LMFDB - Embedded newform 441.2.s.b.374.2

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			374.2
Root			$0.187540 + 0.324828i$ of defining polynomial
Character	$\chi$	$=$	441.374
Dual form			441.2.s.b.362.2

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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	0.263721	−	0.964599i	$-0.415050\pi$
$2$	−0.621951	−	0.359083i	−0.439785	−	0.253910i	−0.703507	+	0.710689i	$0.748383\pi$
$3$	−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	$0.0875015\pi$
$11$			1.80056i			0.542890i	−0.962454	+	0.271445i	$0.912499\pi$
$12$	2.40030	+	0.920553i	0.692908	+	0.265741i
$13$	−1.88867	−	1.09042i	−0.523823	−	0.302429i	0.214675	−	0.976686i	$-0.431131\pi$
$13$	−1.88867	−	1.09042i	−0.523823	−	0.302429i	−0.738497	+	0.674256i	$0.764464\pi$
$14$		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	−0.526037	−	0.850462i	$-0.676323\pi$
$17$	1.95230	−	3.38149i	0.473503	−	0.820131i	0.999540	+	0.0303308i	$0.00965608\pi$
$18$	−1.44067	+	1.60198i	−0.339569	+	0.377591i
$19$	3.47456	−	2.00604i	0.797118	−	0.460216i	−0.0453446	−	0.998971i	$-0.514439\pi$
$19$	3.47456	−	2.00604i	0.797118	−	0.460216i	0.842462	+	0.538755i	$0.181105\pi$
$20$	−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	$-0.798448\pi$
$23$		−	5.67561i		−	1.18345i	0.806141	−	0.591723i	$-0.201552\pi$
$24$	−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	0.582100	−	0.813117i	$-0.302231\pi$
$29$	8.49418	−	4.90412i	1.57733	−	0.910672i	0.995230	−	0.0975551i	$-0.0311022\pi$
$30$	1.77835	−	0.282218i	0.324681	−	0.0515257i
$31$	2.45129	−	1.41525i	0.440264	−	0.254187i	−0.263445	−	0.964674i	$-0.584859\pi$
$31$	2.45129	−	1.41525i	0.440264	−	0.254187i	0.703710	+	0.710488i	$0.251526\pi$
$32$	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	0.830192	−	0.557478i	$-0.188231\pi$
$37$	−0.411767	−	0.713202i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$38$	−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	0.126681	−	0.991943i	$-0.459567\pi$
$41$	5.90617	−	10.2298i	0.922389	−	1.59762i	0.795708	−	0.605681i	$-0.207099\pi$
$42$		0			0
$43$	−3.76766	−	6.52578i	−0.574563	−	0.995172i	−0.996089	−	0.0883555i	$-0.971839\pi$
$43$	−3.76766	−	6.52578i	−0.574563	−	0.995172i	0.421526	−	0.906816i	$-0.361494\pi$
$44$	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	−0.938610	−	0.344979i	$-0.887886\pi$
$47$	−1.16920	+	2.02511i	−0.170545	+	0.295392i	0.768066	+	0.640371i	$0.221219\pi$
$48$	−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	0.429981	−	0.902838i	$-0.358520\pi$
$53$	−0.996713	−	0.575453i	−0.136909	−	0.0790445i	−0.566890	+	0.823793i	$0.691854\pi$
$54$	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	0.986013	+	0.166669i	$0.0533013\pi$
$59$	4.89555	+	8.47934i	0.637346	+	1.10392i	−0.348666	+	0.937247i	$0.613365\pi$
$60$	3.47456	+	1.33255i	0.448563	+	0.172031i
$61$	−2.03980	−	1.17768i	−0.261170	−	0.150786i	0.363698	−	0.931517i	$-0.381514\pi$
$61$	−2.03980	−	1.17768i	−0.261170	−	0.150786i	−0.624868	+	0.780730i	$0.714847\pi$
$62$	−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	0.875421	−	0.483361i	$-0.160584\pi$
$67$	0.156402	+	0.270897i	0.0191076	+	0.0330953i	−0.856313	+	0.516456i	$0.827251\pi$
$68$	−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	$0.0369019\pi$
$71$			1.94933i			0.231343i	−0.993288	+	0.115671i	$0.963098\pi$
$72$	7.34369	+	1.55628i	0.865463	+	0.183410i
$73$	−2.42847	−	1.40208i	−0.284231	−	0.164101i	0.351106	−	0.936336i	$-0.385806\pi$
$73$	−2.42847	−	1.40208i	−0.284231	−	0.164101i	−0.635337	+	0.772235i	$0.719139\pi$
$74$			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	0.269361	+	0.963039i	$0.413187\pi$
$79$	−6.21583	+	10.7661i	−0.699336	+	1.21128i	−0.968697	+	0.248246i	$0.920146\pi$
$80$	−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	0.993248	−	0.116010i	$-0.0370104\pi$
$83$	3.60916	+	6.25124i	0.396157	+	0.686163i	−0.597092	+	0.802173i	$0.703677\pi$
$84$		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	−0.997432	−	0.0716161i	$-0.977184\pi$
$89$	−5.28999	−	9.16253i	−0.560737	−	0.971226i	0.436695	−	0.899610i	$-0.356149\pi$
$90$	−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	−0.990132	−	0.140137i	$-0.955246\pi$
$97$	−13.4322	+	7.75510i	−1.36384	+	0.787411i	−0.373704	+	0.927548i	$0.621912\pi$
$98$		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	$0.0656261\pi$
$103$			4.15522i			0.409426i	−0.978822	+	0.204713i	$0.934374\pi$
$104$	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	−0.243472	−	0.969908i	$-0.578286\pi$
$107$	4.91092	−	2.83532i	0.474757	−	0.274101i	0.718229	+	0.695807i	$0.244953\pi$
$108$	4.19453	−	6.47192i	0.403619	−	0.622761i
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	−0.421468	−	0.906843i	$-0.638485\pi$
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	0.996083	−	0.0884193i	$-0.0281815\pi$
$110$	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	0.765329	−	0.643640i	$-0.222576\pi$
$113$	6.27800	+	3.62461i	0.590585	+	0.340974i	−0.174744	+	0.984614i	$0.555910\pi$
$114$	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	$0.169720\pi$
$137$			11.8986i			1.01657i	−0.861190	+	0.508283i	$0.830280\pi$
$138$	−1.10653	−	6.97264i	−0.0941942	−	0.593551i
$139$	10.4143	+	6.01268i	0.883327	+	0.509989i	0.871754	−	0.489944i	$-0.162983\pi$
$139$	10.4143	+	6.01268i	0.883327	+	0.509989i	0.0115731	+	0.999933i	$0.496316\pi$
$140$		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	$0.0936446\pi$
$149$			7.07901i			0.579935i	−0.957036	+	0.289968i	$0.906355\pi$
$150$	−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	−0.570362	−	0.821393i	$-0.693197\pi$
$157$	−1.80677	+	1.04314i	−0.144196	+	0.0832517i	0.426166	+	0.904645i	$0.359864\pi$
$158$	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	0.559692	−	0.828700i	$-0.310919\pi$
$163$	−5.58983	−	9.68188i	−0.437830	−	0.758343i	−0.997522	+	0.0703575i	$0.977586\pi$
$164$	−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	−0.900801	−	0.434232i	$-0.857020\pi$
$167$	−0.960750	+	1.66407i	−0.0743450	+	0.128769i	0.826456	+	0.563001i	$0.190353\pi$
$168$		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	0.416820	+	0.908989i	$0.363145\pi$
$173$	−7.61290	+	13.1859i	−0.578798	+	1.00251i	−0.995618	+	0.0935182i	$0.970189\pi$
$174$	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	0.488769	−	0.872413i	$-0.337446\pi$
$179$	−0.299401	−	0.172859i	−0.0223783	−	0.0129201i	−0.511147	+	0.859493i	$0.670779\pi$
$180$	−6.12884	+	1.99550i	−0.456816	+	0.148736i
$181$			3.27661i			0.243548i	0.992558	+	0.121774i	$0.0388583\pi$
$181$			3.27661i			0.243548i	−0.992558	+	0.121774i	$0.961142\pi$
$182$		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	0.713371	−	0.700787i	$-0.247167\pi$
$191$	6.40096	+	3.69560i	0.463158	+	0.267404i	−0.250213	+	0.968191i	$0.580501\pi$
$192$	2.49686	−	2.02317i	0.180195	−	0.146010i
$193$	−6.51425	−	11.2830i	−0.468906	−	0.812169i	0.530462	−	0.847708i	$-0.322018\pi$
$193$	−6.51425	−	11.2830i	−0.468906	−	0.812169i	−0.999368	+	0.0355398i	$0.988685\pi$
$194$	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	$-0.954140\pi$
$197$		−	4.03035i		−	0.287151i	0.989639	−	0.143575i	$-0.0458599\pi$
$198$	−2.88447	−	2.59401i	−0.204990	−	0.184348i
$199$	−14.2096	−	8.20390i	−1.00729	−	0.581559i	−0.0968925	−	0.995295i	$-0.530890\pi$
$199$	−14.2096	−	8.20390i	−1.00729	−	0.581559i	−0.910397	+	0.413736i	$0.864224\pi$
$200$		−	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	−0.995283	−	0.0970121i	$-0.969071\pi$
$211$	−6.00827	+	10.4066i	−0.413627	+	0.716422i	0.581657	+	0.813434i	$0.302405\pi$
$212$			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	0.526836	−	0.849967i	$-0.323378\pi$
$223$	22.7932	−	13.1597i	1.52635	−	0.881237i	0.999511	−	0.0312693i	$-0.00995496\pi$
$224$		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	$-0.896184\pi$
$229$		−	9.69691i		−	0.640790i	0.947284	−	0.320395i	$-0.103816\pi$
$230$	−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	−0.561853	−	0.827237i	$-0.689911\pi$
$233$	−1.92897	+	1.11369i	−0.126371	+	0.0729605i	0.435482	+	0.900198i	$0.356578\pi$
$234$	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	−0.115151	−	0.993348i	$-0.536735\pi$
$239$	−15.9697	−	9.22008i	−1.03299	−	0.596398i	−0.917840	+	0.396950i	$0.870068\pi$
$240$	−0.460337	−	2.90075i	−0.0297146	−	0.187242i
$241$		−	6.47181i		−	0.416886i	−0.978035	−	0.208443i	$-0.933160\pi$
$241$		−	6.47181i		−	0.416886i	0.978035	−	0.208443i	$-0.0668396\pi$
$242$	−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	$0.240574\pi$
$263$			22.2456i			1.37172i	−0.727732	+	0.685862i	$0.759426\pi$
$264$	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	0.0394642	−	0.999221i	$-0.487435\pi$
$269$	14.5164	−	25.1432i	0.885083	−	1.53301i	0.845619	−	0.533788i	$-0.179232\pi$
$270$	0.277789	−	5.39467i	0.0169057	−	0.328309i
$271$	−20.8174	+	12.0189i	−1.26456	+	0.730097i	−0.973954	−	0.226745i	$-0.927192\pi$
$271$	−20.8174	+	12.0189i	−1.26456	+	0.730097i	−0.290610	+	0.956842i	$0.593858\pi$
$272$	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	−0.815153	−	0.579246i	$-0.803347\pi$
$281$	−12.0876	+	6.97879i	−0.721087	+	0.416320i	0.0940658	+	0.995566i	$0.470014\pi$
$282$	−1.04157	+	2.71585i	−0.0620245	+	0.161726i
$283$	−13.4559	+	7.76876i	−0.799869	+	0.461805i	−0.843425	−	0.537246i	$-0.819465\pi$
$283$	−13.4559	+	7.76876i	−0.799869	+	0.461805i	0.0435563	+	0.999051i	$0.486131\pi$
$284$	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	−0.992920	−	0.118788i	$-0.962099\pi$
$293$	−6.73712	+	11.6690i	−0.393587	+	0.681712i	0.599333	+	0.800500i	$0.295433\pi$
$294$		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	$-0.920815\pi$
$307$		−	8.62791i		−	0.492421i	0.969216	−	0.246210i	$-0.0791854\pi$
$308$		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	0.998989	−	0.0449616i	$-0.0143165\pi$
$311$	8.12200	+	14.0677i	0.460556	+	0.797707i	−0.538432	+	0.842669i	$0.680983\pi$
$312$	1.48144	+	9.33508i	0.0838701	+	0.528495i
$313$	−5.86899	−	3.38846i	−0.331735	−	0.191527i	0.324876	−	0.945757i	$-0.394677\pi$
$313$	−5.86899	−	3.38846i	−0.331735	−	0.191527i	−0.656611	+	0.754229i	$0.728011\pi$
$314$	1.49830			0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$	19.0245	+	10.9838i	1.06852	+	0.616911i	0.927777	−	0.373135i	$-0.121717\pi$
$317$	19.0245	+	10.9838i	1.06852	+	0.616911i	0.140744	+	0.990046i	$0.455051\pi$
$318$	−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	−0.592546	−	0.805537i	$-0.701877\pi$
$331$	7.30179	−	12.6471i	0.401342	−	0.695145i	0.993888	+	0.110391i	$0.0352104\pi$
$332$	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	−0.0412090	+	0.999151i	$0.513121\pi$
$337$	−16.2629	+	28.1681i	−0.885894	+	1.53441i	−0.844685	+	0.535263i	$0.820212\pi$
$338$			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	−0.424084	−	0.905623i	$-0.639404\pi$
$347$	2.76005	−	1.59352i	0.148167	−	0.0855444i	0.572251	+	0.820079i	$0.306070\pi$
$348$	24.9031	−	3.95203i	1.33495	−	0.211851i
$349$	6.48224	−	3.74252i	0.346986	−	0.200333i	−0.316371	−	0.948636i	$-0.602464\pi$
$349$	6.48224	−	3.74252i	0.346986	−	0.200333i	0.663357	+	0.748303i	$0.269131\pi$
$350$		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	−0.620703	−	0.784046i	$-0.713153\pi$
$359$	−4.77569	+	2.75725i	−0.252051	+	0.145522i	0.368652	+	0.929568i	$0.379819\pi$
$360$	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	$0.185666\pi$
$367$			21.1025i			1.10154i	−0.834657	+	0.550770i	$0.814334\pi$
$368$	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	$-0.958707\pi$
$389$		−	5.10283i		−	0.258724i	0.991597	−	0.129362i	$-0.0412928\pi$
$390$	−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	−0.181969	−	0.983304i	$-0.558247\pi$
$397$	11.5288	−	6.65615i	0.578613	−	0.334062i	0.760582	+	0.649242i	$0.224914\pi$
$398$	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	$0.134013\pi$
$401$			16.3678i			0.817371i	−0.912675	+	0.408685i	$0.865987\pi$
$402$	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	−0.589979	−	0.807418i	$-0.700864\pi$
$409$	−3.75604	+	2.16855i	−0.185724	+	0.107228i	0.404255	+	0.914646i	$0.367531\pi$
$410$	−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	−0.539100	−	0.842241i	$-0.681236\pi$
$419$	9.41294	−	16.3037i	0.459852	−	0.796487i	0.998953	+	0.0457540i	$0.0145690\pi$
$420$		0			0
$421$	0.913453	+	1.58215i	0.0445190	+	0.0771092i	0.887426	−	0.460950i	$-0.152491\pi$
$421$	0.913453	+	1.58215i	0.0445190	+	0.0771092i	−0.842907	+	0.538059i	$0.819158\pi$
$422$	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	0.169149	−	0.985590i	$-0.445898\pi$
$431$	−12.4526	−	7.18954i	−0.599823	−	0.346308i	−0.768972	+	0.639283i	$0.779231\pi$
$432$	−6.07888	−	0.313021i	−0.292470	−	0.0150602i
$433$			2.22130i			0.106749i	0.998575	+	0.0533745i	$0.0169977\pi$
$433$			2.22130i			0.106749i	−0.998575	+	0.0533745i	$0.983002\pi$
$434$		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	0.277831	−	0.960630i	$-0.410385\pi$
$439$	−8.69907	−	5.02241i	−0.415184	−	0.239706i	−0.693015	+	0.720924i	$0.743718\pi$
$440$	−6.52190			−0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$	12.0321	+	6.94672i	0.571661	+	0.330049i	0.757812	−	0.652472i	$-0.226268\pi$
$443$	12.0321	+	6.94672i	0.571661	+	0.330049i	−0.186151	+	0.982521i	$0.559602\pi$
$444$	−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	$-0.919816\pi$
$449$		−	10.5630i		−	0.498498i	0.968439	−	0.249249i	$-0.0801837\pi$
$450$	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	−0.919605	−	0.392844i	$-0.871491\pi$
$457$	−2.55654	+	4.42805i	−0.119590	+	0.207135i	0.800015	+	0.599979i	$0.204825\pi$
$458$	−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	0.946596	−	0.322422i	$-0.104497\pi$
$461$	4.16691	+	7.21730i	0.194072	+	0.336143i	−0.752524	+	0.658565i	$0.771164\pi$
$462$		0			0
$463$	10.0143	−	17.3452i	0.465403	−	0.806102i	−0.533817	−	0.845600i	$-0.679243\pi$
$463$	10.0143	−	17.3452i	0.465403	−	0.806102i	0.999220	+	0.0394986i	$0.0125761\pi$
$464$			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	0.999757	−	0.0220611i	$-0.00702284\pi$
$467$	10.3896	+	17.9953i	0.480773	+	0.832723i	−0.518984	+	0.854784i	$0.673690\pi$
$468$	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	−0.462685	−	0.886523i	$-0.653114\pi$
$487$	11.8375	−	20.5032i	0.536408	−	0.929087i	0.999094	−	0.0425641i	$-0.0135527\pi$
$488$	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	0.806597	−	0.591101i	$-0.201307\pi$
$491$	15.4664	+	8.92951i	0.697987	+	0.402983i	−0.108610	+	0.994084i	$0.534640\pi$
$492$	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	0.270242	+	0.962792i	$0.412896\pi$
$521$	−15.9477	+	27.6222i	−0.698682	+	1.21015i	−0.968924	+	0.247360i	$0.920437\pi$
$522$	−4.38099	+	20.6727i	−0.191751	+	0.904821i
$523$	1.20531	−	0.695886i	0.0527046	−	0.0304290i	−0.473416	−	0.880839i	$-0.656979\pi$
$523$	1.20531	−	0.695886i	0.0527046	−	0.0304290i	0.526121	+	0.850410i	$0.323646\pi$
$524$	−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	0.997682	+	0.0680555i	$0.0216795\pi$
$541$	12.9736	+	22.4709i	0.557779	+	0.966101i	−0.439903	+	0.898045i	$0.644987\pi$
$542$	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	0.594882	−	0.803813i	$-0.297199\pi$
$547$	−9.32438	−	16.1503i	−0.398682	−	0.690537i	−0.993564	+	0.113276i	$0.963865\pi$
$548$	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	0.998808	+	0.0488092i	$0.0155426\pi$
$557$	36.3567	+	20.9905i	1.54048	+	0.889398i	0.541674	+	0.840589i	$0.317791\pi$
$558$	−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	−0.910456	−	0.413606i	$-0.864269\pi$
$563$	−19.3006	−	33.4295i	−0.813422	−	1.40889i	0.0970343	−	0.995281i	$-0.469064\pi$
$564$	−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	−0.300184	−	0.953881i	$-0.597048\pi$
$569$	−30.4460	−	17.5780i	−1.27636	−	0.736908i	−0.976178	+	0.216973i	$0.930382\pi$
$570$	5.61285	−	4.54802i	0.235096	−	0.190496i
$571$	17.6766	+	30.6167i	0.739742	+	1.28127i	0.952611	+	0.304190i	$0.0983857\pi$
$571$	17.6766	+	30.6167i	0.739742	+	1.28127i	−0.212870	+	0.977081i	$0.568281\pi$
$572$	−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	−0.0694761	−	0.997584i	$-0.522133\pi$
$577$	−23.2557	−	13.4267i	−0.968147	−	0.558960i	−0.898671	+	0.438624i	$0.855466\pi$
$578$		−	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	−0.983804	−	0.179246i	$-0.942634\pi$
$587$	−15.6788	−	27.1565i	−0.647134	−	1.12087i	0.336671	−	0.941622i	$-0.390699\pi$
$588$		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	0.944353	−	0.328935i	$-0.106690\pi$
$593$	4.56131	+	7.90043i	0.187311	+	0.324432i	−0.757042	+	0.653366i	$0.773356\pi$
$594$	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	−0.477086	−	0.878856i	$-0.658307\pi$
$599$	1.11316	−	0.642683i	0.0454825	−	0.0262593i	0.522569	+	0.852597i	$0.324974\pi$
$600$	7.92529	+	9.78084i	0.323549	+	0.399301i
$601$	16.7126	−	9.64903i	0.681721	−	0.393592i	−0.118782	−	0.992920i	$-0.537899\pi$
$601$	16.7126	−	9.64903i	0.681721	−	0.393592i	0.800503	+	0.599328i	$0.204566\pi$
$602$		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	$0.290164\pi$
$607$			38.9502i			1.58094i	−0.612501	+	0.790470i	$0.709836\pi$
$608$	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	−0.930277	−	0.366859i	$-0.880433\pi$
$613$	−3.65018	+	6.32229i	−0.147429	+	0.255355i	0.782847	+	0.622214i	$0.213767\pi$
$614$	−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	0.998548	+	0.0538763i	$0.0171577\pi$
$617$	38.3641	+	22.1495i	1.54448	+	0.891706i	0.545932	+	0.837829i	$0.316176\pi$
$618$	0.810113	+	5.10480i	0.0325875	+	0.205345i
$619$			0.471636i			0.0189566i	0.999955	+	0.00947832i	$0.00301709\pi$
$619$			0.471636i			0.0189566i	−0.999955	+	0.00947832i	$0.996983\pi$
$620$	−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	$-0.542679\pi$
$641$		−	50.1815i		−	1.98205i	0.133677	−	0.991025i	$-0.457321\pi$
$642$	5.48042	−	4.44072i	0.216295	−	0.175261i
$643$	−9.18633	−	5.30373i	−0.362274	−	0.209159i	0.307804	−	0.951450i	$-0.400406\pi$
$643$	−9.18633	−	5.30373i	−0.362274	−	0.209159i	−0.670078	+	0.742291i	$0.733739\pi$
$644$		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	0.408100	+	0.912937i	$0.366191\pi$
$647$	−14.9203	+	25.8427i	−0.586577	+	1.01598i	−0.994677	+	0.103044i	$0.967142\pi$
$648$	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	$-0.757681\pi$
$653$		−	35.2561i		−	1.37968i	0.723962	−	0.689839i	$-0.242319\pi$
$654$	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	0.196801	−	0.980443i	$-0.436945\pi$
$659$	29.3751	−	16.9597i	1.14429	−	0.660656i	0.947489	+	0.319787i	$0.103611\pi$
$660$	−2.39933	+	6.25615i	−0.0933938	+	0.243520i
$661$	13.6550	−	7.88371i	0.531117	−	0.306641i	−0.210354	−	0.977625i	$-0.567462\pi$
$661$	13.6550	−	7.88371i	0.531117	−	0.306641i	0.741471	+	0.670985i	$0.234128\pi$
$662$	−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	0.688696	−	0.725050i	$-0.258183\pi$
$673$	−7.35627	−	12.7414i	−0.283563	−	0.491146i	−0.972260	+	0.233904i	$0.924850\pi$
$674$	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	−0.901766	−	0.432225i	$-0.857729\pi$
$677$	−1.99217	+	3.45054i	−0.0765654	+	0.132615i	0.825201	+	0.564840i	$0.191062\pi$
$678$	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	0.0834856	−	0.996509i	$-0.473395\pi$
$683$	−19.2812	−	11.1320i	−0.737774	−	0.425954i	−0.821259	+	0.570555i	$0.806728\pi$
$684$	−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	0.992618	+	0.121287i	$0.0387020\pi$
$691$	41.9003	+	24.1912i	1.59396	+	0.920275i	0.601346	+	0.798989i	$0.294631\pi$
$692$	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	$0.145113\pi$
$701$			23.3129i			0.880514i	−0.897872	+	0.440257i	$0.854887\pi$
$702$	−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	−0.982894	−	0.184172i	$-0.941040\pi$
$709$	−8.83884	+	15.3093i	−0.331949	+	0.574953i	0.650945	+	0.759125i	$0.274373\pi$
$710$	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	−0.996837	−	0.0794749i	$-0.974676\pi$
$719$	−15.2102	−	26.3449i	−0.567246	−	0.982498i	0.429591	−	0.903024i	$-0.358658\pi$
$720$	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	−0.997018	−	0.0771674i	$-0.975412\pi$
$727$	−38.5219	+	22.2406i	−1.42870	+	0.824859i	−0.431680	+	0.902027i	$0.642079\pi$
$728$		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	$-0.684591\pi$
$733$		−	45.2954i		−	1.67302i	0.547949	−	0.836512i	$-0.315409\pi$
$734$	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	−0.990947	−	0.134252i	$-0.957137\pi$
$739$	−10.3086	+	17.8550i	−0.379208	+	0.656808i	0.611739	+	0.791060i	$0.290470\pi$
$740$	−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	0.634529	−	0.772899i	$-0.281194\pi$
$743$	7.69885	+	4.44493i	0.282443	+	0.163069i	−0.352086	+	0.935968i	$0.614527\pi$
$744$	−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	0.454455	−	0.890770i	$-0.349834\pi$
$769$	−2.48873	−	1.43687i	−0.0897460	−	0.0518149i	−0.544201	+	0.838955i	$0.683167\pi$
$770$		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	−0.955247	−	0.295810i	$-0.904410\pi$
$773$	−6.15679	+	10.6639i	−0.221444	+	0.383553i	0.733802	+	0.679363i	$0.237744\pi$
$774$	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	−0.439946	−	0.898024i	$-0.645002\pi$
$787$	3.30450	−	1.90785i	0.117793	−	0.0680076i	0.557739	+	0.830017i	$0.311669\pi$
$788$	−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	−0.00851609	+	0.999964i	$0.502711\pi$
$797$	−24.5682	+	42.5535i	−0.870252	+	1.50732i	−0.861736	+	0.507357i	$0.830623\pi$
$798$		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	0.993146	−	0.116882i	$-0.0372900\pi$
$809$	39.4929	+	22.8012i	1.38850	+	0.801648i	0.395350	+	0.918531i	$0.370623\pi$
$810$	5.50866	+	7.56265i	0.193554	+	0.265725i
$811$		−	39.1391i		−	1.37436i	−0.726488	−	0.687180i	$-0.758849\pi$
$811$		−	39.1391i		−	1.37436i	0.726488	−	0.687180i	$-0.241151\pi$
$812$		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	0.668812	−	0.743432i	$-0.266803\pi$
$821$	10.2976	+	5.94530i	0.359387	+	0.207492i	−0.309425	+	0.950924i	$0.600136\pi$
$822$	2.31978	+	14.6178i	0.0809117	+	0.509853i
$823$	−1.51195	−	2.61877i	−0.0527031	−	0.0912844i	0.838470	−	0.544947i	$-0.183450\pi$
$823$	−1.51195	−	2.61877i	−0.0527031	−	0.0912844i	−0.891173	+	0.453663i	$0.850117\pi$
$824$	−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	$-0.914616\pi$
$827$		−	15.2436i		−	0.530071i	0.964239	−	0.265035i	$-0.0853836\pi$
$828$	7.82405	+	24.0302i	0.271904	+	0.835107i
$829$	29.7306	+	17.1649i	1.03259	+	0.596163i	0.917724	−	0.397218i	$-0.130024\pi$
$829$	29.7306	+	17.1649i	1.03259	+	0.596163i	0.114861	+	0.993382i	$0.463358\pi$
$830$		−	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	0.952551	−	0.304379i	$-0.0984491\pi$
$839$	6.16024	+	10.6698i	0.212675	+	0.368364i	−0.739876	+	0.672744i	$0.765116\pi$
$840$		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	−0.431291	−	0.902213i	$-0.641942\pi$
$853$	3.92537	−	2.26631i	0.134402	−	0.0775971i	0.565693	+	0.824616i	$0.308609\pi$
$854$		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	$0.0972615\pi$
$859$			17.6335i			0.601647i	−0.953680	+	0.300824i	$0.902738\pi$
$860$	−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	−0.876867	−	0.480732i	$-0.840371\pi$
$863$	−26.4091	+	15.2473i	−0.898975	+	0.519023i	−0.0221074	+	0.999756i	$0.507038\pi$
$864$	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	−0.563570	−	0.826069i	$-0.690572\pi$
$911$	−3.92249	+	2.26465i	−0.129958	+	0.0750313i	0.433612	+	0.901100i	$0.357239\pi$
$912$	−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	0.997666	+	0.0682866i	$0.0217532\pi$
$919$	16.9149	+	29.2975i	0.557971	+	0.966434i	−0.439695	+	0.898147i	$0.644913\pi$
$920$	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	0.458928	+	0.888473i	$0.348233\pi$
$929$	−16.4582	+	28.5064i	−0.539976	+	0.935266i	−0.998905	+	0.0467929i	$0.985100\pi$
$930$	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	$0.213854\pi$
$937$			38.1057i			1.24486i	−0.782676	+	0.622430i	$0.786146\pi$
$938$		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	0.981307	−	0.192449i	$-0.0616431\pi$
$941$	9.93855	+	17.2141i	0.323987	+	0.561163i	−0.657319	+	0.753612i	$0.728310\pi$
$942$	−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	0.762695	−	0.646759i	$-0.223876\pi$
$947$	17.9696	+	10.3747i	0.583933	+	0.337134i	−0.178762	+	0.983892i	$0.557209\pi$
$948$	−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	$-0.933345\pi$
$953$		−	12.8345i		−	0.415751i	0.978155	−	0.207876i	$-0.0666549\pi$
$954$	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	0.420557	+	0.907266i	$0.361835\pi$
$967$	−17.8941	+	30.9936i	−0.575437	+	0.996685i	−0.995994	+	0.0894195i	$0.971499\pi$
$968$			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	0.533494	−	0.845804i	$-0.320879\pi$
$971$	−14.5129	−	25.1370i	−0.465740	−	0.806686i	−0.999235	+	0.0391177i	$0.987545\pi$
$972$	−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	−0.371149	−	0.928573i	$-0.621036\pi$
$977$	7.73439	−	4.46545i	0.247445	−	0.142862i	0.618594	+	0.785711i	$0.287703\pi$
$978$	−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	0.273631	+	0.961835i	$0.411775\pi$
$991$	−21.9151	+	37.9581i	−0.696158	+	1.20578i	−0.969789	+	0.243946i	$0.921558\pi$
$992$	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	$0.252456\pi$
$997$			44.9975i			1.42508i	−0.701630	+	0.712542i	$0.747544\pi$
$998$	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.374.2		10
3.2	odd	2		1323.2.s.b.962.4		10
7.2	even	3		63.2.i.b.5.4	✓	10
7.3	odd	6		441.2.o.c.293.4		10
7.4	even	3		441.2.o.d.293.4		10
7.5	odd	6		441.2.i.b.68.4		10
7.6	odd	2		63.2.s.b.59.2	yes	10
9.2	odd	6		441.2.i.b.227.2		10
9.7	even	3		1323.2.i.b.521.4		10
21.2	odd	6		189.2.i.b.152.2		10
21.5	even	6		1323.2.i.b.1097.2		10
21.11	odd	6		1323.2.o.c.881.2		10
21.17	even	6		1323.2.o.d.881.2		10
21.20	even	2		189.2.s.b.17.4		10
28.23	odd	6		1008.2.ca.b.257.3		10
28.27	even	2		1008.2.df.b.689.2		10
63.2	odd	6		63.2.s.b.47.2	yes	10
63.11	odd	6		441.2.o.c.146.4		10
63.13	odd	6		567.2.p.c.80.4		10
63.16	even	3		189.2.s.b.89.4		10
63.20	even	6		63.2.i.b.38.2	yes	10
63.23	odd	6		567.2.p.c.404.4		10
63.25	even	3		1323.2.o.d.440.2		10
63.34	odd	6		189.2.i.b.143.4		10
63.38	even	6		441.2.o.d.146.4		10
63.41	even	6		567.2.p.d.80.2		10
63.47	even	6	inner	441.2.s.b.362.2		10
63.52	odd	6		1323.2.o.c.440.2		10
63.58	even	3		567.2.p.d.404.2		10
63.61	odd	6		1323.2.s.b.656.4		10
84.23	even	6		3024.2.ca.b.2609.4		10
84.83	odd	2		3024.2.df.b.17.4		10
252.79	odd	6		3024.2.df.b.1601.4		10
252.83	odd	6		1008.2.ca.b.353.3		10
252.191	even	6		1008.2.df.b.929.2		10
252.223	even	6		3024.2.ca.b.2033.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	7.2	even	3
63.2.i.b.38.2	yes	10	63.20	even	6
63.2.s.b.47.2	yes	10	63.2	odd	6
63.2.s.b.59.2	yes	10	7.6	odd	2
189.2.i.b.143.4		10	63.34	odd	6
189.2.i.b.152.2		10	21.2	odd	6
189.2.s.b.17.4		10	21.20	even	2
189.2.s.b.89.4		10	63.16	even	3
441.2.i.b.68.4		10	7.5	odd	6
441.2.i.b.227.2		10	9.2	odd	6
441.2.o.c.146.4		10	63.11	odd	6
441.2.o.c.293.4		10	7.3	odd	6
441.2.o.d.146.4		10	63.38	even	6
441.2.o.d.293.4		10	7.4	even	3
441.2.s.b.362.2		10	63.47	even	6	inner
441.2.s.b.374.2		10	1.1	even	1	trivial
567.2.p.c.80.4		10	63.13	odd	6
567.2.p.c.404.4		10	63.23	odd	6
567.2.p.d.80.2		10	63.41	even	6
567.2.p.d.404.2		10	63.58	even	3
1008.2.ca.b.257.3		10	28.23	odd	6
1008.2.ca.b.353.3		10	252.83	odd	6
1008.2.df.b.689.2		10	28.27	even	2
1008.2.df.b.929.2		10	252.191	even	6
1323.2.i.b.521.4		10	9.7	even	3
1323.2.i.b.1097.2		10	21.5	even	6
1323.2.o.c.440.2		10	63.52	odd	6
1323.2.o.c.881.2		10	21.11	odd	6
1323.2.o.d.440.2		10	63.25	even	3
1323.2.o.d.881.2		10	21.17	even	6
1323.2.s.b.656.4		10	63.61	odd	6
1323.2.s.b.962.4		10	3.2	odd	2
3024.2.ca.b.2033.4		10	252.223	even	6
3024.2.ca.b.2609.4		10	84.23	even	6
3024.2.df.b.17.4		10	84.83	odd	2
3024.2.df.b.1601.4		10	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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

Introduction

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