LMFDB - Embedded newform 77.2.e.b.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(23,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("77.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.e (of order $3$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			23.2
Root			$-0.956115 - 1.65604i$ of defining polynomial
Character	$\chi$	$=$	77.23
Dual form			77.2.e.b.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.328310 + 0.568650i) q^{2} +(-0.956115 - 1.65604i) q^{3} +(0.784425 + 1.35866i) q^{4} +(1.78442 - 3.09071i) q^{5} +1.25561 q^{6} +(1.78442 + 1.95341i) q^{7} -2.34338 q^{8} +(-0.328310 + 0.568650i) q^{9} +O(q^{10})$	\(q+(-0.328310 + 0.568650i) q^{2} +(-0.956115 - 1.65604i) q^{3} +(0.784425 + 1.35866i) q^{4} +(1.78442 - 3.09071i) q^{5} +1.25561 q^{6} +(1.78442 + 1.95341i) q^{7} -2.34338 q^{8} +(-0.328310 + 0.568650i) q^{9} +(1.17169 + 2.02943i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} -5.91223 q^{13} +(-1.69665 + 0.373387i) q^{14} -6.82446 q^{15} +(-0.799494 + 1.38476i) q^{16} +(0.828310 + 1.43468i) q^{17} +(-0.215575 - 0.373387i) q^{18} +(-0.740539 + 1.28265i) q^{19} +5.59899 q^{20} +(1.52882 - 4.82277i) q^{21} -0.656620 q^{22} +(-1.67169 + 2.89545i) q^{23} +(2.24054 + 3.88073i) q^{24} +(-3.86834 - 6.70017i) q^{25} +(1.94105 - 3.36199i) q^{26} -4.48108 q^{27} +(-1.25429 + 3.95674i) q^{28} +3.08007 q^{29} +(2.24054 - 3.88073i) q^{30} +(3.54003 + 6.13152i) q^{31} +(-2.86834 - 4.96812i) q^{32} +(0.956115 - 1.65604i) q^{33} -1.08777 q^{34} +(9.22162 - 2.02943i) q^{35} -1.03014 q^{36} +(2.25561 - 3.90683i) q^{37} +(-0.486253 - 0.842215i) q^{38} +(5.65277 + 9.79088i) q^{39} +(-4.18158 + 7.24272i) q^{40} -1.28575 q^{41} +(2.24054 + 2.45272i) q^{42} +1.59899 q^{43} +(-0.784425 + 1.35866i) q^{44} +(1.17169 + 2.02943i) q^{45} +(-1.09767 - 1.90121i) q^{46} +(0.828310 - 1.43468i) q^{47} +3.05763 q^{48} +(-0.631656 + 6.97144i) q^{49} +5.08007 q^{50} +(1.58392 - 2.74343i) q^{51} +(-4.63770 - 8.03273i) q^{52} +(-4.61274 - 7.98949i) q^{53} +(1.47118 - 2.54817i) q^{54} +3.56885 q^{55} +(-4.18158 - 4.57759i) q^{56} +2.83216 q^{57} +(-1.01122 + 1.75148i) q^{58} +(-4.42598 - 7.66602i) q^{59} +(-5.35327 - 9.27214i) q^{60} +(3.34338 - 5.79090i) q^{61} -4.64892 q^{62} +(-1.69665 + 0.373387i) q^{63} +0.568850 q^{64} +(-10.5499 + 18.2730i) q^{65} +(0.627804 + 1.08739i) q^{66} +(4.91223 + 8.50823i) q^{67} +(-1.29949 + 2.25079i) q^{68} +6.39331 q^{69} +(-1.87352 + 5.91015i) q^{70} -8.61878 q^{71} +(0.769355 - 1.33256i) q^{72} +(-2.28057 - 3.95007i) q^{73} +(1.48108 + 2.56530i) q^{74} +(-7.39716 + 12.8123i) q^{75} -2.32359 q^{76} +(-0.799494 + 2.52206i) q^{77} -7.42345 q^{78} +(3.19665 - 5.53677i) q^{79} +(2.85327 + 4.94202i) q^{80} +(5.26936 + 9.12679i) q^{81} +(0.422124 - 0.731140i) q^{82} +0.167838 q^{83} +(7.75176 - 1.70595i) q^{84} +5.91223 q^{85} +(-0.524964 + 0.909265i) q^{86} +(-2.94490 - 5.10071i) q^{87} +(-1.17169 - 2.02943i) q^{88} +(1.28442 - 2.22469i) q^{89} -1.53871 q^{90} +(-10.5499 - 11.5490i) q^{91} -5.24526 q^{92} +(6.76936 - 11.7249i) q^{93} +(0.543885 + 0.942037i) q^{94} +(2.64287 + 4.57759i) q^{95} +(-5.48493 + 9.50018i) q^{96} +9.73669 q^{97} +(-3.75693 - 2.64799i) q^{98} -0.656620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8}+O(q^{10}) $ 6 * q + q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8	\( 6 q + q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} + 9 q^{10} + 3 q^{11} + 9 q^{12} - 22 q^{13} + 12 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} + 28 q^{20} + 10 q^{21} - 12 q^{23} - 2 q^{24} - 3 q^{25} - q^{26} + 4 q^{27} + 13 q^{28} - 18 q^{29} - 2 q^{30} + 3 q^{31} + 3 q^{32} - q^{33} - 20 q^{34} + 9 q^{35} - 18 q^{36} + 4 q^{37} - 8 q^{38} + 5 q^{39} + 3 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} + 4 q^{44} + 9 q^{45} + 10 q^{46} + 3 q^{47} + 20 q^{48} - 24 q^{49} - 6 q^{50} - 2 q^{51} + 7 q^{52} - 17 q^{53} + 8 q^{54} + 4 q^{55} + 3 q^{56} + 40 q^{57} + 13 q^{58} - 8 q^{59} - 6 q^{60} + 24 q^{61} + 26 q^{62} + 12 q^{63} - 14 q^{64} - 15 q^{65} - q^{66} + 16 q^{67} - 5 q^{68} - 6 q^{69} - 27 q^{70} + 14 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} - 25 q^{75} - 78 q^{76} - 2 q^{77} - 12 q^{78} - 3 q^{79} - 9 q^{80} + 17 q^{81} - 41 q^{82} - 22 q^{83} + 12 q^{84} + 22 q^{85} + 21 q^{86} - 30 q^{87} - 9 q^{88} - q^{89} + 20 q^{90} - 15 q^{91} + 50 q^{92} + 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} + 18 q^{97} - 24 q^{98}+O(q^{100}) \) 6 * q + q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8 + 9 * q^10 + 3 * q^11 + 9 * q^12 - 22 * q^13 + 12 * q^14 - 14 * q^15 - 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 + 28 * q^20 + 10 * q^21 - 12 * q^23 - 2 * q^24 - 3 * q^25 - q^26 + 4 * q^27 + 13 * q^28 - 18 * q^29 - 2 * q^30 + 3 * q^31 + 3 * q^32 - q^33 - 20 * q^34 + 9 * q^35 - 18 * q^36 + 4 * q^37 - 8 * q^38 + 5 * q^39 + 3 * q^40 - 10 * q^41 - 2 * q^42 + 4 * q^43 + 4 * q^44 + 9 * q^45 + 10 * q^46 + 3 * q^47 + 20 * q^48 - 24 * q^49 - 6 * q^50 - 2 * q^51 + 7 * q^52 - 17 * q^53 + 8 * q^54 + 4 * q^55 + 3 * q^56 + 40 * q^57 + 13 * q^58 - 8 * q^59 - 6 * q^60 + 24 * q^61 + 26 * q^62 + 12 * q^63 - 14 * q^64 - 15 * q^65 - q^66 + 16 * q^67 - 5 * q^68 - 6 * q^69 - 27 * q^70 + 14 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 - 25 * q^75 - 78 * q^76 - 2 * q^77 - 12 * q^78 - 3 * q^79 - 9 * q^80 + 17 * q^81 - 41 * q^82 - 22 * q^83 + 12 * q^84 + 22 * q^85 + 21 * q^86 - 30 * q^87 - 9 * q^88 - q^89 + 20 * q^90 - 15 * q^91 + 50 * q^92 + 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 + 18 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.328310	+	0.568650i	−0.232150	+	0.402096i	−0.958441	−	0.285292i	$-0.907909\pi$
$2$	−0.328310	+	0.568650i	−0.232150	+	0.402096i	0.726290	+	0.687388i	$0.241243\pi$
$3$	−0.956115	−	1.65604i	−0.552013	−	0.956115i	−0.998129	−	0.0611395i	$-0.980527\pi$
$3$	−0.956115	−	1.65604i	−0.552013	−	0.956115i	0.446116	−	0.894975i	$-0.352807\pi$
$4$	0.784425	+	1.35866i	0.392212	+	0.679332i
$5$	1.78442	−	3.09071i	0.798019	−	1.38221i	−0.122885	−	0.992421i	$-0.539215\pi$
$5$	1.78442	−	3.09071i	0.798019	−	1.38221i	0.920904	−	0.389789i	$-0.127452\pi$
$6$	1.25561			0.512600
$7$	1.78442	+	1.95341i	0.674449	+	0.738321i
$7$	1.78442	+	1.95341i	0.674449	+	0.738321i
$8$	−2.34338			−0.828510
$9$	−0.328310	+	0.568650i	−0.109437	+	0.189550i
$10$	1.17169	+	2.02943i	0.370521	+	0.641761i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	−5.91223			−1.63976			−0.819879	−	0.572537i	$-0.805959\pi$
$13$	−5.91223			−1.63976			−0.819879	+	0.572537i	$0.805959\pi$
$14$	−1.69665	+	0.373387i	−0.453450	+	0.0997919i
$15$	−6.82446			−1.76207
$16$	−0.799494	+	1.38476i	−0.199874	+	0.346191i
$17$	0.828310	+	1.43468i	0.200895	+	0.347960i	0.948817	−	0.315826i	$-0.102282\pi$
$17$	0.828310	+	1.43468i	0.200895	+	0.347960i	−0.747922	+	0.663786i	$0.768948\pi$
$18$	−0.215575	−	0.373387i	−0.0508116	−	0.0880082i
$19$	−0.740539	+	1.28265i	−0.169891	+	0.294261i	−0.938382	−	0.345601i	$-0.887675\pi$
$19$	−0.740539	+	1.28265i	−0.169891	+	0.294261i	0.768490	+	0.639862i	$0.221008\pi$
$20$	5.59899			1.25197
$21$	1.52882	−	4.82277i	0.333615	−	1.05241i
$22$	−0.656620			−0.139992
$23$	−1.67169	+	2.89545i	−0.348571	+	0.603743i	−0.985996	−	0.166769i	$-0.946666\pi$
$23$	−1.67169	+	2.89545i	−0.348571	+	0.603743i	0.637425	+	0.770513i	$0.280000\pi$
$24$	2.24054	+	3.88073i	0.457348	+	0.792150i
$25$	−3.86834	−	6.70017i	−0.773669	−	1.34003i
$26$	1.94105	−	3.36199i	0.380670	−	0.659340i
$27$	−4.48108			−0.862384
$28$	−1.25429	+	3.95674i	−0.237038	+	0.747754i
$29$	3.08007			0.571954			0.285977	−	0.958236i	$-0.407682\pi$
$29$	3.08007			0.571954			0.285977	+	0.958236i	$0.407682\pi$
$30$	2.24054	−	3.88073i	0.409065	−	0.708521i
$31$	3.54003	+	6.13152i	0.635809	+	1.10125i	0.986343	+	0.164703i	$0.0526667\pi$
$31$	3.54003	+	6.13152i	0.635809	+	1.10125i	−0.350534	+	0.936550i	$0.614000\pi$
$32$	−2.86834	−	4.96812i	−0.507056	−	0.878247i
$33$	0.956115	−	1.65604i	0.166438	−	0.288279i
$34$	−1.08777			−0.186551
$35$	9.22162	−	2.02943i	1.55874	−	0.343036i
$36$	−1.03014			−0.171690
$37$	2.25561	−	3.90683i	0.370820	−	0.642279i	−0.618872	−	0.785492i	$-0.712410\pi$
$37$	2.25561	−	3.90683i	0.370820	−	0.642279i	0.989692	+	0.143213i	$0.0457434\pi$
$38$	−0.486253	−	0.842215i	−0.0788807	−	0.136625i
$39$	5.65277	+	9.79088i	0.905167	+	1.56780i
$40$	−4.18158	+	7.24272i	−0.661167	+	1.14517i
$41$	−1.28575			−0.200800			−0.100400	−	0.994947i	$-0.532012\pi$
$41$	−1.28575			−0.200800			−0.100400	+	0.994947i	$0.532012\pi$
$42$	2.24054	+	2.45272i	0.345723	+	0.378464i
$43$	1.59899			0.243843			0.121922	−	0.992540i	$-0.461094\pi$
$43$	1.59899			0.243843			0.121922	+	0.992540i	$0.461094\pi$
$44$	−0.784425	+	1.35866i	−0.118256	+	0.204826i
$45$	1.17169	+	2.02943i	0.174665	+	0.302529i
$46$	−1.09767	−	1.90121i	−0.161842	−	0.280319i
$47$	0.828310	−	1.43468i	0.120821	−	0.209269i	−0.799270	−	0.600972i	$-0.794780\pi$
$47$	0.828310	−	1.43468i	0.120821	−	0.209269i	0.920092	+	0.391703i	$0.128114\pi$
$48$	3.05763			0.441331
$49$	−0.631656	+	6.97144i	−0.0902366	+	0.995920i
$50$	5.08007			0.718430
$51$	1.58392	−	2.74343i	0.221793	−	0.384157i
$52$	−4.63770	−	8.03273i	−0.643133	−	1.11394i
$53$	−4.61274	−	7.98949i	−0.633608	−	1.09744i	−0.986808	−	0.161893i	$-0.948240\pi$
$53$	−4.61274	−	7.98949i	−0.633608	−	1.09744i	0.353200	−	0.935548i	$-0.385093\pi$
$54$	1.47118	−	2.54817i	0.200203	−	0.346761i
$55$	3.56885			0.481224
$56$	−4.18158	−	4.57759i	−0.558788	−	0.611706i
$57$	2.83216			0.375129
$58$	−1.01122	+	1.75148i	−0.132779	+	0.229981i
$59$	−4.42598	−	7.66602i	−0.576213	−	0.998030i	−0.995909	−	0.0903653i	$-0.971197\pi$
$59$	−4.42598	−	7.66602i	−0.576213	−	0.998030i	0.419696	−	0.907665i	$-0.362137\pi$
$60$	−5.35327	−	9.27214i	−0.691105	−	1.19703i
$61$	3.34338	−	5.79090i	0.428076	−	0.741449i	−0.568626	−	0.822596i	$-0.692525\pi$
$61$	3.34338	−	5.79090i	0.428076	−	0.741449i	0.996702	+	0.0811468i	$0.0258583\pi$
$62$	−4.64892			−0.590413
$63$	−1.69665	+	0.373387i	−0.213758	+	0.0470424i
$64$	0.568850			0.0711062
$65$	−10.5499	+	18.2730i	−1.30856	+	2.26649i
$66$	0.627804	+	1.08739i	0.0772774	+	0.133848i
$67$	4.91223	+	8.50823i	0.600124	+	1.03945i	0.992802	+	0.119770i	$0.0382156\pi$
$67$	4.91223	+	8.50823i	0.600124	+	1.03945i	−0.392677	+	0.919676i	$0.628451\pi$
$68$	−1.29949	+	2.25079i	−0.157587	+	0.272948i
$69$	6.39331			0.769664
$70$	−1.87352	+	5.91015i	−0.223928	+	0.706399i
$71$	−8.61878			−1.02286			−0.511430	−	0.859325i	$-0.670884\pi$
$71$	−8.61878			−1.02286			−0.511430	+	0.859325i	$0.670884\pi$
$72$	0.769355	−	1.33256i	0.0906694	−	0.157044i
$73$	−2.28057	−	3.95007i	−0.266921	−	0.462321i	0.701144	−	0.713019i	$-0.252673\pi$
$73$	−2.28057	−	3.95007i	−0.266921	−	0.462321i	−0.968065	+	0.250699i	$0.919340\pi$
$74$	1.48108	+	2.56530i	0.172172	+	0.298210i
$75$	−7.39716	+	12.8123i	−0.854150	+	1.47943i
$76$	−2.32359			−0.266534
$77$	−0.799494	+	2.52206i	−0.0911108	+	0.287416i
$78$	−7.42345			−0.840540
$79$	3.19665	−	5.53677i	0.359652	−	0.622935i	−0.628251	−	0.778011i	$-0.716229\pi$
$79$	3.19665	−	5.53677i	0.359652	−	0.622935i	0.987903	+	0.155076i	$0.0495622\pi$
$80$	2.85327	+	4.94202i	0.319006	+	0.552534i
$81$	5.26936	+	9.12679i	0.585484	+	1.01409i
$82$	0.422124	−	0.731140i	0.0466158	−	0.0807409i
$83$	0.167838			0.0184226			0.00921130	−	0.999958i	$-0.497068\pi$
$83$	0.167838			0.0184226			0.00921130	+	0.999958i	$0.497068\pi$
$84$	7.75176	−	1.70595i	0.845786	−	0.186134i
$85$	5.91223			0.641271
$86$	−0.524964	+	0.909265i	−0.0566083	+	0.0980485i
$87$	−2.94490	−	5.10071i	−0.315726	−	0.546854i
$88$	−1.17169	−	2.02943i	−0.124903	−	0.216338i
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	−0.789887	−	0.613252i	$-0.789861\pi$
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	0.926036	+	0.377436i	$0.123194\pi$
$90$	−1.53871			−0.162194
$91$	−10.5499	−	11.5490i	−1.10593	−	1.21067i
$92$	−5.24526			−0.546856
$93$	6.76936	−	11.7249i	0.701949	−	1.21581i
$94$	0.543885	+	0.942037i	0.0560975	+	0.0971637i
$95$	2.64287	+	4.57759i	0.271153	+	0.469651i
$96$	−5.48493	+	9.50018i	−0.559803	+	0.969608i
$97$	9.73669			0.988611			0.494305	−	0.869288i	$-0.335422\pi$
$97$	9.73669			0.988611			0.494305	+	0.869288i	$0.335422\pi$
$98$	−3.75693	−	2.64799i	−0.379507	−	0.267487i
$99$	−0.656620			−0.0659928
$100$	6.06885	−	10.5116i	0.606885	−	1.05116i
$101$	−0.927299	−	1.60613i	−0.0922697	−	0.159816i	0.816196	−	0.577775i	$-0.196079\pi$
$101$	−0.927299	−	1.60613i	−0.0922697	−	0.159816i	−0.908466	+	0.417959i	$0.862746\pi$
$102$	1.04003	+	1.80139i	0.102979	+	0.178364i
$103$	1.58392	−	2.74343i	0.156068	−	0.270318i	−0.777379	−	0.629032i	$-0.783451\pi$
$103$	1.58392	−	2.74343i	0.156068	−	0.270318i	0.933447	+	0.358714i	$0.116785\pi$
$104$	13.8546			1.35856
$105$	−12.1777	−	13.3310i	−1.18843	−	1.30097i
$106$	6.05763			0.588369
$107$	2.38341	−	4.12819i	0.230413	−	0.399087i	−0.727517	−	0.686090i	$-0.759326\pi$
$107$	2.38341	−	4.12819i	0.230413	−	0.399087i	0.957930	+	0.287003i	$0.0926589\pi$
$108$	−3.51507	−	6.08828i	−0.338238	−	0.585845i
$109$	7.44105	+	12.8883i	0.712723	+	1.23447i	0.963831	+	0.266513i	$0.0858716\pi$
$109$	7.44105	+	12.8883i	0.712723	+	1.23447i	−0.251108	+	0.967959i	$0.580795\pi$
$110$	−1.17169	+	2.02943i	−0.111716	+	0.193498i
$111$	−8.62648			−0.818789
$112$	−4.13166	+	0.909265i	−0.390405	+	0.0859174i
$113$	12.4432			1.17056			0.585281	−	0.810831i	$-0.300984\pi$
$113$	12.4432			1.17056			0.585281	+	0.810831i	$0.300984\pi$
$114$	−0.929828	+	1.61051i	−0.0870863	+	0.150838i
$115$	5.96601	+	10.3334i	0.556333	+	0.963597i
$116$	2.41608	+	4.18478i	0.224327	+	0.388547i
$117$	1.94105	−	3.36199i	0.179450	−	0.310816i
$118$	5.81237			0.535072
$119$	−1.32446	+	4.17810i	−0.121413	+	0.383006i
$120$	15.9923			1.45989
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.19533	+	3.80243i	0.198756	+	0.344255i
$123$	1.22932	+	2.12925i	0.110844	+	0.191988i
$124$	−5.55378	+	9.61943i	−0.498744	+	0.863850i
$125$	−9.76683			−0.873571
$126$	0.344702	−	1.08739i	0.0307085	−	0.0968723i
$127$	−6.62142			−0.587556			−0.293778	−	0.955874i	$-0.594913\pi$
$127$	−6.62142			−0.587556			−0.293778	+	0.955874i	$0.594913\pi$
$128$	5.54993	−	9.61276i	0.490549	−	0.849656i
$129$	−1.52882	−	2.64799i	−0.134605	−	0.233142i
$130$	−6.92730	−	11.9984i	−0.607564	−	1.05233i
$131$	3.02882	−	5.24606i	0.264629	−	0.458351i	−0.702837	−	0.711351i	$-0.748084\pi$
$131$	3.02882	−	5.24606i	0.264629	−	0.458351i	0.967466	+	0.253000i	$0.0814172\pi$
$132$	3.00000			0.261116
$133$	−3.82699	+	0.842215i	−0.331842	+	0.0730293i
$134$	−6.45094			−0.557276
$135$	−7.99615	+	13.8497i	−0.688199	+	1.19200i
$136$	−1.94105	−	3.36199i	−0.166443	−	0.288288i
$137$	3.71172	+	6.42889i	0.317114	+	0.549257i	0.979885	−	0.199565i	$-0.0639529\pi$
$137$	3.71172	+	6.42889i	0.317114	+	0.549257i	−0.662771	+	0.748822i	$0.730620\pi$
$138$	−2.09899	+	3.63555i	−0.178678	+	0.309479i
$139$	−10.8245			−0.918119			−0.459059	−	0.888406i	$-0.651813\pi$
$139$	−10.8245			−0.918119			−0.459059	+	0.888406i	$0.651813\pi$
$140$	9.99097	+	10.9371i	0.844391	+	0.924357i
$141$	−3.16784			−0.266780
$142$	2.82963	−	4.90107i	0.237458	−	0.411288i
$143$	−2.95611	−	5.12014i	−0.247203	−	0.428168i
$144$	−0.524964	−	0.909265i	−0.0437470	−	0.0757721i
$145$	5.49615	−	9.51961i	0.456430	−	0.790560i
$146$	2.99494			0.247863
$147$	12.1489	−	5.61945i	1.00203	−	0.463484i
$148$	7.07742			0.581760
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$	−4.85713	−	8.41279i	−0.396583	−	0.686901i
$151$	−8.21172	−	14.2231i	−0.668261	−	1.15746i	−0.978390	−	0.206767i	$-0.933706\pi$
$151$	−8.21172	−	14.2231i	−0.668261	−	1.15746i	0.310130	−	0.950694i	$-0.399628\pi$
$152$	1.73536	−	3.00574i	0.140757	−	0.243798i
$153$	−1.08777			−0.0879411
$154$	−1.17169	−	1.28265i	−0.0944175	−	0.103359i
$155$	25.2677			2.02955
$156$	−8.86834	+	15.3604i	−0.710036	+	1.22982i
$157$	5.72547	+	9.91681i	0.456942	+	0.791447i	0.998798	−	0.0490246i	$-0.0156113\pi$
$157$	5.72547	+	9.91681i	0.456942	+	0.791447i	−0.541855	+	0.840472i	$0.682278\pi$
$158$	2.09899	+	3.63555i	0.166987	+	0.289229i
$159$	−8.82061	+	15.2777i	−0.699520	+	1.21160i
$160$	−20.4734			−1.61856
$161$	−8.63902	+	1.90121i	−0.680850	+	0.149837i
$162$	−6.91993			−0.543681
$163$	4.46986	−	7.74203i	0.350107	−	0.606402i	−0.636161	−	0.771556i	$-0.719479\pi$
$163$	4.46986	−	7.74203i	0.350107	−	0.606402i	0.986268	+	0.165154i	$0.0528120\pi$
$164$	−1.00857	−	1.74690i	−0.0787563	−	0.136410i
$165$	−3.41223	−	5.91015i	−0.265642	−	0.460105i
$166$	−0.0551029	+	0.0954410i	−0.00427681	+	0.00740766i
$167$	−18.2178			−1.40973			−0.704867	−	0.709340i	$-0.748993\pi$
$167$	−18.2178			−1.40973			−0.704867	+	0.709340i	$0.748993\pi$
$168$	−3.58260	+	11.3016i	−0.276403	+	0.871935i
$169$	21.9545			1.68880
$170$	−1.94105	+	3.36199i	−0.148871	+	0.257853i
$171$	−0.486253	−	0.842215i	−0.0371847	−	0.0644058i
$172$	1.25429	+	2.17249i	0.0956384	+	0.165651i
$173$	−9.78057	+	16.9404i	−0.743603	+	1.28796i	0.207241	+	0.978290i	$0.433551\pi$
$173$	−9.78057	+	16.9404i	−0.743603	+	1.28796i	−0.950845	+	0.309669i	$0.899782\pi$
$174$	3.86736			0.293184
$175$	6.18544	−	19.5124i	0.467575	−	1.47500i
$176$	−1.59899			−0.120528
$177$	−8.46348	+	14.6592i	−0.636154	+	1.10185i
$178$	0.843380	+	1.46078i	0.0632140	+	0.109490i
$179$	−1.62395	−	2.81277i	−0.121380	−	0.210236i	0.798932	−	0.601421i	$-0.205399\pi$
$179$	−1.62395	−	2.81277i	−0.121380	−	0.210236i	−0.920312	+	0.391185i	$0.872065\pi$
$180$	−1.83821	+	3.18386i	−0.137012	+	0.237311i
$181$	−10.3407			−0.768621			−0.384310	−	0.923204i	$-0.625561\pi$
$181$	−10.3407			−0.768621			−0.384310	+	0.923204i	$0.625561\pi$
$182$	10.0310	−	2.20755i	0.743548	−	0.163635i
$183$	−12.7866			−0.945214
$184$	3.91740	−	6.78514i	0.288795	−	0.500207i
$185$	−8.04993	−	13.9429i	−0.591843	−	1.02510i
$186$	4.44490	+	7.69879i	0.325916	+	0.564502i
$187$	−0.828310	+	1.43468i	−0.0605720	+	0.104914i
$188$	2.59899			0.189551
$189$	−7.99615	−	8.75340i	−0.581634	−	0.636716i
$190$	−3.47073			−0.251793
$191$	−5.01122	+	8.67968i	−0.362599	+	0.628040i	−0.988388	−	0.151953i	$-0.951444\pi$
$191$	−5.01122	+	8.67968i	−0.362599	+	0.628040i	0.625789	+	0.779993i	$0.284777\pi$
$192$	−0.543885	−	0.942037i	−0.0392515	−	0.0679857i
$193$	−12.6627	−	21.9324i	−0.911478	−	1.57873i	−0.811977	−	0.583690i	$-0.801609\pi$
$193$	−12.6627	−	21.9324i	−0.911478	−	1.57873i	−0.0995016	−	0.995037i	$-0.531725\pi$
$194$	−3.19665	+	5.53677i	−0.229506	+	0.397517i
$195$	40.3478			2.88936
$196$	−9.96733	+	4.61036i	−0.711952	+	0.329312i
$197$	−24.5809			−1.75132			−0.875660	−	0.482929i	$-0.839573\pi$
$197$	−24.5809			−1.75132			−0.875660	+	0.482929i	$0.839573\pi$
$198$	0.215575	−	0.373387i	0.0153203	−	0.0265355i
$199$	−2.79564	−	4.84219i	−0.198178	−	0.343254i	0.749760	−	0.661710i	$-0.230169\pi$
$199$	−2.79564	−	4.84219i	−0.198178	−	0.343254i	−0.947938	+	0.318456i	$0.896836\pi$
$200$	9.06500	+	15.7010i	0.640992	+	1.11023i
$201$	9.39331	−	16.2697i	0.662553	−	1.14758i
$202$	1.21777			0.0856817
$203$	5.49615	+	6.01665i	0.385754	+	0.422286i
$204$	4.96986			0.347960
$205$	−2.29432	+	3.97388i	−0.160242	+	0.277548i
$206$	1.04003	+	1.80139i	0.0724626	+	0.125509i
$207$	−1.09767	−	1.90121i	−0.0762930	−	0.132143i
$208$	4.72679	−	8.18705i	0.327744	−	0.567669i
$209$	−1.48108			−0.102448
$210$	11.5787	−	2.54817i	0.799009	−	0.175840i
$211$	12.0999			0.832988			0.416494	−	0.909138i	$-0.363259\pi$
$211$	12.0999			0.832988			0.416494	+	0.909138i	$0.363259\pi$
$212$	7.23669	−	12.5343i	0.497018	−	0.860860i
$213$	8.24054	+	14.2730i	0.564632	+	0.977972i
$214$	1.56500	+	2.71066i	0.106981	+	0.185297i
$215$	2.85327	−	4.94202i	0.194592	−	0.337043i
$216$	10.5009			0.714494
$217$	−5.66047	+	17.8564i	−0.384258	+	1.21217i
$218$	−9.77188			−0.661836
$219$	−4.36098	+	7.55344i	−0.294688	+	0.510414i
$220$	2.79949	+	4.84887i	0.188742	+	0.326910i
$221$	−4.89716	−	8.48213i	−0.329419	−	0.570570i
$222$	2.83216	−	4.90545i	0.190082	−	0.329232i
$223$	15.6265			1.04643			0.523213	−	0.852202i	$-0.324733\pi$
$223$	15.6265			1.04643			0.523213	+	0.852202i	$0.324733\pi$
$224$	4.58645	−	14.4683i	0.306445	−	0.966704i
$225$	5.08007			0.338671
$226$	−4.08524	+	7.07585i	−0.271746	+	0.470678i
$227$	7.83435	+	13.5695i	0.519984	+	0.900639i	0.999730	+	0.0232317i	$0.00739554\pi$
$227$	7.83435	+	13.5695i	0.519984	+	0.900639i	−0.479746	+	0.877408i	$0.659271\pi$
$228$	2.22162	+	3.84796i	0.147130	+	0.254837i
$229$	2.78575	−	4.82506i	0.184087	−	0.318849i	−0.759181	−	0.650879i	$-0.774400\pi$
$229$	2.78575	−	4.82506i	0.184087	−	0.318849i	0.943269	+	0.332031i	$0.107734\pi$
$230$	−7.83481			−0.516612
$231$	4.94105	−	1.08739i	0.325097	−	0.0715449i
$232$	−7.21777			−0.473870
$233$	9.63770	−	16.6930i	0.631387	−	1.09359i	−0.355882	−	0.934531i	$-0.615819\pi$
$233$	9.63770	−	16.6930i	0.631387	−	1.09359i	0.987268	−	0.159063i	$-0.0508472\pi$
$234$	1.27453	+	2.20755i	0.0833186	+	0.144312i
$235$	−2.95611	−	5.12014i	−0.192836	−	0.334001i
$236$	6.94369	−	12.0268i	0.451996	−	0.782880i
$237$	−12.2255			−0.794130
$238$	−1.94105	−	2.12487i	−0.125819	−	0.137735i
$239$	−22.1575			−1.43325			−0.716624	−	0.697459i	$-0.754314\pi$
$239$	−22.1575			−1.43325			−0.716624	+	0.697459i	$0.754314\pi$
$240$	5.45611	−	9.45027i	0.352191	−	0.610012i
$241$	9.93719	+	17.2117i	0.640111	+	1.10870i	0.985408	+	0.170211i	$0.0544449\pi$
$241$	9.93719	+	17.2117i	0.640111	+	1.10870i	−0.345297	+	0.938494i	$0.612222\pi$
$242$	−0.328310	−	0.568650i	−0.0211046	−	0.0365542i
$243$	3.35460	−	5.81033i	0.215198	−	0.372733i
$244$	10.4905			0.671587
$245$	20.4196	+	14.3923i	1.30456	+	0.919489i
$246$	−1.61440			−0.102930
$247$	4.37824	−	7.58333i	0.278581	−	0.482516i
$248$	−8.29564	−	14.3685i	−0.526774	−	0.912399i
$249$	−0.160472	−	0.277946i	−0.0101695	−	0.0176141i
$250$	3.20655	−	5.55391i	0.202800	−	0.351260i
$251$	22.1076			1.39542			0.697708	−	0.716382i	$-0.254203\pi$
$251$	22.1076			1.39542			0.697708	+	0.716382i	$0.254203\pi$
$252$	−1.83821	−	2.01229i	−0.115796	−	0.126762i
$253$	−3.34338			−0.210196
$254$	2.17388	−	3.76527i	0.136401	−	0.236254i
$255$	−5.65277	−	9.79088i	−0.353990	−	0.613129i
$256$	4.21305	+	7.29721i	0.263315	+	0.456076i
$257$	−14.5598	+	25.2184i	−0.908217	+	1.57308i	−0.0916768	+	0.995789i	$0.529223\pi$
$257$	−14.5598	+	25.2184i	−0.908217	+	1.57308i	−0.816540	+	0.577289i	$0.804111\pi$
$258$	2.00770			0.124994
$259$	11.6566	−	2.56530i	0.724307	−	0.159400i
$260$	−33.1025			−2.05293
$261$	−1.01122	+	1.75148i	−0.0625928	+	0.108414i
$262$	1.98878	+	3.44467i	0.122867	+	0.212813i
$263$	7.75176	+	13.4264i	0.477994	+	0.827910i	0.999682	−	0.0252268i	$-0.00803080\pi$
$263$	7.75176	+	13.4264i	0.477994	+	0.827910i	−0.521688	+	0.853136i	$0.674697\pi$
$264$	−2.24054	+	3.88073i	−0.137896	+	0.238842i
$265$	−32.9243			−2.02252
$266$	0.777513	−	2.45272i	0.0476724	−	0.150386i
$267$	−4.91223			−0.300624
$268$	−7.70655	+	13.3481i	−0.470752	+	0.815367i
$269$	−0.853274	−	1.47791i	−0.0520251	−	0.0901100i	0.838840	−	0.544378i	$-0.183234\pi$
$269$	−0.853274	−	1.47791i	−0.0520251	−	0.0901100i	−0.890865	+	0.454268i	$0.849901\pi$
$270$	−5.25043	−	9.09402i	−0.319531	−	0.553444i
$271$	10.2642	−	17.7781i	0.623505	−	1.07994i	−0.365323	−	0.930881i	$-0.619042\pi$
$271$	10.2642	−	17.7781i	0.623505	−	1.07994i	0.988828	−	0.149061i	$-0.0476251\pi$
$272$	−2.64892			−0.160614
$273$	−9.03871	+	28.5133i	−0.547048	+	1.72570i
$274$	−4.87439			−0.294472
$275$	3.86834	−	6.70017i	0.233270	−	0.404035i
$276$	5.01507	+	8.68635i	0.301872	+	0.522857i
$277$	13.3305	+	23.0891i	0.800952	+	1.38729i	0.918990	+	0.394281i	$0.129006\pi$
$277$	13.3305	+	23.0891i	0.800952	+	1.38729i	−0.118038	+	0.993009i	$0.537660\pi$
$278$	3.55378	−	6.15533i	0.213142	−	0.369172i
$279$	−4.64892			−0.278323
$280$	−21.6098	+	4.75572i	−1.29143	+	0.284208i
$281$	15.7444			0.939232			0.469616	−	0.882871i	$-0.344392\pi$
$281$	15.7444			0.939232			0.469616	+	0.882871i	$0.344392\pi$
$282$	1.04003	−	1.80139i	0.0619331	−	0.107271i
$283$	8.03486	+	13.9168i	0.477623	+	0.827267i	0.999671	−	0.0256490i	$-0.00816524\pi$
$283$	8.03486	+	13.9168i	0.477623	+	0.827267i	−0.522048	+	0.852916i	$0.674832\pi$
$284$	−6.76078	−	11.7100i	−0.401179	−	0.694862i
$285$	5.05378	−	8.75340i	0.299360	−	0.518507i
$286$	3.88209			0.229553
$287$	−2.29432	−	2.51160i	−0.135429	−	0.148255i
$288$	3.76683			0.221962
$289$	7.12780	−	12.3457i	0.419283	−	0.726219i
$290$	3.60888	+	6.25077i	0.211921	+	0.367058i
$291$	−9.30939	−	16.1243i	−0.545726	−	0.945225i
$292$	3.57788	−	6.19706i	0.209379	−	0.362656i
$293$	15.3357			0.895920			0.447960	−	0.894054i	$-0.352151\pi$
$293$	15.3357			0.895920			0.447960	+	0.894054i	$0.352151\pi$
$294$	−0.793113	+	8.75340i	−0.0462553	+	0.510509i
$295$	−31.5913			−1.83932
$296$	−5.28575	+	9.15518i	−0.307228	+	0.532134i
$297$	−2.24054	−	3.88073i	−0.130009	−	0.225183i
$298$	0.328310	+	0.568650i	0.0190185	+	0.0329410i
$299$	9.88341	−	17.1186i	0.571573	−	0.989993i
$300$	−23.2101			−1.34003
$301$	2.85327	+	3.12349i	0.164460	+	0.180035i
$302$	10.7840			0.620548
$303$	−1.77321	+	3.07129i	−0.101868	+	0.176441i
$304$	−1.18411	−	2.05095i	−0.0679136	−	0.117630i
$305$	−11.9320	−	20.6669i	−0.683225	−	1.18338i
$306$	0.357126	−	0.618561i	0.0204156	−	0.0353608i
$307$	−16.4707			−0.940034			−0.470017	−	0.882657i	$-0.655752\pi$
$307$	−16.4707			−0.940034			−0.470017	+	0.882657i	$0.655752\pi$
$308$	−4.05378	+	0.892126i	−0.230986	+	0.0508336i
$309$	−6.05763			−0.344607
$310$	−8.29564	+	14.3685i	−0.471161	+	0.816074i
$311$	−10.8146	−	18.7314i	−0.613238	−	1.06216i	−0.990691	−	0.136130i	$-0.956533\pi$
$311$	−10.8146	−	18.7314i	−0.613238	−	1.06216i	0.377453	−	0.926029i	$-0.376800\pi$
$312$	−13.2466	−	22.9438i	−0.749940	−	1.29893i
$313$	−8.19412	+	14.1926i	−0.463159	+	0.802215i	−0.999116	−	0.0420298i	$-0.986618\pi$
$313$	−8.19412	+	14.1926i	−0.463159	+	0.802215i	0.535957	+	0.844245i	$0.319951\pi$
$314$	−7.51892			−0.424317
$315$	−1.87352	+	5.91015i	−0.105561	+	0.332999i
$316$	10.0301			0.564239
$317$	−2.23064	+	3.86359i	−0.125285	+	0.217001i	−0.921844	−	0.387560i	$-0.873318\pi$
$317$	−2.23064	+	3.86359i	−0.125285	+	0.217001i	0.796559	+	0.604561i	$0.206651\pi$
$318$	−5.79179	−	10.0317i	−0.324787	−	0.562548i
$319$	1.54003	+	2.66742i	0.0862253	+	0.149347i
$320$	1.01507	−	1.75815i	0.0567441	−	0.0982837i
$321$	−9.11526			−0.508764
$322$	1.75515	−	5.53677i	0.0978109	−	0.308552i
$323$	−2.45359			−0.136521
$324$	−8.26683	+	14.3186i	−0.459268	+	0.795476i
$325$	22.8705	+	39.6129i	1.26863	+	2.19733i
$326$	2.93500	+	5.08357i	0.162555	+	0.281553i
$327$	14.2290	−	24.6453i	0.786865	−	1.36289i
$328$	3.01299			0.166365
$329$	4.28057	−	0.942037i	0.235996	−	0.0519362i
$330$	4.48108			0.246675
$331$	−9.51979	+	16.4888i	−0.523255	+	0.906304i	0.476379	+	0.879240i	$0.341949\pi$
$331$	−9.51979	+	16.4888i	−0.523255	+	0.906304i	−0.999634	+	0.0270640i	$0.991384\pi$
$332$	0.131656	+	0.228035i	0.00722557	+	0.0125151i
$333$	1.48108	+	2.56530i	0.0811626	+	0.140578i
$334$	5.98108	−	10.3595i	0.327270	−	0.566848i
$335$	35.0620			1.91564
$336$	5.45611	+	5.97282i	0.297655	+	0.325844i
$337$	27.0147			1.47159			0.735793	−	0.677206i	$-0.236810\pi$
$337$	27.0147			1.47159			0.735793	+	0.677206i	$0.236810\pi$
$338$	−7.20787	+	12.4844i	−0.392057	+	0.679062i
$339$	−11.8972	−	20.6065i	−0.646165	−	1.11919i
$340$	4.63770	+	8.03273i	0.251515	+	0.435636i
$341$	−3.54003	+	6.13152i	−0.191704	+	0.332040i
$342$	0.638568			0.0345298
$343$	−14.7453	+	11.2061i	−0.796169	+	0.605074i
$344$	−3.74704			−0.202027
$345$	11.4084	−	19.7599i	0.614206	−	1.06384i
$346$	−6.42212	−	11.1234i	−0.345256	−	0.598000i
$347$	10.1089	+	17.5091i	0.542673	+	0.939938i	0.998749	+	0.0499969i	$0.0159211\pi$
$347$	10.1089	+	17.5091i	0.542673	+	0.939938i	−0.456076	+	0.889941i	$0.650746\pi$
$348$	4.62010	−	8.00225i	0.247663	−	0.428966i
$349$	−12.0224			−0.643546			−0.321773	−	0.946817i	$-0.604279\pi$
$349$	−12.0224			−0.643546			−0.321773	+	0.946817i	$0.604279\pi$
$350$	9.06500	+	9.92348i	0.484545	+	0.530432i
$351$	26.4932			1.41410
$352$	2.86834	−	4.96812i	0.152883	−	0.264802i
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	0.972930	−	0.231101i	$-0.0742329\pi$
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	−0.686605	+	0.727031i	$0.740900\pi$
$354$	−5.55729	−	9.62552i	−0.295367	−	0.511590i
$355$	−15.3796	+	26.6382i	−0.816262	+	1.41381i
$356$	4.03014			0.213597
$357$	8.18544	−	1.80139i	0.433219	−	0.0953397i
$358$	2.13264			0.112714
$359$	−12.1451	+	21.0359i	−0.640992	+	1.11023i	0.344220	+	0.938889i	$0.388144\pi$
$359$	−12.1451	+	21.0359i	−0.640992	+	1.11023i	−0.985212	+	0.171342i	$0.945190\pi$
$360$	−2.74571	−	4.75572i	−0.144712	−	0.250648i
$361$	8.40320	+	14.5548i	0.442274	+	0.766041i
$362$	3.39497	−	5.88026i	0.178436	−	0.309060i
$363$	1.91223			0.100366
$364$	7.41563	−	23.3932i	0.388684	−	1.22613i
$365$	−16.2780			−0.852032
$366$	4.19798	−	7.27111i	0.219432	−	0.380067i
$367$	−5.42212	−	9.39139i	−0.283033	−	0.490227i	0.689098	−	0.724669i	$-0.258007\pi$
$367$	−5.42212	−	9.39139i	−0.283033	−	0.490227i	−0.972130	+	0.234442i	$0.924674\pi$
$368$	−2.67301	−	4.62979i	−0.139340	−	0.241345i
$369$	0.422124	−	0.731140i	0.0219749	−	0.0380616i
$370$	10.5715			0.549586
$371$	7.37571	−	23.2672i	0.382928	−	1.20797i
$372$	21.2402			1.10125
$373$	16.5121	−	28.5998i	0.854963	−	1.48084i	−0.0217156	−	0.999764i	$-0.506913\pi$
$373$	16.5121	−	28.5998i	0.854963	−	1.48084i	0.876679	−	0.481076i	$-0.159754\pi$
$374$	−0.543885	−	0.942037i	−0.0281236	−	0.0487116i
$375$	9.33821	+	16.1742i	0.482223	+	0.835234i
$376$	−1.94105	+	3.36199i	−0.100102	+	0.173381i
$377$	−18.2101			−0.937866
$378$	7.60284	−	1.67318i	0.391048	−	0.0860590i
$379$	−21.9320			−1.12657			−0.563286	−	0.826262i	$-0.690463\pi$
$379$	−21.9320			−1.12657			−0.563286	+	0.826262i	$0.690463\pi$
$380$	−4.14627	+	7.18155i	−0.212699	+	0.368406i
$381$	6.33084	+	10.9653i	0.324339	+	0.561771i
$382$	−3.29047	−	5.69926i	−0.168355	−	0.291599i
$383$	−18.2315	+	31.5779i	−0.931587	+	1.61356i	−0.150977	+	0.988537i	$0.548242\pi$
$383$	−18.2315	+	31.5779i	−0.931587	+	1.61356i	−0.780610	+	0.625018i	$0.785091\pi$
$384$	−21.2255			−1.08316
$385$	6.36834	+	6.97144i	0.324561	+	0.355298i
$386$	16.6291			0.846400
$387$	−0.524964	+	0.909265i	−0.0266854	+	0.0462205i
$388$	7.63770	+	13.2289i	0.387745	+	0.671595i
$389$	−9.73801	−	16.8667i	−0.493737	−	0.855177i	0.506237	−	0.862394i	$-0.331036\pi$
$389$	−9.73801	−	16.8667i	−0.493737	−	0.855177i	−0.999974	+	0.00721718i	$0.997703\pi$
$390$	−13.2466	+	22.9438i	−0.670767	+	1.16180i
$391$	−5.53871			−0.280105
$392$	1.48021	−	16.3367i	0.0747619	−	0.825130i
$393$	−11.5836			−0.584314
$394$	8.07017	−	13.9779i	0.406569	−	0.704199i
$395$	−11.4084	−	19.7599i	−0.574018	−	0.994228i
$396$	−0.515069	−	0.892126i	−0.0258832	−	0.0448310i
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	−0.750732	−	0.660606i	$-0.770299\pi$
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	0.947468	+	0.319850i	$0.103633\pi$
$398$	3.67135			0.184028
$399$	5.05378	+	5.53239i	0.253005	+	0.276966i
$400$	12.3709			0.618544
$401$	12.2229	−	21.1708i	0.610385	−	1.05722i	−0.380791	−	0.924661i	$-0.624348\pi$
$401$	12.2229	−	21.1708i	0.610385	−	1.05722i	0.991176	−	0.132556i	$-0.0423184\pi$
$402$	6.16784	+	10.6830i	0.307624	+	0.532820i
$403$	−20.9295	−	36.2509i	−1.04257	−	1.80579i
$404$	1.45479	−	2.51977i	0.0723786	−	0.125363i
$405$	37.6111			1.86891
$406$	−5.22581	+	1.15006i	−0.259353	+	0.0570764i
$407$	4.51122			0.223613
$408$	−3.71172	+	6.42889i	−0.183758	+	0.318278i
$409$	1.17686	+	2.03839i	0.0581922	+	0.100792i	0.893654	−	0.448757i	$-0.148133\pi$
$409$	1.17686	+	2.03839i	0.0581922	+	0.100792i	−0.835462	+	0.549549i	$0.814800\pi$
$410$	−1.50650	−	2.60933i	−0.0744006	−	0.128866i
$411$	7.09767	−	12.2935i	0.350102	−	0.606395i
$412$	4.96986			0.244847
$413$	7.07708	−	22.3252i	0.348241	−	1.09855i
$414$	1.44150			0.0708458
$415$	0.299494	−	0.518739i	0.0147016	−	0.0254639i
$416$	16.9583	+	29.3726i	0.831449	+	1.44011i
$417$	10.3494	+	17.9257i	0.506813	+	0.877827i
$418$	0.486253	−	0.842215i	0.0237834	−	0.0411941i
$419$	9.29081			0.453886			0.226943	−	0.973908i	$-0.427127\pi$
$419$	9.29081			0.453886			0.226943	+	0.973908i	$0.427127\pi$
$420$	8.55982	−	27.0026i	0.417677	−	1.31759i
$421$	−39.0319			−1.90230			−0.951149	−	0.308733i	$-0.900095\pi$
$421$	−39.0319			−1.90230			−0.951149	+	0.308733i	$0.900095\pi$
$422$	−3.97251	+	6.88058i	−0.193379	+	0.334942i
$423$	0.543885	+	0.942037i	0.0264446	+	0.0458034i
$424$	10.8094	+	18.7224i	0.524950	+	0.909241i
$425$	6.40838	−	11.0996i	0.310852	−	0.538411i
$426$	−10.8218			−0.524319
$427$	17.2780	−	3.80243i	0.836143	−	0.184012i
$428$	7.47843			0.361484
$429$	−5.65277	+	9.79088i	−0.272918	+	0.472708i
$430$	1.87352	+	3.24503i	0.0903491	+	0.156489i
$431$	1.90101	+	3.29265i	0.0915685	+	0.158601i	0.908171	−	0.418599i	$-0.137479\pi$
$431$	1.90101	+	3.29265i	0.0915685	+	0.158601i	−0.816603	+	0.577200i	$0.804145\pi$
$432$	3.58260	−	6.20524i	0.172368	−	0.298550i
$433$	8.22041			0.395048			0.197524	−	0.980298i	$-0.436710\pi$
$433$	8.22041			0.395048			0.197524	+	0.980298i	$0.436710\pi$
$434$	−8.29564	−	9.08126i	−0.398204	−	0.435914i
$435$	−21.0198			−1.00782
$436$	−11.6739	+	20.2198i	−0.559077	+	0.968351i
$437$	−2.47590	−	4.28839i	−0.118439	−	0.205142i
$438$	−2.86351	−	4.95974i	−0.136824	−	0.236986i
$439$	−2.27068	+	3.93293i	−0.108374	+	0.187708i	−0.915112	−	0.403201i	$-0.867898\pi$
$439$	−2.27068	+	3.93293i	−0.108374	+	0.187708i	0.806738	+	0.590909i	$0.201231\pi$
$440$	−8.36317			−0.398698
$441$	−3.75693	−	2.64799i	−0.178901	−	0.126095i
$442$	6.43115			0.305899
$443$	−6.87220	+	11.9030i	−0.326508	+	0.565528i	−0.981816	−	0.189833i	$-0.939205\pi$
$443$	−6.87220	+	11.9030i	−0.326508	+	0.565528i	0.655309	+	0.755361i	$0.272539\pi$
$444$	−6.76683	−	11.7205i	−0.321139	−	0.556230i
$445$	−4.58392	−	7.93958i	−0.217299	−	0.376372i
$446$	−5.13033	+	8.88600i	−0.242928	+	0.420764i
$447$	−1.91223			−0.0904453
$448$	1.01507	+	1.11120i	0.0479575	+	0.0524992i
$449$	21.5662			1.01777			0.508886	−	0.860834i	$-0.330057\pi$
$449$	21.5662			1.01777			0.508886	+	0.860834i	$0.330057\pi$
$450$	−1.66784	+	2.88878i	−0.0786226	+	0.136178i
$451$	−0.642874	−	1.11349i	−0.0302717	−	0.0524322i
$452$	9.76078	+	16.9062i	0.459109	+	0.795199i
$453$	−15.7027	+	27.1979i	−0.737777	+	1.27787i
$454$	−10.2884			−0.482858
$455$	−54.5203	+	11.9984i	−2.55595	+	0.562495i
$456$	−6.63683			−0.310798
$457$	1.65277	−	2.86268i	0.0773133	−	0.133910i	−0.824777	−	0.565459i	$-0.808699\pi$
$457$	1.65277	−	2.86268i	0.0773133	−	0.133910i	0.902090	+	0.431548i	$0.142033\pi$
$458$	1.82918	+	3.16823i	0.0854719	+	0.148042i
$459$	−3.71172	−	6.42889i	−0.173248	−	0.300075i
$460$	−9.35977	+	16.2116i	−0.436402	+	0.755870i
$461$	−32.1524			−1.49749			−0.748744	−	0.662859i	$-0.769343\pi$
$461$	−32.1524			−1.49749			−0.748744	+	0.662859i	$0.769343\pi$
$462$	−1.00385	+	3.16673i	−0.0467034	+	0.147329i
$463$	5.82181			0.270563			0.135281	−	0.990807i	$-0.456806\pi$
$463$	5.82181			0.270563			0.135281	+	0.990807i	$0.456806\pi$
$464$	−2.46250	+	4.26517i	−0.114318	+	0.198005i
$465$	−24.1588	−	41.8443i	−1.12034	−	1.94048i
$466$	6.32831	+	10.9610i	0.293153	+	0.507756i
$467$	3.00737	−	5.20891i	0.139164	−	0.241040i	−0.788016	−	0.615654i	$-0.788892\pi$
$467$	3.00737	−	5.20891i	0.139164	−	0.241040i	0.927181	+	0.374615i	$0.122225\pi$
$468$	6.09042			0.281530
$469$	−7.85460	+	24.7779i	−0.362692	+	1.14414i
$470$	3.88209			0.179067
$471$	10.9484	−	18.9632i	0.504476	−	0.873778i
$472$	10.3717	+	17.9644i	0.477398	+	0.826878i
$473$	0.799494	+	1.38476i	0.0367608	+	0.0636715i
$474$	4.01375	−	6.95201i	0.184357	−	0.319317i
$475$	11.4586			0.525759
$476$	−6.71558	+	1.47791i	−0.307808	+	0.0677401i
$477$	6.05763			0.277360
$478$	7.27453	−	12.5999i	0.332729	−	0.576304i
$479$	−8.56753	−	14.8394i	−0.391460	−	0.678029i	0.601182	−	0.799112i	$-0.294697\pi$
$479$	−8.56753	−	14.8394i	−0.391460	−	0.678029i	−0.992642	+	0.121083i	$0.961363\pi$
$480$	19.5749	+	33.9047i	0.893468	+	1.54753i
$481$	−13.3357	+	23.0981i	−0.608054	+	1.05318i
$482$	−13.0499			−0.594408
$483$	11.4084	+	12.4888i	0.519099	+	0.568259i
$484$	−1.56885			−0.0713113
$485$	17.3744	−	30.0933i	0.788930	−	1.36647i
$486$	2.20270	+	3.81518i	0.0999164	+	0.173060i
$487$	−2.85713	−	4.94869i	−0.129469	−	0.224246i	0.794002	−	0.607915i	$-0.207994\pi$
$487$	−2.85713	−	4.94869i	−0.129469	−	0.224246i	−0.923471	+	0.383669i	$0.874661\pi$
$488$	−7.83481	+	13.5703i	−0.354665	+	0.614298i
$489$	−17.0948			−0.773054
$490$	−14.8881	+	6.88647i	−0.672577	+	0.311099i
$491$	24.0673			1.08614			0.543071	−	0.839687i	$-0.317261\pi$
$491$	24.0673			1.08614			0.543071	+	0.839687i	$0.317261\pi$
$492$	−1.92862	+	3.34047i	−0.0869490	+	0.150600i
$493$	2.55125	+	4.41890i	0.114903	+	0.199017i
$494$	2.87484	+	4.97937i	0.129345	+	0.224032i
$495$	−1.17169	+	2.02943i	−0.0526635	+	0.0912159i
$496$	−11.3209			−0.508325
$497$	−15.3796	−	16.8360i	−0.689868	−	0.755200i
$498$	0.210739			0.00944343
$499$	−5.39463	+	9.34377i	−0.241497	+	0.418285i	−0.961141	−	0.276058i	$-0.910972\pi$
$499$	−5.39463	+	9.34377i	−0.241497	+	0.418285i	0.719644	+	0.694343i	$0.244305\pi$
$500$	−7.66134	−	13.2698i	−0.342626	−	0.593445i
$501$	17.4183	+	30.1693i	0.778191	+	1.34787i
$502$	−7.25814	+	12.5715i	−0.323947	+	0.561092i
$503$	28.0121			1.24900			0.624499	−	0.781026i	$-0.285303\pi$
$503$	28.0121			1.24900			0.624499	+	0.781026i	$0.285303\pi$
$504$	3.97590	−	0.874988i	0.177101	−	0.0389751i
$505$	−6.61878			−0.294532
$506$	1.09767	−	1.90121i	0.0487972	−	0.0845192i
$507$	−20.9910	−	36.3574i	−0.932242	−	1.61469i
$508$	−5.19401	−	8.99629i	−0.230447	−	0.399146i
$509$	0.957437	−	1.65833i	0.0424377	−	0.0735042i	−0.844026	−	0.536302i	$-0.819821\pi$
$509$	0.957437	−	1.65833i	0.0424377	−	0.0735042i	0.886464	+	0.462797i	$0.153154\pi$
$510$	7.42345			0.328716
$511$	3.64661	−	11.5035i	0.161317	−	0.508885i
$512$	16.6670			0.736583
$513$	3.31842	−	5.74766i	0.146512	−	0.253766i
$514$	−9.56028	−	16.5589i	−0.421686	−	0.730381i
$515$	−5.65277	−	9.79088i	−0.249091	−	0.431438i
$516$	2.39848	−	4.15429i	0.105587	−	0.182883i
$517$	1.65662			0.0728581
$518$	−2.36823	+	7.47075i	−0.104054	+	0.328246i
$519$	37.4054			1.64191
$520$	24.7225	−	42.8206i	1.08415	−	1.87781i
$521$	−0.789599	−	1.36763i	−0.0345930	−	0.0599168i	0.848211	−	0.529659i	$-0.177680\pi$
$521$	−0.789599	−	1.36763i	−0.0345930	−	0.0599168i	−0.882804	+	0.469742i	$0.844347\pi$
$522$	−0.663986	−	1.15006i	−0.0290619	−	0.0503367i
$523$	4.48493	−	7.76813i	0.196112	−	0.339677i	−0.751152	−	0.660129i	$-0.770502\pi$
$523$	4.48493	−	7.76813i	0.196112	−	0.339677i	0.947265	+	0.320452i	$0.103835\pi$
$524$	9.50351			0.415163
$525$	−38.2273	+	8.41279i	−1.66838	+	0.367164i
$526$	−10.1799			−0.443866
$527$	−5.86449	+	10.1576i	−0.255461	+	0.442472i
$528$	1.52882	+	2.64799i	0.0665332	+	0.115239i
$529$	5.91091	+	10.2380i	0.256996	+	0.445130i
$530$	10.8094	−	18.7224i	0.469530	−	0.813250i
$531$	5.81237			0.252235
$532$	−4.14627	−	4.53893i	−0.179764	−	0.196788i
$533$	7.60163			0.329263
$534$	1.61274	−	2.79334i	0.0697899	−	0.120880i
$535$	−8.50604	−	14.7329i	−0.367748	−	0.636959i
$536$	−11.5112	−	19.9380i	−0.497209	−	0.861191i
$537$	−3.10537	+	5.37866i	−0.134007	+	0.232106i
$538$	1.12055			0.0483105
$539$	−6.35327	+	2.93869i	−0.273655	+	0.126578i
$540$	−25.0895			−1.07968
$541$	−9.05125	+	15.6772i	−0.389144	+	0.674017i	−0.992335	−	0.123580i	$-0.960562\pi$
$541$	−9.05125	+	15.6772i	−0.389144	+	0.674017i	0.603191	+	0.797597i	$0.293896\pi$
$542$	6.73967	+	11.6735i	0.289494	+	0.501418i
$543$	9.88693	+	17.1247i	0.424289	+	0.734889i
$544$	4.75176	−	8.23028i	0.203730	−	0.352871i
$545$	53.1119			2.27507
$546$	−13.2466	−	14.5011i	−0.566901	−	0.620588i
$547$	22.6885			0.970090			0.485045	−	0.874489i	$-0.338803\pi$
$547$	22.6885			0.970090			0.485045	+	0.874489i	$0.338803\pi$
$548$	−5.82314	+	10.0860i	−0.248752	+	0.430851i
$549$	2.19533	+	3.80243i	0.0936945	+	0.162284i
$550$	2.54003	+	4.39947i	0.108307	+	0.187594i
$551$	−2.28091	+	3.95065i	−0.0971701	+	0.168304i
$552$	−14.9819			−0.637674
$553$	16.5198	−	3.63555i	0.702493	−	0.154599i
$554$	−17.5062			−0.743765
$555$	−15.3933	+	26.6620i	−0.653410	+	1.13174i
$556$	−8.49097	−	14.7068i	−0.360097	−	0.623707i
$557$	−19.1777	−	33.2168i	−0.812587	−	1.40744i	−0.911048	−	0.412300i	$-0.864725\pi$
$557$	−19.1777	−	33.2168i	−0.812587	−	1.40744i	0.0984613	−	0.995141i	$-0.468608\pi$
$558$	1.52629	−	2.64361i	0.0646129	−	0.111913i
$559$	−9.45359			−0.399844
$560$	−4.56235	+	14.3923i	−0.192795	+	0.608185i
$561$	3.16784			0.133746
$562$	−5.16904	+	8.95305i	−0.218043	+	0.377662i
$563$	20.8869	+	36.1772i	0.880279	+	1.52469i	0.851031	+	0.525116i	$0.175978\pi$
$563$	20.8869	+	36.1772i	0.880279	+	1.52469i	0.0292482	+	0.999572i	$0.490689\pi$
$564$	−2.48493	−	4.30403i	−0.104634	−	0.181232i
$565$	22.2040	−	38.4585i	0.934130	−	1.61796i
$566$	−10.5517			−0.443521
$567$	−8.42564	+	26.5793i	−0.353844	+	1.11623i
$568$	20.1971			0.847450
$569$	5.93500	−	10.2797i	0.248808	−	0.430949i	−0.714387	−	0.699751i	$-0.753294\pi$
$569$	5.93500	−	10.2797i	0.248808	−	0.430949i	0.963195	+	0.268802i	$0.0866278\pi$
$570$	3.31842	+	5.74766i	0.138993	+	0.240743i
$571$	−9.90067	−	17.1485i	−0.414330	−	0.717641i	0.581028	−	0.813884i	$-0.302651\pi$
$571$	−9.90067	−	17.1485i	−0.414330	−	0.717641i	−0.995358	+	0.0962427i	$0.969317\pi$
$572$	4.63770	−	8.03273i	0.193912	−	0.335865i
$573$	19.1652			0.800637
$574$	2.18147	−	0.480082i	0.0910527	−	0.0200382i
$575$	25.8667			1.07872
$576$	−0.186759	+	0.323476i	−0.00778163	+	0.0134782i
$577$	−14.3395	−	24.8368i	−0.596962	−	1.03397i	−0.993267	−	0.115850i	$-0.963041\pi$
$577$	−14.3395	−	24.8368i	−0.596962	−	1.03397i	0.396304	−	0.918119i	$-0.370293\pi$
$578$	4.68026	+	8.10645i	0.194673	+	0.337184i
$579$	−24.2139	+	41.9397i	−1.00630	+	1.74296i
$580$	17.2453			0.716070
$581$	0.299494	+	0.327857i	0.0124251	+	0.0136018i
$582$	12.2255			0.506762
$583$	4.61274	−	7.98949i	0.191040	−	0.330891i
$584$	5.34425	+	9.25651i	0.221147	+	0.383037i
$585$	−6.92730	−	11.9984i	−0.286409	−	0.496074i
$586$	−5.03486	+	8.72063i	−0.207988	+	0.360246i
$587$	1.01209			0.0417733			0.0208866	−	0.999782i	$-0.493351\pi$
$587$	1.01209			0.0417733			0.0208866	+	0.999782i	$0.493351\pi$
$588$	17.1649	+	12.0983i	0.707867	+	0.498924i
$589$	−10.4861			−0.432074
$590$	10.3717	−	17.9644i	0.426998	−	0.739582i
$591$	23.5022	+	40.7070i	0.966751	+	1.67446i
$592$	3.60669	+	6.24697i	0.148234	+	0.256749i
$593$	−7.11659	+	12.3263i	−0.292243	+	0.506180i	−0.974340	−	0.225082i	$-0.927735\pi$
$593$	−7.11659	+	12.3263i	−0.292243	+	0.506180i	0.682097	+	0.731262i	$0.261068\pi$
$594$	2.94237			0.120727
$595$	10.5499	+	11.5490i	0.432505	+	0.473464i
$596$	1.56885			0.0642626
$597$	−5.34591	+	9.25939i	−0.218793	+	0.378961i
$598$	6.48965	+	11.2404i	0.265382	+	0.459654i
$599$	13.2729	+	22.9893i	0.542315	+	0.939317i	0.998771	+	0.0495706i	$0.0157853\pi$
$599$	13.2729	+	22.9893i	0.542315	+	0.939317i	−0.456456	+	0.889746i	$0.650881\pi$
$600$	17.3344	−	30.0240i	0.707672	−	1.22572i
$601$	−12.1558			−0.495843			−0.247922	−	0.968780i	$-0.579748\pi$
$601$	−12.1558			−0.495843			−0.247922	+	0.968780i	$0.579748\pi$
$602$	−2.71293	+	0.597042i	−0.110571	+	0.0243336i
$603$	−6.45094			−0.262703
$604$	12.8830	−	22.3139i	0.524200	−	0.907941i
$605$	1.78442	+	3.09071i	0.0725472	+	0.125655i
$606$	−1.16432	−	2.01667i	−0.0472974	−	0.0819216i
$607$	−6.98361	+	12.0960i	−0.283456	+	0.490960i	−0.972234	−	0.234013i	$-0.924814\pi$
$607$	−6.98361	+	12.0960i	−0.283456	+	0.490960i	0.688778	+	0.724973i	$0.258148\pi$
$608$	8.49649			0.344578
$609$	4.70886	−	14.8544i	0.190812	−	0.601932i
$610$	15.6696			0.634444
$611$	−4.89716	+	8.48213i	−0.198118	+	0.343150i
$612$	−0.853274	−	1.47791i	−0.0344916	−	0.0597412i
$613$	−2.32094	−	4.01999i	−0.0937421	−	0.162366i	0.815341	−	0.578981i	$-0.196550\pi$
$613$	−2.32094	−	4.01999i	−0.0937421	−	0.162366i	−0.909083	+	0.416615i	$0.863216\pi$
$614$	5.40751	−	9.36608i	0.218229	−	0.377984i
$615$	8.77453			0.353823
$616$	1.87352	−	5.91015i	0.0754862	−	0.238127i
$617$	−26.3960			−1.06266			−0.531331	−	0.847165i	$-0.678308\pi$
$617$	−26.3960			−1.06266			−0.531331	+	0.847165i	$0.678308\pi$
$618$	1.98878	−	3.44467i	0.0800006	−	0.138565i
$619$	−7.34073	−	12.7145i	−0.295049	−	0.511040i	0.679947	−	0.733261i	$-0.262003\pi$
$619$	−7.34073	−	12.7145i	−0.295049	−	0.511040i	−0.974996	+	0.222221i	$0.928669\pi$
$620$	19.8206	+	34.3303i	0.796015	+	1.37874i
$621$	7.49097	−	12.9747i	0.300602	−	0.520659i
$622$	14.2021			0.569453
$623$	6.63770	−	1.46078i	0.265934	−	0.0585248i
$624$	−18.0774			−0.723676
$625$	1.91355	−	3.31437i	0.0765421	−	0.132575i
$626$	−5.38043	−	9.31918i	−0.215045	−	0.372469i
$627$	1.41608	+	2.45272i	0.0565528	+	0.0979524i
$628$	−8.98240	+	15.5580i	−0.358437	+	0.620831i
$629$	7.47338			0.297983
$630$	−2.74571	−	3.00574i	−0.109392	−	0.119752i
$631$	−30.1498			−1.20024			−0.600122	−	0.799908i	$-0.704881\pi$
$631$	−30.1498			−1.20024			−0.600122	+	0.799908i	$0.704881\pi$
$632$	−7.49097	+	12.9747i	−0.297975	+	0.516108i
$633$	−11.5688	−	20.0378i	−0.459820	−	0.796432i
$634$	−1.46469	−	2.53691i	−0.0581701	−	0.100754i
$635$	−11.8154	+	20.4649i	−0.468881	+	0.812126i
$636$	−27.6764			−1.09744
$637$	3.73450	−	41.2168i	0.147966	−	1.63307i
$638$	−2.02243			−0.0800690
$639$	2.82963	−	4.90107i	0.111939	−	0.193883i
$640$	−19.8069	−	34.3065i	−0.782935	−	1.35608i
$641$	8.08909	+	14.0107i	0.319500	+	0.553390i	0.980384	−	0.197098i	$-0.0631517\pi$
$641$	8.08909	+	14.0107i	0.319500	+	0.553390i	−0.660884	+	0.750488i	$0.729818\pi$
$642$	2.99263	−	5.18339i	0.118110	−	0.204572i
$643$	−2.33568			−0.0921101			−0.0460550	−	0.998939i	$-0.514665\pi$
$643$	−2.33568			−0.0921101			−0.0460550	+	0.998939i	$0.514665\pi$
$644$	−9.35977	−	10.2462i	−0.368827	−	0.403756i
$645$	−10.9122			−0.429669
$646$	0.805537	−	1.39523i	0.0316934	−	0.0548946i
$647$	−7.48108	−	12.9576i	−0.294112	−	0.509416i	0.680666	−	0.732594i	$-0.261690\pi$
$647$	−7.48108	−	12.9576i	−0.294112	−	0.509416i	−0.974778	+	0.223177i	$0.928357\pi$
$648$	−12.3481	−	21.3875i	−0.485079	−	0.840182i
$649$	4.42598	−	7.66602i	0.173735	−	0.300917i
$650$	−30.0345			−1.17805
$651$	34.9829	−	7.69879i	1.37109	−	0.301739i
$652$	14.0251			0.549265
$653$	11.4449	−	19.8231i	0.447873	−	0.775740i	−0.550374	−	0.834918i	$-0.685515\pi$
$653$	11.4449	−	19.8231i	0.447873	−	0.775740i	0.998247	+	0.0591787i	$0.0188482\pi$
$654$	9.34304	+	16.1826i	0.365342	+	0.632791i
$655$	−10.8094	−	18.7224i	−0.422358	−	0.731545i
$656$	1.02795	−	1.78046i	0.0401346	−	0.0695152i
$657$	2.99494			0.116844
$658$	−0.869666	+	2.74343i	−0.0339031	+	0.106950i
$659$	−2.20568			−0.0859211			−0.0429606	−	0.999077i	$-0.513679\pi$
$659$	−2.20568			−0.0859211			−0.0429606	+	0.999077i	$0.513679\pi$
$660$	5.35327	−	9.27214i	0.208376	−	0.360918i
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	0.872584	−	0.488463i	$-0.162442\pi$
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	−0.859314	+	0.511449i	$0.829109\pi$
$662$	−6.25089	−	10.8269i	−0.242948	−	0.420798i
$663$	−9.36449	+	16.2198i	−0.363687	+	0.629924i
$664$	−0.393308			−0.0152633
$665$	−4.22592	+	13.3310i	−0.163874	+	0.516954i
$666$	−1.94501			−0.0753677
$667$	−5.14892	+	8.91819i	−0.199367	+	0.345314i
$668$	−14.2905	−	24.7518i	−0.552915	−	0.957677i
$669$	−14.9407	−	25.8781i	−0.577641	−	1.00050i
$670$	−11.5112	+	19.9380i	−0.444717	+	0.770273i
$671$	6.68676			0.258139
$672$	−28.3452	+	6.23801i	−1.09344	+	0.240637i
$673$	−10.8865			−0.419643			−0.209821	−	0.977740i	$-0.567288\pi$
$673$	−10.8865			−0.419643			−0.209821	+	0.977740i	$0.567288\pi$
$674$	−8.86921	+	15.3619i	−0.341629	+	0.591719i
$675$	17.3344	+	30.0240i	0.667200	+	1.15562i
$676$	17.2216	+	29.8287i	0.662370	+	1.14726i
$677$	−22.8327	+	39.5474i	−0.877532	+	1.51993i	−0.0234904	+	0.999724i	$0.507478\pi$
$677$	−22.8327	+	39.5474i	−0.877532	+	1.51993i	−0.854041	+	0.520205i	$0.825855\pi$
$678$	15.6238			0.600030
$679$	17.3744	+	19.0198i	0.666768	+	0.729912i
$680$	−13.8546			−0.531300
$681$	14.9811	−	25.9480i	0.574076	−	0.994329i
$682$	−2.32446	−	4.02608i	−0.0890081	−	0.154167i
$683$	−3.24186	−	5.61507i	−0.124046	−	0.214855i	0.797313	−	0.603566i	$-0.206254\pi$
$683$	−3.24186	−	5.61507i	−0.124046	−	0.214855i	−0.921360	+	0.388711i	$0.872921\pi$
$684$	0.762858	−	1.32131i	0.0291686	−	0.0505215i
$685$	26.4932			1.01225
$686$	−1.53135	−	12.0640i	−0.0584670	−	0.460605i
$687$	−10.6540			−0.406475
$688$	−1.27838	+	2.21422i	−0.0487378	+	0.0844164i
$689$	27.2715	+	47.2357i	1.03896	+	1.79954i
$690$	7.49097	+	12.9747i	0.285176	+	0.493940i
$691$	−5.47338	+	9.48016i	−0.208217	+	0.360642i	−0.951153	−	0.308720i	$-0.900099\pi$
$691$	−5.47338	+	9.48016i	−0.208217	+	0.360642i	0.742936	+	0.669363i	$0.233433\pi$
$692$	−30.6885			−1.16660
$693$	−1.17169	−	1.28265i	−0.0445088	−	0.0487239i
$694$	−13.2754			−0.503927
$695$	−19.3154	+	33.4553i	−0.732676	+	1.26903i
$696$	6.90101	+	11.9529i	0.261582	+	0.453074i
$697$	−1.06500	−	1.84463i	−0.0403397	−	0.0698704i
$698$	3.94709	−	6.83656i	0.149399	−	0.258768i
$699$	−36.8590			−1.39413
$700$	31.3628	−	6.90210i	1.18540	−	0.260875i
$701$	−0.914874			−0.0345543			−0.0172772	−	0.999851i	$-0.505500\pi$
$701$	−0.914874			−0.0345543			−0.0172772	+	0.999851i	$0.505500\pi$
$702$	−8.69798	+	15.0653i	−0.328284	+	0.568605i
$703$	3.34073	+	5.78632i	0.125998	+	0.218235i
$704$	0.284425	+	0.492638i	0.0107197	+	0.0185670i
$705$	−5.65277	+	9.79088i	−0.212896	+	0.368746i
$706$	−7.06466			−0.265882
$707$	1.48274	−	4.67741i	0.0557642	−	0.175912i
$708$	−26.5559			−0.998030
$709$	−22.1562	+	38.3756i	−0.832092	+	1.44123i	0.0642838	+	0.997932i	$0.479524\pi$
$709$	−22.1562	+	38.3756i	−0.832092	+	1.44123i	−0.896376	+	0.443294i	$0.853810\pi$
$710$	−10.0985	−	17.4912i	−0.378991	−	0.656432i
$711$	2.09899	+	3.63555i	0.0787182	+	0.136344i
$712$	−3.00989	+	5.21329i	−0.112801	+	0.195376i
$713$	−23.6714			−0.886499
$714$	−1.66300	+	5.24606i	−0.0622363	+	0.196329i
$715$	−21.0999			−0.789090
$716$	2.54774	−	4.41281i	0.0952134	−	0.164914i
$717$	21.1851	+	36.6937i	0.791172	+	1.37035i
$718$	−7.97470	−	13.8126i	−0.297613	−	0.515481i
$719$	2.60118	−	4.50537i	0.0970076	−	0.168022i	−0.813437	−	0.581653i	$-0.802406\pi$
$719$	2.60118	−	4.50537i	0.0970076	−	0.168022i	0.910445	+	0.413631i	$0.135740\pi$
$720$	−3.74704			−0.139644
$721$	8.18544	−	1.80139i	0.304842	−	0.0670873i
$722$	−11.0354			−0.410696
$723$	19.0022	−	32.9128i	0.706699	−	1.22404i
$724$	−8.11153	−	14.0496i	−0.301463	−	0.522149i
$725$	−11.9148	−	20.6370i	−0.442503	−	0.766438i
$726$	−0.627804	+	1.08739i	−0.0233000	+	0.0403568i
$727$	50.0871			1.85763			0.928814	−	0.370547i	$-0.120830\pi$
$727$	50.0871			1.85763			0.928814	+	0.370547i	$0.120830\pi$
$728$	24.7225	+	27.0638i	0.916276	+	1.00305i
$729$	18.7866			0.695801
$730$	5.34425	−	9.25651i	0.197799	−	0.342599i
$731$	1.32446	+	2.29403i	0.0489869	+	0.0848477i
$732$	−10.0301	−	17.3727i	−0.370725	−	0.642114i
$733$	23.5349	−	40.7636i	0.869280	−	1.50564i	0.00654601	−	0.999979i	$-0.497916\pi$
$733$	23.5349	−	40.7636i	0.869280	−	1.50564i	0.862734	−	0.505658i	$-0.168750\pi$
$734$	7.12055			0.262824
$735$	4.31071	−	47.5763i	0.159003	−	1.75488i
$736$	19.1799			0.706981
$737$	−4.91223	+	8.50823i	−0.180944	+	0.313405i
$738$	0.277175	+	0.480082i	0.0102030	+	0.0176720i
$739$	−23.4957	−	40.6957i	−0.864303	−	1.49702i	−0.867738	−	0.497023i	$-0.834427\pi$
$739$	−23.4957	−	40.6957i	−0.864303	−	1.49702i	0.00343444	−	0.999994i	$-0.498907\pi$
$740$	12.6291	−	21.8743i	0.464256	−	0.804115i
$741$	−16.7444			−0.615121
$742$	10.8094	+	11.8331i	0.396825	+	0.434406i
$743$	−5.19533			−0.190598			−0.0952991	−	0.995449i	$-0.530381\pi$
$743$	−5.19533			−0.190598			−0.0952991	+	0.995449i	$0.530381\pi$
$744$	−15.8632	+	27.4758i	−0.581572	+	1.00731i
$745$	−1.78442	−	3.09071i	−0.0653763	−	0.113235i
$746$	10.8422	+	18.7792i	0.396960	+	0.687555i
$747$	−0.0551029	+	0.0954410i	−0.00201611	+	0.00349200i
$748$	−2.59899			−0.0950284
$749$	12.3171	−	2.71066i	0.450057	−	0.0990452i
$750$	−12.2633			−0.447793
$751$	−16.7268	+	28.9717i	−0.610369	+	1.05719i	0.380809	+	0.924654i	$0.375646\pi$
$751$	−16.7268	+	28.9717i	−0.610369	+	1.05719i	−0.991178	+	0.132537i	$0.957688\pi$
$752$	1.32446	+	2.29403i	0.0482980	+	0.0836546i
$753$	−21.1374	−	36.6110i	−0.770288	−	1.33418i
$754$	5.97855	−	10.3552i	0.217726	−	0.377112i
$755$	−58.6128			−2.13314
$756$	5.62055	−	17.7305i	0.204418	−	0.644851i
$757$	40.0440			1.45542			0.727711	−	0.685884i	$-0.240584\pi$
$757$	40.0440			1.45542			0.727711	+	0.685884i	$0.240584\pi$
$758$	7.20051	−	12.4716i	0.261534	−	0.452990i
$759$	3.19665	+	5.53677i	0.116031	+	0.200972i
$760$	−6.19326	−	10.7270i	−0.224653	−	0.389110i
$761$	3.77925	−	6.54585i	0.136998	−	0.237287i	−0.789361	−	0.613929i	$-0.789588\pi$
$761$	3.77925	−	6.54585i	0.136998	−	0.237287i	0.926359	+	0.376642i	$0.122921\pi$
$762$	−8.31392			−0.301181
$763$	−11.8981	+	37.5336i	−0.430742	+	1.35881i
$764$	−15.7237			−0.568863
$765$	−1.94105	+	3.36199i	−0.0701786	+	0.121553i
$766$	−11.9712	−	20.7347i	−0.432536	−	0.749175i
$767$	26.1674	+	45.3232i	0.944849	+	1.63653i
$768$	8.05631	−	13.9539i	0.290707	−	0.503519i
$769$	51.5407			1.85860			0.929302	−	0.369320i	$-0.120409\pi$
$769$	51.5407			1.85860			0.929302	+	0.369320i	$0.120409\pi$
$770$	−6.05510	+	1.33256i	−0.218211	+	0.0480222i
$771$	55.6834			2.00539
$772$	19.8658	−	34.4086i	0.714986	−	1.23839i
$773$	7.73284	+	13.3937i	0.278131	+	0.481737i	0.970920	−	0.239403i	$-0.0769518\pi$
$773$	7.73284	+	13.3937i	0.278131	+	0.481737i	−0.692789	+	0.721140i	$0.743618\pi$
$774$	−0.344702	−	0.597042i	−0.0123901	−	0.0214602i
$775$	27.3881	−	47.4376i	0.983811	−	1.70401i
$776$	−22.8168			−0.819074
$777$	−15.3933	−	16.8511i	−0.552232	−	0.604530i
$778$	12.7884			0.458485
$779$	0.952147	−	1.64917i	0.0341142	−	0.0590875i
$780$	31.6498	+	54.8190i	1.13324	+	1.96284i
$781$	−4.30939	−	7.46408i	−0.154202	−	0.267086i
$782$	1.81842	−	3.14959i	0.0650264	−	0.112629i
$783$	−13.8020			−0.493244
$784$	−9.14880	−	6.44832i	−0.326743	−	0.230297i
$785$	40.8667			1.45859
$786$	3.80301	−	6.58700i	0.135649	−	0.234951i
$787$	−10.9759	−	19.0108i	−0.391249	−	0.677663i	0.601366	−	0.798974i	$-0.294623\pi$
$787$	−10.9759	−	19.0108i	−0.391249	−	0.677663i	−0.992615	+	0.121311i	$0.961290\pi$
$788$	−19.2819	−	33.3972i	−0.686889	−	1.18973i
$789$	14.8231	−	25.6744i	0.527718	−	0.914034i
$790$	14.9819			0.533034
$791$	22.2040	+	24.3068i	0.789484	+	0.864250i
$792$	1.53871			0.0546757
$793$	−19.7668	+	34.2371i	−0.701941	+	1.21580i
$794$	2.57391	+	4.45814i	0.0913446	+	0.158213i
$795$	31.4794	+	54.5240i	1.11646	+	1.93377i
$796$	4.38594	−	7.59667i	0.155456	−	0.269257i
$797$	42.6258			1.50988			0.754942	−	0.655792i	$-0.227665\pi$
$797$	42.6258			1.50988			0.754942	+	0.655792i	$0.227665\pi$
$798$	−4.80520	+	1.05749i	−0.170102	+	0.0374348i
$799$	2.74439			0.0970896
$800$	−22.1915	+	38.4368i	−0.784587	+	1.35895i
$801$	0.843380	+	1.46078i	0.0297994	+	0.0516140i
$802$	8.02583	+	13.9011i	0.283402	+	0.490867i
$803$	2.28057	−	3.95007i	0.0804797	−	0.139395i
$804$	29.4734			1.03945
$805$	−9.53958	+	30.0933i	−0.336226	+	1.06065i
$806$	27.4855			0.968134
$807$	−1.63166	+	2.82611i	−0.0574370	+	0.0994838i
$808$	2.17301	+	3.76377i	0.0764463	+	0.132409i
$809$	−1.98372	−	3.43591i	−0.0697440	−	0.120800i	0.829045	−	0.559183i	$-0.188885\pi$
$809$	−1.98372	−	3.43591i	−0.0697440	−	0.120800i	−0.898789	+	0.438382i	$0.855552\pi$
$810$	−12.3481	+	21.3875i	−0.433868	+	0.751481i
$811$	−46.9217			−1.64764			−0.823821	−	0.566850i	$-0.808162\pi$
$811$	−46.9217			−1.64764			−0.823821	+	0.566850i	$0.808162\pi$
$812$	−3.86329	+	12.1870i	−0.135575	+	0.427681i
$813$	−39.2549			−1.37673
$814$	−1.48108	+	2.56530i	−0.0519118	+	0.0899138i
$815$	−15.9523	−	27.6301i	−0.558783	−	0.967841i
$816$	2.53267	+	4.38671i	0.0886611	+	0.153566i
$817$	−1.18411	+	2.05095i	−0.0414269	+	0.0717535i
$818$	−1.54551			−0.0540374
$819$	10.0310	−	2.20755i	0.350512	−	0.0771381i
$820$	−7.19888			−0.251396
$821$	25.3000	−	43.8209i	0.882977	−	1.52936i	0.0349620	−	0.999389i	$-0.488869\pi$
$821$	25.3000	−	43.8209i	0.882977	−	1.52936i	0.848015	−	0.529972i	$-0.177798\pi$
$822$	4.66047	+	8.07217i	0.162553	+	0.281549i
$823$	−0.199299	−	0.345196i	−0.00694714	−	0.0120328i	0.862531	−	0.506004i	$-0.168878\pi$
$823$	−0.199299	−	0.345196i	−0.00694714	−	0.0120328i	−0.869478	+	0.493972i	$0.835545\pi$
$824$	−3.71172	+	6.42889i	−0.129304	+	0.223961i
$825$	−14.7943			−0.515072
$826$	10.3717	+	11.3540i	0.360879	+	0.395055i
$827$	−20.4234			−0.710193			−0.355096	−	0.934830i	$-0.615552\pi$
$827$	−20.4234			−0.710193			−0.355096	+	0.934830i	$0.615552\pi$
$828$	1.72207	−	2.98272i	0.0598462	−	0.103657i
$829$	11.6317	+	20.1466i	0.403984	+	0.699721i	0.994203	−	0.107522i	$-0.0342918\pi$
$829$	11.6317	+	20.1466i	0.403984	+	0.699721i	−0.590219	+	0.807244i	$0.700958\pi$
$830$	0.196654	+	0.340615i	0.00682596	+	0.0118229i
$831$	25.4910	−	44.1517i	0.884272	−	1.53160i
$832$	−3.36317			−0.116597
$833$	−10.5250	+	4.86830i	−0.364668	+	0.168676i
$834$	−13.5913			−0.470628
$835$	−32.5082	+	56.3059i	−1.12499	+	1.94855i
$836$	−1.16179	−	2.01229i	−0.0401815	−	0.0695964i
$837$	−15.8632	−	27.4758i	−0.548311	−	0.949703i
$838$	−3.05027	+	5.28322i	−0.105370	+	0.182506i
$839$	−16.4861			−0.569165			−0.284582	−	0.958652i	$-0.591855\pi$
$839$	−16.4861			−0.569165			−0.284582	+	0.958652i	$0.591855\pi$
$840$	28.5371	+	31.2396i	0.984622	+	1.07787i
$841$	−19.5132			−0.672869
$842$	12.8146	−	22.1955i	0.441619	−	0.764907i
$843$	−15.0534	−	26.0733i	−0.518468	−	0.898013i
$844$	9.49143	+	16.4396i	0.326708	+	0.565876i
$845$	39.1761	−	67.8549i	1.34770	−	2.33428i
$846$	−0.714253			−0.0245565
$847$	−2.58392	+	0.568650i	−0.0887845	+	0.0195390i
$848$	14.7514			0.506566
$849$	15.3645	−	26.6121i	0.527308	−	0.913324i
$850$	4.20787	+	7.28825i	0.144329	+	0.249985i
$851$	7.54136	+	13.0620i	0.258514	+	0.447760i
$852$	−12.9282	+	22.3922i	−0.442912	+	0.767146i
$853$	−14.8315			−0.507820			−0.253910	−	0.967228i	$-0.581717\pi$
$853$	−14.8315			−0.507820			−0.253910	+	0.967228i	$0.581717\pi$
$854$	−3.51031	+	11.0735i	−0.120120	+	0.378929i
$855$	−3.47073			−0.118696
$856$	−5.58524	+	9.67392i	−0.190900	+	0.330648i
$857$	2.51594	+	4.35773i	0.0859428	+	0.148857i	0.905793	−	0.423721i	$-0.139276\pi$
$857$	2.51594	+	4.35773i	0.0859428	+	0.148857i	−0.819850	+	0.572579i	$0.805943\pi$
$858$	−3.71172	−	6.42889i	−0.126716	−	0.219479i
$859$	28.0181	−	48.5288i	0.955966	−	1.65578i	0.223825	−	0.974629i	$-0.428146\pi$
$859$	28.0181	−	48.5288i	0.955966	−	1.65578i	0.732141	−	0.681153i	$-0.238521\pi$
$860$	8.95272			0.305285
$861$	−1.96567	+	6.20086i	−0.0669899	+	0.211325i
$862$	−2.49649			−0.0850307
$863$	18.2380	−	31.5892i	0.620829	−	1.07531i	−0.368503	−	0.929627i	$-0.620129\pi$
$863$	18.2380	−	31.5892i	0.620829	−	1.07531i	0.989332	−	0.145681i	$-0.0465372\pi$
$864$	12.8533	+	22.2625i	0.437277	+	0.757386i
$865$	34.9054	+	60.4579i	1.18682	+	2.05563i
$866$	−2.69885	+	4.67454i	−0.0917105	+	0.158847i
$867$	−27.2600			−0.925798
$868$	−28.7010	+	6.31631i	−0.974177	+	0.214390i
$869$	6.39331			0.216878
$870$	6.90101	−	11.9529i	0.233966	−	0.405241i
$871$	−29.0422	−	50.3026i	−0.984058	−	1.70444i
$872$	−17.4372	−	30.2021i	−0.590498	−	1.02277i
$873$	−3.19665	+	5.53677i	−0.108190	+	0.187391i
$874$	3.25146			0.109982
$875$	−17.4282	−	19.0787i	−0.589180	−	0.644976i
$876$	−13.6834			−0.462321
$877$	3.30807	−	5.72974i	0.111705	−	0.193480i	−0.804753	−	0.593610i	$-0.797702\pi$
$877$	3.30807	−	5.72974i	0.111705	−	0.193480i	0.916458	+	0.400131i	$0.131035\pi$
$878$	−1.49097	−	2.58244i	−0.0503179	−	0.0871532i
$879$	−14.6627	−	25.3965i	−0.494559	−	0.856602i
$880$	−2.85327	+	4.94202i	−0.0961839	+	0.166595i
$881$	−22.5286			−0.759008			−0.379504	−	0.925190i	$-0.623905\pi$
$881$	−22.5286			−0.759008			−0.379504	+	0.925190i	$0.623905\pi$
$882$	2.73922	−	1.26702i	0.0922342	−	0.0426627i
$883$	−51.1652			−1.72185			−0.860923	−	0.508735i	$-0.830113\pi$
$883$	−51.1652			−1.72185			−0.860923	+	0.508735i	$0.830113\pi$
$884$	7.68291	−	13.3072i	0.258404	−	0.447569i
$885$	30.2049	+	52.3164i	1.01533	+	1.75860i
$886$	−4.51242	−	7.81575i	−0.151598	−	0.262575i
$887$	3.16904	−	5.48895i	0.106406	−	0.184301i	−0.807906	−	0.589312i	$-0.799399\pi$
$887$	3.16904	−	5.48895i	0.106406	−	0.184301i	0.914312	+	0.405011i	$0.132732\pi$
$888$	20.2151			0.678375
$889$	−11.8154	−	12.9344i	−0.396277	−	0.433805i
$890$	6.01979			0.201784
$891$	−5.26936	+	9.12679i	−0.176530	+	0.305759i
$892$	12.2578	+	21.2311i	0.410421	+	0.710871i
$893$	1.22679	+	2.12487i	0.0410531	+	0.0711060i
$894$	0.627804	−	1.08739i	0.0209969	−	0.0363677i
$895$	−11.5913			−0.387454
$896$	28.6811	−	6.31193i	0.958169	−	0.210867i
$897$	−37.7987			−1.26206
$898$	−7.08041	+	12.2636i	−0.236276	+	0.409242i
$899$	10.9035	+	18.8855i	0.363653	+	0.629866i
$900$	3.98493	+	6.90210i	0.132831	+	0.230070i
$901$	7.64155	−	13.2356i	0.254577	−	0.440940i
$902$	0.844248			0.0281104
$903$	2.44456	−	7.71155i	0.0813498	−	0.256624i
$904$	−29.1592			−0.969821
$905$	−18.4523	+	31.9603i	−0.613374	+	1.06239i
$906$	−10.3107	−	17.8587i	−0.342550	−	0.593315i
$907$	3.44237	+	5.96236i	0.114302	+	0.197977i	0.917500	−	0.397735i	$-0.130204\pi$
$907$	3.44237	+	5.96236i	0.114302	+	0.197977i	−0.803199	+	0.595711i	$0.796870\pi$
$908$	−12.2909	+	21.2885i	−0.407889	+	0.706484i
$909$	1.21777			0.0403908
$910$	11.0767	−	34.9422i	0.367188	−	1.15832i
$911$	−41.0818			−1.36110			−0.680550	−	0.732701i	$-0.738259\pi$
$911$	−41.0818			−1.36110			−0.680550	+	0.732701i	$0.738259\pi$
$912$	−2.26430	+	3.92188i	−0.0749784	+	0.129866i
$913$	0.0839190	+	0.145352i	0.00277731	+	0.00481045i
$914$	1.08524	+	1.87969i	0.0358966	+	0.0621747i
$915$	−22.8168	+	39.5198i	−0.754299	+	1.30648i
$916$	8.74084			0.288805
$917$	15.6524	−	3.44467i	0.516889	−	0.113753i
$918$	4.87439			0.160879
$919$	5.81324	−	10.0688i	0.191761	−	0.332140i	−0.754073	−	0.656791i	$-0.771913\pi$
$919$	5.81324	−	10.0688i	0.191761	−	0.332140i	0.945834	+	0.324651i	$0.105247\pi$
$920$	−13.9806	−	24.2152i	−0.460928	−	0.798350i
$921$	15.7479	+	27.2762i	0.518911	+	0.898780i
$922$	10.5560	−	18.2835i	0.347642	−	0.602134i
$923$	50.9562			1.67724
$924$	5.35327	+	5.86024i	0.176110	+	0.192788i
$925$	−34.9019			−1.14757
$926$	−1.91136	+	3.31057i	−0.0628112	+	0.108792i
$927$	1.04003	+	1.80139i	0.0341592	+	0.0591654i
$928$	−8.83469	−	15.3021i	−0.290013	−	0.502317i
$929$	−12.3834	+	21.4487i	−0.406287	+	0.703709i	−0.994470	−	0.105018i	$-0.966510\pi$
$929$	−12.3834	+	21.4487i	−0.406287	+	0.703709i	0.588184	+	0.808727i	$0.299843\pi$
$930$	31.7263			1.04035
$931$	−8.47417	−	5.97282i	−0.277730	−	0.195751i
$932$	30.2402			0.990551
$933$	−20.6799	+	35.8187i	−0.677030	+	1.17265i
$934$	1.97470	+	3.42028i	0.0646141	+	0.111915i
$935$	2.95611	+	5.12014i	0.0966753	+	0.167447i
$936$	−4.54861	+	7.87842i	−0.148676	+	0.257514i
$937$	1.15046			0.0375839			0.0187920	−	0.999823i	$-0.494018\pi$
$937$	1.15046			0.0375839			0.0187920	+	0.999823i	$0.494018\pi$
$938$	−11.5112	−	12.6014i	−0.375855	−	0.411449i
$939$	31.3381			1.02268
$940$	4.63770	−	8.03273i	0.151265	−	0.261999i
$941$	−5.05510	−	8.75570i	−0.164792	−	0.285428i	0.771790	−	0.635878i	$-0.219362\pi$
$941$	−5.05510	−	8.75570i	−0.164792	−	0.285428i	−0.936581	+	0.350450i	$0.886029\pi$
$942$	7.18895	+	12.4516i	0.234229	+	0.405696i
$943$	2.14937	−	3.72282i	0.0699931	−	0.121232i
$944$	14.1542			0.460679
$945$	−41.3228	+	9.09402i	−1.34423	+	0.295828i
$946$	−1.04993			−0.0341361
$947$	12.2277	−	21.1789i	0.397346	−	0.688223i	−0.596052	−	0.802946i	$-0.703265\pi$
$947$	12.2277	−	21.1789i	0.397346	−	0.688223i	0.993398	+	0.114723i	$0.0365981\pi$
$948$	−9.58996	−	16.6103i	−0.311467	−	0.539478i
$949$	13.4833	+	23.3537i	0.437685	+	0.758093i
$950$	−3.76199	+	6.51596i	−0.122055	+	0.211406i
$951$	8.53101			0.276637
$952$	3.10371	−	9.79088i	0.100592	−	0.317324i
$953$	−16.1696			−0.523784			−0.261892	−	0.965097i	$-0.584346\pi$
$953$	−16.1696			−0.523784			−0.261892	+	0.965097i	$0.584346\pi$
$954$	−1.98878	+	3.44467i	−0.0643892	+	0.111525i
$955$	17.8843	+	30.9765i	0.578722	+	1.00238i
$956$	−17.3809	−	30.1046i	−0.562138	−	0.973652i
$957$	2.94490	−	5.10071i	0.0951950	−	0.164883i
$958$	11.2512			0.363511
$959$	−5.93500	+	18.7224i	−0.191651	+	0.604578i
$960$	−3.88209			−0.125294
$961$	−9.56368	+	16.5648i	−0.308506	+	0.534347i
$962$	−8.75648	−	15.1667i	−0.282320	−	0.488993i
$963$	1.56500	+	2.71066i	0.0504313	+	0.0873497i
$964$	−15.5900	+	27.0026i	−0.502119	+	0.869695i
$965$	−90.3823			−2.90951
$966$	−10.8472	+	2.38718i	−0.349004	+	0.0768062i
$967$	−1.55941			−0.0501472			−0.0250736	−	0.999686i	$-0.507982\pi$
$967$	−1.55941			−0.0501472			−0.0250736	+	0.999686i	$0.507982\pi$
$968$	1.17169	−	2.02943i	0.0376595	−	0.0652282i
$969$	2.34591	+	4.06323i	0.0753614	+	0.130530i
$970$	11.4084	+	19.7599i	0.366301	+	0.634452i
$971$	4.52364	−	7.83518i	0.145171	−	0.251443i	−0.784266	−	0.620425i	$-0.786960\pi$
$971$	4.52364	−	7.83518i	0.145171	−	0.251443i	0.929437	+	0.368982i	$0.120294\pi$
$972$	10.5257			0.337613
$973$	−19.3154	−	21.1447i	−0.619224	−	0.677866i
$974$	3.75209			0.120225
$975$	43.7337	−	75.7490i	1.40060	−	2.42591i
$976$	5.34602	+	9.25959i	0.171122	+	0.296392i
$977$	3.37824	+	5.85128i	0.108079	+	0.187199i	0.914992	−	0.403472i	$-0.132197\pi$
$977$	3.37824	+	5.85128i	0.108079	+	0.187199i	−0.806913	+	0.590671i	$0.798863\pi$
$978$	5.61240	−	9.72096i	0.179465	−	0.310842i
$979$	2.56885			0.0821008
$980$	−3.53664	+	39.0330i	−0.112974	+	1.24686i
$981$	−9.77188			−0.311992
$982$	−7.90154	+	13.6859i	−0.252148	+	0.436734i
$983$	−13.2152	−	22.8895i	−0.421501	−	0.730060i	0.574586	−	0.818444i	$-0.305163\pi$
$983$	−13.2152	−	22.8895i	−0.421501	−	0.730060i	−0.996086	+	0.0883838i	$0.971830\pi$
$984$	−2.88077	−	4.98964i	−0.0918355	−	0.159064i
$985$	−43.8628	+	75.9727i	−1.39759	+	2.42069i
$986$	−3.35041			−0.106699
$987$	−5.65277	−	6.18810i	−0.179930	−	0.196969i
$988$	13.7376			0.437051
$989$	−2.67301	+	4.62979i	−0.0849969	+	0.147219i
$990$	−0.769355	−	1.33256i	−0.0244517	−	0.0423516i
$991$	0.317093	+	0.549221i	0.0100728	+	0.0174466i	0.871018	−	0.491251i	$-0.163460\pi$
$991$	0.317093	+	0.549221i	0.0100728	+	0.0174466i	−0.860945	+	0.508698i	$0.830127\pi$
$992$	20.3081	−	35.1746i	0.644782	−	1.11679i
$993$	36.4080			1.15537
$994$	14.6231	−	3.21814i	0.463816	−	0.102073i
$995$	−19.9545			−0.632599
$996$	0.251757	−	0.436056i	0.00797722	−	0.0138170i
$997$	−5.06368	−	8.77054i	−0.160368	−	0.277766i	0.774633	−	0.632412i	$-0.217935\pi$
$997$	−5.06368	−	8.77054i	−0.160368	−	0.277766i	−0.935001	+	0.354646i	$0.884601\pi$
$998$	−3.54222	−	6.13531i	−0.112127	−	0.194210i
$999$	−10.1076	+	17.5068i	−0.319789	+	0.553891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.e.b.23.2	✓	6
3.2	odd	2		693.2.i.g.100.2		6
4.3	odd	2		1232.2.q.k.177.3		6
7.2	even	3		539.2.a.h.1.2		3
7.3	odd	6		539.2.e.l.67.2		6
7.4	even	3	inner	77.2.e.b.67.2	yes	6
7.5	odd	6		539.2.a.i.1.2		3
7.6	odd	2		539.2.e.l.177.2		6
11.2	odd	10		847.2.n.d.807.2		24
11.3	even	5		847.2.n.e.9.2		24
11.4	even	5		847.2.n.e.632.2		24
11.5	even	5		847.2.n.e.366.2		24
11.6	odd	10		847.2.n.d.366.2		24
11.7	odd	10		847.2.n.d.632.2		24
11.8	odd	10		847.2.n.d.9.2		24
11.9	even	5		847.2.n.e.807.2		24
11.10	odd	2		847.2.e.d.485.2		6
21.2	odd	6		4851.2.a.bo.1.2		3
21.5	even	6		4851.2.a.bn.1.2		3
21.11	odd	6		693.2.i.g.298.2		6
28.11	odd	6		1232.2.q.k.529.3		6
28.19	even	6		8624.2.a.ck.1.3		3
28.23	odd	6		8624.2.a.cl.1.1		3
77.4	even	15		847.2.n.e.753.2		24
77.18	odd	30		847.2.n.d.753.2		24
77.25	even	15		847.2.n.e.130.2		24
77.32	odd	6		847.2.e.d.606.2		6
77.39	odd	30		847.2.n.d.487.2		24
77.46	odd	30		847.2.n.d.81.2		24
77.53	even	15		847.2.n.e.81.2		24
77.54	even	6		5929.2.a.w.1.2		3
77.60	even	15		847.2.n.e.487.2		24
77.65	odd	6		5929.2.a.v.1.2		3
77.74	odd	30		847.2.n.d.130.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.2	✓	6	1.1	even	1	trivial
77.2.e.b.67.2	yes	6	7.4	even	3	inner
539.2.a.h.1.2		3	7.2	even	3
539.2.a.i.1.2		3	7.5	odd	6
539.2.e.l.67.2		6	7.3	odd	6
539.2.e.l.177.2		6	7.6	odd	2
693.2.i.g.100.2		6	3.2	odd	2
693.2.i.g.298.2		6	21.11	odd	6
847.2.e.d.485.2		6	11.10	odd	2
847.2.e.d.606.2		6	77.32	odd	6
847.2.n.d.9.2		24	11.8	odd	10
847.2.n.d.81.2		24	77.46	odd	30
847.2.n.d.130.2		24	77.74	odd	30
847.2.n.d.366.2		24	11.6	odd	10
847.2.n.d.487.2		24	77.39	odd	30
847.2.n.d.632.2		24	11.7	odd	10
847.2.n.d.753.2		24	77.18	odd	30
847.2.n.d.807.2		24	11.2	odd	10
847.2.n.e.9.2		24	11.3	even	5
847.2.n.e.81.2		24	77.53	even	15
847.2.n.e.130.2		24	77.25	even	15
847.2.n.e.366.2		24	11.5	even	5
847.2.n.e.487.2		24	77.60	even	15
847.2.n.e.632.2		24	11.4	even	5
847.2.n.e.753.2		24	77.4	even	15
847.2.n.e.807.2		24	11.9	even	5
1232.2.q.k.177.3		6	4.3	odd	2
1232.2.q.k.529.3		6	28.11	odd	6
4851.2.a.bn.1.2		3	21.5	even	6
4851.2.a.bo.1.2		3	21.2	odd	6
5929.2.a.v.1.2		3	77.65	odd	6
5929.2.a.w.1.2		3	77.54	even	6
8624.2.a.ck.1.3		3	28.19	even	6
8624.2.a.cl.1.1		3	28.23	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.328310 + 0.568650i) q^{2} +(-0.956115 - 1.65604i) q^{3} +(0.784425 + 1.35866i) q^{4} +(1.78442 - 3.09071i) q^{5} +1.25561 q^{6} +(1.78442 + 1.95341i) q^{7} -2.34338 q^{8} +(-0.328310 + 0.568650i) q^{9} +O(q^{10})\)	\(q+(-0.328310 + 0.568650i) q^{2} +(-0.956115 - 1.65604i) q^{3} +(0.784425 + 1.35866i) q^{4} +(1.78442 - 3.09071i) q^{5} +1.25561 q^{6} +(1.78442 + 1.95341i) q^{7} -2.34338 q^{8} +(-0.328310 + 0.568650i) q^{9} +(1.17169 + 2.02943i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} -5.91223 q^{13} +(-1.69665 + 0.373387i) q^{14} -6.82446 q^{15} +(-0.799494 + 1.38476i) q^{16} +(0.828310 + 1.43468i) q^{17} +(-0.215575 - 0.373387i) q^{18} +(-0.740539 + 1.28265i) q^{19} +5.59899 q^{20} +(1.52882 - 4.82277i) q^{21} -0.656620 q^{22} +(-1.67169 + 2.89545i) q^{23} +(2.24054 + 3.88073i) q^{24} +(-3.86834 - 6.70017i) q^{25} +(1.94105 - 3.36199i) q^{26} -4.48108 q^{27} +(-1.25429 + 3.95674i) q^{28} +3.08007 q^{29} +(2.24054 - 3.88073i) q^{30} +(3.54003 + 6.13152i) q^{31} +(-2.86834 - 4.96812i) q^{32} +(0.956115 - 1.65604i) q^{33} -1.08777 q^{34} +(9.22162 - 2.02943i) q^{35} -1.03014 q^{36} +(2.25561 - 3.90683i) q^{37} +(-0.486253 - 0.842215i) q^{38} +(5.65277 + 9.79088i) q^{39} +(-4.18158 + 7.24272i) q^{40} -1.28575 q^{41} +(2.24054 + 2.45272i) q^{42} +1.59899 q^{43} +(-0.784425 + 1.35866i) q^{44} +(1.17169 + 2.02943i) q^{45} +(-1.09767 - 1.90121i) q^{46} +(0.828310 - 1.43468i) q^{47} +3.05763 q^{48} +(-0.631656 + 6.97144i) q^{49} +5.08007 q^{50} +(1.58392 - 2.74343i) q^{51} +(-4.63770 - 8.03273i) q^{52} +(-4.61274 - 7.98949i) q^{53} +(1.47118 - 2.54817i) q^{54} +3.56885 q^{55} +(-4.18158 - 4.57759i) q^{56} +2.83216 q^{57} +(-1.01122 + 1.75148i) q^{58} +(-4.42598 - 7.66602i) q^{59} +(-5.35327 - 9.27214i) q^{60} +(3.34338 - 5.79090i) q^{61} -4.64892 q^{62} +(-1.69665 + 0.373387i) q^{63} +0.568850 q^{64} +(-10.5499 + 18.2730i) q^{65} +(0.627804 + 1.08739i) q^{66} +(4.91223 + 8.50823i) q^{67} +(-1.29949 + 2.25079i) q^{68} +6.39331 q^{69} +(-1.87352 + 5.91015i) q^{70} -8.61878 q^{71} +(0.769355 - 1.33256i) q^{72} +(-2.28057 - 3.95007i) q^{73} +(1.48108 + 2.56530i) q^{74} +(-7.39716 + 12.8123i) q^{75} -2.32359 q^{76} +(-0.799494 + 2.52206i) q^{77} -7.42345 q^{78} +(3.19665 - 5.53677i) q^{79} +(2.85327 + 4.94202i) q^{80} +(5.26936 + 9.12679i) q^{81} +(0.422124 - 0.731140i) q^{82} +0.167838 q^{83} +(7.75176 - 1.70595i) q^{84} +5.91223 q^{85} +(-0.524964 + 0.909265i) q^{86} +(-2.94490 - 5.10071i) q^{87} +(-1.17169 - 2.02943i) q^{88} +(1.28442 - 2.22469i) q^{89} -1.53871 q^{90} +(-10.5499 - 11.5490i) q^{91} -5.24526 q^{92} +(6.76936 - 11.7249i) q^{93} +(0.543885 + 0.942037i) q^{94} +(2.64287 + 4.57759i) q^{95} +(-5.48493 + 9.50018i) q^{96} +9.73669 q^{97} +(-3.75693 - 2.64799i) q^{98} -0.656620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8}+O(q^{10}) \) 6 * q + q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8	\( 6 q + q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} + 9 q^{10} + 3 q^{11} + 9 q^{12} - 22 q^{13} + 12 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} + 28 q^{20} + 10 q^{21} - 12 q^{23} - 2 q^{24} - 3 q^{25} - q^{26} + 4 q^{27} + 13 q^{28} - 18 q^{29} - 2 q^{30} + 3 q^{31} + 3 q^{32} - q^{33} - 20 q^{34} + 9 q^{35} - 18 q^{36} + 4 q^{37} - 8 q^{38} + 5 q^{39} + 3 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} + 4 q^{44} + 9 q^{45} + 10 q^{46} + 3 q^{47} + 20 q^{48} - 24 q^{49} - 6 q^{50} - 2 q^{51} + 7 q^{52} - 17 q^{53} + 8 q^{54} + 4 q^{55} + 3 q^{56} + 40 q^{57} + 13 q^{58} - 8 q^{59} - 6 q^{60} + 24 q^{61} + 26 q^{62} + 12 q^{63} - 14 q^{64} - 15 q^{65} - q^{66} + 16 q^{67} - 5 q^{68} - 6 q^{69} - 27 q^{70} + 14 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} - 25 q^{75} - 78 q^{76} - 2 q^{77} - 12 q^{78} - 3 q^{79} - 9 q^{80} + 17 q^{81} - 41 q^{82} - 22 q^{83} + 12 q^{84} + 22 q^{85} + 21 q^{86} - 30 q^{87} - 9 q^{88} - q^{89} + 20 q^{90} - 15 q^{91} + 50 q^{92} + 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} + 18 q^{97} - 24 q^{98}+O(q^{100}) \) 6 * q + q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8 + 9 * q^10 + 3 * q^11 + 9 * q^12 - 22 * q^13 + 12 * q^14 - 14 * q^15 - 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 + 28 * q^20 + 10 * q^21 - 12 * q^23 - 2 * q^24 - 3 * q^25 - q^26 + 4 * q^27 + 13 * q^28 - 18 * q^29 - 2 * q^30 + 3 * q^31 + 3 * q^32 - q^33 - 20 * q^34 + 9 * q^35 - 18 * q^36 + 4 * q^37 - 8 * q^38 + 5 * q^39 + 3 * q^40 - 10 * q^41 - 2 * q^42 + 4 * q^43 + 4 * q^44 + 9 * q^45 + 10 * q^46 + 3 * q^47 + 20 * q^48 - 24 * q^49 - 6 * q^50 - 2 * q^51 + 7 * q^52 - 17 * q^53 + 8 * q^54 + 4 * q^55 + 3 * q^56 + 40 * q^57 + 13 * q^58 - 8 * q^59 - 6 * q^60 + 24 * q^61 + 26 * q^62 + 12 * q^63 - 14 * q^64 - 15 * q^65 - q^66 + 16 * q^67 - 5 * q^68 - 6 * q^69 - 27 * q^70 + 14 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 - 25 * q^75 - 78 * q^76 - 2 * q^77 - 12 * q^78 - 3 * q^79 - 9 * q^80 + 17 * q^81 - 41 * q^82 - 22 * q^83 + 12 * q^84 + 22 * q^85 + 21 * q^86 - 30 * q^87 - 9 * q^88 - q^89 + 20 * q^90 - 15 * q^91 + 50 * q^92 + 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 + 18 * q^97 - 24 * q^98

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