LMFDB - Embedded newform 650.2.ba.a.73.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(73,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([11, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.ba (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [136] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$17$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.16
Character	$\chi$	$=$	650.73
Dual form			650.2.ba.a.187.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(2.56648 - 1.30768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.585893 + 2.15795i) q^{5} +(-1.30768 + 2.56648i) q^{6} +0.941662i q^{7} +(0.309017 + 0.951057i) q^{8} +(3.11340 - 4.28523i) q^{9} +(-1.74241 - 1.40144i) q^{10} +(-0.313429 + 1.97891i) q^{11} +(-0.450597 - 2.84496i) q^{12} +(-0.365403 + 3.58699i) q^{13} +(-0.553495 - 0.761821i) q^{14} +(4.32559 + 4.77215i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.48766 - 4.88231i) q^{17} +5.29683i q^{18} +(4.66891 + 2.37893i) q^{19} +(2.23338 + 0.109624i) q^{20} +(1.23140 + 2.41675i) q^{21} +(-0.909607 - 1.78520i) q^{22} +(-0.289608 + 1.82851i) q^{23} +(2.03677 + 2.03677i) q^{24} +(-4.31346 + 2.52865i) q^{25} +(-1.81276 - 3.11671i) q^{26} +(1.03495 - 6.53440i) q^{27} +(0.895574 + 0.290990i) q^{28} +(-2.82946 - 0.919348i) q^{29} +(-6.30448 - 1.31823i) q^{30} +(0.399153 - 0.783382i) q^{31} +1.00000 q^{32} +(1.78339 + 5.48870i) q^{33} +(0.857190 + 5.41209i) q^{34} +(-2.03206 + 0.551714i) q^{35} +(-3.11340 - 4.28523i) q^{36} +(-0.998819 + 1.37476i) q^{37} +(-5.17553 + 0.819723i) q^{38} +(3.75285 + 9.68375i) q^{39} +(-1.87128 + 1.22406i) q^{40} +(-1.26808 - 8.00633i) q^{41} +(-2.41675 - 1.23140i) q^{42} +(5.80017 - 5.80017i) q^{43} +(1.78520 + 0.909607i) q^{44} +(11.0714 + 4.20786i) q^{45} +(-0.840474 - 1.64952i) q^{46} +(-6.52422 - 2.11985i) q^{47} +(-2.84496 - 0.450597i) q^{48} +6.11327 q^{49} +(2.00336 - 4.58111i) q^{50} -15.7834i q^{51} +(3.29851 + 1.45596i) q^{52} +(1.13062 - 0.576081i) q^{53} +(3.00354 + 5.89477i) q^{54} +(-4.45402 + 0.483069i) q^{55} +(-0.895574 + 0.290990i) q^{56} +15.0935 q^{57} +(2.82946 - 0.919348i) q^{58} +(-1.51948 - 9.59361i) q^{59} +(5.87527 - 2.63921i) q^{60} +(-2.95793 + 2.14906i) q^{61} +(0.137539 + 0.868386i) q^{62} +(4.03524 + 2.93177i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.95461 + 1.31307i) q^{65} +(-4.66897 - 3.39220i) q^{66} +(-1.38515 - 4.26307i) q^{67} +(-3.87463 - 3.87463i) q^{68} +(1.64784 + 5.07154i) q^{69} +(1.31968 - 1.64076i) q^{70} +(-7.48770 + 3.81518i) q^{71} +(5.03759 + 1.63681i) q^{72} +(0.169310 - 0.123011i) q^{73} -1.69929i q^{74} +(-7.76370 + 12.1304i) q^{75} +(3.70527 - 3.70527i) q^{76} +(-1.86347 - 0.295144i) q^{77} +(-8.72808 - 5.62845i) q^{78} +(1.23956 + 0.402759i) q^{79} +(0.794411 - 2.09019i) q^{80} +(-0.978334 - 3.01100i) q^{81} +(5.73190 + 5.73190i) q^{82} +(5.03495 - 1.63595i) q^{83} +(2.67899 - 0.424311i) q^{84} +(11.9933 + 2.50773i) q^{85} +(-1.28318 + 8.10170i) q^{86} +(-8.46397 + 1.34056i) q^{87} +(-1.97891 + 0.313429i) q^{88} +(-1.10202 - 0.174543i) q^{89} +(-11.4303 + 3.10338i) q^{90} +(-3.37773 - 0.344086i) q^{91} +(1.64952 + 0.840474i) q^{92} -2.53250i q^{93} +(6.52422 - 2.11985i) q^{94} +(-2.39812 + 11.4691i) q^{95} +(2.56648 - 1.30768i) q^{96} +(-3.03050 + 9.32693i) q^{97} +(-4.94574 + 3.59329i) q^{98} +(7.50427 + 7.50427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 34 q^{2} - 34 q^{4} - 34 q^{8} + 20 q^{9} + 6 q^{13} + 32 q^{15} - 34 q^{16} + 4 q^{17} - 20 q^{19} + 6 q^{21} + 12 q^{23} - 14 q^{26} + 36 q^{27} + 20 q^{29} + 12 q^{30} + 6 q^{31} + 136 q^{32}+ \cdots - 40 q^{99}+O(q^{100}) $ 136 * q - 34 * q^2 - 34 * q^4 - 34 * q^8 + 20 * q^9 + 6 * q^13 + 32 * q^15 - 34 * q^16 + 4 * q^17 - 20 * q^19 + 6 * q^21 + 12 * q^23 - 14 * q^26 + 36 * q^27 + 20 * q^29 + 12 * q^30 + 6 * q^31 + 136 * q^32 - 54 * q^33 + 4 * q^34 - 52 * q^35 - 20 * q^36 + 30 * q^37 + 20 * q^39 + 18 * q^41 + 6 * q^42 - 12 * q^43 + 24 * q^45 - 28 * q^46 + 50 * q^47 - 120 * q^49 + 20 * q^50 + 6 * q^52 - 50 * q^53 + 6 * q^54 + 24 * q^55 - 28 * q^57 - 20 * q^58 + 16 * q^59 + 12 * q^60 - 12 * q^61 + 6 * q^62 - 70 * q^63 - 34 * q^64 - 140 * q^65 + 16 * q^66 - 8 * q^67 + 4 * q^68 - 26 * q^69 + 58 * q^70 - 72 * q^71 - 32 * q^73 + 192 * q^75 + 64 * q^77 - 50 * q^78 + 20 * q^79 - 54 * q^81 - 12 * q^82 + 70 * q^83 + 6 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^87 - 108 * q^89 + 44 * q^90 - 94 * q^91 + 12 * q^92 - 50 * q^94 + 110 * q^95 + 28 * q^97 + 50 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	2.56648	−	1.30768i	1.48176	−	0.754992i	0.488679	−	0.872464i	$-0.337479\pi$
$3$	2.56648	−	1.30768i	1.48176	−	0.754992i	0.993076	+	0.117472i	$0.0374789\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.585893	+	2.15795i	0.262019	+	0.965063i
$5$	0.585893	+	2.15795i	0.262019	+	0.965063i
$6$	−1.30768	+	2.56648i	−0.533860	+	1.04776i
$7$			0.941662i			0.355915i	0.984038	+	0.177957i	$0.0569489\pi$
$7$			0.941662i			0.355915i	−0.984038	+	0.177957i	$0.943051\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	3.11340	−	4.28523i	1.03780	−	1.42841i
$10$	−1.74241	−	1.40144i	−0.550997	−	0.443173i
$11$	−0.313429	+	1.97891i	−0.0945024	+	0.596665i	0.894304	+	0.447460i	$0.147671\pi$
$11$	−0.313429	+	1.97891i	−0.0945024	+	0.596665i	−0.988806	+	0.149205i	$0.952329\pi$
$12$	−0.450597	−	2.84496i	−0.130076	−	0.821269i
$13$	−0.365403	+	3.58699i	−0.101345	+	0.994851i
$13$	−0.365403	+	3.58699i	−0.101345	+	0.994851i
$14$	−0.553495	−	0.761821i	−0.147928	−	0.203605i
$15$	4.32559	+	4.77215i	1.11686	+	1.23216i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.48766	−	4.88231i	0.603347	−	1.18414i	−0.364171	−	0.931332i	$-0.618648\pi$
$17$	2.48766	−	4.88231i	0.603347	−	1.18414i	0.967518	−	0.252803i	$-0.0813524\pi$
$18$			5.29683i			1.24848i
$19$	4.66891	+	2.37893i	1.07112	+	0.545764i	0.898387	−	0.439204i	$-0.144740\pi$
$19$	4.66891	+	2.37893i	1.07112	+	0.545764i	0.172735	+	0.984968i	$0.444740\pi$
$20$	2.23338	+	0.109624i	0.499399	+	0.0245127i
$21$	1.23140	+	2.41675i	0.268713	+	0.527379i
$22$	−0.909607	−	1.78520i	−0.193929	−	0.380607i
$23$	−0.289608	+	1.82851i	−0.0603874	+	0.381271i	0.938923	+	0.344128i	$0.111826\pi$
$23$	−0.289608	+	1.82851i	−0.0603874	+	0.381271i	−0.999310	+	0.0371424i	$0.988174\pi$
$24$	2.03677	+	2.03677i	0.415753	+	0.415753i
$25$	−4.31346	+	2.52865i	−0.862692	+	0.505730i
$26$	−1.81276	−	3.11671i	−0.355512	−	0.611238i
$27$	1.03495	−	6.53440i	0.199176	−	1.25755i
$28$	0.895574	+	0.290990i	0.169248	+	0.0549919i
$29$	−2.82946	−	0.919348i	−0.525418	−	0.170719i	0.0342847	−	0.999412i	$-0.489085\pi$
$29$	−2.82946	−	0.919348i	−0.525418	−	0.170719i	−0.559703	+	0.828693i	$0.689085\pi$
$30$	−6.30448	−	1.31823i	−1.15103	−	0.240675i
$31$	0.399153	−	0.783382i	0.0716900	−	0.140700i	−0.852380	−	0.522923i	$-0.824842\pi$
$31$	0.399153	−	0.783382i	0.0716900	−	0.140700i	0.924070	+	0.382223i	$0.124842\pi$
$32$	1.00000			0.176777
$33$	1.78339	+	5.48870i	0.310448	+	0.955460i
$34$	0.857190	+	5.41209i	0.147007	+	0.928165i
$35$	−2.03206	+	0.551714i	−0.343480	+	0.0932566i
$36$	−3.11340	−	4.28523i	−0.518900	−	0.714205i
$37$	−0.998819	+	1.37476i	−0.164205	+	0.226009i	−0.883188	−	0.469019i	$-0.844608\pi$
$37$	−0.998819	+	1.37476i	−0.164205	+	0.226009i	0.718983	+	0.695027i	$0.244608\pi$
$38$	−5.17553	+	0.819723i	−0.839582	+	0.132977i
$39$	3.75285	+	9.68375i	0.600937	+	1.55064i
$40$	−1.87128	+	1.22406i	−0.295875	+	0.193541i
$41$	−1.26808	−	8.00633i	−0.198041	−	1.25038i	−0.863655	−	0.504083i	$-0.831831\pi$
$41$	−1.26808	−	8.00633i	−0.198041	−	1.25038i	0.665615	−	0.746296i	$-0.268169\pi$
$42$	−2.41675	−	1.23140i	−0.372913	−	0.190009i
$43$	5.80017	−	5.80017i	0.884518	−	0.884518i	−0.109472	−	0.993990i	$-0.534916\pi$
$43$	5.80017	−	5.80017i	0.884518	−	0.884518i	0.993990	+	0.109472i	$0.0349159\pi$
$44$	1.78520	+	0.909607i	0.269130	+	0.137128i
$45$	11.0714	+	4.20786i	1.65043	+	0.627271i
$46$	−0.840474	−	1.64952i	−0.123921	−	0.243209i
$47$	−6.52422	−	2.11985i	−0.951656	−	0.309212i	−0.208268	−	0.978072i	$-0.566783\pi$
$47$	−6.52422	−	2.11985i	−0.951656	−	0.309212i	−0.743388	+	0.668860i	$0.766783\pi$
$48$	−2.84496	−	0.450597i	−0.410635	−	0.0650381i
$49$	6.11327			0.873325
$50$	2.00336	−	4.58111i	0.283317	−	0.647867i
$51$		−	15.7834i		−	2.21012i
$52$	3.29851	+	1.45596i	0.457421	+	0.201905i
$53$	1.13062	−	0.576081i	0.155303	−	0.0791308i	−0.374612	−	0.927182i	$-0.622224\pi$
$53$	1.13062	−	0.576081i	0.155303	−	0.0791308i	0.529915	+	0.848051i	$0.322224\pi$
$54$	3.00354	+	5.89477i	0.408729	+	0.802177i
$55$	−4.45402	+	0.483069i	−0.600581	+	0.0651371i
$56$	−0.895574	+	0.290990i	−0.119676	+	0.0388851i
$57$	15.0935			1.99919
$58$	2.82946	−	0.919348i	0.371527	−	0.120716i
$59$	−1.51948	−	9.59361i	−0.197819	−	1.24898i	−0.864115	−	0.503294i	$-0.832121\pi$
$59$	−1.51948	−	9.59361i	−0.197819	−	1.24898i	0.666296	−	0.745687i	$-0.267879\pi$
$60$	5.87527	−	2.63921i	0.758494	−	0.340720i
$61$	−2.95793	+	2.14906i	−0.378724	+	0.275159i	−0.760819	−	0.648964i	$-0.775203\pi$
$61$	−2.95793	+	2.14906i	−0.378724	+	0.275159i	0.382095	+	0.924123i	$0.375203\pi$
$62$	0.137539	+	0.868386i	0.0174674	+	0.110285i
$63$	4.03524	+	2.93177i	0.508392	+	0.369369i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−7.95461	+	1.31307i	−0.986648	+	0.162867i
$66$	−4.66897	−	3.39220i	−0.574710	−	0.417551i
$67$	−1.38515	−	4.26307i	−0.169224	−	0.520817i	0.830099	−	0.557616i	$-0.188284\pi$
$67$	−1.38515	−	4.26307i	−0.169224	−	0.520817i	−0.999323	+	0.0367993i	$0.988284\pi$
$68$	−3.87463	−	3.87463i	−0.469867	−	0.469867i
$69$	1.64784	+	5.07154i	0.198377	+	0.610542i
$70$	1.31968	−	1.64076i	0.157732	−	0.196108i
$71$	−7.48770	+	3.81518i	−0.888627	+	0.452778i	−0.837830	−	0.545931i	$-0.816176\pi$
$71$	−7.48770	+	3.81518i	−0.888627	+	0.452778i	−0.0507967	+	0.998709i	$0.516176\pi$
$72$	5.03759	+	1.63681i	0.593686	+	0.192900i
$73$	0.169310	−	0.123011i	0.0198162	−	0.0143973i	−0.577833	−	0.816155i	$-0.696102\pi$
$73$	0.169310	−	0.123011i	0.0198162	−	0.0143973i	0.597649	+	0.801758i	$0.296102\pi$
$74$		−	1.69929i		−	0.197539i
$75$	−7.76370	+	12.1304i	−0.896475	+	1.40069i
$76$	3.70527	−	3.70527i	0.425024	−	0.425024i
$77$	−1.86347	−	0.295144i	−0.212362	−	0.0336348i
$78$	−8.72808	−	5.62845i	−0.988261	−	0.637296i
$79$	1.23956	+	0.402759i	0.139462	+	0.0453139i	0.377916	−	0.925840i	$-0.376641\pi$
$79$	1.23956	+	0.402759i	0.139462	+	0.0453139i	−0.238454	+	0.971154i	$0.576641\pi$
$80$	0.794411	−	2.09019i	0.0888178	−	0.233691i
$81$	−0.978334	−	3.01100i	−0.108704	−	0.334556i
$82$	5.73190	+	5.73190i	0.632982	+	0.632982i
$83$	5.03495	−	1.63595i	0.552657	−	0.179569i	−0.0193573	−	0.999813i	$-0.506162\pi$
$83$	5.03495	−	1.63595i	0.552657	−	0.179569i	0.572015	+	0.820243i	$0.306162\pi$
$84$	2.67899	−	0.424311i	0.292302	−	0.0462961i
$85$	11.9933	+	2.50773i	1.30085	+	0.272001i
$86$	−1.28318	+	8.10170i	−0.138369	+	0.873628i
$87$	−8.46397	+	1.34056i	−0.907432	+	0.143723i
$88$	−1.97891	+	0.313429i	−0.210953	+	0.0334117i
$89$	−1.10202	−	0.174543i	−0.116814	−	0.0185015i	0.0977537	−	0.995211i	$-0.468834\pi$
$89$	−1.10202	−	0.174543i	−0.116814	−	0.0185015i	−0.214568	+	0.976709i	$0.568834\pi$
$90$	−11.4303	+	3.10338i	−1.20486	+	0.327125i
$91$	−3.37773	−	0.344086i	−0.354082	−	0.0360700i
$92$	1.64952	+	0.840474i	0.171975	+	0.0876255i
$93$		−	2.53250i		−	0.262608i
$94$	6.52422	−	2.11985i	0.672922	−	0.218646i
$95$	−2.39812	+	11.4691i	−0.246042	+	1.17670i
$96$	2.56648	−	1.30768i	0.261940	−	0.133465i
$97$	−3.03050	+	9.32693i	−0.307701	+	0.947006i	0.670955	+	0.741498i	$0.265885\pi$
$97$	−3.03050	+	9.32693i	−0.307701	+	0.947006i	−0.978656	+	0.205508i	$0.934115\pi$
$98$	−4.94574	+	3.59329i	−0.499595	+	0.362977i
$99$	7.50427	+	7.50427i	0.754207	+	0.754207i
$100$	1.07196	+	4.88374i	0.107196	+	0.488374i
$101$		−	18.7528i		−	1.86598i	−0.359908	−	0.932988i	$-0.617192\pi$
$101$		−	18.7528i		−	1.86598i	0.359908	−	0.932988i	$-0.382808\pi$
$102$	9.27726	+	12.7691i	0.918586	+	1.26432i
$103$	0.908431	+	1.78290i	0.0895104	+	0.175674i	0.931422	−	0.363942i	$-0.118569\pi$
$103$	0.908431	+	1.78290i	0.0895104	+	0.175674i	−0.841911	+	0.539616i	$0.818569\pi$
$104$	−3.52434	+	0.760921i	−0.345590	+	0.0746145i
$105$	−4.49375	+	4.07325i	−0.438545	+	0.397508i
$106$	−0.576081	+	1.13062i	−0.0559539	+	0.109816i
$107$	−13.3382	+	13.3382i	−1.28945	+	1.28945i	−0.354333	+	0.935119i	$0.615292\pi$
$107$	−13.3382	+	13.3382i	−1.28945	+	1.28945i	−0.935119	+	0.354333i	$0.884708\pi$
$108$	−5.89477	−	3.00354i	−0.567224	−	0.289015i
$109$	6.34048	−	1.00423i	0.607308	−	0.0961881i	0.154796	−	0.987946i	$-0.450528\pi$
$109$	6.34048	−	1.00423i	0.607308	−	0.0961881i	0.452512	+	0.891758i	$0.350528\pi$
$110$	3.31944	−	3.00882i	0.316496	−	0.286880i
$111$	−0.765697	+	4.83442i	−0.0726767	+	0.458863i
$112$	0.553495	−	0.761821i	0.0523004	−	0.0719853i
$113$	2.54969	+	16.0981i	0.239855	+	1.51438i	0.754112	+	0.656746i	$0.228068\pi$
$113$	2.54969	+	16.0981i	0.239855	+	1.51438i	−0.514257	+	0.857636i	$0.671932\pi$
$114$	−12.2109	+	8.87176i	−1.14366	+	0.830917i
$115$	−4.11551	+	0.446355i	−0.383773	+	0.0416228i
$116$	−1.74870	+	2.40689i	−0.162363	+	0.223474i
$117$	14.2334	+	12.7336i	1.31588	+	1.17722i
$118$	6.86826	+	6.86826i	0.632275	+	0.632275i
$119$	4.59749	+	2.34254i	0.421451	+	0.214740i
$120$	−3.20190	+	5.58856i	−0.292292	+	0.510163i
$121$	6.64376	+	2.15869i	0.603978	+	0.196244i
$122$	1.12983	−	3.47725i	0.102290	−	0.314816i
$123$	−13.7242	−	18.8898i	−1.23747	−	1.70324i
$124$	−0.621696	−	0.621696i	−0.0558299	−	0.0558299i
$125$	−7.98392	−	7.82669i	−0.714104	−	0.700040i
$126$	−4.98783			−0.444351
$127$	−20.9852	−	3.32372i	−1.86213	−	0.294933i	−0.878860	−	0.477080i	$-0.841695\pi$
$127$	−20.9852	−	3.32372i	−1.86213	−	0.294933i	−0.983271	+	0.182147i	$0.941695\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	7.30121	−	22.4708i	0.642835	−	1.97844i
$130$	5.66361	−	5.73790i	0.496732	−	0.503247i
$131$	−4.58089	−	14.0985i	−0.400234	−	1.23179i	−0.924810	−	0.380430i	$-0.875776\pi$
$131$	−4.58089	−	14.0985i	−0.400234	−	1.23179i	0.524576	−	0.851364i	$-0.324224\pi$
$132$	5.77116			0.502315
$133$	−2.24015	+	4.39654i	−0.194246	+	0.381228i
$134$	3.62638	+	2.63472i	0.313272	+	0.227605i
$135$	14.7073	−	1.59510i	1.26580	−	0.137285i
$136$	5.41209	+	0.857190i	0.464083	+	0.0735035i
$137$	−7.30922	+	10.0603i	−0.624469	+	0.859508i	−0.997669	−	0.0682431i	$-0.978261\pi$
$137$	−7.30922	+	10.0603i	−0.624469	+	0.859508i	0.373200	+	0.927751i	$0.378261\pi$
$138$	−4.31411	−	3.13439i	−0.367242	−	0.266817i
$139$	−4.10590	−	5.65128i	−0.348258	−	0.479336i	0.598573	−	0.801068i	$-0.295735\pi$
$139$	−4.10590	−	5.65128i	−0.348258	−	0.479336i	−0.946831	+	0.321733i	$0.895735\pi$
$140$	−0.103229	+	2.10309i	−0.00872443	+	0.177743i
$141$	−19.5164	+	3.09109i	−1.64357	+	0.260317i
$142$	3.81518	−	7.48770i	0.320162	−	0.628354i
$143$	−6.98381	−	1.84737i	−0.584016	−	0.154485i
$144$	−5.03759	+	1.63681i	−0.419799	+	0.136401i
$145$	0.326140	−	6.64447i	0.0270844	−	0.551793i
$146$	−0.0646707	+	0.199036i	−0.00535218	+	0.0164723i
$147$	15.6896	−	7.99423i	1.29405	−	0.659353i
$148$	0.998819	+	1.37476i	0.0821024	+	0.113004i
$149$	11.7202	−	11.7202i	0.960159	−	0.960159i	−0.0390769	−	0.999236i	$-0.512442\pi$
$149$	11.7202	−	11.7202i	0.960159	−	0.960159i	0.999236	+	0.0390769i	$0.0124417\pi$
$150$	−0.849081	−	14.3771i	−0.0693272	−	1.17388i
$151$	7.39086	−	7.39086i	0.601459	−	0.601459i	−0.339240	−	0.940700i	$-0.610170\pi$
$151$	7.39086	−	7.39086i	0.601459	−	0.601459i	0.940700	+	0.339240i	$0.110170\pi$
$152$	−0.819723	+	5.17553i	−0.0664884	+	0.419791i
$153$	−13.1767	−	25.8608i	−1.06528	−	2.09072i
$154$	1.68106	−	0.856542i	0.135464	−	0.0690222i
$155$	1.92436	+	0.402372i	0.154568	+	0.0323193i
$156$	10.3695	−	0.576730i	0.830223	−	0.0461754i
$157$	13.4626	−	13.4626i	1.07443	−	1.07443i	0.0774348	−	0.996997i	$-0.475327\pi$
$157$	13.4626	−	13.4626i	1.07443	−	1.07443i	0.996997	−	0.0774348i	$-0.0246730\pi$
$158$	−1.23956	+	0.402759i	−0.0986144	+	0.0320418i
$159$	2.14838	−	2.95699i	0.170378	−	0.234505i
$160$	0.585893	+	2.15795i	0.0463189	+	0.170601i
$161$	−1.72184	−	0.272713i	−0.135700	−	0.0214928i
$162$	2.56131	+	1.86090i	0.201236	+	0.146206i
$163$	−17.6849	−	12.8488i	−1.38519	−	1.00640i	−0.996374	−	0.0850793i	$-0.972886\pi$
$163$	−17.6849	−	12.8488i	−1.38519	−	1.00640i	−0.388812	−	0.921317i	$-0.627114\pi$
$164$	−8.00633	−	1.26808i	−0.625189	−	0.0990203i
$165$	−10.7994	+	7.06424i	−0.840735	+	0.549951i
$166$	−3.11177	+	4.28298i	−0.241520	+	0.332424i
$167$	−15.8656	+	5.15505i	−1.22772	+	0.398910i	−0.849887	−	0.526965i	$-0.823330\pi$
$167$	−15.8656	+	5.15505i	−1.22772	+	0.398910i	−0.377831	+	0.925875i	$0.623330\pi$
$168$	−1.91795	+	1.91795i	−0.147973	+	0.147973i
$169$	−12.7330	−	2.62139i	−0.979459	−	0.201646i
$170$	−11.1768	+	5.02068i	−0.857219	+	0.385068i
$171$	24.7305	−	12.6008i	1.89119	−	0.963607i
$172$	−3.72394	−	7.30865i	−0.283948	−	0.557279i
$173$	−2.24414	+	14.1689i	−0.170619	+	1.07724i	0.742588	+	0.669748i	$0.233598\pi$
$173$	−2.24414	+	14.1689i	−0.170619	+	1.07724i	−0.913207	+	0.407496i	$0.866402\pi$
$174$	6.05953	−	6.05953i	0.459372	−	0.459372i
$175$	−2.38114	−	4.06182i	−0.179997	−	0.307045i
$176$	1.41675	−	1.41675i	0.106791	−	0.106791i
$177$	−16.4451	−	22.6348i	−1.23609	−	1.70133i
$178$	0.994148	−	0.506544i	0.0745145	−	0.0379671i
$179$	6.71635	−	20.6708i	0.502004	−	1.54501i	−0.303747	−	0.952753i	$-0.598238\pi$
$179$	6.71635	−	20.6708i	0.502004	−	1.54501i	0.805750	−	0.592255i	$-0.201762\pi$
$180$	7.42317	−	9.22924i	0.553290	−	0.687907i
$181$	−22.1712	+	7.20384i	−1.64797	+	0.535457i	−0.978298	−	0.207201i	$-0.933565\pi$
$181$	−22.1712	+	7.20384i	−1.64797	+	0.535457i	−0.669670	+	0.742658i	$0.733565\pi$
$182$	2.93489	−	1.70701i	0.217549	−	0.126532i
$183$	−4.78116	+	9.38355i	−0.353433	+	0.693652i
$184$	−1.82851	+	0.289608i	−0.134800	+	0.0213502i
$185$	−3.55185	−	1.34994i	−0.261137	−	0.0992493i
$186$	1.48856	+	2.04883i	0.109147	+	0.150228i
$187$	8.88197	+	6.45313i	0.649514	+	0.471900i
$188$	−4.03219	+	5.54984i	−0.294078	+	0.404763i
$189$	6.15320	+	0.974571i	0.447579	+	0.0708896i
$190$	−4.80123	−	10.6882i	−0.348318	−	0.775407i
$191$	−0.772921	−	0.561560i	−0.0559266	−	0.0406331i	0.559471	−	0.828850i	$-0.311004\pi$
$191$	−0.772921	−	0.561560i	−0.0559266	−	0.0406331i	−0.615397	+	0.788217i	$0.711004\pi$
$192$	−1.30768	+	2.56648i	−0.0943740	+	0.185219i
$193$	6.19367			0.445830			0.222915	−	0.974838i	$-0.428443\pi$
$193$	6.19367			0.445830			0.222915	+	0.974838i	$0.428443\pi$
$194$	−3.03050	−	9.32693i	−0.217577	−	0.669634i
$195$	−18.6982	+	13.7721i	−1.33901	+	0.986240i
$196$	1.88911	−	5.81407i	0.134936	−	0.415291i
$197$	−1.54979	+	4.76976i	−0.110418	+	0.339832i	−0.990964	−	0.134129i	$-0.957176\pi$
$197$	−1.54979	+	4.76976i	−0.110418	+	0.339832i	0.880546	+	0.473961i	$0.157176\pi$
$198$	−10.4820	−	1.66018i	−0.744922	−	0.117984i
$199$	18.3801			1.30293			0.651467	−	0.758677i	$-0.274154\pi$
$199$	18.3801			1.30293			0.651467	+	0.758677i	$0.274154\pi$
$200$	−3.73782	−	3.32095i	−0.264304	−	0.234826i
$201$	−9.12971	−	9.12971i	−0.643960	−	0.643960i
$202$	11.0226	+	15.1714i	0.775550	+	1.06745i
$203$	0.865716	−	2.66440i	0.0607613	−	0.187004i
$204$	−15.0109	−	4.87734i	−1.05097	−	0.341482i
$205$	16.5343	−	7.42730i	1.15480	−	0.518745i
$206$	−1.78290	−	0.908431i	−0.124220	−	0.0632934i
$207$	6.93392	+	6.93392i	0.481941	+	0.481941i
$208$	2.40400	−	2.68716i	0.166687	−	0.186321i
$209$	−6.17107	+	8.49375i	−0.426862	+	0.587525i
$210$	1.24133	−	5.93669i	0.0856598	−	0.409670i
$211$	18.1657	−	13.1981i	1.25058	−	0.908598i	0.252323	−	0.967643i	$-0.418806\pi$
$211$	18.1657	−	13.1981i	1.25058	−	0.908598i	0.998255	+	0.0590450i	$0.0188056\pi$
$212$	−0.198504	−	1.25330i	−0.0136333	−	0.0860773i
$213$	−14.2280	+	19.5831i	−0.974884	+	1.34181i
$214$	2.95083	−	18.6308i	0.201715	−	1.27358i
$215$	15.9147	+	9.11818i	1.08538	+	0.621855i
$216$	6.53440	−	1.03495i	0.444610	−	0.0704193i
$217$	0.737681	+	0.375867i	0.0500771	+	0.0255155i
$218$	−4.53928	+	4.53928i	−0.307439	+	0.307439i
$219$	0.273670	−	0.537109i	0.0184929	−	0.0362944i
$220$	−0.916943	+	4.38531i	−0.0618203	+	0.295657i
$221$	16.6038	+	10.7072i	1.11689	+	0.720246i
$222$	−2.22214	−	4.36119i	−0.149140	−	0.292704i
$223$	7.88762	+	10.8564i	0.528194	+	0.726997i	0.986854	−	0.161615i	$-0.0516703\pi$
$223$	7.88762	+	10.8564i	0.528194	+	0.726997i	−0.458660	+	0.888612i	$0.651670\pi$
$224$			0.941662i			0.0629175i
$225$	−2.59367	+	26.3569i	−0.172911	+	1.75712i
$226$	−11.5250	−	11.5250i	−0.766630	−	0.766630i
$227$	−15.2829	+	11.1036i	−1.01436	+	0.736975i	−0.965119	−	0.261812i	$-0.915680\pi$
$227$	−15.2829	+	11.1036i	−1.01436	+	0.736975i	−0.0492398	+	0.998787i	$0.515680\pi$
$228$	4.66416	−	14.3548i	0.308892	−	0.950671i
$229$	−23.4942	+	11.9709i	−1.55254	+	0.791060i	−0.999124	−	0.0418429i	$-0.986677\pi$
$229$	−23.4942	+	11.9709i	−1.55254	+	0.791060i	−0.553419	+	0.832903i	$0.686677\pi$
$230$	3.06715	−	2.78014i	0.202242	−	0.183317i
$231$	−5.16850	+	1.67935i	−0.340062	+	0.110493i
$232$		−	2.97507i		−	0.195323i
$233$	−0.824303	−	0.420003i	−0.0540019	−	0.0275153i	0.426781	−	0.904355i	$-0.359648\pi$
$233$	−0.824303	−	0.420003i	−0.0540019	−	0.0275153i	−0.480783	+	0.876840i	$0.659648\pi$
$234$	−18.9997	−	1.93548i	−1.24205	−	0.126526i
$235$	0.752019	−	15.3209i	0.0490563	−	0.999427i
$236$	−9.59361	−	1.51948i	−0.624491	−	0.0989096i
$237$	3.70799	−	0.587288i	0.240860	−	0.0381485i
$238$	−5.09636	+	0.807184i	−0.330348	+	0.0523220i
$239$	0.306957	−	1.93805i	0.0198554	−	0.125362i	−0.975770	−	0.218800i	$-0.929786\pi$
$239$	0.306957	−	1.93805i	0.0198554	−	0.125362i	0.995625	+	0.0934380i	$0.0297857\pi$
$240$	−0.694479	−	6.40327i	−0.0448284	−	0.413329i
$241$	9.83340	−	1.55746i	0.633425	−	0.100325i	0.168539	−	0.985695i	$-0.446095\pi$
$241$	9.83340	−	1.55746i	0.633425	−	0.100325i	0.464886	+	0.885370i	$0.346095\pi$
$242$	−6.64376	+	2.15869i	−0.427077	+	0.138766i
$243$	7.58604	+	7.58604i	0.486645	+	0.486645i
$244$	1.12983	+	3.47725i	0.0723298	+	0.222608i
$245$	3.58173	+	13.1921i	0.228828	+	0.842813i
$246$	22.2063	+	7.21526i	1.41582	+	0.460028i
$247$	−10.2392	+	15.8781i	−0.651506	+	1.01030i
$248$	0.868386	+	0.137539i	0.0551426	+	0.00873372i
$249$	10.7828	−	10.7828i	0.683330	−	0.683330i
$250$	11.0595	+	1.63909i	0.699467	+	0.103665i
$251$			15.5958i			0.984398i	0.870483	+	0.492199i	$0.163807\pi$
$251$			15.5958i			0.984398i	−0.870483	+	0.492199i	$0.836193\pi$
$252$	4.03524	−	2.93177i	0.254196	−	0.184684i
$253$	−3.52769	−	1.14622i	−0.221784	−	0.0720620i
$254$	18.9310	−	9.64582i	1.18784	−	0.605232i
$255$	34.0598	−	9.24740i	2.13290	−	0.579095i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	0.888270	+	0.888270i	0.0554088	+	0.0554088i	0.734268	−	0.678859i	$-0.237525\pi$
$257$	0.888270	+	0.888270i	0.0554088	+	0.0554088i	−0.678859	+	0.734268i	$0.737525\pi$
$258$	7.30121	+	22.4708i	0.454553	+	1.39897i
$259$	−1.29456	−	0.940550i	−0.0804398	−	0.0584429i
$260$	−1.20930	+	7.97105i	−0.0749978	+	0.494343i
$261$	−12.7489	+	9.26260i	−0.789135	+	0.573340i
$262$	11.9929	+	8.71337i	0.740925	+	0.538314i
$263$	−3.91117	−	24.6942i	−0.241173	−	1.52271i	−0.749767	−	0.661702i	$-0.769835\pi$
$263$	−3.91117	−	24.6942i	−0.241173	−	1.52271i	0.508594	−	0.861006i	$-0.330165\pi$
$264$	−4.66897	+	3.39220i	−0.287355	+	0.208776i
$265$	1.90557	+	2.10230i	0.117058	+	0.129143i
$266$	−0.771903	−	4.87360i	−0.0473284	−	0.298820i
$267$	−3.05656	+	0.993136i	−0.187058	+	0.0607789i
$268$	−4.48245			−0.273810
$269$	−20.7199	+	6.73230i	−1.26331	+	0.410476i	−0.862674	−	0.505760i	$-0.831212\pi$
$269$	−20.7199	+	6.73230i	−1.26331	+	0.410476i	−0.400640	+	0.916236i	$0.631212\pi$
$270$	−10.9608	+	9.93517i	−0.667056	+	0.604635i
$271$	5.39848	+	10.5951i	0.327934	+	0.643608i	0.994831	−	0.101543i	$-0.0323778\pi$
$271$	5.39848	+	10.5951i	0.327934	+	0.643608i	−0.666897	+	0.745150i	$0.732378\pi$
$272$	−4.88231	+	2.48766i	−0.296034	+	0.150837i
$273$	−9.11882	+	3.53392i	−0.551896	+	0.213882i
$274$		−	12.4352i		−	0.751237i
$275$	−3.65202	−	9.32851i	−0.220225	−	0.562531i
$276$	5.33254			0.320981
$277$	12.7682	+	2.02229i	0.767169	+	0.121508i	0.527740	−	0.849406i	$-0.323040\pi$
$277$	12.7682	+	2.02229i	0.767169	+	0.121508i	0.239429	+	0.970914i	$0.423040\pi$
$278$	6.64348	+	2.15860i	0.398450	+	0.129464i
$279$	−2.11425	−	4.14945i	−0.126577	−	0.248421i
$280$	−1.15265	−	1.76211i	−0.0688841	−	0.105306i
$281$	−6.09853	−	3.10736i	−0.363808	−	0.185369i	0.262525	−	0.964925i	$-0.415445\pi$
$281$	−6.09853	−	3.10736i	−0.363808	−	0.185369i	−0.626333	+	0.779556i	$0.715445\pi$
$282$	13.9722	−	13.9722i	0.832031	−	0.832031i
$283$	−19.0941	−	9.72895i	−1.13503	−	0.578326i	−0.217526	−	0.976055i	$-0.569799\pi$
$283$	−19.0941	−	9.72895i	−1.13503	−	0.578326i	−0.917503	+	0.397728i	$0.869799\pi$
$284$	1.31462	+	8.30018i	0.0780083	+	0.492525i
$285$	8.84321	+	32.5710i	0.523826	+	1.92934i
$286$	6.73588	−	2.61043i	0.398301	−	0.154358i
$287$	7.53926	−	1.19410i	0.445028	−	0.0704856i
$288$	3.11340	−	4.28523i	0.183459	−	0.252510i
$289$	−7.65617	−	10.5378i	−0.450363	−	0.619872i
$290$	3.64167	+	5.56719i	0.213846	+	0.326917i
$291$	4.41897	+	27.9003i	0.259045	+	1.63554i
$292$	−0.0646707	−	0.199036i	−0.00378456	−	0.0116477i
$293$	9.03303			0.527715			0.263858	−	0.964562i	$-0.415005\pi$
$293$	9.03303			0.527715			0.263858	+	0.964562i	$0.415005\pi$
$294$	−7.99423	+	15.6896i	−0.466233	+	0.915034i
$295$	19.8122	−	8.89978i	1.15351	−	0.518165i
$296$	−1.61612	−	0.525110i	−0.0939352	−	0.0305214i
$297$	12.6066	+	4.09614i	0.731511	+	0.237682i
$298$	−2.59289	+	16.3709i	−0.150202	+	0.948338i
$299$	−6.45302	−	1.70696i	−0.373188	−	0.0987162i
$300$	9.13755	+	11.1322i	0.527556	+	0.642718i
$301$	5.46181	+	5.46181i	0.314813	+	0.314813i
$302$	−1.63509	+	10.3236i	−0.0940890	+	0.594054i
$303$	−24.5228	−	48.1287i	−1.40880	−	2.76492i
$304$	−2.37893	−	4.66891i	−0.136441	−	0.267781i
$305$	−6.37059	−	5.12393i	−0.364779	−	0.293395i
$306$	25.8608	+	13.1767i	1.47836	+	0.753264i
$307$		−	12.9168i		−	0.737200i	−0.929588	−	0.368600i	$-0.879837\pi$
$307$		−	12.9168i		−	0.737200i	0.929588	−	0.368600i	$-0.120163\pi$
$308$	−0.856542	+	1.68106i	−0.0488060	+	0.0957872i
$309$	4.66293	+	3.38782i	0.265265	+	0.192726i
$310$	−1.79335	+	0.805583i	−0.101855	+	0.0457540i
$311$	−17.4631	−	24.0359i	−0.990242	−	1.36295i	−0.931125	−	0.364700i	$-0.881172\pi$
$311$	−17.4631	−	24.0359i	−0.990242	−	1.36295i	−0.0591167	−	0.998251i	$-0.518828\pi$
$312$	−8.05010	+	6.56162i	−0.455747	+	0.371478i
$313$	2.93930	+	18.5580i	0.166139	+	1.04896i	0.919998	+	0.391924i	$0.128190\pi$
$313$	2.93930	+	18.5580i	0.166139	+	1.04896i	−0.753859	+	0.657037i	$0.771810\pi$
$314$	−2.97835	+	18.8046i	−0.168078	+	1.06120i
$315$	−3.96239	+	10.4255i	−0.223255	+	0.587412i
$316$	0.766093	−	1.05444i	0.0430961	−	0.0593167i
$317$	9.15070	+	28.1630i	0.513955	+	1.58179i	0.785176	+	0.619273i	$0.212572\pi$
$317$	9.15070	+	28.1630i	0.513955	+	1.58179i	−0.271222	+	0.962517i	$0.587428\pi$
$318$			3.65504i			0.204965i
$319$	2.70615	−	5.31111i	0.151515	−	0.297365i
$320$	−1.74241	−	1.40144i	−0.0974035	−	0.0783426i
$321$	−16.7900	+	51.6743i	−0.937127	+	2.88418i
$322$	1.55329	−	0.791443i	0.0865617	−	0.0441054i
$323$	23.2294	−	16.8771i	1.29252	−	0.939068i
$324$	−3.16595			−0.175886
$325$	−7.49409	−	16.3963i	−0.415698	−	0.909503i
$326$	21.8597			1.21070
$327$	14.9595	−	10.8687i	0.827260	−	0.601040i
$328$	7.22261	−	3.68011i	0.398802	−	0.203200i
$329$	1.99618	−	6.14362i	0.110053	−	0.338709i
$330$	4.58467	−	12.0628i	0.252378	−	0.664038i
$331$	−5.07033	+	9.95108i	−0.278690	+	0.546961i	−0.987344	−	0.158596i	$-0.949303\pi$
$331$	−5.07033	+	9.95108i	−0.278690	+	0.546961i	0.708653	+	0.705557i	$0.249303\pi$
$332$		−	5.29406i		−	0.290549i
$333$	2.78142	+	8.56034i	0.152421	+	0.469104i
$334$	9.80548	−	13.4961i	0.536532	−	0.738473i
$335$	8.38792	−	5.48679i	0.458281	−	0.299775i
$336$	0.424311	−	2.67899i	0.0231480	−	0.146151i
$337$	1.76966	+	11.1732i	0.0963997	+	0.608644i	0.987836	+	0.155498i	$0.0496982\pi$
$337$	1.76966	+	11.1732i	0.0963997	+	0.608644i	−0.891437	+	0.453146i	$0.850302\pi$
$338$	11.8420	−	5.36350i	0.644120	−	0.291736i
$339$	27.5950	+	37.9812i	1.49875	+	2.06286i
$340$	6.09111	−	10.6314i	0.330337	−	0.576566i
$341$	1.42514	+	1.03542i	0.0771756	+	0.0560714i
$342$	−12.6008	+	24.7305i	−0.681373	+	1.33727i
$343$			12.3483i			0.666744i
$344$	7.30865	+	3.72394i	0.394056	+	0.200781i
$345$	−9.97865	+	6.52734i	−0.537233	+	0.351420i
$346$	−6.51274	−	12.7820i	−0.350127	−	0.687163i
$347$	6.38316	+	12.5277i	0.342666	+	0.672520i	0.996452	−	0.0841593i	$-0.0268205\pi$
$347$	6.38316	+	12.5277i	0.342666	+	0.672520i	−0.653786	+	0.756679i	$0.726820\pi$
$348$	−1.34056	+	8.46397i	−0.0718616	+	0.453716i
$349$	−4.28589	−	4.28589i	−0.229419	−	0.229419i	0.583031	−	0.812450i	$-0.301867\pi$
$349$	−4.28589	−	4.28589i	−0.229419	−	0.229419i	−0.812450	+	0.583031i	$0.801867\pi$
$350$	4.31386	+	1.88649i	0.230585	+	0.100837i
$351$	23.0606	+	6.10004i	1.23089	+	0.325596i
$352$	−0.313429	+	1.97891i	−0.0167058	+	0.105476i
$353$	−21.4552	−	6.97122i	−1.14195	−	0.371040i	−0.323842	−	0.946111i	$-0.604974\pi$
$353$	−21.4552	−	6.97122i	−1.14195	−	0.371040i	−0.818104	+	0.575071i	$0.804974\pi$
$354$	26.6088	+	8.64571i	1.41424	+	0.459514i
$355$	−12.6199	−	13.9228i	−0.669797	−	0.738944i
$356$	−0.506544	+	0.994148i	−0.0268468	+	0.0526897i
$357$	14.8626			0.786615
$358$	6.71635	+	20.6708i	0.354970	+	1.09249i
$359$	−0.635141	−	4.01012i	−0.0335214	−	0.211646i	0.965242	−	0.261357i	$-0.0841700\pi$
$359$	−0.635141	−	4.01012i	−0.0335214	−	0.211646i	−0.998764	+	0.0497109i	$0.984170\pi$
$360$	−0.580661	+	11.8298i	−0.0306035	+	0.623487i
$361$	4.97152	+	6.84271i	0.261659	+	0.360143i
$362$	13.7025	−	18.8599i	0.720189	−	0.991255i
$363$	19.8739	−	3.14772i	1.04311	−	0.165213i
$364$	−1.37102	+	3.10608i	−0.0718611	+	0.162803i
$365$	0.364648	+	0.293290i	0.0190866	+	0.0153515i
$366$	−1.64747	−	10.4017i	−0.0861149	−	0.543708i
$367$	24.6352	+	12.5522i	1.28595	+	0.655222i	0.957263	−	0.289219i	$-0.0933955\pi$
$367$	24.6352	+	12.5522i	1.28595	+	0.655222i	0.328682	+	0.944441i	$0.393396\pi$
$368$	1.30907	−	1.30907i	0.0682399	−	0.0682399i
$369$	−38.2570	−	19.4929i	−1.99158	−	1.01476i
$370$	3.66698	−	0.995604i	0.190637	−	0.0517590i
$371$	0.542473	+	1.06466i	0.0281638	+	0.0552746i
$372$	−2.40855	−	0.782585i	−0.124877	−	0.0405751i
$373$	36.7187	+	5.81568i	1.90122	+	0.301124i	0.993071	−	0.117515i	$-0.0374927\pi$
$373$	36.7187	+	5.81568i	1.90122	+	0.301124i	0.908153	+	0.418639i	$0.137493\pi$
$374$	−10.9787			−0.567696
$375$	−30.7254	−	9.64655i	−1.58665	−	0.498146i
$376$		−	6.85998i		−	0.353776i
$377$	4.33159	−	9.81332i	0.223088	−	0.505412i
$378$	−5.55088	+	2.82832i	−0.285507	+	0.145473i
$379$	10.6166	+	20.8363i	0.545340	+	1.07029i	0.985069	+	0.172160i	$0.0550746\pi$
$379$	10.6166	+	20.8363i	0.545340	+	1.07029i	−0.439729	+	0.898131i	$0.644925\pi$
$380$	10.1667	+	5.82488i	0.521539	+	0.298810i
$381$	−58.2043	+	18.9117i	−2.98189	+	0.968876i
$382$	0.955383			0.0488816
$383$	30.7308	−	9.98505i	1.57027	−	0.510212i	0.610744	−	0.791828i	$-0.290870\pi$
$383$	30.7308	−	9.98505i	1.57027	−	0.510212i	0.959527	+	0.281616i	$0.0908704\pi$
$384$	−0.450597	−	2.84496i	−0.0229945	−	0.145181i
$385$	−0.454888	−	4.19419i	−0.0231833	−	0.213756i
$386$	−5.01078	+	3.64055i	−0.255042	+	0.185299i
$387$	−6.79681	−	42.9134i	−0.345501	−	2.18141i
$388$	7.93396	+	5.76436i	0.402786	+	0.292641i
$389$	3.90966	−	2.84053i	0.198228	−	0.144021i	−0.484244	−	0.874933i	$-0.660905\pi$
$389$	3.90966	−	2.84053i	0.198228	−	0.144021i	0.682471	+	0.730912i	$0.260905\pi$
$390$	7.03215	−	22.1324i	0.356087	−	1.12072i
$391$	8.20692	+	5.96267i	0.415042	+	0.301545i
$392$	1.88911	+	5.81407i	0.0954142	+	0.293655i
$393$	−30.1932	−	30.1932i	−1.52304	−	1.52304i
$394$	−1.54979	−	4.76976i	−0.0780773	−	0.240297i
$395$	−0.142879	+	2.91089i	−0.00718903	+	0.146463i
$396$	9.45593	−	4.81804i	0.475178	−	0.242115i
$397$	2.80522	+	0.911471i	0.140790	+	0.0457454i	0.378564	−	0.925575i	$-0.376418\pi$
$397$	2.80522	+	0.911471i	0.140790	+	0.0457454i	−0.237774	+	0.971320i	$0.576418\pi$
$398$	−14.8699	+	10.8036i	−0.745358	+	0.541535i
$399$			14.2130i			0.711541i
$400$	4.97597	+	0.489664i	0.248798	+	0.0244832i
$401$	−4.17926	+	4.17926i	−0.208702	+	0.208702i	−0.803716	−	0.595013i	$-0.797147\pi$
$401$	−4.17926	+	4.17926i	−0.208702	+	0.208702i	0.595013	+	0.803716i	$0.297147\pi$
$402$	12.7524	+	2.01978i	0.636032	+	0.100738i
$403$	2.66413	+	1.71801i	0.132710	+	0.0855801i
$404$	−17.8350	−	5.79494i	−0.887324	−	0.288309i
$405$	5.92438	−	3.87532i	0.294385	−	0.192566i
$406$	0.865716	+	2.66440i	0.0429647	+	0.132232i
$407$	−2.40747	−	2.40747i	−0.119334	−	0.119334i
$408$	15.0109	−	4.87734i	0.743151	−	0.241465i
$409$	25.4756	−	4.03494i	1.25969	−	0.199515i	0.509345	−	0.860562i	$-0.329888\pi$
$409$	25.4756	−	4.03494i	1.25969	−	0.199515i	0.750344	+	0.661047i	$0.229888\pi$
$410$	−9.01084	+	15.7274i	−0.445014	+	0.776721i
$411$	−5.60327	+	35.3776i	−0.276389	+	1.74505i
$412$	1.97636	−	0.313024i	0.0973681	−	0.0154216i
$413$	9.03394	−	1.43084i	0.444531	−	0.0704068i
$414$	−9.68532	−	1.53400i	−0.476007	−	0.0753922i
$415$	6.48024	+	9.90665i	0.318103	+	0.486298i
$416$	−0.365403	+	3.58699i	−0.0179154	+	0.175867i
$417$	−17.9278	−	9.13466i	−0.877927	−	0.447326i
$418$		−	10.4989i		−	0.513516i
$419$	12.8624	−	4.17924i	0.628368	−	0.204169i	0.0225161	−	0.999746i	$-0.492832\pi$
$419$	12.8624	−	4.17924i	0.628368	−	0.204169i	0.605852	+	0.795577i	$0.292832\pi$
$420$	2.48524	+	5.53252i	0.121267	+	0.269959i
$421$	−2.00424	+	1.02121i	−0.0976809	+	0.0497709i	−0.502148	−	0.864781i	$-0.667457\pi$
$421$	−2.00424	+	1.02121i	−0.0976809	+	0.0497709i	0.404467	+	0.914552i	$0.367457\pi$
$422$	−6.93868	+	21.3551i	−0.337770	+	1.03955i
$423$	−29.3966	+	21.3579i	−1.42931	+	1.03845i
$424$	0.897267	+	0.897267i	0.0435751	+	0.0435751i
$425$	1.61524	+	27.3501i	0.0783508	+	1.32667i
$426$		−	24.2061i		−	1.17279i
$427$	−2.02369	−	2.78537i	−0.0979332	−	0.134794i
$428$	8.56365	+	16.8071i	0.413940	+	0.812403i
$429$	−20.3396	+	4.39140i	−0.982003	+	0.212019i
$430$	−18.2348	+	1.97769i	−0.879362	+	0.0953728i
$431$	14.9382	−	29.3179i	0.719548	−	1.41219i	−0.183661	−	0.982990i	$-0.558795\pi$
$431$	14.9382	−	29.3179i	0.719548	−	1.41219i	0.903209	−	0.429202i	$-0.141205\pi$
$432$	−4.67812	+	4.67812i	−0.225076	+	0.225076i
$433$	5.55106	+	2.82841i	0.266767	+	0.135925i	0.582258	−	0.813004i	$-0.302169\pi$
$433$	5.55106	+	2.82841i	0.266767	+	0.135925i	−0.315491	+	0.948929i	$0.602169\pi$
$434$	−0.817726	+	0.129515i	−0.0392521	+	0.00621692i
$435$	−7.85184	−	17.4794i	−0.376467	−	0.838071i
$436$	1.00423	−	6.34048i	0.0480941	−	0.303654i
$437$	−5.70205	+	7.84820i	−0.272766	+	0.375430i
$438$	0.0943004	+	0.595389i	0.00450585	+	0.0284488i
$439$	−12.5394	+	9.11037i	−0.598471	+	0.434814i	−0.845336	−	0.534236i	$-0.820600\pi$
$439$	−12.5394	+	9.11037i	−0.598471	+	0.434814i	0.246865	+	0.969050i	$0.420600\pi$
$440$	−1.83580	−	4.08675i	−0.0875181	−	0.194828i
$441$	19.0331	−	26.1968i	0.906337	−	1.24747i
$442$	−19.7263	+	1.09714i	−0.938285	+	0.0521855i
$443$	−21.4004	−	21.4004i	−1.01676	−	1.01676i	−0.999857	−	0.0169048i	$-0.994619\pi$
$443$	−21.4004	−	21.4004i	−1.01676	−	1.01676i	−0.0169048	−	0.999857i	$-0.505381\pi$
$444$	4.36119	+	2.22214i	0.206973	+	0.105458i
$445$	−0.269013	−	2.48037i	−0.0127524	−	0.117581i
$446$	−12.7624	−	4.14677i	−0.604319	−	0.196355i
$447$	14.7533	−	45.4061i	0.697809	−	2.14763i
$448$	−0.553495	−	0.761821i	−0.0261502	−	0.0359926i
$449$	18.0817	+	18.0817i	0.853328	+	0.853328i	0.990542	−	0.137213i	$-0.0438145\pi$
$449$	18.0817	+	18.0817i	0.853328	+	0.853328i	−0.137213	+	0.990542i	$0.543815\pi$
$450$	−13.3939	−	22.8477i	−0.631392	−	1.07705i
$451$	16.2413			0.764772
$452$	16.0981	+	2.54969i	0.757191	+	0.119927i
$453$	9.30354	−	28.6334i	0.437119	−	1.34531i
$454$	5.83753	−	17.9661i	0.273969	−	0.843190i
$455$	−1.23647	−	7.49056i	−0.0579666	−	0.351163i
$456$	4.66416	+	14.3548i	0.218419	+	0.672226i
$457$	−32.2055			−1.50651			−0.753256	−	0.657728i	$-0.771518\pi$
$457$	−32.2055			−1.50651			−0.753256	+	0.657728i	$0.771518\pi$
$458$	11.9709	−	23.4942i	0.559364	−	1.09781i
$459$	−29.3284	−	21.3083i	−1.36893	−	0.994588i
$460$	−0.847252	+	4.05201i	−0.0395033	+	0.188926i
$461$	2.30811	+	0.365568i	0.107499	+	0.0170262i	0.209952	−	0.977712i	$-0.432669\pi$
$461$	2.30811	+	0.365568i	0.107499	+	0.0170262i	−0.102453	+	0.994738i	$0.532669\pi$
$462$	3.19431	−	4.39659i	0.148613	−	0.204548i
$463$	11.2643	+	8.18402i	0.523498	+	0.380343i	0.817920	−	0.575332i	$-0.195127\pi$
$463$	11.2643	+	8.18402i	0.523498	+	0.380343i	−0.294422	+	0.955675i	$0.595127\pi$
$464$	1.74870	+	2.40689i	0.0811816	+	0.111737i
$465$	5.46499	−	1.48377i	0.253433	−	0.0688084i
$466$	0.913747	−	0.144723i	0.0423285	−	0.00670418i
$467$	7.43471	−	14.5914i	0.344037	−	0.675211i	−0.652551	−	0.757745i	$-0.726301\pi$
$467$	7.43471	−	14.5914i	0.344037	−	0.675211i	0.996588	+	0.0825337i	$0.0263012\pi$
$468$	16.5087	−	9.60190i	0.763115	−	0.443848i
$469$	4.01437	−	1.30435i	0.185366	−	0.0602292i
$470$	8.39702	+	12.8369i	0.387326	+	0.592123i
$471$	16.9466	−	52.1563i	0.780858	−	2.40323i
$472$	8.65452	−	4.40970i	0.398356	−	0.202973i
$473$	9.66010	+	13.2960i	0.444172	+	0.611350i
$474$	−2.65463	+	2.65463i	−0.121931	+	0.121931i
$475$	−26.1546	+	1.54464i	−1.20006	+	0.0708731i
$476$	3.64859	−	3.64859i	0.167233	−	0.167233i
$477$	1.05144	−	6.63854i	0.0481422	−	0.303958i
$478$	0.890825	+	1.74834i	0.0407454	+	0.0799674i
$479$	15.8414	−	8.07158i	0.723810	−	0.368800i	−0.0529492	−	0.998597i	$-0.516862\pi$
$479$	15.8414	−	8.07158i	0.723810	−	0.368800i	0.776759	+	0.629798i	$0.216862\pi$
$480$	4.32559	+	4.77215i	0.197435	+	0.217818i
$481$	−4.56626	−	4.08509i	−0.208204	−	0.186264i
$482$	−7.03994	+	7.03994i	−0.320660	+	0.320660i
$483$	−4.77568	+	1.55171i	−0.217301	+	0.0706054i
$484$	4.10607	−	5.65152i	0.186640	−	0.256887i
$485$	−21.9026	−	1.07507i	−0.994544	−	0.0488166i
$486$	−10.5962	−	1.67827i	−0.480653	−	0.0761280i
$487$	−14.0623	−	10.2169i	−0.637224	−	0.462970i	0.221671	−	0.975121i	$-0.428849\pi$
$487$	−14.0623	−	10.2169i	−0.637224	−	0.462970i	−0.858895	+	0.512151i	$0.828849\pi$
$488$	−2.95793	−	2.14906i	−0.133899	−	0.0972834i
$489$	−62.1900	−	9.84992i	−2.81233	−	0.445429i
$490$	−10.6518	−	8.56735i	−0.481199	−	0.387034i
$491$	−15.9295	+	21.9250i	−0.718887	+	0.989463i	0.280673	+	0.959803i	$0.409442\pi$
$491$	−15.9295	+	21.9250i	−0.718887	+	0.989463i	−0.999560	+	0.0296598i	$0.990558\pi$
$492$	−22.2063	+	7.21526i	−1.00114	+	0.325289i
$493$	−11.5273	+	11.5273i	−0.519163	+	0.519163i
$494$	−1.04918	−	18.8641i	−0.0472050	−	0.848736i
$495$	−11.7971	+	20.5905i	−0.530240	+	0.925474i
$496$	−0.783382	+	0.399153i	−0.0351749	+	0.0179225i
$497$	−3.59261	−	7.05089i	−0.161150	−	0.316276i
$498$	−2.38549	+	15.0614i	−0.106896	+	0.674917i
$499$	15.5198	−	15.5198i	0.694761	−	0.694761i	−0.268515	−	0.963276i	$-0.586533\pi$
$499$	15.5198	−	15.5198i	0.694761	−	0.694761i	0.963276	+	0.268515i	$0.0865328\pi$
$500$	−9.91079	+	5.17458i	−0.443224	+	0.231414i
$501$	−33.9775	+	33.9775i	−1.51800	+	1.51800i
$502$	−9.16698	−	12.6173i	−0.409142	−	0.563136i
$503$	14.9447	−	7.61468i	0.666349	−	0.339522i	−0.0878820	−	0.996131i	$-0.528010\pi$
$503$	14.9447	−	7.61468i	0.666349	−	0.339522i	0.754231	+	0.656609i	$0.228010\pi$
$504$	−1.54132	+	4.74371i	−0.0686560	+	0.211302i
$505$	40.4676	−	10.9872i	1.80078	−	0.488922i
$506$	3.52769	−	1.14622i	0.156825	−	0.0509556i
$507$	−36.1068	+	9.92296i	−1.60356	+	0.440694i
$508$	−9.64582	+	18.9310i	−0.427964	+	0.839926i
$509$	40.1086	−	6.35258i	1.77778	−	0.281573i	0.820693	−	0.571369i	$-0.193587\pi$
$509$	40.1086	−	6.35258i	1.77778	−	0.281573i	0.957088	+	0.289796i	$0.0935874\pi$
$510$	−22.1194	+	27.5011i	−0.979465	+	1.21777i
$511$	0.115835	+	0.159433i	0.00512423	+	0.00705289i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	20.3770	−	28.0465i	0.899665	−	1.23828i
$514$	−1.24074	−	0.196514i	−0.0547266	−	0.00866784i
$515$	−3.31515	+	3.00493i	−0.146083	+	0.132413i
$516$	−19.1148	−	13.8877i	−0.841483	−	0.611373i
$517$	6.23988	−	12.2465i	0.274430	−	0.538599i
$518$	1.60016			0.0703070
$519$	12.7690	+	39.2988i	0.560496	+	1.72503i
$520$	−3.70692	−	7.15952i	−0.162559	−	0.313966i
$521$	−12.8300	+	39.4866i	−0.562091	+	1.72994i	0.114350	+	0.993441i	$0.463522\pi$
$521$	−12.8300	+	39.4866i	−0.562091	+	1.72994i	−0.676441	+	0.736497i	$0.736478\pi$
$522$	4.86964	−	14.9872i	0.213138	−	0.655972i
$523$	−16.2436	−	2.57274i	−0.710284	−	0.112498i	−0.209170	−	0.977879i	$-0.567076\pi$
$523$	−16.2436	−	2.57274i	−0.710284	−	0.112498i	−0.501114	+	0.865381i	$0.667076\pi$
$524$	−14.8241			−0.647592
$525$	−11.4227	−	7.31079i	−0.498528	−	0.319069i
$526$	17.6791	+	17.6791i	0.770844	+	0.770844i
$527$	−2.83176	−	3.89758i	−0.123353	−	0.169781i
$528$	1.78339	−	5.48870i	0.0776119	−	0.238865i
$529$	18.6147	+	6.04829i	0.809336	+	0.262969i
$530$	−2.77734	−	0.580727i	−0.120640	−	0.0252252i
$531$	−45.8415	−	23.3574i	−1.98935	−	1.01363i
$532$	3.48911	+	3.48911i	0.151272	+	0.151272i
$533$	29.1820	−	1.62304i	1.26401	−	0.0703018i
$534$	1.88906	−	2.60006i	0.0817475	−	0.112516i
$535$	−36.5979	−	20.9683i	−1.58226	−	0.906541i
$536$	3.62638	−	2.63472i	0.156636	−	0.113803i
$537$	−9.79354	−	61.8340i	−0.422622	−	2.66833i
$538$	12.8056	−	17.6254i	0.552089	−	0.759885i
$539$	−1.91608	+	12.0976i	−0.0825313	+	0.521082i
$540$	3.02776	−	14.4803i	0.130294	−	0.623135i
$541$	14.6629	−	2.32238i	0.630409	−	0.0998470i	0.166950	−	0.985965i	$-0.446608\pi$
$541$	14.6629	−	2.32238i	0.630409	−	0.0998470i	0.463459	+	0.886118i	$0.346608\pi$
$542$	−10.5951	−	5.39848i	−0.455099	−	0.231885i
$543$	−47.4814	+	47.4814i	−2.03762	+	2.03762i
$544$	2.48766	−	4.88231i	0.106658	−	0.209327i
$545$	5.88193	+	13.0940i	0.251954	+	0.560887i
$546$	5.30010	−	8.21891i	0.226823	−	0.351737i
$547$	3.58357	+	7.03315i	0.153222	+	0.300716i	0.954840	−	0.297122i	$-0.0960268\pi$
$547$	3.58357	+	7.03315i	0.153222	+	0.300716i	−0.801617	+	0.597838i	$0.796027\pi$
$548$	7.30922	+	10.0603i	0.312235	+	0.429754i
$549$			19.3663i			0.826533i
$550$	8.43771	+	5.40032i	0.359785	+	0.230271i
$551$	−11.0235	−	11.0235i	−0.469615	−	0.469615i
$552$	−4.31411	+	3.13439i	−0.183621	+	0.133408i
$553$	−0.379263	+	1.16725i	−0.0161279	+	0.0496365i
$554$	−11.5184	+	5.86892i	−0.489370	+	0.249346i
$555$	−10.8810	+	1.18012i	−0.461874	+	0.0500934i
$556$	−6.64348	+	2.15860i	−0.281746	+	0.0915450i
$557$			8.97251i			0.380177i	0.981767	+	0.190089i	$0.0608775\pi$
$557$			8.97251i			0.380177i	−0.981767	+	0.190089i	$0.939122\pi$
$558$	4.14945	+	2.11425i	0.175660	+	0.0895033i
$559$	18.6858	+	22.9246i	0.790323	+	0.969605i
$560$	1.96826	+	0.748067i	0.0831740	+	0.0316116i
$561$	31.2340	+	4.94698i	1.31870	+	0.208862i
$562$	6.76027	−	1.07072i	0.285165	−	0.0451657i
$563$	35.8490	−	5.67793i	1.51086	−	0.239296i	0.654651	−	0.755932i	$-0.272816\pi$
$563$	35.8490	−	5.67793i	1.51086	−	0.239296i	0.856205	+	0.516635i	$0.172816\pi$
$564$	−3.09109	+	19.5164i	−0.130158	+	0.821787i
$565$	−33.2450	+	14.9339i	−1.39863	+	0.628273i
$566$	21.1660	−	3.35237i	0.889674	−	0.140911i
$567$	2.83535	−	0.921260i	0.119073	−	0.0386893i
$568$	−5.94227	−	5.94227i	−0.249332	−	0.249332i
$569$	−5.12826	−	15.7832i	−0.214988	−	0.661665i	−0.999154	−	0.0411145i	$-0.986909\pi$
$569$	−5.12826	−	15.7832i	−0.214988	−	0.661665i	0.784166	−	0.620551i	$-0.213091\pi$
$570$	−26.2991	−	21.1526i	−1.10155	−	0.885986i
$571$	8.66674	+	2.81600i	0.362692	+	0.117846i	0.484693	−	0.874684i	$-0.338931\pi$
$571$	8.66674	+	2.81600i	0.362692	+	0.117846i	−0.122001	+	0.992530i	$0.538931\pi$
$572$	−3.91507	+	6.07113i	−0.163697	+	0.253847i
$573$	−2.71803	−	0.430493i	−0.113547	−	0.0179841i
$574$	−5.39751	+	5.39751i	−0.225288	+	0.225288i
$575$	−3.37446	−	8.61952i	−0.140725	−	0.359459i
$576$			5.29683i			0.220701i
$577$	1.30311	−	0.946765i	0.0542492	−	0.0394143i	−0.560330	−	0.828269i	$-0.689326\pi$
$577$	1.30311	−	0.946765i	0.0542492	−	0.0394143i	0.614579	+	0.788855i	$0.289326\pi$
$578$	12.3879	+	4.02509i	0.515271	+	0.167422i
$579$	15.8959	−	8.09936i	0.660611	−	0.336598i
$580$	−6.21848	−	2.36343i	−0.258208	−	0.0981361i
$581$	1.54052	+	4.74122i	0.0639114	+	0.196699i
$582$	−19.9744	−	19.9744i	−0.827965	−	0.827965i
$583$	0.785644	+	2.41796i	0.0325380	+	0.100142i
$584$	0.169310	+	0.123011i	0.00700610	+	0.00509023i
$585$	−19.1391	+	38.1755i	−0.791304	+	1.57836i
$586$	−7.30788	+	5.30948i	−0.301886	+	0.219333i
$587$	−10.0993	−	7.33757i	−0.416843	−	0.302854i	0.359524	−	0.933136i	$-0.382939\pi$
$587$	−10.0993	−	7.33757i	−0.416843	−	0.302854i	−0.776366	+	0.630282i	$0.782939\pi$
$588$	−2.75462	−	17.3920i	−0.113599	−	0.717235i
$589$	3.72722	−	2.70799i	0.153578	−	0.111581i
$590$	−10.7973	+	18.8454i	−0.444517	+	0.775853i
$591$	2.25985	+	14.2681i	0.0929577	+	0.586912i
$592$	1.61612	−	0.525110i	0.0664222	−	0.0215819i
$593$	27.3699			1.12395			0.561974	−	0.827155i	$-0.310042\pi$
$593$	27.3699			1.12395			0.561974	+	0.827155i	$0.310042\pi$
$594$	−12.6066	+	4.09614i	−0.517257	+	0.168067i
$595$	−2.36143	+	11.2936i	−0.0968092	+	0.462993i
$596$	−7.52486	−	14.7684i	−0.308230	−	0.604936i
$597$	47.1722	−	24.0354i	1.93063	−	0.983705i
$598$	6.22393	−	2.41203i	0.254515	−	0.0986352i
$599$			15.6821i			0.640755i	0.947290	+	0.320377i	$0.103810\pi$
$599$			15.6821i			0.640755i	−0.947290	+	0.320377i	$0.896190\pi$
$600$	−13.9358	−	3.63523i	−0.568926	−	0.148408i
$601$	−7.98127			−0.325563			−0.162781	−	0.986662i	$-0.552047\pi$
$601$	−7.98127			−0.325563			−0.162781	+	0.986662i	$0.552047\pi$
$602$	−7.62906	−	1.20832i	−0.310937	−	0.0492476i
$603$	−22.5808	−	7.33694i	−0.919560	−	0.298783i
$604$	−4.74522	−	9.31302i	−0.193080	−	0.378942i
$605$	−0.765797	+	15.6016i	−0.0311341	+	0.634297i
$606$	48.1287	+	24.5228i	1.95509	+	0.996170i
$607$	22.6593	−	22.6593i	0.919713	−	0.919713i	−0.0772954	−	0.997008i	$-0.524628\pi$
$607$	22.6593	−	22.6593i	0.919713	−	0.919713i	0.997008	+	0.0772954i	$0.0246284\pi$
$608$	4.66891	+	2.37893i	0.189349	+	0.0964784i
$609$	−1.26236	−	7.97020i	−0.0511532	−	0.322969i
$610$	8.16568	+	0.400808i	0.330619	+	0.0162282i
$611$	9.98784	−	22.6277i	0.404065	−	0.915419i
$612$	−28.6669	+	4.54040i	−1.15879	+	0.183535i
$613$	26.8587	−	36.9679i	1.08481	−	1.49312i	0.230704	−	0.973024i	$-0.425897\pi$
$613$	26.8587	−	36.9679i	1.08481	−	1.49312i	0.854109	−	0.520094i	$-0.174103\pi$
$614$	7.59230	+	10.4499i	0.306400	+	0.421724i
$615$	32.7222	−	40.6836i	1.31949	−	1.64052i
$616$	−0.295144	−	1.86347i	−0.0118917	−	0.0750813i
$617$	−0.493203	−	1.51792i	−0.0198556	−	0.0611092i	0.940638	−	0.339412i	$-0.110228\pi$
$617$	−0.493203	−	1.51792i	−0.0198556	−	0.0611092i	−0.960493	+	0.278303i	$0.910228\pi$
$618$	−5.76370			−0.231850
$619$	−13.0443	+	25.6008i	−0.524294	+	1.02898i	0.465308	+	0.885149i	$0.345944\pi$
$619$	−13.0443	+	25.6008i	−0.524294	+	1.02898i	−0.989602	+	0.143836i	$0.954056\pi$
$620$	0.977338	−	1.70583i	0.0392508	−	0.0685079i
$621$	11.6485	+	3.78483i	0.467438	+	0.151880i
$622$	28.2559	+	9.18090i	1.13296	+	0.368120i
$623$	0.164361	−	1.03773i	0.00658497	−	0.0415759i
$624$	2.65584	−	10.0402i	0.106319	−	0.401929i
$625$	12.2118	−	21.8145i	0.488473	−	0.872579i
$626$	−13.2861	−	13.2861i	−0.531018	−	0.531018i
$627$	−4.73076	+	29.8688i	−0.188928	+	1.19285i
$628$	−8.64352	−	16.9639i	−0.344914	−	0.676932i
$629$	4.22727	+	8.29648i	0.168552	+	0.330802i
$630$	−2.92234	−	10.7635i	−0.116429	−	0.428827i
$631$	−12.5618	−	6.40054i	−0.500076	−	0.254801i	0.185710	−	0.982605i	$-0.440541\pi$
$631$	−12.5618	−	6.40054i	−0.500076	−	0.254801i	−0.685786	+	0.727803i	$0.740541\pi$
$632$			1.30335i			0.0518447i
$633$	29.3628	−	57.6277i	1.16707	−	2.29050i
$634$	−23.9568	−	17.4057i	−0.951448	−	0.691267i
$635$	−5.12265	−	47.2322i	−0.203286	−	1.87435i
$636$	−2.14838	−	2.95699i	−0.0851889	−	0.117252i
$637$	−2.23381	+	21.9282i	−0.0885067	+	0.868828i
$638$	0.932475	+	5.88741i	0.0369170	+	0.233085i
$639$	−6.96332	+	43.9647i	−0.275465	+	1.73922i
$640$	2.23338	+	0.109624i	0.0882821	+	0.00433327i
$641$	19.9720	−	27.4892i	0.788848	−	1.08576i	−0.205402	−	0.978678i	$-0.565850\pi$
$641$	19.9720	−	27.4892i	0.788848	−	1.08576i	0.994251	−	0.107079i	$-0.0341497\pi$
$642$	−16.7900	−	51.6743i	−0.662649	−	2.03942i
$643$			23.9322i			0.943792i	0.881654	+	0.471896i	$0.156430\pi$
$643$			23.9322i			0.943792i	−0.881654	+	0.471896i	$0.843570\pi$
$644$	−0.791443	+	1.55329i	−0.0311872	+	0.0612083i
$645$	52.7685	+	2.59011i	2.07776	+	0.101986i
$646$	−8.87283	+	27.3078i	−0.349097	+	1.07441i
$647$	−30.4048	+	15.4920i	−1.19534	+	0.609054i	−0.934374	−	0.356294i	$-0.884040\pi$
$647$	−30.4048	+	15.4920i	−1.19534	+	0.609054i	−0.260963	+	0.965349i	$0.584040\pi$
$648$	2.56131	−	1.86090i	0.100618	−	0.0731031i
$649$	19.4612			0.763918
$650$	15.7004	+	8.85997i	0.615818	+	0.347516i
$651$	2.38476			0.0934660
$652$	−17.6849	+	12.8488i	−0.692593	+	0.503198i
$653$	5.04920	−	2.57270i	0.197590	−	0.100677i	−0.352396	−	0.935851i	$-0.614633\pi$
$653$	5.04920	−	2.57270i	0.197590	−	0.100677i	0.549986	+	0.835174i	$0.314633\pi$
$654$	−5.71401	+	17.5859i	−0.223435	+	0.687663i
$655$	27.7399	−	18.1455i	1.08389	−	0.709005i
$656$	−3.68011	+	7.22261i	−0.143684	+	0.281996i
$657$		−	1.10851i		−	0.0432473i
$658$	1.99618	+	6.14362i	0.0778193	+	0.239503i
$659$	−23.4277	+	32.2455i	−0.912616	+	1.25611i	0.0536500	+	0.998560i	$0.482914\pi$
$659$	−23.4277	+	32.2455i	−0.912616	+	1.25611i	−0.966266	+	0.257548i	$0.917086\pi$
$660$	3.38129	+	12.4539i	0.131616	+	0.484765i
$661$	0.178243	−	1.12538i	0.00693285	−	0.0437723i	−0.983979	−	0.178282i	$-0.942946\pi$
$661$	0.178243	−	1.12538i	0.00693285	−	0.0437723i	0.990912	+	0.134510i	$0.0429460\pi$
$662$	−1.74712	−	11.0309i	−0.0679036	−	0.428726i
$663$	56.6149	+	5.76731i	2.19874	+	0.223984i
$664$	3.11177	+	4.28298i	0.120760	+	0.166212i
$665$	−10.8000	−	2.25822i	−0.418805	−	0.0875698i
$666$	−7.28186	−	5.29058i	−0.282166	−	0.205006i
$667$	2.50047	−	4.90745i	0.0968187	−	0.190017i
$668$			16.6821i			0.645449i
$669$	34.4401	+	17.5481i	1.33153	+	0.678449i
$670$	−3.56091	+	9.36920i	−0.137570	+	0.361964i
$671$	−3.32571	−	6.52707i	−0.128387	−	0.251975i
$672$	1.23140	+	2.41675i	0.0475022	+	0.0932283i
$673$	−6.64906	+	41.9805i	−0.256302	+	1.61823i	0.438295	+	0.898831i	$0.355583\pi$
$673$	−6.64906	+	41.9805i	−0.256302	+	1.61823i	−0.694597	+	0.719399i	$0.744417\pi$
$674$	−7.99914	−	7.99914i	−0.308115	−	0.308115i
$675$	12.0590	+	30.8029i	0.464152	+	1.18560i
$676$	−6.42779	+	11.2997i	−0.247223	+	0.434604i
$677$	2.27839	−	14.3852i	0.0875658	−	0.552868i	−0.904432	−	0.426617i	$-0.859705\pi$
$677$	2.27839	−	14.3852i	0.0875658	−	0.552868i	0.991998	−	0.126252i	$-0.0402947\pi$
$678$	−44.6496	−	14.5075i	−1.71476	−	0.557158i
$679$	−8.78282	−	2.85371i	−0.337054	−	0.109515i
$680$	1.32114	+	12.1812i	0.0506632	+	0.467128i
$681$	−24.7030	+	48.4824i	−0.946621	+	1.85785i
$682$	−1.76157			−0.0674540
$683$	7.45137	+	22.9330i	0.285119	+	0.877505i	0.986363	+	0.164584i	$0.0526282\pi$
$683$	7.45137	+	22.9330i	0.285119	+	0.877505i	−0.701244	+	0.712921i	$0.747372\pi$
$684$	−4.34194	−	27.4139i	−0.166018	−	1.04820i
$685$	−25.9920	−	9.87865i	−0.993102	−	0.377444i
$686$	−7.25813	−	9.98996i	−0.277117	−	0.381419i
$687$	−44.6432	+	61.4461i	−1.70324	+	2.34432i
$688$	−8.10170	+	1.28318i	−0.308874	+	0.0489209i
$689$	1.65326	+	4.26603i	0.0629842	+	0.162523i
$690$	4.23622	−	11.1460i	0.161270	−	0.424322i
$691$	1.15532	+	7.29441i	0.0439505	+	0.277492i	0.999870	−	0.0161371i	$-0.00513683\pi$
$691$	1.15532	+	7.29441i	0.0439505	+	0.277492i	−0.955919	+	0.293629i	$0.905137\pi$
$692$	12.7820	+	6.51274i	0.485898	+	0.247577i
$693$	−7.06649	+	7.06649i	−0.268434	+	0.268434i
$694$	−12.5277	−	6.38316i	−0.475543	−	0.242301i
$695$	9.78954	−	12.1714i	0.371339	−	0.461686i
$696$	−3.89046	−	7.63545i	−0.147467	−	0.289421i
$697$	−42.2440	−	13.7259i	−1.60010	−	0.519905i
$698$	5.98654	+	0.948175i	0.226594	+	0.0358890i
$699$	−2.66479			−0.100791
$700$	−4.59883	+	1.00942i	−0.173820	+	0.0381526i
$701$		−	21.9211i		−	0.827949i	−0.910288	−	0.413975i	$-0.864140\pi$
$701$		−	21.9211i		−	0.827949i	0.910288	−	0.413975i	$-0.135860\pi$
$702$	−22.2420	+	8.61968i	−0.839469	+	0.325329i
$703$	−7.93385	+	4.04250i	−0.299231	+	0.152466i
$704$	−0.909607	−	1.78520i	−0.0342821	−	0.0672824i
$705$	−18.1049	−	40.3042i	−0.681870	−	1.51794i
$706$	21.4552	−	6.97122i	0.807477	−	0.262365i
$707$	17.6588			0.664128
$708$	−26.6088	+	8.64571i	−1.00002	+	0.324926i
$709$	5.04656	+	31.8627i	0.189527	+	1.19663i	0.880606	+	0.473849i	$0.157136\pi$
$709$	5.04656	+	31.8627i	0.189527	+	1.19663i	−0.691079	+	0.722780i	$0.742864\pi$
$710$	18.3933	+	3.84594i	0.690290	+	0.144336i
$711$	5.58517	−	4.05787i	0.209460	−	0.152182i
$712$	−0.174543	−	1.10202i	−0.00654128	−	0.0413000i
$713$	1.31682	+	0.956729i	0.0493155	+	0.0358298i
$714$	−12.0241	+	8.73605i	−0.449992	+	0.326938i
$715$	−0.105250	−	16.1530i	−0.00393614	−	0.604090i
$716$	−17.5836	−	12.7753i	−0.657131	−	0.477434i
$717$	−1.74656	−	5.37537i	−0.0652266	−	0.200747i
$718$	2.87093	+	2.87093i	0.107142	+	0.107142i
$719$	5.36436	+	16.5098i	0.200057	+	0.615712i	0.999880	+	0.0154764i	$0.00492648\pi$
$719$	5.36436	+	16.5098i	0.200057	+	0.615712i	−0.799823	+	0.600236i	$0.795074\pi$
$720$	−6.48364	−	9.91185i	−0.241631	−	0.369393i
$721$	−1.67889	+	0.855435i	−0.0625250	+	0.0318581i
$722$	−8.04409	−	2.61368i	−0.299370	−	0.0972713i
$723$	23.2005	−	16.8562i	0.862836	−	0.626887i
$724$			23.3121i			0.866388i
$725$	14.5295	−	3.18916i	0.539611	−	0.118442i
$726$	−14.2282	+	14.2282i	−0.528057	+	0.528057i
$727$	−7.56534	−	1.19823i	−0.280583	−	0.0444400i	0.0145570	−	0.999894i	$-0.495366\pi$
$727$	−7.56534	−	1.19823i	−0.280583	−	0.0444400i	−0.295140	+	0.955454i	$0.595366\pi$
$728$	−0.716531	−	3.31874i	−0.0265564	−	0.123001i
$729$	38.4225	+	12.4842i	1.42306	+	0.462379i
$730$	−0.467399	−	0.0229420i	−0.0172992	−	0.000849121i
$731$	−13.8894	−	42.7472i	−0.513718	−	1.58106i
$732$	7.44683	+	7.44683i	0.275243	+	0.275243i
$733$	−43.8855	+	14.2593i	−1.62095	+	0.526678i	−0.972165	−	0.234296i	$-0.924721\pi$
$733$	−43.8855	+	14.2593i	−1.62095	+	0.526678i	−0.648782	+	0.760974i	$0.724721\pi$
$734$	−27.3083	+	4.32521i	−1.00797	+	0.159646i
$735$	26.4435	+	29.1735i	0.975384	+	1.07608i
$736$	−0.289608	+	1.82851i	−0.0106751	+	0.0673998i
$737$	8.87039	−	1.40493i	0.326745	−	0.0517513i
$738$	42.4082	−	6.71680i	1.56107	−	0.247249i
$739$	−0.761439	−	0.120600i	−0.0280100	−	0.00443635i	0.142414	−	0.989807i	$-0.454514\pi$
$739$	−0.761439	−	0.120600i	−0.0280100	−	0.00443635i	−0.170424	+	0.985371i	$0.554514\pi$
$740$	−2.38145	+	2.96086i	−0.0875438	+	0.108843i
$741$	−5.51523	+	54.1403i	−0.202607	+	1.98890i
$742$	−1.06466	−	0.542473i	−0.0390850	−	0.0199148i
$743$			10.0495i			0.368679i	0.982863	+	0.184339i	$0.0590146\pi$
$743$			10.0495i			0.368679i	−0.982863	+	0.184339i	$0.940985\pi$
$744$	2.40855	−	0.782585i	0.0883017	−	0.0286909i
$745$	32.1584	+	18.4248i	1.17819	+	0.675033i
$746$	−33.1244	+	16.8777i	−1.21277	+	0.617938i
$747$	8.66538	−	26.6693i	0.317050	−	0.975778i
$748$	8.88197	−	6.45313i	0.324757	−	0.235950i
$749$	−12.5601	−	12.5601i	−0.458935	−	0.458935i
$750$	30.5274	−	10.2557i	1.11470	−	0.374485i
$751$		−	10.2228i		−	0.373035i	−0.982452	−	0.186517i	$-0.940280\pi$
$751$		−	10.2228i		−	0.373035i	0.982452	−	0.186517i	$-0.0597200\pi$
$752$	4.03219	+	5.54984i	0.147039	+	0.202382i
$753$	20.3944	+	40.0262i	0.743212	+	1.45864i
$754$	2.26380	+	10.4852i	0.0824426	+	0.381848i
$755$	20.2793	+	11.6188i	0.738040	+	0.422852i
$756$	2.82832	−	5.55088i	0.102865	−	0.201884i
$757$	−1.92755	+	1.92755i	−0.0700580	+	0.0700580i	−0.741268	−	0.671210i	$-0.765775\pi$
$757$	−1.92755	+	1.92755i	−0.0700580	+	0.0700580i	0.671210	+	0.741268i	$0.265775\pi$
$758$	−20.8363	−	10.6166i	−0.756810	−	0.385614i
$759$	−10.5526	+	1.67137i	−0.383036	+	0.0606670i
$760$	−11.6488	+	1.26339i	−0.422546	+	0.0458280i
$761$	−3.62030	+	22.8577i	−0.131236	+	0.828591i	0.830980	+	0.556303i	$0.187780\pi$
$761$	−3.62030	+	22.8577i	−0.131236	+	0.828591i	−0.962216	+	0.272288i	$0.912220\pi$
$762$	35.9722	−	49.5115i	1.30314	−	1.79361i
$763$	0.945649	+	5.97059i	0.0342348	+	0.216150i
$764$	−0.772921	+	0.561560i	−0.0279633	+	0.0203165i
$765$	48.0861	−	43.5864i	1.73855	−	1.57587i
$766$	−18.9927	+	26.1412i	−0.686234	+	0.944520i
$767$	34.9674	−	1.94482i	1.26260	−	0.0702232i
$768$	2.03677	+	2.03677i	0.0734955	+	0.0734955i
$769$	−3.05494	−	1.55657i	−0.110164	−	0.0561314i	0.398040	−	0.917368i	$-0.369690\pi$
$769$	−3.05494	−	1.55657i	−0.110164	−	0.0561314i	−0.508204	+	0.861237i	$0.669690\pi$
$770$	2.83329	+	3.12579i	0.102105	+	0.112646i
$771$	3.44130	+	1.11815i	0.123935	+	0.0402691i
$772$	1.91395	−	5.89053i	0.0688845	−	0.212005i
$773$	−14.6201	−	20.1228i	−0.525847	−	0.723767i	0.460643	−	0.887585i	$-0.347619\pi$
$773$	−14.6201	−	20.1228i	−0.525847	−	0.723767i	−0.986490	+	0.163819i	$0.947619\pi$
$774$	30.7226	+	30.7226i	1.10430	+	1.10430i
$775$	0.259171	+	4.38841i	0.00930968	+	0.157636i
$776$	−9.80691			−0.352048
$777$	−4.55239	−	0.721028i	−0.163316	−	0.0258667i
$778$	−1.49336	+	4.59608i	−0.0535394	+	0.164777i
$779$	13.1260	−	40.3975i	0.470286	−	1.44739i
$780$	7.31997	+	22.0389i	0.262097	+	0.789119i
$781$	−5.20304	−	16.0133i	−0.186179	−	0.573001i
$782$	−10.1443			−0.362760
$783$	−8.93574	+	17.5374i	−0.319337	+	0.626735i
$784$	−4.94574	−	3.59329i	−0.176634	−	0.128332i
$785$	36.9392	+	21.1639i	1.31842	+	0.755372i
$786$	42.1739	+	6.67968i	1.50429	+	0.238256i
$787$	−12.4484	+	17.1338i	−0.443739	+	0.610754i	−0.971038	−	0.238925i	$-0.923205\pi$
$787$	−12.4484	+	17.1338i	−0.443739	+	0.610754i	0.527299	+	0.849680i	$0.323205\pi$
$788$	4.05740	+	2.94788i	0.144539	+	0.105014i
$789$	−42.3301	−	58.2624i	−1.50699	−	2.07420i
$790$	−1.59538	−	2.43894i	−0.0567612	−	0.0867735i
$791$	−15.1590	+	2.40095i	−0.538991	+	0.0853678i
$792$	−4.81804	+	9.45593i	−0.171201	+	0.336002i
$793$	−6.62782	−	11.3953i	−0.235361	−	0.404660i
$794$	−2.80522	+	0.911471i	−0.0995535	+	0.0323469i
$795$	7.63975	+	2.90361i	0.270954	+	0.102980i
$796$	5.67978	−	17.4806i	0.201314	−	0.619582i
$797$	5.93924	−	3.02619i	0.210379	−	0.107193i	−0.345626	−	0.938372i	$-0.612334\pi$
$797$	5.93924	−	3.02619i	0.210379	−	0.107193i	0.556005	+	0.831179i	$0.312334\pi$
$798$	−8.35420	−	11.4986i	−0.295736	−	0.407045i
$799$	−26.5798	+	26.5798i	−0.940327	+	0.940327i
$800$	−4.31346	+	2.52865i	−0.152504	+	0.0894014i
$801$	−4.17899	+	4.17899i	−0.147657	+	0.147657i
$802$	0.924586	−	5.83760i	0.0326483	−	0.206133i
$803$	0.190361	+	0.373605i	0.00671770	+	0.0131842i
$804$	−11.5041	+	5.86164i	−0.405719	+	0.206724i
$805$	−0.420315	−	3.87542i	−0.0148142	−	0.136590i
$806$	−3.16515	+	0.176039i	−0.111488	+	0.00620072i
$807$	−44.3734	+	44.3734i	−1.56202	+	1.56202i
$808$	17.8350	−	5.79494i	0.627433	−	0.203865i
$809$	4.04765	−	5.57111i	0.142308	−	0.195870i	−0.731914	−	0.681397i	$-0.761373\pi$
$809$	4.04765	−	5.57111i	0.142308	−	0.195870i	0.874221	+	0.485528i	$0.161373\pi$
$810$	−2.51507	+	6.61746i	−0.0883705	+	0.232514i
$811$	−43.6313	−	6.91052i	−1.53210	−	0.242661i	−0.667306	−	0.744784i	$-0.732552\pi$
$811$	−43.6313	−	6.91052i	−1.53210	−	0.242661i	−0.864796	+	0.502123i	$0.832552\pi$
$812$	−2.26647	−	1.64669i	−0.0795376	−	0.0577875i
$813$	27.7101	+	20.1326i	0.971837	+	0.706081i
$814$	3.36275	+	0.532608i	0.117864	+	0.0186679i
$815$	17.3656	−	45.6910i	0.608290	−	1.60049i
$816$	−9.27726	+	12.7691i	−0.324769	+	0.447006i
$817$	40.8787	−	13.2823i	1.43017	−	0.464689i
$818$	−18.2385	+	18.2385i	−0.637696	+	0.637696i
$819$	−11.9907	+	13.4031i	−0.418990	+	0.468341i
$820$	−1.95441	−	18.0202i	−0.0682510	−	0.629292i
$821$	−50.1353	+	25.5452i	−1.74974	+	0.891535i	−0.788852	+	0.614584i	$0.789324\pi$
$821$	−50.1353	+	25.5452i	−1.74974	+	0.891535i	−0.960884	+	0.276951i	$0.910676\pi$
$822$	−16.2613	−	31.9146i	−0.567178	−	1.11315i
$823$	−3.71738	+	23.4706i	−0.129580	+	0.818135i	0.834205	+	0.551454i	$0.185927\pi$
$823$	−3.71738	+	23.4706i	−0.129580	+	0.818135i	−0.963785	+	0.266681i	$0.914073\pi$
$824$	−1.41491	+	1.41491i	−0.0492909	+	0.0492909i
$825$	−21.5716	−	19.1657i	−0.751026	−	0.667264i
$826$	−6.46758	+	6.46758i	−0.225036	+	0.225036i
$827$	−12.0924	−	16.6437i	−0.420493	−	0.578759i	0.545245	−	0.838277i	$-0.316437\pi$
$827$	−12.0924	−	16.6437i	−0.420493	−	0.578759i	−0.965738	+	0.259517i	$0.916437\pi$
$828$	8.73725	−	4.45185i	0.303640	−	0.154713i
$829$	−1.32825	+	4.08794i	−0.0461321	+	0.141980i	−0.971469	−	0.237165i	$-0.923782\pi$
$829$	−1.32825	+	4.08794i	−0.0461321	+	0.141980i	0.925337	+	0.379145i	$0.123782\pi$
$830$	−11.0656	−	4.20566i	−0.384093	−	0.145981i
$831$	35.4139	−	11.5067i	1.22849	−	0.399162i
$832$	−1.81276	−	3.11671i	−0.0628462	−	0.108053i
$833$	15.2078	−	29.8469i	0.526918	−	1.03413i
$834$	19.8731	−	3.14759i	0.688149	−	0.108992i
$835$	−20.4199	−	31.2168i	−0.706659	−	1.08030i
$836$	6.17107	+	8.49375i	0.213431	+	0.293763i
$837$	−4.70583	−	3.41899i	−0.162657	−	0.118177i
$838$	−7.94939	+	10.9414i	−0.274607	+	0.377964i
$839$	−47.2059	−	7.47668i	−1.62973	−	0.258124i	−0.726463	−	0.687206i	$-0.758837\pi$
$839$	−47.2059	−	7.47668i	−1.62973	−	0.258124i	−0.903266	+	0.429082i	$0.858837\pi$
$840$	−5.26254	−	3.01511i	−0.181575	−	0.104031i
$841$	−16.3008	−	11.8432i	−0.562098	−	0.408388i
$842$	1.02121	−	2.00424i	0.0351933	−	0.0690708i
$843$	−19.7152			−0.679027
$844$	−6.93868	−	21.3551i	−0.238839	−	0.735071i
$845$	−1.80334	−	29.0129i	−0.0620367	−	0.998074i
$846$	11.2285	−	34.5577i	0.386043	−	1.18812i
$847$	−2.03276	+	6.25618i	−0.0698463	+	0.214965i
$848$	−1.25330	−	0.198504i	−0.0430386	−	0.00681665i
$849$	−61.7270			−2.11847
$850$	−17.3827	−	21.1773i	−0.596223	−	0.726374i
$851$	−2.22449	−	2.22449i	−0.0762546	−	0.0762546i
$852$	14.2280	+	19.5831i	0.487442	+	0.670906i
$853$	12.0423	−	37.0625i	0.412322	−	1.26900i	−0.502302	−	0.864692i	$-0.667514\pi$
$853$	12.0423	−	37.0625i	0.412322	−	1.26900i	0.914624	−	0.404305i	$-0.132486\pi$
$854$	3.27440	+	1.06392i	0.112048	+	0.0364065i
$855$	41.6813	+	45.9843i	1.42547	+	1.57263i
$856$	−16.8071	−	8.56365i	−0.574455	−	0.292700i
$857$	7.18900	+	7.18900i	0.245572	+	0.245572i	0.819150	−	0.573579i	$-0.194445\pi$
$857$	7.18900	+	7.18900i	0.245572	+	0.245572i	−0.573579	+	0.819150i	$0.694445\pi$
$858$	13.8738	−	15.5080i	0.473645	−	0.529435i
$859$	3.15618	−	4.34410i	0.107687	−	0.148219i	−0.751772	−	0.659423i	$-0.770800\pi$
$859$	3.15618	−	4.34410i	0.107687	−	0.148219i	0.859459	+	0.511204i	$0.170800\pi$
$860$	13.5898	−	12.3182i	0.463409	−	0.420045i
$861$	17.7878	−	12.9236i	0.606207	−	0.440435i
$862$	5.14735	+	32.4991i	0.175319	+	1.10692i
$863$	19.1892	−	26.4116i	0.653207	−	0.899062i	−0.346026	−	0.938225i	$-0.612469\pi$
$863$	19.1892	−	26.4116i	0.653207	−	0.899062i	0.999233	+	0.0391626i	$0.0124690\pi$
$864$	1.03495	−	6.53440i	0.0352096	−	0.222305i
$865$	−31.8906	+	3.45876i	−1.08431	+	0.117601i
$866$	−6.15340	+	0.974603i	−0.209101	+	0.0331184i
$867$	−33.4295	−	17.0332i	−1.13533	−	0.578477i
$868$	0.585427	−	0.585427i	0.0198707	−	0.0198707i
$869$	−1.18554	+	2.32675i	−0.0402167	+	0.0789297i
$870$	16.6264	+	9.52590i	0.563687	+	0.322958i
$871$	15.7977	−	3.41080i	0.535285	−	0.115570i
$872$	2.91440	+	5.71983i	0.0986940	+	0.193698i
$873$	30.5329	+	42.0249i	1.03338	+	1.42233i
$874$		−	9.70091i		−	0.328138i
$875$	7.37010	−	7.51816i	0.249155	−	0.254160i
$876$	−0.426252	−	0.426252i	−0.0144017	−	0.0144017i
$877$	−18.8500	+	13.6953i	−0.636519	+	0.462458i	−0.858652	−	0.512558i	$-0.828698\pi$
$877$	−18.8500	+	13.6953i	−0.636519	+	0.462458i	0.222134	+	0.975016i	$0.428698\pi$
$878$	4.78961	−	14.7409i	0.161641	−	0.497481i
$879$	23.1831	−	11.8124i	0.781945	−	0.398421i
$880$	3.88732	+	2.22720i	0.131042	+	0.0750788i
$881$	50.7647	−	16.4945i	1.71031	−	0.555712i	0.719922	−	0.694054i	$-0.244177\pi$
$881$	50.7647	−	16.4945i	1.71031	−	0.555712i	0.990385	+	0.138342i	$0.0441773\pi$
$882$			32.3810i			1.09032i
$883$	1.11013	+	0.565640i	0.0373589	+	0.0190353i	0.472570	−	0.881293i	$-0.343326\pi$
$883$	1.11013	+	0.565640i	0.0373589	+	0.0190353i	−0.435211	+	0.900328i	$0.643326\pi$
$884$	15.3140	−	12.4824i	0.515067	−	0.419830i
$885$	39.2095	−	48.7492i	1.31801	−	1.63869i
$886$	29.8921	+	4.73444i	1.00424	+	0.159057i
$887$	0.413680	−	0.0655204i	0.0138900	−	0.00219996i	−0.149486	−	0.988764i	$-0.547762\pi$
$887$	0.413680	−	0.0655204i	0.0138900	−	0.00219996i	0.163376	+	0.986564i	$0.447762\pi$
$888$	−4.83442	+	0.765697i	−0.162232	+	0.0256951i
$889$	3.12982	−	19.7609i	0.104971	−	0.662760i
$890$	1.67556	+	1.84854i	0.0561648	+	0.0619631i
$891$	6.26515	−	0.992302i	0.209890	−	0.0332434i
$892$	12.7624	−	4.14677i	0.427318	−	0.138844i
$893$	−25.4181	−	25.4181i	−0.850583	−	0.850583i
$894$	14.7533	+	45.4061i	0.493425	+	1.51861i
$895$	48.5415	+	2.38263i	1.62256	+	0.0796426i
$896$	0.895574	+	0.290990i	0.0299190	+	0.00972128i
$897$	−18.7937	+	4.05764i	−0.627503	+	0.135481i
$898$	−25.2566	−	4.00025i	−0.842823	−	0.133490i
$899$	−1.84959	+	1.84959i	−0.0616873	+	0.0616873i
$900$	24.2654	+	10.6114i	0.808846	+	0.353715i
$901$		−	6.95314i		−	0.231643i
$902$	−13.1395	+	9.54639i	−0.437497	+	0.317860i
$903$	21.1599	+	6.87527i	0.704158	+	0.228795i
$904$	−14.5223	+	7.39949i	−0.483005	+	0.246103i
$905$	−28.5354	−	43.6235i	−0.948550	−	1.45009i
$906$	9.30354	+	28.6334i	0.309090	+	0.951280i
$907$	14.8265	+	14.8265i	0.492304	+	0.492304i	0.909032	−	0.416727i	$-0.136823\pi$
$907$	14.8265	+	14.8265i	0.492304	+	0.492304i	−0.416727	+	0.909032i	$0.636823\pi$
$908$	5.83753	+	17.9661i	0.193725	+	0.596225i
$909$	−80.3601	−	58.3851i	−2.66538	−	1.93651i
$910$	5.40317	+	5.33321i	0.179113	+	0.176794i
$911$	4.48496	−	3.25851i	0.148593	−	0.107959i	−0.511005	−	0.859578i	$-0.670727\pi$
$911$	4.48496	−	3.25851i	0.148593	−	0.107959i	0.659598	+	0.751619i	$0.270727\pi$
$912$	−12.2109	−	8.87176i	−0.404344	−	0.293773i
$913$	1.65931	+	10.4765i	0.0549152	+	0.346721i
$914$	26.0548	−	18.9299i	0.861817	−	0.626147i
$915$	−23.0504	−	4.81972i	−0.762024	−	0.159335i
$916$	4.12490	+	26.0436i	0.136290	+	0.860504i
$917$	13.2760	−	4.31365i	0.438414	−	0.142449i
$918$	36.2519			1.19649
$919$	−19.2498	+	6.25464i	−0.634992	+	0.206322i	−0.608785	−	0.793335i	$-0.708343\pi$
$919$	−19.2498	+	6.25464i	−0.634992	+	0.206322i	−0.0262071	+	0.999657i	$0.508343\pi$
$920$	−1.69627	−	3.77615i	−0.0559244	−	0.124496i
$921$	−16.8911	−	33.1506i	−0.556580	−	1.09235i
$922$	−2.08217	+	1.06092i	−0.0685727	+	0.0349395i
$923$	−10.9490	−	28.2524i	−0.360389	−	0.929938i
$924$			5.43448i			0.178781i
$925$	0.832083	−	8.45562i	0.0273587	−	0.278019i
$926$	−13.9235			−0.457554
$927$	10.4684	+	1.65804i	0.343828	+	0.0544571i
$928$	−2.82946	−	0.919348i	−0.0928817	−	0.0301791i
$929$	−11.2956	−	22.1689i	−0.370598	−	0.727339i	0.628112	−	0.778123i	$-0.283828\pi$
$929$	−11.2956	−	22.1689i	−0.370598	−	0.727339i	−0.998710	+	0.0507838i	$0.983828\pi$
$930$	−3.54913	+	4.41264i	−0.116381	+	0.144696i
$931$	28.5423	+	14.5430i	0.935437	+	0.476629i
$932$	−0.654171	+	0.654171i	−0.0214281	+	0.0214281i
$933$	−76.2500	−	38.8513i	−2.49631	−	1.27194i
$934$	2.56183	+	16.1747i	0.0838255	+	0.529253i
$935$	−8.72162	+	22.9477i	−0.285227	+	0.750469i
$936$	−7.71197	+	17.4717i	−0.252074	+	0.571080i
$937$	−3.88462	+	0.615263i	−0.126905	+	0.0200998i	−0.219564	−	0.975598i	$-0.570463\pi$
$937$	−3.88462	+	0.615263i	−0.126905	+	0.0200998i	0.0926588	+	0.995698i	$0.470463\pi$
$938$	−2.48102	+	3.41483i	−0.0810081	+	0.111498i
$939$	31.8117	+	43.7850i	1.03813	+	1.42887i
$940$	−14.3387	−	5.44964i	−0.467676	−	0.177748i
$941$	1.87652	+	11.8479i	0.0611727	+	0.386229i	0.999212	+	0.0396993i	$0.0126400\pi$
$941$	1.87652	+	11.8479i	0.0611727	+	0.386229i	−0.938039	+	0.346530i	$0.887360\pi$
$942$	16.9466	+	52.1563i	0.552150	+	1.69934i
$943$	15.0069			0.488692
$944$	−4.40970	+	8.65452i	−0.143523	+	0.281681i
$945$	1.50205	+	13.8493i	0.0488616	+	0.450517i
$946$	−15.6304	−	5.07862i	−0.508187	−	0.165120i
$947$	−28.9873	−	9.41855i	−0.941961	−	0.306062i	−0.202516	−	0.979279i	$-0.564912\pi$
$947$	−28.9873	−	9.41855i	−0.941961	−	0.306062i	−0.739445	+	0.673217i	$0.764912\pi$
$948$	0.587288	−	3.70799i	0.0190742	−	0.120430i
$949$	0.379372	+	0.652261i	0.0123149	+	0.0211733i
$950$	20.2516	−	16.6230i	0.657050	−	0.539320i
$951$	60.3133	+	60.3133i	1.95579	+	1.95579i
$952$	−0.807184	+	5.09636i	−0.0261610	+	0.165174i
$953$	18.8505	+	36.9962i	0.610627	+	1.19842i	0.964736	+	0.263219i	$0.0847843\pi$
$953$	18.8505	+	36.9962i	0.610627	+	1.19842i	−0.354109	+	0.935204i	$0.615216\pi$
$954$	3.05140	+	5.98872i	0.0987928	+	0.193892i
$955$	0.758967	−	1.99694i	0.0245596	−	0.0646193i
$956$	−1.74834	−	0.890825i	−0.0565455	−	0.0288114i
$957$		−	17.1696i		−	0.555015i
$958$	−8.07158	+	15.8414i	−0.260781	+	0.511811i
$959$	−9.47339	−	6.88282i	−0.305912	−	0.222258i
$960$	−6.30448	−	1.31823i	−0.203476	−	0.0425457i
$961$	17.7670	+	24.4541i	0.573128	+	0.788843i
$962$	6.09534	+	0.620927i	0.196522	+	0.0200195i
$963$	15.6301	+	98.6844i	0.503672	+	3.18006i
$964$	1.55746	−	9.83340i	0.0501623	−	0.316712i
$965$	3.62883	+	13.3656i	0.116816	+	0.430254i
$966$	2.95153	−	4.06244i	0.0949640	−	0.130707i
$967$	−1.35951	−	4.18415i	−0.0437190	−	0.134553i	0.926815	−	0.375519i	$-0.122536\pi$
$967$	−1.35951	−	4.18415i	−0.0437190	−	0.134553i	−0.970533	+	0.240966i	$0.922536\pi$
$968$			6.98566i			0.224528i
$969$	37.5476	−	73.6914i	1.20620	−	2.36731i
$970$	18.3515	−	12.0042i	0.589230	−	0.385433i
$971$	−9.44527	+	29.0696i	−0.303113	+	0.932887i	0.677261	+	0.735743i	$0.263167\pi$
$971$	−9.44527	+	29.0696i	−0.303113	+	0.932887i	−0.980375	+	0.197144i	$0.936833\pi$
$972$	9.55897	−	4.87054i	0.306604	−	0.156223i
$973$	5.32160	−	3.86637i	0.170603	−	0.123950i
$974$	17.3820			0.556954
$975$	−40.6746	−	32.2808i	−1.30263	−	1.03381i
$976$	3.65620			0.117032
$977$	−41.8640	+	30.4160i	−1.33935	+	0.973094i	−0.339881	+	0.940468i	$0.610387\pi$
$977$	−41.8640	+	30.4160i	−1.33935	+	0.973094i	−0.999468	+	0.0326252i	$0.989613\pi$
$978$	56.1024	−	28.5856i	1.79396	−	0.914066i
$979$	0.690811	−	2.12610i	0.0220784	−	0.0679504i
$980$	13.6533	+	0.670162i	0.436137	+	0.0214075i
$981$	15.4371	−	30.2970i	0.492868	−	0.967308i
$982$		−	27.1008i		−	0.864823i
$983$	2.11981	+	6.52409i	0.0676113	+	0.208086i	0.979154	−	0.203119i	$-0.0651079\pi$
$983$	2.11981	+	6.52409i	0.0676113	+	0.208086i	−0.911543	+	0.411205i	$0.865108\pi$
$984$	13.7242	−	18.8898i	0.437513	−	0.602185i
$985$	−11.2009	−	0.549790i	−0.356890	−	0.0175178i
$986$	2.55020	−	16.1014i	0.0812151	−	0.512772i
$987$	−2.91076	−	18.3778i	−0.0926505	−	0.584972i
$988$	11.9368	+	14.6447i	0.379762	+	0.465909i
$989$	8.92591	+	12.2855i	0.283827	+	0.390655i
$990$	−2.55874	−	23.5922i	−0.0813221	−	0.749810i
$991$	21.8668	+	15.8871i	0.694620	+	0.504671i	0.878176	−	0.478338i	$-0.158761\pi$
$991$	21.8668	+	15.8871i	0.694620	+	0.504671i	−0.183555	+	0.983009i	$0.558761\pi$
$992$	0.399153	−	0.783382i	0.0126731	−	0.0248724i
$993$			32.1696i			1.02087i
$994$	7.05089	+	3.59261i	0.223641	+	0.113951i
$995$	10.7688	+	39.6634i	0.341394	+	1.25741i
$996$	−6.92296	−	13.5871i	−0.219362	−	0.430523i
$997$	2.93589	+	5.76202i	0.0929807	+	0.182485i	0.932813	−	0.360361i	$-0.117347\pi$
$997$	2.93589	+	5.76202i	0.0929807	+	0.182485i	−0.839832	+	0.542846i	$0.817347\pi$
$998$	−3.43347	+	21.6781i	−0.108685	+	0.686207i
$999$	7.94949	+	7.94949i	0.251511	+	0.251511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.ba.a.73.16	✓	136
13.5	odd	4		650.2.bd.a.473.16	yes	136
25.12	odd	20		650.2.bd.a.437.16	yes	136
325.187	even	20	inner	650.2.ba.a.187.16	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.a.73.16	✓	136	1.1	even	1	trivial
650.2.ba.a.187.16	yes	136	325.187	even	20	inner
650.2.bd.a.437.16	yes	136	25.12	odd	20
650.2.bd.a.473.16	yes	136	13.5	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.ba (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(2.56648 - 1.30768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.585893 + 2.15795i) q^{5} +(-1.30768 + 2.56648i) q^{6} +0.941662i q^{7} +(0.309017 + 0.951057i) q^{8} +(3.11340 - 4.28523i) q^{9} +(-1.74241 - 1.40144i) q^{10} +(-0.313429 + 1.97891i) q^{11} +(-0.450597 - 2.84496i) q^{12} +(-0.365403 + 3.58699i) q^{13} +(-0.553495 - 0.761821i) q^{14} +(4.32559 + 4.77215i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.48766 - 4.88231i) q^{17} +5.29683i q^{18} +(4.66891 + 2.37893i) q^{19} +(2.23338 + 0.109624i) q^{20} +(1.23140 + 2.41675i) q^{21} +(-0.909607 - 1.78520i) q^{22} +(-0.289608 + 1.82851i) q^{23} +(2.03677 + 2.03677i) q^{24} +(-4.31346 + 2.52865i) q^{25} +(-1.81276 - 3.11671i) q^{26} +(1.03495 - 6.53440i) q^{27} +(0.895574 + 0.290990i) q^{28} +(-2.82946 - 0.919348i) q^{29} +(-6.30448 - 1.31823i) q^{30} +(0.399153 - 0.783382i) q^{31} +1.00000 q^{32} +(1.78339 + 5.48870i) q^{33} +(0.857190 + 5.41209i) q^{34} +(-2.03206 + 0.551714i) q^{35} +(-3.11340 - 4.28523i) q^{36} +(-0.998819 + 1.37476i) q^{37} +(-5.17553 + 0.819723i) q^{38} +(3.75285 + 9.68375i) q^{39} +(-1.87128 + 1.22406i) q^{40} +(-1.26808 - 8.00633i) q^{41} +(-2.41675 - 1.23140i) q^{42} +(5.80017 - 5.80017i) q^{43} +(1.78520 + 0.909607i) q^{44} +(11.0714 + 4.20786i) q^{45} +(-0.840474 - 1.64952i) q^{46} +(-6.52422 - 2.11985i) q^{47} +(-2.84496 - 0.450597i) q^{48} +6.11327 q^{49} +(2.00336 - 4.58111i) q^{50} -15.7834i q^{51} +(3.29851 + 1.45596i) q^{52} +(1.13062 - 0.576081i) q^{53} +(3.00354 + 5.89477i) q^{54} +(-4.45402 + 0.483069i) q^{55} +(-0.895574 + 0.290990i) q^{56} +15.0935 q^{57} +(2.82946 - 0.919348i) q^{58} +(-1.51948 - 9.59361i) q^{59} +(5.87527 - 2.63921i) q^{60} +(-2.95793 + 2.14906i) q^{61} +(0.137539 + 0.868386i) q^{62} +(4.03524 + 2.93177i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.95461 + 1.31307i) q^{65} +(-4.66897 - 3.39220i) q^{66} +(-1.38515 - 4.26307i) q^{67} +(-3.87463 - 3.87463i) q^{68} +(1.64784 + 5.07154i) q^{69} +(1.31968 - 1.64076i) q^{70} +(-7.48770 + 3.81518i) q^{71} +(5.03759 + 1.63681i) q^{72} +(0.169310 - 0.123011i) q^{73} -1.69929i q^{74} +(-7.76370 + 12.1304i) q^{75} +(3.70527 - 3.70527i) q^{76} +(-1.86347 - 0.295144i) q^{77} +(-8.72808 - 5.62845i) q^{78} +(1.23956 + 0.402759i) q^{79} +(0.794411 - 2.09019i) q^{80} +(-0.978334 - 3.01100i) q^{81} +(5.73190 + 5.73190i) q^{82} +(5.03495 - 1.63595i) q^{83} +(2.67899 - 0.424311i) q^{84} +(11.9933 + 2.50773i) q^{85} +(-1.28318 + 8.10170i) q^{86} +(-8.46397 + 1.34056i) q^{87} +(-1.97891 + 0.313429i) q^{88} +(-1.10202 - 0.174543i) q^{89} +(-11.4303 + 3.10338i) q^{90} +(-3.37773 - 0.344086i) q^{91} +(1.64952 + 0.840474i) q^{92} -2.53250i q^{93} +(6.52422 - 2.11985i) q^{94} +(-2.39812 + 11.4691i) q^{95} +(2.56648 - 1.30768i) q^{96} +(-3.03050 + 9.32693i) q^{97} +(-4.94574 + 3.59329i) q^{98} +(7.50427 + 7.50427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 34 q^{2} - 34 q^{4} - 34 q^{8} + 20 q^{9} + 6 q^{13} + 32 q^{15} - 34 q^{16} + 4 q^{17} - 20 q^{19} + 6 q^{21} + 12 q^{23} - 14 q^{26} + 36 q^{27} + 20 q^{29} + 12 q^{30} + 6 q^{31} + 136 q^{32}+ \cdots - 40 q^{99}+O(q^{100}) \) 136 * q - 34 * q^2 - 34 * q^4 - 34 * q^8 + 20 * q^9 + 6 * q^13 + 32 * q^15 - 34 * q^16 + 4 * q^17 - 20 * q^19 + 6 * q^21 + 12 * q^23 - 14 * q^26 + 36 * q^27 + 20 * q^29 + 12 * q^30 + 6 * q^31 + 136 * q^32 - 54 * q^33 + 4 * q^34 - 52 * q^35 - 20 * q^36 + 30 * q^37 + 20 * q^39 + 18 * q^41 + 6 * q^42 - 12 * q^43 + 24 * q^45 - 28 * q^46 + 50 * q^47 - 120 * q^49 + 20 * q^50 + 6 * q^52 - 50 * q^53 + 6 * q^54 + 24 * q^55 - 28 * q^57 - 20 * q^58 + 16 * q^59 + 12 * q^60 - 12 * q^61 + 6 * q^62 - 70 * q^63 - 34 * q^64 - 140 * q^65 + 16 * q^66 - 8 * q^67 + 4 * q^68 - 26 * q^69 + 58 * q^70 - 72 * q^71 - 32 * q^73 + 192 * q^75 + 64 * q^77 - 50 * q^78 + 20 * q^79 - 54 * q^81 - 12 * q^82 + 70 * q^83 + 6 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^87 - 108 * q^89 + 44 * q^90 - 94 * q^91 + 12 * q^92 - 50 * q^94 + 110 * q^95 + 28 * q^97 + 50 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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Database

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