LMFDB - Embedded newform 231.2.y.b.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	231.25
Dual form			231.2.y.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02024 + 0.454240i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.503705 - 0.559421i) q^{4} +(0.0732968 - 0.697372i) q^{5} +(-0.903504 - 0.656434i) q^{6} +(2.46176 - 0.969406i) q^{7} +(-0.950004 - 2.92381i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(1.02024 + 0.454240i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.503705 - 0.559421i) q^{4} +(0.0732968 - 0.697372i) q^{5} +(-0.903504 - 0.656434i) q^{6} +(2.46176 - 0.969406i) q^{7} +(-0.950004 - 2.92381i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.391555 - 0.678193i) q^{10} +(3.03888 - 1.32860i) q^{11} +(0.376388 + 0.651923i) q^{12} +(2.89681 - 2.10465i) q^{13} +(2.95193 + 0.129202i) q^{14} +(-0.216687 + 0.666894i) q^{15} +(0.201508 - 1.91722i) q^{16} +(-3.40872 + 1.51766i) q^{17} +(0.747280 + 0.829938i) q^{18} +(-4.33202 + 4.81120i) q^{19} +(-0.427045 + 0.310266i) q^{20} +(-2.60951 + 0.436394i) q^{21} +(3.70390 + 0.0248887i) q^{22} +(-2.77749 - 4.81076i) q^{23} +(0.321350 + 3.05744i) q^{24} +(4.40978 + 0.937328i) q^{25} +(3.91146 - 0.831406i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.78231 - 0.888864i) q^{28} +(-1.13169 + 3.48298i) q^{29} +(-0.524003 + 0.581964i) q^{30} +(0.204170 + 1.94255i) q^{31} +(-1.99781 + 3.46032i) q^{32} +(-3.24871 + 0.667751i) q^{33} -4.16709 q^{34} +(-0.495598 - 1.78782i) q^{35} +(-0.232620 - 0.715932i) q^{36} +(-1.63297 + 0.347098i) q^{37} +(-6.60515 + 2.94080i) q^{38} +(-3.27109 + 1.45638i) q^{39} +(-2.10862 + 0.448201i) q^{40} +(1.67227 + 5.14670i) q^{41} +(-2.86056 - 0.740119i) q^{42} +12.2117 q^{43} +(-2.27395 - 1.03079i) q^{44} +(0.350607 - 0.607269i) q^{45} +(-0.648470 - 6.16978i) q^{46} +(-6.10795 + 6.78357i) q^{47} +(-0.595716 + 1.83343i) q^{48} +(5.12050 - 4.77289i) q^{49} +(4.07327 + 2.95940i) q^{50} +(3.64977 - 0.775782i) q^{51} +(-2.63652 - 0.560410i) q^{52} +(0.784426 + 7.46332i) q^{53} +(-0.558396 - 0.967170i) q^{54} +(-0.703791 - 2.21662i) q^{55} +(-5.17304 - 6.27678i) q^{56} +(5.23766 - 3.80539i) q^{57} +(-2.73670 + 3.03941i) q^{58} +(-5.57473 - 6.19137i) q^{59} +(0.482221 - 0.214698i) q^{60} +(0.338800 - 3.22346i) q^{61} +(-0.674081 + 2.07461i) q^{62} +(2.64322 + 0.115690i) q^{63} +(-6.72928 + 4.88911i) q^{64} +(-1.25540 - 2.17442i) q^{65} +(-3.61778 - 0.794428i) q^{66} +(2.88249 - 4.99261i) q^{67} +(2.56600 + 1.14246i) q^{68} +(1.71658 + 5.28310i) q^{69} +(0.306469 - 2.04912i) q^{70} +(-1.24843 - 0.907036i) q^{71} +(0.321350 - 3.05744i) q^{72} +(9.86039 + 10.9511i) q^{73} +(-1.82369 - 0.387636i) q^{74} +(-4.11854 - 1.83369i) q^{75} +4.87355 q^{76} +(6.19304 - 6.21661i) q^{77} -3.99884 q^{78} +(-4.64470 - 2.06795i) q^{79} +(-1.32224 - 0.281052i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.631727 + 6.01049i) q^{82} +(-8.27734 - 6.01384i) q^{83} +(1.55855 + 1.24000i) q^{84} +(0.808525 + 2.48838i) q^{85} +(12.4588 + 5.54703i) q^{86} +(1.83111 - 3.17157i) q^{87} +(-6.77154 - 7.62295i) q^{88} +(6.65543 + 11.5275i) q^{89} +(0.633549 - 0.460300i) q^{90} +(5.09097 - 7.98933i) q^{91} +(-1.29220 + 3.97699i) q^{92} +(0.204170 - 1.94255i) q^{93} +(-9.31295 + 4.14639i) q^{94} +(3.03767 + 3.37368i) q^{95} +(2.67360 - 2.96933i) q^{96} +(-2.57932 + 1.87399i) q^{97} +(7.39218 - 2.54355i) q^{98} +(3.31655 + 0.0222859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.02024	+	0.454240i	0.721419	+	0.321196i	0.734398	−	0.678719i	$-0.237465\pi$
$2$	1.02024	+	0.454240i	0.721419	+	0.321196i	−0.0129788	+	0.999916i	$0.504131\pi$
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	−0.503705	−	0.559421i	−0.251853	−	0.279711i
$5$	0.0732968	−	0.697372i	0.0327793	−	0.311874i	−0.965831	−	0.259173i	$-0.916550\pi$
$5$	0.0732968	−	0.697372i	0.0327793	−	0.311874i	0.998610	−	0.0527016i	$-0.0167832\pi$
$6$	−0.903504	−	0.656434i	−0.368854	−	0.267988i
$7$	2.46176	−	0.969406i	0.930457	−	0.366401i
$7$	2.46176	−	0.969406i	0.930457	−	0.366401i
$8$	−0.950004	−	2.92381i	−0.335877	−	1.03372i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.391555	−	0.678193i	0.123821	−	0.214463i
$11$	3.03888	−	1.32860i	0.916258	−	0.400589i
$11$	3.03888	−	1.32860i	0.916258	−	0.400589i
$12$	0.376388	+	0.651923i	0.108654	+	0.188194i
$13$	2.89681	−	2.10465i	0.803430	−	0.583726i	−0.108489	−	0.994098i	$-0.534601\pi$
$13$	2.89681	−	2.10465i	0.803430	−	0.583726i	0.911918	+	0.410372i	$0.134601\pi$
$14$	2.95193	+	0.129202i	0.788936	+	0.0345307i
$15$	−0.216687	+	0.666894i	−0.0559483	+	0.172191i
$16$	0.201508	−	1.91722i	0.0503769	−	0.479305i
$17$	−3.40872	+	1.51766i	−0.826735	+	0.368086i	−0.776083	−	0.630630i	$-0.782796\pi$
$17$	−3.40872	+	1.51766i	−0.826735	+	0.368086i	−0.0506515	+	0.998716i	$0.516130\pi$
$18$	0.747280	+	0.829938i	0.176136	+	0.195618i
$19$	−4.33202	+	4.81120i	−0.993835	+	1.10377i	0.000767219		1.00000i	$0.499756\pi$
$19$	−4.33202	+	4.81120i	−0.993835	+	1.10377i	−0.994602	+	0.103765i	$0.966911\pi$
$20$	−0.427045	+	0.310266i	−0.0954901	+	0.0693776i
$21$	−2.60951	+	0.436394i	−0.569442	+	0.0952291i
$22$	3.70390	+	0.0248887i	0.789673	+	0.00530629i
$23$	−2.77749	−	4.81076i	−0.579147	−	1.00311i	−0.995577	−	0.0939447i	$-0.970052\pi$
$23$	−2.77749	−	4.81076i	−0.579147	−	1.00311i	0.416430	−	0.909168i	$-0.363281\pi$
$24$	0.321350	+	3.05744i	0.0655952	+	0.624097i
$25$	4.40978	+	0.937328i	0.881956	+	0.187466i
$26$	3.91146	−	0.831406i	0.767100	−	0.163052i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.78231	−	0.888864i	−0.336824	−	0.167980i
$29$	−1.13169	+	3.48298i	−0.210149	+	0.646772i	0.789313	+	0.613990i	$0.210437\pi$
$29$	−1.13169	+	3.48298i	−0.210149	+	0.646772i	−0.999463	+	0.0327818i	$0.989563\pi$
$30$	−0.524003	+	0.581964i	−0.0956694	+	0.106252i
$31$	0.204170	+	1.94255i	0.0366700	+	0.348892i	0.997438	+	0.0715380i	$0.0227907\pi$
$31$	0.204170	+	1.94255i	0.0366700	+	0.348892i	−0.960768	+	0.277354i	$0.910543\pi$
$32$	−1.99781	+	3.46032i	−0.353167	+	0.611703i
$33$	−3.24871	+	0.667751i	−0.565528	+	0.116240i
$34$	−4.16709			−0.714650
$35$	−0.495598	−	1.78782i	−0.0837714	−	0.302196i
$36$	−0.232620	−	0.715932i	−0.0387701	−	0.119322i
$37$	−1.63297	+	0.347098i	−0.268458	+	0.0570626i	−0.340174	−	0.940363i	$-0.610486\pi$
$37$	−1.63297	+	0.347098i	−0.268458	+	0.0570626i	0.0717156	+	0.997425i	$0.477153\pi$
$38$	−6.60515	+	2.94080i	−1.07150	+	0.477061i
$39$	−3.27109	+	1.45638i	−0.523793	+	0.233208i
$40$	−2.10862	+	0.448201i	−0.333402	+	0.0708667i
$41$	1.67227	+	5.14670i	0.261164	+	0.803780i	0.992552	+	0.121819i	$0.0388727\pi$
$41$	1.67227	+	5.14670i	0.261164	+	0.803780i	−0.731388	+	0.681961i	$0.761127\pi$
$42$	−2.86056	−	0.740119i	−0.441394	−	0.114203i
$43$	12.2117			1.86226			0.931130	−	0.364688i	$-0.118824\pi$
$43$	12.2117			1.86226			0.931130	+	0.364688i	$0.118824\pi$
$44$	−2.27395	−	1.03079i	−0.342811	−	0.155398i
$45$	0.350607	−	0.607269i	0.0522654	−	0.0905263i
$46$	−0.648470	−	6.16978i	−0.0956117	−	0.909684i
$47$	−6.10795	+	6.78357i	−0.890937	+	0.989485i	−0.999990	−	0.00455063i	$-0.998551\pi$
$47$	−6.10795	+	6.78357i	−0.890937	+	0.989485i	0.109053	+	0.994036i	$0.465218\pi$
$48$	−0.595716	+	1.83343i	−0.0859842	+	0.264632i
$49$	5.12050	−	4.77289i	0.731500	−	0.681841i
$50$	4.07327	+	2.95940i	0.576047	+	0.418522i
$51$	3.64977	−	0.775782i	0.511069	−	0.108631i
$52$	−2.63652	−	0.560410i	−0.365620	−	0.0777149i
$53$	0.784426	+	7.46332i	0.107749	+	1.02517i	0.906126	+	0.423007i	$0.139026\pi$
$53$	0.784426	+	7.46332i	0.107749	+	1.02517i	−0.798377	+	0.602158i	$0.794308\pi$
$54$	−0.558396	−	0.967170i	−0.0759881	−	0.131615i
$55$	−0.703791	−	2.21662i	−0.0948991	−	0.298888i
$56$	−5.17304	−	6.27678i	−0.691277	−	0.838770i
$57$	5.23766	−	3.80539i	0.693746	−	0.504036i
$58$	−2.73670	+	3.03941i	−0.359346	+	0.399095i
$59$	−5.57473	−	6.19137i	−0.725768	−	0.806047i	0.261485	−	0.965208i	$-0.415788\pi$
$59$	−5.57473	−	6.19137i	−0.725768	−	0.806047i	−0.987253	+	0.159160i	$0.949121\pi$
$60$	0.482221	−	0.214698i	0.0622544	−	0.0277175i
$61$	0.338800	−	3.22346i	0.0433789	−	0.412722i	−0.951187	−	0.308615i	$-0.900135\pi$
$61$	0.338800	−	3.22346i	0.0433789	−	0.412722i	0.994566	−	0.104108i	$-0.0331987\pi$
$62$	−0.674081	+	2.07461i	−0.0856083	+	0.263475i
$63$	2.64322	+	0.115690i	0.333015	+	0.0145756i
$64$	−6.72928	+	4.88911i	−0.841160	+	0.611138i
$65$	−1.25540	−	2.17442i	−0.155713	−	0.269703i
$66$	−3.61778	−	0.794428i	−0.445318	−	0.0977874i
$67$	2.88249	−	4.99261i	0.352152	−	0.609945i	−0.634474	−	0.772944i	$-0.718783\pi$
$67$	2.88249	−	4.99261i	0.352152	−	0.609945i	0.986626	+	0.162999i	$0.0521167\pi$
$68$	2.56600	+	1.14246i	0.311173	+	0.138543i
$69$	1.71658	+	5.28310i	0.206653	+	0.636011i
$70$	0.306469	−	2.04912i	0.0366300	−	0.244917i
$71$	−1.24843	−	0.907036i	−0.148161	−	0.107645i	0.511235	−	0.859441i	$-0.329188\pi$
$71$	−1.24843	−	0.907036i	−0.148161	−	0.107645i	−0.659396	+	0.751795i	$0.729188\pi$
$72$	0.321350	−	3.05744i	0.0378714	−	0.360322i
$73$	9.86039	+	10.9511i	1.15407	+	1.28173i	0.953279	+	0.302093i	$0.0976853\pi$
$73$	9.86039	+	10.9511i	1.15407	+	1.28173i	0.200793	+	0.979634i	$0.435648\pi$
$74$	−1.82369	−	0.387636i	−0.211999	−	0.0450618i
$75$	−4.11854	−	1.83369i	−0.475568	−	0.211736i
$76$	4.87355			0.559034
$77$	6.19304	−	6.21661i	0.705762	−	0.708449i
$78$	−3.99884			−0.452780
$79$	−4.64470	−	2.06795i	−0.522569	−	0.232663i	0.128461	−	0.991715i	$-0.458996\pi$
$79$	−4.64470	−	2.06795i	−0.522569	−	0.232663i	−0.651030	+	0.759052i	$0.725663\pi$
$80$	−1.32224	−	0.281052i	−0.147831	−	0.0314225i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.631727	+	6.01049i	−0.0697626	+	0.663747i
$83$	−8.27734	−	6.01384i	−0.908556	−	0.660104i	0.0320934	−	0.999485i	$-0.489783\pi$
$83$	−8.27734	−	6.01384i	−0.908556	−	0.660104i	−0.940649	+	0.339380i	$0.889783\pi$
$84$	1.55855	+	1.24000i	0.170052	+	0.135295i
$85$	0.808525	+	2.48838i	0.0876968	+	0.269903i
$86$	12.4588	+	5.54703i	1.34347	+	0.598151i
$87$	1.83111	−	3.17157i	0.196315	−	0.340028i
$88$	−6.77154	−	7.62295i	−0.721848	−	0.812609i
$89$	6.65543	+	11.5275i	0.705474	+	1.22192i	0.966520	+	0.256591i	$0.0825993\pi$
$89$	6.65543	+	11.5275i	0.705474	+	1.22192i	−0.261046	+	0.965326i	$0.584067\pi$
$90$	0.633549	−	0.460300i	0.0667819	−	0.0485199i
$91$	5.09097	−	7.98933i	0.533679	−	0.837509i
$92$	−1.29220	+	3.97699i	−0.134721	+	0.414630i
$93$	0.204170	−	1.94255i	0.0211714	−	0.201433i
$94$	−9.31295	+	4.14639i	−0.960558	+	0.427668i
$95$	3.03767	+	3.37368i	0.311659	+	0.346132i
$96$	2.67360	−	2.96933i	0.272873	−	0.303056i
$97$	−2.57932	+	1.87399i	−0.261891	+	0.190275i	−0.710980	−	0.703212i	$-0.751748\pi$
$97$	−2.57932	+	1.87399i	−0.261891	+	0.190275i	0.449089	+	0.893487i	$0.351748\pi$
$98$	7.39218	−	2.54355i	0.746723	−	0.256938i
$99$	3.31655	+	0.0222859i	0.333326	+	0.00223981i
$100$	−1.69687	−	2.93906i	−0.169687	−	0.293906i
$101$	−0.747805	−	7.11489i	−0.0744094	−	0.707958i	−0.966598	−	0.256296i	$-0.917498\pi$
$101$	−0.747805	−	7.11489i	−0.0744094	−	0.707958i	0.892189	−	0.451662i	$-0.149169\pi$
$102$	4.07603	+	0.866387i	0.403587	+	0.0857851i
$103$	4.45657	−	0.947272i	0.439119	−	0.0933375i	0.0169530	−	0.999856i	$-0.494603\pi$
$103$	4.45657	−	0.947272i	0.439119	−	0.0933375i	0.422166	+	0.906519i	$0.361270\pi$
$104$	−8.90559	−	6.47029i	−0.873265	−	0.634464i
$105$	0.113060	+	1.85179i	0.0110336	+	0.180716i
$106$	−2.58984	+	7.97069i	−0.251547	+	0.774182i
$107$	3.91178	−	4.34447i	0.378166	−	0.419996i	−0.523774	−	0.851857i	$-0.675476\pi$
$107$	3.91178	−	4.34447i	0.378166	−	0.419996i	0.901940	+	0.431861i	$0.142143\pi$
$108$	0.0786864	+	0.748652i	0.00757161	+	0.0720390i
$109$	−10.2671	+	17.7831i	−0.983410	+	1.70332i	−0.334611	+	0.942356i	$0.608605\pi$
$109$	−10.2671	+	17.7831i	−0.983410	+	1.70332i	−0.648799	+	0.760960i	$0.724729\pi$
$110$	0.288840	−	2.58117i	0.0275399	−	0.246105i
$111$	1.66945			0.158457
$112$	−1.36250	−	4.91507i	−0.128744	−	0.464430i
$113$	3.53371	+	10.8756i	0.332423	+	1.02309i	0.967977	+	0.251038i	$0.0807718\pi$
$113$	3.53371	+	10.8756i	0.332423	+	1.02309i	−0.635554	+	0.772057i	$0.719228\pi$
$114$	7.07224	−	1.50325i	0.662376	−	0.140792i
$115$	−3.55847	+	1.58433i	−0.331829	+	0.147740i
$116$	2.51849	−	1.12130i	0.233836	−	0.104110i
$117$	3.50240	−	0.744459i	0.323797	−	0.0688253i
$118$	−2.87520	−	8.84895i	−0.264683	−	0.814612i
$119$	−6.92020	+	7.04054i	−0.634374	+	0.645405i
$120$	2.15573			0.196790
$121$	7.46963	−	8.07494i	0.679057	−	0.734086i
$122$	1.80988	−	3.13481i	0.163859	−	0.283813i
$123$	−0.565663	−	5.38192i	−0.0510041	−	0.485271i
$124$	0.983861	−	1.09269i	0.0883533	−	0.0981263i
$125$	2.06032	−	6.34103i	0.184281	−	0.567159i
$126$	2.64417	+	1.31869i	0.235561	+	0.117478i
$127$	−3.71593	−	2.69978i	−0.329735	−	0.239567i	0.410583	−	0.911823i	$-0.365325\pi$
$127$	−3.71593	−	2.69978i	−0.329735	−	0.239567i	−0.740318	+	0.672257i	$0.765325\pi$
$128$	−1.26968	+	0.269879i	−0.112225	+	0.0238542i
$129$	−11.9448	−	2.53895i	−1.05168	−	0.223542i
$130$	−0.293102	−	2.78868i	−0.0257068	−	0.244584i
$131$	−2.32547	−	4.02783i	−0.203177	−	0.351913i	0.746373	−	0.665528i	$-0.231793\pi$
$131$	−2.32547	−	4.02783i	−0.203177	−	0.351913i	−0.949550	+	0.313615i	$0.898460\pi$
$132$	2.00994	+	1.48105i	0.174943	+	0.128909i
$133$	−6.00039	+	16.0435i	−0.520299	+	1.39115i
$134$	5.20868	−	3.78433i	0.449961	−	0.326916i
$135$	−0.469203	+	0.521103i	−0.0403826	+	0.0448494i
$136$	7.67564	+	8.52466i	0.658181	+	0.730984i
$137$	−3.32068	+	1.47846i	−0.283705	+	0.126313i	−0.543656	−	0.839308i	$-0.682960\pi$
$137$	−3.32068	+	1.47846i	−0.283705	+	0.126313i	0.259951	+	0.965622i	$0.416294\pi$
$138$	−0.648470	+	6.16978i	−0.0552014	+	0.525206i
$139$	2.15087	−	6.61968i	0.182434	−	0.561474i	−0.817461	−	0.575984i	$-0.804619\pi$
$139$	2.15087	−	6.61968i	0.182434	−	0.561474i	0.999895	+	0.0145102i	$0.00461890\pi$
$140$	−0.750507	+	1.17778i	−0.0634294	+	0.0995406i
$141$	7.38486	−	5.36542i	0.621918	−	0.451850i
$142$	−0.861684	−	1.49248i	−0.0723109	−	0.125246i
$143$	6.00681	−	10.2445i	0.502315	−	0.856689i
$144$	0.963889	−	1.66951i	0.0803241	−	0.139125i
$145$	2.34598	+	1.04450i	0.194823	+	0.0867408i
$146$	5.08555	+	15.6517i	0.420883	+	1.29535i
$147$	−6.00095	+	3.60398i	−0.494950	+	0.297251i
$148$	1.01671	+	0.738682i	0.0835729	+	0.0607193i
$149$	1.15084	−	10.9495i	0.0942802	−	0.897016i	−0.840505	−	0.541803i	$-0.817742\pi$
$149$	1.15084	−	10.9495i	0.0942802	−	0.897016i	0.934785	−	0.355213i	$-0.115592\pi$
$150$	−3.36896	−	3.74161i	−0.275075	−	0.305501i
$151$	2.39273	+	0.508590i	0.194718	+	0.0413885i	0.304238	−	0.952596i	$-0.401598\pi$
$151$	2.39273	+	0.508590i	0.194718	+	0.0413885i	−0.109520	+	0.993985i	$0.534932\pi$
$152$	18.1825	+	8.09536i	1.47479	+	0.656621i
$153$	−3.73130			−0.301658
$154$	9.14222	−	3.52931i	0.736701	−	0.284400i
$155$	1.36964			0.110012
$156$	2.46239	+	1.09633i	0.197149	+	0.0877765i
$157$	10.3689	+	2.20397i	0.827525	+	0.175896i	0.602157	−	0.798378i	$-0.294308\pi$
$157$	10.3689	+	2.20397i	0.827525	+	0.175896i	0.225368	+	0.974274i	$0.427642\pi$
$158$	−3.79936	−	4.21962i	−0.302261	−	0.335695i
$159$	0.784426	−	7.46332i	0.0622090	−	0.591879i
$160$	2.26669	+	1.64685i	0.179198	+	0.130195i
$161$	−11.5011	−	9.15040i	−0.906413	−	0.721153i
$162$	0.345108	+	1.06213i	0.0271142	+	0.0834490i
$163$	−18.2021	−	8.10408i	−1.42570	−	0.634761i	−0.458477	−	0.888706i	$-0.651605\pi$
$163$	−18.2021	−	8.10408i	−1.42570	−	0.634761i	−0.967219	+	0.253945i	$0.918272\pi$
$164$	2.03685	−	3.52792i	0.159051	−	0.275484i
$165$	0.227551	+	2.31450i	0.0177148	+	0.180184i
$166$	−5.71315	−	9.89546i	−0.443426	−	0.768037i
$167$	5.05564	−	3.67314i	0.391217	−	0.284236i	−0.374737	−	0.927131i	$-0.622267\pi$
$167$	5.05564	−	3.67314i	0.391217	−	0.284236i	0.765954	+	0.642895i	$0.222267\pi$
$168$	3.75498	+	7.21515i	0.289703	+	0.556661i
$169$	−0.0552958	+	0.170183i	−0.00425352	+	0.0130910i
$170$	−0.305434	+	2.90601i	−0.0234257	+	0.222881i
$171$	−5.91439	+	2.63326i	−0.452285	+	0.201370i
$172$	−6.15107	−	6.83146i	−0.469015	−	0.520894i
$173$	15.4985	−	17.2128i	1.17833	−	1.30867i	0.236869	−	0.971542i	$-0.423879\pi$
$173$	15.4985	−	17.2128i	1.17833	−	1.30867i	0.941460	−	0.337125i	$-0.109455\pi$
$174$	3.30883	−	2.40400i	0.250842	−	0.182247i
$175$	11.7645	−	1.96740i	0.889310	−	0.148721i
$176$	−1.93486	−	6.09393i	−0.145846	−	0.459347i
$177$	4.16565	+	7.21512i	0.313110	+	0.542322i
$178$	1.55386	+	14.7840i	0.116467	+	1.10811i
$179$	1.43856	+	0.305775i	0.107523	+	0.0228547i	0.261359	−	0.965242i	$-0.415829\pi$
$179$	1.43856	+	0.305775i	0.107523	+	0.0228547i	−0.153836	+	0.988096i	$0.549163\pi$
$180$	−0.516321	+	0.109747i	−0.0384843	+	0.00818010i
$181$	−14.9467	−	10.8594i	−1.11098	−	0.807173i	−0.128160	−	0.991753i	$-0.540907\pi$
$181$	−14.9467	−	10.8594i	−1.11098	−	0.807173i	−0.982817	+	0.184581i	$0.940907\pi$
$182$	8.82309	−	5.83851i	0.654011	−	0.432779i
$183$	−1.00159	+	3.08258i	−0.0740398	+	0.227871i
$184$	−11.4271	+	12.6911i	−0.842419	+	0.935601i
$185$	0.122365	+	1.16423i	0.00899647	+	0.0855957i
$186$	1.09069	−	1.88912i	0.0799730	−	0.138517i
$187$	−8.34232	+	9.14082i	−0.610051	+	0.668443i
$188$	6.87148			0.501154
$189$	−2.56141	−	0.662719i	−0.186315	−	0.0482057i
$190$	1.56670	+	4.82180i	0.113660	+	0.349810i
$191$	−22.7102	+	4.82721i	−1.64326	+	0.349285i	−0.934443	−	0.356113i	$-0.884102\pi$
$191$	−22.7102	+	4.82721i	−1.64326	+	0.349285i	−0.708812	+	0.705397i	$0.750769\pi$
$192$	7.59873	−	3.38317i	0.548391	−	0.244159i
$193$	−21.2485	+	9.46042i	−1.52950	+	0.680976i	−0.987240	−	0.159237i	$-0.949097\pi$
$193$	−21.2485	+	9.46042i	−1.52950	+	0.680976i	−0.542257	+	0.840213i	$0.682430\pi$
$194$	−3.48277	+	0.740286i	−0.250048	+	0.0531494i
$195$	0.775880	+	2.38791i	0.0555619	+	0.171002i
$196$	−5.24928	−	0.460390i	−0.374948	−	0.0328850i
$197$	10.2775			0.732241			0.366120	−	0.930567i	$-0.380686\pi$
$197$	10.2775			0.732241			0.366120	+	0.930567i	$0.380686\pi$
$198$	3.37355	+	1.52925i	0.239748	+	0.108679i
$199$	−6.90174	+	11.9542i	−0.489251	+	0.847408i	−0.999924	−	0.0123674i	$-0.996063\pi$
$199$	−6.90174	+	11.9542i	−0.489251	+	0.847408i	0.510672	+	0.859775i	$0.329397\pi$
$200$	−1.44874	−	13.7838i	−0.102441	−	0.974665i
$201$	−3.85752	+	4.28421i	−0.272089	+	0.302185i
$202$	2.46893	−	7.59858i	0.173713	−	0.534634i
$203$	0.590479	+	9.67131i	0.0414435	+	0.678793i
$204$	−2.27239	−	1.65099i	−0.159099	−	0.115592i
$205$	3.71174	−	0.788955i	0.259239	−	0.0551030i
$206$	4.97706	+	1.05791i	0.346768	+	0.0737078i
$207$	−0.580654	−	5.52455i	−0.0403582	−	0.383983i
$208$	−3.45135	−	5.97792i	−0.239308	−	0.414494i
$209$	−6.77234	+	20.3762i	−0.468453	+	1.40945i
$210$	−0.725808	+	1.94063i	−0.0500855	+	0.133916i
$211$	−10.5364	+	7.65517i	−0.725359	+	0.527004i	−0.888092	−	0.459666i	$-0.847969\pi$
$211$	−10.5364	+	7.65517i	−0.725359	+	0.527004i	0.162733	+	0.986670i	$0.447969\pi$
$212$	3.78002	−	4.19813i	0.259613	−	0.288329i
$213$	1.03256	+	1.14678i	0.0707501	+	0.0785759i
$214$	5.96439	−	2.65552i	0.407717	−	0.181527i
$215$	0.895075	−	8.51607i	0.0610436	−	0.580791i
$216$	−0.950004	+	2.92381i	−0.0646396	+	0.198940i
$217$	2.38573	+	4.58416i	0.161954	+	0.311193i
$218$	−18.5527	+	13.4793i	−1.25655	+	0.912937i
$219$	−7.36806	−	12.7619i	−0.497888	−	0.862367i
$220$	−0.885519	+	1.51024i	−0.0597016	+	0.101820i
$221$	−6.68025	+	11.5705i	−0.449362	+	0.778318i
$222$	1.70324	+	0.758331i	0.114314	+	0.0508959i
$223$	0.937059	+	2.88397i	0.0627501	+	0.193125i	0.977517	−	0.210858i	$-0.0676256\pi$
$223$	0.937059	+	2.88397i	0.0627501	+	0.193125i	−0.914767	+	0.403983i	$0.867626\pi$
$224$	−1.56368	+	10.4552i	−0.104478	+	0.698564i
$225$	3.64729	+	2.64991i	0.243153	+	0.176661i
$226$	−1.33492	+	12.7009i	−0.0887976	+	0.844853i
$227$	−5.94630	−	6.60404i	−0.394670	−	0.438325i	0.512758	−	0.858533i	$-0.328624\pi$
$227$	−5.94630	−	6.60404i	−0.394670	−	0.438325i	−0.907428	+	0.420208i	$0.861957\pi$
$228$	−4.76705	−	1.01327i	−0.315706	−	0.0671053i
$229$	−9.00067	−	4.00736i	−0.594781	−	0.264814i	0.0871911	−	0.996192i	$-0.472211\pi$
$229$	−9.00067	−	4.00736i	−0.594781	−	0.264814i	−0.681972	+	0.731378i	$0.738878\pi$
$230$	−4.35016			−0.286841
$231$	−7.35021	+	4.79316i	−0.483608	+	0.315367i
$232$	11.2587			0.739168
$233$	17.6895	+	7.87585i	1.15888	+	0.515964i	0.893889	−	0.448288i	$-0.147966\pi$
$233$	17.6895	+	7.87585i	1.15888	+	0.515964i	0.264986	+	0.964252i	$0.414633\pi$
$234$	3.91146	+	0.831406i	0.255700	+	0.0543507i
$235$	4.28298	+	4.75673i	0.279391	+	0.310295i
$236$	−0.655561	+	6.23724i	−0.0426734	+	0.406010i
$237$	4.11325	+	2.98845i	0.267184	+	0.194121i
$238$	−10.2584	+	4.03960i	−0.664951	+	0.261849i
$239$	−3.04360	−	9.36722i	−0.196874	−	0.605915i	−0.999950	−	0.0100384i	$-0.996805\pi$
$239$	−3.04360	−	9.36722i	−0.196874	−	0.605915i	0.803076	−	0.595877i	$-0.203195\pi$
$240$	1.23492	+	0.549820i	0.0797135	+	0.0354907i
$241$	9.02876	−	15.6383i	0.581594	−	1.00735i	−0.413697	−	0.910415i	$-0.635763\pi$
$241$	9.02876	−	15.6383i	0.581594	−	1.00735i	0.995291	−	0.0969353i	$-0.0309040\pi$
$242$	11.2888	−	4.84538i	0.725670	−	0.311473i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.97393	+	1.43414i	−0.126368	+	0.0918116i
$245$	−2.95316	−	3.92073i	−0.188671	−	0.250486i
$246$	1.86757	−	5.74780i	0.119072	−	0.366466i
$247$	−2.42313	+	23.0545i	−0.154180	+	1.46692i
$248$	5.48568	−	2.44238i	0.348341	−	0.155091i
$249$	6.84611	+	7.60338i	0.433855	+	0.481844i
$250$	4.98237	−	5.53349i	0.315113	−	0.349969i
$251$	0.120693	−	0.0876883i	0.00761805	−	0.00553484i	−0.583970	−	0.811775i	$-0.698501\pi$
$251$	0.120693	−	0.0876883i	0.00761805	−	0.00553484i	0.591588	+	0.806241i	$0.298501\pi$
$252$	−1.26668	−	1.53695i	−0.0797936	−	0.0968186i
$253$	−14.8321	−	10.9291i	−0.932484	−	0.687110i
$254$	−2.56479	−	4.44235i	−0.160929	−	0.278738i
$255$	−0.273493	−	2.60211i	−0.0171268	−	0.162950i
$256$	14.8542	+	3.15735i	0.928387	+	0.197335i
$257$	−21.0861	+	4.48199i	−1.31531	+	0.279579i	−0.811560	−	0.584269i	$-0.801381\pi$
$257$	−21.0861	+	4.48199i	−1.31531	+	0.279579i	−0.503754	+	0.863847i	$0.668048\pi$
$258$	−11.0333	−	8.01614i	−0.686902	−	0.499063i
$259$	−3.68349	+	2.43748i	−0.228881	+	0.151458i
$260$	−0.584063	+	1.79756i	−0.0362221	+	0.111480i
$261$	−2.45050	+	2.72156i	−0.151682	+	0.168460i
$262$	−0.542934	−	5.16567i	−0.0335426	−	0.319136i
$263$	−7.81562	+	13.5370i	−0.481932	+	0.834730i	−0.999785	−	0.0207394i	$-0.993398\pi$
$263$	−7.81562	+	13.5370i	−0.481932	+	0.834730i	0.517853	+	0.855469i	$0.326731\pi$
$264$	5.03866	+	8.86425i	0.310108	+	0.545557i
$265$	5.26220			0.323255
$266$	−13.4094	+	13.6426i	−0.822186	+	0.836482i
$267$	−4.11328	−	12.6594i	−0.251729	−	0.774742i
$268$	−4.24490	+	0.902281i	−0.259298	+	0.0551156i
$269$	−10.0221	+	4.46214i	−0.611060	+	0.272062i	−0.688845	−	0.724909i	$-0.741882\pi$
$269$	−10.0221	+	4.46214i	−0.611060	+	0.272062i	0.0777848	+	0.996970i	$0.475215\pi$
$270$	−0.715406	+	0.318519i	−0.0435382	+	0.0193845i
$271$	−7.18637	+	1.52751i	−0.436541	+	0.0927896i	−0.420940	−	0.907089i	$-0.638300\pi$
$271$	−7.18637	+	1.52751i	−0.436541	+	0.0927896i	−0.0156013	+	0.999878i	$0.504966\pi$
$272$	2.22280	+	6.84107i	0.134777	+	0.414801i
$273$	−6.64080	+	6.75627i	−0.401919	+	0.408908i
$274$	−4.05947			−0.245241
$275$	14.6462	−	3.01042i	0.883196	−	0.181535i
$276$	2.09083	−	3.62142i	0.125853	−	0.217984i
$277$	−1.71526	−	16.3196i	−0.103060	−	0.980549i	−0.916807	−	0.399330i	$-0.869243\pi$
$277$	−1.71526	−	16.3196i	−0.103060	−	0.980549i	0.813747	−	0.581219i	$-0.197424\pi$
$278$	5.20133	−	5.77666i	0.311955	−	0.346461i
$279$	−0.603587	+	1.85765i	−0.0361358	+	0.111215i
$280$	−4.75642	+	3.14747i	−0.284250	+	0.188097i
$281$	−7.90308	−	5.74193i	−0.471458	−	0.342535i	0.326551	−	0.945180i	$-0.394114\pi$
$281$	−7.90308	−	5.74193i	−0.471458	−	0.342535i	−0.798009	+	0.602645i	$0.794114\pi$
$282$	9.97152	−	2.11951i	0.593796	−	0.126215i
$283$	26.1712	+	5.56286i	1.55572	+	0.330678i	0.903915	−	0.427712i	$-0.140680\pi$
$283$	26.1712	+	5.56286i	1.55572	+	0.330678i	0.651802	+	0.758389i	$0.274013\pi$
$284$	0.121424	+	1.15528i	0.00720521	+	0.0685530i
$285$	−2.26987	−	3.93152i	−0.134455	−	0.232883i
$286$	10.7819	−	7.72332i	0.637545	−	0.456690i
$287$	9.10596	+	11.0488i	0.537508	+	0.652192i
$288$	−3.23253	+	2.34857i	−0.190479	+	0.138391i
$289$	−2.05917	+	2.28694i	−0.121127	+	0.134526i
$290$	1.91901	+	2.13128i	0.112688	+	0.125153i
$291$	2.91258	−	1.29677i	0.170739	−	0.0760178i
$292$	1.15953	−	11.0322i	0.0678566	−	0.645612i
$293$	2.51860	−	7.75146i	0.147138	−	0.452845i	−0.850141	−	0.526554i	$-0.823484\pi$
$293$	2.51860	−	7.75146i	0.147138	−	0.452845i	0.997280	+	0.0737091i	$0.0234836\pi$
$294$	−7.75948	+	0.951050i	−0.452542	+	0.0554664i
$295$	−4.72630	+	3.43386i	−0.275176	+	0.199927i
$296$	2.56618	+	4.44475i	0.149156	+	0.258346i
$297$	−3.23944	−	0.711348i	−0.187971	−	0.0412766i
$298$	6.14783	−	10.6483i	0.356134	−	0.616842i
$299$	−18.1708	−	8.09018i	−1.05085	−	0.467867i
$300$	1.04872	+	3.22764i	0.0605480	+	0.186348i
$301$	30.0621	−	11.8381i	1.73275	−	0.682334i
$302$	2.21014	+	1.60576i	0.127179	+	0.0924010i
$303$	−0.747805	+	7.11489i	−0.0429603	+	0.408740i
$304$	8.35118	+	9.27493i	0.478973	+	0.531954i
$305$	−2.22312	−	0.472539i	−0.127296	−	0.0270575i
$306$	−3.80683	−	1.69491i	−0.217622	−	0.0968915i
$307$	26.3427			1.50346			0.751729	−	0.659472i	$-0.229220\pi$
$307$	26.3427			1.50346			0.751729	+	0.659472i	$0.229220\pi$
$308$	−6.59717	−	0.333178i	−0.375909	−	0.0189846i
$309$	−4.55613			−0.259189
$310$	1.39737	+	0.622147i	0.0793650	+	0.0353356i
$311$	−13.5813	−	2.88680i	−0.770127	−	0.163696i	−0.193940	−	0.981013i	$-0.562127\pi$
$311$	−13.5813	−	2.88680i	−0.770127	−	0.163696i	−0.576187	+	0.817318i	$0.695460\pi$
$312$	7.36573	+	8.18048i	0.417003	+	0.463128i
$313$	0.681133	−	6.48055i	0.0384999	−	0.366302i	−0.958262	−	0.285892i	$-0.907710\pi$
$313$	0.681133	−	6.48055i	0.0384999	−	0.366302i	0.996762	−	0.0804104i	$-0.0256231\pi$
$314$	9.57759	+	6.95853i	0.540495	+	0.392692i
$315$	0.274419	−	1.83483i	0.0154617	−	0.103381i
$316$	1.18270	+	3.63998i	0.0665321	+	0.204765i
$317$	4.24977	+	1.89212i	0.238691	+	0.106272i	0.522596	−	0.852580i	$-0.324963\pi$
$317$	4.24977	+	1.89212i	0.238691	+	0.106272i	−0.283905	+	0.958852i	$0.591630\pi$
$318$	4.19044	−	7.25806i	0.234988	−	0.407012i
$319$	1.18843	+	12.0879i	0.0665391	+	0.676794i
$320$	2.91629	+	5.05117i	0.163026	+	0.282369i
$321$	−4.72956	+	3.43623i	−0.263978	+	0.191792i
$322$	−7.57740	−	14.5599i	−0.422272	−	0.811390i
$323$	7.46488	−	22.9745i	0.415357	−	1.27834i
$324$	0.0786864	−	0.748652i	0.00437147	−	0.0415918i
$325$	14.7470	−	6.56581i	0.818019	−	0.364205i
$326$	−14.8893	−	16.5362i	−0.824641	−	0.915857i
$327$	13.7401	−	15.2599i	0.759827	−	0.843874i
$328$	13.4593	−	9.77878i	0.743167	−	0.539943i
$329$	−8.46027	+	22.6206i	−0.466430	+	1.24711i
$330$	−0.819184	+	2.46471i	−0.0450946	+	0.135678i
$331$	−0.656522	−	1.13713i	−0.0360857	−	0.0625023i	0.847418	−	0.530926i	$-0.178156\pi$
$331$	−0.656522	−	1.13713i	−0.0360857	−	0.0625023i	−0.883504	+	0.468423i	$0.844822\pi$
$332$	0.805069	+	7.65972i	0.0441839	+	0.420382i
$333$	−1.63297	−	0.347098i	−0.0894861	−	0.0190209i
$334$	6.82645	−	1.45101i	0.373527	−	0.0793956i
$335$	−3.27043	−	2.37611i	−0.178683	−	0.129821i
$336$	0.310826	+	5.09094i	0.0169569	+	0.277734i
$337$	1.03602	−	3.18854i	0.0564356	−	0.173691i	−0.918865	−	0.394571i	$-0.870893\pi$
$337$	1.03602	−	3.18854i	0.0564356	−	0.173691i	0.975301	+	0.220881i	$0.0708931\pi$
$338$	−0.133719	+	0.148510i	−0.00727335	+	0.00807787i
$339$	−1.19532	−	11.3727i	−0.0649207	−	0.617679i
$340$	0.984796	−	1.70572i	0.0534081	−	0.0925055i
$341$	3.20132	+	5.63191i	0.173361	+	0.304985i
$342$	−7.23023			−0.390966
$343$	7.97857	−	16.7135i	0.430802	−	0.902446i
$344$	−11.6011	−	35.7046i	−0.625491	−	1.92506i
$345$	3.81011	−	0.809864i	0.205129	−	0.0436016i
$346$	23.6310	−	10.5212i	1.27041	−	0.565622i
$347$	29.0988	−	12.9556i	1.56210	−	0.695493i	0.570085	−	0.821586i	$-0.306910\pi$
$347$	29.0988	−	12.9556i	1.56210	−	0.695493i	0.992018	+	0.126092i	$0.0402436\pi$
$348$	−2.69658	+	0.573176i	−0.144552	+	0.0307255i
$349$	−2.20110	−	6.77428i	−0.117822	−	0.362619i	0.874703	−	0.484659i	$-0.161056\pi$
$349$	−2.20110	−	6.77428i	−0.117822	−	0.362619i	−0.992525	+	0.122040i	$0.961056\pi$
$350$	12.8963	+	3.33668i	0.689334	+	0.178353i
$351$	−3.58065			−0.191121
$352$	−1.47374	+	13.1698i	−0.0785505	+	0.701953i
$353$	4.80505	−	8.32260i	0.255747	−	0.442967i	−0.709351	−	0.704855i	$-0.751012\pi$
$353$	4.80505	−	8.32260i	0.255747	−	0.442967i	0.965098	+	0.261888i	$0.0843452\pi$
$354$	0.972568	+	9.25337i	0.0516914	+	0.491811i
$355$	−0.724048	+	0.804136i	−0.0384285	+	0.0426791i
$356$	3.09638	−	9.52967i	0.164108	−	0.505071i
$357$	8.23279	−	5.44789i	0.435725	−	0.288333i
$358$	1.32878	+	0.965415i	0.0702282	+	0.0510238i
$359$	12.4727	−	2.65116i	0.658286	−	0.139923i	0.133356	−	0.991068i	$-0.457425\pi$
$359$	12.4727	−	2.65116i	0.658286	−	0.139923i	0.524930	+	0.851145i	$0.324091\pi$
$360$	−2.10862	−	0.448201i	−0.111134	−	0.0236222i
$361$	−2.39517	−	22.7886i	−0.126062	−	1.19940i
$362$	−10.3164	−	17.8686i	−0.542219	−	0.939152i
$363$	−8.98527	+	6.34546i	−0.471604	+	0.333050i
$364$	−7.03375	+	1.17627i	−0.368669	+	0.0616532i
$365$	8.35971	−	6.07369i	0.437567	−	0.317911i
$366$	−2.42210	+	2.69001i	−0.126605	+	0.140609i
$367$	−14.1655	−	15.7323i	−0.739431	−	0.821222i	0.249690	−	0.968326i	$-0.419671\pi$
$367$	−14.1655	−	15.7323i	−0.739431	−	0.821222i	−0.989121	+	0.147104i	$0.953005\pi$
$368$	−9.78296	+	4.35565i	−0.509972	+	0.227054i
$369$	−0.565663	+	5.38192i	−0.0294472	+	0.280172i
$370$	−0.403997	+	1.24338i	−0.0210028	+	0.0646400i
$371$	9.16605	+	17.6124i	0.475878	+	0.914393i
$372$	−1.18954	+	0.864254i	−0.0616749	+	0.0448095i
$373$	−9.74084	−	16.8716i	−0.504362	−	0.873580i	−0.999987	−	0.00504375i	$-0.998395\pi$
$373$	−9.74084	−	16.8716i	−0.504362	−	0.873580i	0.495626	−	0.868536i	$-0.334939\pi$
$374$	−12.6633	+	5.53641i	−0.654804	+	0.286281i
$375$	−3.33367	+	5.77409i	−0.172150	+	0.298173i
$376$	25.6365	+	11.4141i	1.32210	+	0.588637i
$377$	4.05218	+	12.4713i	0.208698	+	0.642306i
$378$	−2.31222	−	1.83963i	−0.118928	−	0.0946202i
$379$	4.29651	+	3.12160i	0.220697	+	0.160346i	0.692640	−	0.721283i	$-0.256447\pi$
$379$	4.29651	+	3.12160i	0.220697	+	0.160346i	−0.471943	+	0.881629i	$0.656447\pi$
$380$	0.357215	−	3.39868i	0.0183248	−	0.174349i
$381$	3.07341	+	3.41337i	0.157456	+	0.174872i
$382$	−25.3626	−	5.39099i	−1.29766	−	0.275827i
$383$	17.7556	+	7.90530i	0.907269	+	0.403942i	0.806682	−	0.590986i	$-0.201261\pi$
$383$	17.7556	+	7.90530i	0.907269	+	0.403942i	0.100587	+	0.994928i	$0.467928\pi$
$384$	1.29805			0.0662406
$385$	−3.88136	−	4.77451i	−0.197813	−	0.243332i
$386$	−25.9758			−1.32214
$387$	11.1559	+	4.96693i	0.567086	+	0.252483i
$388$	2.34757	+	0.498991i	0.119180	+	0.0253324i
$389$	24.3605	+	27.0551i	1.23513	+	1.37175i	0.903642	+	0.428288i	$0.140883\pi$
$389$	24.3605	+	27.0551i	1.23513	+	1.37175i	0.331485	+	0.943460i	$0.392450\pi$
$390$	−0.293102	+	2.78868i	−0.0148418	+	0.141210i
$391$	16.7688	+	12.1832i	0.848033	+	0.616132i
$392$	−18.8195	−	10.4371i	−0.950529	−	0.527154i
$393$	1.43722	+	4.42330i	0.0724981	+	0.223126i
$394$	10.4855	+	4.66845i	0.528252	+	0.235193i
$395$	−1.78257	+	3.08751i	−0.0896910	+	0.155349i
$396$	−1.65810	−	1.86657i	−0.0833224	−	0.0937988i
$397$	6.79814	+	11.7747i	0.341189	+	0.590956i	0.984654	−	0.174519i	$-0.0558371\pi$
$397$	6.79814	+	11.7747i	0.341189	+	0.590956i	−0.643465	+	0.765476i	$0.722504\pi$
$398$	−12.4715	+	9.06107i	−0.625140	+	0.454190i
$399$	9.20490	−	14.4454i	0.460821	−	0.723173i
$400$	2.68567	−	8.26564i	0.134283	−	0.413282i
$401$	−2.69495	+	25.6407i	−0.134579	+	1.28044i	0.693758	+	0.720208i	$0.255954\pi$
$401$	−2.69495	+	25.6407i	−0.134579	+	1.28044i	−0.828338	+	0.560229i	$0.810713\pi$
$402$	−5.88166	+	2.61868i	−0.293351	+	0.130608i
$403$	4.67983	+	5.19748i	0.233119	+	0.258905i
$404$	−3.60355	+	4.00214i	−0.179283	+	0.199114i
$405$	0.567294	−	0.412163i	0.0281891	−	0.0204805i
$406$	−3.79067	+	10.1353i	−0.188128	+	0.503005i
$407$	−4.50124	+	3.22436i	−0.223118	+	0.159825i
$408$	−5.73553	−	9.93423i	−0.283951	−	0.491818i
$409$	−0.260958	−	2.48285i	−0.0129035	−	0.122769i	0.986174	−	0.165714i	$-0.0529927\pi$
$409$	−0.260958	−	2.48285i	−0.0129035	−	0.122769i	−0.999077	+	0.0429448i	$0.986326\pi$
$410$	4.14524	+	0.881098i	0.204719	+	0.0435144i
$411$	3.55550	−	0.755745i	0.175380	−	0.0372782i
$412$	−2.77472	−	2.01595i	−0.136701	−	0.0993188i
$413$	−19.7256	−	9.83746i	−0.970633	−	0.484070i
$414$	1.91707	−	5.90013i	0.0942188	−	0.289976i
$415$	−4.80059	+	5.33159i	−0.235651	+	0.261717i
$416$	1.49548	+	14.2286i	0.0733221	+	0.697613i
$417$	−3.48017	+	6.02784i	−0.170425	+	0.295184i
$418$	−16.1651	+	17.7124i	−0.790662	+	0.866340i
$419$	−10.1903			−0.497831			−0.248915	−	0.968525i	$-0.580074\pi$
$419$	−10.1903			−0.497831			−0.248915	+	0.968525i	$0.580074\pi$
$420$	0.978980	−	0.996004i	0.0477694	−	0.0486000i
$421$	−8.82469	−	27.1596i	−0.430089	−	1.32368i	−0.898036	−	0.439922i	$-0.855006\pi$
$421$	−8.82469	−	27.1596i	−0.430089	−	1.32368i	0.467947	−	0.883757i	$-0.344994\pi$
$422$	−14.2270	+	3.02404i	−0.692559	+	0.147208i
$423$	−8.33902	+	3.71277i	−0.405457	+	0.180521i
$424$	21.0761	−	9.38369i	1.02355	−	0.455712i
$425$	−16.4542	+	3.49746i	−0.798148	+	0.169652i
$426$	0.532550	+	1.63902i	0.0258021	+	0.0794108i
$427$	−2.29080	−	8.26382i	−0.110860	−	0.399915i
$428$	−4.40077			−0.212719
$429$	−8.00550	+	8.77175i	−0.386509	+	0.423504i
$430$	4.78153	−	8.28186i	0.230586	−	0.399387i
$431$	0.300802	+	2.86194i	0.0144891	+	0.137855i	0.999375	−	0.0353498i	$-0.0112545\pi$
$431$	0.300802	+	2.86194i	0.0144891	+	0.137855i	−0.984886	+	0.173204i	$0.944588\pi$
$432$	−1.28994	+	1.43262i	−0.0620621	+	0.0689269i
$433$	−8.03123	+	24.7176i	−0.385956	+	1.18785i	0.549828	+	0.835278i	$0.314693\pi$
$433$	−8.03123	+	24.7176i	−0.385956	+	1.18785i	−0.935784	+	0.352574i	$0.885307\pi$
$434$	0.351714	+	5.76064i	0.0168828	+	0.276520i
$435$	−2.07755	−	1.50943i	−0.0996110	−	0.0723716i
$436$	15.1199	−	3.21382i	0.724110	−	0.153914i
$437$	35.1777	+	7.47725i	1.68278	+	0.357685i
$438$	−1.72024	−	16.3670i	−0.0821965	−	0.782047i
$439$	−10.2932	−	17.8283i	−0.491267	−	0.850899i	0.508683	−	0.860954i	$-0.330133\pi$
$439$	−10.2932	−	17.8283i	−0.491267	−	0.850899i	−0.999949	+	0.0100552i	$0.996799\pi$
$440$	−5.81236	+	4.16355i	−0.277094	+	0.198489i
$441$	6.61912	−	2.27755i	0.315196	−	0.108455i
$442$	−12.0713	+	8.77028i	−0.574171	+	0.417160i
$443$	−8.52874	+	9.47213i	−0.405213	+	0.450034i	−0.910866	−	0.412703i	$-0.864585\pi$
$443$	−8.52874	+	9.47213i	−0.405213	+	0.450034i	0.505653	+	0.862737i	$0.331252\pi$
$444$	−0.840910	−	0.933925i	−0.0399078	−	0.0443221i
$445$	8.52681	−	3.79638i	0.404210	−	0.179966i
$446$	−0.353990	+	3.36799i	−0.0167619	+	0.159479i
$447$	−3.40221	+	10.4709i	−0.160919	+	0.495258i
$448$	−11.8263	+	18.5592i	−0.558741	+	0.876840i
$449$	6.71321	−	4.87743i	0.316816	−	0.230180i	−0.418000	−	0.908447i	$-0.637269\pi$
$449$	6.71321	−	4.87743i	0.316816	−	0.230180i	0.734816	+	0.678267i	$0.237269\pi$
$450$	2.51742	+	4.36029i	0.118672	+	0.205546i
$451$	11.9197	+	13.4185i	0.561279	+	0.631850i
$452$	4.30412	−	7.45495i	0.202449	−	0.350651i
$453$	−2.23470	−	0.994953i	−0.104995	−	0.0467470i
$454$	−3.06684	−	9.43875i	−0.143934	−	0.442983i
$455$	−5.19839	−	4.13590i	−0.243704	−	0.193894i
$456$	−16.1020	−	11.6988i	−0.754047	−	0.547847i
$457$	−0.284862	+	2.71028i	−0.0133253	+	0.126782i	−0.999162	−	0.0409251i	$-0.986969\pi$
$457$	−0.284862	+	2.71028i	−0.0133253	+	0.126782i	0.985837	+	0.167707i	$0.0536362\pi$
$458$	−7.36255	−	8.17694i	−0.344029	−	0.382083i
$459$	3.64977	+	0.775782i	0.170356	+	0.0362104i
$460$	2.67873	+	1.19265i	0.124896	+	0.0556075i
$461$	−1.65195			−0.0769390			−0.0384695	−	0.999260i	$-0.512248\pi$
$461$	−1.65195			−0.0769390			−0.0384695	+	0.999260i	$0.512248\pi$
$462$	−9.67623	+	1.55141i	−0.450179	+	0.0721782i
$463$	6.81764			0.316842			0.158421	−	0.987372i	$-0.449360\pi$
$463$	6.81764			0.316842			0.158421	+	0.987372i	$0.449360\pi$
$464$	6.44958	+	2.87154i	0.299414	+	0.133308i
$465$	−1.33971	−	0.284765i	−0.0621277	−	0.0132057i
$466$	14.4700	+	16.0705i	0.670308	+	0.744453i
$467$	3.56213	−	33.8914i	0.164836	−	1.56831i	−0.529281	−	0.848447i	$-0.677538\pi$
$467$	3.56213	−	33.8914i	0.164836	−	1.56831i	0.694117	−	0.719862i	$-0.255795\pi$
$468$	−2.18065	−	1.58433i	−0.100800	−	0.0732357i
$469$	2.25611	−	15.0849i	0.104178	−	0.696556i
$470$	2.20897	+	6.79851i	0.101892	+	0.313592i
$471$	−9.68404	−	4.31161i	−0.446217	−	0.198669i
$472$	−12.8064	+	22.1813i	−0.589461	+	1.02098i
$473$	37.1098	−	16.2244i	1.70631	−	0.746001i
$474$	2.83903	+	4.91734i	0.130401	+	0.225861i
$475$	−23.6130	+	17.1558i	−1.08344	+	0.787163i
$476$	7.42437	+	0.324955i	0.340295	+	0.0148943i
$477$	−2.31899	+	7.13713i	−0.106179	+	0.326787i
$478$	1.14977	−	10.9393i	0.0525893	−	0.500354i
$479$	19.3374	−	8.60956i	0.883547	−	0.393381i	0.0857574	−	0.996316i	$-0.472669\pi$
$479$	19.3374	−	8.60956i	0.883547	−	0.393381i	0.797790	+	0.602935i	$0.206002\pi$
$480$	−1.87476	−	2.08213i	−0.0855708	−	0.0950360i
$481$	−3.99987	+	4.44231i	−0.182379	+	0.202552i
$482$	16.3150	−	11.8536i	0.743130	−	0.539916i
$483$	9.34729	+	11.3417i	0.425317	+	0.516063i
$484$	−8.27978	−	0.111279i	−0.376354	−	0.00505812i
$485$	1.11781	+	1.93611i	0.0507572	+	0.0879141i
$486$	−0.116737	−	1.11067i	−0.00529528	−	0.0503812i
$487$	−3.01124	−	0.640059i	−0.136452	−	0.0290038i	0.139179	−	0.990267i	$-0.455554\pi$
$487$	−3.01124	−	0.640059i	−0.136452	−	0.0290038i	−0.275632	+	0.961263i	$0.588887\pi$
$488$	−9.74667	+	2.07172i	−0.441211	+	0.0937823i
$489$	16.1194	+	11.7114i	0.728943	+	0.529608i
$490$	−1.23198	−	5.34154i	−0.0556552	−	0.241306i
$491$	−5.20970	+	16.0338i	−0.235110	+	0.723596i	0.761996	+	0.647581i	$0.224219\pi$
$491$	−5.20970	+	16.0338i	−0.235110	+	0.723596i	−0.997107	+	0.0760142i	$0.975781\pi$
$492$	−2.72583	+	3.02734i	−0.122890	+	0.136483i
$493$	−1.42836	−	13.5900i	−0.0643303	−	0.612062i
$494$	−12.9445	+	22.4205i	−0.582399	+	1.00875i
$495$	0.258634	−	2.31124i	0.0116247	−	0.103882i
$496$	3.76543			0.169073
$497$	−3.95261	−	1.02267i	−0.177299	−	0.0458730i
$498$	3.53092	+	10.8671i	0.158224	+	0.486964i
$499$	−33.7833	+	7.18086i	−1.51235	+	0.321459i	−0.888057	−	0.459733i	$-0.847945\pi$
$499$	−33.7833	+	7.18086i	−1.51235	+	0.321459i	−0.624290	+	0.781192i	$0.714612\pi$
$500$	−4.58510	+	2.04142i	−0.205052	+	0.0912950i
$501$	−5.70885	+	2.54174i	−0.255053	+	0.113557i
$502$	0.162967	−	0.0346397i	0.00727357	−	0.00154605i
$503$	−9.04217	−	27.8289i	−0.403170	−	1.24083i	−0.922413	−	0.386204i	$-0.873786\pi$
$503$	−9.04217	−	27.8289i	−0.403170	−	1.24083i	0.519243	−	0.854627i	$-0.326214\pi$
$504$	−2.17281	−	7.83819i	−0.0967848	−	0.349141i
$505$	−5.01654			−0.223233
$506$	−10.1678	−	17.8877i	−0.452014	−	0.795204i
$507$	0.0894704	−	0.154967i	0.00397352	−	0.00688234i
$508$	0.361418	+	3.43866i	0.0160353	+	0.152566i
$509$	−18.9212	+	21.0141i	−0.838668	+	0.931435i	−0.998447	−	0.0557181i	$-0.982255\pi$
$509$	−18.9212	+	21.0141i	−0.838668	+	0.931435i	0.159779	+	0.987153i	$0.448922\pi$
$510$	0.902954	−	2.77901i	0.0399835	−	0.123056i
$511$	34.8899	+	17.4002i	1.54344	+	0.769738i
$512$	15.8209	+	11.4946i	0.699193	+	0.507993i
$513$	6.33263	−	1.34604i	0.279593	−	0.0594292i
$514$	−23.5488	−	5.00545i	−1.03869	−	0.220781i
$515$	−0.333950	−	3.17732i	−0.0147156	−	0.140009i
$516$	4.59632	+	7.96105i	0.202342	+	0.350466i
$517$	−9.54869	+	28.7295i	−0.419951	+	1.26352i
$518$	−4.86525	+	0.813626i	−0.213767	+	0.0357487i
$519$	−18.7386	+	13.6144i	−0.822532	+	0.597604i
$520$	−5.16495	+	5.73626i	−0.226498	+	0.251552i
$521$	−9.69060	−	10.7625i	−0.424553	−	0.471514i	0.492481	−	0.870323i	$-0.336090\pi$
$521$	−9.69060	−	10.7625i	−0.424553	−	0.471514i	−0.917034	+	0.398809i	$0.869424\pi$
$522$	−3.73634	+	1.66353i	−0.163535	+	0.0728106i
$523$	−3.02024	+	28.7357i	−0.132066	+	1.25652i	0.704915	+	0.709292i	$0.250985\pi$
$523$	−3.02024	+	28.7357i	−0.132066	+	1.25652i	−0.836981	+	0.547233i	$0.815681\pi$
$524$	−1.08190	+	3.32975i	−0.0472631	+	0.145461i
$525$	−11.9164	−	0.521566i	−0.520076	−	0.0227630i
$526$	−14.1229	+	10.2609i	−0.615787	+	0.447395i
$527$	−3.64408	−	6.31173i	−0.158739	−	0.274943i
$528$	0.625584	+	6.36304i	0.0272250	+	0.276916i
$529$	−3.92893	+	6.80511i	−0.170823	+	0.295874i
$530$	5.36871	+	2.39031i	0.233202	+	0.103828i
$531$	−2.57451	−	7.92354i	−0.111724	−	0.343852i
$532$	11.9975	−	4.72445i	0.520158	−	0.204831i
$533$	15.6763	+	11.3895i	0.679014	+	0.493333i
$534$	1.55386	−	14.7840i	0.0672423	−	0.639768i
$535$	−2.74299	−	3.04640i	−0.118590	−	0.131707i
$536$	−17.3358	−	3.68485i	−0.748794	−	0.159161i
$537$	−1.34355	−	0.598186i	−0.0579784	−	0.0258136i
$538$	−12.2519			−0.528216
$539$	9.21934	−	21.3074i	0.397105	−	0.917773i
$540$	0.527856			0.0227153
$541$	−18.3577	−	8.17338i	−0.789260	−	0.351401i	−0.0278001	−	0.999614i	$-0.508850\pi$
$541$	−18.3577	−	8.17338i	−0.789260	−	0.351401i	−0.761460	+	0.648212i	$0.775517\pi$
$542$	−8.02568	−	1.70591i	−0.344733	−	0.0732752i
$543$	12.3623	+	13.7297i	0.530515	+	0.589197i
$544$	1.55840	−	14.8272i	0.0668160	−	0.635712i
$545$	11.6489	+	8.46344i	0.498985	+	0.362534i
$546$	−9.84418	+	3.87650i	−0.421292	+	0.165899i
$547$	−0.352528	−	1.08497i	−0.0150730	−	0.0463900i	0.943237	−	0.332120i	$-0.107764\pi$
$547$	−0.352528	−	1.08497i	−0.0150730	−	0.0463900i	−0.958310	+	0.285730i	$0.907764\pi$
$548$	2.49972	+	1.11295i	0.106783	+	0.0475428i
$549$	1.62061	−	2.80698i	0.0691660	−	0.119799i
$550$	16.3101	+	3.58152i	0.695463	+	0.152717i
$551$	−11.8548	−	20.5331i	−0.505031	−	0.874740i
$552$	13.8160	−	10.0379i	0.588050	−	0.427243i
$553$	−13.4388	−	0.588199i	−0.571476	−	0.0250127i
$554$	5.66304	−	17.4290i	0.240600	−	0.740489i
$555$	0.122365	−	1.16423i	0.00519412	−	0.0494187i
$556$	−4.78659	+	2.13113i	−0.202997	+	0.0903800i
$557$	−21.4783	−	23.8541i	−0.910065	−	1.01073i	−0.999891	−	0.0147717i	$-0.995298\pi$
$557$	−21.4783	−	23.8541i	−0.910065	−	1.01073i	0.0898263	−	0.995957i	$-0.471369\pi$
$558$	−1.45962	+	1.62107i	−0.0617907	+	0.0686256i
$559$	35.3748	−	25.7013i	1.49620	−	1.08705i
$560$	−3.52750	+	0.589911i	−0.149064	+	0.0249283i
$561$	10.0605	−	7.20660i	0.424755	−	0.304263i
$562$	−5.45483	−	9.44805i	−0.230098	−	0.398542i
$563$	2.34070	+	22.2702i	0.0986486	+	0.938579i	0.926160	+	0.377130i	$0.123089\pi$
$563$	2.34070	+	22.2702i	0.0986486	+	0.938579i	−0.827512	+	0.561448i	$0.810244\pi$
$564$	−6.72132	−	1.42866i	−0.283019	−	0.0601575i
$565$	7.84338	−	1.66716i	0.329973	−	0.0701380i
$566$	24.1740	+	17.5635i	1.01611	+	0.738248i
$567$	2.36765	+	1.18078i	0.0994318	+	0.0495882i
$568$	−1.46599	+	4.51186i	−0.0615116	+	0.189313i
$569$	5.78841	−	6.42869i	0.242663	−	0.269505i	−0.609494	−	0.792791i	$-0.708627\pi$
$569$	5.78841	−	6.42869i	0.242663	−	0.269505i	0.852157	+	0.523286i	$0.175294\pi$
$570$	−0.529953	−	5.04216i	−0.0221973	−	0.211193i
$571$	−23.3636	+	40.4670i	−0.977736	+	1.69349i	−0.307144	+	0.951663i	$0.599373\pi$
$571$	−23.3636	+	40.4670i	−0.977736	+	1.69349i	−0.670592	+	0.741826i	$0.733960\pi$
$572$	−8.75665	+	1.79987i	−0.366134	+	0.0752564i
$573$	23.2176			0.969929
$574$	4.27144	+	15.4088i	0.178287	+	0.643149i
$575$	−7.73888	−	23.8178i	−0.322734	−	0.993272i
$576$	−8.13608	+	1.72938i	−0.339003	+	0.0720574i
$577$	10.3877	−	4.62490i	0.432445	−	0.192537i	−0.178957	−	0.983857i	$-0.557272\pi$
$577$	10.3877	−	4.62490i	0.432445	−	0.192537i	0.611402	+	0.791320i	$0.290606\pi$
$578$	−3.13966	+	1.39787i	−0.130593	+	0.0581436i
$579$	22.7511	−	4.83589i	0.945502	−	0.200973i
$580$	−0.597368	−	1.83851i	−0.0248044	−	0.0763400i
$581$	−26.2067	−	6.78051i	−1.08724	−	0.281303i
$582$	3.56058			0.147591
$583$	12.2996	+	21.6380i	0.509396	+	0.896153i
$584$	22.6515	−	39.2335i	0.937325	−	1.62349i
$585$	−0.262450	−	2.49705i	−0.0108510	−	0.103240i
$586$	6.09061	−	6.76430i	0.251601	−	0.279431i
$587$	−2.56089	+	7.88162i	−0.105699	+	0.325309i	−0.989894	−	0.141810i	$-0.954708\pi$
$587$	−2.56089	+	7.88162i	−0.105699	+	0.325309i	0.884195	+	0.467119i	$0.154708\pi$
$588$	5.03885	+	1.54172i	0.207799	+	0.0635793i
$589$	−10.2305	−	7.43286i	−0.421539	−	0.306266i
$590$	−6.38175	+	1.35648i	−0.262733	+	0.0558456i
$591$	−10.0529	−	2.13681i	−0.413521	−	0.0878966i
$592$	0.336407	+	3.20070i	0.0138262	+	0.131548i
$593$	3.34659	+	5.79646i	0.137428	+	0.238032i	0.926522	−	0.376240i	$-0.122783\pi$
$593$	3.34659	+	5.79646i	0.137428	+	0.238032i	−0.789094	+	0.614272i	$0.789450\pi$
$594$	−2.98189	−	2.19723i	−0.122348	−	0.0901535i
$595$	4.40265	+	5.34201i	0.180491	+	0.219001i
$596$	−6.70505	+	4.87151i	−0.274650	+	0.199545i
$597$	9.23633	−	10.2580i	0.378018	−	0.419831i
$598$	−14.8637	−	16.5079i	−0.607824	−	0.675056i
$599$	31.5802	−	14.0604i	1.29033	−	0.574494i	0.357202	−	0.934027i	$-0.383731\pi$
$599$	31.5802	−	14.0604i	1.29033	−	0.574494i	0.933132	+	0.359534i	$0.117064\pi$
$600$	−1.44874	+	13.7838i	−0.0591446	+	0.562723i
$601$	0.373342	−	1.14903i	0.0152289	−	0.0468698i	−0.943153	−	0.332358i	$-0.892156\pi$
$601$	0.373342	−	1.14903i	0.0152289	−	0.0468698i	0.958382	+	0.285488i	$0.0921558\pi$
$602$	36.0479	+	1.57777i	1.46920	+	0.0643051i
$603$	4.66396	−	3.38857i	0.189931	−	0.137993i
$604$	−0.920714	−	1.59472i	−0.0374633	−	0.0648884i
$605$	−5.08374	−	5.80098i	−0.206683	−	0.235843i
$606$	−3.99481	+	6.91921i	−0.162278	+	0.281074i
$607$	18.5220	+	8.24654i	0.751786	+	0.334717i	0.746603	−	0.665270i	$-0.231683\pi$
$607$	18.5220	+	8.24654i	0.751786	+	0.334717i	0.00518310	+	0.999987i	$0.498350\pi$
$608$	−7.99369	−	24.6021i	−0.324187	−	0.997745i
$609$	1.43320	−	9.58273i	0.0580763	−	0.388312i
$610$	−2.05347	−	1.49194i	−0.0831427	−	0.0604067i
$611$	−3.41650	+	32.5058i	−0.138217	+	1.31504i
$612$	1.87948	+	2.08737i	0.0759733	+	0.0843769i
$613$	−8.05817	−	1.71282i	−0.325467	−	0.0691800i	0.0422809	−	0.999106i	$-0.486538\pi$
$613$	−8.05817	−	1.71282i	−0.325467	−	0.0691800i	−0.367747	+	0.929926i	$0.619871\pi$
$614$	26.8759	+	11.9659i	1.08462	+	0.482905i
$615$	−3.79466			−0.153016
$616$	−24.0596	−	12.2015i	−0.969390	−	0.491611i
$617$	1.43589			0.0578068			0.0289034	−	0.999582i	$-0.490798\pi$
$617$	1.43589			0.0578068			0.0289034	+	0.999582i	$0.490798\pi$
$618$	−4.64835	−	2.06958i	−0.186984	−	0.0832506i
$619$	−37.4688	−	7.96425i	−1.50600	−	0.320110i	−0.620298	−	0.784366i	$-0.712989\pi$
$619$	−37.4688	−	7.96425i	−1.50600	−	0.320110i	−0.885701	+	0.464256i	$0.846322\pi$
$620$	−0.689896	−	0.766208i	−0.0277069	−	0.0307716i
$621$	−0.580654	+	5.52455i	−0.0233008	+	0.221693i
$622$	−12.5449	−	9.11443i	−0.503006	−	0.365455i
$623$	27.5589	+	21.9262i	1.10413	+	0.878455i
$624$	2.13305	+	6.56486i	0.0853904	+	0.262805i
$625$	16.3216	+	7.26686i	0.652866	+	0.290675i
$626$	3.63864	−	6.30232i	0.145429	−	0.251891i
$627$	10.8608	−	18.5229i	0.433739	−	0.739733i
$628$	−3.98990	−	6.91071i	−0.159214	−	0.275767i
$629$	5.03955	−	3.66145i	0.200940	−	0.145991i
$630$	1.11343	−	1.74731i	0.0443600	−	0.0696147i
$631$	−1.02994	+	3.16983i	−0.0410013	+	0.126189i	−0.969462	−	0.245242i	$-0.921133\pi$
$631$	−1.02994	+	3.16983i	−0.0410013	+	0.126189i	0.928461	+	0.371431i	$0.121133\pi$
$632$	−1.63382	+	15.5448i	−0.0649900	+	0.618338i
$633$	11.8978	−	5.29724i	0.472895	−	0.210546i
$634$	3.47631	+	3.86084i	0.138062	+	0.153333i
$635$	−2.15512	+	2.39350i	−0.0855232	+	0.0949831i
$636$	−4.57026	+	3.32048i	−0.181222	+	0.131666i
$637$	4.78783	−	24.6030i	0.189701	−	0.974807i
$638$	−4.27834	+	12.8724i	−0.169381	+	0.509624i
$639$	−0.771571	−	1.33640i	−0.0305229	−	0.0528672i
$640$	0.0951426	+	0.905221i	0.00376084	+	0.0357820i
$641$	−38.6477	−	8.21482i	−1.52649	−	0.324466i	−0.633217	−	0.773975i	$-0.718266\pi$
$641$	−38.6477	−	8.21482i	−1.52649	−	0.324466i	−0.893276	+	0.449509i	$0.851599\pi$
$642$	−6.38616	+	1.35742i	−0.252042	+	0.0535731i
$643$	−38.3893	−	27.8914i	−1.51392	−	1.09993i	−0.964398	−	0.264454i	$-0.914808\pi$
$643$	−38.3893	−	27.8914i	−1.51392	−	1.09993i	−0.549526	−	0.835477i	$-0.685192\pi$
$644$	0.674231	+	11.0431i	0.0265684	+	0.435157i
$645$	−2.64611	+	8.14388i	−0.104190	+	0.320665i
$646$	18.0519	−	20.0487i	0.710244	−	0.788806i
$647$	3.98599	+	37.9242i	0.156706	+	1.49095i	0.736637	+	0.676288i	$0.236413\pi$
$647$	3.98599	+	37.9242i	0.156706	+	1.49095i	−0.579932	+	0.814665i	$0.696921\pi$
$648$	1.53714	−	2.66240i	0.0603845	−	0.104589i
$649$	−25.1668	−	11.4082i	−0.987884	−	0.447812i
$650$	18.0280			0.707116
$651$	−1.38050	−	4.98000i	−0.0541061	−	0.195182i
$652$	4.63488	+	14.2647i	0.181516	+	0.558648i
$653$	34.7208	−	7.38014i	1.35873	−	0.288807i	0.529783	−	0.848133i	$-0.322273\pi$
$653$	34.7208	−	7.38014i	1.35873	−	0.288807i	0.828948	+	0.559326i	$0.188940\pi$
$654$	20.9498	−	9.32746i	0.819203	−	0.364733i
$655$	−2.97935	+	1.32649i	−0.116413	+	0.0518302i
$656$	10.2043	−	2.16900i	0.398412	−	0.0846851i
$657$	4.55371	+	14.0149i	0.177657	+	0.546773i
$658$	−18.9067	+	19.2354i	−0.737059	+	0.749876i
$659$	39.1773			1.52613			0.763065	−	0.646321i	$-0.223693\pi$
$659$	39.1773			1.52613			0.763065	+	0.646321i	$0.223693\pi$
$660$	1.18016	−	1.29312i	0.0459378	−	0.0503348i
$661$	−7.77398	+	13.4649i	−0.302373	+	0.523725i	−0.976673	−	0.214733i	$-0.931112\pi$
$661$	−7.77398	+	13.4649i	−0.302373	+	0.523725i	0.674300	+	0.738457i	$0.264445\pi$
$662$	−0.153280	−	1.45836i	−0.00595741	−	0.0566810i
$663$	8.93992	−	9.92878i	0.347198	−	0.385602i
$664$	−9.71983	+	29.9145i	−0.377202	+	1.16091i
$665$	10.7485	+	5.36044i	0.416808	+	0.207869i
$666$	−1.50835	−	1.09588i	−0.0584475	−	0.0424646i
$667$	19.8990	−	4.22966i	0.770493	−	0.163773i
$668$	−4.60138	−	0.978054i	−0.178033	−	0.0378420i
$669$	−0.316971	−	3.01577i	−0.0122548	−	0.116597i
$670$	−2.25730	−	3.90977i	−0.0872073	−	0.151047i
$671$	−3.25313	−	10.2459i	−0.125586	−	0.395537i
$672$	3.70326	−	9.90157i	0.142856	−	0.381961i
$673$	−18.8644	+	13.7058i	−0.727171	+	0.528321i	−0.888667	−	0.458553i	$-0.848368\pi$
$673$	−18.8644	+	13.7058i	−0.727171	+	0.528321i	0.161496	+	0.986873i	$0.448368\pi$
$674$	2.50535	−	2.78248i	0.0965026	−	0.107177i
$675$	−3.01664	−	3.35032i	−0.116111	−	0.128954i
$676$	0.123057	−	0.0547884i	0.00473295	−	0.00210724i
$677$	3.31217	−	31.5132i	0.127297	−	1.21115i	−0.725244	−	0.688492i	$-0.758273\pi$
$677$	3.31217	−	31.5132i	0.127297	−	1.21115i	0.852541	−	0.522660i	$-0.175060\pi$
$678$	3.94642	−	12.1458i	0.151561	−	0.466458i
$679$	−4.53302	+	7.11372i	−0.173961	+	0.273000i
$680$	6.50746	−	4.72795i	0.249550	−	0.181309i
$681$	4.44330	+	7.69603i	0.170268	+	0.294912i
$682$	0.707877	+	7.20008i	0.0271060	+	0.275705i
$683$	−3.76735	+	6.52524i	−0.144154	+	0.249681i	−0.929057	−	0.369937i	$-0.879379\pi$
$683$	−3.76735	+	6.52524i	−0.144154	+	0.249681i	0.784903	+	0.619618i	$0.212713\pi$
$684$	4.45221	+	1.98225i	0.170234	+	0.0757933i
$685$	0.787643	+	2.42412i	0.0300943	+	0.0926207i
$686$	15.7320	−	13.4276i	0.600651	−	0.512670i
$687$	7.97081	+	5.79113i	0.304105	+	0.220946i
$688$	2.46074	−	23.4124i	0.0938149	−	0.892590i
$689$	17.9800	+	19.9688i	0.684984	+	0.760752i
$690$	4.25510	+	0.904450i	0.161989	+	0.0344318i
$691$	26.0196	+	11.5847i	0.989832	+	0.440701i	0.836793	−	0.547519i	$-0.184428\pi$
$691$	26.0196	+	11.5847i	0.989832	+	0.440701i	0.153038	+	0.988220i	$0.451094\pi$
$692$	−17.4359			−0.662813
$693$	8.18615	−	3.16022i	0.310966	−	0.120047i
$694$	35.5727			1.35032
$695$	−4.45873	−	1.98516i	−0.169129	−	0.0753012i
$696$	−11.0126	−	2.34081i	−0.417433	−	0.0887282i
$697$	−13.5112	−	15.0057i	−0.511774	−	0.568382i
$698$	0.831502	−	7.91122i	0.0314728	−	0.299444i
$699$	−15.6654	−	11.3816i	−0.592521	−	0.430491i
$700$	−7.02642	−	5.59030i	−0.265574	−	0.211294i
$701$	8.37757	+	25.7835i	0.316416	+	0.973830i	0.975167	+	0.221469i	$0.0710851\pi$
$701$	8.37757	+	25.7835i	0.316416	+	0.973830i	−0.658751	+	0.752361i	$0.728915\pi$
$702$	−3.65312	−	1.62648i	−0.137878	−	0.0613874i
$703$	5.40410	−	9.36018i	0.203819	−	0.353026i
$704$	−13.9538	+	23.7980i	−0.525904	+	0.896919i
$705$	−3.20041	−	5.54327i	−0.120534	−	0.208771i
$706$	8.68277	−	6.30840i	0.326780	−	0.237420i
$707$	−8.73813	−	16.7902i	−0.328631	−	0.631461i
$708$	1.93803	−	5.96465i	0.0728357	−	0.224165i
$709$	2.82952	−	26.9211i	0.106265	−	1.01104i	−0.803326	−	0.595539i	$-0.796938\pi$
$709$	2.82952	−	26.9211i	0.106265	−	1.01104i	0.909591	−	0.415505i	$-0.136395\pi$
$710$	−1.10397	+	0.491521i	−0.0414314	+	0.0184464i
$711$	−3.40203	−	3.77834i	−0.127586	−	0.141699i
$712$	27.3817	−	30.4104i	1.02617	−	1.13968i
$713$	8.77804	−	6.37762i	0.328740	−	0.238844i
$714$	10.8741	−	1.81849i	0.406952	−	0.0680554i
$715$	−6.70395	−	4.93987i	−0.250714	−	0.184741i
$716$	−0.553552	−	0.958781i	−0.0206872	−	0.0358313i
$717$	1.02953	+	9.79533i	0.0384485	+	0.365813i
$718$	13.9295	+	2.96080i	0.519843	+	0.110496i
$719$	−46.2101	+	9.82226i	−1.72335	+	0.366309i	−0.960069	−	0.279762i	$-0.909744\pi$
$719$	−46.2101	+	9.82226i	−1.72335	+	0.366309i	−0.763277	+	0.646071i	$0.776411\pi$
$720$	−1.09362	−	0.794559i	−0.0407567	−	0.0296115i
$721$	10.0527	−	6.65218i	0.374382	−	0.247740i
$722$	7.90783	−	24.3378i	0.294299	−	0.905759i
$723$	−12.0828	+	13.4194i	−0.449366	+	0.499071i
$724$	1.45374	+	13.8314i	0.0540278	+	0.514041i
$725$	−8.25519	+	14.2984i	−0.306590	+	0.531029i
$726$	−12.0495	+	2.39242i	−0.447199	+	0.0887912i
$727$	−33.2506			−1.23319			−0.616597	−	0.787279i	$-0.711489\pi$
$727$	−33.2506			−1.23319			−0.616597	+	0.787279i	$0.711489\pi$
$728$	−28.1957	−	7.29515i	−1.04500	−	0.270376i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	11.2878	−	2.39930i	0.417781	−	0.0888021i
$731$	−41.6261	+	18.5331i	−1.53960	+	0.685472i
$732$	2.22897	−	0.992401i	0.0823851	−	0.0366802i
$733$	29.2593	−	6.21926i	1.08072	−	0.229714i	0.367052	−	0.930200i	$-0.380367\pi$
$733$	29.2593	−	6.21926i	1.08072	−	0.229714i	0.713665	+	0.700487i	$0.247034\pi$
$734$	−7.30592	−	22.4853i	−0.269666	−	0.829947i
$735$	2.07346	+	4.44905i	0.0764808	+	0.164106i
$736$	22.1957			0.818143
$737$	2.12634	−	19.0017i	0.0783247	−	0.699935i
$738$	−3.02180	+	5.23391i	−0.111234	+	0.192663i
$739$	0.460340	+	4.37984i	0.0169339	+	0.161115i	0.999721	−	0.0236274i	$-0.00752153\pi$
$739$	0.460340	+	4.37984i	0.0169339	+	0.161115i	−0.982787	+	0.184743i	$0.940855\pi$
$740$	0.589658	−	0.654881i	0.0216762	−	0.0240739i
$741$	7.16348	−	22.0469i	0.263157	−	0.809915i
$742$	1.35129	+	22.1325i	0.0496076	+	0.812510i
$743$	25.2372	+	18.3359i	0.925862	+	0.672678i	0.944976	−	0.327139i	$-0.106085\pi$
$743$	25.2372	+	18.3359i	0.925862	+	0.672678i	−0.0191142	+	0.999817i	$0.506085\pi$
$744$	−5.87361	+	1.24847i	−0.215337	+	0.0457713i
$745$	−7.55151	−	1.60512i	−0.276666	−	0.0588072i
$746$	−2.27422	−	21.6378i	−0.0832653	−	0.792216i
$747$	−5.11568	−	8.86061i	−0.187173	−	0.324193i
$748$	9.31564	+	0.0625973i	0.340613	+	0.00228878i
$749$	5.41829	−	14.4871i	0.197980	−	0.529348i
$750$	−6.02397	+	4.37667i	−0.219964	+	0.159814i
$751$	12.8922	−	14.3182i	0.470442	−	0.522479i	−0.460493	−	0.887663i	$-0.652327\pi$
$751$	12.8922	−	14.3182i	0.470442	−	0.522479i	0.930935	+	0.365184i	$0.118994\pi$
$752$	11.7748	+	13.0772i	0.429382	+	0.476877i
$753$	−0.136287	+	0.0606787i	−0.00496656	+	0.00221125i
$754$	−1.53078	+	14.5644i	−0.0557477	+	0.530404i
$755$	0.530056	−	1.63135i	0.0192907	−	0.0593707i
$756$	0.919455	+	1.76672i	0.0334402	+	0.0642550i
$757$	10.3603	−	7.52718i	0.376551	−	0.273580i	−0.383371	−	0.923594i	$-0.625237\pi$
$757$	10.3603	−	7.52718i	0.376551	−	0.273580i	0.759922	+	0.650014i	$0.225237\pi$
$758$	2.96552	+	5.13643i	0.107712	+	0.186563i
$759$	12.2357	+	13.7741i	0.444126	+	0.499967i
$760$	6.97820	−	12.0866i	0.253126	−	0.438427i
$761$	−8.70253	−	3.87462i	−0.315467	−	0.140455i	0.242895	−	0.970053i	$-0.421903\pi$
$761$	−8.70253	−	3.87462i	−0.315467	−	0.140455i	−0.558361	+	0.829598i	$0.688570\pi$
$762$	1.58513	+	4.87852i	0.0574231	+	0.176730i
$763$	−8.03602	+	53.7308i	−0.290924	+	1.94518i
$764$	14.1397	+	10.2731i	0.511557	+	0.371668i
$765$	−0.273493	+	2.60211i	−0.00988814	+	0.0940794i
$766$	14.5241	+	16.1306i	0.524776	+	0.582823i
$767$	−29.1796	−	6.20232i	−1.05361	−	0.223953i
$768$	−13.8731	−	6.17672i	−0.500604	−	0.222883i
$769$	−28.4799			−1.02701			−0.513505	−	0.858087i	$-0.671653\pi$
$769$	−28.4799			−1.02701			−0.513505	+	0.858087i	$0.671653\pi$
$770$	−1.79115	−	6.63422i	−0.0645485	−	0.239081i
$771$	21.5572			0.776362
$772$	15.9953	+	7.12157i	0.575684	+	0.256311i
$773$	−19.6061	−	4.16740i	−0.705182	−	0.149891i	−0.158657	−	0.987334i	$-0.550716\pi$
$773$	−19.6061	−	4.16740i	−0.705182	−	0.149891i	−0.546525	+	0.837443i	$0.684050\pi$
$774$	9.12552	+	10.1349i	0.328010	+	0.364292i
$775$	−0.920459	+	8.75758i	−0.0330639	+	0.314582i
$776$	7.92956	+	5.76116i	0.284655	+	0.206814i
$777$	4.10978	−	1.61838i	0.147438	−	0.0580589i
$778$	12.5641	+	38.6682i	0.450444	+	1.38632i
$779$	−32.0061	−	14.2500i	−1.14674	−	0.510561i
$780$	0.945034	−	1.63685i	0.0338377	−	0.0586086i
$781$	−4.99892	−	1.09771i	−0.178875	−	0.0392792i
$782$	11.5741	+	20.0469i	0.413888	+	0.716874i
$783$	2.96280	−	2.15260i	0.105882	−	0.0769275i
$784$	−8.11885	−	10.7789i	−0.289959	−	0.384960i
$785$	2.29699	−	7.06941i	0.0819831	−	0.252318i
$786$	−0.542934	+	5.16567i	−0.0193658	+	0.184254i
$787$	5.07134	−	2.25790i	0.180774	−	0.0804856i	−0.314354	−	0.949306i	$-0.601788\pi$
$787$	5.07134	−	2.25790i	0.180774	−	0.0804856i	0.495128	+	0.868820i	$0.335121\pi$
$788$	−5.17682	−	5.74944i	−0.184417	−	0.204815i
$789$	10.4593	−	11.6163i	0.372362	−	0.413550i
$790$	−3.22112	+	2.34028i	−0.114602	+	0.0832636i
$791$	19.2421	+	23.3476i	0.684169	+	0.830145i
$792$	−3.08558	−	9.71814i	−0.109641	−	0.345319i
$793$	−5.80284	−	10.0508i	−0.206065	−	0.356915i
$794$	1.58718	+	15.1010i	0.0563270	+	0.535916i
$795$	−5.14721	−	1.09407i	−0.182553	−	0.0388028i
$796$	10.1639	−	2.16039i	0.360248	−	0.0765731i
$797$	−27.8522	−	20.2358i	−0.986575	−	0.716789i	−0.0274070	−	0.999624i	$-0.508725\pi$
$797$	−27.8522	−	20.2358i	−0.986575	−	0.716789i	−0.959168	+	0.282835i	$0.908725\pi$
$798$	15.9529	−	10.5565i	0.564726	−	0.373696i
$799$	10.5251	−	32.3930i	0.372353	−	1.14598i
$800$	−12.0534	+	13.3866i	−0.426151	+	0.473289i
$801$	1.39136	+	13.2379i	0.0491614	+	0.467740i
$802$	−14.3965	+	24.9355i	−0.508360	+	0.880505i
$803$	44.5142	+	20.1785i	1.57087	+	0.712084i
$804$	4.33973			0.153051
$805$	−7.22423	+	7.34985i	−0.254621	+	0.259048i
$806$	2.41365	+	7.42844i	0.0850171	+	0.261656i
$807$	10.7309	−	2.28091i	0.377744	−	0.0802920i
$808$	−20.0922	+	8.94562i	−0.706840	+	0.314706i
$809$	−9.43347	+	4.20005i	−0.331663	+	0.147666i	−0.565811	−	0.824535i	$-0.691437\pi$
$809$	−9.43347	+	4.20005i	−0.331663	+	0.147666i	0.234148	+	0.972201i	$0.424770\pi$
$810$	0.765997	−	0.162818i	0.0269144	−	0.00572083i
$811$	−11.4662	−	35.2894i	−0.402633	−	1.23918i	−0.922855	−	0.385147i	$-0.874151\pi$
$811$	−11.4662	−	35.2894i	−0.402633	−	1.23918i	0.520222	−	0.854031i	$-0.325849\pi$
$812$	5.11291	−	5.20181i	0.179428	−	0.182548i
$813$	7.34692			0.257668
$814$	−6.05698	+	1.24497i	−0.212297	+	0.0436363i
$815$	−6.98572	+	12.0996i	−0.244699	+	0.423831i
$816$	−0.751886	−	7.15372i	−0.0263213	−	0.250430i
$817$	−52.9012	+	58.7527i	−1.85078	+	2.05550i
$818$	0.861569	−	2.65164i	0.0301240	−	0.0927123i
$819$	7.90039	−	5.22793i	0.276062	−	0.182679i
$820$	−2.31098	−	1.67903i	−0.0807029	−	0.0586341i
$821$	−1.01832	+	0.216451i	−0.0355397	+	0.00755419i	−0.225647	−	0.974209i	$-0.572450\pi$
$821$	−1.01832	+	0.216451i	−0.0355397	+	0.00755419i	0.190108	+	0.981763i	$0.439116\pi$
$822$	3.97076	+	0.844011i	0.138496	+	0.0294382i
$823$	−4.41299	−	41.9868i	−0.153827	−	1.46357i	−0.750387	−	0.660998i	$-0.770133\pi$
$823$	−4.41299	−	41.9868i	−0.153827	−	1.46357i	0.596560	−	0.802568i	$-0.296534\pi$
$824$	−7.00340	−	12.1302i	−0.243975	−	0.422577i
$825$	−14.9520	−	0.100471i	−0.520562	−	0.00349797i
$826$	−15.6563	−	18.9967i	−0.544751	−	0.660981i
$827$	−9.91212	+	7.20158i	−0.344678	+	0.250423i	−0.746633	−	0.665236i	$-0.768331\pi$
$827$	−9.91212	+	7.20158i	−0.344678	+	0.250423i	0.401955	+	0.915659i	$0.368331\pi$
$828$	−2.79807	+	3.10758i	−0.0972398	+	0.107996i
$829$	−13.1384	−	14.5916i	−0.456314	−	0.506788i	0.470453	−	0.882425i	$-0.344091\pi$
$829$	−13.1384	−	14.5916i	−0.456314	−	0.506788i	−0.926767	+	0.375637i	$0.877424\pi$
$830$	−7.31957	+	3.25888i	−0.254066	+	0.113118i
$831$	−1.71526	+	16.3196i	−0.0595017	+	0.566120i
$832$	−9.20354	+	28.3256i	−0.319075	+	0.982013i
$833$	−10.2107	+	24.0406i	−0.353781	+	0.832957i
$834$	−6.28870	+	4.56901i	−0.217760	+	0.158212i
$835$	−2.19098	−	3.79489i	−0.0758220	−	0.131328i
$836$	14.8101	−	6.47501i	0.512220	−	0.223943i
$837$	0.976624	−	1.69156i	0.0337571	−	0.0584689i
$838$	−10.3966	−	4.62887i	−0.359145	−	0.159901i
$839$	8.43938	+	25.9738i	0.291360	+	0.896714i	0.984420	+	0.175834i	$0.0562621\pi$
$839$	8.43938	+	25.9738i	0.291360	+	0.896714i	−0.693060	+	0.720880i	$0.743738\pi$
$840$	5.30687	−	2.08977i	0.183105	−	0.0721041i
$841$	12.6111	+	9.16250i	0.434865	+	0.315948i
$842$	3.33368	−	31.7179i	0.114886	−	1.09307i
$843$	6.53657	+	7.25960i	0.225131	+	0.250034i
$844$	9.58973	+	2.03836i	0.330092	+	0.0701632i
$845$	0.114628	+	0.0510356i	0.00394332	+	0.00175568i
$846$	−10.1943			−0.350487
$847$	10.5605	−	27.1197i	0.362863	−	0.931842i
$848$	14.4669			0.496794
$849$	−24.4427	−	10.8826i	−0.838872	−	0.373490i
$850$	−18.3760	−	3.90593i	−0.630290	−	0.133972i
$851$	6.20536	+	6.89175i	0.212717	+	0.236246i
$852$	0.121424	−	1.15528i	0.00415993	−	0.0395791i
$853$	19.7645	+	14.3598i	0.676725	+	0.491669i	0.872270	−	0.489025i	$-0.162647\pi$
$853$	19.7645	+	14.3598i	0.676725	+	0.491669i	−0.195545	+	0.980695i	$0.562647\pi$
$854$	1.41659	−	9.47166i	0.0484747	−	0.324114i
$855$	1.40285	+	4.31754i	0.0479766	+	0.147657i
$856$	−16.4186	−	7.31004i	−0.561177	−	0.249852i
$857$	−7.06172	+	12.2313i	−0.241224	+	0.417812i	−0.961063	−	0.276329i	$-0.910882\pi$
$857$	−7.06172	+	12.2313i	−0.241224	+	0.417812i	0.719839	+	0.694141i	$0.244215\pi$
$858$	−12.1520	+	5.31287i	−0.414863	+	0.181379i
$859$	10.8367	+	18.7698i	0.369745	+	0.640417i	0.989526	−	0.144358i	$-0.0461117\pi$
$859$	10.8367	+	18.7698i	0.369745	+	0.640417i	−0.619780	+	0.784775i	$0.712778\pi$
$860$	−5.21492	+	3.78886i	−0.177827	+	0.129199i
$861$	−6.60979	−	12.7006i	−0.225261	−	0.432836i
$862$	−0.993117	+	3.05650i	−0.0338257	+	0.104105i
$863$	2.25668	−	21.4709i	0.0768184	−	0.730879i	−0.886538	−	0.462655i	$-0.846897\pi$
$863$	2.25668	−	21.4709i	0.0768184	−	0.730879i	0.963357	−	0.268223i	$-0.0864365\pi$
$864$	3.65019	−	1.62517i	0.124182	−	0.0552893i
$865$	−10.8678	−	12.0699i	−0.369515	−	0.410388i
$866$	−19.4215	+	21.5698i	−0.659970	+	0.732971i
$867$	2.48965	−	1.80884i	0.0845529	−	0.0614313i
$868$	1.36277	−	3.64369i	0.0462553	−	0.123675i
$869$	−16.8622	−	0.113307i	−0.572010	−	0.00384368i
$870$	−1.43396	−	2.48369i	−0.0486158	−	0.0842050i
$871$	−2.15771	−	20.5293i	−0.0731114	−	0.695608i
$872$	61.7483	+	13.1250i	2.09106	+	0.444469i
$873$	−3.11855	+	0.662868i	−0.105547	+	0.0224347i
$874$	32.4932	+	23.6077i	1.09910	+	0.798543i
$875$	−1.07501	−	17.6074i	−0.0363420	−	0.595237i
$876$	−3.42792	+	10.5501i	−0.115819	+	0.356454i
$877$	27.0501	−	30.0422i	0.913418	−	1.01445i	−0.0864164	−	0.996259i	$-0.527542\pi$
$877$	27.0501	−	30.0422i	0.913418	−	1.01445i	0.999834	−	0.0181945i	$-0.00579179\pi$
$878$	−2.40318	−	22.8647i	−0.0811034	−	0.771648i
$879$	−4.07519	+	7.05843i	−0.137453	+	0.238075i
$880$	−4.39155	+	0.902655i	−0.148039	+	0.0304285i
$881$	5.39527			0.181771			0.0908856	−	0.995861i	$-0.471030\pi$
$881$	5.39527			0.181771			0.0908856	+	0.995861i	$0.471030\pi$
$882$	7.78765	+	0.683019i	0.262224	+	0.0229984i
$883$	5.38285	+	16.5667i	0.181147	+	0.557514i	0.999861	−	0.0166883i	$-0.00531229\pi$
$883$	5.38285	+	16.5667i	0.181147	+	0.557514i	−0.818713	+	0.574202i	$0.805312\pi$
$884$	9.83767	−	2.09106i	0.330877	−	0.0703300i
$885$	5.33695	−	2.37617i	0.179400	−	0.0798739i
$886$	−13.0040	+	5.78975i	−0.436877	+	0.194510i
$887$	−4.94924	+	1.05199i	−0.166179	+	0.0353225i	−0.290250	−	0.956951i	$-0.593738\pi$
$887$	−4.94924	+	1.05199i	−0.166179	+	0.0353225i	0.124071	+	0.992273i	$0.460405\pi$
$888$	−1.58598	−	4.88116i	−0.0532221	−	0.163801i
$889$	−11.7649	−	3.04396i	−0.394582	−	0.102091i
$890$	10.4239			0.349409
$891$	3.02075	+	1.36932i	0.101199	+	0.0458740i
$892$	1.14135	−	1.97688i	0.0382153	−	0.0661909i
$893$	−6.17731	−	58.7732i	−0.206716	−	1.96677i
$894$	−8.22740	+	9.13745i	−0.275165	+	0.305602i
$895$	0.318681	−	0.980799i	0.0106523	−	0.0327845i
$896$	−2.86402	+	1.89521i	−0.0956803	+	0.0633146i
$897$	16.0917	+	11.6913i	0.537287	+	0.390362i
$898$	9.06461	−	1.92674i	0.302490	−	0.0642962i
$899$	−6.99690	−	1.48724i	−0.233360	−	0.0496021i
$900$	−0.354742	−	3.37515i	−0.0118247	−	0.112505i
$901$	−14.0006	−	24.2498i	−0.466429	−	0.807879i
$902$	6.06580	+	19.1045i	0.201969	+	0.636110i
$903$	−31.8665	+	5.32910i	−1.06045	+	0.177341i
$904$	28.4413	−	20.6638i	0.945943	−	0.687268i
$905$	−8.66858	+	9.62744i	−0.288153	+	0.320027i
$906$	−1.82798	−	2.03018i	−0.0607307	−	0.0674483i
$907$	−36.1493	+	16.0947i	−1.20032	+	0.534416i	−0.906810	−	0.421540i	$-0.861490\pi$
$907$	−36.1493	+	16.0947i	−1.20032	+	0.534416i	−0.293509	+	0.955956i	$0.594823\pi$
$908$	−0.699255	+	6.65297i	−0.0232056	+	0.220787i
$909$	2.21073	−	6.80393i	0.0733254	−	0.225672i
$910$	−3.42491	−	6.58092i	−0.113535	−	0.218155i
$911$	−22.8923	+	16.6322i	−0.758455	+	0.551050i	−0.898436	−	0.439105i	$-0.855296\pi$
$911$	−22.8923	+	16.6322i	−0.758455	+	0.551050i	0.139981	+	0.990154i	$0.455296\pi$
$912$	−6.24032	−	10.8086i	−0.206638	−	0.357907i
$913$	−33.1439	−	7.27806i	−1.09690	−	0.240868i
$914$	−1.52175	+	2.63574i	−0.0503349	+	0.0871826i
$915$	2.07630	+	0.924426i	0.0686402	+	0.0305606i
$916$	2.29188	+	7.05369i	0.0757260	+	0.233061i
$917$	−9.62934	−	7.66121i	−0.317989	−	0.252996i
$918$	3.37125	+	2.44935i	0.111268	+	0.0808407i
$919$	−5.19270	+	49.4052i	−0.171291	+	1.62973i	0.484503	+	0.874789i	$0.339000\pi$
$919$	−5.19270	+	49.4052i	−0.171291	+	1.62973i	−0.655795	+	0.754939i	$0.727666\pi$
$920$	8.01285	+	8.89918i	0.264176	+	0.293397i
$921$	−25.7671	−	5.47696i	−0.849053	−	0.180472i
$922$	−1.68539	−	0.750382i	−0.0555052	−	0.0247125i
$923$	−5.52545			−0.181872
$924$	6.38373	+	1.69753i	0.210009	+	0.0558445i
$925$	−7.52638			−0.247466
$926$	6.95563	+	3.09684i	0.228576	+	0.101769i
$927$	4.45657	+	0.947272i	0.146373	+	0.0311125i
$928$	−9.79129	−	10.8743i	−0.321415	−	0.356967i
$929$	3.58243	−	34.0845i	0.117536	−	1.11828i	−0.763691	−	0.645582i	$-0.776615\pi$
$929$	3.58243	−	34.0845i	0.117536	−	1.11828i	0.881227	−	0.472694i	$-0.156718\pi$
$930$	−1.23748	−	0.899081i	−0.0405785	−	0.0294820i
$931$	0.781178	+	45.3120i	0.0256021	+	1.48504i
$932$	−4.50435	−	13.8630i	−0.147545	−	0.454097i
$933$	12.6844	+	5.64744i	0.415267	+	0.184889i
$934$	19.0291	−	32.9594i	0.622651	−	1.07846i
$935$	5.76309	+	6.48770i	0.188473	+	0.212170i
$936$	−5.50396	−	9.53313i	−0.179902	−	0.311600i
$937$	−1.62912	+	1.18362i	−0.0532210	+	0.0386673i	−0.614078	−	0.789246i	$-0.710472\pi$
$937$	−1.62912	+	1.18362i	−0.0532210	+	0.0386673i	0.560857	+	0.827913i	$0.310472\pi$
$938$	9.15395	−	14.3654i	0.298887	−	0.469047i
$939$	−2.01363	+	6.19732i	−0.0657123	+	0.202242i
$940$	0.503657	−	4.79198i	0.0164275	−	0.156297i
$941$	−12.9089	+	5.74742i	−0.420819	+	0.187361i	−0.606211	−	0.795304i	$-0.707311\pi$
$941$	−12.9089	+	5.74742i	−0.420819	+	0.187361i	0.185392	+	0.982665i	$0.440645\pi$
$942$	−7.92154	−	8.79776i	−0.258098	−	0.286647i
$943$	20.1148	−	22.3398i	0.655029	−	0.727484i
$944$	−12.9935	+	9.44037i	−0.422904	+	0.307258i
$945$	−0.649904	+	1.73768i	−0.0211414	+	0.0565267i
$946$	45.2307	+	0.303932i	1.47058	+	0.00988168i
$947$	10.6209	+	18.3960i	0.345134	+	0.597790i	0.985378	−	0.170382i	$-0.0545000\pi$
$947$	10.6209	+	18.3960i	0.345134	+	0.597790i	−0.640244	+	0.768172i	$0.721167\pi$
$948$	−0.400062	−	3.80633i	−0.0129934	−	0.123624i
$949$	51.6119	+	10.9704i	1.67539	+	0.356116i
$950$	−31.8838	+	6.77710i	−1.03445	+	0.219878i
$951$	−3.76351	−	2.73435i	−0.122040	−	0.0886674i
$952$	27.1594	+	13.5448i	0.880242	+	0.438991i
$953$	−16.9739	+	52.2403i	−0.549839	+	1.69223i	0.159360	+	0.987221i	$0.449057\pi$
$953$	−16.9739	+	52.2403i	−0.549839	+	1.69223i	−0.709199	+	0.705009i	$0.750943\pi$
$954$	−5.60791	+	6.22821i	−0.181563	+	0.201646i
$955$	1.70178	+	16.1913i	0.0550681	+	0.523938i
$956$	−3.70715	+	6.42097i	−0.119898	+	0.207669i
$957$	1.35076	−	12.0709i	0.0436640	−	0.390195i
$958$	23.6396			0.763760
$959$	−6.74148	+	6.85870i	−0.217694	+	0.221479i
$960$	−1.80237	−	5.54712i	−0.0581712	−	0.179032i
$961$	26.5908	−	5.65204i	0.857767	−	0.182324i
$962$	−6.09871	+	2.71532i	−0.196630	+	0.0875454i
$963$	5.34064	−	2.37781i	0.172100	−	0.0766238i
$964$	−13.2962	+	2.82620i	−0.428242	+	0.0910257i
$965$	5.03999	+	15.5115i	0.162243	+	0.499333i
$966$	4.38465	+	15.8171i	0.141074	+	0.508908i
$967$	−34.1710			−1.09887			−0.549433	−	0.835538i	$-0.685156\pi$
$967$	−34.1710			−1.09887			−0.549433	+	0.835538i	$0.685156\pi$
$968$	−30.7058	−	14.1686i	−0.986921	−	0.455395i
$969$	−12.0784	+	20.9205i	−0.388015	+	0.672062i
$970$	0.260979	+	2.48305i	0.00837953	+	0.0797259i
$971$	20.2257	−	22.4629i	0.649074	−	0.720870i	−0.325348	−	0.945594i	$-0.605482\pi$
$971$	20.2257	−	22.4629i	0.649074	−	0.720870i	0.974422	+	0.224724i	$0.0721482\pi$
$972$	−0.232620	+	0.715932i	−0.00746130	+	0.0229635i
$973$	−1.12225	−	18.3811i	−0.0359778	−	0.589272i
$974$	−2.78145	−	2.02084i	−0.0891234	−	0.0647519i
$975$	−15.7899	+	3.35624i	−0.505681	+	0.107486i
$976$	−6.11181	−	1.29911i	−0.195634	−	0.0415834i
$977$	2.37043	+	22.5531i	0.0758367	+	0.721538i	0.964697	+	0.263361i	$0.0848309\pi$
$977$	2.37043	+	22.5531i	0.0758367	+	0.721538i	−0.888861	+	0.458177i	$0.848502\pi$
$978$	11.1258	+	19.2705i	0.355765	+	0.616203i
$979$	35.5406	+	26.1884i	1.13588	+	0.836986i
$980$	−0.705818	+	3.62695i	−0.0225465	+	0.115859i
$981$	−16.6125	+	12.0697i	−0.530397	+	0.385356i
$982$	−12.5983	+	13.9919i	−0.402029	+	0.446499i
$983$	26.2253	+	29.1262i	0.836457	+	0.928980i	0.998326	−	0.0578322i	$-0.0184188\pi$
$983$	26.2253	+	29.1262i	0.836457	+	0.928980i	−0.161869	+	0.986812i	$0.551752\pi$
$984$	−15.1983	+	6.76674i	−0.484505	+	0.215716i
$985$	0.753307	−	7.16724i	0.0240024	−	0.228367i
$986$	4.71584	−	14.5139i	0.150183	−	0.462216i
$987$	12.9785	−	20.3673i	0.413109	−	0.648298i
$988$	14.1177	−	10.2571i	0.449145	−	0.326323i
$989$	−33.9178	−	58.7473i	−1.07852	−	1.86806i
$990$	1.31373	−	2.24053i	0.0417529	−	0.0712089i
$991$	10.5475	−	18.2688i	0.335052	−	0.580327i	−0.648443	−	0.761263i	$-0.724579\pi$
$991$	10.5475	−	18.2688i	0.335052	−	0.580327i	0.983495	+	0.180936i	$0.0579128\pi$
$992$	−7.12972	−	3.17436i	−0.226369	−	0.100786i
$993$	0.405753	+	1.24878i	0.0128762	+	0.0396288i
$994$	−3.56808	−	2.83880i	−0.113173	−	0.0900414i
$995$	7.83063	+	5.68928i	0.248248	+	0.180362i
$996$	0.805069	−	7.65972i	0.0255096	−	0.242707i
$997$	−39.4123	−	43.7717i	−1.24820	−	1.38626i	−0.892113	−	0.451811i	$-0.850778\pi$
$997$	−39.4123	−	43.7717i	−1.24820	−	1.38626i	−0.356085	−	0.934454i	$-0.615889\pi$
$998$	−37.7289	−	8.01953i	−1.19429	−	0.253854i
$999$	1.52512	+	0.679026i	0.0482526	+	0.0214834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.25.6	yes	64
3.2	odd	2		693.2.by.c.487.3		64
7.2	even	3	inner	231.2.y.b.58.3	yes	64
11.4	even	5	inner	231.2.y.b.4.3	✓	64
21.2	odd	6		693.2.by.c.289.6		64
33.26	odd	10		693.2.by.c.235.6		64
77.37	even	15	inner	231.2.y.b.37.6	yes	64
231.191	odd	30		693.2.by.c.37.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.4.3	✓	64	11.4	even	5	inner
231.2.y.b.25.6	yes	64	1.1	even	1	trivial
231.2.y.b.37.6	yes	64	77.37	even	15	inner
231.2.y.b.58.3	yes	64	7.2	even	3	inner
693.2.by.c.37.3		64	231.191	odd	30
693.2.by.c.235.6		64	33.26	odd	10
693.2.by.c.289.6		64	21.2	odd	6
693.2.by.c.487.3		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02024 + 0.454240i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.503705 - 0.559421i) q^{4} +(0.0732968 - 0.697372i) q^{5} +(-0.903504 - 0.656434i) q^{6} +(2.46176 - 0.969406i) q^{7} +(-0.950004 - 2.92381i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(1.02024 + 0.454240i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.503705 - 0.559421i) q^{4} +(0.0732968 - 0.697372i) q^{5} +(-0.903504 - 0.656434i) q^{6} +(2.46176 - 0.969406i) q^{7} +(-0.950004 - 2.92381i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.391555 - 0.678193i) q^{10} +(3.03888 - 1.32860i) q^{11} +(0.376388 + 0.651923i) q^{12} +(2.89681 - 2.10465i) q^{13} +(2.95193 + 0.129202i) q^{14} +(-0.216687 + 0.666894i) q^{15} +(0.201508 - 1.91722i) q^{16} +(-3.40872 + 1.51766i) q^{17} +(0.747280 + 0.829938i) q^{18} +(-4.33202 + 4.81120i) q^{19} +(-0.427045 + 0.310266i) q^{20} +(-2.60951 + 0.436394i) q^{21} +(3.70390 + 0.0248887i) q^{22} +(-2.77749 - 4.81076i) q^{23} +(0.321350 + 3.05744i) q^{24} +(4.40978 + 0.937328i) q^{25} +(3.91146 - 0.831406i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.78231 - 0.888864i) q^{28} +(-1.13169 + 3.48298i) q^{29} +(-0.524003 + 0.581964i) q^{30} +(0.204170 + 1.94255i) q^{31} +(-1.99781 + 3.46032i) q^{32} +(-3.24871 + 0.667751i) q^{33} -4.16709 q^{34} +(-0.495598 - 1.78782i) q^{35} +(-0.232620 - 0.715932i) q^{36} +(-1.63297 + 0.347098i) q^{37} +(-6.60515 + 2.94080i) q^{38} +(-3.27109 + 1.45638i) q^{39} +(-2.10862 + 0.448201i) q^{40} +(1.67227 + 5.14670i) q^{41} +(-2.86056 - 0.740119i) q^{42} +12.2117 q^{43} +(-2.27395 - 1.03079i) q^{44} +(0.350607 - 0.607269i) q^{45} +(-0.648470 - 6.16978i) q^{46} +(-6.10795 + 6.78357i) q^{47} +(-0.595716 + 1.83343i) q^{48} +(5.12050 - 4.77289i) q^{49} +(4.07327 + 2.95940i) q^{50} +(3.64977 - 0.775782i) q^{51} +(-2.63652 - 0.560410i) q^{52} +(0.784426 + 7.46332i) q^{53} +(-0.558396 - 0.967170i) q^{54} +(-0.703791 - 2.21662i) q^{55} +(-5.17304 - 6.27678i) q^{56} +(5.23766 - 3.80539i) q^{57} +(-2.73670 + 3.03941i) q^{58} +(-5.57473 - 6.19137i) q^{59} +(0.482221 - 0.214698i) q^{60} +(0.338800 - 3.22346i) q^{61} +(-0.674081 + 2.07461i) q^{62} +(2.64322 + 0.115690i) q^{63} +(-6.72928 + 4.88911i) q^{64} +(-1.25540 - 2.17442i) q^{65} +(-3.61778 - 0.794428i) q^{66} +(2.88249 - 4.99261i) q^{67} +(2.56600 + 1.14246i) q^{68} +(1.71658 + 5.28310i) q^{69} +(0.306469 - 2.04912i) q^{70} +(-1.24843 - 0.907036i) q^{71} +(0.321350 - 3.05744i) q^{72} +(9.86039 + 10.9511i) q^{73} +(-1.82369 - 0.387636i) q^{74} +(-4.11854 - 1.83369i) q^{75} +4.87355 q^{76} +(6.19304 - 6.21661i) q^{77} -3.99884 q^{78} +(-4.64470 - 2.06795i) q^{79} +(-1.32224 - 0.281052i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.631727 + 6.01049i) q^{82} +(-8.27734 - 6.01384i) q^{83} +(1.55855 + 1.24000i) q^{84} +(0.808525 + 2.48838i) q^{85} +(12.4588 + 5.54703i) q^{86} +(1.83111 - 3.17157i) q^{87} +(-6.77154 - 7.62295i) q^{88} +(6.65543 + 11.5275i) q^{89} +(0.633549 - 0.460300i) q^{90} +(5.09097 - 7.98933i) q^{91} +(-1.29220 + 3.97699i) q^{92} +(0.204170 - 1.94255i) q^{93} +(-9.31295 + 4.14639i) q^{94} +(3.03767 + 3.37368i) q^{95} +(2.67360 - 2.96933i) q^{96} +(-2.57932 + 1.87399i) q^{97} +(7.39218 - 2.54355i) q^{98} +(3.31655 + 0.0222859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

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