LMFDB - Embedded newform 170.2.k.b.121.2

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			121.2
Root			$-0.0614939i$ of defining polynomial
Character	$\chi$	$=$	170.121
Dual form			170.2.k.b.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.980692 + 0.406216i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.980692 - 0.406216i) q^{6} +(-0.758398 + 1.83094i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.32457 + 1.32457i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.980692 + 0.406216i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.980692 - 0.406216i) q^{6} +(-0.758398 + 1.83094i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.32457 + 1.32457i) q^{9} +(-0.382683 + 0.923880i) q^{10} +(5.09023 + 2.10844i) q^{11} +(-0.406216 - 0.980692i) q^{12} -3.39460i q^{13} +(-1.83094 + 0.758398i) q^{14} +(-0.750590 - 0.750590i) q^{15} -1.00000 q^{16} +(-2.20451 - 3.48427i) q^{17} -1.87323 q^{18} +(1.48774 + 1.48774i) q^{19} +(-0.923880 + 0.382683i) q^{20} -2.10366i q^{21} +(2.10844 + 5.09023i) q^{22} +(1.94049 + 0.803776i) q^{23} +(0.406216 - 0.980692i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(2.40034 - 2.40034i) q^{26} +(1.97958 - 4.77914i) q^{27} +(-1.83094 - 0.758398i) q^{28} +(-1.85710 - 4.48343i) q^{29} -1.06149i q^{30} +(6.95674 - 2.88158i) q^{31} +(-0.707107 - 0.707107i) q^{32} -5.84844 q^{33} +(0.904922 - 4.02258i) q^{34} -1.98179 q^{35} +(-1.32457 - 1.32457i) q^{36} +(6.56031 - 2.71737i) q^{37} +2.10399i q^{38} +(1.37894 + 3.32906i) q^{39} +(-0.923880 - 0.382683i) q^{40} +(2.80101 - 6.76223i) q^{41} +(1.48751 - 1.48751i) q^{42} +(-7.94580 + 7.94580i) q^{43} +(-2.10844 + 5.09023i) q^{44} +(-1.73064 - 0.716854i) q^{45} +(0.803776 + 1.94049i) q^{46} -0.959164i q^{47} +(0.980692 - 0.406216i) q^{48} +(2.17259 + 2.17259i) q^{49} -1.00000 q^{50} +(3.57732 + 2.52149i) q^{51} +3.39460 q^{52} +(-3.52810 - 3.52810i) q^{53} +(4.77914 - 1.97958i) q^{54} +5.50963i q^{55} +(-0.758398 - 1.83094i) q^{56} +(-2.06336 - 0.854673i) q^{57} +(1.85710 - 4.48343i) q^{58} +(0.723071 - 0.723071i) q^{59} +(0.750590 - 0.750590i) q^{60} +(-5.64869 + 13.6371i) q^{61} +(6.95674 + 2.88158i) q^{62} +(-1.42065 - 3.42976i) q^{63} -1.00000i q^{64} +(3.13620 - 1.29906i) q^{65} +(-4.13547 - 4.13547i) q^{66} -10.9274 q^{67} +(3.48427 - 2.20451i) q^{68} -2.22953 q^{69} +(-1.40134 - 1.40134i) q^{70} +(0.614209 - 0.254414i) q^{71} -1.87323i q^{72} +(3.54195 + 8.55102i) q^{73} +(6.56031 + 2.71737i) q^{74} +(0.406216 - 0.980692i) q^{75} +(-1.48774 + 1.48774i) q^{76} +(-7.72085 + 7.72085i) q^{77} +(-1.37894 + 3.32906i) q^{78} +(-1.19449 - 0.494772i) q^{79} +(-0.382683 - 0.923880i) q^{80} -0.128685i q^{81} +(6.76223 - 2.80101i) q^{82} +(-1.36223 - 1.36223i) q^{83} +2.10366 q^{84} +(2.37541 - 3.37008i) q^{85} -11.2371 q^{86} +(3.64248 + 3.64248i) q^{87} +(-5.09023 + 2.10844i) q^{88} -14.7461i q^{89} +(-0.716854 - 1.73064i) q^{90} +(6.21529 + 2.57446i) q^{91} +(-0.803776 + 1.94049i) q^{92} +(-5.65188 + 5.65188i) q^{93} +(0.678231 - 0.678231i) q^{94} +(-0.805161 + 1.94383i) q^{95} +(0.980692 + 0.406216i) q^{96} +(-2.47139 - 5.96646i) q^{97} +3.07251i q^{98} +(-9.53518 + 3.94960i) 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
$3$	−0.980692	+	0.406216i	−0.566203	+	0.234529i	−0.647376	−	0.762171i	$-0.724134\pi$
$3$	−0.980692	+	0.406216i	−0.566203	+	0.234529i	0.0811726	+	0.996700i	$0.474134\pi$
$4$			1.00000i			0.500000i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$	−0.980692	−	0.406216i	−0.400366	−	0.165837i
$7$	−0.758398	+	1.83094i	−0.286648	+	0.692028i	−0.999961	−	0.00881658i	$-0.997194\pi$
$7$	−0.758398	+	1.83094i	−0.286648	+	0.692028i	0.713314	+	0.700845i	$0.247194\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.32457	+	1.32457i	−0.441525	+	0.441525i
$10$	−0.382683	+	0.923880i	−0.121015	+	0.292156i
$11$	5.09023	+	2.10844i	1.53476	+	0.635720i	0.980482	−	0.196610i	$-0.0629931\pi$
$11$	5.09023	+	2.10844i	1.53476	+	0.635720i	0.554281	+	0.832329i	$0.312993\pi$
$12$	−0.406216	−	0.980692i	−0.117264	−	0.283102i
$13$		−	3.39460i		−	0.941493i	−0.882269	−	0.470746i	$-0.843985\pi$
$13$		−	3.39460i		−	0.941493i	0.882269	−	0.470746i	$-0.156015\pi$
$14$	−1.83094	+	0.758398i	−0.489338	+	0.202690i
$15$	−0.750590	−	0.750590i	−0.193801	−	0.193801i
$16$	−1.00000			−0.250000
$17$	−2.20451	−	3.48427i	−0.534673	−	0.845059i
$17$	−2.20451	−	3.48427i	−0.534673	−	0.845059i
$18$	−1.87323			−0.441525
$19$	1.48774	+	1.48774i	0.341312	+	0.341312i	0.856860	−	0.515549i	$-0.172412\pi$
$19$	1.48774	+	1.48774i	0.341312	+	0.341312i	−0.515549	+	0.856860i	$0.672412\pi$
$20$	−0.923880	+	0.382683i	−0.206586	+	0.0855706i
$21$		−	2.10366i		−	0.459056i
$22$	2.10844	+	5.09023i	0.449522	+	1.08524i
$23$	1.94049	+	0.803776i	0.404619	+	0.167599i	0.575705	−	0.817657i	$-0.304728\pi$
$23$	1.94049	+	0.803776i	0.404619	+	0.167599i	−0.171086	+	0.985256i	$0.554728\pi$
$24$	0.406216	−	0.980692i	0.0829185	−	0.200183i
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	2.40034	−	2.40034i	0.470746	−	0.470746i
$27$	1.97958	−	4.77914i	0.380971	−	0.919746i
$28$	−1.83094	−	0.758398i	−0.346014	−	0.143324i
$29$	−1.85710	−	4.48343i	−0.344854	−	0.832551i	−0.997211	−	0.0746391i	$-0.976220\pi$
$29$	−1.85710	−	4.48343i	−0.344854	−	0.832551i	0.652357	−	0.757912i	$-0.273780\pi$
$30$		−	1.06149i		−	0.193801i
$31$	6.95674	−	2.88158i	1.24947	−	0.517546i	0.342806	−	0.939406i	$-0.388623\pi$
$31$	6.95674	−	2.88158i	1.24947	−	0.517546i	0.906661	+	0.421860i	$0.138623\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−5.84844			−1.01808
$34$	0.904922	−	4.02258i	0.155193	−	0.689866i
$35$	−1.98179			−0.334984
$36$	−1.32457	−	1.32457i	−0.220762	−	0.220762i
$37$	6.56031	−	2.71737i	1.07851	−	0.446733i	0.228523	−	0.973539i	$-0.426610\pi$
$37$	6.56031	−	2.71737i	1.07851	−	0.446733i	0.849986	+	0.526806i	$0.176610\pi$
$38$			2.10399i			0.341312i
$39$	1.37894	+	3.32906i	0.220807	+	0.533076i
$40$	−0.923880	−	0.382683i	−0.146078	−	0.0605076i
$41$	2.80101	−	6.76223i	0.437444	−	1.05608i	−0.539385	−	0.842059i	$-0.681343\pi$
$41$	2.80101	−	6.76223i	0.437444	−	1.05608i	0.976829	−	0.214023i	$-0.0686568\pi$
$42$	1.48751	−	1.48751i	0.229528	−	0.229528i
$43$	−7.94580	+	7.94580i	−1.21172	+	1.21172i	−0.241264	+	0.970460i	$0.577562\pi$
$43$	−7.94580	+	7.94580i	−1.21172	+	1.21172i	−0.970460	+	0.241264i	$0.922438\pi$
$44$	−2.10844	+	5.09023i	−0.317860	+	0.767382i
$45$	−1.73064	−	0.716854i	−0.257989	−	0.106862i
$46$	0.803776	+	1.94049i	0.118510	+	0.286109i
$47$		−	0.959164i		−	0.139908i	−0.997550	−	0.0699542i	$-0.977715\pi$
$47$		−	0.959164i		−	0.139908i	0.997550	−	0.0699542i	$-0.0222853\pi$
$48$	0.980692	−	0.406216i	0.141551	−	0.0586322i
$49$	2.17259	+	2.17259i	0.310370	+	0.310370i
$50$	−1.00000			−0.141421
$51$	3.57732	+	2.52149i	0.500924	+	0.353079i
$52$	3.39460			0.470746
$53$	−3.52810	−	3.52810i	−0.484622	−	0.484622i	0.421982	−	0.906604i	$-0.361334\pi$
$53$	−3.52810	−	3.52810i	−0.484622	−	0.484622i	−0.906604	+	0.421982i	$0.861334\pi$
$54$	4.77914	−	1.97958i	0.650359	−	0.269387i
$55$			5.50963i			0.742918i
$56$	−0.758398	−	1.83094i	−0.101345	−	0.244669i
$57$	−2.06336	−	0.854673i	−0.273299	−	0.113204i
$58$	1.85710	−	4.48343i	0.243849	−	0.588703i
$59$	0.723071	−	0.723071i	0.0941359	−	0.0941359i	−0.658471	−	0.752606i	$-0.728796\pi$
$59$	0.723071	−	0.723071i	0.0941359	−	0.0941359i	0.752606	+	0.658471i	$0.228796\pi$
$60$	0.750590	−	0.750590i	0.0969007	−	0.0969007i
$61$	−5.64869	+	13.6371i	−0.723241	+	1.74606i	−0.0593390	+	0.998238i	$0.518899\pi$
$61$	−5.64869	+	13.6371i	−0.723241	+	1.74606i	−0.663902	+	0.747820i	$0.731101\pi$
$62$	6.95674	+	2.88158i	0.883507	+	0.365961i
$63$	−1.42065	−	3.42976i	−0.178986	−	0.432110i
$64$		−	1.00000i		−	0.125000i
$65$	3.13620	−	1.29906i	0.388998	−	0.161128i
$66$	−4.13547	−	4.13547i	−0.509041	−	0.509041i
$67$	−10.9274			−1.33500			−0.667498	−	0.744612i	$-0.732635\pi$
$67$	−10.9274			−1.33500			−0.667498	+	0.744612i	$0.732635\pi$
$68$	3.48427	−	2.20451i	0.422529	−	0.267337i
$69$	−2.22953			−0.268404
$70$	−1.40134	−	1.40134i	−0.167492	−	0.167492i
$71$	0.614209	−	0.254414i	0.0728932	−	0.0301934i	−0.345939	−	0.938257i	$-0.612440\pi$
$71$	0.614209	−	0.254414i	0.0728932	−	0.0301934i	0.418832	+	0.908064i	$0.362440\pi$
$72$		−	1.87323i		−	0.220762i
$73$	3.54195	+	8.55102i	0.414554	+	1.00082i	0.983899	+	0.178723i	$0.0571965\pi$
$73$	3.54195	+	8.55102i	0.414554	+	1.00082i	−0.569346	+	0.822098i	$0.692803\pi$
$74$	6.56031	+	2.71737i	0.762621	+	0.315888i
$75$	0.406216	−	0.980692i	0.0469058	−	0.113241i
$76$	−1.48774	+	1.48774i	−0.170656	+	0.170656i
$77$	−7.72085	+	7.72085i	−0.879872	+	0.879872i
$78$	−1.37894	+	3.32906i	−0.156134	+	0.376942i
$79$	−1.19449	−	0.494772i	−0.134390	−	0.0556662i	0.314475	−	0.949266i	$-0.398172\pi$
$79$	−1.19449	−	0.494772i	−0.134390	−	0.0556662i	−0.448865	+	0.893600i	$0.648172\pi$
$80$	−0.382683	−	0.923880i	−0.0427853	−	0.103293i
$81$		−	0.128685i		−	0.0142984i
$82$	6.76223	−	2.80101i	0.746763	−	0.309319i
$83$	−1.36223	−	1.36223i	−0.149524	−	0.149524i	0.628381	−	0.777906i	$-0.283718\pi$
$83$	−1.36223	−	1.36223i	−0.149524	−	0.149524i	−0.777906	+	0.628381i	$0.783718\pi$
$84$	2.10366			0.229528
$85$	2.37541	−	3.37008i	0.257650	−	0.365536i
$86$	−11.2371			−1.21172
$87$	3.64248	+	3.64248i	0.390515	+	0.390515i
$88$	−5.09023	+	2.10844i	−0.542621	+	0.224761i
$89$		−	14.7461i		−	1.56309i	−0.623851	−	0.781543i	$-0.714433\pi$
$89$		−	14.7461i		−	1.56309i	0.623851	−	0.781543i	$-0.285567\pi$
$90$	−0.716854	−	1.73064i	−0.0755631	−	0.182425i
$91$	6.21529	+	2.57446i	0.651540	+	0.269877i
$92$	−0.803776	+	1.94049i	−0.0837994	+	0.202310i
$93$	−5.65188	+	5.65188i	−0.586073	+	0.586073i
$94$	0.678231	−	0.678231i	0.0699542	−	0.0699542i
$95$	−0.805161	+	1.94383i	−0.0826077	+	0.199433i
$96$	0.980692	+	0.406216i	0.100092	+	0.0414593i
$97$	−2.47139	−	5.96646i	−0.250932	−	0.605803i	0.747348	−	0.664433i	$-0.231327\pi$
$97$	−2.47139	−	5.96646i	−0.250932	−	0.605803i	−0.998280	+	0.0586300i	$0.981327\pi$
$98$			3.07251i			0.310370i
$99$	−9.53518	+	3.94960i	−0.958322	+	0.396950i
$100$	−0.707107	−	0.707107i	−0.0707107	−	0.0707107i
$101$	−4.10929			−0.408890			−0.204445	−	0.978878i	$-0.565539\pi$
$101$	−4.10929			−0.408890			−0.204445	+	0.978878i	$0.565539\pi$
$102$	0.746585	+	4.31250i	0.0739230	+	0.427002i
$103$	9.11950			0.898571			0.449286	−	0.893388i	$-0.351679\pi$
$103$	9.11950			0.898571			0.449286	+	0.893388i	$0.351679\pi$
$104$	2.40034	+	2.40034i	0.235373	+	0.235373i
$105$	1.94353	−	0.805035i	0.189669	−	0.0785634i
$106$		−	4.98948i		−	0.484622i
$107$	4.68155	+	11.3023i	0.452582	+	1.09263i	0.971337	+	0.237707i	$0.0763959\pi$
$107$	4.68155	+	11.3023i	0.452582	+	1.09263i	−0.518754	+	0.854923i	$0.673604\pi$
$108$	4.77914	+	1.97958i	0.459873	+	0.190486i
$109$	−1.50289	+	3.62829i	−0.143950	+	0.347527i	−0.979367	−	0.202091i	$-0.935226\pi$
$109$	−1.50289	+	3.62829i	−0.143950	+	0.347527i	0.835417	+	0.549617i	$0.185226\pi$
$110$	−3.89590	+	3.89590i	−0.371459	+	0.371459i
$111$	−5.32981	+	5.32981i	−0.505883	+	0.505883i
$112$	0.758398	−	1.83094i	0.0716619	−	0.173007i
$113$	−2.23248	−	0.924725i	−0.210014	−	0.0869908i	0.275196	−	0.961388i	$-0.411257\pi$
$113$	−2.23248	−	0.924725i	−0.210014	−	0.0869908i	−0.485211	+	0.874397i	$0.661257\pi$
$114$	−0.854673	−	2.06336i	−0.0800475	−	0.193252i
$115$			2.10037i			0.195860i
$116$	4.48343	−	1.85710i	0.416276	−	0.172427i
$117$	4.49640	+	4.49640i	0.415692	+	0.415692i
$118$	1.02258			0.0941359
$119$	8.05137	−	1.39386i	0.738068	−	0.127775i
$120$	1.06149			0.0969007
$121$	13.6868	+	13.6868i	1.24425	+	1.24425i
$122$	−13.6371	+	5.64869i	−1.23465	+	0.511408i
$123$			7.76948i			0.700551i
$124$	2.88158	+	6.95674i	0.258773	+	0.624734i
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$	1.42065	−	3.42976i	0.126562	−	0.305548i
$127$	8.77568	−	8.77568i	0.778716	−	0.778716i	−0.200897	−	0.979612i	$-0.564386\pi$
$127$	8.77568	−	8.77568i	0.778716	−	0.778716i	0.979612	+	0.200897i	$0.0643856\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.56468	−	11.0201i	0.401897	−	0.970266i
$130$	3.13620	+	1.29906i	0.275063	+	0.113935i
$131$	−5.98001	−	14.4370i	−0.522476	−	1.26137i	−0.936361	−	0.351039i	$-0.885828\pi$
$131$	−5.98001	−	14.4370i	−0.522476	−	1.26137i	0.413885	−	0.910329i	$-0.364172\pi$
$132$		−	5.84844i		−	0.509041i
$133$	−3.85226	+	1.59566i	−0.334033	+	0.138361i
$134$	−7.72685	−	7.72685i	−0.667498	−	0.667498i
$135$	5.17290			0.445213
$136$	4.02258	+	0.904922i	0.344933	+	0.0775964i
$137$	−15.4112			−1.31667			−0.658335	−	0.752725i	$-0.728739\pi$
$137$	−15.4112			−1.31667			−0.658335	+	0.752725i	$0.728739\pi$
$138$	−1.57651	−	1.57651i	−0.134202	−	0.134202i
$139$	−10.8943	+	4.51255i	−0.924039	+	0.382750i	−0.793414	−	0.608682i	$-0.791698\pi$
$139$	−10.8943	+	4.51255i	−0.924039	+	0.382750i	−0.130625	+	0.991432i	$0.541698\pi$
$140$		−	1.98179i		−	0.167492i
$141$	0.389628	+	0.940645i	0.0328126	+	0.0792166i
$142$	0.614209	+	0.254414i	0.0515433	+	0.0213499i
$143$	7.15732	−	17.2793i	0.598526	−	1.44497i
$144$	1.32457	−	1.32457i	0.110381	−	0.110381i
$145$	3.43147	−	3.43147i	0.284968	−	0.284968i
$146$	−3.54195	+	8.55102i	−0.293134	+	0.707687i
$147$	−3.01319	−	1.24810i	−0.248523	−	0.102942i
$148$	2.71737	+	6.56031i	0.223366	+	0.539254i
$149$		−	17.7389i		−	1.45323i	−0.687045	−	0.726614i	$-0.741093\pi$
$149$		−	17.7389i		−	1.45323i	0.687045	−	0.726614i	$-0.258907\pi$
$150$	0.980692	−	0.406216i	0.0800732	−	0.0331674i
$151$	1.47823	+	1.47823i	0.120297	+	0.120297i	0.764692	−	0.644396i	$-0.222891\pi$
$151$	1.47823	+	1.47823i	0.120297	+	0.120297i	−0.644396	+	0.764692i	$0.722891\pi$
$152$	−2.10399			−0.170656
$153$	7.53521	+	1.69513i	0.609186	+	0.137043i
$154$	−10.9189			−0.879872
$155$	5.32446	+	5.32446i	0.427671	+	0.427671i
$156$	−3.32906	+	1.37894i	−0.266538	+	0.110404i
$157$		−	5.38314i		−	0.429622i	−0.976656	−	0.214811i	$-0.931086\pi$
$157$		−	5.38314i		−	0.429622i	0.976656	−	0.214811i	$-0.0689135\pi$
$158$	−0.494772	−	1.19449i	−0.0393620	−	0.0950282i
$159$	4.89315	+	2.02681i	0.388052	+	0.160736i
$160$	0.382683	−	0.923880i	0.0302538	−	0.0730391i
$161$	−2.94332	+	2.94332i	−0.231966	+	0.231966i
$162$	0.0909942	−	0.0909942i	0.00714918	−	0.00714918i
$163$	6.81116	−	16.4436i	0.533491	−	1.28796i	−0.395706	−	0.918377i	$-0.629500\pi$
$163$	6.81116	−	16.4436i	0.533491	−	1.28796i	0.929197	−	0.369585i	$-0.120500\pi$
$164$	6.76223	+	2.80101i	0.528041	+	0.218722i
$165$	−2.23810	−	5.40325i	−0.174236	−	0.420643i
$166$		−	1.92649i		−	0.149524i
$167$	−0.571853	+	0.236869i	−0.0442513	+	0.0183295i	−0.404699	−	0.914450i	$-0.632624\pi$
$167$	−0.571853	+	0.236869i	−0.0442513	+	0.0183295i	0.360448	+	0.932779i	$0.382624\pi$
$168$	1.48751	+	1.48751i	0.114764	+	0.114764i
$169$	1.47669			0.113591
$170$	4.06267	−	0.703335i	0.311593	−	0.0539433i
$171$	−3.94125			−0.301395
$172$	−7.94580	−	7.94580i	−0.605862	−	0.605862i
$173$	19.9059	−	8.24528i	1.51341	−	0.626877i	0.537156	−	0.843483i	$-0.319499\pi$
$173$	19.9059	−	8.24528i	1.51341	−	0.626877i	0.976259	+	0.216606i	$0.0694987\pi$
$174$			5.15124i			0.390515i
$175$	−0.758398	−	1.83094i	−0.0573295	−	0.138406i
$176$	−5.09023	−	2.10844i	−0.383691	−	0.158930i
$177$	−0.415387	+	1.00283i	−0.0312224	+	0.0753776i
$178$	10.4271	−	10.4271i	0.781543	−	0.781543i
$179$	−15.5992	+	15.5992i	−1.16594	+	1.16594i	−0.182790	+	0.983152i	$0.558513\pi$
$179$	−15.5992	+	15.5992i	−1.16594	+	1.16594i	−0.983152	+	0.182790i	$0.941487\pi$
$180$	0.716854	−	1.73064i	0.0534312	−	0.128994i
$181$	−18.9519	−	7.85013i	−1.40868	−	0.583496i	−0.456693	−	0.889624i	$-0.650966\pi$
$181$	−18.9519	−	7.85013i	−1.40868	−	0.583496i	−0.951990	+	0.306129i	$0.900966\pi$
$182$	2.57446	+	6.21529i	0.190832	+	0.460708i
$183$		−	15.6684i		−	1.15824i
$184$	−1.94049	+	0.803776i	−0.143055	+	0.0592551i
$185$	5.02105	+	5.02105i	0.369155	+	0.369155i
$186$	−7.99297			−0.586073
$187$	−3.87511	−	22.3838i	−0.283376	−	1.63687i
$188$	0.959164			0.0699542
$189$	7.24898	+	7.24898i	0.527286	+	0.527286i
$190$	−1.94383	+	0.805161i	−0.141020	+	0.0584125i
$191$		−	20.8063i		−	1.50549i	−0.658313	−	0.752744i	$-0.728730\pi$
$191$		−	20.8063i		−	1.50549i	0.658313	−	0.752744i	$-0.271270\pi$
$192$	0.406216	+	0.980692i	0.0293161	+	0.0707754i
$193$	−0.871268	−	0.360891i	−0.0627153	−	0.0259775i	0.351105	−	0.936336i	$-0.385806\pi$
$193$	−0.871268	−	0.360891i	−0.0627153	−	0.0259775i	−0.413821	+	0.910358i	$0.635806\pi$
$194$	2.47139	−	5.96646i	0.177435	−	0.428367i
$195$	−2.54795	+	2.54795i	−0.182463	+	0.182463i
$196$	−2.17259	+	2.17259i	−0.155185	+	0.155185i
$197$	−2.88154	+	6.95665i	−0.205301	+	0.495641i	−0.992672	−	0.120839i	$-0.961442\pi$
$197$	−2.88154	+	6.95665i	−0.205301	+	0.495641i	0.787371	+	0.616479i	$0.211442\pi$
$198$	−9.53518	−	3.94960i	−0.677636	−	0.280686i
$199$	4.95469	+	11.9617i	0.351229	+	0.847941i	0.996469	+	0.0839616i	$0.0267573\pi$
$199$	4.95469	+	11.9617i	0.351229	+	0.847941i	−0.645240	+	0.763980i	$0.723243\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	10.7164	−	4.43889i	0.755879	−	0.313095i
$202$	−2.90571	−	2.90571i	−0.204445	−	0.204445i
$203$	9.61728			0.675001
$204$	−2.52149	+	3.57732i	−0.176539	+	0.250462i
$205$	7.31938			0.511208
$206$	6.44846	+	6.44846i	0.449286	+	0.449286i
$207$	−3.63498	+	1.50566i	−0.252649	+	0.104650i
$208$			3.39460i			0.235373i
$209$	4.43614	+	10.7098i	0.306854	+	0.740811i
$210$	1.94353	+	0.805035i	0.134116	+	0.0555527i
$211$	−5.15683	+	12.4497i	−0.355011	+	0.857072i	0.640975	+	0.767562i	$0.278530\pi$
$211$	−5.15683	+	12.4497i	−0.355011	+	0.857072i	−0.995986	+	0.0895105i	$0.971470\pi$
$212$	3.52810	−	3.52810i	0.242311	−	0.242311i
$213$	−0.499003	+	0.499003i	−0.0341911	+	0.0341911i
$214$	−4.68155	+	11.3023i	−0.320024	+	0.772606i
$215$	−10.3817	−	4.30024i	−0.708025	−	0.293274i
$216$	1.97958	+	4.77914i	0.134694	+	0.325179i
$217$			14.9227i			1.01302i
$218$	−3.62829	+	1.50289i	−0.245739	+	0.101788i
$219$	−6.94712	−	6.94712i	−0.469443	−	0.469443i
$220$	−5.50963			−0.371459
$221$	−11.8277	+	7.48345i	−0.795617	+	0.503391i
$222$	−7.53749			−0.505883
$223$	3.56198	+	3.56198i	0.238528	+	0.238528i	0.816240	−	0.577712i	$-0.196054\pi$
$223$	3.56198	+	3.56198i	0.238528	+	0.238528i	−0.577712	+	0.816240i	$0.696054\pi$
$224$	1.83094	−	0.758398i	0.122335	−	0.0506726i
$225$		−	1.87323i		−	0.124882i
$226$	−0.924725	−	2.23248i	−0.0615118	−	0.148503i
$227$	2.44249	+	1.01171i	0.162114	+	0.0671497i	0.462265	−	0.886742i	$-0.347037\pi$
$227$	2.44249	+	1.01171i	0.162114	+	0.0671497i	−0.300151	+	0.953892i	$0.597037\pi$
$228$	0.854673	−	2.06336i	0.0566021	−	0.136650i
$229$	9.07617	−	9.07617i	0.599770	−	0.599770i	−0.340481	−	0.940251i	$-0.610590\pi$
$229$	9.07617	−	9.07617i	0.599770	−	0.599770i	0.940251	+	0.340481i	$0.110590\pi$
$230$	−1.48518	+	1.48518i	−0.0979301	+	0.0979301i
$231$	4.43544	−	10.7081i	0.291831	−	0.704542i
$232$	4.48343	+	1.85710i	0.294351	+	0.121924i
$233$	6.68454	+	16.1379i	0.437919	+	1.05723i	0.976666	+	0.214762i	$0.0688977\pi$
$233$	6.68454	+	16.1379i	0.437919	+	1.05723i	−0.538747	+	0.842467i	$0.681102\pi$
$234$			6.35887i			0.415692i
$235$	0.886152	−	0.367056i	0.0578062	−	0.0239441i
$236$	0.723071	+	0.723071i	0.0470679	+	0.0470679i
$237$	1.37241			0.0891475
$238$	6.67878	+	4.70757i	0.432921	+	0.305146i
$239$	−8.10490			−0.524262			−0.262131	−	0.965032i	$-0.584425\pi$
$239$	−8.10490			−0.524262			−0.262131	+	0.965032i	$0.584425\pi$
$240$	0.750590	+	0.750590i	0.0484503	+	0.0484503i
$241$	−6.97258	+	2.88814i	−0.449143	+	0.186041i	−0.595778	−	0.803150i	$-0.703156\pi$
$241$	−6.97258	+	2.88814i	−0.449143	+	0.186041i	0.146634	+	0.989191i	$0.453156\pi$
$242$			19.3560i			1.24425i
$243$	5.99103	+	14.4636i	0.384325	+	0.927842i
$244$	−13.6371	−	5.64869i	−0.873029	−	0.361620i
$245$	−1.17580	+	2.83863i	−0.0751190	+	0.181353i
$246$	−5.49385	+	5.49385i	−0.350275	+	0.350275i
$247$	5.05029	−	5.05029i	0.321342	−	0.321342i
$248$	−2.88158	+	6.95674i	−0.182980	+	0.441753i
$249$	1.88929	+	0.782569i	0.119729	+	0.0495933i
$250$	−0.382683	−	0.923880i	−0.0242030	−	0.0584313i
$251$			13.4087i			0.846347i	0.906049	+	0.423173i	$0.139084\pi$
$251$			13.4087i			0.846347i	−0.906049	+	0.423173i	$0.860916\pi$
$252$	3.42976	−	1.42065i	0.216055	−	0.0894928i
$253$	8.18281	+	8.18281i	0.514449	+	0.514449i
$254$	12.4107			0.778716
$255$	−0.960569	+	4.26994i	−0.0601532	+	0.267394i
$256$	1.00000			0.0625000
$257$	−8.70117	−	8.70117i	−0.542764	−	0.542764i	0.381574	−	0.924338i	$-0.375382\pi$
$257$	−8.70117	−	8.70117i	−0.542764	−	0.542764i	−0.924338	+	0.381574i	$0.875382\pi$
$258$	11.0201	−	4.56468i	0.686082	−	0.284184i
$259$			14.0724i			0.874414i
$260$	1.29906	+	3.13620i	0.0805641	+	0.194499i
$261$	8.39849	+	3.47877i	0.519854	+	0.215330i
$262$	5.98001	−	14.4370i	0.369446	−	0.891922i
$263$	2.11132	−	2.11132i	0.130190	−	0.130190i	−0.639009	−	0.769199i	$-0.720656\pi$
$263$	2.11132	−	2.11132i	0.130190	−	0.130190i	0.769199	+	0.639009i	$0.220656\pi$
$264$	4.13547	−	4.13547i	0.254521	−	0.254521i
$265$	1.90939	−	4.60968i	0.117293	−	0.283171i
$266$	−3.85226	−	1.59566i	−0.236197	−	0.0978361i
$267$	5.99011	+	14.4614i	0.366589	+	0.885024i
$268$		−	10.9274i		−	0.667498i
$269$	5.95467	−	2.46651i	0.363063	−	0.150385i	−0.193692	−	0.981062i	$-0.562046\pi$
$269$	5.95467	−	2.46651i	0.363063	−	0.150385i	0.556755	+	0.830677i	$0.312046\pi$
$270$	3.65780	+	3.65780i	0.222606	+	0.222606i
$271$	−5.46663			−0.332074			−0.166037	−	0.986120i	$-0.553097\pi$
$271$	−5.46663			−0.332074			−0.166037	+	0.986120i	$0.553097\pi$
$272$	2.20451	+	3.48427i	0.133668	+	0.211265i
$273$	−7.14108			−0.432198
$274$	−10.8974	−	10.8974i	−0.658335	−	0.658335i
$275$	−5.09023	+	2.10844i	−0.306953	+	0.127144i
$276$		−	2.22953i		−	0.134202i
$277$	4.29248	+	10.3630i	0.257910	+	0.622649i	0.998800	−	0.0489769i	$-0.0155961\pi$
$277$	4.29248	+	10.3630i	0.257910	+	0.622649i	−0.740890	+	0.671626i	$0.765596\pi$
$278$	−10.8943	−	4.51255i	−0.653394	−	0.270645i
$279$	−5.39786	+	13.0316i	−0.323161	+	0.780180i
$280$	1.40134	−	1.40134i	0.0837459	−	0.0837459i
$281$	−17.6806	+	17.6806i	−1.05474	+	1.05474i	−0.0563230	+	0.998413i	$0.517938\pi$
$281$	−17.6806	+	17.6806i	−1.05474	+	1.05474i	−0.998413	+	0.0563230i	$0.982062\pi$
$282$	−0.389628	+	0.940645i	−0.0232020	+	0.0560146i
$283$	−16.7994	−	6.95853i	−0.998619	−	0.413642i	−0.177328	−	0.984152i	$-0.556745\pi$
$283$	−16.7994	−	6.95853i	−0.998619	−	0.413642i	−0.821291	+	0.570510i	$0.806745\pi$
$284$	0.254414	+	0.614209i	0.0150967	+	0.0364466i
$285$		−	2.23337i		−	0.132293i
$286$	17.2793	−	7.15732i	1.02175	−	0.423221i
$287$	10.2569	+	10.2569i	0.605447	+	0.605447i
$288$	1.87323			0.110381
$289$	−7.28023	+	15.3622i	−0.428249	+	0.903661i
$290$	4.85283			0.284968
$291$	4.84735	+	4.84735i	0.284157	+	0.284157i
$292$	−8.55102	+	3.54195i	−0.500410	+	0.207277i
$293$		−	3.16725i		−	0.185033i	−0.995711	−	0.0925163i	$-0.970509\pi$
$293$		−	3.16725i		−	0.185033i	0.995711	−	0.0925163i	$-0.0294910\pi$
$294$	−1.24810	−	3.01319i	−0.0727908	−	0.175733i
$295$	0.944738	+	0.391323i	0.0550048	+	0.0227837i
$296$	−2.71737	+	6.56031i	−0.157944	+	0.381310i
$297$	20.1531	−	20.1531i	1.16940	−	1.16940i
$298$	12.5433	−	12.5433i	0.726614	−	0.726614i
$299$	2.72850	−	6.58718i	0.157793	−	0.380946i
$300$	0.980692	+	0.406216i	0.0566203	+	0.0234529i
$301$	−8.52217	−	20.5743i	−0.491210	−	1.18588i
$302$			2.09054i			0.120297i
$303$	4.02995	−	1.66926i	0.231515	−	0.0958964i
$304$	−1.48774	−	1.48774i	−0.0853279	−	0.0853279i
$305$	−14.7607			−0.845198
$306$	4.12956	+	6.52684i	0.236071	+	0.373114i
$307$	−20.1863			−1.15209			−0.576046	−	0.817417i	$-0.695405\pi$
$307$	−20.1863			−1.15209			−0.576046	+	0.817417i	$0.695405\pi$
$308$	−7.72085	−	7.72085i	−0.439936	−	0.439936i
$309$	−8.94343	+	3.70449i	−0.508774	+	0.210741i
$310$			7.52992i			0.427671i
$311$	−12.3373	−	29.7849i	−0.699585	−	1.68895i	−0.724515	−	0.689259i	$-0.757936\pi$
$311$	−12.3373	−	29.7849i	−0.699585	−	1.68895i	0.0249300	−	0.999689i	$-0.492064\pi$
$312$	−3.32906	−	1.37894i	−0.188471	−	0.0780672i
$313$	−0.590112	+	1.42466i	−0.0333551	+	0.0805264i	−0.939679	−	0.342057i	$-0.888877\pi$
$313$	−0.590112	+	1.42466i	−0.0333551	+	0.0805264i	0.906324	+	0.422583i	$0.138877\pi$
$314$	3.80646	−	3.80646i	0.214811	−	0.214811i
$315$	2.62503	−	2.62503i	0.147904	−	0.147904i
$316$	0.494772	−	1.19449i	0.0278331	−	0.0671951i
$317$	24.8823	+	10.3066i	1.39753	+	0.578875i	0.949109	−	0.314948i	$-0.101987\pi$
$317$	24.8823	+	10.3066i	1.39753	+	0.578875i	0.448420	+	0.893823i	$0.351987\pi$
$318$	2.02681	+	4.89315i	0.113658	+	0.274394i
$319$		−	26.7373i		−	1.49700i
$320$	0.923880	−	0.382683i	0.0516464	−	0.0213927i
$321$	−9.18232	−	9.18232i	−0.512507	−	0.512507i
$322$	−4.16249			−0.231966
$323$	1.90394	−	8.46344i	0.105938	−	0.470919i
$324$	0.128685			0.00714918
$325$	2.40034	+	2.40034i	0.133147	+	0.133147i
$326$	16.4436	−	6.81116i	0.910727	−	0.377235i
$327$		−	4.16873i		−	0.230531i
$328$	2.80101	+	6.76223i	0.154660	+	0.373382i
$329$	1.75617	+	0.727428i	0.0968206	+	0.0401044i
$330$	2.23810	−	5.40325i	0.123203	−	0.297439i
$331$	−21.1198	+	21.1198i	−1.16085	+	1.16085i	−0.176560	+	0.984290i	$0.556497\pi$
$331$	−21.1198	+	21.1198i	−1.16085	+	1.16085i	−0.984290	+	0.176560i	$0.943503\pi$
$332$	1.36223	−	1.36223i	0.0747621	−	0.0747621i
$333$	−5.09026	+	12.2890i	−0.278945	+	0.673432i
$334$	−0.571853	−	0.236869i	−0.0312904	−	0.0129609i
$335$	−4.18174	−	10.0956i	−0.228473	−	0.551582i
$336$			2.10366i			0.114764i
$337$	−0.678917	+	0.281217i	−0.0369830	+	0.0153189i	−0.401098	−	0.916035i	$-0.631371\pi$
$337$	−0.678917	+	0.281217i	−0.0369830	+	0.0153189i	0.364115	+	0.931354i	$0.381371\pi$
$338$	1.04418	+	1.04418i	0.0567957	+	0.0567957i
$339$	2.56502			0.139313
$340$	3.37008	+	2.37541i	0.182768	+	0.128825i
$341$	41.4871			2.24665
$342$	−2.78689	−	2.78689i	−0.150698	−	0.150698i
$343$	−18.4421	+	7.63897i	−0.995780	+	0.412466i
$344$		−	11.2371i		−	0.605862i
$345$	−0.853203	−	2.05981i	−0.0459349	−	0.110897i
$346$	19.9059	+	8.24528i	1.07015	+	0.443269i
$347$	−10.5321	+	25.4267i	−0.565392	+	1.36498i	0.340010	+	0.940422i	$0.389569\pi$
$347$	−10.5321	+	25.4267i	−0.565392	+	1.36498i	−0.905402	+	0.424555i	$0.860431\pi$
$348$	−3.64248	+	3.64248i	−0.195257	+	0.195257i
$349$	23.9228	−	23.9228i	1.28056	−	1.28056i	0.340205	−	0.940351i	$-0.389504\pi$
$349$	23.9228	−	23.9228i	1.28056	−	1.28056i	0.940351	−	0.340205i	$-0.110496\pi$
$350$	0.758398	−	1.83094i	0.0405381	−	0.0978676i
$351$	−16.2233	−	6.71990i	−0.865934	−	0.358682i
$352$	−2.10844	−	5.09023i	−0.112380	−	0.271310i
$353$			8.60084i			0.457777i	0.973453	+	0.228888i	$0.0735091\pi$
$353$			8.60084i			0.457777i	−0.973453	+	0.228888i	$0.926491\pi$
$354$	−1.00283	+	0.415387i	−0.0533000	+	0.0220776i
$355$	0.470095	+	0.470095i	0.0249501	+	0.0249501i
$356$	14.7461			0.781543
$357$	−7.32971	+	4.63754i	−0.387929	+	0.245445i
$358$	−22.0607			−1.16594
$359$	11.1363	+	11.1363i	0.587752	+	0.587752i	0.937022	−	0.349270i	$-0.113571\pi$
$359$	11.1363	+	11.1363i	0.587752	+	0.587752i	−0.349270	+	0.937022i	$0.613571\pi$
$360$	1.73064	−	0.716854i	0.0912127	−	0.0377815i
$361$		−	14.5732i		−	0.767013i
$362$	−7.85013	−	18.9519i	−0.412594	−	0.996089i
$363$	−18.9823	−	7.86273i	−0.996312	−	0.412686i
$364$	−2.57446	+	6.21529i	−0.134938	+	0.325770i
$365$	−6.54466	+	6.54466i	−0.342563	+	0.342563i
$366$	11.0793	−	11.0793i	0.579122	−	0.579122i
$367$	7.33287	−	17.7031i	0.382773	−	0.924095i	−0.608655	−	0.793435i	$-0.708291\pi$
$367$	7.33287	−	17.7031i	0.382773	−	0.924095i	0.991427	−	0.130659i	$-0.0417095\pi$
$368$	−1.94049	−	0.803776i	−0.101155	−	0.0418997i
$369$	5.24693	+	12.6672i	0.273144	+	0.659429i
$370$			7.10083i			0.369155i
$371$	9.13542	−	3.78402i	0.474287	−	0.196456i
$372$	−5.65188	−	5.65188i	−0.293036	−	0.293036i
$373$	−37.0002			−1.91580			−0.957898	−	0.287109i	$-0.907306\pi$
$373$	−37.0002			−1.91580			−0.957898	+	0.287109i	$0.907306\pi$
$374$	13.0876	−	18.5679i	0.676746	−	0.960122i
$375$	1.06149			0.0548153
$376$	0.678231	+	0.678231i	0.0349771	+	0.0349771i
$377$	−15.2194	+	6.30410i	−0.783841	+	0.324678i
$378$			10.2516i			0.527286i
$379$	−8.79923	−	21.2432i	−0.451986	−	1.09119i	−0.971566	−	0.236769i	$-0.923912\pi$
$379$	−8.79923	−	21.2432i	−0.451986	−	1.09119i	0.519580	−	0.854422i	$-0.326088\pi$
$380$	−1.94383	−	0.805161i	−0.0997164	−	0.0413039i
$381$	−5.04142	+	12.1711i	−0.258280	+	0.623542i
$382$	14.7123	−	14.7123i	0.752744	−	0.752744i
$383$	4.50999	−	4.50999i	0.230450	−	0.230450i	−0.582431	−	0.812880i	$-0.697898\pi$
$383$	4.50999	−	4.50999i	0.230450	−	0.230450i	0.812880	+	0.582431i	$0.197898\pi$
$384$	−0.406216	+	0.980692i	−0.0207296	+	0.0500458i
$385$	−10.0878	−	4.17849i	−0.514121	−	0.212956i
$386$	−0.360891	−	0.871268i	−0.0183689	−	0.0443464i
$387$		−	21.0496i		−	1.07001i
$388$	5.96646	−	2.47139i	0.302901	−	0.125466i
$389$	2.52434	+	2.52434i	0.127989	+	0.127989i	0.768199	−	0.640211i	$-0.221153\pi$
$389$	2.52434	+	2.52434i	0.127989	+	0.127989i	−0.640211	+	0.768199i	$0.721153\pi$
$390$	−3.60335			−0.182463
$391$	−1.47726	−	8.53311i	−0.0747083	−	0.431538i
$392$	−3.07251			−0.155185
$393$	11.7291	+	11.7291i	0.591655	+	0.591655i
$394$	−6.95665	+	2.88154i	−0.350471	+	0.145170i
$395$		−	1.29290i		−	0.0650530i
$396$	−3.94960	−	9.53518i	−0.198475	−	0.479161i
$397$	−1.16269	−	0.481601i	−0.0583536	−	0.0241708i	0.353316	−	0.935504i	$-0.385054\pi$
$397$	−1.16269	−	0.481601i	−0.0583536	−	0.0241708i	−0.411669	+	0.911333i	$0.635054\pi$
$398$	−4.95469	+	11.9617i	−0.248356	+	0.599585i
$399$	3.12970	−	3.12970i	0.156681	−	0.156681i
$400$	0.707107	−	0.707107i	0.0353553	−	0.0353553i
$401$	0.518027	−	1.25063i	0.0258690	−	0.0624534i	−0.910417	−	0.413691i	$-0.864239\pi$
$401$	0.518027	−	1.25063i	0.0258690	−	0.0624534i	0.936286	+	0.351238i	$0.114239\pi$
$402$	10.7164	+	4.43889i	0.534487	+	0.221392i
$403$	−9.78180	−	23.6154i	−0.487266	−	1.17636i
$404$		−	4.10929i		−	0.204445i
$405$	0.118890	−	0.0492457i	0.00590767	−	0.00244704i
$406$	6.80044	+	6.80044i	0.337500	+	0.337500i
$407$	39.1229			1.93925
$408$	−4.31250	+	0.746585i	−0.213501	+	0.0369615i
$409$	17.5855			0.869545			0.434772	−	0.900540i	$-0.356829\pi$
$409$	17.5855			0.869545			0.434772	+	0.900540i	$0.356829\pi$
$410$	5.17559	+	5.17559i	0.255604	+	0.255604i
$411$	15.1137	−	6.26029i	0.745502	−	0.308797i
$412$			9.11950i			0.449286i
$413$	0.775521	+	1.87227i	0.0381609	+	0.0921285i
$414$	−3.63498	−	1.50566i	−0.178649	−	0.0739990i
$415$	0.737234	−	1.77984i	0.0361894	−	0.0873689i
$416$	−2.40034	+	2.40034i	−0.117687	+	0.117687i
$417$	8.85085	−	8.85085i	0.433428	−	0.433428i
$418$	−4.43614	+	10.7098i	−0.216979	+	0.523833i
$419$	8.62951	+	3.57446i	0.421579	+	0.174624i	0.583379	−	0.812200i	$-0.301730\pi$
$419$	8.62951	+	3.57446i	0.421579	+	0.174624i	−0.161800	+	0.986824i	$0.551730\pi$
$420$	0.805035	+	1.94353i	0.0392817	+	0.0948344i
$421$			22.9324i			1.11766i	0.829283	+	0.558830i	$0.188749\pi$
$421$			22.9324i			1.11766i	−0.829283	+	0.558830i	$0.811251\pi$
$422$	−12.4497	+	5.15683i	−0.606042	+	0.251031i
$423$	1.27048	+	1.27048i	0.0617730	+	0.0617730i
$424$	4.98948			0.242311
$425$	4.02258	+	0.904922i	0.195124	+	0.0438951i
$426$	−0.705697			−0.0341911
$427$	−20.6848	−	20.6848i	−1.00101	−	1.00101i
$428$	−11.3023	+	4.68155i	−0.546315	+	0.226291i
$429$			19.8531i			0.958517i
$430$	−4.30024	−	10.3817i	−0.207376	−	0.500650i
$431$	29.9233	+	12.3946i	1.44136	+	0.597029i	0.960127	−	0.279566i	$-0.0901905\pi$
$431$	29.9233	+	12.3946i	1.44136	+	0.597029i	0.481229	+	0.876595i	$0.340191\pi$
$432$	−1.97958	+	4.77914i	−0.0952428	+	0.229937i
$433$	−4.62412	+	4.62412i	−0.222221	+	0.222221i	−0.809433	−	0.587212i	$-0.800225\pi$
$433$	−4.62412	+	4.62412i	−0.222221	+	0.222221i	0.587212	+	0.809433i	$0.300225\pi$
$434$	−10.5520	+	10.5520i	−0.506510	+	0.506510i
$435$	−1.97130	+	4.75913i	−0.0945164	+	0.228183i
$436$	−3.62829	−	1.50289i	−0.173763	−	0.0719752i
$437$	1.69113	+	4.08276i	0.0808979	+	0.195305i
$438$		−	9.82471i		−	0.469443i
$439$	−28.9599	+	11.9956i	−1.38218	+	0.572519i	−0.945064	−	0.326885i	$-0.894001\pi$
$439$	−28.9599	+	11.9956i	−1.38218	+	0.572519i	−0.437118	+	0.899404i	$0.644001\pi$
$440$	−3.89590	−	3.89590i	−0.185730	−	0.185730i
$441$	−5.75552			−0.274072
$442$	−13.6550	−	3.07185i	−0.649504	−	0.146113i
$443$	36.6924			1.74331			0.871655	−	0.490120i	$-0.163047\pi$
$443$	36.6924			1.74331			0.871655	+	0.490120i	$0.163047\pi$
$444$	−5.32981	−	5.32981i	−0.252942	−	0.252942i
$445$	13.6236	−	5.64310i	0.645823	−	0.267508i
$446$			5.03740i			0.238528i
$447$	7.20584	+	17.3964i	0.340824	+	0.822823i
$448$	1.83094	+	0.758398i	0.0865036	+	0.0358309i
$449$	14.9498	−	36.0921i	0.705527	−	1.70329i	−0.00535989	−	0.999986i	$-0.501706\pi$
$449$	14.9498	−	36.0921i	0.705527	−	1.70329i	0.710887	−	0.703307i	$-0.248294\pi$
$450$	1.32457	−	1.32457i	0.0624410	−	0.0624410i
$451$	28.5156	−	28.5156i	1.34275	−	1.34275i
$452$	0.924725	−	2.23248i	0.0434954	−	0.105007i
$453$	−2.05017	−	0.849210i	−0.0963256	−	0.0398994i
$454$	1.01171	+	2.44249i	0.0474820	+	0.114632i
$455$			6.72739i			0.315385i
$456$	2.06336	−	0.854673i	0.0966258	−	0.0400237i
$457$	20.1430	+	20.1430i	0.942249	+	0.942249i	0.998421	−	0.0561719i	$-0.0178895\pi$
$457$	20.1430	+	20.1430i	0.942249	+	0.942249i	−0.0561719	+	0.998421i	$0.517889\pi$
$458$	12.8356			0.599770
$459$	−21.0158	+	3.63828i	−0.980935	+	0.169820i
$460$	−2.10037			−0.0979301
$461$	13.5676	+	13.5676i	0.631906	+	0.631906i	0.948546	−	0.316640i	$-0.102555\pi$
$461$	13.5676	+	13.5676i	0.631906	+	0.631906i	−0.316640	+	0.948546i	$0.602555\pi$
$462$	10.7081	−	4.43544i	0.498186	−	0.206356i
$463$			17.6152i			0.818649i	0.912389	+	0.409324i	$0.134236\pi$
$463$			17.6152i			0.818649i	−0.912389	+	0.409324i	$0.865764\pi$
$464$	1.85710	+	4.48343i	0.0862135	+	0.208138i
$465$	−7.38454	−	3.05878i	−0.342450	−	0.141847i
$466$	−6.68454	+	16.1379i	−0.309655	+	0.747574i
$467$	−18.5150	+	18.5150i	−0.856772	+	0.856772i	−0.990956	−	0.134185i	$-0.957158\pi$
$467$	−18.5150	+	18.5150i	−0.856772	+	0.856772i	0.134185	+	0.990956i	$0.457158\pi$
$468$	−4.49640	+	4.49640i	−0.207846	+	0.207846i
$469$	8.28733	−	20.0074i	0.382673	−	0.923855i
$470$	0.886152	+	0.367056i	0.0408751	+	0.0169310i
$471$	2.18672	+	5.27921i	0.100759	+	0.243253i
$472$			1.02258i			0.0470679i
$473$	−57.1993	+	23.6927i	−2.63003	+	1.08939i
$474$	0.970439	+	0.970439i	0.0445738	+	0.0445738i
$475$	−2.10399			−0.0965375
$476$	1.39386	+	8.05137i	0.0638875	+	0.369034i
$477$	9.34645			0.427945
$478$	−5.73103	−	5.73103i	−0.262131	−	0.262131i
$479$	18.8147	−	7.79330i	0.859665	−	0.356085i	0.0910888	−	0.995843i	$-0.470965\pi$
$479$	18.8147	−	7.79330i	0.859665	−	0.356085i	0.768577	+	0.639758i	$0.220965\pi$
$480$			1.06149i			0.0484503i
$481$	−9.22439	−	22.2696i	−0.420596	−	1.01541i
$482$	−6.97258	−	2.88814i	−0.317592	−	0.131551i
$483$	1.69087	−	4.08212i	0.0769372	−	0.185743i
$484$	−13.6868	+	13.6868i	−0.622126	+	0.622126i
$485$	4.56653	−	4.56653i	0.207356	−	0.207356i
$486$	−5.99103	+	14.4636i	−0.271759	+	0.656083i
$487$	12.0750	+	5.00165i	0.547173	+	0.226646i	0.639106	−	0.769119i	$-0.279305\pi$
$487$	12.0750	+	5.00165i	0.547173	+	0.226646i	−0.0919331	+	0.995765i	$0.529305\pi$
$488$	−5.64869	−	13.6371i	−0.255704	−	0.617325i
$489$			18.8929i			0.854367i
$490$	−2.83863	+	1.17580i	−0.128236	+	0.0531171i
$491$	−6.48279	−	6.48279i	−0.292564	−	0.292564i	0.545528	−	0.838092i	$-0.316329\pi$
$491$	−6.48279	−	6.48279i	−0.292564	−	0.292564i	−0.838092	+	0.545528i	$0.816329\pi$
$492$	−7.76948			−0.350275
$493$	−11.5275	+	16.3544i	−0.519171	+	0.736565i
$494$	7.14219			0.321342
$495$	−7.29791	−	7.29791i	−0.328017	−	0.328017i
$496$	−6.95674	+	2.88158i	−0.312367	+	0.129387i
$497$			1.31752i			0.0590990i
$498$	0.782569	+	1.88929i	0.0350678	+	0.0846611i
$499$	17.6004	+	7.29034i	0.787904	+	0.326361i	0.740101	−	0.672496i	$-0.234778\pi$
$499$	17.6004	+	7.29034i	0.787904	+	0.326361i	0.0478036	+	0.998857i	$0.484778\pi$
$500$	0.382683	−	0.923880i	0.0171141	−	0.0413171i
$501$	0.464592	−	0.464592i	0.0207564	−	0.0207564i
$502$	−9.48135	+	9.48135i	−0.423173	+	0.423173i
$503$	2.69203	−	6.49913i	0.120032	−	0.289782i	−0.852432	−	0.522839i	$-0.824873\pi$
$503$	2.69203	−	6.49913i	0.120032	−	0.289782i	0.972463	+	0.233057i	$0.0748729\pi$
$504$	3.42976	+	1.42065i	0.152774	+	0.0632810i
$505$	−1.57256	−	3.79649i	−0.0699779	−	0.168941i
$506$			11.5722i			0.514449i
$507$	−1.44818	+	0.599855i	−0.0643158	+	0.0266405i
$508$	8.77568	+	8.77568i	0.389358	+	0.389358i
$509$	−39.7595			−1.76231			−0.881155	−	0.472827i	$-0.843234\pi$
$509$	−39.7595			−1.76231			−0.881155	+	0.472827i	$0.843234\pi$
$510$	−3.69853	+	2.34008i	−0.163774	+	0.103620i
$511$	−18.3426			−0.811427
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	10.0552	−	4.16502i	0.443950	−	0.183890i
$514$		−	12.3053i		−	0.542764i
$515$	3.48988	+	8.42532i	0.153783	+	0.371264i
$516$	11.0201	+	4.56468i	0.485133	+	0.200949i
$517$	2.02234	−	4.88237i	0.0889425	−	0.214726i
$518$	−9.95066	+	9.95066i	−0.437207	+	0.437207i
$519$	−16.1722	+	16.1722i	−0.709879	+	0.709879i
$520$	−1.29906	+	3.13620i	−0.0569674	+	0.137532i
$521$	−7.79046	−	3.22692i	−0.341306	−	0.141374i	0.205445	−	0.978669i	$-0.434136\pi$
$521$	−7.79046	−	3.22692i	−0.341306	−	0.141374i	−0.546752	+	0.837295i	$0.684136\pi$
$522$	3.47877	+	8.39849i	0.152262	+	0.367592i
$523$			31.0329i			1.35698i	0.734612	+	0.678488i	$0.237364\pi$
$523$			31.0329i			1.35698i	−0.734612	+	0.678488i	$0.762636\pi$
$524$	14.4370	−	5.98001i	0.630684	−	0.261238i
$525$	1.48751	+	1.48751i	0.0649203	+	0.0649203i
$526$	2.98586			0.130190
$527$	−25.3764	−	17.8867i	−1.10541	−	0.779155i
$528$	5.84844			0.254521
$529$	−13.1440	−	13.1440i	−0.571479	−	0.571479i
$530$	4.60968	−	1.90939i	0.200232	−	0.0829387i
$531$			1.91552i			0.0831266i
$532$	−1.59566	−	3.85226i	−0.0691806	−	0.167017i
$533$	−22.9551	−	9.50830i	−0.994294	−	0.411850i
$534$	−5.99011	+	14.4614i	−0.259218	+	0.625807i
$535$	−8.65037	+	8.65037i	−0.373988	+	0.373988i
$536$	7.72685	−	7.72685i	0.333749	−	0.333749i
$537$	8.96140	−	21.6347i	0.386713	−	0.933607i
$538$	5.95467	+	2.46651i	0.256724	+	0.106339i
$539$	6.47821	+	15.6398i	0.279036	+	0.673653i
$540$			5.17290i			0.222606i
$541$	33.5807	−	13.9096i	1.44375	−	0.598020i	0.483044	−	0.875596i	$-0.339531\pi$
$541$	33.5807	−	13.9096i	1.44375	−	0.598020i	0.960704	+	0.277576i	$0.0895312\pi$
$542$	−3.86549	−	3.86549i	−0.166037	−	0.166037i
$543$	21.7748			0.934447
$544$	−0.904922	+	4.02258i	−0.0387982	+	0.172467i
$545$	−3.92723			−0.168224
$546$	−5.04950	−	5.04950i	−0.216099	−	0.216099i
$547$	14.7662	−	6.11635i	0.631356	−	0.261516i	−0.0439732	−	0.999033i	$-0.514002\pi$
$547$	14.7662	−	6.11635i	0.631356	−	0.261516i	0.675329	+	0.737517i	$0.264002\pi$
$548$		−	15.4112i		−	0.658335i
$549$	−10.5813	−	25.5455i	−0.451599	−	1.09026i
$550$	−5.09023	−	2.10844i	−0.217048	−	0.0899044i
$551$	3.90730	−	9.43307i	0.166457	−	0.401862i
$552$	1.57651	−	1.57651i	0.0671009	−	0.0671009i
$553$	1.81179	−	1.81179i	0.0770453	−	0.0770453i
$554$	−4.29248	+	10.3630i	−0.182370	+	0.440280i
$555$	−6.96373	−	2.88447i	−0.295594	−	0.122439i
$556$	−4.51255	−	10.8943i	−0.191375	−	0.462020i
$557$		−	6.46452i		−	0.273911i	−0.990577	−	0.136955i	$-0.956268\pi$
$557$		−	6.46452i		−	0.273911i	0.990577	−	0.136955i	$-0.0437317\pi$
$558$	−13.0316	+	5.39786i	−0.551671	+	0.228510i
$559$	26.9728	+	26.9728i	1.14083	+	1.14083i
$560$	1.98179			0.0837459
$561$	12.8930	+	20.3775i	0.544341	+	0.860340i
$562$	−25.0041			−1.05474
$563$	−20.4557	−	20.4557i	−0.862107	−	0.862107i	0.129476	−	0.991583i	$-0.458671\pi$
$563$	−20.4557	−	20.4557i	−0.862107	−	0.862107i	−0.991583	+	0.129476i	$0.958671\pi$
$564$	−0.940645	+	0.389628i	−0.0396083	+	0.0164063i
$565$		−	2.41642i		−	0.101660i
$566$	−6.95853	−	16.7994i	−0.292489	−	0.706130i
$567$	0.235614	+	0.0975946i	0.00989487	+	0.00409859i
$568$	−0.254414	+	0.614209i	−0.0106750	+	0.0257716i
$569$	26.1230	−	26.1230i	1.09513	−	1.09513i	0.100164	−	0.994971i	$-0.468063\pi$
$569$	26.1230	−	26.1230i	1.09513	−	1.09513i	0.994971	−	0.100164i	$-0.0319367\pi$
$570$	1.57923	−	1.57923i	0.0661467	−	0.0661467i
$571$	−10.6642	+	25.7456i	−0.446282	+	1.07742i	0.527422	+	0.849603i	$0.323159\pi$
$571$	−10.6642	+	25.7456i	−0.446282	+	1.07742i	−0.973704	+	0.227817i	$0.926841\pi$
$572$	17.2793	+	7.15732i	0.722484	+	0.299263i
$573$	8.45184	+	20.4046i	0.353081	+	0.852412i
$574$			14.5055i			0.605447i
$575$	−1.94049	+	0.803776i	−0.0809239	+	0.0335198i
$576$	1.32457	+	1.32457i	0.0551906	+	0.0551906i
$577$	47.6984			1.98571			0.992856	−	0.119322i	$-0.0380721\pi$
$577$	47.6984			1.98571			0.992856	+	0.119322i	$0.0380721\pi$
$578$	−16.0106	+	5.71484i	−0.665955	+	0.237706i
$579$	1.00105			0.0416020
$580$	3.43147	+	3.43147i	0.142484	+	0.142484i
$581$	3.52727	−	1.46104i	0.146336	−	0.0606143i
$582$			6.85519i			0.284157i
$583$	−10.5200	−	25.3976i	−0.435696	−	1.05186i
$584$	−8.55102	−	3.54195i	−0.353844	−	0.146567i
$585$	−2.43343	+	5.87483i	−0.100610	+	0.242894i
$586$	2.23958	−	2.23958i	0.0925163	−	0.0925163i
$587$	−16.7656	+	16.7656i	−0.691990	+	0.691990i	−0.962670	−	0.270679i	$-0.912752\pi$
$587$	−16.7656	+	16.7656i	−0.691990	+	0.691990i	0.270679	+	0.962670i	$0.412752\pi$
$588$	1.24810	−	3.01319i	0.0514709	−	0.124262i
$589$	14.6369	+	6.06280i	0.603102	+	0.249813i
$590$	0.391323	+	0.944738i	0.0161105	+	0.0388943i
$591$		−	7.99286i		−	0.328782i
$592$	−6.56031	+	2.71737i	−0.269627	+	0.111683i
$593$	−10.0830	−	10.0830i	−0.414057	−	0.414057i	0.469092	−	0.883149i	$-0.344581\pi$
$593$	−10.0830	−	10.0830i	−0.414057	−	0.414057i	−0.883149	+	0.469092i	$0.844581\pi$
$594$	28.5008			1.16940
$595$	4.36888	+	6.90509i	0.179107	+	0.283081i
$596$	17.7389			0.726614
$597$	−9.71806	−	9.71806i	−0.397734	−	0.397734i
$598$	6.58718	−	2.72850i	0.269370	−	0.111577i
$599$			4.30801i			0.176021i	0.996120	+	0.0880103i	$0.0280508\pi$
$599$			4.30801i			0.176021i	−0.996120	+	0.0880103i	$0.971949\pi$
$600$	0.406216	+	0.980692i	0.0165837	+	0.0400366i
$601$	−19.2090	−	7.95664i	−0.783553	−	0.324558i	−0.0452046	−	0.998978i	$-0.514394\pi$
$601$	−19.2090	−	7.95664i	−0.783553	−	0.324558i	−0.738348	+	0.674419i	$0.764394\pi$
$602$	8.52217	−	20.5743i	0.347338	−	0.838547i
$603$	14.4742	−	14.4742i	0.589434	−	0.589434i
$604$	−1.47823	+	1.47823i	−0.0601484	+	0.0601484i
$605$	−7.40723	+	17.8826i	−0.301147	+	0.727032i
$606$	4.02995	+	1.66926i	0.163705	+	0.0678090i
$607$	9.52861	+	23.0041i	0.386755	+	0.933708i	0.990623	+	0.136624i	$0.0436252\pi$
$607$	9.52861	+	23.0041i	0.386755	+	0.933708i	−0.603868	+	0.797084i	$0.706375\pi$
$608$		−	2.10399i		−	0.0853279i
$609$	−9.43160	+	3.90669i	−0.382188	+	0.158307i
$610$	−10.4374	−	10.4374i	−0.422599	−	0.422599i
$611$	−3.25598			−0.131723
$612$	−1.69513	+	7.53521i	−0.0685214	+	0.304593i
$613$	19.4614			0.786040			0.393020	−	0.919530i	$-0.371430\pi$
$613$	19.4614			0.786040			0.393020	+	0.919530i	$0.371430\pi$
$614$	−14.2739	−	14.2739i	−0.576046	−	0.576046i
$615$	−7.17806	+	2.97325i	−0.289447	+	0.119893i
$616$		−	10.9189i		−	0.439936i
$617$	12.7195	+	30.7075i	0.512067	+	1.23624i	0.942679	+	0.333702i	$0.108298\pi$
$617$	12.7195	+	30.7075i	0.512067	+	1.23624i	−0.430612	+	0.902537i	$0.641702\pi$
$618$	−8.94343	−	3.70449i	−0.359758	−	0.149016i
$619$	−6.97953	+	16.8501i	−0.280531	+	0.677261i	−0.999848	−	0.0174203i	$-0.994455\pi$
$619$	−6.97953	+	16.8501i	−0.280531	+	0.677261i	0.719317	+	0.694682i	$0.244455\pi$
$620$	−5.32446	+	5.32446i	−0.213835	+	0.213835i
$621$	7.68272	−	7.68272i	0.308297	−	0.308297i
$622$	12.3373	−	29.7849i	0.494681	−	1.19427i
$623$	26.9992	+	11.1834i	1.08170	+	0.448055i
$624$	−1.37894	−	3.32906i	−0.0552018	−	0.133269i
$625$		−	1.00000i		−	0.0400000i
$626$	−1.42466	+	0.590112i	−0.0569408	+	0.0235856i
$627$	−8.70097	−	8.70097i	−0.347483	−	0.347483i
$628$	5.38314			0.214811
$629$	−23.9303	−	16.8674i	−0.954165	−	0.672547i
$630$	3.71235			0.147904
$631$	−16.3691	−	16.3691i	−0.651643	−	0.651643i	0.301746	−	0.953388i	$-0.402431\pi$
$631$	−16.3691	−	16.3691i	−0.651643	−	0.651643i	−0.953388	+	0.301746i	$0.902431\pi$
$632$	1.19449	−	0.494772i	0.0475141	−	0.0196810i
$633$		−	14.3041i		−	0.568537i
$634$	10.3066	+	24.8823i	0.409327	+	0.988202i
$635$	11.4660	+	4.74936i	0.455013	+	0.188473i
$636$	−2.02681	+	4.89315i	−0.0803682	+	0.194026i
$637$	7.37508	−	7.37508i	0.292211	−	0.292211i
$638$	18.9061	−	18.9061i	0.748500	−	0.748500i
$639$	−0.476576	+	1.15056i	−0.0188530	+	0.0455153i
$640$	0.923880	+	0.382683i	0.0365195	+	0.0151269i
$641$	−6.95241	−	16.7846i	−0.274604	−	0.662952i	0.725065	−	0.688680i	$-0.241810\pi$
$641$	−6.95241	−	16.7846i	−0.274604	−	0.662952i	−0.999669	+	0.0257282i	$0.991810\pi$
$642$		−	12.9858i		−	0.512507i
$643$	0.263485	−	0.109139i	0.0103908	−	0.00430403i	−0.377482	−	0.926017i	$-0.623210\pi$
$643$	0.263485	−	0.109139i	0.0103908	−	0.00430403i	0.387873	+	0.921713i	$0.373210\pi$
$644$	−2.94332	−	2.94332i	−0.115983	−	0.115983i
$645$	11.9281			0.469667
$646$	7.33085	−	4.63827i	0.288428	−	0.182490i
$647$	33.0088			1.29771			0.648854	−	0.760913i	$-0.275249\pi$
$647$	33.0088			1.29771			0.648854	+	0.760913i	$0.275249\pi$
$648$	0.0909942	+	0.0909942i	0.00357459	+	0.00357459i
$649$	5.20516	−	2.15605i	0.204320	−	0.0846322i
$650$			3.39460i			0.133147i
$651$	−6.06185	−	14.6346i	−0.237583	−	0.573575i
$652$	16.4436	+	6.81116i	0.643981	+	0.266746i
$653$	9.28603	−	22.4185i	0.363391	−	0.877302i	−0.631409	−	0.775450i	$-0.717523\pi$
$653$	9.28603	−	22.4185i	0.363391	−	0.877302i	0.994800	−	0.101852i	$-0.0324770\pi$
$654$	2.94774	−	2.94774i	0.115266	−	0.115266i
$655$	11.0496	−	11.0496i	0.431744	−	0.431744i
$656$	−2.80101	+	6.76223i	−0.109361	+	0.264021i
$657$	−16.0180	−	6.63488i	−0.624923	−	0.258851i
$658$	0.727428	+	1.75617i	0.0283581	+	0.0684625i
$659$			10.1667i			0.396037i	0.980198	+	0.198018i	$0.0634506\pi$
$659$			10.1667i			0.396037i	−0.980198	+	0.198018i	$0.936549\pi$
$660$	5.40325	−	2.23810i	0.210321	−	0.0871179i
$661$	−26.3725	−	26.3725i	−1.02577	−	1.02577i	−0.999659	−	0.0261133i	$-0.991687\pi$
$661$	−26.3725	−	26.3725i	−1.02577	−	1.02577i	−0.0261133	−	0.999659i	$-0.508313\pi$
$662$	−29.8679			−1.16085
$663$	8.55943	−	12.1436i	0.332421	−	0.471617i
$664$	1.92649			0.0747621
$665$	−2.94839	−	2.94839i	−0.114334	−	0.114334i
$666$	−12.2890	+	5.09026i	−0.476188	+	0.197244i
$667$		−	10.1927i		−	0.394664i
$668$	−0.236869	−	0.571853i	−0.00916475	−	0.0221257i
$669$	−4.94014	−	2.04627i	−0.190997	−	0.0791135i
$670$	4.18174	−	10.0956i	0.161555	−	0.390028i
$671$	−57.5063	+	57.5063i	−2.22001	+	2.22001i
$672$	−1.48751	+	1.48751i	−0.0573820	+	0.0573820i
$673$	5.12842	−	12.3811i	0.197686	−	0.477256i	−0.793687	−	0.608326i	$-0.791841\pi$
$673$	5.12842	−	12.3811i	0.197686	−	0.477256i	0.991373	+	0.131070i	$0.0418413\pi$
$674$	−0.678917	−	0.281217i	−0.0261509	−	0.0108321i
$675$	1.97958	+	4.77914i	0.0761943	+	0.183949i
$676$			1.47669i			0.0567957i
$677$	−44.2308	+	18.3210i	−1.69993	+	0.704134i	−0.999950	−	0.0100294i	$-0.996807\pi$
$677$	−44.2308	+	18.3210i	−1.69993	+	0.704134i	−0.699979	+	0.714163i	$0.746807\pi$
$678$	1.81374	+	1.81374i	0.0696563	+	0.0696563i
$679$	12.7985			0.491162
$680$	0.703335	+	4.06267i	0.0269716	+	0.155796i
$681$	−2.80631			−0.107538
$682$	29.3358	+	29.3358i	1.12333	+	1.12333i
$683$	7.45575	−	3.08827i	0.285286	−	0.118169i	−0.235452	−	0.971886i	$-0.575657\pi$
$683$	7.45575	−	3.08827i	0.285286	−	0.118169i	0.520738	+	0.853717i	$0.325657\pi$
$684$		−	3.94125i		−	0.150698i
$685$	−5.89762	−	14.2381i	−0.225336	−	0.544010i
$686$	−18.4421	−	7.63897i	−0.704123	−	0.291657i
$687$	−5.21405	+	12.5878i	−0.198928	+	0.480255i
$688$	7.94580	−	7.94580i	0.302931	−	0.302931i
$689$	−11.9765	+	11.9765i	−0.456268	+	0.456268i
$690$	0.853203	−	2.05981i	0.0324809	−	0.0784158i
$691$	30.9832	+	12.8337i	1.17866	+	0.488216i	0.884045	−	0.467401i	$-0.154810\pi$
$691$	30.9832	+	12.8337i	1.17866	+	0.488216i	0.294612	+	0.955617i	$0.404810\pi$
$692$	8.24528	+	19.9059i	0.313438	+	0.756707i
$693$		−	20.4537i		−	0.776971i
$694$	−25.4267	+	10.5321i	−0.965184	+	0.399792i
$695$	−8.33811	−	8.33811i	−0.316282	−	0.316282i
$696$	−5.15124			−0.195257
$697$	−29.7363	+	5.14798i	−1.12634	+	0.194993i
$698$	33.8319			1.28056
$699$	−13.1110	−	13.1110i	−0.495902	−	0.495902i
$700$	1.83094	−	0.758398i	0.0692028	−	0.0286648i
$701$		−	8.74893i		−	0.330442i	−0.986257	−	0.165221i	$-0.947166\pi$
$701$		−	8.74893i		−	0.330442i	0.986257	−	0.165221i	$-0.0528338\pi$
$702$	−6.71990	−	16.2233i	−0.253626	−	0.612308i
$703$	13.8028	+	5.71731i	0.520583	+	0.215632i
$704$	2.10844	−	5.09023i	0.0794650	−	0.191845i
$705$	−0.719938	+	0.719938i	−0.0271144	+	0.0271144i
$706$	−6.08172	+	6.08172i	−0.228888	+	0.228888i
$707$	3.11648	−	7.52384i	0.117207	−	0.282963i
$708$	−1.00283	−	0.415387i	−0.0376888	−	0.0156112i
$709$	0.474224	+	1.14488i	0.0178098	+	0.0429968i	0.932534	−	0.361081i	$-0.117592\pi$
$709$	0.474224	+	1.14488i	0.0178098	+	0.0429968i	−0.914724	+	0.404078i	$0.867592\pi$
$710$			0.664815i			0.0249501i
$711$	2.23755	−	0.926823i	0.0839146	−	0.0347586i
$712$	10.4271	+	10.4271i	0.390772	+	0.390772i
$713$	15.8156			0.592299
$714$	−8.46212	−	1.90365i	−0.316687	−	0.0712421i
$715$	18.7030			0.699452
$716$	−15.5992	−	15.5992i	−0.582971	−	0.582971i
$717$	7.94841	−	3.29234i	0.296839	−	0.122955i
$718$			15.7491i			0.587752i
$719$	−0.754116	−	1.82060i	−0.0281238	−	0.0678969i	0.909194	−	0.416373i	$-0.136699\pi$
$719$	−0.754116	−	1.82060i	−0.0281238	−	0.0678969i	−0.937317	+	0.348477i	$0.886699\pi$
$720$	1.73064	+	0.716854i	0.0644971	+	0.0267156i
$721$	−6.91622	+	16.6972i	−0.257573	+	0.621837i
$722$	10.3048	−	10.3048i	0.383506	−	0.383506i
$723$	5.66475	−	5.66475i	0.210674	−	0.210674i
$724$	7.85013	−	18.9519i	0.291748	−	0.704342i
$725$	4.48343	+	1.85710i	0.166510	+	0.0689708i
$726$	−7.86273	−	18.9823i	−0.291813	−	0.704499i
$727$			5.07291i			0.188144i	0.995565	+	0.0940719i	$0.0299884\pi$
$727$			5.07291i			0.188144i	−0.995565	+	0.0940719i	$0.970012\pi$
$728$	−6.21529	+	2.57446i	−0.230354	+	0.0954158i
$729$	−11.4777	−	11.4777i	−0.425101	−	0.425101i
$730$	−9.25555			−0.342563
$731$	45.2019	+	10.1687i	1.67185	+	0.376101i
$732$	15.6684			0.579122
$733$	6.79670	+	6.79670i	0.251042	+	0.251042i	0.821398	−	0.570356i	$-0.193195\pi$
$733$	6.79670	+	6.79670i	0.251042	+	0.251042i	−0.570356	+	0.821398i	$0.693195\pi$
$734$	17.7031	−	7.33287i	0.653434	−	0.270661i
$735$		−	3.26145i		−	0.120300i
$736$	−0.803776	−	1.94049i	−0.0296276	−	0.0715273i
$737$	−55.6231	−	23.0398i	−2.04890	−	0.848683i
$738$	−5.24693	+	12.6672i	−0.193142	+	0.466287i
$739$	−3.06068	+	3.06068i	−0.112589	+	0.112589i	−0.761157	−	0.648568i	$-0.775368\pi$
$739$	−3.06068	+	3.06068i	−0.112589	+	0.112589i	0.648568	+	0.761157i	$0.275368\pi$
$740$	−5.02105	+	5.02105i	−0.184577	+	0.184577i
$741$	−2.90127	+	7.00429i	−0.106581	+	0.257309i
$742$	9.13542	+	3.78402i	0.335372	+	0.138916i
$743$	−1.29178	−	3.11864i	−0.0473909	−	0.114412i	0.898411	−	0.439155i	$-0.144722\pi$
$743$	−1.29178	−	3.11864i	−0.0473909	−	0.114412i	−0.945802	+	0.324743i	$0.894722\pi$
$744$		−	7.99297i		−	0.293036i
$745$	16.3886	−	6.78839i	0.600433	−	0.248707i
$746$	−26.1631	−	26.1631i	−0.957898	−	0.957898i
$747$	3.60875			0.132037
$748$	22.3838	−	3.87511i	0.818434	−	0.141688i
$749$	−24.2442			−0.885863
$750$	0.750590	+	0.750590i	0.0274077	+	0.0274077i
$751$	−4.11772	+	1.70561i	−0.150258	+	0.0622387i	−0.456545	−	0.889700i	$-0.650913\pi$
$751$	−4.11772	+	1.70561i	−0.150258	+	0.0622387i	0.306287	+	0.951939i	$0.400913\pi$
$752$			0.959164i			0.0349771i
$753$	−5.44681	−	13.1498i	−0.198493	−	0.479204i
$754$	−15.2194	−	6.30410i	−0.554259	−	0.229582i
$755$	−0.800014	+	1.93140i	−0.0291155	+	0.0702910i
$756$	−7.24898	+	7.24898i	−0.263643	+	0.263643i
$757$	−1.78569	+	1.78569i	−0.0649020	+	0.0649020i	−0.738813	−	0.673911i	$-0.764613\pi$
$757$	−1.78569	+	1.78569i	−0.0649020	+	0.0649020i	0.673911	+	0.738813i	$0.264613\pi$
$758$	8.79923	−	21.2432i	0.319602	−	0.771588i
$759$	−11.3488	−	4.70083i	−0.411936	−	0.170629i
$760$	−0.805161	−	1.94383i	−0.0292062	−	0.0705101i
$761$			45.3588i			1.64426i	0.569303	+	0.822128i	$0.307213\pi$
$761$			45.3588i			1.64426i	−0.569303	+	0.822128i	$0.692787\pi$
$762$	−12.1711	+	5.04142i	−0.440911	+	0.182631i
$763$	−5.50337	−	5.50337i	−0.199235	−	0.199235i
$764$	20.8063			0.752744
$765$	1.31751	+	7.61033i	0.0476346	+	0.275152i
$766$	6.37809			0.230450
$767$	−2.45454	−	2.45454i	−0.0886282	−	0.0886282i
$768$	−0.980692	+	0.406216i	−0.0353877	+	0.0146581i
$769$			9.41250i			0.339424i	0.985494	+	0.169712i	$0.0542837\pi$
$769$			9.41250i			0.339424i	−0.985494	+	0.169712i	$0.945716\pi$
$770$	−4.17849	−	10.0878i	−0.150582	−	0.363538i
$771$	12.0677	+	4.99862i	0.434609	+	0.180021i
$772$	0.360891	−	0.871268i	0.0129888	−	0.0313576i
$773$	−6.34812	+	6.34812i	−0.228326	+	0.228326i	−0.811993	−	0.583667i	$-0.801617\pi$
$773$	−6.34812	+	6.34812i	−0.228326	+	0.228326i	0.583667	+	0.811993i	$0.301617\pi$
$774$	14.8843	−	14.8843i	0.535006	−	0.535006i
$775$	−2.88158	+	6.95674i	−0.103509	+	0.249893i
$776$	5.96646	+	2.47139i	0.214184	+	0.0887177i
$777$	−5.71642	−	13.8007i	−0.205075	−	0.495096i
$778$			3.56995i			0.127989i
$779$	14.2276	−	5.89328i	0.509758	−	0.211149i
$780$	−2.54795	−	2.54795i	−0.0912313	−	0.0912313i
$781$	3.66288			0.131068
$782$	4.98924	−	7.07840i	0.178415	−	0.253123i
$783$	−25.1032			−0.897115
$784$	−2.17259	−	2.17259i	−0.0775926	−	0.0775926i
$785$	4.97338	−	2.06004i	0.177507	−	0.0735260i
$786$			16.5875i			0.591655i
$787$	−1.67451	−	4.04261i	−0.0596897	−	0.144104i	0.891221	−	0.453570i	$-0.149850\pi$
$787$	−1.67451	−	4.04261i	−0.0596897	−	0.144104i	−0.950910	+	0.309466i	$0.899850\pi$
$788$	−6.95665	−	2.88154i	−0.247820	−	0.102651i
$789$	−1.21290	+	2.92821i	−0.0431805	+	0.104247i
$790$	0.914220	−	0.914220i	0.0325265	−	0.0325265i
$791$	3.38622	−	3.38622i	0.120400	−	0.120400i
$792$	3.94960	−	9.53518i	0.140343	−	0.338818i
$793$	46.2927	+	19.1750i	1.64390	+	0.680926i
$794$	−0.481601	−	1.16269i	−0.0170914	−	0.0412622i
$795$			5.29631i			0.187841i
$796$	−11.9617	+	4.95469i	−0.423971	+	0.175614i
$797$	−32.0583	−	32.0583i	−1.13556	−	1.13556i	−0.989236	−	0.146328i	$-0.953254\pi$
$797$	−32.0583	−	32.0583i	−1.13556	−	1.13556i	−0.146328	−	0.989236i	$-0.546746\pi$
$798$	4.42607			0.156681
$799$	−3.34198	+	2.11449i	−0.118231	+	0.0748053i
$800$	1.00000			0.0353553
$801$	19.5323	+	19.5323i	0.690141	+	0.690141i
$802$	1.25063	−	0.518027i	0.0441612	−	0.0182922i
$803$			50.9947i			1.79956i
$804$	4.43889	+	10.7164i	0.156548	+	0.377939i
$805$	−3.84564	−	1.59292i	−0.135541	−	0.0561429i
$806$	9.78180	−	23.6154i	0.344549	−	0.831815i
$807$	−4.83777	+	4.83777i	−0.170297	+	0.170297i
$808$	2.90571	−	2.90571i	0.102222	−	0.102222i
$809$	−7.45094	+	17.9882i	−0.261961	+	0.632430i	−0.999060	−	0.0433550i	$-0.986195\pi$
$809$	−7.45094	+	17.9882i	−0.261961	+	0.632430i	0.737099	+	0.675785i	$0.236195\pi$
$810$	0.118890	+	0.0492457i	0.00417736	+	0.00173032i
$811$	8.78671	+	21.2130i	0.308543	+	0.744889i	0.999753	+	0.0222346i	$0.00707809\pi$
$811$	8.78671	+	21.2130i	0.308543	+	0.744889i	−0.691210	+	0.722654i	$0.742922\pi$
$812$			9.61728i			0.337500i
$813$	5.36108	−	2.22063i	0.188021	−	0.0778809i
$814$	27.6641	+	27.6641i	0.969626	+	0.969626i
$815$	17.7984			0.623452
$816$	−3.57732	−	2.52149i	−0.125231	−	0.0882696i
$817$	−23.6426			−0.827151
$818$	12.4348	+	12.4348i	0.434772	+	0.434772i
$819$	−11.6427	+	4.82256i	−0.406828	+	0.168514i
$820$			7.31938i			0.255604i
$821$	−10.5896	−	25.5656i	−0.369580	−	0.892245i	−0.993819	−	0.111011i	$-0.964591\pi$
$821$	−10.5896	−	25.5656i	−0.369580	−	0.892245i	0.624239	−	0.781233i	$-0.285409\pi$
$822$	15.1137	+	6.26029i	0.527150	+	0.218353i
$823$	−9.81637	+	23.6988i	−0.342177	+	0.826088i	0.655318	+	0.755353i	$0.272535\pi$
$823$	−9.81637	+	23.6988i	−0.342177	+	0.826088i	−0.997495	+	0.0707354i	$0.977465\pi$
$824$	−6.44846	+	6.44846i	−0.224643	+	0.224643i
$825$	4.13547	−	4.13547i	0.143979	−	0.143979i
$826$	−0.775521	+	1.87227i	−0.0269838	+	0.0651447i
$827$	6.62629	+	2.74470i	0.230419	+	0.0954426i	0.494906	−	0.868947i	$-0.335203\pi$
$827$	6.62629	+	2.74470i	0.230419	+	0.0954426i	−0.264487	+	0.964389i	$0.585203\pi$
$828$	−1.50566	−	3.63498i	−0.0523252	−	0.126324i
$829$			40.3624i			1.40184i	0.713238	+	0.700922i	$0.247228\pi$
$829$			40.3624i			1.40184i	−0.713238	+	0.700922i	$0.752772\pi$
$830$	1.77984	−	0.737234i	0.0617792	−	0.0255898i
$831$	−8.41920	−	8.41920i	−0.292059	−	0.292059i
$832$	−3.39460			−0.117687
$833$	2.78038	−	12.3594i	0.0963344	−	0.428228i
$834$	12.5170			0.433428
$835$	−0.437677	−	0.437677i	−0.0151464	−	0.0151464i
$836$	−10.7098	+	4.43614i	−0.370406	+	0.153427i
$837$		−	38.9516i		−	1.34636i
$838$	3.57446	+	8.62951i	0.123478	+	0.298101i
$839$	−12.6205	−	5.22757i	−0.435707	−	0.180476i	0.154039	−	0.988065i	$-0.450772\pi$
$839$	−12.6205	−	5.22757i	−0.435707	−	0.180476i	−0.589746	+	0.807589i	$0.700772\pi$
$840$	−0.805035	+	1.94353i	−0.0277763	+	0.0670580i
$841$	3.85379	−	3.85379i	0.132889	−	0.132889i
$842$	−16.2157	+	16.2157i	−0.558830	+	0.558830i
$843$	10.1571	−	24.5214i	0.349828	−	0.844561i
$844$	−12.4497	−	5.15683i	−0.428536	−	0.177505i
$845$	0.565104	+	1.36428i	0.0194402	+	0.0469327i
$846$			1.79673i			0.0617730i
$847$	−35.4396	+	14.6796i	−1.21772	+	0.504396i
$848$	3.52810	+	3.52810i	0.121155	+	0.121155i
$849$	19.3017			0.662432
$850$	2.20451	+	3.48427i	0.0756142	+	0.119509i
$851$	14.9144			0.511258
$852$	−0.499003	−	0.499003i	−0.0170956	−	0.0170956i
$853$	−18.5007	+	7.66323i	−0.633451	+	0.262384i	−0.676219	−	0.736701i	$-0.736382\pi$
$853$	−18.5007	+	7.66323i	−0.633451	+	0.262384i	0.0427677	+	0.999085i	$0.486382\pi$
$854$		−	29.2527i		−	1.00101i
$855$	−1.50825	−	3.64124i	−0.0515811	−	0.124528i
$856$	−11.3023	−	4.68155i	−0.386303	−	0.160012i
$857$	−5.90614	+	14.2587i	−0.201750	+	0.487067i	−0.992079	−	0.125615i	$-0.959910\pi$
$857$	−5.90614	+	14.2587i	−0.201750	+	0.487067i	0.790329	+	0.612682i	$0.209910\pi$
$858$	−14.0383	+	14.0383i	−0.479259	+	0.479259i
$859$	3.12637	−	3.12637i	0.106670	−	0.106670i	−0.651757	−	0.758428i	$-0.725968\pi$
$859$	3.12637	−	3.12637i	0.106670	−	0.106670i	0.758428	+	0.651757i	$0.225968\pi$
$860$	4.30024	−	10.3817i	0.146637	−	0.354013i
$861$	−14.2254	−	5.89236i	−0.484801	−	0.200811i
$862$	12.3946	+	29.9233i	0.422163	+	1.01919i
$863$			37.4831i			1.27594i	0.770061	+	0.637971i	$0.220226\pi$
$863$			37.4831i			1.27594i	−0.770061	+	0.637971i	$0.779774\pi$
$864$	−4.77914	+	1.97958i	−0.162590	+	0.0673468i
$865$	15.2353	+	15.2353i	0.518015	+	0.518015i
$866$	−6.53949			−0.222221
$867$	0.899282	−	18.0230i	0.0305412	−	0.612092i
$868$	−14.9227			−0.506510
$869$	−5.03701	−	5.03701i	−0.170869	−	0.170869i
$870$	−4.75913	+	1.97130i	−0.161350	+	0.0668332i
$871$			37.0942i			1.25689i
$872$	−1.50289	−	3.62829i	−0.0508941	−	0.122869i
$873$	11.1766	+	4.62948i	0.378269	+	0.156684i
$874$	−1.69113	+	4.08276i	−0.0572034	+	0.138101i
$875$	1.40134	−	1.40134i	0.0473738	−	0.0473738i
$876$	6.94712	−	6.94712i	0.234721	−	0.234721i
$877$	−19.1062	+	46.1265i	−0.645172	+	1.55758i	0.174443	+	0.984667i	$0.444187\pi$
$877$	−19.1062	+	46.1265i	−0.645172	+	1.55758i	−0.819615	+	0.572915i	$0.805813\pi$
$878$	−28.9599	−	11.9956i	−0.977350	−	0.404832i
$879$	1.28659	+	3.10610i	0.0433955	+	0.104766i
$880$		−	5.50963i		−	0.185730i
$881$	−16.8369	+	6.97405i	−0.567248	+	0.234962i	−0.647828	−	0.761786i	$-0.724323\pi$
$881$	−16.8369	+	6.97405i	−0.567248	+	0.234962i	0.0805804	+	0.996748i	$0.474323\pi$
$882$	−4.06977	−	4.06977i	−0.137036	−	0.137036i
$883$	−8.84410			−0.297628			−0.148814	−	0.988865i	$-0.547545\pi$
$883$	−8.84410			−0.297628			−0.148814	+	0.988865i	$0.547545\pi$
$884$	−7.48345	−	11.8277i	−0.251696	−	0.397808i
$885$	−1.08546			−0.0364873
$886$	25.9455	+	25.9455i	0.871655	+	0.871655i
$887$	1.66620	−	0.690164i	0.0559456	−	0.0231734i	−0.354535	−	0.935043i	$-0.615361\pi$
$887$	1.66620	−	0.690164i	0.0559456	−	0.0231734i	0.410481	+	0.911869i	$0.365361\pi$
$888$		−	7.53749i		−	0.252942i
$889$	9.41224	+	22.7232i	0.315676	+	0.762110i
$890$	13.6236	+	5.64310i	0.456666	+	0.189157i
$891$	0.271326	−	0.655038i	0.00908975	−	0.0219446i
$892$	−3.56198	+	3.56198i	−0.119264	+	0.119264i
$893$	1.42699	−	1.42699i	0.0477524	−	0.0477524i
$894$	−7.20584	+	17.3964i	−0.240999	+	0.581823i
$895$	−20.3814	−	8.44225i	−0.681275	−	0.282193i
$896$	0.758398	+	1.83094i	0.0253363	+	0.0611673i
$897$			7.56835i			0.252700i
$898$	36.0921	−	14.9498i	1.20441	−	0.498883i
$899$	−25.8387	−	25.8387i	−0.861768	−	0.861768i
$900$	1.87323			0.0624410
$901$	−4.51509	+	20.0706i	−0.150420	+	0.668648i
$902$	40.3271			1.34275
$903$	16.7153	+	16.7153i	0.556249	+	0.556249i
$904$	2.23248	−	0.924725i	0.0742513	−	0.0307559i
$905$		−	20.5134i		−	0.681888i
$906$	−0.849210	−	2.05017i	−0.0282131	−	0.0681125i
$907$	4.77963	+	1.97979i	0.158705	+	0.0657378i	0.460622	−	0.887597i	$-0.347626\pi$
$907$	4.77963	+	1.97979i	0.158705	+	0.0657378i	−0.301917	+	0.953334i	$0.597626\pi$
$908$	−1.01171	+	2.44249i	−0.0335749	+	0.0810569i
$909$	5.44306	−	5.44306i	0.180535	−	0.180535i
$910$	−4.75698	+	4.75698i	−0.157692	+	0.157692i
$911$	−8.94080	+	21.5850i	−0.296222	+	0.715143i	0.703767	+	0.710431i	$0.251500\pi$
$911$	−8.94080	+	21.5850i	−0.296222	+	0.715143i	−0.999989	+	0.00471208i	$0.998500\pi$
$912$	2.06336	+	0.854673i	0.0683248	+	0.0283011i
$913$	−4.06189	−	9.80626i	−0.134429	−	0.324540i
$914$			28.4865i			0.942249i
$915$	14.4757	−	5.99605i	0.478553	−	0.198223i
$916$	9.07617	+	9.07617i	0.299885	+	0.299885i
$917$	30.9685			1.02267
$918$	−17.4331	−	12.2878i	−0.575378	−	0.405557i
$919$	40.5550			1.33779			0.668893	−	0.743358i	$-0.266768\pi$
$919$	40.5550			1.33779			0.668893	+	0.743358i	$0.266768\pi$
$920$	−1.48518	−	1.48518i	−0.0489651	−	0.0489651i
$921$	19.7966	−	8.20000i	0.652319	−	0.270199i
$922$			19.1875i			0.631906i
$923$	−0.863633	−	2.08499i	−0.0284268	−	0.0686284i
$924$	10.7081	+	4.43544i	0.352271	+	0.145915i
$925$	−2.71737	+	6.56031i	−0.0893466	+	0.215702i
$926$	−12.4558	+	12.4558i	−0.409324	+	0.409324i
$927$	−12.0795	+	12.0795i	−0.396742	+	0.396742i
$928$	−1.85710	+	4.48343i	−0.0609622	+	0.147176i
$929$	33.9468	+	14.0612i	1.11376	+	0.461333i	0.862230	−	0.506517i	$-0.169067\pi$
$929$	33.9468	+	14.0612i	1.11376	+	0.461333i	0.251527	+	0.967850i	$0.419067\pi$
$930$	−3.05878	−	7.38454i	−0.100301	−	0.242149i
$931$			6.46451i			0.211866i
$932$	−16.1379	+	6.68454i	−0.528615	+	0.218959i
$933$	24.1982	+	24.1982i	0.792215	+	0.792215i
$934$	−26.1842			−0.856772
$935$	19.1970	−	12.1461i	0.627810	−	0.397219i
$936$	−6.35887			−0.207846
$937$	−21.4800	−	21.4800i	−0.701721	−	0.701721i	0.263059	−	0.964780i	$-0.415269\pi$
$937$	−21.4800	−	21.4800i	−0.701721	−	0.701721i	−0.964780	+	0.263059i	$0.915269\pi$
$938$	20.0074	−	8.28733i	0.653264	−	0.270591i
$939$		−	1.63686i		−	0.0534170i
$940$	0.367056	+	0.886152i	0.0119720	+	0.0289031i
$941$	−33.0480	−	13.6889i	−1.07734	−	0.446247i	−0.227762	−	0.973717i	$-0.573141\pi$
$941$	−33.0480	−	13.6889i	−1.07734	−	0.446247i	−0.849574	+	0.527470i	$0.823141\pi$
$942$	−2.18672	+	5.27921i	−0.0712472	+	0.172006i
$943$	10.8706	−	10.8706i	0.353997	−	0.353997i
$944$	−0.723071	+	0.723071i	−0.0235340	+	0.0235340i
$945$	−3.92312	+	9.47125i	−0.127619	+	0.308100i
$946$	−57.1993	−	23.6927i	−1.85971	−	0.770317i
$947$	−10.4961	−	25.3399i	−0.341078	−	0.823436i	−0.997607	−	0.0691354i	$-0.977976\pi$
$947$	−10.4961	−	25.3399i	−0.341078	−	0.823436i	0.656529	−	0.754301i	$-0.272024\pi$
$948$			1.37241i			0.0445738i
$949$	29.0273	−	12.0235i	0.942265	−	0.390299i
$950$	−1.48774	−	1.48774i	−0.0482687	−	0.0482687i
$951$	−28.5886			−0.927048
$952$	−4.70757	+	6.67878i	−0.152573	+	0.216461i
$953$	8.63559			0.279734			0.139867	−	0.990170i	$-0.455332\pi$
$953$	8.63559			0.279734			0.139867	+	0.990170i	$0.455332\pi$
$954$	6.60894	+	6.60894i	0.213972	+	0.213972i
$955$	19.2225	−	7.96221i	0.622025	−	0.257651i
$956$		−	8.10490i		−	0.262131i
$957$	10.8611	+	26.2210i	0.351090	+	0.847606i
$958$	18.8147	+	7.79330i	0.607875	+	0.251790i
$959$	11.6878	−	28.2170i	0.377420	−	0.911173i
$960$	−0.750590	+	0.750590i	−0.0242252	+	0.0242252i
$961$	18.1724	−	18.1724i	0.586208	−	0.586208i
$962$	9.22439	−	22.2696i	0.297406	−	0.718002i
$963$	−21.1717	−	8.76962i	−0.682250	−	0.282597i
$964$	−2.88814	−	6.97258i	−0.0930206	−	0.224572i
$965$		−	0.943054i		−	0.0303580i
$966$	4.08212	−	1.69087i	0.131340	−	0.0544028i
$967$	16.8424	+	16.8424i	0.541614	+	0.541614i	0.924002	−	0.382388i	$-0.124898\pi$
$967$	16.8424	+	16.8424i	0.541614	+	0.541614i	−0.382388	+	0.924002i	$0.624898\pi$
$968$	−19.3560			−0.622126
$969$	1.57081	+	9.07345i	0.0504615	+	0.291481i
$970$	6.45805			0.207356
$971$	9.81551	+	9.81551i	0.314995	+	0.314995i	0.846841	−	0.531846i	$-0.178502\pi$
$971$	9.81551	+	9.81551i	0.314995	+	0.314995i	−0.531846	+	0.846841i	$0.678502\pi$
$972$	−14.4636	+	5.99103i	−0.463921	+	0.192162i
$973$		−	23.3690i		−	0.749176i
$974$	5.00165	+	12.0750i	0.160263	+	0.386910i
$975$	−3.32906	−	1.37894i	−0.106615	−	0.0441615i
$976$	5.64869	−	13.6371i	0.180810	−	0.436514i
$977$	37.6783	−	37.6783i	1.20544	−	1.20544i	0.232946	−	0.972490i	$-0.425163\pi$
$977$	37.6783	−	37.6783i	1.20544	−	1.20544i	0.972490	−	0.232946i	$-0.0748366\pi$
$978$	−13.3593	+	13.3593i	−0.427184	+	0.427184i
$979$	31.0914	−	75.0612i	0.993685	−	2.39897i
$980$	−2.83863	−	1.17580i	−0.0906766	−	0.0375595i
$981$	−2.81525	−	6.79662i	−0.0898840	−	0.216999i
$982$		−	9.16805i		−	0.292564i
$983$	31.1274	−	12.8934i	0.992810	−	0.411235i	0.173654	−	0.984807i	$-0.444442\pi$
$983$	31.1274	−	12.8934i	0.992810	−	0.411235i	0.819156	+	0.573571i	$0.194442\pi$
$984$	−5.49385	−	5.49385i	−0.175138	−	0.175138i
$985$	−7.52982			−0.239920
$986$	−19.7154	+	3.41316i	−0.627868	+	0.108697i
$987$	−2.01775			−0.0642258
$988$	5.05029	+	5.05029i	0.160671	+	0.160671i
$989$	−21.8054	+	9.03208i	−0.693370	+	0.287203i
$990$		−	10.3208i		−	0.328017i
$991$	−19.2682	−	46.5176i	−0.612075	−	1.47768i	−0.860716	−	0.509085i	$-0.829984\pi$
$991$	−19.2682	−	46.5176i	−0.612075	−	1.47768i	0.248641	−	0.968596i	$-0.420016\pi$
$992$	−6.95674	−	2.88158i	−0.220877	−	0.0914901i
$993$	12.1328	−	29.2913i	0.385024	−	0.929530i
$994$	−0.931630	+	0.931630i	−0.0295495	+	0.0295495i
$995$	−9.15508	+	9.15508i	−0.290235	+	0.290235i
$996$	−0.782569	+	1.88929i	−0.0247967	+	0.0598644i
$997$	−24.7253	−	10.2415i	−0.783057	−	0.324353i	−0.0449086	−	0.998991i	$-0.514300\pi$
$997$	−24.7253	−	10.2415i	−0.783057	−	0.324353i	−0.738149	+	0.674638i	$0.764300\pi$
$998$	7.29034	+	17.6004i	0.230772	+	0.557132i
$999$		−	36.7319i		−	1.16215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.121.2	yes	16
5.2	odd	4		850.2.o.g.699.3		16
5.3	odd	4		850.2.o.j.699.2		16
5.4	even	2		850.2.l.e.801.3		16
17.3	odd	16		2890.2.a.bi.1.4		8
17.5	odd	16		2890.2.b.r.2311.6		16
17.9	even	8	inner	170.2.k.b.111.2	✓	16
17.12	odd	16		2890.2.b.r.2311.11		16
17.14	odd	16		2890.2.a.bj.1.5		8
85.9	even	8		850.2.l.e.451.3		16
85.43	odd	8		850.2.o.g.349.3		16
85.77	odd	8		850.2.o.j.349.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.2	✓	16	17.9	even	8	inner
170.2.k.b.121.2	yes	16	1.1	even	1	trivial
850.2.l.e.451.3		16	85.9	even	8
850.2.l.e.801.3		16	5.4	even	2
850.2.o.g.349.3		16	85.43	odd	8
850.2.o.g.699.3		16	5.2	odd	4
850.2.o.j.349.2		16	85.77	odd	8
850.2.o.j.699.2		16	5.3	odd	4
2890.2.a.bi.1.4		8	17.3	odd	16
2890.2.a.bj.1.5		8	17.14	odd	16
2890.2.b.r.2311.6		16	17.5	odd	16
2890.2.b.r.2311.11		16	17.12	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.980692 + 0.406216i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.980692 - 0.406216i) q^{6} +(-0.758398 + 1.83094i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.32457 + 1.32457i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.980692 + 0.406216i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.980692 - 0.406216i) q^{6} +(-0.758398 + 1.83094i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.32457 + 1.32457i) q^{9} +(-0.382683 + 0.923880i) q^{10} +(5.09023 + 2.10844i) q^{11} +(-0.406216 - 0.980692i) q^{12} -3.39460i q^{13} +(-1.83094 + 0.758398i) q^{14} +(-0.750590 - 0.750590i) q^{15} -1.00000 q^{16} +(-2.20451 - 3.48427i) q^{17} -1.87323 q^{18} +(1.48774 + 1.48774i) q^{19} +(-0.923880 + 0.382683i) q^{20} -2.10366i q^{21} +(2.10844 + 5.09023i) q^{22} +(1.94049 + 0.803776i) q^{23} +(0.406216 - 0.980692i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(2.40034 - 2.40034i) q^{26} +(1.97958 - 4.77914i) q^{27} +(-1.83094 - 0.758398i) q^{28} +(-1.85710 - 4.48343i) q^{29} -1.06149i q^{30} +(6.95674 - 2.88158i) q^{31} +(-0.707107 - 0.707107i) q^{32} -5.84844 q^{33} +(0.904922 - 4.02258i) q^{34} -1.98179 q^{35} +(-1.32457 - 1.32457i) q^{36} +(6.56031 - 2.71737i) q^{37} +2.10399i q^{38} +(1.37894 + 3.32906i) q^{39} +(-0.923880 - 0.382683i) q^{40} +(2.80101 - 6.76223i) q^{41} +(1.48751 - 1.48751i) q^{42} +(-7.94580 + 7.94580i) q^{43} +(-2.10844 + 5.09023i) q^{44} +(-1.73064 - 0.716854i) q^{45} +(0.803776 + 1.94049i) q^{46} -0.959164i q^{47} +(0.980692 - 0.406216i) q^{48} +(2.17259 + 2.17259i) q^{49} -1.00000 q^{50} +(3.57732 + 2.52149i) q^{51} +3.39460 q^{52} +(-3.52810 - 3.52810i) q^{53} +(4.77914 - 1.97958i) q^{54} +5.50963i q^{55} +(-0.758398 - 1.83094i) q^{56} +(-2.06336 - 0.854673i) q^{57} +(1.85710 - 4.48343i) q^{58} +(0.723071 - 0.723071i) q^{59} +(0.750590 - 0.750590i) q^{60} +(-5.64869 + 13.6371i) q^{61} +(6.95674 + 2.88158i) q^{62} +(-1.42065 - 3.42976i) q^{63} -1.00000i q^{64} +(3.13620 - 1.29906i) q^{65} +(-4.13547 - 4.13547i) q^{66} -10.9274 q^{67} +(3.48427 - 2.20451i) q^{68} -2.22953 q^{69} +(-1.40134 - 1.40134i) q^{70} +(0.614209 - 0.254414i) q^{71} -1.87323i q^{72} +(3.54195 + 8.55102i) q^{73} +(6.56031 + 2.71737i) q^{74} +(0.406216 - 0.980692i) q^{75} +(-1.48774 + 1.48774i) q^{76} +(-7.72085 + 7.72085i) q^{77} +(-1.37894 + 3.32906i) q^{78} +(-1.19449 - 0.494772i) q^{79} +(-0.382683 - 0.923880i) q^{80} -0.128685i q^{81} +(6.76223 - 2.80101i) q^{82} +(-1.36223 - 1.36223i) q^{83} +2.10366 q^{84} +(2.37541 - 3.37008i) q^{85} -11.2371 q^{86} +(3.64248 + 3.64248i) q^{87} +(-5.09023 + 2.10844i) q^{88} -14.7461i q^{89} +(-0.716854 - 1.73064i) q^{90} +(6.21529 + 2.57446i) q^{91} +(-0.803776 + 1.94049i) q^{92} +(-5.65188 + 5.65188i) q^{93} +(0.678231 - 0.678231i) q^{94} +(-0.805161 + 1.94383i) q^{95} +(0.980692 + 0.406216i) q^{96} +(-2.47139 - 5.96646i) q^{97} +3.07251i q^{98} +(-9.53518 + 3.94960i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more