66486	+	14.3570i	−0.149625	+	0.460499i
$973$	14.2692	+	10.3672i	0.457451	+	0.332357i
$974$	−2.43151	−	1.76659i	−0.0779106	−	0.0566053i
$975$	−2.45668	+	7.56089i	−0.0786767	+	0.242142i
$976$	0.140984	+	0.433905i	0.00451280	+	0.0138890i
$977$	36.3313	−	26.3962i	1.16234	−	0.844491i	0.172269	−	0.985050i	$-0.444890\pi$
$977$	36.3313	−	26.3962i	1.16234	−	0.844491i	0.990072	+	0.140559i	$0.0448900\pi$
$978$	−1.01816			−0.0325572
$979$	11.0194	−	12.2653i	0.352182	−	0.392002i
$980$	−1.00000			−0.0319438
$981$	13.7604	−	9.99752i	0.439336	−	0.319196i
$982$	10.7143	+	32.9753i	0.341908	+	1.05228i
$983$	3.69704	−	11.3783i	0.117917	−	0.362912i	−0.874627	−	0.484796i	$-0.838894\pi$
$983$	3.69704	−	11.3783i	0.117917	−	0.362912i	0.992544	+	0.121885i	$0.0388938\pi$
$984$	−4.56608	−	3.31745i	−0.145561	−	0.105756i
$985$	21.2171	+	15.4151i	0.676032	+	0.491166i
$986$	−9.25361	+	28.4797i	−0.294695	+	0.906978i
$987$	3.41521	+	10.5109i	0.108707	+	0.334566i
$988$	−19.6524	+	14.2783i	−0.625227	+	0.454254i
$989$	−19.6331			−0.624297
$990$	0.595344	−	5.72472i	0.0189213	−	0.181944i
$991$	25.7714			0.818656			0.409328	−	0.912387i	$-0.365763\pi$
$991$	25.7714			0.818656			0.409328	+	0.912387i	$0.365763\pi$
$992$	3.65793	−	2.65764i	0.116139	−	0.0843801i
$993$	2.29059	+	7.04972i	0.0726898	+	0.223716i
$994$	2.10557	−	6.48027i	0.0667846	−	0.205542i
$995$	4.57064	+	3.32077i	0.144899	+	0.105275i
$996$	6.73553	+	4.89365i	0.213423	+	0.155061i
$997$	2.83274	−	8.71828i	0.0897138	−	0.276111i	−0.896126	−	0.443799i	$-0.853630\pi$
$997$	2.83274	−	8.71828i	0.0897138	−	0.276111i	0.985840	+	0.167689i	$0.0536303\pi$
$998$	−1.62301	−	4.99510i	−0.0513754	−	0.158117i
$999$	3.36285	−	2.44326i	0.106396	−	0.0773012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.k.421.2	✓	16
11.2	odd	10		8470.2.a.dg.1.3		8
11.4	even	5	inner	770.2.n.k.631.2	yes	16
11.9	even	5		8470.2.a.dh.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.k.421.2	✓	16	1.1	even	1	trivial
770.2.n.k.631.2	yes	16	11.4	even	5	inner
8470.2.a.dg.1.3		8	11.2	odd	10
8470.2.a.dh.1.3		8	11.9	even	5

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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.347506 - 1.06951i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.909784 + 0.660997i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.40395 - 1.02003i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.347506 - 1.06951i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.909784 + 0.660997i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.40395 - 1.02003i) q^{9} -1.00000 q^{10} +(-2.21655 + 2.46717i) q^{11} -1.12455 q^{12} +(-5.71931 + 4.15532i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.347506 - 1.06951i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.78688 - 2.02478i) q^{17} +(-0.536261 + 1.65044i) q^{18} +(1.06183 + 3.26798i) q^{19} +(0.809017 - 0.587785i) q^{20} +1.12455 q^{21} +(0.343063 - 3.29883i) q^{22} +3.63913 q^{23} +(0.909784 - 0.660997i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.18458 - 6.72345i) q^{26} +(-4.30817 - 3.13007i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-2.68628 + 8.26751i) q^{29} +(0.347506 + 1.06951i) q^{30} +(3.65793 - 2.65764i) q^{31} +1.00000 q^{32} +(3.40894 + 1.51328i) q^{33} +3.44477 q^{34} +(-0.809017 + 0.587785i) q^{35} +(-0.536261 - 1.65044i) q^{36} +(-0.241211 + 0.742372i) q^{37} +(-2.77991 - 2.01972i) q^{38} +(6.43167 + 4.67288i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-1.55091 - 4.77322i) q^{41} +(-0.909784 + 0.660997i) q^{42} -5.39500 q^{43} +(1.66146 + 2.87046i) q^{44} +1.73538 q^{45} +(-2.94412 + 2.13903i) q^{46} +(3.03694 + 9.34674i) q^{47} +(-0.347506 + 1.06951i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.19708 + 3.68423i) q^{51} +(2.18458 + 6.72345i) q^{52} +(-9.19999 + 6.68419i) q^{53} +5.32519 q^{54} +(-3.24339 + 0.693123i) q^{55} -1.00000 q^{56} +(3.12616 - 2.27129i) q^{57} +(-2.68628 - 8.26751i) q^{58} +(-3.25231 + 10.0096i) q^{59} +(-0.909784 - 0.660997i) q^{60} +(-0.369102 - 0.268168i) q^{61} +(-1.39720 + 4.30015i) q^{62} +(0.536261 + 1.65044i) q^{63} +(-0.809017 + 0.587785i) q^{64} -7.06945 q^{65} +(-3.64737 + 0.779455i) q^{66} +10.4937 q^{67} +(-2.78688 + 2.02478i) q^{68} +(-1.26462 - 3.89211i) q^{69} +(0.309017 - 0.951057i) q^{70} +(5.51245 + 4.00503i) q^{71} +(1.40395 + 1.02003i) q^{72} +(-4.67084 + 14.3754i) q^{73} +(-0.241211 - 0.742372i) q^{74} +(0.909784 - 0.660997i) q^{75} +3.43616 q^{76} +(-1.66146 - 2.87046i) q^{77} -7.94999 q^{78} +(13.1358 - 9.54373i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-0.241755 + 0.744045i) q^{81} +(4.06034 + 2.95001i) q^{82} +(-5.98951 - 4.35163i) q^{83} +(0.347506 - 1.06951i) q^{84} +(-1.06449 - 3.27617i) q^{85} +(4.36464 - 3.17110i) q^{86} +9.77573 q^{87} +(-3.03137 - 1.34567i) q^{88} -4.97143 q^{89} +(-1.40395 + 1.02003i) q^{90} +(-2.18458 - 6.72345i) q^{91} +(1.12455 - 3.46102i) q^{92} +(-4.11354 - 2.98866i) q^{93} +(-7.95082 - 5.77661i) q^{94} +(-1.06183 + 3.26798i) q^{95} +(-0.347506 - 1.06951i) q^{96} +(-2.33800 + 1.69866i) q^{97} +1.00000 q^{98} +(-0.595344 + 5.72472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

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