LMFDB - Embedded newform 360.2.bm.b.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959041 + 1.03935i) q^{2} +(0.0478668 + 1.73139i) q^{3} +(-0.160481 + 1.99355i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.75361 + 1.71022i) q^{6} +(-1.21691 - 0.702581i) q^{7} +(-2.22590 + 1.74510i) q^{8} +(-2.99542 + 0.165752i) q^{9} +O(q^{10})$	\(q+(0.959041 + 1.03935i) q^{2} +(0.0478668 + 1.73139i) q^{3} +(-0.160481 + 1.99355i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.75361 + 1.71022i) q^{6} +(-1.21691 - 0.702581i) q^{7} +(-2.22590 + 1.74510i) q^{8} +(-2.99542 + 0.165752i) q^{9} +(-0.420580 + 1.35023i) q^{10} +(1.54060 + 0.889464i) q^{11} +(-3.45929 - 0.182430i) q^{12} +(1.92926 - 1.11386i) q^{13} +(-0.436838 - 1.93859i) q^{14} +(-1.47549 + 0.907148i) q^{15} +(-3.94849 - 0.639853i) q^{16} -2.44342i q^{17} +(-3.04500 - 2.95431i) q^{18} +2.27508 q^{19} +(-1.80671 + 0.857795i) q^{20} +(1.15819 - 2.14057i) q^{21} +(0.553034 + 2.45424i) q^{22} +(4.09002 + 7.08413i) q^{23} +(-3.12800 - 3.77036i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.00792 + 0.936933i) q^{26} +(-0.430363 - 5.17830i) q^{27} +(1.59592 - 2.31321i) q^{28} +(2.01840 - 3.49598i) q^{29} +(-2.35790 - 0.663556i) q^{30} +(-1.77108 + 1.02254i) q^{31} +(-3.12174 - 4.71750i) q^{32} +(-1.46626 + 2.70995i) q^{33} +(2.53956 - 2.34334i) q^{34} -1.40516i q^{35} +(0.150272 - 5.99812i) q^{36} +0.470507i q^{37} +(2.18189 + 2.36460i) q^{38} +(2.02087 + 3.28698i) q^{39} +(-2.62425 - 1.05513i) q^{40} +(6.26396 - 3.61650i) q^{41} +(3.33554 - 0.849130i) q^{42} +(-3.04567 + 5.27525i) q^{43} +(-2.02043 + 2.92852i) q^{44} +(-1.64125 - 2.51123i) q^{45} +(-3.44036 + 11.0449i) q^{46} +(-6.65955 + 11.5347i) q^{47} +(0.918833 - 6.86700i) q^{48} +(-2.51276 - 4.35223i) q^{49} +(-1.37962 + 0.310881i) q^{50} +(4.23051 - 0.116959i) q^{51} +(1.91093 + 4.02483i) q^{52} +9.04935 q^{53} +(4.96931 - 5.41350i) q^{54} +1.77893i q^{55} +(3.93478 - 0.559752i) q^{56} +(0.108901 + 3.93905i) q^{57} +(5.56926 - 1.25497i) q^{58} +(8.51602 - 4.91673i) q^{59} +(-1.57166 - 3.08705i) q^{60} +(-3.96414 - 2.28870i) q^{61} +(-2.76131 - 0.860115i) q^{62} +(3.76159 + 1.90282i) q^{63} +(1.90924 - 7.76884i) q^{64} +(1.92926 + 1.11386i) q^{65} +(-4.22278 + 1.07499i) q^{66} +(-1.54825 - 2.68165i) q^{67} +(4.87108 + 0.392122i) q^{68} +(-12.0696 + 7.42052i) q^{69} +(1.46045 - 1.34761i) q^{70} +12.8925 q^{71} +(6.37824 - 5.59626i) q^{72} +1.45731 q^{73} +(-0.489020 + 0.451236i) q^{74} +(-1.52336 - 0.824241i) q^{75} +(-0.365107 + 4.53549i) q^{76} +(-1.24984 - 2.16479i) q^{77} +(-1.47822 + 5.25274i) q^{78} +(-7.90843 - 4.56593i) q^{79} +(-1.42012 - 3.73942i) q^{80} +(8.94505 - 0.992994i) q^{81} +(9.76619 + 3.04205i) q^{82} +(5.76713 + 3.32965i) q^{83} +(4.08146 + 2.65243i) q^{84} +(2.11606 - 1.22171i) q^{85} +(-8.40374 + 1.89368i) q^{86} +(6.14951 + 3.32730i) q^{87} +(-4.98141 + 0.708643i) q^{88} -8.82082i q^{89} +(1.03601 - 4.11421i) q^{90} -3.13030 q^{91} +(-14.7789 + 7.01681i) q^{92} +(-1.85518 - 3.01749i) q^{93} +(-18.3753 + 4.14065i) q^{94} +(1.13754 + 1.97028i) q^{95} +(8.01839 - 5.63075i) q^{96} +(-7.48016 + 12.9560i) q^{97} +(2.11363 - 6.78559i) q^{98} +(-4.76216 - 2.40896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.959041	+	1.03935i	0.678144	+	0.734929i
$2$	0.959041	+	1.03935i	0.678144	+	0.734929i
$3$	0.0478668	+	1.73139i	0.0276359	+	0.999618i
$3$	0.0478668	+	1.73139i	0.0276359	+	0.999618i
$4$	−0.160481	+	1.99355i	−0.0802404	+	0.996776i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.75361	+	1.71022i	−0.715907	+	0.698196i
$7$	−1.21691	−	0.702581i	−0.459947	−	0.265551i	0.252075	−	0.967708i	$-0.418887\pi$
$7$	−1.21691	−	0.702581i	−0.459947	−	0.265551i	−0.712022	+	0.702157i	$0.752220\pi$
$8$	−2.22590	+	1.74510i	−0.786974	+	0.616987i
$9$	−2.99542	+	0.165752i	−0.998473	+	0.0552507i
$10$	−0.420580	+	1.35023i	−0.132999	+	0.426979i
$11$	1.54060	+	0.889464i	0.464507	+	0.268183i	0.713938	−	0.700209i	$-0.246910\pi$
$11$	1.54060	+	0.889464i	0.464507	+	0.268183i	−0.249430	+	0.968393i	$0.580243\pi$
$12$	−3.45929	−	0.182430i	−0.998612	−	0.0526629i
$13$	1.92926	−	1.11386i	0.535080	−	0.308929i	−0.208002	−	0.978128i	$-0.566696\pi$
$13$	1.92926	−	1.11386i	0.535080	−	0.308929i	0.743083	+	0.669199i	$0.233363\pi$
$14$	−0.436838	−	1.93859i	−0.116750	−	0.518110i
$15$	−1.47549	+	0.907148i	−0.380971	+	0.234225i
$16$	−3.94849	−	0.639853i	−0.987123	−	0.159963i
$17$		−	2.44342i		−	0.592616i	−0.955092	−	0.296308i	$-0.904244\pi$
$17$		−	2.44342i		−	0.592616i	0.955092	−	0.296308i	$-0.0957555\pi$
$18$	−3.04500	−	2.95431i	−0.717714	−	0.696338i
$19$	2.27508			0.521939			0.260970	−	0.965347i	$-0.415958\pi$
$19$	2.27508			0.521939			0.260970	+	0.965347i	$0.415958\pi$
$20$	−1.80671	+	0.857795i	−0.403992	+	0.191809i
$21$	1.15819	−	2.14057i	0.252738	−	0.467110i
$22$	0.553034	+	2.45424i	0.117907	+	0.523247i
$23$	4.09002	+	7.08413i	0.852829	+	1.47714i	0.878644	+	0.477477i	$0.158448\pi$
$23$	4.09002	+	7.08413i	0.852829	+	1.47714i	−0.0258153	+	0.999667i	$0.508218\pi$
$24$	−3.12800	−	3.77036i	−0.638500	−	0.769622i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.00792	+	0.936933i	0.589902	+	0.183748i
$27$	−0.430363	−	5.17830i	−0.0828233	−	0.996564i
$28$	1.59592	−	2.31321i	0.301601	−	0.437156i
$29$	2.01840	−	3.49598i	0.374808	−	0.649187i	−0.615490	−	0.788145i	$-0.711042\pi$
$29$	2.01840	−	3.49598i	0.374808	−	0.649187i	0.990298	+	0.138958i	$0.0443753\pi$
$30$	−2.35790	−	0.663556i	−0.430492	−	0.121148i
$31$	−1.77108	+	1.02254i	−0.318096	+	0.183653i	−0.650544	−	0.759469i	$-0.725459\pi$
$31$	−1.77108	+	1.02254i	−0.318096	+	0.183653i	0.332448	+	0.943122i	$0.392126\pi$
$32$	−3.12174	−	4.71750i	−0.551850	−	0.833943i
$33$	−1.46626	+	2.70995i	−0.255244	+	0.471741i
$34$	2.53956	−	2.34334i	0.435531	−	0.401879i
$35$		−	1.40516i		−	0.237516i
$36$	0.150272	−	5.99812i	0.0250453	−	0.999686i
$37$			0.470507i			0.0773509i	0.999252	+	0.0386755i	$0.0123139\pi$
$37$			0.470507i			0.0773509i	−0.999252	+	0.0386755i	$0.987686\pi$
$38$	2.18189	+	2.36460i	0.353950	+	0.383588i
$39$	2.02087	+	3.28698i	0.323598	+	0.526339i
$40$	−2.62425	−	1.05513i	−0.414931	−	0.166831i
$41$	6.26396	−	3.61650i	0.978267	−	0.564802i	0.0765203	−	0.997068i	$-0.475619\pi$
$41$	6.26396	−	3.61650i	0.978267	−	0.564802i	0.901746	+	0.432266i	$0.142286\pi$
$42$	3.33554	−	0.849130i	0.514686	−	0.131024i
$43$	−3.04567	+	5.27525i	−0.464460	+	0.804469i	−0.999177	−	0.0405627i	$-0.987085\pi$
$43$	−3.04567	+	5.27525i	−0.464460	+	0.804469i	0.534717	+	0.845031i	$0.320418\pi$
$44$	−2.02043	+	2.92852i	−0.304591	+	0.441490i
$45$	−1.64125	−	2.51123i	−0.244664	−	0.374352i
$46$	−3.44036	+	11.0449i	−0.507254	+	1.62849i
$47$	−6.65955	+	11.5347i	−0.971395	+	1.68251i	−0.280045	+	0.959987i	$0.590349\pi$
$47$	−6.65955	+	11.5347i	−0.971395	+	1.68251i	−0.691351	+	0.722519i	$0.742984\pi$
$48$	0.918833	−	6.86700i	0.132622	−	0.991167i
$49$	−2.51276	−	4.35223i	−0.358966	−	0.621747i
$50$	−1.37962	+	0.310881i	−0.195108	+	0.0439652i
$51$	4.23051	−	0.116959i	0.592390	−	0.0163775i
$52$	1.91093	+	4.02483i	0.264998	+	0.558144i
$53$	9.04935			1.24302			0.621512	−	0.783405i	$-0.286519\pi$
$53$	9.04935			1.24302			0.621512	+	0.783405i	$0.286519\pi$
$54$	4.96931	−	5.41350i	0.676238	−	0.736684i
$55$			1.77893i			0.239871i
$56$	3.93478	−	0.559752i	0.525807	−	0.0748000i
$57$	0.108901	+	3.93905i	0.0144243	+	0.521740i
$58$	5.56926	−	1.25497i	0.731280	−	0.164785i
$59$	8.51602	−	4.91673i	1.10869	−	0.640103i	0.170201	−	0.985409i	$-0.445558\pi$
$59$	8.51602	−	4.91673i	1.10869	−	0.640103i	0.938490	+	0.345306i	$0.112225\pi$
$60$	−1.57166	−	3.08705i	−0.202900	−	0.398537i
$61$	−3.96414	−	2.28870i	−0.507557	−	0.293038i	0.224272	−	0.974527i	$-0.428000\pi$
$61$	−3.96414	−	2.28870i	−0.507557	−	0.293038i	−0.731829	+	0.681489i	$0.761333\pi$
$62$	−2.76131	−	0.860115i	−0.350687	−	0.109235i
$63$	3.76159	+	1.90282i	0.473916	+	0.239733i
$64$	1.90924	−	7.76884i	0.238655	−	0.971104i
$65$	1.92926	+	1.11386i	0.239295	+	0.138157i
$66$	−4.22278	+	1.07499i	−0.519788	+	0.132323i
$67$	−1.54825	−	2.68165i	−0.189149	−	0.327616i	0.755818	−	0.654782i	$-0.227240\pi$
$67$	−1.54825	−	2.68165i	−0.189149	−	0.327616i	−0.944967	+	0.327166i	$0.893906\pi$
$68$	4.87108	+	0.392122i	0.590705	+	0.0475518i
$69$	−12.0696	+	7.42052i	−1.45301	+	0.893326i
$70$	1.46045	−	1.34761i	0.174557	−	0.161070i
$71$	12.8925			1.53006			0.765028	−	0.643997i	$-0.222725\pi$
$71$	12.8925			1.53006			0.765028	+	0.643997i	$0.222725\pi$
$72$	6.37824	−	5.59626i	0.751682	−	0.659525i
$73$	1.45731			0.170565			0.0852824	−	0.996357i	$-0.472821\pi$
$73$	1.45731			0.170565			0.0852824	+	0.996357i	$0.472821\pi$
$74$	−0.489020	+	0.451236i	−0.0568474	+	0.0524551i
$75$	−1.52336	−	0.824241i	−0.175903	−	0.0951751i
$76$	−0.365107	+	4.53549i	−0.0418806	+	0.520256i
$77$	−1.24984	−	2.16479i	−0.142433	−	0.246700i
$78$	−1.47822	+	5.25274i	−0.167375	+	0.594755i
$79$	−7.90843	−	4.56593i	−0.889767	−	0.513707i	−0.0159009	−	0.999874i	$-0.505062\pi$
$79$	−7.90843	−	4.56593i	−0.889767	−	0.513707i	−0.873866	+	0.486166i	$0.838395\pi$
$80$	−1.42012	−	3.73942i	−0.158774	−	0.418080i
$81$	8.94505	−	0.992994i	0.993895	−	0.110333i
$82$	9.76619	+	3.04205i	1.07850	+	0.335939i
$83$	5.76713	+	3.32965i	0.633025	+	0.365477i	0.781923	−	0.623376i	$-0.214239\pi$
$83$	5.76713	+	3.32965i	0.633025	+	0.365477i	−0.148898	+	0.988853i	$0.547573\pi$
$84$	4.08146	+	2.65243i	0.445324	+	0.289404i
$85$	2.11606	−	1.22171i	0.229519	−	0.132513i
$86$	−8.40374	+	1.89368i	−0.906198	+	0.204201i
$87$	6.14951	+	3.32730i	0.659297	+	0.356724i
$88$	−4.98141	+	0.708643i	−0.531021	+	0.0755416i
$89$		−	8.82082i		−	0.935005i	−0.883992	−	0.467503i	$-0.845154\pi$
$89$		−	8.82082i		−	0.935005i	0.883992	−	0.467503i	$-0.154846\pi$
$90$	1.03601	−	4.11421i	0.109205	−	0.433675i
$91$	−3.13030			−0.328145
$92$	−14.7789	+	7.01681i	−1.54081	+	0.731553i
$93$	−1.85518	−	3.01749i	−0.192373	−	0.312899i
$94$	−18.3753	+	4.14065i	−1.89527	+	0.427076i
$95$	1.13754	+	1.97028i	0.116709	+	0.202146i
$96$	8.01839	−	5.63075i	0.818374	−	0.574686i
$97$	−7.48016	+	12.9560i	−0.759495	+	1.31548i	0.183614	+	0.982998i	$0.441220\pi$
$97$	−7.48016	+	12.9560i	−0.759495	+	1.31548i	−0.943109	+	0.332485i	$0.892113\pi$
$98$	2.11363	−	6.78559i	0.213509	−	0.685448i
$99$	−4.76216	−	2.40896i	−0.478615	−	0.242109i
$100$	−1.64623	−	1.13576i	−0.164623	−	0.113576i
$101$	6.50211	−	11.2620i	0.646984	−	1.12061i	−0.336855	−	0.941556i	$-0.609363\pi$
$101$	6.50211	−	11.2620i	0.646984	−	1.12061i	0.983839	−	0.179053i	$-0.0573034\pi$
$102$	4.17879	+	4.28480i	0.413762	+	0.424258i
$103$	7.64894	−	4.41612i	0.753673	−	0.435133i	−0.0733467	−	0.997307i	$-0.523368\pi$
$103$	7.64894	−	4.41612i	0.753673	−	0.435133i	0.827019	+	0.562173i	$0.190035\pi$
$104$	−2.35054	+	5.84609i	−0.230489	+	0.573256i
$105$	2.43288	−	0.0672606i	0.237425	−	0.00656396i
$106$	8.67870	+	9.40541i	0.842950	+	0.913534i
$107$		−	16.3487i		−	1.58049i	−0.612789	−	0.790246i	$-0.709953\pi$
$107$		−	16.3487i		−	1.58049i	0.612789	−	0.790246i	$-0.290047\pi$
$108$	10.3923	−	0.0269320i	0.999997	−	0.00259153i
$109$		−	5.04055i		−	0.482797i	−0.970426	−	0.241398i	$-0.922394\pi$
$109$		−	5.04055i		−	0.482797i	0.970426	−	0.241398i	$-0.0776061\pi$
$110$	−1.84892	+	1.70606i	−0.176288	+	0.162667i
$111$	−0.814631	+	0.0225217i	−0.0773214	+	0.00213766i
$112$	4.35539	+	3.55278i	0.411546	+	0.335706i
$113$	−16.0187	+	9.24838i	−1.50691	+	0.870014i	−0.506941	+	0.861981i	$0.669224\pi$
$113$	−16.0187	+	9.24838i	−1.50691	+	0.870014i	−0.999968	+	0.00803312i	$0.997443\pi$
$114$	−3.98959	+	3.89089i	−0.373660	+	0.364416i
$115$	−4.09002	+	7.08413i	−0.381397	+	0.660599i
$116$	6.64549	+	4.58483i	0.617019	+	0.425691i
$117$	−5.59431	+	3.65625i	−0.517195	+	0.338021i
$118$	13.2774	+	4.13575i	1.22228	+	0.380727i
$119$	−1.71670	+	2.97341i	−0.157370	+	0.272572i
$120$	1.70123	−	4.59411i	0.155300	−	0.419383i
$121$	−3.91771	−	6.78567i	−0.356155	−	0.616879i
$122$	−1.42303	−	6.31508i	−0.128835	−	0.571740i
$123$	6.56141	+	10.6722i	0.591622	+	0.962284i
$124$	−1.75425	−	3.69484i	−0.157536	−	0.331807i
$125$	−1.00000			−0.0894427
$126$	1.62984	+	5.73448i	0.145197	+	0.510868i
$127$		−	11.1726i		−	0.991412i	−0.868490	−	0.495706i	$-0.834909\pi$
$127$		−	11.1726i		−	0.991412i	0.868490	−	0.495706i	$-0.165091\pi$
$128$	9.90555	−	5.46627i	0.875535	−	0.483155i
$129$	−9.27930	−	5.02073i	−0.816997	−	0.442051i
$130$	0.692555	+	3.07340i	0.0607411	+	0.269555i
$131$	−10.1359	+	5.85198i	−0.885580	+	0.511290i	−0.872494	−	0.488624i	$-0.837499\pi$
$131$	−10.1359	+	5.85198i	−0.885580	+	0.511290i	−0.0130860	+	0.999914i	$0.504166\pi$
$132$	−5.16711	−	3.35797i	−0.449739	−	0.292274i
$133$	−2.76856	−	1.59843i	−0.240064	−	0.138601i
$134$	1.30233	−	4.18098i	0.112504	−	0.361182i
$135$	4.26936	−	2.96185i	0.367448	−	0.254916i
$136$	4.26402	+	5.43880i	0.365636	+	0.466373i
$137$	−4.64344	−	2.68089i	−0.396716	−	0.229044i	0.288350	−	0.957525i	$-0.406893\pi$
$137$	−4.64344	−	2.68089i	−0.396716	−	0.229044i	−0.685066	+	0.728481i	$0.740227\pi$
$138$	−19.2877	−	5.42792i	−1.64188	−	0.462055i
$139$	3.33160	+	5.77051i	0.282583	+	0.489448i	0.972020	−	0.234897i	$-0.0754754\pi$
$139$	3.33160	+	5.77051i	0.282583	+	0.489448i	−0.689437	+	0.724345i	$0.742142\pi$
$140$	2.80126	+	0.225501i	0.236750	+	0.0190584i
$141$	−20.2898	−	10.9781i	−1.70871	−	0.924527i
$142$	12.3644	+	13.3997i	1.03760	+	1.12448i
$143$	3.96295			0.331398
$144$	11.9334	+	1.26216i	0.994453	+	0.105180i
$145$	4.03681			0.335239
$146$	1.39762	+	1.51465i	0.115668	+	0.125353i
$147$	7.41512	−	4.55889i	0.611589	−	0.376011i
$148$	−0.937980	−	0.0755074i	−0.0771015	−	0.00620667i
$149$	−2.24781	−	3.89332i	−0.184148	−	0.318954i	0.759141	−	0.650926i	$-0.225619\pi$
$149$	−2.24781	−	3.89332i	−0.184148	−	0.318954i	−0.943289	+	0.331973i	$0.892286\pi$
$150$	−0.604294	−	2.37378i	−0.0493404	−	0.193818i
$151$	−14.3560	−	8.28846i	−1.16828	−	0.674505i	−0.215004	−	0.976613i	$-0.568976\pi$
$151$	−14.3560	−	8.28846i	−1.16828	−	0.674505i	−0.953274	+	0.302108i	$0.902310\pi$
$152$	−5.06409	+	3.97025i	−0.410752	+	0.322030i
$153$	0.405002	+	7.31906i	0.0327425	+	0.591711i
$154$	1.05131	−	3.37514i	0.0847174	−	0.271976i
$155$	−1.77108	−	1.02254i	−0.142257	−	0.0821320i
$156$	−6.87708	+	3.50121i	−0.550607	+	0.280321i
$157$	11.3211	−	6.53624i	0.903522	−	0.521648i	0.0251805	−	0.999683i	$-0.491984\pi$
$157$	11.3211	−	6.53624i	0.903522	−	0.521648i	0.878341	+	0.478035i	$0.158651\pi$
$158$	−2.83892	−	12.5985i	−0.225852	−	1.00228i
$159$	0.433164	+	15.6680i	0.0343521	+	1.24255i
$160$	2.52460	−	5.06225i	0.199587	−	0.400206i
$161$		−	11.4943i		−	0.905877i
$162$	9.61074	+	8.34468i	0.755091	+	0.655620i
$163$	−6.67258			−0.522637			−0.261318	−	0.965253i	$-0.584157\pi$
$163$	−6.67258			−0.522637			−0.261318	+	0.965253i	$0.584157\pi$
$164$	6.20443	+	13.0679i	0.484485	+	1.02043i
$165$	−3.08002	+	0.0851516i	−0.239779	+	0.00662904i
$166$	2.07025	+	9.18732i	0.160683	+	0.713074i
$167$	−2.48102	−	4.29726i	−0.191987	−	0.332532i	0.753921	−	0.656965i	$-0.228160\pi$
$167$	−2.48102	−	4.29726i	−0.191987	−	0.332532i	−0.945909	+	0.324433i	$0.894827\pi$
$168$	1.15749	+	6.78585i	0.0893026	+	0.523539i
$169$	−4.01864	+	6.96048i	−0.309126	+	0.535422i
$170$	3.29917	+	1.02765i	0.253035	+	0.0788174i
$171$	−6.81481	+	0.377099i	−0.521142	+	0.0288375i
$172$	−10.0277	−	6.91827i	−0.764606	−	0.527513i
$173$	6.20403	−	10.7457i	0.471684	−	0.816980i	−0.527791	−	0.849374i	$-0.676980\pi$
$173$	6.20403	−	10.7457i	0.471684	−	0.816980i	0.999475	+	0.0323937i	$0.0103130\pi$
$174$	2.43942	+	9.58249i	0.184932	+	0.726447i
$175$	1.21691	−	0.702581i	0.0919894	−	0.0531101i
$176$	−5.51391	−	4.49780i	−0.415626	−	0.339034i
$177$	8.92040	+	14.5092i	0.670498	+	1.09058i
$178$	9.16789	−	8.45953i	0.687162	−	0.634069i
$179$			2.73138i			0.204153i	0.994777	+	0.102076i	$0.0325486\pi$
$179$			2.73138i			0.204153i	−0.994777	+	0.102076i	$0.967451\pi$
$180$	5.26966	−	2.86892i	0.392777	−	0.213837i
$181$			20.5542i			1.52778i	0.645345	+	0.763892i	$0.276714\pi$
$181$			20.5542i			1.52778i	−0.645345	+	0.763892i	$0.723286\pi$
$182$	−3.00209	−	3.25347i	−0.222530	−	0.241163i
$183$	3.77288	−	6.97303i	0.278899	−	0.515461i
$184$	−21.4665	−	8.63104i	−1.58253	−	0.636288i
$185$	−0.407471	+	0.235254i	−0.0299579	+	0.0172962i
$186$	1.35702	−	4.82207i	0.0995015	−	0.353571i
$187$	2.17333	−	3.76432i	0.158930	−	0.275275i
$188$	−21.9262	−	15.1273i	−1.59914	−	1.10327i
$189$	−3.11446	+	6.60387i	−0.226544	+	0.480361i
$190$	−0.956852	+	3.07187i	−0.0694174	+	0.222857i
$191$	−11.5150	+	19.9446i	−0.833197	+	1.44314i	0.0622936	+	0.998058i	$0.480158\pi$
$191$	−11.5150	+	19.9446i	−0.833197	+	1.44314i	−0.895490	+	0.445081i	$0.853175\pi$
$192$	13.5423	+	2.93376i	0.977329	+	0.211726i
$193$	−2.07419	−	3.59260i	−0.149303	−	0.258601i	0.781667	−	0.623696i	$-0.214370\pi$
$193$	−2.07419	−	3.59260i	−0.149303	−	0.258601i	−0.930970	+	0.365095i	$0.881036\pi$
$194$	−20.6396	+	4.65087i	−1.48183	+	0.333913i
$195$	−1.83618	+	3.39362i	−0.131491	+	0.243022i
$196$	9.07964	−	4.31087i	0.648546	−	0.307919i
$197$	−5.04925			−0.359745			−0.179872	−	0.983690i	$-0.557568\pi$
$197$	−5.04925			−0.359745			−0.179872	+	0.983690i	$0.557568\pi$
$198$	−2.06337	−	7.25982i	−0.146637	−	0.515933i
$199$		−	11.4128i		−	0.809031i	−0.914531	−	0.404515i	$-0.867440\pi$
$199$		−	11.4128i		−	0.809031i	0.914531	−	0.404515i	$-0.132560\pi$
$200$	−0.398354	−	2.80023i	−0.0281679	−	0.198006i
$201$	4.56887	−	2.80899i	0.322263	−	0.198131i
$202$	17.9409	−	4.04276i	1.26232	−	0.284448i
$203$	−4.91241	+	2.83618i	−0.344784	+	0.199061i
$204$	−0.445753	+	8.45251i	−0.0312089	+	0.591794i
$205$	6.26396	+	3.61650i	0.437494	+	0.252587i
$206$	11.9255	+	3.71466i	0.830891	+	0.258813i
$207$	−13.4255	−	20.5420i	−0.933140	−	1.42777i
$208$	−8.33037	+	3.16362i	−0.577607	+	0.219357i
$209$	3.50498	+	2.02360i	0.242445	+	0.139975i
$210$	2.40314	+	2.46410i	0.165832	+	0.170039i
$211$	−4.02192	−	6.96617i	−0.276880	−	0.479571i	0.693727	−	0.720238i	$-0.255967\pi$
$211$	−4.02192	−	6.96617i	−0.276880	−	0.479571i	−0.970608	+	0.240667i	$0.922634\pi$
$212$	−1.45225	+	18.0403i	−0.0997407	+	1.23902i
$213$	0.617122	+	22.3219i	0.0422845	+	1.52947i
$214$	16.9920	−	15.6791i	1.16155	−	1.07180i
$215$	−6.09134			−0.415426
$216$	9.99460	+	10.7753i	0.680047	+	0.733169i
$217$	2.87365			0.195076
$218$	5.23887	−	4.83409i	0.354821	−	0.327406i
$219$	0.0697566	+	2.52316i	0.00471371	+	0.170500i
$220$	−3.54638	−	0.285484i	−0.239097	−	0.0192473i
$221$	−2.72162	−	4.71399i	−0.183076	−	0.317097i
$222$	−0.804673	−	0.825085i	−0.0540061	−	0.0553760i
$223$	−22.1578	−	12.7928i	−1.48379	−	0.856669i	−0.483963	−	0.875088i	$-0.660803\pi$
$223$	−22.1578	−	12.7928i	−1.48379	−	0.856669i	−0.999830	+	0.0184196i	$0.994137\pi$
$224$	0.484437	+	7.93402i	0.0323678	+	0.530114i
$225$	1.35416	−	2.67698i	0.0902775	−	0.178466i
$226$	−24.9748	−	7.77936i	−1.66130	−	0.517475i
$227$	7.16382	+	4.13603i	0.475479	+	0.274518i	0.718531	−	0.695495i	$-0.244815\pi$
$227$	7.16382	+	4.13603i	0.475479	+	0.274518i	−0.243051	+	0.970013i	$0.578148\pi$
$228$	−7.87017	−	0.415042i	−0.521215	−	0.0274869i
$229$	1.65748	−	0.956947i	0.109529	−	0.0632368i	−0.444235	−	0.895911i	$-0.646524\pi$
$229$	1.65748	−	0.956947i	0.109529	−	0.0632368i	0.553764	+	0.832674i	$0.313191\pi$
$230$	−11.2854	+	2.54302i	−0.744135	+	0.167682i
$231$	3.68826	−	2.26758i	0.242670	−	0.149196i
$232$	1.60808	+	11.3040i	0.105576	+	0.742144i
$233$			27.1552i			1.77900i	0.456937	+	0.889499i	$0.348947\pi$
$233$			27.1552i			1.77900i	−0.456937	+	0.889499i	$0.651053\pi$
$234$	−9.16529	−	2.30793i	−0.599154	−	0.150874i
$235$	−13.3191			−0.868843
$236$	8.43509	+	17.7662i	0.549077	+	1.15648i
$237$	7.52685	−	13.9111i	0.488922	−	0.903624i
$238$	−4.73679	+	1.06738i	−0.307040	+	0.0691878i
$239$	−12.8128	−	22.1925i	−0.828793	−	1.43551i	−0.898986	−	0.437978i	$-0.855695\pi$
$239$	−12.8128	−	22.1925i	−0.828793	−	1.43551i	0.0701924	−	0.997533i	$-0.477639\pi$
$240$	6.40642	−	2.63777i	0.413532	−	0.170267i
$241$	13.3246	−	23.0788i	0.858310	−	1.48664i	−0.0152291	−	0.999884i	$-0.504848\pi$
$241$	13.3246	−	23.0788i	0.858310	−	1.48664i	0.873540	−	0.486753i	$-0.161819\pi$
$242$	3.29542	−	10.5796i	0.211837	−	0.680082i
$243$	2.14743	+	15.4398i	0.137758	+	0.990466i
$244$	5.19881	−	7.53543i	0.332820	−	0.482407i
$245$	2.51276	−	4.35223i	0.160534	−	0.278054i
$246$	−4.79950	+	17.0547i	−0.306005	+	1.08737i
$247$	4.38922	−	2.53412i	0.279279	−	0.161242i
$248$	2.15782	−	5.36678i	0.137022	−	0.340791i
$249$	−5.48887	+	10.1445i	−0.347843	+	0.642883i
$250$	−0.959041	−	1.03935i	−0.0606551	−	0.0657340i
$251$			21.0518i			1.32878i	0.747386	+	0.664390i	$0.231309\pi$
$251$			21.0518i			1.32878i	−0.747386	+	0.664390i	$0.768691\pi$
$252$	−4.39703	+	7.19357i	−0.276987	+	0.453152i
$253$			14.5517i			0.914858i
$254$	11.6122	−	10.7150i	0.728617	−	0.672320i
$255$	2.21654	+	3.60525i	0.138805	+	0.225770i
$256$	15.1812	+	5.05291i	0.948823	+	0.315807i
$257$	−11.9304	+	6.88800i	−0.744196	+	0.429662i	−0.823593	−	0.567181i	$-0.808034\pi$
$257$	−11.9304	+	6.88800i	−0.744196	+	0.429662i	0.0793970	+	0.996843i	$0.474701\pi$
$258$	−3.68096	−	14.4595i	−0.229166	−	0.900209i
$259$	0.330569	−	0.572563i	0.0205406	−	0.0355773i
$260$	−2.53014	+	3.66733i	−0.156913	+	0.227438i
$261$	−5.46650	+	10.8065i	−0.338368	+	0.668903i
$262$	−15.8030	−	4.92245i	−0.976313	−	0.304110i
$263$	−4.05001	+	7.01483i	−0.249734	+	0.432553i	−0.963452	−	0.267881i	$-0.913677\pi$
$263$	−4.05001	+	7.01483i	−0.249734	+	0.432553i	0.713718	+	0.700434i	$0.247010\pi$
$264$	−1.46538	−	8.59085i	−0.0901880	−	0.528730i
$265$	4.52468	+	7.83697i	0.277949	+	0.481421i
$266$	−0.993841	−	4.41045i	−0.0609363	−	0.270422i
$267$	15.2723	−	0.422225i	0.934648	−	0.0258397i
$268$	5.59447	−	2.65617i	0.341737	−	0.162251i
$269$	−1.24883			−0.0761426			−0.0380713	−	0.999275i	$-0.512121\pi$
$269$	−1.24883			−0.0761426			−0.0380713	+	0.999275i	$0.512121\pi$
$270$	7.17288	+	1.59680i	0.436528	+	0.0971782i
$271$			2.06863i			0.125660i	0.998024	+	0.0628302i	$0.0200127\pi$
$271$			2.06863i			0.125660i	−0.998024	+	0.0628302i	$0.979987\pi$
$272$	−1.56343	+	9.64782i	−0.0947969	+	0.584985i
$273$	−0.149838	−	5.41977i	−0.00906858	−	0.328020i
$274$	−1.66688	−	7.39723i	−0.100700	−	0.446883i
$275$	−1.54060	+	0.889464i	−0.0929015	+	0.0536367i
$276$	−12.8562	−	25.2522i	−0.773855	−	1.52001i
$277$	17.7407	+	10.2426i	1.06593	+	0.615417i	0.927067	−	0.374895i	$-0.122321\pi$
$277$	17.7407	+	10.2426i	1.06593	+	0.615417i	0.138865	+	0.990311i	$0.455654\pi$
$278$	−2.80241	+	8.99684i	−0.168077	+	0.539595i
$279$	5.13565	−	3.35648i	0.307463	−	0.200947i
$280$	2.45215	+	3.12775i	0.146544	+	0.186919i
$281$	−7.83557	−	4.52387i	−0.467431	−	0.269871i	0.247733	−	0.968828i	$-0.420315\pi$
$281$	−7.83557	−	4.52387i	−0.467431	−	0.269871i	−0.715164	+	0.698957i	$0.753648\pi$
$282$	−8.04865	−	31.6166i	−0.479290	−	1.88274i
$283$	−13.8103	−	23.9201i	−0.820935	−	1.42190i	−0.904987	−	0.425439i	$-0.860120\pi$
$283$	−13.8103	−	23.9201i	−0.820935	−	1.42190i	0.0840524	−	0.996461i	$-0.473214\pi$
$284$	−2.06899	+	25.7018i	−0.122772	+	1.52512i
$285$	−3.35687	+	2.06384i	−0.198844	+	0.122251i
$286$	3.80063	+	4.11887i	0.224736	+	0.243554i
$287$	−10.1635			−0.599935
$288$	10.1328	+	13.6134i	0.597083	+	0.802179i
$289$	11.0297			0.648806
$290$	3.87146	+	4.19564i	0.227340	+	0.246376i
$291$	−22.7899	−	12.3309i	−1.33597	−	0.722850i
$292$	−0.233870	+	2.90521i	−0.0136862	+	0.170015i
$293$	9.29796	+	16.1045i	0.543192	+	0.940837i	0.998718	+	0.0506143i	$0.0161179\pi$
$293$	9.29796	+	16.1045i	0.543192	+	0.940837i	−0.455526	+	0.890223i	$0.650549\pi$
$294$	11.8497	+	3.33471i	0.691087	+	0.194485i
$295$	8.51602	+	4.91673i	0.495822	+	0.286263i
$296$	−0.821083	−	1.04730i	−0.0477245	−	0.0608731i
$297$	3.94289	−	8.36046i	0.228790	−	0.485123i
$298$	1.89077	−	6.07011i	0.109529	−	0.351632i
$299$	15.7814	+	9.11142i	0.912664	+	0.526927i
$300$	1.88764	−	2.90462i	0.108983	−	0.167698i
$301$	7.41258	−	4.27966i	0.427254	−	0.246675i
$302$	−5.15345	−	22.8699i	−0.296547	−	1.31601i
$303$	19.8101	+	10.7186i	1.13806	+	0.615768i
$304$	−8.98313	−	1.45572i	−0.515218	−	0.0834911i
$305$		−	4.57740i		−	0.262101i
$306$	−7.21863	+	7.44022i	−0.412661	+	0.425329i
$307$	21.1402			1.20653			0.603266	−	0.797540i	$-0.293866\pi$
$307$	21.1402			1.20653			0.603266	+	0.797540i	$0.293866\pi$
$308$	4.51619	−	2.14421i	0.257334	−	0.122178i
$309$	8.01215	+	13.0319i	0.455795	+	0.741360i
$310$	−0.635773	−	2.82142i	−0.0361095	−	0.160246i
$311$	0.847692	+	1.46825i	0.0480682	+	0.0832566i	0.889058	−	0.457794i	$-0.151360\pi$
$311$	0.847692	+	1.46825i	0.0480682	+	0.0832566i	−0.840990	+	0.541050i	$0.818027\pi$
$312$	−10.2344	−	3.78986i	−0.579407	−	0.214559i
$313$	12.1754	−	21.0883i	0.688192	−	1.19198i	−0.284230	−	0.958756i	$-0.591738\pi$
$313$	12.1754	−	21.0883i	0.688192	−	1.19198i	0.972422	−	0.233228i	$-0.0749287\pi$
$314$	17.6508	+	5.49802i	0.996092	+	0.310271i
$315$	0.232909	+	4.20905i	0.0131229	+	0.237153i
$316$	10.3716	−	15.0331i	0.583446	−	0.845678i
$317$	−2.70775	+	4.68996i	−0.152082	+	0.263414i	−0.931993	−	0.362477i	$-0.881931\pi$
$317$	−2.70775	+	4.68996i	−0.152082	+	0.263414i	0.779910	+	0.625891i	$0.215265\pi$
$318$	−15.8690	+	15.4764i	−0.889889	+	0.867874i
$319$	6.21909	−	3.59059i	0.348202	−	0.201035i
$320$	7.68263	−	2.23097i	0.429472	−	0.124715i
$321$	28.3060	−	0.782562i	1.57989	−	0.0436784i
$322$	11.9465	−	11.0235i	0.665755	−	0.614315i
$323$		−	5.55897i		−	0.309310i
$324$	0.544075	+	17.9918i	0.0302264	+	0.999543i
$325$			2.22772i			0.123572i
$326$	−6.39928	−	6.93512i	−0.354423	−	0.384101i
$327$	8.72715	−	0.241275i	0.482612	−	0.0133425i
$328$	−7.63177	+	18.9812i	−0.421394	+	1.04806i
$329$	16.2081	−	9.35775i	0.893581	−	0.515909i
$330$	−3.04236	−	3.11954i	−0.167477	−	0.171725i
$331$	0.632649	−	1.09578i	0.0347735	−	0.0602295i	−0.848115	−	0.529812i	$-0.822262\pi$
$331$	0.632649	−	1.09578i	0.0347735	−	0.0602295i	0.882888	+	0.469583i	$0.155596\pi$
$332$	−7.56335	+	10.9627i	−0.415093	+	0.601658i
$333$	−0.0779876	−	1.40937i	−0.00427369	−	0.0772328i
$334$	2.08694	−	6.69989i	0.114192	−	0.366602i
$335$	1.54825	−	2.68165i	0.0845901	−	0.146514i
$336$	−5.94276	+	7.71094i	−0.324204	+	0.420666i
$337$	−6.03951	−	10.4607i	−0.328993	−	0.569833i	0.653319	−	0.757083i	$-0.273376\pi$
$337$	−6.03951	−	10.4607i	−0.328993	−	0.569833i	−0.982312	+	0.187250i	$0.940043\pi$
$338$	−11.0884	+	2.49863i	−0.603129	+	0.135908i
$339$	−16.7793	−	27.2918i	−0.911327	−	1.48229i
$340$	2.09595	+	4.41454i	0.113669	+	0.239412i
$341$	−3.63803			−0.197010
$342$	−6.92762	−	6.72130i	−0.374603	−	0.363446i
$343$			16.8978i			0.912395i
$344$	−2.42651	−	17.0572i	−0.130829	−	0.919661i
$345$	−12.4612	−	6.74233i	−0.670887	−	0.362995i
$346$	17.1184	−	3.85743i	0.920292	−	0.207377i
$347$	−7.42206	+	4.28513i	−0.398437	+	0.230038i	−0.685809	−	0.727781i	$-0.740552\pi$
$347$	−7.42206	+	4.28513i	−0.398437	+	0.230038i	0.287372	+	0.957819i	$0.407218\pi$
$348$	−7.62002	+	11.7254i	−0.408476	+	0.628547i
$349$	28.8682	+	16.6670i	1.54528	+	0.892166i	0.998492	+	0.0548930i	$0.0174818\pi$
$349$	28.8682	+	16.6670i	1.54528	+	0.892166i	0.546785	+	0.837273i	$0.315852\pi$
$350$	1.89729	+	0.590982i	0.101414	+	0.0315893i
$351$	−6.59818	−	9.51092i	−0.352185	−	0.507656i
$352$	−0.613295	−	10.0444i	−0.0326887	−	0.535370i
$353$	−3.64795	−	2.10614i	−0.194161	−	0.112099i	0.399768	−	0.916616i	$-0.369091\pi$
$353$	−3.64795	−	2.10614i	−0.194161	−	0.112099i	−0.593929	+	0.804518i	$0.702424\pi$
$354$	−6.52505	+	23.1863i	−0.346802	+	1.23234i
$355$	6.44624	+	11.1652i	0.342131	+	0.592588i
$356$	17.5848	+	1.41557i	0.931991	+	0.0750252i
$357$	−5.23030	−	2.82995i	−0.276817	−	0.149777i
$358$	−2.83885	+	2.61951i	−0.150038	+	0.138445i
$359$	22.9791			1.21279			0.606396	−	0.795163i	$-0.292615\pi$
$359$	22.9791			1.21279			0.606396	+	0.795163i	$0.292615\pi$
$360$	8.03562	+	2.72559i	0.423514	+	0.143651i
$361$	−13.8240			−0.727580
$362$	−21.3629	+	19.7123i	−1.12281	+	1.03606i
$363$	11.5611	−	7.10789i	0.606801	−	0.373067i
$364$	0.502353	−	6.24042i	0.0263305	−	0.327087i
$365$	0.728653	+	1.26206i	0.0381394	+	0.0660594i
$366$	10.8657	−	2.76609i	0.567961	−	0.144586i
$367$	4.83241	+	2.78999i	0.252250	+	0.145637i	0.620794	−	0.783974i	$-0.286810\pi$
$367$	4.83241	+	2.78999i	0.252250	+	0.145637i	−0.368544	+	0.929610i	$0.620144\pi$
$368$	−11.6166	−	30.5886i	−0.605558	−	1.59454i
$369$	−18.1637	+	11.8712i	−0.945567	+	0.617990i
$370$	−0.635292	−	0.197886i	−0.0330272	−	0.0102876i
$371$	−11.0122	−	6.35790i	−0.571725	−	0.330086i
$372$	6.31324	−	3.21415i	0.327326	−	0.166646i
$373$	−14.7149	+	8.49564i	−0.761907	+	0.439887i	−0.829980	−	0.557793i	$-0.811648\pi$
$373$	−14.7149	+	8.49564i	−0.761907	+	0.439887i	0.0680727	+	0.997680i	$0.478315\pi$
$374$	5.99675	−	1.35129i	0.310085	−	0.0698738i
$375$	−0.0478668	−	1.73139i	−0.00247183	−	0.0894086i
$376$	−5.30572	−	37.2966i	−0.273622	−	1.92343i
$377$		−	8.99287i		−	0.463156i
$378$	−9.85060	+	3.09637i	−0.506660	+	0.159260i
$379$	9.59477			0.492850			0.246425	−	0.969162i	$-0.420744\pi$
$379$	9.59477			0.492850			0.246425	+	0.969162i	$0.420744\pi$
$380$	−4.11040	+	1.95155i	−0.210859	+	0.100113i
$381$	19.3442	−	0.534799i	0.991033	−	0.0273986i
$382$	−31.7727	+	7.15959i	−1.62563	+	0.366316i
$383$	−5.20924	−	9.02267i	−0.266180	−	0.461037i	0.701692	−	0.712480i	$-0.252428\pi$
$383$	−5.20924	−	9.02267i	−0.266180	−	0.461037i	−0.967872	+	0.251443i	$0.919095\pi$
$384$	9.93839	+	16.8887i	0.507167	+	0.861848i
$385$	1.24984	−	2.16479i	0.0636978	−	0.110328i
$386$	1.74472	−	5.60124i	0.0888040	−	0.285096i
$387$	8.24867	−	16.3064i	0.419303	−	0.828902i
$388$	−24.6280	−	16.9913i	−1.25030	−	0.862601i
$389$	11.3009	−	19.5737i	0.572978	−	0.992427i	−0.423280	−	0.905999i	$-0.639121\pi$
$389$	11.3009	−	19.5737i	0.572978	−	0.992427i	0.996258	−	0.0864284i	$-0.0275454\pi$
$390$	−5.28811	+	1.34620i	−0.267774	+	0.0681673i
$391$	17.3095	−	9.99365i	0.875379	−	0.505400i
$392$	13.1882	+	5.30259i	0.666106	+	0.267821i
$393$	−10.6172	−	17.2691i	−0.535569	−	0.871112i
$394$	−4.84244	−	5.24792i	−0.243959	−	0.264387i
$395$		−	9.13186i		−	0.459474i
$396$	5.56662	−	9.10702i	0.279733	−	0.457645i
$397$			37.1633i			1.86517i	0.360948	+	0.932586i	$0.382453\pi$
$397$			37.1633i			1.86517i	−0.360948	+	0.932586i	$0.617547\pi$
$398$	11.8618	−	10.9453i	0.594580	−	0.548640i
$399$	2.63498	−	4.86996i	0.131914	−	0.243803i
$400$	2.52838	−	3.09957i	0.126419	−	0.154978i
$401$	30.0324	−	17.3392i	1.49975	−	0.865880i	0.499749	−	0.866170i	$-0.333426\pi$
$401$	30.0324	−	17.3392i	1.49975	−	0.865880i	1.00000		0.000290061i	$9.23292e-5\pi$
$402$	7.30125	+	2.05470i	0.364153	+	0.102479i
$403$	−2.27792	+	3.94547i	−0.113471	+	0.196538i
$404$	21.4079	+	14.7696i	1.06508	+	0.734816i
$405$	5.33248	+	7.25015i	0.264973	+	0.360263i
$406$	−7.65898	−	2.38568i	−0.380109	−	0.118399i
$407$	−0.418499	+	0.724862i	−0.0207442	+	0.0359301i
$408$	−9.21258	+	7.64301i	−0.456091	+	0.378385i
$409$	8.35161	+	14.4654i	0.412961	+	0.715269i	0.995212	−	0.0977401i	$-0.0311614\pi$
$409$	8.35161	+	14.4654i	0.412961	+	0.715269i	−0.582251	+	0.813009i	$0.697828\pi$
$410$	2.24860	+	9.97880i	0.111050	+	0.492818i
$411$	4.41940	−	8.16793i	0.217993	−	0.402894i
$412$	7.57625	+	15.9573i	0.373255	+	0.786158i
$413$	−13.8176			−0.679919
$414$	8.47460	−	33.6544i	0.416504	−	1.65402i
$415$			6.65931i			0.326893i
$416$	−11.2773	−	5.62410i	−0.552913	−	0.275744i
$417$	−9.83152	+	6.04452i	−0.481452	+	0.296001i
$418$	1.25820	+	5.58360i	0.0615404	+	0.273103i
$419$	19.2665	−	11.1235i	0.941228	−	0.543418i	0.0508830	−	0.998705i	$-0.483796\pi$
$419$	19.2665	−	11.1235i	0.941228	−	0.543418i	0.890345	+	0.455286i	$0.150463\pi$
$420$	−0.256343	+	4.86087i	−0.0125083	+	0.237186i
$421$	−25.6982	−	14.8369i	−1.25245	−	0.723104i	−0.280857	−	0.959749i	$-0.590619\pi$
$421$	−25.6982	−	14.8369i	−1.25245	−	0.723104i	−0.971596	+	0.236645i	$0.923952\pi$
$422$	3.38308	−	10.8610i	0.164686	−	0.528706i
$423$	18.0362	−	35.6550i	0.876952	−	1.73361i
$424$	−20.1429	+	15.7920i	−0.978227	+	0.766929i
$425$	2.11606	+	1.22171i	0.102644	+	0.0592616i
$426$	−22.6083	+	22.0490i	−1.09538	+	1.06828i
$427$	3.21599	+	5.57026i	0.155633	+	0.269564i
$428$	32.5921	+	2.62366i	1.57540	+	0.126819i
$429$	0.189694	+	6.86140i	0.00915849	+	0.331272i
$430$	−5.84184	−	6.33101i	−0.281719	−	0.305308i
$431$	−1.23870			−0.0596661			−0.0298330	−	0.999555i	$-0.509498\pi$
$431$	−1.23870			−0.0596661			−0.0298330	+	0.999555i	$0.509498\pi$
$432$	−1.61407	+	20.7218i	−0.0776569	+	0.996980i
$433$	27.2485			1.30948			0.654739	−	0.755855i	$-0.272779\pi$
$433$	27.2485			1.30948			0.654739	+	0.755855i	$0.272779\pi$
$434$	2.75595	+	2.98672i	0.132290	+	0.143367i
$435$	0.193229	+	6.98928i	0.00926462	+	0.335111i
$436$	10.0486	+	0.808911i	0.481240	+	0.0387398i
$437$	9.30513	+	16.1170i	0.445125	+	0.770979i
$438$	−2.55554	+	2.49232i	−0.122108	+	0.119088i
$439$	1.13429	+	0.654883i	0.0541367	+	0.0312559i	0.526824	−	0.849974i	$-0.323383\pi$
$439$	1.13429	+	0.654883i	0.0541367	+	0.0312559i	−0.472687	+	0.881230i	$0.656716\pi$
$440$	−3.10441	−	3.95971i	−0.147997	−	0.188772i
$441$	8.24816	+	12.6202i	0.392769	+	0.600964i
$442$	2.28932	−	7.34962i	0.108892	−	0.349586i
$443$	−13.9249	−	8.03957i	−0.661594	−	0.381972i	0.131290	−	0.991344i	$-0.458088\pi$
$443$	−13.9249	−	8.03957i	−0.661594	−	0.381972i	−0.792884	+	0.609372i	$0.791421\pi$
$444$	0.0858345	−	1.62762i	0.00407353	−	0.0772436i
$445$	7.63906	−	4.41041i	0.362126	−	0.209074i
$446$	−7.95407	−	35.2984i	−0.376636	−	1.67143i
$447$	6.63326	−	4.07820i	0.313743	−	0.192892i
$448$	−7.78160	+	8.11255i	−0.367646	+	0.383282i
$449$			31.0748i			1.46651i	0.679952	+	0.733256i	$0.262000\pi$
$449$			31.0748i			1.46651i	−0.679952	+	0.733256i	$0.738000\pi$
$450$	4.08101	−	1.15989i	0.192381	−	0.0546779i
$451$	12.8670			0.605883
$452$	−15.8664	−	33.4182i	−0.746294	−	1.57186i
$453$	13.6634	−	25.2526i	0.641961	−	1.18647i
$454$	2.57163	+	11.4123i	0.120692	+	0.535606i
$455$	−1.56515	−	2.71092i	−0.0733754	−	0.127090i
$456$	−7.11644	−	8.57788i	−0.333258	−	0.401696i
$457$	−6.48546	+	11.2332i	−0.303377	+	0.525465i	−0.976899	−	0.213703i	$-0.931448\pi$
$457$	−6.48546	+	11.2332i	−0.303377	+	0.525465i	0.673522	+	0.739168i	$0.264781\pi$
$458$	2.58419	+	0.804945i	0.120751	+	0.0376126i
$459$	−12.6528	+	1.05156i	−0.590580	+	0.0490824i
$460$	−13.4662	−	9.29054i	−0.627865	−	0.433174i
$461$	−12.8548	+	22.2653i	−0.598710	+	1.03700i	0.394302	+	0.918981i	$0.370986\pi$
$461$	−12.8548	+	22.2653i	−0.598710	+	1.03700i	−0.993012	+	0.118015i	$0.962347\pi$
$462$	5.89400	+	1.65868i	0.274214	+	0.0771687i
$463$	−28.1403	+	16.2468i	−1.30779	+	0.755052i	−0.981727	−	0.190296i	$-0.939055\pi$
$463$	−28.1403	+	16.2468i	−1.30779	+	0.755052i	−0.326062	+	0.945348i	$0.605722\pi$
$464$	−10.2066	+	12.5124i	−0.473828	+	0.580872i
$465$	1.68563	−	3.11538i	0.0781692	−	0.144472i
$466$	−28.2237	+	26.0430i	−1.30744	+	1.20642i
$467$			4.35490i			0.201521i	0.994911	+	0.100760i	$0.0321276\pi$
$467$			4.35490i			0.201521i	−0.994911	+	0.100760i	$0.967872\pi$
$468$	−6.39114	−	11.7393i	−0.295431	−	0.542650i
$469$			4.35109i			0.200915i
$470$	−12.7736	−	13.8432i	−0.589201	−	0.638537i
$471$	11.8587	+	19.2883i	0.546419	+	0.888760i
$472$	−10.3756	+	25.8054i	−0.477575	+	1.18779i
$473$	−9.38429	+	5.41802i	−0.431490	+	0.249121i
$474$	21.6770	−	5.51833i	0.995659	−	0.253465i
$475$	−1.13754	+	1.97028i	−0.0521939	+	0.0904025i
$476$	−5.65215	−	3.89950i	−0.259066	−	0.178733i
$477$	−27.1066	+	1.49995i	−1.24113	+	0.0686780i
$478$	10.7776	−	34.6005i	0.492957	−	1.58259i
$479$	−6.74075	+	11.6753i	−0.307993	+	0.533459i	−0.977923	−	0.208965i	$-0.932991\pi$
$479$	−6.74075	+	11.6753i	−0.307993	+	0.533459i	0.669930	+	0.742424i	$0.266324\pi$
$480$	8.88557	+	4.12876i	0.405569	+	0.188451i
$481$	0.524079	+	0.907731i	0.0238959	+	0.0413890i
$482$	36.7657	−	8.28470i	1.67463	−	0.377358i
$483$	19.9011	−	0.550195i	0.905531	−	0.0250347i
$484$	14.1563	−	6.72118i	0.643468	−	0.305508i
$485$	−14.9603			−0.679313
$486$	−13.9879	+	17.0394i	−0.634502	+	0.772921i
$487$		−	3.52103i		−	0.159553i	−0.996813	−	0.0797765i	$-0.974579\pi$
$487$		−	3.52103i		−	0.159553i	0.996813	−	0.0797765i	$-0.0254206\pi$
$488$	12.8178	−	1.82343i	0.580234	−	0.0825426i
$489$	−0.319395	−	11.5528i	−0.0144435	−	0.522437i
$490$	6.93331	−	1.56234i	0.313215	−	0.0705792i
$491$	−33.6029	+	19.4007i	−1.51648	+	0.875539i	−0.516666	+	0.856187i	$0.672827\pi$
$491$	−33.6029	+	19.4007i	−1.51648	+	0.875539i	−0.999813	+	0.0193523i	$0.993840\pi$
$492$	−22.3287	+	11.3678i	−1.00665	+	0.512500i
$493$	−8.54214	−	4.93181i	−0.384719	−	0.222117i
$494$	6.84327	+	2.13160i	0.307893	+	0.0959051i
$495$	−0.294861	−	5.32863i	−0.0132530	−	0.239504i
$496$	7.64738	−	2.90424i	0.343377	−	0.130404i
$497$	−15.6889	−	9.05801i	−0.703744	−	0.406307i
$498$	−15.8077	+	4.02418i	−0.708361	+	0.180328i
$499$	8.31771	+	14.4067i	0.372352	+	0.644932i	0.989927	−	0.141580i	$-0.0452182\pi$
$499$	8.31771	+	14.4067i	0.372352	+	0.644932i	−0.617575	+	0.786512i	$0.711885\pi$
$500$	0.160481	−	1.99355i	0.00717692	−	0.0891543i
$501$	7.32147	−	4.50131i	0.327099	−	0.201104i
$502$	−21.8802	+	20.1896i	−0.976559	+	0.901105i
$503$	−4.70283			−0.209689			−0.104844	−	0.994489i	$-0.533434\pi$
$503$	−4.70283			−0.209689			−0.104844	+	0.994489i	$0.533434\pi$
$504$	−11.6935	+	2.32889i	−0.520871	+	0.103737i
$505$	13.0042			0.578680
$506$	−15.1243	+	13.9557i	−0.672356	+	0.620406i
$507$	−12.2437	−	6.62465i	−0.543760	−	0.294211i
$508$	22.2732	+	1.79299i	0.988215	+	0.0795513i
$509$	−6.15218	−	10.6559i	−0.272691	−	0.472314i	0.696859	−	0.717208i	$-0.254580\pi$
$509$	−6.15218	−	10.6559i	−0.272691	−	0.472314i	−0.969550	+	0.244894i	$0.921247\pi$
$510$	−1.62135	+	5.76134i	−0.0717944	+	0.255116i
$511$	−1.77340	−	1.02388i	−0.0784508	−	0.0452936i
$512$	9.30765	+	20.6244i	0.411344	+	0.911480i
$513$	−0.979109	−	11.7810i	−0.0432287	−	0.520146i
$514$	−18.6007	−	5.79391i	−0.820443	−	0.255558i
$515$	7.64894	+	4.41612i	0.337053	+	0.194597i
$516$	11.4982	−	17.6930i	0.506181	−	0.778892i
$517$	−20.5194	+	11.8469i	−0.902440	+	0.521024i
$518$	0.912121	−	0.205535i	0.0400763	−	0.00903070i
$519$	18.9020	+	10.2272i	0.829704	+	0.448926i
$520$	−6.23813	+	0.887420i	−0.273560	+	0.0389160i
$521$		−	0.855870i		−	0.0374963i	−0.999824	−	0.0187482i	$-0.994032\pi$
$521$		−	0.855870i		−	0.0374963i	0.999824	−	0.0187482i	$-0.00596808\pi$
$522$	−16.4743	+	4.68226i	−0.721058	+	0.204937i
$523$	−10.7179			−0.468659			−0.234330	−	0.972157i	$-0.575290\pi$
$523$	−10.7179			−0.468659			−0.234330	+	0.972157i	$0.575290\pi$
$524$	−10.0396	−	21.1456i	−0.438582	−	0.923751i
$525$	1.27469	+	2.07331i	0.0556320	+	0.0904865i
$526$	−11.1750	+	2.51814i	−0.487252	+	0.109796i
$527$	2.49848	+	4.32750i	0.108836	+	0.188509i
$528$	7.52350	−	9.76201i	0.327418	−	0.424837i
$529$	−21.9566	+	38.0300i	−0.954635	+	1.65348i
$530$	−3.80597	+	12.2187i	−0.165321	+	0.530745i
$531$	−24.6941	+	16.1392i	−1.07163	+	0.700381i
$532$	3.63085	−	5.26274i	0.157417	−	0.228169i
$533$	8.05654	−	13.9543i	0.348968	−	0.604430i
$534$	15.0856	+	15.4683i	0.652817	+	0.669377i
$535$	14.1584	−	8.17437i	0.612122	−	0.353409i
$536$	8.12601	+	3.26722i	0.350990	+	0.141123i
$537$	−4.72908	+	0.130742i	−0.204075	+	0.00564195i
$538$	−1.19768	−	1.29797i	−0.0516357	−	0.0559594i
$539$		−	8.94004i		−	0.385075i
$540$	5.21946	+	8.98650i	0.224610	+	0.386718i
$541$			6.01003i			0.258391i	0.991619	+	0.129196i	$0.0412395\pi$
$541$			6.01003i			0.258391i	−0.991619	+	0.129196i	$0.958760\pi$
$542$	−2.15002	+	1.98390i	−0.0923514	+	0.0852159i
$543$	−35.5874	+	0.983865i	−1.52720	+	0.0422217i
$544$	−11.5268	+	7.62771i	−0.494208	+	0.327035i
$545$	4.36524	−	2.52027i	0.186986	−	0.107957i
$546$	5.48932	−	5.35352i	0.234921	−	0.229109i
$547$	−3.69184	+	6.39445i	−0.157852	+	0.273407i	−0.934094	−	0.357028i	$-0.883790\pi$
$547$	−3.69184	+	6.39445i	−0.157852	+	0.273407i	0.776242	+	0.630435i	$0.217123\pi$
$548$	6.08968	−	8.82671i	0.260138	−	0.377058i
$549$	12.2536	+	6.19855i	0.522972	+	0.264548i
$550$	−2.40196	−	0.748181i	−0.102420	−	0.0319025i
$551$	4.59203	−	7.95363i	0.195627	−	0.338836i
$552$	13.9162	−	37.5800i	0.592311	−	1.59951i
$553$	6.41587	+	11.1126i	0.272831	+	0.472556i
$554$	6.36844	+	28.2617i	0.270569	+	1.20073i
$555$	−0.426820	−	0.694230i	−0.0181175	−	0.0294684i
$556$	−12.0385	+	5.71567i	−0.510544	+	0.242398i
$557$	−33.7176			−1.42866			−0.714331	−	0.699808i	$-0.753269\pi$
$557$	−33.7176			−1.42866			−0.714331	+	0.699808i	$0.753269\pi$
$558$	8.41384	+	2.11871i	0.356186	+	0.0896922i
$559$			13.5698i			0.573941i
$560$	−0.899097	+	5.54827i	−0.0379938	+	0.234457i
$561$	6.62154	+	3.58270i	0.279562	+	0.151262i
$562$	−2.81277	−	12.4824i	−0.118649	−	0.526540i
$563$	9.04056	−	5.21957i	0.381014	−	0.219979i	−0.297245	−	0.954801i	$-0.596068\pi$
$563$	9.04056	−	5.21957i	0.381014	−	0.219979i	0.678259	+	0.734823i	$0.262735\pi$
$564$	25.1416	−	38.6870i	1.05865	−	1.62901i
$565$	−16.0187	−	9.24838i	−0.673910	−	0.389082i
$566$	11.6166	−	37.2940i	0.488283	−	1.56758i
$567$	−11.5829	−	5.07624i	−0.486438	−	0.213182i
$568$	−28.6973	+	22.4987i	−1.20411	+	0.944024i
$569$	1.98850	+	1.14806i	0.0833621	+	0.0481291i	0.541102	−	0.840957i	$-0.318007\pi$
$569$	1.98850	+	1.14806i	0.0833621	+	0.0481291i	−0.457740	+	0.889086i	$0.651341\pi$
$570$	−5.36441	−	1.50964i	−0.224690	−	0.0632320i
$571$	16.4667	+	28.5212i	0.689111	+	1.19357i	0.972126	+	0.234459i	$0.0753319\pi$
$571$	16.4667	+	28.5212i	0.689111	+	1.19357i	−0.283015	+	0.959115i	$0.591335\pi$
$572$	−0.635977	+	7.90034i	−0.0265915	+	0.330330i
$573$	−35.0830	−	18.9823i	−1.46561	−	0.792996i
$574$	−9.74725	−	10.5634i	−0.406842	−	0.440909i
$575$	−8.18005			−0.341132
$576$	−4.43126	+	23.5874i	−0.184636	+	0.982807i
$577$	−40.1965			−1.67340			−0.836700	−	0.547661i	$-0.815518\pi$
$577$	−40.1965			−1.67340			−0.836700	+	0.547661i	$0.815518\pi$
$578$	10.5779	+	11.4637i	0.439984	+	0.476826i
$579$	6.12090	−	3.76319i	0.254376	−	0.156393i
$580$	−0.647830	+	8.04758i	−0.0268997	+	0.334158i
$581$	−4.67870	−	8.10375i	−0.194105	−	0.336200i
$582$	−9.04042	−	35.5125i	−0.374738	−	1.47204i
$583$	13.9414	+	8.04907i	0.577394	+	0.333358i
$584$	−3.24381	+	2.54315i	−0.134230	+	0.105236i
$585$	−5.96356	−	3.01669i	−0.246563	−	0.124725i
$586$	−7.82106	+	25.1087i	−0.323085	+	1.03723i
$587$	19.2022	+	11.0864i	0.792558	+	0.457584i	0.840862	−	0.541249i	$-0.182048\pi$
$587$	19.2022	+	11.0864i	0.792558	+	0.457584i	−0.0483041	+	0.998833i	$0.515382\pi$
$588$	7.89840	+	15.5140i	0.325725	+	0.639788i
$589$	−4.02936	+	2.32635i	−0.166027	+	0.0958556i
$590$	3.05703	+	13.5664i	0.125856	+	0.558521i
$591$	−0.241692	−	8.74223i	−0.00994187	−	0.359607i
$592$	0.301056	−	1.85779i	0.0123733	−	0.0763549i
$593$			34.7611i			1.42747i	0.700417	+	0.713734i	$0.252998\pi$
$593$			34.7611i			1.42747i	−0.700417	+	0.713734i	$0.747002\pi$
$594$	12.4708	−	3.91999i	0.511684	−	0.160839i
$595$	−3.43340			−0.140756
$596$	8.12227	−	3.85632i	0.332701	−	0.157961i
$597$	19.7600	−	0.546293i	0.808722	−	0.0223583i
$598$	5.66513	+	25.1406i	0.231664	+	1.02808i
$599$	−8.84778	−	15.3248i	−0.361510	−	0.626154i	0.626699	−	0.779261i	$-0.284405\pi$
$599$	−8.84778	−	15.3248i	−0.361510	−	0.626154i	−0.988210	+	0.153107i	$0.951072\pi$
$600$	4.82923	−	0.823744i	0.197152	−	0.0336292i
$601$	−7.28596	+	12.6197i	−0.297200	+	0.514766i	−0.975494	−	0.220024i	$-0.929386\pi$
$601$	−7.28596	+	12.6197i	−0.297200	+	0.514766i	0.678294	+	0.734791i	$0.262720\pi$
$602$	11.5570	+	3.59987i	0.471029	+	0.146720i
$603$	5.08215	+	7.77604i	0.206961	+	0.316665i
$604$	18.8273	−	27.2893i	0.766073	−	1.11039i
$605$	3.91771	−	6.78567i	0.159278	−	0.275877i
$606$	7.85837	+	30.8692i	0.319224	+	1.25397i
$607$	−38.3460	+	22.1391i	−1.55642	+	0.898598i	−0.558823	+	0.829287i	$0.688747\pi$
$607$	−38.3460	+	22.1391i	−1.55642	+	0.898598i	−0.997595	+	0.0693110i	$0.977920\pi$
$608$	−7.10220	−	10.7327i	−0.288032	−	0.435268i
$609$	−5.14568	−	8.36954i	−0.208513	−	0.339151i
$610$	4.75750	−	4.38991i	0.192626	−	0.177742i
$611$			29.6712i			1.20037i
$612$	−14.6559	−	0.367177i	−0.592430	−	0.0148422i
$613$		−	38.5861i		−	1.55848i	−0.626727	−	0.779239i	$-0.715606\pi$
$613$		−	38.5861i		−	1.55848i	0.626727	−	0.779239i	$-0.284394\pi$
$614$	20.2743	+	21.9719i	0.818204	+	0.886716i
$615$	−5.96173	+	11.0185i	−0.240400	+	0.444308i
$616$	6.55979	+	2.63749i	0.264301	+	0.106268i
$617$	−4.42105	+	2.55249i	−0.177985	+	0.102759i	−0.586345	−	0.810061i	$-0.699434\pi$
$617$	−4.42105	+	2.55249i	−0.177985	+	0.102759i	0.408361	+	0.912821i	$0.366101\pi$
$618$	−5.86069	+	20.8255i	−0.235751	+	0.837726i
$619$	−4.20314	+	7.28005i	−0.168938	+	0.292610i	−0.938047	−	0.346508i	$-0.887367\pi$
$619$	−4.20314	+	7.28005i	−0.168938	+	0.292610i	0.769109	+	0.639118i	$0.220701\pi$
$620$	2.32270	−	3.36665i	0.0932819	−	0.135208i
$621$	34.9236	−	24.2281i	1.40143	−	0.972241i
$622$	−0.713044	+	2.28915i	−0.0285905	+	0.0917867i
$623$	−6.19734	+	10.7341i	−0.248291	+	0.430053i
$624$	−5.87620	−	14.2717i	−0.235236	−	0.571325i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	33.5948	−	7.57017i	1.34272	−	0.302565i
$627$	−3.33587	+	6.16535i	−0.133222	+	0.246220i
$628$	11.2135	+	23.6181i	0.447467	+	0.942465i
$629$	1.14965			0.0458394
$630$	−4.15129	+	4.27872i	−0.165391	+	0.170468i
$631$			22.0910i			0.879428i	0.898138	+	0.439714i	$0.144920\pi$
$631$			22.0910i			0.879428i	−0.898138	+	0.439714i	$0.855080\pi$
$632$	25.5714	−	3.63771i	1.01717	−	0.144701i
$633$	11.8686	−	7.29696i	0.471736	−	0.290028i
$634$	−7.47134	+	1.68357i	−0.296725	+	0.0668633i
$635$	9.67579	−	5.58632i	0.383972	−	0.221686i
$636$	−31.3044	−	1.65087i	−1.24130	−	0.0654613i
$637$	−9.69554	−	5.59772i	−0.384151	−	0.221790i
$638$	9.69623	+	3.02026i	0.383877	+	0.119573i
$639$	−38.6183	+	2.13696i	−1.52772	+	0.0845366i
$640$	9.68671	+	5.84532i	0.382901	+	0.231056i
$641$	−1.40461	−	0.810952i	−0.0554788	−	0.0320307i	0.472004	−	0.881596i	$-0.343531\pi$
$641$	−1.40461	−	0.810952i	−0.0554788	−	0.0320307i	−0.527483	+	0.849566i	$0.676864\pi$
$642$	27.9600	+	28.6693i	1.10349	+	1.13149i
$643$	−19.7339	−	34.1802i	−0.778231	−	1.34794i	−0.932961	−	0.359979i	$-0.882784\pi$
$643$	−19.7339	−	34.1802i	−0.778231	−	1.34794i	0.154730	−	0.987957i	$-0.450549\pi$
$644$	22.9145	+	1.84461i	0.902956	+	0.0726879i
$645$	−0.291573	−	10.5465i	−0.0114807	−	0.415267i
$646$	5.77770	−	5.33128i	0.227321	−	0.209757i
$647$	27.7156			1.08961			0.544806	−	0.838562i	$-0.316603\pi$
$647$	27.7156			1.08961			0.544806	+	0.838562i	$0.316603\pi$
$648$	−18.1779	+	17.8203i	−0.714095	+	0.700049i
$649$	17.4930			0.686660
$650$	−2.31537	+	2.13647i	−0.0908163	+	0.0837993i
$651$	0.137553	+	4.97541i	0.00539111	+	0.195002i
$652$	1.07082	−	13.3021i	0.0419366	−	0.520952i
$653$	20.0327	+	34.6976i	0.783939	+	1.35782i	0.929631	+	0.368492i	$0.120126\pi$
$653$	20.0327	+	34.6976i	0.783939	+	1.35782i	−0.145692	+	0.989330i	$0.546541\pi$
$654$	8.62046	+	8.83914i	0.337087	+	0.345638i
$655$	−10.1359	−	5.85198i	−0.396044	−	0.228656i
$656$	−27.0472	+	10.2717i	−1.05602	+	0.401043i
$657$	−4.36524	+	0.241552i	−0.170304	+	0.00942382i
$658$	25.2702	+	7.87136i	0.985133	+	0.306857i
$659$	−25.5398	−	14.7454i	−0.994891	−	0.574400i	−0.0881582	−	0.996106i	$-0.528098\pi$
$659$	−25.5398	−	14.7454i	−0.994891	−	0.574400i	−0.906733	+	0.421706i	$0.861431\pi$
$660$	0.324529	−	6.15383i	0.0126323	−	0.239538i
$661$	8.88631	−	5.13051i	0.345637	−	0.199554i	−0.317125	−	0.948384i	$-0.602717\pi$
$661$	8.88631	−	5.13051i	0.345637	−	0.199554i	0.662762	+	0.748830i	$0.269384\pi$
$662$	1.74563	−	0.393357i	0.0678459	−	0.0152883i
$663$	8.03148	−	4.93783i	0.311917	−	0.191770i
$664$	−18.6476	+	2.65276i	−0.723668	+	0.102947i
$665$		−	3.19685i		−	0.123969i
$666$	1.39003	−	1.43270i	0.0538624	−	0.0555158i
$667$	33.0213			1.27859
$668$	8.96496	−	4.25642i	0.346865	−	0.164686i
$669$	21.0887	−	38.9761i	0.815336	−	1.50690i
$670$	4.27200	−	0.962644i	0.165042	−	0.0371902i
$671$	−4.07143	−	7.05193i	−0.157176	−	0.272237i
$672$	−13.7137	+	1.21853i	−0.529017	+	0.0470056i
$673$	21.0722	−	36.4982i	0.812274	−	1.40690i	−0.0989942	−	0.995088i	$-0.531563\pi$
$673$	21.0722	−	36.4982i	0.812274	−	1.40690i	0.911269	−	0.411813i	$-0.135104\pi$
$674$	5.08019	−	16.3094i	0.195682	−	0.628216i
$675$	4.69972	+	2.21644i	0.180892	+	0.0853110i
$676$	−13.2312	−	9.12838i	−0.508891	−	0.351092i
$677$	22.3699	−	38.7459i	0.859746	−	1.48912i	−0.0124242	−	0.999923i	$-0.503955\pi$
$677$	22.3699	−	38.7459i	0.859746	−	1.48912i	0.872171	−	0.489202i	$-0.162712\pi$
$678$	12.2736	−	43.6135i	0.471366	−	1.67497i
$679$	18.2053	−	10.5108i	0.698655	−	0.403369i
$680$	−2.57813	+	6.41215i	−0.0988668	+	0.245895i
$681$	−6.81817	+	12.6013i	−0.261273	+	0.482884i
$682$	−3.48902	−	3.78117i	−0.133602	−	0.144789i
$683$		−	45.1722i		−	1.72846i	−0.503093	−	0.864232i	$-0.667805\pi$
$683$		−	45.1722i		−	1.72846i	0.503093	−	0.864232i	$-0.332195\pi$
$684$	0.341880	−	13.6462i	0.0130721	−	0.521775i
$685$		−	5.36178i		−	0.204863i
$686$	−17.5627	+	16.2057i	−0.670546	+	0.618736i
$687$	1.73619	+	2.82394i	0.0662396	+	0.107740i
$688$	15.4012	−	18.8805i	0.587165	−	0.719813i
$689$	17.4586	−	10.0797i	0.665118	−	0.384006i
$690$	−4.94315	−	19.4176i	−0.188183	−	0.739217i
$691$	8.39067	−	14.5331i	0.319196	−	0.552864i	−0.661124	−	0.750276i	$-0.729920\pi$
$691$	8.39067	−	14.5331i	0.319196	−	0.552864i	0.980321	+	0.197412i	$0.0632537\pi$
$692$	20.4265	+	14.0925i	0.776498	+	0.535718i
$693$	4.10261	+	6.27728i	0.155845	+	0.238454i
$694$	−11.5718	−	3.60448i	−0.439259	−	0.136824i
$695$	−3.33160	+	5.77051i	−0.126375	+	0.218888i
$696$	−19.4947	+	3.32530i	−0.738943	+	0.126045i
$697$	−8.83663	−	15.3055i	−0.334711	−	0.579737i
$698$	10.3629	+	45.9884i	0.392242	+	1.74069i
$699$	−47.0163	+	1.29983i	−1.77832	+	0.0491642i
$700$	1.20534	+	2.53871i	0.0455576	+	0.0959544i
$701$	−24.7544			−0.934961			−0.467480	−	0.884003i	$-0.654838\pi$
$701$	−24.7544			−0.934961			−0.467480	+	0.884003i	$0.654838\pi$
$702$	3.55722	−	15.9792i	0.134259	−	0.603094i
$703$			1.07044i			0.0403725i
$704$	9.85146	−	10.2704i	0.371291	−	0.387082i
$705$	−0.637543	−	23.0606i	−0.0240113	−	0.868511i
$706$	−1.30952	−	5.81135i	−0.0492844	−	0.218713i
$707$	−15.8249	+	9.13652i	−0.595157	+	0.343614i
$708$	−30.3564	+	15.4548i	−1.14086	+	0.580828i
$709$	−28.9637	−	16.7222i	−1.08776	−	0.628016i	−0.154778	−	0.987949i	$-0.549466\pi$
$709$	−28.9637	−	16.7222i	−1.08776	−	0.628016i	−0.932978	+	0.359933i	$0.882799\pi$
$710$	−5.42231	+	17.4078i	−0.203496	+	0.653302i
$711$	24.4458	+	12.3660i	0.916791	+	0.463762i
$712$	15.3932	+	19.6342i	0.576886	+	0.735825i
$713$	−14.4875	−	8.36439i	−0.542563	−	0.313249i
$714$	−2.07478	−	8.15013i	−0.0776467	−	0.305011i
$715$	1.98147	+	3.43201i	0.0741029	+	0.128350i
$716$	−5.44515	−	0.438334i	−0.203495	−	0.0163813i
$717$	37.8105	−	23.2463i	1.41206	−	0.868148i
$718$	22.0379	+	23.8833i	0.822448	+	0.891316i
$719$	−16.1805			−0.603429			−0.301715	−	0.953398i	$-0.597559\pi$
$719$	−16.1805			−0.603429			−0.301715	+	0.953398i	$0.597559\pi$
$720$	4.87366	+	10.9657i	0.181631	+	0.408669i
$721$	−12.4107			−0.462199
$722$	−13.2578	−	14.3679i	−0.493404	−	0.534719i
$723$	40.5962	+	21.9653i	1.50979	+	0.816898i
$724$	−40.9759	−	3.29856i	−1.52286	−	0.122590i
$725$	2.01840	+	3.49598i	0.0749616	+	0.129837i
$726$	18.4751	+	5.19924i	0.685676	+	0.192962i
$727$	23.0048	+	13.2818i	0.853201	+	0.492596i	0.861730	−	0.507368i	$-0.169381\pi$
$727$	23.0048	+	13.2818i	0.853201	+	0.492596i	−0.00852835	+	0.999964i	$0.502715\pi$
$728$	6.96773	−	5.46270i	0.258241	−	0.202461i
$729$	−26.6296	+	4.45709i	−0.986281	+	0.165077i
$730$	−0.612913	+	1.96769i	−0.0226849	+	0.0728276i
$731$	12.8897	+	7.44185i	0.476741	+	0.275247i
$732$	13.2956	+	8.64047i	0.491420	+	0.319361i
$733$	18.7821	−	10.8439i	0.693733	−	0.400527i	−0.111276	−	0.993790i	$-0.535494\pi$
$733$	18.7821	−	10.8439i	0.693733	−	0.400527i	0.805009	+	0.593262i	$0.202160\pi$
$734$	1.73471	+	7.69827i	0.0640294	+	0.284148i
$735$	7.65568	+	4.14224i	0.282384	+	0.152789i
$736$	20.6514	−	41.4095i	0.761220	−	1.52637i
$737$		−	5.50846i		−	0.202907i
$738$	−29.7581	−	7.49345i	−1.09541	−	0.275838i
$739$	−5.29348			−0.194724			−0.0973620	−	0.995249i	$-0.531040\pi$
$739$	−5.29348			−0.194724			−0.0973620	+	0.995249i	$0.531040\pi$
$740$	−0.403599	−	0.850068i	−0.0148366	−	0.0312491i
$741$	4.59764	+	7.47815i	0.168899	+	0.274717i
$742$	−3.95310	−	17.5430i	−0.145123	−	0.644023i
$743$	−5.33472	−	9.24001i	−0.195712	−	0.338983i	0.751422	−	0.659822i	$-0.229368\pi$
$743$	−5.33472	−	9.24001i	−0.195712	−	0.338983i	−0.947134	+	0.320839i	$0.896035\pi$
$744$	9.39527	+	3.47914i	0.344447	+	0.127551i
$745$	2.24781	−	3.89332i	0.0823534	−	0.142640i
$746$	−22.9421	−	7.14619i	−0.839969	−	0.261640i
$747$	−17.8269	−	9.01779i	−0.652251	−	0.329944i
$748$	7.15559	+	4.93675i	0.261634	+	0.180506i
$749$	−11.4863	+	19.8949i	−0.419701	+	0.726943i
$750$	1.75361	−	1.71022i	0.0640327	−	0.0624485i
$751$	−3.82460	+	2.20814i	−0.139562	+	0.0805760i	−0.568155	−	0.822921i	$-0.692343\pi$
$751$	−3.82460	+	2.20814i	−0.139562	+	0.0805760i	0.428593	+	0.903497i	$0.359009\pi$
$752$	33.6757	−	41.2835i	1.22803	−	1.50545i
$753$	−36.4489	+	1.00768i	−1.32827	+	0.0367221i
$754$	9.34670	−	8.62453i	0.340387	−	0.314087i
$755$		−	16.5769i		−	0.603296i
$756$	−12.6653	−	7.26864i	−0.460634	−	0.264358i
$757$		−	35.2525i		−	1.28127i	−0.767844	−	0.640637i	$-0.778670\pi$
$757$		−	35.2525i		−	1.28127i	0.767844	−	0.640637i	$-0.221330\pi$
$758$	9.20178	+	9.97228i	0.334224	+	0.362210i
$759$	−25.1947	+	0.696544i	−0.914509	+	0.0252829i
$760$	−5.97038	−	2.40051i	−0.216569	−	0.0870757i
$761$	−9.26359	+	5.34834i	−0.335805	+	0.193877i	−0.658415	−	0.752655i	$-0.728773\pi$
$761$	−9.26359	+	5.34834i	−0.335805	+	0.193877i	0.322611	+	0.946532i	$0.395440\pi$
$762$	19.1077	+	19.5924i	0.692199	+	0.709758i
$763$	−3.54139	+	6.13387i	−0.128207	+	0.222061i
$764$	−37.9126	−	26.1565i	−1.37163	−	0.946308i
$765$	−6.13599	+	4.01027i	−0.221847	+	0.144992i
$766$	4.38180	−	14.0673i	0.158321	−	0.508273i
$767$	10.9531	−	18.9713i	0.395493	−	0.685013i
$768$	−8.02188	+	26.5264i	−0.289465	+	0.957189i
$769$	−8.46964	−	14.6698i	−0.305423	−	0.529008i	0.671933	−	0.740612i	$-0.265464\pi$
$769$	−8.46964	−	14.6698i	−0.305423	−	0.529008i	−0.977355	+	0.211604i	$0.932131\pi$
$770$	3.44861	−	0.777103i	0.124279	−	0.0280048i
$771$	−12.4969	−	20.3264i	−0.450064	−	0.732038i
$772$	7.49489	−	3.55845i	0.269747	−	0.128072i
$773$	−10.6111			−0.381656			−0.190828	−	0.981623i	$-0.561117\pi$
$773$	−10.6111			−0.381656			−0.190828	+	0.981623i	$0.561117\pi$
$774$	24.8588	−	7.06530i	0.893532	−	0.253957i
$775$		−	2.04507i		−	0.0734611i
$776$	−5.95950	−	41.8924i	−0.213934	−	1.50385i
$777$	1.00715	+	0.544937i	0.0361314	+	0.0195495i
$778$	31.1819	−	7.02646i	1.11793	−	0.251911i
$779$	14.2510	−	8.22783i	0.510596	−	0.294793i
$780$	−6.47068	−	4.20512i	−0.231687	−	0.150567i
$781$	19.8621	+	11.4674i	0.710722	+	0.410335i
$782$	26.9874	+	8.40625i	0.965067	+	0.300607i
$783$	−18.9719	−	8.94736i	−0.677999	−	0.319753i
$784$	7.13683	+	18.7925i	0.254887	+	0.671162i
$785$	11.3211	+	6.53624i	0.404067	+	0.233288i
$786$	7.76624	−	27.5968i	0.277012	−	0.984344i
$787$	−10.6302	−	18.4121i	−0.378926	−	0.656319i	0.611980	−	0.790873i	$-0.290373\pi$
$787$	−10.6302	−	18.4121i	−0.378926	−	0.656319i	−0.990906	+	0.134554i	$0.957040\pi$
$788$	0.810308	−	10.0659i	0.0288660	−	0.358585i
$789$	−12.3393	−	6.67637i	−0.439289	−	0.237685i
$790$	9.49117	−	8.75783i	0.337681	−	0.311590i
$791$	25.9909			0.924131
$792$	14.8040	−	2.94836i	0.526036	−	0.104765i
$793$	−10.1972			−0.362112
$794$	−38.6255	+	35.6411i	−1.37077	+	1.26486i
$795$	−13.3523	+	8.20911i	−0.473556	+	0.291147i
$796$	22.7520	+	1.83153i	0.806422	+	0.0649169i
$797$	20.1692	+	34.9341i	0.714430	+	1.23743i	0.963179	+	0.268860i	$0.0866470\pi$
$797$	20.1692	+	34.9341i	0.714430	+	1.23743i	−0.248750	+	0.968568i	$0.580020\pi$
$798$	7.58863	−	1.93184i	0.268635	−	0.0683864i
$799$	28.1841	+	16.2721i	0.997081	+	0.575665i
$800$	5.64634	−	0.344755i	0.199628	−	0.0121889i
$801$	1.46207	+	26.4220i	0.0516597	+	0.933577i
$802$	46.8238	+	14.5851i	1.65341	+	0.515017i
$803$	2.24512	+	1.29622i	0.0792286	+	0.0457426i
$804$	4.86665	+	9.55907i	0.171633	+	0.337122i
$805$	9.95435	−	5.74715i	0.350845	−	0.202560i
$806$	−6.28533	+	1.41632i	−0.221391	+	0.0498878i
$807$	−0.0597776	−	2.16221i	−0.00210427	−	0.0761135i
$808$	5.18029	+	36.4149i	0.182242	+	1.28107i
$809$		−	25.1721i		−	0.885006i	−0.896767	−	0.442503i	$-0.854091\pi$
$809$		−	25.1721i		−	0.885006i	0.896767	−	0.442503i	$-0.145909\pi$
$810$	−2.42134	+	12.4955i	−0.0850772	+	0.439047i
$811$	24.0913			0.845960			0.422980	−	0.906139i	$-0.360984\pi$
$811$	24.0913			0.845960			0.422980	+	0.906139i	$0.360984\pi$
$812$	−4.86573	−	10.2483i	−0.170754	−	0.359645i
$813$	−3.58161	+	0.0990188i	−0.125612	+	0.00347274i
$814$	−1.15474	+	0.260207i	−0.0404736	+	0.00912024i
$815$	−3.33629	−	5.77862i	−0.116865	−	0.202416i
$816$	−16.7790	−	2.24510i	−0.587382	−	0.0785941i
$817$	−6.92914	+	12.0016i	−0.242420	+	0.419884i
$818$	−7.02504	+	22.5531i	−0.245625	+	0.788552i
$819$	9.37656	−	0.518854i	0.327644	−	0.0181302i
$820$	−8.21492	+	11.9072i	−0.286878	+	0.415816i
$821$	10.1773	−	17.6276i	0.355191	−	0.615208i	−0.631960	−	0.775001i	$-0.717749\pi$
$821$	10.1773	−	17.6276i	0.355191	−	0.615208i	0.987151	+	0.159793i	$0.0510826\pi$
$822$	12.7277	−	3.24009i	0.443929	−	0.113011i
$823$	−17.1275	+	9.88857i	−0.597027	+	0.344694i	−0.767871	−	0.640604i	$-0.778684\pi$
$823$	−17.1275	+	9.88857i	−0.597027	+	0.344694i	0.170844	+	0.985298i	$0.445351\pi$
$824$	−9.31918	+	23.1780i	−0.324649	+	0.807444i
$825$	−1.61375	−	2.62480i	−0.0561836	−	0.0913837i
$826$	−13.2516	−	14.3613i	−0.461083	−	0.499692i
$827$			36.5200i			1.26993i	0.772543	+	0.634963i	$0.218985\pi$
$827$			36.5200i			1.26993i	−0.772543	+	0.634963i	$0.781015\pi$
$828$	43.1061	−	23.4679i	1.49804	−	0.815566i
$829$		−	8.37836i		−	0.290993i	−0.989359	−	0.145496i	$-0.953522\pi$
$829$		−	8.37836i		−	0.290993i	0.989359	−	0.145496i	$-0.0464779\pi$
$830$	−6.92133	+	6.38655i	−0.240243	+	0.221680i
$831$	−16.8847	+	31.2063i	−0.585723	+	1.08253i
$832$	−4.96997	−	17.1147i	−0.172303	−	0.593346i
$833$	−10.6343	+	6.13973i	−0.368457	+	0.212729i
$834$	−15.7112	−	4.42141i	−0.544034	−	0.153101i
$835$	2.48102	−	4.29726i	0.0858594	−	0.148713i
$836$	−4.59663	+	6.66261i	−0.158978	+	0.230431i
$837$	6.05720	+	8.73114i	0.209368	+	0.301792i
$838$	30.0385	+	9.35663i	1.03766	+	0.323219i
$839$	−0.610377	+	1.05720i	−0.0210726	+	0.0364987i	−0.876369	−	0.481640i	$-0.840041\pi$
$839$	−0.610377	+	1.05720i	−0.0210726	+	0.0364987i	0.855297	+	0.518138i	$0.173375\pi$
$840$	−5.29797	+	4.39534i	−0.182797	+	0.151654i
$841$	6.35209	+	11.0022i	0.219038	+	0.379385i
$842$	−9.22499	−	40.9385i	−0.317914	−	1.41083i
$843$	7.45751	−	13.7830i	0.256850	−	0.474710i
$844$	14.5329	−	6.89997i	0.500242	−	0.237507i
$845$	−8.03728			−0.276491
$846$	54.3554	−	15.4487i	1.86878	−	0.531138i
$847$			11.0100i			0.378309i
$848$	−35.7313	−	5.79026i	−1.22702	−	0.198838i
$849$	40.7539	−	25.0559i	1.39867	−	0.859917i
$850$	0.759612	+	3.37099i	0.0260545	+	0.115624i
$851$	−3.33313	+	1.92439i	−0.114258	+	0.0659671i
$852$	−44.5989	−	2.35197i	−1.52793	−	0.0805772i
$853$	−29.7085	−	17.1522i	−1.01720	−	0.587280i	−0.103908	−	0.994587i	$-0.533135\pi$
$853$	−29.7085	−	17.1522i	−1.01720	−	0.587280i	−0.913291	+	0.407307i	$0.866468\pi$
$854$	−2.70516	+	8.68464i	−0.0925688	+	0.297182i
$855$	−3.73398	−	5.71325i	−0.127700	−	0.195389i
$856$	28.5302	+	36.3906i	0.975143	+	1.24381i
$857$	41.5825	+	24.0077i	1.42043	+	0.820086i	0.996336	−	0.0855309i	$-0.0272586\pi$
$857$	41.5825	+	24.0077i	1.42043	+	0.820086i	0.424096	+	0.905617i	$0.360592\pi$
$858$	−6.94945	+	6.77753i	−0.237250	+	0.231381i
$859$	−2.55616	−	4.42740i	−0.0872150	−	0.151061i	0.819118	−	0.573625i	$-0.194463\pi$
$859$	−2.55616	−	4.42740i	−0.0872150	−	0.151061i	−0.906333	+	0.422564i	$0.861130\pi$
$860$	0.977543	−	12.1434i	0.0333339	−	0.414086i
$861$	−0.486496	−	17.5970i	−0.0165797	−	0.599705i
$862$	−1.18796	−	1.28744i	−0.0404622	−	0.0438503i
$863$	4.39998			0.149777			0.0748885	−	0.997192i	$-0.476140\pi$
$863$	4.39998			0.149777			0.0748885	+	0.997192i	$0.476140\pi$
$864$	−23.0851	+	18.1955i	−0.785372	+	0.619024i
$865$	12.4081			0.421887
$866$	26.1324	+	28.3206i	0.888015	+	0.962372i
$867$	0.527957	+	19.0967i	0.0179303	+	0.648558i
$868$	−0.461166	+	5.72878i	−0.0156530	+	0.194447i
$869$	−8.12246	−	14.0685i	−0.275536	−	0.477242i
$870$	−7.07897	+	6.90384i	−0.240000	+	0.234062i
$871$	−5.97396	−	3.44907i	−0.202420	−	0.116867i
$872$	8.79627	+	11.2197i	0.297879	+	0.379948i
$873$	20.2587	−	40.0485i	0.685653	−	1.35544i
$874$	−7.82710	+	25.1281i	−0.264756	+	0.849970i
$875$	1.21691	+	0.702581i	0.0411389	+	0.0237516i
$876$	−5.04125	−	0.265856i	−0.170328	−	0.00898244i
$877$	3.30393	−	1.90752i	0.111566	−	0.0644125i	−0.443179	−	0.896433i	$-0.646149\pi$
$877$	3.30393	−	1.90752i	0.111566	−	0.0644125i	0.554745	+	0.832021i	$0.312816\pi$
$878$	0.407181	+	1.80698i	0.0137417	+	0.0609826i
$879$	−27.4382	+	16.8693i	−0.925466	+	0.568986i
$880$	1.13825	−	7.02408i	0.0383705	−	0.236782i
$881$		−	15.9028i		−	0.535781i	−0.963449	−	0.267890i	$-0.913674\pi$
$881$		−	15.9028i		−	0.535781i	0.963449	−	0.267890i	$-0.0863265\pi$
$882$	−5.20648	+	20.6760i	−0.175311	+	0.696198i
$883$	−0.566973			−0.0190802			−0.00954008	−	0.999954i	$-0.503037\pi$
$883$	−0.566973			−0.0190802			−0.00954008	+	0.999954i	$0.503037\pi$
$884$	9.83435	−	4.66919i	0.330765	−	0.157042i
$885$	−8.10513	+	14.9799i	−0.272451	+	0.503543i
$886$	−4.99870	−	22.1831i	−0.167934	−	0.745256i
$887$	−0.368769	−	0.638726i	−0.0123820	−	0.0214463i	0.859768	−	0.510685i	$-0.170608\pi$
$887$	−0.368769	−	0.638726i	−0.0123820	−	0.0214463i	−0.872150	+	0.489239i	$0.837275\pi$
$888$	1.77398	−	1.47175i	0.0595310	−	0.0493885i
$889$	−7.84968	+	13.5961i	−0.263270	+	0.455997i
$890$	11.9101	+	3.70986i	0.399228	+	0.124355i
$891$	14.6639	+	6.42650i	0.491261	+	0.215296i
$892$	29.0590	−	42.1196i	0.972967	−	1.41027i
$893$	−15.1510	+	26.2423i	−0.507009	+	0.878166i
$894$	10.6002	+	2.98310i	0.354525	+	0.0997697i
$895$	−2.36544	+	1.36569i	−0.0790681	+	0.0456500i
$896$	−15.8946	−	0.307508i	−0.531002	−	0.0102731i
$897$	−15.0200	+	27.7600i	−0.501503	+	0.926878i
$898$	−32.2975	+	29.8021i	−1.07778	+	0.994507i
$899$			8.25555i			0.275338i
$900$	5.11939	+	3.12920i	0.170646	+	0.104307i
$901$		−	22.1114i		−	0.736636i
$902$	12.3400	+	13.3732i	0.410876	+	0.445281i
$903$	7.76457	+	12.6292i	0.258389	+	0.420274i
$904$	19.5165	−	48.5401i	0.649110	−	1.61442i
$905$	−17.8005	+	10.2771i	−0.591708	+	0.341623i
$906$	39.3499	−	10.0173i	1.30731	−	0.332803i
$907$	5.15797	−	8.93386i	0.171267	−	0.296644i	−0.767596	−	0.640934i	$-0.778547\pi$
$907$	5.15797	−	8.93386i	0.171267	−	0.296644i	0.938863	+	0.344290i	$0.111880\pi$
$908$	−9.39504	+	13.6177i	−0.311786	+	0.451919i
$909$	−17.6098	+	34.8121i	−0.584082	+	1.15464i
$910$	1.31654	−	4.22662i	0.0436429	−	0.140111i
$911$	2.54588	−	4.40960i	0.0843489	−	0.146097i	−0.820765	−	0.571266i	$-0.806452\pi$
$911$	2.54588	−	4.40960i	0.0843489	−	0.146097i	0.905114	+	0.425170i	$0.139786\pi$
$912$	2.09042	−	15.6230i	0.0692207	−	0.517329i
$913$	5.92321	+	10.2593i	0.196030	+	0.339533i
$914$	−17.8950	+	4.03241i	−0.591913	+	0.133380i
$915$	7.92526	−	0.219106i	0.262001	−	0.00724340i
$916$	1.64173	+	3.45784i	0.0542442	+	0.114250i
$917$	16.4460			0.543093
$918$	−13.2274	−	12.1421i	−0.436571	−	0.400749i
$919$			47.5059i			1.56708i	0.621344	+	0.783538i	$0.286587\pi$
$919$			47.5059i			1.56708i	−0.621344	+	0.783538i	$0.713413\pi$
$920$	−3.25856	−	22.9061i	−0.107431	−	0.755190i
$921$	1.01191	+	36.6019i	0.0333436	+	1.20607i
$922$	−35.4696	+	7.99265i	−1.16813	+	0.263224i
$923$	24.8729	−	14.3604i	0.818703	−	0.472678i
$924$	3.92864	+	7.71664i	0.129243	+	0.253859i
$925$	−0.407471	−	0.235254i	−0.0133976	−	0.00773509i
$926$	−43.8737	−	13.6661i	−1.44178	−	0.449097i
$927$	−22.1798	+	14.4959i	−0.728480	+	0.476109i
$928$	−22.7932	+	1.39171i	−0.748223	+	0.0456851i
$929$	−38.2693	−	22.0948i	−1.25557	−	0.724906i	−0.283363	−	0.959013i	$-0.591450\pi$
$929$	−38.2693	−	22.0948i	−1.25557	−	0.724906i	−0.972211	+	0.234106i	$0.924784\pi$
$930$	4.85455	−	1.23582i	0.159187	−	0.0405242i
$931$	−5.71673	−	9.90167i	−0.187358	−	0.324514i
$932$	−54.1353	−	4.35789i	−1.77326	−	0.142748i
$933$	−2.50153	+	1.53796i	−0.0818963	+	0.0503507i
$934$	−4.52625	+	4.17653i	−0.148103	+	0.136660i
$935$	4.34667			0.142151
$936$	6.07184	−	17.9011i	0.198464	−	0.585115i
$937$	20.1663			0.658804			0.329402	−	0.944190i	$-0.393153\pi$
$937$	20.1663			0.658804			0.329402	+	0.944190i	$0.393153\pi$
$938$	−4.52229	+	4.17287i	−0.147658	+	0.136249i
$939$	37.0949	+	20.0709i	1.21055	+	0.654988i
$940$	2.13746	−	26.5523i	0.0697163	−	0.866041i
$941$	12.1023	+	20.9617i	0.394522	+	0.683333i	0.993040	−	0.117777i	$-0.0375767\pi$
$941$	12.1023	+	20.9617i	0.394522	+	0.683333i	−0.598518	+	0.801110i	$0.704243\pi$
$942$	−8.67432	+	30.8236i	−0.282625	+	1.00429i
$943$	51.2395	+	29.5832i	1.66859	+	0.963360i
$944$	−36.7714	+	13.9646i	−1.19681	+	0.454511i
$945$	−7.27635	+	0.604729i	−0.236700	+	0.0196718i
$946$	−14.6311	−	4.55742i	−0.475699	−	0.148175i
$947$	−0.752503	−	0.434458i	−0.0244531	−	0.0141180i	0.487724	−	0.872998i	$-0.337827\pi$
$947$	−0.752503	−	0.434458i	−0.0244531	−	0.0141180i	−0.512177	+	0.858880i	$0.671161\pi$
$948$	26.5246	+	17.2376i	0.861479	+	0.559852i
$949$	2.81152	−	1.62323i	0.0912659	−	0.0526924i
$950$	−3.13875	+	0.707279i	−0.101834	+	0.0229471i
$951$	−8.24976	−	4.46368i	−0.267517	−	0.144745i
$952$	−1.36771	−	9.61432i	−0.0443277	−	0.311602i
$953$			37.0893i			1.20144i	0.799459	+	0.600721i	$0.205120\pi$
$953$			37.0893i			1.20144i	−0.799459	+	0.600721i	$0.794880\pi$
$954$	−27.5553	−	26.7346i	−0.892136	−	0.865565i
$955$	−23.0300			−0.745234
$956$	46.2980	−	21.9816i	1.49739	−	0.710935i
$957$	6.51440	+	10.5958i	0.210581	+	0.342513i
$958$	−18.5994	+	4.19114i	−0.600918	+	0.135410i
$959$	3.76709	+	6.52479i	0.121646	+	0.210696i
$960$	4.23042	+	13.1948i	0.136536	+	0.425861i
$961$	−13.4088	+	23.2248i	−0.432543	+	0.749187i
$962$	−0.440834	+	1.41525i	−0.0142130	+	0.0456295i
$963$	2.70984	+	48.9713i	0.0873233	+	1.57808i
$964$	43.8705	+	30.2669i	1.41297	+	0.974831i
$965$	2.07419	−	3.59260i	0.0667704	−	0.115650i
$966$	19.6578	+	20.1565i	0.632480	+	0.648524i
$967$	34.7775	−	20.0788i	1.11837	−	0.645691i	0.177386	−	0.984141i	$-0.443236\pi$
$967$	34.7775	−	20.0788i	1.11837	−	0.645691i	0.940984	+	0.338450i	$0.109903\pi$
$968$	20.5621	+	8.26740i	0.660891	+	0.265724i
$969$	9.62475	−	0.266090i	0.309191	−	0.00854805i
$970$	−14.3476	−	15.5489i	−0.460672	−	0.499246i
$971$			30.4205i			0.976241i	0.872776	+	0.488121i	$0.162317\pi$
$971$			30.4205i			0.976241i	−0.872776	+	0.488121i	$0.837683\pi$
$972$	−31.1247	+	1.80321i	−0.998326	+	0.0578381i
$973$		−	9.36288i		−	0.300160i
$974$	3.65956	−	3.37681i	0.117260	−	0.108200i
$975$	−3.85705	+	0.106634i	−0.123524	+	0.00341501i
$976$	14.1880	+	11.5734i	0.454146	+	0.370455i
$977$	4.68667	−	2.70585i	0.149940	−	0.0865678i	−0.423153	−	0.906058i	$-0.639077\pi$
$977$	4.68667	−	2.70585i	0.149940	−	0.0865678i	0.573093	+	0.819490i	$0.305743\pi$
$978$	11.7011	−	11.4116i	0.374159	−	0.364903i
$979$	7.84580	−	13.5893i	0.250753	−	0.434317i
$980$	8.27314	+	5.70777i	0.264276	+	0.182328i
$981$	0.835481	+	15.0985i	0.0266749	+	0.482059i
$982$	−52.3906	−	16.3190i	−1.67185	−	0.520762i
$983$	8.53588	−	14.7846i	0.272252	−	0.471555i	−0.697186	−	0.716890i	$-0.745565\pi$
$983$	8.53588	−	14.7846i	0.272252	−	0.471555i	0.969438	+	0.245336i	$0.0788981\pi$
$984$	−33.2292	−	12.3050i	−1.05931	−	0.392269i
$985$	−2.52463	−	4.37278i	−0.0804413	−	0.139328i
$986$	−3.06641	−	13.6080i	−0.0976543	−	0.433368i
$987$	16.9777	+	27.6146i	0.540407	+	0.878982i
$988$	4.34751	+	9.15681i	0.138313	+	0.291317i
$989$	−49.8274			−1.58442
$990$	5.25551	−	5.41684i	0.167031	−	0.172158i
$991$		−	19.8811i		−	0.631543i	−0.948835	−	0.315772i	$-0.897737\pi$
$991$		−	19.8811i		−	0.631543i	0.948835	−	0.315772i	$-0.102263\pi$
$992$	10.3527	+	5.16299i	0.328697	+	0.163925i
$993$	1.92751	+	1.04291i	0.0611675	+	0.0330958i
$994$	−5.63192	−	24.9932i	−0.178634	−	0.792737i
$995$	9.88376	−	5.70639i	0.313336	−	0.180905i
$996$	−19.3428	−	12.5704i	−0.612899	−	0.398307i
$997$	−41.6461	−	24.0444i	−1.31894	−	0.761493i	−0.335385	−	0.942081i	$-0.608866\pi$
$997$	−41.6461	−	24.0444i	−1.31894	−	0.761493i	−0.983559	+	0.180589i	$0.942200\pi$
$998$	−6.99652	+	22.4616i	−0.221471	+	0.711009i
$999$	2.43643	−	0.202489i	0.0770852	−	0.00640646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.19	yes	48
3.2	odd	2		1080.2.bm.a.251.6		48
4.3	odd	2		1440.2.cc.b.911.12		48
8.3	odd	2		360.2.bm.a.11.22	✓	48
8.5	even	2		1440.2.cc.a.911.12		48
9.4	even	3		1080.2.bm.b.611.3		48
9.5	odd	6		360.2.bm.a.131.22	yes	48
12.11	even	2		4320.2.cc.a.1871.16		48
24.5	odd	2		4320.2.cc.b.1871.9		48
24.11	even	2		1080.2.bm.b.251.3		48
36.23	even	6		1440.2.cc.a.1391.12		48
36.31	odd	6		4320.2.cc.b.3311.9		48
72.5	odd	6		1440.2.cc.b.1391.12		48
72.13	even	6		4320.2.cc.a.3311.16		48
72.59	even	6	inner	360.2.bm.b.131.19	yes	48
72.67	odd	6		1080.2.bm.a.611.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.22	✓	48	8.3	odd	2
360.2.bm.a.131.22	yes	48	9.5	odd	6
360.2.bm.b.11.19	yes	48	1.1	even	1	trivial
360.2.bm.b.131.19	yes	48	72.59	even	6	inner
1080.2.bm.a.251.6		48	3.2	odd	2
1080.2.bm.a.611.6		48	72.67	odd	6
1080.2.bm.b.251.3		48	24.11	even	2
1080.2.bm.b.611.3		48	9.4	even	3
1440.2.cc.a.911.12		48	8.5	even	2
1440.2.cc.a.1391.12		48	36.23	even	6
1440.2.cc.b.911.12		48	4.3	odd	2
1440.2.cc.b.1391.12		48	72.5	odd	6
4320.2.cc.a.1871.16		48	12.11	even	2
4320.2.cc.a.3311.16		48	72.13	even	6
4320.2.cc.b.1871.9		48	24.5	odd	2
4320.2.cc.b.3311.9		48	36.31	odd	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959041 + 1.03935i) q^{2} +(0.0478668 + 1.73139i) q^{3} +(-0.160481 + 1.99355i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.75361 + 1.71022i) q^{6} +(-1.21691 - 0.702581i) q^{7} +(-2.22590 + 1.74510i) q^{8} +(-2.99542 + 0.165752i) q^{9} +O(q^{10})\)	\(q+(0.959041 + 1.03935i) q^{2} +(0.0478668 + 1.73139i) q^{3} +(-0.160481 + 1.99355i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.75361 + 1.71022i) q^{6} +(-1.21691 - 0.702581i) q^{7} +(-2.22590 + 1.74510i) q^{8} +(-2.99542 + 0.165752i) q^{9} +(-0.420580 + 1.35023i) q^{10} +(1.54060 + 0.889464i) q^{11} +(-3.45929 - 0.182430i) q^{12} +(1.92926 - 1.11386i) q^{13} +(-0.436838 - 1.93859i) q^{14} +(-1.47549 + 0.907148i) q^{15} +(-3.94849 - 0.639853i) q^{16} -2.44342i q^{17} +(-3.04500 - 2.95431i) q^{18} +2.27508 q^{19} +(-1.80671 + 0.857795i) q^{20} +(1.15819 - 2.14057i) q^{21} +(0.553034 + 2.45424i) q^{22} +(4.09002 + 7.08413i) q^{23} +(-3.12800 - 3.77036i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.00792 + 0.936933i) q^{26} +(-0.430363 - 5.17830i) q^{27} +(1.59592 - 2.31321i) q^{28} +(2.01840 - 3.49598i) q^{29} +(-2.35790 - 0.663556i) q^{30} +(-1.77108 + 1.02254i) q^{31} +(-3.12174 - 4.71750i) q^{32} +(-1.46626 + 2.70995i) q^{33} +(2.53956 - 2.34334i) q^{34} -1.40516i q^{35} +(0.150272 - 5.99812i) q^{36} +0.470507i q^{37} +(2.18189 + 2.36460i) q^{38} +(2.02087 + 3.28698i) q^{39} +(-2.62425 - 1.05513i) q^{40} +(6.26396 - 3.61650i) q^{41} +(3.33554 - 0.849130i) q^{42} +(-3.04567 + 5.27525i) q^{43} +(-2.02043 + 2.92852i) q^{44} +(-1.64125 - 2.51123i) q^{45} +(-3.44036 + 11.0449i) q^{46} +(-6.65955 + 11.5347i) q^{47} +(0.918833 - 6.86700i) q^{48} +(-2.51276 - 4.35223i) q^{49} +(-1.37962 + 0.310881i) q^{50} +(4.23051 - 0.116959i) q^{51} +(1.91093 + 4.02483i) q^{52} +9.04935 q^{53} +(4.96931 - 5.41350i) q^{54} +1.77893i q^{55} +(3.93478 - 0.559752i) q^{56} +(0.108901 + 3.93905i) q^{57} +(5.56926 - 1.25497i) q^{58} +(8.51602 - 4.91673i) q^{59} +(-1.57166 - 3.08705i) q^{60} +(-3.96414 - 2.28870i) q^{61} +(-2.76131 - 0.860115i) q^{62} +(3.76159 + 1.90282i) q^{63} +(1.90924 - 7.76884i) q^{64} +(1.92926 + 1.11386i) q^{65} +(-4.22278 + 1.07499i) q^{66} +(-1.54825 - 2.68165i) q^{67} +(4.87108 + 0.392122i) q^{68} +(-12.0696 + 7.42052i) q^{69} +(1.46045 - 1.34761i) q^{70} +12.8925 q^{71} +(6.37824 - 5.59626i) q^{72} +1.45731 q^{73} +(-0.489020 + 0.451236i) q^{74} +(-1.52336 - 0.824241i) q^{75} +(-0.365107 + 4.53549i) q^{76} +(-1.24984 - 2.16479i) q^{77} +(-1.47822 + 5.25274i) q^{78} +(-7.90843 - 4.56593i) q^{79} +(-1.42012 - 3.73942i) q^{80} +(8.94505 - 0.992994i) q^{81} +(9.76619 + 3.04205i) q^{82} +(5.76713 + 3.32965i) q^{83} +(4.08146 + 2.65243i) q^{84} +(2.11606 - 1.22171i) q^{85} +(-8.40374 + 1.89368i) q^{86} +(6.14951 + 3.32730i) q^{87} +(-4.98141 + 0.708643i) q^{88} -8.82082i q^{89} +(1.03601 - 4.11421i) q^{90} -3.13030 q^{91} +(-14.7789 + 7.01681i) q^{92} +(-1.85518 - 3.01749i) q^{93} +(-18.3753 + 4.14065i) q^{94} +(1.13754 + 1.97028i) q^{95} +(8.01839 - 5.63075i) q^{96} +(-7.48016 + 12.9560i) q^{97} +(2.11363 - 6.78559i) q^{98} +(-4.76216 - 2.40896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

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