LMFDB - Embedded newform 273.2.bl.d.121.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.8
Root			$-1.46676i$ of defining polynomial
Character	$\chi$	$=$	273.121
Dual form			273.2.bl.d.88.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27025 - 0.733378i) q^{2} -1.00000 q^{3} +(0.0756874 - 0.131094i) q^{4} +(1.88109 + 1.08605i) q^{5} +(-1.27025 + 0.733378i) q^{6} +(0.427729 + 2.61095i) q^{7} +2.71148i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.27025 - 0.733378i) q^{2} -1.00000 q^{3} +(0.0756874 - 0.131094i) q^{4} +(1.88109 + 1.08605i) q^{5} +(-1.27025 + 0.733378i) q^{6} +(0.427729 + 2.61095i) q^{7} +2.71148i q^{8} +1.00000 q^{9} +3.18593 q^{10} -5.49721i q^{11} +(-0.0756874 + 0.131094i) q^{12} +(3.04222 + 1.93517i) q^{13} +(2.45813 + 3.00287i) q^{14} +(-1.88109 - 1.08605i) q^{15} +(2.13992 + 3.70645i) q^{16} +(-1.99413 + 3.45394i) q^{17} +(1.27025 - 0.733378i) q^{18} -4.33519i q^{19} +(0.284749 - 0.164400i) q^{20} +(-0.427729 - 2.61095i) q^{21} +(-4.03154 - 6.98282i) q^{22} +(-0.862484 - 1.49387i) q^{23} -2.71148i q^{24} +(-0.141010 - 0.244236i) q^{25} +(5.28359 + 0.227044i) q^{26} -1.00000 q^{27} +(0.374655 + 0.141543i) q^{28} +(4.36939 - 7.56801i) q^{29} -3.18593 q^{30} +(-2.95043 + 1.70343i) q^{31} +(0.740028 + 0.427255i) q^{32} +5.49721i q^{33} +5.84981i q^{34} +(-2.03101 + 5.37595i) q^{35} +(0.0756874 - 0.131094i) q^{36} +(-7.86991 + 4.54370i) q^{37} +(-3.17933 - 5.50676i) q^{38} +(-3.04222 - 1.93517i) q^{39} +(-2.94479 + 5.10053i) q^{40} +(6.74826 + 3.89611i) q^{41} +(-2.45813 - 3.00287i) q^{42} +(-2.24984 - 3.89684i) q^{43} +(-0.720654 - 0.416070i) q^{44} +(1.88109 + 1.08605i) q^{45} +(-2.19114 - 1.26505i) q^{46} +(3.33576 + 1.92590i) q^{47} +(-2.13992 - 3.70645i) q^{48} +(-6.63410 + 2.23356i) q^{49} +(-0.358235 - 0.206827i) q^{50} +(1.99413 - 3.45394i) q^{51} +(0.483948 - 0.252351i) q^{52} +(-4.08835 - 7.08123i) q^{53} +(-1.27025 + 0.733378i) q^{54} +(5.97022 - 10.3407i) q^{55} +(-7.07954 + 1.15978i) q^{56} +4.33519i q^{57} -12.8177i q^{58} +(-1.27893 - 0.738389i) q^{59} +(-0.284749 + 0.164400i) q^{60} -3.65055 q^{61} +(-2.49852 + 4.32757i) q^{62} +(0.427729 + 2.61095i) q^{63} -7.30631 q^{64} +(3.62100 + 6.94421i) q^{65} +(4.03154 + 6.98282i) q^{66} -1.10868i q^{67} +(0.301861 + 0.522839i) q^{68} +(0.862484 + 1.49387i) q^{69} +(1.36271 + 8.31829i) q^{70} +(6.60723 - 3.81468i) q^{71} +2.71148i q^{72} +(-6.82323 + 3.93939i) q^{73} +(-6.66450 + 11.5432i) q^{74} +(0.141010 + 0.244236i) q^{75} +(-0.568319 - 0.328119i) q^{76} +(14.3529 - 2.35132i) q^{77} +(-5.28359 - 0.227044i) q^{78} +(7.56487 - 13.1027i) q^{79} +9.29619i q^{80} +1.00000 q^{81} +11.4293 q^{82} -11.9428i q^{83} +(-0.374655 - 0.141543i) q^{84} +(-7.50226 + 4.33143i) q^{85} +(-5.71571 - 3.29997i) q^{86} +(-4.36939 + 7.56801i) q^{87} +14.9056 q^{88} +(3.17206 - 1.83139i) q^{89} +3.18593 q^{90} +(-3.75138 + 8.77081i) q^{91} -0.261117 q^{92} +(2.95043 - 1.70343i) q^{93} +5.64966 q^{94} +(4.70821 - 8.15486i) q^{95} +(-0.740028 - 0.427255i) q^{96} +(-4.57836 + 2.64332i) q^{97} +(-6.78891 + 7.70247i) q^{98} -5.49721i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.27025	−	0.733378i	0.898201	−	0.518577i	0.0215851	−	0.999767i	$-0.493129\pi$
$2$	1.27025	−	0.733378i	0.898201	−	0.518577i	0.876616	+	0.481190i	$0.159795\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.0756874	−	0.131094i	0.0378437	−	0.0655472i
$5$	1.88109	+	1.08605i	0.841247	+	0.485694i	0.857688	−	0.514170i	$-0.171900\pi$
$5$	1.88109	+	1.08605i	0.841247	+	0.485694i	−0.0164407	+	0.999865i	$0.505233\pi$
$6$	−1.27025	+	0.733378i	−0.518577	+	0.299400i
$7$	0.427729	+	2.61095i	0.161666	+	0.986845i
$7$	0.427729	+	2.61095i	0.161666	+	0.986845i
$8$			2.71148i			0.958654i
$9$	1.00000			0.333333
$10$	3.18593			1.00748
$11$		−	5.49721i		−	1.65747i	−0.559640	−	0.828736i	$-0.689061\pi$
$11$		−	5.49721i		−	1.65747i	0.559640	−	0.828736i	$-0.310939\pi$
$12$	−0.0756874	+	0.131094i	−0.0218491	+	0.0378437i
$13$	3.04222	+	1.93517i	0.843761	+	0.536719i
$13$	3.04222	+	1.93517i	0.843761	+	0.536719i
$14$	2.45813	+	3.00287i	0.656964	+	0.802549i
$15$	−1.88109	−	1.08605i	−0.485694	−	0.280416i
$16$	2.13992	+	3.70645i	0.534979	+	0.926612i
$17$	−1.99413	+	3.45394i	−0.483648	+	0.837703i	−0.999824	−	0.0187801i	$-0.994022\pi$
$17$	−1.99413	+	3.45394i	−0.483648	+	0.837703i	0.516176	+	0.856483i	$0.327355\pi$
$18$	1.27025	−	0.733378i	0.299400	−	0.172859i
$19$		−	4.33519i		−	0.994560i	−0.867590	−	0.497280i	$-0.834332\pi$
$19$		−	4.33519i		−	0.994560i	0.867590	−	0.497280i	$-0.165668\pi$
$20$	0.284749	−	0.164400i	0.0636719	−	0.0367610i
$21$	−0.427729	−	2.61095i	−0.0933381	−	0.569756i
$22$	−4.03154	−	6.98282i	−0.859526	−	1.48874i
$23$	−0.862484	−	1.49387i	−0.179840	−	0.311493i	0.761985	−	0.647594i	$-0.224225\pi$
$23$	−0.862484	−	1.49387i	−0.179840	−	0.311493i	−0.941826	+	0.336102i	$0.890891\pi$
$24$		−	2.71148i		−	0.553479i
$25$	−0.141010	−	0.244236i	−0.0282019	−	0.0488472i
$26$	5.28359	+	0.227044i	1.03620	+	0.0445270i
$27$	−1.00000			−0.192450
$28$	0.374655	+	0.141543i	0.0708031	+	0.0267491i
$29$	4.36939	−	7.56801i	0.811376	−	1.40534i	−0.100525	−	0.994934i	$-0.532052\pi$
$29$	4.36939	−	7.56801i	0.811376	−	1.40534i	0.911901	−	0.410410i	$-0.134614\pi$
$30$	−3.18593			−0.581668
$31$	−2.95043	+	1.70343i	−0.529913	+	0.305946i	−0.740981	−	0.671526i	$-0.765639\pi$
$31$	−2.95043	+	1.70343i	−0.529913	+	0.305946i	0.211068	+	0.977471i	$0.432306\pi$
$32$	0.740028	+	0.427255i	0.130820	+	0.0755288i
$33$			5.49721i			0.956942i
$34$			5.84981i			1.00323i
$35$	−2.03101	+	5.37595i	−0.343304	+	0.908702i
$36$	0.0756874	−	0.131094i	0.0126146	−	0.0218491i
$37$	−7.86991	+	4.54370i	−1.29381	+	0.746979i	−0.979327	−	0.202285i	$-0.935163\pi$
$37$	−7.86991	+	4.54370i	−1.29381	+	0.746979i	−0.314479	+	0.949264i	$0.601830\pi$
$38$	−3.17933	−	5.50676i	−0.515756	−	0.893315i
$39$	−3.04222	−	1.93517i	−0.487146	−	0.309875i
$40$	−2.94479	+	5.10053i	−0.465613	+	0.806465i
$41$	6.74826	+	3.89611i	1.05390	+	0.608471i	0.923739	−	0.383022i	$-0.125117\pi$
$41$	6.74826	+	3.89611i	1.05390	+	0.608471i	0.130163	+	0.991493i	$0.458450\pi$
$42$	−2.45813	−	3.00287i	−0.379298	−	0.463352i
$43$	−2.24984	−	3.89684i	−0.343097	−	0.594262i	0.641909	−	0.766781i	$-0.278143\pi$
$43$	−2.24984	−	3.89684i	−0.343097	−	0.594262i	−0.985006	+	0.172519i	$0.944809\pi$
$44$	−0.720654	−	0.416070i	−0.108643	−	0.0627249i
$45$	1.88109	+	1.08605i	0.280416	+	0.161898i
$46$	−2.19114	−	1.26505i	−0.323066	−	0.186522i
$47$	3.33576	+	1.92590i	0.486571	+	0.280922i	0.723151	−	0.690690i	$-0.242693\pi$
$47$	3.33576	+	1.92590i	0.486571	+	0.280922i	−0.236580	+	0.971612i	$0.576027\pi$
$48$	−2.13992	−	3.70645i	−0.308871	−	0.534979i
$49$	−6.63410	+	2.23356i	−0.947728	+	0.319079i
$50$	−0.358235	−	0.206827i	−0.0506621	−	0.0292497i
$51$	1.99413	−	3.45394i	0.279234	−	0.483648i
$52$	0.483948	−	0.252351i	0.0671115	−	0.0349948i
$53$	−4.08835	−	7.08123i	−0.561578	−	0.972681i	−0.997359	−	0.0726288i	$-0.976861\pi$
$53$	−4.08835	−	7.08123i	−0.561578	−	0.972681i	0.435781	−	0.900053i	$-0.356472\pi$
$54$	−1.27025	+	0.733378i	−0.172859	+	0.0998001i
$55$	5.97022	−	10.3407i	0.805025	−	1.39434i
$56$	−7.07954	+	1.15978i	−0.946043	+	0.154982i
$57$			4.33519i			0.574209i
$58$		−	12.8177i		−	1.68304i
$59$	−1.27893	−	0.738389i	−0.166502	−	0.0961301i	0.414433	−	0.910080i	$-0.363980\pi$
$59$	−1.27893	−	0.738389i	−0.166502	−	0.0961301i	−0.580935	+	0.813950i	$0.697313\pi$
$60$	−0.284749	+	0.164400i	−0.0367610	+	0.0212240i
$61$	−3.65055			−0.467406			−0.233703	−	0.972308i	$-0.575084\pi$
$61$	−3.65055			−0.467406			−0.233703	+	0.972308i	$0.575084\pi$
$62$	−2.49852	+	4.32757i	−0.317313	+	0.549602i
$63$	0.427729	+	2.61095i	0.0538888	+	0.328948i
$64$	−7.30631			−0.913289
$65$	3.62100	+	6.94421i	0.449130	+	0.861323i
$66$	4.03154	+	6.98282i	0.496248	+	0.859526i
$67$		−	1.10868i		−	0.135447i	−0.997704	−	0.0677233i	$-0.978427\pi$
$67$		−	1.10868i		−	0.135447i	0.997704	−	0.0677233i	$-0.0215735\pi$
$68$	0.301861	+	0.522839i	0.0366061	+	0.0634036i
$69$	0.862484	+	1.49387i	0.103831	+	0.179840i
$70$	1.36271	+	8.31829i	0.162875	+	0.994226i
$71$	6.60723	−	3.81468i	0.784133	−	0.452720i	−0.0537597	−	0.998554i	$-0.517121\pi$
$71$	6.60723	−	3.81468i	0.784133	−	0.452720i	0.837893	+	0.545834i	$0.183787\pi$
$72$			2.71148i			0.319551i
$73$	−6.82323	+	3.93939i	−0.798599	+	0.461071i	−0.842981	−	0.537943i	$-0.819201\pi$
$73$	−6.82323	+	3.93939i	−0.798599	+	0.461071i	0.0443821	+	0.999015i	$0.485868\pi$
$74$	−6.66450	+	11.5432i	−0.774732	+	1.34188i
$75$	0.141010	+	0.244236i	0.0162824	+	0.0282019i
$76$	−0.568319	−	0.328119i	−0.0651907	−	0.0376378i
$77$	14.3529	−	2.35132i	1.63567	−	0.267957i
$78$	−5.28359	−	0.227044i	−0.598249	−	0.0257077i
$79$	7.56487	−	13.1027i	0.851114	−	1.47417i	−0.0290891	−	0.999577i	$-0.509261\pi$
$79$	7.56487	−	13.1027i	0.851114	−	1.47417i	0.880203	−	0.474597i	$-0.157406\pi$
$80$			9.29619i			1.03935i
$81$	1.00000			0.111111
$82$	11.4293			1.26215
$83$		−	11.9428i		−	1.31089i	−0.755243	−	0.655445i	$-0.772481\pi$
$83$		−	11.9428i		−	1.31089i	0.755243	−	0.655445i	$-0.227519\pi$
$84$	−0.374655	−	0.141543i	−0.0408782	−	0.0154436i
$85$	−7.50226	+	4.33143i	−0.813735	+	0.469810i
$86$	−5.71571	−	3.29997i	−0.616341	−	0.355844i
$87$	−4.36939	+	7.56801i	−0.468448	+	0.811376i
$88$	14.9056			1.58894
$89$	3.17206	−	1.83139i	0.336238	−	0.194127i	−0.322369	−	0.946614i	$-0.604479\pi$
$89$	3.17206	−	1.83139i	0.336238	−	0.194127i	0.658607	+	0.752487i	$0.271146\pi$
$90$	3.18593			0.335826
$91$	−3.75138	+	8.77081i	−0.393251	+	0.919431i
$92$	−0.261117			−0.0272233
$93$	2.95043	−	1.70343i	0.305946	−	0.176638i
$94$	5.64966			0.582718
$95$	4.70821	−	8.15486i	0.483052	−	0.836671i
$96$	−0.740028	−	0.427255i	−0.0755288	−	0.0436066i
$97$	−4.57836	+	2.64332i	−0.464862	+	0.268388i	−0.714086	−	0.700058i	$-0.753158\pi$
$97$	−4.57836	+	2.64332i	−0.464862	+	0.268388i	0.249225	+	0.968446i	$0.419824\pi$
$98$	−6.78891	+	7.70247i	−0.685783	+	0.778067i
$99$		−	5.49721i		−	0.552491i
$100$	−0.0426907			−0.00426907
$101$	2.09045			0.208008			0.104004	−	0.994577i	$-0.466835\pi$
$101$	2.09045			0.208008			0.104004	+	0.994577i	$0.466835\pi$
$102$		−	5.84981i		−	0.579217i
$103$	3.82846	−	6.63109i	0.377230	−	0.653381i	−0.613428	−	0.789750i	$-0.710210\pi$
$103$	3.82846	−	6.63109i	0.377230	−	0.653381i	0.990658	+	0.136369i	$0.0435434\pi$
$104$	−5.24718	+	8.24894i	−0.514528	+	0.808875i
$105$	2.03101	−	5.37595i	0.198207	−	0.524639i
$106$	−10.3864	−	5.99661i	−1.00882	−	0.582443i
$107$	7.59271	+	13.1510i	0.734015	+	1.27135i	0.955154	+	0.296109i	$0.0956892\pi$
$107$	7.59271	+	13.1510i	0.734015	+	1.27135i	−0.221139	+	0.975242i	$0.570977\pi$
$108$	−0.0756874	+	0.131094i	−0.00728303	+	0.0126146i
$109$	11.6292	−	6.71414i	1.11388	−	0.643098i	0.174048	−	0.984737i	$-0.444315\pi$
$109$	11.6292	−	6.71414i	1.11388	−	0.643098i	0.939831	+	0.341639i	$0.110982\pi$
$110$		−	17.5137i		−	1.66987i
$111$	7.86991	−	4.54370i	0.746979	−	0.431269i
$112$	−8.76203	+	7.17257i	−0.827934	+	0.677744i
$113$	2.09697	+	3.63207i	0.197267	+	0.341676i	0.947641	−	0.319337i	$-0.103460\pi$
$113$	2.09697	+	3.63207i	0.197267	+	0.341676i	−0.750375	+	0.661013i	$0.770127\pi$
$114$	3.17933	+	5.50676i	0.297772	+	0.515756i
$115$		−	3.74679i		−	0.349390i
$116$	−0.661416	−	1.14561i	−0.0614110	−	0.106367i
$117$	3.04222	+	1.93517i	0.281254	+	0.178906i
$118$	−2.16607			−0.199403
$119$	−9.87099	−	3.72922i	−0.904873	−	0.341857i
$120$	2.94479	−	5.10053i	0.268822	−	0.465613i
$121$	−19.2193			−1.74721
$122$	−4.63711	+	2.67724i	−0.419824	+	0.242386i
$123$	−6.74826	−	3.89611i	−0.608471	−	0.351301i
$124$			0.515714i			0.0463125i
$125$		−	11.4730i		−	1.02618i
$126$	2.45813	+	3.00287i	0.218988	+	0.267516i
$127$	−7.43604	+	12.8796i	−0.659842	+	1.14288i	0.320814	+	0.947142i	$0.396043\pi$
$127$	−7.43604	+	12.8796i	−0.659842	+	1.14288i	−0.980656	+	0.195738i	$0.937290\pi$
$128$	−10.7609	+	6.21280i	−0.951137	+	0.549139i
$129$	2.24984	+	3.89684i	0.198087	+	0.343097i
$130$	9.69231	+	6.16531i	0.850072	+	0.540733i
$131$	−8.04868	+	13.9407i	−0.703217	+	1.21801i	0.264114	+	0.964491i	$0.414920\pi$
$131$	−8.04868	+	13.9407i	−0.703217	+	1.21801i	−0.967331	+	0.253516i	$0.918413\pi$
$132$	0.720654	+	0.416070i	0.0627249	+	0.0362142i
$133$	11.3189	−	1.85428i	0.981477	−	0.160787i
$134$	−0.813080	−	1.40830i	−0.0702394	−	0.121658i
$135$	−1.88109	−	1.08605i	−0.161898	−	0.0934719i
$136$	−9.36529	−	5.40705i	−0.803067	−	0.463651i
$137$	10.0151	+	5.78222i	0.855648	+	0.494009i	0.862553	−	0.505967i	$-0.168864\pi$
$137$	10.0151	+	5.78222i	0.855648	+	0.494009i	−0.00690436	+	0.999976i	$0.502198\pi$
$138$	2.19114	+	1.26505i	0.186522	+	0.107689i
$139$	−2.24447	−	3.88754i	−0.190374	−	0.329737i	0.755001	−	0.655724i	$-0.227637\pi$
$139$	−2.24447	−	3.88754i	−0.190374	−	0.329737i	−0.945374	+	0.325988i	$0.894303\pi$
$140$	0.551035	+	0.673147i	0.0465710	+	0.0568913i
$141$	−3.33576	−	1.92590i	−0.280922	−	0.162190i
$142$	5.59521	−	9.69119i	0.469540	−	0.813267i
$143$	10.6380	−	16.7237i	0.889597	−	1.39851i
$144$	2.13992	+	3.70645i	0.178326	+	0.308871i
$145$	16.4384	−	9.49072i	1.36514	−	0.788161i
$146$	−5.77813	+	10.0080i	−0.478202	+	0.828270i
$147$	6.63410	−	2.23356i	0.547171	−	0.184221i
$148$			1.37560i			0.113074i
$149$		−	2.01120i		−	0.164764i	−0.996601	−	0.0823819i	$-0.973747\pi$
$149$		−	2.01120i		−	0.164764i	0.996601	−	0.0823819i	$-0.0262527\pi$
$150$	0.358235	+	0.206827i	0.0292497	+	0.0168874i
$151$	−10.2962	+	5.94449i	−0.837890	+	0.483756i	−0.856547	−	0.516070i	$-0.827394\pi$
$151$	−10.2962	+	5.94449i	−0.837890	+	0.483756i	0.0186563	+	0.999826i	$0.494061\pi$
$152$	11.7548			0.953439
$153$	−1.99413	+	3.45394i	−0.161216	+	0.279234i
$154$	16.5074	−	13.5129i	1.33020	−	1.08890i
$155$	−7.40003			−0.594384
$156$	−0.483948	+	0.252351i	−0.0387469	+	0.0202042i
$157$	8.29034	+	14.3593i	0.661641	+	1.14600i	0.980184	+	0.198087i	$0.0634729\pi$
$157$	8.29034	+	14.3593i	0.661641	+	1.14600i	−0.318544	+	0.947908i	$0.603194\pi$
$158$		−	22.1916i		−	1.76547i
$159$	4.08835	+	7.08123i	0.324227	+	0.561578i
$160$	0.928038	+	1.60741i	0.0733678	+	0.127077i
$161$	3.53150	−	2.89087i	0.278321	−	0.227832i
$162$	1.27025	−	0.733378i	0.0998001	−	0.0576196i
$163$			10.7128i			0.839088i	0.907735	+	0.419544i	$0.137810\pi$
$163$			10.7128i			0.839088i	−0.907735	+	0.419544i	$0.862190\pi$
$164$	1.02152	−	0.589774i	0.0797671	−	0.0460536i
$165$	−5.97022	+	10.3407i	−0.464781	+	0.805025i
$166$	−8.75857	−	15.1703i	−0.679797	−	1.17744i
$167$	−17.4633	−	10.0825i	−1.35135	−	0.780205i	−0.362915	−	0.931822i	$-0.618219\pi$
$167$	−17.4633	−	10.0825i	−1.35135	−	0.780205i	−0.988439	+	0.151617i	$0.951552\pi$
$168$	7.07954	−	1.15978i	0.546198	−	0.0894789i
$169$	5.51025	+	11.7744i	0.423865	+	0.905725i
$170$	−6.35316	+	11.0040i	−0.487265	+	0.843968i
$171$		−	4.33519i		−	0.331520i
$172$	−0.681138			−0.0519363
$173$	2.22062			0.168831			0.0844155	−	0.996431i	$-0.473098\pi$
$173$	2.22062			0.168831			0.0844155	+	0.996431i	$0.473098\pi$
$174$			12.8177i			0.971705i
$175$	0.577374	−	0.472636i	0.0436453	−	0.0357279i
$176$	20.3751	−	11.7636i	1.53583	−	0.886713i
$177$	1.27893	+	0.738389i	0.0961301	+	0.0555007i
$178$	2.68621	−	4.65265i	0.201340	−	0.348731i
$179$	−4.92118			−0.367826			−0.183913	−	0.982943i	$-0.558876\pi$
$179$	−4.92118			−0.367826			−0.183913	+	0.982943i	$0.558876\pi$
$180$	0.284749	−	0.164400i	0.0212240	−	0.0122537i
$181$	20.3883			1.51545			0.757727	−	0.652572i	$-0.226310\pi$
$181$	20.3883			1.51545			0.757727	+	0.652572i	$0.226310\pi$
$182$	1.66714	+	13.8923i	0.123577	+	1.02977i
$183$	3.65055			0.269857
$184$	4.05059	−	2.33861i	0.298614	−	0.172405i
$185$	−19.7387			−1.45121
$186$	2.49852	−	4.32757i	0.183201	−	0.317313i
$187$	18.9870	+	10.9622i	1.38847	+	0.801633i
$188$	0.504951	−	0.291533i	0.0368273	−	0.0212623i
$189$	−0.427729	−	2.61095i	−0.0311127	−	0.189919i
$190$		−	13.8116i		−	1.00200i
$191$	−20.4365			−1.47874			−0.739368	−	0.673302i	$-0.764875\pi$
$191$	−20.4365			−1.47874			−0.739368	+	0.673302i	$0.764875\pi$
$192$	7.30631			0.527288
$193$			17.4039i			1.25276i	0.779519	+	0.626379i	$0.215464\pi$
$193$			17.4039i			1.25276i	−0.779519	+	0.626379i	$0.784536\pi$
$194$	−3.87710	+	6.71534i	−0.278360	+	0.482133i
$195$	−3.62100	−	6.94421i	−0.259305	−	0.497285i
$196$	−0.209311	+	1.03875i	−0.0149508	+	0.0741961i
$197$	13.5736	+	7.83670i	0.967077	+	0.558342i	0.898344	−	0.439293i	$-0.144771\pi$
$197$	13.5736	+	7.83670i	0.967077	+	0.558342i	0.0687330	+	0.997635i	$0.478104\pi$
$198$	−4.03154	−	6.98282i	−0.286509	−	0.496248i
$199$	−9.90041	+	17.1480i	−0.701821	+	1.21559i	0.266005	+	0.963972i	$0.414296\pi$
$199$	−9.90041	+	17.1480i	−0.701821	+	1.21559i	−0.967827	+	0.251618i	$0.919037\pi$
$200$	0.662242	−	0.382346i	0.0468276	−	0.0270359i
$201$			1.10868i			0.0782001i
$202$	2.65539	−	1.53309i	0.186833	−	0.107868i
$203$	21.6286	+	8.17120i	1.51803	+	0.573506i
$204$	−0.301861	−	0.522839i	−0.0211345	−	0.0366061i
$205$	8.46271	+	14.6578i	0.591061	+	1.02375i
$206$		−	11.2308i		−	0.782490i
$207$	−0.862484	−	1.49387i	−0.0599468	−	0.103831i
$208$	−0.662490	+	15.4169i	−0.0459354	+	1.06897i
$209$	−23.8314			−1.64845
$210$	−1.36271	−	8.31829i	−0.0940362	−	0.574017i
$211$	−3.63953	+	6.30384i	−0.250555	+	0.433974i	−0.963679	−	0.267064i	$-0.913947\pi$
$211$	−3.63953	+	6.30384i	−0.250555	+	0.433974i	0.713124	+	0.701038i	$0.247280\pi$
$212$	−1.23775			−0.0850088
$213$	−6.60723	+	3.81468i	−0.452720	+	0.261378i
$214$	19.2893	+	11.1367i	1.31859	+	0.761286i
$215$		−	9.77371i		−	0.666562i
$216$		−	2.71148i		−	0.184493i
$217$	−5.70956	−	6.97482i	−0.387590	−	0.473482i
$218$	9.84801	−	17.0573i	0.666992	−	1.15526i
$219$	6.82323	−	3.93939i	0.461071	−	0.266200i
$220$	−0.903742	−	1.56533i	−0.0609303	−	0.105534i
$221$	−12.7505	+	6.64867i	−0.857694	+	0.447238i
$222$	6.66450	−	11.5432i	0.447292	−	0.774732i
$223$	−8.73149	−	5.04113i	−0.584704	−	0.337579i	0.178297	−	0.983977i	$-0.442941\pi$
$223$	−8.73149	−	5.04113i	−0.584704	−	0.337579i	−0.763000	+	0.646398i	$0.776275\pi$
$224$	−0.799010	+	2.11492i	−0.0533861	+	0.141309i
$225$	−0.141010	−	0.244236i	−0.00940065	−	0.0162824i
$226$	5.32736	+	3.07575i	0.354370	+	0.204596i
$227$	−13.1129	−	7.57071i	−0.870331	−	0.502486i	−0.00287297	−	0.999996i	$-0.500914\pi$
$227$	−13.1129	−	7.57071i	−0.870331	−	0.502486i	−0.867458	+	0.497510i	$0.834248\pi$
$228$	0.568319	+	0.328119i	0.0376378	+	0.0217302i
$229$	−19.9091	−	11.4945i	−1.31563	−	0.759581i	−0.332610	−	0.943065i	$-0.607929\pi$
$229$	−19.9091	−	11.4945i	−1.31563	−	0.759581i	−0.983023	+	0.183484i	$0.941263\pi$
$230$	−2.74781	−	4.75935i	−0.181185	−	0.313822i
$231$	−14.3529	+	2.35132i	−0.944354	+	0.154705i
$232$	20.5205	+	11.8475i	1.34724	+	0.777829i
$233$	5.15182	−	8.92321i	0.337507	−	0.584579i	−0.646456	−	0.762951i	$-0.723750\pi$
$233$	5.15182	−	8.92321i	0.337507	−	0.584579i	0.983963	+	0.178372i	$0.0570831\pi$
$234$	5.28359	+	0.227044i	0.345399	+	0.0148423i
$235$	4.18324	+	7.24558i	0.272884	+	0.472649i
$236$	−0.193598	+	0.111774i	−0.0126021	+	0.00727584i
$237$	−7.56487	+	13.1027i	−0.491391	+	0.851114i
$238$	−15.2735	+	2.50213i	−0.990037	+	0.162189i
$239$			3.23395i			0.209187i	0.994515	+	0.104594i	$0.0333542\pi$
$239$			3.23395i			0.209187i	−0.994515	+	0.104594i	$0.966646\pi$
$240$		−	9.29619i		−	0.600067i
$241$	−4.54302	−	2.62291i	−0.292642	−	0.168957i	0.346491	−	0.938053i	$-0.387373\pi$
$241$	−4.54302	−	2.62291i	−0.292642	−	0.168957i	−0.639133	+	0.769097i	$0.720706\pi$
$242$	−24.4133	+	14.0950i	−1.56935	+	0.906064i
$243$	−1.00000			−0.0641500
$244$	−0.276301	+	0.478568i	−0.0176884	+	0.0306372i
$245$	−14.9050	−	3.00342i	−0.952249	−	0.191881i
$246$	−11.4293			−0.728705
$247$	8.38931	−	13.1886i	0.533799	−	0.839171i
$248$	−4.61883	−	8.00005i	−0.293296	−	0.508004i
$249$			11.9428i			0.756842i
$250$	−8.41407	−	14.5736i	−0.532153	−	0.921715i
$251$	3.37240	+	5.84117i	0.212864	+	0.368691i	0.952610	−	0.304195i	$-0.0983875\pi$
$251$	3.37240	+	5.84117i	0.212864	+	0.368691i	−0.739746	+	0.672887i	$0.765054\pi$
$252$	0.374655	+	0.141543i	0.0236010	+	0.00891637i
$253$	−8.21210	+	4.74126i	−0.516290	+	0.298080i
$254$			21.8137i			1.36871i
$255$	7.50226	−	4.33143i	0.469810	−	0.271245i
$256$	−1.80636	+	3.12870i	−0.112897	+	0.195544i
$257$	−0.519430	−	0.899679i	−0.0324011	−	0.0561204i	0.849370	−	0.527798i	$-0.176982\pi$
$257$	−0.519430	−	0.899679i	−0.0324011	−	0.0561204i	−0.881771	+	0.471677i	$0.843649\pi$
$258$	5.71571	+	3.29997i	0.355844	+	0.205447i
$259$	−15.2295	−	18.6045i	−0.946318	−	1.15603i
$260$	1.18441	+	0.0508960i	0.0734541	+	0.00315644i
$261$	4.36939	−	7.56801i	0.270459	−	0.468448i
$262$			23.6109i			1.45869i
$263$	11.3330			0.698824			0.349412	−	0.936969i	$-0.386381\pi$
$263$	11.3330			0.698824			0.349412	+	0.936969i	$0.386381\pi$
$264$	−14.9056			−0.917376
$265$		−	17.7605i		−	1.09102i
$266$	13.0180	−	10.6565i	0.798183	−	0.653390i
$267$	−3.17206	+	1.83139i	−0.194127	+	0.112079i
$268$	−0.145342	−	0.0839130i	−0.00887815	−	0.00512580i
$269$	−11.2083	+	19.4133i	−0.683380	+	1.18365i	0.290563	+	0.956856i	$0.406157\pi$
$269$	−11.2083	+	19.4133i	−0.683380	+	1.18365i	−0.973943	+	0.226793i	$0.927176\pi$
$270$	−3.18593			−0.193889
$271$	5.92452	−	3.42052i	0.359889	−	0.207782i	−0.309143	−	0.951015i	$-0.600042\pi$
$271$	5.92452	−	3.42052i	0.359889	−	0.207782i	0.669032	+	0.743234i	$0.266709\pi$
$272$	−17.0691			−1.03497
$273$	3.75138	−	8.77081i	0.227044	−	0.530834i
$274$	16.9622			1.02473
$275$	−1.34262	+	0.775160i	−0.0809629	+	0.0467439i
$276$	0.261117			0.0157174
$277$	4.21146	−	7.29447i	0.253042	−	0.438282i	−0.711320	−	0.702869i	$-0.751902\pi$
$277$	4.21146	−	7.29447i	0.253042	−	0.438282i	0.964362	+	0.264586i	$0.0852355\pi$
$278$	−5.70207	−	3.29209i	−0.341987	−	0.197447i
$279$	−2.95043	+	1.70343i	−0.176638	+	0.101982i
$280$	−14.5768	−	5.50706i	−0.871130	−	0.329110i
$281$		−	13.5699i		−	0.809510i	−0.914425	−	0.404755i	$-0.867357\pi$
$281$		−	13.5699i		−	0.809510i	0.914425	−	0.404755i	$-0.132643\pi$
$282$	−5.64966			−0.336432
$283$	6.76619			0.402208			0.201104	−	0.979570i	$-0.435547\pi$
$283$	6.76619			0.402208			0.201104	+	0.979570i	$0.435547\pi$
$284$		−	1.15489i		−	0.0685304i
$285$	−4.70821	+	8.15486i	−0.278890	+	0.483052i
$286$	1.24811	−	29.0450i	0.0738022	−	1.71747i
$287$	−7.28612	+	19.2858i	−0.430086	+	1.13841i
$288$	0.740028	+	0.427255i	0.0436066	+	0.0251763i
$289$	0.546883	+	0.947230i	0.0321696	+	0.0557194i
$290$	13.9206	−	24.1111i	0.817444	−	1.41586i
$291$	4.57836	−	2.64332i	0.268388	−	0.154954i
$292$			1.19265i			0.0697946i
$293$	2.62940	−	1.51808i	0.153611	−	0.0886873i	−0.421224	−	0.906957i	$-0.638399\pi$
$293$	2.62940	−	1.51808i	0.153611	−	0.0886873i	0.574835	+	0.818269i	$0.305066\pi$
$294$	6.78891	−	7.70247i	0.395937	−	0.449217i
$295$	−1.60385	−	2.77795i	−0.0933797	−	0.161738i
$296$	−12.3202	−	21.3391i	−0.716095	−	1.24031i
$297$			5.49721i			0.318981i
$298$	−1.47497	−	2.55472i	−0.0854427	−	0.147991i
$299$	0.267013	−	6.21373i	0.0154418	−	0.359349i
$300$	0.0426907			0.00246475
$301$	9.21211	−	7.54100i	0.530977	−	0.434656i
$302$	−8.71913	+	15.1020i	−0.501729	+	0.869021i
$303$	−2.09045			−0.120093
$304$	16.0681	−	9.27694i	0.921571	−	0.532069i
$305$	−6.86701	−	3.96467i	−0.393204	−	0.227016i
$306$			5.84981i			0.334411i
$307$		−	0.123565i		−	0.00705225i	−0.999994	−	0.00352613i	$-0.998878\pi$
$307$		−	0.123565i		−	0.00705225i	0.999994	−	0.00352613i	$-0.00112240\pi$
$308$	0.778092	−	2.05956i	0.0443359	−	0.117354i
$309$	−3.82846	+	6.63109i	−0.217794	+	0.377230i
$310$	−9.39987	+	5.42702i	−0.533877	+	0.308234i
$311$	6.90330	+	11.9569i	0.391450	+	0.678011i	0.992641	−	0.121094i	$-0.0386402\pi$
$311$	6.90330	+	11.9569i	0.391450	+	0.678011i	−0.601191	+	0.799105i	$0.705307\pi$
$312$	5.24718	−	8.24894i	0.297063	−	0.467004i
$313$	−8.94111	+	15.4864i	−0.505381	+	0.875346i	0.494599	+	0.869121i	$0.335315\pi$
$313$	−8.94111	+	15.4864i	−0.505381	+	0.875346i	−0.999981	+	0.00622482i	$0.998019\pi$
$314$	21.0616	+	12.1599i	1.18857	+	0.686223i
$315$	−2.03101	+	5.37595i	−0.114435	+	0.302901i
$316$	−1.14513	−	1.98343i	−0.0644187	−	0.111576i
$317$	−12.7409	−	7.35599i	−0.715603	−	0.413153i	0.0975293	−	0.995233i	$-0.468906\pi$
$317$	−12.7409	−	7.35599i	−0.715603	−	0.413153i	−0.813132	+	0.582079i	$0.802239\pi$
$318$	10.3864	+	5.99661i	0.582443	+	0.336273i
$319$	−41.6030	−	24.0195i	−2.32932	−	1.34483i
$320$	−13.7438	−	7.93499i	−0.768302	−	0.443579i
$321$	−7.59271	−	13.1510i	−0.423784	−	0.734015i
$322$	2.36578	−	6.26205i	0.131840	−	0.348970i
$323$	14.9735	+	8.64493i	0.833145	+	0.481017i
$324$	0.0756874	−	0.131094i	0.00420486	−	0.00728303i
$325$	0.0436547	−	1.01590i	0.00242153	−	0.0563519i
$326$	7.85650	+	13.6079i	0.435131	+	0.753670i
$327$	−11.6292	+	6.71414i	−0.643098	+	0.371293i
$328$	−10.5642	+	18.2978i	−0.583313	+	1.01033i
$329$	−3.60163	+	9.53326i	−0.198564	+	0.525586i
$330$			17.5137i			0.964099i
$331$			17.7857i			0.977591i	0.872398	+	0.488795i	$0.162564\pi$
$331$			17.7857i			0.977591i	−0.872398	+	0.488795i	$0.837436\pi$
$332$	−1.56563	−	0.903917i	−0.0859252	−	0.0496089i
$333$	−7.86991	+	4.54370i	−0.431269	+	0.248993i
$334$	−29.5771			−1.61838
$335$	1.20407	−	2.08552i	0.0657856	−	0.113944i
$336$	8.76203	−	7.17257i	0.478008	−	0.391296i
$337$	−27.7787			−1.51320			−0.756602	−	0.653876i	$-0.773142\pi$
$337$	−27.7787			−1.51320			−0.756602	+	0.653876i	$0.773142\pi$
$338$	15.6345	+	10.9154i	0.850404	+	0.593717i
$339$	−2.09697	−	3.63207i	−0.113892	−	0.197267i
$340$			1.31134i			0.0711174i
$341$	9.36413	+	16.2192i	0.507096	+	0.878317i
$342$	−3.17933	−	5.50676i	−0.171919	−	0.297772i
$343$	−8.66929	−	16.3659i	−0.468098	−	0.883677i
$344$	10.5662	−	6.10040i	0.569691	−	0.328912i
$345$			3.74679i			0.201720i
$346$	2.82075	−	1.62856i	0.151644	−	0.0875518i
$347$	−0.0124421	+	0.0215504i	−0.000667929	+	0.00115689i	−0.866359	−	0.499421i	$-0.833546\pi$
$347$	−0.0124421	+	0.0215504i	−0.000667929	+	0.00115689i	0.865691	+	0.500578i	$0.166879\pi$
$348$	0.661416	+	1.14561i	0.0354556	+	0.0614110i
$349$	27.8290	+	16.0671i	1.48965	+	0.860050i	0.999930	−	0.0118288i	$-0.00376532\pi$
$349$	27.8290	+	16.0671i	1.48965	+	0.860050i	0.489721	+	0.871879i	$0.337099\pi$
$350$	0.386787	−	1.02380i	0.0206746	−	0.0547243i
$351$	−3.04222	−	1.93517i	−0.162382	−	0.103292i
$352$	2.34871	−	4.06809i	0.125187	−	0.216830i
$353$		−	28.4593i		−	1.51474i	−0.652987	−	0.757369i	$-0.726485\pi$
$353$		−	28.4593i		−	1.51474i	0.652987	−	0.757369i	$-0.273515\pi$
$354$	2.16607			0.115126
$355$	16.5717			0.879534
$356$		−	0.554454i		−	0.0293860i
$357$	9.87099	+	3.72922i	0.522428	+	0.197371i
$358$	−6.25112	+	3.60908i	−0.330382	+	0.190746i
$359$	20.8607	+	12.0439i	1.10099	+	0.635654i	0.936480	−	0.350722i	$-0.114064\pi$
$359$	20.8607	+	12.0439i	1.10099	+	0.635654i	0.164506	+	0.986376i	$0.447397\pi$
$360$	−2.94479	+	5.10053i	−0.155204	+	0.268822i
$361$	0.206166			0.0108508
$362$	25.8983	−	14.9524i	1.36118	−	0.785879i
$363$	19.2193			1.00875
$364$	0.865873	+	1.15563i	0.0453841	+	0.0605712i
$365$	−17.1134			−0.895759
$366$	4.63711	−	2.67724i	0.242386	−	0.139941i
$367$	4.22700			0.220648			0.110324	−	0.993896i	$-0.464811\pi$
$367$	4.22700			0.220648			0.110324	+	0.993896i	$0.464811\pi$
$368$	3.69129	−	6.39350i	0.192422	−	0.333284i
$369$	6.74826	+	3.89611i	0.351301	+	0.202824i
$370$	−25.0730	+	14.4759i	−1.30348	+	0.752566i
$371$	16.7400	−	13.7033i	0.869098	−	0.711440i
$372$		−	0.515714i		−	0.0267385i
$373$	5.55455			0.287604			0.143802	−	0.989607i	$-0.454067\pi$
$373$	5.55455			0.287604			0.143802	+	0.989607i	$0.454067\pi$
$374$	32.1576			1.66283
$375$			11.4730i			0.592465i
$376$	−5.22205	+	9.04486i	−0.269307	+	0.466453i
$377$	27.9380	−	14.5681i	1.43888	−	0.750294i
$378$	−2.45813	−	3.00287i	−0.126433	−	0.154451i
$379$	−2.42943	−	1.40263i	−0.124791	−	0.0720482i	0.436305	−	0.899799i	$-0.356287\pi$
$379$	−2.42943	−	1.40263i	−0.124791	−	0.0720482i	−0.561096	+	0.827751i	$0.689620\pi$
$380$	−0.712705	−	1.23444i	−0.0365610	−	0.0633255i
$381$	7.43604	−	12.8796i	0.380960	−	0.659842i
$382$	−25.9595	+	14.9877i	−1.32820	+	0.766838i
$383$			0.968526i			0.0494894i	0.999694	+	0.0247447i	$0.00787728\pi$
$383$			0.968526i			0.0494894i	−0.999694	+	0.0247447i	$0.992123\pi$
$384$	10.7609	−	6.21280i	0.549139	−	0.317046i
$385$	29.5527	+	11.1649i	1.50615	+	0.569017i
$386$	12.7636	+	22.1072i	0.649651	+	1.12523i
$387$	−2.24984	−	3.89684i	−0.114366	−	0.198087i
$388$			0.800263i			0.0406272i
$389$	0.0909948	+	0.157608i	0.00461362	+	0.00799103i	0.868323	−	0.495999i	$-0.165198\pi$
$389$	0.0909948	+	0.157608i	0.00461362	+	0.00799103i	−0.863709	+	0.503990i	$0.831865\pi$
$390$	−9.69231	−	6.16531i	−0.490789	−	0.312193i
$391$	6.87962			0.347918
$392$	−6.05625	−	17.9882i	−0.305887	−	0.908543i
$393$	8.04868	−	13.9407i	0.406002	−	0.703217i
$394$	22.9891			1.15817
$395$	28.4603	−	16.4316i	1.43200	−	0.826763i
$396$	−0.720654	−	0.416070i	−0.0362142	−	0.0209083i
$397$			16.9505i			0.850721i	0.905024	+	0.425360i	$0.139853\pi$
$397$			16.9505i			0.850721i	−0.905024	+	0.425360i	$0.860147\pi$
$398$			29.0430i			1.45579i
$399$	−11.3189	+	1.85428i	−0.566656	+	0.0928303i
$400$	0.603498	−	1.04529i	0.0301749	−	0.0522645i
$401$	−3.28448	+	1.89630i	−0.164019	+	0.0946966i	−0.579763	−	0.814785i	$-0.696855\pi$
$401$	−3.28448	+	1.89630i	−0.164019	+	0.0946966i	0.415743	+	0.909482i	$0.363521\pi$
$402$	0.813080	+	1.40830i	0.0405528	+	0.0702394i
$403$	−12.2723	−	0.527360i	−0.611327	−	0.0262697i
$404$	0.158221	−	0.274047i	0.00787179	−	0.0136343i
$405$	1.88109	+	1.08605i	0.0934719	+	0.0539660i
$406$	33.4663	−	5.48249i	1.66090	−	0.272091i
$407$	24.9777	+	43.2626i	1.23810	+	2.14445i
$408$	9.36529	+	5.40705i	0.463651	+	0.267689i
$409$	−27.2737	−	15.7465i	−1.34860	−	0.778614i	−0.360548	−	0.932741i	$-0.617410\pi$
$409$	−27.2737	−	15.7465i	−1.34860	−	0.778614i	−0.988051	+	0.154127i	$0.950744\pi$
$410$	21.4995	+	12.4127i	1.06178	+	0.613021i
$411$	−10.0151	−	5.78222i	−0.494009	−	0.285216i
$412$	−0.579533	−	1.00378i	−0.0285515	−	0.0494527i
$413$	1.38086	−	3.65504i	0.0679477	−	0.179853i
$414$	−2.19114	−	1.26505i	−0.107689	−	0.0621740i
$415$	12.9704	−	22.4654i	0.636691	−	1.10278i
$416$	1.42452	+	2.73188i	0.0698428	+	0.133942i
$417$	2.24447	+	3.88754i	0.109912	+	0.190374i
$418$	−30.2718	+	17.4775i	−1.48064	+	0.854850i
$419$	−6.42663	+	11.1312i	−0.313961	+	0.543797i	−0.979216	−	0.202819i	$-0.934990\pi$
$419$	−6.42663	+	11.1312i	−0.313961	+	0.543797i	0.665255	+	0.746616i	$0.268323\pi$
$420$	−0.551035	−	0.673147i	−0.0268878	−	0.0328462i
$421$		−	16.5709i		−	0.807618i	−0.914843	−	0.403809i	$-0.867686\pi$
$421$		−	16.5709i		−	0.807618i	0.914843	−	0.403809i	$-0.132314\pi$
$422$			10.6766i			0.519729i
$423$	3.33576	+	1.92590i	0.162190	+	0.0936406i
$424$	19.2006	−	11.0855i	0.932465	−	0.538359i
$425$	1.12477			0.0545592
$426$	−5.59521	+	9.69119i	−0.271089	+	0.469540i
$427$	−1.56145	−	9.53141i	−0.0755638	−	0.461257i
$428$	2.29869			0.111111
$429$	−10.6380	+	16.7237i	−0.513609	+	0.807430i
$430$	−7.16783	−	12.4150i	−0.345663	−	0.598706i
$431$			2.30611i			0.111081i	0.998456	+	0.0555407i	$0.0176883\pi$
$431$			2.30611i			0.111081i	−0.998456	+	0.0555407i	$0.982312\pi$
$432$	−2.13992	−	3.70645i	−0.102957	−	0.178326i
$433$	18.5194	+	32.0765i	0.889984	+	1.54150i	0.839892	+	0.542753i	$0.182618\pi$
$433$	18.5194	+	32.0765i	0.889984	+	1.54150i	0.0500916	+	0.998745i	$0.484049\pi$
$434$	−12.3677	−	4.67249i	−0.593671	−	0.224286i
$435$	−16.4384	+	9.49072i	−0.788161	+	0.455045i
$436$		−	2.03271i		−	0.0973489i
$437$	−6.47619	+	3.73903i	−0.309798	+	0.178862i
$438$	5.77813	−	10.0080i	0.276090	−	0.478202i
$439$	8.57862	+	14.8586i	0.409435	+	0.709163i	0.994827	−	0.101588i	$-0.0323924\pi$
$439$	8.57862	+	14.8586i	0.409435	+	0.709163i	−0.585391	+	0.810751i	$0.699059\pi$
$440$	28.0387	+	16.1882i	1.33669	+	0.771740i
$441$	−6.63410	+	2.23356i	−0.315909	+	0.106360i
$442$	−11.3204	+	17.7964i	−0.538455	+	0.846490i
$443$	12.4916	−	21.6361i	0.593495	−	1.02796i	−0.400263	−	0.916400i	$-0.631081\pi$
$443$	12.4916	−	21.6361i	0.593495	−	1.02796i	0.993757	−	0.111562i	$-0.0355855\pi$
$444$		−	1.37560i		−	0.0652832i
$445$	7.95590			0.377146
$446$	−14.7882			−0.700242
$447$			2.01120i			0.0951264i
$448$	−3.12512	−	19.0764i	−0.147648	−	0.901275i
$449$	17.6481	−	10.1891i	0.832866	−	0.480855i	−0.0219673	−	0.999759i	$-0.506993\pi$
$449$	17.6481	−	10.1891i	0.832866	−	0.480855i	0.854833	+	0.518904i	$0.173660\pi$
$450$	−0.358235	−	0.206827i	−0.0168874	−	0.00974992i
$451$	21.4178	−	37.0966i	1.00852	−	1.74681i
$452$	0.634858			0.0298612
$453$	10.2962	−	5.94449i	0.483756	−	0.279297i
$454$	−22.2088			−1.04231
$455$	−16.5822	+	12.4245i	−0.777384	+	0.582469i
$456$	−11.7548			−0.550468
$457$	17.9309	−	10.3524i	0.838772	−	0.484265i	−0.0180744	−	0.999837i	$-0.505754\pi$
$457$	17.9309	−	10.3524i	0.838772	−	0.484265i	0.856847	+	0.515571i	$0.172420\pi$
$458$	−33.7194			−1.57560
$459$	1.99413	−	3.45394i	0.0930781	−	0.161216i
$460$	−0.491183	−	0.283585i	−0.0229015	−	0.0132222i
$461$	−5.91037	+	3.41236i	−0.275274	+	0.158929i	−0.631282	−	0.775554i	$-0.717471\pi$
$461$	−5.91037	+	3.41236i	−0.275274	+	0.158929i	0.356008	+	0.934483i	$0.384138\pi$
$462$	−16.5074	+	13.5129i	−0.767993	+	0.628676i
$463$		−	25.3595i		−	1.17856i	−0.807930	−	0.589278i	$-0.799412\pi$
$463$		−	25.3595i		−	1.17856i	0.807930	−	0.589278i	$-0.200588\pi$
$464$	37.4006			1.73628
$465$	7.40003			0.343168
$466$		−	15.1129i		−	0.700092i
$467$	−8.81166	+	15.2622i	−0.407755	+	0.706252i	−0.994638	−	0.103419i	$-0.967022\pi$
$467$	−8.81166	+	15.2622i	−0.407755	+	0.706252i	0.586883	+	0.809672i	$0.300355\pi$
$468$	0.483948	−	0.252351i	0.0223705	−	0.0116649i
$469$	2.89470	−	0.474213i	0.133665	−	0.0218971i
$470$	10.6275	+	6.13579i	0.490210	+	0.283023i
$471$	−8.29034	−	14.3593i	−0.381999	−	0.661641i
$472$	2.00213	−	3.46779i	0.0921555	−	0.159618i
$473$	−21.4217	+	12.3678i	−0.984972	+	0.568674i
$474$			22.1916i			1.01930i
$475$	−1.05881	+	0.611303i	−0.0485815	+	0.0280485i
$476$	−1.23599	+	1.01178i	−0.0566515	+	0.0463747i
$477$	−4.08835	−	7.08123i	−0.187193	−	0.324227i
$478$	2.37171	+	4.10792i	0.108480	+	0.187892i
$479$			20.8671i			0.953440i	0.879055	+	0.476720i	$0.158174\pi$
$479$			20.8671i			0.953440i	−0.879055	+	0.476720i	$0.841826\pi$
$480$	−0.928038	−	1.60741i	−0.0423589	−	0.0733678i
$481$	−32.7349	−	1.40667i	−1.49258	−	0.0641385i
$482$	−7.69435			−0.350468
$483$	−3.53150	+	2.89087i	−0.160689	+	0.131539i
$484$	−1.45466	+	2.51955i	−0.0661210	+	0.114525i
$485$	−11.4830			−0.521418
$486$	−1.27025	+	0.733378i	−0.0576196	+	0.0332667i
$487$	−2.34354	−	1.35304i	−0.106196	−	0.0613122i	0.445961	−	0.895052i	$-0.352862\pi$
$487$	−2.34354	−	1.35304i	−0.106196	−	0.0613122i	−0.552157	+	0.833740i	$0.686195\pi$
$488$		−	9.89842i		−	0.448080i
$489$		−	10.7128i		−	0.484448i
$490$	−21.1358	+	7.11595i	−0.954816	+	0.321466i
$491$	−2.79084	+	4.83387i	−0.125949	+	0.218150i	−0.922103	−	0.386944i	$-0.873531\pi$
$491$	−2.79084	+	4.83387i	−0.125949	+	0.218150i	0.796155	+	0.605093i	$0.206864\pi$
$492$	−1.02152	+	0.589774i	−0.0460536	+	0.0265890i
$493$	17.4263	+	30.1832i	0.784840	+	1.35938i
$494$	0.984278	−	22.9053i	0.0442848	−	1.03056i
$495$	5.97022	−	10.3407i	0.268342	−	0.464781i
$496$	−12.6274	−	7.29041i	−0.566986	−	0.327349i
$497$	12.7860	+	15.6195i	0.573532	+	0.700629i
$498$	8.75857	+	15.1703i	0.392481	+	0.679797i
$499$	−9.96935	−	5.75580i	−0.446289	−	0.257665i	0.259973	−	0.965616i	$-0.416286\pi$
$499$	−9.96935	−	5.75580i	−0.446289	−	0.257665i	−0.706262	+	0.707951i	$0.749620\pi$
$500$	−1.50405	−	0.868364i	−0.0672632	−	0.0388344i
$501$	17.4633	+	10.0825i	0.780205	+	0.450452i
$502$	8.56757	+	4.94649i	0.382390	+	0.220773i
$503$	−16.6667	−	28.8676i	−0.743133	−	1.28714i	−0.951062	−	0.309001i	$-0.900005\pi$
$503$	−16.6667	−	28.8676i	−0.743133	−	1.28714i	0.207929	−	0.978144i	$-0.433328\pi$
$504$	−7.07954	+	1.15978i	−0.315348	+	0.0516607i
$505$	3.93232	+	2.27033i	0.174986	+	0.101028i
$506$	−6.95427	+	12.0451i	−0.309155	+	0.535472i
$507$	−5.51025	−	11.7744i	−0.244719	−	0.522921i
$508$	1.12563	+	1.94965i	0.0499417	+	0.0865016i
$509$	−3.86527	+	2.23161i	−0.171325	+	0.0989145i	−0.583210	−	0.812321i	$-0.698204\pi$
$509$	−3.86527	+	2.23161i	−0.171325	+	0.0989145i	0.411885	+	0.911236i	$0.364870\pi$
$510$	6.35316	−	11.0040i	0.281323	−	0.487265i
$511$	−13.2040	−	16.1301i	−0.584113	−	0.713554i
$512$		−	19.5522i		−	0.864095i
$513$			4.33519i			0.191403i
$514$	−1.31961	−	0.761877i	−0.0582055	−	0.0336050i
$515$	14.4033	−	8.31577i	0.634687	−	0.366437i
$516$	0.681138			0.0299854
$517$	10.5871	−	18.3374i	0.465620	−	0.806477i
$518$	−32.9894	−	12.4633i	−1.44947	−	0.547605i
$519$	−2.22062			−0.0974746
$520$	−18.8291	+	9.81829i	−0.825711	+	0.430560i
$521$	−12.9353	−	22.4045i	−0.566704	−	0.981560i	−0.996889	−	0.0788194i	$-0.974885\pi$
$521$	−12.9353	−	22.4045i	−0.566704	−	0.981560i	0.430185	−	0.902741i	$-0.358448\pi$
$522$		−	12.8177i		−	0.561014i
$523$	−4.90970	−	8.50385i	−0.214686	−	0.371848i	0.738489	−	0.674265i	$-0.235540\pi$
$523$	−4.90970	−	8.50385i	−0.214686	−	0.371848i	−0.953175	+	0.302418i	$0.902206\pi$
$524$	1.21837	+	2.11028i	0.0532247	+	0.0921879i
$525$	−0.577374	+	0.472636i	−0.0251986	+	0.0206275i
$526$	14.3957	−	8.31139i	0.627684	−	0.362394i
$527$		−	13.5875i		−	0.591880i
$528$	−20.3751	+	11.7636i	−0.886713	+	0.511944i
$529$	10.0122	−	17.3417i	0.435315	−	0.753988i
$530$	−13.0252	−	22.5603i	−0.565778	−	0.979956i
$531$	−1.27893	−	0.738389i	−0.0555007	−	0.0320434i
$532$	0.613615	−	1.62420i	0.0266036	−	0.0704179i
$533$	12.9901	+	24.9119i	0.562663	+	1.07905i
$534$	−2.68621	+	4.65265i	−0.116244	+	0.201340i
$535$			32.9841i			1.42603i
$536$	3.00616			0.129846
$537$	4.92118			0.212364
$538$			32.8796i			1.41754i
$539$	12.2783	+	36.4690i	0.528865	+	1.57083i
$540$	−0.284749	+	0.164400i	−0.0122537	+	0.00707465i
$541$	−22.8738	−	13.2062i	−0.983422	−	0.567779i	−0.0801204	−	0.996785i	$-0.525530\pi$
$541$	−22.8738	−	13.2062i	−0.983422	−	0.567779i	−0.903302	+	0.429006i	$0.858864\pi$
$542$	5.01707	−	8.68982i	0.215502	−	0.373260i
$543$	−20.3883			−0.874948
$544$	−2.95143	+	1.70401i	−0.126541	+	0.0730587i
$545$	29.1675			1.24940
$546$	−1.66714	−	13.8923i	−0.0713472	−	0.594535i
$547$	9.87823			0.422363			0.211181	−	0.977447i	$-0.432269\pi$
$547$	9.87823			0.422363			0.211181	+	0.977447i	$0.432269\pi$
$548$	1.51604	−	0.875283i	0.0647618	−	0.0373903i
$549$	−3.65055			−0.155802
$550$	−1.13697	+	1.96929i	−0.0484806	+	0.0839709i
$551$	−32.8087	−	18.9421i	−1.39770	−	0.806962i
$552$	−4.05059	+	2.33861i	−0.172405	+	0.0995379i
$553$	37.4463	+	14.1471i	1.59238	+	0.601594i
$554$		−	12.3544i		−	0.524888i
$555$	19.7387			0.837859
$556$	−0.679513			−0.0288178
$557$		−	21.2907i		−	0.902118i	−0.892494	−	0.451059i	$-0.851046\pi$
$557$		−	21.2907i		−	0.902118i	0.892494	−	0.451059i	$-0.148954\pi$
$558$	−2.49852	+	4.32757i	−0.105771	+	0.183201i
$559$	0.696520	−	16.2089i	0.0294596	−	0.685562i
$560$	−24.2719	+	3.97625i	−1.02567	+	0.168027i
$561$	−18.9870	−	10.9622i	−0.801633	−	0.462823i
$562$	−9.95184	−	17.2371i	−0.419793	−	0.727103i
$563$	−13.0548	+	22.6116i	−0.550196	+	0.952967i	0.448064	+	0.894001i	$0.352114\pi$
$563$	−13.0548	+	22.6116i	−0.550196	+	0.952967i	−0.998260	+	0.0589657i	$0.981220\pi$
$564$	−0.504951	+	0.291533i	−0.0212623	+	0.0122758i
$565$			9.10964i			0.383245i
$566$	8.59474	−	4.96218i	0.361264	−	0.208576i
$567$	0.427729	+	2.61095i	0.0179629	+	0.109649i
$568$	10.3435	+	17.9154i	0.434002	+	0.751713i
$569$	1.69004	+	2.92724i	0.0708503	+	0.122716i	0.899274	−	0.437385i	$-0.144095\pi$
$569$	1.69004	+	2.92724i	0.0708503	+	0.122716i	−0.828424	+	0.560102i	$0.810762\pi$
$570$			13.8116i			0.578504i
$571$	19.4728	+	33.7279i	0.814911	+	1.41147i	0.909392	+	0.415940i	$0.136547\pi$
$571$	19.4728	+	33.7279i	0.814911	+	1.41147i	−0.0944813	+	0.995527i	$0.530119\pi$
$572$	−1.38723	−	2.66036i	−0.0580028	−	0.111235i
$573$	20.4365			0.853748
$574$	4.88864	+	29.8413i	0.204048	+	1.24555i
$575$	−0.243237	+	0.421299i	−0.0101437	+	0.0175694i
$576$	−7.30631			−0.304430
$577$	26.9303	−	15.5482i	1.12112	−	0.647281i	0.179436	−	0.983770i	$-0.442573\pi$
$577$	26.9303	−	15.5482i	1.12112	−	0.647281i	0.941687	+	0.336489i	$0.109239\pi$
$578$	1.38936	+	0.802145i	0.0577896	+	0.0333648i
$579$		−	17.4039i		−	0.723280i
$580$		−	2.87331i		−	0.119308i
$581$	31.1819	−	5.10827i	1.29364	−	0.211927i
$582$	3.87710	−	6.71534i	0.160711	−	0.278360i
$583$	−38.9270	+	22.4745i	−1.61219	+	0.930799i
$584$	−10.6816	−	18.5011i	−0.442008	−	0.765580i
$585$	3.62100	+	6.94421i	0.149710	+	0.287108i
$586$	2.22666	−	3.85668i	0.0919824	−	0.159318i
$587$	10.3654	+	5.98444i	0.427824	+	0.247004i	0.698419	−	0.715689i	$-0.253887\pi$
$587$	10.3654	+	5.98444i	0.427824	+	0.247004i	−0.270595	+	0.962693i	$0.587220\pi$
$588$	0.209311	−	1.03875i	0.00863184	−	0.0428371i
$589$	7.38470	+	12.7907i	0.304281	+	0.527031i
$590$	−4.07457	−	2.35246i	−0.167748	−	0.0968491i
$591$	−13.5736	−	7.83670i	−0.558342	−	0.322359i
$592$	−33.6819	−	19.4463i	−1.38432	−	0.799237i
$593$	−33.8407	−	19.5379i	−1.38967	−	0.802327i	−0.396393	−	0.918081i	$-0.629738\pi$
$593$	−33.8407	−	19.5379i	−1.38967	−	0.802327i	−0.993278	+	0.115754i	$0.963072\pi$
$594$	4.03154	+	6.98282i	0.165416	+	0.286509i
$595$	−14.5181	−	17.7353i	−0.595183	−	0.727078i
$596$	−0.263657	−	0.152222i	−0.0107998	−	0.00623528i
$597$	9.90041	−	17.1480i	0.405197	−	0.701821i
$598$	−4.21784	−	8.08880i	−0.172480	−	0.330776i
$599$	−0.912960	−	1.58129i	−0.0373025	−	0.0646099i	0.846771	−	0.531957i	$-0.178543\pi$
$599$	−0.912960	−	1.58129i	−0.0373025	−	0.0646099i	−0.884074	+	0.467347i	$0.845210\pi$
$600$	−0.662242	+	0.382346i	−0.0270359	+	0.0156092i
$601$	−14.6227	+	25.3273i	−0.596473	+	1.03312i	0.396864	+	0.917878i	$0.370099\pi$
$601$	−14.6227	+	25.3273i	−0.596473	+	1.03312i	−0.993337	+	0.115245i	$0.963235\pi$
$602$	6.17126	−	16.3349i	0.251522	−	0.665761i
$603$		−	1.10868i		−	0.0451488i
$604$			1.79969i			0.0732285i
$605$	−36.1532	−	20.8731i	−1.46984	−	0.848611i
$606$	−2.65539	+	1.53309i	−0.107868	+	0.0622776i
$607$	−7.73129			−0.313803			−0.156902	−	0.987614i	$-0.550151\pi$
$607$	−7.73129			−0.313803			−0.156902	+	0.987614i	$0.550151\pi$
$608$	1.85223	−	3.20816i	0.0751179	−	0.130108i
$609$	−21.6286	−	8.17120i	−0.876435	−	0.331114i
$610$	−11.6304			−0.470902
$611$	6.42119	+	12.3143i	0.259773	+	0.498183i
$612$	0.301861	+	0.522839i	0.0122020	+	0.0211345i
$613$		−	8.51853i		−	0.344060i	−0.985092	−	0.172030i	$-0.944967\pi$
$613$		−	8.51853i		−	0.344060i	0.985092	−	0.172030i	$-0.0550326\pi$
$614$	−0.0906202	−	0.156959i	−0.00365713	−	0.00633434i
$615$	−8.46271	−	14.6578i	−0.341249	−	0.591061i
$616$	6.37555	+	38.9177i	0.256878	+	1.56804i
$617$	17.9858	−	10.3841i	0.724083	−	0.418050i	−0.0921706	−	0.995743i	$-0.529381\pi$
$617$	17.9858	−	10.3841i	0.724083	−	0.418050i	0.816254	+	0.577694i	$0.196047\pi$
$618$			11.2308i			0.451771i
$619$	14.5519	−	8.40157i	0.584892	−	0.337688i	−0.178183	−	0.983997i	$-0.557022\pi$
$619$	14.5519	−	8.40157i	0.584892	−	0.337688i	0.763075	+	0.646310i	$0.223689\pi$
$620$	−0.560089	+	0.970103i	−0.0224937	+	0.0389603i
$621$	0.862484	+	1.49387i	0.0346103	+	0.0599468i
$622$	17.5378	+	10.1255i	0.703202	+	0.405994i
$623$	6.13845	+	7.49876i	0.245932	+	0.300431i
$624$	0.662490	−	15.4169i	0.0265208	−	0.617171i
$625$	11.7552	−	20.3606i	0.470207	−	0.814423i
$626$			26.2289i			1.04832i
$627$	23.8314			0.951736
$628$	2.50990			0.100156
$629$		−	36.2429i		−	1.44510i
$630$	1.36271	+	8.31829i	0.0542918	+	0.331409i
$631$	34.8915	−	20.1446i	1.38901	−	0.801945i	0.395806	−	0.918334i	$-0.370465\pi$
$631$	34.8915	−	20.1446i	1.38901	−	0.801945i	0.993204	+	0.116389i	$0.0371320\pi$
$632$	35.5279	+	20.5120i	1.41322	+	0.815924i
$633$	3.63953	−	6.30384i	0.144658	−	0.250555i
$634$	−21.5789			−0.857007
$635$	−27.9757	+	16.1518i	−1.11018	+	0.640963i
$636$	1.23775			0.0490798
$637$	−24.5047	−	6.04312i	−0.970912	−	0.239437i
$638$	−70.4614			−2.78960
$639$	6.60723	−	3.81468i	0.261378	−	0.150907i
$640$	−26.9895			−1.06686
$641$	2.41581	−	4.18430i	0.0954187	−	0.165270i	−0.814365	−	0.580354i	$-0.802914\pi$
$641$	2.41581	−	4.18430i	0.0954187	−	0.165270i	0.909783	+	0.415084i	$0.136248\pi$
$642$	−19.2893	−	11.1367i	−0.761286	−	0.439529i
$643$	−3.33166	+	1.92353i	−0.131388	+	0.0758567i	−0.564253	−	0.825602i	$-0.690836\pi$
$643$	−3.33166	+	1.92353i	−0.131388	+	0.0758567i	0.432866	+	0.901459i	$0.357502\pi$
$644$	−0.111687	−	0.681762i	−0.00440109	−	0.0268652i
$645$			9.77371i			0.384839i
$646$	25.3600			0.997776
$647$	−8.53903			−0.335704			−0.167852	−	0.985812i	$-0.553683\pi$
$647$	−8.53903			−0.335704			−0.167852	+	0.985812i	$0.553683\pi$
$648$			2.71148i			0.106517i
$649$	−4.05908	+	7.03054i	−0.159333	+	0.275973i
$650$	−0.689585	−	1.32246i	−0.0270478	−	0.0518711i
$651$	5.70956	+	6.97482i	0.223775	+	0.273365i
$652$	1.40438	+	0.810821i	0.0549999	+	0.0317542i
$653$	−13.1999	−	22.8628i	−0.516550	−	0.894691i	−0.999815	−	0.0192170i	$-0.993883\pi$
$653$	−13.1999	−	22.8628i	−0.516550	−	0.894691i	0.483265	−	0.875474i	$-0.339451\pi$
$654$	−9.84801	+	17.0573i	−0.385088	+	0.666992i
$655$	−30.2805	+	17.4825i	−1.18316	+	0.683097i
$656$			33.3494i			1.30208i
$657$	−6.82323	+	3.93939i	−0.266200	+	0.153690i
$658$	2.41652	+	14.7510i	0.0942059	+	0.575053i
$659$	13.0931	+	22.6779i	0.510035	+	0.883407i	0.999932	+	0.0116265i	$0.00370091\pi$
$659$	13.0931	+	22.6779i	0.510035	+	0.883407i	−0.489897	+	0.871780i	$0.662966\pi$
$660$	0.903742	+	1.56533i	0.0351781	+	0.0609303i
$661$		−	34.0147i		−	1.32302i	−0.749937	−	0.661510i	$-0.769916\pi$
$661$		−	34.0147i		−	1.32302i	0.749937	−	0.661510i	$-0.230084\pi$
$662$	13.0437	+	22.5923i	0.506956	+	0.878073i
$663$	12.7505	−	6.64867i	0.495190	−	0.258213i
$664$	32.3826			1.25669
$665$	23.3057	+	8.80482i	0.903758	+	0.341436i
$666$	−6.66450	+	11.5432i	−0.258244	+	0.447292i
$667$	−15.0741			−0.583672
$668$	−2.64351	+	1.52623i	−0.102281	+	0.0590517i
$669$	8.73149	+	5.04113i	0.337579	+	0.194901i
$670$		−	3.53217i		−	0.136460i
$671$			20.0679i			0.774712i
$672$	0.799010	−	2.11492i	0.0308225	−	0.0815849i
$673$	−11.8498	+	20.5244i	−0.456775	+	0.791158i	−0.998788	−	0.0492124i	$-0.984329\pi$
$673$	−11.8498	+	20.5244i	−0.456775	+	0.791158i	0.542013	+	0.840370i	$0.317662\pi$
$674$	−35.2859	+	20.3723i	−1.35916	+	0.784712i
$675$	0.141010	+	0.244236i	0.00542747	+	0.00940065i
$676$	1.96062	+	0.168813i	0.0754084	+	0.00649282i
$677$	7.66166	−	13.2704i	0.294461	−	0.510022i	−0.680398	−	0.732843i	$-0.738193\pi$
$677$	7.66166	−	13.2704i	0.294461	−	0.510022i	0.974859	+	0.222821i	$0.0715264\pi$
$678$	−5.32736	−	3.07575i	−0.204596	−	0.118123i
$679$	−8.85985	−	10.8232i	−0.340010	−	0.415357i
$680$	−11.7446	−	20.3423i	−0.450385	−	0.780090i
$681$	13.1129	+	7.57071i	0.502486	+	0.290110i
$682$	23.7896	+	13.7349i	0.910949	+	0.525937i
$683$	−4.85569	−	2.80344i	−0.185798	−	0.107271i	0.404216	−	0.914664i	$-0.367544\pi$
$683$	−4.85569	−	2.80344i	−0.185798	−	0.107271i	−0.590014	+	0.807393i	$0.700878\pi$
$684$	−0.568319	−	0.328119i	−0.0217302	−	0.0125459i
$685$	12.5595	+	21.7537i	0.479875	+	0.831167i
$686$	−23.0146	−	14.4309i	−0.878700	−	0.550975i
$687$	19.9091	+	11.4945i	0.759581	+	0.438544i
$688$	9.62894	−	16.6778i	0.367100	−	0.635836i
$689$	1.26570	−	29.4543i	0.0482192	−	1.12212i
$690$	2.74781	+	4.75935i	0.104607	+	0.181185i
$691$	6.47071	−	3.73587i	0.246158	−	0.142119i	−0.371846	−	0.928294i	$-0.621275\pi$
$691$	6.47071	−	3.73587i	0.246158	−	0.142119i	0.618004	+	0.786175i	$0.287942\pi$
$692$	0.168073	−	0.291112i	0.00638919	−	0.0110664i
$693$	14.3529	−	2.35132i	0.545223	−	0.0893191i
$694$			0.0364992i			0.00138549i
$695$		−	9.75039i		−	0.369853i
$696$	−20.5205	−	11.8475i	−0.777829	−	0.449080i
$697$	−26.9138	+	15.5387i	−1.01943	+	0.588571i
$698$	47.1330			1.78401
$699$	−5.15182	+	8.92321i	−0.194860	+	0.337507i
$700$	−0.0182600	−	0.111463i	−0.000690164	−	0.00421291i
$701$	−49.0133			−1.85120			−0.925602	−	0.378497i	$-0.876441\pi$
$701$	−49.0133			−1.85120			−0.925602	+	0.378497i	$0.876441\pi$
$702$	−5.28359	−	0.227044i	−0.199416	−	0.00856922i
$703$	19.6978	+	34.1175i	0.742916	+	1.28677i
$704$			40.1643i			1.51375i
$705$	−4.18324	−	7.24558i	−0.157550	−	0.272884i
$706$	−20.8715	−	36.1504i	−0.785508	−	1.36054i
$707$	0.894147	+	5.45806i	0.0336279	+	0.205272i
$708$	0.193598	−	0.111774i	0.00727584	−	0.00420071i
$709$			24.4325i			0.917581i	0.888545	+	0.458790i	$0.151717\pi$
$709$			24.4325i			0.917581i	−0.888545	+	0.458790i	$0.848283\pi$
$710$	21.0502	−	12.1533i	0.789998	−	0.456106i
$711$	7.56487	−	13.1027i	0.283705	−	0.491391i
$712$	4.96579	+	8.60100i	0.186101	+	0.322336i
$713$	5.08940	+	2.93837i	0.190600	+	0.110043i
$714$	15.2735	−	2.50213i	0.571598	−	0.0936400i
$715$	38.1738	−	19.9054i	1.42762	−	0.744421i
$716$	−0.372471	+	0.645139i	−0.0139199	+	0.0241100i
$717$		−	3.23395i		−	0.120774i
$718$	35.3310			1.31854
$719$	15.3040			0.570743			0.285372	−	0.958417i	$-0.407883\pi$
$719$	15.3040			0.570743			0.285372	+	0.958417i	$0.407883\pi$
$720$			9.29619i			0.346449i
$721$	18.9510	+	7.15961i	0.705771	+	0.266638i
$722$	0.261882	−	0.151198i	0.00974624	−	0.00562699i
$723$	4.54302	+	2.62291i	0.168957	+	0.0975472i
$724$	1.54314	−	2.67280i	0.0573504	−	0.0993338i
$725$	−2.46451			−0.0915295
$726$	24.4133	−	14.0950i	0.906064	−	0.523116i
$727$	−39.2429			−1.45544			−0.727719	−	0.685875i	$-0.759420\pi$
$727$	−39.2429			−1.45544			−0.727719	+	0.685875i	$0.759420\pi$
$728$	−23.7819	−	10.1718i	−0.881416	−	0.376992i
$729$	1.00000			0.0370370
$730$	−21.7383	+	12.5506i	−0.804572	+	0.464520i
$731$	17.9459			0.663753
$732$	0.276301	−	0.478568i	0.0102124	−	0.0176884i
$733$	38.2863	+	22.1046i	1.41414	+	0.816453i	0.995775	−	0.0918266i	$-0.0292706\pi$
$733$	38.2863	+	22.1046i	1.41414	+	0.816453i	0.418363	+	0.908280i	$0.362604\pi$
$734$	5.36934	−	3.09999i	0.198186	−	0.114423i
$735$	14.9050	+	3.00342i	0.549781	+	0.110783i
$736$		−	1.47400i		−	0.0543325i
$737$	−6.09464			−0.224499
$738$	11.4293			0.420718
$739$		−	35.7288i		−	1.31430i	−0.753758	−	0.657152i	$-0.771761\pi$
$739$		−	35.7288i		−	1.31430i	0.753758	−	0.657152i	$-0.228239\pi$
$740$	−1.49397	+	2.58763i	−0.0549194	+	0.0951231i
$741$	−8.38931	+	13.1886i	−0.308189	+	0.484495i
$742$	11.2143	−	29.6834i	0.411689	−	1.08971i
$743$	−42.7329	−	24.6719i	−1.56772	−	0.905123i	−0.996434	−	0.0843718i	$-0.973112\pi$
$743$	−42.7329	−	24.6719i	−1.56772	−	0.905123i	−0.571285	−	0.820752i	$-0.693555\pi$
$744$	4.61883	+	8.00005i	0.169335	+	0.293296i
$745$	2.18425	−	3.78324i	0.0800249	−	0.138607i
$746$	7.05566	−	4.07359i	0.258326	−	0.149145i
$747$		−	11.9428i		−	0.436963i
$748$	2.87416	−	1.65940i	0.105090	−	0.0606735i
$749$	−31.0888	+	25.4492i	−1.13596	+	0.929894i
$750$	8.41407	+	14.5736i	0.307238	+	0.532153i
$751$	19.3982	+	33.5987i	0.707851	+	1.22603i	0.965653	+	0.259836i	$0.0836685\pi$
$751$	19.3982	+	33.5987i	0.707851	+	1.22603i	−0.257802	+	0.966198i	$0.582998\pi$
$752$			16.4851i			0.601150i
$753$	−3.37240	−	5.84117i	−0.122897	−	0.212864i
$754$	24.8044	−	38.9942i	0.903321	−	1.42009i
$755$	−25.8240			−0.939830
$756$	−0.374655	−	0.141543i	−0.0136261	−	0.00514787i
$757$	8.12196	−	14.0677i	0.295198	−	0.511298i	−0.679833	−	0.733367i	$-0.737948\pi$
$757$	8.12196	−	14.0677i	0.295198	−	0.511298i	0.975031	+	0.222069i	$0.0712811\pi$
$758$	−4.11463			−0.149450
$759$	8.21210	−	4.74126i	0.298080	−	0.172097i
$760$	22.1118	+	12.7662i	0.802078	+	0.463080i
$761$		−	33.6642i		−	1.22033i	−0.792276	−	0.610163i	$-0.791104\pi$
$761$		−	33.6642i		−	1.22033i	0.792276	−	0.610163i	$-0.208896\pi$
$762$		−	21.8137i		−	0.790228i
$763$	22.5044	+	27.4915i	0.814715	+	0.995259i
$764$	−1.54679	+	2.67912i	−0.0559609	+	0.0969270i
$765$	−7.50226	+	4.33143i	−0.271245	+	0.156603i
$766$	0.710296	+	1.23027i	0.0256640	+	0.0444514i
$767$	−2.46188	−	4.72129i	−0.0888932	−	0.170476i
$768$	1.80636	−	3.12870i	0.0651812	−	0.112897i
$769$	5.26215	+	3.03810i	0.189758	+	0.109557i	0.591869	−	0.806034i	$-0.298390\pi$
$769$	5.26215	+	3.03810i	0.189758	+	0.109557i	−0.402111	+	0.915591i	$0.631724\pi$
$770$	45.7274	−	7.49113i	1.64790	−	0.269961i
$771$	0.519430	+	0.899679i	0.0187068	+	0.0324011i
$772$	2.28155	+	1.31725i	0.0821148	+	0.0474090i
$773$	26.7187	+	15.4261i	0.961006	+	0.554837i	0.896483	−	0.443079i	$-0.146114\pi$
$773$	26.7187	+	15.4261i	0.961006	+	0.554837i	0.0645238	+	0.997916i	$0.479447\pi$
$774$	−5.71571	−	3.29997i	−0.205447	−	0.118615i
$775$	0.832080	+	0.480401i	0.0298892	+	0.0172565i
$776$	−7.16731	−	12.4141i	−0.257291	−	0.445642i
$777$	15.2295	+	18.6045i	0.546357	+	0.667431i
$778$	0.231172	+	0.133467i	0.00828792	+	0.00478503i
$779$	16.8904	−	29.2550i	0.605160	−	1.04817i
$780$	−1.18441	−	0.0508960i	−0.0424088	−	0.00182237i
$781$	−20.9701	−	36.3213i	−0.750370	−	1.29968i
$782$	8.73883	−	5.04537i	0.312500	−	0.180422i
$783$	−4.36939	+	7.56801i	−0.156149	+	0.270459i
$784$	−22.4750	−	19.8093i	−0.802678	−	0.707475i
$785$			36.0147i			1.28542i
$786$		−	23.6109i		−	0.842174i
$787$	32.7907	+	18.9317i	1.16886	+	0.674843i	0.953412	−	0.301672i	$-0.0975447\pi$
$787$	32.7907	+	18.9317i	1.16886	+	0.674843i	0.215450	+	0.976515i	$0.430878\pi$
$788$	2.05470	−	1.18628i	0.0731956	−	0.0422595i
$789$	−11.3330			−0.403466
$790$	24.1011	−	41.7444i	0.857480	−	1.48520i
$791$	−8.58620	+	7.02863i	−0.305290	+	0.249909i
$792$	14.9056			0.529647
$793$	−11.1058	−	7.06444i	−0.394379	−	0.250866i
$794$	12.4311	+	21.5313i	0.441164	+	0.764118i
$795$			17.7605i			0.629901i
$796$	1.49867	+	2.59578i	0.0531190	+	0.0920049i
$797$	−10.0472	−	17.4022i	−0.355889	−	0.616418i	0.631381	−	0.775473i	$-0.282489\pi$
$797$	−10.0472	−	17.4022i	−0.355889	−	0.616418i	−0.987270	+	0.159055i	$0.949155\pi$
$798$	−13.0180	+	10.6565i	−0.460831	+	0.377235i
$799$	−13.3039	+	7.68101i	−0.470658	+	0.271734i
$800$		−	0.240989i		−	0.00852023i
$801$	3.17206	−	1.83139i	0.112079	−	0.0647091i
$802$	−2.78141	+	4.81754i	−0.0982149	+	0.170113i
$803$	21.6557	+	37.5087i	0.764213	+	1.32365i
$804$	0.145342	+	0.0839130i	0.00512580	+	0.00295938i
$805$	9.78267	−	1.60261i	0.344794	−	0.0564846i
$806$	−15.9756	+	8.33037i	−0.562718	+	0.293425i
$807$	11.2083	−	19.4133i	0.394550	−	0.683380i
$808$			5.66823i			0.199408i
$809$	−15.1596			−0.532982			−0.266491	−	0.963837i	$-0.585864\pi$
$809$	−15.1596			−0.532982			−0.266491	+	0.963837i	$0.585864\pi$
$810$	3.18593			0.111942
$811$			41.1951i			1.44656i	0.690556	+	0.723279i	$0.257366\pi$
$811$			41.1951i			1.44656i	−0.690556	+	0.723279i	$0.742634\pi$
$812$	2.70821	−	2.21693i	0.0950396	−	0.0777991i
$813$	−5.92452	+	3.42052i	−0.207782	+	0.119963i
$814$	63.4557	+	36.6362i	2.22412	+	1.28410i
$815$	−11.6345	+	20.1516i	−0.407540	+	0.705880i
$816$	17.0691			0.597538
$817$	−16.8935	+	9.75347i	−0.591029	+	0.341231i
$818$	−46.1925			−1.61508
$819$	−3.75138	+	8.77081i	−0.131084	+	0.306477i
$820$	2.56208			0.0894718
$821$	−14.3955	+	8.31122i	−0.502405	+	0.290064i	−0.729706	−	0.683761i	$-0.760343\pi$
$821$	−14.3955	+	8.31122i	−0.502405	+	0.290064i	0.227301	+	0.973825i	$0.427010\pi$
$822$	−16.9622			−0.591626
$823$	−7.47325	+	12.9441i	−0.260501	+	0.451201i	−0.966375	−	0.257136i	$-0.917221\pi$
$823$	−7.47325	+	12.9441i	−0.260501	+	0.451201i	0.705874	+	0.708337i	$0.250554\pi$
$824$	17.9801	+	10.3808i	0.626366	+	0.361633i
$825$	1.34262	−	0.775160i	0.0467439	−	0.0269876i
$826$	−0.926493	−	5.65551i	−0.0322368	−	0.196780i
$827$		−	13.2231i		−	0.459812i	−0.973213	−	0.229906i	$-0.926158\pi$
$827$		−	13.2231i		−	0.459812i	0.973213	−	0.229906i	$-0.0738418\pi$
$828$	−0.261117			−0.00907444
$829$	−24.0008			−0.833583			−0.416791	−	0.909002i	$-0.636845\pi$
$829$	−24.0008			−0.833583			−0.416791	+	0.909002i	$0.636845\pi$
$830$		−	38.0488i		−	1.32069i
$831$	−4.21146	+	7.29447i	−0.146094	+	0.253042i
$832$	−22.2274	−	14.1389i	−0.770598	−	0.490180i
$833$	5.51470	−	27.3677i	0.191073	−	0.948236i
$834$	5.70207	+	3.29209i	0.197447	+	0.113996i
$835$	−21.9000	−	37.9320i	−0.757882	−	1.31269i
$836$	−1.80374	+	3.12417i	−0.0623837	+	0.108052i
$837$	2.95043	−	1.70343i	0.101982	−	0.0588793i
$838$			18.8526i			0.651252i
$839$	−36.5723	+	21.1151i	−1.26262	+	0.728973i	−0.973580	−	0.228345i	$-0.926668\pi$
$839$	−36.5723	+	21.1151i	−1.26262	+	0.728973i	−0.289037	+	0.957318i	$0.593335\pi$
$840$	14.5768	+	5.50706i	0.502947	+	0.190012i
$841$	−23.6832	−	41.0205i	−0.816661	−	1.41450i
$842$	−12.1528	−	21.0492i	−0.418812	−	0.725403i
$843$			13.5699i			0.467371i
$844$	0.550933	+	0.954243i	0.0189639	+	0.0328464i
$845$	−2.42232	+	28.1331i	−0.0833303	+	0.967808i
$846$	5.64966			0.194239
$847$	−8.22066	−	50.1807i	−0.282465	−	1.72423i
$848$	17.4975	−	30.3065i	0.600865	−	1.04073i
$849$	−6.76619			−0.232215
$850$	1.42873	−	0.824880i	0.0490052	−	0.0282932i
$851$	13.5753	+	7.83773i	0.465357	+	0.268674i
$852$			1.15489i			0.0395660i
$853$		−	34.5287i		−	1.18224i	−0.806584	−	0.591120i	$-0.798686\pi$
$853$		−	34.5287i		−	1.18224i	0.806584	−	0.591120i	$-0.201314\pi$
$854$	−8.97355	−	10.9621i	−0.307069	−	0.375116i
$855$	4.70821	−	8.15486i	0.161017	−	0.278890i
$856$	−35.6586	+	20.5875i	−1.21879	+	0.703666i
$857$	16.3930	+	28.3934i	0.559973	+	0.969901i	0.997498	+	0.0706948i	$0.0225216\pi$
$857$	16.3930	+	28.3934i	0.559973	+	0.969901i	−0.437525	+	0.899206i	$0.644145\pi$
$858$	−1.24811	+	29.0450i	−0.0426097	+	0.991580i
$859$	8.25051	−	14.2903i	0.281504	−	0.487579i	−0.690252	−	0.723569i	$-0.742500\pi$
$859$	8.25051	−	14.2903i	0.281504	−	0.487579i	0.971755	+	0.235991i	$0.0758335\pi$
$860$	−1.28128	−	0.739747i	−0.0436913	−	0.0252252i
$861$	7.28612	−	19.2858i	0.248310	−	0.657260i
$862$	1.69125	+	2.92933i	0.0576043	+	0.0997735i
$863$	−11.7134	−	6.76276i	−0.398730	−	0.230207i	0.287206	−	0.957869i	$-0.407274\pi$
$863$	−11.7134	−	6.76276i	−0.398730	−	0.230207i	−0.685936	+	0.727662i	$0.740607\pi$
$864$	−0.740028	−	0.427255i	−0.0251763	−	0.0145355i
$865$	4.17719	+	2.41170i	0.142029	+	0.0820003i
$866$	47.0484	+	27.1634i	1.59877	+	0.923050i
$867$	−0.546883	−	0.947230i	−0.0185731	−	0.0321696i
$868$	−1.34650	+	0.220586i	−0.0457033	+	0.00748717i
$869$	−72.0285	−	41.5857i	−2.44340	−	1.41070i
$870$	−13.9206	+	24.1111i	−0.471952	+	0.817444i
$871$	2.14548	−	3.37285i	0.0726967	−	0.114284i
$872$	18.2053	+	31.5325i	0.616509	+	1.06782i
$873$	−4.57836	+	2.64332i	−0.154954	+	0.0894627i
$874$	−5.48424	+	9.49899i	−0.185507	+	0.321308i
$875$	29.9555	−	4.90735i	1.01268	−	0.165899i
$876$		−	1.19265i		−	0.0402959i
$877$			28.5031i			0.962480i	0.876589	+	0.481240i	$0.159813\pi$
$877$			28.5031i			0.962480i	−0.876589	+	0.481240i	$0.840187\pi$
$878$	21.7940	+	12.5827i	0.735511	+	0.424647i
$879$	−2.62940	+	1.51808i	−0.0886873	+	0.0512037i
$880$	51.1031			1.72269
$881$	12.3238	−	21.3455i	0.415199	−	0.719147i	−0.580250	−	0.814439i	$-0.697045\pi$
$881$	12.3238	−	21.3455i	0.415199	−	0.719147i	0.995449	+	0.0952919i	$0.0303784\pi$
$882$	−6.78891	+	7.70247i	−0.228594	+	0.259356i
$883$	47.2299			1.58941			0.794706	−	0.606995i	$-0.207625\pi$
$883$	47.2299			1.58941			0.794706	+	0.606995i	$0.207625\pi$
$884$	−0.0934522	+	2.17475i	−0.00314314	+	0.0731446i
$885$	1.60385	+	2.77795i	0.0539128	+	0.0933797i
$886$		−	36.6443i		−	1.23109i
$887$	−1.60651	−	2.78257i	−0.0539415	−	0.0934294i	0.837794	−	0.545987i	$-0.183845\pi$
$887$	−1.60651	−	2.78257i	−0.0539415	−	0.0934294i	−0.891735	+	0.452557i	$0.850512\pi$
$888$	12.3202	+	21.3391i	0.413437	+	0.716095i
$889$	−36.8086	−	13.9061i	−1.23452	−	0.466397i
$890$	10.1060	−	5.83469i	0.338753	−	0.195579i
$891$		−	5.49721i		−	0.184164i
$892$	−1.32173	+	0.763100i	−0.0442547	+	0.0255505i
$893$	8.34915	−	14.4611i	0.279394	−	0.483924i
$894$	1.47497	+	2.55472i	0.0493304	+	0.0854427i
$895$	−9.25716	−	5.34462i	−0.309433	−	0.178651i
$896$	−20.8240	−	25.4387i	−0.695682	−	0.849848i
$897$	−0.267013	+	6.21373i	−0.00891532	+	0.207470i
$898$	14.9450	−	25.8855i	0.498721	−	0.863809i
$899$			29.7719i			0.992948i
$900$	−0.0426907			−0.00142302
$901$	32.6108			1.08642
$902$		−	62.8293i		−	2.09199i
$903$	−9.21211	+	7.54100i	−0.306560	+	0.250949i
$904$	−9.84828	+	5.68591i	−0.327549	+	0.189111i
$905$	38.3522	+	22.1427i	1.27487	+	0.736047i
$906$	8.71913	−	15.1020i	0.289674	−	0.501729i
$907$	10.5918			0.351694			0.175847	−	0.984418i	$-0.443734\pi$
$907$	10.5918			0.351694			0.175847	+	0.984418i	$0.443734\pi$
$908$	−1.98496	+	1.14602i	−0.0658731	+	0.0380319i
$909$	2.09045			0.0693360
$910$	−11.9516	+	27.9432i	−0.396192	+	0.926308i
$911$	52.8741			1.75180			0.875899	−	0.482495i	$-0.160269\pi$
$911$	52.8741			1.75180			0.875899	+	0.482495i	$0.160269\pi$
$912$	−16.0681	+	9.27694i	−0.532069	+	0.307190i
$913$	−65.6519			−2.17276
$914$	15.1845	−	26.3003i	0.502258	−	0.869936i
$915$	6.86701	+	3.96467i	0.227016	+	0.131068i
$916$	−3.01374	+	1.73998i	−0.0995769	+	0.0574907i
$917$	−39.8412	−	15.0518i	−1.31567	−	0.497056i
$918$		−	5.84981i		−	0.193072i
$919$	−12.7865			−0.421787			−0.210894	−	0.977509i	$-0.567637\pi$
$919$	−12.7865			−0.421787			−0.210894	+	0.977509i	$0.567637\pi$
$920$	10.1594			0.334944
$921$			0.123565i			0.00407162i
$922$	−5.00509	+	8.66908i	−0.164834	+	0.285501i
$923$	27.4827	+	1.18097i	0.904605	+	0.0388722i
$924$	−0.778092	+	2.05956i	−0.0255973	+	0.0677544i
$925$	2.21947	+	1.28141i	0.0729757	+	0.0421325i
$926$	−18.5981	−	32.2129i	−0.611172	−	1.05858i
$927$	3.82846	−	6.63109i	0.125743	−	0.217794i
$928$	6.46694	−	3.73369i	0.212288	−	0.122564i
$929$		−	26.5386i		−	0.870702i	−0.900261	−	0.435351i	$-0.856624\pi$
$929$		−	26.5386i		−	0.870702i	0.900261	−	0.435351i	$-0.143376\pi$
$930$	9.39987	−	5.42702i	0.308234	−	0.177959i
$931$	9.68288	+	28.7600i	0.317344	+	0.942572i
$932$	−0.779855	−	1.35075i	−0.0255450	−	0.0442453i
$933$	−6.90330	−	11.9569i	−0.226004	−	0.391450i
$934$			25.8491i			0.845809i
$935$	23.8108	+	41.2415i	0.778697	+	1.34874i
$936$	−5.24718	+	8.24894i	−0.171509	+	0.269625i
$937$	−54.9588			−1.79543			−0.897713	−	0.440581i	$-0.854773\pi$
$937$	−54.9588			−1.79543			−0.897713	+	0.440581i	$0.854773\pi$
$938$	3.32921	−	2.72528i	0.108703	−	0.0889835i
$939$	8.94111	−	15.4864i	0.291782	−	0.505381i
$940$	1.26647			0.0413078
$941$	−10.4669	+	6.04305i	−0.341210	+	0.196998i	−0.660807	−	0.750556i	$-0.729786\pi$
$941$	−10.4669	+	6.04305i	−0.341210	+	0.196998i	0.319597	+	0.947554i	$0.396453\pi$
$942$	−21.0616	−	12.1599i	−0.686223	−	0.396191i
$943$		−	13.4413i		−	0.437710i
$944$		−	6.32037i		−	0.205710i
$945$	2.03101	−	5.37595i	0.0660689	−	0.174880i
$946$	−18.1406	+	31.4205i	−0.589802	+	1.02157i
$947$	−31.7263	+	18.3172i	−1.03097	+	0.595229i	−0.917261	−	0.398286i	$-0.869605\pi$
$947$	−31.7263	+	18.3172i	−1.03097	+	0.595229i	−0.113705	+	0.993515i	$0.536272\pi$
$948$	1.14513	+	1.98343i	0.0371921	+	0.0644187i
$949$	−28.3812	−	1.21958i	−0.921292	−	0.0395893i
$950$	−0.896633	+	1.55301i	−0.0290906	+	0.0503864i
$951$	12.7409	+	7.35599i	0.413153	+	0.238534i
$952$	10.1117	−	26.7650i	0.327723	−	0.867460i
$953$	9.08718	+	15.7395i	0.294363	+	0.509851i	0.974836	−	0.222921i	$-0.0715593\pi$
$953$	9.08718	+	15.7395i	0.294363	+	0.509851i	−0.680474	+	0.732772i	$0.738226\pi$
$954$	−10.3864	−	5.99661i	−0.336273	−	0.194148i
$955$	−38.4429	−	22.1950i	−1.24398	−	0.718214i
$956$	0.423953	+	0.244770i	0.0137116	+	0.00791641i
$957$	41.6030	+	24.0195i	1.34483	+	0.776439i
$958$	15.3034	+	26.5063i	0.494432	+	0.856381i
$959$	−10.8133	+	28.6221i	−0.349181	+	0.924257i
$960$	13.7438	+	7.93499i	0.443579	+	0.256101i
$961$	−9.69663	+	16.7951i	−0.312794	+	0.541776i
$962$	−42.6130	+	22.2202i	−1.37390	+	0.716409i
$963$	7.59271	+	13.1510i	0.244672	+	0.423784i
$964$	−0.687699	+	0.397043i	−0.0221493	+	0.0127879i
$965$	−18.9014	+	32.7382i	−0.608457	+	1.05388i
$966$	−2.36578	+	6.26205i	−0.0761176	+	0.201478i
$967$			38.5735i			1.24044i	0.784428	+	0.620220i	$0.212957\pi$
$967$			38.5735i			1.24044i	−0.784428	+	0.620220i	$0.787043\pi$
$968$		−	52.1129i		−	1.67497i
$969$	−14.9735	−	8.64493i	−0.481017	−	0.277715i
$970$	−14.5863	+	8.42142i	−0.468339	+	0.270395i
$971$	14.1186			0.453089			0.226544	−	0.974001i	$-0.427257\pi$
$971$	14.1186			0.453089			0.226544	+	0.974001i	$0.427257\pi$
$972$	−0.0756874	+	0.131094i	−0.00242768	+	0.00420486i
$973$	9.19013	−	7.52301i	0.294622	−	0.241177i
$974$	−3.96917			−0.127180
$975$	−0.0436547	+	1.01590i	−0.00139807	+	0.0325348i
$976$	−7.81189	−	13.5306i	−0.250052	−	0.433103i
$977$			41.4872i			1.32729i	0.748046	+	0.663647i	$0.230992\pi$
$977$			41.4872i			1.32729i	−0.748046	+	0.663647i	$0.769008\pi$
$978$	−7.85650	−	13.6079i	−0.251223	−	0.435131i
$979$	−10.0676	−	17.4375i	−0.321760	−	0.557305i
$980$	−1.52186	+	1.72665i	−0.0486139	+	0.0551558i
$981$	11.6292	−	6.71414i	0.371293	−	0.214366i
$982$			8.18696i			0.261256i
$983$	−15.2419	+	8.79992i	−0.486142	+	0.280674i	−0.722972	−	0.690877i	$-0.757225\pi$
$983$	−15.2419	+	8.79992i	−0.486142	+	0.280674i	0.236831	+	0.971551i	$0.423891\pi$
$984$	10.5642	−	18.2978i	0.336776	−	0.583313i
$985$	17.0220	+	29.4830i	0.542367	+	0.939408i
$986$	44.2714	+	25.5601i	1.40989	+	0.814000i
$987$	3.60163	−	9.53326i	0.114641	−	0.303447i
$988$	−1.09399	−	2.09800i	−0.0348044	−	0.0667464i
$989$	−3.88090	+	6.72192i	−0.123405	+	0.213744i
$990$		−	17.5137i		−	0.556623i
$991$	−9.61380			−0.305392			−0.152696	−	0.988273i	$-0.548796\pi$
$991$	−9.61380			−0.305392			−0.152696	+	0.988273i	$0.548796\pi$
$992$	−2.91120			−0.0924308
$993$		−	17.7857i		−	0.564412i
$994$	27.6964	+	10.4636i	0.878477	+	0.331885i
$995$	−37.2470	+	21.5046i	−1.18081	+	0.681741i
$996$	1.56563	+	0.903917i	0.0496089	+	0.0286417i
$997$	9.50761	−	16.4677i	0.301109	−	0.521536i	−0.675279	−	0.737563i	$-0.735977\pi$
$997$	9.50761	−	16.4677i	0.301109	−	0.521536i	0.976387	+	0.216027i	$0.0693099\pi$
$998$	−16.8847			−0.534477
$999$	7.86991	−	4.54370i	0.248993	−	0.143756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.d.121.8	yes	20
3.2	odd	2		819.2.do.g.667.3		20
7.4	even	3		273.2.t.d.4.8	✓	20
13.10	even	6		273.2.t.d.205.3	yes	20
21.11	odd	6		819.2.bm.g.550.3		20
39.23	odd	6		819.2.bm.g.478.8		20
91.88	even	6	inner	273.2.bl.d.88.8	yes	20
273.179	odd	6		819.2.do.g.361.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.8	✓	20	7.4	even	3
273.2.t.d.205.3	yes	20	13.10	even	6
273.2.bl.d.88.8	yes	20	91.88	even	6	inner
273.2.bl.d.121.8	yes	20	1.1	even	1	trivial
819.2.bm.g.478.8		20	39.23	odd	6
819.2.bm.g.550.3		20	21.11	odd	6
819.2.do.g.361.3		20	273.179	odd	6
819.2.do.g.667.3		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27025 - 0.733378i) q^{2} -1.00000 q^{3} +(0.0756874 - 0.131094i) q^{4} +(1.88109 + 1.08605i) q^{5} +(-1.27025 + 0.733378i) q^{6} +(0.427729 + 2.61095i) q^{7} +2.71148i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.27025 - 0.733378i) q^{2} -1.00000 q^{3} +(0.0756874 - 0.131094i) q^{4} +(1.88109 + 1.08605i) q^{5} +(-1.27025 + 0.733378i) q^{6} +(0.427729 + 2.61095i) q^{7} +2.71148i q^{8} +1.00000 q^{9} +3.18593 q^{10} -5.49721i q^{11} +(-0.0756874 + 0.131094i) q^{12} +(3.04222 + 1.93517i) q^{13} +(2.45813 + 3.00287i) q^{14} +(-1.88109 - 1.08605i) q^{15} +(2.13992 + 3.70645i) q^{16} +(-1.99413 + 3.45394i) q^{17} +(1.27025 - 0.733378i) q^{18} -4.33519i q^{19} +(0.284749 - 0.164400i) q^{20} +(-0.427729 - 2.61095i) q^{21} +(-4.03154 - 6.98282i) q^{22} +(-0.862484 - 1.49387i) q^{23} -2.71148i q^{24} +(-0.141010 - 0.244236i) q^{25} +(5.28359 + 0.227044i) q^{26} -1.00000 q^{27} +(0.374655 + 0.141543i) q^{28} +(4.36939 - 7.56801i) q^{29} -3.18593 q^{30} +(-2.95043 + 1.70343i) q^{31} +(0.740028 + 0.427255i) q^{32} +5.49721i q^{33} +5.84981i q^{34} +(-2.03101 + 5.37595i) q^{35} +(0.0756874 - 0.131094i) q^{36} +(-7.86991 + 4.54370i) q^{37} +(-3.17933 - 5.50676i) q^{38} +(-3.04222 - 1.93517i) q^{39} +(-2.94479 + 5.10053i) q^{40} +(6.74826 + 3.89611i) q^{41} +(-2.45813 - 3.00287i) q^{42} +(-2.24984 - 3.89684i) q^{43} +(-0.720654 - 0.416070i) q^{44} +(1.88109 + 1.08605i) q^{45} +(-2.19114 - 1.26505i) q^{46} +(3.33576 + 1.92590i) q^{47} +(-2.13992 - 3.70645i) q^{48} +(-6.63410 + 2.23356i) q^{49} +(-0.358235 - 0.206827i) q^{50} +(1.99413 - 3.45394i) q^{51} +(0.483948 - 0.252351i) q^{52} +(-4.08835 - 7.08123i) q^{53} +(-1.27025 + 0.733378i) q^{54} +(5.97022 - 10.3407i) q^{55} +(-7.07954 + 1.15978i) q^{56} +4.33519i q^{57} -12.8177i q^{58} +(-1.27893 - 0.738389i) q^{59} +(-0.284749 + 0.164400i) q^{60} -3.65055 q^{61} +(-2.49852 + 4.32757i) q^{62} +(0.427729 + 2.61095i) q^{63} -7.30631 q^{64} +(3.62100 + 6.94421i) q^{65} +(4.03154 + 6.98282i) q^{66} -1.10868i q^{67} +(0.301861 + 0.522839i) q^{68} +(0.862484 + 1.49387i) q^{69} +(1.36271 + 8.31829i) q^{70} +(6.60723 - 3.81468i) q^{71} +2.71148i q^{72} +(-6.82323 + 3.93939i) q^{73} +(-6.66450 + 11.5432i) q^{74} +(0.141010 + 0.244236i) q^{75} +(-0.568319 - 0.328119i) q^{76} +(14.3529 - 2.35132i) q^{77} +(-5.28359 - 0.227044i) q^{78} +(7.56487 - 13.1027i) q^{79} +9.29619i q^{80} +1.00000 q^{81} +11.4293 q^{82} -11.9428i q^{83} +(-0.374655 - 0.141543i) q^{84} +(-7.50226 + 4.33143i) q^{85} +(-5.71571 - 3.29997i) q^{86} +(-4.36939 + 7.56801i) q^{87} +14.9056 q^{88} +(3.17206 - 1.83139i) q^{89} +3.18593 q^{90} +(-3.75138 + 8.77081i) q^{91} -0.261117 q^{92} +(2.95043 - 1.70343i) q^{93} +5.64966 q^{94} +(4.70821 - 8.15486i) q^{95} +(-0.740028 - 0.427255i) q^{96} +(-4.57836 + 2.64332i) q^{97} +(-6.78891 + 7.70247i) q^{98} -5.49721i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

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