LMFDB - Embedded newform 170.2.r.b.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(23,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([12, 15]))

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

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

chi := DirichletCharacter("170.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.r (of order $16$, degree $8$, 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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	170.23
Dual form			170.2.r.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 - 0.382683i) q^{2} +(-2.47936 - 1.65666i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-2.20283 + 0.384106i) q^{5} +(-2.92460 - 0.581740i) q^{6} +(-2.11600 - 0.420899i) q^{7} +(0.382683 - 0.923880i) q^{8} +(2.25467 + 5.44325i) q^{9} +(-1.88816 + 1.19785i) q^{10} +(0.581141 - 2.92159i) q^{11} +(-2.92460 + 0.581740i) q^{12} -5.10274 q^{13} +(-2.11600 + 0.420899i) q^{14} +(6.09794 + 2.69699i) q^{15} -1.00000i q^{16} +(2.91101 - 2.91993i) q^{17} +(4.16608 + 4.16608i) q^{18} +(2.47306 - 5.97048i) q^{19} +(-1.28603 + 1.82924i) q^{20} +(4.54905 + 4.54905i) q^{21} +(-0.581141 - 2.92159i) q^{22} +(0.847753 + 1.26875i) q^{23} +(-2.47936 + 1.65666i) q^{24} +(4.70493 - 1.69224i) q^{25} +(-4.71431 + 1.95273i) q^{26} +(1.68223 - 8.45716i) q^{27} +(-1.79386 + 1.19862i) q^{28} +(-3.82051 + 5.71779i) q^{29} +(6.66586 + 0.158117i) q^{30} +(-0.942552 - 4.73853i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(-6.28093 + 6.28093i) q^{33} +(1.57202 - 3.81166i) q^{34} +(4.82287 + 0.114401i) q^{35} +(5.44325 + 2.25467i) q^{36} +(4.04382 - 6.05201i) q^{37} -6.46241i q^{38} +(12.6515 + 8.45347i) q^{39} +(-0.488119 + 2.18214i) q^{40} +(2.01733 + 3.01915i) q^{41} +(5.94362 + 2.46193i) q^{42} +(-1.73529 - 0.718779i) q^{43} +(-1.65495 - 2.47681i) q^{44} +(-7.05743 - 11.1245i) q^{45} +(1.26875 + 0.847753i) q^{46} +4.65062i q^{47} +(-1.65666 + 2.47936i) q^{48} +(-2.16684 - 0.897536i) q^{49} +(3.69919 - 3.36392i) q^{50} +(-12.0548 + 2.41701i) q^{51} +(-3.60818 + 3.60818i) q^{52} +(1.11881 + 2.70105i) q^{53} +(-1.68223 - 8.45716i) q^{54} +(-0.157954 + 6.65899i) q^{55} +(-1.19862 + 1.79386i) q^{56} +(-16.0226 + 10.7060i) q^{57} +(-1.34158 + 6.74460i) q^{58} +(-3.66553 + 1.51831i) q^{59} +(6.21896 - 2.40483i) q^{60} +(-3.45296 + 2.30720i) q^{61} +(-2.68416 - 4.01713i) q^{62} +(-2.47982 - 12.4669i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(11.2405 - 1.95999i) q^{65} +(-3.39921 + 8.20642i) q^{66} +(-2.25590 - 2.25590i) q^{67} +(-0.00630415 - 4.12310i) q^{68} -4.55013i q^{69} +(4.49953 - 1.73994i) q^{70} +(5.63509 - 1.12089i) q^{71} +5.89173 q^{72} +(9.62889 - 1.91531i) q^{73} +(1.42000 - 7.13883i) q^{74} +(-14.4687 - 3.59877i) q^{75} +(-2.47306 - 5.97048i) q^{76} +(-2.45939 + 5.93749i) q^{77} +(14.9235 + 2.96847i) q^{78} +(-15.1407 - 3.01167i) q^{79} +(0.384106 + 2.20283i) q^{80} +(-5.68322 + 5.68322i) q^{81} +(3.01915 + 2.01733i) q^{82} +(9.03070 - 3.74064i) q^{83} +6.43332 q^{84} +(-5.29091 + 7.55025i) q^{85} -1.87826 q^{86} +(18.9448 - 7.84720i) q^{87} +(-2.47681 - 1.65495i) q^{88} +(-5.41083 + 5.41083i) q^{89} +(-10.7774 - 7.57696i) q^{90} +(10.7974 + 2.14774i) q^{91} +(1.49660 + 0.297691i) q^{92} +(-5.51318 + 13.3100i) q^{93} +(1.77972 + 4.29662i) q^{94} +(-3.15442 + 14.1019i) q^{95} +(-0.581740 + 2.92460i) q^{96} +(-2.63292 + 0.523720i) q^{97} -2.34537 q^{98} +(17.2132 - 3.42392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44}+ \cdots + 160 q^{99}+O(q^{100}) $ 40 * q - 16 * q^10 - 16 * q^18 + 8 * q^25 - 8 * q^26 + 24 * q^27 - 8 * q^28 + 8 * q^29 + 16 * q^30 - 16 * q^31 - 32 * q^33 + 8 * q^34 - 32 * q^35 - 32 * q^39 - 56 * q^41 - 24 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^49 - 32 * q^51 - 16 * q^52 + 16 * q^53 - 24 * q^54 - 8 * q^55 - 8 * q^56 - 120 * q^57 + 16 * q^58 + 8 * q^60 + 24 * q^61 - 8 * q^62 - 24 * q^63 - 32 * q^65 + 16 * q^67 - 8 * q^70 + 24 * q^71 + 56 * q^72 + 88 * q^73 + 32 * q^74 + 8 * q^75 + 24 * q^77 + 32 * q^78 - 104 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 + 136 * q^85 + 96 * q^86 + 136 * q^87 - 16 * q^89 + 24 * q^90 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 136 * q^95 + 16 * q^97 + 72 * q^98 + 160 * q^99

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$3$	−2.47936	−	1.65666i	−1.43146	−	0.956470i	−0.998483	−	0.0550648i	$-0.982463\pi$
$3$	−2.47936	−	1.65666i	−1.43146	−	0.956470i	−0.432976	−	0.901405i	$-0.642537\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	−2.20283	+	0.384106i	−0.985136	+	0.171777i
$5$	−2.20283	+	0.384106i	−0.985136	+	0.171777i
$6$	−2.92460	−	0.581740i	−1.19396	−	0.237494i
$7$	−2.11600	−	0.420899i	−0.799774	−	0.159085i	−0.221749	−	0.975104i	$-0.571176\pi$
$7$	−2.11600	−	0.420899i	−0.799774	−	0.159085i	−0.578025	+	0.816019i	$0.696176\pi$
$8$	0.382683	−	0.923880i	0.135299	−	0.326641i
$9$	2.25467	+	5.44325i	0.751556	+	1.81442i
$10$	−1.88816	+	1.19785i	−0.597088	+	0.378795i
$11$	0.581141	−	2.92159i	0.175220	−	0.880893i	−0.788715	−	0.614758i	$-0.789253\pi$
$11$	0.581141	−	2.92159i	0.175220	−	0.880893i	0.963936	−	0.266134i	$-0.0857465\pi$
$12$	−2.92460	+	0.581740i	−0.844260	+	0.167934i
$13$	−5.10274			−1.41524			−0.707622	−	0.706591i	$-0.750232\pi$
$13$	−5.10274			−1.41524			−0.707622	+	0.706591i	$0.750232\pi$
$14$	−2.11600	+	0.420899i	−0.565526	+	0.112490i
$15$	6.09794	+	2.69699i	1.57448	+	0.696361i
$16$		−	1.00000i		−	0.250000i
$17$	2.91101	−	2.91993i	0.706025	−	0.708187i
$17$	2.91101	−	2.91993i	0.706025	−	0.708187i
$18$	4.16608	+	4.16608i	0.981955	+	0.981955i
$19$	2.47306	−	5.97048i	0.567358	−	1.36972i	−0.336416	−	0.941713i	$-0.609215\pi$
$19$	2.47306	−	5.97048i	0.567358	−	1.36972i	0.903774	−	0.428010i	$-0.140785\pi$
$20$	−1.28603	+	1.82924i	−0.287566	+	0.409031i
$21$	4.54905	+	4.54905i	0.992684	+	0.992684i
$22$	−0.581141	−	2.92159i	−0.123900	−	0.622885i
$23$	0.847753	+	1.26875i	0.176769	+	0.264553i	0.909265	−	0.416218i	$-0.136645\pi$
$23$	0.847753	+	1.26875i	0.176769	+	0.264553i	−0.732496	+	0.680771i	$0.761645\pi$
$24$	−2.47936	+	1.65666i	−0.506097	+	0.338163i
$25$	4.70493	−	1.69224i	0.940985	−	0.338448i
$26$	−4.71431	+	1.95273i	−0.924553	+	0.382962i
$27$	1.68223	−	8.45716i	0.323746	−	1.62758i
$28$	−1.79386	+	1.19862i	−0.339008	+	0.226518i
$29$	−3.82051	+	5.71779i	−0.709450	+	1.06177i	0.285200	+	0.958468i	$0.407940\pi$
$29$	−3.82051	+	5.71779i	−0.709450	+	1.06177i	−0.994650	+	0.103300i	$0.967060\pi$
$30$	6.66586	+	0.158117i	1.21701	+	0.0288681i
$31$	−0.942552	−	4.73853i	−0.169287	−	0.851065i	−0.968308	−	0.249761i	$-0.919648\pi$
$31$	−0.942552	−	4.73853i	−0.169287	−	0.851065i	0.799020	−	0.601304i	$-0.205352\pi$
$32$	−0.382683	−	0.923880i	−0.0676495	−	0.163320i
$33$	−6.28093	+	6.28093i	−1.09337	+	1.09337i
$34$	1.57202	−	3.81166i	0.269599	−	0.653694i
$35$	4.82287	+	0.114401i	0.815213	+	0.0193372i
$36$	5.44325	+	2.25467i	0.907208	+	0.375778i
$37$	4.04382	−	6.05201i	0.664801	−	0.994945i	−0.333830	−	0.942633i	$-0.608341\pi$
$37$	4.04382	−	6.05201i	0.664801	−	0.994945i	0.998631	−	0.0523113i	$-0.0166588\pi$
$38$		−	6.46241i		−	1.04834i
$39$	12.6515	+	8.45347i	2.02586	+	1.35364i
$40$	−0.488119	+	2.18214i	−0.0771784	+	0.345027i
$41$	2.01733	+	3.01915i	0.315054	+	0.471511i	0.954873	−	0.297014i	$-0.0959908\pi$
$41$	2.01733	+	3.01915i	0.315054	+	0.471511i	−0.639819	+	0.768525i	$0.720991\pi$
$42$	5.94362	+	2.46193i	0.917120	+	0.379884i
$43$	−1.73529	−	0.718779i	−0.264629	−	0.109613i	0.246424	−	0.969162i	$-0.420744\pi$
$43$	−1.73529	−	0.718779i	−0.264629	−	0.109613i	−0.511053	+	0.859549i	$0.670744\pi$
$44$	−1.65495	−	2.47681i	−0.249493	−	0.373392i
$45$	−7.05743	−	11.1245i	−1.05206	−	1.65835i
$46$	1.26875	+	0.847753i	0.187067	+	0.124994i
$47$			4.65062i			0.678363i	0.940721	+	0.339182i	$0.110150\pi$
$47$			4.65062i			0.678363i	−0.940721	+	0.339182i	$0.889850\pi$
$48$	−1.65666	+	2.47936i	−0.239118	+	0.357865i
$49$	−2.16684	−	0.897536i	−0.309549	−	0.128219i
$50$	3.69919	−	3.36392i	0.523145	−	0.475731i
$51$	−12.0548	+	2.41701i	−1.68801	+	0.338449i
$52$	−3.60818	+	3.60818i	−0.500364	+	0.500364i
$53$	1.11881	+	2.70105i	0.153680	+	0.371017i	0.981904	−	0.189381i	$-0.0606481\pi$
$53$	1.11881	+	2.70105i	0.153680	+	0.371017i	−0.828223	+	0.560398i	$0.810648\pi$
$54$	−1.68223	−	8.45716i	−0.228923	−	1.15087i
$55$	−0.157954	+	6.65899i	−0.0212986	+	0.897898i
$56$	−1.19862	+	1.79386i	−0.160172	+	0.239715i
$57$	−16.0226	+	10.7060i	−2.12225	+	1.41804i
$58$	−1.34158	+	6.74460i	−0.176159	+	0.885609i
$59$	−3.66553	+	1.51831i	−0.477211	+	0.197667i	−0.608306	−	0.793703i	$-0.708151\pi$
$59$	−3.66553	+	1.51831i	−0.477211	+	0.197667i	0.131095	+	0.991370i	$0.458151\pi$
$60$	6.21896	−	2.40483i	0.802864	−	0.310462i
$61$	−3.45296	+	2.30720i	−0.442107	+	0.295406i	−0.756630	−	0.653844i	$-0.773155\pi$
$61$	−3.45296	+	2.30720i	−0.442107	+	0.295406i	0.314523	+	0.949250i	$0.398155\pi$
$62$	−2.68416	−	4.01713i	−0.340889	−	0.510176i
$63$	−2.47982	−	12.4669i	−0.312428	−	1.57068i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	11.2405	−	1.95999i	1.39421	−	0.243107i
$66$	−3.39921	+	8.20642i	−0.418414	+	1.01014i
$67$	−2.25590	−	2.25590i	−0.275602	−	0.275602i	0.555749	−	0.831350i	$-0.312432\pi$
$67$	−2.25590	−	2.25590i	−0.275602	−	0.275602i	−0.831350	+	0.555749i	$0.812432\pi$
$68$	−0.00630415	−	4.12310i	−0.000764491	−	0.499999i
$69$		−	4.55013i		−	0.547771i
$70$	4.49953	−	1.73994i	0.537796	−	0.207962i
$71$	5.63509	−	1.12089i	0.668762	−	0.133025i	0.150979	−	0.988537i	$-0.451757\pi$
$71$	5.63509	−	1.12089i	0.668762	−	0.133025i	0.517783	+	0.855512i	$0.326757\pi$
$72$	5.89173			0.694347
$73$	9.62889	−	1.91531i	1.12698	−	0.224170i	0.403810	−	0.914843i	$-0.367686\pi$
$73$	9.62889	−	1.91531i	1.12698	−	0.224170i	0.723167	+	0.690674i	$0.242686\pi$
$74$	1.42000	−	7.13883i	0.165072	−	0.829873i
$75$	−14.4687	−	3.59877i	−1.67070	−	0.415550i
$76$	−2.47306	−	5.97048i	−0.283679	−	0.684861i
$77$	−2.45939	+	5.93749i	−0.280274	+	0.676640i
$78$	14.9235	+	2.96847i	1.68975	+	0.336113i
$79$	−15.1407	−	3.01167i	−1.70346	−	0.338839i	−0.754996	−	0.655729i	$-0.772361\pi$
$79$	−15.1407	−	3.01167i	−1.70346	−	0.338839i	−0.948462	+	0.316890i	$0.897361\pi$
$80$	0.384106	+	2.20283i	0.0429443	+	0.246284i
$81$	−5.68322	+	5.68322i	−0.631469	+	0.631469i
$82$	3.01915	+	2.01733i	0.333409	+	0.222777i
$83$	9.03070	−	3.74064i	0.991249	−	0.410589i	0.172668	−	0.984980i	$-0.444761\pi$
$83$	9.03070	−	3.74064i	0.991249	−	0.410589i	0.818581	+	0.574391i	$0.194761\pi$
$84$	6.43332			0.701933
$85$	−5.29091	+	7.55025i	−0.573880	+	0.818940i
$86$	−1.87826			−0.202538
$87$	18.9448	−	7.84720i	2.03110	−	0.841309i
$88$	−2.47681	−	1.65495i	−0.264028	−	0.176418i
$89$	−5.41083	+	5.41083i	−0.573547	+	0.573547i	−0.933118	−	0.359571i	$-0.882923\pi$
$89$	−5.41083	+	5.41083i	−0.573547	+	0.573547i	0.359571	+	0.933118i	$0.382923\pi$
$90$	−10.7774	−	7.57696i	−1.13604	−	0.798681i
$91$	10.7974	+	2.14774i	1.13188	+	0.225144i
$92$	1.49660	+	0.297691i	0.156031	+	0.0310365i
$93$	−5.51318	+	13.3100i	−0.571690	+	1.38018i
$94$	1.77972	+	4.29662i	0.183564	+	0.443162i
$95$	−3.15442	+	14.1019i	−0.323637	+	1.44682i
$96$	−0.581740	+	2.92460i	−0.0593736	+	0.298491i
$97$	−2.63292	+	0.523720i	−0.267332	+	0.0531757i	−0.326936	−	0.945046i	$-0.606016\pi$
$97$	−2.63292	+	0.523720i	−0.267332	+	0.0531757i	0.0596039	+	0.998222i	$0.481016\pi$
$98$	−2.34537			−0.236919
$99$	17.2132	−	3.42392i	1.72999	−	0.344117i
$100$	2.13029	−	4.52348i	0.213029	−	0.452348i
$101$		−	12.8077i		−	1.27441i	−0.770693	−	0.637207i	$-0.780090\pi$
$101$		−	12.8077i		−	1.27441i	0.770693	−	0.637207i	$-0.219910\pi$
$102$	−10.2122	+	6.84619i	−1.01116	+	0.677873i
$103$	−8.68917	−	8.68917i	−0.856170	−	0.856170i	0.134715	−	0.990884i	$-0.456988\pi$
$103$	−8.68917	−	8.68917i	−0.856170	−	0.856170i	−0.990884	+	0.134715i	$0.956988\pi$
$104$	−1.95273	+	4.71431i	−0.191481	+	0.462276i
$105$	−11.7681	−	8.27347i	−1.14845	−	0.807408i
$106$	2.06729	+	2.06729i	0.200793	+	0.200793i
$107$	−0.486150	−	2.44404i	−0.0469978	−	0.236274i	0.950145	−	0.311807i	$-0.100934\pi$
$107$	−0.486150	−	2.44404i	−0.0469978	−	0.236274i	−0.997143	+	0.0755328i	$0.975934\pi$
$108$	−4.79060	−	7.16964i	−0.460976	−	0.689899i
$109$	15.1896	−	10.1494i	1.45490	−	0.972132i	0.458380	−	0.888756i	$-0.348430\pi$
$109$	15.1896	−	10.1494i	1.45490	−	0.972132i	0.996518	−	0.0833759i	$-0.0265702\pi$
$110$	2.40235	+	6.21255i	0.229055	+	0.592343i
$111$	−20.0522	+	8.30589i	−1.90327	+	0.788360i
$112$	−0.420899	+	2.11600i	−0.0397712	+	0.199944i
$113$	10.4494	−	6.98206i	0.982997	−	0.656817i	0.0433845	−	0.999058i	$-0.486186\pi$
$113$	10.4494	−	6.98206i	0.982997	−	0.656817i	0.939612	+	0.342241i	$0.111186\pi$
$114$	−10.7060	+	16.0226i	−1.00271	+	1.50066i
$115$	−2.35479	−	2.46922i	−0.219586	−	0.230256i
$116$	1.34158	+	6.74460i	0.124563	+	0.626220i
$117$	−11.5050	−	27.7755i	−1.06364	−	2.56784i
$118$	−2.80547	+	2.80547i	−0.258265	+	0.258265i
$119$	−7.38871	+	4.95334i	−0.677322	+	0.454072i
$120$	4.82528	−	4.60167i	0.440486	−	0.420073i
$121$	1.96470	+	0.813807i	0.178610	+	0.0739825i
$122$	−2.30720	+	3.45296i	−0.208884	+	0.312617i
$123$		−	10.8276i		−	0.976289i
$124$	−4.01713	−	2.68416i	−0.360749	−	0.241045i
$125$	−9.71415	+	5.53491i	−0.868860	+	0.495057i
$126$	−7.06194	−	10.5689i	−0.629128	−	0.941556i
$127$	2.06022	+	0.853371i	0.182815	+	0.0757245i	0.472213	−	0.881484i	$-0.343455\pi$
$127$	2.06022	+	0.853371i	0.182815	+	0.0757245i	−0.289398	+	0.957209i	$0.593455\pi$
$128$	−0.923880	−	0.382683i	−0.0816602	−	0.0338248i
$129$	3.11163	+	4.65688i	0.273964	+	0.410016i
$130$	9.63478	−	6.11233i	0.845026	−	0.536087i
$131$	10.4931	+	7.01129i	0.916790	+	0.612579i	0.921909	−	0.387407i	$-0.126629\pi$
$131$	10.4931	+	7.01129i	0.916790	+	0.612579i	−0.00511864	+	0.999987i	$0.501629\pi$
$132$			8.88257i			0.773128i
$133$	−7.74596	+	11.5927i	−0.671660	+	1.00521i
$134$	−2.94747	−	1.22088i	−0.254623	−	0.105468i
$135$	−0.457232	+	19.2759i	−0.0393523	+	1.65900i
$136$	−1.58367	−	3.80684i	−0.135798	−	0.326433i
$137$	−2.33320	+	2.33320i	−0.199339	+	0.199339i	−0.799717	−	0.600378i	$-0.795017\pi$
$137$	−2.33320	+	2.33320i	−0.199339	+	0.199339i	0.600378	+	0.799717i	$0.295017\pi$
$138$	−1.74126	−	4.20377i	−0.148226	−	0.357849i
$139$	2.59433	+	13.0426i	0.220049	+	1.10626i	0.919955	+	0.392024i	$0.128225\pi$
$139$	2.59433	+	13.0426i	0.220049	+	1.10626i	−0.699906	+	0.714235i	$0.746775\pi$
$140$	3.49117	−	3.32939i	0.295058	−	0.281385i
$141$	7.70448	−	11.5306i	0.648834	−	0.971049i
$142$	4.77720	−	3.19202i	0.400894	−	0.267869i
$143$	−2.96541	+	14.9081i	−0.247980	+	1.24668i
$144$	5.44325	−	2.25467i	0.453604	−	0.187889i
$145$	6.21969	−	14.0628i	0.516517	−	1.16785i
$146$	8.16298	−	5.45433i	0.675573	−	0.451403i
$147$	3.88548	+	5.81503i	0.320469	+	0.479615i
$148$	−1.42000	−	7.13883i	−0.116723	−	0.586809i
$149$	−5.78244	−	5.78244i	−0.473716	−	0.473716i	0.429399	−	0.903115i	$-0.358725\pi$
$149$	−5.78244	−	5.78244i	−0.473716	−	0.473716i	−0.903115	+	0.429399i	$0.858725\pi$
$150$	−14.7445	+	2.21209i	−1.20388	+	0.180616i
$151$	3.31607	−	8.00571i	0.269858	−	0.651495i	−0.729618	−	0.683855i	$-0.760302\pi$
$151$	3.31607	−	8.00571i	0.269858	−	0.651495i	0.999476	+	0.0323595i	$0.0103021\pi$
$152$	−4.56961	−	4.56961i	−0.370644	−	0.370644i
$153$	22.4573	+	9.26191i	1.81556	+	0.748781i
$154$			6.42670i			0.517878i
$155$	3.89638	+	10.0761i	0.312965	+	0.809335i
$156$	14.9235	−	2.96847i	1.19483	−	0.237667i
$157$	6.12399			0.488747			0.244374	−	0.969681i	$-0.421418\pi$
$157$	6.12399			0.488747			0.244374	+	0.969681i	$0.421418\pi$
$158$	−15.1407	+	3.01167i	−1.20453	+	0.239595i
$159$	1.70077	−	8.55035i	0.134880	−	0.678087i
$160$	1.19785	+	1.88816i	0.0946987	+	0.149272i
$161$	−1.25983	−	3.04150i	−0.0992887	−	0.239704i
$162$	−3.07574	+	7.42549i	−0.241653	+	0.583401i
$163$	−12.9467	−	2.57526i	−1.01407	−	0.201710i	−0.340034	−	0.940413i	$-0.610439\pi$
$163$	−12.9467	−	2.57526i	−1.01407	−	0.201710i	−0.674031	+	0.738703i	$0.735439\pi$
$164$	3.56132	+	0.708391i	0.278093	+	0.0553161i
$165$	11.4233	−	16.2484i	0.889301	−	1.26493i
$166$	6.91180	−	6.91180i	0.536460	−	0.536460i
$167$	14.6882	+	9.81435i	1.13661	+	0.759457i	0.973846	−	0.227209i	$-0.0729599\pi$
$167$	14.6882	+	9.81435i	1.13661	+	0.759457i	0.162761	+	0.986665i	$0.447960\pi$
$168$	5.94362	−	2.46193i	0.458560	−	0.189942i
$169$	13.0379			1.00292
$170$	−1.99881	+	9.00026i	−0.153302	+	0.690289i
$171$	38.0747			2.91165
$172$	−1.73529	+	0.718779i	−0.132314	+	0.0548064i
$173$	8.19533	+	5.47594i	0.623079	+	0.416328i	0.826638	−	0.562734i	$-0.190251\pi$
$173$	8.19533	+	5.47594i	0.623079	+	0.416328i	−0.203558	+	0.979063i	$0.565251\pi$
$174$	14.4997	−	14.4997i	1.09922	−	1.09922i
$175$	−10.6679	+	1.60049i	−0.806417	+	0.120985i
$176$	−2.92159	−	0.581141i	−0.220223	−	0.0438051i
$177$	11.6035	+	2.30807i	0.872170	+	0.173485i
$178$	−2.92832	+	7.06959i	−0.219487	+	0.529888i
$179$	0.836227	+	2.01883i	0.0625026	+	0.150895i	0.952045	−	0.305958i	$-0.0989767\pi$
$179$	0.836227	+	2.01883i	0.0625026	+	0.150895i	−0.889542	+	0.456853i	$0.848977\pi$
$180$	−12.8566	−	2.87587i	−0.958273	−	0.214354i
$181$	2.38233	−	11.9768i	0.177077	−	0.890225i	−0.785426	−	0.618955i	$-0.787556\pi$
$181$	2.38233	−	11.9768i	0.177077	−	0.890225i	0.962503	−	0.271270i	$-0.0874437\pi$
$182$	10.7974	−	2.14774i	0.800357	−	0.159201i
$183$	12.3834			0.915405
$184$	1.49660	−	0.297691i	0.110330	−	0.0219461i
$185$	−6.58325	+	14.8848i	−0.484010	+	1.09435i
$186$			14.4066i			1.05635i
$187$	−6.83913	−	10.2017i	−0.500127	−	0.746021i
$188$	3.28849	+	3.28849i	0.239838	+	0.239838i
$189$	−7.11923	+	17.1873i	−0.517848	+	1.25019i
$190$	2.48225	+	14.2356i	0.180081	+	1.03276i
$191$	−3.12333	−	3.12333i	−0.225996	−	0.225996i	0.585021	−	0.811018i	$-0.301086\pi$
$191$	−3.12333	−	3.12333i	−0.225996	−	0.225996i	−0.811018	+	0.585021i	$0.801086\pi$
$192$	0.581740	+	2.92460i	0.0419835	+	0.211065i
$193$	13.1386	+	19.6632i	0.945734	+	1.41539i	0.909340	+	0.416054i	$0.136587\pi$
$193$	13.1386	+	19.6632i	0.945734	+	1.41539i	0.0363943	+	0.999338i	$0.488413\pi$
$194$	−2.23208	+	1.49143i	−0.160254	+	0.107078i
$195$	−31.1162	−	13.7621i	−2.22828	−	0.985521i
$196$	−2.16684	+	0.897536i	−0.154775	+	0.0641097i
$197$	−0.300658	+	1.51151i	−0.0214210	+	0.107691i	−0.990017	−	0.140951i	$-0.954984\pi$
$197$	−0.300658	+	1.51151i	−0.0214210	+	0.107691i	0.968596	+	0.248641i	$0.0799840\pi$
$198$	14.5927	−	9.75051i	1.03706	−	0.692938i
$199$	−2.72577	+	4.07940i	−0.193224	+	0.289181i	−0.915413	−	0.402515i	$-0.868136\pi$
$199$	−2.72577	+	4.07940i	−0.193224	+	0.289181i	0.722189	+	0.691696i	$0.243136\pi$
$200$	0.237071	−	4.99438i	0.0167635	−	0.353156i
$201$	1.85594	+	9.33042i	0.130908	+	0.658117i
$202$	−4.90129	−	11.8328i	−0.344854	−	0.832551i
$203$	10.4908	−	10.4908i	0.736311	−	0.736311i
$204$	−6.81493	+	10.2331i	−0.477140	+	0.716460i
$205$	−5.60350	−	5.87580i	−0.391366	−	0.410384i
$206$	−11.3530	−	4.70255i	−0.790998	−	0.327642i
$207$	−4.99473	+	7.47515i	−0.347158	+	0.519559i
$208$			5.10274i			0.353811i
$209$	−16.0061	−	10.6949i	−1.10717	−	0.739785i
$210$	−14.0384	−	3.14023i	−0.968743	−	0.216696i
$211$	−14.8005	−	22.1505i	−1.01891	−	1.52490i	−0.841131	−	0.540832i	$-0.818110\pi$
$211$	−14.8005	−	22.1505i	−1.01891	−	1.52490i	−0.177777	−	0.984071i	$-0.556890\pi$
$212$	2.70105	+	1.11881i	0.185509	+	0.0768402i
$213$	−15.8283	−	6.55631i	−1.08454	−	0.449231i
$214$	−1.38444	−	2.07196i	−0.0946381	−	0.141636i
$215$	4.09863	+	0.916815i	0.279524	+	0.0625263i
$216$	−7.16964	−	4.79060i	−0.487832	−	0.325959i
$217$			10.4235i			0.707591i
$218$	10.1494	−	15.1896i	0.687401	−	1.02877i
$219$	−27.0465	−	11.2030i	−1.82763	−	0.757030i
$220$	4.59693	+	4.82031i	0.309925	+	0.324985i
$221$	−14.8541	+	14.8996i	−0.999198	+	1.00226i
$222$	−15.3473	+	15.3473i	−1.03004	+	1.03004i
$223$	−3.78056	−	9.12708i	−0.253165	−	0.611195i	0.745291	−	0.666739i	$-0.232310\pi$
$223$	−3.78056	−	9.12708i	−0.253165	−	0.611195i	−0.998456	+	0.0555446i	$0.982310\pi$
$224$	0.420899	+	2.11600i	0.0281225	+	0.141381i
$225$	19.8193	+	21.7946i	1.32129	+	1.45298i
$226$	6.98206	−	10.4494i	0.464440	−	0.695084i
$227$	−6.88241	+	4.59868i	−0.456801	+	0.305225i	−0.762599	−	0.646872i	$-0.776077\pi$
$227$	−6.88241	+	4.59868i	−0.456801	+	0.305225i	0.305797	+	0.952097i	$0.401077\pi$
$228$	−3.75944	+	18.9000i	−0.248975	+	1.25168i
$229$	21.1923	−	8.77812i	1.40042	−	0.580074i	0.450562	−	0.892745i	$-0.351224\pi$
$229$	21.1923	−	8.77812i	1.40042	−	0.580074i	0.949862	+	0.312671i	$0.101224\pi$
$230$	−3.12047	−	1.38012i	−0.205758	−	0.0910025i
$231$	15.9341	−	10.6468i	1.04839	−	0.700509i
$232$	3.82051	+	5.71779i	0.250829	+	0.375392i
$233$	−5.40843	−	27.1900i	−0.354318	−	1.78128i	−0.587894	−	0.808938i	$-0.700043\pi$
$233$	−5.40843	−	27.1900i	−0.354318	−	1.78128i	0.233576	−	0.972339i	$-0.424957\pi$
$234$	−21.2584	−	21.2584i	−1.38971	−	1.38971i
$235$	−1.78633	−	10.2445i	−0.116527	−	0.668280i
$236$	−1.51831	+	3.66553i	−0.0988336	+	0.238605i
$237$	32.5499	+	32.5499i	2.11434	+	2.11434i
$238$	−4.93072	+	7.40383i	−0.319611	+	0.479919i
$239$		−	21.8340i		−	1.41232i	−0.708051	−	0.706161i	$-0.750425\pi$
$239$		−	21.8340i		−	1.41232i	0.708051	−	0.706161i	$-0.249575\pi$
$240$	2.69699	−	6.09794i	0.174090	−	0.393620i
$241$	−10.9377	+	2.17563i	−0.704556	+	0.140145i	−0.534350	−	0.845264i	$-0.679443\pi$
$241$	−10.9377	+	2.17563i	−0.704556	+	0.140145i	−0.170206	+	0.985408i	$0.554443\pi$
$242$	2.12658			0.136702
$243$	−1.86561	+	0.371092i	−0.119679	+	0.0238056i
$244$	−0.810180	+	4.07305i	−0.0518664	+	0.260750i
$245$	5.11794	+	1.14482i	0.326973	+	0.0731400i
$246$	−4.14353	−	10.0034i	−0.264182	−	0.637791i
$247$	−12.6193	+	30.4658i	−0.802950	+	1.93849i
$248$	−4.73853	−	0.942552i	−0.300897	−	0.0598521i
$249$	−28.5873	−	5.68637i	−1.81165	−	0.360359i
$250$	−6.85659	+	8.83103i	−0.433649	+	0.558524i
$251$	−5.63823	+	5.63823i	−0.355882	+	0.355882i	−0.862292	−	0.506411i	$-0.830972\pi$
$251$	−5.63823	+	5.63823i	−0.355882	+	0.355882i	0.506411	+	0.862292i	$0.330972\pi$
$252$	−10.5689	−	7.06194i	−0.665781	−	0.444861i
$253$	4.19944	−	1.73947i	0.264017	−	0.109359i
$254$	2.22997			0.139921
$255$	25.6262	−	9.95457i	1.60478	−	0.623379i
$256$	−1.00000			−0.0625000
$257$	−11.0133	+	4.56187i	−0.686992	+	0.284561i	−0.698746	−	0.715370i	$-0.746258\pi$
$257$	−11.0133	+	4.56187i	−0.686992	+	0.284561i	0.0117544	+	0.999931i	$0.496258\pi$
$258$	4.65688	+	3.11163i	0.289925	+	0.193722i
$259$	−11.1040	+	11.1040i	−0.689971	+	0.689971i
$260$	6.56229	−	9.33413i	0.406976	−	0.578878i
$261$	−39.7373	−	7.90425i	−2.45968	−	0.489261i
$262$	12.3775	+	2.46204i	0.764685	+	0.152105i
$263$	−5.39184	+	13.0171i	−0.332475	+	0.802666i	0.665919	+	0.746024i	$0.268039\pi$
$263$	−5.39184	+	13.0171i	−0.332475	+	0.802666i	−0.998395	+	0.0566422i	$0.981961\pi$
$264$	3.39921	+	8.20642i	0.209207	+	0.505070i
$265$	−3.50204	−	5.52021i	−0.215129	−	0.339104i
$266$	−2.72002	+	13.6745i	−0.166775	+	0.838436i
$267$	22.3793	−	4.45151i	1.36959	−	0.272428i
$268$	−3.19032			−0.194880
$269$	−4.26081	+	0.847528i	−0.259786	+	0.0516747i	−0.323265	−	0.946308i	$-0.604781\pi$
$269$	−4.26081	+	0.847528i	−0.259786	+	0.0516747i	0.0634787	+	0.997983i	$0.479781\pi$
$270$	6.95412	+	17.9835i	0.423214	+	1.09444i
$271$			3.27703i			0.199065i	0.995034	+	0.0995326i	$0.0317347\pi$
$271$			3.27703i			0.199065i	−0.995034	+	0.0995326i	$0.968265\pi$
$272$	−2.91993	−	2.91101i	−0.177047	−	0.176506i
$273$	−23.2126	−	23.2126i	−1.40489	−	1.40489i
$274$	−1.26272	+	3.04848i	−0.0762837	+	0.184165i
$275$	−2.20981	−	14.7293i	−0.133257	−	0.888210i
$276$	−3.21743	−	3.21743i	−0.193666	−	0.193666i
$277$	3.34480	+	16.8154i	0.200970	+	1.01034i	0.941164	+	0.337950i	$0.109733\pi$
$277$	3.34480	+	16.8154i	0.200970	+	1.01034i	−0.740195	+	0.672393i	$0.765267\pi$
$278$	7.38804	+	11.0570i	0.443105	+	0.663154i
$279$	23.6678	−	15.8143i	1.41696	−	0.946780i
$280$	1.95132	−	4.41197i	0.116614	−	0.263666i
$281$	26.4043	−	10.9370i	1.57515	−	0.652447i	0.587511	−	0.809216i	$-0.300108\pi$
$281$	26.4043	−	10.9370i	1.57515	−	0.652447i	0.987635	+	0.156769i	$0.0501079\pi$
$282$	2.70545	−	13.6012i	0.161107	−	0.809942i
$283$	−2.50708	+	1.67518i	−0.149030	+	0.0995789i	−0.627850	−	0.778334i	$-0.716065\pi$
$283$	−2.50708	+	1.67518i	−0.149030	+	0.0995789i	0.478820	+	0.877913i	$0.341065\pi$
$284$	3.19202	−	4.77720i	0.189412	−	0.283475i
$285$	31.1829	−	29.7378i	1.84712	−	1.76152i
$286$	2.96541	+	14.9081i	0.175348	+	0.881535i
$287$	−2.99792	−	7.23761i	−0.176961	−	0.427223i
$288$	4.16608	−	4.16608i	0.245489	−	0.245489i
$289$	−0.0519853	−	16.9999i	−0.00305796	−	0.999995i
$290$	0.364643	−	15.3725i	0.0214126	−	0.902705i
$291$	7.39558	+	3.06335i	0.433536	+	0.179577i
$292$	5.45433	−	8.16298i	0.319190	−	0.477702i
$293$			7.90877i			0.462035i	0.972950	+	0.231018i	$0.0742055\pi$
$293$			7.90877i			0.462035i	−0.972950	+	0.231018i	$0.925794\pi$
$294$	5.81503	+	3.88548i	0.339139	+	0.226606i
$295$	7.49134	−	4.75253i	0.436163	−	0.276703i
$296$	−4.04382	−	6.05201i	−0.235043	−	0.351766i
$297$	−23.7308	−	9.82960i	−1.37700	−	0.570371i
$298$	−7.55512	−	3.12943i	−0.437656	−	0.181283i
$299$	−4.32586	−	6.47411i	−0.250171	−	0.374407i
$300$	−12.7756	+	7.68617i	−0.737600	+	0.443761i
$301$	3.36934	+	2.25132i	0.194205	+	0.129764i
$302$		−	8.66532i		−	0.498633i
$303$	−21.2179	+	31.7549i	−1.21894	+	1.82427i
$304$	−5.97048	−	2.47306i	−0.342431	−	0.141839i
$305$	6.72009	−	6.40867i	0.384791	−	0.366959i
$306$	24.2922	−	0.0371424i	1.38869	−	0.00212329i
$307$	−10.8126	+	10.8126i	−0.617106	+	0.617106i	−0.944788	−	0.327682i	$-0.893733\pi$
$307$	−10.8126	+	10.8126i	−0.617106	+	0.617106i	0.327682	+	0.944788i	$0.393733\pi$
$308$	2.45939	+	5.93749i	0.140137	+	0.338320i
$309$	7.14862	+	35.9386i	0.406671	+	2.04447i
$310$	7.45575	+	7.81806i	0.423458	+	0.444036i
$311$	0.359069	−	0.537385i	0.0203609	−	0.0304723i	−0.821150	−	0.570713i	$-0.806667\pi$
$311$	0.359069	−	0.537385i	0.0203609	−	0.0304723i	0.841510	+	0.540241i	$0.181667\pi$
$312$	12.6515	−	8.45347i	0.716251	−	0.478584i
$313$	0.645545	−	3.24537i	0.0364883	−	0.183439i	−0.958243	−	0.285955i	$-0.907689\pi$
$313$	0.645545	−	3.24537i	0.0364883	−	0.183439i	0.994731	+	0.102516i	$0.0326892\pi$
$314$	5.65783	−	2.34355i	0.319290	−	0.132254i
$315$	10.2512	+	26.5100i	0.577592	+	1.49367i
$316$	−12.8356	+	8.57650i	−0.722061	+	0.482466i
$317$	−7.87772	−	11.7898i	−0.442457	−	0.662183i	0.541477	−	0.840715i	$-0.317865\pi$
$317$	−7.87772	−	11.7898i	−0.442457	−	0.662183i	−0.983934	+	0.178532i	$0.942865\pi$
$318$	−1.70077	−	8.55035i	−0.0953745	−	0.479480i
$319$	14.4848	+	14.4848i	0.810993	+	0.810993i
$320$	1.82924	+	1.28603i	0.102258	+	0.0718914i
$321$	−2.84359	+	6.86503i	−0.158714	+	0.383169i
$322$	−2.32787	−	2.32787i	−0.129727	−	0.129727i
$323$	−10.2343	−	24.6013i	−0.569451	−	1.36885i
$324$			8.03729i			0.446516i
$325$	−24.0080	+	8.63505i	−1.33172	+	0.478987i
$326$	−12.9467	+	2.57526i	−0.717053	+	0.142631i
$327$	−54.4744			−3.01244
$328$	3.56132	−	0.708391i	0.196641	−	0.0391144i
$329$	1.95744	−	9.84074i	0.107917	−	0.542537i
$330$	4.33575	−	19.3830i	0.238675	−	1.06700i
$331$	10.8628	+	26.2251i	0.597073	+	1.44146i	0.876550	+	0.481310i	$0.159839\pi$
$331$	10.8628	+	26.2251i	0.597073	+	1.44146i	−0.279477	+	0.960152i	$0.590161\pi$
$332$	3.74064	−	9.03070i	0.205294	−	0.495624i
$333$	42.0601	+	8.36627i	2.30488	+	0.458469i
$334$	17.3259	+	3.44634i	0.948032	+	0.188575i
$335$	5.83586	+	4.10285i	0.318847	+	0.224163i
$336$	4.54905	−	4.54905i	0.248171	−	0.248171i
$337$	−2.20255	−	1.47169i	−0.119980	−	0.0801683i	0.494132	−	0.869387i	$-0.335486\pi$
$337$	−2.20255	−	1.47169i	−0.119980	−	0.0801683i	−0.614112	+	0.789219i	$0.710486\pi$
$338$	12.0455	−	4.98940i	0.655187	−	0.271387i
$339$	−37.4747			−2.03535
$340$	1.59759	+	9.08007i	0.0866417	+	0.492436i
$341$	−14.3918			−0.779360
$342$	35.1765	−	14.5706i	1.90213	−	0.787886i
$343$	16.7643	+	11.2015i	0.905187	+	0.604827i
$344$	−1.32813	+	1.32813i	−0.0716080	+	0.0716080i
$345$	1.74773	+	10.0232i	0.0940947	+	0.539629i
$346$	9.66705	+	1.92290i	0.519704	+	0.103376i
$347$	−21.2587	−	4.22862i	−1.14123	−	0.227004i	−0.411940	−	0.911211i	$-0.635149\pi$
$347$	−21.2587	−	4.22862i	−1.14123	−	0.227004i	−0.729288	+	0.684207i	$0.760149\pi$
$348$	7.84720	−	18.9448i	0.420654	−	1.01555i
$349$	2.37113	+	5.72441i	0.126923	+	0.306420i	0.974549	−	0.224174i	$-0.0719686\pi$
$349$	2.37113	+	5.72441i	0.126923	+	0.306420i	−0.847626	+	0.530595i	$0.821969\pi$
$350$	−9.24337	+	5.56108i	−0.494079	+	0.297252i
$351$	−8.58400	+	43.1547i	−0.458180	+	2.30343i
$352$	−2.92159	+	0.581141i	−0.155721	+	0.0309749i
$353$	18.7851			0.999831			0.499915	−	0.866074i	$-0.333364\pi$
$353$	18.7851			0.999831			0.499915	+	0.866074i	$0.333364\pi$
$354$	11.6035	−	2.30807i	0.616718	−	0.122673i
$355$	−11.9826	+	4.63360i	−0.635971	+	0.245926i
$356$			7.65207i			0.405559i
$357$	26.5252	−	0.0405567i	1.40386	−	0.00214649i
$358$	1.54515	+	1.54515i	0.0816635	+	0.0816635i
$359$	−0.798627	+	1.92806i	−0.0421499	+	0.101759i	−0.943552	−	0.331223i	$-0.892539\pi$
$359$	−0.798627	+	1.92806i	−0.0421499	+	0.101759i	0.901402	+	0.432982i	$0.142539\pi$
$360$	−12.9785	+	2.26305i	−0.684026	+	0.119273i
$361$	−16.0956	−	16.0956i	−0.847139	−	0.847139i
$362$	−2.38233	−	11.9768i	−0.125212	−	0.629484i
$363$	−3.52301	−	5.27256i	−0.184910	−	0.276738i
$364$	9.15360	−	6.11624i	0.479779	−	0.320578i
$365$	−20.4751	+	7.91760i	−1.07172	+	0.414426i
$366$	11.4407	−	4.73891i	0.598017	−	0.247707i
$367$	−0.264915	+	1.33182i	−0.0138285	+	0.0695204i	−0.987083	−	0.160208i	$-0.948784\pi$
$367$	−0.264915	+	1.33182i	−0.0138285	+	0.0695204i	0.973255	+	0.229728i	$0.0737837\pi$
$368$	1.26875	−	0.847753i	0.0661383	−	0.0441922i
$369$	−11.8856	+	17.7880i	−0.618737	+	0.926006i
$370$	−0.385957	+	16.2711i	−0.0200650	+	0.845893i
$371$	−1.23054	−	6.18633i	−0.0638863	−	0.321178i
$372$	5.51318	+	13.3100i	0.285845	+	0.690091i
$373$	−6.12982	+	6.12982i	−0.317390	+	0.317390i	−0.847764	−	0.530374i	$-0.822052\pi$
$373$	−6.12982	+	6.12982i	−0.317390	+	0.317390i	0.530374	+	0.847764i	$0.322052\pi$
$374$	−10.2226	−	6.80790i	−0.528596	−	0.352028i
$375$	33.2543	+	2.36998i	1.71725	+	0.122385i
$376$	4.29662	+	1.77972i	0.221581	+	0.0917819i
$377$	19.4950	−	29.1764i	1.00405	−	1.50266i
$378$			18.6034i			0.956857i
$379$	9.90108	+	6.61569i	0.508584	+	0.339825i	0.783242	−	0.621717i	$-0.213565\pi$
$379$	9.90108	+	6.61569i	0.508584	+	0.339825i	−0.274658	+	0.961542i	$0.588565\pi$
$380$	7.74102	+	12.2020i	0.397106	+	0.625952i
$381$	−3.69429	−	5.52889i	−0.189264	−	0.283254i
$382$	−4.08083	−	1.69034i	−0.208793	−	0.0864851i
$383$	−13.9138	−	5.76328i	−0.710962	−	0.294490i	−0.00225919	−	0.999997i	$-0.500719\pi$
$383$	−13.9138	−	5.76328i	−0.710962	−	0.294490i	−0.708702	+	0.705507i	$0.750719\pi$
$384$	1.65666	+	2.47936i	0.0845408	+	0.126524i
$385$	3.13700	−	14.0240i	0.159876	−	0.714727i
$386$	19.6632	+	13.1386i	1.00083	+	0.668735i
$387$		−	11.0662i		−	0.562527i
$388$	−1.49143	+	2.23208i	−0.0757158	+	0.113317i
$389$	24.1120	+	9.98753i	1.22253	+	0.506388i	0.898213	−	0.439561i	$-0.144866\pi$
$389$	24.1120	+	9.98753i	1.22253	+	0.506388i	0.324315	+	0.945949i	$0.394866\pi$
$390$	−34.0141	−	0.806830i	−1.72237	−	0.0408554i
$391$	6.17249	+	1.21798i	0.312156	+	0.0615957i
$392$	−1.65843	+	1.65843i	−0.0837634	+	0.0837634i
$393$	−14.4010	−	34.7670i	−0.726433	−	1.75376i
$394$	0.300658	+	1.51151i	0.0151469	+	0.0761487i
$395$	34.5091	+	0.818573i	1.73634	+	0.0411869i
$396$	9.75051	−	14.5927i	0.489981	−	0.733309i
$397$	21.0338	−	14.0544i	1.05566	−	0.705368i	0.0985598	−	0.995131i	$-0.468576\pi$
$397$	21.0338	−	14.0544i	1.05566	−	0.705368i	0.957098	+	0.289763i	$0.0935764\pi$
$398$	−0.957161	+	4.81198i	−0.0479782	+	0.241203i
$399$	38.4101	−	15.9100i	1.92291	−	0.796495i
$400$	−1.69224	−	4.70493i	−0.0846120	−	0.235246i
$401$	−8.53692	+	5.70419i	−0.426314	+	0.284854i	−0.750160	−	0.661256i	$-0.770024\pi$
$401$	−8.53692	+	5.70419i	−0.426314	+	0.284854i	0.323847	+	0.946110i	$0.395024\pi$
$402$	5.28526	+	7.90995i	0.263605	+	0.394512i
$403$	4.80959	+	24.1795i	0.239583	+	1.20446i
$404$	−9.05641	−	9.05641i	−0.450573	−	0.450573i
$405$	10.3362	−	14.7021i	0.513611	−	0.730555i
$406$	5.67759	−	13.7069i	0.281774	−	0.680263i
$407$	−15.3315	−	15.3315i	−0.759953	−	0.759953i
$408$	−2.38014	+	12.0621i	−0.117834	+	0.597163i
$409$			18.8720i			0.933158i	0.884480	+	0.466579i	$0.154514\pi$
$409$			18.8720i			0.933158i	−0.884480	+	0.466579i	$0.845486\pi$
$410$	−7.42553	−	3.28416i	−0.366721	−	0.162193i
$411$	9.65016	−	1.91954i	0.476007	−	0.0946838i
$412$	−12.2883			−0.605403
$413$	8.39532	−	1.66993i	0.413107	−	0.0821720i
$414$	−1.75392	+	8.81754i	−0.0862003	+	0.433358i
$415$	−18.4563	+	11.7087i	−0.905985	+	0.574760i
$416$	1.95273	+	4.71431i	0.0957406	+	0.231138i
$417$	15.1748	−	36.6352i	0.743113	−	1.79403i
$418$	−18.8805	−	3.75557i	−0.923476	−	0.183691i
$419$	2.17804	+	0.433238i	0.106404	+	0.0211651i	0.248005	−	0.968759i	$-0.420225\pi$
$419$	2.17804	+	0.433238i	0.106404	+	0.0211651i	−0.141601	+	0.989924i	$0.545225\pi$
$420$	−14.1715	+	2.47108i	−0.691500	+	0.120576i
$421$	−19.5353	+	19.5353i	−0.952094	+	0.952094i	−0.998904	−	0.0468096i	$-0.985095\pi$
$421$	−19.5353	+	19.5353i	−0.952094	+	0.952094i	0.0468096	+	0.998904i	$0.485095\pi$
$422$	−22.1505	−	14.8005i	−1.07827	−	0.720476i
$423$	−25.3145	+	10.4856i	−1.23083	+	0.509828i
$424$	2.92359			0.141982
$425$	8.75489	−	18.6642i	0.424674	−	0.905346i
$426$	−17.1325			−0.830071
$427$	8.27758	−	3.42869i	0.400580	−	0.165926i
$428$	−2.07196	−	1.38444i	−0.100152	−	0.0669193i
$429$	32.0499	−	32.0499i	1.54738	−	1.54738i
$430$	4.13749	−	0.721451i	0.199527	−	0.0347914i
$431$	26.3843	+	5.24817i	1.27089	+	0.252796i	0.784051	−	0.620697i	$-0.213150\pi$
$431$	26.3843	+	5.24817i	1.27089	+	0.252796i	0.486838	+	0.873492i	$0.338150\pi$
$432$	−8.45716	−	1.68223i	−0.406895	−	0.0809365i
$433$	2.65966	−	6.42099i	0.127815	−	0.308573i	−0.846998	−	0.531596i	$-0.821592\pi$
$433$	2.65966	−	6.42099i	0.127815	−	0.308573i	0.974813	+	0.223023i	$0.0715925\pi$
$434$	3.98889	+	9.63002i	0.191473	+	0.462256i
$435$	−38.7181	+	24.5629i	−1.85639	+	1.17770i
$436$	3.56398	−	17.9173i	0.170684	−	0.858085i
$437$	9.67161	−	1.92380i	0.462656	−	0.0920279i
$438$	−29.2749			−1.39881
$439$	11.9718	−	2.38134i	0.571382	−	0.113655i	0.0990609	−	0.995081i	$-0.468416\pi$
$439$	11.9718	−	2.38134i	0.571382	−	0.113655i	0.472321	+	0.881426i	$0.343416\pi$
$440$	6.09166	+	2.69422i	0.290408	+	0.128442i
$441$		−	13.8183i		−	0.658015i
$442$	−8.02159	+	19.4499i	−0.381548	+	0.925137i
$443$	18.3210	+	18.3210i	0.870456	+	0.870456i	0.992522	−	0.122066i	$-0.0389519\pi$
$443$	18.3210	+	18.3210i	0.870456	+	0.870456i	−0.122066	+	0.992522i	$0.538952\pi$
$444$	−8.30589	+	20.0522i	−0.394180	+	0.951635i
$445$	9.84081	−	13.9975i	0.466499	−	0.663544i
$446$	−6.98556	−	6.98556i	−0.330776	−	0.330776i
$447$	4.75724	+	23.9163i	0.225010	+	1.13120i
$448$	1.19862	+	1.79386i	0.0566294	+	0.0847520i
$449$	−31.2145	+	20.8568i	−1.47310	+	0.984295i	−0.478773	+	0.877939i	$0.658918\pi$
$449$	−31.2145	+	20.8568i	−1.47310	+	0.984295i	−0.994328	+	0.106356i	$0.966082\pi$
$450$	26.6511	+	12.5511i	1.25635	+	0.591664i
$451$	9.99306	−	4.13926i	0.470555	−	0.194910i
$452$	2.45178	−	12.3259i	0.115322	−	0.579762i
$453$	−21.4844	+	14.3554i	−1.00943	+	0.674478i
$454$	−4.59868	+	6.88241i	−0.215827	+	0.323007i
$455$	−24.6098	−	0.583756i	−1.15373	−	0.0273669i
$456$	3.75944	+	18.9000i	0.176052	+	0.885072i
$457$	−6.88648	−	16.6254i	−0.322136	−	0.777705i	−0.999130	−	0.0417158i	$-0.986718\pi$
$457$	−6.88648	−	16.6254i	−0.322136	−	0.777705i	0.676994	−	0.735989i	$-0.263282\pi$
$458$	16.2199	−	16.2199i	0.757904	−	0.757904i
$459$	−19.7973	−	29.5309i	−0.924060	−	1.37839i
$460$	−3.41109	−	0.0809127i	−0.159043	−	0.00377257i
$461$	22.1601	+	9.17900i	1.03210	+	0.427508i	0.833469	−	0.552566i	$-0.186351\pi$
$461$	22.1601	+	9.17900i	1.03210	+	0.427508i	0.198628	+	0.980075i	$0.436351\pi$
$462$	10.6468	−	15.9341i	0.495335	−	0.741321i
$463$		−	35.3808i		−	1.64428i	−0.569283	−	0.822142i	$-0.692779\pi$
$463$		−	35.3808i		−	1.64428i	0.569283	−	0.822142i	$-0.307221\pi$
$464$	5.71779	+	3.82051i	0.265442	+	0.177363i
$465$	7.03216	−	31.4373i	0.326109	−	1.45787i
$466$	−15.4019	−	23.0506i	−0.713479	−	1.06780i
$467$	20.7488	+	8.59445i	0.960142	+	0.397704i	0.807033	−	0.590506i	$-0.201072\pi$
$467$	20.7488	+	8.59445i	0.960142	+	0.397704i	0.153108	+	0.988209i	$0.451072\pi$
$468$	−27.7755	−	11.5050i	−1.28392	−	0.531818i
$469$	3.82398	+	5.72299i	0.176575	+	0.264263i
$470$	−5.57077	−	8.78112i	−0.256960	−	0.405043i
$471$	−15.1836	−	10.1453i	−0.699622	−	0.467472i
$472$			3.96754i			0.182621i
$473$	−3.10842	+	4.65208i	−0.142925	+	0.213903i
$474$	42.5285	+	17.6159i	1.95340	+	0.809123i
$475$	1.53205	−	32.2757i	0.0702953	−	1.48091i
$476$	−1.72207	+	8.72715i	−0.0789310	+	0.400008i
$477$	−12.1799	+	12.1799i	−0.557681	+	0.557681i
$478$	−8.35550	−	20.1720i	−0.382172	−	0.922644i
$479$	−3.75915	−	18.8985i	−0.171760	−	0.863496i	−0.966524	−	0.256577i	$-0.917405\pi$
$479$	−3.75915	−	18.8985i	−0.171760	−	0.863496i	0.794764	−	0.606919i	$-0.207595\pi$
$480$	0.158117	−	6.66586i	0.00721703	−	0.304253i
$481$	−20.6346	+	30.8818i	−0.940856	+	1.40809i
$482$	−9.27249	+	6.19568i	−0.422350	+	0.282206i
$483$	−1.91515	+	9.62809i	−0.0871421	+	0.438093i
$484$	1.96470	−	0.813807i	0.0893048	−	0.0369912i
$485$	5.59871	−	2.16499i	0.254224	−	0.0983070i
$486$	−1.58158	+	1.05678i	−0.0717422	+	0.0479366i
$487$	17.2975	+	25.8876i	0.783826	+	1.17308i	0.981246	+	0.192760i	$0.0617437\pi$
$487$	17.2975	+	25.8876i	0.783826	+	1.17308i	−0.197420	+	0.980319i	$0.563256\pi$
$488$	0.810180	+	4.07305i	0.0366751	+	0.184378i
$489$	27.8333	+	27.8333i	1.25866	+	1.25866i
$490$	5.16646	−	0.900872i	0.233397	−	0.0406972i
$491$	−12.1296	+	29.2835i	−0.547403	+	1.32155i	0.372001	+	0.928232i	$0.378672\pi$
$491$	−12.1296	+	29.2835i	−0.547403	+	1.32155i	−0.919404	+	0.393315i	$0.871328\pi$
$492$	−7.65624	−	7.65624i	−0.345170	−	0.345170i
$493$	5.57400	+	27.8002i	0.251041	+	1.25206i
$494$			32.9759i			1.48366i
$495$	−36.6027	+	14.1540i	−1.64517	+	0.636176i
$496$	−4.73853	+	0.942552i	−0.212766	+	0.0423218i
$497$	−12.3957			−0.556021
$498$	−28.5873	+	5.68637i	−1.28103	+	0.254812i
$499$	−5.07928	+	25.5353i	−0.227380	+	1.14312i	0.683343	+	0.730098i	$0.260525\pi$
$499$	−5.07928	+	25.5353i	−0.227380	+	1.14312i	−0.910723	+	0.413018i	$0.864475\pi$
$500$	−2.95517	+	10.7827i	−0.132159	+	0.482218i
$501$	−20.1584	−	48.6666i	−0.900609	−	2.17426i
$502$	−3.05139	+	7.36670i	−0.136190	+	0.328792i
$503$	19.6945	+	3.91748i	0.878134	+	0.174672i	0.613517	−	0.789682i	$-0.289754\pi$
$503$	19.6945	+	3.91748i	0.878134	+	0.174672i	0.264617	+	0.964353i	$0.414754\pi$
$504$	−12.4669	−	2.47982i	−0.555321	−	0.110460i
$505$	4.91951	+	28.2132i	0.218915	+	1.25547i
$506$	3.21411	−	3.21411i	0.142885	−	0.142885i
$507$	−32.3257	−	21.5993i	−1.43563	−	0.959260i
$508$	2.06022	−	0.853371i	0.0914075	−	0.0378622i
$509$	−2.28523			−0.101291			−0.0506455	−	0.998717i	$-0.516128\pi$
$509$	−2.28523			−0.101291			−0.0506455	+	0.998717i	$0.516128\pi$
$510$	19.8661	−	19.0036i	0.879686	−	0.841492i
$511$	−21.1809			−0.936988
$512$	−0.923880	+	0.382683i	−0.0408301	+	0.0169124i
$513$	−46.3331	−	30.9588i	−2.04566	−	1.36686i
$514$	−8.42923	+	8.42923i	−0.371797	+	0.371797i
$515$	22.4783	+	15.8032i	0.990514	+	0.696373i
$516$	5.49317	+	1.09266i	0.241823	+	0.0481016i
$517$	13.5872	+	2.70267i	0.597565	+	0.118863i
$518$	−6.00946	+	14.5081i	−0.264040	+	0.637450i
$519$	−11.2474	−	27.1537i	−0.493707	−	1.19191i
$520$	2.49074	−	11.1349i	0.109226	−	0.488297i
$521$	4.26245	−	21.4288i	0.186741	−	0.938812i	−0.767790	−	0.640701i	$-0.778644\pi$
$521$	4.26245	−	21.4288i	0.186741	−	0.938812i	0.954531	−	0.298110i	$-0.0963563\pi$
$522$	−39.7373	+	7.90425i	−1.73926	+	0.345960i
$523$	38.7971			1.69648			0.848239	−	0.529614i	$-0.177663\pi$
$523$	38.7971			1.69648			0.848239	+	0.529614i	$0.177663\pi$
$524$	12.3775	−	2.46204i	0.540714	−	0.107555i
$525$	29.1010	+	13.7049i	1.27007	+	0.598129i
$526$			14.0896i			0.614334i
$527$	−16.5800	−	11.0417i	−0.722234	−	0.480986i
$528$	6.28093	+	6.28093i	0.273342	+	0.273342i
$529$	7.91067	−	19.0981i	0.343942	−	0.830350i
$530$	−5.34795	−	3.75984i	−0.232300	−	0.163317i
$531$	−16.5291	−	16.5291i	−0.717301	−	0.717301i
$532$	2.72002	+	13.6745i	0.117928	+	0.592863i
$533$	−10.2939	−	15.4059i	−0.445878	−	0.667304i
$534$	18.9722	−	12.6768i	0.821008	−	0.548580i
$535$	2.00967	+	5.19707i	0.0868858	+	0.224689i
$536$	−2.94747	+	1.22088i	−0.127311	+	0.0527341i
$537$	1.27120	−	6.39075i	0.0548563	−	0.275781i
$538$	−3.61214	+	2.41356i	−0.155731	+	0.104056i
$539$	−3.88147	+	5.80904i	−0.167187	+	0.250213i
$540$	13.3068	+	13.9534i	0.572632	+	0.600459i
$541$	2.10863	+	10.6008i	0.0906572	+	0.455765i	0.999273	+	0.0381310i	$0.0121404\pi$
$541$	2.10863	+	10.6008i	0.0906572	+	0.455765i	−0.908616	+	0.417634i	$0.862860\pi$
$542$	1.25406	+	3.02758i	0.0538666	+	0.130046i
$543$	−25.7480	+	25.7480i	−1.10495	+	1.10495i
$544$	−3.81166	−	1.57202i	−0.163424	−	0.0673997i
$545$	−29.5617	+	28.1917i	−1.26628	+	1.20760i
$546$	−30.3287	−	12.5626i	−1.29795	−	0.537628i
$547$	13.3892	−	20.0384i	0.572482	−	0.856780i	−0.426376	−	0.904546i	$-0.640210\pi$
$547$	13.3892	−	20.0384i	0.572482	−	0.856780i	0.998859	+	0.0477657i	$0.0152101\pi$
$548$			3.29965i			0.140954i
$549$	−20.3439	−	13.5934i	−0.868258	−	0.580151i
$550$	−7.67826	−	12.7624i	−0.327402	−	0.544192i
$551$	24.6897	+	36.9507i	1.05182	+	1.57415i
$552$	−4.20377	−	1.74126i	−0.178924	−	0.0741129i
$553$	30.7701	+	12.7454i	1.30848	+	0.541989i
$554$	9.52519	+	14.2554i	0.404686	+	0.605656i
$555$	40.9812	−	25.9986i	1.73956	−	1.10358i
$556$	11.0570	+	7.38804i	0.468921	+	0.313323i
$557$			33.9956i			1.44044i	0.693746	+	0.720220i	$0.255959\pi$
$557$			33.9956i			1.44044i	−0.693746	+	0.720220i	$0.744041\pi$
$558$	15.8143	−	23.6678i	0.669475	−	1.00194i
$559$	8.85471	+	3.66774i	0.374514	+	0.155129i
$560$	0.114401	−	4.82287i	0.00483431	−	0.203803i
$561$	0.0559971	+	36.6237i	0.00236420	+	1.54626i
$562$	20.2089	−	20.2089i	0.852463	−	0.852463i
$563$	−2.94572	−	7.11160i	−0.124147	−	0.299718i	0.849571	−	0.527475i	$-0.176861\pi$
$563$	−2.94572	−	7.11160i	−0.124147	−	0.299718i	−0.973718	+	0.227756i	$0.926861\pi$
$564$	−2.70545	−	13.6012i	−0.113920	−	0.572715i
$565$	−20.3364	+	19.3940i	−0.855559	+	0.815911i
$566$	−1.67518	+	2.50708i	−0.0704129	+	0.105380i
$567$	14.4178	−	9.63365i	0.605490	−	0.404575i
$568$	1.12089	−	5.63509i	0.0470315	−	0.236443i
$569$	−18.4941	+	7.66052i	−0.775314	+	0.321146i	−0.735023	−	0.678042i	$-0.762829\pi$
$569$	−18.4941	+	7.66052i	−0.775314	+	0.321146i	−0.0402912	+	0.999188i	$0.512829\pi$
$570$	17.4291	−	39.4074i	0.730023	−	1.65059i
$571$	8.82341	−	5.89561i	0.369248	−	0.246724i	−0.357077	−	0.934075i	$-0.616227\pi$
$571$	8.82341	−	5.89561i	0.369248	−	0.246724i	0.726325	+	0.687351i	$0.241227\pi$
$572$	8.44477	+	12.6385i	0.353093	+	0.528442i
$573$	2.56958	+	12.9181i	0.107346	+	0.539663i
$574$	−5.53943	−	5.53943i	−0.231211	−	0.231211i
$575$	6.13565	+	4.53478i	0.255874	+	0.189114i
$576$	2.25467	−	5.44325i	0.0939445	−	0.226802i
$577$	−26.0481	−	26.0481i	−1.08440	−	1.08440i	−0.996094	−	0.0883015i	$-0.971856\pi$
$577$	−26.0481	−	26.0481i	−1.08440	−	1.08440i	−0.0883015	−	0.996094i	$-0.528144\pi$
$578$	−6.55362	−	15.6860i	−0.272594	−	0.652451i
$579$		−	70.5183i		−	2.93064i
$580$	−5.54592	−	14.3419i	−0.230282	−	0.595515i
$581$	−20.6834	+	4.11419i	−0.858093	+	0.170685i
$582$	8.00491			0.331814
$583$	8.54154	−	1.69902i	0.353755	−	0.0703662i
$584$	1.91531	−	9.62889i	0.0792559	−	0.398446i
$585$	36.0122	+	56.7655i	1.48892	+	2.34696i
$586$	3.02656	+	7.30675i	0.125026	+	0.301839i
$587$	6.90430	−	16.6684i	0.284971	−	0.687980i	−0.714967	−	0.699159i	$-0.753558\pi$
$587$	6.90430	−	16.6684i	0.284971	−	0.687980i	0.999938	+	0.0111781i	$0.00355817\pi$
$588$	6.85929	+	1.36440i	0.282872	+	0.0562668i
$589$	−30.6223	−	6.09115i	−1.26177	−	0.250982i
$590$	5.10238	−	7.25758i	0.210062	−	0.298790i
$591$	3.24949	−	3.24949i	0.133666	−	0.133666i
$592$	−6.05201	−	4.04382i	−0.248736	−	0.166200i
$593$	19.0530	−	7.89203i	0.782414	−	0.324087i	0.0445250	−	0.999008i	$-0.485823\pi$
$593$	19.0530	−	7.89203i	0.782414	−	0.324087i	0.737889	+	0.674922i	$0.235823\pi$
$594$	−25.6860			−1.05391
$595$	14.3735	−	13.7494i	0.589255	−	0.563671i
$596$	−8.17761			−0.334968
$597$	13.5163	−	5.59864i	0.553185	−	0.229137i
$598$	−6.47411	−	4.32586i	−0.264746	−	0.176898i
$599$	8.03343	−	8.03343i	0.328237	−	0.328237i	−0.523679	−	0.851916i	$-0.675441\pi$
$599$	8.03343	−	8.03343i	0.328237	−	0.328237i	0.851916	+	0.523679i	$0.175441\pi$
$600$	−8.86174	+	11.9901i	−0.361779	+	0.489494i
$601$	16.8364	+	3.34896i	0.686770	+	0.136607i	0.526127	−	0.850406i	$-0.323644\pi$
$601$	16.8364	+	3.34896i	0.686770	+	0.136607i	0.160642	+	0.987013i	$0.448644\pi$
$602$	3.97440	+	0.790558i	0.161985	+	0.0322207i
$603$	7.19311	−	17.3657i	0.292926	−	0.707186i
$604$	−3.31607	−	8.00571i	−0.134929	−	0.325748i
$605$	−4.64050	−	1.03803i	−0.188663	−	0.0422017i
$606$	−7.45075	+	37.4574i	−0.302666	+	1.52160i
$607$	−15.0490	+	2.99343i	−0.610821	+	0.121500i	−0.490801	−	0.871272i	$-0.663296\pi$
$607$	−15.0490	+	2.99343i	−0.610821	+	0.121500i	−0.120020	+	0.992772i	$0.538296\pi$
$608$	−6.46241			−0.262085
$609$	−43.3902	+	8.63085i	−1.75826	+	0.349740i
$610$	3.75606	−	8.49250i	0.152078	−	0.343851i
$611$		−	23.7309i		−	0.960050i
$612$	22.4288	−	9.33054i	0.906632	−	0.377165i
$613$	−5.02517	−	5.02517i	−0.202965	−	0.202965i	0.598304	−	0.801269i	$-0.295841\pi$
$613$	−5.02517	−	5.02517i	−0.202965	−	0.202965i	−0.801269	+	0.598304i	$0.795841\pi$
$614$	−5.85173	+	14.1273i	−0.236156	+	0.570132i
$615$	4.15893	+	23.8513i	0.167704	+	0.961777i
$616$	4.54436	+	4.54436i	0.183098	+	0.183098i
$617$	−1.51726	−	7.62776i	−0.0610824	−	0.307082i	0.938151	−	0.346226i	$-0.112537\pi$
$617$	−1.51726	−	7.62776i	−0.0610824	−	0.307082i	−0.999234	+	0.0391439i	$0.987537\pi$
$618$	20.3576	+	30.4672i	0.818901	+	1.22557i
$619$	23.2443	−	15.5314i	0.934268	−	0.624258i	0.00753243	−	0.999972i	$-0.497602\pi$
$619$	23.2443	−	15.5314i	0.934268	−	0.624258i	0.926736	+	0.375714i	$0.122602\pi$
$620$	9.88006	+	4.36975i	0.396793	+	0.175493i
$621$	12.1562	−	5.03525i	0.487810	−	0.202058i
$622$	0.126088	−	0.633889i	0.00505568	−	0.0254166i
$623$	13.7267	−	9.17192i	0.549950	−	0.367465i
$624$	8.45347	−	12.6515i	0.338410	−	0.506466i
$625$	19.2726	−	15.9237i	0.770906	−	0.636949i
$626$	−0.645545	−	3.24537i	−0.0258011	−	0.129711i
$627$	21.9671	+	53.0332i	0.877281	+	2.11794i
$628$	4.33031	−	4.33031i	0.172798	−	0.172798i
$629$	−5.89982	−	29.4252i	−0.235241	−	1.17326i
$630$	19.6159	+	20.5691i	0.781514	+	0.819491i
$631$	16.9058	+	7.00260i	0.673008	+	0.278769i	0.692901	−	0.721033i	$-0.256332\pi$
$631$	16.9058	+	7.00260i	0.673008	+	0.278769i	−0.0198927	+	0.999802i	$0.506332\pi$
$632$	−8.57650	+	12.8356i	−0.341155	+	0.510574i
$633$			79.4383i			3.15739i
$634$	−11.7898	−	7.87772i	−0.468234	−	0.312864i
$635$	−4.86610	−	1.08849i	−0.193105	−	0.0431954i
$636$	−4.84339	−	7.24864i	−0.192053	−	0.287427i
$637$	11.0568	+	4.57989i	0.438088	+	0.181462i
$638$	18.9253	+	7.83912i	0.749260	+	0.310354i
$639$	18.8065	+	28.1460i	0.743975	+	1.11344i
$640$	2.18214	+	0.488119i	0.0862567	+	0.0192946i
$641$	−29.4328	−	19.6664i	−1.16253	−	0.776776i	−0.184007	−	0.982925i	$-0.558907\pi$
$641$	−29.4328	−	19.6664i	−1.16253	−	0.776776i	−0.978521	+	0.206149i	$0.933907\pi$
$642$			7.43066i			0.293265i
$643$	5.81925	−	8.70912i	0.229489	−	0.343454i	−0.698798	−	0.715319i	$-0.746281\pi$
$643$	5.81925	−	8.70912i	0.229489	−	0.343454i	0.928287	+	0.371865i	$0.121281\pi$
$644$	−3.04150	−	1.25983i	−0.119852	−	0.0496443i
$645$	−8.64313	−	9.06313i	−0.340323	−	0.356860i
$646$	−18.8698	−	18.8122i	−0.742421	−	0.740154i
$647$	1.76443	−	1.76443i	0.0693668	−	0.0693668i	−0.671572	−	0.740939i	$-0.734381\pi$
$647$	1.76443	−	1.76443i	0.0693668	−	0.0693668i	0.740939	+	0.671572i	$0.234381\pi$
$648$	3.07574	+	7.42549i	0.120826	+	0.291701i
$649$	2.30570	+	11.5915i	0.0905065	+	0.455007i
$650$	−18.8760	+	17.1652i	−0.740378	+	0.673275i
$651$	17.2681	−	25.8435i	0.676789	−	1.01289i
$652$	−10.9757	+	7.33373i	−0.429842	+	0.287211i
$653$	2.34838	−	11.8061i	0.0918991	−	0.462008i	−0.907243	−	0.420606i	$-0.861818\pi$
$653$	2.34838	−	11.8061i	0.0918991	−	0.462008i	0.999143	−	0.0414020i	$-0.0131824\pi$
$654$	−50.3278	+	20.8465i	−1.96797	+	0.815161i
$655$	−25.8077	−	11.4142i	−1.00839	−	0.445990i
$656$	3.01915	−	2.01733i	0.117878	−	0.0787634i
$657$	32.1354	+	48.0941i	1.25372	+	1.87633i
$658$	−1.95744	−	9.84074i	−0.0763091	−	0.383632i
$659$	−21.1376	−	21.1376i	−0.823403	−	0.823403i	0.163192	−	0.986594i	$-0.447821\pi$
$659$	−21.1376	−	21.1376i	−0.823403	−	0.823403i	−0.986594	+	0.163192i	$0.947821\pi$
$660$	−3.41185	−	19.5668i	−0.132806	−	0.761637i
$661$	−7.99380	+	19.2988i	−0.310923	+	0.750634i	0.688748	+	0.725000i	$0.258160\pi$
$661$	−7.99380	+	19.2988i	−0.310923	+	0.750634i	−0.999671	+	0.0256340i	$0.991840\pi$
$662$	20.0718	+	20.0718i	0.780114	+	0.780114i
$663$	61.5123	−	12.3334i	2.38894	−	0.478988i
$664$		−	9.77476i		−	0.379334i
$665$	12.6102	−	28.5119i	0.489004	−	1.10565i
$666$	42.0601	−	8.36627i	1.62980	−	0.324186i
$667$	−10.4933			−0.406303
$668$	17.3259	−	3.44634i	0.670360	−	0.133343i
$669$	−5.74706	+	28.8924i	−0.222194	+	1.11704i
$670$	6.96173	+	1.55726i	0.268955	+	0.0601621i
$671$	4.73403	+	11.4290i	0.182755	+	0.441210i
$672$	2.46193	−	5.94362i	0.0949709	−	0.229280i
$673$	−35.6232	−	7.08590i	−1.37317	−	0.273141i	−0.547272	−	0.836955i	$-0.684334\pi$
$673$	−35.6232	−	7.08590i	−1.37317	−	0.273141i	−0.825902	+	0.563813i	$0.809334\pi$
$674$	−2.59808	−	0.516790i	−0.100074	−	0.0199060i
$675$	−6.39676	−	42.6371i	−0.246211	−	1.64110i
$676$	9.21920	−	9.21920i	0.354585	−	0.354585i
$677$	5.06304	+	3.38302i	0.194588	+	0.130020i	0.649048	−	0.760748i	$-0.275168\pi$
$677$	5.06304	+	3.38302i	0.194588	+	0.130020i	−0.454459	+	0.890767i	$0.650168\pi$
$678$	−34.6221	+	14.3409i	−1.32965	+	0.550761i
$679$	5.79170			0.222265
$680$	4.95078	+	7.77752i	0.189854	+	0.298254i
$681$	24.6824			0.945831
$682$	−13.2963	+	5.50750i	−0.509141	+	0.210893i
$683$	−20.5178	−	13.7095i	−0.785091	−	0.524581i	0.0972115	−	0.995264i	$-0.469008\pi$
$683$	−20.5178	−	13.7095i	−0.785091	−	0.524581i	−0.882303	+	0.470683i	$0.844008\pi$
$684$	26.9229	−	26.9229i	1.02942	−	1.02942i
$685$	4.24346	−	6.03585i	0.162134	−	0.230618i
$686$	19.7748	+	3.93346i	0.755007	+	0.150180i
$687$	−67.0855	−	13.3441i	−2.55947	−	0.509111i
$688$	−0.718779	+	1.73529i	−0.0274032	+	0.0661572i
$689$	−5.70900	−	13.7827i	−0.217495	−	0.525080i
$690$	5.45039	+	8.59137i	0.207493	+	0.327068i
$691$	−5.00947	+	25.1843i	−0.190569	+	0.958057i	0.760561	+	0.649267i	$0.224924\pi$
$691$	−5.00947	+	25.1843i	−0.190569	+	0.958057i	−0.951130	+	0.308790i	$0.900076\pi$
$692$	9.66705	−	1.92290i	0.367486	−	0.0730975i
$693$	−37.8644			−1.43835
$694$	−21.2587	+	4.22862i	−0.806970	+	0.160516i
$695$	−10.7246	−	27.7341i	−0.406808	−	1.05202i
$696$		−	20.5057i		−	0.777268i
$697$	14.6882	+	2.89832i	0.556354	+	0.109782i
$698$	4.38127	+	4.38127i	0.165834	+	0.165834i
$699$	−31.6350	+	76.3737i	−1.19655	+	2.88872i
$700$	−6.41163	+	8.67506i	−0.242337	+	0.327886i
$701$	−11.3764	−	11.3764i	−0.429679	−	0.429679i	0.458840	−	0.888519i	$-0.348265\pi$
$701$	−11.3764	−	11.3764i	−0.429679	−	0.429679i	−0.888519	+	0.458840i	$0.848265\pi$
$702$	8.58400	+	43.1547i	0.323982	+	1.62877i
$703$	−26.1328	−	39.1106i	−0.985619	−	1.47508i
$704$	−2.47681	+	1.65495i	−0.0933481	+	0.0623732i
$705$	−12.5427	+	28.3592i	−0.472386	+	1.06807i
$706$	17.3552	−	7.18875i	0.653171	−	0.270552i
$707$	−5.39075	+	27.1011i	−0.202740	+	1.01924i
$708$	9.83695	−	6.57284i	0.369695	−	0.247022i
$709$	−3.94521	+	5.90443i	−0.148165	+	0.221745i	−0.898127	−	0.439736i	$-0.855072\pi$
$709$	−3.94521	+	5.90443i	−0.148165	+	0.221745i	0.749962	+	0.661481i	$0.230072\pi$
$710$	−9.29729	+	8.86643i	−0.348921	+	0.332751i
$711$	−17.7439	−	89.2047i	−0.665449	−	3.34544i
$712$	2.92832	+	7.06959i	0.109743	+	0.264944i
$713$	5.21297	−	5.21297i	0.195227	−	0.195227i
$714$	24.4906	−	10.1882i	0.916538	−	0.381285i
$715$	0.805999	−	33.9791i	0.0301427	−	1.27075i
$716$	2.01883	+	0.836227i	0.0754473	+	0.0312513i
$717$	−36.1714	+	54.1343i	−1.35084	+	2.02168i
$718$			2.08691i			0.0778829i
$719$	29.9430	+	20.0073i	1.11669	+	0.746146i	0.970016	−	0.243040i	$-0.0781446\pi$
$719$	29.9430	+	20.0073i	1.11669	+	0.746146i	0.146670	+	0.989186i	$0.453145\pi$
$720$	−11.1245	+	7.05743i	−0.414587	+	0.263015i
$721$	14.7291	+	22.0436i	0.548539	+	0.820946i
$722$	−21.0300	−	8.71090i	−0.782655	−	0.324186i
$723$	30.7226	+	12.7257i	1.14259	+	0.473275i
$724$	−6.78429	−	10.1534i	−0.252136	−	0.377348i
$725$	−8.29933	+	33.3670i	−0.308229	+	1.23922i
$726$	−5.27256	−	3.52301i	−0.195683	−	0.130751i
$727$		−	32.6875i		−	1.21231i	−0.795345	−	0.606156i	$-0.792711\pi$
$727$		−	32.6875i		−	1.21231i	0.795345	−	0.606156i	$-0.207289\pi$
$728$	6.11624	−	9.15360i	0.226683	−	0.339255i
$729$	27.5167	+	11.3978i	1.01914	+	0.422141i
$730$	−15.8866	+	15.1504i	−0.587990	+	0.560742i
$731$	−7.15023	+	2.97454i	−0.264461	+	0.110017i
$732$	8.75636	−	8.75636i	0.323645	−	0.323645i
$733$	8.14076	+	19.6535i	0.300686	+	0.725920i	0.999939	+	0.0110459i	$0.00351609\pi$
$733$	8.14076	+	19.6535i	0.300686	+	0.725920i	−0.699253	+	0.714874i	$0.746484\pi$
$734$	0.264915	+	1.33182i	0.00977821	+	0.0491584i
$735$	−10.7926	−	11.3171i	−0.398092	−	0.417437i
$736$	0.847753	−	1.26875i	0.0312486	−	0.0467668i
$737$	−7.90180	+	5.27981i	−0.291066	+	0.194484i
$738$	−4.17365	+	20.9824i	−0.153634	+	0.772371i
$739$	−29.6823	+	12.2948i	−1.09188	+	0.452271i	−0.854662	−	0.519185i	$-0.826236\pi$
$739$	−29.6823	+	12.2948i	−1.09188	+	0.452271i	−0.237218	+	0.971456i	$0.576236\pi$
$740$	5.87009	+	15.1802i	0.215789	+	0.558036i
$741$	81.7592	−	54.6298i	3.00350	−	2.00687i
$742$	−3.50428	−	5.24452i	−0.128646	−	0.192532i
$743$	−2.43650	−	12.2491i	−0.0893863	−	0.449375i	−0.999395	−	0.0347858i	$-0.988925\pi$
$743$	−2.43650	−	12.2491i	−0.0893863	−	0.449375i	0.910008	−	0.414590i	$-0.136075\pi$
$744$	10.1870	+	10.1870i	0.373475	+	0.373475i
$745$	14.9588	+	10.5167i	0.548048	+	0.385301i
$746$	−3.31743	+	8.00899i	−0.121460	+	0.293230i
$747$	40.7225	+	40.7225i	1.48996	+	1.48996i
$748$	−12.0497	−	2.37768i	−0.440580	−	0.0869367i
$749$			5.37621i			0.196443i
$750$	31.6299	−	10.5363i	1.15496	−	0.384731i
$751$	1.41399	−	0.281260i	0.0515972	−	0.0102633i	−0.169224	−	0.985578i	$-0.554126\pi$
$751$	1.41399	−	0.281260i	0.0515972	−	0.0102633i	0.220821	+	0.975314i	$0.429126\pi$
$752$	4.65062			0.169591
$753$	23.3198	−	4.63859i	0.849820	−	0.169040i
$754$	6.84575	−	34.4159i	0.249307	−	1.25335i
$755$	−4.22971	+	18.9089i	−0.153935	+	0.688167i
$756$	7.11923	+	17.1873i	0.258924	+	0.625097i
$757$	10.3778	−	25.0542i	0.377187	−	0.910610i	−0.615304	−	0.788290i	$-0.710967\pi$
$757$	10.3778	−	25.0542i	0.377187	−	0.910610i	0.992491	−	0.122320i	$-0.0390334\pi$
$758$	11.6791	+	2.32312i	0.424205	+	0.0843796i
$759$	−13.2936	−	2.64426i	−0.482528	−	0.0959807i
$760$	11.8213	+	8.31086i	0.428803	+	0.301467i
$761$	−23.9731	+	23.9731i	−0.869023	+	0.869023i	−0.992364	−	0.123342i	$-0.960639\pi$
$761$	−23.9731	+	23.9731i	−0.869023	+	0.869023i	0.123342	+	0.992364i	$0.460639\pi$
$762$	−5.52889	−	3.69429i	−0.200291	−	0.133830i
$763$	−36.4131	+	15.0828i	−1.31824	+	0.546034i
$764$	−4.41706			−0.159804
$765$	−53.0271	−	11.7764i	−1.91720	−	0.425778i
$766$	−15.0602			−0.544146
$767$	18.7042	−	7.74754i	0.675370	−	0.279747i
$768$	2.47936	+	1.65666i	0.0894662	+	0.0597794i
$769$	15.9323	−	15.9323i	0.574535	−	0.574535i	−0.358858	−	0.933392i	$-0.616834\pi$
$769$	15.9323	−	15.9323i	0.574535	−	0.574535i	0.933392	+	0.358858i	$0.116834\pi$
$770$	−2.46853	−	14.1569i	−0.0889597	−	0.510180i
$771$	34.8634	+	6.93476i	1.25558	+	0.249749i
$772$	23.1944	+	4.61365i	0.834784	+	0.166049i
$773$	−13.5036	+	32.6005i	−0.485690	+	1.17256i	0.471178	+	0.882038i	$0.343829\pi$
$773$	−13.5036	+	32.6005i	−0.485690	+	1.17256i	−0.956868	+	0.290522i	$0.906171\pi$
$774$	−4.23485	−	10.2238i	−0.152219	−	0.367488i
$775$	−12.4534	−	20.6994i	−0.447338	−	0.743544i
$776$	−0.523720	+	2.63292i	−0.0188005	+	0.0945163i
$777$	45.9264	−	9.13534i	1.64760	−	0.327728i
$778$	26.0987			0.935683
$779$	23.0147	−	4.57791i	0.824588	−	0.164021i
$780$	−31.7337	+	12.2712i	−1.13625	+	0.439380i
$781$		−	17.1148i		−	0.612417i
$782$	6.16874	−	1.23685i	0.220594	−	0.0442295i
$783$	41.9293	+	41.9293i	1.49843	+	1.49843i
$784$	−0.897536	+	2.16684i	−0.0320549	+	0.0773873i
$785$	−13.4901	+	2.35226i	−0.481483	+	0.0839557i
$786$	−26.6095	−	26.6095i	−0.949131	−	0.949131i
$787$	−7.92509	−	39.8421i	−0.282499	−	1.42022i	−0.817774	−	0.575540i	$-0.804792\pi$
$787$	−7.92509	−	39.8421i	−0.282499	−	1.42022i	0.535275	−	0.844678i	$-0.320208\pi$
$788$	0.856201	+	1.28139i	0.0305009	+	0.0456478i
$789$	34.9331	−	23.3415i	1.24365	−	0.830981i
$790$	32.1955	−	12.4498i	1.14547	−	0.442944i
$791$	−25.0497	+	10.3759i	−0.890665	+	0.368926i
$792$	3.42392	−	17.2132i	0.121664	−	0.611645i
$793$	17.6196	−	11.7730i	0.625689	−	0.418072i
$794$	14.0544	−	21.0338i	0.498771	−	0.746463i
$795$	−0.462270	+	19.4883i	−0.0163950	+	0.691177i
$796$	0.957161	+	4.81198i	0.0339257	+	0.170556i
$797$	−12.3988	−	29.9332i	−0.439186	−	1.06029i	−0.976230	−	0.216736i	$-0.930459\pi$
$797$	−12.3988	−	29.9332i	−0.439186	−	1.06029i	0.537044	−	0.843554i	$-0.319541\pi$
$798$	29.3978	−	29.3978i	1.04067	−	1.04067i
$799$	13.5795	+	13.5380i	0.480408	+	0.478941i
$800$	−3.36392	−	3.69919i	−0.118933	−	0.130786i
$801$	−41.6521	−	17.2529i	−1.47170	−	0.609600i
$802$	−5.70419	+	8.53692i	−0.201422	+	0.301449i
$803$		−	29.2447i		−	1.03202i
$804$	7.90995	+	5.28526i	0.278962	+	0.186397i
$805$	3.94345	+	6.21601i	0.138989	+	0.219085i
$806$	13.6966	+	20.4984i	0.482441	+	0.722024i
$807$	11.9681	+	4.95737i	0.421299	+	0.174508i
$808$	−11.8328	−	4.90129i	−0.416275	−	0.172427i
$809$	2.83469	+	4.24242i	0.0996626	+	0.149156i	0.877950	−	0.478753i	$-0.158911\pi$
$809$	2.83469	+	4.24242i	0.0996626	+	0.149156i	−0.778287	+	0.627909i	$0.783911\pi$
$810$	3.92316	−	17.5385i	0.137846	−	0.616240i
$811$	−17.3551	−	11.5963i	−0.609421	−	0.407202i	0.212208	−	0.977224i	$-0.431934\pi$
$811$	−17.3551	−	11.5963i	−0.609421	−	0.407202i	−0.821629	+	0.570022i	$0.806934\pi$
$812$		−	14.8363i		−	0.520651i
$813$	5.42890	−	8.12493i	0.190400	−	0.284954i
$814$	−20.0315	−	8.29733i	−0.702105	−	0.290821i
$815$	29.5086	+	0.699958i	1.03364	+	0.0245185i
$816$	2.41701	+	12.0548i	0.0846123	+	0.422001i
$817$	−8.58292	+	8.58292i	−0.300278	+	0.300278i
$818$	7.22198	+	17.4354i	0.252511	+	0.609615i
$819$	12.6539	+	63.6154i	0.442163	+	2.22290i
$820$	−8.11709	−	0.192541i	−0.283461	−	0.00672383i
$821$	−12.5463	+	18.7769i	−0.437870	+	0.655318i	−0.983121	−	0.182954i	$-0.941434\pi$
$821$	−12.5463	+	18.7769i	−0.437870	+	0.655318i	0.545252	+	0.838272i	$0.316434\pi$
$822$	8.18101	−	5.46638i	0.285346	−	0.190662i
$823$	5.50950	−	27.6981i	0.192049	−	0.965496i	−0.757728	−	0.652570i	$-0.773691\pi$
$823$	5.50950	−	27.6981i	0.192049	−	0.965496i	0.949777	−	0.312926i	$-0.101309\pi$
$824$	−11.3530	+	4.70255i	−0.395499	+	0.163821i
$825$	−18.9225	+	40.1801i	−0.658795	+	1.39889i
$826$	7.11721	−	4.75557i	0.247639	−	0.165467i
$827$	13.1935	+	19.7455i	0.458783	+	0.686617i	0.986677	−	0.162693i	$-0.0520181\pi$
$827$	13.1935	+	19.7455i	0.458783	+	0.686617i	−0.527894	+	0.849310i	$0.677018\pi$
$828$	1.75392	+	8.81754i	0.0609528	+	0.306431i
$829$	−29.1861	−	29.1861i	−1.01367	−	1.01367i	−0.999905	−	0.0137698i	$-0.995617\pi$
$829$	−29.1861	−	29.1861i	−1.01367	−	1.01367i	−0.0137698	−	0.999905i	$-0.504383\pi$
$830$	−12.5707	+	17.8804i	−0.436334	+	0.620637i
$831$	19.5644	−	47.2327i	0.678683	−	1.63848i
$832$	3.60818	+	3.60818i	0.125091	+	0.125091i
$833$	−8.92846	+	3.71429i	−0.309353	+	0.128693i
$834$		−	39.6537i		−	1.37309i
$835$	−36.1254	−	15.9775i	−1.25017	−	0.552925i
$836$	−18.8805	+	3.75557i	−0.652996	+	0.129889i
$837$	−41.6601			−1.43998
$838$	2.17804	−	0.433238i	0.0752390	−	0.0149660i
$839$	−2.28546	+	11.4898i	−0.0789027	+	0.396671i	0.921071	+	0.389395i	$0.127316\pi$
$839$	−2.28546	+	11.4898i	−0.0789027	+	0.396671i	−0.999974	+	0.00727558i	$0.997684\pi$
$840$	−12.1471	+	7.70619i	−0.419116	+	0.265889i
$841$	−6.99907	−	16.8972i	−0.241347	−	0.582664i
$842$	−10.5724	+	25.5242i	−0.364351	+	0.879620i
$843$	−83.5845	−	16.6260i	−2.87880	−	0.572630i
$844$	−26.1283	−	5.19724i	−0.899373	−	0.178896i
$845$	−28.7203	+	5.00794i	−0.988009	+	0.172278i
$846$	−19.3749	+	19.3749i	−0.666122	+	0.666122i
$847$	−3.81479	−	2.54896i	−0.131078	−	0.0875834i
$848$	2.70105	−	1.11881i	0.0927544	−	0.0384201i
$849$	8.99114			0.308575
$850$	0.945983	−	20.5938i	0.0324470	−	0.706362i
$851$	11.1067			0.380732
$852$	−15.8283	+	6.55631i	−0.542270	+	0.224616i
$853$	−7.11121	−	4.75156i	−0.243483	−	0.162690i	0.427841	−	0.903854i	$-0.359274\pi$
$853$	−7.11121	−	4.75156i	−0.243483	−	0.162690i	−0.671324	+	0.741164i	$0.734274\pi$
$854$	6.33539	−	6.33539i	0.216792	−	0.216792i
$855$	−83.8722	+	14.6247i	−2.86837	+	0.500155i
$856$	−2.44404	−	0.486150i	−0.0835355	−	0.0166162i
$857$	−38.0331	−	7.56525i	−1.29919	−	0.258424i	−0.503427	−	0.864038i	$-0.667928\pi$
$857$	−38.0331	−	7.56525i	−1.29919	−	0.258424i	−0.795759	+	0.605614i	$0.792928\pi$
$858$	17.3453	−	41.8752i	0.592158	−	1.42960i
$859$	3.49731	+	8.44324i	0.119327	+	0.288080i	0.972245	−	0.233964i	$-0.0751698\pi$
$859$	3.49731	+	8.44324i	0.119327	+	0.288080i	−0.852919	+	0.522044i	$0.825170\pi$
$860$	3.54645	−	2.24988i	0.120933	−	0.0767203i
$861$	−4.55731	+	22.9112i	−0.155313	+	0.780810i
$862$	26.3843	−	5.24817i	0.898654	−	0.178753i
$863$	−40.0088			−1.36191			−0.680957	−	0.732323i	$-0.738436\pi$
$863$	−40.0088			−1.36191			−0.680957	+	0.732323i	$0.738436\pi$
$864$	−8.45716	+	1.68223i	−0.287719	+	0.0572308i
$865$	−20.1563	−	8.91471i	−0.685334	−	0.303109i
$866$		−	6.95003i		−	0.236172i
$867$	−28.0341	+	42.2350i	−0.952088	+	1.43438i
$868$	7.37050	+	7.37050i	0.250171	+	0.250171i
$869$	−17.5977	+	42.4846i	−0.596962	+	1.44119i
$870$	−26.3710	+	37.5099i	−0.894062	+	1.27170i
$871$	11.5112	+	11.5112i	0.390044	+	0.390044i
$872$	−3.56398	−	17.9173i	−0.120692	−	0.606758i
$873$	−8.78710	−	13.1508i	−0.297398	−	0.445088i
$874$	8.19919	−	5.47853i	0.277342	−	0.185314i
$875$	22.8848	−	7.62320i	0.773648	−	0.257711i
$876$	−27.0465	+	11.2030i	−0.913816	+	0.378515i
$877$	0.434606	−	2.18491i	0.0146756	−	0.0737792i	−0.972753	−	0.231842i	$-0.925525\pi$
$877$	0.434606	−	2.18491i	0.0146756	−	0.0737792i	0.987429	+	0.158063i	$0.0505248\pi$
$878$	10.1492	−	6.78147i	0.342519	−	0.228864i
$879$	13.1021	−	19.6087i	0.441923	−	0.661385i
$880$	6.65899	+	0.157954i	0.224474	+	0.00532464i
$881$	−6.84061	−	34.3901i	−0.230466	−	1.15863i	−0.906645	−	0.421894i	$-0.861365\pi$
$881$	−6.84061	−	34.3901i	−0.230466	−	1.15863i	0.676179	−	0.736737i	$-0.263635\pi$
$882$	−5.28804	−	12.7665i	−0.178058	−	0.429869i
$883$	−8.59552	+	8.59552i	−0.289262	+	0.289262i	−0.836788	−	0.547526i	$-0.815570\pi$
$883$	−8.59552	+	8.59552i	−0.289262	+	0.289262i	0.547526	+	0.836788i	$0.315570\pi$
$884$	0.0321684	+	21.0391i	0.00108194	+	0.707621i
$885$	−26.4470	−	0.627336i	−0.889007	−	0.0210877i
$886$	23.9375	+	9.91525i	0.804197	+	0.333109i
$887$	−3.09981	+	4.63920i	−0.104082	+	0.155769i	−0.879855	−	0.475243i	$-0.842360\pi$
$887$	−3.09981	+	4.63920i	−0.104082	+	0.155769i	0.775773	+	0.631012i	$0.217360\pi$
$888$			21.7043i			0.728350i
$889$	−4.00025	−	2.67288i	−0.134164	−	0.0896456i
$890$	3.73512	−	16.6979i	0.125202	−	0.559714i
$891$	13.3013	+	19.9068i	0.445610	+	0.666903i
$892$	−9.12708	−	3.78056i	−0.305597	−	0.126583i
$893$	27.7665	+	11.5013i	0.929170	+	0.384875i
$894$	13.5475	+	20.2752i	0.453095	+	0.678105i
$895$	−2.61751	−	4.12594i	−0.0874938	−	0.137915i
$896$	1.79386	+	1.19862i	0.0599287	+	0.0400431i
$897$			23.2181i			0.775230i
$898$	−20.8568	+	31.2145i	−0.696002	+	1.04164i
$899$	30.6950	+	12.7143i	1.02373	+	0.424045i
$900$	29.4255	+	1.39676i	0.980851	+	0.0465587i
$901$	11.1437	+	4.59594i	0.371252	+	0.153113i
$902$	7.64836	−	7.64836i	0.254662	−	0.254662i
$903$	−4.62414	−	11.1637i	−0.153882	−	0.371503i
$904$	−2.45178	−	12.3259i	−0.0815448	−	0.409954i
$905$	−0.647517	+	27.2978i	−0.0215242	+	0.907411i
$906$	−14.3554	+	21.4844i	−0.476928	+	0.713773i
$907$	0.544935	−	0.364114i	0.0180943	−	0.0120902i	−0.546490	−	0.837465i	$-0.684036\pi$
$907$	0.544935	−	0.364114i	0.0180943	−	0.0120902i	0.564584	+	0.825375i	$0.309036\pi$
$908$	−1.61484	+	8.11835i	−0.0535904	+	0.269417i
$909$	69.7155	−	28.8771i	2.31232	−	0.957793i
$910$	−22.9599	+	8.87845i	−0.761113	+	0.294318i
$911$	−0.784565	+	0.524230i	−0.0259938	+	0.0173685i	−0.568499	−	0.822684i	$-0.692476\pi$
$911$	−0.784565	+	0.524230i	−0.0259938	+	0.0173685i	0.542505	+	0.840052i	$0.317476\pi$
$912$	10.7060	+	16.0226i	0.354510	+	0.530562i
$913$	−5.68051	−	28.5579i	−0.187998	−	0.945127i
$914$	−12.7246	−	12.7246i	−0.420891	−	0.420891i
$915$	−27.2785	+	4.75652i	−0.901798	+	0.157246i
$916$	8.77812	−	21.1923i	0.290037	−	0.700212i
$917$	−19.2525	−	19.2525i	−0.635773	−	0.635773i
$918$	−29.5913	−	19.7069i	−0.976660	−	0.650425i
$919$			7.40165i			0.244158i	0.992520	+	0.122079i	$0.0389561\pi$
$919$			7.40165i			0.244158i	−0.992520	+	0.122079i	$0.961044\pi$
$920$	−3.18240	+	1.23061i	−0.104921	+	0.0405722i
$921$	44.7210	−	8.89556i	1.47361	−	0.293119i
$922$	23.9859			0.789933
$923$	−28.7544	+	5.71960i	−0.946462	+	0.188263i
$924$	3.73867	−	18.7955i	0.122993	−	0.618328i
$925$	8.78444	−	35.3174i	0.288831	−	1.16123i
$926$	−13.5396	−	32.6876i	−0.444940	−	1.07418i
$927$	27.7061	−	66.8885i	0.909989	−	2.19691i
$928$	6.74460	+	1.34158i	0.221402	+	0.0440397i
$929$	45.9163	+	9.13333i	1.50647	+	0.299655i	0.878181	−	0.478328i	$-0.158757\pi$
$929$	45.9163	+	9.13333i	1.50647	+	0.299655i	0.628285	+	0.777983i	$0.283757\pi$
$930$	−5.53367	−	31.7354i	−0.181456	−	1.04064i
$931$	−10.7174	+	10.7174i	−0.351250	+	0.351250i
$932$	−23.0506	−	15.4019i	−0.755047	−	0.504506i
$933$	−1.78052	+	0.737517i	−0.0582917	+	0.0241452i
$934$	22.4584			0.734861
$935$	18.9840	+	19.8456i	0.620842	+	0.649022i
$936$	−30.0639			−0.982671
$937$	−20.4567	+	8.47343i	−0.668291	+	0.276815i	−0.690923	−	0.722929i	$-0.742795\pi$
$937$	−20.4567	+	8.47343i	−0.668291	+	0.276815i	0.0226319	+	0.999744i	$0.492795\pi$
$938$	5.72299	+	3.82398i	0.186862	+	0.124857i
$939$	−6.97700	+	6.97700i	−0.227686	+	0.227686i
$940$	−8.50711	−	5.98085i	−0.277471	−	0.195074i
$941$	16.4307	+	3.26827i	0.535626	+	0.106543i	0.455489	−	0.890241i	$-0.349464\pi$
$941$	16.4307	+	3.26827i	0.535626	+	0.106543i	0.0801364	+	0.996784i	$0.474464\pi$
$942$	−17.9102	−	3.56257i	−0.583547	−	0.116075i
$943$	−2.12035	+	5.11898i	−0.0690481	+	0.166697i
$944$	1.51831	+	3.66553i	0.0494168	+	0.119303i
$945$	9.08070	−	40.5953i	0.295395	−	1.32057i
$946$	−1.09153	+	5.48751i	−0.0354888	+	0.178414i
$947$	41.4186	−	8.23868i	1.34592	−	0.267721i	0.531041	−	0.847346i	$-0.321801\pi$
$947$	41.4186	−	8.23868i	1.34592	−	0.267721i	0.814883	+	0.579625i	$0.196801\pi$
$948$	46.0325			1.49507
$949$	−49.1337	+	9.77330i	−1.59495	+	0.317255i
$950$	−10.9359	−	30.4051i	−0.354809	−	0.986473i
$951$			42.2819i			1.37109i
$952$	1.74875	+	8.72184i	0.0566773	+	0.282676i
$953$	24.8733	+	24.8733i	0.805725	+	0.805725i	0.983984	−	0.178259i	$-0.0570464\pi$
$953$	24.8733	+	24.8733i	0.805725	+	0.805725i	−0.178259	+	0.983984i	$0.557046\pi$
$954$	−6.59173	+	15.9138i	−0.213415	+	0.515230i
$955$	8.07986	+	5.68048i	0.261458	+	0.183816i
$956$	−15.4390	−	15.4390i	−0.499332	−	0.499332i
$957$	−11.9167	−	59.9094i	−0.385213	−	1.93659i
$958$	−10.7052	−	16.0214i	−0.345868	−	0.517628i
$959$	5.91911	−	3.95502i	0.191138	−	0.127714i
$960$	−2.40483	−	6.21896i	−0.0776156	−	0.200716i
$961$	7.07502	−	2.93057i	0.228226	−	0.0945345i
$962$	−7.24590	+	36.4276i	−0.233617	+	1.17447i
$963$	12.2074	−	8.15673i	0.393378	−	0.262847i
$964$	−6.19568	+	9.27249i	−0.199549	+	0.298647i
$965$	−36.4948	−	38.2682i	−1.17481	−	1.23190i
$966$	1.91515	+	9.62809i	0.0616188	+	0.309779i
$967$	17.9448	+	43.3226i	0.577066	+	1.39316i	0.895435	+	0.445193i	$0.146865\pi$
$967$	17.9448	+	43.3226i	0.577066	+	1.39316i	−0.318369	+	0.947967i	$0.603135\pi$
$968$	1.50372	−	1.50372i	0.0483314	−	0.0483314i
$969$	−15.3814	+	77.9502i	−0.494122	+	2.50412i
$970$	4.34403	−	4.14272i	0.139478	−	0.133015i
$971$	4.40078	+	1.82286i	0.141228	+	0.0584985i	0.452178	−	0.891928i	$-0.350647\pi$
$971$	4.40078	+	1.82286i	0.141228	+	0.0584985i	−0.310950	+	0.950426i	$0.600647\pi$
$972$	−1.05678	+	1.58158i	−0.0338963	+	0.0507294i
$973$		−	28.6901i		−	0.919764i
$974$	25.8876	+	17.2975i	0.829492	+	0.554249i
$975$	73.8298	+	18.3636i	2.36444	+	0.588105i
$976$	2.30720	+	3.45296i	0.0738516	+	0.110527i
$977$	−2.57938	−	1.06842i	−0.0825218	−	0.0341816i	0.341041	−	0.940049i	$-0.389221\pi$
$977$	−2.57938	−	1.06842i	−0.0825218	−	0.0341816i	−0.423562	+	0.905867i	$0.639221\pi$
$978$	36.3659	+	15.0633i	1.16285	+	0.481670i
$979$	12.6638	+	18.9527i	0.404736	+	0.605730i
$980$	4.42844	−	2.80942i	0.141461	−	0.0897435i
$981$	89.4929	+	59.7973i	2.85729	+	1.90918i
$982$			31.6963i			1.01147i
$983$	7.38005	−	11.0450i	0.235387	−	0.352281i	−0.694905	−	0.719102i	$-0.744554\pi$
$983$	7.38005	−	11.0450i	0.235387	−	0.352281i	0.930292	+	0.366820i	$0.119554\pi$
$984$	−10.0034	−	4.14353i	−0.318896	−	0.132091i
$985$	0.0817189	−	3.44508i	0.00260378	−	0.109769i
$986$	15.7884	+	23.5510i	0.502805	+	0.750015i
$987$	−21.1559	+	21.1559i	−0.673400	+	0.673400i
$988$	12.6193	+	30.4658i	0.401475	+	0.969246i
$989$	−0.559142	−	2.81100i	−0.0177797	−	0.0893845i
$990$	−28.3999	+	27.0838i	−0.902610	+	0.860781i
$991$	7.46029	−	11.1651i	0.236984	−	0.354671i	−0.693847	−	0.720123i	$-0.744085\pi$
$991$	7.46029	−	11.1651i	0.236984	−	0.354671i	0.930830	+	0.365451i	$0.119085\pi$
$992$	−4.01713	+	2.68416i	−0.127544	+	0.0852222i
$993$	16.5132	−	83.0174i	0.524030	−	2.63448i
$994$	−11.4521	+	4.74361i	−0.363238	+	0.150458i
$995$	4.43748	−	10.0332i	0.140678	−	0.318074i
$996$	−24.2352	+	16.1934i	−0.767920	+	0.513108i
$997$	−3.11894	−	4.66783i	−0.0987780	−	0.147832i	0.778789	−	0.627286i	$-0.215834\pi$
$997$	−3.11894	−	4.66783i	−0.0987780	−	0.147832i	−0.877567	+	0.479455i	$0.840834\pi$
$998$	5.07928	+	25.5353i	0.160782	+	0.808305i
$999$	−44.3802	−	44.3802i	−1.40413	−	1.40413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.r.b.23.1	yes	40
5.2	odd	4		170.2.o.b.57.1	yes	40
5.3	odd	4		850.2.s.d.57.5		40
5.4	even	2		850.2.v.d.193.5		40
17.3	odd	16		170.2.o.b.3.1	✓	40
85.3	even	16		850.2.v.d.207.5		40
85.37	even	16	inner	170.2.r.b.37.1	yes	40
85.54	odd	16		850.2.s.d.343.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.3.1	✓	40	17.3	odd	16
170.2.o.b.57.1	yes	40	5.2	odd	4
170.2.r.b.23.1	yes	40	1.1	even	1	trivial
170.2.r.b.37.1	yes	40	85.37	even	16	inner
850.2.s.d.57.5		40	5.3	odd	4
850.2.s.d.343.5		40	85.54	odd	16
850.2.v.d.193.5		40	5.4	even	2
850.2.v.d.207.5		40	85.3	even	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.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{2} +(-2.47936 - 1.65666i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-2.20283 + 0.384106i) q^{5} +(-2.92460 - 0.581740i) q^{6} +(-2.11600 - 0.420899i) q^{7} +(0.382683 - 0.923880i) q^{8} +(2.25467 + 5.44325i) q^{9} +(-1.88816 + 1.19785i) q^{10} +(0.581141 - 2.92159i) q^{11} +(-2.92460 + 0.581740i) q^{12} -5.10274 q^{13} +(-2.11600 + 0.420899i) q^{14} +(6.09794 + 2.69699i) q^{15} -1.00000i q^{16} +(2.91101 - 2.91993i) q^{17} +(4.16608 + 4.16608i) q^{18} +(2.47306 - 5.97048i) q^{19} +(-1.28603 + 1.82924i) q^{20} +(4.54905 + 4.54905i) q^{21} +(-0.581141 - 2.92159i) q^{22} +(0.847753 + 1.26875i) q^{23} +(-2.47936 + 1.65666i) q^{24} +(4.70493 - 1.69224i) q^{25} +(-4.71431 + 1.95273i) q^{26} +(1.68223 - 8.45716i) q^{27} +(-1.79386 + 1.19862i) q^{28} +(-3.82051 + 5.71779i) q^{29} +(6.66586 + 0.158117i) q^{30} +(-0.942552 - 4.73853i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(-6.28093 + 6.28093i) q^{33} +(1.57202 - 3.81166i) q^{34} +(4.82287 + 0.114401i) q^{35} +(5.44325 + 2.25467i) q^{36} +(4.04382 - 6.05201i) q^{37} -6.46241i q^{38} +(12.6515 + 8.45347i) q^{39} +(-0.488119 + 2.18214i) q^{40} +(2.01733 + 3.01915i) q^{41} +(5.94362 + 2.46193i) q^{42} +(-1.73529 - 0.718779i) q^{43} +(-1.65495 - 2.47681i) q^{44} +(-7.05743 - 11.1245i) q^{45} +(1.26875 + 0.847753i) q^{46} +4.65062i q^{47} +(-1.65666 + 2.47936i) q^{48} +(-2.16684 - 0.897536i) q^{49} +(3.69919 - 3.36392i) q^{50} +(-12.0548 + 2.41701i) q^{51} +(-3.60818 + 3.60818i) q^{52} +(1.11881 + 2.70105i) q^{53} +(-1.68223 - 8.45716i) q^{54} +(-0.157954 + 6.65899i) q^{55} +(-1.19862 + 1.79386i) q^{56} +(-16.0226 + 10.7060i) q^{57} +(-1.34158 + 6.74460i) q^{58} +(-3.66553 + 1.51831i) q^{59} +(6.21896 - 2.40483i) q^{60} +(-3.45296 + 2.30720i) q^{61} +(-2.68416 - 4.01713i) q^{62} +(-2.47982 - 12.4669i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(11.2405 - 1.95999i) q^{65} +(-3.39921 + 8.20642i) q^{66} +(-2.25590 - 2.25590i) q^{67} +(-0.00630415 - 4.12310i) q^{68} -4.55013i q^{69} +(4.49953 - 1.73994i) q^{70} +(5.63509 - 1.12089i) q^{71} +5.89173 q^{72} +(9.62889 - 1.91531i) q^{73} +(1.42000 - 7.13883i) q^{74} +(-14.4687 - 3.59877i) q^{75} +(-2.47306 - 5.97048i) q^{76} +(-2.45939 + 5.93749i) q^{77} +(14.9235 + 2.96847i) q^{78} +(-15.1407 - 3.01167i) q^{79} +(0.384106 + 2.20283i) q^{80} +(-5.68322 + 5.68322i) q^{81} +(3.01915 + 2.01733i) q^{82} +(9.03070 - 3.74064i) q^{83} +6.43332 q^{84} +(-5.29091 + 7.55025i) q^{85} -1.87826 q^{86} +(18.9448 - 7.84720i) q^{87} +(-2.47681 - 1.65495i) q^{88} +(-5.41083 + 5.41083i) q^{89} +(-10.7774 - 7.57696i) q^{90} +(10.7974 + 2.14774i) q^{91} +(1.49660 + 0.297691i) q^{92} +(-5.51318 + 13.3100i) q^{93} +(1.77972 + 4.29662i) q^{94} +(-3.15442 + 14.1019i) q^{95} +(-0.581740 + 2.92460i) q^{96} +(-2.63292 + 0.523720i) q^{97} -2.34537 q^{98} +(17.2132 - 3.42392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44}+ \cdots + 160 q^{99}+O(q^{100}) \) 40 * q - 16 * q^10 - 16 * q^18 + 8 * q^25 - 8 * q^26 + 24 * q^27 - 8 * q^28 + 8 * q^29 + 16 * q^30 - 16 * q^31 - 32 * q^33 + 8 * q^34 - 32 * q^35 - 32 * q^39 - 56 * q^41 - 24 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^49 - 32 * q^51 - 16 * q^52 + 16 * q^53 - 24 * q^54 - 8 * q^55 - 8 * q^56 - 120 * q^57 + 16 * q^58 + 8 * q^60 + 24 * q^61 - 8 * q^62 - 24 * q^63 - 32 * q^65 + 16 * q^67 - 8 * q^70 + 24 * q^71 + 56 * q^72 + 88 * q^73 + 32 * q^74 + 8 * q^75 + 24 * q^77 + 32 * q^78 - 104 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 + 136 * q^85 + 96 * q^86 + 136 * q^87 - 16 * q^89 + 24 * q^90 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 136 * q^95 + 16 * q^97 + 72 * q^98 + 160 * q^99

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