LMFDB - Embedded newform 768.2.z.a.685.28

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			685.28
Character	$\chi$	$=$	768.685
Dual form			768.2.z.a.37.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.268514 - 1.38849i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(-1.85580 + 0.745657i) q^{4} +(-0.0355676 + 0.0994047i) q^{5} +(-1.05290 + 0.944138i) q^{6} +(0.550047 + 0.166855i) q^{7} +(1.53364 + 2.37654i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(-0.268514 - 1.38849i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(-1.85580 + 0.745657i) q^{4} +(-0.0355676 + 0.0994047i) q^{5} +(-1.05290 + 0.944138i) q^{6} +(0.550047 + 0.166855i) q^{7} +(1.53364 + 2.37654i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(0.147573 + 0.0226936i) q^{10} +(0.784890 - 0.582114i) q^{11} +(1.59364 + 1.20843i) q^{12} +(-2.67374 + 5.65315i) q^{13} +(0.0839809 - 0.808537i) q^{14} +(0.103548 - 0.0205969i) q^{15} +(2.88799 - 2.76758i) q^{16} +(-0.333374 - 0.0663123i) q^{17} +(1.35111 + 0.417721i) q^{18} +(6.92114 + 0.340014i) q^{19} +(-0.00811550 - 0.210997i) q^{20} +(-0.139665 - 0.557572i) q^{21} +(-1.01901 - 0.933505i) q^{22} +(-0.257680 + 2.61627i) q^{23} +(1.24997 - 2.53724i) q^{24} +(3.85644 + 3.16490i) q^{25} +(8.56727 + 2.19451i) q^{26} +(0.998795 - 0.0490677i) q^{27} +(-1.14519 + 0.100497i) q^{28} +(4.87539 - 0.723196i) q^{29} +(-0.0564026 - 0.138244i) q^{30} +(-6.12801 + 2.53830i) q^{31} +(-4.61822 - 3.26681i) q^{32} +(-0.902810 - 0.373956i) q^{33} +(-0.00255818 + 0.480692i) q^{34} +(-0.0361500 + 0.0487427i) q^{35} +(0.217208 - 1.98817i) q^{36} +(-3.68570 - 3.34052i) q^{37} +(-1.38632 - 9.70122i) q^{38} +(6.22345 - 0.612956i) q^{39} +(-0.290787 + 0.0679238i) q^{40} +(2.53423 - 2.07979i) q^{41} +(-0.736680 + 0.343638i) q^{42} +(9.80504 + 5.87692i) q^{43} +(-1.02254 + 1.66555i) q^{44} +(-0.0709007 - 0.0782268i) q^{45} +(3.70185 - 0.344719i) q^{46} +(7.39908 - 4.94391i) q^{47} +(-3.85856 - 1.05429i) q^{48} +(-5.54558 - 3.70544i) q^{49} +(3.35891 - 6.20444i) q^{50} +(0.114511 + 0.320036i) q^{51} +(0.746619 - 12.4848i) q^{52} +(1.01797 + 0.151001i) q^{53} +(-0.336320 - 1.37364i) q^{54} +(0.0299483 + 0.0987262i) q^{55} +(0.447040 + 1.56310i) q^{56} +(-3.26654 - 6.11126i) q^{57} +(-2.31326 - 6.57524i) q^{58} +(4.89345 + 10.3463i) q^{59} +(-0.176806 + 0.115435i) q^{60} +(1.96827 - 7.85779i) q^{61} +(5.16986 + 7.82710i) q^{62} +(-0.406444 + 0.406444i) q^{63} +(-3.29587 + 7.28953i) q^{64} +(-0.466851 - 0.466851i) q^{65} +(-0.276817 + 1.35395i) q^{66} +(-1.21038 - 0.303184i) q^{67} +(0.668122 - 0.125521i) q^{68} +(2.37652 - 1.12401i) q^{69} +(0.0773854 + 0.0371058i) q^{70} +(5.25824 - 2.81059i) q^{71} +(-2.81887 + 0.232261i) q^{72} +(-11.0448 + 3.35041i) q^{73} +(-3.64861 + 6.01452i) q^{74} +(0.732017 - 4.93486i) q^{75} +(-13.0978 + 4.52980i) q^{76} +(0.528856 - 0.189228i) q^{77} +(-2.52216 - 8.47660i) q^{78} +(-6.81504 + 10.1994i) q^{79} +(0.172392 + 0.385516i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(-3.56824 - 2.96030i) q^{82} +(7.76169 - 7.03479i) q^{83} +(0.674947 + 0.930601i) q^{84} +(0.0184491 - 0.0307804i) q^{85} +(5.52724 - 15.1922i) q^{86} +(-3.12676 - 3.80997i) q^{87} +(2.58716 + 0.972565i) q^{88} +(-1.10302 - 11.1991i) q^{89} +(-0.0895793 + 0.119450i) q^{90} +(-2.41394 + 2.66337i) q^{91} +(-1.47264 - 5.04741i) q^{92} +(5.32760 + 3.95122i) q^{93} +(-8.85131 - 8.94603i) q^{94} +(-0.279967 + 0.675900i) q^{95} +(-0.427795 + 5.64066i) q^{96} +(3.78616 + 9.14061i) q^{97} +(-3.65589 + 8.69493i) q^{98} +(0.143384 + 0.966618i) 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{39}{64}\right)$

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 $

$2$	−0.268514	−	1.38849i	−0.189868	−	0.981810i
$2$	−0.268514	−	1.38849i	−0.189868	−	0.981810i
$3$	−0.514103	−	0.857729i	−0.296817	−	0.495210i
$3$	−0.514103	−	0.857729i	−0.296817	−	0.495210i
$4$	−1.85580	+	0.745657i	−0.927900	+	0.372829i
$5$	−0.0355676	+	0.0994047i	−0.0159063	+	0.0444551i	−0.949235	−	0.314568i	$-0.898140\pi$
$5$	−0.0355676	+	0.0994047i	−0.0159063	+	0.0444551i	0.933329	+	0.359024i	$0.116890\pi$
$6$	−1.05290	+	0.944138i	−0.429846	+	0.385443i
$7$	0.550047	+	0.166855i	0.207898	+	0.0630653i	0.392516	−	0.919745i	$-0.371605\pi$
$7$	0.550047	+	0.166855i	0.207898	+	0.0630653i	−0.184618	+	0.982810i	$0.559105\pi$
$8$	1.53364	+	2.37654i	0.542225	+	0.840233i
$9$	−0.471397	+	0.881921i	−0.157132	+	0.293974i
$10$	0.147573	+	0.0226936i	0.0466666	+	0.00717635i
$11$	0.784890	−	0.582114i	0.236653	−	0.175514i	−0.470873	−	0.882201i	$-0.656061\pi$
$11$	0.784890	−	0.582114i	0.236653	−	0.175514i	0.707526	+	0.706687i	$0.249811\pi$
$12$	1.59364	+	1.20843i	0.460045	+	0.348843i
$13$	−2.67374	+	5.65315i	−0.741562	+	1.56790i	0.0793493	+	0.996847i	$0.474716\pi$
$13$	−2.67374	+	5.65315i	−0.741562	+	1.56790i	−0.820912	+	0.571055i	$0.806534\pi$
$14$	0.0839809	−	0.808537i	0.0224448	−	0.216091i
$15$	0.103548	−	0.0205969i	0.0267359	−	0.00531810i
$16$	2.88799	−	2.76758i	0.721998	−	0.691895i
$17$	−0.333374	−	0.0663123i	−0.0808551	−	0.0160831i	0.154497	−	0.987993i	$-0.450624\pi$
$17$	−0.333374	−	0.0663123i	−0.0808551	−	0.0160831i	−0.235352	+	0.971910i	$0.575624\pi$
$18$	1.35111	+	0.417721i	0.318461	+	0.0984577i
$19$	6.92114	+	0.340014i	1.58782	+	0.0780045i	0.823682	−	0.567052i	$-0.191916\pi$
$19$	6.92114	+	0.340014i	1.58782	+	0.0780045i	0.764135	+	0.645056i	$0.223166\pi$
$20$	−0.00811550	−	0.210997i	−0.00181468	−	0.0471803i
$21$	−0.139665	−	0.557572i	−0.0304773	−	0.121672i
$22$	−1.01901	−	0.933505i	−0.217254	−	0.199024i
$23$	−0.257680	+	2.61627i	−0.0537299	+	0.545529i	0.930210	+	0.367028i	$0.119625\pi$
$23$	−0.257680	+	2.61627i	−0.0537299	+	0.545529i	−0.983940	+	0.178501i	$0.942875\pi$
$24$	1.24997	−	2.53724i	0.255150	−	0.517911i
$25$	3.85644	+	3.16490i	0.771287	+	0.632979i
$26$	8.56727	+	2.19451i	1.68018	+	0.430379i
$27$	0.998795	−	0.0490677i	0.192218	−	0.00944308i
$28$	−1.14519	+	0.100497i	−0.216421	+	0.0189921i
$29$	4.87539	−	0.723196i	0.905337	−	0.134294i	0.322204	−	0.946670i	$-0.395576\pi$
$29$	4.87539	−	0.723196i	0.905337	−	0.134294i	0.583134	+	0.812376i	$0.301826\pi$
$30$	−0.0564026	−	0.138244i	−0.0102977	−	0.0252398i
$31$	−6.12801	+	2.53830i	−1.10062	+	0.455893i	−0.857699	−	0.514152i	$-0.828107\pi$
$31$	−6.12801	+	2.53830i	−1.10062	+	0.455893i	−0.242924	+	0.970045i	$0.578107\pi$
$32$	−4.61822	−	3.26681i	−0.816394	−	0.577496i
$33$	−0.902810	−	0.373956i	−0.157159	−	0.0650974i
$34$	−0.00255818	+	0.480692i	−0.000438723	+	0.0824380i
$35$	−0.0361500	+	0.0487427i	−0.00611047	+	0.00823901i
$36$	0.217208	−	1.98817i	0.0362013	−	0.331362i
$37$	−3.68570	−	3.34052i	−0.605925	−	0.549178i	0.309893	−	0.950771i	$-0.399707\pi$
$37$	−3.68570	−	3.34052i	−0.605925	−	0.549178i	−0.915818	+	0.401593i	$0.868457\pi$
$38$	−1.38632	−	9.70122i	−0.224890	−	1.57375i
$39$	6.22345	−	0.612956i	0.996549	−	0.0981515i
$40$	−0.290787	+	0.0679238i	−0.0459775	+	0.0107397i
$41$	2.53423	−	2.07979i	0.395780	−	0.324808i	−0.415363	−	0.909656i	$-0.636346\pi$
$41$	2.53423	−	2.07979i	0.395780	−	0.324808i	0.811143	+	0.584847i	$0.198846\pi$
$42$	−0.736680	+	0.343638i	−0.113672	+	0.0530246i
$43$	9.80504	+	5.87692i	1.49525	+	0.896221i	0.999616	+	0.0276923i	$0.00881587\pi$
$43$	9.80504	+	5.87692i	1.49525	+	0.896221i	0.495638	+	0.868529i	$0.334934\pi$
$44$	−1.02254	+	1.66555i	−0.154154	+	0.251091i
$45$	−0.0709007	−	0.0782268i	−0.0105692	−	0.0116614i
$46$	3.70185	−	0.344719i	0.545807	−	0.0508260i
$47$	7.39908	−	4.94391i	1.07927	−	0.721143i	0.116967	−	0.993136i	$-0.462683\pi$
$47$	7.39908	−	4.94391i	1.07927	−	0.721143i	0.962299	+	0.271993i	$0.0876827\pi$
$48$	−3.85856	−	1.05429i	−0.556935	−	0.152174i
$49$	−5.54558	−	3.70544i	−0.792225	−	0.529348i
$50$	3.35891	−	6.20444i	0.475022	−	0.877440i
$51$	0.114511	+	0.320036i	0.0160347	+	0.0448140i
$52$	0.746619	−	12.4848i	0.103537	−	1.73133i
$53$	1.01797	+	0.151001i	0.139829	+	0.0207416i	0.216278	−	0.976332i	$-0.430608\pi$
$53$	1.01797	+	0.151001i	0.139829	+	0.0207416i	−0.0764493	+	0.997073i	$0.524358\pi$
$54$	−0.336320	−	1.37364i	−0.0457674	−	0.186929i
$55$	0.0299483	+	0.0987262i	0.00403822	+	0.0133122i
$56$	0.447040	+	1.56310i	0.0597382	+	0.208879i
$57$	−3.26654	−	6.11126i	−0.432663	−	0.809456i
$58$	−2.31326	−	6.57524i	−0.303746	−	0.863371i
$59$	4.89345	+	10.3463i	0.637074	+	1.34698i	0.921536	+	0.388292i	$0.126935\pi$
$59$	4.89345	+	10.3463i	0.637074	+	1.34698i	−0.284463	+	0.958687i	$0.591815\pi$
$60$	−0.176806	+	0.115435i	−0.0228255	+	0.0149026i
$61$	1.96827	−	7.85779i	0.252012	−	1.00609i	−0.703396	−	0.710798i	$-0.748334\pi$
$61$	1.96827	−	7.85779i	0.252012	−	1.00609i	0.955408	−	0.295289i	$-0.0954160\pi$
$62$	5.16986	+	7.82710i	0.656573	+	0.994043i
$63$	−0.406444	+	0.406444i	−0.0512071	+	0.0512071i
$64$	−3.29587	+	7.28953i	−0.411984	+	0.911191i
$65$	−0.466851	−	0.466851i	−0.0579058	−	0.0579058i
$66$	−0.276817	+	1.35395i	−0.0340738	+	0.166660i
$67$	−1.21038	−	0.303184i	−0.147871	−	0.0370398i	0.168338	−	0.985729i	$-0.446160\pi$
$67$	−1.21038	−	0.303184i	−0.147871	−	0.0370398i	−0.316209	+	0.948690i	$0.602410\pi$
$68$	0.668122	−	0.125521i	0.0810217	−	0.0152216i
$69$	2.37652	−	1.12401i	0.286099	−	0.135315i
$70$	0.0773854	+	0.0371058i	0.00924933	+	0.00443499i
$71$	5.25824	−	2.81059i	0.624038	−	0.333555i	−0.128889	−	0.991659i	$-0.541141\pi$
$71$	5.25824	−	2.81059i	0.624038	−	0.333555i	0.752927	+	0.658104i	$0.228641\pi$
$72$	−2.81887	+	0.232261i	−0.332208	+	0.0273723i
$73$	−11.0448	+	3.35041i	−1.29270	+	0.392135i	−0.860411	−	0.509601i	$-0.829793\pi$
$73$	−11.0448	+	3.35041i	−1.29270	+	0.392135i	−0.432286	+	0.901736i	$0.642293\pi$
$74$	−3.64861	+	6.01452i	−0.424143	+	0.699174i
$75$	0.732017	−	4.93486i	0.0845260	−	0.569828i
$76$	−13.0978	+	4.52980i	−1.50242	+	0.519603i
$77$	0.528856	−	0.189228i	0.0602687	−	0.0215645i
$78$	−2.52216	−	8.47660i	−0.285579	−	0.959786i
$79$	−6.81504	+	10.1994i	−0.766752	+	1.14753i	0.218403	+	0.975859i	$0.429915\pi$
$79$	−6.81504	+	10.1994i	−0.766752	+	1.14753i	−0.985155	+	0.171667i	$0.945085\pi$
$80$	0.172392	+	0.385516i	0.0192740	+	0.0431020i
$81$	−0.555570	−	0.831470i	−0.0617300	−	0.0923855i
$82$	−3.56824	−	2.96030i	−0.394046	−	0.326910i
$83$	7.76169	−	7.03479i	0.851956	−	0.772168i	−0.123504	−	0.992344i	$-0.539413\pi$
$83$	7.76169	−	7.03479i	0.851956	−	0.772168i	0.975460	+	0.220176i	$0.0706631\pi$
$84$	0.674947	+	0.930601i	0.0736427	+	0.101537i
$85$	0.0184491	−	0.0307804i	0.00200108	−	0.00333860i
$86$	5.52724	−	15.1922i	0.596018	−	1.63822i
$87$	−3.12676	−	3.80997i	−0.335224	−	0.408471i
$88$	2.58716	+	0.972565i	0.275792	+	0.103676i
$89$	−1.10302	−	11.1991i	−0.116920	−	1.18710i	−0.857264	−	0.514877i	$-0.827838\pi$
$89$	−1.10302	−	11.1991i	−0.116920	−	1.18710i	0.740344	−	0.672228i	$-0.234662\pi$
$90$	−0.0895793	+	0.119450i	−0.00944248	+	0.0125911i
$91$	−2.41394	+	2.66337i	−0.253050	+	0.279197i
$92$	−1.47264	−	5.04741i	−0.153533	−	0.526229i
$93$	5.32760	+	3.95122i	0.552447	+	0.409722i
$94$	−8.85131	−	8.94603i	−0.912943	−	0.922712i
$95$	−0.279967	+	0.675900i	−0.0287240	+	0.0693459i
$96$	−0.427795	+	5.64066i	−0.0436616	+	0.575697i
$97$	3.78616	+	9.14061i	0.384427	+	0.928088i	0.991098	+	0.133135i	$0.0425044\pi$
$97$	3.78616	+	9.14061i	0.384427	+	0.928088i	−0.606671	+	0.794953i	$0.707496\pi$
$98$	−3.65589	+	8.69493i	−0.369301	+	0.878320i
$99$	0.143384	+	0.966618i	0.0144107	+	0.0971488i
$100$	−9.51670	−	2.99784i	−0.951670	−	0.299784i
$101$	0.455037	+	9.26248i	0.0452778	+	0.921651i	0.908772	+	0.417293i	$0.137021\pi$
$101$	0.455037	+	9.26248i	0.0452778	+	0.921651i	−0.863494	+	0.504359i	$0.831729\pi$
$102$	0.413619	−	0.244931i	0.0409543	−	0.0242518i
$103$	−2.56295	+	3.12297i	−0.252535	+	0.307715i	−0.883812	−	0.467843i	$-0.845031\pi$
$103$	−2.56295	+	3.12297i	−0.252535	+	0.307715i	0.631276	+	0.775558i	$0.282531\pi$
$104$	−17.5355	+	2.31568i	−1.71950	+	0.227071i
$105$	0.0603928	+	0.00594817i	0.00589373	+	0.000580482i
$106$	−0.0636750	−	1.45398i	−0.00618466	−	0.141223i
$107$	6.11546	−	1.53184i	0.591204	−	0.148089i	0.0641784	−	0.997938i	$-0.479557\pi$
$107$	6.11546	−	1.53184i	0.591204	−	0.148089i	0.527025	+	0.849850i	$0.323307\pi$
$108$	−1.81698	+	0.835819i	−0.174839	+	0.0804267i
$109$	−0.0834703	+	1.69908i	−0.00799501	+	0.162742i	0.991478	+	0.130276i	$0.0415862\pi$
$109$	−0.0834703	+	1.69908i	−0.00799501	+	0.162742i	−0.999473	+	0.0324665i	$0.989664\pi$
$110$	0.129039	−	0.0680922i	0.0123034	−	0.00649233i
$111$	−0.970433	+	4.87870i	−0.0921095	+	0.463065i
$112$	2.05032	−	1.04042i	0.193737	−	0.0983109i
$113$	3.94266	+	19.8211i	0.370894	+	1.86461i	0.489992	+	0.871727i	$0.337000\pi$
$113$	3.94266	+	19.8211i	0.370894	+	1.86461i	−0.119098	+	0.992883i	$0.538000\pi$
$114$	−7.60830	+	6.17651i	−0.712583	+	0.578483i
$115$	−0.250904	−	0.118669i	−0.0233969	−	0.0110659i
$116$	−8.50850	+	4.97748i	−0.789994	+	0.462147i
$117$	−3.72524	−	5.02291i	−0.344399	−	0.464368i
$118$	13.0518	−	9.57264i	1.20152	−	0.881233i
$119$	−0.172307	−	0.0921001i	−0.0157954	−	0.00844280i
$120$	0.207755	+	0.214497i	0.0189653	+	0.0195808i
$121$	−2.91594	+	9.61255i	−0.265085	+	0.873868i
$122$	−11.4390	−	0.623000i	−1.03564	−	0.0564037i
$123$	−3.08675	−	1.10446i	−0.278323	−	0.0995854i
$124$	9.47966	−	9.27998i	0.851298	−	0.833367i
$125$	−0.904548	+	0.542165i	−0.0809053	+	0.0484928i
$126$	0.673478	+	0.455206i	0.0599982	+	0.0405530i
$127$			13.3381i			1.18357i	0.806097	+	0.591784i	$0.201576\pi$
$127$			13.3381i			1.18357i	−0.806097	+	0.591784i	$0.798424\pi$
$128$	11.0064	+	2.61894i	0.972839	+	0.231483i
$129$		−	11.4314i		−	1.00648i
$130$	−0.522862	+	0.773574i	−0.0458580	+	0.0678469i
$131$	17.5133	−	10.4971i	1.53015	−	0.917134i	0.532656	−	0.846332i	$-0.321194\pi$
$131$	17.5133	−	10.4971i	1.53015	−	0.917134i	0.997490	−	0.0708020i	$-0.0225559\pi$
$132$	1.95428	+	0.0208014i	0.170098	+	0.00181053i
$133$	3.75022	+	1.34185i	0.325185	+	0.116353i
$134$	−0.0959640	+	1.76201i	−0.00829003	+	0.152214i
$135$	−0.0306472	+	0.101030i	−0.00263769	+	0.00869529i
$136$	−0.353684	−	0.893976i	−0.0303282	−	0.0766578i
$137$	−13.3592	−	7.14064i	−1.14135	−	0.610066i	−0.211275	−	0.977427i	$-0.567762\pi$
$137$	−13.3592	−	7.14064i	−1.14135	−	0.610066i	−0.930079	+	0.367361i	$0.880262\pi$
$138$	−2.19880	−	2.99796i	−0.187175	−	0.255203i
$139$	−2.90709	−	3.91976i	−0.246576	−	0.332470i	0.662529	−	0.749036i	$-0.269483\pi$
$139$	−2.90709	−	3.91976i	−0.246576	−	0.332470i	−0.909105	+	0.416567i	$0.863233\pi$
$140$	0.0307419	−	0.117412i	0.00259817	−	0.00992314i
$141$	−8.04442	−	3.80473i	−0.677462	−	0.320416i
$142$	−5.31438	−	6.54632i	−0.445973	−	0.549355i
$143$	1.19219	+	5.99353i	0.0996957	+	0.501204i
$144$	1.07940	+	3.85161i	0.0899499	+	0.320967i
$145$	−0.101517	+	0.510359i	−0.00843051	+	0.0423830i
$146$	7.61769	+	14.4360i	0.630444	+	1.19473i
$147$	−0.327262	+	6.66157i	−0.0269921	+	0.549437i
$148$	9.33080	+	3.45107i	0.766987	+	0.283677i
$149$	−1.52480	+	0.381942i	−0.124916	+	0.0312899i	−0.304934	−	0.952373i	$-0.598634\pi$
$149$	−1.52480	+	0.381942i	−0.124916	+	0.0312899i	0.180018	+	0.983663i	$0.442384\pi$
$150$	−7.04855	+	0.308681i	−0.575512	+	0.0252037i
$151$	9.00117	+	0.886538i	0.732505	+	0.0721454i	0.457390	−	0.889266i	$-0.348784\pi$
$151$	9.00117	+	0.886538i	0.732505	+	0.0721454i	0.275115	+	0.961411i	$0.411284\pi$
$152$	9.80651	+	16.9698i	0.795413	+	1.37643i
$153$	0.215634	−	0.262750i	0.0174330	−	0.0212421i
$154$	−0.404745	−	0.683500i	−0.0326153	−	0.0550780i
$155$	−0.0343610	−	0.699434i	−0.00275994	−	0.0561799i
$156$	−11.0924	+	5.77808i	−0.888104	+	0.462617i
$157$	−0.511823	−	3.45043i	−0.0408479	−	0.275374i	0.959123	−	0.282989i	$-0.0913260\pi$
$157$	−0.511823	−	3.45043i	−0.0408479	−	0.275374i	−0.999971	+	0.00761504i	$0.997576\pi$
$158$	15.9917	+	6.72392i	1.27223	+	0.534926i
$159$	−0.393822	−	0.950770i	−0.0312321	−	0.0754009i
$160$	0.488995	−	0.342880i	0.0386584	−	0.0271071i
$161$	−0.578273	+	1.39608i	−0.0455743	+	0.110026i
$162$	−1.00531	+	0.994664i	−0.0789844	+	0.0781482i
$163$	12.3951	+	9.19286i	0.970862	+	0.720040i	0.960029	−	0.279901i	$-0.0903016\pi$
$163$	12.3951	+	9.19286i	0.970862	+	0.720040i	0.0108332	+	0.999941i	$0.496552\pi$
$164$	−3.15221	+	5.74934i	−0.246147	+	0.448948i
$165$	0.0692838	−	0.0764429i	0.00539374	−	0.00595107i
$166$	−11.8518	−	8.88808i	−0.919881	−	0.689849i
$167$	0.767537	+	7.79294i	0.0593938	+	0.603036i	0.978106	+	0.208108i	$0.0667304\pi$
$167$	0.767537	+	7.79294i	0.0593938	+	0.603036i	−0.918712	+	0.394928i	$0.870770\pi$
$168$	1.11090	−	1.18704i	0.0857074	−	0.0915818i
$169$	−16.5621	−	20.1810i	−1.27401	−	1.55238i
$170$	−0.0476921	−	0.0173513i	−0.00365781	−	0.00133079i
$171$	−3.56247	+	5.94362i	−0.272429	+	0.454520i
$172$	−22.5784	−	3.59519i	−1.72158	−	0.274130i
$173$	−13.6365	+	12.3594i	−1.03677	+	0.939671i	−0.998223	−	0.0595861i	$-0.981022\pi$
$173$	−13.6365	+	12.3594i	−1.03677	+	0.939671i	−0.0385438	+	0.999257i	$0.512272\pi$
$174$	−4.45051	+	5.36450i	−0.337393	+	0.406681i
$175$	1.59314	+	2.38431i	0.120430	+	0.180237i
$176$	0.655707	−	3.85339i	0.0494258	−	0.290460i
$177$	6.35861	−	9.51634i	0.477943	−	0.715292i
$178$	−15.2537	+	4.53865i	−1.14331	+	0.340186i
$179$	2.09420	−	0.749316i	0.156528	−	0.0560065i	−0.257460	−	0.966289i	$-0.582886\pi$
$179$	2.09420	−	0.749316i	0.156528	−	0.0560065i	0.413988	+	0.910282i	$0.364136\pi$
$180$	0.189908	+	0.0923058i	0.0141549	+	0.00688007i
$181$	−0.297897	+	2.00826i	−0.0221425	+	0.149273i	−0.997428	−	0.0716759i	$-0.977165\pi$
$181$	−0.297897	+	2.00826i	−0.0221425	+	0.149273i	0.975285	+	0.220948i	$0.0709153\pi$
$182$	4.34624	+	2.63658i	0.322165	+	0.195436i
$183$	−7.75175	+	2.35147i	−0.573026	+	0.173825i
$184$	−6.61285	+	3.40004i	−0.487505	+	0.250654i
$185$	0.463155	−	0.247561i	0.0340518	−	0.0182011i
$186$	4.05569	−	8.45827i	0.297377	−	0.620191i
$187$	−0.300264	+	0.142014i	−0.0219574	+	0.0103851i
$188$	−10.0448	+	14.6921i	−0.732589	+	1.07153i
$189$	0.557572	+	0.139665i	0.0405574	+	0.0101591i
$190$	1.01365	+	0.207242i	0.0735382	+	0.0150349i
$191$	−8.77751	−	8.77751i	−0.635118	−	0.635118i	0.314229	−	0.949347i	$-0.398254\pi$
$191$	−8.77751	−	8.77751i	−0.635118	−	0.635118i	−0.949347	+	0.314229i	$0.898254\pi$
$192$	7.94685	−	0.920606i	0.573515	−	0.0664390i
$193$	10.6760	−	10.6760i	0.768474	−	0.768474i	−0.209363	−	0.977838i	$-0.567139\pi$
$193$	10.6760	−	10.6760i	0.768474	−	0.768474i	0.977838	+	0.209363i	$0.0671392\pi$
$194$	11.6750	−	7.71142i	0.838215	−	0.553648i
$195$	−0.160422	+	0.640441i	−0.0114881	+	0.0458630i
$196$	13.0545	+	2.74145i	0.932462	+	0.195818i
$197$	10.8943	+	23.0340i	0.776185	+	1.64111i	0.767421	+	0.641144i	$0.221540\pi$
$197$	10.8943	+	23.0340i	0.776185	+	1.64111i	0.00876410	+	0.999962i	$0.497210\pi$
$198$	1.30364	−	0.458638i	0.0926455	−	0.0325940i
$199$	−4.91794	−	9.20081i	−0.348623	−	0.652228i	0.645100	−	0.764099i	$-0.276816\pi$
$199$	−4.91794	−	9.20081i	−0.348623	−	0.652228i	−0.993723	+	0.111870i	$0.964316\pi$
$200$	−1.60709	+	14.0188i	−0.113639	+	0.991278i
$201$	0.362209	+	1.19404i	0.0255483	+	0.0842214i
$202$	12.7387	−	3.11892i	0.896289	−	0.219446i
$203$	2.80236	+	0.415692i	0.196687	+	0.0291758i
$204$	−0.451146	−	0.508537i	−0.0315865	−	0.0356047i
$205$	0.116604	+	0.325887i	0.00814400	+	0.0227610i
$206$	5.02440	+	2.72007i	0.350066	+	0.189516i
$207$	−2.18587	−	1.46055i	−0.151929	−	0.101515i
$208$	7.92381	+	23.7260i	0.549418	+	1.64511i
$209$	5.63026	−	3.76202i	0.389453	−	0.260224i
$210$	−0.00795734	−	0.0854519i	−0.000549109	−	0.00589674i
$211$	0.0709698	+	0.0783031i	0.00488576	+	0.00539060i	0.743389	−	0.668859i	$-0.233217\pi$
$211$	0.0709698	+	0.0783031i	0.00488576	+	0.00539060i	−0.738503	+	0.674250i	$0.764467\pi$
$212$	−2.00174	+	0.478826i	−0.137480	+	0.0328859i
$213$	−5.11400	−	3.06521i	−0.350405	−	0.210025i
$214$	−3.76903	−	8.07992i	−0.257646	−	0.552332i
$215$	−0.932935	+	0.765640i	−0.0636256	+	0.0522162i
$216$	1.64841	+	2.29842i	0.112160	+	0.156388i
$217$	−3.79422	+	0.373698i	−0.257569	+	0.0253683i
$218$	2.38156	−	0.340328i	0.161300	−	0.0230499i
$219$	8.55191	+	7.75100i	0.577884	+	0.523764i
$220$	−0.129194	−	0.160885i	−0.00871025	−	0.0108469i
$221$	1.26623	−	1.70731i	0.0851758	−	0.114846i
$222$	7.03459	+	0.0374371i	0.472131	+	0.00251261i
$223$	−2.97354	−	1.23168i	−0.199123	−	0.0824793i	0.280893	−	0.959739i	$-0.409369\pi$
$223$	−2.97354	−	1.23168i	−0.199123	−	0.0824793i	−0.480016	+	0.877260i	$0.659369\pi$
$224$	−1.99516	−	2.56747i	−0.133307	−	0.171546i
$225$	−4.60910	+	1.90915i	−0.307273	+	0.127277i
$226$	26.4627	−	10.7966i	1.76027	−	0.718177i
$227$	−11.3681	+	1.68630i	−0.754529	+	0.111924i	−0.512904	−	0.858446i	$-0.671430\pi$
$227$	−11.3681	+	1.68630i	−0.754529	+	0.111924i	−0.241625	+	0.970370i	$0.577680\pi$
$228$	10.6189	+	8.90556i	0.703257	+	0.589785i
$229$	−17.3008	+	0.849935i	−1.14327	+	0.0561653i	−0.611872	−	0.790957i	$-0.709583\pi$
$229$	−17.3008	+	0.849935i	−1.14327	+	0.0561653i	−0.531398	+	0.847122i	$0.678333\pi$
$230$	−0.0973990	+	0.380242i	−0.00642230	+	0.0250724i
$231$	−0.434192	−	0.356332i	−0.0285677	−	0.0234449i
$232$	9.19582	+	10.4774i	0.603735	+	0.687877i
$233$	0.764487	−	7.76197i	0.0500832	−	0.508504i	−0.937117	−	0.349016i	$-0.886516\pi$
$233$	0.764487	−	7.76197i	0.0500832	−	0.508504i	0.987200	−	0.159487i	$-0.0509842\pi$
$234$	−5.97397	+	6.52117i	−0.390531	+	0.426303i
$235$	0.228280	+	0.911346i	0.0148914	+	0.0594497i
$236$	−16.7961	−	15.5519i	−1.09333	−	1.01234i
$237$	12.2520	+	0.601901i	0.795852	+	0.0390977i
$238$	−0.0816130	+	0.263977i	−0.00529019	+	0.0171111i
$239$	−29.1563	−	5.79954i	−1.88596	−	0.375141i	−0.889339	−	0.457248i	$-0.848835\pi$
$239$	−29.1563	−	5.79954i	−1.88596	−	0.375141i	−0.996624	+	0.0821068i	$0.973835\pi$
$240$	0.242041	−	0.346060i	0.0156237	−	0.0223381i
$241$	24.6963	−	4.91240i	1.59083	−	0.316435i	0.681276	−	0.732027i	$-0.261425\pi$
$241$	24.6963	−	4.91240i	1.59083	−	0.316435i	0.909551	+	0.415591i	$0.136425\pi$
$242$	14.1299	+	1.46764i	0.908304	+	0.0943434i
$243$	−0.427555	+	0.903989i	−0.0274277	+	0.0579909i
$244$	2.20649	+	16.0502i	0.141256	+	1.02751i
$245$	0.565580	−	0.419463i	0.0361336	−	0.0267985i
$246$	−0.704690	+	4.58247i	−0.0449294	+	0.292168i
$247$	−20.4275	+	38.2171i	−1.29977	+	2.43170i
$248$	−15.4306	−	10.6706i	−0.979842	−	0.677583i
$249$	−10.0242	−	3.04082i	−0.635261	−	0.192704i
$250$	0.995674	+	1.11038i	0.0629720	+	0.0702263i
$251$	−1.14977	+	3.21338i	−0.0725726	+	0.202827i	−0.972353	−	0.233517i	$-0.924977\pi$
$251$	−1.14977	+	3.21338i	−0.0725726	+	0.202827i	0.899780	+	0.436343i	$0.143727\pi$
$252$	0.451211	−	1.05735i	0.0284236	−	0.0666065i
$253$	1.32072	+	2.20348i	0.0830327	+	0.138532i
$254$	18.5198	−	3.58147i	1.16204	−	0.224722i
$255$	−0.0358860			−0.00224727
$256$	0.680986	−	15.9855i	0.0425616	−	0.999094i
$257$	−11.7312			−0.731773			−0.365886	−	0.930659i	$-0.619234\pi$
$257$	−11.7312			−0.731773			−0.365886	+	0.930659i	$0.619234\pi$
$258$	−15.8724	+	3.06949i	−0.988171	+	0.191098i
$259$	−1.46992	−	2.45242i	−0.0913367	−	0.152386i
$260$	1.21449	+	0.518272i	0.0753197	+	0.0321419i
$261$	−1.66044	+	4.64062i	−0.102779	+	0.287247i
$262$	−19.2776	−	21.4984i	−1.19098	−	1.32818i
$263$	3.48662	+	1.05766i	0.214994	+	0.0652178i	0.395944	−	0.918274i	$-0.370417\pi$
$263$	3.48662	+	1.05766i	0.214994	+	0.0652178i	−0.180950	+	0.983492i	$0.557917\pi$
$264$	−0.495869	−	2.71908i	−0.0305186	−	0.167348i
$265$	−0.0512168	+	0.0958200i	−0.00314623	+	0.00588617i
$266$	0.856157	−	5.56744i	0.0524944	−	0.341362i
$267$	−9.03874	+	6.70359i	−0.553162	+	0.410253i
$268$	2.47229	−	0.339878i	0.151019	−	0.0207614i
$269$	5.93953	−	12.5581i	0.362140	−	0.765680i	−0.637850	−	0.770160i	$-0.720176\pi$
$269$	5.93953	−	12.5581i	0.362140	−	0.765680i	0.999990	+	0.00448029i	$0.00142612\pi$
$270$	0.148508	+	0.0154252i	0.00903794	+	0.000938750i
$271$	3.36155	−	0.668654i	0.204200	−	0.0406178i	−0.0919305	−	0.995765i	$-0.529304\pi$
$271$	3.36155	−	0.668654i	0.204200	−	0.0406178i	0.296130	+	0.955148i	$0.404304\pi$
$272$	−1.14631	+	0.731131i	−0.0695050	+	0.0443313i
$273$	3.52547	+	0.701259i	0.213371	+	0.0424421i
$274$	−6.32757	+	20.4665i	−0.382262	+	1.23642i
$275$	4.86921	+	0.239209i	0.293624	+	0.0144248i
$276$	−3.57222	+	3.85801i	−0.215022	+	0.232225i
$277$	1.45524	+	5.80966i	0.0874372	+	0.349069i	0.997919	−	0.0644804i	$-0.0205390\pi$
$277$	1.45524	+	5.80966i	0.0874372	+	0.349069i	−0.910482	+	0.413549i	$0.864289\pi$
$278$	−4.66195	+	5.08897i	−0.279605	+	0.305216i
$279$	0.650139	−	6.60097i	0.0389228	−	0.395190i
$280$	−0.171280	−	0.0111580i	−0.0102359	−	0.000666818i
$281$	−18.1837	−	14.9230i	−1.08475	−	0.890230i	−0.0903477	−	0.995910i	$-0.528798\pi$
$281$	−18.1837	−	14.9230i	−1.08475	−	0.890230i	−0.994400	+	0.105681i	$0.966298\pi$
$282$	−3.12278	+	12.1912i	−0.185959	+	0.725975i
$283$	16.5658	−	0.813825i	0.984734	−	0.0483769i	0.449675	−	0.893192i	$-0.351540\pi$
$283$	16.5658	−	0.813825i	0.984734	−	0.0483769i	0.535058	+	0.844815i	$0.320290\pi$
$284$	−7.66251	+	9.13674i	−0.454686	+	0.542165i
$285$	0.723671	−	0.107346i	0.0428665	−	0.00635865i
$286$	8.00182	−	3.26468i	0.473158	−	0.193045i
$287$	1.74097	−	0.721133i	0.102766	−	0.0425671i
$288$	5.05808	−	2.53294i	0.298050	−	0.149255i
$289$	−15.5992	−	6.46140i	−0.917601	−	0.380083i
$290$	0.735886	+	0.00391628i	0.0432127	+	0.000229972i
$291$	5.89368	−	7.94671i	0.345494	−	0.465844i
$292$	17.9987	−	14.4533i	1.05329	−	0.845817i
$293$	−8.72264	−	7.90574i	−0.509582	−	0.461858i	0.375814	−	0.926695i	$-0.377363\pi$
$293$	−8.72264	−	7.90574i	−0.509582	−	0.461858i	−0.885396	+	0.464837i	$0.846113\pi$
$294$	9.33739	−	1.33433i	0.544568	−	0.0778195i
$295$	−1.20252	+	0.118438i	−0.0700136	+	0.00689574i
$296$	2.28633	−	13.8824i	0.132890	−	0.806896i
$297$	0.755382	−	0.619926i	0.0438317	−	0.0359718i
$298$	0.939752	+	2.01461i	0.0544384	+	0.116703i
$299$	−14.1012	−	8.45192i	−0.815492	−	0.488787i
$300$	2.32123	+	9.70394i	0.134016	+	0.560257i
$301$	4.41264	+	4.86860i	0.254341	+	0.280622i
$302$	−1.18599	−	12.7361i	−0.0682462	−	0.732879i
$303$	7.71076	−	5.15217i	0.442972	−	0.295984i
$304$	20.9292	−	18.1729i	1.20037	−	1.04228i
$305$	0.711095	+	0.475138i	0.0407172	+	0.0272063i
$306$	−0.422727	−	0.228853i	−0.0241657	−	0.0130826i
$307$	−8.90121	−	24.8772i	−0.508019	−	1.41982i	−0.872503	−	0.488608i	$-0.837505\pi$
$307$	−8.90121	−	24.8772i	−0.508019	−	1.41982i	0.364484	−	0.931209i	$-0.381245\pi$
$308$	−0.840352	+	0.745513i	−0.0478835	+	0.0424796i
$309$	3.99628	+	0.592792i	0.227341	+	0.0337228i
$310$	−0.961930	+	0.235518i	−0.0546339	+	0.0133765i
$311$	−9.38635	−	30.9427i	−0.532251	−	1.75460i	−0.648333	−	0.761357i	$-0.724533\pi$
$311$	−9.38635	−	30.9427i	−0.532251	−	1.75460i	0.116082	−	0.993240i	$-0.462967\pi$
$312$	11.0013	+	13.8502i	0.622824	+	0.784113i
$313$	−6.13531	−	11.4784i	−0.346788	−	0.648795i	0.646698	−	0.762746i	$-0.276149\pi$
$313$	−6.13531	−	11.4784i	−0.346788	−	0.648795i	−0.993486	+	0.113951i	$0.963649\pi$
$314$	−4.65345	+	1.63715i	−0.262609	+	0.0923896i
$315$	−0.0259462	−	0.0548586i	−0.00146190	−	0.00309093i
$316$	5.04208	−	24.0098i	0.283639	−	1.35066i
$317$	3.27046	−	13.0564i	0.183687	−	0.733320i	−0.806222	−	0.591614i	$-0.798491\pi$
$317$	3.27046	−	13.0564i	0.183687	−	0.733320i	0.989909	−	0.141706i	$-0.0452589\pi$
$318$	−1.21439	+	0.802112i	−0.0680994	+	0.0449802i
$319$	3.40566	−	3.40566i	0.190681	−	0.190681i
$320$	−0.607388	−	0.586896i	−0.0339540	−	0.0328085i
$321$	−4.45788	−	4.45788i	−0.248815	−	0.248815i
$322$	2.09371	+	0.428060i	0.116678	+	0.0238549i
$323$	−2.28478	−	0.572308i	−0.127129	−	0.0318441i
$324$	1.65102	+	1.12878i	0.0917233	+	0.0627098i
$325$	−28.2027	+	13.3389i	−1.56441	+	0.739909i
$326$	9.43591	−	19.6789i	0.522607	−	1.08991i
$327$	1.50026	−	0.801905i	0.0829645	−	0.0443455i
$328$	8.82930	+	2.83304i	0.487517	+	0.156428i
$329$	4.89476	−	1.48481i	0.269857	−	0.0818602i
$330$	−0.124744	−	0.0756738i	−0.00686692	−	0.00416570i
$331$	−2.70823	+	18.2574i	−0.148858	+	1.00352i	0.778043	+	0.628211i	$0.216213\pi$
$331$	−2.70823	+	18.2574i	−0.148858	+	1.00352i	−0.926901	+	0.375307i	$0.877537\pi$
$332$	−9.15861	+	18.8427i	−0.502644	+	1.03413i
$333$	4.68350	−	1.67578i	0.256654	−	0.0918324i
$334$	10.6143	−	3.15823i	0.580789	−	0.172811i
$335$	0.0731881	−	0.109534i	0.00399870	−	0.00598447i
$336$	−1.94648	−	1.22373i	−0.106189	−	0.0667599i
$337$	2.90679	+	4.35032i	0.158343	+	0.236977i	0.902155	−	0.431412i	$-0.141984\pi$
$337$	2.90679	+	4.35032i	0.158343	+	0.236977i	−0.743812	+	0.668389i	$0.766984\pi$
$338$	−23.5739	+	28.4152i	−1.28225	+	1.54558i
$339$	14.9742	−	13.5718i	0.813285	−	0.737119i
$340$	−0.0112862	+	0.0708790i	−0.000612078	+	0.00384395i
$341$	−3.33223	+	5.55949i	−0.180450	+	0.301063i
$342$	9.20921	+	3.35050i	0.497977	+	0.181174i
$343$	−4.98459	−	6.07375i	−0.269143	−	0.327951i
$344$	1.07073	+	32.3152i	0.0577301	+	1.74232i
$345$	0.0272049	+	0.276216i	0.00146466	+	0.0148709i
$346$	20.8225	+	15.6155i	1.11943	+	0.839494i
$347$	13.0959	−	14.4491i	0.703027	−	0.775671i	−0.279828	−	0.960050i	$-0.590278\pi$
$347$	13.0959	−	14.4491i	0.703027	−	0.775671i	0.982855	+	0.184379i	$0.0590275\pi$
$348$	8.64357	+	4.73905i	0.463344	+	0.254040i
$349$	−12.9050	−	9.57101i	−0.690789	−	0.512324i	0.192415	−	0.981314i	$-0.438368\pi$
$349$	−12.9050	−	9.57101i	−0.690789	−	0.512324i	−0.883204	+	0.468990i	$0.844618\pi$
$350$	2.88280	−	2.85228i	0.154092	−	0.152461i
$351$	−2.39313	+	5.77754i	−0.127736	+	0.308382i
$352$	−5.52645	+	0.124246i	−0.294561	+	0.00662236i
$353$	−7.80346	−	18.8392i	−0.415336	−	1.00271i	−0.983681	−	0.179920i	$-0.942416\pi$
$353$	−7.80346	−	18.8392i	−0.415336	−	1.00271i	0.568345	−	0.822790i	$-0.307584\pi$
$354$	−14.9207	−	6.27359i	−0.793026	−	0.333438i
$355$	0.0923628	+	0.622660i	0.00490211	+	0.0330473i
$356$	10.3977	+	19.9609i	0.551076	+	1.05792i
$357$	0.00958669	+	0.195142i	0.000507382	+	0.0103280i
$358$	−1.60274	−	2.70657i	−0.0847073	−	0.143047i
$359$	17.6239	−	21.4748i	0.930155	−	1.13340i	−0.0606582	−	0.998159i	$-0.519320\pi$
$359$	17.6239	−	21.4748i	0.930155	−	1.13340i	0.990813	−	0.135238i	$-0.0431800\pi$
$360$	0.0771727	−	0.288470i	0.00406736	−	0.0152037i
$361$	28.8780	+	2.84424i	1.51990	+	0.149697i
$362$	2.86843	−	0.125619i	0.150761	−	0.00660238i
$363$	9.74405	−	2.44076i	0.511430	−	0.128107i
$364$	2.49383	−	6.74266i	0.130712	−	0.353411i
$365$	0.0597909	−	1.21707i	0.00312960	−	0.0637044i
$366$	5.34644	+	10.1318i	0.279463	+	0.529598i
$367$	−6.23463	+	31.3436i	−0.325445	+	1.63612i	0.378310	+	0.925679i	$0.376505\pi$
$367$	−6.23463	+	31.3436i	−0.325445	+	1.63612i	−0.703755	+	0.710443i	$0.748495\pi$
$368$	6.49655	+	8.26890i	0.338656	+	0.431046i
$369$	0.639582	+	3.21540i	0.0332953	+	0.167387i
$370$	−0.468100	−	0.576611i	−0.0243353	−	0.0299766i
$371$	0.534735	+	0.252911i	0.0277620	+	0.0131305i
$372$	−12.8332	−	3.36011i	−0.665371	−	0.174214i
$373$	−1.44859	−	1.95320i	−0.0750051	−	0.101133i	0.764112	−	0.645084i	$-0.223178\pi$
$373$	−1.44859	−	1.95320i	−0.0750051	−	0.101133i	−0.839117	+	0.543951i	$0.816928\pi$
$374$	0.277810	+	0.378780i	0.0143652	+	0.0195862i
$375$	0.930062	+	0.497128i	0.0480282	+	0.0256716i
$376$	23.0969	+	10.0020i	1.19113	+	0.515814i
$377$	−8.94720	+	29.4950i	−0.460804	+	1.51907i
$378$	0.0442067	−	0.811684i	0.00227375	−	0.0417485i
$379$	−8.95875	−	3.20549i	−0.460180	−	0.164655i	0.0965855	−	0.995325i	$-0.469208\pi$
$379$	−8.95875	−	3.20549i	−0.460180	−	0.164655i	−0.556766	+	0.830670i	$0.687958\pi$
$380$	0.0155732	−	1.46310i	0.000798889	−	0.0750552i
$381$	11.4405	−	6.85717i	0.586114	−	0.351303i
$382$	−9.83058	+	14.5443i	−0.502976	+	0.744154i
$383$			8.56864i			0.437837i	0.975743	+	0.218918i	$0.0702529\pi$
$383$			8.56864i			0.437837i	−0.975743	+	0.218918i	$0.929747\pi$
$384$	−3.41209	−	10.7869i	−0.174123	−	0.550468i
$385$			0.0593011i			0.00302226i
$386$	−17.6901	−	11.9568i	−0.900404	−	0.608587i
$387$	−9.80504	+	5.87692i	−0.498418	+	0.298740i
$388$	−13.8421	−	14.1400i	−0.702727	−	0.717848i
$389$	33.4165	+	11.9566i	1.69428	+	0.606224i	0.994172	−	0.107810i	$-0.0343837\pi$
$389$	33.4165	+	11.9566i	1.69428	+	0.606224i	0.700111	+	0.714034i	$0.253134\pi$
$390$	0.932321	+	0.0507769i	0.0472099	+	0.00257119i
$391$	0.259394	−	0.855109i	0.0131181	−	0.0432447i
$392$	0.301167	−	18.8621i	0.0152112	−	0.952680i
$393$	−18.0073	−	9.62510i	−0.908348	−	0.485522i
$394$	29.0572	−	21.3115i	1.46388	−	1.07366i
$395$	−0.771477	−	1.04022i	−0.0388172	−	0.0523390i
$396$	−0.986858	−	1.68694i	−0.0495915	−	0.0847717i
$397$	14.2948	+	6.76094i	0.717436	+	0.339322i	0.751170	−	0.660109i	$-0.229490\pi$
$397$	14.2948	+	6.76094i	0.717436	+	0.339322i	−0.0337342	+	0.999431i	$0.510740\pi$
$398$	−11.4547	+	9.29904i	−0.574172	+	0.466119i
$399$	−0.777055	−	3.90652i	−0.0389014	−	0.195571i
$400$	19.8965	−	1.53281i	0.994823	−	0.0766406i
$401$	3.72926	−	18.7483i	0.186230	−	0.936244i	−0.768744	−	0.639556i	$-0.779118\pi$
$401$	3.72926	−	18.7483i	0.186230	−	0.936244i	0.954975	−	0.296687i	$-0.0958820\pi$
$402$	1.56066	−	0.823541i	0.0778386	−	0.0410745i
$403$	2.03529	−	41.4293i	0.101385	−	2.06374i
$404$	−7.75109	−	16.8500i	−0.385631	−	0.838320i
$405$	0.102412	−	0.0256529i	0.00508891	−	0.00127470i
$406$	−0.175291	−	4.00267i	−0.00869955	−	0.198649i
$407$	−4.83743	−	0.476445i	−0.239783	−	0.0236165i
$408$	−0.584959	+	0.762961i	−0.0289598	+	0.0377722i
$409$	2.23196	−	2.71965i	0.110363	−	0.134478i	−0.714899	−	0.699228i	$-0.753527\pi$
$409$	2.23196	−	2.71965i	0.110363	−	0.134478i	0.825262	+	0.564750i	$0.191027\pi$
$410$	0.421181	−	0.249409i	0.0208006	−	0.0123174i
$411$	0.743269	+	15.1296i	0.0366628	+	0.746288i
$412$	2.42767	−	7.70669i	0.119603	−	0.379681i
$413$	0.965293	+	6.50747i	0.0474989	+	0.320212i
$414$	−1.44102	+	3.42724i	−0.0708224	+	0.168439i
$415$	0.423226	+	1.02176i	0.0207754	+	0.0501562i
$416$	30.8157	−	17.3729i	1.51086	−	0.851776i
$417$	−1.86755	+	4.50866i	−0.0914541	+	0.220790i
$418$	−6.73532	−	6.80740i	−0.329435	−	0.332961i
$419$	−14.0068	−	10.3882i	−0.684277	−	0.507494i	0.196814	−	0.980441i	$-0.436940\pi$
$419$	−14.0068	−	10.3882i	−0.684277	−	0.507494i	−0.881091	+	0.472946i	$0.843190\pi$
$420$	−0.116512	+	0.0339937i	−0.00568522	+	0.00165872i
$421$	11.1046	−	12.2521i	0.541206	−	0.597129i	−0.407533	−	0.913191i	$-0.633611\pi$
$421$	11.1046	−	12.2521i	0.541206	−	0.597129i	0.948739	+	0.316062i	$0.102361\pi$
$422$	0.0896665	−	0.119566i	0.00436490	−	0.00582039i
$423$	0.872235	+	8.85595i	0.0424095	+	0.430591i
$424$	1.20234	+	2.65082i	0.0583908	+	0.128735i
$425$	−1.07577	−	1.31082i	−0.0521823	−	0.0635843i
$426$	−2.88283	+	7.92378i	−0.139674	+	0.383908i
$427$	2.39376	−	3.99374i	0.115842	−	0.193271i
$428$	−10.2068	+	7.40283i	−0.493366	+	0.357829i
$429$	4.52791	−	4.10386i	0.218610	−	0.198136i
$430$	1.31359	+	1.08978i	0.0633468	+	0.0525541i
$431$	−5.27998	−	7.90205i	−0.254328	−	0.380628i	0.682232	−	0.731135i	$-0.261009\pi$
$431$	−5.27998	−	7.90205i	−0.254328	−	0.380628i	−0.936560	+	0.350507i	$0.886009\pi$
$432$	2.74871	−	2.90595i	0.132248	−	0.139813i
$433$	−10.2479	+	15.3371i	−0.492483	+	0.737053i	−0.991580	−	0.129493i	$-0.958665\pi$
$433$	−10.2479	+	15.3371i	−0.492483	+	0.737053i	0.499097	+	0.866546i	$0.333665\pi$
$434$	1.53768	+	5.16789i	0.0738109	+	0.248067i
$435$	0.489940	−	0.175303i	0.0234908	−	0.00840515i
$436$	−1.11202	−	3.21539i	−0.0532563	−	0.153989i
$437$	−2.67300	+	18.0199i	−0.127867	+	0.862010i
$438$	8.46586	−	13.9555i	0.404515	−	0.666818i
$439$	22.4092	−	6.79777i	1.06953	−	0.324440i	0.294040	−	0.955793i	$-0.405000\pi$
$439$	22.4092	−	6.79777i	1.06953	−	0.324440i	0.775495	+	0.631353i	$0.217500\pi$
$440$	−0.188697	+	0.222584i	−0.00899576	+	0.0106113i
$441$	5.88207	−	3.14403i	0.280099	−	0.149716i
$442$	−2.71059	−	1.29971i	−0.128929	−	0.0618208i
$443$	4.05022	−	1.91561i	0.192432	−	0.0910136i	−0.328910	−	0.944361i	$-0.606681\pi$
$443$	4.05022	−	1.91561i	0.192432	−	0.0910136i	0.521342	+	0.853348i	$0.325431\pi$
$444$	−1.83690	−	9.77750i	−0.0871756	−	0.464020i
$445$	1.15248	+	0.288681i	0.0546327	+	0.0136848i
$446$	−0.911736	+	4.45944i	−0.0431720	+	0.211161i
$447$	1.11151	+	1.11151i	0.0525724	+	0.0525724i
$448$	−3.02918	+	3.45965i	−0.143115	+	0.163453i
$449$	−19.6260	+	19.6260i	−0.926206	+	0.926206i	−0.997458	−	0.0712521i	$-0.977301\pi$
$449$	−19.6260	+	19.6260i	−0.926206	+	0.926206i	0.0712521	+	0.997458i	$0.477301\pi$
$450$	3.88844	+	5.88705i	0.183303	+	0.277518i
$451$	0.778417	−	3.10762i	0.0366542	−	0.146332i
$452$	−22.0965	−	33.8441i	−1.03933	−	1.59189i
$453$	−3.86712	−	8.17633i	−0.181693	−	0.384158i
$454$	5.39391	+	15.3317i	0.253149	+	0.719553i
$455$	−0.178894	−	0.334687i	−0.00838667	−	0.0156904i
$456$	9.51394	−	17.1355i	0.445531	−	0.802445i
$457$	−9.34393	−	30.8028i	−0.437091	−	1.44089i	−0.848379	−	0.529389i	$-0.822421\pi$
$457$	−9.34393	−	30.8028i	−0.437091	−	1.44089i	0.411288	−	0.911505i	$-0.365079\pi$
$458$	5.82564	+	23.7938i	0.272214	+	1.11181i
$459$	−0.336227	−	0.0498745i	−0.0156937	−	0.00232794i
$460$	0.554114	+	0.0331372i	0.0258357	+	0.00154503i
$461$	10.6203	+	29.6818i	0.494638	+	1.38242i	0.886642	+	0.462457i	$0.153032\pi$
$461$	10.6203	+	29.6818i	0.494638	+	1.38242i	−0.392004	+	0.919964i	$0.628218\pi$
$462$	−0.378176	+	0.698551i	−0.0175944	+	0.0324995i
$463$	−12.9794	−	8.67254i	−0.603202	−	0.403047i	0.216131	−	0.976364i	$-0.430656\pi$
$463$	−12.9794	−	8.67254i	−0.603202	−	0.403047i	−0.819333	+	0.573317i	$0.805656\pi$
$464$	12.0786	−	15.5816i	0.560734	−	0.723359i
$465$	−0.582260	+	0.389053i	−0.0270016	+	0.0180419i
$466$	−10.9827	+	1.02272i	−0.508763	+	0.0473764i
$467$	−25.5166	−	28.1532i	−1.18077	−	1.30277i	−0.943516	−	0.331326i	$-0.892504\pi$
$467$	−25.5166	−	28.1532i	−1.18077	−	1.30277i	−0.237250	−	0.971449i	$-0.576246\pi$
$468$	10.6587	+	6.54376i	0.492697	+	0.302485i
$469$	−0.615178	−	0.368723i	−0.0284063	−	0.0170261i
$470$	1.20410	−	0.561674i	0.0555408	−	0.0259081i
$471$	−2.69640	+	2.21288i	−0.124244	+	0.101964i
$472$	−17.0837	+	27.4971i	−0.786339	+	1.26566i
$473$	11.1169	−	1.09492i	0.511157	−	0.0503445i
$474$	−2.45409	−	17.1733i	−0.112720	−	0.788798i
$475$	25.6148	+	23.2159i	1.17529	+	1.06522i
$476$	0.388443	+	0.0424373i	0.0178042	+	0.00194511i
$477$	−0.613037	+	0.826585i	−0.0280691	+	0.0378467i
$478$	−0.223733	+	42.0404i	−0.0102333	+	1.92288i
$479$	−19.7622	−	8.18577i	−0.902958	−	0.374017i	−0.117601	−	0.993061i	$-0.537520\pi$
$479$	−19.7622	−	8.18577i	−0.902958	−	0.374017i	−0.785357	+	0.619044i	$0.787520\pi$
$480$	−0.545492	−	0.243149i	−0.0248982	−	0.0110982i
$481$	28.7391	−	11.9041i	1.31039	−	0.542781i
$482$	−13.4521	−	32.9715i	−0.612726	−	1.50181i
$483$	1.49475	−	0.221725i	0.0680133	−	0.0100888i
$484$	−1.75627	−	20.0133i	−0.0798305	−	0.909694i
$485$	−1.04328	+	0.0512533i	−0.0473731	+	0.00232729i
$486$	1.36998	+	0.350922i	0.0621437	+	0.0159181i
$487$	20.7671	+	17.0431i	0.941048	+	0.772299i	0.973857	−	0.227163i	$-0.0729451\pi$
$487$	20.7671	+	17.0431i	0.941048	+	0.772299i	−0.0328082	+	0.999462i	$0.510445\pi$
$488$	21.6930	−	7.37338i	0.981995	−	0.333777i
$489$	1.51261	−	15.3577i	0.0684024	−	0.694501i
$490$	−0.734286	−	0.672670i	−0.0331716	−	0.0303881i
$491$	−6.22640	−	24.8572i	−0.280993	−	1.12179i	−0.931925	−	0.362652i	$-0.881871\pi$
$491$	−6.22640	−	24.8572i	−0.280993	−	1.12179i	0.650931	−	0.759137i	$-0.274379\pi$
$492$	6.55193	−	0.252005i	0.295384	−	0.0113613i
$493$	−1.67329	−	0.0822033i	−0.0753610	−	0.00370225i
$494$	58.5491	+	18.1015i	2.63425	+	0.814424i
$495$	−0.101186	−	0.0201272i	−0.00454798	−	0.000904650i
$496$	−10.6727	+	24.2904i	−0.479217	+	1.09067i
$497$	3.36124	−	0.668593i	0.150772	−	0.0299905i
$498$	−1.53050	+	14.7351i	−0.0685832	+	0.660293i
$499$	−0.744318	+	1.57373i	−0.0333202	+	0.0704497i	−0.919963	−	0.392006i	$-0.871781\pi$
$499$	−0.744318	+	1.57373i	−0.0333202	+	0.0704497i	0.886643	+	0.462455i	$0.153031\pi$
$500$	1.27439	−	1.68063i	0.0569925	−	0.0751602i
$501$	6.28963	−	4.66471i	0.281000	−	0.208404i
$502$	4.77047	+	0.733600i	0.212917	+	0.0327422i
$503$	7.28896	−	13.6367i	0.324999	−	0.608030i	−0.665366	−	0.746518i	$-0.731724\pi$
$503$	7.28896	−	13.6367i	0.324999	−	0.608030i	0.990364	+	0.138488i	$0.0442243\pi$
$504$	−1.58927	−	0.342589i	−0.0707916	−	0.0152601i
$505$	−0.936919	−	0.284211i	−0.0416923	−	0.0126472i
$506$	2.70488	−	2.42546i	0.120246	−	0.107825i
$507$	−8.79519	+	24.5809i	−0.390608	+	1.09168i
$508$	−9.94567	−	24.7529i	−0.441268	−	1.09823i
$509$	0.576063	+	0.961103i	0.0255335	+	0.0426002i	0.870231	−	0.492644i	$-0.163970\pi$
$509$	0.576063	+	0.961103i	0.0255335	+	0.0426002i	−0.844697	+	0.535244i	$0.820220\pi$
$510$	0.00963588	+	0.0498272i	0.000426684	+	0.00220639i
$511$	−6.63420			−0.293480
$512$	−22.3785	+	3.34679i	−0.989001	+	0.147909i
$513$	6.92948			0.305944
$514$	3.14999	+	16.2887i	0.138940	+	0.718462i
$515$	−0.219280	−	0.365846i	−0.00966262	−	0.0161211i
$516$	8.52391	+	21.2144i	0.375244	+	0.933912i
$517$	2.92955	−	8.18753i	0.128841	−	0.360087i
$518$	−3.01046	+	2.69948i	−0.132272	+	0.118608i
$519$	17.6116	+	5.34243i	0.773065	+	0.234507i
$520$	0.393506	−	1.82547i	0.0172564	−	0.0800523i
$521$	0.653815	−	1.22320i	0.0286442	−	0.0535894i	−0.867192	−	0.497974i	$-0.834078\pi$
$521$	0.653815	−	1.22320i	0.0286442	−	0.0535894i	0.895836	+	0.444384i	$0.146578\pi$
$522$	6.88930	+	1.05943i	0.301537	+	0.0463701i
$523$	2.47214	−	1.83346i	0.108099	−	0.0801717i	−0.540300	−	0.841473i	$-0.681689\pi$
$523$	2.47214	−	1.83346i	0.108099	−	0.0801717i	0.648399	+	0.761301i	$0.275439\pi$
$524$	−24.6740	+	32.5394i	−1.07789	+	1.42149i
$525$	1.22605	−	2.59226i	0.0535092	−	0.113136i
$526$	0.532336	−	5.12513i	0.0232109	−	0.223466i
$527$	2.21124	−	0.439843i	0.0963232	−	0.0191599i
$528$	−3.64226	+	1.41862i	−0.158509	+	0.0617375i
$529$	15.7796	+	3.13876i	0.686070	+	0.136468i
$530$	0.146797	+	0.0453850i	0.00637647	+	0.00197140i
$531$	−11.4314	−	0.561589i	−0.496081	−	0.0243709i
$532$	−7.96022	+	0.306172i	−0.345119	+	0.0132742i
$533$	4.98148	+	19.8872i	0.215772	+	0.861410i
$534$	11.7349	+	10.7502i	0.507818	+	0.465206i
$535$	−0.0652396	+	0.662389i	−0.00282056	+	0.0286376i
$536$	−1.13576	−	3.34149i	−0.0490574	−	0.144330i
$537$	−1.71934	−	1.41103i	−0.0741951	−	0.0608903i
$538$	−19.0316	−	4.87495i	−0.820511	−	0.210174i
$539$	−6.50966	+	0.319799i	−0.280391	+	0.0137747i
$540$	−0.0184588	−	0.210344i	−0.000794342	−	0.00905177i
$541$	19.0069	−	2.81941i	0.817171	−	0.121216i	0.274957	−	0.961457i	$-0.411336\pi$
$541$	19.0069	−	2.81941i	0.817171	−	0.121216i	0.542214	+	0.840241i	$0.317586\pi$
$542$	−1.83104	−	4.48793i	−0.0786500	−	0.192773i
$543$	1.87569	−	0.776936i	0.0804935	−	0.0333415i
$544$	1.32297	+	1.39531i	0.0567217	+	0.0598236i
$545$	−0.165927	−	0.0687294i	−0.00710755	−	0.00294404i
$546$	0.0270530	−	5.08337i	0.00115776	−	0.217548i
$547$	9.52634	−	12.8448i	0.407317	−	0.549203i	−0.551150	−	0.834406i	$-0.685811\pi$
$547$	9.52634	−	12.8448i	0.407317	−	0.549203i	0.958467	+	0.285203i	$0.0920609\pi$
$548$	30.1165	+	3.29022i	1.28651	+	0.140551i
$549$	6.00212	+	5.44000i	0.256164	+	0.232174i
$550$	−0.975312	−	6.82507i	−0.0415874	−	0.291022i
$551$	33.9891	−	3.34764i	1.44799	−	0.142614i
$552$	6.31599	+	3.92406i	0.268826	+	0.167019i
$553$	−5.45042	+	4.47305i	−0.231776	+	0.190213i
$554$	7.67589	−	3.58057i	0.326117	−	0.152124i
$555$	−0.450450	−	0.269989i	−0.0191205	−	0.0114604i
$556$	8.31778	+	5.10660i	0.352752	+	0.216568i
$557$	−19.7460	−	21.7864i	−0.836666	−	0.923118i	0.161298	−	0.986906i	$-0.448432\pi$
$557$	−19.7460	−	21.7864i	−0.836666	−	0.923118i	−0.997964	+	0.0637875i	$0.979682\pi$
$558$	−9.33994	+	0.869742i	−0.395391	+	0.0368191i
$559$	−59.4392	+	39.7160i	−2.51401	+	1.67981i
$560$	0.0304983	+	0.240817i	0.00128879	+	0.0101764i
$561$	0.276176	+	0.184535i	0.0116602	+	0.00779107i
$562$	−15.8378	+	29.2549i	−0.668077	+	1.23404i
$563$	1.57463	+	4.40079i	0.0663627	+	0.185471i	0.970147	−	0.242516i	$-0.0779727\pi$
$563$	1.57463	+	4.40079i	0.0663627	+	0.185471i	−0.903785	+	0.427987i	$0.859223\pi$
$564$	17.7659	+	1.06244i	0.748077	+	0.0447366i
$565$	−2.11054	−	0.313069i	−0.0887910	−	0.0131709i
$566$	−5.57813	−	22.7829i	−0.234466	−	0.957636i
$567$	−0.166855	−	0.550047i	−0.00700725	−	0.0230998i
$568$	14.7437	+	8.18597i	0.618634	+	0.343476i
$569$	−0.441179	−	0.825387i	−0.0184952	−	0.0346020i	0.872504	−	0.488607i	$-0.162495\pi$
$569$	−0.441179	−	0.825387i	−0.0184952	−	0.0346020i	−0.890999	+	0.454005i	$0.849995\pi$
$570$	−0.343365	−	0.975984i	−0.0143820	−	0.0408795i
$571$	6.89197	+	14.5718i	0.288420	+	0.609813i	0.995226	−	0.0975943i	$-0.0311148\pi$
$571$	6.89197	+	14.5718i	0.288420	+	0.609813i	−0.706806	+	0.707407i	$0.749865\pi$
$572$	−6.68158	−	10.2338i	−0.279371	−	0.427898i
$573$	−3.01618	+	12.0413i	−0.126003	+	0.503031i
$574$	−1.46876	−	2.22368i	−0.0613048	−	0.0928146i
$575$	−9.27393	+	9.27393i	−0.386750	+	0.386750i
$576$	−4.87513	−	6.34296i	−0.203130	−	0.264290i
$577$	10.5559	+	10.5559i	0.439446	+	0.439446i	0.891826	−	0.452379i	$-0.149425\pi$
$577$	10.5559	+	10.5559i	0.439446	+	0.439446i	−0.452379	+	0.891826i	$0.649425\pi$
$578$	−4.78298	+	23.3943i	−0.198946	+	0.973075i
$579$	−14.6457	−	3.66855i	−0.608653	−	0.152460i
$580$	−0.192158	−	1.02282i	−0.00797893	−	0.0424703i
$581$	5.44309	−	2.57439i	0.225817	−	0.106804i
$582$	−12.6165	−	6.04951i	−0.522969	−	0.250760i
$583$	0.886892	−	0.474054i	0.0367313	−	0.0196333i
$584$	−24.9012	−	21.1101i	−1.03042	−	0.873541i
$585$	0.631798	−	0.191654i	0.0261216	−	0.00792391i
$586$	−8.63488	+	14.2341i	−0.356703	+	0.588005i
$587$	3.41706	−	23.0359i	0.141037	−	0.950795i	−0.796930	−	0.604071i	$-0.793544\pi$
$587$	3.41706	−	23.0359i	0.141037	−	0.950795i	0.937967	−	0.346724i	$-0.112706\pi$
$588$	−4.35992	−	12.6066i	−0.179800	−	0.519886i
$589$	−43.2758	+	15.4843i	−1.78315	+	0.638021i
$590$	0.487344	+	1.63789i	0.0200636	+	0.0674308i
$591$	14.1562	−	21.1862i	0.582306	−	0.871483i
$592$	−19.8894	+	0.553071i	−0.817450	+	0.0227311i
$593$	15.6510	+	23.4233i	0.642709	+	0.961882i	0.999615	+	0.0277415i	$0.00883152\pi$
$593$	15.6510	+	23.4233i	0.642709	+	0.961882i	−0.356906	+	0.934140i	$0.616168\pi$
$594$	−1.06359	−	0.882380i	−0.0436396	−	0.0362045i
$595$	0.0152837	−	0.0138524i	0.000626572	−	0.000567891i
$596$	2.54492	−	1.84578i	0.104244	−	0.0756063i
$597$	−5.36347	+	8.94842i	−0.219512	+	0.366234i
$598$	−7.94903	+	21.8488i	−0.325060	+	0.893463i
$599$	5.24948	+	6.39651i	0.214488	+	0.261354i	0.869129	−	0.494586i	$-0.164680\pi$
$599$	5.24948	+	6.39651i	0.214488	+	0.261354i	−0.654641	+	0.755940i	$0.727180\pi$
$600$	12.8505	−	5.82865i	0.524621	−	0.237954i
$601$	1.00294	+	10.1830i	0.0409108	+	0.415375i	0.993728	+	0.111828i	$0.0356707\pi$
$601$	1.00294	+	10.1830i	0.0409108	+	0.415375i	−0.952817	+	0.303546i	$0.901829\pi$
$602$	5.57514	−	7.43419i	0.227226	−	0.302995i
$603$	0.837953	−	0.924539i	0.0341241	−	0.0376501i
$604$	−17.3654	+	5.06655i	−0.706589	+	0.206155i
$605$	−0.851820	−	0.631753i	−0.0346314	−	0.0256844i
$606$	−9.22417	−	9.32287i	−0.374706	−	0.378716i
$607$	12.3525	−	29.8217i	0.501374	−	1.21042i	−0.447362	−	0.894353i	$-0.647636\pi$
$607$	12.3525	−	29.8217i	0.501374	−	1.21042i	0.948736	−	0.316071i	$-0.102364\pi$
$608$	−30.8526	−	24.1803i	−1.25124	−	0.980640i
$609$	−1.08415	−	2.61738i	−0.0439321	−	0.106061i
$610$	0.468785	−	1.11493i	0.0189806	−	0.0451421i
$611$	8.16543	+	55.0468i	0.330338	+	2.22696i
$612$	−0.204251	+	0.648401i	−0.00825638	+	0.0262101i
$613$	1.16410	+	23.6959i	0.0470177	+	0.957068i	0.900206	+	0.435465i	$0.143416\pi$
$613$	1.16410	+	23.6959i	0.0470177	+	0.957068i	−0.853188	+	0.521603i	$0.825334\pi$
$614$	−32.1516	+	19.0391i	−1.29753	+	0.768356i
$615$	0.219576	−	0.267554i	0.00885417	−	0.0107888i
$616$	1.26078	+	0.966638i	0.0507984	+	0.0389469i
$617$	−11.1731	−	1.10046i	−0.449814	−	0.0443028i	−0.129426	−	0.991589i	$-0.541313\pi$
$617$	−11.1731	−	1.10046i	−0.449814	−	0.0443028i	−0.320388	+	0.947286i	$0.603813\pi$
$618$	−0.249972	−	5.70796i	−0.0100553	−	0.229608i
$619$	−6.84326	+	1.71415i	−0.275054	+	0.0688974i	−0.378053	−	0.925784i	$-0.623406\pi$
$619$	−6.84326	+	1.71415i	−0.275054	+	0.0688974i	0.102999	+	0.994681i	$0.467156\pi$
$620$	0.585305	+	1.27239i	0.0235064	+	0.0511004i
$621$	−0.128995	+	2.62576i	−0.00517640	+	0.105368i
$622$	−40.4432	+	21.3414i	−1.62162	+	0.855711i
$623$	1.26192	−	6.34409i	0.0505577	−	0.254171i
$624$	16.2769	−	18.9941i	0.651596	−	0.760373i
$625$	4.84466	+	24.3558i	0.193787	+	0.974231i
$626$	−14.2901	+	11.6009i	−0.571149	+	0.463665i
$627$	−6.12132	−	2.89517i	−0.244462	−	0.115622i
$628$	3.52268	+	6.02166i	0.140570	+	0.240290i
$629$	1.00720	+	1.35805i	0.0401596	+	0.0541490i
$630$	−0.0692036	+	0.0507563i	−0.00275714	+	0.00202218i
$631$	−31.0545	−	16.5990i	−1.23626	−	0.660794i	−0.281897	−	0.959445i	$-0.590964\pi$
$631$	−31.0545	−	16.5990i	−1.23626	−	0.660794i	−0.954363	+	0.298651i	$0.903464\pi$
$632$	−34.6912	−	0.553907i	−1.37994	−	0.0220332i
$633$	0.0306770	−	0.101129i	0.00121930	−	0.00401950i
$634$	−19.0068	−	1.03517i	−0.754857	−	0.0411117i
$635$	−1.32587	−	0.474405i	−0.0526157	−	0.0188262i
$636$	1.43980	+	1.47078i	0.0570919	+	0.0583203i
$637$	35.7748	−	21.4426i	1.41745	−	0.849587i
$638$	−5.64319	−	3.81426i	−0.223416	−	0.151008i
$639$			5.96226i			0.235863i
$640$	−0.651806	+	1.00094i	−0.0257649	+	0.0395656i
$641$			16.1013i			0.635962i	0.948097	+	0.317981i	$0.103005\pi$
$641$			16.1013i			0.635962i	−0.948097	+	0.317981i	$0.896995\pi$
$642$	−4.99271	+	7.38672i	−0.197047	+	0.291530i
$643$	4.64636	−	2.78492i	0.183234	−	0.109826i	−0.419544	−	0.907735i	$-0.637810\pi$
$643$	4.64636	−	2.78492i	0.183234	−	0.109826i	0.602779	+	0.797908i	$0.294060\pi$
$644$	0.0321665	−	3.02203i	0.00126754	−	0.119085i
$645$	1.13634	+	0.406587i	0.0447432	+	0.0160094i
$646$	−0.181147	+	3.32607i	−0.00712715	+	0.130862i
$647$	5.49199	−	18.1047i	0.215912	−	0.711768i	−0.780346	−	0.625348i	$-0.784957\pi$
$647$	5.49199	−	18.1047i	0.215912	−	0.711768i	0.996259	−	0.0864203i	$-0.0275428\pi$
$648$	1.12397	−	2.59551i	0.0441538	−	0.101961i
$649$	9.86358	+	5.27219i	0.387179	+	0.206952i
$650$	26.0937	+	35.5775i	1.02348	+	1.39546i
$651$	2.27115	+	3.06229i	0.0890135	+	0.120021i
$652$	−29.8576	−	7.81759i	−1.16931	−	0.306161i
$653$	−8.23031	−	3.89265i	−0.322077	−	0.152331i	0.259678	−	0.965695i	$-0.416384\pi$
$653$	−8.23031	−	3.89265i	−0.322077	−	0.152331i	−0.581755	+	0.813364i	$0.697634\pi$
$654$	−1.51628	−	1.86777i	−0.0592911	−	0.0730356i
$655$	0.420553	+	2.11426i	0.0164324	+	0.0826111i
$656$	1.56285	−	13.0201i	0.0610190	−	0.508349i
$657$	2.25169	−	11.3200i	0.0878469	−	0.441636i
$658$	−3.37595	−	6.39762i	−0.131608	−	0.249405i
$659$	0.271707	−	5.53072i	0.0105842	−	0.215446i	−0.987677	−	0.156505i	$-0.949977\pi$
$659$	0.271707	−	5.53072i	0.0105842	−	0.215446i	0.998261	−	0.0589417i	$-0.0187726\pi$
$660$	−0.0715767	+	0.193525i	−0.00278612	+	0.00753294i
$661$	−19.8154	+	4.96349i	−0.770728	+	0.193057i	−0.608347	−	0.793671i	$-0.708167\pi$
$661$	−19.8154	+	4.96349i	−0.770728	+	0.193057i	−0.162381	+	0.986728i	$0.551917\pi$
$662$	26.0774	−	1.14202i	1.01353	−	0.0443859i
$663$	−2.11538	−	0.208347i	−0.0821547	−	0.00809153i
$664$	28.6221	+	7.65709i	1.11075	+	0.297153i
$665$	−0.266772	+	0.325063i	−0.0103450	+	0.0126054i
$666$	−3.58439	−	6.05302i	−0.138892	−	0.234550i
$667$	0.635784	+	12.9417i	0.0246176	+	0.501104i
$668$	−7.23525	−	13.8898i	−0.279940	−	0.537413i
$669$	0.472257	+	3.18370i	0.0182585	+	0.123089i
$670$	−0.171738	−	0.0722095i	−0.00663483	−	0.00278970i
$671$	−3.02925	−	7.31327i	−0.116943	−	0.282326i
$672$	−1.17648	+	3.03125i	−0.0453837	+	0.116933i
$673$	3.18098	−	7.67956i	0.122618	−	0.296025i	−0.850637	−	0.525753i	$-0.823784\pi$
$673$	3.18098	−	7.67956i	0.122618	−	0.296025i	0.973255	+	0.229728i	$0.0737836\pi$
$674$	5.25986	−	5.20417i	0.202602	−	0.200457i
$675$	4.00708	+	2.97186i	0.154233	+	0.114387i
$676$	45.7841	+	25.1022i	1.76093	+	0.965471i
$677$	−32.0669	+	35.3804i	−1.23243	+	1.35978i	−0.321666	+	0.946853i	$0.604243\pi$
$677$	−32.0669	+	35.3804i	−1.23243	+	1.35978i	−0.910765	+	0.412925i	$0.864507\pi$
$678$	−22.8651	−	17.1472i	−0.878127	−	0.658536i
$679$	0.557413	+	5.65951i	0.0213915	+	0.217192i
$680$	0.101445	−	0.00336129i	0.00389024	−	0.000128900i
$681$	7.29078	+	8.88384i	0.279383	+	0.340429i
$682$	8.61404	+	3.13396i	0.329849	+	0.120006i
$683$	−21.5621	+	35.9741i	−0.825049	+	1.37651i	0.0993371	+	0.995054i	$0.468328\pi$
$683$	−21.5621	+	35.9741i	−0.825049	+	1.37651i	−0.924386	+	0.381458i	$0.875422\pi$
$684$	2.17933	−	13.6865i	0.0833287	−	0.523318i
$685$	1.18497	−	1.07399i	0.0452753	−	0.0410351i
$686$	−7.09489	+	8.55194i	−0.270884	+	0.326514i
$687$	9.62341	+	14.4025i	0.367156	+	0.549488i
$688$	44.5817	−	10.1638i	1.69966	−	0.387490i
$689$	−3.57541	+	5.35098i	−0.136212	+	0.203856i
$690$	0.376217	−	0.111941i	0.0143223	−	0.00426154i
$691$	22.0729	−	7.89782i	0.839694	−	0.300447i	0.118305	−	0.992977i	$-0.462254\pi$
$691$	22.0729	−	7.89782i	0.839694	−	0.300447i	0.721389	+	0.692530i	$0.243504\pi$
$692$	16.0908	−	33.1048i	0.611680	−	1.25846i
$693$	−0.0824170	+	0.555610i	−0.00313076	+	0.0211059i
$694$	−23.5789	−	14.3038i	−0.895043	−	0.542964i
$695$	0.493041	−	0.149562i	0.0187021	−	0.00567322i
$696$	4.25919	−	13.2740i	0.161444	−	0.503149i
$697$	−0.982762	+	0.525297i	−0.0372248	+	0.0198971i
$698$	−9.82406	+	20.4884i	−0.371846	+	0.775497i
$699$	−7.05069	+	3.33473i	−0.266682	+	0.126131i
$700$	−4.73443	−	3.23686i	−0.178945	−	0.122342i
$701$	36.1708	+	9.06032i	1.36615	+	0.342203i	0.855598	−	0.517642i	$-0.173190\pi$
$701$	36.1708	+	9.06032i	1.36615	+	0.342203i	0.510555	+	0.859845i	$0.329440\pi$
$702$	8.66463	+	1.77149i	0.327025	+	0.0668606i
$703$	−24.3734	−	24.3734i	−0.919260	−	0.919260i
$704$	1.65644	+	7.64005i	0.0624296	+	0.287945i
$705$	0.664328	−	0.664328i	0.0250200	−	0.0250200i
$706$	−24.0627	+	15.8936i	−0.905612	+	0.598164i
$707$	−1.29520	+	5.17073i	−0.0487110	+	0.194465i
$708$	−4.70439	+	22.4018i	−0.176802	+	0.841910i
$709$	−0.592816	−	1.25340i	−0.0222637	−	0.0470726i	0.892551	−	0.450946i	$-0.148913\pi$
$709$	−0.592816	−	1.25340i	−0.0222637	−	0.0470726i	−0.914815	+	0.403874i	$0.867663\pi$
$710$	0.839755	−	0.295438i	0.0315154	−	0.0110876i
$711$	−5.78251	−	10.8183i	−0.216861	−	0.405718i
$712$	24.9235	−	19.7968i	0.934048	−	0.741918i
$713$	−5.06182	−	16.6866i	−0.189566	−	0.624917i
$714$	0.268378	−	0.0657093i	0.0100438	−	0.00245911i
$715$	−0.638188	−	0.0946662i	−0.0238669	−	0.00354032i
$716$	−3.32768	+	2.95213i	−0.124361	+	0.110326i
$717$	10.0149	+	27.9897i	0.374013	+	1.04530i
$718$	−34.5498	−	18.7043i	−1.28939	−	0.698039i
$719$	0.300868	+	0.201034i	0.0112205	+	0.00749729i	0.561168	−	0.827702i	$-0.310352\pi$
$719$	0.300868	+	0.201034i	0.0112205	+	0.00749729i	−0.549947	+	0.835199i	$0.685352\pi$
$720$	−0.421260	−	0.0296950i	−0.0156994	−	0.00110667i
$721$	−1.93083	+	1.29014i	−0.0719078	+	0.0480473i
$722$	−3.80496	−	40.8605i	−0.141606	−	1.52067i
$723$	−16.9099	−	18.6572i	−0.628887	−	0.693870i
$724$	−0.944634	−	3.94905i	−0.0351070	−	0.146765i
$725$	21.0905	+	12.6411i	0.783280	+	0.469480i
$726$	−6.00538	−	12.8741i	−0.222880	−	0.477804i
$727$	−27.5216	+	22.5864i	−1.02072	+	0.837682i	−0.986833	−	0.161744i	$-0.948288\pi$
$727$	−27.5216	+	22.5864i	−1.02072	+	0.837682i	−0.0338853	+	0.999426i	$0.510788\pi$
$728$	−10.0317	−	1.65216i	−0.371801	−	0.0612329i
$729$	0.995185	−	0.0980171i	0.0368587	−	0.00363026i
$730$	−1.70594	+	0.243782i	−0.0631398	+	0.00902277i
$731$	−2.87904	−	2.60941i	−0.106485	−	0.0965124i
$732$	12.6323	−	10.1440i	0.466904	−	0.374933i
$733$	1.70350	−	2.29690i	0.0629200	−	0.0848379i	−0.770627	−	0.637287i	$-0.780057\pi$
$733$	1.70350	−	2.29690i	0.0629200	−	0.0848379i	0.833547	+	0.552449i	$0.186307\pi$
$734$	45.1943	+	0.240518i	1.66815	+	0.00887767i
$735$	−0.650552	−	0.269467i	−0.0239960	−	0.00993945i
$736$	9.73686	−	11.2407i	0.358905	−	0.414338i
$737$	−1.12650	+	0.466612i	−0.0414952	+	0.0171879i
$738$	4.29280	−	1.75143i	0.158020	−	0.0644711i
$739$	−7.48376	+	1.11011i	−0.275295	+	0.0408361i	−0.282950	−	0.959135i	$-0.591313\pi$
$739$	−7.48376	+	1.11011i	−0.275295	+	0.0408361i	0.00765560	+	0.999971i	$0.497563\pi$
$740$	−0.674927	+	0.804779i	−0.0248108	+	0.0295843i
$741$	43.2817	−	2.12630i	1.58999	−	0.0781114i
$742$	0.207580	−	0.810383i	0.00762050	−	0.0297501i
$743$	31.6843	+	26.0026i	1.16238	+	0.953944i	0.999465	−	0.0326959i	$-0.0104093\pi$
$743$	31.6843	+	26.0026i	1.16238	+	0.953944i	0.162918	+	0.986640i	$0.447909\pi$
$744$	−1.21958	+	18.7210i	−0.0447118	+	0.686346i
$745$	0.0162665	−	0.165157i	0.000595960	−	0.00605088i
$746$	−2.32303	+	2.53581i	−0.0850520	+	0.0928426i
$747$	2.54529	+	10.1614i	0.0931274	+	0.371785i
$748$	0.451336	−	0.487444i	0.0165025	−	0.0178227i
$749$	3.61939	+	0.177809i	0.132250	+	0.00649700i
$750$	0.440522	−	1.42487i	0.0160856	−	0.0520287i
$751$	25.4330	+	5.05895i	0.928065	+	0.184604i	0.635906	−	0.771766i	$-0.280627\pi$
$751$	25.4330	+	5.05895i	0.928065	+	0.184604i	0.292158	+	0.956370i	$0.405627\pi$
$752$	7.68581	−	34.7555i	0.280273	−	1.26740i
$753$	3.34731	−	0.665821i	0.121983	−	0.0242639i
$754$	43.3559	+	4.50327i	1.57893	+	0.164000i
$755$	−0.408276	+	0.863227i	−0.0148587	+	0.0314160i
$756$	−1.13888	+	0.156568i	−0.0414208	+	0.00569432i
$757$	−10.0452	+	7.45000i	−0.365098	+	0.270775i	−0.762659	−	0.646801i	$-0.776107\pi$
$757$	−10.0452	+	7.45000i	−0.365098	+	0.270775i	0.397561	+	0.917576i	$0.369857\pi$
$758$	−2.04524	+	13.2998i	−0.0742865	+	0.483072i
$759$	1.21101	−	2.26563i	0.0439567	−	0.0822372i
$760$	−2.03567	+	0.371238i	−0.0738416	+	0.0134662i
$761$	2.35651	+	0.714840i	0.0854234	+	0.0259129i	0.332707	−	0.943030i	$-0.392038\pi$
$761$	2.35651	+	0.714840i	0.0854234	+	0.0259129i	−0.247284	+	0.968943i	$0.579538\pi$
$762$	−12.5930	−	14.0437i	−0.456197	−	0.508751i
$763$	−0.329412	+	0.920645i	−0.0119255	+	0.0333296i
$764$	22.8343	+	9.74429i	0.826116	+	0.352536i
$765$	0.0184491	+	0.0307804i	0.000667027	+	0.00111287i
$766$	11.8975	−	2.30080i	0.429872	−	0.0831312i
$767$	−71.5733			−2.58436
$768$	−14.0613	+	7.63409i	−0.507394	+	0.275471i
$769$	−47.1435			−1.70004			−0.850019	−	0.526752i	$-0.823409\pi$
$769$	−47.1435			−1.70004			−0.850019	+	0.526752i	$0.823409\pi$
$770$	0.0823389	−	0.0159232i	0.00296729	−	0.000573831i
$771$	6.03105	+	10.0622i	0.217203	+	0.362381i
$772$	−11.8519	+	27.7731i	−0.426558	+	0.999577i
$773$	−10.5392	+	29.4550i	−0.379068	+	1.05942i	0.588868	+	0.808229i	$0.299574\pi$
$773$	−10.5392	+	29.4550i	−0.379068	+	1.05942i	−0.967936	+	0.251195i	$0.919176\pi$
$774$	10.7928	+	12.0362i	0.387940	+	0.432631i
$775$	−31.6657	−	9.60570i	−1.13747	−	0.345047i
$776$	−15.9164	+	23.0164i	−0.571365	+	0.826241i
$777$	−1.34782	+	2.52159i	−0.0483528	+	0.0904616i
$778$	7.62882	−	49.6089i	0.273506	−	1.77857i
$779$	18.2469	−	13.5328i	0.653763	−	0.484864i
$780$	−0.179838	−	1.30815i	−0.00643923	−	0.0468393i
$781$	2.49106	−	5.26690i	0.0891371	−	0.188465i
$782$	−1.25696	−	0.130557i	−0.0449488	−	0.00466873i
$783$	4.83403	−	0.961549i	0.172754	−	0.0343630i
$784$	−26.2707	+	4.64657i	−0.938238	+	0.165949i
$785$	0.361193	+	0.0718458i	0.0128915	+	0.00256428i
$786$	−8.52913	+	27.5874i	−0.304224	+	0.984010i
$787$	18.5409	+	0.910857i	0.660912	+	0.0324685i	0.376760	−	0.926311i	$-0.377038\pi$
$787$	18.5409	+	0.910857i	0.660912	+	0.0324685i	0.284152	+	0.958779i	$0.408288\pi$
$788$	−37.3931	−	34.6231i	−1.33207	−	1.23340i
$789$	−0.885301	−	3.53432i	−0.0315175	−	0.125825i
$790$	−1.23718	+	1.35050i	−0.0440168	+	0.0480486i
$791$	−1.13860	+	11.5604i	−0.0404839	+	0.411040i
$792$	−2.07730	+	1.82321i	−0.0738138	+	0.0647848i
$793$	39.1586	+	32.1367i	1.39056	+	1.14121i
$794$	5.54913	−	21.6636i	0.196931	−	0.768811i
$795$	0.108518	−	0.00533116i	0.00384875	−	0.000189077i
$796$	15.9874	+	13.4078i	0.566657	+	0.475226i
$797$	−4.81941	+	0.714893i	−0.170712	+	0.0253228i	−0.231539	−	0.972826i	$-0.574376\pi$
$797$	−4.81941	+	0.714893i	−0.170712	+	0.0253228i	0.0608270	+	0.998148i	$0.480626\pi$
$798$	−5.21551	+	2.12789i	−0.184627	+	0.0753264i
$799$	−2.79450	+	1.15752i	−0.0988625	+	0.0409502i
$800$	−7.47077	−	27.2144i	−0.264132	−	0.962175i
$801$	10.3967	+	4.30646i	0.367349	+	0.152161i
$802$	−27.0331	−	0.143866i	−0.954573	−	0.00508010i
$803$	−6.71864	+	9.05904i	−0.237096	+	0.319687i
$804$	−1.56254	−	1.94582i	−0.0551064	−	0.0686239i
$805$	−0.118209	−	0.107138i	−0.00416631	−	0.00377612i
$806$	−58.0706	+	8.29837i	−2.04545	+	0.292298i
$807$	−13.8250	+	1.36164i	−0.486662	+	0.0479320i
$808$	−21.3148	+	15.2868i	−0.749851	+	0.537787i
$809$	13.2946	−	10.9106i	0.467415	−	0.383597i	−0.370998	−	0.928634i	$-0.620984\pi$
$809$	13.2946	−	10.9106i	0.467415	−	0.383597i	0.838412	+	0.545036i	$0.183484\pi$
$810$	−0.0631179	−	0.135310i	−0.00221774	−	0.00475431i
$811$	−13.8082	−	8.27634i	−0.484873	−	0.290622i	0.250703	−	0.968064i	$-0.419338\pi$
$811$	−13.8082	−	8.27634i	−0.484873	−	0.290622i	−0.735576	+	0.677442i	$0.763088\pi$
$812$	−5.51059	+	1.31816i	−0.193384	+	0.0462584i
$813$	−2.30171	−	2.53954i	−0.0807243	−	0.0890656i
$814$	0.637379	+	6.84465i	0.0223401	+	0.239905i
$815$	−1.35468	+	0.905167i	−0.0474523	+	0.0317066i
$816$	1.21643	+	0.607343i	0.0425836	+	0.0212613i
$817$	65.8638	+	44.0088i	2.30428	+	1.53967i
$818$	−4.37552	−	2.36879i	−0.152986	−	0.0828227i
$819$	−1.21096	−	3.38441i	−0.0423144	−	0.118261i
$820$	−0.459394	−	0.517835i	−0.0160428	−	0.0180836i
$821$	−43.0853	−	6.39110i	−1.50369	−	0.223051i	−0.656492	−	0.754333i	$-0.727960\pi$
$821$	−43.0853	−	6.39110i	−1.50369	−	0.223051i	−0.847195	+	0.531282i	$0.821710\pi$
$822$	20.8077	−	5.09453i	0.725751	−	0.177692i
$823$	1.32019	+	4.35207i	0.0460188	+	0.151704i	0.976939	−	0.213520i	$-0.0684927\pi$
$823$	1.32019	+	4.35207i	0.0460188	+	0.151704i	−0.930920	+	0.365223i	$0.880993\pi$
$824$	−11.3525	−	1.30144i	−0.395484	−	0.0453376i
$825$	−2.29810	−	4.29944i	−0.0800095	−	0.149687i
$826$	8.77636	−	3.08765i	0.305369	−	0.107433i
$827$	−14.8587	−	31.4161i	−0.516688	−	1.09245i	−0.978648	−	0.205545i	$-0.934103\pi$
$827$	−14.8587	−	31.4161i	−0.516688	−	1.09245i	0.461959	−	0.886901i	$-0.347147\pi$
$828$	5.14561	+	1.08058i	0.178822	+	0.0375529i
$829$	8.50259	−	33.9442i	0.295307	−	1.17893i	−0.622730	−	0.782437i	$-0.713976\pi$
$829$	8.50259	−	33.9442i	0.295307	−	1.17893i	0.918037	−	0.396495i	$-0.129774\pi$
$830$	1.30506	−	0.862001i	0.0452992	−	0.0299205i
$831$	4.23497	−	4.23497i	0.146909	−	0.146909i
$832$	−32.3965	−	38.1224i	−1.12315	−	1.32166i
$833$	1.60304	+	1.60304i	0.0555419	+	0.0555419i
$834$	6.76168	+	1.38243i	0.234138	+	0.0478696i
$835$	−0.801954	−	0.200879i	−0.0277528	−	0.00695171i
$836$	−7.64346	+	11.1798i	−0.264355	+	0.386662i
$837$	−5.99608	+	2.83593i	−0.207255	+	0.0980242i
$838$	−10.6628	+	22.2376i	−0.368341	+	0.768187i
$839$	22.8851	−	12.2323i	0.790080	−	0.422306i	−0.0264209	−	0.999651i	$-0.508411\pi$
$839$	22.8851	−	12.2323i	0.790080	−	0.422306i	0.816501	+	0.577344i	$0.195911\pi$
$840$	0.0784850	+	0.152648i	0.00270799	+	0.00526686i
$841$	−4.50485	+	1.36653i	−0.155340	+	0.0471217i
$842$	−19.9936	−	12.1288i	−0.689025	−	0.417986i
$843$	−3.45157	+	23.2686i	−0.118878	+	0.801413i
$844$	−0.190093	−	0.0923958i	−0.00654327	−	0.00318039i
$845$	2.59516	−	0.928563i	0.0892762	−	0.0319435i
$846$	12.0622	−	3.58903i	0.414706	−	0.123393i
$847$	−3.20781	+	4.80082i	−0.110221	+	0.164958i
$848$	3.35779	−	2.38122i	0.115307	−	0.0817713i
$849$	−9.21456	−	13.7906i	−0.316243	−	0.473291i
$850$	−1.53121	+	1.84566i	−0.0525199	+	0.0633057i
$851$	9.68942	−	8.78198i	0.332149	−	0.301042i
$852$	11.7762	+	1.87513i	0.403444	+	0.0642410i
$853$	7.20703	−	12.0242i	0.246764	−	0.411701i	−0.709279	−	0.704928i	$-0.750979\pi$
$853$	7.20703	−	12.0242i	0.246764	−	0.411701i	0.956043	+	0.293227i	$0.0947293\pi$
$854$	−6.18802	−	2.25133i	−0.211750	−	0.0770389i
$855$	−0.464115	−	0.565526i	−0.0158724	−	0.0193406i
$856$	13.0194	+	12.1843i	0.444995	+	0.416451i
$857$	−0.390834	−	3.96821i	−0.0133506	−	0.135551i	0.986199	−	0.165565i	$-0.0529449\pi$
$857$	−0.390834	−	3.96821i	−0.0133506	−	0.135551i	−0.999549	+	0.0300139i	$0.990445\pi$
$858$	−6.91397	−	5.18501i	−0.236039	−	0.177013i
$859$	15.4729	−	17.0717i	0.527929	−	0.582480i	−0.417349	−	0.908746i	$-0.637041\pi$
$859$	15.4729	−	17.0717i	0.527929	−	0.582480i	0.945278	+	0.326266i	$0.105791\pi$
$860$	1.16044	−	2.11652i	0.0395705	−	0.0721729i
$861$	−1.51357	−	1.12254i	−0.0515824	−	0.0382561i
$862$	−9.55416	+	9.45300i	−0.325416	+	0.321971i
$863$	9.32922	−	22.5227i	0.317570	−	0.766683i	−0.681812	−	0.731528i	$-0.738808\pi$
$863$	9.32922	−	22.5227i	0.317570	−	0.766683i	0.999382	−	0.0351548i	$-0.0111924\pi$
$864$	−4.77295	−	3.03627i	−0.162379	−	0.103296i
$865$	−0.743568	−	1.79513i	−0.0252821	−	0.0610363i
$866$	24.0471	+	10.1109i	0.817153	+	0.343582i
$867$	2.47747	+	16.7017i	0.0841391	+	0.567220i
$868$	6.76267	−	3.52270i	0.229540	−	0.119568i
$869$	0.588175	+	11.9726i	0.0199525	+	0.406142i
$870$	−0.374962	−	0.633204i	−0.0127124	−	0.0214676i
$871$	4.95018	−	6.03182i	0.167731	−	0.204380i
$872$	−4.16594	+	2.40741i	−0.141076	+	0.0815252i
$873$	−9.84608	−	0.969754i	−0.333239	−	0.0328212i
$874$	25.7382	−	1.12717i	0.870607	−	0.0381270i
$875$	−0.588007	+	0.147288i	−0.0198783	+	0.00497925i
$876$	−21.6502	−	8.00751i	−0.731493	−	0.270549i
$877$	0.995278	−	20.2594i	0.0336082	−	0.684110i	−0.921594	−	0.388155i	$-0.873112\pi$
$877$	0.995278	−	20.2594i	0.0336082	−	0.684110i	0.955202	−	0.295954i	$-0.0956376\pi$
$878$	−15.4558	−	29.2897i	−0.521609	−	0.988479i
$879$	−2.29665	+	11.5460i	−0.0774639	+	0.389438i
$880$	0.359723	+	0.202236i	0.0121263	+	0.00681738i
$881$	2.89491	+	14.5537i	0.0975321	+	0.490327i	0.998416	+	0.0562663i	$0.0179196\pi$
$881$	2.89491	+	14.5537i	0.0975321	+	0.490327i	−0.900884	+	0.434060i	$0.857080\pi$
$882$	−5.94487	−	7.32297i	−0.200174	−	0.246577i
$883$	10.6739	+	5.04838i	0.359205	+	0.169891i	0.598634	−	0.801022i	$-0.295710\pi$
$883$	10.6739	+	5.04838i	0.359205	+	0.169891i	−0.239429	+	0.970914i	$0.576960\pi$
$884$	−1.07680	+	4.11261i	−0.0362167	+	0.138322i
$885$	0.719808	+	0.970549i	0.0241961	+	0.0326247i
$886$	−3.74735	−	5.10932i	−0.125895	−	0.171651i
$887$	2.38952	+	1.27723i	0.0802323	+	0.0428851i	0.511025	−	0.859566i	$-0.329266\pi$
$887$	2.38952	+	1.27723i	0.0802323	+	0.0428851i	−0.430793	+	0.902451i	$0.641766\pi$
$888$	−13.0827	+	5.17592i	−0.439027	+	0.173692i
$889$	−2.22553	+	7.33660i	−0.0746420	+	0.246062i
$890$	0.0913734	−	1.67772i	0.00306284	−	0.0562372i
$891$	−0.920072	−	0.329207i	−0.0308236	−	0.0110289i
$892$	6.43670	+	0.0685124i	0.215517	+	0.00229396i
$893$	52.8910	−	31.7017i	1.76993	−	1.06086i
$894$	1.24486	−	1.84177i	0.0416343	−	0.0615979i
$895$			0.234824i			0.00784931i
$896$	5.61707	+	3.27701i	0.187653	+	0.109477i
$897$			16.4401i			0.548920i
$898$	32.5203	+	21.9806i	1.08522	+	0.733501i
$899$	−28.0407	+	16.8070i	−0.935211	+	0.560544i
$900$	7.13000	−	6.97981i	0.237667	−	0.232660i
$901$	−0.329351	−	0.117844i	−0.0109723	−	0.00392594i
$902$	−4.52391	−	0.246385i	−0.150630	−	0.00820373i
$903$	1.90739	−	6.28781i	0.0634739	−	0.209245i
$904$	−41.0589	+	39.7684i	−1.36560	+	1.32268i
$905$	−0.189035	−	0.101041i	−0.00628373	−	0.00335872i
$906$	−10.3144	+	7.56491i	−0.342672	+	0.251327i
$907$	−28.2559	−	38.0987i	−0.938221	−	1.26505i	−0.964144	−	0.265381i	$-0.914502\pi$
$907$	−28.2559	−	38.0987i	−0.938221	−	1.26505i	0.0259222	−	0.999664i	$-0.491748\pi$
$908$	19.8396	−	11.6062i	0.658399	−	0.385164i
$909$	−8.38328	−	3.96500i	−0.278056	−	0.131511i
$910$	−0.416673	+	0.338260i	−0.0138126	+	0.0112132i
$911$	−2.84920	−	14.3239i	−0.0943982	−	0.474572i	−0.998848	−	0.0479912i	$-0.984718\pi$
$911$	−2.84920	−	14.3239i	−0.0943982	−	0.474572i	0.904450	−	0.426581i	$-0.140282\pi$
$912$	−26.3471	−	8.60886i	−0.872441	−	0.285068i
$913$	1.99703	−	10.0397i	0.0660919	−	0.332266i
$914$	−40.2604	+	21.2449i	−1.33169	+	0.702720i
$915$	0.0419640	−	0.854196i	0.00138729	−	0.0282389i
$916$	31.4731	−	14.4778i	1.03990	−	0.478360i
$917$	11.3846	−	2.85171i	0.375954	−	0.0941716i
$918$	0.0210314	+	0.480239i	0.000694138	+	0.0158502i
$919$	8.46035	+	0.833272i	0.279081	+	0.0274871i	0.236589	−	0.971610i	$-0.423970\pi$
$919$	8.46035	+	0.833272i	0.279081	+	0.0274871i	0.0424917	+	0.999097i	$0.486470\pi$
$920$	−0.102777	−	0.778279i	−0.00338845	−	0.0256591i
$921$	−16.7618	+	20.4243i	−0.552319	+	0.673002i
$922$	38.3612	−	22.7162i	1.26336	−	0.748118i
$923$	1.82950	+	37.2404i	0.0602189	+	1.22578i
$924$	1.07148	+	0.337523i	0.0352489	+	0.0111037i
$925$	−3.64125	−	24.5473i	−0.119724	−	0.807112i
$926$	−8.55658	+	20.3504i	−0.281187	+	0.668756i
$927$	−1.54604	−	3.73248i	−0.0507788	−	0.122591i
$928$	−24.8782	−	12.5871i	−0.816666	−	0.413191i
$929$	−0.0918435	+	0.221730i	−0.00301329	+	0.00727472i	−0.925379	−	0.379043i	$-0.876253\pi$
$929$	−0.0918435	+	0.221730i	−0.00301329	+	0.00727472i	0.922366	+	0.386318i	$0.126253\pi$
$930$	0.696541	+	0.703994i	0.0228405	+	0.0230849i
$931$	−37.1218	−	27.5314i	−1.21662	−	0.902305i
$932$	4.36903	+	14.9747i	0.143112	+	0.490513i
$933$	−21.7148	+	23.9586i	−0.710912	+	0.784371i
$934$	−32.2388	+	42.9890i	−1.05489	+	1.40664i
$935$	−0.00343722	−	0.0348987i	−0.000112409	−	0.00114131i
$936$	6.22393	−	16.5565i	0.203436	−	0.541167i
$937$	10.1534	+	12.3720i	0.331697	+	0.404174i	0.911976	−	0.410244i	$-0.134556\pi$
$937$	10.1534	+	12.3720i	0.331697	+	0.404174i	−0.580279	+	0.814418i	$0.697056\pi$
$938$	−0.346784	+	0.953174i	−0.0113229	+	0.0311222i
$939$	−6.69114	+	11.1635i	−0.218357	+	0.364307i
$940$	−1.10319	−	1.52106i	−0.0359822	−	0.0496114i
$941$	20.0458	−	18.1684i	0.653474	−	0.592274i	−0.276002	−	0.961157i	$-0.589010\pi$
$941$	20.0458	−	18.1684i	0.653474	−	0.592274i	0.929476	+	0.368883i	$0.120260\pi$
$942$	3.79658	+	3.14973i	0.123699	+	0.102624i
$943$	4.78826	+	7.16614i	0.155927	+	0.233361i
$944$	42.7666	+	16.3371i	1.39193	+	0.531727i
$945$	−0.0337148	+	0.0504577i	−0.00109674	+	0.00164139i
$946$	−4.50533	−	15.1417i	−0.146481	−	0.492300i
$947$	−20.6137	+	7.37571i	−0.669856	+	0.239678i	−0.649782	−	0.760120i	$-0.725140\pi$
$947$	−20.6137	+	7.37571i	−0.669856	+	0.239678i	−0.0200735	+	0.999799i	$0.506390\pi$
$948$	−23.1860	+	8.01877i	−0.753048	+	0.260437i
$949$	10.5906	−	71.3961i	0.343786	−	2.31762i
$950$	25.3571	−	41.7997i	0.822693	−	1.35616i
$951$	−12.8802	+	3.90716i	−0.417669	+	0.126698i
$952$	−0.0453785	−	0.550743i	−0.00147073	−	0.0178497i
$953$	−9.06631	+	4.84605i	−0.293687	+	0.156979i	−0.611660	−	0.791121i	$-0.709498\pi$
$953$	−9.06631	+	4.84605i	−0.293687	+	0.156979i	0.317973	+	0.948100i	$0.396998\pi$
$954$	1.31231	+	0.629246i	0.0424877	+	0.0203726i
$955$	1.18472	−	0.560331i	0.0383366	−	0.0181319i
$956$	58.4327	−	10.9778i	1.88985	−	0.355047i
$957$	−4.67200	−	1.17027i	−0.151024	−	0.0378296i
$958$	−6.05942	+	29.6376i	−0.195771	+	0.957547i
$959$	−6.15674	−	6.15674i	−0.198812	−	0.198812i
$960$	−0.191138	+	0.822698i	−0.00616894	+	0.0265525i
$961$	9.18919	−	9.18919i	0.296425	−	0.296425i
$962$	−24.2456	−	36.7074i	−0.781708	−	1.18350i
$963$	−1.53184	+	6.11546i	−0.0493629	+	0.197068i
$964$	−42.1684	+	27.5314i	−1.35815	+	0.886726i
$965$	0.681524	+	1.44096i	0.0219390	+	0.0463862i
$966$	−0.709222	−	2.01590i	−0.0228188	−	0.0648605i
$967$	24.5055	+	45.8465i	0.788043	+	1.47432i	0.878146	+	0.478393i	$0.158780\pi$
$967$	24.5055	+	45.8465i	0.788043	+	1.47432i	−0.0901030	+	0.995932i	$0.528720\pi$
$968$	−27.3166	+	7.81240i	−0.877989	+	0.251100i
$969$	0.683728	+	2.25395i	0.0219645	+	0.0724072i
$970$	0.351301	+	1.43483i	0.0112796	+	0.0460695i
$971$	17.3076	+	2.56734i	0.555428	+	0.0823900i	0.418543	−	0.908197i	$-0.362541\pi$
$971$	17.3076	+	2.56734i	0.555428	+	0.0823900i	0.136885	+	0.990587i	$0.456291\pi$
$972$	0.119391	−	1.99643i	0.00382947	−	0.0640356i
$973$	−0.945007	−	2.64112i	−0.0302955	−	0.0846703i
$974$	18.0879	−	33.4112i	0.579575	−	1.07057i
$975$	25.9403	+	17.3327i	0.830753	+	0.555092i
$976$	−16.0627	−	28.1406i	−0.514155	−	0.900759i
$977$	6.99544	−	4.67420i	0.223804	−	0.149541i	−0.438614	−	0.898676i	$-0.644530\pi$
$977$	6.99544	−	4.67420i	0.223804	−	0.149541i	0.662418	+	0.749135i	$0.269530\pi$
$978$	−21.7302	+	2.02353i	−0.694855	+	0.0647054i
$979$	−7.38492	−	8.14800i	−0.236023	−	0.260411i
$980$	−0.736829	+	1.20017i	−0.0235371	+	0.0383380i
$981$	−1.45910	−	0.874554i	−0.0465856	−	0.0279224i
$982$	−32.8420	+	15.3198i	−1.04803	+	0.488874i
$983$	8.91254	−	7.31433i	0.284266	−	0.233291i	−0.481444	−	0.876477i	$-0.659888\pi$
$983$	8.91254	−	7.31433i	0.284266	−	0.233291i	0.765710	+	0.643186i	$0.222388\pi$
$984$	−2.10919	−	9.02962i	−0.0672386	−	0.287854i
$985$	−2.67717	+	0.263678i	−0.0853018	+	0.00840149i
$986$	0.335162	+	2.34541i	0.0106737	+	0.0746931i
$987$	−3.78997	−	3.43503i	−0.120636	−	0.109338i
$988$	9.41246	−	86.1552i	0.299450	−	2.74096i
$989$	−17.9021	+	24.1382i	−0.569255	+	0.767551i
$990$	−0.000776461		0.145900i	−2.46776e−5		0.00463702i
$991$	24.2884	+	10.0606i	0.771546	+	0.319585i	0.733499	−	0.679691i	$-0.237886\pi$
$991$	24.2884	+	10.0606i	0.771546	+	0.319585i	0.0380478	+	0.999276i	$0.487886\pi$
$992$	36.5926	+	8.29658i	1.16182	+	0.263417i
$993$	17.0522	−	7.06326i	0.541136	−	0.224146i
$994$	−1.83087	−	4.48752i	−0.0580718	−	0.142335i
$995$	1.08952	−	0.161615i	0.0345402	−	0.00512355i
$996$	20.8704	−	1.83149i	0.661304	−	0.0580330i
$997$	−41.5407	+	2.04076i	−1.31561	+	0.0646316i	−0.694727	−	0.719274i	$-0.744475\pi$
$997$	−41.5407	+	2.04076i	−1.31561	+	0.0646316i	−0.620880	+	0.783905i	$0.713225\pi$
$998$	2.38496	+	0.610909i	0.0754947	+	0.0193380i
$999$	−3.84517	−	3.15565i	−0.121656	−	0.0998403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.685.28	yes	2048
256.37	even	64	inner	768.2.z.a.37.28	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.37.28	✓	2048	256.37	even	64	inner
768.2.z.a.685.28	yes	2048	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.268514 - 1.38849i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(-1.85580 + 0.745657i) q^{4} +(-0.0355676 + 0.0994047i) q^{5} +(-1.05290 + 0.944138i) q^{6} +(0.550047 + 0.166855i) q^{7} +(1.53364 + 2.37654i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(-0.268514 - 1.38849i) q^{2} +(-0.514103 - 0.857729i) q^{3} +(-1.85580 + 0.745657i) q^{4} +(-0.0355676 + 0.0994047i) q^{5} +(-1.05290 + 0.944138i) q^{6} +(0.550047 + 0.166855i) q^{7} +(1.53364 + 2.37654i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(0.147573 + 0.0226936i) q^{10} +(0.784890 - 0.582114i) q^{11} +(1.59364 + 1.20843i) q^{12} +(-2.67374 + 5.65315i) q^{13} +(0.0839809 - 0.808537i) q^{14} +(0.103548 - 0.0205969i) q^{15} +(2.88799 - 2.76758i) q^{16} +(-0.333374 - 0.0663123i) q^{17} +(1.35111 + 0.417721i) q^{18} +(6.92114 + 0.340014i) q^{19} +(-0.00811550 - 0.210997i) q^{20} +(-0.139665 - 0.557572i) q^{21} +(-1.01901 - 0.933505i) q^{22} +(-0.257680 + 2.61627i) q^{23} +(1.24997 - 2.53724i) q^{24} +(3.85644 + 3.16490i) q^{25} +(8.56727 + 2.19451i) q^{26} +(0.998795 - 0.0490677i) q^{27} +(-1.14519 + 0.100497i) q^{28} +(4.87539 - 0.723196i) q^{29} +(-0.0564026 - 0.138244i) q^{30} +(-6.12801 + 2.53830i) q^{31} +(-4.61822 - 3.26681i) q^{32} +(-0.902810 - 0.373956i) q^{33} +(-0.00255818 + 0.480692i) q^{34} +(-0.0361500 + 0.0487427i) q^{35} +(0.217208 - 1.98817i) q^{36} +(-3.68570 - 3.34052i) q^{37} +(-1.38632 - 9.70122i) q^{38} +(6.22345 - 0.612956i) q^{39} +(-0.290787 + 0.0679238i) q^{40} +(2.53423 - 2.07979i) q^{41} +(-0.736680 + 0.343638i) q^{42} +(9.80504 + 5.87692i) q^{43} +(-1.02254 + 1.66555i) q^{44} +(-0.0709007 - 0.0782268i) q^{45} +(3.70185 - 0.344719i) q^{46} +(7.39908 - 4.94391i) q^{47} +(-3.85856 - 1.05429i) q^{48} +(-5.54558 - 3.70544i) q^{49} +(3.35891 - 6.20444i) q^{50} +(0.114511 + 0.320036i) q^{51} +(0.746619 - 12.4848i) q^{52} +(1.01797 + 0.151001i) q^{53} +(-0.336320 - 1.37364i) q^{54} +(0.0299483 + 0.0987262i) q^{55} +(0.447040 + 1.56310i) q^{56} +(-3.26654 - 6.11126i) q^{57} +(-2.31326 - 6.57524i) q^{58} +(4.89345 + 10.3463i) q^{59} +(-0.176806 + 0.115435i) q^{60} +(1.96827 - 7.85779i) q^{61} +(5.16986 + 7.82710i) q^{62} +(-0.406444 + 0.406444i) q^{63} +(-3.29587 + 7.28953i) q^{64} +(-0.466851 - 0.466851i) q^{65} +(-0.276817 + 1.35395i) q^{66} +(-1.21038 - 0.303184i) q^{67} +(0.668122 - 0.125521i) q^{68} +(2.37652 - 1.12401i) q^{69} +(0.0773854 + 0.0371058i) q^{70} +(5.25824 - 2.81059i) q^{71} +(-2.81887 + 0.232261i) q^{72} +(-11.0448 + 3.35041i) q^{73} +(-3.64861 + 6.01452i) q^{74} +(0.732017 - 4.93486i) q^{75} +(-13.0978 + 4.52980i) q^{76} +(0.528856 - 0.189228i) q^{77} +(-2.52216 - 8.47660i) q^{78} +(-6.81504 + 10.1994i) q^{79} +(0.172392 + 0.385516i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(-3.56824 - 2.96030i) q^{82} +(7.76169 - 7.03479i) q^{83} +(0.674947 + 0.930601i) q^{84} +(0.0184491 - 0.0307804i) q^{85} +(5.52724 - 15.1922i) q^{86} +(-3.12676 - 3.80997i) q^{87} +(2.58716 + 0.972565i) q^{88} +(-1.10302 - 11.1991i) q^{89} +(-0.0895793 + 0.119450i) q^{90} +(-2.41394 + 2.66337i) q^{91} +(-1.47264 - 5.04741i) q^{92} +(5.32760 + 3.95122i) q^{93} +(-8.85131 - 8.94603i) q^{94} +(-0.279967 + 0.675900i) q^{95} +(-0.427795 + 5.64066i) q^{96} +(3.78616 + 9.14061i) q^{97} +(-3.65589 + 8.69493i) q^{98} +(0.143384 + 0.966618i) 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

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