LMFDB - Embedded newform 170.2.r.b.37.1

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			37.1
Character	$\chi$	$=$	170.37
Dual form			170.2.r.b.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 + 0.382683i) q^{2} +(-2.47936 + 1.65666i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.20283 - 0.384106i) q^{5} +(-2.92460 + 0.581740i) q^{6} +(-2.11600 + 0.420899i) q^{7} +(0.382683 + 0.923880i) q^{8} +(2.25467 - 5.44325i) q^{9} +O(q^{10})$	\(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+O(q^{10}) $ 40 * 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} + 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.432976	+	0.901405i	$0.642537\pi$
$3$	−2.47936	+	1.65666i	−1.43146	+	0.956470i	−0.998483	+	0.0550648i	$0.982463\pi$
$4$	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	−0.578025	−	0.816019i	$-0.696176\pi$
$7$	−2.11600	+	0.420899i	−0.799774	+	0.159085i	−0.221749	+	0.975104i	$0.571176\pi$
$8$	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	0.963936	+	0.266134i	$0.0857465\pi$
$11$	0.581141	+	2.92159i	0.175220	+	0.880893i	−0.788715	+	0.614758i	$0.789253\pi$
$12$	−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	0.903774	+	0.428010i	$0.140785\pi$
$19$	2.47306	+	5.97048i	0.567358	+	1.36972i	−0.336416	+	0.941713i	$0.609215\pi$
$20$	−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	−0.732496	−	0.680771i	$-0.761645\pi$
$23$	0.847753	−	1.26875i	0.176769	−	0.264553i	0.909265	+	0.416218i	$0.136645\pi$
$24$	−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	−0.994650	−	0.103300i	$-0.967060\pi$
$29$	−3.82051	−	5.71779i	−0.709450	−	1.06177i	0.285200	−	0.958468i	$-0.407940\pi$
$30$	6.66586	−	0.158117i	1.21701	−	0.0288681i
$31$	−0.942552	+	4.73853i	−0.169287	+	0.851065i	0.799020	+	0.601304i	$0.205352\pi$
$31$	−0.942552	+	4.73853i	−0.169287	+	0.851065i	−0.968308	+	0.249761i	$0.919648\pi$
$32$	−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	0.998631	+	0.0523113i	$0.0166588\pi$
$37$	4.04382	+	6.05201i	0.664801	+	0.994945i	−0.333830	+	0.942633i	$0.608341\pi$
$38$			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	−0.639819	−	0.768525i	$-0.720991\pi$
$41$	2.01733	−	3.01915i	0.315054	−	0.471511i	0.954873	+	0.297014i	$0.0959908\pi$
$42$	5.94362	−	2.46193i	0.917120	−	0.379884i
$43$	−1.73529	+	0.718779i	−0.264629	+	0.109613i	−0.511053	−	0.859549i	$-0.670744\pi$
$43$	−1.73529	+	0.718779i	−0.264629	+	0.109613i	0.246424	+	0.969162i	$0.420744\pi$
$44$	−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	$-0.889850\pi$
$47$		−	4.65062i		−	0.678363i	0.940721	−	0.339182i	$-0.110150\pi$
$48$	−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	−0.828223	−	0.560398i	$-0.810648\pi$
$53$	1.11881	−	2.70105i	0.153680	−	0.371017i	0.981904	+	0.189381i	$0.0606481\pi$
$54$	−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	0.131095	−	0.991370i	$-0.458151\pi$
$59$	−3.66553	−	1.51831i	−0.477211	−	0.197667i	−0.608306	+	0.793703i	$0.708151\pi$
$60$	6.21896	+	2.40483i	0.802864	+	0.310462i
$61$	−3.45296	−	2.30720i	−0.442107	−	0.295406i	0.314523	−	0.949250i	$-0.398155\pi$
$61$	−3.45296	−	2.30720i	−0.442107	−	0.295406i	−0.756630	+	0.653844i	$0.773155\pi$
$62$	−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	−0.831350	−	0.555749i	$-0.812432\pi$
$67$	−2.25590	+	2.25590i	−0.275602	+	0.275602i	0.555749	+	0.831350i	$0.312432\pi$
$68$	−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	0.517783	−	0.855512i	$-0.326757\pi$
$71$	5.63509	+	1.12089i	0.668762	+	0.133025i	0.150979	+	0.988537i	$0.451757\pi$
$72$	5.89173			0.694347
$73$	9.62889	+	1.91531i	1.12698	+	0.224170i	0.723167	−	0.690674i	$-0.242686\pi$
$73$	9.62889	+	1.91531i	1.12698	+	0.224170i	0.403810	+	0.914843i	$0.367686\pi$
$74$	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	−0.948462	−	0.316890i	$-0.897361\pi$
$79$	−15.1407	+	3.01167i	−1.70346	+	0.338839i	−0.754996	+	0.655729i	$0.772361\pi$
$80$	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	0.818581	−	0.574391i	$-0.194761\pi$
$83$	9.03070	+	3.74064i	0.991249	+	0.410589i	0.172668	+	0.984980i	$0.444761\pi$
$84$	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	0.359571	−	0.933118i	$-0.382923\pi$
$89$	−5.41083	−	5.41083i	−0.573547	−	0.573547i	−0.933118	+	0.359571i	$0.882923\pi$
$90$	−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	0.0596039	−	0.998222i	$-0.481016\pi$
$97$	−2.63292	−	0.523720i	−0.267332	−	0.0531757i	−0.326936	+	0.945046i	$0.606016\pi$
$98$	−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	$0.219910\pi$
$101$			12.8077i			1.27441i	−0.770693	+	0.637207i	$0.780090\pi$
$102$	−10.2122	−	6.84619i	−1.01116	−	0.677873i
$103$	−8.68917	+	8.68917i	−0.856170	+	0.856170i	−0.990884	−	0.134715i	$-0.956988\pi$
$103$	−8.68917	+	8.68917i	−0.856170	+	0.856170i	0.134715	+	0.990884i	$0.456988\pi$
$104$	−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	−0.997143	−	0.0755328i	$-0.975934\pi$
$107$	−0.486150	+	2.44404i	−0.0469978	+	0.236274i	0.950145	+	0.311807i	$0.100934\pi$
$108$	−4.79060	+	7.16964i	−0.460976	+	0.689899i
$109$	15.1896	+	10.1494i	1.45490	+	0.972132i	0.996518	+	0.0833759i	$0.0265702\pi$
$109$	15.1896	+	10.1494i	1.45490	+	0.972132i	0.458380	+	0.888756i	$0.348430\pi$
$110$	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	0.939612	−	0.342241i	$-0.111186\pi$
$113$	10.4494	+	6.98206i	0.982997	+	0.656817i	0.0433845	+	0.999058i	$0.486186\pi$
$114$	−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	−0.289398	−	0.957209i	$-0.593455\pi$
$127$	2.06022	−	0.853371i	0.182815	−	0.0757245i	0.472213	+	0.881484i	$0.343455\pi$
$128$	−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	−0.00511864	−	0.999987i	$-0.501629\pi$
$131$	10.4931	−	7.01129i	0.916790	−	0.612579i	0.921909	+	0.387407i	$0.126629\pi$
$132$		−	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	0.600378	−	0.799717i	$-0.295017\pi$
$137$	−2.33320	−	2.33320i	−0.199339	−	0.199339i	−0.799717	+	0.600378i	$0.795017\pi$
$138$	−1.74126	+	4.20377i	−0.148226	+	0.357849i
$139$	2.59433	−	13.0426i	0.220049	−	1.10626i	−0.699906	−	0.714235i	$-0.746775\pi$
$139$	2.59433	−	13.0426i	0.220049	−	1.10626i	0.919955	−	0.392024i	$-0.128225\pi$
$140$	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	−0.903115	−	0.429399i	$-0.858725\pi$
$149$	−5.78244	+	5.78244i	−0.473716	+	0.473716i	0.429399	+	0.903115i	$0.358725\pi$
$150$	−14.7445	−	2.21209i	−1.20388	−	0.180616i
$151$	3.31607	+	8.00571i	0.269858	+	0.651495i	0.999476	−	0.0323595i	$-0.0103021\pi$
$151$	3.31607	+	8.00571i	0.269858	+	0.651495i	−0.729618	+	0.683855i	$0.760302\pi$
$152$	−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	−0.674031	−	0.738703i	$-0.735439\pi$
$163$	−12.9467	+	2.57526i	−1.01407	+	0.201710i	−0.340034	+	0.940413i	$0.610439\pi$
$164$	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	0.162761	−	0.986665i	$-0.447960\pi$
$167$	14.6882	−	9.81435i	1.13661	−	0.759457i	0.973846	+	0.227209i	$0.0729599\pi$
$168$	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	−0.203558	−	0.979063i	$-0.565251\pi$
$173$	8.19533	−	5.47594i	0.623079	−	0.416328i	0.826638	+	0.562734i	$0.190251\pi$
$174$	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	−0.889542	−	0.456853i	$-0.848977\pi$
$179$	0.836227	−	2.01883i	0.0625026	−	0.150895i	0.952045	+	0.305958i	$0.0989767\pi$
$180$	−12.8566	+	2.87587i	−0.958273	+	0.214354i
$181$	2.38233	+	11.9768i	0.177077	+	0.890225i	0.962503	+	0.271270i	$0.0874437\pi$
$181$	2.38233	+	11.9768i	0.177077	+	0.890225i	−0.785426	+	0.618955i	$0.787556\pi$
$182$	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	−0.811018	−	0.585021i	$-0.801086\pi$
$191$	−3.12333	+	3.12333i	−0.225996	+	0.225996i	0.585021	+	0.811018i	$0.301086\pi$
$192$	0.581740	−	2.92460i	0.0419835	−	0.211065i
$193$	13.1386	−	19.6632i	0.945734	−	1.41539i	0.0363943	−	0.999338i	$-0.488413\pi$
$193$	13.1386	−	19.6632i	0.945734	−	1.41539i	0.909340	−	0.416054i	$-0.136587\pi$
$194$	−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	0.968596	−	0.248641i	$-0.0799840\pi$
$197$	−0.300658	−	1.51151i	−0.0214210	−	0.107691i	−0.990017	+	0.140951i	$0.954984\pi$
$198$	14.5927	+	9.75051i	1.03706	+	0.692938i
$199$	−2.72577	−	4.07940i	−0.193224	−	0.289181i	0.722189	−	0.691696i	$-0.243136\pi$
$199$	−2.72577	−	4.07940i	−0.193224	−	0.289181i	−0.915413	+	0.402515i	$0.868136\pi$
$200$	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	−0.177777	+	0.984071i	$0.556890\pi$
$211$	−14.8005	+	22.1505i	−1.01891	+	1.52490i	−0.841131	+	0.540832i	$0.818110\pi$
$212$	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	−0.998456	−	0.0555446i	$-0.982310\pi$
$223$	−3.78056	+	9.12708i	−0.253165	+	0.611195i	0.745291	+	0.666739i	$0.232310\pi$
$224$	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	0.305797	−	0.952097i	$-0.401077\pi$
$227$	−6.88241	−	4.59868i	−0.456801	−	0.305225i	−0.762599	+	0.646872i	$0.776077\pi$
$228$	−3.75944	−	18.9000i	−0.248975	−	1.25168i
$229$	21.1923	+	8.77812i	1.40042	+	0.580074i	0.949862	−	0.312671i	$-0.101224\pi$
$229$	21.1923	+	8.77812i	1.40042	+	0.580074i	0.450562	+	0.892745i	$0.351224\pi$
$230$	−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	0.233576	+	0.972339i	$0.424957\pi$
$233$	−5.40843	+	27.1900i	−0.354318	+	1.78128i	−0.587894	+	0.808938i	$0.700043\pi$
$234$	−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	$0.249575\pi$
$239$			21.8340i			1.41232i	−0.708051	+	0.706161i	$0.750425\pi$
$240$	2.69699	+	6.09794i	0.174090	+	0.393620i
$241$	−10.9377	−	2.17563i	−0.704556	−	0.140145i	−0.170206	−	0.985408i	$-0.554443\pi$
$241$	−10.9377	−	2.17563i	−0.704556	−	0.140145i	−0.534350	+	0.845264i	$0.679443\pi$
$242$	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	0.506411	−	0.862292i	$-0.330972\pi$
$251$	−5.63823	−	5.63823i	−0.355882	−	0.355882i	−0.862292	+	0.506411i	$0.830972\pi$
$252$	−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	0.0117544	−	0.999931i	$-0.496258\pi$
$257$	−11.0133	−	4.56187i	−0.686992	−	0.284561i	−0.698746	+	0.715370i	$0.746258\pi$
$258$	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	−0.998395	−	0.0566422i	$-0.981961\pi$
$263$	−5.39184	−	13.0171i	−0.332475	−	0.802666i	0.665919	−	0.746024i	$-0.268039\pi$
$264$	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	0.0634787	−	0.997983i	$-0.479781\pi$
$269$	−4.26081	−	0.847528i	−0.259786	−	0.0516747i	−0.323265	+	0.946308i	$0.604781\pi$
$270$	6.95412	−	17.9835i	0.423214	−	1.09444i
$271$		−	3.27703i		−	0.199065i	−0.995034	−	0.0995326i	$-0.968265\pi$
$271$		−	3.27703i		−	0.199065i	0.995034	−	0.0995326i	$-0.0317347\pi$
$272$	−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	−0.740195	−	0.672393i	$-0.765267\pi$
$277$	3.34480	−	16.8154i	0.200970	−	1.01034i	0.941164	−	0.337950i	$-0.109733\pi$
$278$	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	0.987635	−	0.156769i	$-0.0501079\pi$
$281$	26.4043	+	10.9370i	1.57515	+	0.652447i	0.587511	+	0.809216i	$0.300108\pi$
$282$	2.70545	+	13.6012i	0.161107	+	0.809942i
$283$	−2.50708	−	1.67518i	−0.149030	−	0.0995789i	0.478820	−	0.877913i	$-0.341065\pi$
$283$	−2.50708	−	1.67518i	−0.149030	−	0.0995789i	−0.627850	+	0.778334i	$0.716065\pi$
$284$	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	$-0.925794\pi$
$293$		−	7.90877i		−	0.462035i	0.972950	−	0.231018i	$-0.0742055\pi$
$294$	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	0.327682	−	0.944788i	$-0.393733\pi$
$307$	−10.8126	−	10.8126i	−0.617106	−	0.617106i	−0.944788	+	0.327682i	$0.893733\pi$
$308$	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	0.841510	−	0.540241i	$-0.181667\pi$
$311$	0.359069	+	0.537385i	0.0203609	+	0.0304723i	−0.821150	+	0.570713i	$0.806667\pi$
$312$	12.6515	+	8.45347i	0.716251	+	0.478584i
$313$	0.645545	+	3.24537i	0.0364883	+	0.183439i	0.994731	−	0.102516i	$-0.0326892\pi$
$313$	0.645545	+	3.24537i	0.0364883	+	0.183439i	−0.958243	+	0.285955i	$0.907689\pi$
$314$	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	−0.983934	−	0.178532i	$-0.942865\pi$
$317$	−7.87772	+	11.7898i	−0.442457	+	0.662183i	0.541477	+	0.840715i	$0.317865\pi$
$318$	−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	−0.279477	−	0.960152i	$-0.590161\pi$
$331$	10.8628	−	26.2251i	0.597073	−	1.44146i	0.876550	−	0.481310i	$-0.159839\pi$
$332$	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	−0.614112	−	0.789219i	$-0.710486\pi$
$337$	−2.20255	+	1.47169i	−0.119980	+	0.0801683i	0.494132	+	0.869387i	$0.335486\pi$
$338$	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	−0.729288	−	0.684207i	$-0.760149\pi$
$347$	−21.2587	+	4.22862i	−1.14123	+	0.227004i	−0.411940	+	0.911211i	$0.635149\pi$
$348$	7.84720	+	18.9448i	0.420654	+	1.01555i
$349$	2.37113	−	5.72441i	0.126923	−	0.306420i	−0.847626	−	0.530595i	$-0.821969\pi$
$349$	2.37113	−	5.72441i	0.126923	−	0.306420i	0.974549	+	0.224174i	$0.0719686\pi$
$350$	−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	0.901402	−	0.432982i	$-0.142539\pi$
$359$	−0.798627	−	1.92806i	−0.0421499	−	0.101759i	−0.943552	+	0.331223i	$0.892539\pi$
$360$	−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	0.973255	−	0.229728i	$-0.0737837\pi$
$367$	−0.264915	−	1.33182i	−0.0138285	−	0.0695204i	−0.987083	+	0.160208i	$0.948784\pi$
$368$	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	0.530374	−	0.847764i	$-0.322052\pi$
$373$	−6.12982	−	6.12982i	−0.317390	−	0.317390i	−0.847764	+	0.530374i	$0.822052\pi$
$374$	−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	−0.274658	−	0.961542i	$-0.588565\pi$
$379$	9.90108	−	6.61569i	0.508584	−	0.339825i	0.783242	+	0.621717i	$0.213565\pi$
$380$	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	−0.708702	−	0.705507i	$-0.750719\pi$
$383$	−13.9138	+	5.76328i	−0.710962	+	0.294490i	−0.00225919	+	0.999997i	$0.500719\pi$
$384$	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	0.324315	−	0.945949i	$-0.394866\pi$
$389$	24.1120	−	9.98753i	1.22253	−	0.506388i	0.898213	+	0.439561i	$0.144866\pi$
$390$	−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	0.957098	−	0.289763i	$-0.0935764\pi$
$397$	21.0338	+	14.0544i	1.05566	+	0.705368i	0.0985598	+	0.995131i	$0.468576\pi$
$398$	−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	0.323847	−	0.946110i	$-0.395024\pi$
$401$	−8.53692	−	5.70419i	−0.426314	−	0.284854i	−0.750160	+	0.661256i	$0.770024\pi$
$402$	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	$-0.845486\pi$
$409$		−	18.8720i		−	0.933158i	0.884480	−	0.466579i	$-0.154514\pi$
$410$	−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	−0.141601	−	0.989924i	$-0.545225\pi$
$419$	2.17804	−	0.433238i	0.106404	−	0.0211651i	0.248005	+	0.968759i	$0.420225\pi$
$420$	−14.1715	−	2.47108i	−0.691500	−	0.120576i
$421$	−19.5353	−	19.5353i	−0.952094	−	0.952094i	0.0468096	−	0.998904i	$-0.485095\pi$
$421$	−19.5353	−	19.5353i	−0.952094	−	0.952094i	−0.998904	+	0.0468096i	$0.985095\pi$
$422$	−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	0.486838	−	0.873492i	$-0.338150\pi$
$431$	26.3843	−	5.24817i	1.27089	−	0.252796i	0.784051	+	0.620697i	$0.213150\pi$
$432$	−8.45716	+	1.68223i	−0.406895	+	0.0809365i
$433$	2.65966	+	6.42099i	0.127815	+	0.308573i	0.974813	−	0.223023i	$-0.0715925\pi$
$433$	2.65966	+	6.42099i	0.127815	+	0.308573i	−0.846998	+	0.531596i	$0.821592\pi$
$434$	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	0.472321	−	0.881426i	$-0.343416\pi$
$439$	11.9718	+	2.38134i	0.571382	+	0.113655i	0.0990609	+	0.995081i	$0.468416\pi$
$440$	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	−0.122066	−	0.992522i	$-0.538952\pi$
$443$	18.3210	−	18.3210i	0.870456	−	0.870456i	0.992522	+	0.122066i	$0.0389519\pi$
$444$	−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	−0.994328	−	0.106356i	$-0.966082\pi$
$449$	−31.2145	−	20.8568i	−1.47310	−	0.984295i	−0.478773	−	0.877939i	$-0.658918\pi$
$450$	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	0.676994	+	0.735989i	$0.263282\pi$
$457$	−6.88648	+	16.6254i	−0.322136	+	0.777705i	−0.999130	+	0.0417158i	$0.986718\pi$
$458$	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	0.198628	−	0.980075i	$-0.436351\pi$
$461$	22.1601	−	9.17900i	1.03210	−	0.427508i	0.833469	+	0.552566i	$0.186351\pi$
$462$	10.6468	+	15.9341i	0.495335	+	0.741321i
$463$			35.3808i			1.64428i	0.569283	+	0.822142i	$0.307221\pi$
$463$			35.3808i			1.64428i	−0.569283	+	0.822142i	$0.692779\pi$
$464$	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	0.153108	−	0.988209i	$-0.451072\pi$
$467$	20.7488	−	8.59445i	0.960142	−	0.397704i	0.807033	+	0.590506i	$0.201072\pi$
$468$	−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	0.794764	+	0.606919i	$0.207595\pi$
$479$	−3.75915	+	18.8985i	−0.171760	+	0.863496i	−0.966524	+	0.256577i	$0.917405\pi$
$480$	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	−0.197420	−	0.980319i	$-0.563256\pi$
$487$	17.2975	−	25.8876i	0.783826	−	1.17308i	0.981246	−	0.192760i	$-0.0617437\pi$
$488$	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	−0.919404	−	0.393315i	$-0.871328\pi$
$491$	−12.1296	−	29.2835i	−0.547403	−	1.32155i	0.372001	−	0.928232i	$-0.378672\pi$
$492$	−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	−0.910723	−	0.413018i	$-0.864475\pi$
$499$	−5.07928	−	25.5353i	−0.227380	−	1.14312i	0.683343	−	0.730098i	$-0.260525\pi$
$500$	−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	0.264617	−	0.964353i	$-0.414754\pi$
$503$	19.6945	−	3.91748i	0.878134	−	0.174672i	0.613517	+	0.789682i	$0.289754\pi$
$504$	−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	0.954531	+	0.298110i	$0.0963563\pi$
$521$	4.26245	+	21.4288i	0.186741	+	0.938812i	−0.767790	+	0.640701i	$0.778644\pi$
$522$	−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	−0.908616	−	0.417634i	$-0.862860\pi$
$541$	2.10863	−	10.6008i	0.0906572	−	0.455765i	0.999273	−	0.0381310i	$-0.0121404\pi$
$542$	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	0.998859	−	0.0477657i	$-0.0152101\pi$
$547$	13.3892	+	20.0384i	0.572482	+	0.856780i	−0.426376	+	0.904546i	$0.640210\pi$
$548$		−	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	$-0.744041\pi$
$557$		−	33.9956i		−	1.44044i	0.693746	−	0.720220i	$-0.255959\pi$
$558$	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	−0.973718	−	0.227756i	$-0.926861\pi$
$563$	−2.94572	+	7.11160i	−0.124147	+	0.299718i	0.849571	+	0.527475i	$0.176861\pi$
$564$	−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	−0.0402912	−	0.999188i	$-0.512829\pi$
$569$	−18.4941	−	7.66052i	−0.775314	−	0.321146i	−0.735023	+	0.678042i	$0.762829\pi$
$570$	17.4291	+	39.4074i	0.730023	+	1.65059i
$571$	8.82341	+	5.89561i	0.369248	+	0.246724i	0.726325	−	0.687351i	$-0.241227\pi$
$571$	8.82341	+	5.89561i	0.369248	+	0.246724i	−0.357077	+	0.934075i	$0.616227\pi$
$572$	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	−0.0883015	+	0.996094i	$0.528144\pi$
$577$	−26.0481	+	26.0481i	−1.08440	+	1.08440i	−0.996094	+	0.0883015i	$0.971856\pi$
$578$	−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	0.999938	−	0.0111781i	$-0.00355817\pi$
$587$	6.90430	+	16.6684i	0.284971	+	0.687980i	−0.714967	+	0.699159i	$0.753558\pi$
$588$	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	0.737889	−	0.674922i	$-0.235823\pi$
$593$	19.0530	+	7.89203i	0.782414	+	0.324087i	0.0445250	+	0.999008i	$0.485823\pi$
$594$	−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	0.851916	−	0.523679i	$-0.175441\pi$
$599$	8.03343	+	8.03343i	0.328237	+	0.328237i	−0.523679	+	0.851916i	$0.675441\pi$
$600$	−8.86174	−	11.9901i	−0.361779	−	0.489494i
$601$	16.8364	−	3.34896i	0.686770	−	0.136607i	0.160642	−	0.987013i	$-0.448644\pi$
$601$	16.8364	−	3.34896i	0.686770	−	0.136607i	0.526127	+	0.850406i	$0.323644\pi$
$602$	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	−0.120020	−	0.992772i	$-0.538296\pi$
$607$	−15.0490	−	2.99343i	−0.610821	−	0.121500i	−0.490801	+	0.871272i	$0.663296\pi$
$608$	−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	−0.801269	−	0.598304i	$-0.795841\pi$
$613$	−5.02517	+	5.02517i	−0.202965	+	0.202965i	0.598304	+	0.801269i	$0.295841\pi$
$614$	−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	−0.999234	−	0.0391439i	$-0.987537\pi$
$617$	−1.51726	+	7.62776i	−0.0610824	+	0.307082i	0.938151	+	0.346226i	$0.112537\pi$
$618$	20.3576	−	30.4672i	0.818901	−	1.22557i
$619$	23.2443	+	15.5314i	0.934268	+	0.624258i	0.926736	−	0.375714i	$-0.122602\pi$
$619$	23.2443	+	15.5314i	0.934268	+	0.624258i	0.00753243	+	0.999972i	$0.497602\pi$
$620$	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	−0.0198927	−	0.999802i	$-0.506332\pi$
$631$	16.9058	−	7.00260i	0.673008	−	0.278769i	0.692901	+	0.721033i	$0.256332\pi$
$632$	−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	−0.978521	−	0.206149i	$-0.933907\pi$
$641$	−29.4328	+	19.6664i	−1.16253	+	0.776776i	−0.184007	+	0.982925i	$0.558907\pi$
$642$		−	7.43066i		−	0.293265i
$643$	5.81925	+	8.70912i	0.229489	+	0.343454i	0.928287	−	0.371865i	$-0.121281\pi$
$643$	5.81925	+	8.70912i	0.229489	+	0.343454i	−0.698798	+	0.715319i	$0.746281\pi$
$644$	−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	0.740939	−	0.671572i	$-0.234381\pi$
$647$	1.76443	+	1.76443i	0.0693668	+	0.0693668i	−0.671572	+	0.740939i	$0.734381\pi$
$648$	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	0.999143	+	0.0414020i	$0.0131824\pi$
$653$	2.34838	+	11.8061i	0.0918991	+	0.462008i	−0.907243	+	0.420606i	$0.861818\pi$
$654$	−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	−0.986594	−	0.163192i	$-0.947821\pi$
$659$	−21.1376	+	21.1376i	−0.823403	+	0.823403i	0.163192	+	0.986594i	$0.447821\pi$
$660$	−3.41185	+	19.5668i	−0.132806	+	0.761637i
$661$	−7.99380	−	19.2988i	−0.310923	−	0.750634i	−0.999671	−	0.0256340i	$-0.991840\pi$
$661$	−7.99380	−	19.2988i	−0.310923	−	0.750634i	0.688748	−	0.725000i	$-0.258160\pi$
$662$	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	−0.825902	−	0.563813i	$-0.809334\pi$
$673$	−35.6232	+	7.08590i	−1.37317	+	0.273141i	−0.547272	+	0.836955i	$0.684334\pi$
$674$	−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	−0.454459	−	0.890767i	$-0.650168\pi$
$677$	5.06304	−	3.38302i	0.194588	−	0.130020i	0.649048	+	0.760748i	$0.275168\pi$
$678$	−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	−0.882303	−	0.470683i	$-0.844008\pi$
$683$	−20.5178	+	13.7095i	−0.785091	+	0.524581i	0.0972115	+	0.995264i	$0.469008\pi$
$684$	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	−0.951130	−	0.308790i	$-0.900076\pi$
$691$	−5.00947	−	25.1843i	−0.190569	−	0.958057i	0.760561	−	0.649267i	$-0.224924\pi$
$692$	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	−0.888519	−	0.458840i	$-0.848265\pi$
$701$	−11.3764	+	11.3764i	−0.429679	+	0.429679i	0.458840	+	0.888519i	$0.348265\pi$
$702$	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	0.749962	−	0.661481i	$-0.230072\pi$
$709$	−3.94521	−	5.90443i	−0.148165	−	0.221745i	−0.898127	+	0.439736i	$0.855072\pi$
$710$	−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	0.146670	−	0.989186i	$-0.453145\pi$
$719$	29.9430	−	20.0073i	1.11669	−	0.746146i	0.970016	+	0.243040i	$0.0781446\pi$
$720$	−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	$0.207289\pi$
$727$			32.6875i			1.21231i	−0.795345	+	0.606156i	$0.792711\pi$
$728$	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	−0.699253	−	0.714874i	$-0.746484\pi$
$733$	8.14076	−	19.6535i	0.300686	−	0.725920i	0.999939	−	0.0110459i	$-0.00351609\pi$
$734$	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	−0.237218	−	0.971456i	$-0.576236\pi$
$739$	−29.6823	−	12.2948i	−1.09188	−	0.452271i	−0.854662	+	0.519185i	$0.826236\pi$
$740$	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	0.910008	+	0.414590i	$0.136075\pi$
$743$	−2.43650	+	12.2491i	−0.0893863	+	0.449375i	−0.999395	+	0.0347858i	$0.988925\pi$
$744$	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	0.220821	−	0.975314i	$-0.429126\pi$
$751$	1.41399	+	0.281260i	0.0515972	+	0.0102633i	−0.169224	+	0.985578i	$0.554126\pi$
$752$	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	0.992491	+	0.122320i	$0.0390334\pi$
$757$	10.3778	+	25.0542i	0.377187	+	0.910610i	−0.615304	+	0.788290i	$0.710967\pi$
$758$	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	0.123342	−	0.992364i	$-0.460639\pi$
$761$	−23.9731	−	23.9731i	−0.869023	−	0.869023i	−0.992364	+	0.123342i	$0.960639\pi$
$762$	−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	0.933392	−	0.358858i	$-0.116834\pi$
$769$	15.9323	+	15.9323i	0.574535	+	0.574535i	−0.358858	+	0.933392i	$0.616834\pi$
$770$	−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	−0.956868	−	0.290522i	$-0.906171\pi$
$773$	−13.5036	−	32.6005i	−0.485690	−	1.17256i	0.471178	−	0.882038i	$-0.343829\pi$
$774$	−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	0.535275	+	0.844678i	$0.320208\pi$
$787$	−7.92509	+	39.8421i	−0.282499	+	1.42022i	−0.817774	+	0.575540i	$0.804792\pi$
$788$	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	0.537044	+	0.843554i	$0.319541\pi$
$797$	−12.3988	+	29.9332i	−0.439186	+	1.06029i	−0.976230	+	0.216736i	$0.930459\pi$
$798$	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	−0.778287	−	0.627909i	$-0.783911\pi$
$809$	2.83469	−	4.24242i	0.0996626	−	0.149156i	0.877950	+	0.478753i	$0.158911\pi$
$810$	3.92316	+	17.5385i	0.137846	+	0.616240i
$811$	−17.3551	+	11.5963i	−0.609421	+	0.407202i	−0.821629	−	0.570022i	$-0.806934\pi$
$811$	−17.3551	+	11.5963i	−0.609421	+	0.407202i	0.212208	+	0.977224i	$0.431934\pi$
$812$			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	0.545252	−	0.838272i	$-0.316434\pi$
$821$	−12.5463	−	18.7769i	−0.437870	−	0.655318i	−0.983121	+	0.182954i	$0.941434\pi$
$822$	8.18101	+	5.46638i	0.285346	+	0.190662i
$823$	5.50950	+	27.6981i	0.192049	+	0.965496i	0.949777	+	0.312926i	$0.101309\pi$
$823$	5.50950	+	27.6981i	0.192049	+	0.965496i	−0.757728	+	0.652570i	$0.773691\pi$
$824$	−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	−0.527894	−	0.849310i	$-0.677018\pi$
$827$	13.1935	−	19.7455i	0.458783	−	0.686617i	0.986677	+	0.162693i	$0.0520181\pi$
$828$	1.75392	−	8.81754i	0.0609528	−	0.306431i
$829$	−29.1861	+	29.1861i	−1.01367	+	1.01367i	−0.0137698	+	0.999905i	$0.504383\pi$
$829$	−29.1861	+	29.1861i	−1.01367	+	1.01367i	−0.999905	+	0.0137698i	$0.995617\pi$
$830$	−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	−0.999974	−	0.00727558i	$-0.997684\pi$
$839$	−2.28546	−	11.4898i	−0.0789027	−	0.396671i	0.921071	−	0.389395i	$-0.127316\pi$
$840$	−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	−0.671324	−	0.741164i	$-0.734274\pi$
$853$	−7.11121	+	4.75156i	−0.243483	+	0.162690i	0.427841	+	0.903854i	$0.359274\pi$
$854$	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	−0.795759	−	0.605614i	$-0.792928\pi$
$857$	−38.0331	+	7.56525i	−1.29919	+	0.258424i	−0.503427	+	0.864038i	$0.667928\pi$
$858$	17.3453	+	41.8752i	0.592158	+	1.42960i
$859$	3.49731	−	8.44324i	0.119327	−	0.288080i	−0.852919	−	0.522044i	$-0.825170\pi$
$859$	3.49731	−	8.44324i	0.119327	−	0.288080i	0.972245	+	0.233964i	$0.0751698\pi$
$860$	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	0.987429	−	0.158063i	$-0.0505248\pi$
$877$	0.434606	+	2.18491i	0.0146756	+	0.0737792i	−0.972753	+	0.231842i	$0.925525\pi$
$878$	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	0.676179	+	0.736737i	$0.263635\pi$
$881$	−6.84061	+	34.3901i	−0.230466	+	1.15863i	−0.906645	+	0.421894i	$0.861365\pi$
$882$	−5.28804	+	12.7665i	−0.178058	+	0.429869i
$883$	−8.59552	−	8.59552i	−0.289262	−	0.289262i	0.547526	−	0.836788i	$-0.315570\pi$
$883$	−8.59552	−	8.59552i	−0.289262	−	0.289262i	−0.836788	+	0.547526i	$0.815570\pi$
$884$	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	0.775773	−	0.631012i	$-0.217360\pi$
$887$	−3.09981	−	4.63920i	−0.104082	−	0.155769i	−0.879855	+	0.475243i	$0.842360\pi$
$888$		−	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	0.564584	−	0.825375i	$-0.309036\pi$
$907$	0.544935	+	0.364114i	0.0180943	+	0.0120902i	−0.546490	+	0.837465i	$0.684036\pi$
$908$	−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	0.542505	−	0.840052i	$-0.317476\pi$
$911$	−0.784565	−	0.524230i	−0.0259938	−	0.0173685i	−0.568499	+	0.822684i	$0.692476\pi$
$912$	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	$-0.961044\pi$
$919$		−	7.40165i		−	0.244158i	0.992520	−	0.122079i	$-0.0389561\pi$
$920$	−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	0.628285	−	0.777983i	$-0.283757\pi$
$929$	45.9163	−	9.13333i	1.50647	−	0.299655i	0.878181	+	0.478328i	$0.158757\pi$
$930$	−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	0.0226319	−	0.999744i	$-0.492795\pi$
$937$	−20.4567	−	8.47343i	−0.668291	−	0.276815i	−0.690923	+	0.722929i	$0.742795\pi$
$938$	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	0.0801364	−	0.996784i	$-0.474464\pi$
$941$	16.4307	−	3.26827i	0.535626	−	0.106543i	0.455489	+	0.890241i	$0.349464\pi$
$942$	−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	0.814883	−	0.579625i	$-0.196801\pi$
$947$	41.4186	+	8.23868i	1.34592	+	0.267721i	0.531041	+	0.847346i	$0.321801\pi$
$948$	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	−0.178259	−	0.983984i	$-0.557046\pi$
$953$	24.8733	−	24.8733i	0.805725	−	0.805725i	0.983984	+	0.178259i	$0.0570464\pi$
$954$	−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	−0.318369	−	0.947967i	$-0.603135\pi$
$967$	17.9448	−	43.3226i	0.577066	−	1.39316i	0.895435	−	0.445193i	$-0.146865\pi$
$968$	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	−0.310950	−	0.950426i	$-0.600647\pi$
$971$	4.40078	−	1.82286i	0.141228	−	0.0584985i	0.452178	+	0.891928i	$0.350647\pi$
$972$	−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	−0.423562	−	0.905867i	$-0.639221\pi$
$977$	−2.57938	+	1.06842i	−0.0825218	+	0.0341816i	0.341041	+	0.940049i	$0.389221\pi$
$978$	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	0.930292	−	0.366820i	$-0.119554\pi$
$983$	7.38005	+	11.0450i	0.235387	+	0.352281i	−0.694905	+	0.719102i	$0.744554\pi$
$984$	−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	0.930830	−	0.365451i	$-0.119085\pi$
$991$	7.46029	+	11.1651i	0.236984	+	0.354671i	−0.693847	+	0.720123i	$0.744085\pi$
$992$	−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	−0.877567	−	0.479455i	$-0.840834\pi$
$997$	−3.11894	+	4.66783i	−0.0987780	+	0.147832i	0.778789	+	0.627286i	$0.215834\pi$
$998$	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.37.1	yes	40
5.2	odd	4		850.2.s.d.343.5		40
5.3	odd	4		170.2.o.b.3.1	✓	40
5.4	even	2		850.2.v.d.207.5		40
17.6	odd	16		170.2.o.b.57.1	yes	40
85.23	even	16	inner	170.2.r.b.23.1	yes	40
85.57	even	16		850.2.v.d.193.5		40
85.74	odd	16		850.2.s.d.57.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.3.1	✓	40	5.3	odd	4
170.2.o.b.57.1	yes	40	17.6	odd	16
170.2.r.b.23.1	yes	40	85.23	even	16	inner
170.2.r.b.37.1	yes	40	1.1	even	1	trivial
850.2.s.d.57.5		40	85.74	odd	16
850.2.s.d.343.5		40	5.2	odd	4
850.2.v.d.193.5		40	85.57	even	16
850.2.v.d.207.5		40	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{2} +(-2.47936 + 1.65666i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.20283 - 0.384106i) q^{5} +(-2.92460 + 0.581740i) q^{6} +(-2.11600 + 0.420899i) q^{7} +(0.382683 + 0.923880i) q^{8} +(2.25467 - 5.44325i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44} + 24 q^{45} + 16 q^{49} - 32 q^{51} - 16 q^{52} + 16 q^{53} - 24 q^{54} - 8 q^{55} - 8 q^{56} - 120 q^{57} + 16 q^{58} + 8 q^{60} + 24 q^{61} - 8 q^{62} - 24 q^{63} - 32 q^{65} + 16 q^{67} - 8 q^{70} + 24 q^{71} + 56 q^{72} + 88 q^{73} + 32 q^{74} + 8 q^{75} + 24 q^{77} + 32 q^{78} - 104 q^{79} + 8 q^{80} + 48 q^{81} + 16 q^{82} + 16 q^{83} + 136 q^{85} + 96 q^{86} + 136 q^{87} - 16 q^{89} + 24 q^{90} + 48 q^{91} - 8 q^{92} - 8 q^{93} - 8 q^{94} - 136 q^{95} + 16 q^{97} + 72 q^{98} + 160 q^{99}+O(q^{100}) \) 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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