LMFDB - Embedded newform 770.2.n.a.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.a.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.11803 + 1.53884i) q^{9} +1.00000 q^{10} +(3.04508 + 1.31433i) q^{11} -0.618034 q^{12} +(-2.73607 - 1.98787i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-0.190983 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.92705 + 1.40008i) q^{17} +(-0.809017 - 2.48990i) q^{18} +(-0.236068 + 0.726543i) q^{19} +(-0.809017 - 0.587785i) q^{20} -0.618034 q^{21} +(-1.69098 - 2.85317i) q^{22} -0.472136 q^{23} +(0.500000 + 0.363271i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.04508 + 3.21644i) q^{26} +(-2.80902 + 2.04087i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(0.263932 + 0.812299i) q^{29} +(-0.190983 + 0.587785i) q^{30} +(-0.618034 - 0.449028i) q^{31} +1.00000 q^{32} +(-1.35410 + 1.53884i) q^{33} +2.38197 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-0.809017 + 2.48990i) q^{36} +(3.00000 + 9.23305i) q^{37} +(0.618034 - 0.449028i) q^{38} +(1.69098 - 1.22857i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-2.76393 + 8.50651i) q^{41} +(0.500000 + 0.363271i) q^{42} -1.23607 q^{43} +(-0.309017 + 3.30220i) q^{44} -2.61803 q^{45} +(0.381966 + 0.277515i) q^{46} +(-0.590170 + 1.81636i) q^{47} +(-0.190983 - 0.587785i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.454915 - 1.40008i) q^{51} +(1.04508 - 3.21644i) q^{52} +(2.00000 + 1.45309i) q^{53} +3.47214 q^{54} +(-3.23607 + 0.726543i) q^{55} +1.00000 q^{56} +(-0.381966 - 0.277515i) q^{57} +(0.263932 - 0.812299i) q^{58} +(2.85410 + 8.78402i) q^{59} +(0.500000 - 0.363271i) q^{60} +(-1.38197 + 1.00406i) q^{61} +(0.236068 + 0.726543i) q^{62} +(-0.809017 + 2.48990i) q^{63} +(-0.809017 - 0.587785i) q^{64} +3.38197 q^{65} +(2.00000 - 0.449028i) q^{66} +3.23607 q^{67} +(-1.92705 - 1.40008i) q^{68} +(0.0901699 - 0.277515i) q^{69} +(0.309017 + 0.951057i) q^{70} +(-6.73607 + 4.89404i) q^{71} +(2.11803 - 1.53884i) q^{72} +(-3.50000 - 10.7719i) q^{73} +(3.00000 - 9.23305i) q^{74} +(0.500000 + 0.363271i) q^{75} -0.763932 q^{76} +(-0.309017 + 3.30220i) q^{77} -2.09017 q^{78} +(-4.73607 - 3.44095i) q^{79} +(0.309017 - 0.951057i) q^{80} +(1.76393 + 5.42882i) q^{81} +(7.23607 - 5.25731i) q^{82} +(-9.20820 + 6.69015i) q^{83} +(-0.190983 - 0.587785i) q^{84} +(0.736068 - 2.26538i) q^{85} +(1.00000 + 0.726543i) q^{86} -0.527864 q^{87} +(2.19098 - 2.48990i) q^{88} +13.7082 q^{89} +(2.11803 + 1.53884i) q^{90} +(1.04508 - 3.21644i) q^{91} +(-0.145898 - 0.449028i) q^{92} +(0.381966 - 0.277515i) q^{93} +(1.54508 - 1.12257i) q^{94} +(-0.236068 - 0.726543i) q^{95} +(-0.190983 + 0.587785i) q^{96} +(4.54508 + 3.30220i) q^{97} +1.00000 q^{98} +(4.42705 + 7.46969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9	\( 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9} + 4 q^{10} + q^{11} + 2 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - q^{17} - q^{18} + 8 q^{19} - q^{20} + 2 q^{21} - 9 q^{22} + 16 q^{23} + 2 q^{24} - q^{25} - 7 q^{26} - 9 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 14 q^{34} - q^{35} - q^{36} + 12 q^{37} - 2 q^{38} + 9 q^{39} - q^{40} - 20 q^{41} + 2 q^{42} + 4 q^{43} + q^{44} - 6 q^{45} + 6 q^{46} + 20 q^{47} - 3 q^{48} - q^{49} - q^{50} - 13 q^{51} - 7 q^{52} + 8 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 6 q^{57} + 10 q^{58} - 2 q^{59} + 2 q^{60} - 10 q^{61} - 8 q^{62} - q^{63} - q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} - q^{68} - 22 q^{69} - q^{70} - 18 q^{71} + 4 q^{72} - 14 q^{73} + 12 q^{74} + 2 q^{75} - 12 q^{76} + q^{77} + 14 q^{78} - 10 q^{79} - q^{80} + 16 q^{81} + 20 q^{82} - 10 q^{83} - 3 q^{84} - 6 q^{85} + 4 q^{86} - 20 q^{87} + 11 q^{88} + 28 q^{89} + 4 q^{90} - 7 q^{91} - 14 q^{92} + 6 q^{93} - 5 q^{94} + 8 q^{95} - 3 q^{96} + 7 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9 + 4 * q^10 + q^11 + 2 * q^12 - 2 * q^13 - q^14 - 3 * q^15 - q^16 - q^17 - q^18 + 8 * q^19 - q^20 + 2 * q^21 - 9 * q^22 + 16 * q^23 + 2 * q^24 - q^25 - 7 * q^26 - 9 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 14 * q^34 - q^35 - q^36 + 12 * q^37 - 2 * q^38 + 9 * q^39 - q^40 - 20 * q^41 + 2 * q^42 + 4 * q^43 + q^44 - 6 * q^45 + 6 * q^46 + 20 * q^47 - 3 * q^48 - q^49 - q^50 - 13 * q^51 - 7 * q^52 + 8 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 6 * q^57 + 10 * q^58 - 2 * q^59 + 2 * q^60 - 10 * q^61 - 8 * q^62 - q^63 - q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 - q^68 - 22 * q^69 - q^70 - 18 * q^71 + 4 * q^72 - 14 * q^73 + 12 * q^74 + 2 * q^75 - 12 * q^76 + q^77 + 14 * q^78 - 10 * q^79 - q^80 + 16 * q^81 + 20 * q^82 - 10 * q^83 - 3 * q^84 - 6 * q^85 + 4 * q^86 - 20 * q^87 + 11 * q^88 + 28 * q^89 + 4 * q^90 - 7 * q^91 - 14 * q^92 + 6 * q^93 - 5 * q^94 + 8 * q^95 - 3 * q^96 + 7 * 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
$3$	−0.190983	+	0.587785i	−0.110264	+	0.339358i	−0.990930	−	0.134380i	$-0.957096\pi$
$3$	−0.190983	+	0.587785i	−0.110264	+	0.339358i	0.880666	+	0.473738i	$0.157096\pi$
$4$	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
$6$	0.500000	−	0.363271i	0.204124	−	0.148305i
$7$	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
$9$	2.11803	+	1.53884i	0.706011	+	0.512947i
$10$	1.00000			0.316228
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$11$	3.04508	+	1.31433i	0.918128	+	0.396285i
$12$	−0.618034			−0.178411
$13$	−2.73607	−	1.98787i	−0.758849	−	0.551336i	0.139708	−	0.990193i	$-0.455384\pi$
$13$	−2.73607	−	1.98787i	−0.758849	−	0.551336i	−0.898557	+	0.438857i	$0.855384\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	−0.190983	−	0.587785i	−0.0493116	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.92705	+	1.40008i	−0.467379	+	0.339570i	−0.796419	−	0.604746i	$-0.793275\pi$
$17$	−1.92705	+	1.40008i	−0.467379	+	0.339570i	0.329040	+	0.944316i	$0.393275\pi$
$18$	−0.809017	−	2.48990i	−0.190687	−	0.586875i
$19$	−0.236068	+	0.726543i	−0.0541577	+	0.166680i	−0.974477	−	0.224488i	$-0.927929\pi$
$19$	−0.236068	+	0.726543i	−0.0541577	+	0.166680i	0.920319	+	0.391168i	$0.127929\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	−0.618034			−0.134866
$22$	−1.69098	−	2.85317i	−0.360519	−	0.608298i
$23$	−0.472136			−0.0984472			−0.0492236	−	0.998788i	$-0.515675\pi$
$23$	−0.472136			−0.0984472			−0.0492236	+	0.998788i	$0.515675\pi$
$24$	0.500000	+	0.363271i	0.102062	+	0.0741524i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	1.04508	+	3.21644i	0.204958	+	0.630796i
$27$	−2.80902	+	2.04087i	−0.540596	+	0.392766i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	0.263932	+	0.812299i	0.0490109	+	0.150840i	0.972567	−	0.232624i	$-0.0747311\pi$
$29$	0.263932	+	0.812299i	0.0490109	+	0.150840i	−0.923556	+	0.383464i	$0.874731\pi$
$30$	−0.190983	+	0.587785i	−0.0348686	+	0.107314i
$31$	−0.618034	−	0.449028i	−0.111002	−	0.0806478i	0.530899	−	0.847435i	$-0.321854\pi$
$31$	−0.618034	−	0.449028i	−0.111002	−	0.0806478i	−0.641902	+	0.766787i	$0.721854\pi$
$32$	1.00000			0.176777
$33$	−1.35410	+	1.53884i	−0.235719	+	0.267878i
$34$	2.38197			0.408504
$35$	−0.809017	−	0.587785i	−0.136749	−	0.0993538i
$36$	−0.809017	+	2.48990i	−0.134836	+	0.414983i
$37$	3.00000	+	9.23305i	0.493197	+	1.51790i	0.819748	+	0.572725i	$0.194114\pi$
$37$	3.00000	+	9.23305i	0.493197	+	1.51790i	−0.326551	+	0.945180i	$0.605886\pi$
$38$	0.618034	−	0.449028i	0.100258	−	0.0728420i
$39$	1.69098	−	1.22857i	0.270774	−	0.196729i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	−2.76393	+	8.50651i	−0.431654	+	1.32849i	0.464823	+	0.885403i	$0.346118\pi$
$41$	−2.76393	+	8.50651i	−0.431654	+	1.32849i	−0.896477	+	0.443090i	$0.853882\pi$
$42$	0.500000	+	0.363271i	0.0771517	+	0.0560540i
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$	−0.309017	+	3.30220i	−0.0465861	+	0.497825i
$45$	−2.61803			−0.390273
$46$	0.381966	+	0.277515i	0.0563178	+	0.0409173i
$47$	−0.590170	+	1.81636i	−0.0860851	+	0.264943i	−0.984828	−	0.173533i	$-0.944482\pi$
$47$	−0.590170	+	1.81636i	−0.0860851	+	0.264943i	0.898743	+	0.438476i	$0.144482\pi$
$48$	−0.190983	−	0.587785i	−0.0275660	−	0.0848395i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	−0.454915	−	1.40008i	−0.0637008	−	0.196051i
$52$	1.04508	−	3.21644i	0.144927	−	0.446040i
$53$	2.00000	+	1.45309i	0.274721	+	0.199597i	0.716612	−	0.697472i	$-0.245692\pi$
$53$	2.00000	+	1.45309i	0.274721	+	0.199597i	−0.441891	+	0.897069i	$0.645692\pi$
$54$	3.47214			0.472498
$55$	−3.23607	+	0.726543i	−0.436351	+	0.0979670i
$56$	1.00000			0.133631
$57$	−0.381966	−	0.277515i	−0.0505926	−	0.0367577i
$58$	0.263932	−	0.812299i	0.0346560	−	0.106660i
$59$	2.85410	+	8.78402i	0.371572	+	1.14358i	0.945762	+	0.324860i	$0.105317\pi$
$59$	2.85410	+	8.78402i	0.371572	+	1.14358i	−0.574190	+	0.818722i	$0.694683\pi$
$60$	0.500000	−	0.363271i	0.0645497	−	0.0468981i
$61$	−1.38197	+	1.00406i	−0.176943	+	0.128556i	−0.672731	−	0.739887i	$-0.734879\pi$
$61$	−1.38197	+	1.00406i	−0.176943	+	0.128556i	0.495789	+	0.868443i	$0.334879\pi$
$62$	0.236068	+	0.726543i	0.0299807	+	0.0922710i
$63$	−0.809017	+	2.48990i	−0.101927	+	0.313698i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.38197			0.419481
$66$	2.00000	−	0.449028i	0.246183	−	0.0552715i
$67$	3.23607			0.395349			0.197674	−	0.980268i	$-0.436661\pi$
$67$	3.23607			0.395349			0.197674	+	0.980268i	$0.436661\pi$
$68$	−1.92705	−	1.40008i	−0.233689	−	0.169785i
$69$	0.0901699	−	0.277515i	0.0108552	−	0.0334088i
$70$	0.309017	+	0.951057i	0.0369346	+	0.113673i
$71$	−6.73607	+	4.89404i	−0.799424	+	0.580816i	−0.910745	−	0.412969i	$-0.864492\pi$
$71$	−6.73607	+	4.89404i	−0.799424	+	0.580816i	0.111321	+	0.993785i	$0.464492\pi$
$72$	2.11803	−	1.53884i	0.249613	−	0.181354i
$73$	−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	$-0.330640\pi$
$74$	3.00000	−	9.23305i	0.348743	−	1.07332i
$75$	0.500000	+	0.363271i	0.0577350	+	0.0419470i
$76$	−0.763932			−0.0876290
$77$	−0.309017	+	3.30220i	−0.0352158	+	0.376320i
$78$	−2.09017			−0.236665
$79$	−4.73607	−	3.44095i	−0.532849	−	0.387138i	0.288573	−	0.957458i	$-0.406819\pi$
$79$	−4.73607	−	3.44095i	−0.532849	−	0.387138i	−0.821422	+	0.570320i	$0.806819\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	1.76393	+	5.42882i	0.195992	+	0.603203i
$82$	7.23607	−	5.25731i	0.799090	−	0.580573i
$83$	−9.20820	+	6.69015i	−1.01073	+	0.734340i	−0.964362	−	0.264585i	$-0.914765\pi$
$83$	−9.20820	+	6.69015i	−1.01073	+	0.734340i	−0.0463693	+	0.998924i	$0.514765\pi$
$84$	−0.190983	−	0.587785i	−0.0208380	−	0.0641326i
$85$	0.736068	−	2.26538i	0.0798378	−	0.245715i
$86$	1.00000	+	0.726543i	0.107833	+	0.0783451i
$87$	−0.527864			−0.0565930
$88$	2.19098	−	2.48990i	0.233560	−	0.265424i
$89$	13.7082			1.45307			0.726533	−	0.687131i	$-0.241130\pi$
$89$	13.7082			1.45307			0.726533	+	0.687131i	$0.241130\pi$
$90$	2.11803	+	1.53884i	0.223260	+	0.162208i
$91$	1.04508	−	3.21644i	0.109555	−	0.337175i
$92$	−0.145898	−	0.449028i	−0.0152109	−	0.0468144i
$93$	0.381966	−	0.277515i	0.0396080	−	0.0287769i
$94$	1.54508	−	1.12257i	0.159363	−	0.115784i
$95$	−0.236068	−	0.726543i	−0.0242201	−	0.0745417i
$96$	−0.190983	+	0.587785i	−0.0194921	+	0.0599906i
$97$	4.54508	+	3.30220i	0.461483	+	0.335287i	0.794113	−	0.607770i	$-0.207936\pi$
$97$	4.54508	+	3.30220i	0.461483	+	0.335287i	−0.332629	+	0.943058i	$0.607936\pi$
$98$	1.00000			0.101015
$99$	4.42705	+	7.46969i	0.444935	+	0.750733i
$100$	1.00000			0.100000
$101$	0.618034	+	0.449028i	0.0614967	+	0.0446800i	0.618109	−	0.786092i	$-0.287899\pi$
$101$	0.618034	+	0.449028i	0.0614967	+	0.0446800i	−0.556612	+	0.830772i	$0.687899\pi$
$102$	−0.454915	+	1.40008i	−0.0450433	+	0.138629i
$103$	−5.11803	−	15.7517i	−0.504295	−	1.55206i	−0.801953	−	0.597387i	$-0.796205\pi$
$103$	−5.11803	−	15.7517i	−0.504295	−	1.55206i	0.297658	−	0.954673i	$-0.403795\pi$
$104$	−2.73607	+	1.98787i	−0.268294	+	0.194927i
$105$	0.500000	−	0.363271i	0.0487950	−	0.0354516i
$106$	−0.763932	−	2.35114i	−0.0741996	−	0.228363i
$107$	−4.70820	+	14.4904i	−0.455159	+	1.40084i	0.415789	+	0.909461i	$0.363506\pi$
$107$	−4.70820	+	14.4904i	−0.455159	+	1.40084i	−0.870948	+	0.491375i	$0.836494\pi$
$108$	−2.80902	−	2.04087i	−0.270298	−	0.196383i
$109$	12.4721			1.19461			0.597307	−	0.802013i	$-0.296237\pi$
$109$	12.4721			1.19461			0.597307	+	0.802013i	$0.296237\pi$
$110$	3.04508	+	1.31433i	0.290337	+	0.125316i
$111$	−6.00000			−0.569495
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	−3.23607	+	9.95959i	−0.304424	+	0.936920i	0.675468	+	0.737389i	$0.263942\pi$
$113$	−3.23607	+	9.95959i	−0.304424	+	0.936920i	−0.979892	+	0.199530i	$0.936058\pi$
$114$	0.145898	+	0.449028i	0.0136646	+	0.0420553i
$115$	0.381966	−	0.277515i	0.0356185	−	0.0258784i
$116$	−0.690983	+	0.502029i	−0.0641562	+	0.0466122i
$117$	−2.73607	−	8.42075i	−0.252950	−	0.778499i
$118$	2.85410	−	8.78402i	0.262741	−	0.808635i
$119$	−1.92705	−	1.40008i	−0.176652	−	0.128346i
$120$	−0.618034			−0.0564185
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$	1.70820			0.154654
$123$	−4.47214	−	3.24920i	−0.403239	−	0.292970i
$124$	0.236068	−	0.726543i	0.0211995	−	0.0652454i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	2.11803	−	1.53884i	0.188689	−	0.137091i
$127$	1.76393	−	1.28157i	0.156524	−	0.113721i	−0.506767	−	0.862083i	$-0.669159\pi$
$127$	1.76393	−	1.28157i	0.156524	−	0.113721i	0.663290	+	0.748362i	$0.269159\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.236068	−	0.726543i	0.0207846	−	0.0639685i
$130$	−2.73607	−	1.98787i	−0.239969	−	0.174348i
$131$	15.4164			1.34694			0.673469	−	0.739216i	$-0.264804\pi$
$131$	15.4164			1.34694			0.673469	+	0.739216i	$0.264804\pi$
$132$	−1.88197	−	0.812299i	−0.163804	−	0.0707016i
$133$	−0.763932			−0.0662413
$134$	−2.61803	−	1.90211i	−0.226164	−	0.164318i
$135$	1.07295	−	3.30220i	0.0923447	−	0.284208i
$136$	0.736068	+	2.26538i	0.0631173	+	0.194255i
$137$	12.9443	−	9.40456i	1.10590	−	0.803486i	0.123890	−	0.992296i	$-0.460463\pi$
$137$	12.9443	−	9.40456i	1.10590	−	0.803486i	0.982014	+	0.188810i	$0.0604630\pi$
$138$	−0.236068	+	0.171513i	−0.0200954	+	0.0146002i
$139$	−2.76393	−	8.50651i	−0.234434	−	0.721513i	−0.997196	−	0.0748337i	$-0.976157\pi$
$139$	−2.76393	−	8.50651i	−0.234434	−	0.721513i	0.762762	−	0.646679i	$-0.223843\pi$
$140$	0.309017	−	0.951057i	0.0261167	−	0.0803789i
$141$	−0.954915	−	0.693786i	−0.0804184	−	0.0584274i
$142$	8.32624			0.698722
$143$	−5.71885	−	9.64932i	−0.478234	−	0.806917i
$144$	−2.61803			−0.218169
$145$	−0.690983	−	0.502029i	−0.0573830	−	0.0416912i
$146$	−3.50000	+	10.7719i	−0.289662	+	0.891488i
$147$	−0.190983	−	0.587785i	−0.0157520	−	0.0484797i
$148$	−7.85410	+	5.70634i	−0.645603	+	0.469058i
$149$	−11.4443	+	8.31475i	−0.937551	+	0.681171i	−0.947830	−	0.318776i	$-0.896728\pi$
$149$	−11.4443	+	8.31475i	−0.937551	+	0.681171i	0.0102787	+	0.999947i	$0.496728\pi$
$150$	−0.190983	−	0.587785i	−0.0155937	−	0.0479925i
$151$	7.29837	−	22.4621i	0.593933	−	1.82794i	0.0339673	−	0.999423i	$-0.489186\pi$
$151$	7.29837	−	22.4621i	0.593933	−	1.82794i	0.559966	−	0.828516i	$-0.310814\pi$
$152$	0.618034	+	0.449028i	0.0501292	+	0.0364210i
$153$	−6.23607			−0.504156
$154$	2.19098	−	2.48990i	0.176554	−	0.200642i
$155$	0.763932			0.0613605
$156$	1.69098	+	1.22857i	0.135387	+	0.0983644i
$157$	0.0278640	−	0.0857567i	0.00222379	−	0.00684413i	−0.949938	−	0.312437i	$-0.898855\pi$
$157$	0.0278640	−	0.0857567i	0.00222379	−	0.00684413i	0.952162	+	0.305593i	$0.0988547\pi$
$158$	1.80902	+	5.56758i	0.143918	+	0.442933i
$159$	−1.23607	+	0.898056i	−0.0980266	+	0.0712205i
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	−0.145898	−	0.449028i	−0.0114984	−	0.0353884i
$162$	1.76393	−	5.42882i	0.138588	−	0.426529i
$163$	−13.4721	−	9.78808i	−1.05522	−	0.766662i	−0.0820212	−	0.996631i	$-0.526138\pi$
$163$	−13.4721	−	9.78808i	−1.05522	−	0.766662i	−0.973198	+	0.229969i	$0.926138\pi$
$164$	−8.94427			−0.698430
$165$	0.190983	−	2.04087i	0.0148680	−	0.158882i
$166$	11.3820			0.883412
$167$	−16.1803	−	11.7557i	−1.25207	−	0.909684i	−0.253732	−	0.967275i	$-0.581658\pi$
$167$	−16.1803	−	11.7557i	−1.25207	−	0.909684i	−0.998340	+	0.0575908i	$0.981658\pi$
$168$	−0.190983	+	0.587785i	−0.0147347	+	0.0453486i
$169$	−0.482779	−	1.48584i	−0.0371369	−	0.114295i
$170$	−1.92705	+	1.40008i	−0.147798	+	0.107382i
$171$	−1.61803	+	1.17557i	−0.123734	+	0.0898981i
$172$	−0.381966	−	1.17557i	−0.0291246	−	0.0896364i
$173$	6.95492	−	21.4050i	0.528772	−	1.62739i	−0.227961	−	0.973670i	$-0.573206\pi$
$173$	6.95492	−	21.4050i	0.528772	−	1.62739i	0.756733	−	0.653724i	$-0.226794\pi$
$174$	0.427051	+	0.310271i	0.0323747	+	0.0235216i
$175$	1.00000			0.0755929
$176$	−3.23607	+	0.726543i	−0.243928	+	0.0547652i
$177$	−5.70820			−0.429055
$178$	−11.0902	−	8.05748i	−0.831243	−	0.603934i
$179$	0.173762	−	0.534785i	0.0129876	−	0.0399717i	−0.944353	−	0.328935i	$-0.893310\pi$
$179$	0.173762	−	0.534785i	0.0129876	−	0.0399717i	0.957340	+	0.288963i	$0.0933104\pi$
$180$	−0.809017	−	2.48990i	−0.0603006	−	0.185586i
$181$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$181$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$182$	−2.73607	+	1.98787i	−0.202811	+	0.147351i
$183$	−0.326238	−	1.00406i	−0.0241162	−	0.0742220i
$184$	−0.145898	+	0.449028i	−0.0107557	+	0.0331028i
$185$	−7.85410	−	5.70634i	−0.577445	−	0.419538i
$186$	−0.472136			−0.0346187
$187$	−7.70820	+	1.73060i	−0.563680	+	0.126554i
$188$	−1.90983			−0.139289
$189$	−2.80902	−	2.04087i	−0.204326	−	0.148451i
$190$	−0.236068	+	0.726543i	−0.0171262	+	0.0527089i
$191$	−1.80902	−	5.56758i	−0.130896	−	0.402856i	0.864033	−	0.503435i	$-0.167931\pi$
$191$	−1.80902	−	5.56758i	−0.130896	−	0.402856i	−0.994929	+	0.100579i	$0.967931\pi$
$192$	0.500000	−	0.363271i	0.0360844	−	0.0262168i
$193$	4.00000	−	2.90617i	0.287926	−	0.209191i	−0.434441	−	0.900700i	$-0.643054\pi$
$193$	4.00000	−	2.90617i	0.287926	−	0.209191i	0.722367	+	0.691510i	$0.243054\pi$
$194$	−1.73607	−	5.34307i	−0.124642	−	0.383610i
$195$	−0.645898	+	1.98787i	−0.0462537	+	0.142354i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	11.4164			0.813385			0.406693	−	0.913565i	$-0.366682\pi$
$197$	11.4164			0.813385			0.406693	+	0.913565i	$0.366682\pi$
$198$	0.809017	−	8.64527i	0.0574943	−	0.614392i
$199$	6.94427			0.492266			0.246133	−	0.969236i	$-0.420840\pi$
$199$	6.94427			0.492266			0.246133	+	0.969236i	$0.420840\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	−0.618034	+	1.90211i	−0.0435928	+	0.134165i
$202$	−0.236068	−	0.726543i	−0.0166097	−	0.0511194i
$203$	−0.690983	+	0.502029i	−0.0484975	+	0.0352355i
$204$	1.19098	−	0.865300i	0.0833855	−	0.0605831i
$205$	−2.76393	−	8.50651i	−0.193041	−	0.594120i
$206$	−5.11803	+	15.7517i	−0.356590	+	1.09747i
$207$	−1.00000	−	0.726543i	−0.0695048	−	0.0504982i
$208$	3.38197			0.234497
$209$	−1.67376	+	1.90211i	−0.115777	+	0.131572i
$210$	−0.618034			−0.0426484
$211$	0.263932	+	0.191758i	0.0181698	+	0.0132012i	0.596833	−	0.802365i	$-0.296425\pi$
$211$	0.263932	+	0.191758i	0.0181698	+	0.0132012i	−0.578663	+	0.815567i	$0.696425\pi$
$212$	−0.763932	+	2.35114i	−0.0524671	+	0.161477i
$213$	−1.59017	−	4.89404i	−0.108957	−	0.335334i
$214$	12.3262	−	8.95554i	0.842604	−	0.612188i
$215$	1.00000	−	0.726543i	0.0681994	−	0.0495498i
$216$	1.07295	+	3.30220i	0.0730049	+	0.224686i
$217$	0.236068	−	0.726543i	0.0160253	−	0.0493209i
$218$	−10.0902	−	7.33094i	−0.683393	−	0.496514i
$219$	7.00000			0.473016
$220$	−1.69098	−	2.85317i	−0.114006	−	0.192361i
$221$	8.05573			0.541887
$222$	4.85410	+	3.52671i	0.325786	+	0.236697i
$223$	−2.94427	+	9.06154i	−0.197163	+	0.606805i	0.802782	+	0.596273i	$0.203353\pi$
$223$	−2.94427	+	9.06154i	−0.197163	+	0.606805i	−0.999945	+	0.0105321i	$0.996647\pi$
$224$	0.309017	+	0.951057i	0.0206471	+	0.0635451i
$225$	2.11803	−	1.53884i	0.141202	−	0.102589i
$226$	8.47214	−	6.15537i	0.563558	−	0.409449i
$227$	4.28115	+	13.1760i	0.284150	+	0.874524i	0.986652	+	0.162842i	$0.0520662\pi$
$227$	4.28115	+	13.1760i	0.284150	+	0.874524i	−0.702502	+	0.711682i	$0.747934\pi$
$228$	0.145898	−	0.449028i	0.00966233	−	0.0297376i
$229$	4.61803	+	3.35520i	0.305168	+	0.221718i	0.729820	−	0.683639i	$-0.239604\pi$
$229$	4.61803	+	3.35520i	0.305168	+	0.221718i	−0.424652	+	0.905357i	$0.639604\pi$
$230$	−0.472136			−0.0311317
$231$	−1.88197	−	0.812299i	−0.123824	−	0.0534454i
$232$	0.854102			0.0560745
$233$	−11.8541	−	8.61251i	−0.776588	−	0.564224i	0.127365	−	0.991856i	$-0.459348\pi$
$233$	−11.8541	−	8.61251i	−0.776588	−	0.564224i	−0.903953	+	0.427632i	$0.859348\pi$
$234$	−2.73607	+	8.42075i	−0.178862	+	0.550482i
$235$	−0.590170	−	1.81636i	−0.0384984	−	0.118486i
$236$	−7.47214	+	5.42882i	−0.486395	+	0.353386i
$237$	2.92705	−	2.12663i	0.190132	−	0.138139i
$238$	0.736068	+	2.26538i	0.0477122	+	0.146843i
$239$	0.663119	−	2.04087i	0.0428936	−	0.132013i	−0.927316	−	0.374278i	$-0.877890\pi$
$239$	0.663119	−	2.04087i	0.0428936	−	0.132013i	0.970210	+	0.242265i	$0.0778905\pi$
$240$	0.500000	+	0.363271i	0.0322749	+	0.0234491i
$241$	9.70820			0.625360			0.312680	−	0.949858i	$-0.398773\pi$
$241$	9.70820			0.625360			0.312680	+	0.949858i	$0.398773\pi$
$242$	−1.39919	−	10.9106i	−0.0899431	−	0.701363i
$243$	−13.9443			−0.894525
$244$	−1.38197	−	1.00406i	−0.0884713	−	0.0642782i
$245$	0.309017	−	0.951057i	0.0197424	−	0.0607608i
$246$	1.70820	+	5.25731i	0.108911	+	0.335194i
$247$	2.09017	−	1.51860i	0.132994	−	0.0966260i
$248$	−0.618034	+	0.449028i	−0.0392452	+	0.0285133i
$249$	−2.17376	−	6.69015i	−0.137757	−	0.423971i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−4.23607	−	3.07768i	−0.267378	−	0.194262i	0.446015	−	0.895025i	$-0.352843\pi$
$251$	−4.23607	−	3.07768i	−0.267378	−	0.194262i	−0.713393	+	0.700764i	$0.752843\pi$
$252$	−2.61803			−0.164921
$253$	−1.43769	−	0.620541i	−0.0903871	−	0.0390131i
$254$	−2.18034			−0.136807
$255$	1.19098	+	0.865300i	0.0745822	+	0.0541872i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.26393	+	19.2784i	0.390733	+	1.20255i	0.932235	+	0.361854i	$0.117856\pi$
$257$	6.26393	+	19.2784i	0.390733	+	1.20255i	−0.541502	+	0.840700i	$0.682144\pi$
$258$	−0.618034	+	0.449028i	−0.0384771	+	0.0279553i
$259$	−7.85410	+	5.70634i	−0.488030	+	0.354575i
$260$	1.04508	+	3.21644i	0.0648134	+	0.199475i
$261$	−0.690983	+	2.12663i	−0.0427708	+	0.131635i
$262$	−12.4721	−	9.06154i	−0.770531	−	0.559824i
$263$	27.7082			1.70856			0.854281	−	0.519812i	$-0.173998\pi$
$263$	27.7082			1.70856			0.854281	+	0.519812i	$0.173998\pi$
$264$	1.04508	+	1.76336i	0.0643205	+	0.108527i
$265$	−2.47214			−0.151862
$266$	0.618034	+	0.449028i	0.0378941	+	0.0275317i
$267$	−2.61803	+	8.05748i	−0.160221	+	0.493110i
$268$	1.00000	+	3.07768i	0.0610847	+	0.187999i
$269$	−5.09017	+	3.69822i	−0.310353	+	0.225485i	−0.732048	−	0.681253i	$-0.761435\pi$
$269$	−5.09017	+	3.69822i	−0.310353	+	0.225485i	0.421695	+	0.906738i	$0.361435\pi$
$270$	−2.80902	+	2.04087i	−0.170951	+	0.124203i
$271$	−7.76393	−	23.8949i	−0.471625	−	1.45151i	−0.850455	−	0.526047i	$-0.823674\pi$
$271$	−7.76393	−	23.8949i	−0.471625	−	1.45151i	0.378830	−	0.925466i	$-0.376326\pi$
$272$	0.736068	−	2.26538i	0.0446307	−	0.137359i
$273$	1.69098	+	1.22857i	0.102343	+	0.0743565i
$274$	−16.0000			−0.966595
$275$	2.19098	−	2.48990i	0.132121	−	0.150147i
$276$	0.291796			0.0175641
$277$	10.8541	+	7.88597i	0.652160	+	0.473822i	0.864006	−	0.503481i	$-0.167948\pi$
$277$	10.8541	+	7.88597i	0.652160	+	0.473822i	−0.211846	+	0.977303i	$0.567948\pi$
$278$	−2.76393	+	8.50651i	−0.165770	+	0.510186i
$279$	−0.618034	−	1.90211i	−0.0370007	−	0.113877i
$280$	−0.809017	+	0.587785i	−0.0483480	+	0.0351269i
$281$	21.3262	−	15.4944i	1.27222	−	0.924320i	0.272928	−	0.962034i	$-0.412008\pi$
$281$	21.3262	−	15.4944i	1.27222	−	0.924320i	0.999289	+	0.0377149i	$0.0120079\pi$
$282$	0.364745	+	1.12257i	0.0217203	+	0.0668481i
$283$	0.409830	−	1.26133i	0.0243619	−	0.0749781i	−0.938136	−	0.346266i	$-0.887450\pi$
$283$	0.409830	−	1.26133i	0.0243619	−	0.0749781i	0.962498	+	0.271288i	$0.0874495\pi$
$284$	−6.73607	−	4.89404i	−0.399712	−	0.290408i
$285$	0.472136			0.0279669
$286$	−1.04508	+	11.1679i	−0.0617972	+	0.660373i
$287$	−8.94427			−0.527964
$288$	2.11803	+	1.53884i	0.124806	+	0.0906771i
$289$	−3.50000	+	10.7719i	−0.205882	+	0.633641i
$290$	0.263932	+	0.812299i	0.0154986	+	0.0476999i
$291$	−2.80902	+	2.04087i	−0.164667	+	0.119638i
$292$	9.16312	−	6.65740i	0.536231	−	0.389595i
$293$	0.437694	+	1.34708i	0.0255704	+	0.0786975i	0.963027	−	0.269404i	$-0.0868266\pi$
$293$	0.437694	+	1.34708i	0.0255704	+	0.0786975i	−0.937457	+	0.348101i	$0.886827\pi$
$294$	−0.190983	+	0.587785i	−0.0111384	+	0.0342803i
$295$	−7.47214	−	5.42882i	−0.435045	−	0.316078i
$296$	9.70820			0.564278
$297$	−11.2361	+	2.52265i	−0.651983	+	0.146379i
$298$	14.1459			0.819450
$299$	1.29180	+	0.938545i	0.0747065	+	0.0542774i
$300$	−0.190983	+	0.587785i	−0.0110264	+	0.0339358i
$301$	−0.381966	−	1.17557i	−0.0220162	−	0.0677588i
$302$	−19.1074	+	13.8823i	−1.09951	+	0.798838i
$303$	−0.381966	+	0.277515i	−0.0219434	+	0.0159428i
$304$	−0.236068	−	0.726543i	−0.0135394	−	0.0416701i
$305$	0.527864	−	1.62460i	0.0302254	−	0.0930242i
$306$	5.04508	+	3.66547i	0.288408	+	0.209541i
$307$	22.4508			1.28134			0.640669	−	0.767817i	$-0.278657\pi$
$307$	22.4508			1.28134			0.640669	+	0.767817i	$0.278657\pi$
$308$	−3.23607	+	0.726543i	−0.184392	+	0.0413986i
$309$	10.2361			0.582310
$310$	−0.618034	−	0.449028i	−0.0351020	−	0.0255031i
$311$	−3.76393	+	11.5842i	−0.213433	+	0.656879i	0.785828	+	0.618445i	$0.212237\pi$
$311$	−3.76393	+	11.5842i	−0.213433	+	0.656879i	−0.999261	+	0.0384343i	$0.987763\pi$
$312$	−0.645898	−	1.98787i	−0.0365668	−	0.112541i
$313$	19.3262	−	14.0413i	1.09238	−	0.793663i	0.112583	−	0.993642i	$-0.464087\pi$
$313$	19.3262	−	14.0413i	1.09238	−	0.793663i	0.979800	+	0.199979i	$0.0640874\pi$
$314$	−0.0729490	+	0.0530006i	−0.00411675	+	0.00299099i
$315$	−0.809017	−	2.48990i	−0.0455829	−	0.140290i
$316$	1.80902	−	5.56758i	0.101765	−	0.313201i
$317$	14.4721	+	10.5146i	0.812836	+	0.590560i	0.914651	−	0.404243i	$-0.132465\pi$
$317$	14.4721	+	10.5146i	0.812836	+	0.590560i	−0.101815	+	0.994803i	$0.532465\pi$
$318$	1.52786			0.0856784
$319$	−0.263932	+	2.82041i	−0.0147774	+	0.157913i
$320$	1.00000			0.0559017
$321$	−7.61803	−	5.53483i	−0.425197	−	0.308924i
$322$	−0.145898	+	0.449028i	−0.00813058	+	0.0250234i
$323$	−0.562306	−	1.73060i	−0.0312875	−	0.0962931i
$324$	−4.61803	+	3.35520i	−0.256557	+	0.186400i
$325$	−2.73607	+	1.98787i	−0.151770	+	0.110267i
$326$	5.14590	+	15.8374i	0.285005	+	0.877155i
$327$	−2.38197	+	7.33094i	−0.131723	+	0.405402i
$328$	7.23607	+	5.25731i	0.399545	+	0.290286i
$329$	−1.90983			−0.105292
$330$	−1.35410	+	1.53884i	−0.0745409	+	0.0847105i
$331$	−8.61803			−0.473690			−0.236845	−	0.971547i	$-0.576113\pi$
$331$	−8.61803			−0.473690			−0.236845	+	0.971547i	$0.576113\pi$
$332$	−9.20820	−	6.69015i	−0.505366	−	0.367170i
$333$	−7.85410	+	24.1724i	−0.430402	+	1.32464i
$334$	6.18034	+	19.0211i	0.338173	+	1.04079i
$335$	−2.61803	+	1.90211i	−0.143038	+	0.103924i
$336$	0.500000	−	0.363271i	0.0272772	−	0.0198181i
$337$	2.47214	+	7.60845i	0.134666	+	0.414459i	0.995538	−	0.0943627i	$-0.0300813\pi$
$337$	2.47214	+	7.60845i	0.134666	+	0.414459i	−0.860872	+	0.508821i	$0.830081\pi$
$338$	−0.482779	+	1.48584i	−0.0262597	+	0.0808191i
$339$	−5.23607	−	3.80423i	−0.284384	−	0.206617i
$340$	2.38197			0.129180
$341$	−1.29180	−	2.17963i	−0.0699547	−	0.118033i
$342$	2.00000			0.108148
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−0.381966	+	1.17557i	−0.0205942	+	0.0633825i
$345$	0.0901699	+	0.277515i	0.00485459	+	0.0149409i
$346$	−18.2082	+	13.2290i	−0.978879	+	0.711197i
$347$	8.00000	−	5.81234i	0.429463	−	0.312023i	−0.351971	−	0.936011i	$-0.614489\pi$
$347$	8.00000	−	5.81234i	0.429463	−	0.312023i	0.781434	+	0.623988i	$0.214489\pi$
$348$	−0.163119	−	0.502029i	−0.00874409	−	0.0269116i
$349$	−2.79837	+	8.61251i	−0.149794	+	0.461017i	−0.997596	−	0.0692947i	$-0.977925\pi$
$349$	−2.79837	+	8.61251i	−0.149794	+	0.461017i	0.847803	+	0.530312i	$0.177925\pi$
$350$	−0.809017	−	0.587785i	−0.0432438	−	0.0314184i
$351$	11.7426			0.626776
$352$	3.04508	+	1.31433i	0.162304	+	0.0700539i
$353$	31.4508			1.67396			0.836980	−	0.547234i	$-0.184319\pi$
$353$	31.4508			1.67396			0.836980	+	0.547234i	$0.184319\pi$
$354$	4.61803	+	3.35520i	0.245446	+	0.178327i
$355$	2.57295	−	7.91872i	0.136558	−	0.420282i
$356$	4.23607	+	13.0373i	0.224511	+	0.690974i
$357$	1.19098	−	0.865300i	0.0630335	−	0.0457965i
$358$	−0.454915	+	0.330515i	−0.0240430	+	0.0174683i
$359$	−8.95492	−	27.5604i	−0.472622	−	1.45458i	−0.849138	−	0.528172i	$-0.822878\pi$
$359$	−8.95492	−	27.5604i	−0.472622	−	1.45458i	0.376515	−	0.926410i	$-0.377122\pi$
$360$	−0.809017	+	2.48990i	−0.0426389	+	0.131229i
$361$	14.8992	+	10.8249i	0.784168	+	0.569731i
$362$		0			0
$363$	−6.14590	+	2.90617i	−0.322576	+	0.152534i
$364$	3.38197			0.177263
$365$	9.16312	+	6.65740i	0.479620	+	0.348464i
$366$	−0.326238	+	1.00406i	−0.0170527	+	0.0524829i
$367$	6.07953	+	18.7109i	0.317349	+	0.976699i	0.974777	+	0.223182i	$0.0716443\pi$
$367$	6.07953	+	18.7109i	0.317349	+	0.976699i	−0.657428	+	0.753517i	$0.728356\pi$
$368$	0.381966	−	0.277515i	0.0199114	−	0.0144664i
$369$	−18.9443	+	13.7638i	−0.986199	+	0.716516i
$370$	3.00000	+	9.23305i	0.155963	+	0.480003i
$371$	−0.763932	+	2.35114i	−0.0396614	+	0.122065i
$372$	0.381966	+	0.277515i	0.0198040	+	0.0143885i
$373$	28.6525			1.48357			0.741784	−	0.670638i	$-0.233980\pi$
$373$	28.6525			1.48357			0.741784	+	0.670638i	$0.233980\pi$
$374$	7.25329	+	3.13068i	0.375059	+	0.161884i
$375$	−0.618034			−0.0319151
$376$	1.54508	+	1.12257i	0.0796817	+	0.0578921i
$377$	0.892609	−	2.74717i	0.0459717	−	0.141486i
$378$	1.07295	+	3.30220i	0.0551865	+	0.169847i
$379$	−18.4894	+	13.4333i	−0.949734	+	0.690022i	−0.950744	−	0.309977i	$-0.899679\pi$
$379$	−18.4894	+	13.4333i	−0.949734	+	0.690022i	0.00100958	+	0.999999i	$0.499679\pi$
$380$	0.618034	−	0.449028i	0.0317045	−	0.0230346i
$381$	0.416408	+	1.28157i	0.0213332	+	0.0656569i
$382$	−1.80902	+	5.56758i	−0.0925574	+	0.284862i
$383$	−1.73607	−	1.26133i	−0.0887089	−	0.0644508i	0.542547	−	0.840026i	$-0.317460\pi$
$383$	−1.73607	−	1.26133i	−0.0887089	−	0.0644508i	−0.631256	+	0.775575i	$0.717460\pi$
$384$	−0.618034			−0.0315389
$385$	−1.69098	−	2.85317i	−0.0861805	−	0.145411i
$386$	−4.94427			−0.251657
$387$	−2.61803	−	1.90211i	−0.133082	−	0.0966898i
$388$	−1.73607	+	5.34307i	−0.0881355	+	0.271253i
$389$	4.10081	+	12.6210i	0.207919	+	0.639910i	0.999581	+	0.0289502i	$0.00921643\pi$
$389$	4.10081	+	12.6210i	0.207919	+	0.639910i	−0.791661	+	0.610960i	$0.790784\pi$
$390$	1.69098	−	1.22857i	0.0856263	−	0.0622111i
$391$	0.909830	−	0.661030i	0.0460121	−	0.0334297i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	−2.94427	+	9.06154i	−0.148519	+	0.457094i
$394$	−9.23607	−	6.71040i	−0.465306	−	0.338065i
$395$	5.85410			0.294552
$396$	−5.73607	+	6.51864i	−0.288248	+	0.327574i
$397$	−10.4377			−0.523853			−0.261926	−	0.965088i	$-0.584358\pi$
$397$	−10.4377			−0.523853			−0.261926	+	0.965088i	$0.584358\pi$
$398$	−5.61803	−	4.08174i	−0.281607	−	0.204599i
$399$	0.145898	−	0.449028i	0.00730404	−	0.0224795i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	27.8156	−	20.2092i	1.38904	−	1.00920i	0.393075	−	0.919506i	$-0.371411\pi$
$401$	27.8156	−	20.2092i	1.38904	−	1.00920i	0.995969	−	0.0896935i	$-0.0285888\pi$
$402$	1.61803	−	1.17557i	0.0807002	−	0.0586321i
$403$	0.798374	+	2.45714i	0.0397698	+	0.122399i
$404$	−0.236068	+	0.726543i	−0.0117448	+	0.0361468i
$405$	−4.61803	−	3.35520i	−0.229472	−	0.166721i
$406$	0.854102			0.0423884
$407$	−3.00000	+	32.0584i	−0.148704	+	1.58908i
$408$	−1.47214			−0.0728816
$409$	−0.618034	−	0.449028i	−0.0305598	−	0.0222030i	0.572400	−	0.819974i	$-0.306012\pi$
$409$	−0.618034	−	0.449028i	−0.0305598	−	0.0222030i	−0.602960	+	0.797771i	$0.706012\pi$
$410$	−2.76393	+	8.50651i	−0.136501	+	0.420106i
$411$	3.05573	+	9.40456i	0.150728	+	0.463893i
$412$	13.3992	−	9.73508i	0.660131	−	0.479613i
$413$	−7.47214	+	5.42882i	−0.367680	+	0.267135i
$414$	0.381966	+	1.17557i	0.0187726	+	0.0577761i
$415$	3.51722	−	10.8249i	0.172654	−	0.531373i
$416$	−2.73607	−	1.98787i	−0.134147	−	0.0974633i
$417$	5.52786			0.270701
$418$	2.47214	−	0.555029i	0.120916	−	0.0271474i
$419$	−10.9443			−0.534663			−0.267331	−	0.963605i	$-0.586142\pi$
$419$	−10.9443			−0.534663			−0.267331	+	0.963605i	$0.586142\pi$
$420$	0.500000	+	0.363271i	0.0243975	+	0.0177258i
$421$	1.33688	−	4.11450i	0.0651556	−	0.200528i	−0.913179	−	0.407559i	$-0.866380\pi$
$421$	1.33688	−	4.11450i	0.0651556	−	0.200528i	0.978334	+	0.207031i	$0.0663800\pi$
$422$	−0.100813	−	0.310271i	−0.00490750	−	0.0151037i
$423$	−4.04508	+	2.93893i	−0.196679	+	0.142895i
$424$	2.00000	−	1.45309i	0.0971286	−	0.0705680i
$425$	0.736068	+	2.26538i	0.0357045	+	0.109887i
$426$	−1.59017	+	4.89404i	−0.0770440	+	0.237117i
$427$	−1.38197	−	1.00406i	−0.0668780	−	0.0485897i
$428$	−15.2361			−0.736463
$429$	6.76393	−	1.51860i	0.326566	−	0.0733186i
$430$	−1.23607			−0.0596085
$431$	−3.69098	−	2.68166i	−0.177788	−	0.129171i	0.495332	−	0.868704i	$-0.335046\pi$
$431$	−3.69098	−	2.68166i	−0.177788	−	0.129171i	−0.673120	+	0.739533i	$0.735046\pi$
$432$	1.07295	−	3.30220i	0.0516223	−	0.158877i
$433$	−2.19098	−	6.74315i	−0.105292	−	0.324055i	0.884507	−	0.466527i	$-0.154495\pi$
$433$	−2.19098	−	6.74315i	−0.105292	−	0.324055i	−0.989799	+	0.142472i	$0.954495\pi$
$434$	−0.618034	+	0.449028i	−0.0296666	+	0.0215540i
$435$	0.427051	−	0.310271i	0.0204755	−	0.0148763i
$436$	3.85410	+	11.8617i	0.184578	+	0.568073i
$437$	0.111456	−	0.343027i	0.00533167	−	0.0164092i
$438$	−5.66312	−	4.11450i	−0.270594	−	0.196598i
$439$	20.6525			0.985689			0.492844	−	0.870117i	$-0.335957\pi$
$439$	20.6525			0.985689			0.492844	+	0.870117i	$0.335957\pi$
$440$	−0.309017	+	3.30220i	−0.0147318	+	0.157426i
$441$	−2.61803			−0.124668
$442$	−6.51722	−	4.73504i	−0.309993	−	0.225223i
$443$	−3.32624	+	10.2371i	−0.158034	+	0.486380i	−0.998456	−	0.0555539i	$-0.982308\pi$
$443$	−3.32624	+	10.2371i	−0.158034	+	0.486380i	0.840421	+	0.541934i	$0.182308\pi$
$444$	−1.85410	−	5.70634i	−0.0879918	−	0.270811i
$445$	−11.0902	+	8.05748i	−0.525724	+	0.381961i
$446$	7.70820	−	5.60034i	0.364994	−	0.265184i
$447$	−2.70163	−	8.31475i	−0.127783	−	0.393274i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−14.9721	−	10.8779i	−0.706579	−	0.513360i	0.175489	−	0.984481i	$-0.443849\pi$
$449$	−14.9721	−	10.8779i	−0.706579	−	0.513360i	−0.882068	+	0.471122i	$0.843849\pi$
$450$	−2.61803			−0.123415
$451$	−19.5967	+	22.2703i	−0.922775	+	1.04867i
$452$	−10.4721			−0.492568
$453$	11.8090	+	8.57975i	0.554836	+	0.403112i
$454$	4.28115	−	13.1760i	0.200924	−	0.618382i
$455$	1.04508	+	3.21644i	0.0489943	+	0.150789i
$456$	−0.381966	+	0.277515i	−0.0178872	+	0.0129958i
$457$	11.3262	−	8.22899i	0.529819	−	0.384936i	−0.290471	−	0.956884i	$-0.593812\pi$
$457$	11.3262	−	8.22899i	0.529819	−	0.384936i	0.820290	+	0.571948i	$0.193812\pi$
$458$	−1.76393	−	5.42882i	−0.0824231	−	0.253672i
$459$	2.55573	−	7.86572i	0.119291	−	0.367140i
$460$	0.381966	+	0.277515i	0.0178093	+	0.0129392i
$461$	−15.1246			−0.704423			−0.352212	−	0.935920i	$-0.614570\pi$
$461$	−15.1246			−0.704423			−0.352212	+	0.935920i	$0.614570\pi$
$462$	1.04508	+	1.76336i	0.0486218	+	0.0820387i
$463$	8.18034			0.380173			0.190086	−	0.981767i	$-0.439123\pi$
$463$	8.18034			0.380173			0.190086	+	0.981767i	$0.439123\pi$
$464$	−0.690983	−	0.502029i	−0.0320781	−	0.0233061i
$465$	−0.145898	+	0.449028i	−0.00676586	+	0.0208232i
$466$	4.52786	+	13.9353i	0.209749	+	0.645542i
$467$	−15.6803	+	11.3924i	−0.725600	+	0.527179i	−0.888168	−	0.459518i	$-0.848022\pi$
$467$	−15.6803	+	11.3924i	−0.725600	+	0.527179i	0.162569	+	0.986697i	$0.448022\pi$
$468$	7.16312	−	5.20431i	0.331115	−	0.240569i
$469$	1.00000	+	3.07768i	0.0461757	+	0.142114i
$470$	−0.590170	+	1.81636i	−0.0272225	+	0.0837823i
$471$	0.0450850	+	0.0327561i	0.00207741	+	0.00150932i
$472$	9.23607			0.425124
$473$	−3.76393	−	1.62460i	−0.173066	−	0.0746991i
$474$	−3.61803			−0.166182
$475$	0.618034	+	0.449028i	0.0283573	+	0.0206028i
$476$	0.736068	−	2.26538i	0.0337376	−	0.103834i
$477$	2.00000	+	6.15537i	0.0915737	+	0.281835i
$478$	−1.73607	+	1.26133i	−0.0794059	+	0.0576918i
$479$	−4.14590	+	3.01217i	−0.189431	+	0.137630i	−0.678459	−	0.734639i	$-0.737352\pi$
$479$	−4.14590	+	3.01217i	−0.189431	+	0.137630i	0.489028	+	0.872268i	$0.337352\pi$
$480$	−0.190983	−	0.587785i	−0.00871714	−	0.0268286i
$481$	10.1459	−	31.2259i	0.462613	−	1.42378i
$482$	−7.85410	−	5.70634i	−0.357745	−	0.259917i
$483$	0.291796			0.0132772
$484$	−5.28115	+	9.64932i	−0.240052	+	0.438606i
$485$	−5.61803			−0.255102
$486$	11.2812	+	8.19624i	0.511723	+	0.371789i
$487$	10.5623	−	32.5074i	0.478624	−	1.47305i	−0.362384	−	0.932029i	$-0.618037\pi$
$487$	10.5623	−	32.5074i	0.478624	−	1.47305i	0.841007	−	0.541023i	$-0.181963\pi$
$488$	0.527864	+	1.62460i	0.0238953	+	0.0735421i
$489$	8.32624	−	6.04937i	0.376525	−	0.273562i
$490$	−0.809017	+	0.587785i	−0.0365477	+	0.0265534i
$491$	−5.23607	−	16.1150i	−0.236300	−	0.727258i	−0.996946	−	0.0780908i	$-0.975118\pi$
$491$	−5.23607	−	16.1150i	−0.236300	−	0.727258i	0.760646	−	0.649167i	$-0.224882\pi$
$492$	1.70820	−	5.25731i	0.0770118	−	0.237018i
$493$	−1.64590	−	1.19581i	−0.0741275	−	0.0538568i
$494$	−2.58359			−0.116241
$495$	−7.97214	−	3.44095i	−0.358321	−	0.154659i
$496$	0.763932			0.0343016
$497$	−6.73607	−	4.89404i	−0.302154	−	0.219528i
$498$	−2.17376	+	6.69015i	−0.0974086	+	0.299793i
$499$	−0.0623059	−	0.191758i	−0.00278920	−	0.00858426i	0.949652	−	0.313306i	$-0.101437\pi$
$499$	−0.0623059	−	0.191758i	−0.00278920	−	0.00858426i	−0.952441	+	0.304722i	$0.901437\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	10.0000	−	7.26543i	0.446767	−	0.324595i
$502$	1.61803	+	4.97980i	0.0722164	+	0.222259i
$503$	−6.48278	+	19.9519i	−0.289053	+	0.889613i	0.696102	+	0.717943i	$0.254916\pi$
$503$	−6.48278	+	19.9519i	−0.289053	+	0.889613i	−0.985155	+	0.171670i	$0.945084\pi$
$504$	2.11803	+	1.53884i	0.0943447	+	0.0685455i
$505$	−0.763932			−0.0339945
$506$	0.798374	+	1.34708i	0.0354920	+	0.0598852i
$507$	0.965558			0.0428819
$508$	1.76393	+	1.28157i	0.0782618	+	0.0568605i
$509$	4.90983	−	15.1109i	0.217624	−	0.669779i	−0.781332	−	0.624115i	$-0.785460\pi$
$509$	4.90983	−	15.1109i	0.217624	−	0.669779i	0.998957	−	0.0456640i	$-0.0145403\pi$
$510$	−0.454915	−	1.40008i	−0.0201440	−	0.0619968i
$511$	9.16312	−	6.65740i	0.405353	−	0.294506i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.819660	−	2.52265i	−0.0361889	−	0.111378i
$514$	6.26393	−	19.2784i	0.276290	−	0.850334i
$515$	13.3992	+	9.73508i	0.590439	+	0.428979i
$516$	0.763932			0.0336302
$517$	−4.18441	+	4.75528i	−0.184030	+	0.209137i
$518$	9.70820			0.426554
$519$	11.2533	+	8.17599i	0.493965	+	0.358886i
$520$	1.04508	−	3.21644i	0.0458300	−	0.141050i
$521$	10.6738	+	32.8505i	0.467626	+	1.43920i	0.855650	+	0.517555i	$0.173158\pi$
$521$	10.6738	+	32.8505i	0.467626	+	1.43920i	−0.388024	+	0.921649i	$0.626842\pi$
$522$	1.80902	−	1.31433i	0.0791785	−	0.0575266i
$523$	−26.4894	+	19.2456i	−1.15830	+	0.841553i	−0.989562	−	0.144108i	$-0.953969\pi$
$523$	−26.4894	+	19.2456i	−1.15830	+	0.841553i	−0.168737	+	0.985661i	$0.553969\pi$
$524$	4.76393	+	14.6619i	0.208113	+	0.640507i
$525$	−0.190983	+	0.587785i	−0.00833518	+	0.0256531i
$526$	−22.4164	−	16.2865i	−0.977402	−	0.710124i
$527$	1.81966			0.0792656
$528$	0.190983	−	2.04087i	0.00831147	−	0.0888175i
$529$	−22.7771			−0.990308
$530$	2.00000	+	1.45309i	0.0868744	+	0.0631180i
$531$	−7.47214	+	22.9969i	−0.324263	+	0.997979i
$532$	−0.236068	−	0.726543i	−0.0102348	−	0.0314996i
$533$	24.4721	−	17.7800i	1.06001	−	0.770139i
$534$	6.85410	−	4.97980i	0.296606	−	0.215497i
$535$	−4.70820	−	14.4904i	−0.203553	−	0.626473i
$536$	1.00000	−	3.07768i	0.0431934	−	0.132936i
$537$	0.281153	+	0.204270i	0.0121326	+	0.00881488i
$538$	6.29180			0.271259
$539$	−3.23607	+	0.726543i	−0.139387	+	0.0312944i
$540$	3.47214			0.149417
$541$	−2.50000	−	1.81636i	−0.107483	−	0.0780913i	0.532745	−	0.846276i	$-0.321160\pi$
$541$	−2.50000	−	1.81636i	−0.107483	−	0.0780913i	−0.640229	+	0.768184i	$0.721160\pi$
$542$	−7.76393	+	23.8949i	−0.333489	+	1.02637i
$543$		0			0
$544$	−1.92705	+	1.40008i	−0.0826216	+	0.0600281i
$545$	−10.0902	+	7.33094i	−0.432215	+	0.314023i
$546$	−0.645898	−	1.98787i	−0.0276419	−	0.0850730i
$547$	0.0557281	−	0.171513i	0.00238276	−	0.00733338i	−0.949858	−	0.312681i	$-0.898773\pi$
$547$	0.0557281	−	0.171513i	0.00238276	−	0.00733338i	0.952241	+	0.305348i	$0.0987728\pi$
$548$	12.9443	+	9.40456i	0.552952	+	0.401743i
$549$	−4.47214			−0.190866
$550$	−3.23607	+	0.726543i	−0.137986	+	0.0309799i
$551$	−0.652476			−0.0277964
$552$	−0.236068	−	0.171513i	−0.0100477	−	0.00730010i
$553$	1.80902	−	5.56758i	0.0769272	−	0.236758i
$554$	−4.14590	−	12.7598i	−0.176142	−	0.542110i
$555$	4.85410	−	3.52671i	0.206045	−	0.149701i
$556$	7.23607	−	5.25731i	0.306878	−	0.222960i
$557$	1.11146	+	3.42071i	0.0470939	+	0.144940i	0.971838	−	0.235648i	$-0.0757214\pi$
$557$	1.11146	+	3.42071i	0.0470939	+	0.144940i	−0.924744	+	0.380589i	$0.875721\pi$
$558$	−0.618034	+	1.90211i	−0.0261635	+	0.0805229i
$559$	3.38197	+	2.45714i	0.143042	+	0.103926i
$560$	1.00000			0.0422577
$561$	0.454915	−	4.86128i	0.0192065	−	0.205244i
$562$	−26.3607			−1.11196
$563$	2.78115	+	2.02063i	0.117212	+	0.0851592i	0.644847	−	0.764312i	$-0.276921\pi$
$563$	2.78115	+	2.02063i	0.117212	+	0.0851592i	−0.527635	+	0.849471i	$0.676921\pi$
$564$	0.364745	−	1.12257i	0.0153585	−	0.0472687i
$565$	−3.23607	−	9.95959i	−0.136142	−	0.419003i
$566$	−1.07295	+	0.779543i	−0.0450994	+	0.0327666i
$567$	−4.61803	+	3.35520i	−0.193939	+	0.140905i
$568$	2.57295	+	7.91872i	0.107959	+	0.332262i
$569$	−1.79180	+	5.51458i	−0.0751160	+	0.231183i	−0.981564	−	0.191134i	$-0.938783\pi$
$569$	−1.79180	+	5.51458i	−0.0751160	+	0.231183i	0.906448	+	0.422318i	$0.138783\pi$
$570$	−0.381966	−	0.277515i	−0.0159988	−	0.0116238i
$571$	−37.1459			−1.55451			−0.777254	−	0.629187i	$-0.783388\pi$
$571$	−37.1459			−1.55451			−0.777254	+	0.629187i	$0.783388\pi$
$572$	7.40983	−	8.42075i	0.309821	−	0.352089i
$573$	3.61803			0.151146
$574$	7.23607	+	5.25731i	0.302028	+	0.219436i
$575$	−0.145898	+	0.449028i	−0.00608437	+	0.0187258i
$576$	−0.809017	−	2.48990i	−0.0337090	−	0.103746i
$577$	7.45492	−	5.41631i	0.310352	−	0.225484i	−0.421695	−	0.906738i	$-0.638565\pi$
$577$	7.45492	−	5.41631i	0.310352	−	0.225484i	0.732048	+	0.681253i	$0.238565\pi$
$578$	9.16312	−	6.65740i	0.381136	−	0.276911i
$579$	0.944272	+	2.90617i	0.0392426	+	0.120776i
$580$	0.263932	−	0.812299i	0.0109592	−	0.0337289i
$581$	−9.20820	−	6.69015i	−0.382021	−	0.277554i
$582$	3.47214			0.143925
$583$	4.18034	+	7.05342i	0.173132	+	0.292123i
$584$	−11.3262			−0.468683
$585$	7.16312	+	5.20431i	0.296159	+	0.215172i
$586$	0.437694	−	1.34708i	0.0180810	−	0.0556475i
$587$	−5.71885	−	17.6008i	−0.236042	−	0.726463i	−0.996981	−	0.0776399i	$-0.975262\pi$
$587$	−5.71885	−	17.6008i	−0.236042	−	0.726463i	0.760939	−	0.648823i	$-0.224738\pi$
$588$	0.500000	−	0.363271i	0.0206197	−	0.0149811i
$589$	0.472136	−	0.343027i	0.0194540	−	0.0141342i
$590$	2.85410	+	8.78402i	0.117502	+	0.361632i
$591$	−2.18034	+	6.71040i	−0.0896872	+	0.276029i
$592$	−7.85410	−	5.70634i	−0.322802	−	0.234529i
$593$	−9.79837			−0.402371			−0.201185	−	0.979553i	$-0.564479\pi$
$593$	−9.79837			−0.402371			−0.201185	+	0.979553i	$0.564479\pi$
$594$	10.5729	+	4.56352i	0.433813	+	0.187244i
$595$	2.38197			0.0976511
$596$	−11.4443	−	8.31475i	−0.468776	−	0.340585i
$597$	−1.32624	+	4.08174i	−0.0542793	+	0.167055i
$598$	−0.493422	−	1.51860i	−0.0201775	−	0.0621001i
$599$	28.6353	−	20.8047i	1.17000	−	0.850058i	0.178995	−	0.983850i	$-0.442715\pi$
$599$	28.6353	−	20.8047i	1.17000	−	0.850058i	0.991009	+	0.133792i	$0.0427153\pi$
$600$	0.500000	−	0.363271i	0.0204124	−	0.0148305i
$601$	−2.47214	−	7.60845i	−0.100841	−	0.310355i	0.887891	−	0.460053i	$-0.152170\pi$
$601$	−2.47214	−	7.60845i	−0.100841	−	0.310355i	−0.988732	+	0.149698i	$0.952170\pi$
$602$	−0.381966	+	1.17557i	−0.0155678	+	0.0479127i
$603$	6.85410	+	4.97980i	0.279121	+	0.202793i
$604$	23.6180			0.961004
$605$	−10.8090	−	2.04087i	−0.439449	−	0.0829732i
$606$	0.472136			0.0191792
$607$	−17.5451	−	12.7473i	−0.712133	−	0.517395i	0.171728	−	0.985144i	$-0.445065\pi$
$607$	−17.5451	−	12.7473i	−0.712133	−	0.517395i	−0.883861	+	0.467749i	$0.845065\pi$
$608$	−0.236068	+	0.726543i	−0.00957382	+	0.0294652i
$609$	−0.163119	−	0.502029i	−0.00660991	−	0.0203432i
$610$	−1.38197	+	1.00406i	−0.0559542	+	0.0406531i
$611$	5.22542	−	3.79649i	0.211398	−	0.153590i
$612$	−1.92705	−	5.93085i	−0.0778964	−	0.239741i
$613$	−1.56231	+	4.80828i	−0.0631009	+	0.194205i	−0.977637	−	0.210300i	$-0.932556\pi$
$613$	−1.56231	+	4.80828i	−0.0631009	+	0.194205i	0.914536	+	0.404504i	$0.132556\pi$
$614$	−18.1631	−	13.1963i	−0.733004	−	0.532558i
$615$	5.52786			0.222905
$616$	3.04508	+	1.31433i	0.122690	+	0.0529558i
$617$	−26.1803			−1.05398			−0.526990	−	0.849871i	$-0.676680\pi$
$617$	−26.1803			−1.05398			−0.526990	+	0.849871i	$0.676680\pi$
$618$	−8.28115	−	6.01661i	−0.333117	−	0.242024i
$619$	8.47214	−	26.0746i	0.340524	−	1.04802i	−0.623413	−	0.781893i	$-0.714254\pi$
$619$	8.47214	−	26.0746i	0.340524	−	1.04802i	0.963937	−	0.266132i	$-0.0857457\pi$
$620$	0.236068	+	0.726543i	0.00948072	+	0.0291787i
$621$	1.32624	−	0.963568i	0.0532201	−	0.0386667i
$622$	9.85410	−	7.15942i	0.395113	−	0.287067i
$623$	4.23607	+	13.0373i	0.169714	+	0.522327i
$624$	−0.645898	+	1.98787i	−0.0258566	+	0.0795785i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−23.8885			−0.954778
$627$	−0.798374	−	1.34708i	−0.0318840	−	0.0537974i
$628$	0.0901699			0.00359817
$629$	−18.7082	−	13.5923i	−0.745945	−	0.541961i
$630$	−0.809017	+	2.48990i	−0.0322320	+	0.0991999i
$631$	−14.3541	−	44.1774i	−0.571428	−	1.75867i	−0.648033	−	0.761612i	$-0.724408\pi$
$631$	−14.3541	−	44.1774i	−0.571428	−	1.75867i	0.0766051	−	0.997062i	$-0.475592\pi$
$632$	−4.73607	+	3.44095i	−0.188391	+	0.136874i
$633$	−0.163119	+	0.118513i	−0.00648340	+	0.00471046i
$634$	−5.52786	−	17.0130i	−0.219540	−	0.675673i
$635$	−0.673762	+	2.07363i	−0.0267374	+	0.0822894i
$636$	−1.23607	−	0.898056i	−0.0490133	−	0.0356102i
$637$	3.38197			0.133998
$638$	1.87132	−	2.12663i	0.0740864	−	0.0841940i
$639$	−21.7984			−0.862330
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−4.57295	+	14.0741i	−0.180621	+	0.555893i	−0.999845	−	0.0175793i	$-0.994404\pi$
$641$	−4.57295	+	14.0741i	−0.180621	+	0.555893i	0.819225	+	0.573472i	$0.194404\pi$
$642$	2.90983	+	8.95554i	0.114842	+	0.353447i
$643$	17.6803	−	12.8455i	0.697245	−	0.506578i	−0.181789	−	0.983338i	$-0.558189\pi$
$643$	17.6803	−	12.8455i	0.697245	−	0.506578i	0.879034	+	0.476760i	$0.158189\pi$
$644$	0.381966	−	0.277515i	0.0150516	−	0.0109356i
$645$	0.236068	+	0.726543i	0.00929517	+	0.0286076i
$646$	−0.562306	+	1.73060i	−0.0221236	+	0.0680895i
$647$	−0.600813	−	0.436516i	−0.0236204	−	0.0171612i	0.575912	−	0.817511i	$-0.304647\pi$
$647$	−0.600813	−	0.436516i	−0.0236204	−	0.0171612i	−0.599533	+	0.800350i	$0.704647\pi$
$648$	5.70820			0.224239
$649$	−2.85410	+	30.4993i	−0.112033	+	1.19720i
$650$	3.38197			0.132652
$651$	0.381966	+	0.277515i	0.0149704	+	0.0108767i
$652$	5.14590	−	15.8374i	0.201529	−	0.620242i
$653$	−8.56231	−	26.3521i	−0.335069	−	1.03124i	−0.966688	−	0.255957i	$-0.917609\pi$
$653$	−8.56231	−	26.3521i	−0.335069	−	1.03124i	0.631619	−	0.775279i	$-0.282391\pi$
$654$	6.23607	−	4.53077i	0.243850	−	0.177167i
$655$	−12.4721	+	9.06154i	−0.487327	+	0.354064i
$656$	−2.76393	−	8.50651i	−0.107913	−	0.332123i
$657$	9.16312	−	28.2012i	0.357487	−	1.10023i
$658$	1.54508	+	1.12257i	0.0602337	+	0.0437623i
$659$	47.7426			1.85979			0.929895	−	0.367826i	$-0.119898\pi$
$659$	47.7426			1.85979			0.929895	+	0.367826i	$0.119898\pi$
$660$	2.00000	−	0.449028i	0.0778499	−	0.0174784i
$661$	−1.05573			−0.0410631			−0.0205315	−	0.999789i	$-0.506536\pi$
$661$	−1.05573			−0.0410631			−0.0205315	+	0.999789i	$0.506536\pi$
$662$	6.97214	+	5.06555i	0.270980	+	0.196878i
$663$	−1.53851	+	4.73504i	−0.0597507	+	0.183894i
$664$	3.51722	+	10.8249i	0.136495	+	0.420087i
$665$	0.618034	−	0.449028i	0.0239663	−	0.0174126i
$666$	20.5623	−	14.9394i	0.796773	−	0.578890i
$667$	−0.124612	−	0.383516i	−0.00482499	−	0.0148498i
$668$	6.18034	−	19.0211i	0.239125	−	0.735950i
$669$	−4.76393	−	3.46120i	−0.184184	−	0.133818i
$670$	3.23607			0.125020
$671$	−5.52786	+	1.24108i	−0.213401	+	0.0479115i
$672$	−0.618034			−0.0238412
$673$	25.4164	+	18.4661i	0.979731	+	0.711816i	0.957648	−	0.287940i	$-0.0929705\pi$
$673$	25.4164	+	18.4661i	0.979731	+	0.711816i	0.0220822	+	0.999756i	$0.492970\pi$
$674$	2.47214	−	7.60845i	0.0952231	−	0.293067i
$675$	1.07295	+	3.30220i	0.0412978	+	0.127102i
$676$	1.26393	−	0.918300i	0.0486128	−	0.0353192i
$677$	−41.1976	+	29.9318i	−1.58335	+	1.15037i	−0.670627	+	0.741795i	$0.733975\pi$
$677$	−41.1976	+	29.9318i	−1.58335	+	1.15037i	−0.912724	+	0.408577i	$0.866025\pi$
$678$	2.00000	+	6.15537i	0.0768095	+	0.236395i
$679$	−1.73607	+	5.34307i	−0.0666242	+	0.205048i
$680$	−1.92705	−	1.40008i	−0.0738990	−	0.0536908i
$681$	−8.56231			−0.328108
$682$	−0.236068	+	2.52265i	−0.00903951	+	0.0965974i
$683$	5.59675			0.214154			0.107077	−	0.994251i	$-0.465851\pi$
$683$	5.59675			0.214154			0.107077	+	0.994251i	$0.465851\pi$
$684$	−1.61803	−	1.17557i	−0.0618671	−	0.0449491i
$685$	−4.94427	+	15.2169i	−0.188911	+	0.581408i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	−2.85410	+	2.07363i	−0.108891	+	0.0791138i
$688$	1.00000	−	0.726543i	0.0381246	−	0.0276992i
$689$	−2.58359	−	7.95148i	−0.0984270	−	0.302927i
$690$	0.0901699	−	0.277515i	0.00343271	−	0.0105648i
$691$	5.23607	+	3.80423i	0.199189	+	0.144720i	0.682909	−	0.730503i	$-0.260715\pi$
$691$	5.23607	+	3.80423i	0.199189	+	0.144720i	−0.483720	+	0.875223i	$0.660715\pi$
$692$	22.5066			0.855572
$693$	−5.73607	+	6.51864i	−0.217895	+	0.247623i
$694$	−9.88854			−0.375364
$695$	7.23607	+	5.25731i	0.274480	+	0.199421i
$696$	−0.163119	+	0.502029i	−0.00618301	+	0.0190293i
$697$	−6.58359	−	20.2622i	−0.249371	−	0.767486i
$698$	7.32624	−	5.32282i	0.277302	−	0.201472i
$699$	7.32624	−	5.32282i	0.277104	−	0.201328i
$700$	0.309017	+	0.951057i	0.0116797	+	0.0359466i
$701$	14.9787	−	46.0997i	0.565738	−	1.74116i	−0.100010	−	0.994986i	$-0.531887\pi$
$701$	14.9787	−	46.0997i	0.565738	−	1.74116i	0.665748	−	0.746177i	$-0.268113\pi$
$702$	−9.50000	−	6.90215i	−0.358554	−	0.260505i
$703$	−7.41641			−0.279715
$704$	−1.69098	−	2.85317i	−0.0637313	−	0.107533i
$705$	1.18034			0.0444542
$706$	−25.4443	−	18.4863i	−0.957608	−	0.695743i
$707$	−0.236068	+	0.726543i	−0.00887825	+	0.0273244i
$708$	−1.76393	−	5.42882i	−0.0662926	−	0.204028i
$709$	−29.1525	+	21.1805i	−1.09484	+	0.795451i	−0.980211	−	0.197957i	$-0.936569\pi$
$709$	−29.1525	+	21.1805i	−1.09484	+	0.795451i	−0.114634	+	0.993408i	$0.536569\pi$
$710$	−6.73607	+	4.89404i	−0.252800	+	0.183670i
$711$	−4.73607	−	14.5761i	−0.177616	−	0.546647i
$712$	4.23607	−	13.0373i	0.158753	−	0.488593i
$713$	0.291796	+	0.212002i	0.0109278	+	0.00793955i
$714$	−1.47214			−0.0550933
$715$	10.2984	+	4.44501i	0.385137	+	0.166234i
$716$	0.562306			0.0210144
$717$	1.07295	+	0.779543i	0.0400700	+	0.0291126i
$718$	−8.95492	+	27.5604i	−0.334194	+	1.02854i
$719$	3.81966	+	11.7557i	0.142449	+	0.438414i	0.996674	−	0.0814899i	$-0.0259678\pi$
$719$	3.81966	+	11.7557i	0.142449	+	0.438414i	−0.854225	+	0.519904i	$0.825968\pi$
$720$	2.11803	−	1.53884i	0.0789345	−	0.0573492i
$721$	13.3992	−	9.73508i	0.499012	−	0.362553i
$722$	−5.69098	−	17.5150i	−0.211796	−	0.651842i
$723$	−1.85410	+	5.70634i	−0.0689548	+	0.212221i
$724$		0			0
$725$	0.854102			0.0317206
$726$	6.68034	+	1.26133i	0.247931	+	0.0468122i
$727$	23.6738			0.878011			0.439006	−	0.898484i	$-0.355331\pi$
$727$	23.6738			0.878011			0.439006	+	0.898484i	$0.355331\pi$
$728$	−2.73607	−	1.98787i	−0.101405	−	0.0736754i
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$	−3.50000	−	10.7719i	−0.129541	−	0.398686i
$731$	2.38197	−	1.73060i	0.0881002	−	0.0640085i
$732$	0.854102	−	0.620541i	0.0315685	−	0.0229359i
$733$	14.7533	+	45.4060i	0.544925	+	1.67711i	0.721168	+	0.692760i	$0.243606\pi$
$733$	14.7533	+	45.4060i	0.544925	+	1.67711i	−0.176243	+	0.984347i	$0.556394\pi$
$734$	6.07953	−	18.7109i	0.224399	−	0.690630i
$735$	0.500000	+	0.363271i	0.0184428	+	0.0133995i
$736$	−0.472136			−0.0174032
$737$	9.85410	+	4.25325i	0.362981	+	0.156671i
$738$	23.4164			0.861970
$739$	16.1803	+	11.7557i	0.595203	+	0.432441i	0.844173	−	0.536071i	$-0.180092\pi$
$739$	16.1803	+	11.7557i	0.595203	+	0.432441i	−0.248970	+	0.968511i	$0.580092\pi$
$740$	3.00000	−	9.23305i	0.110282	−	0.339414i
$741$	0.493422	+	1.51860i	0.0181263	+	0.0557871i
$742$	2.00000	−	1.45309i	0.0734223	−	0.0533444i
$743$	−17.0902	+	12.4167i	−0.626978	+	0.455526i	−0.855352	−	0.518048i	$-0.826659\pi$
$743$	−17.0902	+	12.4167i	−0.626978	+	0.455526i	0.228374	+	0.973573i	$0.426659\pi$
$744$	−0.145898	−	0.449028i	−0.00534888	−	0.0164622i
$745$	4.37132	−	13.4535i	0.160153	−	0.492900i
$746$	−23.1803	−	16.8415i	−0.848693	−	0.616611i
$747$	−29.7984			−1.09027
$748$	−4.02786	−	6.79615i	−0.147273	−	0.248492i
$749$	−15.2361			−0.556714
$750$	0.500000	+	0.363271i	0.0182574	+	0.0132648i
$751$	5.64590	−	17.3763i	0.206022	−	0.634070i	−0.793648	−	0.608377i	$-0.791821\pi$
$751$	5.64590	−	17.3763i	0.206022	−	0.634070i	0.999670	−	0.0256927i	$-0.00817914\pi$
$752$	−0.590170	−	1.81636i	−0.0215213	−	0.0662357i
$753$	2.61803	−	1.90211i	0.0954065	−	0.0693169i
$754$	−2.33688	+	1.69784i	−0.0851042	+	0.0618318i
$755$	7.29837	+	22.4621i	0.265615	+	0.817479i
$756$	1.07295	−	3.30220i	0.0390228	−	0.120100i
$757$	−15.0902	−	10.9637i	−0.548462	−	0.398481i	0.278756	−	0.960362i	$-0.410078\pi$
$757$	−15.0902	−	10.9637i	−0.548462	−	0.398481i	−0.827218	+	0.561881i	$0.810078\pi$
$758$	22.8541			0.830098
$759$	0.639320	−	0.726543i	0.0232059	−	0.0263718i
$760$	−0.763932			−0.0277107
$761$	−36.7426	−	26.6951i	−1.33192	−	0.967696i	−0.999700	−	0.0244945i	$-0.992202\pi$
$761$	−36.7426	−	26.6951i	−1.33192	−	0.967696i	−0.332220	−	0.943202i	$-0.607798\pi$
$762$	0.416408	−	1.28157i	0.0150849	−	0.0464264i
$763$	3.85410	+	11.8617i	0.139528	+	0.429423i
$764$	4.73607	−	3.44095i	0.171345	−	0.124489i
$765$	5.04508	−	3.66547i	0.182405	−	0.132525i
$766$	0.663119	+	2.04087i	0.0239595	+	0.0737396i
$767$	9.65248	−	29.7073i	0.348531	−	1.07267i
$768$	0.500000	+	0.363271i	0.0180422	+	0.0131084i
$769$	−8.29180			−0.299010			−0.149505	−	0.988761i	$-0.547768\pi$
$769$	−8.29180			−0.299010			−0.149505	+	0.988761i	$0.547768\pi$
$770$	−0.309017	+	3.30220i	−0.0111362	+	0.119003i
$771$	−12.5279			−0.451180
$772$	4.00000	+	2.90617i	0.143963	+	0.104595i
$773$	0.461493	−	1.42033i	0.0165987	−	0.0510857i	−0.942414	−	0.334448i	$-0.891450\pi$
$773$	0.461493	−	1.42033i	0.0165987	−	0.0510857i	0.959013	+	0.283363i	$0.0914500\pi$
$774$	1.00000	+	3.07768i	0.0359443	+	0.110625i
$775$	−0.618034	+	0.449028i	−0.0222004	+	0.0161296i
$776$	4.54508	−	3.30220i	0.163159	−	0.118542i
$777$	−1.85410	−	5.70634i	−0.0665155	−	0.204714i
$778$	4.10081	−	12.6210i	0.147021	−	0.452485i
$779$	−5.52786	−	4.01623i	−0.198056	−	0.143896i
$780$	−2.09017			−0.0748401
$781$	−26.9443	+	6.04937i	−0.964142	+	0.216463i
$782$	−1.12461			−0.0402160
$783$	−2.39919	−	1.74311i	−0.0857399	−	0.0622937i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	0.0278640	+	0.0857567i	0.000994510	+	0.00306079i
$786$	7.70820	−	5.60034i	0.274943	−	0.199757i
$787$	21.9164	−	15.9232i	0.781236	−	0.567601i	−0.124114	−	0.992268i	$-0.539609\pi$
$787$	21.9164	−	15.9232i	0.781236	−	0.567601i	0.905350	+	0.424667i	$0.139609\pi$
$788$	3.52786	+	10.8576i	0.125675	+	0.386788i
$789$	−5.29180	+	16.2865i	−0.188393	+	0.579814i
$790$	−4.73607	−	3.44095i	−0.168502	−	0.122424i
$791$	−10.4721			−0.372346
$792$	8.47214	−	1.90211i	0.301044	−	0.0675886i
$793$	5.77709			0.205150
$794$	8.44427	+	6.13512i	0.299676	+	0.217727i
$795$	0.472136	−	1.45309i	0.0167449	−	0.0515356i
$796$	2.14590	+	6.60440i	0.0760593	+	0.234087i
$797$	39.0967	−	28.4054i	1.38488	−	1.00617i	0.388472	−	0.921460i	$-0.373003\pi$
$797$	39.0967	−	28.4054i	1.38488	−	1.00617i	0.996405	−	0.0847123i	$-0.0269971\pi$
$798$	−0.381966	+	0.277515i	−0.0135215	+	0.00982391i
$799$	−1.40576	−	4.32650i	−0.0497324	−	0.153061i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	29.0344	+	21.0948i	1.02588	+	0.745347i
$802$	−34.3820			−1.21407
$803$	3.50000	−	37.4015i	0.123512	−	1.31987i
$804$	−2.00000			−0.0705346
$805$	0.381966	+	0.277515i	0.0134625	+	0.00978110i
$806$	0.798374	−	2.45714i	0.0281215	−	0.0865491i
$807$	−1.20163	−	3.69822i	−0.0422992	−	0.130184i
$808$	0.618034	−	0.449028i	0.0217424	−	0.0157967i
$809$	−26.4443	+	19.2129i	−0.929731	+	0.675489i	−0.945927	−	0.324380i	$-0.894844\pi$
$809$	−26.4443	+	19.2129i	−0.929731	+	0.675489i	0.0161959	+	0.999869i	$0.494844\pi$
$810$	1.76393	+	5.42882i	0.0619783	+	0.190749i
$811$	−16.6525	+	51.2511i	−0.584748	+	1.79967i	0.0155344	+	0.999879i	$0.495055\pi$
$811$	−16.6525	+	51.2511i	−0.584748	+	1.79967i	−0.600282	+	0.799788i	$0.704945\pi$
$812$	−0.690983	−	0.502029i	−0.0242487	−	0.0176177i
$813$	15.5279			0.544586
$814$	21.2705	−	24.1724i	0.745531	−	0.847244i
$815$	16.6525			0.583311
$816$	1.19098	+	0.865300i	0.0416927	+	0.0302916i
$817$	0.291796	−	0.898056i	0.0102087	−	0.0314190i
$818$	0.236068	+	0.726543i	0.00825392	+	0.0254030i
$819$	7.16312	−	5.20431i	0.250300	−	0.181853i
$820$	7.23607	−	5.25731i	0.252694	−	0.183593i
$821$	−11.5000	−	35.3934i	−0.401353	−	1.23524i	−0.923902	−	0.382628i	$-0.875019\pi$
$821$	−11.5000	−	35.3934i	−0.401353	−	1.23524i	0.522550	−	0.852609i	$-0.324981\pi$
$822$	3.05573	−	9.40456i	0.106581	−	0.328022i
$823$	−3.52786	−	2.56314i	−0.122974	−	0.0893456i	0.524598	−	0.851350i	$-0.324215\pi$
$823$	−3.52786	−	2.56314i	−0.122974	−	0.0893456i	−0.647572	+	0.762004i	$0.724215\pi$
$824$	−16.5623			−0.576975
$825$	1.04508	+	1.76336i	0.0363852	+	0.0613922i
$826$	9.23607			0.321364
$827$	12.1803	+	8.84953i	0.423552	+	0.307728i	0.779065	−	0.626943i	$-0.215694\pi$
$827$	12.1803	+	8.84953i	0.423552	+	0.307728i	−0.355513	+	0.934671i	$0.615694\pi$
$828$	0.381966	−	1.17557i	0.0132742	−	0.0408539i
$829$	−1.81966	−	5.60034i	−0.0631994	−	0.194508i	0.914471	−	0.404651i	$-0.132607\pi$
$829$	−1.81966	−	5.60034i	−0.0631994	−	0.194508i	−0.977671	+	0.210143i	$0.932607\pi$
$830$	−9.20820	+	6.69015i	−0.319621	+	0.232219i
$831$	−6.70820	+	4.87380i	−0.232705	+	0.169070i
$832$	1.04508	+	3.21644i	0.0362318	+	0.111510i
$833$	0.736068	−	2.26538i	0.0255032	−	0.0784909i
$834$	−4.47214	−	3.24920i	−0.154857	−	0.112510i
$835$	20.0000			0.692129
$836$	−2.32624	−	1.00406i	−0.0804546	−	0.0347260i
$837$	2.65248			0.0916830
$838$	8.85410	+	6.43288i	0.305860	+	0.222220i
$839$	13.7082	−	42.1895i	0.473260	−	1.45654i	−0.375031	−	0.927012i	$-0.622368\pi$
$839$	13.7082	−	42.1895i	0.473260	−	1.45654i	0.848290	−	0.529531i	$-0.177632\pi$
$840$	−0.190983	−	0.587785i	−0.00658954	−	0.0202805i
$841$	22.8713	−	16.6170i	0.788666	−	0.573000i
$842$	−3.50000	+	2.54290i	−0.120618	+	0.0876341i
$843$	5.03444	+	15.4944i	0.173395	+	0.533656i
$844$	−0.100813	+	0.310271i	−0.00347013	+	0.0106800i
$845$	1.26393	+	0.918300i	0.0434806	+	0.0315905i
$846$	5.00000			0.171904
$847$	−5.28115	+	9.64932i	−0.181463	+	0.331555i
$848$	−2.47214			−0.0848935
$849$	0.663119	+	0.481784i	0.0227582	+	0.0165348i
$850$	0.736068	−	2.26538i	0.0252469	−	0.0777020i
$851$	−1.41641	−	4.35926i	−0.0485538	−	0.149433i
$852$	4.16312	−	3.02468i	0.142626	−	0.103624i
$853$	20.4443	−	14.8536i	0.699999	−	0.508579i	−0.179933	−	0.983679i	$-0.557588\pi$
$853$	20.4443	−	14.8536i	0.699999	−	0.508579i	0.879932	+	0.475100i	$0.157588\pi$
$854$	0.527864	+	1.62460i	0.0180631	+	0.0555926i
$855$	0.618034	−	1.90211i	0.0211363	−	0.0650509i
$856$	12.3262	+	8.95554i	0.421302	+	0.306094i
$857$	6.58359			0.224891			0.112446	−	0.993658i	$-0.464132\pi$
$857$	6.58359			0.224891			0.112446	+	0.993658i	$0.464132\pi$
$858$	−6.36475	−	2.74717i	−0.217289	−	0.0937868i
$859$	28.5836			0.975260			0.487630	−	0.873051i	$-0.337862\pi$
$859$	28.5836			0.975260			0.487630	+	0.873051i	$0.337862\pi$
$860$	1.00000	+	0.726543i	0.0340997	+	0.0247749i
$861$	1.70820	−	5.25731i	0.0582154	−	0.179169i
$862$	1.40983	+	4.33901i	0.0480190	+	0.147787i
$863$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$863$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$864$	−2.80902	+	2.04087i	−0.0955647	+	0.0694318i
$865$	6.95492	+	21.4050i	0.236474	+	0.727793i
$866$	−2.19098	+	6.74315i	−0.0744526	+	0.229142i
$867$	−5.66312	−	4.11450i	−0.192330	−	0.139736i
$868$	0.763932			0.0259295
$869$	−9.89919	−	16.7027i	−0.335807	−	0.566602i
$870$	−0.527864			−0.0178963
$871$	−8.85410	−	6.43288i	−0.300010	−	0.217970i
$872$	3.85410	−	11.8617i	0.130516	−	0.401688i
$873$	4.54508	+	13.9883i	0.153828	+	0.473433i
$874$	−0.291796	+	0.212002i	−0.00987015	+	0.00717108i
$875$	−0.809017	+	0.587785i	−0.0273498	+	0.0198708i
$876$	2.16312	+	6.65740i	0.0730850	+	0.224933i
$877$	−12.5279	+	38.5568i	−0.423036	+	1.30197i	0.481827	+	0.876267i	$0.339974\pi$
$877$	−12.5279	+	38.5568i	−0.423036	+	1.30197i	−0.904862	+	0.425704i	$0.860026\pi$
$878$	−16.7082	−	12.1392i	−0.563875	−	0.409679i
$879$	−0.875388			−0.0295261
$880$	2.19098	−	2.48990i	0.0738580	−	0.0839345i
$881$	−47.4853			−1.59982			−0.799910	−	0.600120i	$-0.795120\pi$
$881$	−47.4853			−1.59982			−0.799910	+	0.600120i	$0.795120\pi$
$882$	2.11803	+	1.53884i	0.0713179	+	0.0518155i
$883$	−11.9787	+	36.8667i	−0.403116	+	1.24066i	0.519342	+	0.854566i	$0.326177\pi$
$883$	−11.9787	+	36.8667i	−0.403116	+	1.24066i	−0.922458	+	0.386097i	$0.873823\pi$
$884$	2.48936	+	7.66145i	0.0837261	+	0.257683i
$885$	4.61803	−	3.35520i	0.155234	−	0.112784i
$886$	8.70820	−	6.32688i	0.292558	−	0.212556i
$887$	9.00658	+	27.7194i	0.302411	+	0.930726i	0.980631	+	0.195867i	$0.0627520\pi$
$887$	9.00658	+	27.7194i	0.302411	+	0.930726i	−0.678219	+	0.734860i	$0.737248\pi$
$888$	−1.85410	+	5.70634i	−0.0622196	+	0.191492i
$889$	1.76393	+	1.28157i	0.0591604	+	0.0429825i
$890$	13.7082			0.459500
$891$	−1.76393	+	18.8496i	−0.0590939	+	0.631486i
$892$	−9.52786			−0.319016
$893$	−1.18034	−	0.857567i	−0.0394986	−	0.0286974i
$894$	−2.70163	+	8.31475i	−0.0903559	+	0.278087i
$895$	0.173762	+	0.534785i	0.00580823	+	0.0178759i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	−0.798374	+	0.580053i	−0.0266569	+	0.0193674i
$898$	5.71885	+	17.6008i	0.190840	+	0.587346i
$899$	0.201626	−	0.620541i	0.00672461	−	0.0206962i
$900$	2.11803	+	1.53884i	0.0706011	+	0.0512947i
$901$	−5.88854			−0.196176
$902$	28.9443	−	6.49839i	0.963739	−	0.216373i
$903$	0.763932			0.0254221
$904$	8.47214	+	6.15537i	0.281779	+	0.204724i
$905$		0			0
$906$	−4.51064	−	13.8823i	−0.149856	−	0.461210i
$907$	−11.6180	+	8.44100i	−0.385770	+	0.280279i	−0.763720	−	0.645547i	$-0.776629\pi$
$907$	−11.6180	+	8.44100i	−0.385770	+	0.280279i	0.377950	+	0.925826i	$0.376629\pi$
$908$	−11.2082	+	8.14324i	−0.371957	+	0.270243i
$909$	0.618034	+	1.90211i	0.0204989	+	0.0630891i
$910$	1.04508	−	3.21644i	0.0346442	−	0.106624i
$911$	31.1074	+	22.6008i	1.03063	+	0.748799i	0.968435	−	0.249264i	$-0.0801888\pi$
$911$	31.1074	+	22.6008i	1.03063	+	0.748799i	0.0621984	+	0.998064i	$0.480189\pi$
$912$	0.472136			0.0156340
$913$	−36.8328	+	8.26948i	−1.21899	+	0.273680i
$914$	−14.0000			−0.463079
$915$	0.854102	+	0.620541i	0.0282357	+	0.0205145i
$916$	−1.76393	+	5.42882i	−0.0582820	+	0.179373i
$917$	4.76393	+	14.6619i	0.157319	+	0.484178i
$918$	−6.69098	+	4.86128i	−0.220835	+	0.160446i
$919$	−11.7254	+	8.51902i	−0.386786	+	0.281017i	−0.764137	−	0.645054i	$-0.776835\pi$
$919$	−11.7254	+	8.51902i	−0.386786	+	0.281017i	0.377351	+	0.926070i	$0.376835\pi$
$920$	−0.145898	−	0.449028i	−0.00481012	−	0.0148040i
$921$	−4.28773	+	13.1963i	−0.141286	+	0.434832i
$922$	12.2361	+	8.89002i	0.402973	+	0.292777i
$923$	28.1591			0.926867
$924$	0.190983	−	2.04087i	0.00628288	−	0.0671397i
$925$	9.70820			0.319204
$926$	−6.61803	−	4.80828i	−0.217482	−	0.158010i
$927$	13.3992	−	41.2385i	0.440087	−	1.35445i
$928$	0.263932	+	0.812299i	0.00866399	+	0.0266650i
$929$	35.4164	−	25.7315i	1.16197	−	0.844224i	0.171948	−	0.985106i	$-0.444994\pi$
$929$	35.4164	−	25.7315i	1.16197	−	0.844224i	0.990026	+	0.140882i	$0.0449938\pi$
$930$	0.381966	−	0.277515i	0.0125252	−	0.00910006i
$931$	−0.236068	−	0.726543i	−0.00773682	−	0.0238115i
$932$	4.52786	−	13.9353i	0.148315	−	0.456467i
$933$	−6.09017	−	4.42477i	−0.199383	−	0.144860i
$934$	19.3820			0.634197
$935$	5.21885	−	5.93085i	0.170675	−	0.193960i
$936$	−8.85410			−0.289405
$937$	−29.4443	−	21.3925i	−0.961902	−	0.698863i	−0.00831064	−	0.999965i	$-0.502645\pi$
$937$	−29.4443	−	21.3925i	−0.961902	−	0.698863i	−0.953592	+	0.301102i	$0.902645\pi$
$938$	1.00000	−	3.07768i	0.0326512	−	0.100490i
$939$	4.56231	+	14.0413i	0.148885	+	0.458222i
$940$	1.54508	−	1.12257i	0.0503951	−	0.0366142i
$941$	−9.18034	+	6.66991i	−0.299271	+	0.217433i	−0.727279	−	0.686342i	$-0.759215\pi$
$941$	−9.18034	+	6.66991i	−0.299271	+	0.217433i	0.428008	+	0.903775i	$0.359215\pi$
$942$	−0.0172209	−	0.0530006i	−0.000561088	−	0.00172685i
$943$	1.30495	−	4.01623i	0.0424951	−	0.130786i
$944$	−7.47214	−	5.42882i	−0.243197	−	0.176693i
$945$	3.47214			0.112949
$946$	2.09017	+	3.52671i	0.0679573	+	0.114663i
$947$	1.34752			0.0437887			0.0218943	−	0.999760i	$-0.493030\pi$
$947$	1.34752			0.0437887			0.0218943	+	0.999760i	$0.493030\pi$
$948$	2.92705	+	2.12663i	0.0950662	+	0.0690696i
$949$	−11.8369	+	36.4302i	−0.384241	+	1.18257i
$950$	−0.236068	−	0.726543i	−0.00765906	−	0.0235722i
$951$	−8.94427	+	6.49839i	−0.290038	+	0.210725i
$952$	−1.92705	+	1.40008i	−0.0624561	+	0.0453770i
$953$	9.09017	+	27.9767i	0.294459	+	0.906253i	0.983402	+	0.181438i	$0.0580750\pi$
$953$	9.09017	+	27.9767i	0.294459	+	0.906253i	−0.688943	+	0.724816i	$0.741925\pi$
$954$	2.00000	−	6.15537i	0.0647524	−	0.199287i
$955$	4.73607	+	3.44095i	0.153256	+	0.111347i
$956$	2.14590			0.0694033
$957$	−1.60739	−	0.693786i	−0.0519596	−	0.0224269i
$958$	5.12461			0.165569
$959$	12.9443	+	9.40456i	0.417992	+	0.303689i
$960$	−0.190983	+	0.587785i	−0.00616395	+	0.0189707i
$961$	−9.39919	−	28.9277i	−0.303200	−	0.933152i
$962$	−26.5623	+	19.2986i	−0.856403	+	0.622213i
$963$	−32.2705	+	23.4459i	−1.03990	+	0.755533i
$964$	3.00000	+	9.23305i	0.0966235	+	0.297377i
$965$	−1.52786	+	4.70228i	−0.0491837	+	0.151372i
$966$	−0.236068	−	0.171513i	−0.00759536	−	0.00551835i
$967$	−17.7082			−0.569457			−0.284729	−	0.958608i	$-0.591904\pi$
$967$	−17.7082			−0.569457			−0.284729	+	0.958608i	$0.591904\pi$
$968$	9.94427	−	4.70228i	0.319621	−	0.151137i
$969$	1.12461			0.0361277
$970$	4.54508	+	3.30220i	0.145934	+	0.106027i
$971$	−0.729490	+	2.24514i	−0.0234105	+	0.0720500i	−0.962079	−	0.272770i	$-0.912060\pi$
$971$	−0.729490	+	2.24514i	−0.0234105	+	0.0720500i	0.938669	+	0.344820i	$0.112060\pi$
$972$	−4.30902	−	13.2618i	−0.138212	−	0.425372i
$973$	7.23607	−	5.25731i	0.231978	−	0.168542i
$974$	−27.6525	+	20.0907i	−0.886042	+	0.643748i
$975$	−0.645898	−	1.98787i	−0.0206853	−	0.0636628i
$976$	0.527864	−	1.62460i	0.0168965	−	0.0520021i
$977$	47.6525	+	34.6216i	1.52454	+	1.10764i	0.959180	+	0.282796i	$0.0912618\pi$
$977$	47.6525	+	34.6216i	1.52454	+	1.10764i	0.565358	+	0.824846i	$0.308738\pi$
$978$	−10.2918			−0.329095
$979$	41.7426	+	18.0171i	1.33410	+	0.575828i
$980$	1.00000			0.0319438
$981$	26.4164	+	19.1926i	0.843411	+	0.612774i
$982$	−5.23607	+	16.1150i	−0.167090	+	0.514249i
$983$	−0.298374	−	0.918300i	−0.00951665	−	0.0292892i	0.946185	−	0.323625i	$-0.104902\pi$
$983$	−0.298374	−	0.918300i	−0.00951665	−	0.0292892i	−0.955702	+	0.294336i	$0.904902\pi$
$984$	−4.47214	+	3.24920i	−0.142566	+	0.103581i
$985$	−9.23607	+	6.71040i	−0.294286	+	0.213811i
$986$	0.628677	+	1.93487i	0.0200212	+	0.0616188i
$987$	0.364745	−	1.12257i	0.0116100	−	0.0357318i
$988$	2.09017	+	1.51860i	0.0664972	+	0.0483130i
$989$	0.583592			0.0185572
$990$	4.42705	+	7.46969i	0.140701	+	0.237402i
$991$	−53.9230			−1.71292			−0.856460	−	0.516213i	$-0.827341\pi$
$991$	−53.9230			−1.71292			−0.856460	+	0.516213i	$0.827341\pi$
$992$	−0.618034	−	0.449028i	−0.0196226	−	0.0142567i
$993$	1.64590	−	5.06555i	0.0522310	−	0.160750i
$994$	2.57295	+	7.91872i	0.0816090	+	0.251167i
$995$	−5.61803	+	4.08174i	−0.178104	+	0.129400i
$996$	5.69098	−	4.13474i	0.180326	−	0.131014i
$997$	−0.791796	−	2.43690i	−0.0250764	−	0.0771773i	0.937735	−	0.347351i	$-0.112919\pi$
$997$	−0.791796	−	2.43690i	−0.0250764	−	0.0771773i	−0.962812	+	0.270174i	$0.912919\pi$
$998$	−0.0623059	+	0.191758i	−0.00197226	+	0.00606999i
$999$	−27.2705	−	19.8132i	−0.862801	−	0.626861i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.a.421.1	✓	4	11.3	even	5	inner
770.2.n.a.631.1	yes	4	1.1	even	1	trivial
8470.2.a.bq.1.1		2	11.6	odd	10
8470.2.a.cc.1.1		2	11.5	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.11803 + 1.53884i) q^{9} +1.00000 q^{10} +(3.04508 + 1.31433i) q^{11} -0.618034 q^{12} +(-2.73607 - 1.98787i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-0.190983 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.92705 + 1.40008i) q^{17} +(-0.809017 - 2.48990i) q^{18} +(-0.236068 + 0.726543i) q^{19} +(-0.809017 - 0.587785i) q^{20} -0.618034 q^{21} +(-1.69098 - 2.85317i) q^{22} -0.472136 q^{23} +(0.500000 + 0.363271i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.04508 + 3.21644i) q^{26} +(-2.80902 + 2.04087i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(0.263932 + 0.812299i) q^{29} +(-0.190983 + 0.587785i) q^{30} +(-0.618034 - 0.449028i) q^{31} +1.00000 q^{32} +(-1.35410 + 1.53884i) q^{33} +2.38197 q^{34} +(-0.809017 - 0.587785i) q^{35} +(-0.809017 + 2.48990i) q^{36} +(3.00000 + 9.23305i) q^{37} +(0.618034 - 0.449028i) q^{38} +(1.69098 - 1.22857i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-2.76393 + 8.50651i) q^{41} +(0.500000 + 0.363271i) q^{42} -1.23607 q^{43} +(-0.309017 + 3.30220i) q^{44} -2.61803 q^{45} +(0.381966 + 0.277515i) q^{46} +(-0.590170 + 1.81636i) q^{47} +(-0.190983 - 0.587785i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.454915 - 1.40008i) q^{51} +(1.04508 - 3.21644i) q^{52} +(2.00000 + 1.45309i) q^{53} +3.47214 q^{54} +(-3.23607 + 0.726543i) q^{55} +1.00000 q^{56} +(-0.381966 - 0.277515i) q^{57} +(0.263932 - 0.812299i) q^{58} +(2.85410 + 8.78402i) q^{59} +(0.500000 - 0.363271i) q^{60} +(-1.38197 + 1.00406i) q^{61} +(0.236068 + 0.726543i) q^{62} +(-0.809017 + 2.48990i) q^{63} +(-0.809017 - 0.587785i) q^{64} +3.38197 q^{65} +(2.00000 - 0.449028i) q^{66} +3.23607 q^{67} +(-1.92705 - 1.40008i) q^{68} +(0.0901699 - 0.277515i) q^{69} +(0.309017 + 0.951057i) q^{70} +(-6.73607 + 4.89404i) q^{71} +(2.11803 - 1.53884i) q^{72} +(-3.50000 - 10.7719i) q^{73} +(3.00000 - 9.23305i) q^{74} +(0.500000 + 0.363271i) q^{75} -0.763932 q^{76} +(-0.309017 + 3.30220i) q^{77} -2.09017 q^{78} +(-4.73607 - 3.44095i) q^{79} +(0.309017 - 0.951057i) q^{80} +(1.76393 + 5.42882i) q^{81} +(7.23607 - 5.25731i) q^{82} +(-9.20820 + 6.69015i) q^{83} +(-0.190983 - 0.587785i) q^{84} +(0.736068 - 2.26538i) q^{85} +(1.00000 + 0.726543i) q^{86} -0.527864 q^{87} +(2.19098 - 2.48990i) q^{88} +13.7082 q^{89} +(2.11803 + 1.53884i) q^{90} +(1.04508 - 3.21644i) q^{91} +(-0.145898 - 0.449028i) q^{92} +(0.381966 - 0.277515i) q^{93} +(1.54508 - 1.12257i) q^{94} +(-0.236068 - 0.726543i) q^{95} +(-0.190983 + 0.587785i) q^{96} +(4.54508 + 3.30220i) q^{97} +1.00000 q^{98} +(4.42705 + 7.46969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9	\( 4 q - q^{2} - 3 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + 4 q^{9} + 4 q^{10} + q^{11} + 2 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - q^{17} - q^{18} + 8 q^{19} - q^{20} + 2 q^{21} - 9 q^{22} + 16 q^{23} + 2 q^{24} - q^{25} - 7 q^{26} - 9 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 14 q^{34} - q^{35} - q^{36} + 12 q^{37} - 2 q^{38} + 9 q^{39} - q^{40} - 20 q^{41} + 2 q^{42} + 4 q^{43} + q^{44} - 6 q^{45} + 6 q^{46} + 20 q^{47} - 3 q^{48} - q^{49} - q^{50} - 13 q^{51} - 7 q^{52} + 8 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 6 q^{57} + 10 q^{58} - 2 q^{59} + 2 q^{60} - 10 q^{61} - 8 q^{62} - q^{63} - q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} - q^{68} - 22 q^{69} - q^{70} - 18 q^{71} + 4 q^{72} - 14 q^{73} + 12 q^{74} + 2 q^{75} - 12 q^{76} + q^{77} + 14 q^{78} - 10 q^{79} - q^{80} + 16 q^{81} + 20 q^{82} - 10 q^{83} - 3 q^{84} - 6 q^{85} + 4 q^{86} - 20 q^{87} + 11 q^{88} + 28 q^{89} + 4 q^{90} - 7 q^{91} - 14 q^{92} + 6 q^{93} - 5 q^{94} + 8 q^{95} - 3 q^{96} + 7 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 - q^4 - q^5 + 2 * q^6 - q^7 - q^8 + 4 * q^9 + 4 * q^10 + q^11 + 2 * q^12 - 2 * q^13 - q^14 - 3 * q^15 - q^16 - q^17 - q^18 + 8 * q^19 - q^20 + 2 * q^21 - 9 * q^22 + 16 * q^23 + 2 * q^24 - q^25 - 7 * q^26 - 9 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 14 * q^34 - q^35 - q^36 + 12 * q^37 - 2 * q^38 + 9 * q^39 - q^40 - 20 * q^41 + 2 * q^42 + 4 * q^43 + q^44 - 6 * q^45 + 6 * q^46 + 20 * q^47 - 3 * q^48 - q^49 - q^50 - 13 * q^51 - 7 * q^52 + 8 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 6 * q^57 + 10 * q^58 - 2 * q^59 + 2 * q^60 - 10 * q^61 - 8 * q^62 - q^63 - q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 - q^68 - 22 * q^69 - q^70 - 18 * q^71 + 4 * q^72 - 14 * q^73 + 12 * q^74 + 2 * q^75 - 12 * q^76 + q^77 + 14 * q^78 - 10 * q^79 - q^80 + 16 * q^81 + 20 * q^82 - 10 * q^83 - 3 * q^84 - 6 * q^85 + 4 * q^86 - 20 * q^87 + 11 * q^88 + 28 * q^89 + 4 * q^90 - 7 * q^91 - 14 * q^92 + 6 * q^93 - 5 * q^94 + 8 * q^95 - 3 * q^96 + 7 * q^97 + 4 * q^98 + 11 * q^99

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