LMFDB - Embedded newform 1110.2.x.c.751.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{13} + 398 x^{12} - 136 x^{11} + 32 x^{10} - 824 x^{9} + 17825 x^{8} - 11480 x^{7} + \cdots + 20736 $ x^16 - 8x^13 + 398x^12 - 136x^11 + 32x^10 - 824x^9 + 17825x^8 - 11480x^7 + 3104x^6 + 11296x^5 + 68320x^4 - 21120x^3 + 4608x^2 + 13824*x + 20736
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.5
Root			$1.14718 - 1.14718i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.c.841.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-1.41697 + 2.45427i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-1.41697 + 2.45427i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +1.83395 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.486978 + 0.281157i) q^{13} +2.83395i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.254444 - 0.146903i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.71426 + 1.56708i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-1.41697 - 2.45427i) q^{21} +(1.58824 - 0.916973i) q^{22} +8.04225i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +0.562314 q^{26} +1.00000 q^{27} +(1.41697 + 2.45427i) q^{28} +0.994151i q^{29} +(0.500000 - 0.866025i) q^{30} +10.1537i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.916973 + 1.58824i) q^{33} +(0.146903 - 0.254444i) q^{34} +(2.45427 - 1.41697i) q^{35} -1.00000 q^{36} +(-4.07258 + 4.51820i) q^{37} +3.13416 q^{38} +(-0.486978 + 0.281157i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.81845 - 3.14965i) q^{41} +(-2.45427 - 1.41697i) q^{42} +4.77620i q^{43} +(0.916973 - 1.58824i) q^{44} +1.00000i q^{45} +(4.02112 + 6.96479i) q^{46} -3.85999 q^{47} +1.00000 q^{48} +(-0.515627 - 0.893091i) q^{49} +(0.866025 + 0.500000i) q^{50} +0.293806i q^{51} +(0.486978 - 0.281157i) q^{52} +(2.65825 + 4.60422i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.58824 - 0.916973i) q^{55} +(2.45427 + 1.41697i) q^{56} +(-2.71426 + 1.56708i) q^{57} +(0.497075 + 0.860960i) q^{58} +(4.33464 - 2.50260i) q^{59} -1.00000i q^{60} +(3.14965 + 1.81845i) q^{61} +(5.07684 + 8.79334i) q^{62} +2.83395 q^{63} -1.00000 q^{64} +(-0.281157 - 0.486978i) q^{65} +1.83395i q^{66} +(3.43814 - 5.95503i) q^{67} -0.293806i q^{68} +(-6.96479 - 4.02112i) q^{69} +(1.41697 - 2.45427i) q^{70} +(4.91693 - 8.51638i) q^{71} +(-0.866025 + 0.500000i) q^{72} -6.07908 q^{73} +(-1.26786 + 5.94916i) q^{74} -1.00000 q^{75} +(2.71426 - 1.56708i) q^{76} +(-2.59865 + 4.50100i) q^{77} +(-0.281157 + 0.486978i) q^{78} +(-10.8779 - 6.28035i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -3.63691i q^{82} +(4.84237 + 8.38723i) q^{83} -2.83395 q^{84} -0.293806 q^{85} +(2.38810 + 4.13631i) q^{86} +(-0.860960 - 0.497075i) q^{87} -1.83395i q^{88} +(6.70890 - 3.87338i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-1.38007 + 0.796783i) q^{91} +(6.96479 + 4.02112i) q^{92} +(-8.79334 - 5.07684i) q^{93} +(-3.34285 + 1.93000i) q^{94} +(-1.56708 - 2.71426i) q^{95} +(0.866025 - 0.500000i) q^{96} -12.9879i q^{97} +(-0.893091 - 0.515627i) q^{98} +(-0.916973 - 1.58824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$			1.00000i			0.408248i
$7$	−1.41697	+	2.45427i	−0.535566	+	0.927627i	0.463570	+	0.886060i	$0.346568\pi$
$7$	−1.41697	+	2.45427i	−0.535566	+	0.927627i	−0.999136	+	0.0415666i	$0.986765\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	1.83395			0.552956			0.276478	−	0.961020i	$-0.410833\pi$
$11$	1.83395			0.552956			0.276478	+	0.961020i	$0.410833\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.486978	+	0.281157i	0.135063	+	0.0779789i	0.566009	−	0.824399i	$-0.308487\pi$
$13$	0.486978	+	0.281157i	0.135063	+	0.0779789i	−0.430946	+	0.902378i	$0.641820\pi$
$14$			2.83395i			0.757404i
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.254444	−	0.146903i	0.0617116	−	0.0356292i	−0.468827	−	0.883290i	$-0.655323\pi$
$17$	0.254444	−	0.146903i	0.0617116	−	0.0356292i	0.530538	+	0.847661i	$0.321990\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	2.71426	+	1.56708i	0.622694	+	0.359513i	0.777917	−	0.628367i	$-0.216276\pi$
$19$	2.71426	+	1.56708i	0.622694	+	0.359513i	−0.155223	+	0.987879i	$0.549610\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	−1.41697	−	2.45427i	−0.309209	−	0.535566i
$22$	1.58824	−	0.916973i	0.338615	−	0.195499i
$23$			8.04225i			1.67692i	0.544960	+	0.838462i	$0.316545\pi$
$23$			8.04225i			1.67692i	−0.544960	+	0.838462i	$0.683455\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.562314			0.110279
$27$	1.00000			0.192450
$28$	1.41697	+	2.45427i	0.267783	+	0.463813i
$29$			0.994151i			0.184609i	0.995731	+	0.0923046i	$0.0294233\pi$
$29$			0.994151i			0.184609i	−0.995731	+	0.0923046i	$0.970577\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$			10.1537i			1.82365i	0.410575	+	0.911827i	$0.365328\pi$
$31$			10.1537i			1.82365i	−0.410575	+	0.911827i	$0.634672\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.916973	+	1.58824i	−0.159625	+	0.276478i
$34$	0.146903	−	0.254444i	0.0251937	−	0.0436367i
$35$	2.45427	−	1.41697i	0.414847	−	0.239512i
$36$	−1.00000			−0.166667
$37$	−4.07258	+	4.51820i	−0.669527	+	0.742787i
$37$	−4.07258	+	4.51820i	−0.669527	+	0.742787i
$38$	3.13416			0.508428
$39$	−0.486978	+	0.281157i	−0.0779789	+	0.0450211i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	1.81845	−	3.14965i	0.283995	−	0.491893i	−0.688370	−	0.725360i	$-0.741674\pi$
$41$	1.81845	−	3.14965i	0.283995	−	0.491893i	0.972365	+	0.233466i	$0.0750069\pi$
$42$	−2.45427	−	1.41697i	−0.378702	−	0.218644i
$43$			4.77620i			0.728363i	0.931328	+	0.364182i	$0.118651\pi$
$43$			4.77620i			0.728363i	−0.931328	+	0.364182i	$0.881349\pi$
$44$	0.916973	−	1.58824i	0.138239	−	0.239437i
$45$			1.00000i			0.149071i
$46$	4.02112	+	6.96479i	0.592882	+	1.02690i
$47$	−3.85999			−0.563038			−0.281519	−	0.959556i	$-0.590838\pi$
$47$	−3.85999			−0.563038			−0.281519	+	0.959556i	$0.590838\pi$
$48$	1.00000			0.144338
$49$	−0.515627	−	0.893091i	−0.0736609	−	0.127584i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$			0.293806i			0.0411411i
$52$	0.486978	−	0.281157i	0.0675317	−	0.0389894i
$53$	2.65825	+	4.60422i	0.365139	+	0.632439i	0.988798	−	0.149257i	$-0.0476883\pi$
$53$	2.65825	+	4.60422i	0.365139	+	0.632439i	−0.623660	+	0.781696i	$0.714355\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−1.58824	−	0.916973i	−0.214159	−	0.123645i
$56$	2.45427	+	1.41697i	0.327966	+	0.189351i
$57$	−2.71426	+	1.56708i	−0.359513	+	0.207565i
$58$	0.497075	+	0.860960i	0.0652692	+	0.113050i
$59$	4.33464	−	2.50260i	0.564322	−	0.325811i	−0.190557	−	0.981676i	$-0.561029\pi$
$59$	4.33464	−	2.50260i	0.564322	−	0.325811i	0.754878	+	0.655865i	$0.227696\pi$
$60$		−	1.00000i		−	0.129099i
$61$	3.14965	+	1.81845i	0.403272	+	0.232829i	0.687895	−	0.725810i	$-0.258535\pi$
$61$	3.14965	+	1.81845i	0.403272	+	0.232829i	−0.284623	+	0.958640i	$0.591868\pi$
$62$	5.07684	+	8.79334i	0.644759	+	1.11676i
$63$	2.83395			0.357044
$64$	−1.00000			−0.125000
$65$	−0.281157	−	0.486978i	−0.0348732	−	0.0604022i
$66$			1.83395i			0.225743i
$67$	3.43814	−	5.95503i	0.420035	−	0.727523i	−0.575907	−	0.817515i	$-0.695351\pi$
$67$	3.43814	−	5.95503i	0.420035	−	0.727523i	0.995942	+	0.0899926i	$0.0286843\pi$
$68$		−	0.293806i		−	0.0356292i
$69$	−6.96479	−	4.02112i	−0.838462	−	0.484086i
$70$	1.41697	−	2.45427i	0.169361	−	0.293341i
$71$	4.91693	−	8.51638i	0.583532	−	1.01071i	−0.411524	−	0.911399i	$-0.635003\pi$
$71$	4.91693	−	8.51638i	0.583532	−	1.01071i	0.995057	−	0.0993091i	$-0.0316633\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−6.07908			−0.711503			−0.355751	−	0.934581i	$-0.615775\pi$
$73$	−6.07908			−0.711503			−0.355751	+	0.934581i	$0.615775\pi$
$74$	−1.26786	+	5.94916i	−0.147385	+	0.691576i
$75$	−1.00000			−0.115470
$76$	2.71426	−	1.56708i	0.311347	−	0.179756i
$77$	−2.59865	+	4.50100i	−0.296144	+	0.512936i
$78$	−0.281157	+	0.486978i	−0.0318347	+	0.0551394i
$79$	−10.8779	−	6.28035i	−1.22386	−	0.706595i	−0.258120	−	0.966113i	$-0.583103\pi$
$79$	−10.8779	−	6.28035i	−1.22386	−	0.706595i	−0.965738	+	0.259518i	$0.916436\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	3.63691i		−	0.401629i
$83$	4.84237	+	8.38723i	0.531519	+	0.920618i	0.999323	+	0.0367857i	$0.0117119\pi$
$83$	4.84237	+	8.38723i	0.531519	+	0.920618i	−0.467804	+	0.883832i	$0.654955\pi$
$84$	−2.83395			−0.309209
$85$	−0.293806			−0.0318678
$86$	2.38810	+	4.13631i	0.257515	+	0.446029i
$87$	−0.860960	−	0.497075i	−0.0923046	−	0.0532921i
$88$		−	1.83395i		−	0.195499i
$89$	6.70890	−	3.87338i	0.711142	−	0.410578i	−0.100342	−	0.994953i	$-0.531994\pi$
$89$	6.70890	−	3.87338i	0.711142	−	0.410578i	0.811484	+	0.584375i	$0.198660\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−1.38007	+	0.796783i	−0.144671	+	0.0835256i
$92$	6.96479	+	4.02112i	0.726130	+	0.419231i
$93$	−8.79334	−	5.07684i	−0.911827	−	0.526444i
$94$	−3.34285	+	1.93000i	−0.344789	+	0.199064i
$95$	−1.56708	−	2.71426i	−0.160779	−	0.278477i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	12.9879i		−	1.31872i	−0.751827	−	0.659360i	$-0.770827\pi$
$97$		−	12.9879i		−	1.31872i	0.751827	−	0.659360i	$-0.229173\pi$
$98$	−0.893091	−	0.515627i	−0.0902158	−	0.0520861i
$99$	−0.916973	−	1.58824i	−0.0921593	−	0.159625i
$100$	1.00000			0.100000
$101$	5.25648			0.523039			0.261520	−	0.965198i	$-0.415776\pi$
$101$	5.25648			0.523039			0.261520	+	0.965198i	$0.415776\pi$
$102$	0.146903	+	0.254444i	0.0145456	+	0.0251937i
$103$			4.71049i			0.464138i	0.972699	+	0.232069i	$0.0745495\pi$
$103$			4.71049i			0.464138i	−0.972699	+	0.232069i	$0.925450\pi$
$104$	0.281157	−	0.486978i	0.0275697	−	0.0477521i
$105$			2.83395i			0.276565i
$106$	4.60422	+	2.65825i	0.447202	+	0.258192i
$107$	6.72696	−	11.6514i	0.650320	−	1.12639i	−0.332725	−	0.943024i	$-0.607968\pi$
$107$	6.72696	−	11.6514i	0.650320	−	1.12639i	0.983045	−	0.183364i	$-0.0586986\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−0.0968558	+	0.0559197i	−0.00927710	+	0.00535614i	−0.504631	−	0.863335i	$-0.668372\pi$
$109$	−0.0968558	+	0.0559197i	−0.00927710	+	0.00535614i	0.495354	+	0.868691i	$0.335038\pi$
$110$	−1.83395			−0.174860
$111$	−1.87659	−	5.78605i	−0.178118	−	0.549188i
$112$	2.83395			0.267783
$113$	−16.1160	+	9.30455i	−1.51606	+	0.875299i	−0.516240	+	0.856444i	$0.672669\pi$
$113$	−16.1160	+	9.30455i	−1.51606	+	0.875299i	−0.999822	+	0.0188545i	$0.993998\pi$
$114$	−1.56708	+	2.71426i	−0.146770	+	0.254214i
$115$	4.02112	−	6.96479i	0.374972	−	0.649470i
$116$	0.860960	+	0.497075i	0.0799381	+	0.0461523i
$117$		−	0.562314i		−	0.0519859i
$118$	2.50260	−	4.33464i	0.230383	−	0.399036i
$119$			0.832631i			0.0763272i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−7.63664			−0.694240
$122$	3.63691			0.329270
$123$	1.81845	+	3.14965i	0.163964	+	0.283995i
$124$	8.79334	+	5.07684i	0.789665	+	0.455913i
$125$		−	1.00000i		−	0.0894427i
$126$	2.45427	−	1.41697i	0.218644	−	0.126234i
$127$	3.08317	+	5.34021i	0.273587	+	0.473867i	0.969778	−	0.243990i	$-0.0784564\pi$
$127$	3.08317	+	5.34021i	0.273587	+	0.473867i	−0.696190	+	0.717857i	$0.745123\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−4.13631	−	2.38810i	−0.364182	−	0.210260i
$130$	−0.486978	−	0.281157i	−0.0427108	−	0.0246591i
$131$	3.81966	−	2.20528i	0.333725	−	0.192676i	−0.323768	−	0.946136i	$-0.604950\pi$
$131$	3.81966	−	2.20528i	0.333725	−	0.192676i	0.657494	+	0.753460i	$0.271617\pi$
$132$	0.916973	+	1.58824i	0.0798123	+	0.138239i
$133$	−7.69207	+	4.44102i	−0.666987	+	0.385085i
$134$		−	6.87628i		−	0.594020i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	−0.146903	−	0.254444i	−0.0125968	−	0.0218184i
$137$	8.22403			0.702626			0.351313	−	0.936258i	$-0.385735\pi$
$137$	8.22403			0.702626			0.351313	+	0.936258i	$0.385735\pi$
$138$	−8.04225			−0.684601
$139$	4.71732	+	8.17063i	0.400118	+	0.693024i	0.993740	−	0.111720i	$-0.0356359\pi$
$139$	4.71732	+	8.17063i	0.400118	+	0.693024i	−0.593622	+	0.804744i	$0.702303\pi$
$140$		−	2.83395i		−	0.239512i
$141$	1.93000	−	3.34285i	0.162535	−	0.281519i
$142$		−	9.83386i		−	0.825240i
$143$	0.893091	+	0.515627i	0.0746841	+	0.0431189i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.497075	−	0.860960i	0.0412799	−	0.0714988i
$146$	−5.26464	+	3.03954i	−0.435705	+	0.251554i
$147$	1.03125			0.0850563
$148$	1.87659	+	5.78605i	0.154254	+	0.475611i
$149$	−0.629941			−0.0516068			−0.0258034	−	0.999667i	$-0.508214\pi$
$149$	−0.629941			−0.0516068			−0.0258034	+	0.999667i	$0.508214\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	−0.868970	+	1.50510i	−0.0707158	+	0.122483i	−0.899215	−	0.437507i	$-0.855862\pi$
$151$	−0.868970	+	1.50510i	−0.0707158	+	0.122483i	0.828499	+	0.559990i	$0.189195\pi$
$152$	1.56708	−	2.71426i	0.127107	−	0.220156i
$153$	−0.254444	−	0.146903i	−0.0205705	−	0.0118764i
$154$			5.19731i			0.418811i
$155$	5.07684	−	8.79334i	0.407781	−	0.706298i
$156$			0.562314i			0.0450211i
$157$	−8.02127	−	13.8932i	−0.640167	−	1.10880i	−0.985395	−	0.170283i	$-0.945532\pi$
$157$	−8.02127	−	13.8932i	−0.640167	−	1.10880i	0.345228	−	0.938519i	$-0.387802\pi$
$158$	−12.5607			−0.999276
$159$	−5.31650			−0.421626
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−19.7378	−	11.3956i	−1.55556	−	0.898103i
$162$			1.00000i			0.0785674i
$163$	−11.0344	+	6.37070i	−0.864279	+	0.498991i	−0.865443	−	0.501008i	$-0.832963\pi$
$163$	−11.0344	+	6.37070i	−0.864279	+	0.498991i	0.00116419	+	0.999999i	$0.499629\pi$
$164$	−1.81845	−	3.14965i	−0.141997	−	0.245947i
$165$	1.58824	−	0.916973i	0.123645	−	0.0713863i
$166$	8.38723	+	4.84237i	0.650975	+	0.375841i
$167$	12.7548	+	7.36397i	0.986994	+	0.569841i	0.904374	−	0.426740i	$-0.140338\pi$
$167$	12.7548	+	7.36397i	0.986994	+	0.569841i	0.0826197	+	0.996581i	$0.473671\pi$
$168$	−2.45427	+	1.41697i	−0.189351	+	0.109322i
$169$	−6.34190	−	10.9845i	−0.487839	−	0.844961i
$170$	−0.254444	+	0.146903i	−0.0195149	+	0.0112670i
$171$		−	3.13416i		−	0.239675i
$172$	4.13631	+	2.38810i	0.315390	+	0.182091i
$173$	3.52677	+	6.10854i	0.268135	+	0.464423i	0.968380	−	0.249479i	$-0.0802593\pi$
$173$	3.52677	+	6.10854i	0.268135	+	0.464423i	−0.700245	+	0.713902i	$0.746926\pi$
$174$	−0.994151			−0.0753664
$175$	−2.83395			−0.214226
$176$	−0.916973	−	1.58824i	−0.0691195	−	0.119718i
$177$			5.00521i			0.376215i
$178$	3.87338	−	6.70890i	0.290322	−	0.502853i
$179$		−	11.3637i		−	0.849362i	−0.905343	−	0.424681i	$-0.860386\pi$
$179$		−	11.3637i		−	0.849362i	0.905343	−	0.424681i	$-0.139614\pi$
$180$	0.866025	+	0.500000i	0.0645497	+	0.0372678i
$181$	−2.67102	+	4.62635i	−0.198536	+	0.343874i	−0.948054	−	0.318110i	$-0.896952\pi$
$181$	−2.67102	+	4.62635i	−0.198536	+	0.343874i	0.749518	+	0.661984i	$0.230285\pi$
$182$	−0.796783	+	1.38007i	−0.0590615	+	0.102298i
$183$	−3.14965	+	1.81845i	−0.232829	+	0.134424i
$184$	8.04225			0.592882
$185$	5.78605	−	1.87659i	0.425399	−	0.137969i
$186$	−10.1537			−0.744504
$187$	0.466636	−	0.269412i	0.0341238	−	0.0197014i
$188$	−1.93000	+	3.34285i	−0.140759	+	0.243802i
$189$	−1.41697	+	2.45427i	−0.103070	+	0.178522i
$190$	−2.71426	−	1.56708i	−0.196913	−	0.113688i
$191$		−	5.12182i		−	0.370602i	−0.982682	−	0.185301i	$-0.940674\pi$
$191$		−	5.12182i		−	0.370602i	0.982682	−	0.185301i	$-0.0593260\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$		−	8.96618i		−	0.645400i	−0.946501	−	0.322700i	$-0.895410\pi$
$193$		−	8.96618i		−	0.645400i	0.946501	−	0.322700i	$-0.104590\pi$
$194$	−6.49394	−	11.2478i	−0.466238	−	0.807548i
$195$	0.562314			0.0402681
$196$	−1.03125			−0.0736609
$197$	−0.417665	−	0.723416i	−0.0297574	−	0.0515413i	0.850763	−	0.525549i	$-0.176140\pi$
$197$	−0.417665	−	0.723416i	−0.0297574	−	0.0515413i	−0.880521	+	0.474008i	$0.842807\pi$
$198$	−1.58824	−	0.916973i	−0.112872	−	0.0651665i
$199$		−	3.98931i		−	0.282795i	−0.989953	−	0.141397i	$-0.954840\pi$
$199$		−	3.98931i		−	0.282795i	0.989953	−	0.141397i	$-0.0451595\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	3.43814	+	5.95503i	0.242508	+	0.420035i
$202$	4.55224	−	2.62824i	0.320295	−	0.184922i
$203$	−2.43991	−	1.40869i	−0.171248	−	0.0988703i
$204$	0.254444	+	0.146903i	0.0178146	+	0.0102853i
$205$	−3.14965	+	1.81845i	−0.219981	+	0.127006i
$206$	2.35524	+	4.07940i	0.164098	+	0.284225i
$207$	6.96479	−	4.02112i	0.484086	−	0.279487i
$208$		−	0.562314i		−	0.0389894i
$209$	4.97781	+	2.87394i	0.344322	+	0.198795i
$210$	1.41697	+	2.45427i	0.0977804	+	0.169361i
$211$	−24.2184			−1.66726			−0.833630	−	0.552323i	$-0.813741\pi$
$211$	−24.2184			−1.66726			−0.833630	+	0.552323i	$0.813741\pi$
$212$	5.31650			0.365139
$213$	4.91693	+	8.51638i	0.336903	+	0.583532i
$214$		−	13.4539i		−	0.919692i
$215$	2.38810	−	4.13631i	0.162867	−	0.282094i
$216$		−	1.00000i		−	0.0680414i
$217$	−24.9199	−	14.3875i	−1.69167	−	0.976686i
$218$	−0.0559197	+	0.0968558i	−0.00378736	+	0.00655990i
$219$	3.03954	−	5.26464i	0.205393	−	0.355751i
$220$	−1.58824	+	0.916973i	−0.107079	+	0.0618223i
$221$	0.165211			0.0111133
$222$	−4.51820	−	4.07258i	−0.303242	−	0.273333i
$223$	12.1808			0.815686			0.407843	−	0.913052i	$-0.366281\pi$
$223$	12.1808			0.815686			0.407843	+	0.913052i	$0.366281\pi$
$224$	2.45427	−	1.41697i	0.163983	−	0.0946755i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−9.30455	+	16.1160i	−0.618930	+	1.07202i
$227$	−2.06996	−	1.19509i	−0.137388	−	0.0793212i	0.429730	−	0.902957i	$-0.358609\pi$
$227$	−2.06996	−	1.19509i	−0.137388	−	0.0793212i	−0.567119	+	0.823636i	$0.691942\pi$
$228$			3.13416i			0.207565i
$229$	5.34859	−	9.26404i	0.353445	−	0.612185i	−0.633406	−	0.773820i	$-0.718343\pi$
$229$	5.34859	−	9.26404i	0.353445	−	0.612185i	0.986851	+	0.161635i	$0.0516768\pi$
$230$		−	8.04225i		−	0.530290i
$231$	−2.59865	−	4.50100i	−0.170979	−	0.296144i
$232$	0.994151			0.0652692
$233$	6.63544			0.434702			0.217351	−	0.976093i	$-0.430258\pi$
$233$	6.63544			0.434702			0.217351	+	0.976093i	$0.430258\pi$
$234$	−0.281157	−	0.486978i	−0.0183798	−	0.0318347i
$235$	3.34285	+	1.93000i	0.218063	+	0.125899i
$236$		−	5.00521i		−	0.325811i
$237$	10.8779	−	6.28035i	0.706595	−	0.407953i
$238$	0.416316	+	0.721080i	0.0269857	+	0.0467407i
$239$	19.3145	−	11.1512i	1.24935	−	0.721314i	0.278372	−	0.960473i	$-0.410205\pi$
$239$	19.3145	−	11.1512i	1.24935	−	0.721314i	0.970980	+	0.239159i	$0.0768718\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	17.1735	+	9.91510i	1.10624	+	0.638688i	0.937853	−	0.347034i	$-0.112811\pi$
$241$	17.1735	+	9.91510i	1.10624	+	0.638688i	0.168387	+	0.985721i	$0.446144\pi$
$242$	−6.61352	+	3.81832i	−0.425133	+	0.245451i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.14965	−	1.81845i	0.201636	−	0.116415i
$245$			1.03125i			0.0658843i
$246$	3.14965	+	1.81845i	0.200815	+	0.115940i
$247$	0.881190	+	1.52627i	0.0560688	+	0.0971140i
$248$	10.1537			0.644759
$249$	−9.68474			−0.613745
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		−	16.1807i		−	1.02132i	−0.859784	−	0.510658i	$-0.829402\pi$
$251$		−	16.1807i		−	1.02132i	0.859784	−	0.510658i	$-0.170598\pi$
$252$	1.41697	−	2.45427i	0.0892609	−	0.154604i
$253$			14.7491i			0.927265i
$254$	5.34021	+	3.08317i	0.335075	+	0.193455i
$255$	0.146903	−	0.254444i	0.00919943	−	0.0159339i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	19.6743	−	11.3590i	1.22725	−	0.708554i	0.260798	−	0.965393i	$-0.416014\pi$
$257$	19.6743	−	11.3590i	1.22725	−	0.708554i	0.966454	+	0.256839i	$0.0826810\pi$
$258$	−4.77620			−0.297353
$259$	−5.31815	−	16.3974i	−0.330453	−	1.01888i
$260$	−0.562314			−0.0348732
$261$	0.860960	−	0.497075i	0.0532921	−	0.0307682i
$262$	2.20528	−	3.81966i	0.136243	−	0.235980i
$263$	8.59540	−	14.8877i	0.530015	−	0.918013i	−0.469372	−	0.883001i	$-0.655520\pi$
$263$	8.59540	−	14.8877i	0.530015	−	0.918013i	0.999387	−	0.0350122i	$-0.0111470\pi$
$264$	1.58824	+	0.916973i	0.0977497	+	0.0564358i
$265$		−	5.31650i		−	0.326590i
$266$	−4.44102	+	7.69207i	−0.272296	+	0.471631i
$267$			7.74677i			0.474094i
$268$	−3.43814	−	5.95503i	−0.210018	−	0.363761i
$269$	−30.8565			−1.88135			−0.940676	−	0.339306i	$-0.889808\pi$
$269$	−30.8565			−1.88135			−0.940676	+	0.339306i	$0.889808\pi$
$270$	−1.00000			−0.0608581
$271$	2.02802	+	3.51263i	0.123193	+	0.213377i	0.921025	−	0.389503i	$-0.127353\pi$
$271$	2.02802	+	3.51263i	0.123193	+	0.213377i	−0.797832	+	0.602880i	$0.794020\pi$
$272$	−0.254444	−	0.146903i	−0.0154279	−	0.00890731i
$273$		−	1.59357i		−	0.0964470i
$274$	7.12222	−	4.11201i	0.430269	−	0.248416i
$275$	0.916973	+	1.58824i	0.0552956	+	0.0957747i
$276$	−6.96479	+	4.02112i	−0.419231	+	0.242043i
$277$	−9.40109	−	5.42772i	−0.564857	−	0.326120i	0.190236	−	0.981738i	$-0.439075\pi$
$277$	−9.40109	−	5.42772i	−0.564857	−	0.326120i	−0.755092	+	0.655618i	$0.772408\pi$
$278$	8.17063	+	4.71732i	0.490042	+	0.282926i
$279$	8.79334	−	5.07684i	0.526444	−	0.303942i
$280$	−1.41697	−	2.45427i	−0.0846803	−	0.146671i
$281$	−13.8236	+	7.98107i	−0.824648	+	0.476111i	−0.852017	−	0.523514i	$-0.824621\pi$
$281$	−13.8236	+	7.98107i	−0.824648	+	0.476111i	0.0273684	+	0.999625i	$0.491287\pi$
$282$		−	3.85999i		−	0.229859i
$283$	19.5503	+	11.2874i	1.16215	+	0.670966i	0.951818	−	0.306664i	$-0.0992129\pi$
$283$	19.5503	+	11.2874i	1.16215	+	0.670966i	0.210330	+	0.977631i	$0.432546\pi$
$284$	−4.91693	−	8.51638i	−0.291766	−	0.505354i
$285$	3.13416			0.185652
$286$	1.03125			0.0609793
$287$	5.15340	+	8.92595i	0.304196	+	0.526882i
$288$			1.00000i			0.0589256i
$289$	−8.45684	+	14.6477i	−0.497461	+	0.861628i
$290$		−	0.994151i		−	0.0583786i
$291$	11.2478	+	6.49394i	0.659360	+	0.380682i
$292$	−3.03954	+	5.26464i	−0.177876	+	0.308090i
$293$	−6.12499	+	10.6088i	−0.357826	+	0.619773i	−0.987597	−	0.157008i	$-0.949815\pi$
$293$	−6.12499	+	10.6088i	−0.357826	+	0.619773i	0.629771	+	0.776781i	$0.283149\pi$
$294$	0.893091	−	0.515627i	0.0520861	−	0.0300719i
$295$	−5.00521			−0.291415
$296$	4.51820	+	4.07258i	0.262615	+	0.236714i
$297$	1.83395			0.106416
$298$	−0.545545	+	0.314970i	−0.0316026	+	0.0182458i
$299$	−2.26113	+	3.91640i	−0.130765	+	0.226491i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−11.7221	−	6.76774i	−0.675649	−	0.390086i
$302$			1.73794i			0.100007i
$303$	−2.62824	+	4.55224i	−0.150988	+	0.261520i
$304$		−	3.13416i		−	0.179756i
$305$	−1.81845	−	3.14965i	−0.104124	−	0.180349i
$306$	−0.293806			−0.0167958
$307$	−29.6095			−1.68990			−0.844952	−	0.534842i	$-0.820371\pi$
$307$	−29.6095			−1.68990			−0.844952	+	0.534842i	$0.820371\pi$
$308$	2.59865	+	4.50100i	0.148072	+	0.256468i
$309$	−4.07940	−	2.35524i	−0.232069	−	0.133985i
$310$		−	10.1537i		−	0.576690i
$311$	19.5885	−	11.3094i	1.11076	−	0.641299i	0.171736	−	0.985143i	$-0.445062\pi$
$311$	19.5885	−	11.3094i	1.11076	−	0.641299i	0.939027	+	0.343844i	$0.111729\pi$
$312$	0.281157	+	0.486978i	0.0159174	+	0.0275697i
$313$	1.39466	−	0.805205i	0.0788306	−	0.0455129i	−0.460067	−	0.887884i	$-0.652174\pi$
$313$	1.39466	−	0.805205i	0.0788306	−	0.0455129i	0.538897	+	0.842372i	$0.318841\pi$
$314$	−13.8932	−	8.02127i	−0.784041	−	0.452666i
$315$	−2.45427	−	1.41697i	−0.138282	−	0.0798374i
$316$	−10.8779	+	6.28035i	−0.611929	+	0.353297i
$317$	4.23824	+	7.34084i	0.238043	+	0.412303i	0.960153	−	0.279476i	$-0.0901607\pi$
$317$	4.23824	+	7.34084i	0.238043	+	0.412303i	−0.722110	+	0.691779i	$0.756827\pi$
$318$	−4.60422	+	2.65825i	−0.258192	+	0.149067i
$319$			1.82322i			0.102081i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	6.72696	+	11.6514i	0.375463	+	0.650320i
$322$	−22.7913			−1.27011
$323$	0.920836			0.0512367
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			0.562314i			0.0311915i
$326$	−6.37070	+	11.0344i	−0.352840	+	0.611137i
$327$		−	0.111839i		−	0.00618473i
$328$	−3.14965	−	1.81845i	−0.173911	−	0.100407i
$329$	5.46950	−	9.47346i	0.301544	−	0.522289i
$330$	0.916973	−	1.58824i	0.0504777	−	0.0874300i
$331$	2.92211	−	1.68708i	0.160613	−	0.0927302i	−0.417539	−	0.908659i	$-0.637107\pi$
$331$	2.92211	−	1.68708i	0.160613	−	0.0927302i	0.578152	+	0.815929i	$0.303774\pi$
$332$	9.68474			0.531519
$333$	5.94916	+	1.26786i	0.326012	+	0.0694781i
$334$	14.7279			0.805877
$335$	−5.95503	+	3.43814i	−0.325358	+	0.187846i
$336$	−1.41697	+	2.45427i	−0.0773022	+	0.133891i
$337$	−8.24363	+	14.2784i	−0.449059	+	0.777793i	−0.998325	−	0.0578543i	$-0.981574\pi$
$337$	−8.24363	+	14.2784i	−0.449059	+	0.777793i	0.549266	+	0.835648i	$0.314907\pi$
$338$	−10.9845	−	6.34190i	−0.597478	−	0.344954i
$339$		−	18.6091i		−	1.01071i
$340$	−0.146903	+	0.254444i	−0.00796694	+	0.0137991i
$341$			18.6213i			1.00840i
$342$	−1.56708	−	2.71426i	−0.0847380	−	0.146770i
$343$	−16.9151			−0.913330
$344$	4.77620			0.257515
$345$	4.02112	+	6.96479i	0.216490	+	0.374972i
$346$	6.10854	+	3.52677i	0.328397	+	0.189600i
$347$			6.67143i			0.358141i	0.983836	+	0.179071i	$0.0573091\pi$
$347$			6.67143i			0.358141i	−0.983836	+	0.179071i	$0.942691\pi$
$348$	−0.860960	+	0.497075i	−0.0461523	+	0.0266460i
$349$	5.08048	+	8.79965i	0.271952	+	0.471035i	0.969362	−	0.245638i	$-0.0789975\pi$
$349$	5.08048	+	8.79965i	0.271952	+	0.471035i	−0.697410	+	0.716673i	$0.745664\pi$
$350$	−2.45427	+	1.41697i	−0.131186	+	0.0757404i
$351$	0.486978	+	0.281157i	0.0259930	+	0.0150070i
$352$	−1.58824	−	0.916973i	−0.0846537	−	0.0488748i
$353$	−5.13435	+	2.96432i	−0.273274	+	0.157775i	−0.630375	−	0.776291i	$-0.717099\pi$
$353$	−5.13435	+	2.96432i	−0.273274	+	0.157775i	0.357101	+	0.934066i	$0.383765\pi$
$354$	2.50260	+	4.33464i	0.133012	+	0.230383i
$355$	−8.51638	+	4.91693i	−0.452002	+	0.260964i
$356$		−	7.74677i		−	0.410578i
$357$	−0.721080	−	0.416316i	−0.0381636	−	0.0220338i
$358$	−5.68184	−	9.84124i	−0.300295	−	0.520126i
$359$	−10.9155			−0.576096			−0.288048	−	0.957616i	$-0.593006\pi$
$359$	−10.9155			−0.576096			−0.288048	+	0.957616i	$0.593006\pi$
$360$	1.00000			0.0527046
$361$	−4.58852	−	7.94755i	−0.241501	−	0.418292i
$362$			5.34205i			0.280772i
$363$	3.81832	−	6.61352i	0.200410	−	0.347120i
$364$			1.59357i			0.0835256i
$365$	5.26464	+	3.03954i	0.275564	+	0.159097i
$366$	−1.81845	+	3.14965i	−0.0950521	+	0.164635i
$367$	1.57721	−	2.73180i	0.0823295	−	0.142599i	−0.821921	−	0.569602i	$-0.807097\pi$
$367$	1.57721	−	2.73180i	0.0823295	−	0.142599i	0.904250	+	0.427003i	$0.140431\pi$
$368$	6.96479	−	4.02112i	0.363065	−	0.209616i
$369$	−3.63691			−0.189330
$370$	4.07258	−	4.51820i	0.211723	−	0.234890i
$371$	−15.0667			−0.782223
$372$	−8.79334	+	5.07684i	−0.455913	+	0.263222i
$373$	−14.8254	+	25.6784i	−0.767632	+	1.32958i	0.171212	+	0.985234i	$0.445232\pi$
$373$	−14.8254	+	25.6784i	−0.767632	+	1.32958i	−0.938844	+	0.344344i	$0.888102\pi$
$374$	0.269412	−	0.466636i	0.0139310	−	0.0241292i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$			3.85999i			0.199064i
$377$	−0.279512	+	0.484129i	−0.0143956	+	0.0249339i
$378$			2.83395i			0.145762i
$379$	−17.1242	−	29.6599i	−0.879609	−	1.52353i	−0.851771	−	0.523915i	$-0.824471\pi$
$379$	−17.1242	−	29.6599i	−0.879609	−	1.52353i	−0.0278385	−	0.999612i	$-0.508862\pi$
$380$	−3.13416			−0.160779
$381$	−6.16635			−0.315911
$382$	−2.56091	−	4.43563i	−0.131028	−	0.226946i
$383$	8.58359	+	4.95574i	0.438601	+	0.253226i	0.703004	−	0.711186i	$-0.251842\pi$
$383$	8.58359	+	4.95574i	0.438601	+	0.253226i	−0.264403	+	0.964412i	$0.585175\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	4.50100	−	2.59865i	0.229392	−	0.132440i
$386$	−4.48309	−	7.76494i	−0.228183	−	0.395225i
$387$	4.13631	−	2.38810i	0.210260	−	0.121394i
$388$	−11.2478	−	6.49394i	−0.571023	−	0.329680i
$389$	22.5243	+	13.0044i	1.14203	+	0.659349i	0.946931	−	0.321436i	$-0.104165\pi$
$389$	22.5243	+	13.0044i	1.14203	+	0.659349i	0.195094	+	0.980785i	$0.437499\pi$
$390$	0.486978	−	0.281157i	0.0246591	−	0.0142369i
$391$	1.18143	+	2.04630i	0.0597475	+	0.103486i
$392$	−0.893091	+	0.515627i	−0.0451079	+	0.0260431i
$393$			4.41057i			0.222484i
$394$	−0.723416	−	0.417665i	−0.0364452	−	0.0210416i
$395$	6.28035	+	10.8779i	0.315999	+	0.547326i
$396$	−1.83395			−0.0921593
$397$	9.25882			0.464687			0.232343	−	0.972634i	$-0.425361\pi$
$397$	9.25882			0.464687			0.232343	+	0.972634i	$0.425361\pi$
$398$	−1.99466	−	3.45485i	−0.0999831	−	0.173176i
$399$		−	8.88204i		−	0.444658i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			23.4901i			1.17304i	0.809935	+	0.586520i	$0.199502\pi$
$401$			23.4901i			1.17304i	−0.809935	+	0.586520i	$0.800498\pi$
$402$	5.95503	+	3.43814i	0.297010	+	0.171479i
$403$	−2.85477	+	4.94461i	−0.142206	+	0.246309i
$404$	2.62824	−	4.55224i	0.130760	−	0.226483i
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−2.81737			−0.139824
$407$	−7.46889	+	8.28613i	−0.370219	+	0.410728i
$408$	0.293806			0.0145456
$409$	22.0190	−	12.7127i	1.08877	−	0.628601i	0.155520	−	0.987833i	$-0.450295\pi$
$409$	22.0190	−	12.7127i	1.08877	−	0.628601i	0.933248	+	0.359232i	$0.116961\pi$
$410$	−1.81845	+	3.14965i	−0.0898070	+	0.155550i
$411$	−4.11201	+	7.12222i	−0.202831	+	0.351313i
$412$	4.07940	+	2.35524i	0.200978	+	0.116035i
$413$			14.1845i			0.697973i
$414$	4.02112	−	6.96479i	0.197627	−	0.342301i
$415$		−	9.68474i		−	0.475405i
$416$	−0.281157	−	0.486978i	−0.0137848	−	0.0238761i
$417$	−9.43463			−0.462016
$418$	5.74788			0.281138
$419$	17.9333	+	31.0615i	0.876101	+	1.51745i	0.855585	+	0.517662i	$0.173198\pi$
$419$	17.9333	+	31.0615i	0.876101	+	1.51745i	0.0205164	+	0.999790i	$0.493469\pi$
$420$	2.45427	+	1.41697i	0.119756	+	0.0691412i
$421$		−	18.8623i		−	0.919293i	−0.888102	−	0.459646i	$-0.847976\pi$
$421$		−	18.8623i		−	0.919293i	0.888102	−	0.459646i	$-0.152024\pi$
$422$	−20.9737	+	12.1092i	−1.02098	+	0.589466i
$423$	1.93000	+	3.34285i	0.0938396	+	0.162535i
$424$	4.60422	−	2.65825i	0.223601	−	0.129096i
$425$	0.254444	+	0.146903i	0.0123423	+	0.00712585i
$426$	8.51638	+	4.91693i	0.412620	+	0.238226i
$427$	−8.92595	+	5.15340i	−0.431957	+	0.249390i
$428$	−6.72696	−	11.6514i	−0.325160	−	0.563194i
$429$	−0.893091	+	0.515627i	−0.0431189	+	0.0248947i
$430$		−	4.77620i		−	0.230329i
$431$	−23.8370	−	13.7623i	−1.14819	−	0.662907i	−0.199743	−	0.979848i	$-0.564011\pi$
$431$	−23.8370	−	13.7623i	−1.14819	−	0.662907i	−0.948445	+	0.316942i	$0.897344\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	23.6642			1.13723			0.568613	−	0.822605i	$-0.307480\pi$
$433$	23.6642			1.13723			0.568613	+	0.822605i	$0.307480\pi$
$434$	−28.7750			−1.38124
$435$	0.497075	+	0.860960i	0.0238329	+	0.0412799i
$436$			0.111839i			0.00535614i
$437$	−12.6028	+	21.8288i	−0.602876	+	1.04421i
$438$		−	6.07908i		−	0.290470i
$439$	18.4034	+	10.6252i	0.878347	+	0.507114i	0.870113	−	0.492852i	$-0.164046\pi$
$439$	18.4034	+	10.6252i	0.878347	+	0.507114i	0.00823426	+	0.999966i	$0.497379\pi$
$440$	−0.916973	+	1.58824i	−0.0437150	+	0.0757166i
$441$	−0.515627	+	0.893091i	−0.0245536	+	0.0425282i
$442$	0.143077	−	0.0826056i	0.00680548	−	0.00392915i
$443$	34.4183			1.63526			0.817632	−	0.575741i	$-0.195286\pi$
$443$	34.4183			1.63526			0.817632	+	0.575741i	$0.195286\pi$
$444$	−5.94916	−	1.26786i	−0.282335	−	0.0601698i
$445$	−7.74677			−0.367232
$446$	10.5489	−	6.09040i	0.499504	−	0.288389i
$447$	0.314970	−	0.545545i	0.0148976	−	0.0258034i
$448$	1.41697	−	2.45427i	0.0669457	−	0.115953i
$449$	−1.22020	−	0.704482i	−0.0575847	−	0.0332465i	0.470931	−	0.882170i	$-0.343918\pi$
$449$	−1.22020	−	0.704482i	−0.0575847	−	0.0332465i	−0.528516	+	0.848923i	$0.677251\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	3.33495	−	5.77630i	0.157036	−	0.271995i
$452$			18.6091i			0.875299i
$453$	−0.868970	−	1.50510i	−0.0408278	−	0.0707158i
$454$	−2.39019			−0.112177
$455$	1.59357			0.0747076
$456$	1.56708	+	2.71426i	0.0733852	+	0.127107i
$457$	−20.7484	−	11.9791i	−0.970570	−	0.560359i	−0.0711598	−	0.997465i	$-0.522670\pi$
$457$	−20.7484	−	11.9791i	−0.970570	−	0.560359i	−0.899410	+	0.437106i	$0.856003\pi$
$458$		−	10.6972i		−	0.499847i
$459$	0.254444	−	0.146903i	0.0118764	−	0.00685685i
$460$	−4.02112	−	6.96479i	−0.187486	−	0.324735i
$461$	5.15659	−	2.97716i	0.240166	−	0.138660i	−0.375087	−	0.926990i	$-0.622387\pi$
$461$	5.15659	−	2.97716i	0.240166	−	0.138660i	0.615253	+	0.788330i	$0.289054\pi$
$462$	−4.50100	−	2.59865i	−0.209405	−	0.120900i
$463$	19.0347	+	10.9897i	0.884618	+	0.510734i	0.872178	−	0.489188i	$-0.162707\pi$
$463$	19.0347	+	10.9897i	0.884618	+	0.510734i	0.0124397	+	0.999923i	$0.496040\pi$
$464$	0.860960	−	0.497075i	0.0399691	−	0.0230761i
$465$	5.07684	+	8.79334i	0.235433	+	0.407781i
$466$	5.74646	−	3.31772i	0.266200	−	0.153690i
$467$		−	5.14968i		−	0.238299i	−0.992876	−	0.119149i	$-0.961983\pi$
$467$		−	5.14968i		−	0.238299i	0.992876	−	0.119149i	$-0.0380167\pi$
$468$	−0.486978	−	0.281157i	−0.0225106	−	0.0129965i
$469$	9.74350	+	16.8762i	0.449913	+	0.779272i
$470$	3.85999			0.178048
$471$	16.0425			0.739201
$472$	−2.50260	−	4.33464i	−0.115192	−	0.199518i
$473$			8.75929i			0.402753i
$474$	6.28035	−	10.8779i	0.288466	−	0.499638i
$475$			3.13416i			0.143805i
$476$	0.721080	+	0.416316i	0.0330506	+	0.0190818i
$477$	2.65825	−	4.60422i	0.121713	−	0.210813i
$478$	11.1512	−	19.3145i	0.510046	−	0.883426i
$479$	7.12652	−	4.11450i	0.325619	−	0.187996i	−0.328275	−	0.944582i	$-0.606467\pi$
$479$	7.12652	−	4.11450i	0.325619	−	0.187996i	0.653894	+	0.756586i	$0.273134\pi$
$480$	−1.00000			−0.0456435
$481$	−3.25358	+	1.05523i	−0.148350	+	0.0481143i
$482$	19.8302			0.903241
$483$	19.7378	−	11.3956i	0.898103	−	0.518520i
$484$	−3.81832	+	6.61352i	−0.173560	+	0.300615i
$485$	−6.49394	+	11.2478i	−0.294875	+	0.510738i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$			17.7139i			0.802696i	0.915926	+	0.401348i	$0.131458\pi$
$487$			17.7139i			0.802696i	−0.915926	+	0.401348i	$0.868542\pi$
$488$	1.81845	−	3.14965i	0.0823175	−	0.142578i
$489$		−	12.7414i		−	0.576186i
$490$	0.515627	+	0.893091i	0.0232936	+	0.0403458i
$491$	−15.4747			−0.698365			−0.349183	−	0.937055i	$-0.613541\pi$
$491$	−15.4747			−0.698365			−0.349183	+	0.937055i	$0.613541\pi$
$492$	3.63691			0.163964
$493$	0.146044	+	0.252955i	0.00657748	+	0.0113925i
$494$	1.52627	+	0.881190i	0.0686700	+	0.0396466i
$495$			1.83395i			0.0824298i
$496$	8.79334	−	5.07684i	0.394833	−	0.227957i
$497$	13.9343	+	24.1350i	0.625040	+	1.08260i
$498$	−8.38723	+	4.84237i	−0.375841	+	0.216992i
$499$	33.6502	+	19.4280i	1.50639	+	0.869715i	0.999972	+	0.00742676i	$0.00236403\pi$
$499$	33.6502	+	19.4280i	1.50639	+	0.869715i	0.506418	+	0.862288i	$0.330969\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−12.7548	+	7.36397i	−0.569841	+	0.328998i
$502$	−8.09035	−	14.0129i	−0.361090	−	0.625426i
$503$	26.6601	−	15.3922i	1.18871	−	0.686304i	0.230699	−	0.973025i	$-0.425899\pi$
$503$	26.6601	−	15.3922i	1.18871	−	0.686304i	0.958014	+	0.286721i	$0.0925654\pi$
$504$		−	2.83395i		−	0.126234i
$505$	−4.55224	−	2.62824i	−0.202572	−	0.116955i
$506$	7.37453	+	12.7731i	0.327838	+	0.567831i
$507$	12.6838			0.563307
$508$	6.16635			0.273587
$509$	−10.5045	−	18.1943i	−0.465602	−	0.806446i	0.533627	−	0.845720i	$-0.320829\pi$
$509$	−10.5045	−	18.1943i	−0.465602	−	0.806446i	−0.999228	+	0.0392740i	$0.987495\pi$
$510$		−	0.293806i		−	0.0130100i
$511$	8.61390	−	14.9197i	0.381056	−	0.660009i
$512$			1.00000i			0.0441942i
$513$	2.71426	+	1.56708i	0.119838	+	0.0691883i
$514$	11.3590	−	19.6743i	0.501024	−	0.867798i
$515$	2.35524	−	4.07940i	0.103784	−	0.179760i
$516$	−4.13631	+	2.38810i	−0.182091	+	0.105130i
$517$	−7.07902			−0.311335
$518$	−12.8043	−	11.5415i	−0.562590	−	0.507103i
$519$	−7.05353			−0.309616
$520$	−0.486978	+	0.281157i	−0.0213554	+	0.0123295i
$521$	9.39950	−	16.2804i	0.411800	−	0.713258i	−0.583287	−	0.812266i	$-0.698234\pi$
$521$	9.39950	−	16.2804i	0.411800	−	0.713258i	0.995087	+	0.0990081i	$0.0315670\pi$
$522$	0.497075	−	0.860960i	0.0217564	−	0.0376832i
$523$	32.4318	+	18.7245i	1.41814	+	0.818766i	0.996136	−	0.0878256i	$-0.0279918\pi$
$523$	32.4318	+	18.7245i	1.41814	+	0.818766i	0.422009	+	0.906592i	$0.361325\pi$
$524$		−	4.41057i		−	0.192676i
$525$	1.41697	−	2.45427i	0.0618418	−	0.107113i
$526$		−	17.1908i		−	0.749554i
$527$	1.49161	+	2.58354i	0.0649754	+	0.112541i
$528$	1.83395			0.0798123
$529$	−41.6777			−1.81208
$530$	−2.65825	−	4.60422i	−0.115467	−	0.199995i
$531$	−4.33464	−	2.50260i	−0.188107	−	0.108604i
$532$			8.88204i			0.385085i
$533$	1.77109	−	1.02254i	0.0767145	−	0.0442912i
$534$	3.87338	+	6.70890i	0.167618	+	0.290322i
$535$	−11.6514	+	6.72696i	−0.503736	+	0.290832i
$536$	−5.95503	−	3.43814i	−0.257218	−	0.148505i
$537$	9.84124	+	5.68184i	0.424681	+	0.245190i
$538$	−26.7225	+	15.4282i	−1.15209	+	0.665158i
$539$	−0.945631	−	1.63788i	−0.0407312	−	0.0705486i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$			26.8453i			1.15417i	0.816684	+	0.577085i	$0.195810\pi$
$541$			26.8453i			1.15417i	−0.816684	+	0.577085i	$0.804190\pi$
$542$	3.51263	+	2.02802i	0.150881	+	0.0871109i
$543$	−2.67102	−	4.62635i	−0.114625	−	0.198536i
$544$	−0.293806			−0.0125968
$545$	0.111839			0.00479067
$546$	−0.796783	−	1.38007i	−0.0340992	−	0.0590615i
$547$		−	2.35688i		−	0.100773i	−0.998730	−	0.0503865i	$-0.983955\pi$
$547$		−	2.35688i		−	0.100773i	0.998730	−	0.0503865i	$-0.0160453\pi$
$548$	4.11201	−	7.12222i	0.175656	−	0.304246i
$549$		−	3.63691i		−	0.155219i
$550$	1.58824	+	0.916973i	0.0677230	+	0.0390999i
$551$	−1.55791	+	2.69839i	−0.0663694	+	0.114955i
$552$	−4.02112	+	6.96479i	−0.171150	+	0.296441i
$553$	30.8274	−	17.7982i	1.31091	−	0.756856i
$554$	−10.8554			−0.461203
$555$	−1.26786	+	5.94916i	−0.0538175	+	0.252528i
$556$	9.43463			0.400118
$557$	21.1417	−	12.2061i	0.895801	−	0.517191i	0.0199657	−	0.999801i	$-0.493644\pi$
$557$	21.1417	−	12.2061i	0.895801	−	0.517191i	0.875836	+	0.482610i	$0.160311\pi$
$558$	5.07684	−	8.79334i	0.214920	−	0.372252i
$559$	−1.34286	+	2.32590i	−0.0567969	+	0.0983752i
$560$	−2.45427	−	1.41697i	−0.103712	−	0.0598780i
$561$			0.538825i			0.0227492i
$562$	−7.98107	+	13.8236i	−0.336661	+	0.583114i
$563$			3.54306i			0.149322i	0.997209	+	0.0746611i	$0.0237875\pi$
$563$			3.54306i			0.149322i	−0.997209	+	0.0746611i	$0.976212\pi$
$564$	−1.93000	−	3.34285i	−0.0812675	−	0.140759i
$565$	18.6091			0.782891
$566$	22.5748			0.948889
$567$	−1.41697	−	2.45427i	−0.0595073	−	0.103070i
$568$	−8.51638	−	4.91693i	−0.357339	−	0.206310i
$569$		−	41.3205i		−	1.73224i	−0.499833	−	0.866122i	$-0.666605\pi$
$569$		−	41.3205i		−	1.73224i	0.499833	−	0.866122i	$-0.333395\pi$
$570$	2.71426	−	1.56708i	0.113688	−	0.0656378i
$571$	12.1942	+	21.1210i	0.510311	+	0.883885i	0.999929	+	0.0119473i	$0.00380304\pi$
$571$	12.1942	+	21.1210i	0.510311	+	0.883885i	−0.489618	+	0.871937i	$0.662864\pi$
$572$	0.893091	−	0.515627i	0.0373420	−	0.0215594i
$573$	4.43563	+	2.56091i	0.185301	+	0.106984i
$574$	8.92595	+	5.15340i	0.372562	+	0.215099i
$575$	−6.96479	+	4.02112i	−0.290452	+	0.167692i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	7.91829	−	4.57163i	0.329643	−	0.190319i	−0.326040	−	0.945356i	$-0.605714\pi$
$577$	7.91829	−	4.57163i	0.329643	−	0.190319i	0.655682	+	0.755037i	$0.272381\pi$
$578$			16.9137i			0.703516i
$579$	7.76494	+	4.48309i	0.322700	+	0.186311i
$580$	−0.497075	−	0.860960i	−0.0206399	−	0.0357494i
$581$	−27.4460			−1.13865
$582$	12.9879			0.538365
$583$	4.87509	+	8.44390i	0.201905	+	0.349710i
$584$			6.07908i			0.251554i
$585$	−0.281157	+	0.486978i	−0.0116244	+	0.0201341i
$586$			12.2500i			0.506042i
$587$	−31.0743	−	17.9408i	−1.28257	−	0.740495i	−0.305256	−	0.952270i	$-0.598742\pi$
$587$	−31.0743	−	17.9408i	−1.28257	−	0.740495i	−0.977318	+	0.211775i	$0.932075\pi$
$588$	0.515627	−	0.893091i	0.0212641	−	0.0368305i
$589$	−15.9116	+	27.5597i	−0.655627	+	1.13558i
$590$	−4.33464	+	2.50260i	−0.178454	+	0.103031i
$591$	0.835329			0.0343609
$592$	5.94916	+	1.26786i	0.244509	+	0.0521085i
$593$	−26.1766			−1.07494			−0.537472	−	0.843281i	$-0.680621\pi$
$593$	−26.1766			−1.07494			−0.537472	+	0.843281i	$0.680621\pi$
$594$	1.58824	−	0.916973i	0.0651665	−	0.0376239i
$595$	0.416316	−	0.721080i	0.0170673	−	0.0295614i
$596$	−0.314970	+	0.545545i	−0.0129017	+	0.0223464i
$597$	3.45485	+	1.99466i	0.141397	+	0.0816359i
$598$			4.52226i			0.184929i
$599$	12.7578	−	22.0972i	0.521271	−	0.902869i	−0.478423	−	0.878130i	$-0.658791\pi$
$599$	12.7578	−	22.0972i	0.521271	−	0.902869i	0.999694	−	0.0247388i	$-0.00787540\pi$
$600$			1.00000i			0.0408248i
$601$	−16.2959	−	28.2252i	−0.664722	−	1.15133i	−0.979361	−	0.202120i	$-0.935217\pi$
$601$	−16.2959	−	28.2252i	−0.664722	−	1.15133i	0.314639	−	0.949211i	$-0.398117\pi$
$602$	−13.5355			−0.551665
$603$	−6.87628			−0.280024
$604$	0.868970	+	1.50510i	0.0353579	+	0.0612417i
$605$	6.61352	+	3.81832i	0.268878	+	0.155237i
$606$			5.25648i			0.213530i
$607$	13.5455	−	7.82049i	0.549795	−	0.317424i	−0.199245	−	0.979950i	$-0.563849\pi$
$607$	13.5455	−	7.82049i	0.549795	−	0.317424i	0.749039	+	0.662526i	$0.230515\pi$
$608$	−1.56708	−	2.71426i	−0.0635535	−	0.110078i
$609$	2.43991	−	1.40869i	0.0988703	−	0.0570828i
$610$	−3.14965	−	1.81845i	−0.127526	−	0.0736270i
$611$	−1.87973	−	1.08526i	−0.0760457	−	0.0439050i
$612$	−0.254444	+	0.146903i	−0.0102853	+	0.00593821i
$613$	13.7929	+	23.8899i	0.557088	+	0.964905i	0.997738	+	0.0672260i	$0.0214149\pi$
$613$	13.7929	+	23.8899i	0.557088	+	0.964905i	−0.440649	+	0.897679i	$0.645252\pi$
$614$	−25.6426	+	14.8048i	−1.03485	+	0.597471i
$615$		−	3.63691i		−	0.146654i
$616$	4.50100	+	2.59865i	0.181350	+	0.104703i
$617$	10.5365	+	18.2498i	0.424184	+	0.734708i	0.996344	−	0.0854343i	$-0.0272278\pi$
$617$	10.5365	+	18.2498i	0.424184	+	0.734708i	−0.572160	+	0.820142i	$0.693894\pi$
$618$	−4.71049			−0.189484
$619$	28.7412			1.15521			0.577604	−	0.816317i	$-0.303988\pi$
$619$	28.7412			1.15521			0.577604	+	0.816317i	$0.303988\pi$
$620$	−5.07684	−	8.79334i	−0.203891	−	0.353149i
$621$			8.04225i			0.322724i
$622$	11.3094	−	19.5885i	0.453467	−	0.785428i
$623$			21.9539i			0.879565i
$624$	0.486978	+	0.281157i	0.0194947	+	0.0112553i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.805205	−	1.39466i	0.0321824	−	0.0557416i
$627$	−4.97781	+	2.87394i	−0.198795	+	0.114774i
$628$	−16.0425			−0.640167
$629$	−0.372504	+	1.74790i	−0.0148527	+	0.0696934i
$630$	−2.83395			−0.112907
$631$	16.9950	−	9.81209i	0.676562	−	0.390613i	−0.121996	−	0.992531i	$-0.538930\pi$
$631$	16.9950	−	9.81209i	0.676562	−	0.390613i	0.798558	+	0.601917i	$0.205596\pi$
$632$	−6.28035	+	10.8779i	−0.249819	+	0.432699i
$633$	12.1092	−	20.9737i	0.481297	−	0.833630i
$634$	7.34084	+	4.23824i	0.291542	+	0.168322i
$635$		−	6.16635i		−	0.244704i
$636$	−2.65825	+	4.60422i	−0.105406	+	0.182569i
$637$		−	0.579888i		−	0.0229760i
$638$	0.911610	+	1.57895i	0.0360910	+	0.0625114i
$639$	−9.83386			−0.389022
$640$	1.00000			0.0395285
$641$	−3.86384	−	6.69237i	−0.152613	−	0.264333i	0.779575	−	0.626309i	$-0.215435\pi$
$641$	−3.86384	−	6.69237i	−0.152613	−	0.264333i	−0.932187	+	0.361977i	$0.882102\pi$
$642$	11.6514	+	6.72696i	0.459846	+	0.265492i
$643$		−	8.92987i		−	0.352160i	−0.984376	−	0.176080i	$-0.943658\pi$
$643$		−	8.92987i		−	0.352160i	0.984376	−	0.176080i	$-0.0563417\pi$
$644$	−19.7378	+	11.3956i	−0.777780	+	0.449051i
$645$	2.38810	+	4.13631i	0.0940313	+	0.162867i
$646$	0.797467	−	0.460418i	0.0313759	−	0.0181149i
$647$	−8.07382	−	4.66142i	−0.317414	−	0.183259i	0.332825	−	0.942989i	$-0.391998\pi$
$647$	−8.07382	−	4.66142i	−0.317414	−	0.183259i	−0.650240	+	0.759729i	$0.725331\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	7.94949	−	4.58964i	0.312045	−	0.180159i
$650$	0.281157	+	0.486978i	0.0110279	+	0.0191008i
$651$	24.9199	−	14.3875i	0.976686	−	0.563890i
$652$			12.7414i			0.498991i
$653$	−15.0613	−	8.69566i	−0.589395	−	0.340288i	0.175463	−	0.984486i	$-0.443858\pi$
$653$	−15.0613	−	8.69566i	−0.589395	−	0.340288i	−0.764858	+	0.644198i	$0.777191\pi$
$654$	−0.0559197	−	0.0968558i	−0.00218663	−	0.00378736i
$655$	−4.41057			−0.172335
$656$	−3.63691			−0.141997
$657$	3.03954	+	5.26464i	0.118584	+	0.205393i
$658$		−	10.9390i		−	0.426447i
$659$	4.69587	−	8.13349i	0.182925	−	0.316836i	−0.759950	−	0.649981i	$-0.774777\pi$
$659$	4.69587	−	8.13349i	0.182925	−	0.316836i	0.942875	+	0.333145i	$0.108110\pi$
$660$		−	1.83395i		−	0.0713863i
$661$	11.7631	+	6.79143i	0.457532	+	0.264156i	0.711006	−	0.703186i	$-0.248240\pi$
$661$	11.7631	+	6.79143i	0.457532	+	0.264156i	−0.253474	+	0.967342i	$0.581573\pi$
$662$	1.68708	−	2.92211i	0.0655702	−	0.113571i
$663$	−0.0826056	+	0.143077i	−0.00320814	+	0.00555665i
$664$	8.38723	−	4.84237i	0.325488	−	0.187920i
$665$	8.88204			0.344431
$666$	5.78605	−	1.87659i	0.224205	−	0.0727162i
$667$	−7.99521			−0.309576
$668$	12.7548	−	7.36397i	0.493497	−	0.284921i
$669$	−6.09040	+	10.5489i	−0.235468	+	0.407843i
$670$	−3.43814	+	5.95503i	−0.132827	+	0.230063i
$671$	5.77630	+	3.33495i	0.222991	+	0.128744i
$672$			2.83395i			0.109322i
$673$	16.2206	−	28.0950i	0.625260	−	1.08298i	−0.363231	−	0.931699i	$-0.618326\pi$
$673$	16.2206	−	28.0950i	0.625260	−	1.08298i	0.988491	−	0.151282i	$-0.0483402\pi$
$674$			16.4873i			0.635066i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−12.6838			−0.487839
$677$	−8.16129			−0.313664			−0.156832	−	0.987625i	$-0.550128\pi$
$677$	−8.16129			−0.313664			−0.156832	+	0.987625i	$0.550128\pi$
$678$	−9.30455	−	16.1160i	−0.357339	−	0.618930i
$679$	31.8758	+	18.4035i	1.22328	+	0.706261i
$680$			0.293806i			0.0112670i
$681$	2.06996	−	1.19509i	0.0793212	−	0.0457961i
$682$	9.31065	+	16.1265i	0.356523	+	0.617516i
$683$	−37.3666	+	21.5736i	−1.42979	+	0.825492i	−0.997104	−	0.0760509i	$-0.975769\pi$
$683$	−37.3666	+	21.5736i	−1.42979	+	0.825492i	−0.432690	+	0.901543i	$0.642436\pi$
$684$	−2.71426	−	1.56708i	−0.103782	−	0.0599188i
$685$	−7.12222	−	4.11201i	−0.272126	−	0.157112i
$686$	−14.6489	+	8.45755i	−0.559298	+	0.322911i
$687$	5.34859	+	9.26404i	0.204062	+	0.353445i
$688$	4.13631	−	2.38810i	0.157695	−	0.0910454i
$689$			2.98954i			0.113892i
$690$	6.96479	+	4.02112i	0.265145	+	0.153082i
$691$	22.2826	+	38.5947i	0.847671	+	1.46821i	0.883281	+	0.468844i	$0.155329\pi$
$691$	22.2826	+	38.5947i	0.847671	+	1.46821i	−0.0356096	+	0.999366i	$0.511337\pi$
$692$	7.05353			0.268135
$693$	5.19731			0.197429
$694$	3.33572	+	5.77763i	0.126622	+	0.219316i
$695$		−	9.43463i		−	0.357876i
$696$	−0.497075	+	0.860960i	−0.0188416	+	0.0326346i
$697$		−	1.06855i		−	0.0404741i
$698$	8.79965	+	5.08048i	0.333072	+	0.192299i
$699$	−3.31772	+	5.74646i	−0.125488	+	0.217351i
$700$	−1.41697	+	2.45427i	−0.0535566	+	0.0927627i
$701$	24.3770	−	14.0741i	0.920708	−	0.531571i	0.0368474	−	0.999321i	$-0.488268\pi$
$701$	24.3770	−	14.0741i	0.920708	−	0.531571i	0.883861	+	0.467750i	$0.154935\pi$
$702$	0.562314			0.0212232
$703$	−18.1344	+	5.88152i	−0.683953	+	0.221826i
$704$	−1.83395			−0.0691195
$705$	−3.34285	+	1.93000i	−0.125899	+	0.0726878i
$706$	−2.96432	+	5.13435i	−0.111564	+	0.193234i
$707$	−7.44829	+	12.9008i	−0.280122	+	0.485185i
$708$	4.33464	+	2.50260i	0.162906	+	0.0940536i
$709$			0.882826i			0.0331552i	0.999863	+	0.0165776i	$0.00527706\pi$
$709$			0.882826i			0.0331552i	−0.999863	+	0.0165776i	$0.994723\pi$
$710$	−4.91693	+	8.51638i	−0.184529	+	0.319614i
$711$			12.5607i			0.471063i
$712$	−3.87338	−	6.70890i	−0.145161	−	0.251427i
$713$	−81.6584			−3.05813
$714$	−0.832631			−0.0311604
$715$	−0.515627	−	0.893091i	−0.0192833	−	0.0333997i
$716$	−9.84124	−	5.68184i	−0.367784	−	0.212340i
$717$			22.3025i			0.832902i
$718$	−9.45307	+	5.45773i	−0.352785	+	0.203681i
$719$	−4.11308	−	7.12407i	−0.153392	−	0.265683i	0.779080	−	0.626924i	$-0.215686\pi$
$719$	−4.11308	−	7.12407i	−0.153392	−	0.265683i	−0.932472	+	0.361241i	$0.882353\pi$
$720$	0.866025	−	0.500000i	0.0322749	−	0.0186339i
$721$	−11.5608	−	6.67464i	−0.430547	−	0.248576i
$722$	−7.94755	−	4.58852i	−0.295777	−	0.170767i
$723$	−17.1735	+	9.91510i	−0.638688	+	0.368746i
$724$	2.67102	+	4.62635i	0.0992678	+	0.171937i
$725$	−0.860960	+	0.497075i	−0.0319752	+	0.0184609i
$726$		−	7.63664i		−	0.283422i
$727$	−28.4163	−	16.4062i	−1.05390	−	0.608471i	−0.130164	−	0.991493i	$-0.541550\pi$
$727$	−28.4163	−	16.4062i	−1.05390	−	0.608471i	−0.923740	+	0.383021i	$0.874884\pi$
$728$	0.796783	+	1.38007i	0.0295308	+	0.0511488i
$729$	1.00000			0.0370370
$730$	6.07908			0.224997
$731$	0.701638	+	1.21527i	0.0259510	+	0.0449485i
$732$			3.63691i			0.134424i
$733$	−6.70846	+	11.6194i	−0.247783	+	0.429172i	−0.962910	−	0.269822i	$-0.913035\pi$
$733$	−6.70846	+	11.6194i	−0.247783	+	0.429172i	0.715128	+	0.698994i	$0.246369\pi$
$734$		−	3.15441i		−	0.116432i
$735$	−0.893091	−	0.515627i	−0.0329422	−	0.0190192i
$736$	4.02112	−	6.96479i	0.148221	−	0.256726i
$737$	6.30536	−	10.9212i	0.232261	−	0.402288i
$738$	−3.14965	+	1.81845i	−0.115940	+	0.0669382i
$739$	−0.120314			−0.00442582			−0.00221291	−	0.999998i	$-0.500704\pi$
$739$	−0.120314			−0.00442582			−0.00221291	+	0.999998i	$0.500704\pi$
$740$	1.26786	−	5.94916i	0.0466073	−	0.218696i
$741$	−1.76238			−0.0647427
$742$	−13.0481	+	7.53334i	−0.479012	+	0.276557i
$743$	−16.2272	+	28.1063i	−0.595317	+	1.03112i	0.398185	+	0.917305i	$0.369640\pi$
$743$	−16.2272	+	28.1063i	−0.595317	+	1.03112i	−0.993502	+	0.113814i	$0.963693\pi$
$744$	−5.07684	+	8.79334i	−0.186126	+	0.322380i
$745$	0.545545	+	0.314970i	0.0199872	+	0.0115396i
$746$			29.6509i			1.08560i
$747$	4.84237	−	8.38723i	0.177173	−	0.306873i
$748$		−	0.538825i		−	0.0197014i
$749$	19.0639	+	33.0196i	0.696578	+	1.20651i
$750$	1.00000			0.0365148
$751$	19.5104			0.711943			0.355972	−	0.934497i	$-0.384150\pi$
$751$	19.5104			0.711943			0.355972	+	0.934497i	$0.384150\pi$
$752$	1.93000	+	3.34285i	0.0703797	+	0.121901i
$753$	14.0129	+	8.09035i	0.510658	+	0.294829i
$754$			0.559025i			0.0203585i
$755$	1.50510	−	0.868970i	0.0547762	−	0.0316251i
$756$	1.41697	+	2.45427i	0.0515348	+	0.0892609i
$757$	−16.1156	+	9.30436i	−0.585732	+	0.338173i	−0.763408	−	0.645916i	$-0.776475\pi$
$757$	−16.1156	+	9.30436i	−0.585732	+	0.338173i	0.177676	+	0.984089i	$0.443142\pi$
$758$	−29.6599	−	17.1242i	−1.07730	−	0.621978i
$759$	−12.7731	−	7.37453i	−0.463632	−	0.267678i
$760$	−2.71426	+	1.56708i	−0.0984566	+	0.0568440i
$761$	−4.56307	−	7.90348i	−0.165411	−	0.286501i	0.771390	−	0.636363i	$-0.219562\pi$
$761$	−4.56307	−	7.90348i	−0.165411	−	0.286501i	−0.936801	+	0.349862i	$0.886229\pi$
$762$	−5.34021	+	3.08317i	−0.193455	+	0.111692i
$763$		−	0.316947i		−	0.0114742i
$764$	−4.43563	−	2.56091i	−0.160475	−	0.0926505i
$765$	0.146903	+	0.254444i	0.00531129	+	0.00919943i
$766$	9.91148			0.358116
$767$	2.81450			0.101626
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$			2.11219i			0.0761674i	0.999275	+	0.0380837i	$0.0121253\pi$
$769$			2.11219i			0.0761674i	−0.999275	+	0.0380837i	$0.987875\pi$
$770$	2.59865	−	4.50100i	0.0936490	−	0.162205i
$771$			22.7180i			0.818168i
$772$	−7.76494	−	4.48309i	−0.279466	−	0.161350i
$773$	14.1527	−	24.5132i	0.509038	−	0.881679i	−0.490907	−	0.871212i	$-0.663335\pi$
$773$	14.1527	−	24.5132i	0.509038	−	0.881679i	0.999945	−	0.0104676i	$-0.00333201\pi$
$774$	2.38810	−	4.13631i	0.0858384	−	0.148676i
$775$	−8.79334	+	5.07684i	−0.315866	+	0.182365i
$776$	−12.9879			−0.466238
$777$	16.8596	+	3.59303i	0.604835	+	0.128899i
$778$	26.0088			0.932460
$779$	9.87152	−	5.69932i	0.353684	−	0.204199i
$780$	0.281157	−	0.486978i	0.0100670	−	0.0174366i
$781$	9.01739	−	15.6186i	0.322668	−	0.558877i
$782$	2.04630	+	1.18143i	0.0731755	+	0.0422479i
$783$			0.994151i			0.0355281i
$784$	−0.515627	+	0.893091i	−0.0184152	+	0.0318961i
$785$			16.0425i			0.572583i
$786$	2.20528	+	3.81966i	0.0786598	+	0.136243i
$787$	3.20692			0.114314			0.0571572	−	0.998365i	$-0.481796\pi$
$787$	3.20692			0.114314			0.0571572	+	0.998365i	$0.481796\pi$
$788$	−0.835329			−0.0297574
$789$	8.59540	+	14.8877i	0.306004	+	0.530015i
$790$	10.8779	+	6.28035i	0.387018	+	0.223445i
$791$		−	52.7372i		−	1.87512i
$792$	−1.58824	+	0.916973i	−0.0564358	+	0.0325832i
$793$	1.02254	+	1.77109i	0.0363115	+	0.0628934i
$794$	8.01837	−	4.62941i	0.284561	−	0.164292i
$795$	4.60422	+	2.65825i	0.163295	+	0.0942784i
$796$	−3.45485	−	1.99466i	−0.122454	−	0.0706987i
$797$	18.8025	−	10.8556i	0.666019	−	0.384526i	−0.128548	−	0.991703i	$-0.541032\pi$
$797$	18.8025	−	10.8556i	0.666019	−	0.384526i	0.794566	+	0.607177i	$0.207698\pi$
$798$	−4.44102	−	7.69207i	−0.157210	−	0.272296i
$799$	−0.982150	+	0.567045i	−0.0347460	+	0.0200606i
$800$		−	1.00000i		−	0.0353553i
$801$	−6.70890	−	3.87338i	−0.237047	−	0.136859i
$802$	11.7451	+	20.3430i	0.414732	+	0.718337i
$803$	−11.1487			−0.393429
$804$	6.87628			0.242508
$805$	11.3956	+	19.7378i	0.401644	+	0.695668i
$806$			5.70955i			0.201110i
$807$	15.4282	−	26.7225i	0.543100	−	0.940676i
$808$		−	5.25648i		−	0.184922i
$809$	−8.40721	−	4.85390i	−0.295582	−	0.170654i	0.344875	−	0.938649i	$-0.387921\pi$
$809$	−8.40721	−	4.85390i	−0.295582	−	0.170654i	−0.640456	+	0.767995i	$0.721255\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	7.77068	−	13.4592i	0.272866	−	0.472617i	−0.696729	−	0.717335i	$-0.745362\pi$
$811$	7.77068	−	13.4592i	0.272866	−	0.472617i	0.969594	+	0.244718i	$0.0786952\pi$
$812$	−2.43991	+	1.40869i	−0.0856242	+	0.0494352i
$813$	−4.05604			−0.142252
$814$	−2.32518	+	10.9104i	−0.0814975	+	0.382411i
$815$	12.7414			0.446312
$816$	0.254444	−	0.146903i	0.00890731	−	0.00514264i
$817$	−7.48468	+	12.9638i	−0.261856	+	0.453548i
$818$	12.7127	−	22.0190i	0.444488	−	0.769876i
$819$	1.38007	+	0.796783i	0.0482235	+	0.0278419i
$820$			3.63691i			0.127006i
$821$	−5.54261	+	9.60008i	−0.193438	+	0.335045i	−0.946387	−	0.323034i	$-0.895297\pi$
$821$	−5.54261	+	9.60008i	−0.193438	+	0.335045i	0.752949	+	0.658079i	$0.228631\pi$
$822$			8.22403i			0.286846i
$823$	16.1553	+	27.9818i	0.563138	+	0.975384i	0.997220	+	0.0745107i	$0.0237395\pi$
$823$	16.1553	+	27.9818i	0.563138	+	0.975384i	−0.434082	+	0.900873i	$0.642927\pi$
$824$	4.71049			0.164098
$825$	−1.83395			−0.0638498
$826$	7.09225	+	12.2841i	0.246771	+	0.427420i
$827$	17.3791	+	10.0338i	0.604330	+	0.348910i	0.770743	−	0.637146i	$-0.219885\pi$
$827$	17.3791	+	10.0338i	0.604330	+	0.348910i	−0.166413	+	0.986056i	$0.553219\pi$
$828$		−	8.04225i		−	0.279487i
$829$	2.61624	−	1.51049i	0.0908659	−	0.0524614i	−0.453879	−	0.891064i	$-0.649960\pi$
$829$	2.61624	−	1.51049i	0.0908659	−	0.0524614i	0.544744	+	0.838602i	$0.316627\pi$
$830$	−4.84237	−	8.38723i	−0.168081	−	0.291125i
$831$	9.40109	−	5.42772i	0.326120	−	0.188286i
$832$	−0.486978	−	0.281157i	−0.0168829	−	0.00974736i
$833$	−0.262396	−	0.151494i	−0.00909148	−	0.00524897i
$834$	−8.17063	+	4.71732i	−0.282926	+	0.163347i
$835$	−7.36397	−	12.7548i	−0.254841	−	0.441397i
$836$	4.97781	−	2.87394i	0.172161	−	0.0993973i
$837$			10.1537i			0.350962i
$838$	31.0615	+	17.9333i	1.07300	+	0.619497i
$839$	−10.2920	−	17.8263i	−0.355319	−	0.615431i	0.631853	−	0.775088i	$-0.282294\pi$
$839$	−10.2920	−	17.8263i	−0.355319	−	0.615431i	−0.987173	+	0.159657i	$0.948961\pi$
$840$	2.83395			0.0977804
$841$	28.0117			0.965919
$842$	−9.43115	−	16.3352i	−0.325019	−	0.562949i
$843$		−	15.9621i		−	0.549766i
$844$	−12.1092	+	20.9737i	−0.416815	+	0.721945i
$845$			12.6838i			0.436336i
$846$	3.34285	+	1.93000i	0.114930	+	0.0663546i
$847$	10.8209	−	18.7424i	0.371811	−	0.643996i
$848$	2.65825	−	4.60422i	0.0912846	−	0.158110i
$849$	−19.5503	+	11.2874i	−0.670966	+	0.387382i
$850$	0.293806			0.0100775
$851$	−36.3365	−	32.7527i	−1.24560	−	1.12275i
$852$	9.83386			0.336903
$853$	12.8202	−	7.40172i	0.438954	−	0.253430i	−0.264200	−	0.964468i	$-0.585108\pi$
$853$	12.8202	−	7.40172i	0.438954	−	0.253430i	0.703154	+	0.711038i	$0.251775\pi$
$854$	−5.15340	+	8.92595i	−0.176346	+	0.305440i
$855$	−1.56708	+	2.71426i	−0.0535930	+	0.0928258i
$856$	−11.6514	−	6.72696i	−0.398238	−	0.229923i
$857$			5.04927i			0.172480i	0.996274	+	0.0862398i	$0.0274851\pi$
$857$			5.04927i			0.172480i	−0.996274	+	0.0862398i	$0.972515\pi$
$858$	−0.515627	+	0.893091i	−0.0176032	+	0.0304896i
$859$			40.4119i			1.37884i	0.724363	+	0.689418i	$0.242134\pi$
$859$			40.4119i			1.37884i	−0.724363	+	0.689418i	$0.757866\pi$
$860$	−2.38810	−	4.13631i	−0.0814335	−	0.141047i
$861$	−10.3068			−0.351255
$862$	−27.5246			−0.937491
$863$	0.717387	+	1.24255i	0.0244202	+	0.0422969i	0.877977	−	0.478702i	$-0.158893\pi$
$863$	0.717387	+	1.24255i	0.0244202	+	0.0422969i	−0.853557	+	0.520999i	$0.825559\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		−	7.05353i		−	0.239827i
$866$	20.4938	−	11.8321i	0.696406	−	0.402070i
$867$	−8.45684	−	14.6477i	−0.287209	−	0.497461i
$868$	−24.9199	+	14.3875i	−0.845835	+	0.488343i
$869$	−19.9495	−	11.5178i	−0.676739	−	0.390716i
$870$	0.860960	+	0.497075i	0.0291893	+	0.0168524i
$871$	3.34859	−	1.93331i	0.113463	−	0.0655078i
$872$	0.0559197	+	0.0968558i	0.00189368	+	0.00327995i
$873$	−11.2478	+	6.49394i	−0.380682	+	0.219787i
$874$			25.2057i			0.852595i
$875$	2.45427	+	1.41697i	0.0829695	+	0.0479024i
$876$	−3.03954	−	5.26464i	−0.102697	−	0.177876i
$877$	28.1596			0.950882			0.475441	−	0.879748i	$-0.342288\pi$
$877$	28.1596			0.950882			0.475441	+	0.879748i	$0.342288\pi$
$878$	21.2504			0.717168
$879$	−6.12499	−	10.6088i	−0.206591	−	0.357826i
$880$			1.83395i			0.0618223i
$881$	−9.21608	+	15.9627i	−0.310498	+	0.537798i	−0.978470	−	0.206388i	$-0.933829\pi$
$881$	−9.21608	+	15.9627i	−0.310498	+	0.537798i	0.667973	+	0.744186i	$0.267162\pi$
$882$			1.03125i			0.0347241i
$883$	−16.8785	−	9.74478i	−0.568005	−	0.327938i	0.188347	−	0.982103i	$-0.439687\pi$
$883$	−16.8785	−	9.74478i	−0.568005	−	0.327938i	−0.756352	+	0.654164i	$0.773020\pi$
$884$	0.0826056	−	0.143077i	0.00277833	−	0.00481220i
$885$	2.50260	−	4.33464i	0.0841241	−	0.145707i
$886$	29.8071	−	17.2092i	1.00139	−	0.578153i
$887$	−43.6339			−1.46508			−0.732542	−	0.680722i	$-0.761666\pi$
$887$	−43.6339			−1.46508			−0.732542	+	0.680722i	$0.761666\pi$
$888$	−5.78605	+	1.87659i	−0.194167	+	0.0629741i
$889$	−17.4751			−0.586096
$890$	−6.70890	+	3.87338i	−0.224883	+	0.129836i
$891$	−0.916973	+	1.58824i	−0.0307198	+	0.0532082i
$892$	6.09040	−	10.5489i	0.203922	−	0.353202i
$893$	−10.4770	−	6.04891i	−0.350600	−	0.202419i
$894$		−	0.629941i		−	0.0210684i
$895$	−5.68184	+	9.84124i	−0.189923	+	0.328956i
$896$		−	2.83395i		−	0.0946755i
$897$	−2.26113	−	3.91640i	−0.0754970	−	0.130765i
$898$	−1.40896			−0.0470177
$899$	−10.0943			−0.336663
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	1.35275	+	0.781010i	0.0450666	+	0.0260192i
$902$		−	6.66989i		−	0.222083i
$903$	11.7221	−	6.76774i	0.390086	−	0.225216i
$904$	9.30455	+	16.1160i	0.309465	+	0.536009i
$905$	4.62635	−	2.67102i	0.153785	−	0.0887878i
$906$	−1.50510	−	0.868970i	−0.0500036	−	0.0288696i
$907$	−9.36593	−	5.40742i	−0.310991	−	0.179550i	0.336379	−	0.941727i	$-0.390798\pi$
$907$	−9.36593	−	5.40742i	−0.310991	−	0.179550i	−0.647370	+	0.762176i	$0.724131\pi$
$908$	−2.06996	+	1.19509i	−0.0686942	+	0.0396606i
$909$	−2.62824	−	4.55224i	−0.0871732	−	0.150988i
$910$	1.38007	−	0.796783i	0.0457488	−	0.0264131i
$911$			49.5010i			1.64004i	0.572335	+	0.820020i	$0.306038\pi$
$911$			49.5010i			1.64004i	−0.572335	+	0.820020i	$0.693962\pi$
$912$	2.71426	+	1.56708i	0.0898782	+	0.0518912i
$913$	8.88064	+	15.3817i	0.293906	+	0.509061i
$914$	−23.9582			−0.792467
$915$	3.63691			0.120232
$916$	−5.34859	−	9.26404i	−0.176722	−	0.306092i
$917$			12.4993i			0.412764i
$918$	0.146903	−	0.254444i	0.00484852	−	0.00839789i
$919$		−	45.5587i		−	1.50284i	−0.659822	−	0.751422i	$-0.729368\pi$
$919$		−	45.5587i		−	1.50284i	0.659822	−	0.751422i	$-0.270632\pi$
$920$	−6.96479	−	4.02112i	−0.229622	−	0.132573i
$921$	14.8048	−	25.6426i	0.487833	−	0.844952i
$922$	2.97716	−	5.15659i	0.0980474	−	0.169823i
$923$	4.78887	−	2.76486i	0.157628	−	0.0910064i
$924$	−5.19731			−0.170979
$925$	−5.94916	−	1.26786i	−0.195607	−	0.0416868i
$926$	21.9794			0.722288
$927$	4.07940	−	2.35524i	0.133985	−	0.0773564i
$928$	0.497075	−	0.860960i	0.0163173	−	0.0282624i
$929$	−19.4300	+	33.6538i	−0.637479	+	1.10415i	0.348506	+	0.937307i	$0.386689\pi$
$929$	−19.4300	+	33.6538i	−0.637479	+	1.10415i	−0.985984	+	0.166839i	$0.946644\pi$
$930$	8.79334	+	5.07684i	0.288345	+	0.166476i
$931$		−	3.23211i		−	0.105928i
$932$	3.31772	−	5.74646i	0.108676	−	0.188232i
$933$			22.6189i			0.740508i
$934$	−2.57484	−	4.45975i	−0.0842513	−	0.145928i
$935$	−0.538825			−0.0176215
$936$	−0.562314			−0.0183798
$937$	−9.37194	−	16.2327i	−0.306168	−	0.530299i	0.671353	−	0.741138i	$-0.265714\pi$
$937$	−9.37194	−	16.2327i	−0.306168	−	0.530299i	−0.977521	+	0.210839i	$0.932380\pi$
$938$	16.8762	+	9.74350i	0.551029	+	0.318136i
$939$			1.61041i			0.0525537i
$940$	3.34285	−	1.93000i	0.109032	−	0.0629495i
$941$	−0.436169	−	0.755466i	−0.0142187	−	0.0246275i	0.858829	−	0.512263i	$-0.171193\pi$
$941$	−0.436169	−	0.755466i	−0.0142187	−	0.0246275i	−0.873047	+	0.487636i	$0.837859\pi$
$942$	13.8932	−	8.02127i	0.452666	−	0.261347i
$943$	25.3303	+	14.6244i	0.824868	+	0.476238i
$944$	−4.33464	−	2.50260i	−0.141080	−	0.0814528i
$945$	2.45427	−	1.41697i	0.0798374	−	0.0460941i
$946$	4.37964	+	7.58577i	0.142395	+	0.246635i
$947$	−43.7942	+	25.2846i	−1.42312	+	0.821638i	−0.996564	−	0.0828239i	$-0.973606\pi$
$947$	−43.7942	+	25.2846i	−1.42312	+	0.821638i	−0.426555	+	0.904462i	$0.640273\pi$
$948$		−	12.5607i		−	0.407953i
$949$	−2.96038	−	1.70918i	−0.0960979	−	0.0554822i
$950$	1.56708	+	2.71426i	0.0508428	+	0.0880623i
$951$	−8.47647			−0.274868
$952$	0.832631			0.0269857
$953$	−29.3193	−	50.7826i	−0.949746	−	1.64501i	−0.745958	−	0.665993i	$-0.768008\pi$
$953$	−29.3193	−	50.7826i	−0.949746	−	1.64501i	−0.203789	−	0.979015i	$-0.565325\pi$
$954$		−	5.31650i		−	0.172128i
$955$	−2.56091	+	4.43563i	−0.0828691	+	0.143534i
$956$		−	22.3025i		−	0.721314i
$957$	−1.57895	−	0.911610i	−0.0510404	−	0.0294682i
$958$	4.11450	−	7.12652i	0.132933	−	0.230247i
$959$	−11.6532	+	20.1840i	−0.376302	+	0.651775i
$960$	−0.866025	+	0.500000i	−0.0279508	+	0.0161374i
$961$	−72.0971			−2.32571
$962$	−2.29007	+	2.54064i	−0.0738347	+	0.0819137i
$963$	−13.4539			−0.433547
$964$	17.1735	−	9.91510i	0.553120	−	0.319344i
$965$	−4.48309	+	7.76494i	−0.144316	+	0.249962i
$966$	11.3956	−	19.7378i	0.366649	−	0.635055i
$967$	−16.4537	−	9.49955i	−0.529116	−	0.305485i	0.211541	−	0.977369i	$-0.432152\pi$
$967$	−16.4537	−	9.49955i	−0.529116	−	0.305485i	−0.740656	+	0.671884i	$0.765485\pi$
$968$			7.63664i			0.245451i
$969$	−0.460418	+	0.797467i	−0.0147908	+	0.0256183i
$970$			12.9879i			0.417016i
$971$	9.60234	+	16.6317i	0.308154	+	0.533738i	0.977959	−	0.208799i	$-0.0669555\pi$
$971$	9.60234	+	16.6317i	0.308154	+	0.533738i	−0.669805	+	0.742537i	$0.733622\pi$
$972$	−1.00000			−0.0320750
$973$	−26.7372			−0.857157
$974$	8.85697	+	15.3407i	0.283796	+	0.491549i
$975$	−0.486978	−	0.281157i	−0.0155958	−	0.00900422i
$976$		−	3.63691i		−	0.116415i
$977$	22.5029	−	12.9921i	0.719932	−	0.415653i	−0.0947956	−	0.995497i	$-0.530220\pi$
$977$	22.5029	−	12.9921i	0.719932	−	0.415653i	0.814728	+	0.579844i	$0.196886\pi$
$978$	−6.37070	−	11.0344i	−0.203712	−	0.352840i
$979$	12.3038	−	7.10358i	0.393230	−	0.227031i
$980$	0.893091	+	0.515627i	0.0285288	+	0.0164711i
$981$	0.0968558	+	0.0559197i	0.00309237	+	0.00178538i
$982$	−13.4015	+	7.73737i	−0.427660	+	0.246909i
$983$	−19.9032	−	34.4734i	−0.634815	−	1.09953i	−0.986554	−	0.163434i	$-0.947743\pi$
$983$	−19.9032	−	34.4734i	−0.634815	−	1.09953i	0.351739	−	0.936098i	$-0.385590\pi$
$984$	3.14965	−	1.81845i	0.100407	−	0.0579702i
$985$			0.835329i			0.0266158i
$986$	0.252955	+	0.146044i	0.00805574	+	0.00465098i
$987$	5.46950	+	9.47346i	0.174096	+	0.301544i
$988$	1.76238			0.0560688
$989$	−38.4113			−1.22141
$990$	0.916973	+	1.58824i	0.0291433	+	0.0504777i
$991$			18.1949i			0.577981i	0.957332	+	0.288991i	$0.0933196\pi$
$991$			18.1949i			0.577981i	−0.957332	+	0.288991i	$0.906680\pi$
$992$	5.07684	−	8.79334i	0.161190	−	0.279189i
$993$			3.37416i			0.107076i
$994$	24.1350	+	13.9343i	0.765514	+	0.441970i
$995$	−1.99466	+	3.45485i	−0.0632349	+	0.109526i
$996$	−4.84237	+	8.38723i	−0.153436	+	0.265759i
$997$	−3.64267	+	2.10310i	−0.115365	+	0.0666058i	−0.556572	−	0.830799i	$-0.687884\pi$
$997$	−3.64267	+	2.10310i	−0.115365	+	0.0666058i	0.441207	+	0.897405i	$0.354550\pi$
$998$	38.8559			1.22996
$999$	−4.07258	+	4.51820i	−0.128851	+	0.142949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.c.751.5	✓	16
37.27	even	6	inner	1110.2.x.c.841.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.c.751.5	✓	16	1.1	even	1	trivial
1110.2.x.c.841.5	yes	16	37.27	even	6	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-1.41697 + 2.45427i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +1.00000i q^{6} +(-1.41697 + 2.45427i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +1.83395 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.486978 + 0.281157i) q^{13} +2.83395i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.254444 - 0.146903i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.71426 + 1.56708i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-1.41697 - 2.45427i) q^{21} +(1.58824 - 0.916973i) q^{22} +8.04225i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +0.562314 q^{26} +1.00000 q^{27} +(1.41697 + 2.45427i) q^{28} +0.994151i q^{29} +(0.500000 - 0.866025i) q^{30} +10.1537i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.916973 + 1.58824i) q^{33} +(0.146903 - 0.254444i) q^{34} +(2.45427 - 1.41697i) q^{35} -1.00000 q^{36} +(-4.07258 + 4.51820i) q^{37} +3.13416 q^{38} +(-0.486978 + 0.281157i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.81845 - 3.14965i) q^{41} +(-2.45427 - 1.41697i) q^{42} +4.77620i q^{43} +(0.916973 - 1.58824i) q^{44} +1.00000i q^{45} +(4.02112 + 6.96479i) q^{46} -3.85999 q^{47} +1.00000 q^{48} +(-0.515627 - 0.893091i) q^{49} +(0.866025 + 0.500000i) q^{50} +0.293806i q^{51} +(0.486978 - 0.281157i) q^{52} +(2.65825 + 4.60422i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.58824 - 0.916973i) q^{55} +(2.45427 + 1.41697i) q^{56} +(-2.71426 + 1.56708i) q^{57} +(0.497075 + 0.860960i) q^{58} +(4.33464 - 2.50260i) q^{59} -1.00000i q^{60} +(3.14965 + 1.81845i) q^{61} +(5.07684 + 8.79334i) q^{62} +2.83395 q^{63} -1.00000 q^{64} +(-0.281157 - 0.486978i) q^{65} +1.83395i q^{66} +(3.43814 - 5.95503i) q^{67} -0.293806i q^{68} +(-6.96479 - 4.02112i) q^{69} +(1.41697 - 2.45427i) q^{70} +(4.91693 - 8.51638i) q^{71} +(-0.866025 + 0.500000i) q^{72} -6.07908 q^{73} +(-1.26786 + 5.94916i) q^{74} -1.00000 q^{75} +(2.71426 - 1.56708i) q^{76} +(-2.59865 + 4.50100i) q^{77} +(-0.281157 + 0.486978i) q^{78} +(-10.8779 - 6.28035i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -3.63691i q^{82} +(4.84237 + 8.38723i) q^{83} -2.83395 q^{84} -0.293806 q^{85} +(2.38810 + 4.13631i) q^{86} +(-0.860960 - 0.497075i) q^{87} -1.83395i q^{88} +(6.70890 - 3.87338i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-1.38007 + 0.796783i) q^{91} +(6.96479 + 4.02112i) q^{92} +(-8.79334 - 5.07684i) q^{93} +(-3.34285 + 1.93000i) q^{94} +(-1.56708 - 2.71426i) q^{95} +(0.866025 - 0.500000i) q^{96} -12.9879i q^{97} +(-0.893091 - 0.515627i) q^{98} +(-0.916973 - 1.58824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

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