LMFDB - Embedded newform 170.2.k.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
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} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			121.3
Root			$2.47571i$ of defining polynomial
Character	$\chi$	$=$	170.121
Dual form			170.2.k.b.111.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.36338 - 0.564729i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(1.36338 + 0.564729i) q^{6} +(1.35785 - 3.27815i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.581445 + 0.581445i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.36338 - 0.564729i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(1.36338 + 0.564729i) q^{6} +(1.35785 - 3.27815i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.581445 + 0.581445i) q^{9} +(-0.382683 + 0.923880i) q^{10} +(-4.35013 - 1.80188i) q^{11} +(0.564729 + 1.36338i) q^{12} +5.47699i q^{13} +(3.27815 - 1.35785i) q^{14} +(1.04348 + 1.04348i) q^{15} -1.00000 q^{16} +(2.52894 - 3.25645i) q^{17} -0.822287 q^{18} +(0.857748 + 0.857748i) q^{19} +(-0.923880 + 0.382683i) q^{20} -5.23617i q^{21} +(-1.80188 - 4.35013i) q^{22} +(-5.28485 - 2.18906i) q^{23} +(-0.564729 + 1.36338i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-3.87282 + 3.87282i) q^{26} +(-2.15856 + 5.21121i) q^{27} +(3.27815 + 1.35785i) q^{28} +(-1.77710 - 4.29029i) q^{29} +1.47571i q^{30} +(6.72892 - 2.78721i) q^{31} +(-0.707107 - 0.707107i) q^{32} -6.94843 q^{33} +(4.09089 - 0.514430i) q^{34} +3.54824 q^{35} +(-0.581445 - 0.581445i) q^{36} +(-8.58444 + 3.55579i) q^{37} +1.21304i q^{38} +(3.09302 + 7.46720i) q^{39} +(-0.923880 - 0.382683i) q^{40} +(0.0547598 - 0.132202i) q^{41} +(3.70253 - 3.70253i) q^{42} +(-0.587013 + 0.587013i) q^{43} +(1.80188 - 4.35013i) q^{44} +(-0.759695 - 0.314676i) q^{45} +(-2.18906 - 5.28485i) q^{46} -5.85635i q^{47} +(-1.36338 + 0.564729i) q^{48} +(-3.95275 - 3.95275i) q^{49} -1.00000 q^{50} +(1.60888 - 5.86793i) q^{51} -5.47699 q^{52} +(6.54226 + 6.54226i) q^{53} +(-5.21121 + 2.15856i) q^{54} -4.70854i q^{55} +(1.35785 + 3.27815i) q^{56} +(1.65383 + 0.685038i) q^{57} +(1.77710 - 4.29029i) q^{58} +(-3.33507 + 3.33507i) q^{59} +(-1.04348 + 1.04348i) q^{60} +(4.76261 - 11.4980i) q^{61} +(6.72892 + 2.78721i) q^{62} +(1.11655 + 2.69558i) q^{63} -1.00000i q^{64} +(-5.06008 + 2.09595i) q^{65} +(-4.91328 - 4.91328i) q^{66} +8.66703 q^{67} +(3.25645 + 2.52894i) q^{68} -8.44146 q^{69} +(2.50899 + 2.50899i) q^{70} +(4.75235 - 1.96849i) q^{71} -0.822287i q^{72} +(6.17351 + 14.9042i) q^{73} +(-8.58444 - 3.55579i) q^{74} +(-0.564729 + 1.36338i) q^{75} +(-0.857748 + 0.857748i) q^{76} +(-11.8137 + 11.8137i) q^{77} +(-3.09302 + 7.46720i) q^{78} +(9.34587 + 3.87118i) q^{79} +(-0.382683 - 0.923880i) q^{80} +5.85698i q^{81} +(0.132202 - 0.0547598i) q^{82} +(2.40841 + 2.40841i) q^{83} +5.23617 q^{84} +(3.97635 + 1.09024i) q^{85} -0.830161 q^{86} +(-4.84570 - 4.84570i) q^{87} +(4.35013 - 1.80188i) q^{88} +2.24175i q^{89} +(-0.314676 - 0.759695i) q^{90} +(17.9544 + 7.43696i) q^{91} +(2.18906 - 5.28485i) q^{92} +(7.60004 - 7.60004i) q^{93} +(4.14106 - 4.14106i) q^{94} +(-0.464210 + 1.12070i) q^{95} +(-1.36338 - 0.564729i) q^{96} +(1.66675 + 4.02389i) q^{97} -5.59004i q^{98} +(3.57705 - 1.48166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.36338	−	0.564729i	0.787145	−	0.326046i	0.0473502	−	0.998878i	$-0.484922\pi$
$3$	1.36338	−	0.564729i	0.787145	−	0.326046i	0.739795	+	0.672832i	$0.234922\pi$
$4$			1.00000i			0.500000i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$	1.36338	+	0.564729i	0.556596	+	0.230550i
$7$	1.35785	−	3.27815i	0.513221	−	1.23902i	−0.428779	−	0.903410i	$-0.641056\pi$
$7$	1.35785	−	3.27815i	0.513221	−	1.23902i	0.941999	−	0.335615i	$-0.108944\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.581445	+	0.581445i	−0.193815	+	0.193815i
$10$	−0.382683	+	0.923880i	−0.121015	+	0.292156i
$11$	−4.35013	−	1.80188i	−1.31161	−	0.543288i	−0.386258	−	0.922391i	$-0.626232\pi$
$11$	−4.35013	−	1.80188i	−1.31161	−	0.543288i	−0.925354	+	0.379103i	$0.876232\pi$
$12$	0.564729	+	1.36338i	0.163023	+	0.393573i
$13$			5.47699i			1.51904i	0.650481	+	0.759522i	$0.274567\pi$
$13$			5.47699i			1.51904i	−0.650481	+	0.759522i	$0.725433\pi$
$14$	3.27815	−	1.35785i	0.876123	−	0.362902i
$15$	1.04348	+	1.04348i	0.269426	+	0.269426i
$16$	−1.00000			−0.250000
$17$	2.52894	−	3.25645i	0.613358	−	0.789805i
$17$	2.52894	−	3.25645i	0.613358	−	0.789805i
$18$	−0.822287			−0.193815
$19$	0.857748	+	0.857748i	0.196781	+	0.196781i	0.798619	−	0.601838i	$-0.205565\pi$
$19$	0.857748	+	0.857748i	0.196781	+	0.196781i	−0.601838	+	0.798619i	$0.705565\pi$
$20$	−0.923880	+	0.382683i	−0.206586	+	0.0855706i
$21$		−	5.23617i		−	1.14263i
$22$	−1.80188	−	4.35013i	−0.384162	−	0.927450i
$23$	−5.28485	−	2.18906i	−1.10197	−	0.456450i	−0.243803	−	0.969825i	$-0.578395\pi$
$23$	−5.28485	−	2.18906i	−1.10197	−	0.456450i	−0.858165	+	0.513375i	$0.828395\pi$
$24$	−0.564729	+	1.36338i	−0.115275	+	0.278298i
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	−3.87282	+	3.87282i	−0.759522	+	0.759522i
$27$	−2.15856	+	5.21121i	−0.415414	+	1.00290i
$28$	3.27815	+	1.35785i	0.619512	+	0.256610i
$29$	−1.77710	−	4.29029i	−0.329999	−	0.796687i	−0.998591	−	0.0530586i	$-0.983103\pi$
$29$	−1.77710	−	4.29029i	−0.329999	−	0.796687i	0.668593	−	0.743629i	$-0.266897\pi$
$30$			1.47571i			0.269426i
$31$	6.72892	−	2.78721i	1.20855	−	0.500598i	0.314798	−	0.949159i	$-0.398063\pi$
$31$	6.72892	−	2.78721i	1.20855	−	0.500598i	0.893752	+	0.448561i	$0.148063\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−6.94843			−1.20957
$34$	4.09089	−	0.514430i	0.701581	−	0.0882239i
$35$	3.54824			0.599763
$36$	−0.581445	−	0.581445i	−0.0969075	−	0.0969075i
$37$	−8.58444	+	3.55579i	−1.41127	+	0.584569i	−0.952652	−	0.304063i	$-0.901657\pi$
$37$	−8.58444	+	3.55579i	−1.41127	+	0.584569i	−0.458622	+	0.888631i	$0.651657\pi$
$38$			1.21304i			0.196781i
$39$	3.09302	+	7.46720i	0.495279	+	1.19571i
$40$	−0.923880	−	0.382683i	−0.146078	−	0.0605076i
$41$	0.0547598	−	0.132202i	0.00855205	−	0.0206465i	−0.919546	−	0.392983i	$-0.871443\pi$
$41$	0.0547598	−	0.132202i	0.00855205	−	0.0206465i	0.928098	+	0.372336i	$0.121443\pi$
$42$	3.70253	−	3.70253i	0.571313	−	0.571313i
$43$	−0.587013	+	0.587013i	−0.0895186	+	0.0895186i	−0.750448	−	0.660929i	$-0.770162\pi$
$43$	−0.587013	+	0.587013i	−0.0895186	+	0.0895186i	0.660929	+	0.750448i	$0.270162\pi$
$44$	1.80188	−	4.35013i	0.271644	−	0.655806i
$45$	−0.759695	−	0.314676i	−0.113249	−	0.0469091i
$46$	−2.18906	−	5.28485i	−0.322759	−	0.779209i
$47$		−	5.85635i		−	0.854236i	−0.904196	−	0.427118i	$-0.859529\pi$
$47$		−	5.85635i		−	0.854236i	0.904196	−	0.427118i	$-0.140471\pi$
$48$	−1.36338	+	0.564729i	−0.196786	+	0.0815116i
$49$	−3.95275	−	3.95275i	−0.564679	−	0.564679i
$50$	−1.00000			−0.141421
$51$	1.60888	−	5.86793i	0.225288	−	0.821675i
$52$	−5.47699			−0.759522
$53$	6.54226	+	6.54226i	0.898648	+	0.898648i	0.995317	−	0.0966687i	$-0.0308187\pi$
$53$	6.54226	+	6.54226i	0.898648	+	0.898648i	−0.0966687	+	0.995317i	$0.530819\pi$
$54$	−5.21121	+	2.15856i	−0.709156	+	0.293742i
$55$		−	4.70854i		−	0.634900i
$56$	1.35785	+	3.27815i	0.181451	+	0.438061i
$57$	1.65383	+	0.685038i	0.219055	+	0.0907355i
$58$	1.77710	−	4.29029i	0.233344	−	0.563343i
$59$	−3.33507	+	3.33507i	−0.434189	+	0.434189i	−0.890051	−	0.455861i	$-0.849331\pi$
$59$	−3.33507	+	3.33507i	−0.434189	+	0.434189i	0.455861	+	0.890051i	$0.349331\pi$
$60$	−1.04348	+	1.04348i	−0.134713	+	0.134713i
$61$	4.76261	−	11.4980i	0.609790	−	1.47216i	−0.253439	−	0.967351i	$-0.581562\pi$
$61$	4.76261	−	11.4980i	0.609790	−	1.47216i	0.863229	−	0.504812i	$-0.168438\pi$
$62$	6.72892	+	2.78721i	0.854574	+	0.353976i
$63$	1.11655	+	2.69558i	0.140672	+	0.339611i
$64$		−	1.00000i		−	0.125000i
$65$	−5.06008	+	2.09595i	−0.627626	+	0.259971i
$66$	−4.91328	−	4.91328i	−0.604783	−	0.604783i
$67$	8.66703			1.05885			0.529423	−	0.848358i	$-0.322408\pi$
$67$	8.66703			1.05885			0.529423	+	0.848358i	$0.322408\pi$
$68$	3.25645	+	2.52894i	0.394903	+	0.306679i
$69$	−8.44146			−1.01623
$70$	2.50899	+	2.50899i	0.299881	+	0.299881i
$71$	4.75235	−	1.96849i	0.564000	−	0.233617i	−0.0824206	−	0.996598i	$-0.526265\pi$
$71$	4.75235	−	1.96849i	0.564000	−	0.233617i	0.646421	+	0.762981i	$0.276265\pi$
$72$		−	0.822287i		−	0.0969075i
$73$	6.17351	+	14.9042i	0.722555	+	1.74440i	0.665939	+	0.746006i	$0.268031\pi$
$73$	6.17351	+	14.9042i	0.722555	+	1.74440i	0.0566159	+	0.998396i	$0.481969\pi$
$74$	−8.58444	−	3.55579i	−0.997921	−	0.413353i
$75$	−0.564729	+	1.36338i	−0.0652093	+	0.157429i
$76$	−0.857748	+	0.857748i	−0.0983905	+	0.0983905i
$77$	−11.8137	+	11.8137i	−1.34629	+	1.34629i
$78$	−3.09302	+	7.46720i	−0.350215	+	0.845494i
$79$	9.34587	+	3.87118i	1.05149	+	0.435542i	0.840424	−	0.541929i	$-0.182306\pi$
$79$	9.34587	+	3.87118i	1.05149	+	0.435542i	0.211068	+	0.977471i	$0.432306\pi$
$80$	−0.382683	−	0.923880i	−0.0427853	−	0.103293i
$81$			5.85698i			0.650776i
$82$	0.132202	−	0.0547598i	0.0145993	−	0.00604721i
$83$	2.40841	+	2.40841i	0.264358	+	0.264358i	0.826822	−	0.562464i	$-0.190147\pi$
$83$	2.40841	+	2.40841i	0.264358	+	0.264358i	−0.562464	+	0.826822i	$0.690147\pi$
$84$	5.23617			0.571313
$85$	3.97635	+	1.09024i	0.431296	+	0.118254i
$86$	−0.830161			−0.0895186
$87$	−4.84570	−	4.84570i	−0.519514	−	0.519514i
$88$	4.35013	−	1.80188i	0.463725	−	0.192081i
$89$			2.24175i			0.237625i	0.992917	+	0.118813i	$0.0379088\pi$
$89$			2.24175i			0.237625i	−0.992917	+	0.118813i	$0.962091\pi$
$90$	−0.314676	−	0.759695i	−0.0331697	−	0.0800788i
$91$	17.9544	+	7.43696i	1.88213	+	0.779605i
$92$	2.18906	−	5.28485i	0.228225	−	0.550984i
$93$	7.60004	−	7.60004i	0.788087	−	0.788087i
$94$	4.14106	−	4.14106i	0.427118	−	0.427118i
$95$	−0.464210	+	1.12070i	−0.0476269	+	0.114982i
$96$	−1.36338	−	0.564729i	−0.139149	−	0.0576374i
$97$	1.66675	+	4.02389i	0.169233	+	0.408564i	0.985628	−	0.168929i	$-0.0540309\pi$
$97$	1.66675	+	4.02389i	0.169233	+	0.408564i	−0.816395	+	0.577493i	$0.804031\pi$
$98$		−	5.59004i		−	0.564679i
$99$	3.57705	−	1.48166i	0.359507	−	0.148913i
$100$	−0.707107	−	0.707107i	−0.0707107	−	0.0707107i
$101$	−10.7393			−1.06860			−0.534301	−	0.845294i	$-0.679425\pi$
$101$	−10.7393			−1.06860			−0.534301	+	0.845294i	$0.679425\pi$
$102$	5.28690	−	3.01160i	0.523482	−	0.298193i
$103$	−7.43306			−0.732401			−0.366200	−	0.930536i	$-0.619342\pi$
$103$	−7.43306			−0.732401			−0.366200	+	0.930536i	$0.619342\pi$
$104$	−3.87282	−	3.87282i	−0.379761	−	0.379761i
$105$	4.83759	−	2.00380i	0.472101	−	0.195550i
$106$			9.25215i			0.898648i
$107$	6.01999	+	14.5335i	0.581974	+	1.40501i	0.891020	+	0.453963i	$0.149990\pi$
$107$	6.01999	+	14.5335i	0.581974	+	1.40501i	−0.309046	+	0.951047i	$0.600010\pi$
$108$	−5.21121	−	2.15856i	−0.501449	−	0.207707i
$109$	2.46089	−	5.94112i	0.235711	−	0.569056i	−0.761120	−	0.648611i	$-0.775350\pi$
$109$	2.46089	−	5.94112i	0.235711	−	0.569056i	0.996830	+	0.0795553i	$0.0253500\pi$
$110$	3.32944	−	3.32944i	0.317450	−	0.317450i
$111$	−9.69577	+	9.69577i	−0.920281	+	0.920281i
$112$	−1.35785	+	3.27815i	−0.128305	+	0.309756i
$113$	−8.90782	−	3.68974i	−0.837978	−	0.347102i	−0.0779218	−	0.996959i	$-0.524828\pi$
$113$	−8.90782	−	3.68974i	−0.837978	−	0.347102i	−0.760056	+	0.649858i	$0.774828\pi$
$114$	0.685038	+	1.65383i	0.0641597	+	0.154895i
$115$		−	5.72028i		−	0.533419i
$116$	4.29029	−	1.77710i	0.398344	−	0.164999i
$117$	−3.18457	−	3.18457i	−0.294414	−	0.294414i
$118$	−4.71650			−0.434189
$119$	−7.24121	−	12.7120i	−0.663800	−	1.16531i
$120$	−1.47571			−0.134713
$121$	7.89864	+	7.89864i	0.718058	+	0.718058i
$122$	11.4980	−	4.76261i	1.04098	−	0.431187i
$123$		−	0.211165i		−	0.0190401i
$124$	2.78721	+	6.72892i	0.250299	+	0.604275i
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$	−1.11655	+	2.69558i	−0.0994699	+	0.240142i
$127$	2.26692	−	2.26692i	0.201157	−	0.201157i	−0.599339	−	0.800496i	$-0.704570\pi$
$127$	2.26692	−	2.26692i	0.201157	−	0.201157i	0.800496	+	0.599339i	$0.204570\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−0.468816	+	1.13182i	−0.0412769	+	0.0996513i
$130$	−5.06008	−	2.09595i	−0.443798	−	0.183827i
$131$	−1.36747	−	3.30136i	−0.119476	−	0.288441i	0.852815	−	0.522213i	$-0.174893\pi$
$131$	−1.36747	−	3.30136i	−0.119476	−	0.288441i	−0.972292	+	0.233771i	$0.924893\pi$
$132$		−	6.94843i		−	0.604783i
$133$	3.97653	−	1.64713i	0.344808	−	0.142824i
$134$	6.12852	+	6.12852i	0.529423	+	0.529423i
$135$	−5.64058			−0.485464
$136$	0.514430	+	4.09089i	0.0441120	+	0.350791i
$137$	3.30950			0.282750			0.141375	−	0.989956i	$-0.454848\pi$
$137$	3.30950			0.282750			0.141375	+	0.989956i	$0.454848\pi$
$138$	−5.96902	−	5.96902i	−0.508116	−	0.508116i
$139$	−1.66295	+	0.688816i	−0.141049	+	0.0584246i	−0.452092	−	0.891972i	$-0.649322\pi$
$139$	−1.66295	+	0.688816i	−0.141049	+	0.0584246i	0.311042	+	0.950396i	$0.399322\pi$
$140$			3.54824i			0.299881i
$141$	−3.30725	−	7.98440i	−0.278520	−	0.672408i
$142$	4.75235	+	1.96849i	0.398808	+	0.165192i
$143$	9.86889	−	23.8256i	0.825278	−	1.99240i
$144$	0.581445	−	0.581445i	0.0484538	−	0.0484538i
$145$	3.28365	−	3.28365i	0.272692	−	0.272692i
$146$	−6.17351	+	14.9042i	−0.510924	+	1.23348i
$147$	−7.62132	−	3.15686i	−0.628596	−	0.260373i
$148$	−3.55579	−	8.58444i	−0.292284	−	0.705637i
$149$		−	4.16768i		−	0.341430i	−0.985320	−	0.170715i	$-0.945392\pi$
$149$		−	4.16768i		−	0.341430i	0.985320	−	0.170715i	$-0.0546077\pi$
$150$	−1.36338	+	0.564729i	−0.111319	+	0.0461099i
$151$	−3.24744	−	3.24744i	−0.264273	−	0.264273i	0.562514	−	0.826788i	$-0.309834\pi$
$151$	−3.24744	−	3.24744i	−0.264273	−	0.264273i	−0.826788	+	0.562514i	$0.809834\pi$
$152$	−1.21304			−0.0983905
$153$	0.423009	+	3.36389i	0.0341982	+	0.271954i
$154$	−16.7071			−1.34629
$155$	5.15010	+	5.15010i	0.413666	+	0.413666i
$156$	−7.46720	+	3.09302i	−0.597854	+	0.247639i
$157$		−	15.5482i		−	1.24088i	−0.784253	−	0.620442i	$-0.786953\pi$
$157$		−	15.5482i		−	1.24088i	0.784253	−	0.620442i	$-0.213047\pi$
$158$	3.87118	+	9.34587i	0.307975	+	0.743517i
$159$	12.6142	+	5.22495i	1.00037	+	0.414366i
$160$	0.382683	−	0.923880i	0.0302538	−	0.0730391i
$161$	−14.3521	+	14.3521i	−1.13111	+	1.13111i
$162$	−4.14151	+	4.14151i	−0.325388	+	0.325388i
$163$	3.87956	−	9.36608i	0.303870	−	0.733608i	−0.696008	−	0.718034i	$-0.745042\pi$
$163$	3.87956	−	9.36608i	0.303870	−	0.733608i	0.999879	−	0.0155742i	$-0.00495762\pi$
$164$	0.132202	+	0.0547598i	0.0103232	+	0.00427602i
$165$	−2.65905	−	6.41951i	−0.207007	−	0.499758i
$166$			3.40601i			0.264358i
$167$	−11.5038	+	4.76501i	−0.890187	+	0.368728i	−0.780439	−	0.625232i	$-0.785004\pi$
$167$	−11.5038	+	4.76501i	−0.890187	+	0.368728i	−0.109748	+	0.993959i	$0.535004\pi$
$168$	3.70253	+	3.70253i	0.285657	+	0.285657i
$169$	−16.9974			−1.30750
$170$	2.04079	+	3.58262i	0.156521	+	0.274775i
$171$	−0.997467			−0.0762782
$172$	−0.587013	−	0.587013i	−0.0447593	−	0.0447593i
$173$	−3.27672	+	1.35726i	−0.249125	+	0.103191i	−0.503752	−	0.863849i	$-0.668047\pi$
$173$	−3.27672	+	1.35726i	−0.249125	+	0.103191i	0.254627	+	0.967039i	$0.418047\pi$
$174$		−	6.85286i		−	0.519514i
$175$	1.35785	+	3.27815i	0.102644	+	0.247805i
$176$	4.35013	+	1.80188i	0.327903	+	0.135822i
$177$	−2.66354	+	6.43037i	−0.200204	+	0.483336i
$178$	−1.58516	+	1.58516i	−0.118813	+	0.118813i
$179$	−9.26485	+	9.26485i	−0.692487	+	0.692487i	−0.962779	−	0.270291i	$-0.912880\pi$
$179$	−9.26485	+	9.26485i	−0.692487	+	0.692487i	0.270291	+	0.962779i	$0.412880\pi$
$180$	0.314676	−	0.759695i	0.0234545	−	0.0566243i
$181$	1.68821	+	0.699281i	0.125484	+	0.0519772i	0.444542	−	0.895758i	$-0.353366\pi$
$181$	1.68821	+	0.699281i	0.125484	+	0.0519772i	−0.319058	+	0.947735i	$0.603366\pi$
$182$	7.43696	+	17.9544i	0.551264	+	1.33087i
$183$		−	18.3656i		−	1.35763i
$184$	5.28485	−	2.18906i	0.389604	−	0.161379i
$185$	−6.57025	−	6.57025i	−0.483054	−	0.483054i
$186$	10.7481			0.788087
$187$	−16.8689	+	9.60913i	−1.23358	+	0.702689i
$188$	5.85635			0.427118
$189$	14.1521	+	14.1521i	1.02942	+	1.02942i
$190$	−1.12070	+	0.464210i	−0.0813043	+	0.0336773i
$191$		−	16.8319i		−	1.21791i	−0.793205	−	0.608955i	$-0.791589\pi$
$191$		−	16.8319i		−	1.21791i	0.793205	−	0.608955i	$-0.208411\pi$
$192$	−0.564729	−	1.36338i	−0.0407558	−	0.0983932i
$193$	−5.38504	−	2.23056i	−0.387624	−	0.160559i	0.180356	−	0.983601i	$-0.442275\pi$
$193$	−5.38504	−	2.23056i	−0.387624	−	0.160559i	−0.567980	+	0.823042i	$0.692275\pi$
$194$	−1.66675	+	4.02389i	−0.119666	+	0.288899i
$195$	−5.71515	+	5.71515i	−0.409270	+	0.409270i
$196$	3.95275	−	3.95275i	0.282340	−	0.282340i
$197$	1.34760	−	3.25339i	0.0960123	−	0.231794i	−0.868575	−	0.495557i	$-0.834964\pi$
$197$	1.34760	−	3.25339i	0.0960123	−	0.231794i	0.964587	+	0.263763i	$0.0849638\pi$
$198$	3.57705	+	1.48166i	0.254210	+	0.105297i
$199$	−6.42910	−	15.5212i	−0.455747	−	1.10027i	−0.970103	−	0.242694i	$-0.921969\pi$
$199$	−6.42910	−	15.5212i	−0.455747	−	1.10027i	0.514356	−	0.857577i	$-0.328031\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	11.8164	−	4.89452i	0.833466	−	0.345233i
$202$	−7.59384	−	7.59384i	−0.534301	−	0.534301i
$203$	−16.4773			−1.15648
$204$	5.86793	+	1.60888i	0.410837	+	0.112644i
$205$	0.143094			0.00999414
$206$	−5.25597	−	5.25597i	−0.366200	−	0.366200i
$207$	4.34567	−	1.80003i	0.302045	−	0.125111i
$208$		−	5.47699i		−	0.379761i
$209$	−2.18575	−	5.27687i	−0.151192	−	0.365009i
$210$	4.83759	+	2.00380i	0.333826	+	0.138275i
$211$	−8.73280	+	21.0828i	−0.601191	+	1.45140i	0.271166	+	0.962533i	$0.412591\pi$
$211$	−8.73280	+	21.0828i	−0.601191	+	1.45140i	−0.872357	+	0.488870i	$0.837409\pi$
$212$	−6.54226	+	6.54226i	−0.449324	+	0.449324i
$213$	5.36758	−	5.36758i	0.367780	−	0.367780i
$214$	−6.01999	+	14.5335i	−0.411518	+	0.993492i
$215$	−0.766969	−	0.317689i	−0.0523068	−	0.0216662i
$216$	−2.15856	−	5.21121i	−0.146871	−	0.354578i
$217$		−	25.8431i		−	1.75434i
$218$	5.94112	−	2.46089i	0.402383	−	0.166673i
$219$	16.8336	+	16.8336i	1.13751	+	1.13751i
$220$	4.70854			0.317450
$221$	17.8356	+	13.8510i	1.19975	+	0.931717i
$222$	−13.7119			−0.920281
$223$	−6.41246	−	6.41246i	−0.429410	−	0.429410i	0.459017	−	0.888427i	$-0.348202\pi$
$223$	−6.41246	−	6.41246i	−0.429410	−	0.429410i	−0.888427	+	0.459017i	$0.848202\pi$
$224$	−3.27815	+	1.35785i	−0.219031	+	0.0907255i
$225$		−	0.822287i		−	0.0548192i
$226$	−3.68974	−	8.90782i	−0.245438	−	0.592540i
$227$	14.5491	+	6.02643i	0.965658	+	0.399988i	0.809094	−	0.587679i	$-0.199958\pi$
$227$	14.5491	+	6.02643i	0.965658	+	0.399988i	0.156564	+	0.987668i	$0.449958\pi$
$228$	−0.685038	+	1.65383i	−0.0453678	+	0.109527i
$229$	14.2262	−	14.2262i	0.940092	−	0.940092i	−0.0582124	−	0.998304i	$-0.518540\pi$
$229$	14.2262	−	14.2262i	0.940092	−	0.940092i	0.998304	+	0.0582124i	$0.0185401\pi$
$230$	4.04485	−	4.04485i	0.266710	−	0.266710i
$231$	−9.43496	+	22.7780i	−0.620775	+	1.49868i
$232$	4.29029	+	1.77710i	0.281672	+	0.116672i
$233$	−7.37613	−	17.8076i	−0.483227	−	1.16661i	−0.958068	−	0.286541i	$-0.907495\pi$
$233$	−7.37613	−	17.8076i	−0.483227	−	1.16661i	0.474841	−	0.880071i	$-0.342505\pi$
$234$		−	4.50366i		−	0.294414i
$235$	5.41056	−	2.24113i	0.352946	−	0.146195i
$236$	−3.33507	−	3.33507i	−0.217095	−	0.217095i
$237$	14.9281			0.969684
$238$	3.86845	−	14.1091i	0.250755	−	0.914555i
$239$	14.2040			0.918778			0.459389	−	0.888235i	$-0.348068\pi$
$239$	14.2040			0.918778			0.459389	+	0.888235i	$0.348068\pi$
$240$	−1.04348	−	1.04348i	−0.0673565	−	0.0673565i
$241$	−4.22633	+	1.75060i	−0.272242	+	0.112766i	−0.514628	−	0.857414i	$-0.672070\pi$
$241$	−4.22633	+	1.75060i	−0.272242	+	0.112766i	0.242386	+	0.970180i	$0.422070\pi$
$242$			11.1704i			0.718058i
$243$	−3.16806	−	7.64838i	−0.203231	−	0.490644i
$244$	11.4980	+	4.76261i	0.736082	+	0.304895i
$245$	2.13922	−	5.16452i	0.136669	−	0.329949i
$246$	0.149316	−	0.149316i	0.00952007	−	0.00952007i
$247$	−4.69788	+	4.69788i	−0.298919	+	0.298919i
$248$	−2.78721	+	6.72892i	−0.176988	+	0.427287i
$249$	4.64367	+	1.92347i	0.294281	+	0.121895i
$250$	−0.382683	−	0.923880i	−0.0242030	−	0.0584313i
$251$		−	9.00712i		−	0.568524i	−0.958747	−	0.284262i	$-0.908251\pi$
$251$		−	9.00712i		−	0.568524i	0.958747	−	0.284262i	$-0.0917486\pi$
$252$	−2.69558	+	1.11655i	−0.169806	+	0.0703358i
$253$	19.0453	+	19.0453i	1.19737	+	1.19737i
$254$	3.20591			0.201157
$255$	6.03695	−	0.759148i	0.378049	−	0.0475397i
$256$	1.00000			0.0625000
$257$	20.2643	+	20.2643i	1.26405	+	1.26405i	0.949112	+	0.314938i	$0.101984\pi$
$257$	20.2643	+	20.2643i	1.26405	+	1.26405i	0.314938	+	0.949112i	$0.398016\pi$
$258$	−1.13182	+	0.468816i	−0.0704641	+	0.0291872i
$259$			32.9693i			2.04862i
$260$	−2.09595	−	5.06008i	−0.129986	−	0.313813i
$261$	3.52785	+	1.46129i	0.218369	+	0.0904513i
$262$	1.36747	−	3.30136i	0.0844825	−	0.203959i
$263$	−4.27498	+	4.27498i	−0.263606	+	0.263606i	−0.826517	−	0.562911i	$-0.809681\pi$
$263$	−4.27498	+	4.27498i	−0.263606	+	0.263606i	0.562911	+	0.826517i	$0.309681\pi$
$264$	4.91328	−	4.91328i	0.302392	−	0.302392i
$265$	−3.54064	+	8.54787i	−0.217500	+	0.525091i
$266$	3.97653	+	1.64713i	0.243816	+	0.100992i
$267$	1.26598	+	3.05635i	0.0774769	+	0.187046i
$268$			8.66703i			0.529423i
$269$	−15.6073	+	6.46477i	−0.951596	+	0.394164i	−0.803830	−	0.594858i	$-0.797208\pi$
$269$	−15.6073	+	6.46477i	−0.951596	+	0.394164i	−0.147765	+	0.989022i	$0.547208\pi$
$270$	−3.98849	−	3.98849i	−0.242732	−	0.242732i
$271$	−22.9305			−1.39293			−0.696463	−	0.717593i	$-0.745244\pi$
$271$	−22.9305			−1.39293			−0.696463	+	0.717593i	$0.745244\pi$
$272$	−2.52894	+	3.25645i	−0.153339	+	0.197451i
$273$	28.6785			1.73570
$274$	2.34017	+	2.34017i	0.141375	+	0.141375i
$275$	4.35013	−	1.80188i	0.262322	−	0.108658i
$276$		−	8.44146i		−	0.508116i
$277$	7.65435	+	18.4792i	0.459905	+	1.11031i	0.968435	+	0.249265i	$0.0801891\pi$
$277$	7.65435	+	18.4792i	0.459905	+	1.11031i	−0.508530	+	0.861044i	$0.669811\pi$
$278$	−1.66295	−	0.688816i	−0.0997370	−	0.0413124i
$279$	−2.29189	+	5.53311i	−0.137212	+	0.331259i
$280$	−2.50899	+	2.50899i	−0.149941	+	0.149941i
$281$	16.4633	−	16.4633i	0.982118	−	0.982118i	−0.0177247	−	0.999843i	$-0.505642\pi$
$281$	16.4633	−	16.4633i	0.982118	−	0.982118i	0.999843	+	0.0177247i	$0.00564226\pi$
$282$	3.30725	−	7.98440i	0.196944	−	0.475464i
$283$	−23.2363	−	9.62478i	−1.38125	−	0.572134i	−0.436437	−	0.899735i	$-0.643760\pi$
$283$	−23.2363	−	9.62478i	−1.38125	−	0.572134i	−0.944816	+	0.327601i	$0.893760\pi$
$284$	1.96849	+	4.75235i	0.116808	+	0.282000i
$285$			1.79009i			0.106036i
$286$	23.8256	−	9.86889i	1.40884	−	0.583560i
$287$	−0.359022	−	0.359022i	−0.0211924	−	0.0211924i
$288$	0.822287			0.0484538
$289$	−4.20895	−	16.4707i	−0.247585	−	0.968866i
$290$	4.64378			0.272692
$291$	4.54481	+	4.54481i	0.266422	+	0.266422i
$292$	−14.9042	+	6.17351i	−0.872201	+	0.361278i
$293$			25.5251i			1.49119i	0.666399	+	0.745595i	$0.267835\pi$
$293$			25.5251i			1.49119i	−0.666399	+	0.745595i	$0.732165\pi$
$294$	−3.15686	−	7.62132i	−0.184112	−	0.444485i
$295$	−4.35748	−	1.80493i	−0.253702	−	0.105087i
$296$	3.55579	−	8.58444i	0.206676	−	0.498961i
$297$	18.7800	−	18.7800i	1.08972	−	1.08972i
$298$	2.94700	−	2.94700i	0.170715	−	0.170715i
$299$	11.9894	−	28.9451i	0.693368	−	1.67394i
$300$	−1.36338	−	0.564729i	−0.0787145	−	0.0326046i
$301$	1.12724	+	2.72139i	0.0649729	+	0.156858i
$302$		−	4.59258i		−	0.264273i
$303$	−14.6417	+	6.06480i	−0.841145	+	0.348414i
$304$	−0.857748	−	0.857748i	−0.0491952	−	0.0491952i
$305$	12.4453			0.712616
$306$	−2.07951	+	2.67774i	−0.118878	+	0.153076i
$307$	−14.2382			−0.812616			−0.406308	−	0.913736i	$-0.633184\pi$
$307$	−14.2382			−0.812616			−0.406308	+	0.913736i	$0.633184\pi$
$308$	−11.8137	−	11.8137i	−0.673147	−	0.673147i
$309$	−10.1341	+	4.19766i	−0.576506	+	0.238797i
$310$			7.28334i			0.413666i
$311$	−4.65012	−	11.2264i	−0.263684	−	0.636590i	0.735477	−	0.677550i	$-0.236958\pi$
$311$	−4.65012	−	11.2264i	−0.263684	−	0.636590i	−0.999161	+	0.0409602i	$0.986958\pi$
$312$	−7.46720	−	3.09302i	−0.422747	−	0.175108i
$313$	−8.33854	+	20.1310i	−0.471322	+	1.13787i	0.492257	+	0.870450i	$0.336172\pi$
$313$	−8.33854	+	20.1310i	−0.471322	+	1.13787i	−0.963579	+	0.267422i	$0.913828\pi$
$314$	10.9943	−	10.9943i	0.620442	−	0.620442i
$315$	−2.06311	+	2.06311i	−0.116243	+	0.116243i
$316$	−3.87118	+	9.34587i	−0.217771	+	0.525746i
$317$	9.47130	+	3.92314i	0.531961	+	0.220346i	0.632462	−	0.774591i	$-0.282044\pi$
$317$	9.47130	+	3.92314i	0.531961	+	0.220346i	−0.100501	+	0.994937i	$0.532044\pi$
$318$	5.22495	+	12.6142i	0.293001	+	0.707367i
$319$			21.8654i			1.22423i
$320$	0.923880	−	0.382683i	0.0516464	−	0.0213927i
$321$	16.4150	+	16.4150i	0.916197	+	0.916197i
$322$	−20.2970			−1.13111
$323$	4.96241	−	0.624023i	0.276116	−	0.0347216i
$324$	−5.85698			−0.325388
$325$	−3.87282	−	3.87282i	−0.214825	−	0.214825i
$326$	9.36608	−	3.87956i	0.518739	−	0.214869i
$327$		−	9.48972i		−	0.524783i
$328$	0.0547598	+	0.132202i	0.00302360	+	0.00729963i
$329$	−19.1980	−	7.95207i	−1.05842	−	0.438412i
$330$	2.65905	−	6.41951i	0.146376	−	0.353383i
$331$	−0.209438	+	0.209438i	−0.0115117	+	0.0115117i	−0.712839	−	0.701327i	$-0.752591\pi$
$331$	−0.209438	+	0.209438i	−0.0115117	+	0.0115117i	0.701327	+	0.712839i	$0.252591\pi$
$332$	−2.40841	+	2.40841i	−0.132179	+	0.132179i
$333$	2.92388	−	7.05888i	0.160228	−	0.386824i
$334$	−11.5038	−	4.76501i	−0.629457	−	0.260730i
$335$	3.31673	+	8.00729i	0.181212	+	0.437485i
$336$			5.23617i			0.285657i
$337$	−12.9824	+	5.37748i	−0.707196	+	0.292930i	−0.707144	−	0.707070i	$-0.750017\pi$
$337$	−12.9824	+	5.37748i	−0.707196	+	0.292930i	−5.22341e−5		1.00000i	$0.500017\pi$
$338$	−12.0190	−	12.0190i	−0.653748	−	0.653748i
$339$	−14.2284			−0.772782
$340$	−1.09024	+	3.97635i	−0.0591268	+	0.215648i
$341$	−34.2939			−1.85712
$342$	−0.705316	−	0.705316i	−0.0381391	−	0.0381391i
$343$	4.62206	−	1.91452i	0.249568	−	0.103374i
$344$		−	0.830161i		−	0.0447593i
$345$	−3.23041	−	7.79889i	−0.173919	−	0.419878i
$346$	−3.27672	−	1.35726i	−0.176158	−	0.0729669i
$347$	−4.26669	+	10.3007i	−0.229048	+	0.552971i	−0.996062	−	0.0886594i	$-0.971742\pi$
$347$	−4.26669	+	10.3007i	−0.229048	+	0.552971i	0.767014	+	0.641631i	$0.221742\pi$
$348$	4.84570	−	4.84570i	0.259757	−	0.259757i
$349$	−1.77671	+	1.77671i	−0.0951051	+	0.0951051i	−0.753059	−	0.657953i	$-0.771422\pi$
$349$	−1.77671	+	1.77671i	−0.0951051	+	0.0951051i	0.657953	+	0.753059i	$0.271422\pi$
$350$	−1.35785	+	3.27815i	−0.0725804	+	0.175225i
$351$	−28.5418	−	11.8224i	−1.52345	−	0.631033i
$352$	1.80188	+	4.35013i	0.0960406	+	0.231862i
$353$		−	10.0823i		−	0.536629i	−0.963331	−	0.268314i	$-0.913533\pi$
$353$		−	10.0823i		−	0.536629i	0.963331	−	0.268314i	$-0.0864666\pi$
$354$	−6.43037	+	2.66354i	−0.341770	+	0.141566i
$355$	3.63729	+	3.63729i	0.193047	+	0.193047i
$356$	−2.24175			−0.118813
$357$	−17.0513	−	13.2420i	−0.902452	−	0.700838i
$358$	−13.1025			−0.692487
$359$	−17.4429	−	17.4429i	−0.920599	−	0.920599i	0.0764723	−	0.997072i	$-0.475634\pi$
$359$	−17.4429	−	17.4429i	−0.920599	−	0.920599i	−0.997072	+	0.0764723i	$0.975634\pi$
$360$	0.759695	−	0.314676i	0.0400394	−	0.0165849i
$361$		−	17.5285i		−	0.922555i
$362$	0.699281	+	1.68821i	0.0367534	+	0.0887306i
$363$	15.2294	+	6.30823i	0.799337	+	0.331096i
$364$	−7.43696	+	17.9544i	−0.389803	+	0.941067i
$365$	−11.4072	+	11.4072i	−0.597078	+	0.597078i
$366$	12.9865	−	12.9865i	0.678813	−	0.678813i
$367$	11.3939	−	27.5072i	0.594755	−	1.43587i	−0.284108	−	0.958792i	$-0.591698\pi$
$367$	11.3939	−	27.5072i	0.594755	−	1.43587i	0.878863	−	0.477073i	$-0.158302\pi$
$368$	5.28485	+	2.18906i	0.275492	+	0.114112i
$369$	0.0450283	+	0.108708i	0.00234408	+	0.00565911i
$370$		−	9.29174i		−	0.483054i
$371$	30.3299	−	12.5631i	1.57465	−	0.652242i
$372$	7.60004	+	7.60004i	0.394043	+	0.394043i
$373$	20.8039			1.07718			0.538592	−	0.842567i	$-0.318956\pi$
$373$	20.8039			1.07718			0.538592	+	0.842567i	$0.318956\pi$
$374$	−18.7228	−	5.13346i	−0.968134	−	0.265445i
$375$	−1.47571			−0.0762052
$376$	4.14106	+	4.14106i	0.213559	+	0.213559i
$377$	23.4979	−	9.73315i	1.21020	−	0.501283i
$378$			20.0142i			1.02942i
$379$	3.99706	+	9.64974i	0.205315	+	0.495674i	0.992674	−	0.120820i	$-0.0385524\pi$
$379$	3.99706	+	9.64974i	0.205315	+	0.495674i	−0.787359	+	0.616494i	$0.788552\pi$
$380$	−1.12070	−	0.464210i	−0.0574908	−	0.0238135i
$381$	1.81047	−	4.37087i	0.0927533	−	0.223926i
$382$	11.9019	−	11.9019i	0.608955	−	0.608955i
$383$	−14.2495	+	14.2495i	−0.728113	+	0.728113i	−0.970244	−	0.242130i	$-0.922154\pi$
$383$	−14.2495	+	14.2495i	−0.728113	+	0.728113i	0.242130	+	0.970244i	$0.422154\pi$
$384$	0.564729	−	1.36338i	0.0288187	−	0.0695745i
$385$	−15.4353	−	6.39351i	−0.786656	−	0.325844i
$386$	−2.23056	−	5.38504i	−0.113532	−	0.274091i
$387$		−	0.682631i		−	0.0347001i
$388$	−4.02389	+	1.66675i	−0.204282	+	0.0846164i
$389$	−13.9058	−	13.9058i	−0.705051	−	0.705051i	0.260440	−	0.965490i	$-0.416133\pi$
$389$	−13.9058	−	13.9058i	−0.705051	−	0.705051i	−0.965490	+	0.260440i	$0.916133\pi$
$390$	−8.08244			−0.409270
$391$	−20.4936	+	11.6739i	−1.03641	+	0.590373i
$392$	5.59004			0.282340
$393$	−3.72875	−	3.72875i	−0.188090	−	0.188090i
$394$	3.25339	−	1.34760i	0.163903	−	0.0678909i
$395$			10.1159i			0.508986i
$396$	1.48166	+	3.57705i	0.0744564	+	0.179754i
$397$	−22.1250	−	9.16446i	−1.11042	−	0.459951i	−0.249338	−	0.968416i	$-0.580213\pi$
$397$	−22.1250	−	9.16446i	−1.11042	−	0.459951i	−0.861083	+	0.508465i	$0.830213\pi$
$398$	6.42910	−	15.5212i	0.322262	−	0.778009i
$399$	4.49132	−	4.49132i	0.224847	−	0.224847i
$400$	0.707107	−	0.707107i	0.0353553	−	0.0353553i
$401$	−8.81734	+	21.2869i	−0.440317	+	1.06302i	0.535521	+	0.844522i	$0.320115\pi$
$401$	−8.81734	+	21.2869i	−0.440317	+	1.06302i	−0.975838	+	0.218497i	$0.929885\pi$
$402$	11.8164	+	4.89452i	0.589350	+	0.244117i
$403$	15.2655	+	36.8543i	0.760431	+	1.83584i
$404$		−	10.7393i		−	0.534301i
$405$	−5.41114	+	2.24137i	−0.268882	+	0.111375i
$406$	−11.6512	−	11.6512i	−0.578239	−	0.578239i
$407$	43.7505			2.16863
$408$	3.01160	+	5.28690i	0.149097	+	0.261741i
$409$	12.7488			0.630389			0.315195	−	0.949027i	$-0.397930\pi$
$409$	12.7488			0.630389			0.315195	+	0.949027i	$0.397930\pi$
$410$	0.101183	+	0.101183i	0.00499707	+	0.00499707i
$411$	4.51209	−	1.86897i	0.222565	−	0.0921895i
$412$		−	7.43306i		−	0.366200i
$413$	6.40432	+	15.4614i	0.315136	+	0.760806i
$414$	4.34567	+	1.80003i	0.213578	+	0.0884669i
$415$	−1.30342	+	3.14674i	−0.0639826	+	0.154468i
$416$	3.87282	−	3.87282i	0.189881	−	0.189881i
$417$	−1.87823	+	1.87823i	−0.0919773	+	0.0919773i
$418$	2.18575	−	5.27687i	0.106909	−	0.258100i
$419$	25.2883	+	10.4748i	1.23541	+	0.511725i	0.902279	−	0.431153i	$-0.141893\pi$
$419$	25.2883	+	10.4748i	1.23541	+	0.511725i	0.333136	+	0.942879i	$0.391893\pi$
$420$	2.00380	+	4.83759i	0.0977752	+	0.236050i
$421$			33.6813i			1.64153i	0.571268	+	0.820764i	$0.306452\pi$
$421$			33.6813i			1.64153i	−0.571268	+	0.820764i	$0.693548\pi$
$422$	−21.0828	+	8.73280i	−1.02630	+	0.425106i
$423$	3.40514	+	3.40514i	0.165564	+	0.165564i
$424$	−9.25215			−0.449324
$425$	0.514430	+	4.09089i	0.0249535	+	0.198437i
$426$	7.59090			0.367780
$427$	−31.2251	−	31.2251i	−1.51109	−	1.51109i
$428$	−14.5335	+	6.01999i	−0.702505	+	0.290987i
$429$		−	38.0565i		−	1.83739i
$430$	−0.317689	−	0.766969i	−0.0153203	−	0.0369865i
$431$	−16.7963	−	6.95725i	−0.809049	−	0.335119i	−0.0604746	−	0.998170i	$-0.519261\pi$
$431$	−16.7963	−	6.95725i	−0.809049	−	0.335119i	−0.748575	+	0.663051i	$0.769261\pi$
$432$	2.15856	−	5.21121i	0.103854	−	0.250725i
$433$	−5.73034	+	5.73034i	−0.275382	+	0.275382i	−0.831262	−	0.555880i	$-0.812381\pi$
$433$	−5.73034	+	5.73034i	−0.275382	+	0.275382i	0.555880	+	0.831262i	$0.312381\pi$
$434$	18.2738	−	18.2738i	0.877170	−	0.877170i
$435$	2.62248	−	6.33122i	0.125738	−	0.303559i
$436$	5.94112	+	2.46089i	0.284528	+	0.117855i
$437$	−2.65541	−	6.41073i	−0.127026	−	0.306667i
$438$			23.8064i			1.13751i
$439$	22.1522	−	9.17574i	1.05727	−	0.437934i	0.214786	−	0.976661i	$-0.431095\pi$
$439$	22.1522	−	9.17574i	1.05727	−	0.437934i	0.842480	+	0.538727i	$0.181095\pi$
$440$	3.32944	+	3.32944i	0.158725	+	0.158725i
$441$	4.59662			0.218887
$442$	2.81753	+	22.4058i	0.134016	+	1.06573i
$443$	0.244075			0.0115964			0.00579819	−	0.999983i	$-0.498154\pi$
$443$	0.244075			0.0115964			0.00579819	+	0.999983i	$0.498154\pi$
$444$	−9.69577	−	9.69577i	−0.460141	−	0.460141i
$445$	−2.07111	+	0.857882i	−0.0981800	+	0.0406675i
$446$		−	9.06859i		−	0.429410i
$447$	−2.35361	−	5.68212i	−0.111322	−	0.268755i
$448$	−3.27815	−	1.35785i	−0.154878	−	0.0641526i
$449$	−0.0315454	+	0.0761574i	−0.00148872	+	0.00359409i	−0.924622	−	0.380886i	$-0.875619\pi$
$449$	−0.0315454	+	0.0761574i	−0.00148872	+	0.00359409i	0.923133	+	0.384480i	$0.125619\pi$
$450$	0.581445	−	0.581445i	0.0274096	−	0.0274096i
$451$	−0.476424	+	0.476424i	−0.0224339	+	0.0224339i
$452$	3.68974	−	8.90782i	0.173551	−	0.418989i
$453$	−6.26141	−	2.59356i	−0.294187	−	0.121856i
$454$	6.02643	+	14.5491i	0.282835	+	0.682823i
$455$			19.4337i			0.911066i
$456$	−1.65383	+	0.685038i	−0.0774476	+	0.0320799i
$457$	17.2461	+	17.2461i	0.806737	+	0.806737i	0.984139	−	0.177402i	$-0.0567692\pi$
$457$	17.2461	+	17.2461i	0.806737	+	0.806737i	−0.177402	+	0.984139i	$0.556769\pi$
$458$	20.1188			0.940092
$459$	11.5112	+	20.2081i	0.537297	+	0.943232i
$460$	5.72028			0.266710
$461$	20.5839	+	20.5839i	0.958687	+	0.958687i	0.999180	−	0.0404924i	$-0.0128926\pi$
$461$	20.5839	+	20.5839i	0.958687	+	0.958687i	−0.0404924	+	0.999180i	$0.512893\pi$
$462$	−22.7780	+	9.43496i	−1.05973	+	0.438954i
$463$			27.9762i			1.30016i	0.759865	+	0.650081i	$0.225265\pi$
$463$			27.9762i			1.30016i	−0.759865	+	0.650081i	$0.774735\pi$
$464$	1.77710	+	4.29029i	0.0824997	+	0.199172i
$465$	9.92992	+	4.11311i	0.460489	+	0.190741i
$466$	7.37613	−	17.8076i	0.341693	−	0.824919i
$467$	22.1173	−	22.1173i	1.02347	−	1.02347i	0.0237504	−	0.999718i	$-0.492439\pi$
$467$	22.1173	−	22.1173i	1.02347	−	1.02347i	0.999718	−	0.0237504i	$-0.00756069\pi$
$468$	3.18457	−	3.18457i	0.147207	−	0.147207i
$469$	11.7686	−	28.4118i	0.543422	−	1.31194i
$470$	5.41056	+	2.24113i	0.249570	+	0.103375i
$471$	−8.78053	−	21.1981i	−0.404586	−	0.976756i
$472$		−	4.71650i		−	0.217095i
$473$	3.61131	−	1.49585i	0.166048	−	0.0687793i
$474$	10.5558	+	10.5558i	0.484842	+	0.484842i
$475$	−1.21304			−0.0556581
$476$	12.7120	−	7.24121i	0.582655	−	0.331900i
$477$	−7.60792			−0.348343
$478$	10.0437	+	10.0437i	0.459389	+	0.459389i
$479$	−11.1564	+	4.62112i	−0.509748	+	0.211144i	−0.622707	−	0.782455i	$-0.713967\pi$
$479$	−11.1564	+	4.62112i	−0.509748	+	0.211144i	0.112959	+	0.993600i	$0.463967\pi$
$480$		−	1.47571i		−	0.0673565i
$481$	−19.4751	−	47.0169i	−0.887986	−	2.14379i
$482$	−4.22633	−	1.75060i	−0.192504	−	0.0797378i
$483$	−11.4623	+	27.6724i	−0.521552	+	1.25914i
$484$	−7.89864	+	7.89864i	−0.359029	+	0.359029i
$485$	−3.07975	+	3.07975i	−0.139844	+	0.139844i
$486$	3.16806	−	7.64838i	0.143706	−	0.346937i
$487$	4.63377	+	1.91937i	0.209976	+	0.0869749i	0.485192	−	0.874407i	$-0.338750\pi$
$487$	4.63377	+	1.91937i	0.209976	+	0.0869749i	−0.275217	+	0.961382i	$0.588750\pi$
$488$	4.76261	+	11.4980i	0.215593	+	0.520488i
$489$		−	14.9604i		−	0.676532i
$490$	5.16452	−	2.13922i	0.233309	−	0.0966399i
$491$	−18.6988	−	18.6988i	−0.843865	−	0.843865i	0.145494	−	0.989359i	$-0.453523\pi$
$491$	−18.6988	−	18.6988i	−0.843865	−	0.843865i	−0.989359	+	0.145494i	$0.953523\pi$
$492$	0.211165			0.00952007
$493$	−18.4653	−	5.06285i	−0.831635	−	0.228019i
$494$	−6.64381			−0.298919
$495$	2.73776	+	2.73776i	0.123053	+	0.123053i
$496$	−6.72892	+	2.78721i	−0.302138	+	0.125150i
$497$		−	18.2518i		−	0.818707i
$498$	1.92347	+	4.64367i	0.0861929	+	0.208088i
$499$	−27.6595	−	11.4569i	−1.23821	−	0.512882i	−0.335053	−	0.942199i	$-0.608754\pi$
$499$	−27.6595	−	11.4569i	−1.23821	−	0.512882i	−0.903154	+	0.429317i	$0.858754\pi$
$500$	0.382683	−	0.923880i	0.0171141	−	0.0413171i
$501$	−12.9930	+	12.9930i	−0.580484	+	0.580484i
$502$	6.36899	−	6.36899i	0.284262	−	0.284262i
$503$	13.0499	−	31.5052i	0.581865	−	1.40475i	−0.309255	−	0.950979i	$-0.600080\pi$
$503$	13.0499	−	31.5052i	0.581865	−	1.40475i	0.891120	−	0.453768i	$-0.149920\pi$
$504$	−2.69558	−	1.11655i	−0.120071	−	0.0497349i
$505$	−4.10976	−	9.92183i	−0.182882	−	0.441516i
$506$			26.9342i			1.19737i
$507$	−23.1739	+	9.59895i	−1.02919	+	0.426304i
$508$	2.26692	+	2.26692i	0.100578	+	0.100578i
$509$	28.0939			1.24524			0.622620	−	0.782525i	$-0.286068\pi$
$509$	28.0939			1.24524			0.622620	+	0.782525i	$0.286068\pi$
$510$	4.80557	+	3.73197i	0.212794	+	0.165255i
$511$	57.2409			2.53219
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−6.32141	+	2.61841i	−0.279097	+	0.115606i
$514$			28.6580i			1.26405i
$515$	−2.84451	−	6.86725i	−0.125344	−	0.302607i
$516$	−1.13182	−	0.468816i	−0.0498257	−	0.0206385i
$517$	−10.5524	+	25.4758i	−0.464096	+	1.12043i
$518$	−23.3129	+	23.3129i	−1.02431	+	1.02431i
$519$	−3.70092	+	3.70092i	−0.162452	+	0.162452i
$520$	2.09595	−	5.06008i	0.0919137	−	0.221899i
$521$	17.6215	+	7.29907i	0.772013	+	0.319778i	0.733687	−	0.679487i	$-0.237798\pi$
$521$	17.6215	+	7.29907i	0.772013	+	0.319778i	0.0383252	+	0.999265i	$0.487798\pi$
$522$	1.46129	+	3.52785i	0.0639587	+	0.154410i
$523$			6.69653i			0.292819i	0.989224	+	0.146409i	$0.0467717\pi$
$523$			6.69653i			0.292819i	−0.989224	+	0.146409i	$0.953228\pi$
$524$	3.30136	−	1.36747i	0.144221	−	0.0597381i
$525$	3.70253	+	3.70253i	0.161592	+	0.161592i
$526$	−6.04573			−0.263606
$527$	7.94061	−	28.9611i	0.345899	−	1.26157i
$528$	6.94843			0.302392
$529$	6.87423	+	6.87423i	0.298879	+	0.298879i
$530$	−8.54787	+	3.54064i	−0.371296	+	0.153796i
$531$		−	3.87832i		−	0.168305i
$532$	1.64713	+	3.97653i	0.0714122	+	0.172404i
$533$	0.724069	+	0.299919i	0.0313629	+	0.0129909i
$534$	−1.26598	+	3.05635i	−0.0547844	+	0.132261i
$535$	−11.1235	+	11.1235i	−0.480910	+	0.480910i
$536$	−6.12852	+	6.12852i	−0.264712	+	0.264712i
$537$	−7.39935	+	17.8636i	−0.319305	+	0.770871i
$538$	−15.6073	−	6.46477i	−0.672880	−	0.278716i
$539$	10.0726	+	24.3174i	0.433857	+	1.04742i
$540$		−	5.64058i		−	0.242732i
$541$	−6.32639	+	2.62047i	−0.271993	+	0.112663i	−0.514511	−	0.857484i	$-0.672027\pi$
$541$	−6.32639	+	2.62047i	−0.271993	+	0.112663i	0.242518	+	0.970147i	$0.422027\pi$
$542$	−16.2143	−	16.2143i	−0.696463	−	0.696463i
$543$	2.69657			0.115721
$544$	−4.09089	+	0.514430i	−0.175395	+	0.0220560i
$545$	6.43062			0.275458
$546$	20.2787	+	20.2787i	0.867850	+	0.867850i
$547$	−3.26202	+	1.35117i	−0.139474	+	0.0577719i	−0.451329	−	0.892358i	$-0.649050\pi$
$547$	−3.26202	+	1.35117i	−0.139474	+	0.0577719i	0.311855	+	0.950130i	$0.399050\pi$
$548$			3.30950i			0.141375i
$549$	3.91624	+	9.45463i	0.167141	+	0.403514i
$550$	4.35013	+	1.80188i	0.185490	+	0.0768325i
$551$	2.15569	−	5.20429i	0.0918355	−	0.221710i
$552$	5.96902	−	5.96902i	0.254058	−	0.254058i
$553$	25.3806	−	25.3806i	1.07929	−	1.07929i
$554$	−7.65435	+	18.4792i	−0.325202	+	0.785108i
$555$	−12.6681	−	5.24731i	−0.537732	−	0.222736i
$556$	−0.688816	−	1.66295i	−0.0292123	−	0.0705247i
$557$			45.7591i			1.93888i	0.245338	+	0.969438i	$0.421101\pi$
$557$			45.7591i			1.93888i	−0.245338	+	0.969438i	$0.578899\pi$
$558$	−5.53311	+	2.29189i	−0.234235	+	0.0970234i
$559$	−3.21506	−	3.21506i	−0.135983	−	0.135983i
$560$	−3.54824			−0.149941
$561$	−17.5721	+	22.6272i	−0.741897	+	0.955322i
$562$	23.2826			0.982118
$563$	−7.05601	−	7.05601i	−0.297375	−	0.297375i	0.542610	−	0.839985i	$-0.317436\pi$
$563$	−7.05601	−	7.05601i	−0.297375	−	0.297375i	−0.839985	+	0.542610i	$0.817436\pi$
$564$	7.98440	−	3.30725i	0.336204	−	0.139260i
$565$		−	9.64176i		−	0.405632i
$566$	−9.62478	−	23.2363i	−0.404560	−	0.976693i
$567$	19.2001	+	7.95293i	0.806327	+	0.333992i
$568$	−1.96849	+	4.75235i	−0.0825959	+	0.199404i
$569$	−9.56020	+	9.56020i	−0.400784	+	0.400784i	−0.878509	−	0.477725i	$-0.841462\pi$
$569$	−9.56020	+	9.56020i	−0.400784	+	0.400784i	0.477725	+	0.878509i	$0.341462\pi$
$570$	−1.26579	+	1.26579i	−0.0530179	+	0.0530179i
$571$	6.49469	−	15.6796i	0.271794	−	0.656169i	−0.727766	−	0.685826i	$-0.759441\pi$
$571$	6.49469	−	15.6796i	0.271794	−	0.656169i	0.999560	+	0.0296562i	$0.00944125\pi$
$572$	23.8256	+	9.86889i	0.996199	+	0.412639i
$573$	−9.50543	−	22.9481i	−0.397095	−	0.958673i
$574$		−	0.507734i		−	0.0211924i
$575$	5.28485	−	2.18906i	0.220394	−	0.0912900i
$576$	0.581445	+	0.581445i	0.0242269	+	0.0242269i
$577$	−9.67374			−0.402723			−0.201361	−	0.979517i	$-0.564537\pi$
$577$	−9.67374			−0.402723			−0.201361	+	0.979517i	$0.564537\pi$
$578$	8.67039	−	14.6227i	0.360641	−	0.608226i
$579$	−8.60150			−0.357466
$580$	3.28365	+	3.28365i	0.136346	+	0.136346i
$581$	11.1654	−	4.62487i	0.463220	−	0.191872i
$582$			6.42734i			0.266422i
$583$	−16.6713	−	40.2480i	−0.690453	−	1.66690i
$584$	−14.9042	−	6.17351i	−0.616739	−	0.255462i
$585$	1.72348	−	4.16084i	0.0712570	−	0.172030i
$586$	−18.0489	+	18.0489i	−0.745595	+	0.745595i
$587$	3.24694	−	3.24694i	0.134015	−	0.134015i	−0.636917	−	0.770932i	$-0.719791\pi$
$587$	3.24694	−	3.24694i	0.134015	−	0.134015i	0.770932	+	0.636917i	$0.219791\pi$
$588$	3.15686	−	7.62132i	0.130187	−	0.314298i
$589$	8.16245	+	3.38100i	0.336328	+	0.139312i
$590$	−1.80493	−	4.35748i	−0.0743077	−	0.179395i
$591$		−	5.19661i		−	0.213760i
$592$	8.58444	−	3.55579i	0.352818	−	0.146142i
$593$	−0.550724	−	0.550724i	−0.0226155	−	0.0226155i	0.695709	−	0.718324i	$-0.255090\pi$
$593$	−0.550724	−	0.550724i	−0.0226155	−	0.0226155i	−0.718324	+	0.695709i	$0.755090\pi$
$594$	26.5589			1.08972
$595$	8.97329	−	11.5547i	0.367869	−	0.473696i
$596$	4.16768			0.170715
$597$	−17.5306	−	17.5306i	−0.717478	−	0.717478i
$598$	28.9451	−	11.9894i	1.18365	−	0.490285i
$599$		−	10.4846i		−	0.428391i	−0.976791	−	0.214196i	$-0.931287\pi$
$599$		−	10.4846i		−	0.428391i	0.976791	−	0.214196i	$-0.0687130\pi$
$600$	−0.564729	−	1.36338i	−0.0230550	−	0.0556596i
$601$	−14.1755	−	5.87170i	−0.578233	−	0.239512i	0.0743464	−	0.997232i	$-0.476313\pi$
$601$	−14.1755	−	5.87170i	−0.578233	−	0.239512i	−0.652579	+	0.757721i	$0.726313\pi$
$602$	−1.12724	+	2.72139i	−0.0459428	+	0.110916i
$603$	−5.03940	+	5.03940i	−0.205220	+	0.205220i
$604$	3.24744	−	3.24744i	0.132137	−	0.132137i
$605$	−4.27471	+	10.3201i	−0.173792	+	0.419571i
$606$	−14.6417	−	6.06480i	−0.594779	−	0.246366i
$607$	8.27458	+	19.9766i	0.335855	+	0.810825i	0.998105	+	0.0615418i	$0.0196018\pi$
$607$	8.27458	+	19.9766i	0.335855	+	0.810825i	−0.662250	+	0.749283i	$0.730398\pi$
$608$		−	1.21304i		−	0.0491952i
$609$	−22.4647	+	9.30519i	−0.910316	+	0.377065i
$610$	8.80016	+	8.80016i	0.356308	+	0.356308i
$611$	32.0752			1.29762
$612$	−3.36389	+	0.423009i	−0.135977	+	0.0170991i
$613$	−18.6071			−0.751535			−0.375768	−	0.926714i	$-0.622621\pi$
$613$	−18.6071			−0.751535			−0.375768	+	0.926714i	$0.622621\pi$
$614$	−10.0679	−	10.0679i	−0.406308	−	0.406308i
$615$	0.195091	−	0.0808095i	0.00786684	−	0.00325855i
$616$		−	16.7071i		−	0.673147i
$617$	2.18286	+	5.26989i	0.0878787	+	0.212158i	0.961709	−	0.274074i	$-0.0883712\pi$
$617$	2.18286	+	5.26989i	0.0878787	+	0.212158i	−0.873830	+	0.486231i	$0.838371\pi$
$618$	−10.1341	−	4.19766i	−0.407651	−	0.168855i
$619$	11.1868	−	27.0073i	0.449635	−	1.08552i	−0.522823	−	0.852441i	$-0.675121\pi$
$619$	11.1868	−	27.0073i	0.449635	−	1.08552i	0.972459	−	0.233075i	$-0.0748787\pi$
$620$	−5.15010	+	5.15010i	−0.206833	+	0.206833i
$621$	22.8153	−	22.8153i	0.915546	−	0.915546i
$622$	4.65012	−	11.2264i	0.186453	−	0.450137i
$623$	7.34881	+	3.04397i	0.294424	+	0.121954i
$624$	−3.09302	−	7.46720i	−0.123820	−	0.298927i
$625$		−	1.00000i		−	0.0400000i
$626$	−20.1310	+	8.33854i	−0.804597	+	0.333275i
$627$	−5.96000	−	5.96000i	−0.238020	−	0.238020i
$628$	15.5482			0.620442
$629$	−10.1303	+	36.9472i	−0.403920	+	1.47318i
$630$	−2.91768			−0.116243
$631$	30.9574	+	30.9574i	1.23239	+	1.23239i	0.963042	+	0.269351i	$0.0868092\pi$
$631$	30.9574	+	30.9574i	1.23239	+	1.23239i	0.269351	+	0.963042i	$0.413191\pi$
$632$	−9.34587	+	3.87118i	−0.371759	+	0.153987i
$633$			33.6755i			1.33848i
$634$	3.92314	+	9.47130i	0.155808	+	0.376153i
$635$	2.96188	+	1.22685i	0.117539	+	0.0486861i
$636$	−5.22495	+	12.6142i	−0.207183	+	0.500184i
$637$	21.6492	−	21.6492i	0.857773	−	0.857773i
$638$	−15.4612	+	15.4612i	−0.612115	+	0.612115i
$639$	−1.61866	+	3.90780i	−0.0640333	+	0.154590i
$640$	0.923880	+	0.382683i	0.0365195	+	0.0151269i
$641$	−16.6913	−	40.2963i	−0.659265	−	1.59161i	−0.798941	−	0.601410i	$-0.794606\pi$
$641$	−16.6913	−	40.2963i	−0.659265	−	1.59161i	0.139676	−	0.990197i	$-0.455394\pi$
$642$			23.2143i			0.916197i
$643$	−5.12401	+	2.12244i	−0.202071	+	0.0837007i	−0.481424	−	0.876488i	$-0.659880\pi$
$643$	−5.12401	+	2.12244i	−0.202071	+	0.0837007i	0.279353	+	0.960189i	$0.409880\pi$
$644$	−14.3521	−	14.3521i	−0.565553	−	0.565553i
$645$	−1.22508			−0.0482373
$646$	3.95020	+	3.06770i	0.155419	+	0.120697i
$647$	−25.3893			−0.998155			−0.499078	−	0.866557i	$-0.666328\pi$
$647$	−25.3893			−0.998155			−0.499078	+	0.866557i	$0.666328\pi$
$648$	−4.14151	−	4.14151i	−0.162694	−	0.162694i
$649$	20.5174	−	8.49858i	0.805378	−	0.333598i
$650$		−	5.47699i		−	0.214825i
$651$	−14.5943	−	35.2338i	−0.571996	−	1.38092i
$652$	9.36608	+	3.87956i	0.366804	+	0.151935i
$653$	15.0457	−	36.3236i	0.588784	−	1.42145i	−0.295882	−	0.955225i	$-0.595613\pi$
$653$	15.0457	−	36.3236i	0.588784	−	1.42145i	0.884666	−	0.466226i	$-0.154387\pi$
$654$	6.71024	−	6.71024i	0.262391	−	0.262391i
$655$	2.52675	−	2.52675i	0.0987284	−	0.0987284i
$656$	−0.0547598	+	0.132202i	−0.00213801	+	0.00516162i
$657$	−12.2555	−	5.07640i	−0.478133	−	0.198049i
$658$	−7.95207	−	19.1980i	−0.310004	−	0.748415i
$659$			39.5179i			1.53940i	0.638408	+	0.769698i	$0.279593\pi$
$659$			39.5179i			1.53940i	−0.638408	+	0.769698i	$0.720407\pi$
$660$	6.41951	−	2.65905i	0.249879	−	0.103503i
$661$	−2.21986	−	2.21986i	−0.0863427	−	0.0863427i	0.662616	−	0.748959i	$-0.269446\pi$
$661$	−2.21986	−	2.21986i	−0.0863427	−	0.0863427i	−0.748959	+	0.662616i	$0.769446\pi$
$662$	−0.296190			−0.0115117
$663$	32.1386	+	8.81183i	1.24816	+	0.342223i
$664$	−3.40601			−0.132179
$665$	3.04350	+	3.04350i	0.118022	+	0.118022i
$666$	7.05888	−	2.92388i	0.273526	−	0.113298i
$667$			26.5637i			1.02855i
$668$	−4.76501	−	11.5038i	−0.184364	−	0.445093i
$669$	−12.3639	−	5.12129i	−0.478016	−	0.198001i
$670$	−3.31673	+	8.00729i	−0.128136	+	0.309349i
$671$	−41.4359	+	41.4359i	−1.59962	+	1.59962i
$672$	−3.70253	+	3.70253i	−0.142828	+	0.142828i
$673$	−8.91195	+	21.5153i	−0.343530	+	0.829355i	0.653823	+	0.756647i	$0.273164\pi$
$673$	−8.91195	+	21.5153i	−0.343530	+	0.829355i	−0.997353	+	0.0727079i	$0.976836\pi$
$674$	−12.9824	−	5.37748i	−0.500063	−	0.207133i
$675$	−2.15856	−	5.21121i	−0.0830829	−	0.200580i
$676$		−	16.9974i		−	0.653748i
$677$	−38.1349	+	15.7960i	−1.46564	+	0.607089i	−0.965861	−	0.259062i	$-0.916587\pi$
$677$	−38.1349	+	15.7960i	−1.46564	+	0.607089i	−0.499782	+	0.866151i	$0.666587\pi$
$678$	−10.0610	−	10.0610i	−0.386391	−	0.386391i
$679$	15.4541			0.593075
$680$	−3.58262	+	2.04079i	−0.137387	+	0.0782606i
$681$	23.2392			0.890528
$682$	−24.2494	−	24.2494i	−0.928559	−	0.928559i
$683$	5.77636	−	2.39265i	0.221026	−	0.0915521i	−0.269423	−	0.963022i	$-0.586833\pi$
$683$	5.77636	−	2.39265i	0.221026	−	0.0915521i	0.490449	+	0.871470i	$0.336833\pi$
$684$		−	0.997467i		−	0.0381391i
$685$	1.26649	+	3.05758i	0.0483901	+	0.116824i
$686$	4.62206	+	1.91452i	0.176471	+	0.0730968i
$687$	11.3617	−	27.4295i	0.433476	−	1.04650i
$688$	0.587013	−	0.587013i	0.0223796	−	0.0223796i
$689$	−35.8319	+	35.8319i	−1.36509	+	1.36509i
$690$	3.23041	−	7.79889i	0.122980	−	0.296899i
$691$	−29.6992	−	12.3018i	−1.12981	−	0.467983i	−0.262094	−	0.965042i	$-0.584413\pi$
$691$	−29.6992	−	12.3018i	−1.12981	−	0.467983i	−0.867716	+	0.497060i	$0.834413\pi$
$692$	−1.35726	−	3.27672i	−0.0515954	−	0.124562i
$693$		−	13.7380i		−	0.521864i
$694$	−10.3007	+	4.26669i	−0.391010	+	0.161961i
$695$	−1.27277	−	1.27277i	−0.0482788	−	0.0482788i
$696$	6.85286			0.259757
$697$	−0.292025	−	0.512653i	−0.0110612	−	0.0194181i
$698$	−2.51265			−0.0951051
$699$	−20.1129	−	20.1129i	−0.760739	−	0.760739i
$700$	−3.27815	+	1.35785i	−0.123902	+	0.0513221i
$701$		−	12.7609i		−	0.481972i	−0.970529	−	0.240986i	$-0.922529\pi$
$701$		−	12.7609i		−	0.481972i	0.970529	−	0.240986i	$-0.0774708\pi$
$702$	−11.8224	−	28.5418i	−0.446208	−	1.07724i
$703$	−10.4133	−	4.31332i	−0.392744	−	0.162680i
$704$	−1.80188	+	4.35013i	−0.0679109	+	0.163952i
$705$	6.11100	−	6.11100i	0.230153	−	0.230153i
$706$	7.12929	−	7.12929i	0.268314	−	0.268314i
$707$	−14.5824	+	35.2051i	−0.548429	+	1.32402i
$708$	−6.43037	−	2.66354i	−0.241668	−	0.100102i
$709$	12.8274	+	30.9681i	0.481744	+	1.16303i	0.958780	+	0.284149i	$0.0917110\pi$
$709$	12.8274	+	30.9681i	0.481744	+	1.16303i	−0.477036	+	0.878884i	$0.658289\pi$
$710$			5.14391i			0.193047i
$711$	−7.68499	+	3.18323i	−0.288210	+	0.119380i
$712$	−1.58516	−	1.58516i	−0.0594063	−	0.0594063i
$713$	−41.6627			−1.56028
$714$	−2.69364	−	21.4206i	−0.100807	−	0.801645i
$715$	25.7886			0.964441
$716$	−9.26485	−	9.26485i	−0.346244	−	0.346244i
$717$	19.3653	−	8.02139i	0.723212	−	0.299564i
$718$		−	24.6679i		−	0.920599i
$719$	−10.9707	−	26.4857i	−0.409140	−	0.987750i	−0.985365	−	0.170459i	$-0.945475\pi$
$719$	−10.9707	−	26.4857i	−0.409140	−	0.987750i	0.576225	−	0.817291i	$-0.304525\pi$
$720$	0.759695	+	0.314676i	0.0283121	+	0.0117273i
$721$	−10.0930	+	24.3667i	−0.375883	+	0.907463i
$722$	12.3945	−	12.3945i	0.461277	−	0.461277i
$723$	−4.77346	+	4.77346i	−0.177527	+	0.177527i
$724$	−0.699281	+	1.68821i	−0.0259886	+	0.0627420i
$725$	4.29029	+	1.77710i	0.159337	+	0.0659998i
$726$	6.30823	+	15.2294i	0.234120	+	0.565216i
$727$			21.0302i			0.779966i	0.920822	+	0.389983i	$0.127519\pi$
$727$			21.0302i			0.779966i	−0.920822	+	0.389983i	$0.872481\pi$
$728$	−17.9544	+	7.43696i	−0.665435	+	0.275632i
$729$	−21.0631	−	21.0631i	−0.780113	−	0.780113i
$730$	−16.1322			−0.597078
$731$	0.427059	+	3.39610i	0.0157954	+	0.125609i
$732$	18.3656			0.678813
$733$	−6.38248	−	6.38248i	−0.235742	−	0.235742i	0.579342	−	0.815084i	$-0.303310\pi$
$733$	−6.38248	−	6.38248i	−0.235742	−	0.235742i	−0.815084	+	0.579342i	$0.803310\pi$
$734$	27.5072	−	11.3939i	1.01531	−	0.420555i
$735$		−	8.24926i		−	0.304279i
$736$	2.18906	+	5.28485i	0.0806897	+	0.194802i
$737$	−37.7027	−	15.6170i	−1.38880	−	0.575258i
$738$	−0.0450283	+	0.108708i	−0.00165751	+	0.00400160i
$739$	10.1850	−	10.1850i	0.374662	−	0.374662i	−0.494510	−	0.869172i	$-0.664653\pi$
$739$	10.1850	−	10.1850i	0.374662	−	0.374662i	0.869172	+	0.494510i	$0.164653\pi$
$740$	6.57025	−	6.57025i	0.241527	−	0.241527i
$741$	−3.75195	+	9.05801i	−0.137831	+	0.332754i
$742$	30.3299	+	12.5631i	1.11345	+	0.461205i
$743$	12.6717	+	30.5921i	0.464879	+	1.12232i	0.966370	+	0.257154i	$0.0827847\pi$
$743$	12.6717	+	30.5921i	0.464879	+	1.12232i	−0.501492	+	0.865162i	$0.667215\pi$
$744$			10.7481i			0.394043i
$745$	3.85044	−	1.59490i	0.141069	−	0.0584327i
$746$	14.7106	+	14.7106i	0.538592	+	0.538592i
$747$	−2.80072			−0.102473
$748$	−9.60913	−	16.8689i	−0.351344	−	0.616789i
$749$	55.8174			2.03952
$750$	−1.04348	−	1.04348i	−0.0381026	−	0.0381026i
$751$	−5.92242	+	2.45315i	−0.216112	+	0.0895166i	−0.488113	−	0.872780i	$-0.662315\pi$
$751$	−5.92242	+	2.45315i	−0.216112	+	0.0895166i	0.272001	+	0.962297i	$0.412315\pi$
$752$			5.85635i			0.213559i
$753$	−5.08658	−	12.2801i	−0.185365	−	0.447511i
$754$	23.4979	+	9.73315i	0.855743	+	0.354460i
$755$	1.75750	−	4.24299i	0.0639621	−	0.154418i
$756$	−14.1521	+	14.1521i	−0.514708	+	0.514708i
$757$	34.6660	−	34.6660i	1.25996	−	1.25996i	0.308847	−	0.951112i	$-0.400057\pi$
$757$	34.6660	−	34.6660i	1.25996	−	1.25996i	0.951112	−	0.308847i	$-0.0999430\pi$
$758$	−3.99706	+	9.64974i	−0.145180	+	0.350495i
$759$	36.7214	+	15.2105i	1.33290	+	0.552107i
$760$	−0.464210	−	1.12070i	−0.0168387	−	0.0406521i
$761$			42.6819i			1.54722i	0.633662	+	0.773610i	$0.281551\pi$
$761$			42.6819i			1.54722i	−0.633662	+	0.773610i	$0.718449\pi$
$762$	4.37087	−	1.81047i	0.158340	−	0.0655865i
$763$	−16.1344	−	16.1344i	−0.584103	−	0.584103i
$764$	16.8319			0.608955
$765$	−2.94595	+	1.67811i	−0.106511	+	0.0606723i
$766$	−20.1518			−0.728113
$767$	−18.2662	−	18.2662i	−0.659553	−	0.659553i
$768$	1.36338	−	0.564729i	0.0491966	−	0.0203779i
$769$			14.6429i			0.528035i	0.964518	+	0.264018i	$0.0850477\pi$
$769$			14.6429i			0.528035i	−0.964518	+	0.264018i	$0.914952\pi$
$770$	−6.39351	−	15.4353i	−0.230406	−	0.556250i
$771$	39.0716	+	16.1840i	1.40713	+	0.582853i
$772$	2.23056	−	5.38504i	0.0802795	−	0.193812i
$773$	10.5010	−	10.5010i	0.377696	−	0.377696i	−0.492575	−	0.870270i	$-0.663944\pi$
$773$	10.5010	−	10.5010i	0.377696	−	0.377696i	0.870270	+	0.492575i	$0.163944\pi$
$774$	0.482693	−	0.482693i	0.0173500	−	0.0173500i
$775$	−2.78721	+	6.72892i	−0.100120	+	0.241710i
$776$	−4.02389	−	1.66675i	−0.144449	−	0.0598328i
$777$	18.6187	+	44.9496i	0.667944	+	1.61256i
$778$		−	19.6657i		−	0.705051i
$779$	0.160366	−	0.0664258i	0.00574571	−	0.00237995i
$780$	−5.71515	−	5.71515i	−0.204635	−	0.204635i
$781$	−24.2203			−0.866670
$782$	−22.7458	−	6.23650i	−0.813390	−	0.223017i
$783$	26.1936			0.936083
$784$	3.95275	+	3.95275i	0.141170	+	0.141170i
$785$	14.3647	−	5.95005i	0.512698	−	0.212366i
$786$		−	5.27324i		−	0.188090i
$787$	8.22589	+	19.8591i	0.293221	+	0.707899i	1.00000		0.000464022i	$0.000147703\pi$
$787$	8.22589	+	19.8591i	0.293221	+	0.707899i	−0.706779	+	0.707435i	$0.749852\pi$
$788$	3.25339	+	1.34760i	0.115897	+	0.0480061i
$789$	−3.41420	+	8.24261i	−0.121549	+	0.293445i
$790$	−7.15302	+	7.15302i	−0.254493	+	0.254493i
$791$	−24.1911	+	24.1911i	−0.860135	+	0.860135i
$792$	−1.48166	+	3.57705i	−0.0526486	+	0.127105i
$793$	62.9743	+	26.0848i	2.23628	+	0.926298i
$794$	−9.16446	−	22.1250i	−0.325235	−	0.785186i
$795$			13.6535i			0.484238i
$796$	15.5212	−	6.42910i	0.550135	−	0.227874i
$797$	14.8934	+	14.8934i	0.527550	+	0.527550i	0.919841	−	0.392291i	$-0.128317\pi$
$797$	14.8934	+	14.8934i	0.527550	+	0.527550i	−0.392291	+	0.919841i	$0.628317\pi$
$798$	6.35168			0.224847
$799$	−19.0709	−	14.8103i	−0.674680	−	0.523952i
$800$	1.00000			0.0353553
$801$	−1.30346	−	1.30346i	−0.0460554	−	0.0460554i
$802$	−21.2869	+	8.81734i	−0.751668	+	0.311351i
$803$		−	75.9590i		−	2.68053i
$804$	4.89452	+	11.8164i	0.172617	+	0.416733i
$805$	−18.7519	−	7.76731i	−0.660919	−	0.273762i
$806$	−15.2655	+	36.8543i	−0.537706	+	1.29814i
$807$	−17.6278	+	17.6278i	−0.620529	+	0.620529i
$808$	7.59384	−	7.59384i	0.267150	−	0.267150i
$809$	−6.98690	+	16.8679i	−0.245646	+	0.593042i	−0.997825	−	0.0659166i	$-0.979003\pi$
$809$	−6.98690	+	16.8679i	−0.245646	+	0.593042i	0.752179	+	0.658959i	$0.229003\pi$
$810$	−5.41114	−	2.24137i	−0.190128	−	0.0787537i
$811$	−5.56638	−	13.4384i	−0.195462	−	0.471887i	0.795512	−	0.605937i	$-0.207202\pi$
$811$	−5.56638	−	13.4384i	−0.195462	−	0.471887i	−0.990975	+	0.134050i	$0.957202\pi$
$812$		−	16.4773i		−	0.578239i
$813$	−31.2628	+	12.9495i	−1.09644	+	0.454158i
$814$	30.9363	+	30.9363i	1.08432	+	1.08432i
$815$	10.1378			0.355111
$816$	−1.60888	+	5.86793i	−0.0563221	+	0.205419i
$817$	−1.00702			−0.0352311
$818$	9.01479	+	9.01479i	0.315195	+	0.315195i
$819$	−14.7637	+	6.11532i	−0.515885	+	0.213686i
$820$			0.143094i			0.00499707i
$821$	15.6230	+	37.7172i	0.545246	+	1.31634i	0.920979	+	0.389613i	$0.127391\pi$
$821$	15.6230	+	37.7172i	0.545246	+	1.31634i	−0.375733	+	0.926728i	$0.622609\pi$
$822$	4.51209	+	1.86897i	0.157377	+	0.0651878i
$823$	0.697439	−	1.68377i	0.0243112	−	0.0586925i	−0.911258	−	0.411837i	$-0.864887\pi$
$823$	0.697439	−	1.68377i	0.0243112	−	0.0586925i	0.935569	+	0.353144i	$0.114887\pi$
$824$	5.25597	−	5.25597i	0.183100	−	0.183100i
$825$	4.91328	−	4.91328i	0.171059	−	0.171059i
$826$	−6.40432	+	15.4614i	−0.222835	+	0.537971i
$827$	42.9008	+	17.7701i	1.49181	+	0.617927i	0.971709	−	0.236180i	$-0.0758955\pi$
$827$	42.9008	+	17.7701i	1.49181	+	0.617927i	0.520098	+	0.854107i	$0.325896\pi$
$828$	1.80003	+	4.34567i	0.0625555	+	0.151022i
$829$		−	34.9749i		−	1.21473i	−0.794424	−	0.607364i	$-0.792227\pi$
$829$		−	34.9749i		−	1.21473i	0.794424	−	0.607364i	$-0.207773\pi$
$830$	−3.14674	+	1.30342i	−0.109225	+	0.0452425i
$831$	20.8715	+	20.8715i	0.724025	+	0.724025i
$832$	5.47699			0.189881
$833$	−22.8682	+	2.87568i	−0.792337	+	0.0996365i
$834$	−2.65622			−0.0919773
$835$	−8.80459	−	8.80459i	−0.304695	−	0.304695i
$836$	5.27687	−	2.18575i	0.182504	−	0.0755958i
$837$			41.0822i			1.42001i
$838$	10.4748	+	25.2883i	0.361845	+	0.873570i
$839$	39.6860	+	16.4385i	1.37011	+	0.567520i	0.941819	−	0.336120i	$-0.109115\pi$
$839$	39.6860	+	16.4385i	1.37011	+	0.567520i	0.428294	+	0.903639i	$0.359115\pi$
$840$	−2.00380	+	4.83759i	−0.0691375	+	0.166913i
$841$	5.25756	−	5.25756i	0.181295	−	0.181295i
$842$	−23.8163	+	23.8163i	−0.820764	+	0.820764i
$843$	13.1484	−	31.7430i	0.452854	−	1.09329i
$844$	−21.0828	−	8.73280i	−0.725701	−	0.300595i
$845$	−6.50464	−	15.7036i	−0.223766	−	0.540220i
$846$			4.81560i			0.165564i
$847$	36.6181	−	15.1677i	1.25821	−	0.521169i
$848$	−6.54226	−	6.54226i	−0.224662	−	0.224662i
$849$	−37.1152			−1.27379
$850$	−2.52894	+	3.25645i	−0.0867419	+	0.111695i
$851$	53.1513			1.82200
$852$	5.36758	+	5.36758i	0.183890	+	0.183890i
$853$	−8.59031	+	3.55822i	−0.294127	+	0.121831i	−0.524867	−	0.851184i	$-0.675885\pi$
$853$	−8.59031	+	3.55822i	−0.294127	+	0.121831i	0.230741	+	0.973015i	$0.425885\pi$
$854$		−	44.1590i		−	1.51109i
$855$	−0.381714	−	0.921539i	−0.0130543	−	0.0315160i
$856$	−14.5335	−	6.01999i	−0.496746	−	0.205759i
$857$	−11.8527	+	28.6150i	−0.404881	+	0.977469i	0.581582	+	0.813488i	$0.302434\pi$
$857$	−11.8527	+	28.6150i	−0.404881	+	0.977469i	−0.986463	+	0.163982i	$0.947566\pi$
$858$	26.9100	−	26.9100i	0.918693	−	0.918693i
$859$	13.1008	−	13.1008i	0.446994	−	0.446994i	−0.447360	−	0.894354i	$-0.647636\pi$
$859$	13.1008	−	13.1008i	0.446994	−	0.446994i	0.894354	+	0.447360i	$0.147636\pi$
$860$	0.317689	−	0.766969i	0.0108331	−	0.0261534i
$861$	−0.692232	−	0.286732i	−0.0235912	−	0.00977179i
$862$	−6.95725	−	16.7963i	−0.236965	−	0.572084i
$863$		−	18.5377i		−	0.631030i	−0.948921	−	0.315515i	$-0.897823\pi$
$863$		−	18.5377i		−	0.631030i	0.948921	−	0.315515i	$-0.102177\pi$
$864$	5.21121	−	2.15856i	0.177289	−	0.0734356i
$865$	−2.50790	−	2.50790i	−0.0852710	−	0.0852710i
$866$	−8.10392			−0.275382
$867$	−15.0399	−	20.0789i	−0.510781	−	0.681914i
$868$	25.8431			0.877170
$869$	−33.6803	−	33.6803i	−1.14253	−	1.14253i
$870$	6.33122	−	2.62248i	0.214648	−	0.0889103i
$871$			47.4693i			1.60843i
$872$	2.46089	+	5.94112i	0.0833363	+	0.201192i
$873$	−3.30880	−	1.37055i	−0.111986	−	0.0463860i
$874$	2.65541	−	6.41073i	0.0898207	−	0.216846i
$875$	−2.50899	+	2.50899i	−0.0848193	+	0.0848193i
$876$	−16.8336	+	16.8336i	−0.568756	+	0.568756i
$877$	16.3998	−	39.5926i	0.553781	−	1.33695i	−0.360837	−	0.932629i	$-0.617509\pi$
$877$	16.3998	−	39.5926i	0.553781	−	1.33695i	0.914619	−	0.404318i	$-0.132491\pi$
$878$	22.1522	+	9.17574i	0.747600	+	0.309666i
$879$	14.4147	+	34.8003i	0.486197	+	1.17378i
$880$			4.70854i			0.158725i
$881$	37.7646	−	15.6426i	1.27232	−	0.527014i	0.358653	−	0.933471i	$-0.383236\pi$
$881$	37.7646	−	15.6426i	1.27232	−	0.527014i	0.913670	+	0.406457i	$0.133236\pi$
$882$	3.25030	+	3.25030i	0.109443	+	0.109443i
$883$	52.3174			1.76062			0.880310	−	0.474398i	$-0.157334\pi$
$883$	52.3174			1.76062			0.880310	+	0.474398i	$0.157334\pi$
$884$	−13.8510	+	17.8356i	−0.465859	+	0.599875i
$885$	−6.96018			−0.233964
$886$	0.172587	+	0.172587i	0.00579819	+	0.00579819i
$887$	−13.9607	+	5.78272i	−0.468755	+	0.194165i	−0.604542	−	0.796573i	$-0.706644\pi$
$887$	−13.9607	+	5.78272i	−0.468755	+	0.194165i	0.135787	+	0.990738i	$0.456644\pi$
$888$		−	13.7119i		−	0.460141i
$889$	−4.35317	−	10.5095i	−0.146000	−	0.352476i
$890$	−2.07111	−	0.857882i	−0.0694238	−	0.0287563i
$891$	10.5536	−	25.4786i	0.353558	−	0.853565i
$892$	6.41246	−	6.41246i	0.214705	−	0.214705i
$893$	5.02327	−	5.02327i	0.168097	−	0.168097i
$894$	2.35361	−	5.68212i	0.0787165	−	0.190038i
$895$	−12.1051	−	5.01410i	−0.404629	−	0.167603i
$896$	−1.35785	−	3.27815i	−0.0453627	−	0.109515i
$897$		−	46.2338i		−	1.54370i
$898$	−0.0761574	+	0.0315454i	−0.00254140	+	0.00105268i
$899$	−23.9159	−	23.9159i	−0.797640	−	0.797640i
$900$	0.822287			0.0274096
$901$	37.8495	−	4.75958i	1.26095	−	0.158565i
$902$	−0.673765			−0.0224339
$903$	3.07370	+	3.07370i	0.102286	+	0.102286i
$904$	8.90782	−	3.68974i	0.296270	−	0.122719i
$905$			1.82731i			0.0607418i
$906$	−2.59356	−	6.26141i	−0.0861653	−	0.208022i
$907$	−23.1561	−	9.59155i	−0.768884	−	0.318482i	−0.0364638	−	0.999335i	$-0.511609\pi$
$907$	−23.1561	−	9.59155i	−0.768884	−	0.318482i	−0.732420	+	0.680853i	$0.761609\pi$
$908$	−6.02643	+	14.5491i	−0.199994	+	0.482829i
$909$	6.24432	−	6.24432i	0.207111	−	0.207111i
$910$	−13.7417	+	13.7417i	−0.455533	+	0.455533i
$911$	−1.10387	+	2.66499i	−0.0365730	+	0.0882950i	−0.941111	−	0.338099i	$-0.890216\pi$
$911$	−1.10387	+	2.66499i	−0.0365730	+	0.0882950i	0.904538	+	0.426394i	$0.140216\pi$
$912$	−1.65383	−	0.685038i	−0.0547637	−	0.0226839i
$913$	−6.13723	−	14.8166i	−0.203113	−	0.490357i
$914$			24.3896i			0.806737i
$915$	16.9676	−	7.02822i	0.560933	−	0.232346i
$916$	14.2262	+	14.2262i	0.470046	+	0.470046i
$917$	−12.6792			−0.418703
$918$	−6.14961	+	22.4289i	−0.202967	+	0.740265i
$919$	−48.0746			−1.58584			−0.792918	−	0.609328i	$-0.791439\pi$
$919$	−48.0746			−1.58584			−0.792918	+	0.609328i	$0.791439\pi$
$920$	4.04485	+	4.04485i	0.133355	+	0.133355i
$921$	−19.4120	+	8.04071i	−0.639647	+	0.264950i
$922$			29.1100i			0.958687i
$923$	10.7814	+	26.0286i	0.354874	+	0.856741i
$924$	−22.7780	−	9.43496i	−0.749341	−	0.310387i
$925$	3.55579	−	8.58444i	0.116914	−	0.282255i
$926$	−19.7821	+	19.7821i	−0.650081	+	0.650081i
$927$	4.32191	−	4.32191i	0.141950	−	0.141950i
$928$	−1.77710	+	4.29029i	−0.0583361	+	0.140836i
$929$	25.3430	+	10.4974i	0.831478	+	0.344409i	0.757487	−	0.652850i	$-0.226427\pi$
$929$	25.3430	+	10.4974i	0.831478	+	0.344409i	0.0739901	+	0.997259i	$0.476427\pi$
$930$	4.11311	+	9.92992i	0.134874	+	0.325615i
$931$		−	6.78094i		−	0.222236i
$932$	17.8076	−	7.37613i	0.583306	−	0.241613i
$933$	−12.6797	−	12.6797i	−0.415116	−	0.415116i
$934$	31.2786			1.02347
$935$	−15.3331	−	11.9076i	−0.501447	−	0.389420i
$936$	4.50366			0.147207
$937$	−10.3762	−	10.3762i	−0.338975	−	0.338975i	0.517007	−	0.855981i	$-0.327046\pi$
$937$	−10.3762	−	10.3762i	−0.338975	−	0.338975i	−0.855981	+	0.517007i	$0.827046\pi$
$938$	28.4118	−	11.7686i	0.927679	−	0.384257i
$939$			32.1552i			1.04934i
$940$	2.24113	+	5.41056i	0.0730975	+	0.176473i
$941$	22.8397	+	9.46050i	0.744552	+	0.308404i	0.722517	−	0.691354i	$-0.242985\pi$
$941$	22.8397	+	9.46050i	0.744552	+	0.308404i	0.0220356	+	0.999757i	$0.492985\pi$
$942$	8.78053	−	21.1981i	0.286085	−	0.690671i
$943$	−0.578795	+	0.578795i	−0.0188482	+	0.0188482i
$944$	3.33507	−	3.33507i	0.108547	−	0.108547i
$945$	−7.65908	+	18.4907i	−0.249150	+	0.601501i
$946$	3.61131	+	1.49585i	0.117414	+	0.0486343i
$947$	−2.49335	−	6.01947i	−0.0810228	−	0.195606i	0.878177	−	0.478336i	$-0.158760\pi$
$947$	−2.49335	−	6.01947i	−0.0810228	−	0.195606i	−0.959200	+	0.282730i	$0.908760\pi$
$948$			14.9281i			0.484842i
$949$	−81.6301	+	33.8123i	−2.64982	+	1.09759i
$950$	−0.857748	−	0.857748i	−0.0278290	−	0.0278290i
$951$	15.1285			0.490574
$952$	14.1091	+	3.86845i	0.457277	+	0.125377i
$953$	13.6944			0.443607			0.221803	−	0.975091i	$-0.428806\pi$
$953$	13.6944			0.443607			0.221803	+	0.975091i	$0.428806\pi$
$954$	−5.37961	−	5.37961i	−0.174171	−	0.174171i
$955$	15.5506	−	6.44127i	0.503206	−	0.208435i
$956$			14.2040i			0.459389i
$957$	12.3480	+	29.8108i	0.399155	+	0.963646i
$958$	−11.1564	−	4.62112i	−0.360446	−	0.149302i
$959$	4.49382	−	10.8490i	0.145113	−	0.350334i
$960$	1.04348	−	1.04348i	0.0336783	−	0.0336783i
$961$	15.5896	−	15.5896i	0.502889	−	0.502889i
$962$	19.4751	−	47.0169i	0.627901	−	1.51589i
$963$	−11.9507	−	4.95016i	−0.385107	−	0.159517i
$964$	−1.75060	−	4.22633i	−0.0563832	−	0.136121i
$965$		−	5.82873i		−	0.187633i
$966$	−27.6724	+	11.4623i	−0.890344	+	0.368793i
$967$	11.5376	+	11.5376i	0.371026	+	0.371026i	0.867851	−	0.496825i	$-0.165501\pi$
$967$	11.5376	+	11.5376i	0.371026	+	0.371026i	−0.496825	+	0.867851i	$0.665501\pi$
$968$	−11.1704			−0.359029
$969$	6.41322	−	3.65319i	0.206022	−	0.117357i
$970$	−4.35543			−0.139844
$971$	−19.0136	−	19.0136i	−0.610176	−	0.610176i	0.332816	−	0.942992i	$-0.392001\pi$
$971$	−19.0136	−	19.0136i	−0.610176	−	0.610176i	−0.942992	+	0.332816i	$0.892001\pi$
$972$	7.64838	−	3.16806i	0.245322	−	0.101616i
$973$			6.38671i			0.204748i
$974$	1.91937	+	4.63377i	0.0615005	+	0.148475i
$975$	−7.46720	−	3.09302i	−0.239142	−	0.0990558i
$976$	−4.76261	+	11.4980i	−0.152448	+	0.368041i
$977$	−14.1423	+	14.1423i	−0.452451	+	0.452451i	−0.896167	−	0.443716i	$-0.853660\pi$
$977$	−14.1423	+	14.1423i	−0.452451	+	0.452451i	0.443716	+	0.896167i	$0.353660\pi$
$978$	10.5786	−	10.5786i	0.338266	−	0.338266i
$979$	4.03937	−	9.75191i	0.129099	−	0.311672i
$980$	5.16452	+	2.13922i	0.164975	+	0.0683347i
$981$	2.02356	+	4.88531i	0.0646073	+	0.155976i
$982$		−	26.4441i		−	0.843865i
$983$	−26.6406	+	11.0349i	−0.849704	+	0.351959i	−0.764672	−	0.644419i	$-0.777099\pi$
$983$	−26.6406	+	11.0349i	−0.849704	+	0.351959i	−0.0850316	+	0.996378i	$0.527099\pi$
$984$	0.149316	+	0.149316i	0.00476003	+	0.00476003i
$985$	3.52144			0.112202
$986$	−9.47696	−	16.6369i	−0.301808	−	0.529827i
$987$	−30.6648			−0.976072
$988$	−4.69788	−	4.69788i	−0.149460	−	0.149460i
$989$	4.38728	−	1.81727i	0.139507	−	0.0577858i
$990$			3.87177i			0.123053i
$991$	−10.2929	−	24.8494i	−0.326966	−	0.789366i	−0.998815	−	0.0486775i	$-0.984499\pi$
$991$	−10.2929	−	24.8494i	−0.326966	−	0.789366i	0.671848	−	0.740689i	$-0.265501\pi$
$992$	−6.72892	−	2.78721i	−0.213644	−	0.0884941i
$993$	−0.167267	+	0.403818i	−0.00530805	+	0.0128148i
$994$	12.9060	−	12.9060i	0.409353	−	0.409353i
$995$	11.8794	−	11.8794i	0.376603	−	0.376603i
$996$	−1.92347	+	4.64367i	−0.0609476	+	0.147140i
$997$	28.1434	+	11.6574i	0.891310	+	0.369193i	0.780872	−	0.624690i	$-0.214775\pi$
$997$	28.1434	+	11.6574i	0.891310	+	0.369193i	0.110437	+	0.993883i	$0.464775\pi$
$998$	−11.4569	−	27.6595i	−0.362663	−	0.875545i
$999$		−	52.4108i		−	1.65820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.121.3	yes	16
5.2	odd	4		850.2.o.g.699.2		16
5.3	odd	4		850.2.o.j.699.3		16
5.4	even	2		850.2.l.e.801.2		16
17.3	odd	16		2890.2.a.bi.1.7		8
17.5	odd	16		2890.2.b.r.2311.12		16
17.9	even	8	inner	170.2.k.b.111.3	✓	16
17.12	odd	16		2890.2.b.r.2311.5		16
17.14	odd	16		2890.2.a.bj.1.2		8
85.9	even	8		850.2.l.e.451.2		16
85.43	odd	8		850.2.o.g.349.2		16
85.77	odd	8		850.2.o.j.349.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.3	✓	16	17.9	even	8	inner
170.2.k.b.121.3	yes	16	1.1	even	1	trivial
850.2.l.e.451.2		16	85.9	even	8
850.2.l.e.801.2		16	5.4	even	2
850.2.o.g.349.2		16	85.43	odd	8
850.2.o.g.699.2		16	5.2	odd	4
850.2.o.j.349.3		16	85.77	odd	8
850.2.o.j.699.3		16	5.3	odd	4
2890.2.a.bi.1.7		8	17.3	odd	16
2890.2.a.bj.1.2		8	17.14	odd	16
2890.2.b.r.2311.5		16	17.12	odd	16
2890.2.b.r.2311.12		16	17.5	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.36338 - 0.564729i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(1.36338 + 0.564729i) q^{6} +(1.35785 - 3.27815i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.581445 + 0.581445i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.36338 - 0.564729i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(1.36338 + 0.564729i) q^{6} +(1.35785 - 3.27815i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.581445 + 0.581445i) q^{9} +(-0.382683 + 0.923880i) q^{10} +(-4.35013 - 1.80188i) q^{11} +(0.564729 + 1.36338i) q^{12} +5.47699i q^{13} +(3.27815 - 1.35785i) q^{14} +(1.04348 + 1.04348i) q^{15} -1.00000 q^{16} +(2.52894 - 3.25645i) q^{17} -0.822287 q^{18} +(0.857748 + 0.857748i) q^{19} +(-0.923880 + 0.382683i) q^{20} -5.23617i q^{21} +(-1.80188 - 4.35013i) q^{22} +(-5.28485 - 2.18906i) q^{23} +(-0.564729 + 1.36338i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-3.87282 + 3.87282i) q^{26} +(-2.15856 + 5.21121i) q^{27} +(3.27815 + 1.35785i) q^{28} +(-1.77710 - 4.29029i) q^{29} +1.47571i q^{30} +(6.72892 - 2.78721i) q^{31} +(-0.707107 - 0.707107i) q^{32} -6.94843 q^{33} +(4.09089 - 0.514430i) q^{34} +3.54824 q^{35} +(-0.581445 - 0.581445i) q^{36} +(-8.58444 + 3.55579i) q^{37} +1.21304i q^{38} +(3.09302 + 7.46720i) q^{39} +(-0.923880 - 0.382683i) q^{40} +(0.0547598 - 0.132202i) q^{41} +(3.70253 - 3.70253i) q^{42} +(-0.587013 + 0.587013i) q^{43} +(1.80188 - 4.35013i) q^{44} +(-0.759695 - 0.314676i) q^{45} +(-2.18906 - 5.28485i) q^{46} -5.85635i q^{47} +(-1.36338 + 0.564729i) q^{48} +(-3.95275 - 3.95275i) q^{49} -1.00000 q^{50} +(1.60888 - 5.86793i) q^{51} -5.47699 q^{52} +(6.54226 + 6.54226i) q^{53} +(-5.21121 + 2.15856i) q^{54} -4.70854i q^{55} +(1.35785 + 3.27815i) q^{56} +(1.65383 + 0.685038i) q^{57} +(1.77710 - 4.29029i) q^{58} +(-3.33507 + 3.33507i) q^{59} +(-1.04348 + 1.04348i) q^{60} +(4.76261 - 11.4980i) q^{61} +(6.72892 + 2.78721i) q^{62} +(1.11655 + 2.69558i) q^{63} -1.00000i q^{64} +(-5.06008 + 2.09595i) q^{65} +(-4.91328 - 4.91328i) q^{66} +8.66703 q^{67} +(3.25645 + 2.52894i) q^{68} -8.44146 q^{69} +(2.50899 + 2.50899i) q^{70} +(4.75235 - 1.96849i) q^{71} -0.822287i q^{72} +(6.17351 + 14.9042i) q^{73} +(-8.58444 - 3.55579i) q^{74} +(-0.564729 + 1.36338i) q^{75} +(-0.857748 + 0.857748i) q^{76} +(-11.8137 + 11.8137i) q^{77} +(-3.09302 + 7.46720i) q^{78} +(9.34587 + 3.87118i) q^{79} +(-0.382683 - 0.923880i) q^{80} +5.85698i q^{81} +(0.132202 - 0.0547598i) q^{82} +(2.40841 + 2.40841i) q^{83} +5.23617 q^{84} +(3.97635 + 1.09024i) q^{85} -0.830161 q^{86} +(-4.84570 - 4.84570i) q^{87} +(4.35013 - 1.80188i) q^{88} +2.24175i q^{89} +(-0.314676 - 0.759695i) q^{90} +(17.9544 + 7.43696i) q^{91} +(2.18906 - 5.28485i) q^{92} +(7.60004 - 7.60004i) q^{93} +(4.14106 - 4.14106i) q^{94} +(-0.464210 + 1.12070i) q^{95} +(-1.36338 - 0.564729i) q^{96} +(1.66675 + 4.02389i) q^{97} -5.59004i q^{98} +(3.57705 - 1.48166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Introduction

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