LMFDB - Embedded newform 850.2.v.d.143.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			143.5
Character	$\chi$	$=$	850.143
Dual form			850.2.v.d.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.382683 + 0.923880i) q^{2} +(2.87914 - 0.572697i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(1.63090 + 2.44082i) q^{6} +(0.222469 + 0.332949i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(5.18983 - 2.14970i) q^{9} +(3.38193 - 2.25974i) q^{11} +(-1.63090 + 2.44082i) q^{12} -1.42762 q^{13} +(-0.222469 + 0.332949i) q^{14} -1.00000i q^{16} +(-2.04427 + 3.58064i) q^{17} +(3.97212 + 3.97212i) q^{18} +(3.96552 + 1.64257i) q^{19} +(0.831199 + 0.831199i) q^{21} +(3.38193 + 2.25974i) q^{22} +(1.20785 - 6.07227i) q^{23} +(-2.87914 - 0.572697i) q^{24} +(-0.546327 - 1.31895i) q^{26} +(6.38867 - 4.26877i) q^{27} +(-0.392740 - 0.0781209i) q^{28} +(0.790417 + 3.97370i) q^{29} +(-5.97330 - 3.99123i) q^{31} +(0.923880 - 0.382683i) q^{32} +(8.44292 - 8.44292i) q^{33} +(-4.09039 - 0.518404i) q^{34} +(-2.14970 + 5.18983i) q^{36} +(0.940802 + 4.72973i) q^{37} +4.29225i q^{38} +(-4.11032 + 0.817593i) q^{39} +(-1.63154 + 8.20230i) q^{41} +(-0.449842 + 1.08601i) q^{42} +(-4.46330 + 10.7754i) q^{43} +(-0.793514 + 3.98926i) q^{44} +(6.07227 - 1.20785i) q^{46} -7.15983i q^{47} +(-0.572697 - 2.87914i) q^{48} +(2.61742 - 6.31901i) q^{49} +(-3.83511 + 11.4799i) q^{51} +(1.00948 - 1.00948i) q^{52} +(-4.41860 + 1.83025i) q^{53} +(6.38867 + 4.26877i) q^{54} +(-0.0781209 - 0.392740i) q^{56} +(12.3580 + 2.45816i) q^{57} +(-3.36874 + 2.25092i) q^{58} +(-1.95801 - 4.72705i) q^{59} +(-10.8073 - 2.14971i) q^{61} +(1.40153 - 7.04599i) q^{62} +(1.87032 + 1.24971i) q^{63} +(0.707107 + 0.707107i) q^{64} +(11.0312 + 4.56928i) q^{66} +(0.229043 + 0.229043i) q^{67} +(-1.08638 - 3.97741i) q^{68} -18.1747i q^{69} +(2.55467 - 3.82333i) q^{71} -5.61743 q^{72} +(7.33833 - 10.9826i) q^{73} +(-4.00967 + 2.67918i) q^{74} +(-3.96552 + 1.64257i) q^{76} +(1.50475 + 0.623289i) q^{77} +(-2.32831 - 3.48456i) q^{78} +(-0.586248 - 0.877382i) q^{79} +(4.03280 - 4.03280i) q^{81} +(-8.20230 + 1.63154i) q^{82} +(-0.476166 - 1.14957i) q^{83} -1.17549 q^{84} -11.6632 q^{86} +(4.55144 + 10.9882i) q^{87} +(-3.98926 + 0.793514i) q^{88} +(-9.95430 + 9.95430i) q^{89} +(-0.317602 - 0.475325i) q^{91} +(3.43967 + 5.14783i) q^{92} +(-19.4837 - 8.07043i) q^{93} +(6.61482 - 2.73995i) q^{94} +(2.44082 - 1.63090i) q^{96} +(-1.65138 + 2.47147i) q^{97} +6.83965 q^{98} +(12.6939 - 18.9978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$3$	2.87914	−	0.572697i	1.66227	−	0.330647i	0.727558	−	0.686046i	$-0.240655\pi$
$3$	2.87914	−	0.572697i	1.66227	−	0.330647i	0.934714	+	0.355400i	$0.115655\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	1.63090	+	2.44082i	0.665813	+	0.996460i
$7$	0.222469	+	0.332949i	0.0840855	+	0.125843i	0.871128	−	0.491056i	$-0.163389\pi$
$7$	0.222469	+	0.332949i	0.0840855	+	0.125843i	−0.787043	+	0.616899i	$0.788389\pi$
$8$	−0.923880	−	0.382683i	−0.326641	−	0.135299i
$9$	5.18983	−	2.14970i	1.72994	−	0.716566i
$10$		0			0
$11$	3.38193	−	2.25974i	1.01969	−	0.681336i	0.0709797	−	0.997478i	$-0.477387\pi$
$11$	3.38193	−	2.25974i	1.01969	−	0.681336i	0.948712	+	0.316142i	$0.102387\pi$
$12$	−1.63090	+	2.44082i	−0.470801	+	0.704603i
$13$	−1.42762			−0.395951			−0.197975	−	0.980207i	$-0.563437\pi$
$13$	−1.42762			−0.395951			−0.197975	+	0.980207i	$0.563437\pi$
$14$	−0.222469	+	0.332949i	−0.0594574	+	0.0889843i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−2.04427	+	3.58064i	−0.495807	+	0.868433i
$17$	−2.04427	+	3.58064i	−0.495807	+	0.868433i
$18$	3.97212	+	3.97212i	0.936239	+	0.936239i
$19$	3.96552	+	1.64257i	0.909753	+	0.376832i	0.787962	−	0.615724i	$-0.211136\pi$
$19$	3.96552	+	1.64257i	0.909753	+	0.376832i	0.121791	+	0.992556i	$0.461136\pi$
$20$		0			0
$21$	0.831199	+	0.831199i	0.181383	+	0.181383i
$22$	3.38193	+	2.25974i	0.721031	+	0.481777i
$23$	1.20785	−	6.07227i	0.251854	−	1.26616i	−0.623173	−	0.782084i	$-0.714157\pi$
$23$	1.20785	−	6.07227i	0.251854	−	1.26616i	0.875028	−	0.484073i	$-0.160843\pi$
$24$	−2.87914	−	0.572697i	−0.587702	−	0.116901i
$25$		0			0
$26$	−0.546327	−	1.31895i	−0.107143	−	0.258667i
$27$	6.38867	−	4.26877i	1.22950	−	0.821526i
$28$	−0.392740	−	0.0781209i	−0.0742209	−	0.0147635i
$29$	0.790417	+	3.97370i	0.146777	+	0.737897i	0.982133	+	0.188188i	$0.0602614\pi$
$29$	0.790417	+	3.97370i	0.146777	+	0.737897i	−0.835356	+	0.549709i	$0.814739\pi$
$30$		0			0
$31$	−5.97330	−	3.99123i	−1.07284	−	0.716847i	−0.111929	−	0.993716i	$-0.535703\pi$
$31$	−5.97330	−	3.99123i	−1.07284	−	0.716847i	−0.960908	+	0.276869i	$0.910703\pi$
$32$	0.923880	−	0.382683i	0.163320	−	0.0676495i
$33$	8.44292	−	8.44292i	1.46972	−	1.46972i
$34$	−4.09039	−	0.518404i	−0.701495	−	0.0889055i
$35$		0			0
$36$	−2.14970	+	5.18983i	−0.358283	+	0.864972i
$37$	0.940802	+	4.72973i	0.154667	+	0.777563i	0.977771	+	0.209673i	$0.0672401\pi$
$37$	0.940802	+	4.72973i	0.154667	+	0.777563i	−0.823105	+	0.567890i	$0.807760\pi$
$38$			4.29225i			0.696295i
$39$	−4.11032	+	0.817593i	−0.658178	+	0.130920i
$40$		0			0
$41$	−1.63154	+	8.20230i	−0.254804	+	1.28098i	0.615370	+	0.788238i	$0.289007\pi$
$41$	−1.63154	+	8.20230i	−0.254804	+	1.28098i	−0.870173	+	0.492746i	$0.835993\pi$
$42$	−0.449842	+	1.08601i	−0.0694121	+	0.167576i
$43$	−4.46330	+	10.7754i	−0.680647	+	1.64323i	0.0821731	+	0.996618i	$0.473814\pi$
$43$	−4.46330	+	10.7754i	−0.680647	+	1.64323i	−0.762821	+	0.646610i	$0.776186\pi$
$44$	−0.793514	+	3.98926i	−0.119627	+	0.601404i
$45$		0			0
$46$	6.07227	−	1.20785i	0.895308	−	0.178088i
$47$		−	7.15983i		−	1.04437i	−0.852833	−	0.522184i	$-0.825117\pi$
$47$		−	7.15983i		−	1.04437i	0.852833	−	0.522184i	$-0.174883\pi$
$48$	−0.572697	−	2.87914i	−0.0826616	−	0.415568i
$49$	2.61742	−	6.31901i	0.373917	−	0.902716i
$50$		0			0
$51$	−3.83511	+	11.4799i	−0.537022	+	1.60751i
$52$	1.00948	−	1.00948i	0.139990	−	0.139990i
$53$	−4.41860	+	1.83025i	−0.606942	+	0.251404i	−0.664920	−	0.746914i	$-0.731535\pi$
$53$	−4.41860	+	1.83025i	−0.606942	+	0.251404i	0.0579785	+	0.998318i	$0.481535\pi$
$54$	6.38867	+	4.26877i	0.869388	+	0.580907i
$55$		0			0
$56$	−0.0781209	−	0.392740i	−0.0104393	−	0.0524821i
$57$	12.3580	+	2.45816i	1.63686	+	0.325591i
$58$	−3.36874	+	2.25092i	−0.442337	+	0.295560i
$59$	−1.95801	−	4.72705i	−0.254911	−	0.615410i	0.743677	−	0.668540i	$-0.233080\pi$
$59$	−1.95801	−	4.72705i	−0.254911	−	0.615410i	−0.998588	+	0.0531298i	$0.983080\pi$
$60$		0			0
$61$	−10.8073	−	2.14971i	−1.38373	−	0.275242i	−0.553589	−	0.832790i	$-0.686742\pi$
$61$	−10.8073	−	2.14971i	−1.38373	−	0.275242i	−0.830144	+	0.557549i	$0.811742\pi$
$62$	1.40153	−	7.04599i	0.177995	−	0.894842i
$63$	1.87032	+	1.24971i	0.235638	+	0.157448i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	11.0312	+	4.56928i	1.35785	+	0.562439i
$67$	0.229043	+	0.229043i	0.0279820	+	0.0279820i	0.720959	−	0.692977i	$-0.243701\pi$
$67$	0.229043	+	0.229043i	0.0279820	+	0.0279820i	−0.692977	+	0.720959i	$0.743701\pi$
$68$	−1.08638	−	3.97741i	−0.131743	−	0.482332i
$69$		−	18.1747i		−	2.18797i
$70$		0			0
$71$	2.55467	−	3.82333i	0.303183	−	0.453746i	−0.648327	−	0.761362i	$-0.724531\pi$
$71$	2.55467	−	3.82333i	0.303183	−	0.453746i	0.951511	+	0.307616i	$0.0995312\pi$
$72$	−5.61743			−0.662021
$73$	7.33833	−	10.9826i	0.858886	−	1.28541i	−0.0980694	−	0.995180i	$-0.531267\pi$
$73$	7.33833	−	10.9826i	0.858886	−	1.28541i	0.956956	−	0.290234i	$-0.0937333\pi$
$74$	−4.00967	+	2.67918i	−0.466115	+	0.311448i
$75$		0			0
$76$	−3.96552	+	1.64257i	−0.454876	+	0.188416i
$77$	1.50475	+	0.623289i	0.171483	+	0.0710304i
$78$	−2.32831	−	3.48456i	−0.263629	−	0.394549i
$79$	−0.586248	−	0.877382i	−0.0659581	−	0.0987132i	0.797024	−	0.603947i	$-0.206406\pi$
$79$	−0.586248	−	0.877382i	−0.0659581	−	0.0987132i	−0.862982	+	0.505234i	$0.831406\pi$
$80$		0			0
$81$	4.03280	−	4.03280i	0.448089	−	0.448089i
$82$	−8.20230	+	1.63154i	−0.905792	+	0.180173i
$83$	−0.476166	−	1.14957i	−0.0522660	−	0.126181i	0.895590	−	0.444881i	$-0.146754\pi$
$83$	−0.476166	−	1.14957i	−0.0522660	−	0.126181i	−0.947856	+	0.318699i	$0.896754\pi$
$84$	−1.17549			−0.128257
$85$		0			0
$86$	−11.6632			−1.25767
$87$	4.55144	+	10.9882i	0.487966	+	1.17805i
$88$	−3.98926	+	0.793514i	−0.425257	+	0.0845889i
$89$	−9.95430	+	9.95430i	−1.05515	+	1.05515i	−0.0567663	+	0.998387i	$0.518079\pi$
$89$	−9.95430	+	9.95430i	−1.05515	+	1.05515i	−0.998387	+	0.0567663i	$0.981921\pi$
$90$		0			0
$91$	−0.317602	−	0.475325i	−0.0332937	−	0.0498276i
$92$	3.43967	+	5.14783i	0.358610	+	0.536698i
$93$	−19.4837	−	8.07043i	−2.02037	−	0.836865i
$94$	6.61482	−	2.73995i	0.682267	−	0.282604i
$95$		0			0
$96$	2.44082	−	1.63090i	0.249115	−	0.166453i
$97$	−1.65138	+	2.47147i	−0.167672	+	0.250939i	−0.905785	−	0.423739i	$-0.860718\pi$
$97$	−1.65138	+	2.47147i	−0.167672	+	0.250939i	0.738112	+	0.674678i	$0.235718\pi$
$98$	6.83965			0.690909
$99$	12.6939	−	18.9978i	1.27579	−	1.90935i
$100$		0			0
$101$		−	1.16189i		−	0.115612i	−0.998328	−	0.0578061i	$-0.981589\pi$
$101$		−	1.16189i		−	0.115612i	0.998328	−	0.0578061i	$-0.0184105\pi$
$102$	−12.0737	+	0.849993i	−1.19547	+	0.0841619i
$103$	−8.86578	−	8.86578i	−0.873571	−	0.873571i	0.119289	−	0.992860i	$-0.461939\pi$
$103$	−8.86578	−	8.86578i	−0.873571	−	0.873571i	−0.992860	+	0.119289i	$0.961939\pi$
$104$	1.31895	+	0.546327i	0.129334	+	0.0535717i
$105$		0			0
$106$	−3.38185	−	3.38185i	−0.328475	−	0.328475i
$107$	−10.7012	−	7.15030i	−1.03452	−	0.691246i	−0.0822866	−	0.996609i	$-0.526222\pi$
$107$	−10.7012	−	7.15030i	−1.03452	−	0.691246i	−0.952236	+	0.305363i	$0.901222\pi$
$108$	−1.49899	+	7.53595i	−0.144241	+	0.725147i
$109$	−2.53399	−	0.504041i	−0.242712	−	0.0482784i	0.0722352	−	0.997388i	$-0.476987\pi$
$109$	−2.53399	−	0.504041i	−0.242712	−	0.0482784i	−0.314947	+	0.949109i	$0.601987\pi$
$110$		0			0
$111$	5.41740	+	13.0788i	0.514197	+	1.24138i
$112$	0.332949	−	0.222469i	0.0314607	−	0.0210214i
$113$	17.7638	+	3.53343i	1.67107	+	0.332397i	0.937705	−	0.347433i	$-0.112947\pi$
$113$	17.7638	+	3.53343i	1.67107	+	0.332397i	0.733370	+	0.679830i	$0.237947\pi$
$114$	2.45816	+	12.3580i	0.230227	+	1.15743i
$115$		0			0
$116$	−3.36874	−	2.25092i	−0.312779	−	0.208992i
$117$	−7.40911	+	3.06895i	−0.684972	+	0.283725i
$118$	3.61793	−	3.61793i	0.333057	−	0.333057i
$119$	−1.64696	+	0.115947i	−0.150976	+	0.0106288i
$120$		0			0
$121$	2.12156	−	5.12189i	0.192869	−	0.465626i
$122$	−2.14971	−	10.8073i	−0.194625	−	0.978447i
$123$			24.5499i			2.21359i
$124$	7.04599	−	1.40153i	0.632749	−	0.125862i
$125$		0			0
$126$	−0.438839	+	2.20619i	−0.0390948	+	0.196543i
$127$	1.02712	−	2.47968i	0.0911419	−	0.220036i	−0.871735	−	0.489978i	$-0.837005\pi$
$127$	1.02712	−	2.47968i	0.0911419	−	0.220036i	0.962876	+	0.269942i	$0.0870047\pi$
$128$	−0.382683	+	0.923880i	−0.0338248	+	0.0816602i
$129$	−6.67946	+	33.5799i	−0.588094	+	2.95655i
$130$		0			0
$131$	−0.529027	+	0.105230i	−0.0462213	+	0.00919399i	−0.218147	−	0.975916i	$-0.570001\pi$
$131$	−0.529027	+	0.105230i	−0.0462213	+	0.00919399i	0.171925	+	0.985110i	$0.445001\pi$
$132$			11.9401i			1.03925i
$133$	0.335314	+	1.68574i	0.0290754	+	0.146172i
$134$	−0.123957	+	0.299259i	−0.0107083	+	0.0258520i
$135$		0			0
$136$	3.25891	−	2.52577i	0.279449	−	0.216583i
$137$	−10.3299	+	10.3299i	−0.882540	+	0.882540i	−0.993792	−	0.111252i	$-0.964514\pi$
$137$	−10.3299	+	10.3299i	−0.882540	+	0.882540i	0.111252	+	0.993792i	$0.464514\pi$
$138$	16.7912	−	6.95514i	1.42936	−	0.592061i
$139$	9.81373	+	6.55733i	0.832390	+	0.556185i	0.897155	−	0.441715i	$-0.145630\pi$
$139$	9.81373	+	6.55733i	0.832390	+	0.556185i	−0.0647652	+	0.997901i	$0.520630\pi$
$140$		0			0
$141$	−4.10041	−	20.6142i	−0.345317	−	1.73603i
$142$	4.50992	+	0.897080i	0.378464	+	0.0752812i
$143$	−4.82812	+	3.22605i	−0.403748	+	0.269776i
$144$	−2.14970	−	5.18983i	−0.179142	−	0.432486i
$145$		0			0
$146$	12.9548	+	2.57688i	1.07215	+	0.213264i
$147$	3.91705	−	19.6923i	0.323073	−	1.62420i
$148$	−4.00967	−	2.67918i	−0.329593	−	0.220227i
$149$	5.72365	+	5.72365i	0.468900	+	0.468900i	0.901558	−	0.432658i	$-0.142424\pi$
$149$	5.72365	+	5.72365i	0.468900	+	0.468900i	−0.432658	+	0.901558i	$0.642424\pi$
$150$		0			0
$151$	−20.2121	−	8.37213i	−1.64484	−	0.681315i	−0.648066	−	0.761584i	$-0.724422\pi$
$151$	−20.2121	−	8.37213i	−1.64484	−	0.681315i	−0.996773	+	0.0802696i	$0.974422\pi$
$152$	−3.03508	−	3.03508i	−0.246177	−	0.246177i
$153$	−2.91210	+	22.9775i	−0.235429	+	1.85762i
$154$			1.62873i			0.131247i
$155$		0			0
$156$	2.32831	−	3.48456i	0.186414	−	0.278988i
$157$	7.75079			0.618580			0.309290	−	0.950968i	$-0.399909\pi$
$157$	7.75079			0.618580			0.309290	+	0.950968i	$0.399909\pi$
$158$	0.586248	−	0.877382i	0.0466394	−	0.0698008i
$159$	−11.6736	+	7.80005i	−0.925777	+	0.618584i
$160$		0			0
$161$	2.29047	−	0.948742i	0.180514	−	0.0747714i
$162$	5.26911	+	2.18254i	0.413980	+	0.171476i
$163$	−4.44289	−	6.64926i	−0.347994	−	0.520810i	0.615643	−	0.788026i	$-0.288897\pi$
$163$	−4.44289	−	6.64926i	−0.347994	−	0.520810i	−0.963637	+	0.267215i	$0.913897\pi$
$164$	−4.64623	−	6.95357i	−0.362810	−	0.542983i
$165$		0			0
$166$	0.879841	−	0.879841i	0.0682889	−	0.0682889i
$167$	15.6593	−	3.11484i	1.21176	−	0.241033i	0.452463	−	0.891783i	$-0.350545\pi$
$167$	15.6593	−	3.11484i	1.21176	−	0.241033i	0.759292	+	0.650750i	$0.225545\pi$
$168$	−0.449842	−	1.08601i	−0.0347061	−	0.0837878i
$169$	−10.9619			−0.843223
$170$		0			0
$171$	24.1114			1.84385
$172$	−4.46330	−	10.7754i	−0.340324	−	0.821614i
$173$	10.6405	−	2.11653i	0.808982	−	0.160917i	0.226765	−	0.973950i	$-0.427185\pi$
$173$	10.6405	−	2.11653i	0.808982	−	0.160917i	0.582218	+	0.813033i	$0.302185\pi$
$174$	−8.40997	+	8.40997i	−0.637558	+	0.637558i
$175$		0			0
$176$	−2.25974	−	3.38193i	−0.170334	−	0.254923i
$177$	−8.34455	−	12.4885i	−0.627215	−	0.938693i
$178$	−13.0059	−	5.38723i	−0.974835	−	0.403790i
$179$	−5.35501	+	2.21812i	−0.400253	+	0.165790i	−0.573724	−	0.819049i	$-0.694502\pi$
$179$	−5.35501	+	2.21812i	−0.400253	+	0.165790i	0.173471	+	0.984839i	$0.444502\pi$
$180$		0			0
$181$	−10.1235	+	6.76432i	−0.752475	+	0.502788i	−0.871676	−	0.490082i	$-0.836967\pi$
$181$	−10.1235	+	6.76432i	−0.752475	+	0.502788i	0.119201	+	0.992870i	$0.461967\pi$
$182$	0.317602	−	0.475325i	0.0235422	−	0.0352334i
$183$	−32.3469			−2.39115
$184$	−3.43967	+	5.14783i	−0.253576	+	0.379503i
$185$		0			0
$186$		−	21.0891i		−	1.54632i
$187$	1.17773	+	16.7290i	0.0861241	+	1.22335i
$188$	5.06277	+	5.06277i	0.369240	+	0.369240i
$189$	2.84257	+	1.17743i	0.206766	+	0.0856454i
$190$		0			0
$191$	4.69675	+	4.69675i	0.339845	+	0.339845i	0.856309	−	0.516464i	$-0.172752\pi$
$191$	4.69675	+	4.69675i	0.339845	+	0.339845i	−0.516464	+	0.856309i	$0.672752\pi$
$192$	2.44082	+	1.63090i	0.176151	+	0.117700i
$193$	−1.47105	+	7.39545i	−0.105888	+	0.532336i	0.891034	+	0.453937i	$0.149981\pi$
$193$	−1.47105	+	7.39545i	−0.105888	+	0.532336i	−0.996922	+	0.0783992i	$0.975019\pi$
$194$	−2.91529	−	0.579888i	−0.209306	−	0.0416335i
$195$		0			0
$196$	2.61742	+	6.31901i	0.186959	+	0.451358i
$197$	−11.0633	+	7.39225i	−0.788226	+	0.526676i	−0.883308	−	0.468793i	$-0.844689\pi$
$197$	−11.0633	+	7.39225i	−0.788226	+	0.526676i	0.0950814	+	0.995470i	$0.469689\pi$
$198$	22.4094	+	4.45751i	1.59257	+	0.316781i
$199$	−1.64904	−	8.29026i	−0.116897	−	0.587681i	−0.994182	−	0.107711i	$-0.965648\pi$
$199$	−1.64904	−	8.29026i	−0.116897	−	0.587681i	0.877285	−	0.479969i	$-0.159352\pi$
$200$		0			0
$201$	0.790618	+	0.528274i	0.0557659	+	0.0372616i
$202$	1.07345	−	0.444636i	0.0755274	−	0.0312845i
$203$	−1.14719	+	1.14719i	−0.0805172	+	0.0805172i
$204$	−5.40569	−	10.8294i	−0.378474	−	0.758206i
$205$		0			0
$206$	4.79812	−	11.5837i	0.334301	−	0.807074i
$207$	−6.78502	−	34.1106i	−0.471591	−	2.37085i
$208$			1.42762i			0.0989877i
$209$	17.1229	−	3.40596i	1.18442	−	0.235595i
$210$		0			0
$211$	1.27654	−	6.41761i	0.0878808	−	0.441807i	−0.911644	−	0.410981i	$-0.865186\pi$
$211$	1.27654	−	6.41761i	0.0878808	−	0.441807i	0.999525	−	0.0308257i	$-0.00981368\pi$
$212$	1.83025	−	4.41860i	0.125702	−	0.303471i
$213$	5.16564	−	12.4709i	0.353944	−	0.854495i
$214$	2.51085	−	12.6229i	0.171638	−	0.862884i
$215$		0			0
$216$	−7.53595	+	1.49899i	−0.512757	+	0.101994i
$217$		−	2.87673i		−	0.195285i
$218$	−0.504041	−	2.53399i	−0.0341380	−	0.171623i
$219$	14.8384	−	35.8230i	1.00269	−	2.42070i
$220$		0			0
$221$	2.91843	−	5.11179i	0.196315	−	0.343856i
$222$	−10.0101	+	10.0101i	−0.671831	+	0.671831i
$223$	11.5196	−	4.77157i	0.771408	−	0.319528i	0.0379655	−	0.999279i	$-0.487912\pi$
$223$	11.5196	−	4.77157i	0.771408	−	0.319528i	0.733443	+	0.679751i	$0.237912\pi$
$224$	0.332949	+	0.222469i	0.0222461	+	0.0148644i
$225$		0			0
$226$	3.53343	+	17.7638i	0.235040	+	1.18163i
$227$	12.0457	+	2.39605i	0.799504	+	0.159031i	0.577902	−	0.816106i	$-0.303871\pi$
$227$	12.0457	+	2.39605i	0.799504	+	0.159031i	0.221602	+	0.975137i	$0.428871\pi$
$228$	−10.4766	+	7.00024i	−0.693830	+	0.463602i
$229$	−4.51607	−	10.9028i	−0.298430	−	0.720474i	−0.999969	−	0.00784330i	$-0.997503\pi$
$229$	−4.51607	−	10.9028i	−0.298430	−	0.720474i	0.701539	−	0.712631i	$-0.252497\pi$
$230$		0			0
$231$	4.68935	+	0.932770i	0.308537	+	0.0613718i
$232$	0.790417	−	3.97370i	0.0518934	−	0.260886i
$233$	6.56815	+	4.38870i	0.430294	+	0.287513i	0.751796	−	0.659396i	$-0.229188\pi$
$233$	6.56815	+	4.38870i	0.430294	+	0.287513i	−0.321502	+	0.946909i	$0.604188\pi$
$234$	−5.67068	−	5.67068i	−0.370704	−	0.370704i
$235$		0			0
$236$	4.72705	+	1.95801i	0.307705	+	0.127456i
$237$	−2.19036	−	2.19036i	−0.142279	−	0.142279i
$238$	−0.737384	−	1.47722i	−0.0477975	−	0.0957539i
$239$			25.7864i			1.66798i	0.551778	+	0.833991i	$0.313950\pi$
$239$			25.7864i			1.66798i	−0.551778	+	0.833991i	$0.686050\pi$
$240$		0			0
$241$	6.67849	−	9.99506i	0.430199	−	0.643839i	−0.551523	−	0.834160i	$-0.685953\pi$
$241$	6.67849	−	9.99506i	0.430199	−	0.643839i	0.981722	+	0.190321i	$0.0609530\pi$
$242$	5.54389			0.356375
$243$	−3.50489	+	5.24544i	−0.224839	+	0.336495i
$244$	9.16199	−	6.12184i	0.586536	−	0.391911i
$245$		0			0
$246$	−22.6812	+	9.39486i	−1.44610	+	0.598994i
$247$	−5.66126	−	2.34497i	−0.360217	−	0.149207i
$248$	3.99123	+	5.97330i	0.253444	+	0.379305i
$249$	−2.02930	−	3.03707i	−0.128602	−	0.192466i
$250$		0			0
$251$	7.42678	−	7.42678i	0.468774	−	0.468774i	−0.432743	−	0.901517i	$-0.642454\pi$
$251$	7.42678	−	7.42678i	0.468774	−	0.468774i	0.901517	+	0.432743i	$0.142454\pi$
$252$	−2.20619	+	0.438839i	−0.138977	+	0.0276442i
$253$	−9.63687	−	23.2655i	−0.605865	−	1.46269i
$254$	2.68399			0.168408
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−7.31385	−	17.6572i	−0.456226	−	1.10143i	−0.969914	−	0.243449i	$-0.921721\pi$
$257$	−7.31385	−	17.6572i	−0.456226	−	1.10143i	0.513688	−	0.857977i	$-0.328279\pi$
$258$	−33.5799	+	6.67946i	−2.09059	+	0.415845i
$259$	−1.36546	+	1.36546i	−0.0848455	+	0.0848455i
$260$		0			0
$261$	12.6444	+	18.9236i	0.782667	+	1.17134i
$262$	−0.299670	−	0.448488i	−0.0185137	−	0.0277077i
$263$	18.2366	+	7.55384i	1.12452	+	0.465790i	0.865913	−	0.500194i	$-0.166738\pi$
$263$	18.2366	+	7.55384i	1.12452	+	0.465790i	0.258603	+	0.965984i	$0.416738\pi$
$264$	−11.0312	+	4.56928i	−0.678924	+	0.281220i
$265$		0			0
$266$	−1.42910	+	0.954894i	−0.0876237	+	0.0585483i
$267$	−22.9590	+	34.3606i	−1.40507	+	2.10284i
$268$	−0.323915			−0.0197863
$269$	−0.192478	+	0.288064i	−0.0117356	+	0.0175636i	−0.837291	−	0.546757i	$-0.815862\pi$
$269$	−0.192478	+	0.288064i	−0.0117356	+	0.0175636i	0.825555	+	0.564321i	$0.190862\pi$
$270$		0			0
$271$		−	7.29707i		−	0.443266i	−0.975130	−	0.221633i	$-0.928861\pi$
$271$		−	7.29707i		−	0.443266i	0.975130	−	0.221633i	$-0.0711386\pi$
$272$	3.58064	+	2.04427i	0.217108	+	0.123952i
$273$	−1.18664	−	1.18664i	−0.0718185	−	0.0718185i
$274$	−13.4966	−	5.59048i	−0.815361	−	0.337734i
$275$		0			0
$276$	12.8514	+	12.8514i	0.773565	+	0.773565i
$277$	−13.3490	−	8.91951i	−0.802063	−	0.535921i	0.0856464	−	0.996326i	$-0.472704\pi$
$277$	−13.3490	−	8.91951i	−0.802063	−	0.535921i	−0.887709	+	0.460404i	$0.847704\pi$
$278$	−2.30263	+	11.5761i	−0.138102	+	0.694288i
$279$	−39.5804	−	7.87303i	−2.36962	−	0.471346i
$280$		0			0
$281$	−2.31954	−	5.59987i	−0.138372	−	0.334060i	0.839469	−	0.543408i	$-0.182866\pi$
$281$	−2.31954	−	5.59987i	−0.138372	−	0.334060i	−0.977841	+	0.209347i	$0.932866\pi$
$282$	17.4758	−	11.6770i	1.04067	−	0.695354i
$283$	16.1947	+	3.22133i	0.962676	+	0.191488i	0.651318	−	0.758805i	$-0.274216\pi$
$283$	16.1947	+	3.22133i	0.962676	+	0.191488i	0.311358	+	0.950293i	$0.399216\pi$
$284$	0.897080	+	4.50992i	0.0532319	+	0.267615i
$285$		0			0
$286$	−4.82812	−	3.22605i	−0.285493	−	0.190760i
$287$	−3.09391	+	1.28154i	−0.182628	+	0.0756470i
$288$	3.97212	−	3.97212i	0.234060	−	0.234060i
$289$	−8.64196	−	14.6396i	−0.508350	−	0.861150i
$290$		0			0
$291$	−3.33916	+	8.06144i	−0.195745	+	0.472570i
$292$	2.57688	+	12.9548i	0.150800	+	0.758125i
$293$		−	6.51197i		−	0.380433i	−0.981742	−	0.190217i	$-0.939081\pi$
$293$		−	6.51197i		−	0.380433i	0.981742	−	0.190217i	$-0.0609190\pi$
$294$	19.6923	−	3.91705i	1.14848	−	0.228447i
$295$		0			0
$296$	0.940802	−	4.72973i	0.0546830	−	0.274910i
$297$	11.9598	−	28.8734i	0.693976	−	1.67541i
$298$	−3.09762	+	7.47831i	−0.179440	+	0.433207i
$299$	−1.72435	+	8.66890i	−0.0997218	+	0.501336i
$300$		0			0
$301$	−4.58060	+	0.911137i	−0.264021	+	0.0525171i
$302$		−	21.8774i		−	1.25891i
$303$	−0.665410	−	3.34524i	−0.0382268	−	0.192179i
$304$	1.64257	−	3.96552i	0.0942080	−	0.227438i
$305$		0			0
$306$	−22.3428	+	6.10267i	−1.27725	+	0.348866i
$307$	0.765848	−	0.765848i	0.0437092	−	0.0437092i	−0.684914	−	0.728624i	$-0.740160\pi$
$307$	0.765848	−	0.765848i	0.0437092	−	0.0437092i	0.728624	+	0.684914i	$0.240160\pi$
$308$	−1.50475	+	0.623289i	−0.0857413	+	0.0355152i
$309$	−30.6032	−	20.4484i	−1.74096	−	1.16327i
$310$		0			0
$311$	3.49706	+	17.5809i	0.198300	+	0.996921i	0.943826	+	0.330444i	$0.107199\pi$
$311$	3.49706	+	17.5809i	0.198300	+	0.996921i	−0.745526	+	0.666477i	$0.767801\pi$
$312$	4.11032	+	0.817593i	0.232701	+	0.0462871i
$313$	2.63946	−	1.76363i	0.149191	−	0.0996864i	−0.478734	−	0.877960i	$-0.658904\pi$
$313$	2.63946	−	1.76363i	0.149191	−	0.0996864i	0.627925	+	0.778273i	$0.283904\pi$
$314$	2.96610	+	7.16079i	0.167387	+	0.404107i
$315$		0			0
$316$	1.03494	+	0.205863i	0.0582201	+	0.0115807i
$317$	−3.02578	+	15.2116i	−0.169945	+	0.854370i	0.797894	+	0.602798i	$0.205948\pi$
$317$	−3.02578	+	15.2116i	−0.169945	+	0.854370i	−0.967839	+	0.251572i	$0.919052\pi$
$318$	−11.6736	−	7.80005i	−0.654623	−	0.437405i
$319$	11.6526	+	11.6526i	0.652423	+	0.652423i
$320$		0			0
$321$	−34.9052	−	14.4582i	−1.94822	−	0.806978i
$322$	1.75305	+	1.75305i	0.0976935	+	0.0976935i
$323$	−13.9880	+	10.8412i	−0.778315	+	0.603223i
$324$			5.70324i			0.316847i
$325$		0			0
$326$	4.44289	−	6.64926i	0.246069	−	0.368268i
$327$	−7.58437			−0.419417
$328$	4.64623	−	6.95357i	0.256545	−	0.383947i
$329$	2.38386	−	1.59284i	0.131426	−	0.0878163i
$330$		0			0
$331$	26.8797	−	11.1340i	1.47744	−	0.611977i	0.508901	−	0.860825i	$-0.330052\pi$
$331$	26.8797	−	11.1340i	1.47744	−	0.611977i	0.968543	+	0.248847i	$0.0800518\pi$
$332$	1.14957	+	0.476166i	0.0630907	+	0.0261330i
$333$	15.0501	+	22.5241i	0.824740	+	1.23431i
$334$	8.87030	+	13.2753i	0.485361	+	0.726394i
$335$		0			0
$336$	0.831199	−	0.831199i	0.0453456	−	0.0453456i
$337$	9.11334	−	1.81276i	0.496435	−	0.0987471i	0.0594785	−	0.998230i	$-0.481056\pi$
$337$	9.11334	−	1.81276i	0.496435	−	0.0987471i	0.436957	+	0.899482i	$0.356056\pi$
$338$	−4.19494	−	10.1275i	−0.228175	−	0.550862i
$339$	53.1680			2.88769
$340$		0			0
$341$	−29.2205			−1.58238
$342$	9.22704	+	22.2760i	0.498941	+	1.20455i
$343$	5.43539	−	1.08117i	0.293483	−	0.0583774i
$344$	8.24711	−	8.24711i	0.444654	−	0.444654i
$345$		0			0
$346$	6.02736	+	9.02058i	0.324033	+	0.484950i
$347$	3.92971	+	5.88122i	0.210958	+	0.315721i	0.921826	−	0.387605i	$-0.126698\pi$
$347$	3.92971	+	5.88122i	0.210958	+	0.315721i	−0.710868	+	0.703326i	$0.751698\pi$
$348$	−10.9882	−	4.55144i	−0.589027	−	0.243983i
$349$	−3.78588	+	1.56816i	−0.202653	+	0.0839418i	−0.481702	−	0.876335i	$-0.659981\pi$
$349$	−3.78588	+	1.56816i	−0.202653	+	0.0839418i	0.279048	+	0.960277i	$0.409981\pi$
$350$		0			0
$351$	−9.12060	+	6.09419i	−0.486822	+	0.325284i
$352$	2.25974	−	3.38193i	0.120444	−	0.180258i
$353$	−8.78110			−0.467371			−0.233685	−	0.972312i	$-0.575079\pi$
$353$	−8.78110			−0.467371			−0.233685	+	0.972312i	$0.575079\pi$
$354$	8.34455	−	12.4885i	0.443508	−	0.663756i
$355$		0			0
$356$		−	14.0775i		−	0.746106i
$357$	−4.67542	+	1.27703i	−0.247449	+	0.0675877i
$358$	−4.09855	−	4.09855i	−0.216615	−	0.216615i
$359$	12.2545	+	5.07599i	0.646769	+	0.267901i	0.681859	−	0.731484i	$-0.261172\pi$
$359$	12.2545	+	5.07599i	0.646769	+	0.267901i	−0.0350899	+	0.999384i	$0.511172\pi$
$360$		0			0
$361$	−0.407718	−	0.407718i	−0.0214588	−	0.0214588i
$362$	−10.1235	−	6.76432i	−0.532080	−	0.355525i
$363$	3.17497	−	15.9616i	0.166643	−	0.837769i
$364$	0.560684	+	0.111527i	0.0293878	+	0.00584560i
$365$		0			0
$366$	−12.3786	−	29.8846i	−0.647040	−	1.56209i
$367$	−10.7937	+	7.21215i	−0.563429	+	0.376471i	−0.804424	−	0.594055i	$-0.797526\pi$
$367$	−10.7937	+	7.21215i	−0.563429	+	0.376471i	0.240996	+	0.970526i	$0.422526\pi$
$368$	−6.07227	−	1.20785i	−0.316539	−	0.0629636i
$369$	9.16506	+	46.0759i	0.477114	+	2.39861i
$370$		0			0
$371$	−1.59238	−	1.06400i	−0.0826724	−	0.0552399i
$372$	19.4837	−	8.07043i	1.01019	−	0.418432i
$373$	26.5715	−	26.5715i	1.37582	−	1.37582i	0.524263	−	0.851557i	$-0.324341\pi$
$373$	26.5715	−	26.5715i	1.37582	−	1.37582i	0.851557	−	0.524263i	$-0.175659\pi$
$374$	−15.0049	+	7.48999i	−0.775884	+	0.387298i
$375$		0			0
$376$	−2.73995	+	6.61482i	−0.141302	+	0.341133i
$377$	−1.12842	−	5.67293i	−0.0581164	−	0.292171i
$378$			3.07677i			0.158252i
$379$	−19.3776	+	3.85445i	−0.995363	+	0.197990i	−0.665789	−	0.746140i	$-0.731905\pi$
$379$	−19.3776	+	3.85445i	−0.995363	+	0.197990i	−0.329574	+	0.944130i	$0.606905\pi$
$380$		0			0
$381$	1.53711	−	7.72757i	0.0787485	−	0.395896i
$382$	−2.54186	+	6.13660i	−0.130053	+	0.313976i
$383$	3.37058	−	8.13729i	0.172228	−	0.415796i	−0.814070	−	0.580767i	$-0.802753\pi$
$383$	3.37058	−	8.13729i	0.172228	−	0.415796i	0.986298	+	0.164971i	$0.0527529\pi$
$384$	−0.572697	+	2.87914i	−0.0292253	+	0.146926i
$385$		0			0
$386$	−7.39545	+	1.47105i	−0.376418	+	0.0748743i
$387$			65.5171i			3.33042i
$388$	−0.579888	−	2.91529i	−0.0294393	−	0.148002i
$389$	0.346119	−	0.835604i	0.0175489	−	0.0423668i	−0.914862	−	0.403766i	$-0.867701\pi$
$389$	0.346119	−	0.835604i	0.0175489	−	0.0423668i	0.932411	+	0.361399i	$0.117701\pi$
$390$		0			0
$391$	19.2735	+	16.7382i	0.974701	+	0.846488i
$392$	−4.83636	+	4.83636i	−0.244273	+	0.244273i
$393$	−1.46288	+	0.605944i	−0.0737925	+	0.0305658i
$394$	−11.0633	−	7.39225i	−0.557360	−	0.372416i
$395$		0			0
$396$	4.45751	+	22.4094i	0.223998	+	1.12612i
$397$	9.40611	+	1.87099i	0.472079	+	0.0939023i	0.425396	−	0.905007i	$-0.360135\pi$
$397$	9.40611	+	1.87099i	0.472079	+	0.0939023i	0.0466831	+	0.998910i	$0.485135\pi$
$398$	7.02814	−	4.69606i	0.352289	−	0.235392i
$399$	1.93083	+	4.66144i	0.0966626	+	0.233364i
$400$		0			0
$401$	26.8075	+	5.33235i	1.33870	+	0.266285i	0.811947	−	0.583731i	$-0.198408\pi$
$401$	26.8075	+	5.33235i	1.33870	+	0.266285i	0.526757	+	0.850016i	$0.323408\pi$
$402$	−0.185505	+	0.932598i	−0.00925216	+	0.0465138i
$403$	8.52761	+	5.69797i	0.424790	+	0.283836i
$404$	0.821580	+	0.821580i	0.0408751	+	0.0408751i
$405$		0			0
$406$	−1.49888	−	0.620857i	−0.0743882	−	0.0308126i
$407$	13.8697	+	13.8697i	0.687495	+	0.687495i
$408$	7.93635	−	9.13842i	0.392908	−	0.452419i
$409$			14.7541i			0.729542i	0.931097	+	0.364771i	$0.118853\pi$
$409$			14.7541i			0.729542i	−0.931097	+	0.364771i	$0.881147\pi$
$410$		0			0
$411$	−23.8253	+	35.6570i	−1.17521	+	1.75883i
$412$	12.5381			0.617708
$413$	1.13827	−	1.70354i	0.0560106	−	0.0838258i
$414$	28.9176	−	19.3221i	1.42122	−	0.949629i
$415$		0			0
$416$	−1.31895	+	0.546327i	−0.0646668	+	0.0267859i
$417$	32.0105	+	13.2592i	1.56756	+	0.649305i
$418$	9.69935	+	14.5161i	0.474411	+	0.710006i
$419$	19.8198	+	29.6624i	0.968259	+	1.44910i	0.892011	+	0.452014i	$0.149294\pi$
$419$	19.8198	+	29.6624i	0.968259	+	1.44910i	0.0762483	+	0.997089i	$0.475706\pi$
$420$		0			0
$421$	−19.9963	+	19.9963i	−0.974561	+	0.974561i	−0.999684	−	0.0251238i	$-0.992002\pi$
$421$	−19.9963	+	19.9963i	−0.974561	+	0.974561i	0.0251238	+	0.999684i	$0.492002\pi$
$422$	6.41761	−	1.27654i	0.312404	−	0.0621411i
$423$	−15.3915	−	37.1583i	−0.748359	−	1.80670i
$424$	4.78266			0.232267
$425$		0			0
$426$	13.4985			0.654002
$427$	−1.68855	−	4.07652i	−0.0817147	−	0.197277i
$428$	12.6229	−	2.51085i	0.610151	−	0.121367i
$429$	−12.0533	+	12.0533i	−0.581938	+	0.581938i
$430$		0			0
$431$	19.4844	+	29.1604i	0.938529	+	1.40461i	0.914361	+	0.404900i	$0.132694\pi$
$431$	19.4844	+	29.1604i	0.938529	+	1.40461i	0.0241685	+	0.999708i	$0.492306\pi$
$432$	−4.26877	−	6.38867i	−0.205382	−	0.307375i
$433$	−8.33104	−	3.45083i	−0.400364	−	0.165836i	0.173410	−	0.984850i	$-0.444521\pi$
$433$	−8.33104	−	3.45083i	−0.400364	−	0.165836i	−0.573774	+	0.819013i	$0.694521\pi$
$434$	2.65775	−	1.10088i	0.127576	−	0.0528438i
$435$		0			0
$436$	2.14821	−	1.43539i	0.102881	−	0.0687426i
$437$	14.7639	−	22.0957i	0.706253	−	1.05698i
$438$	38.7746			1.85272
$439$	0.450506	−	0.674229i	0.0215015	−	0.0321792i	−0.820563	−	0.571556i	$-0.806340\pi$
$439$	0.450506	−	0.674229i	0.0215015	−	0.0321792i	0.842065	+	0.539377i	$0.181340\pi$
$440$		0			0
$441$		−	38.4213i		−	1.82958i
$442$	5.83952	+	0.740084i	0.277758	+	0.0352022i
$443$	21.1731	+	21.1731i	1.00597	+	1.00597i	0.999982	+	0.00598344i	$0.00190460\pi$
$443$	21.1731	+	21.1731i	1.00597	+	1.00597i	0.00598344	+	0.999982i	$0.498095\pi$
$444$	−13.0788	−	5.41740i	−0.620691	−	0.257099i
$445$		0			0
$446$	8.81671	+	8.81671i	0.417483	+	0.417483i
$447$	19.7571	+	13.2013i	0.934480	+	0.624399i
$448$	−0.0781209	+	0.392740i	−0.00369086	+	0.0185552i
$449$	31.7252	+	6.31053i	1.49720	+	0.297812i	0.874646	−	0.484762i	$-0.161094\pi$
$449$	31.7252	+	6.31053i	1.49720	+	0.297812i	0.622558	+	0.782574i	$0.286094\pi$
$450$		0			0
$451$	13.0173	+	31.4265i	0.612960	+	1.47982i
$452$	−15.0594	+	10.0624i	−0.708334	+	0.473294i
$453$	−62.9882	−	12.5291i	−2.95945	−	0.588670i
$454$	2.39605	+	12.0457i	0.112452	+	0.565335i
$455$		0			0
$456$	−10.4766	−	7.00024i	−0.490612	−	0.327816i
$457$	−2.69908	+	1.11799i	−0.126258	+	0.0522976i	−0.444918	−	0.895571i	$-0.646767\pi$
$457$	−2.69908	+	1.11799i	−0.126258	+	0.0522976i	0.318660	+	0.947869i	$0.396767\pi$
$458$	8.34461	−	8.34461i	0.389918	−	0.389918i
$459$	2.22480	+	31.6020i	0.103845	+	1.47506i
$460$		0			0
$461$	0.778333	−	1.87906i	0.0362506	−	0.0875167i	−0.904717	−	0.426012i	$-0.859918\pi$
$461$	0.778333	−	1.87906i	0.0362506	−	0.0875167i	0.940968	+	0.338496i	$0.109918\pi$
$462$	0.932770	+	4.68935i	0.0433964	+	0.218168i
$463$			27.6489i			1.28495i	0.766306	+	0.642476i	$0.222093\pi$
$463$			27.6489i			1.28495i	−0.766306	+	0.642476i	$0.777907\pi$
$464$	3.97370	−	0.790417i	0.184474	−	0.0366942i
$465$		0			0
$466$	−1.54111	+	7.74767i	−0.0713904	+	0.358904i
$467$	0.528111	−	1.27497i	0.0244380	−	0.0589987i	−0.911189	−	0.411988i	$-0.864835\pi$
$467$	0.528111	−	1.27497i	0.0244380	−	0.0589987i	0.935627	+	0.352989i	$0.114835\pi$
$468$	3.06895	−	7.40911i	0.141862	−	0.342486i
$469$	−0.0253045	+	0.127215i	−0.00116846	+	0.00587422i
$470$		0			0
$471$	22.3156	−	4.43885i	1.02825	−	0.204531i
$472$			5.11652i			0.235507i
$473$	9.25489	+	46.5275i	0.425540	+	2.13934i
$474$	1.18542	−	2.86185i	0.0544480	−	0.131449i
$475$		0			0
$476$	1.08259	−	1.24656i	0.0496203	−	0.0571360i
$477$	−18.9973	+	18.9973i	−0.869828	+	0.869828i
$478$	−23.8235	+	9.86802i	−1.08966	+	0.451353i
$479$	−20.9063	−	13.9692i	−0.955234	−	0.638267i	−0.0228511	−	0.999739i	$-0.507274\pi$
$479$	−20.9063	−	13.9692i	−0.955234	−	0.638267i	−0.932383	+	0.361472i	$0.882274\pi$
$480$		0			0
$481$	−1.34311	−	6.75226i	−0.0612405	−	0.307877i
$482$	11.7900	+	2.34517i	0.537019	+	0.106820i
$483$	6.05123	−	4.04331i	0.275341	−	0.183977i
$484$	2.12156	+	5.12189i	0.0964344	+	0.232813i
$485$		0			0
$486$	−6.18742	−	1.23075i	−0.280667	−	0.0558282i
$487$	−4.82518	+	24.2578i	−0.218650	+	1.09923i	0.702995	+	0.711194i	$0.251845\pi$
$487$	−4.82518	+	24.2578i	−0.218650	+	1.09923i	−0.921645	+	0.388033i	$0.873155\pi$
$488$	9.16199	+	6.12184i	0.414744	+	0.277123i
$489$	−16.5997	−	16.5997i	−0.750665	−	0.750665i
$490$		0			0
$491$	−14.0845	−	5.83401i	−0.635627	−	0.263285i	0.0415151	−	0.999138i	$-0.486782\pi$
$491$	−14.0845	−	5.83401i	−0.635627	−	0.263285i	−0.677142	+	0.735853i	$0.736782\pi$
$492$	−17.3594	−	17.3594i	−0.782624	−	0.782624i
$493$	−15.8442	−	5.29309i	−0.713587	−	0.238389i
$494$		−	6.12770i		−	0.275698i
$495$		0			0
$496$	−3.99123	+	5.97330i	−0.179212	+	0.268209i
$497$	1.84131			0.0825940
$498$	2.02930	−	3.03707i	0.0909352	−	0.136094i
$499$	4.13838	−	2.76518i	0.185260	−	0.123786i	−0.459482	−	0.888187i	$-0.651965\pi$
$499$	4.13838	−	2.76518i	0.185260	−	0.123786i	0.644742	+	0.764401i	$0.276965\pi$
$500$		0			0
$501$	43.3016	−	17.9361i	1.93457	−	0.801326i
$502$	9.70355	+	4.01934i	0.433091	+	0.179392i
$503$	11.8866	+	17.7895i	0.529997	+	0.793196i	0.995787	−	0.0916992i	$-0.0292298\pi$
$503$	11.8866	+	17.7895i	0.529997	+	0.793196i	−0.465790	+	0.884895i	$0.654230\pi$
$504$	−1.24971	−	1.87032i	−0.0556663	−	0.0833106i
$505$		0			0
$506$	17.8066	−	17.8066i	0.791600	−	0.791600i
$507$	−31.5609	+	6.27784i	−1.40167	+	0.278809i
$508$	1.02712	+	2.47968i	0.0455709	+	0.110018i
$509$	42.8646			1.89994			0.949969	−	0.312343i	$-0.101114\pi$
$509$	42.8646			1.89994			0.949969	+	0.312343i	$0.101114\pi$
$510$		0			0
$511$	5.28919			0.233980
$512$	−0.382683	−	0.923880i	−0.0169124	−	0.0408301i
$513$	32.3462	−	6.43406i	1.42812	−	0.284071i
$514$	13.5142	−	13.5142i	0.596088	−	0.596088i
$515$		0			0
$516$	−19.0215	−	28.4677i	−0.837375	−	1.25322i
$517$	−16.1793	−	24.2141i	−0.711566	−	1.06493i
$518$	−1.78406	−	0.738981i	−0.0783871	−	0.0324690i
$519$	29.4234	−	12.1876i	1.29154	−	0.534975i
$520$		0			0
$521$	−0.196842	+	0.131526i	−0.00862380	+	0.00576224i	−0.559875	−	0.828577i	$-0.689151\pi$
$521$	−0.196842	+	0.131526i	−0.00862380	+	0.00576224i	0.551251	+	0.834340i	$0.314151\pi$
$522$	−12.6444	+	18.9236i	−0.553429	+	0.828266i
$523$	−1.81889			−0.0795345			−0.0397673	−	0.999209i	$-0.512662\pi$
$523$	−1.81889			−0.0795345			−0.0397673	+	0.999209i	$0.512662\pi$
$524$	0.299670	−	0.448488i	0.0130911	−	0.0195923i
$525$		0			0
$526$			19.7391i			0.860667i
$527$	26.5022	−	13.2291i	1.15445	−	0.576269i
$528$	−8.44292	−	8.44292i	−0.367431	−	0.367431i
$529$	−14.1644	−	5.86708i	−0.615843	−	0.255090i
$530$		0			0
$531$	−20.3235	−	20.3235i	−0.881964	−	0.881964i
$532$	−1.42910	−	0.954894i	−0.0619593	−	0.0413999i
$533$	2.32922	−	11.7098i	0.100890	−	0.507206i
$534$	−40.5311	−	8.06214i	−1.75395	−	0.348883i
$535$		0			0
$536$	−0.123957	−	0.299259i	−0.00535413	−	0.0129260i
$537$	−14.1475	+	9.45308i	−0.610511	+	0.407930i
$538$	−0.339795	−	0.0675894i	−0.0146496	−	0.00291399i
$539$	−5.42736	−	27.2852i	−0.233773	−	1.17526i
$540$		0			0
$541$	−0.619318	−	0.413815i	−0.0266266	−	0.0177913i	0.542186	−	0.840259i	$-0.317597\pi$
$541$	−0.619318	−	0.413815i	−0.0266266	−	0.0177913i	−0.568812	+	0.822467i	$0.692597\pi$
$542$	6.74162	−	2.79247i	0.289577	−	0.119947i
$543$	−25.2731	+	25.2731i	−1.08457	+	1.08457i
$544$	−0.518404	+	4.09039i	−0.0222264	+	0.175374i
$545$		0			0
$546$	0.642203	−	1.55042i	0.0274838	−	0.0663517i
$547$	−6.30620	−	31.7034i	−0.269634	−	1.35554i	−0.843737	−	0.536757i	$-0.819649\pi$
$547$	−6.30620	−	31.7034i	−0.269634	−	1.35554i	0.574103	−	0.818783i	$-0.305351\pi$
$548$		−	14.6086i		−	0.624050i
$549$	−60.7093	+	12.0758i	−2.59101	+	0.515384i
$550$		0			0
$551$	−3.39267	+	17.0561i	−0.144532	+	0.726614i
$552$	−6.95514	+	16.7912i	−0.296031	+	0.714681i
$553$	0.161701	−	0.390381i	0.00687624	−	0.0166007i
$554$	3.13211	−	15.7462i	0.133071	−	0.668992i
$555$		0			0
$556$	−11.5761	+	2.30263i	−0.490936	+	0.0976531i
$557$			5.88641i			0.249415i	0.992194	+	0.124708i	$0.0397993\pi$
$557$			5.88641i			0.249415i	−0.992194	+	0.124708i	$0.960201\pi$
$558$	−7.87303	−	39.5804i	−0.333292	−	1.67557i
$559$	6.37190	−	15.3831i	0.269503	−	0.650637i
$560$		0			0
$561$	12.9715	+	47.4906i	0.547657	+	2.00506i
$562$	4.28596	−	4.28596i	0.180792	−	0.180792i
$563$	15.6628	−	6.48773i	0.660107	−	0.273425i	−0.0273765	−	0.999625i	$-0.508715\pi$
$563$	15.6628	−	6.48773i	0.660107	−	0.273425i	0.687484	+	0.726200i	$0.258715\pi$
$564$	17.4758	+	11.6770i	0.735866	+	0.491690i
$565$		0			0
$566$	3.22133	+	16.1947i	0.135403	+	0.680715i
$567$	2.23989	+	0.445542i	0.0940666	+	0.0187110i
$568$	−3.82333	+	2.55467i	−0.160423	+	0.107191i
$569$	−8.50960	−	20.5440i	−0.356741	−	0.861249i	−0.995754	−	0.0920531i	$-0.970657\pi$
$569$	−8.50960	−	20.5440i	−0.356741	−	0.861249i	0.639013	−	0.769196i	$-0.279343\pi$
$570$		0			0
$571$	−26.9713	−	5.36493i	−1.12872	−	0.224515i	−0.404801	−	0.914405i	$-0.632659\pi$
$571$	−26.9713	−	5.36493i	−1.12872	−	0.224515i	−0.723915	+	0.689890i	$0.757659\pi$
$572$	1.13284	−	5.69515i	0.0473663	−	0.238126i
$573$	16.2124	+	10.8328i	0.677283	+	0.452546i
$574$	−2.36798	−	2.36798i	−0.0988376	−	0.0988376i
$575$		0			0
$576$	5.18983	+	2.14970i	0.216243	+	0.0895708i
$577$	15.7178	+	15.7178i	0.654339	+	0.654339i	0.954035	−	0.299696i	$-0.0968853\pi$
$577$	15.7178	+	15.7178i	0.654339	+	0.654339i	−0.299696	+	0.954035i	$0.596885\pi$
$578$	10.2181	−	13.5864i	0.425015	−	0.565121i
$579$			22.1350i			0.919899i
$580$		0			0
$581$	0.276815	−	0.414283i	0.0114842	−	0.0171873i
$582$	−8.72564			−0.361689
$583$	−10.8076	+	16.1747i	−0.447603	+	0.669886i
$584$	−10.9826	+	7.33833i	−0.454462	+	0.303662i
$585$		0			0
$586$	6.01627	−	2.49202i	0.248530	−	0.102944i
$587$	20.3915	+	8.44643i	0.841646	+	0.348621i	0.761503	−	0.648162i	$-0.224462\pi$
$587$	20.3915	+	8.44643i	0.841646	+	0.348621i	0.0801439	+	0.996783i	$0.474462\pi$
$588$	11.1548	+	16.6943i	0.460016	+	0.688463i
$589$	−17.1314	−	25.6389i	−0.705886	−	1.05643i
$590$		0			0
$591$	−27.6192	+	27.6192i	−1.13610	+	1.13610i
$592$	4.72973	−	0.940802i	0.194391	−	0.0386667i
$593$	−5.63746	−	13.6100i	−0.231503	−	0.558897i	0.764852	−	0.644206i	$-0.222812\pi$
$593$	−5.63746	−	13.6100i	−0.231503	−	0.558897i	−0.996355	+	0.0853090i	$0.972812\pi$
$594$	31.2524			1.28230
$595$		0			0
$596$	−8.09447			−0.331562
$597$	−9.49561	−	22.9244i	−0.388629	−	0.938234i
$598$	−8.66890	+	1.72435i	−0.354498	+	0.0705140i
$599$	−9.31709	+	9.31709i	−0.380686	+	0.380686i	−0.871349	−	0.490663i	$-0.836754\pi$
$599$	−9.31709	+	9.31709i	−0.380686	+	0.380686i	0.490663	+	0.871349i	$0.336754\pi$
$600$		0			0
$601$	−20.2161	−	30.2555i	−0.824632	−	1.23415i	−0.969596	−	0.244712i	$-0.921307\pi$
$601$	−20.2161	−	30.2555i	−0.824632	−	1.23415i	0.144964	−	0.989437i	$-0.453693\pi$
$602$	−2.59470	−	3.88324i	−0.105752	−	0.158269i
$603$	1.68107	+	0.696320i	0.0684583	+	0.0283564i
$604$	20.2121	−	8.37213i	0.822420	−	0.340657i
$605$		0			0
$606$	2.83596	−	1.89493i	0.115203	−	0.0769762i
$607$	−20.8064	+	31.1390i	−0.844506	+	1.26389i	0.118104	+	0.993001i	$0.462318\pi$
$607$	−20.8064	+	31.1390i	−0.844506	+	1.26389i	−0.962610	+	0.270891i	$0.912682\pi$
$608$	4.29225			0.174074
$609$	−2.64594	+	3.95993i	−0.107219	+	0.160464i
$610$		0			0
$611$			10.2215i			0.413519i
$612$	−14.1884	−	18.3067i	−0.573530	−	0.740004i
$613$	−9.23647	−	9.23647i	−0.373058	−	0.373058i	0.495532	−	0.868590i	$-0.334973\pi$
$613$	−9.23647	−	9.23647i	−0.373058	−	0.373058i	−0.868590	+	0.495532i	$0.834973\pi$
$614$	1.00063	+	0.414474i	0.0403821	+	0.0167268i
$615$		0			0
$616$	−1.15169	−	1.15169i	−0.0464029	−	0.0464029i
$617$	−18.8949	−	12.6251i	−0.760679	−	0.508269i	0.113699	−	0.993515i	$-0.463730\pi$
$617$	−18.8949	−	12.6251i	−0.760679	−	0.508269i	−0.874378	+	0.485246i	$0.838730\pi$
$618$	7.18053	−	36.0990i	0.288843	−	1.45211i
$619$	−2.56570	−	0.510350i	−0.103124	−	0.0205127i	0.143258	−	0.989685i	$-0.454242\pi$
$619$	−2.56570	−	0.510350i	−0.103124	−	0.0205127i	−0.246383	+	0.969173i	$0.579242\pi$
$620$		0			0
$621$	−18.2046	−	43.9498i	−0.730526	−	1.76365i
$622$	−14.9044	+	9.95878i	−0.597611	+	0.399311i
$623$	−5.52880	−	1.09975i	−0.221507	−	0.0440604i
$624$	0.817593	+	4.11032i	0.0327299	+	0.164544i
$625$		0			0
$626$	2.63946	+	1.76363i	0.105494	+	0.0704889i
$627$	47.3487	−	19.6125i	1.89092	−	0.783247i
$628$	−5.48064	+	5.48064i	−0.218701	+	0.218701i
$629$	−18.8587	−	6.30016i	−0.751946	−	0.251204i
$630$		0			0
$631$	0.670871	−	1.61962i	0.0267069	−	0.0644762i	−0.909963	−	0.414689i	$-0.863891\pi$
$631$	0.670871	−	1.61962i	0.0267069	−	0.0644762i	0.936670	+	0.350212i	$0.113891\pi$
$632$	0.205863	+	1.03494i	0.00818879	+	0.0411678i
$633$		−	19.2083i		−	0.763460i
$634$	−15.2116	+	3.02578i	−0.604131	+	0.120169i
$635$		0			0
$636$	2.73901	−	13.7700i	0.108609	−	0.546014i
$637$	−3.73668	+	9.02115i	−0.148053	+	0.357431i
$638$	−6.30637	+	15.2249i	−0.249671	+	0.602760i
$639$	5.03928	−	25.3342i	0.199351	−	1.00220i
$640$		0			0
$641$	40.7308	−	8.10186i	1.60877	−	0.320004i	0.692763	−	0.721165i	$-0.256393\pi$
$641$	40.7308	−	8.10186i	1.60877	−	0.320004i	0.916008	+	0.401161i	$0.131393\pi$
$642$		−	37.7811i		−	1.49110i
$643$	−2.48698	−	12.5029i	−0.0980769	−	0.493066i	−0.998334	−	0.0577063i	$-0.981621\pi$
$643$	−2.48698	−	12.5029i	−0.0980769	−	0.493066i	0.900257	−	0.435359i	$-0.143379\pi$
$644$	−0.948742	+	2.29047i	−0.0373857	+	0.0902570i
$645$		0			0
$646$	−15.3690	−	8.77450i	−0.604685	−	0.345228i
$647$	33.2038	−	33.2038i	1.30538	−	1.30538i	0.380661	−	0.924715i	$-0.375697\pi$
$647$	33.2038	−	33.2038i	1.30538	−	1.30538i	0.924715	−	0.380661i	$-0.124303\pi$
$648$	−5.26911	+	2.18254i	−0.206990	+	0.0857381i
$649$	−17.3038	−	11.5620i	−0.679232	−	0.453848i
$650$		0			0
$651$	−1.64749	−	8.28252i	−0.0645704	−	0.324617i
$652$	7.84334	+	1.56014i	0.307169	+	0.0610997i
$653$	−18.1599	+	12.1341i	−0.710652	+	0.474843i	−0.857610	−	0.514300i	$-0.828052\pi$
$653$	−18.1599	+	12.1341i	−0.710652	+	0.474843i	0.146958	+	0.989143i	$0.453052\pi$
$654$	−2.90241	−	7.00704i	−0.113493	−	0.273997i
$655$		0			0
$656$	8.20230	+	1.63154i	0.320246	+	0.0637009i
$657$	14.4754	−	72.7729i	0.564740	−	2.83914i
$658$	2.38386	+	1.59284i	0.0929325	+	0.0620955i
$659$	−5.08209	−	5.08209i	−0.197970	−	0.197970i	0.601159	−	0.799129i	$-0.294706\pi$
$659$	−5.08209	−	5.08209i	−0.197970	−	0.197970i	−0.799129	+	0.601159i	$0.794706\pi$
$660$		0			0
$661$	45.0992	+	18.6807i	1.75416	+	0.726596i	0.997334	+	0.0729758i	$0.0232496\pi$
$661$	45.0992	+	18.6807i	1.75416	+	0.726596i	0.756823	+	0.653620i	$0.226750\pi$
$662$	20.5729	+	20.5729i	0.799587	+	0.799587i
$663$	5.47508	−	16.3889i	0.212634	−	0.636494i
$664$			1.24428i			0.0482875i
$665$		0			0
$666$	−15.0501	+	22.5241i	−0.583180	+	0.872790i
$667$	25.0841			0.971259
$668$	−8.87030	+	13.2753i	−0.343202	+	0.513638i
$669$	30.4338	−	20.3352i	1.17664	−	0.786206i
$670$		0			0
$671$	−41.4074	+	17.1515i	−1.59851	+	0.662126i
$672$	1.08601	+	0.449842i	0.0418939	+	0.0173530i
$673$	−5.46823	−	8.18378i	−0.210785	−	0.315461i	0.710979	−	0.703213i	$-0.248252\pi$
$673$	−5.46823	−	8.18378i	−0.210785	−	0.315461i	−0.921764	+	0.387751i	$0.873252\pi$
$674$	5.16229	+	7.72592i	0.198844	+	0.297591i
$675$		0			0
$676$	7.75123	−	7.75123i	0.298124	−	0.298124i
$677$	−12.9461	+	2.57514i	−0.497560	+	0.0989707i	−0.437490	−	0.899223i	$-0.644132\pi$
$677$	−12.9461	+	2.57514i	−0.497560	+	0.0989707i	−0.0600699	+	0.998194i	$0.519132\pi$
$678$	20.3465	+	49.1208i	0.781403	+	1.88647i
$679$	−1.19025			−0.0456777
$680$		0			0
$681$	36.0536			1.38158
$682$	−11.1822	−	26.9962i	−0.428188	−	1.03374i
$683$	0.146970	−	0.0292342i	0.00562366	−	0.00111862i	−0.192278	−	0.981341i	$-0.561587\pi$
$683$	0.146970	−	0.0292342i	0.00562366	−	0.00111862i	0.197901	+	0.980222i	$0.436587\pi$
$684$	−17.0493	+	17.0493i	−0.651898	+	0.651898i
$685$		0			0
$686$	3.07890	+	4.60790i	0.117553	+	0.175930i
$687$	−19.2464	−	28.8042i	−0.734295	−	1.09895i
$688$	10.7754	+	4.46330i	0.410807	+	0.170162i
$689$	6.30809	−	2.61290i	0.240319	−	0.0995434i
$690$		0			0
$691$	−5.65974	+	3.78171i	−0.215306	+	0.143863i	−0.658547	−	0.752539i	$-0.728829\pi$
$691$	−5.65974	+	3.78171i	−0.215306	+	0.143863i	0.443241	+	0.896403i	$0.353829\pi$
$692$	−6.02736	+	9.02058i	−0.229126	+	0.342911i
$693$	9.14930			0.347553
$694$	−3.92971	+	5.88122i	−0.149170	+	0.223248i
$695$		0			0
$696$		−	11.8935i		−	0.450822i
$697$	−26.0342	−	22.6096i	−0.986115	−	0.856401i
$698$	−2.89759	−	2.89759i	−0.109675	−	0.109675i
$699$	21.4240	+	8.87412i	0.810331	+	0.335650i
$700$		0			0
$701$	7.74147	+	7.74147i	0.292391	+	0.292391i	0.838024	−	0.545633i	$-0.183711\pi$
$701$	7.74147	+	7.74147i	0.292391	+	0.292391i	−0.545633	+	0.838024i	$0.683711\pi$
$702$	−9.12060	−	6.09419i	−0.344235	−	0.230010i
$703$	−4.03816	+	20.3012i	−0.152302	+	0.765674i
$704$	3.98926	+	0.793514i	0.150351	+	0.0299067i
$705$		0			0
$706$	−3.36038	−	8.11268i	−0.126470	−	0.305325i
$707$	0.386850	−	0.258485i	0.0145490	−	0.00972132i
$708$	14.7312	+	2.93022i	0.553632	+	0.110124i
$709$	4.93399	+	24.8048i	0.185300	+	0.931565i	0.955776	+	0.294096i	$0.0950185\pi$
$709$	4.93399	+	24.8048i	0.185300	+	0.931565i	−0.770476	+	0.637469i	$0.779982\pi$
$710$		0			0
$711$	−4.92864	−	3.29321i	−0.184838	−	0.123505i
$712$	13.0059	−	5.38723i	0.487418	−	0.201895i
$713$	−31.4507	+	31.4507i	−1.17784	+	1.17784i
$714$	−2.96903	−	3.83082i	−0.111113	−	0.143365i
$715$		0			0
$716$	2.21812	−	5.35501i	0.0828950	−	0.200126i
$717$	14.7678	+	74.2426i	0.551513	+	2.77264i
$718$			13.2642i			0.495016i
$719$	−22.3307	+	4.44185i	−0.832795	+	0.165653i	−0.593033	−	0.805179i	$-0.702069\pi$
$719$	−22.3307	+	4.44185i	−0.832795	+	0.165653i	−0.239762	+	0.970832i	$0.577069\pi$
$720$		0			0
$721$	0.979487	−	4.92421i	0.0364780	−	0.183387i
$722$	0.220655	−	0.532709i	0.00821194	−	0.0198254i
$723$	13.5042	−	32.6019i	0.502225	−	1.21248i
$724$	2.37531	−	11.9415i	0.0882778	−	0.443802i
$725$		0			0
$726$	15.9616	−	3.17497i	0.592392	−	0.117834i
$727$		−	15.5794i		−	0.577807i	−0.957358	−	0.288903i	$-0.906709\pi$
$727$		−	15.5794i		−	0.577807i	0.957358	−	0.288903i	$-0.0932906\pi$
$728$	0.111527	+	0.560684i	0.00413346	+	0.0207803i
$729$	−13.6346	+	32.9169i	−0.504987	+	1.21915i
$730$		0			0
$731$	−29.4585	−	38.0092i	−1.08956	−	1.40582i
$732$	22.8727	−	22.8727i	0.845399	−	0.845399i
$733$	−31.8427	+	13.1897i	−1.17614	+	0.487171i	−0.883216	−	0.468966i	$-0.844627\pi$
$733$	−31.8427	+	13.1897i	−1.17614	+	0.487171i	−0.292919	+	0.956137i	$0.594627\pi$
$734$	−10.7937	−	7.21215i	−0.398404	−	0.266205i
$735$		0			0
$736$	−1.20785	−	6.07227i	−0.0445220	−	0.223827i
$737$	1.29218	+	0.257031i	0.0475982	+	0.00946787i
$738$	−39.0612	+	26.0999i	−1.43786	+	0.960750i
$739$	−2.32988	−	5.62482i	−0.0857058	−	0.206912i	0.875216	−	0.483733i	$-0.160719\pi$
$739$	−2.32988	−	5.62482i	−0.0857058	−	0.206912i	−0.960922	+	0.276820i	$0.910719\pi$
$740$		0			0
$741$	−17.6425	−	3.50931i	−0.648114	−	0.128918i
$742$	0.373626	−	1.87834i	0.0137162	−	0.0689561i
$743$	16.3416	+	10.9191i	0.599516	+	0.400584i	0.817968	−	0.575264i	$-0.195101\pi$
$743$	16.3416	+	10.9191i	0.599516	+	0.400584i	−0.218452	+	0.975848i	$0.570101\pi$
$744$	14.9122	+	14.9122i	0.546708	+	0.546708i
$745$		0			0
$746$	34.7173	+	14.3804i	1.27109	+	0.526503i
$747$	−4.94244	−	4.94244i	−0.180835	−	0.180835i
$748$	−12.6620	−	10.9964i	−0.462967	−	0.402068i
$749$		−	5.15367i		−	0.188311i
$750$		0			0
$751$	21.4221	−	32.0605i	0.781705	−	1.16990i	−0.200056	−	0.979785i	$-0.564112\pi$
$751$	21.4221	−	32.0605i	0.781705	−	1.16990i	0.981761	−	0.190120i	$-0.0608877\pi$
$752$	−7.15983			−0.261092
$753$	17.1294	−	25.6360i	0.624232	−	0.934229i
$754$	4.80928	−	3.21346i	0.175144	−	0.117027i
$755$		0			0
$756$	−2.84257	+	1.17743i	−0.103383	+	0.0428227i
$757$	2.48797	+	1.03055i	0.0904267	+	0.0374559i	0.427438	−	0.904045i	$-0.359416\pi$
$757$	2.48797	+	1.03055i	0.0904267	+	0.0374559i	−0.337012	+	0.941501i	$0.609416\pi$
$758$	−10.9766	−	16.4276i	−0.398686	−	0.596676i
$759$	−41.0700	−	61.4655i	−1.49074	−	2.23106i
$760$		0			0
$761$	11.4396	−	11.4396i	0.414686	−	0.414686i	−0.468681	−	0.883367i	$-0.655271\pi$
$761$	11.4396	−	11.4396i	0.414686	−	0.414686i	0.883367	+	0.468681i	$0.155271\pi$
$762$	7.72757	−	1.53711i	0.279940	−	0.0556836i
$763$	−0.395915	−	0.955822i	−0.0143331	−	0.0346031i
$764$	−6.64220			−0.240306
$765$		0			0
$766$	8.80774			0.318237
$767$	2.79529	+	6.74844i	0.100932	+	0.243672i
$768$	−2.87914	+	0.572697i	−0.103892	+	0.0206654i
$769$	9.04894	−	9.04894i	0.326313	−	0.326313i	−0.524870	−	0.851183i	$-0.675886\pi$
$769$	9.04894	−	9.04894i	0.326313	−	0.326313i	0.851183	+	0.524870i	$0.175886\pi$
$770$		0			0
$771$	−31.1698	−	46.6490i	−1.12255	−	1.68002i
$772$	−4.18919	−	6.26956i	−0.150772	−	0.225646i
$773$	30.6341	+	12.6891i	1.10183	+	0.456394i	0.858118	−	0.513453i	$-0.171634\pi$
$773$	30.6341	+	12.6891i	1.10183	+	0.456394i	0.243715	+	0.969847i	$0.421634\pi$
$774$	−60.5299	+	25.0723i	−2.17570	+	0.901205i
$775$		0			0
$776$	2.47147	−	1.65138i	0.0887205	−	0.0592811i
$777$	−3.14936	+	4.71334i	−0.112983	+	0.169090i
$778$	0.904451			0.0324262
$779$	−19.9428	+	29.8465i	−0.714524	+	1.06936i
$780$		0			0
$781$		−	18.7031i		−	0.669250i
$782$	−8.08846	+	24.2118i	−0.289243	+	0.865812i
$783$	22.0125	+	22.0125i	0.786664	+	0.786664i
$784$	−6.31901	−	2.61742i	−0.225679	−	0.0934793i
$785$		0			0
$786$	−1.11964	−	1.11964i	−0.0399362	−	0.0399362i
$787$	6.71110	+	4.48421i	0.239225	+	0.159845i	0.669404	−	0.742899i	$-0.266550\pi$
$787$	6.71110	+	4.48421i	0.239225	+	0.159845i	−0.430179	+	0.902744i	$0.641550\pi$
$788$	2.59581	−	13.0500i	0.0924720	−	0.464888i
$789$	56.8318	+	11.3045i	2.02326	+	0.402452i
$790$		0			0
$791$	2.77544	+	6.70051i	0.0986833	+	0.238243i
$792$	−18.9978	+	12.6939i	−0.675057	+	0.451059i
$793$	15.4287	+	3.06896i	0.547890	+	0.108982i
$794$	1.87099	+	9.40611i	0.0663990	+	0.333810i
$795$		0			0
$796$	7.02814	+	4.69606i	0.249106	+	0.166447i
$797$	−12.2303	+	5.06596i	−0.433219	+	0.179445i	−0.588626	−	0.808405i	$-0.700331\pi$
$797$	−12.2303	+	5.06596i	−0.433219	+	0.179445i	0.155407	+	0.987851i	$0.450331\pi$
$798$	−3.56771	+	3.56771i	−0.126296	+	0.126296i
$799$	25.6368	+	14.6366i	0.906964	+	0.517806i
$800$		0			0
$801$	−30.2624	+	73.0599i	−1.06927	+	2.58144i
$802$	5.33235	+	26.8075i	0.188292	+	0.946607i
$803$		−	53.7251i		−	1.89592i
$804$	−0.932598	+	0.185505i	−0.0328902	+	0.00654227i
$805$		0			0
$806$	−2.00086	+	10.0590i	−0.0704773	+	0.354313i
$807$	−0.389199	+	0.939609i	−0.0137005	+	0.0330758i
$808$	−0.444636	+	1.07345i	−0.0156422	+	0.0377637i
$809$	2.50901	−	12.6137i	0.0882122	−	0.443473i	−0.911285	−	0.411775i	$-0.864909\pi$
$809$	2.50901	−	12.6137i	0.0882122	−	0.443473i	0.999498	−	0.0316971i	$-0.0100912\pi$
$810$		0			0
$811$	36.3575	−	7.23195i	1.27668	−	0.253948i	0.490227	−	0.871595i	$-0.336914\pi$
$811$	36.3575	−	7.23195i	1.27668	−	0.253948i	0.786456	+	0.617647i	$0.211914\pi$
$812$		−	1.62238i		−	0.0569343i
$813$	−4.17901	−	21.0093i	−0.146564	−	0.736828i
$814$	−7.50622	+	18.1216i	−0.263093	+	0.635162i
$815$		0			0
$816$	11.4799	+	3.83511i	0.401877	+	0.134256i
$817$	−35.3986	+	35.3986i	−1.23844	+	1.23844i
$818$	−13.6310	+	5.64614i	−0.476596	+	0.197413i
$819$	−2.67010	−	1.78411i	−0.0933010	−	0.0623417i
$820$		0			0
$821$	−0.0441357	−	0.221885i	−0.00154035	−	0.00774385i	0.980007	−	0.198961i	$-0.0637566\pi$
$821$	−0.0441357	−	0.221885i	−0.00154035	−	0.00774385i	−0.981548	+	0.191217i	$0.938757\pi$
$822$	−42.0603	−	8.36632i	−1.46702	−	0.291809i
$823$	−10.3503	+	6.91586i	−0.360789	+	0.241072i	−0.722732	−	0.691129i	$-0.757114\pi$
$823$	−10.3503	+	6.91586i	−0.360789	+	0.241072i	0.361942	+	0.932201i	$0.382114\pi$
$824$	4.79812	+	11.5837i	0.167151	+	0.403537i
$825$		0			0
$826$	2.00946	+	0.399707i	0.0699182	+	0.0139076i
$827$	−7.57291	+	38.0716i	−0.263336	+	1.32388i	0.592056	+	0.805897i	$0.298317\pi$
$827$	−7.57291	+	38.0716i	−0.263336	+	1.32388i	−0.855392	+	0.517982i	$0.826683\pi$
$828$	28.9176	+	19.3221i	1.00495	+	0.671489i
$829$	3.17422	+	3.17422i	0.110245	+	0.110245i	0.760078	−	0.649832i	$-0.225161\pi$
$829$	3.17422	+	3.17422i	0.110245	+	0.110245i	−0.649832	+	0.760078i	$0.725161\pi$
$830$		0			0
$831$	−43.5418	−	18.0356i	−1.51045	−	0.625648i
$832$	−1.00948	−	1.00948i	−0.0349974	−	0.0349974i
$833$	17.2754	+	22.2898i	0.598557	+	0.772295i
$834$			34.6479i			1.19976i
$835$		0			0
$836$	−9.69935	+	14.5161i	−0.335459	+	0.502050i
$837$	−55.1992			−1.90796
$838$	−19.8198	+	29.6624i	−0.684663	+	1.02467i
$839$	3.56762	−	2.38381i	0.123168	−	0.0822982i	−0.492460	−	0.870335i	$-0.663902\pi$
$839$	3.56762	−	2.38381i	0.123168	−	0.0822982i	0.615628	+	0.788037i	$0.288902\pi$
$840$		0			0
$841$	11.6270	−	4.81606i	0.400931	−	0.166071i
$842$	−26.1264	−	10.8219i	−0.900377	−	0.372948i
$843$	−9.88532	−	14.7944i	−0.340468	−	0.509547i
$844$	3.63528	+	5.44059i	0.125132	+	0.187273i
$845$		0			0
$846$	28.4397	−	28.4397i	0.977779	−	0.977779i
$847$	2.17731	−	0.433094i	0.0748132	−	0.0148813i
$848$	1.83025	+	4.41860i	0.0628509	+	0.151735i
$849$	48.4717			1.66354
$850$		0			0
$851$	29.8566			1.02347
$852$	5.16564	+	12.4709i	0.176972	+	0.427248i
$853$	−42.4704	+	8.44788i	−1.45416	+	0.289250i	−0.858013	−	0.513627i	$-0.828301\pi$
$853$	−42.4704	+	8.44788i	−1.45416	+	0.289250i	−0.596144	+	0.802877i	$0.703301\pi$
$854$	3.12004	−	3.12004i	0.106765	−	0.106765i
$855$		0			0
$856$	7.15030	+	10.7012i	0.244392	+	0.365759i
$857$	4.34733	+	6.50624i	0.148502	+	0.222249i	0.898261	−	0.439462i	$-0.144831\pi$
$857$	4.34733	+	6.50624i	0.148502	+	0.222249i	−0.749759	+	0.661711i	$0.769831\pi$
$858$	−15.7484	−	6.52319i	−0.537641	−	0.222698i
$859$	23.8872	−	9.89439i	0.815020	−	0.337592i	0.0640648	−	0.997946i	$-0.479594\pi$
$859$	23.8872	−	9.89439i	0.815020	−	0.337592i	0.750955	+	0.660354i	$0.229594\pi$
$860$		0			0
$861$	−8.17388	+	5.46161i	−0.278565	+	0.186131i
$862$	−19.4844	+	29.1604i	−0.663640	+	0.993208i
$863$	13.4218			0.456883			0.228441	−	0.973558i	$-0.426637\pi$
$863$	13.4218			0.456883			0.228441	+	0.973558i	$0.426637\pi$
$864$	4.26877	−	6.38867i	0.145227	−	0.217347i
$865$		0			0
$866$		−	9.01745i		−	0.306426i
$867$	−33.2654	−	37.2001i	−1.12975	−	1.26338i
$868$	2.03416	+	2.03416i	0.0690438	+	0.0690438i
$869$	−3.96531	−	1.64248i	−0.134514	−	0.0557174i
$870$		0			0
$871$	−0.326986	−	0.326986i	−0.0110795	−	0.0110795i
$872$	2.14821	+	1.43539i	0.0727476	+	0.0486084i
$873$	−3.25748	+	16.3765i	−0.110249	+	0.554259i
$874$	26.0637	+	5.18439i	0.881618	+	0.175365i
$875$		0			0
$876$	14.8384	+	35.8230i	0.501343	+	1.21035i
$877$	26.7175	−	17.8520i	0.902185	−	0.602820i	−0.0156091	−	0.999878i	$-0.504969\pi$
$877$	26.7175	−	17.8520i	0.902185	−	0.602820i	0.917794	+	0.397058i	$0.129969\pi$
$878$	0.795308	+	0.158197i	0.0268403	+	0.00533887i
$879$	−3.72938	−	18.7489i	−0.125789	−	0.632384i
$880$		0			0
$881$	−33.7511	−	22.5517i	−1.13710	−	0.759788i	−0.163164	−	0.986599i	$-0.552170\pi$
$881$	−33.7511	−	22.5517i	−1.13710	−	0.759788i	−0.973939	+	0.226811i	$0.927170\pi$
$882$	35.4966	−	14.7032i	1.19523	−	0.495082i
$883$	2.77493	−	2.77493i	0.0933838	−	0.0933838i	−0.658872	−	0.752255i	$-0.728966\pi$
$883$	2.77493	−	2.77493i	0.0933838	−	0.0933838i	0.752255	+	0.658872i	$0.228966\pi$
$884$	1.55094	+	5.67823i	0.0521637	+	0.190980i
$885$		0			0
$886$	−11.4588	+	27.6640i	−0.384966	+	0.929391i
$887$	−7.82501	−	39.3390i	−0.262738	−	1.32087i	−0.856464	−	0.516206i	$-0.827344\pi$
$887$	−7.82501	−	39.3390i	−0.262738	−	1.32087i	0.593726	−	0.804667i	$-0.297656\pi$
$888$		−	14.1564i		−	0.475056i
$889$	1.05411	−	0.209675i	0.0353537	−	0.00703228i
$890$		0			0
$891$	4.52560	−	22.7517i	0.151613	−	0.762212i
$892$	−4.77157	+	11.5196i	−0.159764	+	0.385704i
$893$	11.7605	−	28.3925i	0.393552	−	0.950118i
$894$	−4.63568	+	23.3051i	−0.155040	+	0.779440i
$895$		0			0
$896$	−0.392740	+	0.0781209i	−0.0131205	+	0.00260983i
$897$			25.9465i			0.866329i
$898$	6.31053	+	31.7252i	0.210585	+	1.05868i
$899$	11.1385	−	26.8908i	0.371491	−	0.896859i
$900$		0			0
$901$	2.47935	−	19.5629i	0.0825991	−	0.651736i
$902$	−24.0528	+	24.0528i	−0.800870	+	0.800870i
$903$	−12.6664	+	5.24658i	−0.421511	+	0.174595i
$904$	−15.0594	−	10.0624i	−0.500868	−	0.334669i
$905$		0			0
$906$	−12.5291	−	62.9882i	−0.416253	−	2.09264i
$907$	−32.5891	−	6.48238i	−1.08210	−	0.215244i	−0.378332	−	0.925670i	$-0.623502\pi$
$907$	−32.5891	−	6.48238i	−1.08210	−	0.215244i	−0.703772	+	0.710426i	$0.748502\pi$
$908$	−10.2119	+	6.82337i	−0.338894	+	0.226441i
$909$	−2.49771	−	6.03001i	−0.0828438	−	0.200003i
$910$		0			0
$911$	25.0330	+	4.97937i	0.829379	+	0.164974i	0.591484	−	0.806317i	$-0.298542\pi$
$911$	25.0330	+	4.97937i	0.829379	+	0.164974i	0.237895	+	0.971291i	$0.423542\pi$
$912$	2.45816	−	12.3580i	0.0813977	−	0.409214i
$913$	−4.20808	−	2.81175i	−0.139267	−	0.0930554i
$914$	−2.06579	−	2.06579i	−0.0683301	−	0.0683301i
$915$		0			0
$916$	10.9028	+	4.51607i	0.360237	+	0.149215i
$917$	−0.152729	−	0.152729i	−0.00504354	−	0.00504354i
$918$	−28.3451	+	14.1490i	−0.935527	+	0.466987i
$919$			20.7776i			0.685390i	0.939447	+	0.342695i	$0.111340\pi$
$919$			20.7776i			0.685390i	−0.939447	+	0.342695i	$0.888660\pi$
$920$		0			0
$921$	1.76638	−	2.64358i	0.0582044	−	0.0871090i
$922$	2.03388			0.0669824
$923$	−3.64709	+	5.45826i	−0.120046	+	0.179661i
$924$	−3.97544	+	2.65631i	−0.130782	+	0.0873860i
$925$		0			0
$926$	−25.5442	+	10.5808i	−0.839435	+	0.347705i
$927$	−65.0706	−	26.9531i	−2.13720	−	0.885257i
$928$	2.25092	+	3.36874i	0.0738900	+	0.110584i
$929$	−27.9157	−	41.7788i	−0.915884	−	1.37072i	−0.928713	−	0.370800i	$-0.879084\pi$
$929$	−27.9157	−	41.7788i	−0.915884	−	1.37072i	0.0128290	−	0.999918i	$-0.495916\pi$
$930$		0			0
$931$	20.7589	−	20.7589i	0.680345	−	0.680345i
$932$	−7.74767	+	1.54111i	−0.253783	+	0.0504806i
$933$	20.1370	+	48.6151i	0.659257	+	1.59159i
$934$	1.38002			0.0451556
$935$		0			0
$936$	8.01956			0.262127
$937$	−6.94921	−	16.7769i	−0.227021	−	0.548077i	0.768791	−	0.639500i	$-0.220858\pi$
$937$	−6.94921	−	16.7769i	−0.227021	−	0.548077i	−0.995812	+	0.0914231i	$0.970858\pi$
$938$	−0.127215	+	0.0253045i	−0.00415370	+	0.000826223i
$939$	6.58936	−	6.58936i	0.215036	−	0.215036i
$940$		0			0
$941$	−17.8596	−	26.7288i	−0.582206	−	0.871332i	0.417090	−	0.908865i	$-0.363050\pi$
$941$	−17.8596	−	26.7288i	−0.582206	−	0.871332i	−0.999295	+	0.0375329i	$0.988050\pi$
$942$	12.6408	+	18.9183i	0.411859	+	0.616390i
$943$	47.8360	+	19.8143i	1.55775	+	0.645242i
$944$	−4.72705	+	1.95801i	−0.153852	+	0.0637278i
$945$		0			0
$946$	−39.4441	+	26.3557i	−1.28244	+	0.856898i
$947$	11.3655	−	17.0097i	0.369329	−	0.552739i	−0.599530	−	0.800352i	$-0.704646\pi$
$947$	11.3655	−	17.0097i	0.369329	−	0.552739i	0.968859	+	0.247612i	$0.0796460\pi$
$948$	3.09764			0.100607
$949$	−10.4763	+	15.6790i	−0.340077	+	0.508960i
$950$		0			0
$951$			45.5293i			1.47639i
$952$	1.56596	+	0.523142i	0.0507531	+	0.0169551i
$953$	−38.6958	−	38.6958i	−1.25348	−	1.25348i	−0.954149	−	0.299332i	$-0.903236\pi$
$953$	−38.6958	−	38.6958i	−1.25348	−	1.25348i	−0.299332	−	0.954149i	$-0.596764\pi$
$954$	−24.8212	−	10.2813i	−0.803616	−	0.332869i
$955$		0			0
$956$	−18.2337	−	18.2337i	−0.589721	−	0.589721i
$957$	40.2230	+	26.8762i	1.30023	+	0.868783i
$958$	4.90532	−	24.6607i	0.158484	−	0.796751i
$959$	−5.73740	−	1.14124i	−0.185270	−	0.0368525i
$960$		0			0
$961$	7.88722	+	19.0414i	0.254426	+	0.614240i
$962$	5.72429	−	3.82485i	0.184559	−	0.123318i
$963$	−70.9083	−	14.1045i	−2.28499	−	0.454513i
$964$	2.34517	+	11.7900i	0.0755329	+	0.379730i
$965$		0			0
$966$	6.05123	+	4.04331i	0.194695	+	0.130091i
$967$	49.8534	−	20.6500i	1.60318	−	0.664058i	0.611317	−	0.791386i	$-0.290640\pi$
$967$	49.8534	−	20.6500i	1.60318	−	0.664058i	0.991861	+	0.127328i	$0.0406402\pi$
$968$	−3.92012	+	3.92012i	−0.125998	+	0.125998i
$969$	−34.0648	+	39.2244i	−1.09432	+	1.26007i
$970$		0			0
$971$	11.6245	−	28.0639i	0.373046	−	0.900614i	−0.620184	−	0.784456i	$-0.712942\pi$
$971$	11.6245	−	28.0639i	0.373046	−	0.900614i	0.993231	−	0.116158i	$-0.0370578\pi$
$972$	−1.23075	−	6.18742i	−0.0394765	−	0.198462i
$973$			4.72628i			0.151517i
$974$	−24.2578	+	4.82518i	−0.777271	+	0.154609i
$975$		0			0
$976$	−2.14971	+	10.8073i	−0.0688104	+	0.345933i
$977$	6.15349	−	14.8558i	0.196868	−	0.475281i	−0.794360	−	0.607448i	$-0.792193\pi$
$977$	6.15349	−	14.8558i	0.196868	−	0.475281i	0.991227	+	0.132167i	$0.0421935\pi$
$978$	8.98371	−	21.6886i	0.287267	−	0.693524i
$979$	−11.1707	+	56.1589i	−0.357017	+	1.79485i
$980$		0			0
$981$	−14.2345	+	2.83142i	−0.454473	+	0.0904002i
$982$		−	15.2450i		−	0.486487i
$983$	2.37200	+	11.9248i	0.0756549	+	0.380343i	0.999999	−	0.00121635i	$-0.000387175\pi$
$983$	2.37200	+	11.9248i	0.0756549	+	0.380343i	−0.924344	+	0.381559i	$0.875387\pi$
$984$	9.39486	−	22.6812i	0.299497	−	0.723050i
$985$		0			0
$986$	−1.17313	−	16.6637i	−0.0373602	−	0.530680i
$987$	5.95125	−	5.95125i	0.189430	−	0.189430i
$988$	5.66126	−	2.34497i	0.180109	−	0.0746034i
$989$	60.0400	+	40.1174i	1.90916	+	1.27566i
$990$		0			0
$991$	0.553654	+	2.78341i	0.0175874	+	0.0884178i	0.988582	−	0.150683i	$-0.0481473\pi$
$991$	0.553654	+	2.78341i	0.0175874	+	0.0884178i	−0.970995	+	0.239101i	$0.923147\pi$
$992$	−7.04599	−	1.40153i	−0.223710	−	0.0444988i
$993$	71.0142	−	47.4502i	2.25357	−	1.50579i
$994$	0.704638	+	1.70115i	0.0223498	+	0.0539571i
$995$		0			0
$996$	3.58246	+	0.712596i	0.113515	+	0.0225795i
$997$	−6.38435	+	32.0963i	−0.202194	+	1.01650i	0.737725	+	0.675102i	$0.235900\pi$
$997$	−6.38435	+	32.0963i	−0.202194	+	1.01650i	−0.939919	+	0.341398i	$0.889100\pi$
$998$	4.13838	+	2.76518i	0.130998	+	0.0875302i
$999$	26.2006	+	26.2006i	0.828952	+	0.828952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.143.5		40
5.2	odd	4		850.2.s.d.7.1		40
5.3	odd	4		170.2.o.b.7.5	✓	40
5.4	even	2		170.2.r.b.143.1	yes	40
17.5	odd	16		850.2.s.d.243.1		40
85.22	even	16	inner	850.2.v.d.107.5		40
85.39	odd	16		170.2.o.b.73.5	yes	40
85.73	even	16		170.2.r.b.107.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.7.5	✓	40	5.3	odd	4
170.2.o.b.73.5	yes	40	85.39	odd	16
170.2.r.b.107.1	yes	40	85.73	even	16
170.2.r.b.143.1	yes	40	5.4	even	2
850.2.s.d.7.1		40	5.2	odd	4
850.2.s.d.243.1		40	17.5	odd	16
850.2.v.d.107.5		40	85.22	even	16	inner
850.2.v.d.143.5		40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{2} +(2.87914 - 0.572697i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(1.63090 + 2.44082i) q^{6} +(0.222469 + 0.332949i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(5.18983 - 2.14970i) q^{9} +(3.38193 - 2.25974i) q^{11} +(-1.63090 + 2.44082i) q^{12} -1.42762 q^{13} +(-0.222469 + 0.332949i) q^{14} -1.00000i q^{16} +(-2.04427 + 3.58064i) q^{17} +(3.97212 + 3.97212i) q^{18} +(3.96552 + 1.64257i) q^{19} +(0.831199 + 0.831199i) q^{21} +(3.38193 + 2.25974i) q^{22} +(1.20785 - 6.07227i) q^{23} +(-2.87914 - 0.572697i) q^{24} +(-0.546327 - 1.31895i) q^{26} +(6.38867 - 4.26877i) q^{27} +(-0.392740 - 0.0781209i) q^{28} +(0.790417 + 3.97370i) q^{29} +(-5.97330 - 3.99123i) q^{31} +(0.923880 - 0.382683i) q^{32} +(8.44292 - 8.44292i) q^{33} +(-4.09039 - 0.518404i) q^{34} +(-2.14970 + 5.18983i) q^{36} +(0.940802 + 4.72973i) q^{37} +4.29225i q^{38} +(-4.11032 + 0.817593i) q^{39} +(-1.63154 + 8.20230i) q^{41} +(-0.449842 + 1.08601i) q^{42} +(-4.46330 + 10.7754i) q^{43} +(-0.793514 + 3.98926i) q^{44} +(6.07227 - 1.20785i) q^{46} -7.15983i q^{47} +(-0.572697 - 2.87914i) q^{48} +(2.61742 - 6.31901i) q^{49} +(-3.83511 + 11.4799i) q^{51} +(1.00948 - 1.00948i) q^{52} +(-4.41860 + 1.83025i) q^{53} +(6.38867 + 4.26877i) q^{54} +(-0.0781209 - 0.392740i) q^{56} +(12.3580 + 2.45816i) q^{57} +(-3.36874 + 2.25092i) q^{58} +(-1.95801 - 4.72705i) q^{59} +(-10.8073 - 2.14971i) q^{61} +(1.40153 - 7.04599i) q^{62} +(1.87032 + 1.24971i) q^{63} +(0.707107 + 0.707107i) q^{64} +(11.0312 + 4.56928i) q^{66} +(0.229043 + 0.229043i) q^{67} +(-1.08638 - 3.97741i) q^{68} -18.1747i q^{69} +(2.55467 - 3.82333i) q^{71} -5.61743 q^{72} +(7.33833 - 10.9826i) q^{73} +(-4.00967 + 2.67918i) q^{74} +(-3.96552 + 1.64257i) q^{76} +(1.50475 + 0.623289i) q^{77} +(-2.32831 - 3.48456i) q^{78} +(-0.586248 - 0.877382i) q^{79} +(4.03280 - 4.03280i) q^{81} +(-8.20230 + 1.63154i) q^{82} +(-0.476166 - 1.14957i) q^{83} -1.17549 q^{84} -11.6632 q^{86} +(4.55144 + 10.9882i) q^{87} +(-3.98926 + 0.793514i) q^{88} +(-9.95430 + 9.95430i) q^{89} +(-0.317602 - 0.475325i) q^{91} +(3.43967 + 5.14783i) q^{92} +(-19.4837 - 8.07043i) q^{93} +(6.61482 - 2.73995i) q^{94} +(2.44082 - 1.63090i) q^{96} +(-1.65138 + 2.47147i) q^{97} +6.83965 q^{98} +(12.6939 - 18.9978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

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