LMFDB - Embedded newform 726.2.i.c.595.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(67,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 20])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			595.4
Character	$\chi$	$=$	726.595
Dual form			726.2.i.c.133.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841254 + 0.540641i) q^{2} -1.00000 q^{3} +(0.415415 + 0.909632i) q^{4} +(0.245189 + 1.70533i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.219849 - 0.253720i) q^{7} +(-0.142315 + 0.989821i) q^{8} +1.00000 q^{9} +(-0.715703 + 1.56717i) q^{10} +(3.10400 + 1.16841i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.869158 + 1.90319i) q^{13} +(-0.0477778 - 0.332302i) q^{14} +(-0.245189 - 1.70533i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.22415 - 0.359443i) q^{17} +(0.841254 + 0.540641i) q^{18} +(-4.77272 - 1.40140i) q^{19} +(-1.44936 + 0.931450i) q^{20} +(0.219849 + 0.253720i) q^{21} +(1.97956 + 2.66108i) q^{22} +(-5.97110 + 6.89102i) q^{23} +(0.142315 - 0.989821i) q^{24} +(1.94944 - 0.572408i) q^{25} +(-0.297760 + 2.07097i) q^{26} -1.00000 q^{27} +(0.139463 - 0.305381i) q^{28} +(0.602673 + 0.176961i) q^{29} +(0.715703 - 1.56717i) q^{30} +(-2.71032 + 5.93476i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-3.10400 - 1.16841i) q^{33} +(1.22415 + 0.359443i) q^{34} +(0.378770 - 0.437124i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-4.19767 + 9.19162i) q^{37} +(-3.25742 - 3.75926i) q^{38} +(-0.869158 - 1.90319i) q^{39} -1.72286 q^{40} +(7.23190 + 4.64766i) q^{41} +(0.0477778 + 0.332302i) q^{42} +(-0.507147 + 3.52729i) q^{43} +(0.226624 + 3.30887i) q^{44} +(0.245189 + 1.70533i) q^{45} +(-8.74878 + 2.56887i) q^{46} +(9.85415 - 6.33288i) q^{47} +(0.654861 - 0.755750i) q^{48} +(0.980164 - 6.81719i) q^{49} +(1.94944 + 0.572408i) q^{50} +(-1.22415 + 0.359443i) q^{51} +(-1.37014 + 1.58123i) q^{52} +(-7.04126 - 8.12605i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-1.23146 + 5.57982i) q^{55} +(0.282425 - 0.181504i) q^{56} +(4.77272 + 1.40140i) q^{57} +(0.411329 + 0.474699i) q^{58} +(5.61779 - 3.61034i) q^{59} +(1.44936 - 0.931450i) q^{60} +(2.64105 - 1.69730i) q^{61} +(-5.48864 + 3.52733i) q^{62} +(-0.219849 - 0.253720i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-3.03246 + 1.94884i) q^{65} +(-1.97956 - 2.66108i) q^{66} +(-1.98094 - 1.27308i) q^{67} +(0.835491 + 0.964207i) q^{68} +(5.97110 - 6.89102i) q^{69} +(0.554969 - 0.162954i) q^{70} +(-11.5086 - 3.37924i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(4.36034 - 5.03210i) q^{73} +(-8.50067 + 5.46305i) q^{74} +(-1.94944 + 0.572408i) q^{75} +(-0.707904 - 4.92358i) q^{76} +(-0.385964 - 1.04442i) q^{77} +(0.297760 - 2.07097i) q^{78} +(-0.329412 - 2.29111i) q^{79} +(-1.44936 - 0.931450i) q^{80} +1.00000 q^{81} +(3.57114 + 7.81972i) q^{82} +(11.3139 + 13.0570i) q^{83} +(-0.139463 + 0.305381i) q^{84} +(0.913115 + 1.99944i) q^{85} +(-2.33363 + 2.69316i) q^{86} +(-0.602673 - 0.176961i) q^{87} +(-1.59826 + 2.90612i) q^{88} +(14.5089 - 4.26019i) q^{89} +(-0.715703 + 1.56717i) q^{90} +(0.291793 - 0.638938i) q^{91} +(-8.74878 - 2.56887i) q^{92} +(2.71032 - 5.93476i) q^{93} +11.7137 q^{94} +(1.21962 - 8.48265i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-1.27952 + 8.89926i) q^{97} +(4.51022 - 5.20507i) q^{98} +(3.10400 + 1.16841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{2} - 60 q^{3} - 6 q^{4} - 2 q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 60 q^{9} - 13 q^{10} - 10 q^{11} + 6 q^{12} - 17 q^{13} - 6 q^{14} + 2 q^{15} - 6 q^{16} + 10 q^{17} - 6 q^{18} - 4 q^{19} - 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) $ 60 * q - 6 * q^2 - 60 * q^3 - 6 * q^4 - 2 * q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 60 * q^9 - 13 * q^10 - 10 * q^11 + 6 * q^12 - 17 * q^13 - 6 * q^14 + 2 * q^15 - 6 * q^16 + 10 * q^17 - 6 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 10 * q^22 - 26 * q^23 + 6 * q^24 - 2 * q^25 + 5 * q^26 - 60 * q^27 + 5 * q^28 - 6 * q^29 + 13 * q^30 - 52 * q^31 - 6 * q^32 + 10 * q^33 + 10 * q^34 + 63 * q^35 - 6 * q^36 - 47 * q^37 + 18 * q^38 + 17 * q^39 - 2 * q^40 + 27 * q^41 + 6 * q^42 + 84 * q^43 + q^44 - 2 * q^45 + 7 * q^46 + 10 * q^47 + 6 * q^48 - 33 * q^49 - 2 * q^50 - 10 * q^51 + 5 * q^52 + 42 * q^53 + 6 * q^54 + 13 * q^55 - 6 * q^56 + 4 * q^57 + 16 * q^58 - 11 * q^59 + 2 * q^60 - 24 * q^61 + 14 * q^62 + 5 * q^63 - 6 * q^64 - 80 * q^65 + 10 * q^66 - 2 * q^67 - q^68 + 26 * q^69 - 14 * q^70 - 30 * q^71 - 6 * q^72 - 51 * q^73 + 8 * q^74 + 2 * q^75 - 4 * q^76 + 73 * q^77 - 5 * q^78 - 30 * q^79 - 2 * q^80 + 60 * q^81 - 6 * q^82 + 4 * q^83 - 5 * q^84 + 45 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 44 * q^89 - 13 * q^90 - 90 * q^91 + 7 * q^92 + 52 * q^93 - 78 * q^94 - 65 * q^95 + 6 * q^96 - 41 * q^97 + 33 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	0.245189	+	1.70533i	0.109652	+	0.762645i	0.968248	+	0.249992i	$0.0804281\pi$
$5$	0.245189	+	1.70533i	0.109652	+	0.762645i	−0.858596	+	0.512653i	$0.828663\pi$
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	−0.219849	−	0.253720i	−0.0830953	−	0.0958971i	0.712679	−	0.701490i	$-0.247481\pi$
$7$	−0.219849	−	0.253720i	−0.0830953	−	0.0958971i	−0.795775	+	0.605593i	$0.792936\pi$
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	1.00000			0.333333
$10$	−0.715703	+	1.56717i	−0.226325	+	0.495583i
$11$	3.10400	+	1.16841i	0.935891	+	0.352289i
$11$	3.10400	+	1.16841i	0.935891	+	0.352289i
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	0.869158	+	1.90319i	0.241061	+	0.527850i	0.991033	−	0.133620i	$-0.0426601\pi$
$13$	0.869158	+	1.90319i	0.241061	+	0.527850i	−0.749971	+	0.661470i	$0.769933\pi$
$14$	−0.0477778	−	0.332302i	−0.0127692	−	0.0888115i
$15$	−0.245189	−	1.70533i	−0.0633075	−	0.440313i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.22415	−	0.359443i	0.296900	−	0.0871776i	−0.129890	−	0.991528i	$-0.541463\pi$
$17$	1.22415	−	0.359443i	0.296900	−	0.0871776i	0.426790	+	0.904351i	$0.359644\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	−4.77272	−	1.40140i	−1.09494	−	0.321503i	−0.316098	−	0.948726i	$-0.602373\pi$
$19$	−4.77272	−	1.40140i	−1.09494	−	0.321503i	−0.778839	+	0.627224i	$0.784191\pi$
$20$	−1.44936	+	0.931450i	−0.324088	+	0.208279i
$21$	0.219849	+	0.253720i	0.0479751	+	0.0553662i
$22$	1.97956	+	2.66108i	0.422044	+	0.567344i
$23$	−5.97110	+	6.89102i	−1.24506	+	1.43688i	−0.388002	+	0.921659i	$0.626835\pi$
$23$	−5.97110	+	6.89102i	−1.24506	+	1.43688i	−0.857059	+	0.515218i	$0.827711\pi$
$24$	0.142315	−	0.989821i	0.0290499	−	0.202046i
$25$	1.94944	−	0.572408i	0.389889	−	0.114482i
$26$	−0.297760	+	2.07097i	−0.0583956	+	0.406150i
$27$	−1.00000			−0.192450
$28$	0.139463	−	0.305381i	0.0263560	−	0.0577116i
$29$	0.602673	+	0.176961i	0.111914	+	0.0328608i	0.337210	−	0.941430i	$-0.390517\pi$
$29$	0.602673	+	0.176961i	0.111914	+	0.0328608i	−0.225296	+	0.974290i	$0.572335\pi$
$30$	0.715703	−	1.56717i	0.130669	−	0.286125i
$31$	−2.71032	+	5.93476i	−0.486787	+	1.06591i	0.493754	+	0.869602i	$0.335624\pi$
$31$	−2.71032	+	5.93476i	−0.486787	+	1.06591i	−0.980541	+	0.196313i	$0.937103\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	−3.10400	−	1.16841i	−0.540337	−	0.203394i
$34$	1.22415	+	0.359443i	0.209940	+	0.0616439i
$35$	0.378770	−	0.437124i	0.0640239	−	0.0738875i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−4.19767	+	9.19162i	−0.690093	+	1.51109i	0.161491	+	0.986874i	$0.448370\pi$
$37$	−4.19767	+	9.19162i	−0.690093	+	1.51109i	−0.851584	+	0.524218i	$0.824358\pi$
$38$	−3.25742	−	3.75926i	−0.528423	−	0.609832i
$39$	−0.869158	−	1.90319i	−0.139177	−	0.304755i
$40$	−1.72286			−0.272409
$41$	7.23190	+	4.64766i	1.12943	+	0.725842i	0.965442	−	0.260620i	$-0.0839269\pi$
$41$	7.23190	+	4.64766i	1.12943	+	0.725842i	0.163991	+	0.986462i	$0.447563\pi$
$42$	0.0477778	+	0.332302i	0.00737228	+	0.0512753i
$43$	−0.507147	+	3.52729i	−0.0773392	+	0.537906i	0.913911	+	0.405914i	$0.133047\pi$
$43$	−0.507147	+	3.52729i	−0.0773392	+	0.537906i	−0.991251	+	0.131993i	$0.957863\pi$
$44$	0.226624	+	3.30887i	0.0341649	+	0.498831i
$45$	0.245189	+	1.70533i	0.0365506	+	0.254215i
$46$	−8.74878	+	2.56887i	−1.28994	+	0.378760i
$47$	9.85415	−	6.33288i	1.43738	−	0.923745i	0.437679	−	0.899131i	$-0.355801\pi$
$47$	9.85415	−	6.33288i	1.43738	−	0.923745i	0.999697	−	0.0246139i	$-0.00783565\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	0.980164	−	6.81719i	0.140023	−	0.973884i
$50$	1.94944	+	0.572408i	0.275693	+	0.0809507i
$51$	−1.22415	+	0.359443i	−0.171415	+	0.0503320i
$52$	−1.37014	+	1.58123i	−0.190005	+	0.219277i
$53$	−7.04126	−	8.12605i	−0.967191	−	1.11620i	−0.993186	−	0.116536i	$-0.962821\pi$
$53$	−7.04126	−	8.12605i	−0.967191	−	1.11620i	0.0259949	−	0.999662i	$-0.491725\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	−1.23146	+	5.57982i	−0.166049	+	0.752382i
$56$	0.282425	−	0.181504i	0.0377406	−	0.0242544i
$57$	4.77272	+	1.40140i	0.632162	+	0.185620i
$58$	0.411329	+	0.474699i	0.0540101	+	0.0623310i
$59$	5.61779	−	3.61034i	0.731374	−	0.470026i	−0.121202	−	0.992628i	$-0.538675\pi$
$59$	5.61779	−	3.61034i	0.731374	−	0.470026i	0.852577	+	0.522602i	$0.175039\pi$
$60$	1.44936	−	0.931450i	0.187112	−	0.120250i
$61$	2.64105	−	1.69730i	0.338152	−	0.217317i	−0.360533	−	0.932746i	$-0.617405\pi$
$61$	2.64105	−	1.69730i	0.338152	−	0.217317i	0.698685	+	0.715429i	$0.253769\pi$
$62$	−5.48864	+	3.52733i	−0.697058	+	0.447972i
$63$	−0.219849	−	0.253720i	−0.0276984	−	0.0319657i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−3.03246	+	1.94884i	−0.376130	+	0.241724i
$66$	−1.97956	−	2.66108i	−0.243667	−	0.327556i
$67$	−1.98094	−	1.27308i	−0.242011	−	0.155531i	0.414013	−	0.910271i	$-0.364127\pi$
$67$	−1.98094	−	1.27308i	−0.242011	−	0.155531i	−0.656024	+	0.754740i	$0.727763\pi$
$68$	0.835491	+	0.964207i	0.101318	+	0.116927i
$69$	5.97110	−	6.89102i	0.718836	−	0.829581i
$70$	0.554969	−	0.162954i	0.0663315	−	0.0194767i
$71$	−11.5086	−	3.37924i	−1.36582	−	0.401042i	−0.485011	−	0.874508i	$-0.661185\pi$
$71$	−11.5086	−	3.37924i	−1.36582	−	0.401042i	−0.880812	+	0.473466i	$0.843003\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	4.36034	−	5.03210i	0.510339	−	0.588963i	−0.440846	−	0.897583i	$-0.645322\pi$
$73$	4.36034	−	5.03210i	0.510339	−	0.588963i	0.951185	+	0.308620i	$0.0998671\pi$
$74$	−8.50067	+	5.46305i	−0.988183	+	0.635066i
$75$	−1.94944	+	0.572408i	−0.225102	+	0.0660960i
$76$	−0.707904	−	4.92358i	−0.0812022	−	0.564773i
$77$	−0.385964	−	1.04442i	−0.0439846	−	0.119023i
$78$	0.297760	−	2.07097i	0.0337147	−	0.234491i
$79$	−0.329412	−	2.29111i	−0.0370618	−	0.257770i	0.962864	−	0.269988i	$-0.0870199\pi$
$79$	−0.329412	−	2.29111i	−0.0370618	−	0.257770i	−0.999925	+	0.0122180i	$0.996111\pi$
$80$	−1.44936	−	0.931450i	−0.162044	−	0.104139i
$81$	1.00000			0.111111
$82$	3.57114	+	7.81972i	0.394367	+	0.863543i
$83$	11.3139	+	13.0570i	1.24186	+	1.43319i	0.861038	+	0.508541i	$0.169815\pi$
$83$	11.3139	+	13.0570i	1.24186	+	1.43319i	0.380826	+	0.924647i	$0.375640\pi$
$84$	−0.139463	+	0.305381i	−0.0152166	+	0.0333198i
$85$	0.913115	+	1.99944i	0.0990412	+	0.216870i
$86$	−2.33363	+	2.69316i	−0.251642	+	0.290411i
$87$	−0.602673	−	0.176961i	−0.0646133	−	0.0189722i
$88$	−1.59826	+	2.90612i	−0.170375	+	0.309794i
$89$	14.5089	−	4.26019i	1.53794	−	0.451580i	0.600470	−	0.799647i	$-0.294980\pi$
$89$	14.5089	−	4.26019i	1.53794	−	0.451580i	0.937469	+	0.348068i	$0.113162\pi$
$90$	−0.715703	+	1.56717i	−0.0754417	+	0.165194i
$91$	0.291793	−	0.638938i	0.0305883	−	0.0669789i
$92$	−8.74878	−	2.56887i	−0.912123	−	0.267823i
$93$	2.71032	−	5.93476i	0.281047	−	0.615406i
$94$	11.7137			1.20817
$95$	1.21962	−	8.48265i	0.125131	−	0.870302i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	−1.27952	+	8.89926i	−0.129916	+	0.903583i	0.815741	+	0.578417i	$0.196329\pi$
$97$	−1.27952	+	8.89926i	−0.129916	+	0.903583i	−0.945657	+	0.325166i	$0.894580\pi$
$98$	4.51022	−	5.20507i	0.455601	−	0.525791i
$99$	3.10400	+	1.16841i	0.311964	+	0.117430i
$100$	1.33051	+	1.53549i	0.133051	+	0.153549i
$101$	−1.04261	+	0.670044i	−0.103743	+	0.0666719i	−0.591484	−	0.806317i	$-0.701458\pi$
$101$	−1.04261	+	0.670044i	−0.103743	+	0.0666719i	0.487740	+	0.872989i	$0.337821\pi$
$102$	−1.22415	−	0.359443i	−0.121209	−	0.0355901i
$103$	0.324536	+	0.208567i	0.0319775	+	0.0205507i	0.556532	−	0.830826i	$-0.312132\pi$
$103$	0.324536	+	0.208567i	0.0319775	+	0.0205507i	−0.524554	+	0.851377i	$0.675768\pi$
$104$	−2.00751	+	0.589459i	−0.196853	+	0.0578012i
$105$	−0.378770	+	0.437124i	−0.0369642	+	0.0426590i
$106$	−1.53021	−	10.6429i	−0.148627	−	1.03373i
$107$	−2.85610	−	19.8646i	−0.276110	−	1.92039i	−0.378420	−	0.925634i	$-0.623532\pi$
$107$	−2.85610	−	19.8646i	−0.276110	−	1.92039i	0.102310	−	0.994753i	$-0.467377\pi$
$108$	−0.415415	−	0.909632i	−0.0399733	−	0.0875294i
$109$	4.47452	+	9.79783i	0.428581	+	0.938462i	0.993555	+	0.113353i	$0.0361590\pi$
$109$	4.47452	+	9.79783i	0.428581	+	0.938462i	−0.564974	+	0.825109i	$0.691114\pi$
$110$	−4.05264	+	4.02826i	−0.386404	+	0.384080i
$111$	4.19767	−	9.19162i	0.398425	−	0.872430i
$112$	0.335719			0.0317225
$113$	0.231801	−	1.61221i	0.0218060	−	0.151664i	−0.976009	−	0.217729i	$-0.930135\pi$
$113$	0.231801	−	1.61221i	0.0218060	−	0.151664i	0.997815	+	0.0660645i	$0.0210443\pi$
$114$	3.25742	+	3.75926i	0.305085	+	0.352087i
$115$	−13.2155	−	8.49308i	−1.23235	−	0.791984i
$116$	0.0893903	+	0.621723i	0.00829968	+	0.0577255i
$117$	0.869158	+	1.90319i	0.0803537	+	0.175950i
$118$	6.67788			0.614749
$119$	−0.360326	−	0.231568i	−0.0330311	−	0.0212278i
$120$	1.72286			0.157275
$121$	8.26963	+	7.25349i	0.751785	+	0.659409i
$122$	3.13942			0.284230
$123$	−7.23190	−	4.64766i	−0.652078	−	0.419065i
$124$	−6.52436			−0.585904
$125$	5.03264	+	11.0199i	0.450133	+	0.985654i
$126$	−0.0477778	−	0.332302i	−0.00425639	−	0.0296038i
$127$	−6.23955	−	4.00991i	−0.553670	−	0.355822i	0.233694	−	0.972310i	$-0.424919\pi$
$127$	−6.23955	−	4.00991i	−0.553670	−	0.355822i	−0.787364	+	0.616488i	$0.788555\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	0.507147	−	3.52729i	0.0446518	−	0.310560i
$130$	−3.60469			−0.316152
$131$	4.30222	−	9.42056i	0.375887	−	0.823078i	−0.623269	−	0.782007i	$-0.714196\pi$
$131$	4.30222	−	9.42056i	0.375887	−	0.823078i	0.999156	−	0.0410705i	$-0.0130768\pi$
$132$	−0.226624	−	3.30887i	−0.0197251	−	0.288000i
$133$	0.693718	+	1.51903i	0.0601530	+	0.131717i
$134$	−0.978200	−	2.14196i	−0.0845036	−	0.185037i
$135$	−0.245189	−	1.70533i	−0.0211025	−	0.146771i
$136$	0.181569	+	1.26284i	0.0155695	+	0.108288i
$137$	7.55905	−	8.72361i	0.645813	−	0.745308i	−0.334578	−	0.942368i	$-0.608594\pi$
$137$	7.55905	−	8.72361i	0.645813	−	0.745308i	0.980392	+	0.197060i	$0.0631393\pi$
$138$	8.74878	−	2.56887i	0.744745	−	0.218677i
$139$	−10.7541	−	6.91126i	−0.912153	−	0.586205i	−0.00178234	−	0.999998i	$-0.500567\pi$
$139$	−10.7541	−	6.91126i	−0.912153	−	0.586205i	−0.910371	+	0.413793i	$0.864204\pi$
$140$	0.554969	+	0.162954i	0.0469035	+	0.0137721i
$141$	−9.85415	+	6.33288i	−0.829869	+	0.533325i
$142$	−7.85472	−	9.06483i	−0.659154	−	0.760704i
$143$	0.474158	+	6.92304i	0.0396511	+	0.578934i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.154007	+	1.07114i	−0.0127896	+	0.0889536i
$146$	6.38871	−	1.87589i	0.528733	−	0.155250i
$147$	−0.980164	+	6.81719i	−0.0808426	+	0.562272i
$148$	−10.1048			−0.830607
$149$	9.66898	−	21.1721i	0.792114	−	1.73449i	0.121614	−	0.992577i	$-0.461193\pi$
$149$	9.66898	−	21.1721i	0.792114	−	1.73449i	0.670500	−	0.741910i	$-0.266080\pi$
$150$	−1.94944	−	0.572408i	−0.159171	−	0.0467369i
$151$	5.06092	−	11.0819i	0.411852	−	0.901829i	−0.584078	−	0.811697i	$-0.698544\pi$
$151$	5.06092	−	11.0819i	0.411852	−	0.901829i	0.995930	−	0.0901318i	$-0.0287288\pi$
$152$	2.06636	−	4.52470i	0.167604	−	0.367002i
$153$	1.22415	−	0.359443i	0.0989666	−	0.0290592i
$154$	0.239963	−	1.08729i	0.0193368	−	0.0876163i
$155$	−10.7852	−	3.16683i	−0.866292	−	0.254366i
$156$	1.37014	−	1.58123i	0.109699	−	0.126600i
$157$	3.12189	+	6.83600i	0.249154	+	0.545572i	0.992343	−	0.123510i	$-0.0394150\pi$
$157$	3.12189	+	6.83600i	0.249154	+	0.545572i	−0.743189	+	0.669081i	$0.766688\pi$
$158$	0.961550	−	2.10550i	0.0764968	−	0.167505i
$159$	7.04126	+	8.12605i	0.558408	+	0.644437i
$160$	−0.715703	−	1.56717i	−0.0565813	−	0.123896i
$161$	3.06113			0.241251
$162$	0.841254	+	0.540641i	0.0660951	+	0.0424768i
$163$	−1.12694	−	7.83801i	−0.0882685	−	0.613921i	−0.985156	−	0.171662i	$-0.945086\pi$
$163$	−1.12694	−	7.83801i	−0.0882685	−	0.613921i	0.896887	−	0.442259i	$-0.145823\pi$
$164$	−1.22342	+	8.50907i	−0.0955330	+	0.664447i
$165$	1.23146	−	5.57982i	0.0958687	−	0.434388i
$166$	2.45875	+	17.1010i	0.190836	+	1.32729i
$167$	6.23274	−	1.83010i	0.482304	−	0.141617i	−0.0315371	−	0.999503i	$-0.510040\pi$
$167$	6.23274	−	1.83010i	0.482304	−	0.141617i	0.513841	+	0.857885i	$0.328222\pi$
$168$	−0.282425	+	0.181504i	−0.0217896	+	0.0140033i
$169$	5.64649	−	6.51639i	0.434345	−	0.501261i
$170$	−0.312819	+	2.17571i	−0.0239921	+	0.166869i
$171$	−4.77272	−	1.40140i	−0.364979	−	0.107168i
$172$	−3.41921	+	1.00397i	−0.260712	+	0.0765520i
$173$	7.69745	−	8.88333i	0.585226	−	0.675387i	−0.383494	−	0.923543i	$-0.625279\pi$
$173$	7.69745	−	8.88333i	0.585226	−	0.675387i	0.968720	+	0.248156i	$0.0798247\pi$
$174$	−0.411329	−	0.474699i	−0.0311827	−	0.0359868i
$175$	−0.573815	−	0.368769i	−0.0433764	−	0.0278763i
$176$	−2.91571	+	1.58070i	−0.219780	+	0.119150i
$177$	−5.61779	+	3.61034i	−0.422259	+	0.271369i
$178$	14.5089	+	4.26019i	1.08749	+	0.319315i
$179$	−8.13657	−	9.39011i	−0.608156	−	0.701850i	0.365257	−	0.930907i	$-0.380981\pi$
$179$	−8.13657	−	9.39011i	−0.608156	−	0.701850i	−0.973413	+	0.229057i	$0.926436\pi$
$180$	−1.44936	+	0.931450i	−0.108029	+	0.0694262i
$181$	−2.59373	+	1.66689i	−0.192791	+	0.123899i	−0.633475	−	0.773763i	$-0.718372\pi$
$181$	−2.59373	+	1.66689i	−0.192791	+	0.123899i	0.440685	+	0.897662i	$0.354736\pi$
$182$	0.590908	−	0.379754i	0.0438010	−	0.0281492i
$183$	−2.64105	+	1.69730i	−0.195232	+	0.125468i
$184$	−5.97110	−	6.89102i	−0.440195	−	0.508013i
$185$	−16.7039	−	4.90472i	−1.22810	−	0.360602i
$186$	5.48864	−	3.52733i	0.402446	−	0.258637i
$187$	4.21974	+	0.314599i	0.308578	+	0.0230058i
$188$	9.85415	+	6.33288i	0.718688	+	0.461873i
$189$	0.219849	+	0.253720i	0.0159917	+	0.0184554i
$190$	5.61208	−	6.47669i	0.407143	−	0.469868i
$191$	4.91370	−	1.44279i	0.355543	−	0.104397i	−0.0990832	−	0.995079i	$-0.531591\pi$
$191$	4.91370	−	1.44279i	0.355543	−	0.104397i	0.454626	+	0.890682i	$0.349773\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	−2.24759	+	15.6323i	−0.161785	+	1.12524i	0.733482	+	0.679709i	$0.237894\pi$
$193$	−2.24759	+	15.6323i	−0.161785	+	1.12524i	−0.895267	+	0.445530i	$0.853015\pi$
$194$	−5.88771	+	6.79478i	−0.422713	+	0.487836i
$195$	3.03246	−	1.94884i	0.217159	−	0.139559i
$196$	6.60831	−	1.94037i	0.472022	−	0.138598i
$197$	0.0207275	+	0.144163i	0.00147677	+	0.0102712i	0.990547	−	0.137177i	$-0.0438030\pi$
$197$	0.0207275	+	0.144163i	0.00147677	+	0.0102712i	−0.989070	+	0.147449i	$0.952894\pi$
$198$	1.97956	+	2.66108i	0.140681	+	0.189115i
$199$	1.34389	−	9.34697i	0.0952659	−	0.662589i	−0.885100	−	0.465401i	$-0.845910\pi$
$199$	1.34389	−	9.34697i	0.0952659	−	0.662589i	0.980366	−	0.197188i	$-0.0631809\pi$
$200$	0.289147	+	2.01106i	0.0204458	+	0.142204i
$201$	1.98094	+	1.27308i	0.139725	+	0.0897958i
$202$	−1.23935			−0.0872005
$203$	−0.0875989	−	0.191815i	−0.00614824	−	0.0134628i
$204$	−0.835491	−	0.964207i	−0.0584960	−	0.0675080i
$205$	−6.15259	+	13.4723i	−0.429716	+	0.940946i
$206$	0.160257	+	0.350915i	0.0111657	+	0.0244494i
$207$	−5.97110	+	6.89102i	−0.415020	+	0.478959i
$208$	−2.00751	−	0.589459i	−0.139196	−	0.0408716i
$209$	−13.1771	−	9.92643i	−0.911480	−	0.686626i
$210$	−0.554969	+	0.162954i	−0.0382965	+	0.0112449i
$211$	−11.2017	+	24.5283i	−0.771156	+	1.68860i	−0.0470646	+	0.998892i	$0.514987\pi$
$211$	−11.2017	+	24.5283i	−0.771156	+	1.68860i	−0.724091	+	0.689704i	$0.757741\pi$
$212$	4.46667	−	9.78064i	0.306772	−	0.671737i
$213$	11.5086	+	3.37924i	0.788559	+	0.231542i
$214$	8.33693	−	18.2553i	0.569900	−	1.24791i
$215$	−6.13952			−0.418712
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	2.10163	−	0.617094i	0.142668	−	0.0418910i
$218$	−1.53290	+	10.6616i	−0.103821	+	0.722092i
$219$	−4.36034	+	5.03210i	−0.294644	+	0.340038i
$220$	−5.58714	+	1.19777i	−0.376685	+	0.0807535i
$221$	1.74807	+	2.01738i	0.117588	+	0.135704i
$222$	8.50067	−	5.46305i	0.570528	−	0.366656i
$223$	2.79241	+	0.819927i	0.186994	+	0.0549064i	0.373889	−	0.927474i	$-0.378024\pi$
$223$	2.79241	+	0.819927i	0.186994	+	0.0549064i	−0.186895	+	0.982380i	$0.559842\pi$
$224$	0.282425	+	0.181504i	0.0188703	+	0.0121272i
$225$	1.94944	−	0.572408i	0.129963	−	0.0381605i
$226$	1.06663	−	1.23096i	0.0709513	−	0.0818821i
$227$	3.21706	+	22.3752i	0.213524	+	1.48509i	0.761264	+	0.648442i	$0.224579\pi$
$227$	3.21706	+	22.3752i	0.213524	+	1.48509i	−0.547740	+	0.836649i	$0.684512\pi$
$228$	0.707904	+	4.92358i	0.0468821	+	0.326072i
$229$	3.59128	+	7.86381i	0.237319	+	0.519655i	0.990393	−	0.138280i	$-0.0441574\pi$
$229$	3.59128	+	7.86381i	0.237319	+	0.519655i	−0.753075	+	0.657935i	$0.771430\pi$
$230$	−6.52587	−	14.2897i	−0.430303	−	0.942233i
$231$	0.385964	+	1.04442i	0.0253945	+	0.0687178i
$232$	−0.260929	+	0.571355i	−0.0171308	+	0.0375113i
$233$	23.6558			1.54974			0.774870	−	0.632120i	$-0.217815\pi$
$233$	23.6558			1.54974			0.774870	+	0.632120i	$0.217815\pi$
$234$	−0.297760	+	2.07097i	−0.0194652	+	0.135383i
$235$	13.2158	+	15.2518i	0.862101	+	0.994918i
$236$	5.61779	+	3.61034i	0.365687	+	0.235013i
$237$	0.329412	+	2.29111i	0.0213976	+	0.148824i
$238$	−0.177931	−	0.389614i	−0.0115335	−	0.0252549i
$239$	1.88865			0.122167			0.0610833	−	0.998133i	$-0.480544\pi$
$239$	1.88865			0.122167			0.0610833	+	0.998133i	$0.480544\pi$
$240$	1.44936	+	0.931450i	0.0935561	+	0.0601248i
$241$	13.0906			0.843238			0.421619	−	0.906773i	$-0.361462\pi$
$241$	13.0906			0.843238			0.421619	+	0.906773i	$0.361462\pi$
$242$	3.03532	+	10.5729i	0.195118	+	0.679654i
$243$	−1.00000			−0.0641500
$244$	2.64105	+	1.69730i	0.169076	+	0.108658i
$245$	11.8659			0.758082
$246$	−3.57114	−	7.81972i	−0.227688	−	0.498567i
$247$	−1.48112	−	10.3014i	−0.0942416	−	0.655465i
$248$	−5.48864	−	3.52733i	−0.348529	−	0.223986i
$249$	−11.3139	−	13.0570i	−0.716991	−	0.827451i
$250$	−1.72411	+	11.9914i	−0.109042	+	0.758404i
$251$	−7.96650			−0.502841			−0.251421	−	0.967878i	$-0.580898\pi$
$251$	−7.96650			−0.502841			−0.251421	+	0.967878i	$0.580898\pi$
$252$	0.139463	−	0.305381i	0.00878533	−	0.0192372i
$253$	−26.5858	+	14.4130i	−1.67144	+	0.906139i
$254$	−3.08112	−	6.74671i	−0.193327	−	0.423326i
$255$	−0.913115	−	1.99944i	−0.0571815	−	0.125210i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	0.678566	+	4.71953i	0.0423278	+	0.294396i	0.999979	+	0.00646569i	$0.00205811\pi$
$257$	0.678566	+	4.71953i	0.0423278	+	0.294396i	−0.957651	+	0.287930i	$0.907033\pi$
$258$	2.33363	−	2.69316i	0.145286	−	0.167669i
$259$	3.25495	−	0.955740i	0.202253	−	0.0593868i
$260$	−3.03246	−	1.94884i	−0.188065	−	0.120862i
$261$	0.602673	+	0.176961i	0.0373045	+	0.0109536i
$262$	8.71240	−	5.59912i	0.538254	−	0.345915i
$263$	10.2263	+	11.8018i	0.630584	+	0.727732i	0.977681	−	0.210097i	$-0.0673779\pi$
$263$	10.2263	+	11.8018i	0.630584	+	0.727732i	−0.347097	+	0.937829i	$0.612832\pi$
$264$	1.59826	−	2.90612i	0.0983663	−	0.178860i
$265$	12.1311	−	14.0001i	0.745209	−	0.860017i
$266$	−0.237657	+	1.65294i	−0.0145717	+	0.101348i
$267$	−14.5089	+	4.26019i	−0.887930	+	0.260720i
$268$	0.335116	−	2.33078i	0.0204705	−	0.142375i
$269$	−7.53229			−0.459252			−0.229626	−	0.973279i	$-0.573750\pi$
$269$	−7.53229			−0.459252			−0.229626	+	0.973279i	$0.573750\pi$
$270$	0.715703	−	1.56717i	0.0435563	−	0.0953750i
$271$	−27.6670	−	8.12376i	−1.68065	−	0.493483i	−0.704341	−	0.709862i	$-0.748757\pi$
$271$	−27.6670	−	8.12376i	−1.68065	−	0.493483i	−0.976310	+	0.216379i	$0.930575\pi$
$272$	−0.529999	+	1.16054i	−0.0321359	+	0.0703678i
$273$	−0.291793	+	0.638938i	−0.0176601	+	0.0386703i
$274$	11.0754	−	3.25204i	0.669091	−	0.196463i
$275$	6.71988	+	0.500995i	0.405224	+	0.0302112i
$276$	8.74878	+	2.56887i	0.526614	+	0.154628i
$277$	−14.1644	+	16.3466i	−0.851054	+	0.982169i	−0.999978	−	0.00667964i	$-0.997874\pi$
$277$	−14.1644	+	16.3466i	−0.851054	+	0.982169i	0.148923	+	0.988849i	$0.452419\pi$
$278$	−5.31044	−	11.6282i	−0.318499	−	0.697416i
$279$	−2.71032	+	5.93476i	−0.162262	+	0.355305i
$280$	0.378770	+	0.437124i	0.0226359	+	0.0261232i
$281$	4.33189	+	9.48551i	0.258419	+	0.565858i	0.993722	−	0.111881i	$-0.0356874\pi$
$281$	4.33189	+	9.48551i	0.258419	+	0.565858i	−0.735303	+	0.677739i	$0.762960\pi$
$282$	−11.7137			−0.697538
$283$	20.4618	+	13.1500i	1.21633	+	0.781685i	0.981706	−	0.190402i	$-0.0609792\pi$
$283$	20.4618	+	13.1500i	1.21633	+	0.781685i	0.234620	+	0.972087i	$0.424616\pi$
$284$	−1.70699	−	11.8724i	−0.101291	−	0.704498i
$285$	−1.21962	+	8.48265i	−0.0722442	+	0.502469i
$286$	−3.34399	+	6.08038i	−0.197734	+	0.359541i
$287$	−0.410726	−	2.85666i	−0.0242444	−	0.168623i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	−12.9320	+	8.31087i	−0.760704	+	0.488875i
$290$	−0.708663	+	0.817841i	−0.0416141	+	0.0480253i
$291$	1.27952	−	8.89926i	0.0750068	−	0.521684i
$292$	6.38871	+	1.87589i	0.373871	+	0.109778i
$293$	−9.64986	+	2.83346i	−0.563751	+	0.165532i	−0.551176	−	0.834389i	$-0.685821\pi$
$293$	−9.64986	+	2.83346i	−0.563751	+	0.165532i	−0.0125746	+	0.999921i	$0.504003\pi$
$294$	−4.51022	+	5.20507i	−0.263041	+	0.303566i
$295$	7.53422	+	8.69496i	0.438659	+	0.506240i
$296$	−8.50067	−	5.46305i	−0.494091	−	0.317533i
$297$	−3.10400	−	1.16841i	−0.180112	−	0.0677981i
$298$	19.5806	−	12.5837i	1.13427	−	0.728953i
$299$	−18.3048	−	5.37476i	−1.05859	−	0.310831i
$300$	−1.33051	−	1.53549i	−0.0768170	−	0.0886515i
$301$	1.00644	−	0.646799i	0.0580101	−	0.0372808i
$302$	10.2488	−	6.58652i	0.589753	−	0.379011i
$303$	1.04261	−	0.670044i	0.0598963	−	0.0384930i
$304$	4.18457	−	2.68926i	0.240002	−	0.154240i
$305$	3.54201	+	4.08769i	0.202815	+	0.234061i
$306$	1.22415	+	0.359443i	0.0699800	+	0.0205480i
$307$	−0.170083	+	0.109306i	−0.00970718	+	0.00623842i	−0.545485	−	0.838120i	$-0.683655\pi$
$307$	−0.170083	+	0.109306i	−0.00970718	+	0.00623842i	0.535778	+	0.844359i	$0.320018\pi$
$308$	0.789703	−	0.784953i	0.0449975	−	0.0447268i
$309$	−0.324536	−	0.208567i	−0.0184622	−	0.0118649i
$310$	−7.36101	−	8.49506i	−0.418077	−	0.482487i
$311$	19.8582	−	22.9176i	1.12605	−	1.29954i	0.177075	−	0.984197i	$-0.443336\pi$
$311$	19.8582	−	22.9176i	1.12605	−	1.29954i	0.948979	−	0.315339i	$-0.102118\pi$
$312$	2.00751	−	0.589459i	0.113653	−	0.0333716i
$313$	−25.7518	−	7.56141i	−1.45558	−	0.427396i	−0.544196	−	0.838958i	$-0.683165\pi$
$313$	−25.7518	−	7.56141i	−1.45558	−	0.427396i	−0.911382	+	0.411562i	$0.864983\pi$
$314$	−1.06951	+	7.43863i	−0.0603561	+	0.419786i
$315$	0.378770	−	0.437124i	0.0213413	−	0.0246292i
$316$	1.94723	−	1.25141i	0.109540	−	0.0703972i
$317$	−27.8671	+	8.18251i	−1.56517	+	0.459575i	−0.945591	−	0.325359i	$-0.894515\pi$
$317$	−27.8671	+	8.18251i	−1.56517	+	0.459575i	−0.619579	+	0.784934i	$0.712697\pi$
$318$	1.53021	+	10.6429i	0.0858100	+	0.596822i
$319$	1.66393	+	1.25346i	0.0931624	+	0.0701801i
$320$	0.245189	−	1.70533i	0.0137065	−	0.0953307i
$321$	2.85610	+	19.8646i	0.159412	+	1.10874i
$322$	2.57519	+	1.65497i	0.143510	+	0.0922280i
$323$	−6.34624			−0.353114
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	2.78378	+	3.21265i	0.154416	+	0.178206i
$326$	3.28951	−	7.20302i	0.182189	−	0.398939i
$327$	−4.47452	−	9.79783i	−0.247441	−	0.541821i
$328$	−5.62956	+	6.49685i	−0.310840	+	0.358729i
$329$	−3.77321	−	1.10791i	−0.208024	−	0.0610812i
$330$	4.05264	−	4.02826i	0.223091	−	0.221749i
$331$	8.51186	−	2.49931i	0.467854	−	0.137374i	−0.0393041	−	0.999227i	$-0.512514\pi$
$331$	8.51186	−	2.49931i	0.467854	−	0.137374i	0.507158	+	0.861853i	$0.330696\pi$
$332$	−7.17706	+	15.7156i	−0.393892	+	0.862503i
$333$	−4.19767	+	9.19162i	−0.230031	+	0.503698i
$334$	6.23274	+	1.83010i	0.341040	+	0.100139i
$335$	1.68530	−	3.69030i	0.0920780	−	0.201623i
$336$	−0.335719			−0.0183150
$337$	4.51437	−	31.3982i	0.245914	−	1.71037i	−0.375449	−	0.926843i	$-0.622511\pi$
$337$	4.51437	−	31.3982i	0.245914	−	1.71037i	0.621362	−	0.783523i	$-0.286580\pi$
$338$	8.27316	−	2.42922i	0.450000	−	0.132132i
$339$	−0.231801	+	1.61221i	−0.0125897	+	0.0875634i
$340$	−1.43944	+	1.66120i	−0.0780644	+	0.0900911i
$341$	−15.3471	+	15.2547i	−0.831090	+	0.826091i
$342$	−3.25742	−	3.75926i	−0.176141	−	0.203277i
$343$	−3.92212	+	2.52059i	−0.211775	+	0.136099i
$344$	−3.41921	−	1.00397i	−0.184351	−	0.0541304i
$345$	13.2155	+	8.49308i	0.711498	+	0.457252i
$346$	11.2782	−	3.31158i	0.606320	−	0.178031i
$347$	−16.6849	+	19.2554i	−0.895692	+	1.03368i	0.103545	+	0.994625i	$0.466981\pi$
$347$	−16.6849	+	19.2554i	−0.895692	+	1.03368i	−0.999237	+	0.0390587i	$0.987564\pi$
$348$	−0.0893903	−	0.621723i	−0.00479182	−	0.0333278i
$349$	−1.42953	−	9.94261i	−0.0765211	−	0.532216i	−0.991640	−	0.129033i	$-0.958813\pi$
$349$	−1.42953	−	9.94261i	−0.0765211	−	0.532216i	0.915119	−	0.403183i	$-0.132096\pi$
$350$	−0.283353	−	0.620456i	−0.0151458	−	0.0331648i
$351$	−0.869158	−	1.90319i	−0.0463922	−	0.101585i
$352$	−3.30745	−	0.246584i	−0.176287	−	0.0131430i
$353$	−9.47976	+	20.7578i	−0.504557	+	1.10483i	0.470404	+	0.882451i	$0.344108\pi$
$353$	−9.47976	+	20.7578i	−0.504557	+	1.10483i	−0.974961	+	0.222375i	$0.928619\pi$
$354$	−6.67788			−0.354925
$355$	2.94092	−	20.4545i	0.156088	−	1.08561i
$356$	9.90242	+	11.4280i	0.524827	+	0.605683i
$357$	0.360326	+	0.231568i	0.0190705	+	0.0122559i
$358$	−1.76825	−	12.2984i	−0.0934547	−	0.649992i
$359$	−5.42603	−	11.8813i	−0.286375	−	0.627073i	0.710701	−	0.703494i	$-0.248378\pi$
$359$	−5.42603	−	11.8813i	−0.286375	−	0.627073i	−0.997076	+	0.0764210i	$0.975651\pi$
$360$	−1.72286			−0.0908029
$361$	4.83113	+	3.10478i	0.254270	+	0.163409i
$362$	−3.08318			−0.162048
$363$	−8.26963	−	7.25349i	−0.434043	−	0.380710i
$364$	0.702414			0.0368165
$365$	9.65048	+	6.20199i	0.505129	+	0.324627i
$366$	−3.13942			−0.164100
$367$	−10.8898	−	23.8453i	−0.568443	−	1.24472i	−0.947622	−	0.319393i	$-0.896521\pi$
$367$	−10.8898	−	23.8453i	−0.568443	−	1.24472i	0.379180	−	0.925323i	$-0.376206\pi$
$368$	−1.29764	−	9.02532i	−0.0676444	−	0.470477i
$369$	7.23190	+	4.64766i	0.376477	+	0.241947i
$370$	−11.4006	−	13.1569i	−0.592686	−	0.683997i
$371$	−0.513722	+	3.57301i	−0.0266711	+	0.185502i
$372$	6.52436			0.338272
$373$	4.15679	−	9.10210i	0.215230	−	0.471289i	−0.770964	−	0.636878i	$-0.780225\pi$
$373$	4.15679	−	9.10210i	0.215230	−	0.471289i	0.986195	+	0.165589i	$0.0529526\pi$
$374$	3.37978	+	2.54602i	0.174764	+	0.131652i
$375$	−5.03264	−	11.0199i	−0.259884	−	0.569068i
$376$	4.86603	+	10.6551i	0.250946	+	0.549496i
$377$	0.187028	+	1.30081i	0.00963244	+	0.0669951i
$378$	0.0477778	+	0.332302i	0.00245743	+	0.0170918i
$379$	7.62300	−	8.79741i	0.391567	−	0.451893i	−0.525400	−	0.850855i	$-0.676084\pi$
$379$	7.62300	−	8.79741i	0.391567	−	0.451893i	0.916967	+	0.398963i	$0.130630\pi$
$380$	8.22274	−	2.41442i	0.421818	−	0.123857i
$381$	6.23955	+	4.00991i	0.319662	+	0.205434i
$382$	4.91370	+	1.44279i	0.251407	+	0.0738198i
$383$	−6.18074	+	3.97212i	−0.315821	+	0.202966i	−0.688941	−	0.724817i	$-0.741924\pi$
$383$	−6.18074	+	3.97212i	−0.315821	+	0.202966i	0.373120	+	0.927783i	$0.378288\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	1.68644	−	0.914275i	0.0859492	−	0.0465958i
$386$	−10.3423	+	11.9356i	−0.526407	+	0.607506i
$387$	−0.507147	+	3.52729i	−0.0257797	+	0.179302i
$388$	−8.62659	+	2.53299i	−0.437949	+	0.128593i
$389$	0.634634	−	4.41397i	0.0321772	−	0.223797i	−0.967387	−	0.253301i	$-0.918484\pi$
$389$	0.634634	−	4.41397i	0.0321772	−	0.223797i	0.999565	+	0.0295038i	$0.00939272\pi$
$390$	3.60469			0.182530
$391$	−4.83259	+	10.5819i	−0.244395	+	0.535150i
$392$	6.60831	+	1.94037i	0.333770	+	0.0980037i
$393$	−4.30222	+	9.42056i	−0.217019	+	0.475204i
$394$	−0.0605033	+	0.132484i	−0.00304811	+	0.00667443i
$395$	3.82633	−	1.12351i	0.192524	−	0.0565300i
$396$	0.226624	+	3.30887i	0.0113883	+	0.166277i
$397$	12.0465	+	3.53717i	0.604597	+	0.177526i	0.569683	−	0.821865i	$-0.307066\pi$
$397$	12.0465	+	3.53717i	0.604597	+	0.177526i	0.0349140	+	0.999390i	$0.488884\pi$
$398$	6.18391	−	7.13661i	0.309971	−	0.357726i
$399$	−0.693718	−	1.51903i	−0.0347293	−	0.0760466i
$400$	−0.844017	+	1.84814i	−0.0422008	+	0.0924069i
$401$	−25.1627	−	29.0393i	−1.25657	−	1.45016i	−0.841402	−	0.540410i	$-0.818269\pi$
$401$	−25.1627	−	29.0393i	−1.25657	−	1.45016i	−0.415165	−	0.909746i	$-0.636276\pi$
$402$	0.978200	+	2.14196i	0.0487882	+	0.106831i
$403$	−13.6507			−0.679989
$404$	−1.04261	−	0.670044i	−0.0518717	−	0.0333359i
$405$	0.245189	+	1.70533i	0.0121835	+	0.0847384i
$406$	0.0300100	−	0.208724i	0.00148937	−	0.0103588i
$407$	−23.7692	+	23.6262i	−1.17819	+	1.17111i
$408$	−0.181569	−	1.26284i	−0.00898903	−	0.0625201i
$409$	4.05319	−	1.19012i	0.200417	−	0.0588478i	−0.179983	−	0.983670i	$-0.557604\pi$
$409$	4.05319	−	1.19012i	0.200417	−	0.0588478i	0.380400	+	0.924822i	$0.375786\pi$
$410$	−12.4596	+	8.00728i	−0.615334	+	0.395451i
$411$	−7.55905	+	8.72361i	−0.372861	+	0.430304i
$412$	−0.0549018	+	0.381850i	−0.00270482	+	0.0188124i
$413$	−2.15108	−	0.631615i	−0.105848	−	0.0310797i
$414$	−8.74878	+	2.56887i	−0.429979	+	0.126253i
$415$	−19.4923	+	22.4954i	−0.956841	+	1.10425i
$416$	−1.37014	−	1.58123i	−0.0671768	−	0.0775261i
$417$	10.7541	+	6.91126i	0.526632	+	0.338446i
$418$	−5.71866	−	15.4747i	−0.279709	−	0.756894i
$419$	25.7144	−	16.5256i	1.25623	−	0.807329i	0.268465	−	0.963289i	$-0.413483\pi$
$419$	25.7144	−	16.5256i	1.25623	−	0.807329i	0.987763	+	0.155960i	$0.0498471\pi$
$420$	−0.554969	−	0.162954i	−0.0270797	−	0.00795133i
$421$	8.01009	+	9.24413i	0.390388	+	0.450531i	0.916590	−	0.399828i	$-0.130930\pi$
$421$	8.01009	+	9.24413i	0.390388	+	0.450531i	−0.526203	+	0.850359i	$0.676385\pi$
$422$	−22.6844	+	14.5784i	−1.10426	+	0.709666i
$423$	9.85415	−	6.33288i	0.479125	−	0.307915i
$424$	9.04541	−	5.81313i	0.439284	−	0.282311i
$425$	2.18066	−	1.40143i	0.105778	−	0.0679791i
$426$	7.85472	+	9.06483i	0.380563	+	0.439193i
$427$	−1.01127	−	0.296936i	−0.0489389	−	0.0143697i
$428$	16.8830	−	10.8501i	0.816073	−	0.524458i
$429$	−0.474158	−	6.92304i	−0.0228926	−	0.334248i
$430$	−5.16489	−	3.31928i	−0.249073	−	0.160070i
$431$	18.1980	+	21.0016i	0.876566	+	1.01161i	0.999815	+	0.0192350i	$0.00612306\pi$
$431$	18.1980	+	21.0016i	0.876566	+	1.01161i	−0.123249	+	0.992376i	$0.539331\pi$
$432$	0.654861	−	0.755750i	0.0315070	−	0.0363610i
$433$	24.3594	−	7.15258i	1.17064	−	0.343731i	0.362082	−	0.932146i	$-0.382066\pi$
$433$	24.3594	−	7.15258i	1.17064	−	0.343731i	0.808559	+	0.588415i	$0.200248\pi$
$434$	2.10163	+	0.617094i	0.100881	+	0.0296214i
$435$	0.154007	−	1.07114i	0.00738408	−	0.0513574i
$436$	−7.05364	+	8.14033i	−0.337808	+	0.389851i
$437$	38.1555	−	24.5210i	1.82522	−	1.17300i
$438$	−6.38871	+	1.87589i	−0.305264	+	0.0896337i
$439$	−2.32197	−	16.1497i	−0.110822	−	0.770781i	−0.967124	−	0.254306i	$-0.918153\pi$
$439$	−2.32197	−	16.1497i	−0.110822	−	0.770781i	0.856302	−	0.516475i	$-0.172756\pi$
$440$	−5.34777	−	2.01301i	−0.254945	−	0.0959666i
$441$	0.980164	−	6.81719i	0.0466745	−	0.324628i
$442$	0.379891	+	2.64220i	0.0180696	+	0.125677i
$443$	4.24470	+	2.72790i	0.201672	+	0.129607i	0.637579	−	0.770385i	$-0.279936\pi$
$443$	4.24470	+	2.72790i	0.201672	+	0.129607i	−0.435907	+	0.899992i	$0.643572\pi$
$444$	10.1048			0.479551
$445$	10.8224	+	23.6978i	0.513033	+	1.12339i
$446$	1.90584	+	2.19946i	0.0902442	+	0.104147i
$447$	−9.66898	+	21.1721i	−0.457327	+	1.00141i
$448$	0.139463	+	0.305381i	0.00658900	+	0.0144279i
$449$	5.09545	−	5.88046i	0.240469	−	0.277516i	−0.622668	−	0.782486i	$-0.713951\pi$
$449$	5.09545	−	5.88046i	0.240469	−	0.277516i	0.863137	+	0.504970i	$0.168497\pi$
$450$	1.94944	+	0.572408i	0.0918976	+	0.0269836i
$451$	17.0174	+	22.8762i	0.801320	+	1.07720i
$452$	1.56281	−	0.458884i	0.0735086	−	0.0215841i
$453$	−5.06092	+	11.0819i	−0.237783	+	0.520671i
$454$	−9.39056	+	20.5625i	−0.440721	+	0.965044i
$455$	1.16114	+	0.340942i	0.0544352	+	0.0159836i
$456$	−2.06636	+	4.52470i	−0.0967663	+	0.211889i
$457$	3.71783			0.173913			0.0869563	−	0.996212i	$-0.472286\pi$
$457$	3.71783			0.173913			0.0869563	+	0.996212i	$0.472286\pi$
$458$	−1.23032	+	8.55705i	−0.0574890	+	0.399845i
$459$	−1.22415	+	0.359443i	−0.0571384	+	0.0167773i
$460$	2.23566	−	15.5494i	0.104238	−	0.724994i
$461$	−15.1646	+	17.5009i	−0.706286	+	0.815097i	−0.989587	−	0.143934i	$-0.954025\pi$
$461$	−15.1646	+	17.5009i	−0.706286	+	0.815097i	0.283302	+	0.959031i	$0.408570\pi$
$462$	−0.239963	+	1.08729i	−0.0111641	+	0.0505853i
$463$	−19.6922	−	22.7260i	−0.915173	−	1.05617i	−0.998221	−	0.0596203i	$-0.981011\pi$
$463$	−19.6922	−	22.7260i	−0.915173	−	1.05617i	0.0830482	−	0.996546i	$-0.473534\pi$
$464$	−0.528405	+	0.339585i	−0.0245306	+	0.0157648i
$465$	10.7852	+	3.16683i	0.500154	+	0.146858i
$466$	19.9005	+	12.7893i	0.921873	+	0.592452i
$467$	−23.1844	+	6.80756i	−1.07285	+	0.315016i	−0.770014	−	0.638027i	$-0.779751\pi$
$467$	−23.1844	+	6.80756i	−1.07285	+	0.315016i	−0.302833	+	0.953044i	$0.597933\pi$
$468$	−1.37014	+	1.58123i	−0.0633349	+	0.0730923i
$469$	0.112505	+	0.782490i	0.00519500	+	0.0361320i
$470$	2.87206	+	19.9756i	0.132478	+	0.921406i
$471$	−3.12189	−	6.83600i	−0.143849	−	0.314986i
$472$	2.77409	+	6.07442i	0.127688	+	0.279598i
$473$	−5.69550	+	10.3561i	−0.261880	+	0.476176i
$474$	−0.961550	+	2.10550i	−0.0441655	+	0.0967089i
$475$	−10.1063			−0.463710
$476$	0.0609564	−	0.423961i	0.00279393	−	0.0194322i
$477$	−7.04126	−	8.12605i	−0.322397	−	0.372066i
$478$	1.58883	+	1.02108i	0.0726715	+	0.0467031i
$479$	2.49967	+	17.3856i	0.114213	+	0.794368i	0.963744	+	0.266829i	$0.0859759\pi$
$479$	2.49967	+	17.3856i	0.114213	+	0.794368i	−0.849531	+	0.527539i	$0.823115\pi$
$480$	0.715703	+	1.56717i	0.0326672	+	0.0715313i
$481$	−21.1418			−0.963985
$482$	11.0125	+	7.07730i	0.501605	+	0.322362i
$483$	−3.06113			−0.139286
$484$	−3.16268	+	10.5355i	−0.143758	+	0.478888i
$485$	−15.4899			−0.703359
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−25.0954			−1.13718			−0.568590	−	0.822621i	$-0.692511\pi$
$487$	−25.0954			−1.13718			−0.568590	+	0.822621i	$0.692511\pi$
$488$	1.30416	+	2.85572i	0.0590367	+	0.129272i
$489$	1.12694	+	7.83801i	0.0509618	+	0.354447i
$490$	9.98220	+	6.41517i	0.450950	+	0.289808i
$491$	20.1066	+	23.2042i	0.907397	+	1.04719i	0.998680	+	0.0513670i	$0.0163578\pi$
$491$	20.1066	+	23.2042i	0.907397	+	1.04719i	−0.0912828	+	0.995825i	$0.529097\pi$
$492$	1.22342	−	8.50907i	0.0551560	−	0.383618i
$493$	0.801369			0.0360918
$494$	4.32338	−	9.46688i	0.194518	−	0.425935i
$495$	−1.23146	+	5.57982i	−0.0553498	+	0.250794i
$496$	−2.71032	−	5.93476i	−0.121697	−	0.266479i
$497$	1.67279	+	3.66289i	0.0750347	+	0.164303i
$498$	−2.45875	−	17.1010i	−0.110179	−	0.766313i
$499$	−2.46275	−	17.1288i	−0.110248	−	0.766790i	−0.967678	−	0.252189i	$-0.918849\pi$
$499$	−2.46275	−	17.1288i	−0.110248	−	0.766790i	0.857430	−	0.514600i	$-0.172060\pi$
$500$	−7.93346	+	9.15570i	−0.354795	+	0.409455i
$501$	−6.23274	+	1.83010i	−0.278458	+	0.0817628i
$502$	−6.70185	−	4.30702i	−0.299118	−	0.192232i
$503$	19.2978	+	5.66635i	0.860447	+	0.252650i	0.682048	−	0.731308i	$-0.261090\pi$
$503$	19.2978	+	5.66635i	0.860447	+	0.252650i	0.178400	+	0.983958i	$0.442908\pi$
$504$	0.282425	−	0.181504i	0.0125802	−	0.00808481i
$505$	−1.39828	−	1.61370i	−0.0622226	−	0.0718088i
$506$	−30.1577	−	2.24838i	−1.34067	−	0.0999529i
$507$	−5.64649	+	6.51639i	−0.250769	+	0.289403i
$508$	1.05554	−	7.34147i	0.0468322	−	0.325725i
$509$	4.11601	−	1.20857i	0.182439	−	0.0535689i	−0.189237	−	0.981931i	$-0.560601\pi$
$509$	4.11601	−	1.20857i	0.182439	−	0.0535689i	0.371676	+	0.928363i	$0.378783\pi$
$510$	0.312819	−	2.17571i	0.0138519	−	0.0963419i
$511$	−2.23536			−0.0988866
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	4.77272	+	1.40140i	0.210721	+	0.0618732i
$514$	−1.98072	+	4.33718i	−0.0873660	+	0.191305i
$515$	−0.276102	+	0.604578i	−0.0121665	+	0.0266409i
$516$	3.41921	−	1.00397i	0.150522	−	0.0441973i
$517$	37.9867	−	8.14356i	1.67065	−	0.358153i
$518$	3.25495	+	0.955740i	0.143014	+	0.0419928i
$519$	−7.69745	+	8.88333i	−0.337880	+	0.389935i
$520$	−1.49744	−	3.27894i	−0.0656671	−	0.143791i
$521$	4.73055	−	10.3585i	0.207249	−	0.453812i	−0.777252	−	0.629189i	$-0.783387\pi$
$521$	4.73055	−	10.3585i	0.207249	−	0.453812i	0.984501	+	0.175377i	$0.0561144\pi$
$522$	0.411329	+	0.474699i	0.0180034	+	0.0207770i
$523$	0.878481	+	1.92360i	0.0384133	+	0.0841134i	0.927866	−	0.372914i	$-0.121641\pi$
$523$	0.878481	+	1.92360i	0.0384133	+	0.0841134i	−0.889453	+	0.457027i	$0.848914\pi$
$524$	10.3564			0.452424
$525$	0.573815	+	0.368769i	0.0250434	+	0.0160944i
$526$	2.22240	+	15.4571i	0.0969012	+	0.673962i
$527$	−1.18462	+	8.23924i	−0.0516030	+	0.358907i
$528$	2.91571	−	1.58070i	0.126890	−	0.0687912i
$529$	−8.55884	−	59.5281i	−0.372124	−	2.58818i
$530$	17.7744	−	5.21902i	0.772069	−	0.226700i
$531$	5.61779	−	3.61034i	0.243791	−	0.156675i
$532$	−1.09358	+	1.26206i	−0.0474126	+	0.0547171i
$533$	−2.55972	+	17.8032i	−0.110874	+	0.771144i
$534$	−14.5089	−	4.26019i	−0.627861	−	0.184357i
$535$	33.1754	−	9.74118i	1.43430	−	0.421148i
$536$	1.54204	−	1.77960i	0.0666058	−	0.0768672i
$537$	8.13657	+	9.39011i	0.351119	+	0.405213i
$538$	−6.33657	−	4.07226i	−0.273189	−	0.175568i
$539$	11.0077	−	20.0153i	0.474136	−	0.862121i
$540$	1.44936	−	0.931450i	0.0623707	−	0.0400832i
$541$	−16.9500	−	4.97697i	−0.728737	−	0.213977i	−0.103741	−	0.994604i	$-0.533081\pi$
$541$	−16.9500	−	4.97697i	−0.728737	−	0.213977i	−0.624996	+	0.780628i	$0.714900\pi$
$542$	−18.8829	−	21.7921i	−0.811091	−	0.936049i
$543$	2.59373	−	1.66689i	0.111308	−	0.0715331i
$544$	−1.07330	+	0.689765i	−0.0460172	+	0.0295734i
$545$	−15.6114	+	10.0328i	−0.668719	+	0.429759i
$546$	−0.590908	+	0.379754i	−0.0252885	+	0.0162520i
$547$	9.88186	+	11.4043i	0.422518	+	0.487611i	0.926602	−	0.376043i	$-0.122715\pi$
$547$	9.88186	+	11.4043i	0.422518	+	0.487611i	−0.504085	+	0.863654i	$0.668170\pi$
$548$	11.0754	+	3.25204i	0.473118	+	0.138920i
$549$	2.64105	−	1.69730i	0.112717	−	0.0724390i
$550$	5.38226	+	4.05451i	0.229500	+	0.172885i
$551$	−2.62840	−	1.68917i	−0.111974	−	0.0719610i
$552$	5.97110	+	6.89102i	0.254147	+	0.293301i
$553$	−0.508880	+	0.587279i	−0.0216398	+	0.0249736i
$554$	−20.7534	+	6.09376i	−0.881729	+	0.258899i
$555$	16.7039	+	4.90472i	0.709042	+	0.208194i
$556$	1.81928	−	12.6533i	0.0771545	−	0.536621i
$557$	−4.53746	+	5.23651i	−0.192258	+	0.221878i	−0.843692	−	0.536828i	$-0.819623\pi$
$557$	−4.53746	+	5.23651i	−0.192258	+	0.221878i	0.651433	+	0.758706i	$0.274168\pi$
$558$	−5.48864	+	3.52733i	−0.232353	+	0.149324i
$559$	−7.15389	+	2.10057i	−0.302577	+	0.0888447i
$560$	0.0823147	+	0.572511i	0.00347843	+	0.0241930i
$561$	−4.21974	−	0.314599i	−0.178157	−	0.0132824i
$562$	−1.48404	+	10.3217i	−0.0626004	+	0.435395i
$563$	4.38059	+	30.4677i	0.184620	+	1.28406i	0.845665	+	0.533714i	$0.179204\pi$
$563$	4.38059	+	30.4677i	0.184620	+	1.28406i	−0.661045	+	0.750346i	$0.729887\pi$
$564$	−9.85415	−	6.33288i	−0.414935	−	0.266662i
$565$	2.80618			0.118057
$566$	10.1041	+	22.1249i	0.424708	+	0.929980i
$567$	−0.219849	−	0.253720i	−0.00923281	−	0.0106552i
$568$	4.98269	−	10.9106i	0.209069	−	0.457798i
$569$	7.83657	+	17.1597i	0.328526	+	0.719372i	0.999761	−	0.0218732i	$-0.00696301\pi$
$569$	7.83657	+	17.1597i	0.328526	+	0.719372i	−0.671235	+	0.741245i	$0.734236\pi$
$570$	−5.61208	+	6.47669i	−0.235064	+	0.271279i
$571$	19.3713	+	5.68794i	0.810665	+	0.238033i	0.660692	−	0.750657i	$-0.270263\pi$
$571$	19.3713	+	5.68794i	0.810665	+	0.238033i	0.149973	+	0.988690i	$0.452081\pi$
$572$	−6.10045	+	3.30724i	−0.255072	+	0.138283i
$573$	−4.91370	+	1.44279i	−0.205273	+	0.0602736i
$574$	1.19890	−	2.62523i	0.0500412	−	0.109575i
$575$	−7.69585	+	16.8516i	−0.320939	+	0.702759i
$576$	−0.959493	−	0.281733i	−0.0399789	−	0.0117389i
$577$	−4.96472	+	10.8712i	−0.206684	+	0.452575i	−0.984378	−	0.176068i	$-0.943662\pi$
$577$	−4.96472	+	10.8712i	−0.206684	+	0.452575i	0.777694	+	0.628643i	$0.216389\pi$
$578$	−15.3723			−0.639402
$579$	2.24759	−	15.6323i	0.0934065	−	0.649657i
$580$	−1.03832	+	0.304879i	−0.0431140	+	0.0126594i
$581$	0.825450	−	5.74113i	0.0342454	−	0.238182i
$582$	5.88771	−	6.79478i	0.244053	−	0.281653i
$583$	−12.3615	−	33.4503i	−0.511961	−	1.38537i
$584$	4.36034	+	5.03210i	0.180432	+	0.208230i
$585$	−3.03246	+	1.94884i	−0.125377	+	0.0805746i
$586$	−9.64986	−	2.83346i	−0.398632	−	0.117049i
$587$	12.3969	+	7.96701i	0.511675	+	0.328834i	0.770871	−	0.636991i	$-0.219821\pi$
$587$	12.3969	+	7.96701i	0.511675	+	0.328834i	−0.259196	+	0.965825i	$0.583458\pi$
$588$	−6.60831	+	1.94037i	−0.272522	+	0.0800197i
$589$	21.2525	−	24.5267i	0.875696	−	1.01061i
$590$	1.63734	+	11.3880i	0.0674084	+	0.468835i
$591$	−0.0207275	−	0.144163i	−0.000852615	−	0.00593007i
$592$	−4.19767	−	9.19162i	−0.172523	−	0.377773i
$593$	0.324856	+	0.711335i	0.0133402	+	0.0292110i	0.916185	−	0.400756i	$-0.131252\pi$
$593$	0.324856	+	0.711335i	0.0133402	+	0.0292110i	−0.902845	+	0.429967i	$0.858525\pi$
$594$	−1.97956	−	2.66108i	−0.0812223	−	0.109185i
$595$	0.306550	−	0.671252i	0.0125673	−	0.0275186i
$596$	23.2755			0.953401
$597$	−1.34389	+	9.34697i	−0.0550018	+	0.382546i
$598$	−12.4931	−	14.4178i	−0.510882	−	0.589589i
$599$	−14.3690	−	9.23437i	−0.587100	−	0.377306i	0.213108	−	0.977029i	$-0.431641\pi$
$599$	−14.3690	−	9.23437i	−0.587100	−	0.377306i	−0.800208	+	0.599722i	$0.795278\pi$
$600$	−0.289147	−	2.01106i	−0.0118044	−	0.0821013i
$601$	−1.04725	−	2.29316i	−0.0427183	−	0.0935399i	0.887070	−	0.461636i	$-0.152737\pi$
$601$	−1.04725	−	2.29316i	−0.0427183	−	0.0935399i	−0.929788	+	0.368096i	$0.880010\pi$
$602$	1.19636			0.0487598
$603$	−1.98094	−	1.27308i	−0.0806703	−	0.0518436i
$604$	12.1828			0.495711
$605$	−10.3420	+	15.8809i	−0.420460	+	0.645650i
$606$	1.23935			0.0503452
$607$	−26.3689	−	16.9463i	−1.07028	−	0.687828i	−0.117989	−	0.993015i	$-0.537645\pi$
$607$	−26.3689	−	16.9463i	−1.07028	−	0.687828i	−0.952293	+	0.305187i	$0.901281\pi$
$608$	4.97421			0.201731
$609$	0.0875989	+	0.191815i	0.00354969	+	0.00777273i
$610$	0.769752	+	5.35374i	0.0311663	+	0.216767i
$611$	20.6175	+	13.2501i	0.834095	+	0.536040i
$612$	0.835491	+	0.964207i	0.0337727	+	0.0389758i
$613$	4.84940	−	33.7283i	0.195865	−	1.36227i	−0.620259	−	0.784397i	$-0.712972\pi$
$613$	4.84940	−	33.7283i	0.195865	−	1.36227i	0.816124	−	0.577877i	$-0.196118\pi$
$614$	−0.202179			−0.00815926
$615$	6.15259	−	13.4723i	0.248096	−	0.543256i
$616$	1.08872	−	0.233399i	0.0438657	−	0.00940390i
$617$	−7.28606	−	15.9543i	−0.293326	−	0.642294i	0.704392	−	0.709811i	$-0.251220\pi$
$617$	−7.28606	−	15.9543i	−0.293326	−	0.642294i	−0.997718	+	0.0675169i	$0.978492\pi$
$618$	−0.160257	−	0.350915i	−0.00644650	−	0.0141159i
$619$	1.36325	+	9.48161i	0.0547936	+	0.381098i	0.998704	+	0.0508962i	$0.0162078\pi$
$619$	1.36325	+	9.48161i	0.0547936	+	0.381098i	−0.943910	+	0.330202i	$0.892883\pi$
$620$	−1.59970	−	11.1262i	−0.0642455	−	0.446837i
$621$	5.97110	−	6.89102i	0.239612	−	0.276527i
$622$	29.0959	−	8.54334i	1.16664	−	0.342557i
$623$	−4.27067	−	2.74459i	−0.171101	−	0.109960i
$624$	2.00751	+	0.589459i	0.0803649	+	0.0235973i
$625$	−9.01261	+	5.79205i	−0.360504	+	0.231682i
$626$	−17.5758	−	20.2835i	−0.702469	−	0.810693i
$627$	13.1771	+	9.92643i	0.526243	+	0.396424i
$628$	−4.92136	+	5.67955i	−0.196384	+	0.226639i
$629$	−1.83472	+	12.7607i	−0.0731549	+	0.508804i
$630$	0.554969	−	0.162954i	0.0221105	−	0.00649223i
$631$	−2.55718	+	17.7856i	−0.101800	+	0.708034i	0.873448	+	0.486918i	$0.161879\pi$
$631$	−2.55718	+	17.7856i	−0.101800	+	0.708034i	−0.975248	+	0.221116i	$0.929030\pi$
$632$	2.31467			0.0920728
$633$	11.2017	−	24.5283i	0.445227	−	0.974911i
$634$	−27.8671	−	8.18251i	−1.10674	−	0.324969i
$635$	5.30835	−	11.6237i	0.210655	−	0.461271i
$636$	−4.46667	+	9.78064i	−0.177115	+	0.387828i
$637$	13.8263	−	4.05978i	0.547819	−	0.160854i
$638$	0.722121	+	1.95407i	0.0285891	+	0.0773622i
$639$	−11.5086	−	3.37924i	−0.455274	−	0.133681i
$640$	1.12824	−	1.30205i	0.0445974	−	0.0514682i
$641$	−5.99460	−	13.1263i	−0.236772	−	0.518459i	0.753526	−	0.657418i	$-0.228352\pi$
$641$	−5.99460	−	13.1263i	−0.236772	−	0.518459i	−0.990298	+	0.138959i	$0.955624\pi$
$642$	−8.33693	+	18.2553i	−0.329032	+	0.720480i
$643$	−19.5700	−	22.5850i	−0.771767	−	0.890666i	0.224719	−	0.974424i	$-0.427853\pi$
$643$	−19.5700	−	22.5850i	−0.771767	−	0.890666i	−0.996486	+	0.0837571i	$0.973308\pi$
$644$	1.27164	+	2.78450i	0.0501096	+	0.109725i
$645$	6.13952			0.241743
$646$	−5.33880	−	3.43104i	−0.210052	−	0.134992i
$647$	−2.79960	−	19.4717i	−0.110064	−	0.765510i	−0.967854	−	0.251511i	$-0.919073\pi$
$647$	−2.79960	−	19.4717i	−0.110064	−	0.765510i	0.857791	−	0.513999i	$-0.171837\pi$
$648$	−0.142315	+	0.989821i	−0.00559065	+	0.0388839i
$649$	21.6560	−	4.64259i	0.850072	−	0.182238i
$650$	0.604973	+	4.20768i	0.0237290	+	0.165039i
$651$	−2.10163	+	0.617094i	−0.0823693	+	0.0241858i
$652$	6.66156	−	4.28113i	0.260887	−	0.167662i
$653$	6.71935	−	7.75454i	0.262948	−	0.303459i	−0.608888	−	0.793257i	$-0.708384\pi$
$653$	6.71935	−	7.75454i	0.262948	−	0.303459i	0.871836	+	0.489798i	$0.162929\pi$
$654$	1.53290	−	10.6616i	0.0599412	−	0.416900i
$655$	17.1200	+	5.02688i	0.668933	+	0.196417i
$656$	−8.24835	+	2.42193i	−0.322044	+	0.0945606i
$657$	4.36034	−	5.03210i	0.170113	−	0.196321i
$658$	−2.57524	−	2.97199i	−0.100393	−	0.115860i
$659$	8.78476	+	5.64562i	0.342206	+	0.219922i	0.700443	−	0.713708i	$-0.252986\pi$
$659$	8.78476	+	5.64562i	0.342206	+	0.219922i	−0.358237	+	0.933631i	$0.616622\pi$
$660$	5.58714	−	1.19777i	0.217479	−	0.0466230i
$661$	21.5073	−	13.8219i	0.836536	−	0.537609i	−0.0508123	−	0.998708i	$-0.516181\pi$
$661$	21.5073	−	13.8219i	0.836536	−	0.537609i	0.887349	+	0.461099i	$0.152545\pi$
$662$	8.51186	+	2.49931i	0.330823	+	0.0971384i
$663$	−1.74807	−	2.01738i	−0.0678893	−	0.0783485i
$664$	−14.5342	+	9.34056i	−0.564036	+	0.362484i
$665$	−2.42035	+	1.55546i	−0.0938572	+	0.0603183i
$666$	−8.50067	+	5.46305i	−0.329394	+	0.211689i
$667$	−4.81806	+	3.09638i	−0.186556	+	0.119892i
$668$	4.25389	+	4.90925i	0.164588	+	0.189945i
$669$	−2.79241	−	0.819927i	−0.107961	−	0.0317002i
$670$	3.41290	−	2.19333i	0.131852	−	0.0847359i
$671$	10.1810	−	2.18259i	0.393032	−	0.0842578i
$672$	−0.282425	−	0.181504i	−0.0108948	−	0.00700165i
$673$	−19.5341	−	22.5436i	−0.752985	−	0.868991i	0.241870	−	0.970309i	$-0.422239\pi$
$673$	−19.5341	−	22.5436i	−0.752985	−	0.868991i	−0.994854	+	0.101318i	$0.967694\pi$
$674$	20.7729	−	23.9732i	0.800141	−	0.923411i
$675$	−1.94944	+	0.572408i	−0.0750341	+	0.0220320i
$676$	8.27316	+	2.42922i	0.318198	+	0.0934315i
$677$	−6.10677	+	42.4735i	−0.234702	+	1.63239i	0.442624	+	0.896707i	$0.354048\pi$
$677$	−6.10677	+	42.4735i	−0.234702	+	1.63239i	−0.677326	+	0.735683i	$0.736861\pi$
$678$	−1.06663	+	1.23096i	−0.0409637	+	0.0472747i
$679$	2.53922	−	1.63186i	0.0974464	−	0.0626250i
$680$	−2.10904	+	0.619270i	−0.0808780	+	0.0237479i
$681$	−3.21706	−	22.3752i	−0.123278	−	0.857418i
$682$	−21.1581	+	4.53586i	−0.810186	+	0.173687i
$683$	−1.63635	+	11.3810i	−0.0626131	+	0.435484i	0.934268	+	0.356571i	$0.116054\pi$
$683$	−1.63635	+	11.3810i	−0.0626131	+	0.435484i	−0.996881	+	0.0789131i	$0.974855\pi$
$684$	−0.707904	−	4.92358i	−0.0270674	−	0.188258i
$685$	16.7300	+	10.7517i	0.639221	+	0.410802i
$686$	−4.66223			−0.178005
$687$	−3.59128	−	7.86381i	−0.137016	−	0.300023i
$688$	−2.33363	−	2.69316i	−0.0889690	−	0.102676i
$689$	9.34545	−	20.4637i	0.356033	−	0.779604i
$690$	6.52587	+	14.2897i	0.248436	+	0.543998i
$691$	0.890358	−	1.02753i	0.0338708	−	0.0390890i	−0.738561	−	0.674186i	$-0.764495\pi$
$691$	0.890358	−	1.02753i	0.0338708	−	0.0390890i	0.772432	+	0.635097i	$0.219040\pi$
$692$	11.2782	+	3.31158i	0.428733	+	0.125887i
$693$	−0.385964	−	1.04442i	−0.0146615	−	0.0396743i
$694$	−24.4465	+	7.17813i	−0.927975	+	0.272478i
$695$	9.14916	−	20.0339i	0.347047	−	0.759928i
$696$	0.260929	−	0.571355i	0.00989048	−	0.0216571i
$697$	10.5235	+	3.08997i	0.398605	+	0.117041i
$698$	4.17278	−	9.13712i	0.157942	−	0.345845i
$699$	−23.6558			−0.894743
$700$	0.0970723	−	0.675153i	0.00366899	−	0.0255184i
$701$	10.4069	−	3.05575i	0.393064	−	0.115414i	−0.0792272	−	0.996857i	$-0.525245\pi$
$701$	10.4069	−	3.05575i	0.393064	−	0.115414i	0.472291	+	0.881443i	$0.343427\pi$
$702$	0.297760	−	2.07097i	0.0112382	−	0.0781637i
$703$	32.9154	−	37.9864i	1.24143	−	1.43268i
$704$	−2.64909	−	1.99558i	−0.0998412	−	0.0752112i
$705$	−13.2158	−	15.2518i	−0.497734	−	0.574416i
$706$	−19.1974	+	12.3374i	−0.722503	+	0.464325i
$707$	0.399220	+	0.117222i	0.0150142	+	0.00440857i
$708$	−5.61779	−	3.61034i	−0.211130	−	0.135685i
$709$	13.1789	−	3.86968i	0.494945	−	0.145329i	−0.0247280	−	0.999694i	$-0.507872\pi$
$709$	13.1789	−	3.86968i	0.494945	−	0.145329i	0.519673	+	0.854365i	$0.326054\pi$
$710$	13.5326	−	15.6175i	0.507870	−	0.586113i
$711$	−0.329412	−	2.29111i	−0.0123539	−	0.0859235i
$712$	2.15200	+	14.9675i	0.0806497	+	0.560931i
$713$	−24.7130	−	54.1139i	−0.925509	−	2.02658i
$714$	0.177931	+	0.389614i	0.00665889	+	0.0145809i
$715$	−11.6898	+	2.50605i	−0.437173	+	0.0937209i
$716$	5.16149	−	11.3021i	0.192894	−	0.422379i
$717$	−1.88865			−0.0705329
$718$	1.85887	−	12.9288i	0.0693726	−	0.482497i
$719$	7.43293	+	8.57806i	0.277202	+	0.319908i	0.877229	−	0.480071i	$-0.159389\pi$
$719$	7.43293	+	8.57806i	0.277202	+	0.319908i	−0.600028	+	0.799979i	$0.704844\pi$
$720$	−1.44936	−	0.931450i	−0.0540146	−	0.0347131i
$721$	−0.0184316	−	0.128195i	−0.000686428	−	0.00477421i
$722$	2.38563	+	5.22381i	0.0887841	+	0.194410i
$723$	−13.0906			−0.486844
$724$	−2.59373	−	1.66689i	−0.0963953	−	0.0619495i
$725$	1.27617			0.0473958
$726$	−3.03532	−	10.5729i	−0.112651	−	0.392398i
$727$	32.7492			1.21460			0.607301	−	0.794472i	$-0.292252\pi$
$727$	32.7492			1.21460			0.607301	+	0.794472i	$0.292252\pi$
$728$	0.590908	+	0.379754i	0.0219005	+	0.0140746i
$729$	1.00000			0.0370370
$730$	4.76545	+	10.4349i	0.176377	+	0.386213i
$731$	0.647033	+	4.50021i	0.0239314	+	0.166446i
$732$	−2.64105	−	1.69730i	−0.0976160	−	0.0627340i
$733$	−0.387659	−	0.447382i	−0.0143185	−	0.0165244i	0.748545	−	0.663084i	$-0.230753\pi$
$733$	−0.387659	−	0.447382i	−0.0143185	−	0.0165244i	−0.762864	+	0.646559i	$0.776207\pi$
$734$	3.73068	−	25.9474i	0.137702	−	0.957737i
$735$	−11.8659			−0.437679
$736$	3.78781	−	8.29414i	0.139620	−	0.305726i
$737$	−4.66138	−	6.26618i	−0.171704	−	0.230818i
$738$	3.57114	+	7.81972i	0.131456	+	0.287848i
$739$	0.991837	+	2.17182i	0.0364853	+	0.0798917i	0.926997	−	0.375068i	$-0.122381\pi$
$739$	0.991837	+	2.17182i	0.0364853	+	0.0798917i	−0.890512	+	0.454960i	$0.849654\pi$
$740$	−2.47758	−	17.2319i	−0.0910775	−	0.633458i
$741$	1.48112	+	10.3014i	0.0544104	+	0.378433i
$742$	−2.36389	+	2.72807i	−0.0867810	+	0.100151i
$743$	15.0455	−	4.41774i	0.551964	−	0.162071i	0.00615532	−	0.999981i	$-0.498041\pi$
$743$	15.0455	−	4.41774i	0.551964	−	0.162071i	0.545809	+	0.837910i	$0.316223\pi$
$744$	5.48864	+	3.52733i	0.201223	+	0.129318i
$745$	38.4761	+	11.2976i	1.40966	+	0.413912i
$746$	8.41788	−	5.40985i	0.308201	−	0.198069i
$747$	11.3139	+	13.0570i	0.413955	+	0.477729i
$748$	1.46677	+	3.96910i	0.0536305	+	0.145125i
$749$	−4.41214	+	5.09188i	−0.161216	+	0.186053i
$750$	1.72411	−	11.9914i	0.0629554	−	0.437865i
$751$	21.8052	−	6.40257i	0.795682	−	0.233633i	0.141468	−	0.989943i	$-0.454818\pi$
$751$	21.8052	−	6.40257i	0.795682	−	0.233633i	0.654214	+	0.756310i	$0.273000\pi$
$752$	−1.66703	+	11.5944i	−0.0607902	+	0.422805i
$753$	7.96650			0.290316
$754$	−0.545932	+	1.19543i	−0.0198817	+	0.0435348i
$755$	20.1391	+	5.91337i	0.732936	+	0.215209i
$756$	−0.139463	+	0.305381i	−0.00507222	+	0.0111066i
$757$	−9.25814	+	20.2725i	−0.336493	+	0.736816i	−0.999935	−	0.0114112i	$-0.996368\pi$
$757$	−9.25814	+	20.2725i	−0.336493	+	0.736816i	0.663442	+	0.748228i	$0.269095\pi$
$758$	11.1691	−	3.27955i	0.405681	−	0.119119i
$759$	26.5858	−	14.4130i	0.965005	−	0.523160i
$760$	8.22274	+	2.41442i	0.298270	+	0.0875800i
$761$	24.4102	−	28.1709i	0.884869	−	1.02119i	−0.114745	−	0.993395i	$-0.536605\pi$
$761$	24.4102	−	28.1709i	0.884869	−	1.02119i	0.999614	−	0.0277981i	$-0.00884955\pi$
$762$	3.08112	+	6.74671i	0.111617	+	0.244407i
$763$	1.50218	−	3.28932i	0.0543826	−	0.119081i
$764$	3.35364	+	3.87030i	0.121330	+	0.140023i
$765$	0.913115	+	1.99944i	0.0330137	+	0.0722900i
$766$	−7.34706			−0.265460
$767$	11.7539	+	7.55378i	0.424409	+	0.272751i
$768$	0.142315	+	0.989821i	0.00513534	+	0.0357171i
$769$	−3.12155	+	21.7109i	−0.112566	+	0.782914i	0.852842	+	0.522169i	$0.174877\pi$
$769$	−3.12155	+	21.7109i	−0.112566	+	0.782914i	−0.965408	+	0.260744i	$0.916032\pi$
$770$	1.91302	+	0.142624i	0.0689405	+	0.00513981i
$771$	−0.678566	−	4.71953i	−0.0244380	−	0.169970i
$772$	−15.1533	+	4.44942i	−0.545380	+	0.160138i
$773$	−1.10454	+	0.709847i	−0.0397277	+	0.0255314i	−0.560354	−	0.828253i	$-0.689335\pi$
$773$	−1.10454	+	0.709847i	−0.0397277	+	0.0255314i	0.520626	+	0.853785i	$0.325699\pi$
$774$	−2.33363	+	2.69316i	−0.0838807	+	0.0968035i
$775$	−1.88650	+	13.1209i	−0.0677650	+	0.471316i
$776$	−8.62659	−	2.53299i	−0.309676	−	0.0909292i
$777$	−3.25495	+	0.955740i	−0.116771	+	0.0342870i
$778$	2.92026	−	3.37016i	0.104696	−	0.120826i
$779$	−28.0026	−	32.3167i	−1.00330	−	1.15787i
$780$	3.03246	+	1.94884i	0.108579	+	0.0697797i
$781$	−31.7745	−	23.9360i	−1.13698	−	0.856496i
$782$	−9.78645	+	6.28937i	−0.349963	+	0.224907i
$783$	−0.602673	−	0.176961i	−0.0215378	−	0.00632406i
$784$	4.51022	+	5.20507i	0.161079	+	0.185895i
$785$	−10.8922	+	6.99996i	−0.388758	+	0.249839i
$786$	−8.71240	+	5.59912i	−0.310761	+	0.199714i
$787$	−27.3488	+	17.5760i	−0.974878	+	0.626516i	−0.928077	−	0.372388i	$-0.878539\pi$
$787$	−27.3488	+	17.5760i	−0.974878	+	0.626516i	−0.0468009	+	0.998904i	$0.514903\pi$
$788$	−0.122525	+	0.0787418i	−0.00436476	+	0.00280506i
$789$	−10.2263	−	11.8018i	−0.364068	−	0.420157i
$790$	3.82633	+	1.12351i	0.136135	+	0.0399728i
$791$	−0.460012	+	0.295631i	−0.0163561	+	0.0105114i
$792$	−1.59826	+	2.90612i	−0.0567918	+	0.103265i
$793$	5.52578	+	3.55120i	0.196226	+	0.126107i
$794$	8.22182	+	9.48849i	0.291782	+	0.336734i
$795$	−12.1311	+	14.0001i	−0.430247	+	0.496531i
$796$	9.06058	−	2.66043i	0.321144	−	0.0942963i
$797$	−32.9973	−	9.68889i	−1.16883	−	0.343198i	−0.360969	−	0.932578i	$-0.617554\pi$
$797$	−32.9973	−	9.68889i	−1.16883	−	0.343198i	−0.807856	+	0.589380i	$0.799372\pi$
$798$	0.237657	−	1.65294i	0.00841297	−	0.0585135i
$799$	9.78665	−	11.2944i	0.346227	−	0.399567i
$800$	−1.70921	+	1.09844i	−0.0604297	+	0.0388358i
$801$	14.5089	−	4.26019i	0.512646	−	0.150527i
$802$	−5.46839	−	38.0335i	−0.193095	−	1.34301i
$803$	19.4141	−	10.5250i	0.685107	−	0.371418i
$804$	−0.335116	+	2.33078i	−0.0118186	+	0.0822004i
$805$	0.750556	+	5.22023i	0.0264536	+	0.183989i
$806$	−11.4837	−	7.38012i	−0.404496	−	0.259954i
$807$	7.53229			0.265149
$808$	−0.514845	−	1.12735i	−0.0181122	−	0.0396602i
$809$	−36.2458	−	41.8299i	−1.27433	−	1.47066i	−0.811660	−	0.584131i	$-0.801436\pi$
$809$	−36.2458	−	41.8299i	−1.27433	−	1.47066i	−0.462674	−	0.886529i	$-0.653110\pi$
$810$	−0.715703	+	1.56717i	−0.0251472	+	0.0550648i
$811$	3.41549	+	7.47888i	0.119934	+	0.262619i	0.960072	−	0.279755i	$-0.0902531\pi$
$811$	3.41549	+	7.47888i	0.119934	+	0.262619i	−0.840138	+	0.542373i	$0.817526\pi$
$812$	0.138091	−	0.159366i	0.00484604	−	0.00559263i
$813$	27.6670	+	8.12376i	0.970324	+	0.284913i
$814$	−32.7692	+	7.02503i	−1.14856	+	0.246227i
$815$	13.0901	−	3.84359i	0.458525	−	0.134635i
$816$	0.529999	−	1.16054i	0.0185537	−	0.0406269i
$817$	7.36360	−	16.1240i	0.257620	−	0.564109i
$818$	4.05319	+	1.19012i	0.141716	+	0.0416117i
$819$	0.291793	−	0.638938i	0.0101961	−	0.0223263i
$820$	−14.8107			−0.517213
$821$	−3.07666	+	21.3986i	−0.107376	+	0.746818i	0.862997	+	0.505208i	$0.168584\pi$
$821$	−3.07666	+	21.3986i	−0.107376	+	0.746818i	−0.970374	+	0.241609i	$0.922325\pi$
$822$	−11.0754	+	3.25204i	−0.386300	+	0.113428i
$823$	−0.232371	+	1.61618i	−0.00809995	+	0.0563364i	−0.993471	−	0.114089i	$-0.963605\pi$
$823$	−0.232371	+	1.61618i	−0.00809995	+	0.0563364i	0.985371	+	0.170425i	$0.0545142\pi$
$824$	−0.252630	+	0.291551i	−0.00880079	+	0.0101566i
$825$	−6.71988	−	0.500995i	−0.233956	−	0.0174424i
$826$	−1.46813	−	1.69431i	−0.0510827	−	0.0589526i
$827$	−8.57270	+	5.50934i	−0.298102	+	0.191578i	−0.681138	−	0.732155i	$-0.738515\pi$
$827$	−8.57270	+	5.50934i	−0.298102	+	0.191578i	0.383036	+	0.923733i	$0.374878\pi$
$828$	−8.74878	−	2.56887i	−0.304041	−	0.0892745i
$829$	−0.376774	−	0.242138i	−0.0130859	−	0.00840980i	0.534082	−	0.845433i	$-0.320658\pi$
$829$	−0.376774	−	0.242138i	−0.0130859	−	0.00840980i	−0.547167	+	0.837023i	$0.684294\pi$
$830$	−28.5599	+	8.38594i	−0.991329	+	0.291080i
$831$	14.1644	−	16.3466i	0.491356	−	0.567056i
$832$	−0.297760	−	2.07097i	−0.0103230	−	0.0717979i
$833$	−1.25052	−	8.69757i	−0.0433280	−	0.301353i
$834$	5.31044	+	11.6282i	0.183886	+	0.402653i
$835$	4.64912	+	10.1801i	0.160889	+	0.352298i
$836$	3.55543	−	16.1099i	0.122967	−	0.557173i
$837$	2.71032	−	5.93476i	0.0936822	−	0.205135i
$838$	30.5667			1.05591
$839$	0.503952	−	3.50506i	0.0173983	−	0.121008i	−0.979271	−	0.202553i	$-0.935076\pi$
$839$	0.503952	−	3.50506i	0.0173983	−	0.121008i	0.996670	+	0.0815446i	$0.0259853\pi$
$840$	−0.378770	−	0.437124i	−0.0130688	−	0.0150822i
$841$	−24.0645	−	15.4653i	−0.829809	−	0.533286i
$842$	1.74076	+	12.1072i	0.0599905	+	0.417243i
$843$	−4.33189	−	9.48551i	−0.149198	−	0.326698i
$844$	−26.9651			−0.928175
$845$	12.4970	+	8.03136i	0.429911	+	0.276287i
$846$	11.7137			0.402724
$847$	0.0222809	−	3.69285i	0.000765581	−	0.126888i
$848$	10.7523			0.369236
$849$	−20.4618	−	13.1500i	−0.702246	−	0.451306i
$850$	2.59216			0.0889103
$851$	−38.2749	−	83.8103i	−1.31205	−	2.87298i
$852$	1.70699	+	11.8724i	0.0584807	+	0.406742i
$853$	1.80010	+	1.15686i	0.0616344	+	0.0396100i	0.571095	−	0.820884i	$-0.306519\pi$
$853$	1.80010	+	1.15686i	0.0616344	+	0.0396100i	−0.509461	+	0.860494i	$0.670155\pi$
$854$	−0.690200	−	0.796533i	−0.0236182	−	0.0272568i
$855$	1.21962	−	8.48265i	0.0417102	−	0.290101i
$856$	20.0689			0.685941
$857$	2.71882	−	5.95339i	0.0928732	−	0.203364i	−0.857494	−	0.514493i	$-0.827980\pi$
$857$	2.71882	−	5.95339i	0.0928732	−	0.203364i	0.950368	+	0.311129i	$0.100707\pi$
$858$	3.34399	−	6.08038i	0.114162	−	0.207581i
$859$	−21.0944	−	46.1904i	−0.719733	−	1.57599i	−0.814279	−	0.580474i	$-0.802867\pi$
$859$	−21.0944	−	46.1904i	−0.719733	−	1.57599i	0.0945462	−	0.995520i	$-0.469860\pi$
$860$	−2.55045	−	5.58471i	−0.0869696	−	0.190437i
$861$	0.410726	+	2.85666i	0.0139975	+	0.0973547i
$862$	3.95480	+	27.5062i	0.134701	+	0.936866i
$863$	−28.7023	+	33.1242i	−0.977038	+	1.12756i	0.0147781	+	0.999891i	$0.495296\pi$
$863$	−28.7023	+	33.1242i	−0.977038	+	1.12756i	−0.991816	+	0.127672i	$0.959250\pi$
$864$	0.959493	−	0.281733i	0.0326426	−	0.00958474i
$865$	17.0363	+	10.9486i	0.579252	+	0.372263i
$866$	24.3594	+	7.15258i	0.827768	+	0.243055i
$867$	12.9320	−	8.31087i	0.439193	−	0.282252i
$868$	1.43438	+	1.65536i	0.0486859	+	0.0561865i
$869$	1.65447	−	7.49651i	0.0561239	−	0.254302i
$870$	0.708663	−	0.817841i	0.0240259	−	0.0277274i
$871$	0.701152	−	4.87662i	0.0237576	−	0.165238i
$872$	−10.3349	+	3.03460i	−0.349984	+	0.102764i
$873$	−1.27952	+	8.89926i	−0.0433052	+	0.301194i
$874$	45.3555			1.53417
$875$	1.68955	−	3.69961i	0.0571174	−	0.125070i
$876$	−6.38871	−	1.87589i	−0.215855	−	0.0633806i
$877$	−16.4098	+	35.9324i	−0.554119	+	1.21335i	0.400712	+	0.916204i	$0.368763\pi$
$877$	−16.4098	+	35.9324i	−0.554119	+	1.21335i	−0.954831	+	0.297148i	$0.903965\pi$
$878$	6.77780	−	14.8413i	0.228740	−	0.500870i
$879$	9.64986	−	2.83346i	0.325482	−	0.0955701i
$880$	−3.41051	−	4.58467i	−0.114968	−	0.154549i
$881$	−17.7109	−	5.20040i	−0.596697	−	0.175206i	−0.0305819	−	0.999532i	$-0.509736\pi$
$881$	−17.7109	−	5.20040i	−0.596697	−	0.175206i	−0.566115	+	0.824326i	$0.691554\pi$
$882$	4.51022	−	5.20507i	0.151867	−	0.175264i
$883$	0.356333	+	0.780261i	0.0119916	+	0.0262579i	0.915533	−	0.402243i	$-0.131769\pi$
$883$	0.356333	+	0.780261i	0.0119916	+	0.0262579i	−0.903541	+	0.428501i	$0.859042\pi$
$884$	−1.10890	+	2.42815i	−0.0372963	+	0.0816674i
$885$	−7.53422	−	8.69496i	−0.253260	−	0.292278i
$886$	2.09605	+	4.58972i	0.0704183	+	0.154195i
$887$	49.1744			1.65111			0.825557	−	0.564318i	$-0.190861\pi$
$887$	49.1744			1.65111			0.825557	+	0.564318i	$0.190861\pi$
$888$	8.50067	+	5.46305i	0.285264	+	0.183328i
$889$	0.354367	+	2.46467i	0.0118851	+	0.0826625i
$890$	−3.70760	+	25.7870i	−0.124279	+	0.864381i
$891$	3.10400	+	1.16841i	0.103988	+	0.0391432i
$892$	0.414179	+	2.88068i	0.0138677	+	0.0964523i
$893$	−55.9060	+	16.4155i	−1.87082	+	0.549323i
$894$	−19.5806	+	12.5837i	−0.654872	+	0.420861i
$895$	14.0182	−	16.1779i	0.468577	−	0.540766i
$896$	−0.0477778	+	0.332302i	−0.00159615	+	0.0111014i
$897$	18.3048	+	5.37476i	0.611178	+	0.179458i
$898$	7.46578	−	2.19215i	0.249136	−	0.0731531i
$899$	−2.68365	+	3.09710i	−0.0895049	+	0.103294i
$900$	1.33051	+	1.53549i	0.0443503	+	0.0511830i
$901$	−11.5404	−	7.41657i	−0.384467	−	0.247082i
$902$	1.94819	+	28.4450i	0.0648677	+	0.947114i
$903$	−1.00644	+	0.646799i	−0.0334922	+	0.0215241i
$904$	1.56281	+	0.458884i	0.0519784	+	0.0152622i
$905$	−3.47855	−	4.01446i	−0.115631	−	0.133445i
$906$	−10.2488	+	6.58652i	−0.340494	+	0.218822i
$907$	−26.4777	+	17.0162i	−0.879176	+	0.565012i	−0.900547	−	0.434760i	$-0.856833\pi$
$907$	−26.4777	+	17.0162i	−0.879176	+	0.565012i	0.0213706	+	0.999772i	$0.493197\pi$
$908$	−19.0167	+	12.2213i	−0.631093	+	0.405579i
$909$	−1.04261	+	0.670044i	−0.0345811	+	0.0222240i
$910$	0.792488	+	0.914580i	0.0262707	+	0.0303180i
$911$	34.4908	+	10.1274i	1.14273	+	0.335536i	0.797700	−	0.603055i	$-0.206050\pi$
$911$	34.4908	+	10.1274i	1.14273	+	0.335536i	0.345032	+	0.938591i	$0.387868\pi$
$912$	−4.18457	+	2.68926i	−0.138565	+	0.0890503i
$913$	19.8625	+	53.7481i	0.657353	+	1.77880i
$914$	3.12764	+	2.01001i	0.103453	+	0.0664852i
$915$	−3.54201	−	4.08769i	−0.117095	−	0.135135i
$916$	−5.66130	+	6.53349i	−0.187055	+	0.215873i
$917$	−3.33602	+	0.979545i	−0.110165	+	0.0323474i
$918$	−1.22415	−	0.359443i	−0.0404029	−	0.0118634i
$919$	−7.83201	+	54.4728i	−0.258354	+	1.79689i	0.286202	+	0.958169i	$0.407607\pi$
$919$	−7.83201	+	54.4728i	−0.258354	+	1.79689i	−0.544557	+	0.838724i	$0.683302\pi$
$920$	10.2874	−	11.8723i	0.339165	−	0.391418i
$921$	0.170083	−	0.109306i	0.00560444	−	0.00360176i
$922$	−22.2190	+	6.52407i	−0.731742	+	0.214859i
$923$	−3.57149	−	24.8402i	−0.117557	−	0.817626i
$924$	−0.789703	+	0.784953i	−0.0259793	+	0.0258231i
$925$	−2.92176	+	20.3213i	−0.0960670	+	0.668161i
$926$	−4.27952	−	29.7647i	−0.140634	−	0.978129i
$927$	0.324536	+	0.208567i	0.0106592	+	0.00685023i
$928$	−0.628116			−0.0206189
$929$	2.73266	+	5.98369i	0.0896557	+	0.196318i	0.949148	−	0.314830i	$-0.101947\pi$
$929$	2.73266	+	5.98369i	0.0896557	+	0.196318i	−0.859492	+	0.511148i	$0.829220\pi$
$930$	7.36101	+	8.49506i	0.241377	+	0.278564i
$931$	−14.2316	+	31.1629i	−0.466423	+	1.02132i
$932$	9.82696	+	21.5180i	0.321893	+	0.704847i
$933$	−19.8582	+	22.9176i	−0.650128	+	0.750288i
$934$	−23.1844	−	6.80756i	−0.758617	−	0.222750i
$935$	0.498138	+	7.27317i	0.0162909	+	0.237858i
$936$	−2.00751	+	0.589459i	−0.0656176	+	0.0192671i
$937$	7.47956	−	16.3779i	0.244347	−	0.535044i	−0.747230	−	0.664565i	$-0.768617\pi$
$937$	7.47956	−	16.3779i	0.244347	−	0.535044i	0.991577	+	0.129521i	$0.0413440\pi$
$938$	−0.328401	+	0.719097i	−0.0107227	+	0.0234793i
$939$	25.7518	+	7.56141i	0.840378	+	0.246757i
$940$	−8.38350	+	18.3573i	−0.273440	+	0.598749i
$941$	37.4965			1.22235			0.611175	−	0.791495i	$-0.290697\pi$
$941$	37.4965			1.22235			0.611175	+	0.791495i	$0.290697\pi$
$942$	1.06951	−	7.43863i	0.0348466	−	0.242364i
$943$	−75.2095	+	22.0835i	−2.44916	+	0.719138i
$944$	−0.950362	+	6.60991i	−0.0309316	+	0.215134i
$945$	−0.378770	+	0.437124i	−0.0123214	+	0.0142197i
$946$	−10.3903	+	5.63292i	−0.337818	+	0.183142i
$947$	33.9240	+	39.1504i	1.10238	+	1.27222i	0.959264	+	0.282510i	$0.0911672\pi$
$947$	33.9240	+	39.1504i	1.10238	+	1.27222i	0.143117	+	0.989706i	$0.454287\pi$
$948$	−1.94723	+	1.25141i	−0.0632430	+	0.0406438i
$949$	13.3669	+	3.92487i	0.433907	+	0.127407i
$950$	−8.50198	−	5.46389i	−0.275841	−	0.177272i
$951$	27.8671	−	8.18251i	0.903651	−	0.265336i
$952$	0.280490	−	0.323703i	0.00909074	−	0.0104913i
$953$	−0.789657	−	5.49218i	−0.0255795	−	0.177909i	0.973026	−	0.230694i	$-0.0740995\pi$
$953$	−0.789657	−	5.49218i	−0.0255795	−	0.177909i	−0.998606	+	0.0527844i	$0.983190\pi$
$954$	−1.53021	−	10.6429i	−0.0495424	−	0.344575i
$955$	3.66522	+	8.02572i	0.118604	+	0.259706i
$956$	0.784573	+	1.71798i	0.0253749	+	0.0555633i
$957$	−1.66393	−	1.25346i	−0.0537874	−	0.0405185i
$958$	−7.29650	+	15.9771i	−0.235739	+	0.516197i
$959$	−3.87521			−0.125137
$960$	−0.245189	+	1.70533i	−0.00791344	+	0.0550392i
$961$	−7.57492	−	8.74192i	−0.244352	−	0.281997i
$962$	−17.7857	−	11.4301i	−0.573433	−	0.368523i
$963$	−2.85610	−	19.8646i	−0.0920366	−	0.640129i
$964$	5.43802	+	11.9076i	0.175147	+	0.383518i
$965$	−27.2093			−0.875898
$966$	−2.57519	−	1.65497i	−0.0828553	−	0.0532479i
$967$	1.32191			0.0425097			0.0212549	−	0.999774i	$-0.493234\pi$
$967$	1.32191			0.0425097			0.0212549	+	0.999774i	$0.493234\pi$
$968$	−8.35656	+	7.15318i	−0.268590	+	0.229912i
$969$	6.34624			0.203871
$970$	−13.0309	−	8.37446i	−0.418397	−	0.268888i
$971$	−22.9661			−0.737016			−0.368508	−	0.929625i	$-0.620131\pi$
$971$	−22.9661			−0.737016			−0.368508	+	0.929625i	$0.620131\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	0.610766	+	4.24797i	0.0195803	+	0.136184i
$974$	−21.1116	−	13.5676i	−0.676459	−	0.434734i
$975$	−2.78378	−	3.21265i	−0.0891522	−	0.102887i
$976$	−0.446786	+	3.10747i	−0.0143013	+	0.0994676i
$977$	7.50112			0.239982			0.119991	−	0.992775i	$-0.461713\pi$
$977$	7.50112			0.239982			0.119991	+	0.992775i	$0.461713\pi$
$978$	−3.28951	+	7.20302i	−0.105187	+	0.230327i
$979$	50.0133	+	3.72870i	1.59843	+	0.119170i
$980$	4.92926	+	10.7936i	0.157459	+	0.344788i
$981$	4.47452	+	9.79783i	0.142860	+	0.312821i
$982$	4.36958	+	30.3911i	0.139439	+	0.969818i
$983$	5.47875	+	38.1056i	0.174745	+	1.21538i	0.868692	+	0.495353i	$0.164961\pi$
$983$	5.47875	+	38.1056i	0.174745	+	1.21538i	−0.693947	+	0.720026i	$0.744130\pi$
$984$	5.62956	−	6.49685i	0.179464	−	0.207112i
$985$	−0.240763	+	0.0706943i	−0.00767134	+	0.00225251i
$986$	0.674155	+	0.433253i	0.0214695	+	0.0137976i
$987$	3.77321	+	1.10791i	0.120102	+	0.0352653i
$988$	8.75524	−	5.62665i	0.278541	−	0.179008i
$989$	−21.2784	−	24.5565i	−0.676613	−	0.780853i
$990$	−4.05264	+	4.02826i	−0.128801	+	0.128027i
$991$	1.26447	−	1.45927i	0.0401671	−	0.0463553i	−0.735311	−	0.677730i	$-0.762964\pi$
$991$	1.26447	−	1.45927i	0.0401671	−	0.0463553i	0.775478	+	0.631375i	$0.217509\pi$
$992$	0.928513	−	6.45795i	0.0294803	−	0.205040i
$993$	−8.51186	+	2.49931i	−0.270116	+	0.0793132i
$994$	−0.573071	+	3.98580i	−0.0181767	+	0.126422i
$995$	16.2691			0.515767
$996$	7.17706	−	15.7156i	0.227414	−	0.497967i
$997$	30.1045	+	8.83949i	0.953421	+	0.279950i	0.721210	−	0.692716i	$-0.243586\pi$
$997$	30.1045	+	8.83949i	0.953421	+	0.279950i	0.232210	+	0.972666i	$0.425404\pi$
$998$	7.18873	−	15.7411i	0.227555	−	0.498276i
$999$	4.19767	−	9.19162i	0.132808	−	0.290810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.i.c.595.4	yes	60
121.12	even	11	inner	726.2.i.c.133.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.i.c.133.4	✓	60	121.12	even	11	inner
726.2.i.c.595.4	yes	60	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} -1.00000 q^{3} +(0.415415 + 0.909632i) q^{4} +(0.245189 + 1.70533i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.219849 - 0.253720i) q^{7} +(-0.142315 + 0.989821i) q^{8} +1.00000 q^{9} +(-0.715703 + 1.56717i) q^{10} +(3.10400 + 1.16841i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(0.869158 + 1.90319i) q^{13} +(-0.0477778 - 0.332302i) q^{14} +(-0.245189 - 1.70533i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.22415 - 0.359443i) q^{17} +(0.841254 + 0.540641i) q^{18} +(-4.77272 - 1.40140i) q^{19} +(-1.44936 + 0.931450i) q^{20} +(0.219849 + 0.253720i) q^{21} +(1.97956 + 2.66108i) q^{22} +(-5.97110 + 6.89102i) q^{23} +(0.142315 - 0.989821i) q^{24} +(1.94944 - 0.572408i) q^{25} +(-0.297760 + 2.07097i) q^{26} -1.00000 q^{27} +(0.139463 - 0.305381i) q^{28} +(0.602673 + 0.176961i) q^{29} +(0.715703 - 1.56717i) q^{30} +(-2.71032 + 5.93476i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-3.10400 - 1.16841i) q^{33} +(1.22415 + 0.359443i) q^{34} +(0.378770 - 0.437124i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-4.19767 + 9.19162i) q^{37} +(-3.25742 - 3.75926i) q^{38} +(-0.869158 - 1.90319i) q^{39} -1.72286 q^{40} +(7.23190 + 4.64766i) q^{41} +(0.0477778 + 0.332302i) q^{42} +(-0.507147 + 3.52729i) q^{43} +(0.226624 + 3.30887i) q^{44} +(0.245189 + 1.70533i) q^{45} +(-8.74878 + 2.56887i) q^{46} +(9.85415 - 6.33288i) q^{47} +(0.654861 - 0.755750i) q^{48} +(0.980164 - 6.81719i) q^{49} +(1.94944 + 0.572408i) q^{50} +(-1.22415 + 0.359443i) q^{51} +(-1.37014 + 1.58123i) q^{52} +(-7.04126 - 8.12605i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-1.23146 + 5.57982i) q^{55} +(0.282425 - 0.181504i) q^{56} +(4.77272 + 1.40140i) q^{57} +(0.411329 + 0.474699i) q^{58} +(5.61779 - 3.61034i) q^{59} +(1.44936 - 0.931450i) q^{60} +(2.64105 - 1.69730i) q^{61} +(-5.48864 + 3.52733i) q^{62} +(-0.219849 - 0.253720i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-3.03246 + 1.94884i) q^{65} +(-1.97956 - 2.66108i) q^{66} +(-1.98094 - 1.27308i) q^{67} +(0.835491 + 0.964207i) q^{68} +(5.97110 - 6.89102i) q^{69} +(0.554969 - 0.162954i) q^{70} +(-11.5086 - 3.37924i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(4.36034 - 5.03210i) q^{73} +(-8.50067 + 5.46305i) q^{74} +(-1.94944 + 0.572408i) q^{75} +(-0.707904 - 4.92358i) q^{76} +(-0.385964 - 1.04442i) q^{77} +(0.297760 - 2.07097i) q^{78} +(-0.329412 - 2.29111i) q^{79} +(-1.44936 - 0.931450i) q^{80} +1.00000 q^{81} +(3.57114 + 7.81972i) q^{82} +(11.3139 + 13.0570i) q^{83} +(-0.139463 + 0.305381i) q^{84} +(0.913115 + 1.99944i) q^{85} +(-2.33363 + 2.69316i) q^{86} +(-0.602673 - 0.176961i) q^{87} +(-1.59826 + 2.90612i) q^{88} +(14.5089 - 4.26019i) q^{89} +(-0.715703 + 1.56717i) q^{90} +(0.291793 - 0.638938i) q^{91} +(-8.74878 - 2.56887i) q^{92} +(2.71032 - 5.93476i) q^{93} +11.7137 q^{94} +(1.21962 - 8.48265i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-1.27952 + 8.89926i) q^{97} +(4.51022 - 5.20507i) q^{98} +(3.10400 + 1.16841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{2} - 60 q^{3} - 6 q^{4} - 2 q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 60 q^{9} - 13 q^{10} - 10 q^{11} + 6 q^{12} - 17 q^{13} - 6 q^{14} + 2 q^{15} - 6 q^{16} + 10 q^{17} - 6 q^{18} - 4 q^{19} - 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) \) 60 * q - 6 * q^2 - 60 * q^3 - 6 * q^4 - 2 * q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 60 * q^9 - 13 * q^10 - 10 * q^11 + 6 * q^12 - 17 * q^13 - 6 * q^14 + 2 * q^15 - 6 * q^16 + 10 * q^17 - 6 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 10 * q^22 - 26 * q^23 + 6 * q^24 - 2 * q^25 + 5 * q^26 - 60 * q^27 + 5 * q^28 - 6 * q^29 + 13 * q^30 - 52 * q^31 - 6 * q^32 + 10 * q^33 + 10 * q^34 + 63 * q^35 - 6 * q^36 - 47 * q^37 + 18 * q^38 + 17 * q^39 - 2 * q^40 + 27 * q^41 + 6 * q^42 + 84 * q^43 + q^44 - 2 * q^45 + 7 * q^46 + 10 * q^47 + 6 * q^48 - 33 * q^49 - 2 * q^50 - 10 * q^51 + 5 * q^52 + 42 * q^53 + 6 * q^54 + 13 * q^55 - 6 * q^56 + 4 * q^57 + 16 * q^58 - 11 * q^59 + 2 * q^60 - 24 * q^61 + 14 * q^62 + 5 * q^63 - 6 * q^64 - 80 * q^65 + 10 * q^66 - 2 * q^67 - q^68 + 26 * q^69 - 14 * q^70 - 30 * q^71 - 6 * q^72 - 51 * q^73 + 8 * q^74 + 2 * q^75 - 4 * q^76 + 73 * q^77 - 5 * q^78 - 30 * q^79 - 2 * q^80 + 60 * q^81 - 6 * q^82 + 4 * q^83 - 5 * q^84 + 45 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 44 * q^89 - 13 * q^90 - 90 * q^91 + 7 * q^92 + 52 * q^93 - 78 * q^94 - 65 * q^95 + 6 * q^96 - 41 * q^97 + 33 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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