LMFDB - Embedded newform 441.2.s.b.362.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.2
Root			$0.187540 - 0.324828i$ of defining polynomial
Character	$\chi$	$=$	441.362
Dual form			441.2.s.b.374.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.621951 + 0.359083i) q^{2} +(-1.34572 - 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} +1.44755 q^{5} +(1.22853 + 0.194963i) q^{6} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +O(q^{10})$	\(q+(-0.621951 + 0.359083i) q^{2} +(-1.34572 - 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} +1.44755 q^{5} +(1.22853 + 0.194963i) q^{6} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +(-0.900304 + 0.519791i) q^{10} -1.80056i q^{11} +(2.40030 - 0.920553i) q^{12} +(-1.88867 + 1.09042i) q^{13} +(-1.94800 - 1.57844i) q^{15} +(-0.585716 - 1.01449i) q^{16} +(1.95230 + 3.38149i) q^{17} +(-1.44067 - 1.60198i) q^{18} +(3.47456 + 2.00604i) q^{19} +(-1.07425 + 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} +5.67561i q^{23} +(-2.72853 + 3.36736i) q^{24} -2.90460 q^{25} +(0.783106 - 1.35638i) q^{26} +(2.36323 - 4.62765i) q^{27} +(8.49418 + 4.90412i) q^{29} +(1.77835 + 0.282218i) q^{30} +(2.45129 + 1.41525i) q^{31} +(5.06262 + 2.92290i) q^{32} +(-1.96338 + 2.42306i) q^{33} +(-2.42847 - 1.40208i) q^{34} +(-4.23394 - 1.37854i) q^{36} +(-0.411767 + 0.713202i) q^{37} -2.88134 q^{38} +(3.73065 + 0.592040i) q^{39} -3.62215i q^{40} +(5.90617 + 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +(2.31442 + 1.33623i) q^{44} +(0.900304 + 4.24830i) q^{45} +(-2.03802 - 3.52995i) q^{46} +(-1.16920 - 2.02511i) q^{47} +(-0.318012 + 2.00390i) q^{48} +(1.80652 - 1.04299i) q^{50} +(1.05999 - 6.67939i) q^{51} -3.23689i q^{52} +(-0.996713 + 0.575453i) q^{53} +(0.191903 + 3.72677i) q^{54} -2.60640i q^{55} +(-2.48837 - 6.48831i) q^{57} -7.04395 q^{58} +(4.89555 - 8.47934i) q^{59} +(3.47456 - 1.33255i) q^{60} +(-2.03980 + 1.17768i) q^{61} -2.03277 q^{62} -1.85540 q^{64} +(-2.73394 + 1.57844i) q^{65} +(0.351042 - 2.21204i) q^{66} +(0.156402 - 0.270897i) q^{67} -5.79536 q^{68} +(6.18882 - 7.63781i) q^{69} -1.94933i q^{71} +(7.34369 - 1.55628i) q^{72} +(-2.42847 + 1.40208i) q^{73} -0.591435i q^{74} +(3.90880 + 3.16725i) q^{75} +(-5.15706 + 2.97743i) q^{76} +(-2.53287 + 0.971396i) q^{78} +(-6.21583 - 10.7661i) q^{79} +(-0.847852 - 1.46852i) q^{80} +(-8.22635 + 3.65063i) q^{81} +(-7.34669 - 4.24162i) q^{82} +(3.60916 - 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} -5.41161i q^{86} +(-6.08326 - 15.8619i) q^{87} -4.50548 q^{88} +(-5.28999 + 9.16253i) q^{89} +(-2.08544 - 2.31895i) q^{90} +(-7.29536 - 4.21198i) q^{92} +(-1.75553 - 4.57748i) q^{93} +(1.45436 + 0.839677i) q^{94} +(5.02959 + 2.90383i) q^{95} +(-3.62569 - 9.45383i) q^{96} +(-13.4322 - 7.75510i) q^{97} +(5.28433 - 1.11986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 12 q^{6}+O(q^{10}) $ 10 * q + 4 * q^4 + 12 * q^6	$ 10 q + 4 q^{4} + 12 q^{6} + 15 q^{10} - 6 q^{13} - 3 q^{15} - 6 q^{16} + 12 q^{17} - 18 q^{18} - 3 q^{19} + 3 q^{20} + 5 q^{22} - 27 q^{24} - 14 q^{25} - 3 q^{26} - 27 q^{27} - 15 q^{29} + 9 q^{31} + 48 q^{32} + 9 q^{33} - 3 q^{34} - 18 q^{36} + 6 q^{37} - 36 q^{38} + 12 q^{39} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 15 q^{45} - 13 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} - 24 q^{51} - 9 q^{53} - 27 q^{54} - 36 q^{57} - 16 q^{58} + 18 q^{59} - 3 q^{60} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} + 33 q^{66} - 10 q^{67} + 54 q^{68} + 3 q^{69} + 18 q^{72} - 3 q^{73} + 21 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} + 30 q^{80} - 48 q^{81} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 30 q^{87} + 16 q^{88} - 24 q^{89} - 24 q^{90} + 39 q^{92} + 6 q^{93} + 3 q^{94} - 3 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 4 * q^4 + 12 * q^6 + 15 * q^10 - 6 * q^13 - 3 * q^15 - 6 * q^16 + 12 * q^17 - 18 * q^18 - 3 * q^19 + 3 * q^20 + 5 * q^22 - 27 * q^24 - 14 * q^25 - 3 * q^26 - 27 * q^27 - 15 * q^29 + 9 * q^31 + 48 * q^32 + 9 * q^33 - 3 * q^34 - 18 * q^36 + 6 * q^37 - 36 * q^38 + 12 * q^39 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 15 * q^45 - 13 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 - 24 * q^51 - 9 * q^53 - 27 * q^54 - 36 * q^57 - 16 * q^58 + 18 * q^59 - 3 * q^60 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 + 33 * q^66 - 10 * q^67 + 54 * q^68 + 3 * q^69 + 18 * q^72 - 3 * q^73 + 21 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 + 30 * q^80 - 48 * q^81 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 30 * q^87 + 16 * q^88 - 24 * q^89 - 24 * q^90 + 39 * q^92 + 6 * q^93 + 3 * q^94 - 3 * q^96 - 6 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.621951	+	0.359083i	−0.439785	+	0.253910i	−0.703507	−	0.710689i	$-0.748383\pi$
$2$	−0.621951	+	0.359083i	−0.439785	+	0.253910i	0.263721	+	0.964599i	$0.415050\pi$
$3$	−1.34572	−	1.09042i	−0.776955	−	0.629557i
$3$	−1.34572	−	1.09042i	−0.776955	−	0.629557i
$4$	−0.742118	+	1.28539i	−0.371059	+	0.642693i
$5$	1.44755			0.647363			0.323682	−	0.946166i	$-0.395079\pi$
$5$	1.44755			0.647363			0.323682	+	0.946166i	$0.395079\pi$
$6$	1.22853	+	0.194963i	0.501544	+	0.0795931i
$7$		0			0
$7$		0			0
$8$		−	2.50226i		−	0.884683i
$9$	0.621951	+	2.93482i	0.207317	+	0.978274i
$10$	−0.900304	+	0.519791i	−0.284701	+	0.164372i
$11$		−	1.80056i		−	0.542890i	−0.962454	−	0.271445i	$-0.912499\pi$
$11$		−	1.80056i		−	0.542890i	0.962454	−	0.271445i	$-0.0875015\pi$
$12$	2.40030	−	0.920553i	0.692908	−	0.265741i
$13$	−1.88867	+	1.09042i	−0.523823	+	0.302429i	−0.738497	−	0.674256i	$-0.764464\pi$
$13$	−1.88867	+	1.09042i	−0.523823	+	0.302429i	0.214675	+	0.976686i	$0.431131\pi$
$14$		0			0
$15$	−1.94800	−	1.57844i	−0.502972	−	0.407552i
$16$	−0.585716	−	1.01449i	−0.146429	−	0.253622i
$17$	1.95230	+	3.38149i	0.473503	+	0.820131i	0.999540	−	0.0303308i	$-0.00965608\pi$
$17$	1.95230	+	3.38149i	0.473503	+	0.820131i	−0.526037	+	0.850462i	$0.676323\pi$
$18$	−1.44067	−	1.60198i	−0.339569	−	0.377591i
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	0.842462	−	0.538755i	$-0.181105\pi$
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	−0.0453446	+	0.998971i	$0.514439\pi$
$20$	−1.07425	+	1.86066i	−0.240210	+	0.416056i
$21$		0			0
$22$	0.646552	+	1.11986i	0.137845	+	0.238755i
$23$			5.67561i			1.18345i	0.806141	+	0.591723i	$0.201552\pi$
$23$			5.67561i			1.18345i	−0.806141	+	0.591723i	$0.798448\pi$
$24$	−2.72853	+	3.36736i	−0.556958	+	0.687359i
$25$	−2.90460			−0.580921
$26$	0.783106	−	1.35638i	0.153580	−	0.266008i
$27$	2.36323	−	4.62765i	0.454803	−	0.890592i
$28$		0			0
$29$	8.49418	+	4.90412i	1.57733	+	0.910672i	0.995230	+	0.0975551i	$0.0311022\pi$
$29$	8.49418	+	4.90412i	1.57733	+	0.910672i	0.582100	+	0.813117i	$0.302231\pi$
$30$	1.77835	+	0.282218i	0.324681	+	0.0515257i
$31$	2.45129	+	1.41525i	0.440264	+	0.254187i	0.703710	−	0.710488i	$-0.251526\pi$
$31$	2.45129	+	1.41525i	0.440264	+	0.254187i	−0.263445	+	0.964674i	$0.584859\pi$
$32$	5.06262	+	2.92290i	0.894953	+	0.516701i
$33$	−1.96338	+	2.42306i	−0.341780	+	0.421801i
$34$	−2.42847	−	1.40208i	−0.416479	−	0.240454i
$35$		0			0
$36$	−4.23394	−	1.37854i	−0.705657	−	0.229756i
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$38$	−2.88134			−0.467414
$39$	3.73065	+	0.592040i	0.597383	+	0.0948023i
$40$		−	3.62215i		−	0.572712i
$41$	5.90617	+	10.2298i	0.922389	+	1.59762i	0.795708	+	0.605681i	$0.207099\pi$
$41$	5.90617	+	10.2298i	0.922389	+	1.59762i	0.126681	+	0.991943i	$0.459567\pi$
$42$		0			0
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	0.421526	+	0.906816i	$0.361494\pi$
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	−0.996089	+	0.0883555i	$0.971839\pi$
$44$	2.31442	+	1.33623i	0.348912	+	0.201444i
$45$	0.900304	+	4.24830i	0.134209	+	0.633299i
$46$	−2.03802	−	3.52995i	−0.300489	−	0.520463i
$47$	−1.16920	−	2.02511i	−0.170545	−	0.295392i	0.768066	−	0.640371i	$-0.221219\pi$
$47$	−1.16920	−	2.02511i	−0.170545	−	0.295392i	−0.938610	+	0.344979i	$0.887886\pi$
$48$	−0.318012	+	2.00390i	−0.0459010	+	0.289238i
$49$		0			0
$50$	1.80652	−	1.04299i	0.255480	−	0.147502i
$51$	1.05999	−	6.67939i	0.148429	−	0.935301i
$52$		−	3.23689i		−	0.448877i
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	−0.566890	−	0.823793i	$-0.691854\pi$
$53$	−0.996713	+	0.575453i	−0.136909	+	0.0790445i	0.429981	+	0.902838i	$0.358520\pi$
$54$	0.191903	+	3.72677i	0.0261147	+	0.507149i
$55$		−	2.60640i		−	0.351447i
$56$		0			0
$57$	−2.48837	−	6.48831i	−0.329592	−	0.859398i
$58$	−7.04395			−0.924916
$59$	4.89555	−	8.47934i	0.637346	−	1.10392i	−0.348666	−	0.937247i	$-0.613365\pi$
$59$	4.89555	−	8.47934i	0.637346	−	1.10392i	0.986013	−	0.166669i	$-0.0533013\pi$
$60$	3.47456	−	1.33255i	0.448563	−	0.172031i
$61$	−2.03980	+	1.17768i	−0.261170	+	0.150786i	−0.624868	−	0.780730i	$-0.714847\pi$
$61$	−2.03980	+	1.17768i	−0.261170	+	0.150786i	0.363698	+	0.931517i	$0.381514\pi$
$62$	−2.03277			−0.258163
$63$		0			0
$64$	−1.85540			−0.231925
$65$	−2.73394	+	1.57844i	−0.339104	+	0.195782i
$66$	0.351042	−	2.21204i	0.0432103	−	0.272283i
$67$	0.156402	−	0.270897i	0.0191076	−	0.0330953i	−0.856313	−	0.516456i	$-0.827251\pi$
$67$	0.156402	−	0.270897i	0.0191076	−	0.0330953i	0.875421	+	0.483361i	$0.160584\pi$
$68$	−5.79536			−0.702790
$69$	6.18882	−	7.63781i	0.745047	−	0.919484i
$70$		0			0
$71$		−	1.94933i		−	0.231343i	−0.993288	−	0.115671i	$-0.963098\pi$
$71$		−	1.94933i		−	0.231343i	0.993288	−	0.115671i	$-0.0369019\pi$
$72$	7.34369	−	1.55628i	0.865463	−	0.183410i
$73$	−2.42847	+	1.40208i	−0.284231	+	0.164101i	−0.635337	−	0.772235i	$-0.719139\pi$
$73$	−2.42847	+	1.40208i	−0.284231	+	0.164101i	0.351106	+	0.936336i	$0.385806\pi$
$74$		−	0.591435i		−	0.0687529i
$75$	3.90880	+	3.16725i	0.451349	+	0.365722i
$76$	−5.15706	+	2.97743i	−0.591556	+	0.341535i
$77$		0			0
$78$	−2.53287	+	0.971396i	−0.286792	+	0.109989i
$79$	−6.21583	−	10.7661i	−0.699336	−	1.21128i	−0.968697	−	0.248246i	$-0.920146\pi$
$79$	−6.21583	−	10.7661i	−0.699336	−	1.21128i	0.269361	−	0.963039i	$-0.413187\pi$
$80$	−0.847852	−	1.46852i	−0.0947927	−	0.164186i
$81$	−8.22635	+	3.65063i	−0.914039	+	0.405625i
$82$	−7.34669	−	4.24162i	−0.811306	−	0.468408i
$83$	3.60916	−	6.25124i	0.396157	−	0.686163i	−0.597092	−	0.802173i	$-0.703677\pi$
$83$	3.60916	−	6.25124i	0.396157	−	0.686163i	0.993248	+	0.116010i	$0.0370104\pi$
$84$		0			0
$85$	2.82605	+	4.89486i	0.306528	+	0.530923i
$86$		−	5.41161i		−	0.583549i
$87$	−6.08326	−	15.8619i	−0.652194	−	1.70057i
$88$	−4.50548			−0.480286
$89$	−5.28999	+	9.16253i	−0.560737	+	0.971226i	0.436695	+	0.899610i	$0.356149\pi$
$89$	−5.28999	+	9.16253i	−0.560737	+	0.971226i	−0.997432	+	0.0716161i	$0.977184\pi$
$90$	−2.08544	−	2.31895i	−0.219824	−	0.244438i
$91$		0			0
$92$	−7.29536	−	4.21198i	−0.760593	−	0.439129i
$93$	−1.75553	−	4.57748i	−0.182040	−	0.474663i
$94$	1.45436	+	0.839677i	0.150006	+	0.0866061i
$95$	5.02959	+	2.90383i	0.516025	+	0.297927i
$96$	−3.62569	−	9.45383i	−0.370045	−	0.964877i
$97$	−13.4322	−	7.75510i	−1.36384	−	0.787411i	−0.373704	−	0.927548i	$-0.621912\pi$
$97$	−13.4322	−	7.75510i	−1.36384	−	0.787411i	−0.990132	+	0.140137i	$0.955246\pi$
$98$		0			0
$99$	5.28433	−	1.11986i	0.531095	−	0.112550i
$100$	2.15556	−	3.73354i	0.215556	−	0.373354i
$101$	3.94618			0.392659			0.196330	−	0.980538i	$-0.437098\pi$
$101$	3.94618			0.392659			0.196330	+	0.980538i	$0.437098\pi$
$102$	1.73919	+	4.53487i	0.172206	+	0.449019i
$103$		−	4.15522i		−	0.409426i	−0.978822	−	0.204713i	$-0.934374\pi$
$103$		−	4.15522i		−	0.409426i	0.978822	−	0.204713i	$-0.0656261\pi$
$104$	2.72853	+	4.72595i	0.267554	+	0.463417i
$105$		0			0
$106$	0.413271	−	0.715806i	0.0401404	−	0.0695253i
$107$	4.91092	+	2.83532i	0.474757	+	0.274101i	0.718229	−	0.695807i	$-0.244953\pi$
$107$	4.91092	+	2.83532i	0.474757	+	0.274101i	−0.243472	+	0.969908i	$0.578286\pi$
$108$	4.19453	+	6.47192i	0.403619	+	0.622761i
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	0.996083	+	0.0884193i	$0.0281815\pi$
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	−0.421468	+	0.906843i	$0.638485\pi$
$110$	0.935915	+	1.62105i	0.0892360	+	0.154561i
$111$	1.33182	−	0.510772i	0.126411	−	0.0484804i
$112$		0			0
$113$	6.27800	−	3.62461i	0.590585	−	0.340974i	−0.174744	−	0.984614i	$-0.555910\pi$
$113$	6.27800	−	3.62461i	0.590585	−	0.340974i	0.765329	+	0.643640i	$0.222576\pi$
$114$	3.87749	+	3.14188i	0.363160	+	0.294264i
$115$			8.21572i			0.766120i
$116$	−12.6074	+	7.27887i	−1.17057	+	0.675826i
$117$	−4.37486	−	4.86472i	−0.404456	−	0.449743i
$118$			7.03164i			0.647315i
$119$		0			0
$120$	−3.94968	+	4.87441i	−0.360554	+	0.444971i
$121$	7.75798			0.705271
$122$	0.845770	−	1.46492i	0.0765724	−	0.132627i
$123$	3.20673	−	20.2067i	0.289141	−	1.82198i
$124$	−3.63829	+	2.10057i	−0.326728	+	0.188637i
$125$	−11.4423			−1.02343
$126$		0			0
$127$	−0.881336			−0.0782059			−0.0391030	−	0.999235i	$-0.512450\pi$
$127$	−0.881336			−0.0782059			−0.0391030	+	0.999235i	$0.512450\pi$
$128$	−8.97127	+	5.17956i	−0.792956	+	0.457813i
$129$	12.1861	−	4.67355i	1.07293	−	0.411483i
$130$	1.13358	−	1.96343i	0.0994219	−	0.172204i
$131$	2.97441			0.259876			0.129938	−	0.991522i	$-0.458522\pi$
$131$	2.97441			0.259876			0.129938	+	0.991522i	$0.458522\pi$
$132$	−1.65751	−	4.32189i	−0.144268	−	0.376173i
$133$		0			0
$134$			0.224646i			0.0194065i
$135$	3.42088	−	6.69875i	0.294423	−	0.576537i
$136$	8.46137	−	4.88517i	0.725556	−	0.418900i
$137$		−	11.8986i		−	1.01657i	−0.861190	−	0.508283i	$-0.830280\pi$
$137$		−	11.8986i		−	1.01657i	0.861190	−	0.508283i	$-0.169720\pi$
$138$	−1.10653	+	6.97264i	−0.0941942	+	0.593551i
$139$	10.4143	−	6.01268i	0.883327	−	0.509989i	0.0115731	−	0.999933i	$-0.496316\pi$
$139$	10.4143	−	6.01268i	0.883327	−	0.509989i	0.871754	+	0.489944i	$0.162983\pi$
$140$		0			0
$141$	−0.634809	+	4.00015i	−0.0534606	+	0.336874i
$142$	0.699971	+	1.21239i	0.0587403	+	0.101741i
$143$	1.96338	+	3.40067i	0.164186	+	0.284378i
$144$	2.61306	−	2.34993i	0.217755	−	0.195828i
$145$	12.2957	+	7.09895i	1.02111	+	0.589536i
$146$	1.00693	−	1.74405i	0.0833338	−	0.144338i
$147$		0			0
$148$	−0.611160	−	1.05856i	−0.0502370	−	0.0870131i
$149$		−	7.07901i		−	0.579935i	−0.957036	−	0.289968i	$-0.906355\pi$
$149$		−	7.07901i		−	0.579935i	0.957036	−	0.289968i	$-0.0936446\pi$
$150$	−3.56838	−	0.566289i	−0.291357	−	0.0462373i
$151$	15.5819			1.26803			0.634017	−	0.773319i	$-0.281405\pi$
$151$	15.5819			1.26803			0.634017	+	0.773319i	$0.281405\pi$
$152$	5.01963	−	8.69425i	0.407146	−	0.705197i
$153$	−8.70982	+	7.83277i	−0.704147	+	0.633242i
$154$		0			0
$155$	3.54836	+	2.04865i	0.285011	+	0.164551i
$156$	−3.52959	+	4.35597i	−0.282593	+	0.348757i
$157$	−1.80677	−	1.04314i	−0.144196	−	0.0832517i	0.426166	−	0.904645i	$-0.359864\pi$
$157$	−1.80677	−	1.04314i	−0.144196	−	0.0832517i	−0.570362	+	0.821393i	$0.693197\pi$
$158$	7.73188	+	4.46400i	0.615115	+	0.355137i
$159$	1.96879	+	0.312439i	0.156135	+	0.0247780i
$160$	7.32839	+	4.23105i	0.579360	+	0.334494i
$161$		0			0
$162$	3.80551	−	5.22446i	0.298989	−	0.410472i
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	−0.997522	−	0.0703575i	$-0.977586\pi$
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	0.559692	+	0.828700i	$0.310919\pi$
$164$	−17.5323			−1.36904
$165$	−2.84208	+	3.50750i	−0.221256	+	0.273058i
$166$			5.18395i			0.402353i
$167$	−0.960750	−	1.66407i	−0.0743450	−	0.128769i	0.826456	−	0.563001i	$-0.190353\pi$
$167$	−0.960750	−	1.66407i	−0.0743450	−	0.128769i	−0.900801	+	0.434232i	$0.857020\pi$
$168$		0			0
$169$	−4.12195	+	7.13943i	−0.317073	+	0.549187i
$170$	−3.51533	−	2.02958i	−0.269613	−	0.155661i
$171$	−3.72635	+	11.4449i	−0.284961	+	0.875210i
$172$	−5.59210	−	9.68580i	−0.426393	−	0.738535i
$173$	−7.61290	−	13.1859i	−0.578798	−	1.00251i	−0.995618	−	0.0935182i	$-0.970189\pi$
$173$	−7.61290	−	13.1859i	−0.578798	−	1.00251i	0.416820	−	0.908989i	$-0.363145\pi$
$174$	9.47922	+	7.68089i	0.718618	+	0.582287i
$175$		0			0
$176$	−1.82665	+	1.05462i	−0.137689	+	0.0794948i
$177$	−15.8341	+	6.07263i	−1.19017	+	0.456447i
$178$		−	7.59818i		−	0.569508i
$179$	−0.299401	+	0.172859i	−0.0223783	+	0.0129201i	−0.511147	−	0.859493i	$-0.670779\pi$
$179$	−0.299401	+	0.172859i	−0.0223783	+	0.0129201i	0.488769	+	0.872413i	$0.337446\pi$
$180$	−6.12884	−	1.99550i	−0.456816	−	0.148736i
$181$		−	3.27661i		−	0.243548i	−0.992558	−	0.121774i	$-0.961142\pi$
$181$		−	3.27661i		−	0.243548i	0.992558	−	0.121774i	$-0.0388583\pi$
$182$		0			0
$183$	4.02918	+	0.639415i	0.297846	+	0.0472669i
$184$	14.2019			1.04698
$185$	−0.596053	+	1.03239i	−0.0438227	+	0.0759031i
$186$	2.73555	+	2.21659i	0.200581	+	0.162528i
$187$	6.08857	−	3.51524i	0.445241	−	0.257060i
$188$	3.47073			0.253129
$189$		0			0
$190$	−4.17087			−0.302587
$191$	6.40096	−	3.69560i	0.463158	−	0.267404i	−0.250213	−	0.968191i	$-0.580501\pi$
$191$	6.40096	−	3.69560i	0.463158	−	0.267404i	0.713371	+	0.700787i	$0.247167\pi$
$192$	2.49686	+	2.02317i	0.180195	+	0.146010i
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	−0.999368	−	0.0355398i	$-0.988685\pi$
$193$	−6.51425	+	11.2830i	−0.468906	+	0.812169i	0.530462	+	0.847708i	$0.322018\pi$
$194$	11.1389			0.799727
$195$	5.40030	+	0.857007i	0.386724	+	0.0613716i
$196$		0			0
$197$			4.03035i			0.287151i	0.989639	+	0.143575i	$0.0458599\pi$
$197$			4.03035i			0.287151i	−0.989639	+	0.143575i	$0.954140\pi$
$198$	−2.88447	+	2.59401i	−0.204990	+	0.184348i
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.910397	−	0.413736i	$-0.864224\pi$
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.0968925	+	0.995295i	$0.530890\pi$
$200$			7.26808i			0.513931i
$201$	−0.505867	+	0.194008i	−0.0356811	+	0.0136843i
$202$	−2.45433	+	1.41701i	−0.172686	+	0.0997003i
$203$		0			0
$204$	7.79895	+	6.31940i	0.546036	+	0.442446i
$205$	8.54947	+	14.8081i	0.597121	+	1.03424i
$206$	1.49207	+	2.58434i	0.103957	+	0.180060i
$207$	−16.6569	+	3.52995i	−1.15774	+	0.245348i
$208$	2.21245	+	1.27736i	0.153406	+	0.0885688i
$209$	3.61199	−	6.25615i	0.249847	−	0.432747i
$210$		0			0
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	0.581657	−	0.813434i	$-0.302405\pi$
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	−0.995283	+	0.0970121i	$0.969071\pi$
$212$		−	1.70822i		−	0.117321i
$213$	−2.12559	+	2.62326i	−0.145643	+	0.179743i
$214$	−4.07247			−0.278388
$215$	−5.45387	+	9.44638i	−0.371951	+	0.644238i
$216$	−11.5796	−	5.91341i	−0.787892	−	0.402357i
$217$		0			0
$218$	−7.46236	−	4.30839i	−0.505415	−	0.291801i
$219$	4.79691	+	0.761251i	0.324145	+	0.0514406i
$220$	3.35023	+	1.93426i	0.225873	+	0.130408i
$221$	−7.37451	−	4.25767i	−0.496063	−	0.286402i
$222$	−0.644915	+	0.795909i	−0.0432839	+	0.0534179i
$223$	22.7932	+	13.1597i	1.52635	+	0.881237i	0.999511	+	0.0312693i	$0.00995496\pi$
$223$	22.7932	+	13.1597i	1.52635	+	0.881237i	0.526836	+	0.849967i	$0.323378\pi$
$224$		0			0
$225$	−1.80652	−	8.52449i	−0.120435	−	0.568300i
$226$	−2.60307	+	4.50865i	−0.173154	+	0.299911i
$227$	−10.8082			−0.717366			−0.358683	−	0.933459i	$-0.616774\pi$
$227$	−10.8082			−0.717366			−0.358683	+	0.933459i	$0.616774\pi$
$228$	10.1867	+	1.61658i	0.674627	+	0.107061i
$229$			9.69691i			0.640790i	0.947284	+	0.320395i	$0.103816\pi$
$229$			9.69691i			0.640790i	−0.947284	+	0.320395i	$0.896184\pi$
$230$	−2.95013	−	5.10977i	−0.194526	−	0.336928i
$231$		0			0
$232$	12.2714	−	21.2547i	0.805657	−	1.39544i
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	0.435482	−	0.900198i	$-0.356578\pi$
$233$	−1.92897	−	1.11369i	−0.126371	−	0.0729605i	−0.561853	+	0.827237i	$0.689911\pi$
$234$	4.46779	+	1.45468i	0.292068	+	0.0950951i
$235$	−1.69247	−	2.93144i	−0.110404	−	0.191226i
$236$	7.26616	+	12.5854i	0.472986	+	0.819237i
$237$	−3.37486	+	21.2661i	−0.219220	+	1.38138i
$238$		0			0
$239$	−15.9697	+	9.22008i	−1.03299	+	0.596398i	−0.917840	−	0.396950i	$-0.870068\pi$
$239$	−15.9697	+	9.22008i	−1.03299	+	0.596398i	−0.115151	+	0.993348i	$0.536735\pi$
$240$	−0.460337	+	2.90075i	−0.0297146	+	0.187242i
$241$			6.47181i			0.416886i	0.978035	+	0.208443i	$0.0668396\pi$
$241$			6.47181i			0.416886i	−0.978035	+	0.208443i	$0.933160\pi$
$242$	−4.82508	+	2.78576i	−0.310168	+	0.179075i
$243$	15.0511	+	4.05748i	0.965531	+	0.260287i
$244$		−	3.49591i		−	0.223803i
$245$		0			0
$246$	5.26147	+	13.7191i	0.335459	+	0.874695i
$247$	−8.74972			−0.556731
$248$	3.54133	−	6.13377i	0.224875	−	0.389495i
$249$	−11.6734	+	4.47694i	−0.739774	+	0.283715i
$250$	7.11654	−	4.10874i	0.450090	−	0.259859i
$251$	−0.416679			−0.0263005			−0.0131503	−	0.999914i	$-0.504186\pi$
$251$	−0.416679			−0.0263005			−0.0131503	+	0.999914i	$0.504186\pi$
$252$		0			0
$253$	10.2193			0.642481
$254$	0.548147	−	0.316473i	0.0343938	−	0.0198573i
$255$	1.53439	−	9.66874i	0.0960873	−	0.605480i
$256$	5.57519	−	9.65652i	0.348449	−	0.603532i
$257$	21.1284			1.31795			0.658976	−	0.752164i	$-0.270990\pi$
$257$	21.1284			1.31795			0.658976	+	0.752164i	$0.270990\pi$
$258$	−5.90095	+	7.28254i	−0.367377	+	0.453391i
$259$		0			0
$260$		−	4.68556i		−	0.290586i
$261$	−9.10975	+	27.9790i	−0.563880	+	1.73186i
$262$	−1.84994	+	1.06806i	−0.114290	+	0.0659851i
$263$		−	22.2456i		−	1.37172i	−0.727732	−	0.685862i	$-0.759426\pi$
$263$		−	22.2456i		−	1.37172i	0.727732	−	0.685862i	$-0.240574\pi$
$264$	6.06313	+	4.91288i	0.373160	+	0.302367i
$265$	−1.44279	+	0.832996i	−0.0886299	+	0.0511705i
$266$		0			0
$267$	17.1099	−	6.56191i	1.04711	−	0.401582i
$268$	0.232138	+	0.402075i	0.0141801	+	0.0245607i
$269$	14.5164	+	25.1432i	0.885083	+	1.53301i	0.845619	+	0.533788i	$0.179232\pi$
$269$	14.5164	+	25.1432i	0.885083	+	1.53301i	0.0394642	+	0.999221i	$0.487435\pi$
$270$	0.277789	+	5.39467i	0.0169057	+	0.328309i
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.290610	−	0.956842i	$-0.593858\pi$
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.973954	+	0.226745i	$0.927192\pi$
$272$	2.28699	−	3.96118i	0.138669	−	0.240182i
$273$		0			0
$274$	4.27259	+	7.40034i	0.258117	+	0.447071i
$275$			5.22992i			0.315376i
$276$	5.22470	+	13.6232i	0.314490	+	0.820020i
$277$	8.06485			0.484570			0.242285	−	0.970205i	$-0.422103\pi$
$277$	8.06485			0.484570			0.242285	+	0.970205i	$0.422103\pi$
$278$	−4.31811	+	7.47918i	−0.258983	+	0.448572i
$279$	−2.62893	+	8.07431i	−0.157390	+	0.483396i
$280$		0			0
$281$	−12.0876	−	6.97879i	−0.721087	−	0.416320i	0.0940658	−	0.995566i	$-0.470014\pi$
$281$	−12.0876	−	6.97879i	−0.721087	−	0.416320i	−0.815153	+	0.579246i	$0.803347\pi$
$282$	−1.04157	−	2.71585i	−0.0620245	−	0.161726i
$283$	−13.4559	−	7.76876i	−0.799869	−	0.461805i	0.0435563	−	0.999051i	$-0.486131\pi$
$283$	−13.4559	−	7.76876i	−0.799869	−	0.461805i	−0.843425	+	0.537246i	$0.819465\pi$
$284$	2.50564	+	1.44663i	0.148682	+	0.0858418i
$285$	−3.60203	−	9.39215i	−0.213366	−	0.556343i
$286$	−2.44225	−	1.41003i	−0.144413	−	0.0833769i
$287$		0			0
$288$	−5.42950	+	16.6758i	−0.319937	+	0.982630i
$289$	0.877036	−	1.51907i	0.0515904	−	0.0893571i
$290$	−10.1965			−0.598757
$291$	9.61973	+	25.0831i	0.563919	+	1.47039i
$292$		−	4.16203i		−	0.243564i
$293$	−6.73712	−	11.6690i	−0.393587	−	0.681712i	0.599333	−	0.800500i	$-0.295433\pi$
$293$	−6.73712	−	11.6690i	−0.393587	−	0.681712i	−0.992920	+	0.118788i	$0.962099\pi$
$294$		0			0
$295$	7.08655	−	12.2743i	0.412595	−	0.714635i
$296$	1.78462	+	1.03035i	0.103729	+	0.0598879i
$297$	−8.33237	−	4.25513i	−0.483493	−	0.246908i
$298$	2.54196	+	4.40280i	0.147252	+	0.255047i
$299$	−6.18882	−	10.7194i	−0.357909	−	0.619916i
$300$	−6.97193	+	2.67384i	−0.402525	+	0.154374i
$301$		0			0
$302$	−9.69114	+	5.59518i	−0.557663	+	0.321967i
$303$	−5.31047	−	4.30301i	−0.305079	−	0.247201i
$304$		−	4.69987i		−	0.269556i
$305$	−2.95271	+	1.70475i	−0.169072	+	0.0976136i
$306$	2.60446	−	7.99915i	0.148887	−	0.457281i
$307$			8.62791i			0.492421i	0.969216	+	0.246210i	$0.0791854\pi$
$307$			8.62791i			0.492421i	−0.969216	+	0.246210i	$0.920815\pi$
$308$		0			0
$309$	−4.53095	+	5.59178i	−0.257757	+	0.318106i
$310$	−2.94254			−0.167125
$311$	8.12200	−	14.0677i	0.460556	−	0.797707i	−0.538432	−	0.842669i	$-0.680983\pi$
$311$	8.12200	−	14.0677i	0.460556	−	0.797707i	0.998989	+	0.0449616i	$0.0143165\pi$
$312$	1.48144	−	9.33508i	0.0838701	−	0.528495i
$313$	−5.86899	+	3.38846i	−0.331735	+	0.191527i	−0.656611	−	0.754229i	$-0.728011\pi$
$313$	−5.86899	+	3.38846i	−0.331735	+	0.191527i	0.324876	+	0.945757i	$0.394677\pi$
$314$	1.49830			0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$	19.0245	−	10.9838i	1.06852	−	0.616911i	0.140744	−	0.990046i	$-0.455051\pi$
$317$	19.0245	−	10.9838i	1.06852	−	0.616911i	0.927777	+	0.373135i	$0.121717\pi$
$318$	−1.33668	+	0.512638i	−0.0749574	+	0.0287473i
$319$	8.83017	−	15.2943i	0.494395	−	0.856316i
$320$	−2.68578			−0.150140
$321$	−3.51705	−	9.17056i	−0.196302	−	0.511850i
$322$		0			0
$323$			15.6655i			0.871654i
$324$	1.41246	−	13.2832i	0.0784700	−	0.737958i
$325$	5.48584	−	3.16725i	0.304299	−	0.175687i
$326$		−	8.02886i		−	0.444678i
$327$	3.25721	−	20.5248i	0.180124	−	1.13503i
$328$	25.5976	−	14.7788i	1.41339	−	0.816022i
$329$		0			0
$330$	0.508150	−	3.20203i	0.0279728	−	0.176266i
$331$	7.30179	+	12.6471i	0.401342	+	0.695145i	0.993888	−	0.110391i	$-0.0352104\pi$
$331$	7.30179	+	12.6471i	0.401342	+	0.695145i	−0.592546	+	0.805537i	$0.701877\pi$
$332$	5.35684	+	9.27833i	0.293995	+	0.509214i
$333$	−2.34922	−	0.764887i	−0.128736	−	0.0419156i
$334$	1.19508	+	0.689978i	0.0653917	+	0.0377539i
$335$	0.226400	−	0.392137i	0.0123696	−	0.0214247i
$336$		0			0
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.844685	−	0.535263i	$-0.820212\pi$
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.0412090	−	0.999151i	$-0.513121\pi$
$338$		−	5.92049i		−	0.322032i
$339$	−12.4008	−	1.96796i	−0.673520	−	0.106885i
$340$	−8.38906			−0.454961
$341$	2.54825	−	4.41370i	0.137995	−	0.239015i
$342$	−1.79205	−	8.45621i	−0.0969029	−	0.457259i
$343$		0			0
$344$	16.3292	+	9.42767i	0.880412	+	0.508306i
$345$	8.95862	−	11.0561i	0.482316	−	0.595241i
$346$	9.46969	+	5.46733i	0.509094	+	0.293925i
$347$	2.76005	+	1.59352i	0.148167	+	0.0855444i	0.572251	−	0.820079i	$-0.306070\pi$
$347$	2.76005	+	1.59352i	0.148167	+	0.0855444i	−0.424084	+	0.905623i	$0.639404\pi$
$348$	24.9031	+	3.95203i	1.33495	+	0.211851i
$349$	6.48224	+	3.74252i	0.346986	+	0.200333i	0.663357	−	0.748303i	$-0.269131\pi$
$349$	6.48224	+	3.74252i	0.346986	+	0.200333i	−0.316371	+	0.948636i	$0.602464\pi$
$350$		0			0
$351$	0.582750	+	11.3170i	0.0311049	+	0.604058i
$352$	5.26287	−	9.11556i	0.280512	−	0.485861i
$353$	11.3808			0.605739			0.302869	−	0.953032i	$-0.402055\pi$
$353$	11.3808			0.605739			0.302869	+	0.953032i	$0.402055\pi$
$354$	7.66747	−	9.46266i	0.407522	−	0.502934i
$355$		−	2.82175i		−	0.149763i
$356$	−7.85159	−	13.5994i	−0.416134	−	0.720764i
$357$		0			0
$358$	0.124142	−	0.215020i	0.00656109	−	0.0113641i
$359$	−4.77569	−	2.75725i	−0.252051	−	0.145522i	0.368652	−	0.929568i	$-0.379819\pi$
$359$	−4.77569	−	2.75725i	−0.252051	−	0.145522i	−0.620703	+	0.784046i	$0.713153\pi$
$360$	10.6304	−	2.25280i	0.560269	−	0.118733i
$361$	−1.45164	−	2.51432i	−0.0764022	−	0.132332i
$362$	1.17657	+	2.03789i	0.0618394	+	0.107109i
$363$	−10.4401	−	8.45949i	−0.547963	−	0.444008i
$364$		0			0
$365$	−3.51533	+	2.02958i	−0.184001	+	0.106233i
$366$	−2.73555	+	1.04913i	−0.142990	+	0.0548387i
$367$		−	21.1025i		−	1.10154i	−0.834657	−	0.550770i	$-0.814334\pi$
$367$		−	21.1025i		−	1.10154i	0.834657	−	0.550770i	$-0.185666\pi$
$368$	5.75785	−	3.32430i	0.300149	−	0.173291i
$369$	−26.3493	+	23.6960i	−1.37169	+	1.23356i
$370$		−	0.856131i		−	0.0445081i
$371$		0			0
$372$	7.18665	+	1.14049i	0.372611	+	0.0591318i
$373$	15.3700			0.795826			0.397913	−	0.917423i	$-0.369735\pi$
$373$	15.3700			0.795826			0.397913	+	0.917423i	$0.369735\pi$
$374$	−2.52453	+	4.37261i	−0.130540	+	0.226102i
$375$	15.3982	+	12.4770i	0.795159	+	0.644307i
$376$	−5.06735	+	2.92563i	−0.261328	+	0.150878i
$377$	−21.3903			−1.10166
$378$		0			0
$379$	−32.3630			−1.66238			−0.831188	−	0.555991i	$-0.812339\pi$
$379$	−32.3630			−1.66238			−0.831188	+	0.555991i	$0.812339\pi$
$380$	−7.46510	+	4.30998i	−0.382951	+	0.221097i
$381$	1.18604	+	0.961030i	0.0607625	+	0.0492351i
$382$	−2.65406	+	4.59696i	−0.135793	+	0.235201i
$383$	−19.8346			−1.01350			−0.506750	−	0.862093i	$-0.669153\pi$
$383$	−19.8346			−1.01350			−0.506750	+	0.862093i	$0.669153\pi$
$384$	17.7208	+	2.81222i	0.904310	+	0.143510i
$385$		0			0
$386$		−	9.35663i		−	0.476240i
$387$	−21.4953	−	6.99870i	−1.09267	−	0.355764i
$388$	19.9366	−	11.5104i	1.01213	−	0.584352i
$389$			5.10283i			0.258724i	0.991597	+	0.129362i	$0.0412928\pi$
$389$			5.10283i			0.258724i	−0.991597	+	0.129362i	$0.958707\pi$
$390$	−3.66646	+	1.40614i	−0.185658	+	0.0712028i
$391$	−19.1920	+	11.0805i	−0.970581	+	0.560365i
$392$		0			0
$393$	−4.00274	−	3.24337i	−0.201912	−	0.163607i
$394$	−1.44723	−	2.50668i	−0.0729105	−	0.126285i
$395$	−8.99772	−	15.5845i	−0.452724	−	0.784141i
$396$	−2.48214	+	7.62347i	−0.124732	+	0.383094i
$397$	11.5288	+	6.65615i	0.578613	+	0.334062i	0.760582	−	0.649242i	$-0.224914\pi$
$397$	11.5288	+	6.65615i	0.578613	+	0.334062i	−0.181969	+	0.983304i	$0.558247\pi$
$398$	5.89177	−	10.2048i	0.295328	−	0.511522i
$399$		0			0
$400$	1.70127	+	2.94669i	0.0850636	+	0.147334i
$401$		−	16.3678i		−	0.817371i	−0.912675	−	0.408685i	$-0.865987\pi$
$401$		−	16.3678i		−	0.817371i	0.912675	−	0.408685i	$-0.134013\pi$
$402$	0.244959	−	0.302312i	0.0122175	−	0.0150779i
$403$	−6.17290			−0.307494
$404$	−2.92853	+	5.07237i	−0.145700	+	0.252360i
$405$	−11.9080	+	5.28446i	−0.591716	+	0.262587i
$406$		0			0
$407$	1.28416	+	0.741412i	0.0636536	+	0.0367504i
$408$	−16.7136	−	2.65238i	−0.827445	−	0.131312i
$409$	−3.75604	−	2.16855i	−0.185724	−	0.107228i	0.404255	−	0.914646i	$-0.367531\pi$
$409$	−3.75604	−	2.16855i	−0.185724	−	0.107228i	−0.589979	+	0.807418i	$0.700864\pi$
$410$	−10.6347	−	6.13994i	−0.525210	−	0.303230i
$411$	−12.9745	+	16.0122i	−0.639986	+	0.789826i
$412$	5.34107	+	3.08367i	0.263135	+	0.151921i
$413$		0			0
$414$	9.09223	−	8.17667i	0.446859	−	0.401862i
$415$	5.22443	−	9.04898i	0.256457	−	0.444197i
$416$	−12.7488			−0.625062
$417$	−20.5711	−	3.26456i	−1.00737	−	0.159866i
$418$			5.18802i			0.253754i
$419$	9.41294	+	16.3037i	0.459852	+	0.796487i	0.998953	−	0.0457540i	$-0.0145690\pi$
$419$	9.41294	+	16.3037i	0.459852	+	0.796487i	−0.539100	+	0.842241i	$0.681236\pi$
$420$		0			0
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	−0.842907	−	0.538059i	$-0.819158\pi$
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	0.887426	+	0.460950i	$0.152491\pi$
$422$	7.47370	+	4.31494i	0.363814	+	0.210048i
$423$	5.21614	−	4.69090i	0.253618	−	0.228079i
$424$	1.43993	+	2.49404i	0.0699294	+	0.121121i
$425$	−5.67066	−	9.82187i	−0.275068	−	0.476431i
$426$	0.380046	−	2.39480i	0.0184133	−	0.116029i
$427$		0			0
$428$	−7.28897	+	4.20829i	−0.352326	+	0.203415i
$429$	1.06601	−	6.71727i	0.0514672	−	0.324313i
$430$		−	7.83357i		−	0.377768i
$431$	−12.4526	+	7.18954i	−0.599823	+	0.346308i	−0.768972	−	0.639283i	$-0.779231\pi$
$431$	−12.4526	+	7.18954i	−0.599823	+	0.346308i	0.169149	+	0.985590i	$0.445898\pi$
$432$	−6.07888	+	0.313021i	−0.292470	+	0.0150602i
$433$		−	2.22130i		−	0.106749i	−0.998575	−	0.0533745i	$-0.983002\pi$
$433$		−	2.22130i		−	0.106749i	0.998575	−	0.0533745i	$-0.0169977\pi$
$434$		0			0
$435$	−8.80582	−	22.9608i	−0.422207	−	1.10089i
$436$	−17.8083			−0.852865
$437$	−11.3855	+	19.7202i	−0.544641	+	0.943347i
$438$	−3.25680	+	1.24903i	−0.155616	+	0.0596810i
$439$	−8.69907	+	5.02241i	−0.415184	+	0.239706i	−0.693015	−	0.720924i	$-0.743718\pi$
$439$	−8.69907	+	5.02241i	−0.415184	+	0.239706i	0.277831	+	0.960630i	$0.410385\pi$
$440$	−6.52190			−0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$	12.0321	−	6.94672i	0.571661	−	0.330049i	−0.186151	−	0.982521i	$-0.559602\pi$
$443$	12.0321	−	6.94672i	0.571661	−	0.330049i	0.757812	+	0.652472i	$0.226268\pi$
$444$	−0.331826	+	2.09095i	−0.0157478	+	0.0992323i
$445$	−7.65751	+	13.2632i	−0.363001	+	0.628736i
$446$	−18.9017			−0.895020
$447$	−7.71913	+	9.52640i	−0.365102	+	0.450583i
$448$		0			0
$449$			10.5630i			0.498498i	0.968439	+	0.249249i	$0.0801837\pi$
$449$			10.5630i			0.498498i	−0.968439	+	0.249249i	$0.919816\pi$
$450$	4.18457	+	4.65312i	0.197262	+	0.219350i
$451$	18.4194	−	10.6344i	0.867334	−	0.500755i
$452$			10.7595i			0.506086i
$453$	−20.9689	−	16.9908i	−0.985204	−	0.798299i
$454$	6.72217	−	3.88105i	0.315487	−	0.182147i
$455$		0			0
$456$	−16.2355	+	6.22655i	−0.760295	+	0.291585i
$457$	−2.55654	−	4.42805i	−0.119590	−	0.207135i	0.800015	−	0.599979i	$-0.204825\pi$
$457$	−2.55654	−	4.42805i	−0.119590	−	0.207135i	−0.919605	+	0.392844i	$0.871491\pi$
$458$	−3.48200	−	6.03100i	−0.162703	−	0.281810i
$459$	20.2621	−	1.04336i	0.945752	−	0.0486998i
$460$	−10.5604	−	6.09704i	−0.492380	−	0.284276i
$461$	4.16691	−	7.21730i	0.194072	−	0.336143i	−0.752524	−	0.658565i	$-0.771164\pi$
$461$	4.16691	−	7.21730i	0.194072	−	0.336143i	0.946596	+	0.322422i	$0.104497\pi$
$462$		0			0
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	0.999220	−	0.0394986i	$-0.0125761\pi$
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	−0.533817	+	0.845600i	$0.679243\pi$
$464$		−	11.4897i		−	0.533395i
$465$	−2.54122	−	6.62613i	−0.117846	−	0.307279i
$466$	1.59963			0.0741016
$467$	10.3896	−	17.9953i	0.480773	−	0.832723i	−0.518984	−	0.854784i	$-0.673690\pi$
$467$	10.3896	−	17.9953i	0.480773	−	0.832723i	0.999757	+	0.0220611i	$0.00702284\pi$
$468$	9.49971	−	2.01319i	0.439124	−	0.0930597i
$469$		0			0
$470$	2.10526	+	1.21547i	0.0971085	+	0.0560656i
$471$	1.29395	+	3.37393i	0.0596222	+	0.155462i
$472$	−21.2175	−	12.2500i	−0.976616	−	0.563850i
$473$	11.7501	+	6.78390i	0.540268	+	0.311924i
$474$	−5.53733	−	14.4383i	−0.254338	−	0.663175i
$475$	−10.0922	−	5.82674i	−0.463062	−	0.267349i
$476$		0			0
$477$	−2.30876	−	2.56727i	−0.105711	−	0.117547i
$478$	6.62156	−	11.4689i	0.302863	−	0.524574i
$479$	32.0617			1.46494			0.732468	−	0.680802i	$-0.238368\pi$
$479$	32.0617			1.46494			0.732468	+	0.680802i	$0.238368\pi$
$480$	−5.24836	−	13.6849i	−0.239554	−	0.624626i
$481$		−	1.79600i		−	0.0818907i
$482$	−2.32392	−	4.02515i	−0.105852	−	0.183340i
$483$		0			0
$484$	−5.75734	+	9.97200i	−0.261697	+	0.453273i
$485$	−19.4438	−	11.2259i	−0.882897	−	0.509741i
$486$	−10.8180	+	2.88107i	−0.490716	+	0.130688i
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	0.999094	+	0.0425641i	$0.0135527\pi$
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	−0.462685	+	0.886523i	$0.653114\pi$
$488$	2.94686	+	5.10412i	0.133398	+	0.231052i
$489$	18.0797	−	6.93385i	0.817594	−	0.313560i
$490$		0			0
$491$	15.4664	−	8.92951i	0.697987	−	0.402983i	−0.108610	−	0.994084i	$-0.534640\pi$
$491$	15.4664	−	8.92951i	0.697987	−	0.402983i	0.806597	+	0.591101i	$0.201307\pi$
$492$	23.5937	+	19.1177i	1.06368	+	0.861890i
$493$			38.2973i			1.72482i
$494$	5.44189	−	3.14188i	0.244842	−	0.141360i
$495$	7.64932	−	1.62105i	0.343811	−	0.0728609i
$496$		−	3.31574i		−	0.148881i
$497$		0			0
$498$	5.65271	−	6.97617i	0.253304	−	0.312610i
$499$	−23.1204			−1.03501			−0.517506	−	0.855680i	$-0.673139\pi$
$499$	−23.1204			−1.03501			−0.517506	+	0.855680i	$0.673139\pi$
$500$	8.49154	−	14.7078i	0.379753	−	0.657752i
$501$	−0.521634	+	3.28700i	−0.0233049	+	0.146852i
$502$	0.259154	−	0.149622i	0.0115666	−	0.00667798i
$503$	13.9995			0.624206			0.312103	−	0.950048i	$-0.398967\pi$
$503$	13.9995			0.624206			0.312103	+	0.950048i	$0.398967\pi$
$504$		0			0
$505$	5.71228			0.254193
$506$	−6.35589	+	3.66958i	−0.282554	+	0.163133i
$507$	13.3320	−	5.11303i	0.592096	−	0.227078i
$508$	0.654056	−	1.13286i	0.0290190	−	0.0502624i
$509$	13.5834			0.602074			0.301037	−	0.953612i	$-0.402667\pi$
$509$	13.5834			0.602074			0.301037	+	0.953612i	$0.402667\pi$
$510$	2.51757	+	6.56445i	0.111480	+	0.290679i
$511$		0			0
$512$		−	12.7104i		−	0.561727i
$513$	17.4944	−	11.3383i	0.772396	−	0.500599i
$514$	−13.1408	+	7.58684i	−0.579616	+	0.334641i
$515$		−	6.01488i		−	0.265047i
$516$	−3.03620	+	19.1322i	−0.133661	+	0.842247i
$517$	−3.64633	+	2.10521i	−0.160365	+	0.0925870i
$518$		0			0
$519$	−4.13339	+	26.0459i	−0.181435	+	1.14329i
$520$	3.94968	+	6.84104i	0.173205	+	0.299999i
$521$	−15.9477	−	27.6222i	−0.698682	−	1.21015i	−0.968924	−	0.247360i	$-0.920437\pi$
$521$	−15.9477	−	27.6222i	−0.698682	−	1.21015i	0.270242	−	0.962792i	$-0.412896\pi$
$522$	−4.38099	−	20.6727i	−0.191751	−	0.904821i
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	0.526121	−	0.850410i	$-0.323646\pi$
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	−0.473416	+	0.880839i	$0.656979\pi$
$524$	−2.20737	+	3.82327i	−0.0964293	+	0.167020i
$525$		0			0
$526$	7.98803	+	13.8357i	0.348295	+	0.603264i
$527$			11.0520i			0.481433i
$528$	3.60815	+	0.572599i	0.157025	+	0.0249192i
$529$	−9.21257			−0.400546
$530$	0.598230	−	1.03616i	0.0259854	−	0.0450081i
$531$	27.9301	+	9.09384i	1.21207	+	0.394639i
$532$		0			0
$533$	−22.3096	−	12.8805i	−0.966337	−	0.557915i
$534$	−8.28524	+	10.2251i	−0.358538	+	0.442482i
$535$	7.10880	+	4.10427i	0.307340	+	0.177443i
$536$	−0.677855	−	0.391360i	−0.0292789	−	0.0169042i
$537$	0.591401	+	0.0938530i	0.0255208	+	0.00405006i
$538$	−18.0570	−	10.4252i	−0.778493	−	0.449463i
$539$		0			0
$540$	6.07178	+	9.36842i	0.261288	+	0.403153i
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	−0.439903	−	0.898045i	$-0.644987\pi$
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	0.997682	−	0.0680555i	$-0.0216795\pi$
$542$	17.2632			0.741516
$543$	−3.57289	+	4.40941i	−0.153327	+	0.189226i
$544$			22.8256i			0.978638i
$545$	8.68407	+	15.0413i	0.371985	+	0.644296i
$546$		0			0
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	−0.993564	−	0.113276i	$-0.963865\pi$
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	0.594882	+	0.803813i	$0.297199\pi$
$548$	15.2943	+	8.83017i	0.653340	+	0.377206i
$549$	−4.72493	−	5.25399i	−0.201655	−	0.224235i
$550$	−1.87798	−	3.25275i	−0.0800772	−	0.138698i
$551$	19.6757	+	34.0793i	0.838212	+	1.45183i
$552$	−19.1118	−	15.4861i	−0.813453	−	0.659131i
$553$		0			0
$554$	−5.01594	+	2.89595i	−0.213107	+	0.123037i
$555$	1.92787	−	0.739368i	0.0818336	−	0.0313844i
$556$			17.8485i			0.756944i
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.541674	−	0.840589i	$-0.317791\pi$
$557$	36.3567	−	20.9905i	1.54048	−	0.889398i	0.998808	−	0.0488092i	$-0.0155426\pi$
$558$	−1.26428	−	5.96583i	−0.0535214	−	0.252554i
$559$		−	16.4334i		−	0.695058i
$560$		0			0
$561$	−12.0266	−	1.90858i	−0.507765	−	0.0805804i
$562$	10.0239			0.422831
$563$	−19.3006	+	33.4295i	−0.813422	+	1.40889i	0.0970343	+	0.995281i	$0.469064\pi$
$563$	−19.3006	+	33.4295i	−0.813422	+	1.40889i	−0.910456	+	0.413606i	$0.864269\pi$
$564$	−4.67064	−	3.78456i	−0.196669	−	0.159359i
$565$	9.08771	−	5.24679i	0.382323	−	0.220734i
$566$	11.1585			0.469028
$567$		0			0
$568$	−4.87773			−0.204665
$569$	−30.4460	+	17.5780i	−1.27636	+	0.736908i	−0.976178	−	0.216973i	$-0.930382\pi$
$569$	−30.4460	+	17.5780i	−1.27636	+	0.736908i	−0.300184	+	0.953881i	$0.597048\pi$
$570$	5.61285	+	4.54802i	0.235096	+	0.190496i
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	−0.212870	−	0.977081i	$-0.568281\pi$
$571$	17.6766	−	30.6167i	0.739742	−	1.28127i	0.952611	−	0.304190i	$-0.0983857\pi$
$572$	−5.82823			−0.243690
$573$	−12.6437	−	2.00651i	−0.528198	−	0.0838230i
$574$		0			0
$575$		−	16.4854i		−	0.687489i
$576$	−1.15397	−	5.44527i	−0.0480820	−	0.226886i
$577$	−23.2557	+	13.4267i	−0.968147	+	0.558960i	−0.898671	−	0.438624i	$-0.855466\pi$
$577$	−23.2557	+	13.4267i	−0.968147	+	0.558960i	−0.0694761	+	0.997584i	$0.522133\pi$
$578$			1.25972i			0.0523973i
$579$	21.0696	−	8.08053i	0.875625	−	0.335815i
$580$	−18.2498	+	10.5365i	−0.757781	+	0.437505i
$581$		0			0
$582$	−14.9899	−	12.1461i	−0.621352	−	0.503473i
$583$	1.03614	+	1.79464i	0.0429125	+	0.0743266i
$584$	3.50837	+	6.07667i	0.145177	+	0.251454i
$585$	−6.33282	−	7.04192i	−0.261830	−	0.291147i
$586$	8.38031	+	4.83837i	0.346187	+	0.199871i
$587$	−15.6788	+	27.1565i	−0.647134	+	1.12087i	0.336671	+	0.941622i	$0.390699\pi$
$587$	−15.6788	+	27.1565i	−0.647134	+	1.12087i	−0.983804	+	0.179246i	$0.942634\pi$
$588$		0			0
$589$	5.67809	+	9.83474i	0.233962	+	0.405234i
$590$			10.1786i			0.419048i
$591$	4.39479	−	5.42374i	0.180778	−	0.223103i
$592$	0.964714			0.0396495
$593$	4.56131	−	7.90043i	0.187311	−	0.324432i	−0.757042	−	0.653366i	$-0.773356\pi$
$593$	4.56131	−	7.90043i	0.187311	−	0.324432i	0.944353	+	0.328935i	$0.106690\pi$
$594$	6.71027	−	0.345533i	0.275326	−	0.0141774i
$595$		0			0
$596$	9.09927	+	5.25347i	0.372721	+	0.215190i
$597$	28.0679	+	4.45427i	1.14874	+	0.182301i
$598$	7.69828	+	4.44461i	0.314806	+	0.181753i
$599$	1.11316	+	0.642683i	0.0454825	+	0.0262593i	0.522569	−	0.852597i	$-0.324974\pi$
$599$	1.11316	+	0.642683i	0.0454825	+	0.0262593i	−0.477086	+	0.878856i	$0.658307\pi$
$600$	7.92529	−	9.78084i	0.323549	−	0.399301i
$601$	16.7126	+	9.64903i	0.681721	+	0.393592i	0.800503	−	0.599328i	$-0.204566\pi$
$601$	16.7126	+	9.64903i	0.681721	+	0.393592i	−0.118782	+	0.992920i	$0.537899\pi$
$602$		0			0
$603$	0.892309	+	0.290529i	0.0363376	+	0.0118312i
$604$	−11.5636	+	20.0287i	−0.470515	+	0.814956i
$605$	11.2300			0.456566
$606$	4.84799	+	0.769357i	0.196936	+	0.0312530i
$607$		−	38.9502i		−	1.58094i	−0.612501	−	0.790470i	$-0.709836\pi$
$607$		−	38.9502i		−	1.58094i	0.612501	−	0.790470i	$-0.290164\pi$
$608$	11.7269	+	20.3116i	0.475589	+	0.823744i
$609$		0			0
$610$	1.22429	−	2.12054i	0.0495702	−	0.0858581i
$611$	4.41645	+	2.54984i	0.178670	+	0.103155i
$612$	−3.60442	−	17.0083i	−0.145700	−	0.687521i
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	0.782847	−	0.622214i	$-0.213767\pi$
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	−0.930277	+	0.366859i	$0.880433\pi$
$614$	−3.09814	−	5.36613i	−0.125031	−	0.216560i
$615$	4.64189	−	29.2502i	0.187179	−	1.17948i
$616$		0			0
$617$	38.3641	−	22.1495i	1.54448	−	0.891706i	0.545932	−	0.837829i	$-0.316176\pi$
$617$	38.3641	−	22.1495i	1.54448	−	0.891706i	0.998548	−	0.0538763i	$-0.0171577\pi$
$618$	0.810113	−	5.10480i	0.0325875	−	0.205345i
$619$		−	0.471636i		−	0.0189566i	−0.999955	−	0.00947832i	$-0.996983\pi$
$619$		−	0.471636i		−	0.0189566i	0.999955	−	0.00947832i	$-0.00301709\pi$
$620$	−5.26660	+	3.04068i	−0.211512	+	0.122116i
$621$	26.2648	+	13.4128i	1.05397	+	0.538235i
$622$			11.6659i			0.467760i
$623$		0			0
$624$	−1.58448	−	4.13148i	−0.0634302	−	0.165391i
$625$	−2.04026			−0.0816105
$626$	2.43348	−	4.21491i	0.0972614	−	0.168462i
$627$	−11.6826	+	4.48046i	−0.466558	+	0.178932i
$628$	2.68168	−	1.54827i	0.107011	−	0.0617826i
$629$	−3.21558			−0.128213
$630$		0			0
$631$	10.2247			0.407038			0.203519	−	0.979071i	$-0.434762\pi$
$631$	10.2247			0.407038			0.203519	+	0.979071i	$0.434762\pi$
$632$	−26.9397	+	15.5536i	−1.07160	+	0.618691i
$633$	−3.26216	+	20.5560i	−0.129659	+	0.817029i
$634$	−7.88819	+	13.6627i	−0.313280	+	0.542617i
$635$	−1.27578			−0.0506277
$636$	−1.86268	+	2.29879i	−0.0738601	+	0.0911529i
$637$		0			0
$638$			12.6831i			0.502127i
$639$	5.72093	−	1.21239i	0.226316	−	0.0479612i
$640$	−12.9863	+	7.49767i	−0.513330	+	0.296371i
$641$			50.1815i			1.98205i	0.133677	+	0.991025i	$0.457321\pi$
$641$			50.1815i			1.98205i	−0.133677	+	0.991025i	$0.542679\pi$
$642$	5.48042	+	4.44072i	0.216295	+	0.175261i
$643$	−9.18633	+	5.30373i	−0.362274	+	0.209159i	−0.670078	−	0.742291i	$-0.733739\pi$
$643$	−9.18633	+	5.30373i	−0.362274	+	0.209159i	0.307804	+	0.951450i	$0.400406\pi$
$644$		0			0
$645$	17.6400	−	6.76520i	0.694573	−	0.266379i
$646$	−5.62524	−	9.74320i	−0.221322	−	0.383341i
$647$	−14.9203	−	25.8427i	−0.586577	−	1.01598i	−0.994677	−	0.103044i	$-0.967142\pi$
$647$	−14.9203	−	25.8427i	−0.586577	−	1.01598i	0.408100	−	0.912937i	$-0.366191\pi$
$648$	9.13483	+	20.5845i	0.358850	+	0.808636i
$649$	−15.2676	−	8.81474i	−0.599305	−	0.346009i
$650$	−2.27461	+	3.93975i	−0.0892177	+	0.154530i
$651$		0			0
$652$	−8.29664	−	14.3702i	−0.324921	−	0.562780i
$653$			35.2561i			1.37968i	0.723962	+	0.689839i	$0.242319\pi$
$653$			35.2561i			1.37968i	−0.723962	+	0.689839i	$0.757681\pi$
$654$	5.34430	+	13.9350i	0.208979	+	0.544904i
$655$	4.30561			0.168234
$656$	6.91868	−	11.9835i	0.270129	−	0.467877i
$657$	−5.62524	−	6.25510i	−0.219461	−	0.244035i
$658$		0			0
$659$	29.3751	+	16.9597i	1.14429	+	0.660656i	0.947489	−	0.319787i	$-0.103611\pi$
$659$	29.3751	+	16.9597i	1.14429	+	0.660656i	0.196801	+	0.980443i	$0.436945\pi$
$660$	−2.39933	−	6.25615i	−0.0933938	−	0.243520i
$661$	13.6550	+	7.88371i	0.531117	+	0.306641i	0.741471	−	0.670985i	$-0.234128\pi$
$661$	13.6550	+	7.88371i	0.531117	+	0.306641i	−0.210354	+	0.977625i	$0.567462\pi$
$662$	−9.08270	−	5.24390i	−0.353009	−	0.203810i
$663$	5.28139	+	13.7710i	0.205112	+	0.534821i
$664$	−15.6423	−	9.03106i	−0.607037	−	0.350473i
$665$		0			0
$666$	1.73576	−	0.367843i	0.0672592	−	0.0142536i
$667$	−27.8339	+	48.2097i	−1.07773	+	1.86669i
$668$	2.85196			0.110346
$669$	−16.3238	−	42.5636i	−0.631114	−	1.64560i
$670$			0.325186i			0.0125630i
$671$	2.12048	+	3.67279i	0.0818604	+	0.141786i
$672$		0			0
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	−0.972260	−	0.233904i	$-0.924850\pi$
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	0.688696	+	0.725050i	$0.258183\pi$
$674$	20.2294	+	11.6794i	0.779207	+	0.449875i
$675$	−6.86423	+	13.4415i	−0.264204	+	0.517363i
$676$	−6.11795	−	10.5966i	−0.235306	−	0.407562i
$677$	−1.99217	−	3.45054i	−0.0765654	−	0.132615i	0.825201	−	0.564840i	$-0.191062\pi$
$677$	−1.99217	−	3.45054i	−0.0765654	−	0.132615i	−0.901766	+	0.432225i	$0.857729\pi$
$678$	8.41936	−	3.22895i	0.323344	−	0.124007i
$679$		0			0
$680$	12.2482	−	7.07152i	0.469698	−	0.271181i
$681$	14.5449	+	11.7855i	0.557361	+	0.451623i
$682$			3.66013i			0.140154i
$683$	−19.2812	+	11.1320i	−0.737774	+	0.425954i	−0.821259	−	0.570555i	$-0.806728\pi$
$683$	−19.2812	+	11.1320i	−0.737774	+	0.425954i	0.0834856	+	0.996509i	$0.473395\pi$
$684$	−11.9457	−	13.2832i	−0.456754	−	0.507898i
$685$		−	17.2238i		−	0.658088i
$686$		0			0
$687$	10.5737	−	13.0494i	0.403414	−	0.497865i
$688$	8.82711			0.336530
$689$	1.25498	−	2.17368i	0.0478107	−	0.0828106i
$690$	−1.60176	+	10.0932i	−0.0609779	+	0.384243i
$691$	41.9003	−	24.1912i	1.59396	−	0.920275i	0.601346	−	0.798989i	$-0.294631\pi$
$691$	41.9003	−	24.1912i	1.59396	−	0.920275i	0.992618	−	0.121287i	$-0.0387020\pi$
$692$	22.5987			0.859073
$693$		0			0
$694$	−2.28882			−0.0868824
$695$	15.0752	−	8.70365i	0.571834	−	0.330148i
$696$	−39.6905	+	15.2219i	−1.50447	+	0.576986i
$697$	−23.0613	+	39.9433i	−0.873507	+	1.51296i
$698$	−5.37551			−0.203466
$699$	1.38147	+	3.60212i	0.0522520	+	0.136245i
$700$		0			0
$701$		−	23.3129i		−	0.880514i	−0.897872	−	0.440257i	$-0.854887\pi$
$701$		−	23.3129i		−	0.880514i	0.897872	−	0.440257i	$-0.145113\pi$
$702$	−4.42620	−	6.82937i	−0.167056	−	0.257758i
$703$	−2.86142	+	1.65204i	−0.107920	+	0.0623079i
$704$			3.34076i			0.125910i
$705$	−0.918917	+	5.79042i	−0.0346084	+	0.218080i
$706$	−7.07830	+	4.08666i	−0.266395	+	0.153803i
$707$		0			0
$708$	3.94512	−	24.8596i	0.148267	−	0.934281i
$709$	−8.83884	−	15.3093i	−0.331949	−	0.574953i	0.650945	−	0.759125i	$-0.274373\pi$
$709$	−8.83884	−	15.3093i	−0.331949	−	0.574953i	−0.982894	+	0.184172i	$0.941040\pi$
$710$	1.01324	+	1.75499i	0.0380263	+	0.0658635i
$711$	27.7307	−	24.9384i	1.03998	−	0.935262i
$712$	22.9270	+	13.2369i	0.859227	+	0.496075i
$713$	−8.03242	+	13.9126i	−0.300817	+	0.521030i
$714$		0			0
$715$	2.84208	+	4.92263i	0.106288	+	0.184096i
$716$		−	0.513128i		−	0.0191765i
$717$	31.5446	+	5.00600i	1.17805	+	0.186952i
$718$	3.96033			0.147798
$719$	−15.2102	+	26.3449i	−0.567246	+	0.982498i	0.429591	+	0.903024i	$0.358658\pi$
$719$	−15.2102	+	26.3449i	−0.567246	+	0.982498i	−0.996837	+	0.0794749i	$0.974676\pi$
$720$	3.78253	−	3.40164i	0.140967	−	0.126772i
$721$		0			0
$722$	1.80570	+	1.04252i	0.0672011	+	0.0387986i
$723$	7.05702	−	8.70928i	0.262453	−	0.323902i
$724$	4.21171	+	2.43163i	0.156527	+	0.0903708i
$725$	−24.6722	−	14.2445i	−0.916304	−	0.529028i
$726$	9.53089	+	1.51252i	0.353724	+	0.0561347i
$727$	−38.5219	−	22.2406i	−1.42870	−	0.824859i	−0.431680	−	0.902027i	$-0.642079\pi$
$727$	−38.5219	−	22.2406i	−1.42870	−	0.824859i	−0.997018	+	0.0771674i	$0.975412\pi$
$728$		0			0
$729$	−15.8303	−	21.8724i	−0.586308	−	0.810088i
$730$	1.45757	−	2.52459i	0.0539472	−	0.0934393i
$731$	−29.4224			−1.08823
$732$	−3.81202	+	4.70453i	−0.140896	+	0.173885i
$733$			45.2954i			1.67302i	0.547949	+	0.836512i	$0.315409\pi$
$733$			45.2954i			1.67302i	−0.547949	+	0.836512i	$0.684591\pi$
$734$	7.57755	+	13.1247i	0.279692	+	0.484442i
$735$		0			0
$736$	−16.5893	+	28.7335i	−0.611489	+	1.05913i
$737$	−0.487767	−	0.281612i	−0.0179671	−	0.0103733i
$738$	7.87910	−	24.1993i	0.290034	−	0.890789i
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	0.611739	−	0.791060i	$-0.290470\pi$
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	−0.990947	+	0.134252i	$0.957137\pi$
$740$	−0.884684	−	1.53232i	−0.0325216	−	0.0563291i
$741$	11.7747	+	9.54090i	0.432555	+	0.350494i
$742$		0			0
$743$	7.69885	−	4.44493i	0.282443	−	0.163069i	−0.352086	−	0.935968i	$-0.614527\pi$
$743$	7.69885	−	4.44493i	0.282443	−	0.163069i	0.634529	+	0.772899i	$0.281194\pi$
$744$	−11.4541	+	4.39281i	−0.419926	+	0.161048i
$745$		−	10.2472i		−	0.375429i
$746$	−9.55935	+	5.51909i	−0.349993	+	0.202068i
$747$	20.5910	+	6.70427i	0.753385	+	0.245296i
$748$			10.4349i			0.381538i
$749$		0			0
$750$	−14.0572	−	2.23082i	−0.513295	−	0.0814580i
$751$	−25.0017			−0.912324			−0.456162	−	0.889897i	$-0.650776\pi$
$751$	−25.0017			−0.912324			−0.456162	+	0.889897i	$0.650776\pi$
$752$	−1.36963	+	2.37227i	−0.0499454	+	0.0865079i
$753$	0.560735	+	0.454357i	0.0204343	+	0.0165577i
$754$	13.3037	−	7.68089i	0.484492	−	0.279722i
$755$	22.5555			0.820878
$756$		0			0
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$	20.1282	−	11.6210i	0.731089	−	0.422094i
$759$	−13.7523	−	11.1434i	−0.499179	−	0.404478i
$760$	7.26616	−	12.5854i	0.263571	−	0.456519i
$761$	3.16732			0.114815			0.0574075	−	0.998351i	$-0.481717\pi$
$761$	3.16732			0.114815			0.0574075	+	0.998351i	$0.481717\pi$
$762$	−1.08275	−	0.171828i	−0.0392237	−	0.00622465i
$763$		0			0
$764$			10.9703i			0.396891i
$765$	−12.6079	+	11.3383i	−0.455839	+	0.409938i
$766$	12.3361	−	7.12228i	0.445723	−	0.257338i
$767$			21.3529i			0.771009i
$768$	−18.0324	+	6.91569i	−0.650687	+	0.249548i
$769$	−2.48873	+	1.43687i	−0.0897460	+	0.0518149i	−0.544201	−	0.838955i	$-0.683167\pi$
$769$	−2.48873	+	1.43687i	−0.0897460	+	0.0518149i	0.454455	+	0.890770i	$0.349834\pi$
$770$		0			0
$771$	−28.4330	−	23.0389i	−1.02399	−	0.829725i
$772$	−9.66868	−	16.7467i	−0.347984	−	0.602725i
$773$	−6.15679	−	10.6639i	−0.221444	−	0.383553i	0.733802	−	0.679363i	$-0.237744\pi$
$773$	−6.15679	−	10.6639i	−0.221444	−	0.383553i	−0.955247	+	0.295810i	$0.904410\pi$
$774$	15.8821	−	3.36576i	0.570871	−	0.120980i
$775$	−7.12002	−	4.11075i	−0.255759	−	0.147662i
$776$	−19.4053	+	33.6110i	−0.696610	+	1.20656i
$777$		0			0
$778$	−1.83234	−	3.17371i	−0.0656926	−	0.113783i
$779$			47.3920i			1.69799i
$780$	−5.10925	+	6.30548i	−0.182940	+	0.225772i
$781$	−3.50988			−0.125594
$782$	7.95765	−	13.7831i	0.284565	−	0.492881i
$783$	42.7682	−	27.7186i	1.52841	−	0.990581i
$784$		0			0
$785$	−2.61539	−	1.51000i	−0.0933473	−	0.0538941i
$786$	3.65415	+	0.579899i	0.130339	+	0.0206843i
$787$	3.30450	+	1.90785i	0.117793	+	0.0680076i	0.557739	−	0.830017i	$-0.311669\pi$
$787$	3.30450	+	1.90785i	0.117793	+	0.0680076i	−0.439946	+	0.898024i	$0.645002\pi$
$788$	−5.18056	−	2.99100i	−0.184550	−	0.106550i
$789$	−24.2572	+	29.9365i	−0.863577	+	1.06577i
$790$	11.1923	+	6.46186i	0.398203	+	0.229903i
$791$		0			0
$792$	−2.80218	−	13.2228i	−0.0995713	−	0.469851i
$793$	2.56834	−	4.44849i	0.0912044	−	0.157971i
$794$	−9.56045			−0.339288
$795$	2.84992	+	0.452271i	0.101076	+	0.0160404i
$796$		−	24.3530i		−	0.863171i
$797$	−24.5682	−	42.5535i	−0.870252	−	1.50732i	−0.861736	−	0.507357i	$-0.830623\pi$
$797$	−24.5682	−	42.5535i	−0.870252	−	1.50732i	−0.00851609	−	0.999964i	$-0.502711\pi$
$798$		0			0
$799$	4.56524	−	7.90724i	0.161507	−	0.279738i
$800$	−14.7049	−	8.48988i	−0.519897	−	0.300162i
$801$	−30.1805	−	9.82653i	−1.06638	−	0.347203i
$802$	5.87742	+	10.1800i	0.207539	+	0.359468i
$803$	2.52453	+	4.37261i	0.0890886	+	0.154306i
$804$	0.126038	−	0.794212i	0.00444503	−	0.0280097i
$805$		0			0
$806$	3.83924	−	2.21659i	0.135231	−	0.0780759i
$807$	7.88163	−	49.6649i	0.277446	−	1.74829i
$808$		−	9.87437i		−	0.347379i
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.395350	−	0.918531i	$-0.370623\pi$
$809$	39.4929	−	22.8012i	1.38850	−	0.801648i	0.993146	+	0.116882i	$0.0372900\pi$
$810$	5.50866	−	7.56265i	0.193554	−	0.265725i
$811$			39.1391i			1.37436i	0.726488	+	0.687180i	$0.241151\pi$
$811$			39.1391i			1.37436i	−0.726488	+	0.687180i	$0.758849\pi$
$812$		0			0
$813$	14.9087	+	38.8739i	0.522872	+	1.36337i
$814$	−1.06492			−0.0373253
$815$	−8.09155	+	14.0150i	−0.283435	+	0.490923i
$816$	−7.39702	+	2.83687i	−0.258948	+	0.0993103i
$817$	−26.1819	+	15.1161i	−0.915988	+	0.528846i
$818$	3.11476			0.108905
$819$		0			0
$820$	−25.3789			−0.886269
$821$	10.2976	−	5.94530i	0.359387	−	0.207492i	−0.309425	−	0.950924i	$-0.600136\pi$
$821$	10.2976	−	5.94530i	0.359387	−	0.207492i	0.668812	+	0.743432i	$0.266803\pi$
$822$	2.31978	−	14.6178i	0.0809117	−	0.509853i
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	−0.891173	−	0.453663i	$-0.850117\pi$
$823$	−1.51195	+	2.61877i	−0.0527031	+	0.0912844i	0.838470	+	0.544947i	$0.183450\pi$
$824$	−10.3975			−0.362213
$825$	5.70283	−	7.03803i	0.198547	−	0.245033i
$826$		0			0
$827$			15.2436i			0.530071i	0.964239	+	0.265035i	$0.0853836\pi$
$827$			15.2436i			0.530071i	−0.964239	+	0.265035i	$0.914616\pi$
$828$	7.82405	−	24.0302i	0.271904	−	0.835107i
$829$	29.7306	−	17.1649i	1.03259	−	0.596163i	0.114861	−	0.993382i	$-0.463358\pi$
$829$	29.7306	−	17.1649i	1.03259	−	0.596163i	0.917724	+	0.397218i	$0.130024\pi$
$830$			7.50402i			0.260468i
$831$	−10.8531	−	8.79411i	−0.376489	−	0.305064i
$832$	3.50424	−	2.02317i	0.121488	−	0.0701409i
$833$		0			0
$834$	13.9665	−	5.35635i	0.483619	−	0.185475i
$835$	−1.39073	−	2.40882i	−0.0481283	−	0.0833606i
$836$	5.36105	+	9.28561i	0.185416	+	0.321150i
$837$	12.3422	−	7.99915i	0.426610	−	0.276491i
$838$	−11.7088	−	6.76006i	−0.404473	−	0.233522i
$839$	6.16024	−	10.6698i	0.212675	−	0.368364i	−0.739876	−	0.672744i	$-0.765116\pi$
$839$	6.16024	−	10.6698i	0.212675	−	0.368364i	0.952551	+	0.304379i	$0.0984491\pi$
$840$		0			0
$841$	33.6008	+	58.1983i	1.15865	+	2.00684i
$842$			1.31202i			0.0452153i
$843$	8.65677	+	22.5722i	0.298155	+	0.777426i
$844$	17.8354			0.613920
$845$	−5.96672	+	10.3347i	−0.205262	+	0.355523i
$846$	−1.55976	+	4.79054i	−0.0536257	+	0.164702i
$847$		0			0
$848$	1.16758	+	0.674104i	0.0400949	+	0.0231488i
$849$	9.63667	+	25.1272i	0.330730	+	0.862364i
$850$	7.05374	+	4.07248i	0.241941	+	0.139685i
$851$	−4.04786	−	2.33703i	−0.138759	−	0.0801124i
$852$	−1.79446	−	4.67898i	−0.0614772	−	0.160299i
$853$	3.92537	+	2.26631i	0.134402	+	0.0775971i	0.565693	−	0.824616i	$-0.308609\pi$
$853$	3.92537	+	2.26631i	0.134402	+	0.0775971i	−0.431291	+	0.902213i	$0.641942\pi$
$854$		0			0
$855$	−5.39408	+	16.5670i	−0.184474	+	0.566579i
$856$	7.09472	−	12.2884i	0.242493	−	0.420010i
$857$	32.2614			1.10203			0.551014	−	0.834496i	$-0.314241\pi$
$857$	32.2614			1.10203			0.551014	+	0.834496i	$0.314241\pi$
$858$	1.74906	+	4.56060i	0.0597119	+	0.155696i
$859$		−	17.6335i		−	0.601647i	−0.953680	−	0.300824i	$-0.902738\pi$
$859$		−	17.6335i		−	0.601647i	0.953680	−	0.300824i	$-0.0972615\pi$
$860$	−8.09483	−	14.0207i	−0.276032	−	0.478101i
$861$		0			0
$862$	5.16329	−	8.94307i	0.175862	−	0.304602i
$863$	−26.4091	−	15.2473i	−0.898975	−	0.519023i	−0.0221074	−	0.999756i	$-0.507038\pi$
$863$	−26.4091	−	15.2473i	−0.898975	−	0.519023i	−0.876867	+	0.480732i	$0.840371\pi$
$864$	25.4903	−	16.5206i	0.867197	−	0.562041i
$865$	−11.0200	−	19.0873i	−0.374693	−	0.648987i
$866$	0.797632	+	1.38154i	0.0271046	+	0.0469466i
$867$	−2.83668	+	1.08791i	−0.0963388	+	0.0369474i
$868$		0			0
$869$	−19.3851	+	11.1920i	−0.657594	+	0.379662i
$870$	13.7216	+	11.1185i	0.465207	+	0.376951i
$871$			0.682180i			0.0231148i
$872$	26.0006	−	15.0115i	0.880492	−	0.508352i
$873$	14.4057	−	44.2445i	0.487557	−	1.49745i
$874$		−	16.3533i		−	0.553160i
$875$		0			0
$876$	−4.53838	+	5.60095i	−0.153338	+	0.189239i
$877$	8.80725			0.297400			0.148700	−	0.988882i	$-0.452491\pi$
$877$	8.80725			0.297400			0.148700	+	0.988882i	$0.452491\pi$
$878$	3.60693	−	6.24738i	0.121728	−	0.210839i
$879$	−3.65788	+	23.0496i	−0.123377	+	0.777444i
$880$	−2.64417	+	1.52661i	−0.0891348	+	0.0514620i
$881$	38.6776			1.30308			0.651540	−	0.758614i	$-0.274123\pi$
$881$	38.6776			1.30308			0.651540	+	0.758614i	$0.274123\pi$
$882$		0			0
$883$	37.4489			1.26026			0.630128	−	0.776491i	$-0.283002\pi$
$883$	37.4489			1.26026			0.630128	+	0.776491i	$0.283002\pi$
$884$	10.9455	−	6.31940i	0.368137	−	0.212544i
$885$	−22.9207	+	8.79043i	−0.770471	+	0.295487i
$886$	−4.98890	+	8.64103i	−0.167605	+	0.290301i
$887$	−27.4050			−0.920171			−0.460086	−	0.887875i	$-0.652181\pi$
$887$	−27.4050			−0.920171			−0.460086	+	0.887875i	$0.652181\pi$
$888$	−1.27809	−	3.33256i	−0.0428898	−	0.111833i
$889$		0			0
$890$		−	10.9987i		−	0.368679i
$891$	6.57318	+	14.8121i	0.220210	+	0.496223i
$892$	−33.8305	+	19.5321i	−1.13273	+	0.653982i
$893$		−	9.38179i		−	0.313950i
$894$	1.38014	−	8.69676i	0.0461589	−	0.290863i
$895$	−0.433397	+	0.250222i	−0.0144869	+	0.00836400i
$896$		0			0
$897$	−3.36019	+	21.1737i	−0.112194	+	0.706971i
$898$	−3.79299	−	6.56965i	−0.126574	−	0.219232i
$899$	13.8811	+	24.0428i	0.462962	+	0.801873i
$900$	12.2979	+	4.00411i	0.409931	+	0.133470i
$901$	−3.89177	−	2.24691i	−0.129654	−	0.0748556i
$902$	−7.63729	+	13.2282i	−0.254294	+	0.440450i
$903$		0			0
$904$	−9.06971	−	15.7092i	−0.301654	−	0.522480i
$905$		−	4.74305i		−	0.157664i
$906$	19.1427	+	3.03788i	0.635975	+	0.100927i
$907$	−23.6433			−0.785062			−0.392531	−	0.919739i	$-0.628400\pi$
$907$	−23.6433			−0.785062			−0.392531	+	0.919739i	$0.628400\pi$
$908$	8.02097	−	13.8927i	0.266185	−	0.461046i
$909$	2.45433	+	11.5813i	0.0814049	+	0.384128i
$910$		0			0
$911$	−3.92249	−	2.26465i	−0.129958	−	0.0750313i	0.433612	−	0.901100i	$-0.357239\pi$
$911$	−3.92249	−	2.26465i	−0.129958	−	0.0750313i	−0.563570	+	0.826069i	$0.690572\pi$
$912$	−5.12485	+	6.32473i	−0.169701	+	0.209433i
$913$	−11.2557	−	6.49851i	−0.372511	−	0.215069i
$914$	3.18008	+	1.83602i	0.105188	+	0.0607301i
$915$	5.83243	+	0.925585i	0.192814	+	0.0305989i
$916$	−12.4643	−	7.19626i	−0.411832	−	0.237771i
$917$		0			0
$918$	−12.2274	+	7.92469i	−0.403563	+	0.261554i
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	−0.439695	−	0.898147i	$-0.644913\pi$
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	0.997666	−	0.0682866i	$-0.0217532\pi$
$920$	20.5579			0.677774
$921$	9.40808	−	11.6108i	0.310007	−	0.382589i
$922$			5.98508i			0.197108i
$923$	2.12559	+	3.68164i	0.0699648	+	0.121183i
$924$		0			0
$925$	1.19602	−	2.07157i	0.0393249	−	0.0681127i
$926$	−12.4568	−	7.19192i	−0.409355	−	0.236341i
$927$	12.1948	−	2.58434i	0.400531	−	0.0848809i
$928$	28.6685	+	49.6554i	0.941091	+	1.63002i
$929$	−16.4582	−	28.5064i	−0.539976	−	0.935266i	−0.998905	−	0.0467929i	$-0.985100\pi$
$929$	−16.4582	−	28.5064i	−0.539976	−	0.935266i	0.458928	−	0.888473i	$-0.348233\pi$
$930$	3.95985	+	3.20861i	0.129849	+	0.105215i
$931$		0			0
$932$	2.86305	−	1.65298i	0.0937824	−	0.0541453i
$933$	−26.2698	+	10.0749i	−0.860033	+	0.329836i
$934$			14.9229i			0.488293i
$935$	8.81350	−	5.08848i	0.288232	−	0.166411i
$936$	−12.1728	+	10.9470i	−0.397881	+	0.357815i
$937$		−	38.1057i		−	1.24486i	−0.782676	−	0.622430i	$-0.786146\pi$
$937$		−	38.1057i		−	1.24486i	0.782676	−	0.622430i	$-0.213854\pi$
$938$		0			0
$939$	11.5929	+	1.83975i	0.378320	+	0.0600379i
$940$	5.02404			0.163866
$941$	9.93855	−	17.2141i	0.323987	−	0.561163i	−0.657319	−	0.753612i	$-0.728310\pi$
$941$	9.93855	−	17.2141i	0.323987	−	0.561163i	0.981307	+	0.192449i	$0.0616431\pi$
$942$	−2.01630	−	1.63378i	−0.0656945	−	0.0532314i
$943$	−58.0603	+	33.5211i	−1.89070	+	1.09160i
$944$	−11.4696			−0.373304
$945$		0			0
$946$	−9.74394			−0.316803
$947$	17.9696	−	10.3747i	0.583933	−	0.337134i	−0.178762	−	0.983892i	$-0.557209\pi$
$947$	17.9696	−	10.3747i	0.583933	−	0.337134i	0.762695	+	0.646759i	$0.223876\pi$
$948$	−24.8307	−	20.1200i	−0.806463	−	0.653467i
$949$	3.05772	−	5.29613i	0.0992578	−	0.171919i
$950$	8.36914			0.271531
$951$	−37.5787	−	5.96359i	−1.21857	−	0.193383i
$952$		0			0
$953$			12.8345i			0.415751i	0.978155	+	0.207876i	$0.0666549\pi$
$953$			12.8345i			0.415751i	−0.978155	+	0.207876i	$0.933345\pi$
$954$	2.35780	+	0.767680i	0.0763365	+	0.0248546i
$955$	9.26571	−	5.34956i	0.299831	−	0.173108i
$956$		−	27.3696i		−	0.885195i
$957$	−28.5603	+	10.9533i	−0.923222	+	0.354070i
$958$	−19.9408	+	11.5128i	−0.644258	+	0.371962i
$959$		0			0
$960$	3.61433	+	2.92864i	0.116652	+	0.0945215i
$961$	−11.4941	−	19.9084i	−0.370778	−	0.642207i
$962$	0.644915	+	1.11703i	0.0207929	+	0.0360143i
$963$	−5.26682	+	16.1761i	−0.169721	+	0.521268i
$964$	−8.31878	−	4.80285i	−0.267930	−	0.154689i
$965$	−9.42969	+	16.3327i	−0.303552	+	0.525768i
$966$		0			0
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	−0.995994	−	0.0894195i	$-0.971499\pi$
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	0.420557	−	0.907266i	$-0.361835\pi$
$968$		−	19.4125i		−	0.623941i
$969$	17.0821	−	21.0815i	0.548756	−	0.677236i
$970$	16.1241			0.517714
$971$	−14.5129	+	25.1370i	−0.465740	+	0.806686i	−0.999235	−	0.0391177i	$-0.987545\pi$
$971$	−14.5129	+	25.1370i	−0.465740	+	0.806686i	0.533494	+	0.845804i	$0.320879\pi$
$972$	−16.3852	+	16.3354i	−0.525554	+	0.523959i
$973$		0			0
$974$	−14.7247	−	8.50130i	−0.471809	−	0.272399i
$975$	−10.8361	−	1.71964i	−0.347032	−	0.0550726i
$976$	2.38949	+	1.37957i	0.0764856	+	0.0441590i
$977$	7.73439	+	4.46545i	0.247445	+	0.142862i	0.618594	−	0.785711i	$-0.287703\pi$
$977$	7.73439	+	4.46545i	0.247445	+	0.142862i	−0.371149	+	0.928573i	$0.621036\pi$
$978$	−8.75487	+	10.8046i	−0.279950	+	0.345494i
$979$	16.4977	+	9.52495i	0.527268	+	0.304419i
$980$		0			0
$981$	−26.7641	+	24.0690i	−0.854512	+	0.768466i
$982$	−6.41288	+	11.1074i	−0.204643	+	0.354452i
$983$	52.2693			1.66713			0.833566	−	0.552420i	$-0.186296\pi$
$983$	52.2693			1.66713			0.833566	+	0.552420i	$0.186296\pi$
$984$	−50.5625	−	8.02407i	−1.61187	−	0.255798i
$985$			5.83413i			0.185891i
$986$	−13.7519	−	23.8190i	−0.437950	−	0.758552i
$987$		0			0
$988$	6.49333	−	11.2468i	0.206580	−	0.357807i
$989$	−37.0378	−	21.3838i	−1.17773	−	0.679964i
$990$	−4.17541	+	3.75496i	−0.132703	+	0.119340i
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	−0.969789	−	0.243946i	$-0.921558\pi$
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	0.273631	−	0.961835i	$-0.411775\pi$
$992$	8.27329	+	14.3298i	0.262677	+	0.454970i
$993$	3.96447	−	24.9815i	0.125809	−	0.792764i
$994$		0			0
$995$	−20.5690	+	11.8755i	−0.652082	+	0.376480i
$996$	2.90847	−	18.3273i	0.0921585	−	0.580723i
$997$		−	44.9975i		−	1.42508i	−0.701630	−	0.712542i	$-0.747544\pi$
$997$		−	44.9975i		−	1.42508i	0.701630	−	0.712542i	$-0.252456\pi$
$998$	14.3797	−	8.30215i	0.455183	−	0.262800i
$999$	2.32735	+	3.59097i	0.0736341	+	0.113613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.b.362.2		10
3.2	odd	2		1323.2.s.b.656.4		10
7.2	even	3		441.2.o.d.146.4		10
7.3	odd	6		441.2.i.b.227.2		10
7.4	even	3		63.2.i.b.38.2	yes	10
7.5	odd	6		441.2.o.c.146.4		10
7.6	odd	2		63.2.s.b.47.2	yes	10
9.4	even	3		1323.2.i.b.1097.2		10
9.5	odd	6		441.2.i.b.68.4		10
21.2	odd	6		1323.2.o.c.440.2		10
21.5	even	6		1323.2.o.d.440.2		10
21.11	odd	6		189.2.i.b.143.4		10
21.17	even	6		1323.2.i.b.521.4		10
21.20	even	2		189.2.s.b.89.4		10
28.11	odd	6		1008.2.ca.b.353.3		10
28.27	even	2		1008.2.df.b.929.2		10
63.4	even	3		189.2.s.b.17.4		10
63.5	even	6		441.2.o.d.293.4		10
63.11	odd	6		567.2.p.c.80.4		10
63.13	odd	6		189.2.i.b.152.2		10
63.20	even	6		567.2.p.d.404.2		10
63.23	odd	6		441.2.o.c.293.4		10
63.25	even	3		567.2.p.d.80.2		10
63.31	odd	6		1323.2.s.b.962.4		10
63.32	odd	6		63.2.s.b.59.2	yes	10
63.34	odd	6		567.2.p.c.404.4		10
63.40	odd	6		1323.2.o.c.881.2		10
63.41	even	6		63.2.i.b.5.4	✓	10
63.58	even	3		1323.2.o.d.881.2		10
63.59	even	6	inner	441.2.s.b.374.2		10
84.11	even	6		3024.2.ca.b.2033.4		10
84.83	odd	2		3024.2.df.b.1601.4		10
252.67	odd	6		3024.2.df.b.17.4		10
252.95	even	6		1008.2.df.b.689.2		10
252.139	even	6		3024.2.ca.b.2609.4		10
252.167	odd	6		1008.2.ca.b.257.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	63.41	even	6
63.2.i.b.38.2	yes	10	7.4	even	3
63.2.s.b.47.2	yes	10	7.6	odd	2
63.2.s.b.59.2	yes	10	63.32	odd	6
189.2.i.b.143.4		10	21.11	odd	6
189.2.i.b.152.2		10	63.13	odd	6
189.2.s.b.17.4		10	63.4	even	3
189.2.s.b.89.4		10	21.20	even	2
441.2.i.b.68.4		10	9.5	odd	6
441.2.i.b.227.2		10	7.3	odd	6
441.2.o.c.146.4		10	7.5	odd	6
441.2.o.c.293.4		10	63.23	odd	6
441.2.o.d.146.4		10	7.2	even	3
441.2.o.d.293.4		10	63.5	even	6
441.2.s.b.362.2		10	1.1	even	1	trivial
441.2.s.b.374.2		10	63.59	even	6	inner
567.2.p.c.80.4		10	63.11	odd	6
567.2.p.c.404.4		10	63.34	odd	6
567.2.p.d.80.2		10	63.25	even	3
567.2.p.d.404.2		10	63.20	even	6
1008.2.ca.b.257.3		10	252.167	odd	6
1008.2.ca.b.353.3		10	28.11	odd	6
1008.2.df.b.689.2		10	252.95	even	6
1008.2.df.b.929.2		10	28.27	even	2
1323.2.i.b.521.4		10	21.17	even	6
1323.2.i.b.1097.2		10	9.4	even	3
1323.2.o.c.440.2		10	21.2	odd	6
1323.2.o.c.881.2		10	63.40	odd	6
1323.2.o.d.440.2		10	21.5	even	6
1323.2.o.d.881.2		10	63.58	even	3
1323.2.s.b.656.4		10	3.2	odd	2
1323.2.s.b.962.4		10	63.31	odd	6
3024.2.ca.b.2033.4		10	84.11	even	6
3024.2.ca.b.2609.4		10	252.139	even	6
3024.2.df.b.17.4		10	252.67	odd	6
3024.2.df.b.1601.4		10	84.83	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.621951 + 0.359083i) q^{2} +(-1.34572 - 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} +1.44755 q^{5} +(1.22853 + 0.194963i) q^{6} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +O(q^{10})\)	\(q+(-0.621951 + 0.359083i) q^{2} +(-1.34572 - 1.09042i) q^{3} +(-0.742118 + 1.28539i) q^{4} +1.44755 q^{5} +(1.22853 + 0.194963i) q^{6} -2.50226i q^{8} +(0.621951 + 2.93482i) q^{9} +(-0.900304 + 0.519791i) q^{10} -1.80056i q^{11} +(2.40030 - 0.920553i) q^{12} +(-1.88867 + 1.09042i) q^{13} +(-1.94800 - 1.57844i) q^{15} +(-0.585716 - 1.01449i) q^{16} +(1.95230 + 3.38149i) q^{17} +(-1.44067 - 1.60198i) q^{18} +(3.47456 + 2.00604i) q^{19} +(-1.07425 + 1.86066i) q^{20} +(0.646552 + 1.11986i) q^{22} +5.67561i q^{23} +(-2.72853 + 3.36736i) q^{24} -2.90460 q^{25} +(0.783106 - 1.35638i) q^{26} +(2.36323 - 4.62765i) q^{27} +(8.49418 + 4.90412i) q^{29} +(1.77835 + 0.282218i) q^{30} +(2.45129 + 1.41525i) q^{31} +(5.06262 + 2.92290i) q^{32} +(-1.96338 + 2.42306i) q^{33} +(-2.42847 - 1.40208i) q^{34} +(-4.23394 - 1.37854i) q^{36} +(-0.411767 + 0.713202i) q^{37} -2.88134 q^{38} +(3.73065 + 0.592040i) q^{39} -3.62215i q^{40} +(5.90617 + 10.2298i) q^{41} +(-3.76766 + 6.52578i) q^{43} +(2.31442 + 1.33623i) q^{44} +(0.900304 + 4.24830i) q^{45} +(-2.03802 - 3.52995i) q^{46} +(-1.16920 - 2.02511i) q^{47} +(-0.318012 + 2.00390i) q^{48} +(1.80652 - 1.04299i) q^{50} +(1.05999 - 6.67939i) q^{51} -3.23689i q^{52} +(-0.996713 + 0.575453i) q^{53} +(0.191903 + 3.72677i) q^{54} -2.60640i q^{55} +(-2.48837 - 6.48831i) q^{57} -7.04395 q^{58} +(4.89555 - 8.47934i) q^{59} +(3.47456 - 1.33255i) q^{60} +(-2.03980 + 1.17768i) q^{61} -2.03277 q^{62} -1.85540 q^{64} +(-2.73394 + 1.57844i) q^{65} +(0.351042 - 2.21204i) q^{66} +(0.156402 - 0.270897i) q^{67} -5.79536 q^{68} +(6.18882 - 7.63781i) q^{69} -1.94933i q^{71} +(7.34369 - 1.55628i) q^{72} +(-2.42847 + 1.40208i) q^{73} -0.591435i q^{74} +(3.90880 + 3.16725i) q^{75} +(-5.15706 + 2.97743i) q^{76} +(-2.53287 + 0.971396i) q^{78} +(-6.21583 - 10.7661i) q^{79} +(-0.847852 - 1.46852i) q^{80} +(-8.22635 + 3.65063i) q^{81} +(-7.34669 - 4.24162i) q^{82} +(3.60916 - 6.25124i) q^{83} +(2.82605 + 4.89486i) q^{85} -5.41161i q^{86} +(-6.08326 - 15.8619i) q^{87} -4.50548 q^{88} +(-5.28999 + 9.16253i) q^{89} +(-2.08544 - 2.31895i) q^{90} +(-7.29536 - 4.21198i) q^{92} +(-1.75553 - 4.57748i) q^{93} +(1.45436 + 0.839677i) q^{94} +(5.02959 + 2.90383i) q^{95} +(-3.62569 - 9.45383i) q^{96} +(-13.4322 - 7.75510i) q^{97} +(5.28433 - 1.11986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 12 q^{6}+O(q^{10}) \) 10 * q + 4 * q^4 + 12 * q^6	\( 10 q + 4 q^{4} + 12 q^{6} + 15 q^{10} - 6 q^{13} - 3 q^{15} - 6 q^{16} + 12 q^{17} - 18 q^{18} - 3 q^{19} + 3 q^{20} + 5 q^{22} - 27 q^{24} - 14 q^{25} - 3 q^{26} - 27 q^{27} - 15 q^{29} + 9 q^{31} + 48 q^{32} + 9 q^{33} - 3 q^{34} - 18 q^{36} + 6 q^{37} - 36 q^{38} + 12 q^{39} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 15 q^{45} - 13 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} - 24 q^{51} - 9 q^{53} - 27 q^{54} - 36 q^{57} - 16 q^{58} + 18 q^{59} - 3 q^{60} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} + 33 q^{66} - 10 q^{67} + 54 q^{68} + 3 q^{69} + 18 q^{72} - 3 q^{73} + 21 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} + 30 q^{80} - 48 q^{81} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 30 q^{87} + 16 q^{88} - 24 q^{89} - 24 q^{90} + 39 q^{92} + 6 q^{93} + 3 q^{94} - 3 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 4 * q^4 + 12 * q^6 + 15 * q^10 - 6 * q^13 - 3 * q^15 - 6 * q^16 + 12 * q^17 - 18 * q^18 - 3 * q^19 + 3 * q^20 + 5 * q^22 - 27 * q^24 - 14 * q^25 - 3 * q^26 - 27 * q^27 - 15 * q^29 + 9 * q^31 + 48 * q^32 + 9 * q^33 - 3 * q^34 - 18 * q^36 + 6 * q^37 - 36 * q^38 + 12 * q^39 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 15 * q^45 - 13 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 - 24 * q^51 - 9 * q^53 - 27 * q^54 - 36 * q^57 - 16 * q^58 + 18 * q^59 - 3 * q^60 - 12 * q^61 - 12 * q^62 + 6 * q^64 - 3 * q^65 + 33 * q^66 - 10 * q^67 + 54 * q^68 + 3 * q^69 + 18 * q^72 - 3 * q^73 + 21 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 + 30 * q^80 - 48 * q^81 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 30 * q^87 + 16 * q^88 - 24 * q^89 - 24 * q^90 + 39 * q^92 + 6 * q^93 + 3 * q^94 - 3 * q^96 - 6 * q^97 + 21 * q^99

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