LMFDB - Embedded newform 768.2.z.a.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	768.157
Dual form			768.2.z.a.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37117 + 0.346269i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.76020 - 0.949585i) q^{4} +(0.359277 + 1.43432i) q^{5} +(0.783427 - 1.17739i) q^{6} +(2.14599 + 1.76117i) q^{7} +(-2.08471 + 1.91154i) q^{8} +(0.0980171 - 0.995185i) q^{9} +O(q^{10})$	\(q+(-1.37117 + 0.346269i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.76020 - 0.949585i) q^{4} +(0.359277 + 1.43432i) q^{5} +(0.783427 - 1.17739i) q^{6} +(2.14599 + 1.76117i) q^{7} +(-2.08471 + 1.91154i) q^{8} +(0.0980171 - 0.995185i) q^{9} +(-0.989289 - 1.84228i) q^{10} +(-2.92962 + 1.38561i) q^{11} +(-0.666516 + 1.88567i) q^{12} +(-1.91901 + 1.15021i) q^{13} +(-3.55234 - 1.67176i) q^{14} +(-1.22943 - 0.821482i) q^{15} +(2.19658 - 3.34291i) q^{16} +(-2.64206 + 1.76537i) q^{17} +(0.210204 + 1.39850i) q^{18} +(-1.15988 + 1.56392i) q^{19} +(1.99440 + 2.18351i) q^{20} +(-2.77280 + 0.136219i) q^{21} +(3.53720 - 2.91434i) q^{22} +(3.61766 - 1.09741i) q^{23} +(0.260955 - 2.81636i) q^{24} +(2.48142 - 1.32635i) q^{25} +(2.23300 - 2.24162i) q^{26} +(0.595699 + 0.803208i) q^{27} +(5.44973 + 1.06220i) q^{28} +(-3.19993 + 1.14495i) q^{29} +(1.97021 + 0.700673i) q^{30} +(1.75317 + 4.23252i) q^{31} +(-1.85432 + 5.34429i) q^{32} +(1.24019 - 2.99408i) q^{33} +(3.01141 - 3.33547i) q^{34} +(-1.75506 + 3.71077i) q^{35} +(-0.772483 - 1.84480i) q^{36} +(0.956568 - 6.44866i) q^{37} +(1.04885 - 2.54602i) q^{38} +(0.649458 - 2.14098i) q^{39} +(-3.49074 - 2.30336i) q^{40} +(-5.30615 - 2.83620i) q^{41} +(3.75480 - 1.14691i) q^{42} +(-5.15955 + 5.69268i) q^{43} +(-3.84095 + 5.22086i) q^{44} +(1.46262 - 0.216960i) q^{45} +(-4.58042 + 2.75741i) q^{46} +(-1.14740 + 5.76835i) q^{47} +(0.617407 + 3.95206i) q^{48} +(0.137922 + 0.693381i) q^{49} +(-2.94317 + 2.67789i) q^{50} +(0.772088 - 3.08235i) q^{51} +(-2.28561 + 3.84685i) q^{52} +(1.49186 + 0.533797i) q^{53} +(-1.09493 - 0.895059i) q^{54} +(-3.03995 - 3.70418i) q^{55} +(-7.84030 + 0.430623i) q^{56} +(-0.190848 - 1.93772i) q^{57} +(3.99118 - 2.67796i) q^{58} +(-3.43562 - 2.05923i) q^{59} +(-2.94411 - 0.278516i) q^{60} +(-6.70590 - 0.329440i) q^{61} +(-3.86947 - 5.19642i) q^{62} +(1.96303 - 1.96303i) q^{63} +(0.692023 - 7.97001i) q^{64} +(-2.33922 - 2.33922i) q^{65} +(-0.663748 + 4.53482i) q^{66} +(0.0170645 - 0.347357i) q^{67} +(-2.97417 + 5.61625i) q^{68} +(-1.94354 + 3.24260i) q^{69} +(1.12156 - 5.69581i) q^{70} +(3.61624 - 0.356169i) q^{71} +(1.69800 + 2.26203i) q^{72} +(-9.98821 + 8.19712i) q^{73} +(0.921357 + 9.17341i) q^{74} +(-0.947893 + 2.64918i) q^{75} +(-0.556543 + 3.85421i) q^{76} +(-8.72721 - 2.18605i) q^{77} +(-0.149161 + 3.16052i) q^{78} +(-3.58970 + 0.714035i) q^{79} +(5.58397 + 1.94955i) q^{80} +(-0.980785 - 0.195090i) q^{81} +(8.25770 + 2.05154i) q^{82} +(0.558008 + 3.76178i) q^{83} +(-4.75132 + 2.87278i) q^{84} +(-3.48133 - 3.15529i) q^{85} +(5.10340 - 9.59221i) q^{86} +(1.60209 - 2.99730i) q^{87} +(3.45876 - 8.48868i) q^{88} +(-12.2562 - 3.71786i) q^{89} +(-1.93038 + 0.803950i) q^{90} +(-6.14388 - 0.911358i) q^{91} +(5.32571 - 5.36692i) q^{92} +(-4.14139 - 1.95873i) q^{93} +(-0.424130 - 8.30668i) q^{94} +(-2.65987 - 1.10176i) q^{95} +(-2.21505 - 5.20515i) q^{96} +(14.6752 - 6.07866i) q^{97} +(-0.429211 - 0.902983i) q^{98} +(1.09178 + 3.05133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{64}\right)$

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 $

$2$	−1.37117	+	0.346269i	−0.969561	+	0.244849i
$2$	−1.37117	+	0.346269i	−0.969561	+	0.244849i
$3$	−0.740951	+	0.671559i	−0.427788	+	0.387725i
$3$	−0.740951	+	0.671559i	−0.427788	+	0.387725i
$4$	1.76020	−	0.949585i	0.880098	−	0.474793i
$5$	0.359277	+	1.43432i	0.160674	+	0.641446i	0.995814	+	0.0914079i	$0.0291367\pi$
$5$	0.359277	+	1.43432i	0.160674	+	0.641446i	−0.835140	+	0.550038i	$0.814613\pi$
$6$	0.783427	−	1.17739i	0.319833	−	0.480667i
$7$	2.14599	+	1.76117i	0.811107	+	0.665658i	0.945627	−	0.325253i	$-0.105449\pi$
$7$	2.14599	+	1.76117i	0.811107	+	0.665658i	−0.134520	+	0.990911i	$0.542949\pi$
$8$	−2.08471	+	1.91154i	−0.737056	+	0.675832i
$9$	0.0980171	−	0.995185i	0.0326724	−	0.331728i
$10$	−0.989289	−	1.84228i	−0.312841	−	0.582580i
$11$	−2.92962	+	1.38561i	−0.883314	+	0.417776i	−0.814711	−	0.579868i	$-0.803104\pi$
$11$	−2.92962	+	1.38561i	−0.883314	+	0.417776i	−0.0686031	+	0.997644i	$0.521854\pi$
$12$	−0.666516	+	1.88567i	−0.192407	+	0.544346i
$13$	−1.91901	+	1.15021i	−0.532237	+	0.319011i	−0.754851	−	0.655896i	$-0.772291\pi$
$13$	−1.91901	+	1.15021i	−0.532237	+	0.319011i	0.222614	+	0.974907i	$0.428541\pi$
$14$	−3.55234	−	1.67176i	−0.949404	−	0.446797i
$15$	−1.22943	−	0.821482i	−0.317439	−	0.212106i
$16$	2.19658	−	3.34291i	0.549144	−	0.835728i
$17$	−2.64206	+	1.76537i	−0.640793	+	0.428164i	−0.833063	−	0.553178i	$-0.813415\pi$
$17$	−2.64206	+	1.76537i	−0.640793	+	0.428164i	0.192270	+	0.981342i	$0.438415\pi$
$18$	0.210204	+	1.39850i	0.0495455	+	0.329631i
$19$	−1.15988	+	1.56392i	−0.266095	+	0.358788i	−0.915965	−	0.401258i	$-0.868573\pi$
$19$	−1.15988	+	1.56392i	−0.266095	+	0.358788i	0.649870	+	0.760045i	$0.274823\pi$
$20$	1.99440	+	2.18351i	0.445962	+	0.488248i
$21$	−2.77280	+	0.136219i	−0.605074	+	0.0297254i
$22$	3.53720	−	2.91434i	0.754134	−	0.621338i
$23$	3.61766	−	1.09741i	0.754334	−	0.228825i	0.110381	−	0.993889i	$-0.464793\pi$
$23$	3.61766	−	1.09741i	0.754334	−	0.228825i	0.643954	+	0.765065i	$0.277293\pi$
$24$	0.260955	−	2.81636i	0.0532672	−	0.574888i
$25$	2.48142	−	1.32635i	0.496285	−	0.265270i
$26$	2.23300	−	2.24162i	0.437927	−	0.439618i
$27$	0.595699	+	0.803208i	0.114642	+	0.154577i
$28$	5.44973	+	1.06220i	1.02990	+	0.200737i
$29$	−3.19993	+	1.14495i	−0.594212	+	0.212612i	−0.616784	−	0.787133i	$-0.711565\pi$
$29$	−3.19993	+	1.14495i	−0.594212	+	0.212612i	0.0225715	+	0.999745i	$0.492815\pi$
$30$	1.97021	+	0.700673i	0.359710	+	0.127925i
$31$	1.75317	+	4.23252i	0.314878	+	0.760182i	0.999510	+	0.0312938i	$0.00996275\pi$
$31$	1.75317	+	4.23252i	0.314878	+	0.760182i	−0.684632	+	0.728889i	$0.740037\pi$
$32$	−1.85432	+	5.34429i	−0.327801	+	0.944747i
$33$	1.24019	−	2.99408i	0.215889	−	0.521202i
$34$	3.01141	−	3.33547i	0.516452	−	0.572029i
$35$	−1.75506	+	3.71077i	−0.296660	+	0.627235i
$36$	−0.772483	−	1.84480i	−0.128747	−	0.307466i
$37$	0.956568	−	6.44866i	0.157259	−	1.06015i	−0.756529	−	0.653960i	$-0.773106\pi$
$37$	0.956568	−	6.44866i	0.157259	−	1.06015i	0.913788	−	0.406192i	$-0.133144\pi$
$38$	1.04885	−	2.54602i	0.170147	−	0.413020i
$39$	0.649458	−	2.14098i	0.103997	−	0.342831i
$40$	−3.49074	−	2.30336i	−0.551935	−	0.364193i
$41$	−5.30615	−	2.83620i	−0.828682	−	0.442940i	0.00179140	−	0.999998i	$-0.499430\pi$
$41$	−5.30615	−	2.83620i	−0.828682	−	0.442940i	−0.830473	+	0.557059i	$0.811930\pi$
$42$	3.75480	−	1.14691i	0.579378	−	0.176973i
$43$	−5.15955	+	5.69268i	−0.786823	+	0.868126i	−0.993910	−	0.110197i	$-0.964852\pi$
$43$	−5.15955	+	5.69268i	−0.786823	+	0.868126i	0.207086	+	0.978323i	$0.433602\pi$
$44$	−3.84095	+	5.22086i	−0.579045	+	0.787075i
$45$	1.46262	−	0.216960i	0.218035	−	0.0323425i
$46$	−4.58042	+	2.75741i	−0.675346	+	0.406558i
$47$	−1.14740	+	5.76835i	−0.167365	+	0.841400i	0.802292	+	0.596931i	$0.203614\pi$
$47$	−1.14740	+	5.76835i	−0.167365	+	0.841400i	−0.969657	+	0.244469i	$0.921386\pi$
$48$	0.617407	+	3.95206i	0.0891150	+	0.570431i
$49$	0.137922	+	0.693381i	0.0197031	+	0.0990544i
$50$	−2.94317	+	2.67789i	−0.416227	+	0.378710i
$51$	0.772088	−	3.08235i	0.108114	−	0.431615i
$52$	−2.28561	+	3.84685i	−0.316957	+	0.533463i
$53$	1.49186	+	0.533797i	0.204923	+	0.0733227i	0.437351	−	0.899291i	$-0.355917\pi$
$53$	1.49186	+	0.533797i	0.204923	+	0.0733227i	−0.232428	+	0.972614i	$0.574667\pi$
$54$	−1.09493	−	0.895059i	−0.149001	−	0.121802i
$55$	−3.03995	−	3.70418i	−0.409906	−	0.499472i
$56$	−7.84030	+	0.430623i	−1.04770	+	0.0575445i
$57$	−0.190848	−	1.93772i	−0.0252785	−	0.256657i
$58$	3.99118	−	2.67796i	0.524067	−	0.351633i
$59$	−3.43562	−	2.05923i	−0.447280	−	0.268089i	0.272680	−	0.962105i	$-0.412090\pi$
$59$	−3.43562	−	2.05923i	−0.447280	−	0.268089i	−0.719960	+	0.694015i	$0.755840\pi$
$60$	−2.94411	−	0.278516i	−0.380083	−	0.0359562i
$61$	−6.70590	−	0.329440i	−0.858602	−	0.0421804i	−0.384997	−	0.922918i	$-0.625798\pi$
$61$	−6.70590	−	0.329440i	−0.858602	−	0.0421804i	−0.473605	+	0.880737i	$0.657048\pi$
$62$	−3.86947	−	5.19642i	−0.491423	−	0.659946i
$63$	1.96303	−	1.96303i	0.247318	−	0.247318i
$64$	0.692023	−	7.97001i	0.0865028	−	0.996252i
$65$	−2.33922	−	2.33922i	−0.290145	−	0.290145i
$66$	−0.663748	+	4.53482i	−0.0817017	+	0.558198i
$67$	0.0170645	−	0.347357i	0.00208476	−	0.0424364i	−0.997528	−	0.0702748i	$-0.977612\pi$
$67$	0.0170645	−	0.347357i	0.00208476	−	0.0424364i	0.999612	+	0.0278384i	$0.00886239\pi$
$68$	−2.97417	+	5.61625i	−0.360671	+	0.681070i
$69$	−1.94354	+	3.24260i	−0.233974	+	0.390363i
$70$	1.12156	−	5.69581i	0.134052	−	0.680779i
$71$	3.61624	−	0.356169i	0.429169	−	0.0422695i	0.118873	−	0.992909i	$-0.462072\pi$
$71$	3.61624	−	0.356169i	0.429169	−	0.0422695i	0.310296	+	0.950640i	$0.399572\pi$
$72$	1.69800	+	2.26203i	0.200111	+	0.266583i
$73$	−9.98821	+	8.19712i	−1.16903	+	0.959400i	−0.999658	−	0.0261521i	$-0.991675\pi$
$73$	−9.98821	+	8.19712i	−1.16903	+	0.959400i	−0.169374	+	0.985552i	$0.554175\pi$
$74$	0.921357	+	9.17341i	0.107106	+	1.06639i
$75$	−0.947893	+	2.64918i	−0.109453	+	0.305901i
$76$	−0.556543	+	3.85421i	−0.0638399	+	0.442108i
$77$	−8.72721	−	2.18605i	−0.994558	−	0.249124i
$78$	−0.149161	+	3.16052i	−0.0168892	+	0.357859i
$79$	−3.58970	+	0.714035i	−0.403872	+	0.0803352i	−0.392847	−	0.919604i	$-0.628510\pi$
$79$	−3.58970	+	0.714035i	−0.403872	+	0.0803352i	−0.0110258	+	0.999939i	$0.503510\pi$
$80$	5.58397	+	1.94955i	0.624307	+	0.217966i
$81$	−0.980785	−	0.195090i	−0.108976	−	0.0216767i
$82$	8.25770	+	2.05154i	0.911911	+	0.226555i
$83$	0.558008	+	3.76178i	0.0612493	+	0.412909i	0.998016	+	0.0629557i	$0.0200527\pi$
$83$	0.558008	+	3.76178i	0.0612493	+	0.412909i	−0.936767	+	0.349954i	$0.886197\pi$
$84$	−4.75132	+	2.87278i	−0.518411	+	0.313446i
$85$	−3.48133	−	3.15529i	−0.377603	−	0.342239i
$86$	5.10340	−	9.59221i	0.550313	−	1.03435i
$87$	1.60209	−	2.99730i	0.171762	−	0.321344i
$88$	3.45876	−	8.48868i	0.368705	−	0.904896i
$89$	−12.2562	−	3.71786i	−1.29915	−	0.394093i	−0.436413	−	0.899746i	$-0.643751\pi$
$89$	−12.2562	−	3.71786i	−1.29915	−	0.394093i	−0.862737	+	0.505654i	$0.831251\pi$
$90$	−1.93038	+	0.803950i	−0.203479	+	0.0847438i
$91$	−6.14388	−	0.911358i	−0.644053	−	0.0955363i
$92$	5.32571	−	5.36692i	0.555243	−	0.559541i
$93$	−4.14139	−	1.95873i	−0.429443	−	0.203111i
$94$	−0.424130	−	8.30668i	−0.0437457	−	0.856768i
$95$	−2.65987	−	1.10176i	−0.272897	−	0.113038i
$96$	−2.21505	−	5.20515i	−0.226072	−	0.531248i
$97$	14.6752	−	6.07866i	1.49004	−	0.617194i	0.518713	−	0.854948i	$-0.326411\pi$
$97$	14.6752	−	6.07866i	1.49004	−	0.617194i	0.971325	+	0.237754i	$0.0764113\pi$
$98$	−0.429211	−	0.902983i	−0.0433568	−	0.0912150i
$99$	1.09178	+	3.05133i	0.109728	+	0.306670i
$100$	3.10831	−	4.69096i	0.310831	−	0.469096i
$101$	−5.25478	+	3.89721i	−0.522870	+	0.387787i	−0.824696	−	0.565576i	$-0.808654\pi$
$101$	−5.25478	+	3.89721i	−0.522870	+	0.387787i	0.301826	+	0.953363i	$0.402404\pi$
$102$	0.00866077	+	4.49376i	0.000857544	+	0.444949i
$103$	2.40470	+	4.49887i	0.236942	+	0.443287i	0.972086	−	0.234624i	$-0.0753858\pi$
$103$	2.40470	+	4.49887i	0.236942	+	0.443287i	−0.735145	+	0.677910i	$0.762886\pi$
$104$	1.80190	−	6.06611i	0.176691	−	0.594831i
$105$	−1.19158	−	3.92813i	−0.116287	−	0.383346i
$106$	−2.23043	−	0.215339i	−0.216639	−	0.0209155i
$107$	0.472075	+	9.60930i	0.0456372	+	0.928966i	0.907040	+	0.421044i	$0.138336\pi$
$107$	0.472075	+	9.60930i	0.0456372	+	0.928966i	−0.861403	+	0.507922i	$0.830414\pi$
$108$	1.81126	+	0.848135i	0.174289	+	0.0816118i
$109$	−12.2601	−	9.09272i	−1.17431	−	0.870925i	−0.180668	−	0.983544i	$-0.557826\pi$
$109$	−12.2601	−	9.09272i	−1.17431	−	0.870925i	−0.993638	+	0.112619i	$0.964076\pi$
$110$	5.45092	+	4.02641i	0.519724	+	0.383904i
$111$	3.62188	+	5.42053i	0.343774	+	0.514494i
$112$	10.6012	−	3.30531i	1.00172	−	0.312322i
$113$	−1.45321	+	2.17489i	−0.136707	+	0.204596i	−0.893506	−	0.449051i	$-0.851762\pi$
$113$	−1.45321	+	2.17489i	−0.136707	+	0.204596i	0.756799	+	0.653647i	$0.226762\pi$
$114$	0.932656	+	2.59085i	0.0873513	+	0.242655i
$115$	2.87377	+	4.79459i	0.267980	+	0.447098i
$116$	−4.54527	+	5.05395i	−0.422018	+	0.469247i
$117$	0.956575	+	2.02251i	0.0884354	+	0.186981i
$118$	5.42386	+	1.63390i	0.499307	+	0.150413i
$119$	−8.77892	−	0.864649i	−0.804763	−	0.0792622i
$120$	4.13331	−	0.637564i	0.377318	−	0.0582014i
$121$	−0.315559	+	0.384509i	−0.0286871	+	0.0349554i
$122$	9.30898	−	1.87033i	0.842795	−	0.169332i
$123$	5.83627	−	1.46191i	0.526239	−	0.131816i
$124$	7.10505	+	5.78527i	0.638052	+	0.519533i
$125$	7.75885	+	8.56058i	0.693973	+	0.765681i
$126$	−2.01190	+	3.37138i	−0.179235	+	0.300346i
$127$		−	3.34318i		−	0.296659i	−0.988938	−	0.148330i	$-0.952610\pi$
$127$		−	3.34318i		−	0.296659i	0.988938	−	0.148330i	$-0.0473896\pi$
$128$	1.81089	+	11.1678i	0.160062	+	0.987107i
$129$		−	7.68294i		−	0.676445i
$130$	4.01746	+	2.39746i	0.352355	+	0.210271i
$131$	−0.555991	−	0.613441i	−0.0485771	−	0.0535966i	0.716178	−	0.697918i	$-0.245890\pi$
$131$	−0.555991	−	0.613441i	−0.0485771	−	0.0535966i	−0.764755	+	0.644321i	$0.777140\pi$
$132$	−0.660160	−	6.44783i	−0.0574596	−	0.561212i
$133$	−5.24341	+	1.31341i	−0.454661	+	0.113887i
$134$	0.0968805	+	0.482193i	0.00836920	+	0.0416551i
$135$	−0.938032	+	1.14300i	−0.0807330	+	0.0983734i
$136$	2.13335	−	8.73068i	0.182933	−	0.748649i
$137$	20.7357	+	2.04228i	1.77157	+	0.174484i	0.930462	−	0.366389i	$-0.119406\pi$
$137$	20.7357	+	2.04228i	1.77157	+	0.174484i	0.841104	+	0.540873i	$0.181906\pi$
$138$	1.54210	−	5.11913i	0.131272	−	0.435769i
$139$	5.23016	+	11.0582i	0.443616	+	0.937948i	0.994634	+	0.103454i	$0.0329896\pi$
$139$	5.23016	+	11.0582i	0.443616	+	0.937948i	−0.551018	+	0.834493i	$0.685760\pi$
$140$	0.434438	+	8.19826i	0.0367167	+	0.692880i
$141$	−3.02362	−	5.04461i	−0.254635	−	0.424833i
$142$	−4.83514	+	1.74056i	−0.405756	+	0.146065i
$143$	4.02823	−	6.02867i	0.336857	−	0.504143i
$144$	−3.11151	−	2.51366i	−0.259293	−	0.209472i
$145$	−2.79189	−	4.17836i	−0.231854	−	0.346994i
$146$	10.8571	−	14.6982i	0.898540	−	1.21643i
$147$	−0.567840	−	0.421139i	−0.0468346	−	0.0347349i
$148$	−4.43980	−	12.2592i	−0.364950	−	1.00770i
$149$	−0.303498	−	6.17785i	−0.0248635	−	0.506109i	−0.978639	−	0.205588i	$-0.934089\pi$
$149$	−0.303498	−	6.17785i	−0.0248635	−	0.506109i	0.953775	−	0.300521i	$-0.0971606\pi$
$150$	0.382389	−	3.96070i	0.0312219	−	0.323389i
$151$	3.26306	+	10.7569i	0.265544	+	0.875382i	0.983749	+	0.179550i	$0.0574642\pi$
$151$	3.26306	+	10.7569i	0.265544	+	0.875382i	−0.718204	+	0.695832i	$0.755036\pi$
$152$	−0.571480	−	5.47748i	−0.0463532	−	0.444282i
$153$	1.49790	+	2.80237i	0.121098	+	0.226558i
$154$	12.7234	−	0.0245217i	1.02528	−	0.00197601i
$155$	−5.44089	+	4.03524i	−0.437023	+	0.324118i
$156$	−0.889866	−	4.38525i	−0.0712463	−	0.351101i
$157$	−2.95112	−	8.24783i	−0.235525	−	0.658249i	−0.999909	−	0.0134874i	$-0.995707\pi$
$157$	−2.95112	−	8.24783i	−0.235525	−	0.658249i	0.764384	−	0.644761i	$-0.223043\pi$
$158$	4.67482	−	2.22206i	0.371909	−	0.176778i
$159$	−1.46387	+	0.606357i	−0.116093	+	0.0480872i
$160$	−8.33162	−	0.739602i	−0.658673	−	0.0584707i
$161$	9.69616	+	4.01628i	0.764165	+	0.316527i
$162$	1.41237	−	0.0721143i	0.110967	−	0.00566584i
$163$	14.9651	+	7.07798i	1.17216	+	0.554390i	0.911604	−	0.411069i	$-0.134845\pi$
$163$	14.9651	+	7.07798i	1.17216	+	0.554390i	0.260555	+	0.965459i	$0.416095\pi$
$164$	−12.0331	+	0.0463825i	−0.939625	+	0.00362187i
$165$	4.74003	+	0.703117i	0.369011	+	0.0547376i
$166$	−2.06771	−	4.96481i	−0.160485	−	0.385344i
$167$	−1.62260	−	0.492210i	−0.125561	−	0.0380884i	0.226879	−	0.973923i	$-0.427148\pi$
$167$	−1.62260	−	0.492210i	−0.125561	−	0.0380884i	−0.352440	+	0.935835i	$0.614648\pi$
$168$	5.52009	−	5.58429i	0.425884	−	0.430838i
$169$	−3.76855	+	7.05045i	−0.289888	+	0.542343i
$170$	5.86606	+	3.12095i	0.449906	+	0.239366i
$171$	1.44270	+	1.30759i	0.110326	+	0.0999937i
$172$	−3.67612	+	14.9197i	−0.280302	+	1.13761i
$173$	−1.72414	−	11.6232i	−0.131084	−	0.883695i	−0.950551	−	0.310569i	$-0.899480\pi$
$173$	−1.72414	−	11.6232i	−0.131084	−	0.883695i	0.819467	−	0.573126i	$-0.194270\pi$
$174$	−1.15886	+	4.66455i	−0.0878528	+	0.353618i
$175$	7.66102	+	1.52387i	0.579119	+	0.115194i
$176$	−1.80317	+	12.8371i	−0.135919	+	0.967629i
$177$	3.92853	−	0.781432i	0.295286	−	0.0587361i
$178$	18.0926	+	0.853883i	1.35610	+	0.0640012i
$179$	17.5039	+	4.38451i	1.30831	+	0.327714i	0.833570	−	0.552414i	$-0.186293\pi$
$179$	17.5039	+	4.38451i	1.30831	+	0.327714i	0.474737	+	0.880128i	$0.342543\pi$
$180$	2.36848	−	1.77078i	0.176536	−	0.131986i
$181$	−7.00202	+	19.5693i	−0.520456	+	1.45458i	0.337732	+	0.941242i	$0.390340\pi$
$181$	−7.00202	+	19.5693i	−0.520456	+	1.45458i	−0.858188	+	0.513336i	$0.828410\pi$
$182$	8.73985	−	0.877811i	0.647841	−	0.0650677i
$183$	5.18998	−	4.25931i	0.383654	−	0.314857i
$184$	−5.44403	+	9.20308i	−0.401339	+	0.678460i
$185$	9.59309	−	0.944837i	0.705298	−	0.0694658i
$186$	6.35679	+	1.25171i	0.466102	+	0.0917800i
$187$	5.29412	−	8.83271i	0.387144	−	0.645912i
$188$	3.45790	+	11.2430i	0.252193	+	0.819978i
$189$	−0.136219	+	2.77280i	−0.00990846	+	0.201691i
$190$	4.02863	+	0.589658i	0.292268	+	0.0427783i
$191$	−7.32997	−	7.32997i	−0.530378	−	0.530378i	0.390307	−	0.920685i	$-0.372369\pi$
$191$	−7.32997	−	7.32997i	−0.530378	−	0.530378i	−0.920685	+	0.390307i	$0.872369\pi$
$192$	4.83958	+	6.37012i	0.349267	+	0.459724i
$193$	18.2275	−	18.2275i	1.31204	−	1.31204i	0.392135	−	0.919908i	$-0.371737\pi$
$193$	18.2275	−	18.2275i	1.31204	−	1.31204i	0.919908	−	0.392135i	$-0.128263\pi$
$194$	−18.0173	+	13.4164i	−1.29356	+	0.963242i
$195$	3.30417	+	0.162324i	0.236617	+	0.0116242i
$196$	0.901194	+	1.08952i	0.0643710	+	0.0778227i
$197$	14.7167	+	8.82085i	1.04852	+	0.628460i	0.931153	−	0.364629i	$-0.118804\pi$
$197$	14.7167	+	8.82085i	1.04852	+	0.628460i	0.117369	+	0.993088i	$0.462554\pi$
$198$	−2.55360	−	3.80583i	−0.181476	−	0.270468i
$199$	1.20945	+	12.2798i	0.0857360	+	0.870492i	0.937828	+	0.347100i	$0.112834\pi$
$199$	1.20945	+	12.2798i	0.0857360	+	0.870492i	−0.852092	+	0.523392i	$0.824666\pi$
$200$	−2.63768	+	7.50839i	−0.186512	+	0.530924i
$201$	0.220626	+	0.268834i	0.0155618	+	0.0189621i
$202$	5.85570	−	7.16330i	0.412005	−	0.504008i
$203$	−8.88346	−	3.17855i	−0.623497	−	0.223091i
$204$	−1.56793	−	6.15870i	−0.109777	−	0.431195i
$205$	2.16162	−	8.62968i	0.150974	−	0.602723i
$206$	−4.85506	−	5.33603i	−0.338268	−	0.371779i
$207$	−0.737528	−	3.70780i	−0.0512618	−	0.257710i
$208$	−0.370199	+	8.94160i	−0.0256687	+	0.619988i
$209$	1.23103	−	6.18883i	0.0851525	−	0.428090i
$210$	2.99405	+	4.97351i	0.206609	+	0.343205i
$211$	3.32245	−	0.492838i	0.228727	−	0.0339284i	−0.0313832	−	0.999507i	$-0.509991\pi$
$211$	3.32245	−	0.492838i	0.228727	−	0.0339284i	0.260110	+	0.965579i	$0.416241\pi$
$212$	3.13286	−	0.477064i	0.215166	−	0.0327649i
$213$	−2.44027	+	2.69242i	−0.167205	+	0.184482i
$214$	−3.97470	−	13.0125i	−0.271705	−	0.889516i
$215$	−10.0188	−	5.35517i	−0.683277	−	0.365219i
$216$	−2.77722	−	0.535750i	−0.188966	−	0.0364532i
$217$	−3.69189	+	12.1705i	−0.250622	+	0.826190i
$218$	19.9592	+	8.22234i	1.35181	+	0.556887i
$219$	1.89593	−	12.7813i	0.128115	−	0.863683i
$220$	−8.86834	−	3.63340i	−0.597903	−	0.244964i
$221$	3.03959	−	6.42667i	0.204465	−	0.432305i
$222$	−6.84317	−	6.17831i	−0.459283	−	0.414661i
$223$	−3.26875	+	7.89147i	−0.218892	+	0.528452i	−0.994736	−	0.102473i	$-0.967324\pi$
$223$	−3.26875	+	7.89147i	−0.218892	+	0.528452i	0.775844	+	0.630925i	$0.217324\pi$
$224$	−13.3915	+	8.20301i	−0.894760	+	0.548087i
$225$	−1.07674	−	2.59948i	−0.0717827	−	0.173299i
$226$	1.23950	−	3.48534i	0.0824504	−	0.231841i
$227$	13.1550	−	4.70694i	0.873128	−	0.312410i	0.138077	−	0.990422i	$-0.455908\pi$
$227$	13.1550	−	4.70694i	0.873128	−	0.312410i	0.735052	+	0.678011i	$0.237158\pi$
$228$	−2.17596	−	3.22953i	−0.144106	−	0.213881i
$229$	−1.39733	−	1.88408i	−0.0923383	−	0.124504i	0.754622	−	0.656159i	$-0.227820\pi$
$229$	−1.39733	−	1.88408i	−0.0923383	−	0.124504i	−0.846961	+	0.531656i	$0.821570\pi$
$230$	−5.60064	−	5.57909i	−0.369295	−	0.367874i
$231$	7.93450	−	4.24108i	0.522052	−	0.279042i
$232$	4.48230	−	8.50369i	0.294277	−	0.558295i
$233$	22.6324	−	6.86548i	1.48270	−	0.449772i	0.557798	−	0.829977i	$-0.311646\pi$
$233$	22.6324	−	6.86548i	1.48270	−	0.449772i	0.924902	+	0.380204i	$0.124146\pi$
$234$	−2.01196	−	2.44196i	−0.131526	−	0.159636i
$235$	−8.68587	+	0.426709i	−0.566604	+	0.0278355i
$236$	−8.00279	−	0.362236i	−0.520937	−	0.0235795i
$237$	2.18027	−	2.93976i	0.141624	−	0.190958i
$238$	12.3368	−	1.85429i	0.799674	−	0.120196i
$239$	7.03815	−	4.70274i	0.455260	−	0.304195i	−0.306715	−	0.951801i	$-0.599230\pi$
$239$	7.03815	−	4.70274i	0.455260	−	0.304195i	0.761975	+	0.647606i	$0.224230\pi$
$240$	−5.44669	+	2.30544i	−0.351582	+	0.148816i
$241$	6.01059	+	4.01615i	0.387176	+	0.258703i	0.733890	−	0.679268i	$-0.237703\pi$
$241$	6.01059	+	4.01615i	0.387176	+	0.258703i	−0.346714	+	0.937971i	$0.612703\pi$
$242$	0.299540	−	0.636494i	0.0192551	−	0.0409154i
$243$	0.857729	−	0.514103i	0.0550233	−	0.0329797i
$244$	−12.1165	+	5.78794i	−0.775681	+	0.370535i
$245$	−0.944975	+	0.446940i	−0.0603723	+	0.0285539i
$246$	−7.49629	+	4.02544i	−0.477946	+	0.256653i
$247$	0.426988	−	4.33528i	0.0271686	−	0.275847i
$248$	−11.7455	−	5.47232i	−0.745838	−	0.347492i
$249$	−2.93972	−	2.41256i	−0.186297	−	0.152890i
$250$	−13.6029	−	9.05133i	−0.860326	−	0.572456i
$251$	1.80303	+	7.19809i	0.113806	+	0.454339i	0.999959	−	0.00905348i	$-0.00288185\pi$
$251$	1.80303	+	7.19809i	0.113806	+	0.454339i	−0.886153	+	0.463393i	$0.846632\pi$
$252$	1.59125	−	5.31938i	0.100239	−	0.335089i
$253$	−9.07780	+	8.22764i	−0.570716	+	0.517267i
$254$	1.15764	+	4.58406i	0.0726368	+	0.287629i
$255$	4.69845			0.294229
$256$	−6.35011	−	14.6859i	−0.396882	−	0.917870i
$257$	−7.74527			−0.483136			−0.241568	−	0.970384i	$-0.577662\pi$
$257$	−7.74527			−0.483136			−0.241568	+	0.970384i	$0.577662\pi$
$258$	2.66036	+	10.5346i	0.165627	+	0.655855i
$259$	13.4099	−	12.1541i	0.833253	−	0.755217i
$260$	−6.33877	−	1.89620i	−0.393114	−	0.117597i
$261$	0.825792	+	3.29675i	0.0511152	+	0.204063i
$262$	0.974772	+	0.648608i	0.0602216	+	0.0400711i
$263$	−15.4465	−	12.6766i	−0.952475	−	0.781676i	0.0234633	−	0.999725i	$-0.492531\pi$
$263$	−15.4465	−	12.6766i	−0.952475	−	0.781676i	−0.975938	+	0.218049i	$0.930031\pi$
$264$	3.13787	+	8.61246i	0.193123	+	0.530060i
$265$	−0.229641	+	2.33159i	−0.0141067	+	0.143228i
$266$	6.73480	−	3.61653i	0.412937	−	0.221744i
$267$	11.5780	−	5.47598i	0.708561	−	0.335124i
$268$	−0.299808	−	0.627620i	−0.0183137	−	0.0383380i
$269$	14.4311	−	8.64964i	0.879877	−	0.527378i	−0.00138880	−	0.999999i	$-0.500442\pi$
$269$	14.4311	−	8.64964i	0.879877	−	0.527378i	0.881266	+	0.472621i	$0.156692\pi$
$270$	0.890414	−	1.89205i	0.0541889	−	0.115146i
$271$	10.0778	+	6.73375i	0.612181	+	0.409046i	0.822645	−	0.568555i	$-0.192497\pi$
$271$	10.0778	+	6.73375i	0.612181	+	0.409046i	−0.210464	+	0.977602i	$0.567497\pi$
$272$	0.0979845	+	12.7099i	0.00594118	+	0.770652i
$273$	5.16434	−	3.45070i	0.312560	−	0.208846i
$274$	−29.1392	+	4.37981i	−1.76036	+	0.264594i
$275$	−5.43183	+	7.32398i	−0.327552	+	0.441652i
$276$	−0.341884	+	7.55316i	−0.0205790	+	0.454647i
$277$	−21.1583	+	1.03944i	−1.27128	+	0.0624539i	−0.673488	−	0.739198i	$-0.735205\pi$
$277$	−21.1583	+	1.03944i	−1.27128	+	0.0624539i	−0.597791	+	0.801652i	$0.703955\pi$
$278$	−11.0005	−	13.3516i	−0.659769	−	0.800779i
$279$	4.38398	−	1.32986i	0.262462	−	0.0796169i
$280$	−3.43449	−	11.0908i	−0.205250	−	0.662799i
$281$	17.3450	−	9.27112i	1.03472	−	0.553069i	0.135595	−	0.990764i	$-0.456705\pi$
$281$	17.3450	−	9.27112i	1.03472	−	0.553069i	0.899123	+	0.437696i	$0.144205\pi$
$282$	5.89268	+	5.87001i	0.350904	+	0.349554i
$283$	−0.223732	−	0.301668i	−0.0132995	−	0.0179323i	0.796508	−	0.604628i	$-0.206678\pi$
$283$	−0.223732	−	0.301668i	−0.0132995	−	0.0179323i	−0.809807	+	0.586696i	$0.800428\pi$
$284$	6.02708	−	4.06086i	0.357641	−	0.240968i
$285$	2.71073	−	0.969915i	0.160570	−	0.0574528i
$286$	−3.43583	+	9.66116i	−0.203165	+	0.571276i
$287$	−6.39192	−	15.4315i	−0.377303	−	0.910890i
$288$	5.13680	+	2.36923i	0.302689	+	0.139608i
$289$	−2.64167	+	6.37755i	−0.155392	+	0.375150i
$290$	5.27498	+	4.76248i	0.309757	+	0.279662i
$291$	−6.79141	+	14.3592i	−0.398120	+	0.841753i
$292$	−9.79735	+	23.9132i	−0.573346	+	1.39941i
$293$	−2.52700	+	17.0356i	−0.147629	+	0.995232i	0.781083	+	0.624428i	$0.214668\pi$
$293$	−2.52700	+	17.0356i	−0.147629	+	0.995232i	−0.928711	+	0.370804i	$0.879082\pi$
$294$	0.924430	+	0.380826i	0.0539139	+	0.0222102i
$295$	1.71925	−	5.66761i	0.100099	−	0.329981i
$296$	10.3327	+	15.2721i	0.600576	+	0.887672i
$297$	−2.85810	−	1.52769i	−0.165844	−	0.0886454i
$298$	2.55534	+	8.36576i	0.148027	+	0.484616i
$299$	−5.68007	+	6.26700i	−0.328487	+	0.362430i
$300$	0.847148	+	5.56318i	0.0489101	+	0.321191i
$301$	−21.0981	+	3.12960i	−1.21607	+	0.180387i
$302$	−8.19898	−	13.6196i	−0.471798	−	0.783718i
$303$	1.27633	−	6.41654i	0.0733232	−	0.368621i
$304$	2.68028	+	7.31265i	0.153724	+	0.419409i
$305$	−1.93676	−	9.73674i	−0.110898	−	0.557524i
$306$	−3.02424	−	3.32384i	−0.172884	−	0.190011i
$307$	−3.01972	+	12.0554i	−0.172345	+	0.688038i	0.820807	+	0.571205i	$0.193524\pi$
$307$	−3.01972	+	12.0554i	−0.172345	+	0.688038i	−0.993152	+	0.116832i	$0.962726\pi$
$308$	−17.4374	+	4.43935i	−0.993590	+	0.252956i
$309$	−4.80302	−	1.71855i	−0.273234	−	0.0977647i
$310$	6.06309	−	7.41700i	0.344360	−	0.421257i
$311$	−17.5134	−	21.3402i	−0.993096	−	1.21009i	−0.977656	−	0.210211i	$-0.932585\pi$
$311$	−17.5134	−	21.3402i	−0.993096	−	1.21009i	−0.0154404	−	0.999881i	$-0.504915\pi$
$312$	2.73863	+	5.70478i	0.155045	+	0.322969i
$313$	2.91055	+	29.5513i	0.164514	+	1.67034i	0.623444	+	0.781868i	$0.285733\pi$
$313$	2.91055	+	29.5513i	0.164514	+	1.67034i	−0.458930	+	0.888472i	$0.651767\pi$
$314$	6.90245	+	10.2873i	0.389528	+	0.580544i
$315$	3.52088	+	2.11033i	0.198379	+	0.118904i
$316$	−5.64053	+	4.66556i	−0.317305	+	0.262459i
$317$	−1.48635	−	0.0730197i	−0.0834818	−	0.00410120i	0.00728391	−	0.999973i	$-0.497681\pi$
$317$	−1.48635	−	0.0730197i	−0.0834818	−	0.00410120i	−0.0907657	+	0.995872i	$0.528931\pi$
$318$	1.79725	−	1.33831i	0.100785	−	0.0750487i
$319$	7.78812	−	7.78812i	0.436051	−	0.436051i
$320$	11.6801	−	1.87087i	0.652940	−	0.104585i
$321$	−6.80300	−	6.80300i	−0.379706	−	0.379706i
$322$	−14.6858	−	2.14951i	−0.818406	−	0.119788i
$323$	0.303583	−	6.17958i	0.0168918	−	0.343841i
$324$	−1.91163	+	0.587942i	−0.106202	+	0.0326635i
$325$	−3.23629	+	5.39943i	−0.179517	+	0.299507i
$326$	−22.9706	−	4.52312i	−1.27222	−	0.250513i
$327$	15.1904	−	1.49613i	0.840034	−	0.0827361i
$328$	16.4833	−	4.23028i	0.910137	−	0.233578i
$329$	−12.6213	+	10.3580i	−0.695836	+	0.571058i
$330$	−6.74284	+	0.677235i	−0.371181	+	0.0372806i
$331$	−10.5665	+	29.5313i	−0.580785	+	1.62319i	0.186915	+	0.982376i	$0.440151\pi$
$331$	−10.5665	+	29.5313i	−0.580785	+	1.62319i	−0.767700	+	0.640809i	$0.778599\pi$
$332$	4.55434	+	6.09160i	0.249952	+	0.334320i
$333$	−6.32385	−	1.58404i	−0.346545	−	0.0868049i
$334$	2.39529	+	0.113046i	0.131065	+	0.00618560i
$335$	0.504350	−	0.100321i	0.0275556	−	0.00548115i
$336$	−5.63529	+	9.56843i	−0.307430	+	0.522001i
$337$	−2.96434	−	0.589644i	−0.161478	−	0.0321200i	0.113689	−	0.993516i	$-0.463733\pi$
$337$	−2.96434	−	0.589644i	−0.161478	−	0.0321200i	−0.275167	+	0.961396i	$0.588733\pi$
$338$	2.72595	−	10.9723i	0.148272	−	0.596813i
$339$	−0.383805	−	2.58741i	−0.0208454	−	0.140529i
$340$	−9.12403	−	2.24811i	−0.494820	−	0.121921i
$341$	−11.0007	−	9.97047i	−0.595722	−	0.539931i
$342$	−2.43096	−	1.29336i	−0.131451	−	0.0699368i
$343$	8.23547	−	15.4075i	0.444674	−	0.831926i
$344$	−0.125643	−	21.7303i	−0.00677420	−	1.17162i
$345$	−5.34918	−	1.62265i	−0.287990	−	0.0873608i
$346$	6.38883	+	15.3403i	0.343466	+	0.824701i
$347$	−9.66967	−	1.43436i	−0.519095	−	0.0770005i	−0.117958	−	0.993019i	$-0.537635\pi$
$347$	−9.66967	−	1.43436i	−0.519095	−	0.0770005i	−0.401137	+	0.916018i	$0.631385\pi$
$348$	−0.0262002	−	6.79715i	−0.00140448	−	0.364365i
$349$	−8.46548	−	4.00387i	−0.453147	−	0.214322i	0.187335	−	0.982296i	$-0.440015\pi$
$349$	−8.46548	−	4.00387i	−0.453147	−	0.214322i	−0.640481	+	0.767974i	$0.721265\pi$
$350$	−11.0322	+	0.563293i	−0.589696	+	0.0301093i
$351$	−2.06701	−	0.856183i	−0.110329	−	0.0456997i
$352$	−1.97263	−	18.2261i	−0.105141	−	0.971455i
$353$	10.4977	−	4.34828i	0.558735	−	0.231436i	−0.0854007	−	0.996347i	$-0.527217\pi$
$353$	10.4977	−	4.34828i	0.558735	−	0.231436i	0.644136	+	0.764911i	$0.277217\pi$
$354$	−5.11608	+	2.43180i	−0.271916	+	0.129249i
$355$	1.81009	+	5.05887i	0.0960698	+	0.268497i
$356$	−25.1037	+	5.09410i	−1.33049	+	0.269987i
$357$	7.08542	−	5.25490i	0.375000	−	0.278119i
$358$	−25.5190	+	0.0491825i	−1.34872	+	0.00259938i
$359$	16.1594	+	30.2322i	0.852863	+	1.59559i	0.802337	+	0.596871i	$0.203590\pi$
$359$	16.1594	+	30.2322i	0.852863	+	1.59559i	0.0505260	+	0.998723i	$0.483910\pi$
$360$	−2.63442	+	3.24817i	−0.138846	+	0.171193i
$361$	4.41489	+	14.5539i	0.232363	+	0.765997i
$362$	2.82468	−	29.2574i	0.148462	−	1.53774i
$363$	−0.0244071	−	0.496819i	−0.00128104	−	0.0260762i
$364$	−11.6798	+	4.22997i	−0.612190	+	0.221710i
$365$	−15.3458	−	11.3812i	−0.803236	−	0.595720i
$366$	−5.64146	+	7.63735i	−0.294884	+	0.399211i
$367$	−13.2707	−	19.8610i	−0.692724	−	1.03673i	−0.996467	−	0.0839808i	$-0.973237\pi$
$367$	−13.2707	−	19.8610i	−0.692724	−	1.03673i	0.303743	−	0.952754i	$-0.401763\pi$
$368$	4.27794	−	14.5040i	0.223003	−	0.756076i
$369$	−3.34263	+	5.00260i	−0.174011	+	0.260425i
$370$	−12.8266	+	4.61732i	−0.666821	+	0.240043i
$371$	2.26141	+	3.77294i	0.117407	+	0.195881i
$372$	−9.14965	+	0.484853i	−0.474387	+	0.0251385i
$373$	6.82029	+	14.4203i	0.353141	+	0.746654i	0.999871	−	0.0160649i	$-0.00511383\pi$
$373$	6.82029	+	14.4203i	0.353141	+	0.746654i	−0.646730	+	0.762719i	$0.723864\pi$
$374$	−4.20063	+	13.9443i	−0.217209	+	0.721043i
$375$	−11.4979	−	1.13244i	−0.593747	−	0.0584790i
$376$	−8.63445	−	14.2186i	−0.445288	−	0.733270i
$377$	4.82376	−	5.87776i	0.248436	−	0.302720i
$378$	−0.773356	−	3.84914i	−0.0397771	−	0.197978i
$379$	30.9686	−	7.75723i	1.59075	−	0.398462i	0.656283	−	0.754515i	$-0.272128\pi$
$379$	30.9686	−	7.75723i	1.59075	−	0.398462i	0.934466	+	0.356053i	$0.115878\pi$
$380$	−5.72811	+	0.586472i	−0.293846	+	0.0300854i
$381$	2.24514	+	2.47713i	0.115022	+	0.126907i
$382$	12.5888	+	7.51247i	0.644097	+	0.384371i
$383$		−	33.0167i		−	1.68707i	−0.537073	−	0.843536i	$-0.680470\pi$
$383$		−	33.0167i		−	1.68707i	0.537073	−	0.843536i	$-0.319530\pi$
$384$	−8.84165	−	7.05870i	−0.451198	−	0.360213i
$385$		−	13.3030i		−	0.677983i
$386$	−18.6813	+	31.3045i	−0.950853	+	1.59336i
$387$	5.15955	+	5.69268i	0.262274	+	0.289375i
$388$	20.0590	−	24.6350i	1.01834	−	1.25065i
$389$	32.1075	−	8.04251i	1.62791	−	0.407771i	0.681783	−	0.731554i	$-0.261205\pi$
$389$	32.1075	−	8.04251i	1.62791	−	0.407771i	0.946131	+	0.323783i	$0.104955\pi$
$390$	−4.58678	+	0.921560i	−0.232261	+	0.0466650i
$391$	−7.62074	+	9.28590i	−0.385398	+	0.469608i
$392$	−1.61295	−	1.18185i	−0.0814665	−	0.0596926i
$393$	0.823924	+	0.0811494i	0.0415615	+	0.00409345i
$394$	−23.2334	−	6.99892i	−1.17048	−	0.352600i
$395$	−2.31385	−	4.89222i	−0.116422	−	0.246154i
$396$	4.81924	+	4.33419i	0.242176	+	0.217801i
$397$	14.5101	+	24.2086i	0.728239	+	1.21499i	0.969633	+	0.244565i	$0.0786453\pi$
$397$	14.5101	+	24.2086i	0.728239	+	1.21499i	−0.241394	+	0.970427i	$0.577605\pi$
$398$	−5.91048	−	16.4189i	−0.296266	−	0.823003i
$399$	3.00308	−	4.49443i	0.150342	−	0.225003i
$400$	1.01677	−	11.2086i	0.0508384	−	0.560430i
$401$	1.11235	+	1.66475i	0.0555481	+	0.0831336i	0.858204	−	0.513309i	$-0.171580\pi$
$401$	1.11235	+	1.66475i	0.0555481	+	0.0831336i	−0.802656	+	0.596442i	$0.796580\pi$
$402$	−0.395604	−	0.292220i	−0.0197310	−	0.0145746i
$403$	−8.23262	−	6.10573i	−0.410096	−	0.304148i
$404$	−5.54871	+	11.8497i	−0.276059	+	0.589546i
$405$	−0.0725529	−	1.47685i	−0.00360518	−	0.0733852i
$406$	13.2813	+	1.28226i	0.659142	+	0.0636374i
$407$	6.13293	+	20.2175i	0.303998	+	1.00215i
$408$	4.28246	+	7.90168i	0.212013	+	0.391191i
$409$	−16.4215	−	30.7224i	−0.811989	−	1.51912i	−0.854158	−	0.520013i	$-0.825927\pi$
$409$	−16.4215	−	30.7224i	−0.811989	−	1.51912i	0.0421696	−	0.999110i	$-0.486573\pi$
$410$	0.0242476	+	12.5812i	0.00119751	+	0.621343i
$411$	−16.7356	+	12.4120i	−0.825507	+	0.612238i
$412$	8.50479	+	5.63542i	0.419001	+	0.277637i
$413$	−3.74615	−	10.4698i	−0.184336	−	0.515185i
$414$	2.29517	+	4.82863i	0.112802	+	0.237314i
$415$	−5.19511	+	2.15188i	−0.255018	+	0.105632i
$416$	−2.58859	−	12.3886i	−0.126916	−	0.607401i
$417$	−11.3016	−	4.68126i	−0.553439	−	0.229242i
$418$	0.455047	+	8.91219i	0.0222571	+	0.435909i
$419$	24.0140	+	11.3578i	1.17316	+	0.554864i	0.911903	−	0.410405i	$-0.134613\pi$
$419$	24.0140	+	11.3578i	1.17316	+	0.554864i	0.261258	+	0.965269i	$0.415863\pi$
$420$	−5.82752	−	5.78276i	−0.284354	−	0.282170i
$421$	−9.71000	−	1.44034i	−0.473236	−	0.0701980i	−0.0941474	−	0.995558i	$-0.530013\pi$
$421$	−9.71000	−	1.44034i	−0.473236	−	0.0701980i	−0.379089	+	0.925360i	$0.623763\pi$
$422$	−4.38497	+	1.82622i	−0.213457	+	0.0888992i
$423$	5.62811	+	1.70727i	0.273648	+	0.0830102i
$424$	−4.13048	+	1.73895i	−0.200594	+	0.0844507i
$425$	−4.21457	+	7.88491i	−0.204437	+	0.382474i
$426$	2.41371	−	4.53675i	0.116945	−	0.219806i
$427$	−13.8106	−	12.5172i	−0.668340	−	0.605748i
$428$	9.95580	+	16.4660i	0.481232	+	0.795913i
$429$	1.06389	+	7.17214i	0.0513649	+	0.346274i
$430$	15.5918	+	3.87362i	0.751903	+	0.186803i
$431$	14.8675	+	2.95733i	0.716141	+	0.142449i	0.539695	−	0.841861i	$-0.318540\pi$
$431$	14.8675	+	2.95733i	0.716141	+	0.142449i	0.176447	+	0.984310i	$0.443540\pi$
$432$	3.99355	−	0.227064i	0.192140	−	0.0109246i
$433$	11.1632	−	2.22050i	0.536469	−	0.106710i	0.0805818	−	0.996748i	$-0.474322\pi$
$433$	11.1632	−	2.22050i	0.536469	−	0.106710i	0.455887	+	0.890038i	$0.349322\pi$
$434$	0.847918	−	17.9662i	0.0407014	−	0.862406i
$435$	4.87466	+	1.22104i	0.233722	+	0.0585444i
$436$	−30.2145	−	4.36294i	−1.44701	−	0.208947i
$437$	−2.47980	+	6.93059i	−0.118625	+	0.331535i
$438$	1.82614	+	18.1818i	0.0872565	+	0.868762i
$439$	−3.09731	+	2.54190i	−0.147827	+	0.121318i	−0.705400	−	0.708809i	$-0.749233\pi$
$439$	−3.09731	+	2.54190i	−0.147827	+	0.121318i	0.557573	+	0.830128i	$0.311733\pi$
$440$	13.4181	+	1.91117i	0.639683	+	0.0911112i
$441$	0.703561	−	0.0692947i	0.0335029	−	0.00329975i
$442$	−1.94243	+	9.86455i	−0.0923917	+	0.469209i
$443$	−9.33171	+	15.5690i	−0.443363	+	0.739707i	−0.995572	−	0.0939990i	$-0.970035\pi$
$443$	−9.33171	+	15.5690i	−0.443363	+	0.739707i	0.552209	+	0.833706i	$0.313785\pi$
$444$	11.5225	+	6.10191i	0.546833	+	0.289584i
$445$	0.929232	−	18.9149i	0.0440498	−	0.896654i
$446$	1.74943	−	11.9524i	0.0828380	−	0.565962i
$447$	4.37366	+	4.37366i	0.206867	+	0.206867i
$448$	15.5216	−	15.8848i	0.733326	−	0.750485i
$449$	2.38233	−	2.38233i	0.112429	−	0.112429i	−0.648654	−	0.761083i	$-0.724668\pi$
$449$	2.38233	−	2.38233i	0.112429	−	0.112429i	0.761083	+	0.648654i	$0.224668\pi$
$450$	2.37651	+	3.19148i	0.112030	+	0.150448i
$451$	19.4749	+	0.956739i	0.917036	+	0.0450511i
$452$	−0.492699	+	5.20818i	−0.0231746	+	0.244972i
$453$	−9.64165	−	5.77898i	−0.453004	−	0.271520i
$454$	−16.4078	+	11.0092i	−0.770058	+	0.516686i
$455$	−0.900181	−	9.13969i	−0.0422011	−	0.428475i
$456$	4.10189	+	3.67476i	0.192088	+	0.172086i
$457$	19.4341	+	23.6806i	0.909090	+	1.10773i	0.993784	+	0.111323i	$0.0355087\pi$
$457$	19.4341	+	23.6806i	0.909090	+	1.10773i	−0.0846939	+	0.996407i	$0.526991\pi$
$458$	2.56838	+	2.09954i	0.120012	+	0.0981051i
$459$	−2.99183	−	1.07049i	−0.139647	−	0.0499663i
$460$	9.61127	+	5.71053i	0.448128	+	0.266255i
$461$	−6.23712	+	24.9000i	−0.290491	+	1.15971i	0.632399	+	0.774643i	$0.282071\pi$
$461$	−6.23712	+	24.9000i	−0.290491	+	1.15971i	−0.922890	+	0.385064i	$0.874179\pi$
$462$	−9.41097	+	8.56270i	−0.437838	+	0.398373i
$463$	−0.701200	−	3.52517i	−0.0325875	−	0.163828i	0.961065	−	0.276323i	$-0.0891159\pi$
$463$	−0.701200	−	3.52517i	−0.0325875	−	0.163828i	−0.993652	+	0.112494i	$0.964116\pi$
$464$	−3.20141	+	13.2121i	−0.148622	+	0.613354i
$465$	1.32153	−	6.64380i	0.0612846	−	0.308099i
$466$	−28.6555	+	17.2506i	−1.32744	+	0.799120i
$467$	−18.0748	+	2.68114i	−0.836402	+	0.124069i	−0.551173	−	0.834391i	$-0.685820\pi$
$467$	−18.0748	+	2.68114i	−0.836402	+	0.124069i	−0.285229	+	0.958459i	$0.592070\pi$
$468$	3.60430	+	2.65166i	0.166609	+	0.122573i
$469$	0.648373	−	0.715369i	0.0299391	−	0.0330327i
$470$	11.7620	−	3.59274i	0.542541	−	0.165721i
$471$	7.72554	+	4.12939i	0.355974	+	0.190272i
$472$	11.0986	−	2.27443i	0.510854	−	0.104689i
$473$	7.22769	−	23.8265i	0.332330	−	1.09554i
$474$	−1.97157	+	4.78586i	−0.0905572	+	0.219822i
$475$	−0.803856	+	5.41915i	−0.0368834	+	0.248648i
$476$	−16.2737	+	6.81439i	−0.745903	+	0.312337i
$477$	0.677455	−	1.43236i	0.0310185	−	0.0655832i
$478$	−8.02206	+	8.88534i	−0.366921	+	0.406406i
$479$	13.9199	−	33.6056i	0.636016	−	1.53548i	−0.195928	−	0.980618i	$-0.562772\pi$
$479$	13.9199	−	33.6056i	0.636016	−	1.53548i	0.831944	−	0.554860i	$-0.187228\pi$
$480$	6.67001	−	5.04717i	0.304443	−	0.230371i
$481$	5.58164	+	13.4753i	0.254501	+	0.614420i
$482$	−9.63219	−	3.42553i	−0.438734	−	0.156028i
$483$	−9.88155	+	3.53568i	−0.449626	+	0.160879i
$484$	−0.190320	+	0.976461i	−0.00865093	+	0.0443846i
$485$	13.9912	+	18.8649i	0.635307	+	0.856612i
$486$	−0.998071	+	1.00193i	−0.0452734	+	0.0454483i
$487$	−29.9751	+	16.0220i	−1.35830	+	0.726027i	−0.979876	−	0.199606i	$-0.936034\pi$
$487$	−29.9751	+	16.0220i	−1.35830	+	0.726027i	−0.378424	+	0.925632i	$0.623534\pi$
$488$	14.6096	−	12.1318i	0.661345	−	0.549181i
$489$	−15.8417	+	4.80553i	−0.716387	+	0.217313i
$490$	1.14096	−	0.940045i	0.0515432	−	0.0424669i
$491$	−28.9166	+	1.42058i	−1.30499	+	0.0641100i	−0.689645	−	0.724148i	$-0.742233\pi$
$491$	−28.9166	+	1.42058i	−1.30499	+	0.0641100i	−0.615345	+	0.788258i	$0.710983\pi$
$492$	8.88477	−	8.11529i	0.400556	−	0.365865i
$493$	6.43314	−	8.67408i	0.289734	−	0.390661i
$494$	0.915702	+	6.09224i	0.0411994	+	0.274103i
$495$	−3.98431	+	2.66223i	−0.179082	+	0.119659i
$496$	17.9999	+	3.43636i	0.808219	+	0.154297i
$497$	8.38768	+	5.60447i	0.376239	+	0.251395i
$498$	4.86624	+	2.29009i	0.218061	+	0.102621i
$499$	3.36705	−	2.01813i	0.150730	−	0.0903440i	−0.436749	−	0.899583i	$-0.643870\pi$
$499$	3.36705	−	2.01813i	0.150730	−	0.0903440i	0.587479	+	0.809239i	$0.300120\pi$
$500$	21.7861	+	7.70059i	0.974304	+	0.344381i
$501$	1.53282	−	0.724968i	0.0684812	−	0.0323892i
$502$	−4.96473	−	9.24545i	−0.221587	−	0.412645i
$503$	−3.31404	+	33.6480i	−0.147766	+	1.50029i	0.580085	+	0.814556i	$0.303019\pi$
$503$	−3.31404	+	33.6480i	−0.147766	+	1.50029i	−0.727851	+	0.685735i	$0.759481\pi$
$504$	−0.339934	+	7.84475i	−0.0151419	+	0.349433i
$505$	−7.47776	−	6.13684i	−0.332756	−	0.273086i
$506$	9.59820	−	14.4248i	0.426692	−	0.641261i
$507$	−1.94249	−	7.75484i	−0.0862689	−	0.344405i
$508$	−3.17463	−	5.88465i	−0.140852	−	0.261089i
$509$	26.0509	−	23.6112i	1.15469	−	1.04655i	0.156420	−	0.987691i	$-0.450005\pi$
$509$	26.0509	−	23.6112i	1.15469	−	1.04655i	0.998266	−	0.0588561i	$-0.0187453\pi$
$510$	−6.44236	+	1.62693i	−0.285273	+	0.0720417i
$511$	−35.8711			−1.58684
$512$	13.7923	+	17.9380i	0.609541	+	0.792754i
$513$	−1.94709			−0.0859662
$514$	10.6200	−	2.68195i	0.468430	−	0.118296i
$515$	−5.58885	+	5.06543i	−0.246274	+	0.223210i
$516$	−7.29560	−	13.5235i	−0.321171	−	0.595338i
$517$	−4.63123	−	18.4889i	−0.203681	−	0.813142i
$518$	−14.1787	+	21.3087i	−0.622976	+	0.936250i
$519$	9.08316	+	7.45436i	0.398706	+	0.327210i
$520$	9.34811	+	0.405078i	0.409942	+	0.0177638i
$521$	−0.970195	+	9.85056i	−0.0425050	+	0.431561i	0.950257	+	0.311466i	$0.100820\pi$
$521$	−0.970195	+	9.85056i	−0.0425050	+	0.431561i	−0.992762	+	0.120095i	$0.961680\pi$
$522$	−2.27386	−	4.23444i	−0.0995242	−	0.185337i
$523$	24.6892	−	11.6771i	1.07959	−	0.510606i	0.196829	−	0.980438i	$-0.436936\pi$
$523$	24.6892	−	11.6771i	1.07959	−	0.510606i	0.882756	+	0.469832i	$0.155686\pi$
$524$	−1.56117	−	0.551816i	−0.0681999	−	0.0241062i
$525$	−6.69981	+	4.01571i	−0.292404	+	0.175260i
$526$	25.5693	+	12.0331i	1.11488	+	0.524670i
$527$	−12.1039	−	8.08757i	−0.527254	−	0.352300i
$528$	−7.28478	−	10.7226i	−0.317029	−	0.466640i
$529$	−7.24064	+	4.83804i	−0.314810	+	0.210349i
$530$	−0.492480	−	3.27651i	−0.0213920	−	0.142322i
$531$	−2.38607	+	3.21724i	−0.103547	+	0.139616i
$532$	−7.98224	+	7.29092i	−0.346074	+	0.316101i
$533$	13.4448	−	0.660499i	0.582358	−	0.0286094i
$534$	−13.9792	+	11.5176i	−0.604938	+	0.498414i
$535$	−13.6132	+	4.12951i	−0.588549	+	0.178534i
$536$	0.628412	+	0.756757i	0.0271432	+	0.0326869i
$537$	−15.9140	+	8.50622i	−0.686741	+	0.367071i
$538$	−16.7923	+	16.8571i	−0.723966	+	0.726762i
$539$	−1.36481	−	1.84024i	−0.0587867	−	0.0792646i
$540$	−0.565748	+	2.90264i	−0.0243459	+	0.124910i
$541$	9.65101	−	3.45319i	0.414929	−	0.148464i	−0.121145	−	0.992635i	$-0.538657\pi$
$541$	9.65101	−	3.45319i	0.414929	−	0.148464i	0.536074	+	0.844171i	$0.319907\pi$
$542$	−16.1500	−	5.74347i	−0.693702	−	0.246703i
$543$	−7.95381	−	19.2022i	−0.341331	−	0.824045i
$544$	−4.53541	−	17.3935i	−0.194454	−	0.745740i
$545$	8.63705	−	20.8517i	0.369971	−	0.893188i
$546$	−5.88630	+	6.51974i	−0.251910	+	0.279019i
$547$	17.9561	−	37.9650i	0.767748	−	1.62327i	−0.0141824	−	0.999899i	$-0.504515\pi$
$547$	17.9561	−	37.9650i	0.767748	−	1.62327i	0.781930	−	0.623366i	$-0.214235\pi$
$548$	38.4381	−	16.0955i	1.64200	−	0.687564i
$549$	−0.985146	+	6.64132i	−0.0420450	+	0.283444i
$550$	4.91188	−	11.9233i	0.209443	−	0.508410i
$551$	1.92093	−	6.33244i	0.0818342	−	0.269771i
$552$	−2.14665	−	10.4750i	−0.0913673	−	0.445846i
$553$	−8.96098	−	4.78974i	−0.381059	−	0.203681i
$554$	28.6516	−	8.75171i	1.21729	−	0.371824i
$555$	−6.47349	+	7.14240i	−0.274785	+	0.303178i
$556$	19.7068	+	14.4982i	0.835756	+	0.614860i
$557$	4.80717	−	0.713076i	0.203686	−	0.0302140i	−0.0441075	−	0.999027i	$-0.514044\pi$
$557$	4.80717	−	0.713076i	0.203686	−	0.0302140i	0.247794	+	0.968813i	$0.420294\pi$
$558$	−5.55067	+	3.34150i	−0.234979	+	0.141457i
$559$	3.35344	−	16.8589i	0.141835	−	0.713054i
$560$	8.54965	+	14.0180i	0.361289	+	0.592369i
$561$	2.00900	+	10.0999i	0.0848200	+	0.426419i
$562$	−20.5726	+	18.7183i	−0.867805	+	0.789584i
$563$	1.42645	−	5.69469i	0.0601176	−	0.240003i	−0.932521	−	0.361115i	$-0.882396\pi$
$563$	1.42645	−	5.69469i	0.0601176	−	0.240003i	0.992639	+	0.121112i	$0.0386461\pi$
$564$	−10.1125	−	6.00831i	−0.425811	−	0.252996i
$565$	−3.64159	−	1.30298i	−0.153203	−	0.0548168i
$566$	0.411232	+	0.336165i	0.0172854	+	0.0141301i
$567$	−1.76117	−	2.14599i	−0.0739620	−	0.0901230i
$568$	−6.85798	+	7.65510i	−0.287755	+	0.321201i
$569$	0.709938	+	7.20812i	0.0297621	+	0.302180i	0.998530	+	0.0542092i	$0.0172638\pi$
$569$	0.709938	+	7.20812i	0.0297621	+	0.302180i	−0.968767	+	0.247971i	$0.920236\pi$
$570$	−3.38101	+	2.26856i	−0.141615	+	0.0950194i
$571$	−2.49131	−	1.49323i	−0.104258	−	0.0624898i	0.461023	−	0.887388i	$-0.347482\pi$
$571$	−2.49131	−	1.49323i	−0.104258	−	0.0624898i	−0.565281	+	0.824898i	$0.691232\pi$
$572$	1.36573	−	14.4368i	0.0571041	−	0.603632i
$573$	10.3537	+	0.508643i	0.432530	+	0.0212489i
$574$	14.1078	+	18.9458i	0.588849	+	0.790781i
$575$	7.52141	−	7.52141i	0.313664	−	0.313664i
$576$	−7.86380	−	1.46989i	−0.327659	−	0.0612453i
$577$	15.7323	+	15.7323i	0.654945	+	0.654945i	0.954179	−	0.299235i	$-0.0967314\pi$
$577$	15.7323	+	15.7323i	0.654945	+	0.654945i	−0.299235	+	0.954179i	$0.596731\pi$
$578$	1.41382	−	9.65941i	0.0588071	−	0.401779i
$579$	−1.26484	+	25.7465i	−0.0525651	+	1.06999i
$580$	−8.88197	−	4.70359i	−0.368804	−	0.195306i
$581$	−5.42765	+	9.05548i	−0.225177	+	0.375685i
$582$	4.34000	−	22.0406i	0.179899	−	0.913610i
$583$	−5.11023	+	0.503313i	−0.211644	+	0.0208451i
$584$	5.15340	−	36.1815i	0.213249	−	1.49720i
$585$	−2.55724	+	2.09867i	−0.105729	+	0.0867694i
$586$	−2.43398	−	24.2337i	−0.100547	−	1.00108i
$587$	−10.2117	+	28.5398i	−0.421482	+	1.17796i	0.523838	+	0.851818i	$0.324500\pi$
$587$	−10.2117	+	28.5398i	−0.421482	+	1.17796i	−0.945320	+	0.326145i	$0.894250\pi$
$588$	−1.39942	−	0.202074i	−0.0577109	−	0.00833339i
$589$	−8.65278	−	2.16741i	−0.356531	−	0.0893065i
$590$	−0.394860	+	8.36655i	−0.0162561	+	0.344446i
$591$	−16.8281	+	3.34731i	−0.692215	+	0.137690i
$592$	−19.4561	−	17.3627i	−0.799641	−	0.713602i
$593$	11.5061	+	2.28870i	0.472497	+	0.0939856i	0.425595	−	0.904914i	$-0.360065\pi$
$593$	11.5061	+	2.28870i	0.472497	+	0.0939856i	0.0469027	+	0.998899i	$0.485065\pi$
$594$	4.44793	+	1.10504i	0.182501	+	0.0453404i
$595$	−1.91389	−	12.9024i	−0.0784619	−	0.528947i
$596$	−6.40061	−	10.5860i	−0.262179	−	0.433620i
$597$	−9.14276	−	8.28651i	−0.374188	−	0.339144i
$598$	5.61826	−	10.5599i	0.229748	−	0.431828i
$599$	11.7189	−	21.9245i	0.478820	−	0.895810i	−0.520304	−	0.853981i	$-0.674181\pi$
$599$	11.7189	−	21.9245i	0.478820	−	0.895810i	0.999125	−	0.0418292i	$-0.0133185\pi$
$600$	−3.08794	−	7.33471i	−0.126065	−	0.299438i
$601$	−21.2289	−	6.43973i	−0.865946	−	0.262682i	−0.174101	−	0.984728i	$-0.555702\pi$
$601$	−21.2289	−	6.43973i	−0.865946	−	0.262682i	−0.691845	+	0.722046i	$0.743202\pi$
$602$	27.8453	−	11.5968i	1.13489	−	0.472651i
$603$	−0.344011	−	0.0510293i	−0.0140092	−	0.00207807i
$604$	15.9582	+	15.8357i	0.649330	+	0.644343i
$605$	−0.664881	−	0.314465i	−0.0270312	−	0.0127848i
$606$	0.471790	+	9.24010i	0.0191652	+	0.375353i
$607$	−0.0656541	−	0.0271948i	−0.00266482	−	0.00110380i	0.381351	−	0.924430i	$-0.375459\pi$
$607$	−0.0656541	−	0.0271948i	−0.00266482	−	0.00110380i	−0.384015	+	0.923327i	$0.625459\pi$
$608$	−6.20725	−	9.09876i	−0.251737	−	0.369003i
$609$	8.71680	−	3.61062i	0.353222	−	0.146310i
$610$	6.02715	+	12.6800i	0.244032	+	0.513400i
$611$	−4.43295	−	12.3893i	−0.179338	−	0.501216i
$612$	5.29769	+	3.51034i	0.214146	+	0.141897i
$613$	14.9229	−	11.0676i	0.602730	−	0.447015i	−0.250815	−	0.968035i	$-0.580698\pi$
$613$	14.9229	−	11.0676i	0.602730	−	0.447015i	0.853544	+	0.521020i	$0.174448\pi$
$614$	−0.0338732	−	17.5756i	−0.00136701	−	0.709293i
$615$	4.19368	+	7.84583i	0.169106	+	0.316374i
$616$	22.3724	−	12.1251i	0.901411	−	0.488536i
$617$	7.63646	+	25.1740i	0.307432	+	1.01347i	0.965477	+	0.260489i	$0.0838838\pi$
$617$	7.63646	+	25.1740i	0.307432	+	1.01347i	−0.658045	+	0.752979i	$0.728616\pi$
$618$	7.18082	+	0.693277i	0.288855	+	0.0278877i
$619$	−0.821047	−	16.7128i	−0.0330006	−	0.671744i	−0.957129	−	0.289662i	$-0.906457\pi$
$619$	−0.821047	−	16.7128i	−0.0330006	−	0.671744i	0.924128	−	0.382082i	$-0.124793\pi$
$620$	−5.74523	+	12.2694i	−0.230734	+	0.492751i
$621$	3.03648	+	2.25201i	0.121850	+	0.0903700i
$622$	31.4033	+	23.1966i	1.25916	+	0.930099i
$623$	−19.7538	−	29.5636i	−0.791418	−	1.18444i
$624$	−5.73051	−	6.87390i	−0.229404	−	0.275176i
$625$	−1.67507	+	2.50692i	−0.0670029	+	0.100277i
$626$	−14.2236	−	39.5120i	−0.568488	−	1.57922i
$627$	3.24403	+	5.41233i	0.129554	+	0.216148i
$628$	−13.0266	−	11.7155i	−0.519817	−	0.467498i
$629$	8.85694	+	18.7264i	0.353149	+	0.746671i
$630$	−5.55845	−	1.67445i	−0.221454	−	0.0667115i
$631$	−38.9584	−	3.83707i	−1.55091	−	0.152751i	−0.714020	−	0.700125i	$-0.753128\pi$
$631$	−38.9584	−	3.83707i	−1.55091	−	0.152751i	−0.836888	+	0.547374i	$0.815628\pi$
$632$	6.11857	−	8.35041i	0.243383	−	0.332161i
$633$	−2.13080	+	2.59639i	−0.0846917	+	0.103197i
$634$	2.06332	−	0.414555i	0.0819449	−	0.0164641i
$635$	4.79518	−	1.20113i	0.190291	−	0.0476653i
$636$	−2.00092	+	2.45738i	−0.0793415	+	0.0974414i
$637$	−1.06221	−	1.17196i	−0.0420862	−	0.0464349i
$638$	−7.98203	+	13.3756i	−0.316012	+	0.529545i
$639$		−	3.63374i		−	0.143749i
$640$	−15.3676	+	6.60974i	−0.607458	+	0.261273i
$641$			25.2963i			0.999143i	0.866273	+	0.499572i	$0.166509\pi$
$641$			25.2963i			0.999143i	−0.866273	+	0.499572i	$0.833491\pi$
$642$	11.6837	+	6.97238i	0.461119	+	0.275178i
$643$	20.7914	+	22.9398i	0.819933	+	0.904657i	0.996829	−	0.0795725i	$-0.0253555\pi$
$643$	20.7914	+	22.9398i	0.819933	+	0.904657i	−0.176896	+	0.984230i	$0.556606\pi$
$644$	20.8809	−	2.13789i	0.822824	−	0.0842448i
$645$	11.0198	−	2.76031i	0.433903	−	0.108687i
$646$	1.72353	+	8.57836i	0.0678116	+	0.337511i
$647$	−10.0058	+	12.1921i	−0.393368	+	0.479320i	−0.931605	−	0.363474i	$-0.881591\pi$
$647$	−10.0058	+	12.1921i	−0.393368	+	0.479320i	0.538237	+	0.842794i	$0.319091\pi$
$648$	2.41757	−	1.46810i	0.0949713	−	0.0576726i
$649$	12.9184	+	1.27235i	0.507090	+	0.0499440i
$650$	2.56784	−	8.52415i	0.100719	−	0.334345i
$651$	−5.43772	−	11.4971i	−0.213121	−	0.450607i
$652$	33.0627	−	1.75204i	1.29483	−	0.0686152i
$653$	−1.61711	−	2.69799i	−0.0632824	−	0.105580i	0.824461	−	0.565918i	$-0.191478\pi$
$653$	−1.61711	−	2.69799i	−0.0632824	−	0.105580i	−0.887744	+	0.460338i	$0.847728\pi$
$654$	−20.3106	+	7.31142i	−0.794206	+	0.285899i
$655$	0.680114	−	1.01786i	0.0265742	−	0.0397712i
$656$	−21.1365	+	11.5081i	−0.825242	+	0.449315i
$657$	7.17863	+	10.7436i	0.280065	+	0.419147i
$658$	13.7193	−	18.5730i	0.534832	−	0.724050i
$659$	−26.6474	−	19.7631i	−1.03803	−	0.769859i	−0.0643892	−	0.997925i	$-0.520510\pi$
$659$	−26.6474	−	19.7631i	−1.03803	−	0.769859i	−0.973646	+	0.228066i	$0.926760\pi$
$660$	9.01105	−	3.26344i	0.350754	−	0.127029i
$661$	−1.27407	−	25.9344i	−0.0495558	−	1.00873i	−0.886873	−	0.462013i	$-0.847127\pi$
$661$	−1.27407	−	25.9344i	−0.0495558	−	1.00873i	0.837317	−	0.546717i	$-0.184123\pi$
$662$	4.26260	−	44.1511i	0.165671	−	1.71598i
$663$	2.06370	+	6.80311i	0.0801475	+	0.264211i
$664$	−8.35409	−	6.77557i	−0.324201	−	0.262943i
$665$	−3.76768	−	7.04883i	−0.146104	−	0.273342i
$666$	9.21955	−	0.0177687i	0.357250	−	0.000688524i
$667$	−10.3198	+	7.65367i	−0.399584	+	0.296351i
$668$	−3.32349	+	0.674411i	−0.128590	+	0.0260937i
$669$	−2.87760	−	8.04235i	−0.111254	−	0.310935i
$670$	−0.656810	+	0.312198i	−0.0253748	+	0.0120613i
$671$	20.1022	−	8.32661i	0.776037	−	0.321445i
$672$	4.41367	−	15.0712i	0.170261	−	0.581386i
$673$	14.4172	+	5.97180i	0.555742	+	0.230196i	0.642836	−	0.766004i	$-0.277758\pi$
$673$	14.4172	+	5.97180i	0.555742	+	0.230196i	−0.0870933	+	0.996200i	$0.527758\pi$
$674$	4.26878	−	0.217960i	0.164427	−	0.00839549i
$675$	2.54352	+	1.20299i	0.0979000	+	0.0463032i
$676$	0.0616300	+	15.9887i	0.00237038	+	0.614951i
$677$	44.0460	+	6.53361i	1.69283	+	0.251107i	0.922348	−	0.386359i	$-0.126267\pi$
$677$	44.0460	+	6.53361i	1.69283	+	0.251107i	0.770478	+	0.637466i	$0.220017\pi$
$678$	1.42220	+	3.41486i	0.0546192	+	0.131147i
$679$	42.1983	+	12.8007i	1.61942	+	0.491246i
$680$	13.2890	−	0.0768360i	0.509610	−	0.00294653i
$681$	−6.58623	+	12.3220i	−0.252385	+	0.472179i
$682$	18.5363	+	9.86196i	0.709791	+	0.377634i
$683$	−11.2283	−	10.1767i	−0.429638	−	0.389401i	0.427897	−	0.903828i	$-0.359255\pi$
$683$	−11.2283	−	10.1767i	−0.429638	−	0.389401i	−0.857534	+	0.514427i	$0.828005\pi$
$684$	3.78110	+	0.931642i	0.144574	+	0.0356222i
$685$	4.52057	+	30.4752i	0.172722	+	1.16440i
$686$	−5.95707	+	23.9779i	−0.227442	+	0.915481i
$687$	2.30063	+	0.457623i	0.0877745	+	0.0174594i
$688$	7.69680	+	29.7523i	0.293438	+	1.13430i
$689$	−3.47688	+	0.691594i	−0.132458	+	0.0263476i
$690$	7.89649	+	0.372675i	0.300614	+	0.0141875i
$691$	−11.4670	−	2.87234i	−0.436226	−	0.109269i	0.0186454	−	0.999826i	$-0.494065\pi$
$691$	−11.4670	−	2.87234i	−0.436226	−	0.109269i	−0.454871	+	0.890557i	$0.650315\pi$
$692$	−14.0720	−	18.8219i	−0.534938	−	0.715500i
$693$	−3.03094	+	8.47092i	−0.115136	+	0.321784i
$694$	13.7554	−	1.38156i	0.522148	−	0.0524434i
$695$	−13.9819	+	11.4747i	−0.530365	+	0.435259i
$696$	2.38957	+	9.31095i	0.0905763	+	0.352931i
$697$	19.0261	−	1.87391i	0.720664	−	0.0709792i
$698$	12.9940	+	2.55864i	0.491830	+	0.0968461i
$699$	−12.1590	+	20.2860i	−0.459894	+	0.767287i
$700$	14.9319	−	4.59248i	0.564374	−	0.173580i
$701$	0.826933	−	16.8326i	0.0312328	−	0.635759i	−0.931244	−	0.364396i	$-0.881276\pi$
$701$	0.826933	−	16.8326i	0.0312328	−	0.635759i	0.962477	−	0.271363i	$-0.0874744\pi$
$702$	3.13068	+	0.458228i	0.118160	+	0.0172947i
$703$	8.97567	+	8.97567i	0.338524	+	0.338524i
$704$	9.01594	+	24.3080i	0.339801	+	0.916142i
$705$	6.14925	−	6.14925i	0.231594	−	0.231594i
$706$	−12.8884	+	9.59725i	−0.485061	+	0.361197i
$707$	−18.1403	−	0.891177i	−0.682237	−	0.0335162i
$708$	6.17294	−	5.10594i	0.231993	−	0.191893i
$709$	−6.36032	−	3.81223i	−0.238867	−	0.143171i	0.389661	−	0.920958i	$-0.372592\pi$
$709$	−6.36032	−	3.81223i	−0.238867	−	0.143171i	−0.628528	+	0.777787i	$0.716342\pi$
$710$	−4.23367	−	6.30978i	−0.158887	−	0.236802i
$711$	0.358745	+	3.64240i	0.0134540	+	0.136601i
$712$	32.6574	−	15.6775i	1.22389	−	0.587538i
$713$	10.9871	+	13.3879i	0.411472	+	0.501380i
$714$	−7.89567	+	9.65881i	−0.295488	+	0.361472i
$715$	10.0943	+	3.61179i	0.377504	+	0.135073i
$716$	34.9738	−	8.90390i	1.30703	−	0.332754i
$717$	−2.05676	+	8.21104i	−0.0768110	+	0.306647i
$718$	−32.6258	−	35.8579i	−1.21758	−	1.33820i
$719$	−0.440004	−	2.21205i	−0.0164094	−	0.0824955i	0.971713	−	0.236165i	$-0.0758907\pi$
$719$	−0.440004	−	2.21205i	−0.0164094	−	0.0824955i	−0.988122	+	0.153670i	$0.950891\pi$
$720$	2.48749	−	5.36599i	0.0927032	−	0.199979i
$721$	−2.76281	+	13.8896i	−0.102892	+	0.517275i
$722$	−11.0931	−	18.4271i	−0.412844	−	0.685787i
$723$	−7.15064	+	1.06070i	−0.265935	+	0.0394477i
$724$	6.25783	+	41.0949i	0.232571	+	1.52728i
$725$	−6.42178	+	7.08534i	−0.238499	+	0.263143i
$726$	0.205499	+	0.672770i	0.00762679	+	0.0249688i
$727$	12.7144	+	6.79598i	0.471550	+	0.252049i	0.690014	−	0.723796i	$-0.257604\pi$
$727$	12.7144	+	6.79598i	0.471550	+	0.252049i	−0.218463	+	0.975845i	$0.570104\pi$
$728$	14.5503	−	9.84435i	0.539270	−	0.364856i
$729$	−0.290285	+	0.956940i	−0.0107513	+	0.0354422i
$730$	24.9826	+	10.2918i	0.924648	+	0.380915i
$731$	3.58215	−	24.1489i	0.132491	−	0.893179i
$732$	5.09080	−	12.4255i	0.188162	−	0.459261i
$733$	2.03400	−	4.30053i	0.0751274	−	0.158844i	−0.862930	−	0.505324i	$-0.831373\pi$
$733$	2.03400	−	4.30053i	0.0751274	−	0.158844i	0.938057	+	0.346480i	$0.112623\pi$
$734$	25.0736	+	22.6375i	0.925482	+	0.835565i
$735$	0.400034	−	0.965767i	0.0147555	−	0.0356229i
$736$	−0.843457	+	21.3688i	−0.0310902	+	0.787664i
$737$	0.431307	+	1.04127i	0.0158874	+	0.0383556i
$738$	2.85106	−	8.01686i	0.104949	−	0.295105i
$739$	32.5501	−	11.6466i	1.19738	−	0.428428i	0.338674	−	0.940904i	$-0.390022\pi$
$739$	32.5501	−	11.6466i	1.19738	−	0.428428i	0.858702	+	0.512476i	$0.171272\pi$
$740$	15.9885	−	10.7726i	0.587749	−	0.396007i
$741$	2.59502	+	3.49898i	0.0953304	+	0.128538i
$742$	−4.40723	−	4.39027i	−0.161794	−	0.161172i
$743$	5.87015	−	3.13766i	0.215355	−	0.115110i	−0.360192	−	0.932878i	$-0.617289\pi$
$743$	5.87015	−	3.13766i	0.215355	−	0.115110i	0.575548	+	0.817768i	$0.304789\pi$
$744$	12.3778	−	3.83305i	0.453792	−	0.140527i
$745$	8.75194	−	2.65487i	0.320646	−	0.0972670i
$746$	−14.3451	−	17.4110i	−0.525210	−	0.637461i
$747$	3.79836	−	0.186602i	0.138975	−	0.00682740i
$748$	0.931278	−	20.5745i	0.0340509	−	0.752279i
$749$	−15.9105	+	21.4528i	−0.581357	+	0.783870i
$750$	16.1576	−	2.42859i	0.589993	−	0.0886796i
$751$	−19.4533	+	12.9983i	−0.709860	+	0.474313i	−0.857339	−	0.514752i	$-0.827884\pi$
$751$	−19.4533	+	12.9983i	−0.709860	+	0.474313i	0.147479	+	0.989065i	$0.452884\pi$
$752$	16.7627	+	16.5063i	0.611274	+	0.601921i
$753$	−6.16990	−	4.12259i	−0.224844	−	0.150236i
$754$	−4.57888	+	9.72971i	−0.166753	+	0.354335i
$755$	−14.2564	+	8.54497i	−0.518844	+	0.310983i
$756$	2.39324	+	5.01002i	0.0870412	+	0.182213i
$757$	23.8286	−	11.2701i	0.866063	−	0.409618i	0.0577229	−	0.998333i	$-0.481616\pi$
$757$	23.8286	−	11.2701i	0.866063	−	0.409618i	0.808341	+	0.588715i	$0.200366\pi$
$758$	−39.7770	+	21.3599i	−1.44477	+	0.775827i
$759$	1.20086	−	12.1926i	0.0435885	−	0.442562i
$760$	7.65111	−	2.78762i	0.277535	−	0.101118i
$761$	5.43516	+	4.46052i	0.197024	+	0.161694i	0.727733	−	0.685861i	$-0.240574\pi$
$761$	5.43516	+	4.46052i	0.197024	+	0.161694i	−0.530708	+	0.847554i	$0.678074\pi$
$762$	−3.93622	−	2.61914i	−0.142594	−	0.0948813i
$763$	−10.2963	−	41.1050i	−0.372750	−	1.48810i
$764$	−19.8626	−	5.94175i	−0.718604	−	0.214965i
$765$	−3.48133	+	3.15529i	−0.125868	+	0.114080i
$766$	11.4326	+	45.2713i	0.413078	+	1.63572i
$767$	8.96154			0.323582
$768$	14.5676	+	6.61707i	0.525662	+	0.238773i
$769$	39.3987			1.42076			0.710378	−	0.703821i	$-0.248524\pi$
$769$	39.3987			1.42076			0.710378	+	0.703821i	$0.248524\pi$
$770$	4.60641	+	18.2406i	0.166004	+	0.657346i
$771$	5.73886	−	5.20140i	0.206680	−	0.187324i
$772$	14.7754	−	49.3925i	0.531777	−	1.77767i
$773$	7.11630	+	28.4099i	0.255956	+	1.02183i	0.952554	+	0.304370i	$0.0984460\pi$
$773$	7.11630	+	28.4099i	0.255956	+	1.02183i	−0.696598	+	0.717461i	$0.745304\pi$
$774$	−9.04580	−	6.01902i	−0.325144	−	0.216349i
$775$	9.96414	+	8.17736i	0.357922	+	0.293739i
$776$	−18.9739	+	40.7244i	−0.681122	+	1.46192i
$777$	−1.77394	+	18.0111i	−0.0636398	+	0.646146i
$778$	−41.2399	+	22.1455i	−1.47852	+	0.793953i
$779$	10.5901	−	5.00874i	0.379429	−	0.179457i
$780$	5.97013	−	2.85187i	0.213765	−	0.102113i
$781$	−10.1007	+	6.05413i	−0.361432	+	0.216634i
$782$	7.23389	−	15.3713i	0.258683	−	0.549678i
$783$	−2.82583	−	1.88816i	−0.100987	−	0.0674773i
$784$	2.62087	+	1.06200i	0.0936024	+	0.0379287i
$785$	10.7697	−	7.19610i	0.384388	−	0.256840i
$786$	−1.15784	+	0.174030i	−0.0412987	+	0.00620745i
$787$	−21.6508	+	29.1927i	−0.771767	+	1.04061i	0.226021	+	0.974123i	$0.427428\pi$
$787$	−21.6508	+	29.1927i	−0.771767	+	1.04061i	−0.997787	+	0.0664847i	$0.978822\pi$
$788$	34.2804	+	1.55166i	1.22119	+	0.0552755i
$789$	19.9582	−	0.980486i	0.710532	−	0.0349062i
$790$	4.86670	+	5.90684i	0.173149	+	0.210156i
$791$	−6.94892	+	2.10793i	−0.247075	+	0.0749494i
$792$	−8.10878	−	4.27414i	−0.288133	−	0.151875i
$793$	13.2476	−	7.08099i	0.470436	−	0.251453i
$794$	−28.2784	−	28.1696i	−1.00356	−	0.999701i
$795$	−1.39564	−	1.88181i	−0.0494984	−	0.0667409i
$796$	13.7896	+	20.4664i	0.488759	+	0.725411i
$797$	−43.0756	+	15.4127i	−1.52582	+	0.545945i	−0.960343	−	0.278822i	$-0.910056\pi$
$797$	−43.0756	+	15.4127i	−1.52582	+	0.545945i	−0.565472	+	0.824767i	$0.691306\pi$
$798$	−2.56144	+	7.20249i	−0.0906741	+	0.254965i
$799$	−7.15176	−	17.2659i	−0.253011	−	0.610823i
$800$	2.48703	+	15.7209i	0.0879300	+	0.555819i
$801$	−4.90127	+	11.8327i	−0.173178	+	0.418089i
$802$	−2.10167	−	1.89748i	−0.0742125	−	0.0670022i
$803$	17.9037	−	37.8542i	0.631808	−	1.33584i
$804$	0.643626	+	0.263697i	0.0226990	+	0.00929987i
$805$	−2.27701	+	15.3503i	−0.0802539	+	0.541028i
$806$	13.4025	+	5.52127i	0.472083	+	0.194478i
$807$	−4.88396	+	16.1003i	−0.171924	+	0.566756i
$808$	3.50501	−	18.1693i	0.123306	−	0.639193i
$809$	−3.21473	−	1.71831i	−0.113024	−	0.0604125i	0.413916	−	0.910315i	$-0.364161\pi$
$809$	−3.21473	−	1.71831i	−0.113024	−	0.0604125i	−0.526940	+	0.849903i	$0.676661\pi$
$810$	0.610869	+	1.99988i	0.0214637	+	0.0702687i
$811$	4.37023	−	4.82180i	0.153459	−	0.169316i	−0.659369	−	0.751819i	$-0.729177\pi$
$811$	4.37023	−	4.82180i	0.153459	−	0.169316i	0.812829	+	0.582503i	$0.197927\pi$
$812$	−18.6549	+	2.84073i	−0.654660	+	0.0996901i
$813$	−11.9892	+	1.77844i	−0.420481	+	0.0623725i
$814$	−15.4100	−	25.5980i	−0.540119	−	0.897209i
$815$	−4.77542	+	24.0077i	−0.167276	+	0.840952i
$816$	−8.60807	−	9.35163i	−0.301343	−	0.327373i
$817$	−2.91843	−	14.6719i	−0.102103	−	0.513306i
$818$	33.1548	+	36.4393i	1.15923	+	1.27407i
$819$	−1.50917	+	6.02496i	−0.0527348	+	0.210529i
$820$	−4.38974	−	17.2426i	−0.153296	−	0.602137i
$821$	3.19729	+	1.14401i	0.111586	+	0.0399261i	0.392091	−	0.919926i	$-0.371752\pi$
$821$	3.19729	+	1.14401i	0.111586	+	0.0399261i	−0.280505	+	0.959853i	$0.590502\pi$
$822$	18.6494	−	22.8139i	0.650474	−	0.795727i
$823$	7.93198	+	9.66514i	0.276491	+	0.336906i	0.892678	−	0.450694i	$-0.148824\pi$
$823$	7.93198	+	9.66514i	0.276491	+	0.336906i	−0.616187	+	0.787600i	$0.711324\pi$
$824$	−13.6129	−	4.78216i	−0.474226	−	0.166594i
$825$	−0.893761	−	9.07450i	−0.0311168	−	0.315934i
$826$	8.76196	+	13.0587i	0.304868	+	0.454369i
$827$	−17.7297	−	10.6268i	−0.616523	−	0.369530i	0.171492	−	0.985186i	$-0.445141\pi$
$827$	−17.7297	−	10.6268i	−0.616523	−	0.369530i	−0.788015	+	0.615656i	$0.788891\pi$
$828$	−4.81907	−	5.82611i	−0.167474	−	0.202471i
$829$	−43.4920	−	2.13663i	−1.51054	−	0.0742081i	−0.723162	−	0.690678i	$-0.757312\pi$
$829$	−43.4920	−	2.13663i	−1.51054	−	0.0742081i	−0.787378	+	0.616470i	$0.788562\pi$
$830$	6.37822	−	4.74950i	0.221391	−	0.164857i
$831$	14.9792	−	14.9792i	0.519623	−	0.519623i
$832$	7.83919	+	16.0905i	0.271775	+	0.557837i
$833$	−1.58847	−	1.58847i	−0.0550372	−	0.0550372i
$834$	17.1173	+	2.50540i	0.592723	+	0.0867550i
$835$	0.123022	−	2.50416i	0.00425734	−	0.0866601i
$836$	−3.70996	−	12.0625i	−0.128312	−	0.417191i
$837$	−2.35523	+	3.92946i	−0.0814086	+	0.135822i
$838$	−36.8601	−	7.25810i	−1.27331	−	0.250727i
$839$	−8.22426	+	0.810019i	−0.283933	+	0.0279650i	−0.238981	−	0.971024i	$-0.576813\pi$
$839$	−8.22426	+	0.810019i	−0.283933	+	0.0279650i	−0.0449519	+	0.998989i	$0.514313\pi$
$840$	9.99289	+	5.91124i	0.344787	+	0.203957i
$841$	−13.4887	+	11.0699i	−0.465126	+	0.381719i
$842$	13.8128	−	1.38732i	0.476019	−	0.0478103i
$843$	−6.62573	+	18.5177i	−0.228202	+	0.637782i
$844$	5.38016	−	4.02244i	0.185193	−	0.138458i
$845$	−11.4665	−	2.87222i	−0.394461	−	0.0988073i
$846$	−8.30825	−	0.392109i	−0.285644	−	0.0134810i
$847$	−1.35437	+	0.269401i	−0.0465367	+	0.00925672i
$848$	5.06143	−	3.81464i	0.173810	−	0.130995i
$849$	0.368362	+	0.0732718i	0.0126422	+	0.00251468i
$850$	3.04858	−	12.2709i	0.104565	−	0.420889i
$851$	−3.61625	−	24.3788i	−0.123964	−	0.835694i
$852$	−1.73867	+	7.05644i	−0.0595658	+	0.241750i
$853$	−19.2261	−	17.4255i	−0.658290	−	0.596639i	0.272517	−	0.962151i	$-0.412144\pi$
$853$	−19.2261	−	17.4255i	−0.658290	−	0.596639i	−0.930807	+	0.365512i	$0.880894\pi$
$854$	23.2709	+	12.3810i	0.796314	+	0.423667i
$855$	−1.35716	+	2.53907i	−0.0464140	+	0.0868345i
$856$	−19.3527	−	19.1302i	−0.661462	−	0.653857i
$857$	−47.6986	−	14.4692i	−1.62935	−	0.494259i	−0.662388	−	0.749161i	$-0.730457\pi$
$857$	−47.6986	−	14.4692i	−1.62935	−	0.494259i	−0.966967	+	0.254902i	$0.917957\pi$
$858$	−3.94226	−	9.46581i	−0.134586	−	0.323157i
$859$	−14.4623	−	2.14528i	−0.493447	−	0.0731960i	−0.104631	−	0.994511i	$-0.533366\pi$
$859$	−14.4623	−	2.14528i	−0.493447	−	0.0731960i	−0.388817	+	0.921315i	$0.627116\pi$
$860$	−22.7203	+	0.0875772i	−0.774754	+	0.00298636i
$861$	15.0992	+	7.14140i	0.514580	+	0.243378i
$862$	−21.4098	+	1.09316i	−0.729221	+	0.0372333i
$863$	39.3510	+	16.2997i	1.33952	+	0.554849i	0.933357	−	0.358949i	$-0.116865\pi$
$863$	39.3510	+	16.2997i	1.33952	+	0.554849i	0.406168	+	0.913799i	$0.366865\pi$
$864$	−5.39720	+	1.69419i	−0.183616	+	0.0576374i
$865$	16.0519	−	6.64891i	0.545781	−	0.226070i
$866$	−14.5377	+	6.91014i	−0.494011	+	0.234816i
$867$	−2.32556	−	6.49949i	−0.0789800	−	0.220734i
$868$	5.05851	+	24.9283i	0.171697	+	0.846121i
$869$	9.52708	−	7.06576i	0.323184	−	0.239690i
$870$	−7.10679	+	0.0136968i	−0.240943	+	0.000464365i
$871$	0.366786	+	0.686208i	0.0124281	+	0.0232513i
$872$	42.9399	−	4.48004i	1.45413	−	0.151713i
$873$	−4.61097	−	15.2003i	−0.156058	−	0.514453i
$874$	1.00038	−	10.3617i	0.0338382	−	0.350489i
$875$	1.57380	+	32.0355i	0.0532043	+	1.08300i
$876$	−8.79976	−	24.2980i	−0.297316	−	0.820953i
$877$	−13.2782	−	9.84781i	−0.448374	−	0.332537i	0.347838	−	0.937555i	$-0.386916\pi$
$877$	−13.2782	−	9.84781i	−0.448374	−	0.332537i	−0.796212	+	0.605018i	$0.793166\pi$
$878$	3.36675	−	4.55787i	0.113622	−	0.153821i
$879$	−9.56804	−	14.3196i	−0.322722	−	0.482988i
$880$	−19.0602	+	2.02575i	−0.642520	+	0.0682879i
$881$	−30.3586	+	45.4349i	−1.02281	+	1.53074i	−0.186518	+	0.982452i	$0.559720\pi$
$881$	−30.3586	+	45.4349i	−1.02281	+	1.53074i	−0.836289	+	0.548288i	$0.815280\pi$
$882$	−0.940705	+	0.338636i	−0.0316752	+	0.0114025i
$883$	14.3884	+	24.0056i	0.484208	+	0.807853i	0.998769	−	0.0496012i	$-0.0157950\pi$
$883$	14.3884	+	24.0056i	0.484208	+	0.807853i	−0.514561	+	0.857454i	$0.672045\pi$
$884$	−0.752402	−	14.1985i	−0.0253060	−	0.477549i
$885$	2.53225	+	5.35400i	0.0851207	+	0.179973i
$886$	7.40426	−	24.5790i	0.248751	−	0.825748i
$887$	−46.0380	−	4.53435i	−1.54581	−	0.152249i	−0.711158	−	0.703033i	$-0.751829\pi$
$887$	−46.0380	−	4.53435i	−1.54581	−	0.152249i	−0.834648	+	0.550784i	$0.814329\pi$
$888$	−17.9121	−	4.37685i	−0.601092	−	0.146878i
$889$	5.88789	−	7.17442i	0.197474	−	0.240622i
$890$	5.27553	+	26.2573i	0.176836	+	0.880147i
$891$	3.14365	−	0.787443i	0.105316	−	0.0263803i
$892$	1.73998	+	16.9945i	0.0582588	+	0.569017i
$893$	−7.69039	−	8.48504i	−0.257349	−	0.283941i
$894$	−7.51149	−	4.48256i	−0.251222	−	0.149919i
$895$			26.6815i			0.891863i
$896$	−15.7823	+	27.1553i	−0.527249	+	0.907196i
$897$		−	8.45804i		−	0.282406i
$898$	−2.44165	+	4.09151i	−0.0814789	+	0.136535i
$899$	−10.4560	−	11.5365i	−0.348728	−	0.384763i
$900$	−4.36370	−	3.55314i	−0.145457	−	0.118438i
$901$	−4.88394	+	1.22336i	−0.162708	+	0.0407561i
$902$	−27.0346	+	5.43170i	−0.900153	+	0.180856i
$903$	13.5309	−	16.4875i	0.450281	−	0.548669i
$904$	−1.12786	−	7.31189i	−0.0375121	−	0.243190i
$905$	−30.5843	−	3.01229i	−1.01666	−	0.100132i
$906$	15.2214	+	4.58534i	0.505697	+	0.152338i
$907$	−20.2779	−	42.8740i	−0.673317	−	1.42361i	−0.893911	−	0.448244i	$-0.852050\pi$
$907$	−20.2779	−	42.8740i	−0.673317	−	1.42361i	0.220594	−	0.975366i	$-0.429200\pi$
$908$	18.6857	−	20.7769i	0.620108	−	0.689507i
$909$	3.36339	+	5.61147i	0.111557	+	0.186121i
$910$	4.39909	+	12.2203i	0.145828	+	0.405100i
$911$	−24.0410	+	35.9799i	−0.796513	+	1.19207i	0.181473	+	0.983396i	$0.441913\pi$
$911$	−24.0410	+	35.9799i	−0.796513	+	1.19207i	−0.977986	+	0.208670i	$0.933087\pi$
$912$	−6.89683	−	3.61835i	−0.228377	−	0.119816i
$913$	−6.84710	−	10.2474i	−0.226606	−	0.339140i
$914$	−34.8473	−	25.7405i	−1.15265	−	0.851422i
$915$	7.97384	+	5.91380i	0.263607	+	0.195504i
$916$	−4.24868	−	1.98947i	−0.140380	−	0.0657340i
$917$	−0.112777	−	2.29563i	−0.00372422	−	0.0758083i
$918$	4.47297	+	0.431847i	0.147630	+	0.0142531i
$919$	−9.46977	−	31.2177i	−0.312379	−	1.02978i	−0.962803	−	0.270204i	$-0.912909\pi$
$919$	−9.46977	−	31.2177i	−0.312379	−	1.02978i	0.650424	−	0.759571i	$-0.274591\pi$
$920$	−15.1560	−	4.50201i	−0.499680	−	0.148427i
$921$	−5.85845	−	10.9604i	−0.193042	−	0.361157i
$922$	−0.0699638	−	36.3017i	−0.00230414	−	1.19553i
$923$	−6.52993	+	4.84293i	−0.214935	+	0.159407i
$924$	9.93900	−	14.9996i	0.326969	−	0.493451i
$925$	−6.17952	−	17.2706i	−0.203181	−	0.567854i
$926$	2.18212	+	4.59079i	0.0717089	+	0.150863i
$927$	4.71291	−	1.95215i	0.154792	−	0.0641170i
$928$	−0.185261	−	19.2245i	−0.00608149	−	0.631075i
$929$	−21.5869	−	8.94160i	−0.708244	−	0.293364i	−0.000666242	−	1.00000i	$-0.500212\pi$
$929$	−21.5869	−	8.94160i	−0.708244	−	0.293364i	−0.707578	+	0.706636i	$0.750212\pi$
$930$	0.488499	+	9.56736i	0.0160185	+	0.313726i
$931$	−1.24437	−	0.588541i	−0.0407824	−	0.0192886i
$932$	33.3182	−	33.5760i	1.09137	−	1.09982i
$933$	27.3078	+	4.05073i	0.894018	+	0.132615i
$934$	23.8552	−	9.93504i	0.780565	−	0.325084i
$935$	14.5710	+	4.42005i	0.476521	+	0.144551i
$936$	−5.86029	−	2.38781i	−0.191549	−	0.0780479i
$937$	−16.1757	+	30.2626i	−0.528437	+	0.988637i	0.466147	+	0.884707i	$0.345642\pi$
$937$	−16.1757	+	30.2626i	−0.528437	+	0.988637i	−0.994585	+	0.103930i	$0.966858\pi$
$938$	−0.641317	+	1.20540i	−0.0209397	+	0.0393578i
$939$	−22.0020	−	19.9415i	−0.718010	−	0.650766i
$940$	−14.8836	+	8.99907i	−0.485451	+	0.293517i
$941$	2.22585	+	15.0054i	0.0725605	+	0.489163i	0.994743	+	0.102407i	$0.0326545\pi$
$941$	2.22585	+	15.0054i	0.0725605	+	0.489163i	−0.922182	+	0.386756i	$0.873596\pi$
$942$	−12.0229	−	2.98696i	−0.391727	−	0.0973205i
$943$	−22.3083	−	4.43740i	−0.726458	−	0.144502i
$944$	−14.4304	+	6.96172i	−0.469671	+	0.226585i
$945$	−4.02601	+	0.800823i	−0.130966	+	0.0260508i
$946$	−1.65998	+	35.1728i	−0.0539708	+	1.14357i
$947$	−1.97811	−	0.495491i	−0.0642800	−	0.0161013i	0.210707	−	0.977549i	$-0.432423\pi$
$947$	−1.97811	−	0.495491i	−0.0642800	−	0.0161013i	−0.274987	+	0.961448i	$0.588673\pi$
$948$	1.04616	−	7.24490i	0.0339776	−	0.235304i
$949$	9.73907	−	27.2189i	0.316143	−	0.883562i
$950$	−0.774266	−	7.70891i	−0.0251205	−	0.250110i
$951$	1.15035	−	0.944068i	0.0373027	−	0.0306135i
$952$	19.9543	−	14.9787i	0.646723	−	0.485463i
$953$	−0.118520	+	0.0116732i	−0.00383925	+	0.000378133i	−0.0999366	−	0.994994i	$-0.531864\pi$
$953$	−0.118520	+	0.0116732i	−0.00383925	+	0.000378133i	0.0960973	+	0.995372i	$0.469364\pi$
$954$	−0.432922	+	2.19858i	−0.0140164	+	0.0711818i
$955$	7.88000	−	13.1470i	0.254991	−	0.425427i
$956$	7.92287	−	14.9611i	0.256244	−	0.483876i
$957$	−0.540435	+	11.0008i	−0.0174698	+	0.355606i
$958$	−7.44991	+	50.8989i	−0.240696	+	1.64447i
$959$	40.9016	+	40.9016i	1.32078	+	1.32078i
$960$	−7.39802	+	9.23013i	−0.238770	+	0.297901i
$961$	7.07971	−	7.07971i	0.228378	−	0.228378i
$962$	−12.3194	−	16.5441i	−0.397195	−	0.533403i
$963$	9.60930	+	0.472075i	0.309655	+	0.0152124i
$964$	14.3935	+	1.36164i	0.463583	+	0.0438554i
$965$	32.6927	+	19.5952i	1.05241	+	0.630793i
$966$	12.3250	−	8.26968i	0.396549	−	0.266073i
$967$	3.00213	+	30.4811i	0.0965418	+	0.980206i	0.914407	+	0.404796i	$0.132657\pi$
$967$	3.00213	+	30.4811i	0.0965418	+	0.980206i	−0.817865	+	0.575410i	$0.804843\pi$
$968$	−0.0771574	−	1.40479i	−0.00247993	−	0.0451518i
$969$	3.92501	+	4.78264i	0.126090	+	0.153641i
$970$	−25.7166	−	21.0222i	−0.825709	−	0.674983i
$971$	−4.55559	−	1.63002i	−0.146196	−	0.0523097i	0.262775	−	0.964857i	$-0.415362\pi$
$971$	−4.55559	−	1.63002i	−0.146196	−	0.0523097i	−0.408971	+	0.912547i	$0.634112\pi$
$972$	1.02159	−	1.71941i	0.0327674	−	0.0551500i
$973$	−8.25154	+	32.9420i	−0.264532	+	1.05607i
$974$	35.5529	−	32.3483i	1.13919	−	1.03651i
$975$	−1.22810	−	6.17408i	−0.0393307	−	0.197729i
$976$	−15.8313	+	21.6936i	−0.506747	+	0.694395i
$977$	3.86766	−	19.4440i	0.123737	−	0.622070i	−0.868291	−	0.496055i	$-0.834781\pi$
$977$	3.86766	−	19.4440i	0.123737	−	0.622070i	0.992028	−	0.126015i	$-0.0402187\pi$
$978$	20.0576	−	12.0747i	0.641372	−	0.386105i
$979$	41.0574	−	6.09029i	1.31220	−	0.194646i
$980$	−1.23893	+	1.68404i	−0.0395763	+	0.0537946i
$981$	−10.2506	+	11.3098i	−0.327278	+	0.361095i
$982$	39.1576	−	11.9608i	1.24957	−	0.381684i
$983$	25.3541	+	13.5520i	0.808670	+	0.432243i	0.823270	−	0.567650i	$-0.192147\pi$
$983$	25.3541	+	13.5520i	0.808670	+	0.432243i	−0.0145997	+	0.999893i	$0.504647\pi$
$984$	−9.37243	+	14.2039i	−0.298782	+	0.452805i
$985$	−7.36451	+	24.2775i	−0.234653	+	0.773547i
$986$	−5.81734	+	14.1212i	−0.185262	+	0.449711i
$987$	2.39574	−	16.1508i	0.0762572	−	0.514085i
$988$	−3.36514	−	8.03640i	−0.107059	−	0.255672i
$989$	−12.4183	+	26.2563i	−0.394879	+	0.834902i
$990$	4.54131	−	5.03001i	0.144332	−	0.159864i
$991$	12.7527	−	30.7877i	0.405103	−	0.978005i	−0.581305	−	0.813686i	$-0.697457\pi$
$991$	12.7527	−	30.7877i	0.405103	−	0.978005i	0.986407	−	0.164319i	$-0.0525425\pi$
$992$	−25.8707	+	1.52098i	−0.821397	+	0.0482911i
$993$	−12.0028	−	28.9772i	−0.380896	−	0.919564i
$994$	−13.4416	−	4.78027i	−0.426341	−	0.151621i
$995$	−17.1786	+	6.14660i	−0.544598	+	0.194860i
$996$	−7.46541	−	1.45507i	−0.236550	−	0.0461057i
$997$	−20.4143	−	27.5255i	−0.646527	−	0.871741i	0.351391	−	0.936229i	$-0.385709\pi$
$997$	−20.4143	−	27.5255i	−0.646527	−	0.871741i	−0.997919	+	0.0644876i	$0.979459\pi$
$998$	−3.91797	+	3.93310i	−0.124021	+	0.124500i
$999$	5.74944	−	3.07314i	0.181904	−	0.0972298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.157.5	✓	2048
256.181	even	64	inner	768.2.z.a.181.5	yes	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.157.5	✓	2048	1.1	even	1	trivial
768.2.z.a.181.5	yes	2048	256.181	even	64	inner

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37117 + 0.346269i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.76020 - 0.949585i) q^{4} +(0.359277 + 1.43432i) q^{5} +(0.783427 - 1.17739i) q^{6} +(2.14599 + 1.76117i) q^{7} +(-2.08471 + 1.91154i) q^{8} +(0.0980171 - 0.995185i) q^{9} +O(q^{10})\)	\(q+(-1.37117 + 0.346269i) q^{2} +(-0.740951 + 0.671559i) q^{3} +(1.76020 - 0.949585i) q^{4} +(0.359277 + 1.43432i) q^{5} +(0.783427 - 1.17739i) q^{6} +(2.14599 + 1.76117i) q^{7} +(-2.08471 + 1.91154i) q^{8} +(0.0980171 - 0.995185i) q^{9} +(-0.989289 - 1.84228i) q^{10} +(-2.92962 + 1.38561i) q^{11} +(-0.666516 + 1.88567i) q^{12} +(-1.91901 + 1.15021i) q^{13} +(-3.55234 - 1.67176i) q^{14} +(-1.22943 - 0.821482i) q^{15} +(2.19658 - 3.34291i) q^{16} +(-2.64206 + 1.76537i) q^{17} +(0.210204 + 1.39850i) q^{18} +(-1.15988 + 1.56392i) q^{19} +(1.99440 + 2.18351i) q^{20} +(-2.77280 + 0.136219i) q^{21} +(3.53720 - 2.91434i) q^{22} +(3.61766 - 1.09741i) q^{23} +(0.260955 - 2.81636i) q^{24} +(2.48142 - 1.32635i) q^{25} +(2.23300 - 2.24162i) q^{26} +(0.595699 + 0.803208i) q^{27} +(5.44973 + 1.06220i) q^{28} +(-3.19993 + 1.14495i) q^{29} +(1.97021 + 0.700673i) q^{30} +(1.75317 + 4.23252i) q^{31} +(-1.85432 + 5.34429i) q^{32} +(1.24019 - 2.99408i) q^{33} +(3.01141 - 3.33547i) q^{34} +(-1.75506 + 3.71077i) q^{35} +(-0.772483 - 1.84480i) q^{36} +(0.956568 - 6.44866i) q^{37} +(1.04885 - 2.54602i) q^{38} +(0.649458 - 2.14098i) q^{39} +(-3.49074 - 2.30336i) q^{40} +(-5.30615 - 2.83620i) q^{41} +(3.75480 - 1.14691i) q^{42} +(-5.15955 + 5.69268i) q^{43} +(-3.84095 + 5.22086i) q^{44} +(1.46262 - 0.216960i) q^{45} +(-4.58042 + 2.75741i) q^{46} +(-1.14740 + 5.76835i) q^{47} +(0.617407 + 3.95206i) q^{48} +(0.137922 + 0.693381i) q^{49} +(-2.94317 + 2.67789i) q^{50} +(0.772088 - 3.08235i) q^{51} +(-2.28561 + 3.84685i) q^{52} +(1.49186 + 0.533797i) q^{53} +(-1.09493 - 0.895059i) q^{54} +(-3.03995 - 3.70418i) q^{55} +(-7.84030 + 0.430623i) q^{56} +(-0.190848 - 1.93772i) q^{57} +(3.99118 - 2.67796i) q^{58} +(-3.43562 - 2.05923i) q^{59} +(-2.94411 - 0.278516i) q^{60} +(-6.70590 - 0.329440i) q^{61} +(-3.86947 - 5.19642i) q^{62} +(1.96303 - 1.96303i) q^{63} +(0.692023 - 7.97001i) q^{64} +(-2.33922 - 2.33922i) q^{65} +(-0.663748 + 4.53482i) q^{66} +(0.0170645 - 0.347357i) q^{67} +(-2.97417 + 5.61625i) q^{68} +(-1.94354 + 3.24260i) q^{69} +(1.12156 - 5.69581i) q^{70} +(3.61624 - 0.356169i) q^{71} +(1.69800 + 2.26203i) q^{72} +(-9.98821 + 8.19712i) q^{73} +(0.921357 + 9.17341i) q^{74} +(-0.947893 + 2.64918i) q^{75} +(-0.556543 + 3.85421i) q^{76} +(-8.72721 - 2.18605i) q^{77} +(-0.149161 + 3.16052i) q^{78} +(-3.58970 + 0.714035i) q^{79} +(5.58397 + 1.94955i) q^{80} +(-0.980785 - 0.195090i) q^{81} +(8.25770 + 2.05154i) q^{82} +(0.558008 + 3.76178i) q^{83} +(-4.75132 + 2.87278i) q^{84} +(-3.48133 - 3.15529i) q^{85} +(5.10340 - 9.59221i) q^{86} +(1.60209 - 2.99730i) q^{87} +(3.45876 - 8.48868i) q^{88} +(-12.2562 - 3.71786i) q^{89} +(-1.93038 + 0.803950i) q^{90} +(-6.14388 - 0.911358i) q^{91} +(5.32571 - 5.36692i) q^{92} +(-4.14139 - 1.95873i) q^{93} +(-0.424130 - 8.30668i) q^{94} +(-2.65987 - 1.10176i) q^{95} +(-2.21505 - 5.20515i) q^{96} +(14.6752 - 6.07866i) q^{97} +(-0.429211 - 0.902983i) q^{98} +(1.09178 + 3.05133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more