LMFDB - Embedded newform 1110.2.x.e.751.3

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} + 44x^{14} + 724x^{12} + 5750x^{10} + 23344x^{8} + 47024x^{6} + 43297x^{4} + 13976x^{2} + 676 $ x^16 + 44x^14 + 724x^12 + 5750x^10 + 23344x^8 + 47024x^6 + 43297x^4 + 13976*x^2 + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.3
Root			$-1.35087i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.e.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.60020 - 2.77163i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(1.60020 - 2.77163i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +2.56098 q^{11} +(-0.500000 - 0.866025i) q^{12} +(4.60015 + 2.65590i) q^{13} +3.20040i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.12715 + 2.96016i) q^{17} +(0.866025 + 0.500000i) q^{18} +(5.09130 + 2.93946i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.60020 - 2.77163i) q^{21} +(-2.21788 + 1.28049i) q^{22} -2.37042i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.31179 q^{26} -1.00000 q^{27} +(-1.60020 - 2.77163i) q^{28} -3.05766i q^{29} +(-0.500000 + 0.866025i) q^{30} -0.762353i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.28049 - 2.21788i) q^{33} +(2.96016 - 5.12715i) q^{34} +(2.77163 - 1.60020i) q^{35} -1.00000 q^{36} +(4.95102 + 3.53375i) q^{37} -5.87892 q^{38} +(4.60015 - 2.65590i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.168873 + 0.292497i) q^{41} +(2.77163 + 1.60020i) q^{42} -9.72879i q^{43} +(1.28049 - 2.21788i) q^{44} -1.00000i q^{45} +(1.18521 + 2.05285i) q^{46} -8.59819 q^{47} -1.00000 q^{48} +(-1.62128 - 2.80814i) q^{49} +(-0.866025 - 0.500000i) q^{50} +5.92032i q^{51} +(4.60015 - 2.65590i) q^{52} +(5.08919 + 8.81474i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.21788 + 1.28049i) q^{55} +(2.77163 + 1.60020i) q^{56} +(5.09130 - 2.93946i) q^{57} +(1.52883 + 2.64802i) q^{58} +(6.08519 - 3.51328i) q^{59} -1.00000i q^{60} +(-11.3999 - 6.58176i) q^{61} +(0.381177 + 0.660217i) q^{62} -3.20040 q^{63} -1.00000 q^{64} +(2.65590 + 4.60015i) q^{65} +2.56098i q^{66} +(4.31103 - 7.46693i) q^{67} +5.92032i q^{68} +(-2.05285 - 1.18521i) q^{69} +(-1.60020 + 2.77163i) q^{70} +(-1.79585 + 3.11050i) q^{71} +(0.866025 - 0.500000i) q^{72} -12.7576 q^{73} +(-6.05458 - 0.584810i) q^{74} +1.00000 q^{75} +(5.09130 - 2.93946i) q^{76} +(4.09809 - 7.09809i) q^{77} +(-2.65590 + 4.60015i) q^{78} +(13.5126 + 7.80151i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -0.337747i q^{82} +(-0.0857892 - 0.148591i) q^{83} -3.20040 q^{84} -5.92032 q^{85} +(4.86439 + 8.42538i) q^{86} +(-2.64802 - 1.52883i) q^{87} +2.56098i q^{88} +(6.85256 - 3.95633i) q^{89} +(0.500000 + 0.866025i) q^{90} +(14.7223 - 8.49992i) q^{91} +(-2.05285 - 1.18521i) q^{92} +(-0.660217 - 0.381177i) q^{93} +(7.44625 - 4.29909i) q^{94} +(2.93946 + 5.09130i) q^{95} +(0.866025 - 0.500000i) q^{96} -13.9813i q^{97} +(2.80814 + 1.62128i) q^{98} +(-1.28049 - 2.21788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * 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
$7$	1.60020	−	2.77163i	0.604819	−	1.04758i	−0.387262	−	0.921970i	$-0.626579\pi$
$7$	1.60020	−	2.77163i	0.604819	−	1.04758i	0.992080	−	0.125607i	$-0.0400877\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	2.56098			0.772166			0.386083	−	0.922464i	$-0.373828\pi$
$11$	2.56098			0.772166			0.386083	+	0.922464i	$0.373828\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	4.60015	+	2.65590i	1.27585	+	0.736613i	0.976083	−	0.217399i	$-0.0697574\pi$
$13$	4.60015	+	2.65590i	1.27585	+	0.736613i	0.299768	+	0.954012i	$0.403091\pi$
$14$			3.20040i			0.855343i
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.12715	+	2.96016i	−1.24352	+	0.717944i	−0.969808	−	0.243869i	$-0.921583\pi$
$17$	−5.12715	+	2.96016i	−1.24352	+	0.717944i	−0.273707	+	0.961813i	$0.588250\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	5.09130	+	2.93946i	1.16802	+	0.674359i	0.953214	−	0.302297i	$-0.0977535\pi$
$19$	5.09130	+	2.93946i	1.16802	+	0.674359i	0.214810	+	0.976656i	$0.431087\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	−1.60020	−	2.77163i	−0.349192	−	0.604819i
$22$	−2.21788	+	1.28049i	−0.472853	+	0.273002i
$23$		−	2.37042i		−	0.494268i	−0.968981	−	0.247134i	$-0.920511\pi$
$23$		−	2.37042i		−	0.494268i	0.968981	−	0.247134i	$-0.0794887\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.31179			−1.04173
$27$	−1.00000			−0.192450
$28$	−1.60020	−	2.77163i	−0.302409	−	0.523788i
$29$		−	3.05766i		−	0.567794i	−0.958855	−	0.283897i	$-0.908373\pi$
$29$		−	3.05766i		−	0.567794i	0.958855	−	0.283897i	$-0.0916274\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$		−	0.762353i		−	0.136923i	−0.997654	−	0.0684613i	$-0.978191\pi$
$31$		−	0.762353i		−	0.136923i	0.997654	−	0.0684613i	$-0.0218090\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.28049	−	2.21788i	0.222905	−	0.386083i
$34$	2.96016	−	5.12715i	0.507663	−	0.879298i
$35$	2.77163	−	1.60020i	0.468490	−	0.270483i
$36$	−1.00000			−0.166667
$37$	4.95102	+	3.53375i	0.813943	+	0.580945i
$37$	4.95102	+	3.53375i	0.813943	+	0.580945i
$38$	−5.87892			−0.953687
$39$	4.60015	−	2.65590i	0.736613	−	0.425284i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−0.168873	+	0.292497i	−0.0263736	+	0.0456804i	−0.878911	−	0.476986i	$-0.841729\pi$
$41$	−0.168873	+	0.292497i	−0.0263736	+	0.0456804i	0.852537	+	0.522666i	$0.175063\pi$
$42$	2.77163	+	1.60020i	0.427671	+	0.246916i
$43$		−	9.72879i		−	1.48363i	−0.670607	−	0.741813i	$-0.733966\pi$
$43$		−	9.72879i		−	1.48363i	0.670607	−	0.741813i	$-0.266034\pi$
$44$	1.28049	−	2.21788i	0.193041	−	0.334358i
$45$		−	1.00000i		−	0.149071i
$46$	1.18521	+	2.05285i	0.174750	+	0.302676i
$47$	−8.59819			−1.25417			−0.627087	−	0.778949i	$-0.715753\pi$
$47$	−8.59819			−1.25417			−0.627087	+	0.778949i	$0.715753\pi$
$48$	−1.00000			−0.144338
$49$	−1.62128	−	2.80814i	−0.231611	−	0.401162i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$			5.92032i			0.829010i
$52$	4.60015	−	2.65590i	0.637925	−	0.368306i
$53$	5.08919	+	8.81474i	0.699054	+	1.21080i	0.968795	+	0.247864i	$0.0797287\pi$
$53$	5.08919	+	8.81474i	0.699054	+	1.21080i	−0.269741	+	0.962933i	$0.586938\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	2.21788	+	1.28049i	0.299058	+	0.172661i
$56$	2.77163	+	1.60020i	0.370374	+	0.213836i
$57$	5.09130	−	2.93946i	0.674359	−	0.389341i
$58$	1.52883	+	2.64802i	0.200746	+	0.347701i
$59$	6.08519	−	3.51328i	0.792224	−	0.457391i	−0.0485211	−	0.998822i	$-0.515451\pi$
$59$	6.08519	−	3.51328i	0.792224	−	0.457391i	0.840745	+	0.541432i	$0.182117\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−11.3999	−	6.58176i	−1.45961	−	0.842708i	−0.460621	−	0.887597i	$-0.652373\pi$
$61$	−11.3999	−	6.58176i	−1.45961	−	0.842708i	−0.998992	+	0.0448893i	$0.985706\pi$
$62$	0.381177	+	0.660217i	0.0484095	+	0.0838477i
$63$	−3.20040			−0.403212
$64$	−1.00000			−0.125000
$65$	2.65590	+	4.60015i	0.329423	+	0.570578i
$66$			2.56098i			0.315235i
$67$	4.31103	−	7.46693i	0.526676	−	0.912230i	−0.472840	−	0.881148i	$-0.656771\pi$
$67$	4.31103	−	7.46693i	0.526676	−	0.912230i	0.999517	−	0.0310823i	$-0.00989540\pi$
$68$			5.92032i			0.717944i
$69$	−2.05285	−	1.18521i	−0.247134	−	0.142683i
$70$	−1.60020	+	2.77163i	−0.191260	+	0.331273i
$71$	−1.79585	+	3.11050i	−0.213128	+	0.369148i	−0.952692	−	0.303938i	$-0.901698\pi$
$71$	−1.79585	+	3.11050i	−0.213128	+	0.369148i	0.739564	+	0.673086i	$0.235032\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−12.7576			−1.49317			−0.746583	−	0.665293i	$-0.768307\pi$
$73$	−12.7576			−1.49317			−0.746583	+	0.665293i	$0.768307\pi$
$74$	−6.05458	−	0.584810i	−0.703831	−	0.0679828i
$75$	1.00000			0.115470
$76$	5.09130	−	2.93946i	0.584012	−	0.337179i
$77$	4.09809	−	7.09809i	0.467020	−	0.808903i
$78$	−2.65590	+	4.60015i	−0.300721	+	0.520864i
$79$	13.5126	+	7.80151i	1.52029	+	0.877739i	0.999714	+	0.0239223i	$0.00761543\pi$
$79$	13.5126	+	7.80151i	1.52029	+	0.877739i	0.520574	+	0.853816i	$0.325718\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	0.337747i		−	0.0372979i
$83$	−0.0857892	−	0.148591i	−0.00941659	−	0.0163100i	0.861279	−	0.508133i	$-0.169664\pi$
$83$	−0.0857892	−	0.148591i	−0.00941659	−	0.0163100i	−0.870695	+	0.491823i	$0.836331\pi$
$84$	−3.20040			−0.349192
$85$	−5.92032			−0.642149
$86$	4.86439	+	8.42538i	0.524541	+	0.908532i
$87$	−2.64802	−	1.52883i	−0.283897	−	0.163908i
$88$			2.56098i			0.273002i
$89$	6.85256	−	3.95633i	0.726370	−	0.419370i	−0.0907229	−	0.995876i	$-0.528918\pi$
$89$	6.85256	−	3.95633i	0.726370	−	0.419370i	0.817093	+	0.576506i	$0.195584\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	14.7223	−	8.49992i	1.54332	−	0.891034i
$92$	−2.05285	−	1.18521i	−0.214024	−	0.123567i
$93$	−0.660217	−	0.381177i	−0.0684613	−	0.0395262i
$94$	7.44625	−	4.29909i	0.768022	−	0.443418i
$95$	2.93946	+	5.09130i	0.301582	+	0.522356i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	13.9813i		−	1.41959i	−0.704410	−	0.709793i	$-0.748788\pi$
$97$		−	13.9813i		−	1.41959i	0.704410	−	0.709793i	$-0.251212\pi$
$98$	2.80814	+	1.62128i	0.283665	+	0.163774i
$99$	−1.28049	−	2.21788i	−0.128694	−	0.222905i
$100$	1.00000			0.100000
$101$	6.97754			0.694291			0.347146	−	0.937811i	$-0.387151\pi$
$101$	6.97754			0.694291			0.347146	+	0.937811i	$0.387151\pi$
$102$	−2.96016	−	5.12715i	−0.293099	−	0.507663i
$103$		−	4.31626i		−	0.425294i	−0.977129	−	0.212647i	$-0.931792\pi$
$103$		−	4.31626i		−	0.425294i	0.977129	−	0.212647i	$-0.0682084\pi$
$104$	−2.65590	+	4.60015i	−0.260432	+	0.451081i
$105$		−	3.20040i		−	0.312327i
$106$	−8.81474	−	5.08919i	−0.856163	−	0.494306i
$107$	−2.72950	+	4.72763i	−0.263870	+	0.457037i	−0.967267	−	0.253761i	$-0.918332\pi$
$107$	−2.72950	+	4.72763i	−0.263870	+	0.457037i	0.703397	+	0.710798i	$0.251666\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	8.30226	−	4.79331i	0.795212	−	0.459116i	−0.0465821	−	0.998914i	$-0.514833\pi$
$109$	8.30226	−	4.79331i	0.795212	−	0.459116i	0.841794	+	0.539799i	$0.181500\pi$
$110$	−2.56098			−0.244180
$111$	5.53583	−	2.52083i	0.525438	−	0.239267i
$112$	−3.20040			−0.302409
$113$	−4.69088	+	2.70828i	−0.441281	+	0.254773i	−0.704141	−	0.710060i	$-0.748668\pi$
$113$	−4.69088	+	2.70828i	−0.441281	+	0.254773i	0.262860	+	0.964834i	$0.415334\pi$
$114$	−2.93946	+	5.09130i	−0.275306	+	0.476844i
$115$	1.18521	−	2.05285i	0.110522	−	0.191429i
$116$	−2.64802	−	1.52883i	−0.245862	−	0.141949i
$117$		−	5.31179i		−	0.491075i
$118$	−3.51328	+	6.08519i	−0.323424	+	0.560187i
$119$			18.9474i			1.73690i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−4.44136			−0.403760
$122$	13.1635			1.19177
$123$	0.168873	+	0.292497i	0.0152268	+	0.0263736i
$124$	−0.660217	−	0.381177i	−0.0592893	−	0.0342307i
$125$			1.00000i			0.0894427i
$126$	2.77163	−	1.60020i	0.246916	−	0.142557i
$127$	2.31158	+	4.00377i	0.205120	+	0.355277i	0.950171	−	0.311730i	$-0.100908\pi$
$127$	2.31158	+	4.00377i	0.205120	+	0.355277i	−0.745051	+	0.667007i	$0.767575\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−8.42538	−	4.86439i	−0.741813	−	0.428286i
$130$	−4.60015	−	2.65590i	−0.403459	−	0.232937i
$131$	8.41964	−	4.86108i	0.735628	−	0.424715i	−0.0848498	−	0.996394i	$-0.527041\pi$
$131$	8.41964	−	4.86108i	0.735628	−	0.424715i	0.820477	+	0.571679i	$0.193708\pi$
$132$	−1.28049	−	2.21788i	−0.111453	−	0.193041i
$133$	16.2942	−	9.40745i	1.41288	−	0.815729i
$134$			8.62207i			0.744833i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	−2.96016	−	5.12715i	−0.253832	−	0.439649i
$137$	−22.2165			−1.89808			−0.949040	−	0.315155i	$-0.897943\pi$
$137$	−22.2165			−1.89808			−0.949040	+	0.315155i	$0.897943\pi$
$138$	2.37042			0.201784
$139$	3.24034	+	5.61243i	0.274842	+	0.476040i	0.970095	−	0.242724i	$-0.0780411\pi$
$139$	3.24034	+	5.61243i	0.274842	+	0.476040i	−0.695253	+	0.718765i	$0.744708\pi$
$140$		−	3.20040i		−	0.270483i
$141$	−4.29909	+	7.44625i	−0.362049	+	0.627087i
$142$		−	3.59169i		−	0.301408i
$143$	11.7809	+	6.80170i	0.985168	+	0.568787i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.52883	−	2.64802i	0.126963	−	0.219906i
$146$	11.0484	−	6.37880i	0.914373	−	0.527914i
$147$	−3.24256			−0.267441
$148$	5.53583	−	2.52083i	0.455042	−	0.207211i
$149$	22.1515			1.81472			0.907362	−	0.420350i	$-0.138093\pi$
$149$	22.1515			1.81472			0.907362	+	0.420350i	$0.138093\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	−4.29303	+	7.43575i	−0.349362	+	0.605113i	−0.986136	−	0.165937i	$-0.946935\pi$
$151$	−4.29303	+	7.43575i	−0.349362	+	0.605113i	0.636774	+	0.771050i	$0.280268\pi$
$152$	−2.93946	+	5.09130i	−0.238422	+	0.412959i
$153$	5.12715	+	2.96016i	0.414505	+	0.239315i
$154$			8.19617i			0.660466i
$155$	0.381177	−	0.660217i	0.0306168	−	0.0530299i
$156$		−	5.31179i		−	0.425284i
$157$	1.84211	+	3.19063i	0.147017	+	0.254640i	0.930124	−	0.367247i	$-0.119700\pi$
$157$	1.84211	+	3.19063i	0.147017	+	0.254640i	−0.783107	+	0.621887i	$0.786366\pi$
$158$	−15.6030			−1.24131
$159$	10.1784			0.807198
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−6.56993	−	3.79315i	−0.517783	−	0.298942i
$162$		−	1.00000i		−	0.0785674i
$163$	−4.53990	+	2.62111i	−0.355593	+	0.205302i	−0.667146	−	0.744927i	$-0.732484\pi$
$163$	−4.53990	+	2.62111i	−0.355593	+	0.205302i	0.311553	+	0.950229i	$0.399151\pi$
$164$	0.168873	+	0.292497i	0.0131868	+	0.0228402i
$165$	2.21788	−	1.28049i	0.172661	−	0.0996862i
$166$	0.148591	+	0.0857892i	0.0115329	+	0.00665853i
$167$	−17.4530	−	10.0765i	−1.35055	−	0.779742i	−0.362226	−	0.932090i	$-0.617983\pi$
$167$	−17.4530	−	10.0765i	−1.35055	−	0.779742i	−0.988327	+	0.152349i	$0.951316\pi$
$168$	2.77163	−	1.60020i	0.213836	−	0.123458i
$169$	7.60756	+	13.1767i	0.585197	+	1.01359i
$170$	5.12715	−	2.96016i	0.393234	−	0.227034i
$171$		−	5.87892i		−	0.449573i
$172$	−8.42538	−	4.86439i	−0.642429	−	0.370907i
$173$	0.121488	+	0.210424i	0.00923659	+	0.0159982i	0.870607	−	0.491980i	$-0.163727\pi$
$173$	0.121488	+	0.210424i	0.00923659	+	0.0159982i	−0.861370	+	0.507978i	$0.830393\pi$
$174$	3.05766			0.231801
$175$	3.20040			0.241927
$176$	−1.28049	−	2.21788i	−0.0965207	−	0.167179i
$177$		−	7.02657i		−	0.528149i
$178$	−3.95633	+	6.85256i	−0.296539	+	0.513621i
$179$			19.6818i			1.47108i	0.677479	+	0.735542i	$0.263072\pi$
$179$			19.6818i			1.47108i	−0.677479	+	0.735542i	$0.736928\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	−12.1318	+	21.0129i	−0.901750	+	1.56188i	−0.0765290	+	0.997067i	$0.524384\pi$
$181$	−12.1318	+	21.0129i	−0.901750	+	1.56188i	−0.825221	+	0.564810i	$0.808950\pi$
$182$	−8.49992	+	14.7223i	−0.630056	+	1.09129i
$183$	−11.3999	+	6.58176i	−0.842708	+	0.486538i
$184$	2.37042			0.174750
$185$	2.52083	+	5.53583i	0.185335	+	0.407002i
$186$	0.762353			0.0558984
$187$	−13.1305	+	7.58092i	−0.960200	+	0.554372i
$188$	−4.29909	+	7.44625i	−0.313544	+	0.543073i
$189$	−1.60020	+	2.77163i	−0.116397	+	0.201606i
$190$	−5.09130	−	2.93946i	−0.369362	−	0.213251i
$191$		−	2.90706i		−	0.210347i	−0.994454	−	0.105174i	$-0.966460\pi$
$191$		−	2.90706i		−	0.210347i	0.994454	−	0.105174i	$-0.0335398\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$		−	0.195945i		−	0.0141044i	−0.999975	−	0.00705220i	$-0.997755\pi$
$193$		−	0.195945i		−	0.0141044i	0.999975	−	0.00705220i	$-0.00224480\pi$
$194$	6.99065	+	12.1082i	0.501899	+	0.869315i
$195$	5.31179			0.380385
$196$	−3.24256			−0.231611
$197$	−10.2760	−	17.7986i	−0.732135	−	1.26810i	−0.955969	−	0.293468i	$-0.905190\pi$
$197$	−10.2760	−	17.7986i	−0.732135	−	1.26810i	0.223833	−	0.974627i	$-0.428143\pi$
$198$	2.21788	+	1.28049i	0.157618	+	0.0910006i
$199$		−	10.6683i		−	0.756258i	−0.925753	−	0.378129i	$-0.876568\pi$
$199$		−	10.6683i		−	0.756258i	0.925753	−	0.378129i	$-0.123432\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−4.31103	−	7.46693i	−0.304077	−	0.526676i
$202$	−6.04273	+	3.48877i	−0.425165	+	0.245469i
$203$	−8.47471	−	4.89287i	−0.594808	−	0.343412i
$204$	5.12715	+	2.96016i	0.358972	+	0.207253i
$205$	−0.292497	+	0.168873i	−0.0204289	+	0.0117946i
$206$	2.15813	+	3.73799i	0.150364	+	0.260438i
$207$	−2.05285	+	1.18521i	−0.142683	+	0.0823780i
$208$		−	5.31179i		−	0.368306i
$209$	13.0387	+	7.52791i	0.901908	+	0.520717i
$210$	1.60020	+	2.77163i	0.110424	+	0.191260i
$211$	−11.8395			−0.815066			−0.407533	−	0.913191i	$-0.633611\pi$
$211$	−11.8395			−0.815066			−0.407533	+	0.913191i	$0.633611\pi$
$212$	10.1784			0.699054
$213$	1.79585	+	3.11050i	0.123049	+	0.213128i
$214$		−	5.45899i		−	0.373169i
$215$	4.86439	−	8.42538i	0.331749	−	0.574606i
$216$		−	1.00000i		−	0.0680414i
$217$	−2.11296	−	1.21992i	−0.143437	−	0.0828134i
$218$	−4.79331	+	8.30226i	−0.324644	+	0.562300i
$219$	−6.37880	+	11.0484i	−0.431040	+	0.746583i
$220$	2.21788	−	1.28049i	0.149529	−	0.0863307i
$221$	−31.4475			−2.11539
$222$	−3.53375	+	4.95102i	−0.237170	+	0.332291i
$223$	−21.2549			−1.42333			−0.711667	−	0.702517i	$-0.752059\pi$
$223$	−21.2549			−1.42333			−0.711667	+	0.702517i	$0.752059\pi$
$224$	2.77163	−	1.60020i	0.185187	−	0.106918i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	2.70828	−	4.69088i	0.180152	−	0.312032i
$227$	4.22423	+	2.43886i	0.280372	+	0.161873i	0.633592	−	0.773668i	$-0.281580\pi$
$227$	4.22423	+	2.43886i	0.280372	+	0.161873i	−0.353220	+	0.935540i	$0.614913\pi$
$228$		−	5.87892i		−	0.389341i
$229$	3.33494	−	5.77628i	0.220379	−	0.381707i	−0.734544	−	0.678561i	$-0.762604\pi$
$229$	3.33494	−	5.77628i	0.220379	−	0.381707i	0.954923	+	0.296854i	$0.0959373\pi$
$230$			2.37042i			0.156301i
$231$	−4.09809	−	7.09809i	−0.269634	−	0.467020i
$232$	3.05766			0.200746
$233$	−16.9894			−1.11301			−0.556507	−	0.830843i	$-0.687859\pi$
$233$	−16.9894			−1.11301			−0.556507	+	0.830843i	$0.687859\pi$
$234$	2.65590	+	4.60015i	0.173621	+	0.300721i
$235$	−7.44625	−	4.29909i	−0.485740	−	0.280442i
$236$		−	7.02657i		−	0.457391i
$237$	13.5126	−	7.80151i	0.877739	−	0.506763i
$238$	−9.47369	−	16.4089i	−0.614088	−	1.06363i
$239$	−11.0481	+	6.37865i	−0.714645	+	0.412600i	−0.812778	−	0.582573i	$-0.802046\pi$
$239$	−11.0481	+	6.37865i	−0.714645	+	0.412600i	0.0981338	+	0.995173i	$0.468713\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	16.6996	+	9.64155i	1.07572	+	0.621067i	0.929738	−	0.368221i	$-0.120033\pi$
$241$	16.6996	+	9.64155i	1.07572	+	0.621067i	0.145981	+	0.989287i	$0.453366\pi$
$242$	3.84633	−	2.22068i	0.247252	−	0.142751i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−11.3999	+	6.58176i	−0.729806	+	0.421354i
$245$		−	3.24256i		−	0.207159i
$246$	−0.292497	−	0.168873i	−0.0186489	−	0.0107670i
$247$	15.6138	+	27.0439i	0.993483	+	1.72076i
$248$	0.762353			0.0484095
$249$	−0.171578			−0.0108733
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$			8.33751i			0.526259i	0.964761	+	0.263129i	$0.0847546\pi$
$251$			8.33751i			0.526259i	−0.964761	+	0.263129i	$0.915245\pi$
$252$	−1.60020	+	2.77163i	−0.100803	+	0.174596i
$253$		−	6.07062i		−	0.381657i
$254$	−4.00377	−	2.31158i	−0.251219	−	0.145041i
$255$	−2.96016	+	5.12715i	−0.185372	+	0.321074i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.05340	−	4.07228i	0.439979	−	0.254022i	−0.263610	−	0.964629i	$-0.584913\pi$
$257$	7.05340	−	4.07228i	0.439979	−	0.254022i	0.703589	+	0.710607i	$0.251580\pi$
$258$	9.72879			0.605688
$259$	17.7169	−	8.06767i	1.10087	−	0.501301i
$260$	5.31179			0.329423
$261$	−2.64802	+	1.52883i	−0.163908	+	0.0946323i
$262$	−4.86108	+	8.41964i	−0.300319	+	0.520167i
$263$	2.49556	−	4.32244i	0.153883	−	0.266533i	−0.778769	−	0.627311i	$-0.784155\pi$
$263$	2.49556	−	4.32244i	0.153883	−	0.266533i	0.932652	+	0.360778i	$0.117489\pi$
$264$	2.21788	+	1.28049i	0.136501	+	0.0788088i
$265$			10.1784i			0.625253i
$266$	−9.40745	+	16.2942i	−0.576808	+	0.999060i
$267$		−	7.91265i		−	0.484246i
$268$	−4.31103	−	7.46693i	−0.263338	−	0.456115i
$269$	−26.0312			−1.58715			−0.793574	−	0.608474i	$-0.791782\pi$
$269$	−26.0312			−1.58715			−0.793574	+	0.608474i	$0.791782\pi$
$270$	1.00000			0.0608581
$271$	−0.127875	−	0.221485i	−0.00776783	−	0.0134543i	0.862115	−	0.506712i	$-0.169139\pi$
$271$	−0.127875	−	0.221485i	−0.00776783	−	0.0134543i	−0.869883	+	0.493258i	$0.835806\pi$
$272$	5.12715	+	2.96016i	0.310879	+	0.179486i
$273$		−	16.9998i		−	1.02888i
$274$	19.2400	−	11.1082i	1.16233	−	0.671073i
$275$	1.28049	+	2.21788i	0.0772166	+	0.133743i
$276$	−2.05285	+	1.18521i	−0.123567	+	0.0713414i
$277$	−20.3140	−	11.7283i	−1.22055	−	0.704684i	−0.255513	−	0.966806i	$-0.582245\pi$
$277$	−20.3140	−	11.7283i	−1.22055	−	0.704684i	−0.965035	+	0.262122i	$0.915578\pi$
$278$	−5.61243	−	3.24034i	−0.336611	−	0.194343i
$279$	−0.660217	+	0.381177i	−0.0395262	+	0.0228204i
$280$	1.60020	+	2.77163i	0.0956302	+	0.165636i
$281$	1.91946	−	1.10820i	0.114506	−	0.0661099i	−0.441653	−	0.897186i	$-0.645608\pi$
$281$	1.91946	−	1.10820i	0.114506	−	0.0661099i	0.556159	+	0.831076i	$0.312275\pi$
$282$		−	8.59819i		−	0.512015i
$283$	15.5342	+	8.96867i	0.923411	+	0.533132i	0.884722	−	0.466119i	$-0.154348\pi$
$283$	15.5342	+	8.96867i	0.923411	+	0.533132i	0.0386897	+	0.999251i	$0.487682\pi$
$284$	1.79585	+	3.11050i	0.106564	+	0.184574i
$285$	5.87892			0.348237
$286$	−13.6034			−0.804386
$287$	0.540462	+	0.936108i	0.0319025	+	0.0552567i
$288$		−	1.00000i		−	0.0589256i
$289$	9.02508	−	15.6319i	0.530887	−	0.919523i
$290$			3.05766i			0.179552i
$291$	−12.1082	−	6.99065i	−0.709793	−	0.409799i
$292$	−6.37880	+	11.0484i	−0.373291	+	0.646560i
$293$	8.47194	−	14.6738i	0.494936	−	0.857254i	−0.505047	−	0.863092i	$-0.668525\pi$
$293$	8.47194	−	14.6738i	0.494936	−	0.857254i	0.999983	+	0.00583766i	$0.00185820\pi$
$294$	2.80814	−	1.62128i	0.163774	−	0.0945548i
$295$	7.02657			0.409103
$296$	−3.53375	+	4.95102i	−0.205395	+	0.287772i
$297$	−2.56098			−0.148603
$298$	−19.1838	+	11.0758i	−1.11129	+	0.641602i
$299$	6.29560	−	10.9043i	0.364084	−	0.630612i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−26.9646	−	15.5680i	−1.55421	−	0.897325i
$302$		−	8.58607i		−	0.494073i
$303$	3.48877	−	6.04273i	0.200425	−	0.347146i
$304$		−	5.87892i		−	0.337179i
$305$	−6.58176	−	11.3999i	−0.376870	−	0.652759i
$306$	−5.92032			−0.338442
$307$	−14.9191			−0.851478			−0.425739	−	0.904846i	$-0.639986\pi$
$307$	−14.9191			−0.851478			−0.425739	+	0.904846i	$0.639986\pi$
$308$	−4.09809	−	7.09809i	−0.233510	−	0.404451i
$309$	−3.73799	−	2.15813i	−0.212647	−	0.122772i
$310$			0.762353i			0.0432988i
$311$	−28.2023	+	16.2826i	−1.59921	+	0.923302i	−0.607567	+	0.794269i	$0.707854\pi$
$311$	−28.2023	+	16.2826i	−1.59921	+	0.923302i	−0.991640	+	0.129034i	$0.958812\pi$
$312$	2.65590	+	4.60015i	0.150360	+	0.260432i
$313$	−10.0322	+	5.79211i	−0.567055	+	0.327389i	−0.755972	−	0.654604i	$-0.772835\pi$
$313$	−10.0322	+	5.79211i	−0.567055	+	0.327389i	0.188917	+	0.981993i	$0.439502\pi$
$314$	−3.19063	−	1.84211i	−0.180058	−	0.103956i
$315$	−2.77163	−	1.60020i	−0.156163	−	0.0901610i
$316$	13.5126	−	7.80151i	0.760144	−	0.438869i
$317$	10.2928	+	17.8276i	0.578101	+	1.00130i	0.995697	+	0.0926677i	$0.0295394\pi$
$317$	10.2928	+	17.8276i	0.578101	+	1.00130i	−0.417596	+	0.908633i	$0.637127\pi$
$318$	−8.81474	+	5.08919i	−0.494306	+	0.285388i
$319$		−	7.83063i		−	0.438431i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	2.72950	+	4.72763i	0.152346	+	0.263870i
$322$	7.58631			0.422768
$323$	−34.8051			−1.93661
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			5.31179i			0.294645i
$326$	2.62111	−	4.53990i	0.145170	−	0.251442i
$327$		−	9.58662i		−	0.530141i
$328$	−0.292497	−	0.168873i	−0.0161505	−	0.00932447i
$329$	−13.7588	+	23.8310i	−0.758548	+	1.31384i
$330$	−1.28049	+	2.21788i	−0.0704888	+	0.122090i
$331$	−3.67434	+	2.12138i	−0.201960	+	0.116602i	−0.597569	−	0.801817i	$-0.703867\pi$
$331$	−3.67434	+	2.12138i	−0.201960	+	0.116602i	0.395609	+	0.918419i	$0.370533\pi$
$332$	−0.171578			−0.00941659
$333$	0.584810	−	6.05458i	0.0320474	−	0.331789i
$334$	20.1530			1.10272
$335$	7.46693	−	4.31103i	0.407962	−	0.235537i
$336$	−1.60020	+	2.77163i	−0.0872980	+	0.151205i
$337$	−14.6707	+	25.4103i	−0.799162	+	1.38419i	0.121000	+	0.992653i	$0.461390\pi$
$337$	−14.6707	+	25.4103i	−0.799162	+	1.38419i	−0.920162	+	0.391537i	$0.871943\pi$
$338$	−13.1767	−	7.60756i	−0.716717	−	0.413797i
$339$			5.41656i			0.294187i
$340$	−2.96016	+	5.12715i	−0.160537	+	0.278058i
$341$		−	1.95237i		−	0.105727i
$342$	2.93946	+	5.09130i	0.158948	+	0.275306i
$343$	12.0253			0.649306
$344$	9.72879			0.524541
$345$	−1.18521	−	2.05285i	−0.0638097	−	0.110522i
$346$	−0.210424	−	0.121488i	−0.0113125	−	0.00653126i
$347$			21.4879i			1.15353i	0.816909	+	0.576766i	$0.195686\pi$
$347$			21.4879i			1.15353i	−0.816909	+	0.576766i	$0.804314\pi$
$348$	−2.64802	+	1.52883i	−0.141949	+	0.0819540i
$349$	−16.5986	−	28.7497i	−0.888505	−	1.53894i	−0.841643	−	0.540034i	$-0.818411\pi$
$349$	−16.5986	−	28.7497i	−0.888505	−	1.53894i	−0.0468619	−	0.998901i	$-0.514922\pi$
$350$	−2.77163	+	1.60020i	−0.148150	+	0.0855343i
$351$	−4.60015	−	2.65590i	−0.245538	−	0.141761i
$352$	2.21788	+	1.28049i	0.118213	+	0.0682504i
$353$	−4.16924	+	2.40711i	−0.221906	+	0.128118i	−0.606833	−	0.794830i	$-0.707560\pi$
$353$	−4.16924	+	2.40711i	−0.221906	+	0.128118i	0.384926	+	0.922947i	$0.374227\pi$
$354$	3.51328	+	6.08519i	0.186729	+	0.323424i
$355$	−3.11050	+	1.79585i	−0.165088	+	0.0953136i
$356$		−	7.91265i		−	0.419370i
$357$	16.4089	+	9.47369i	0.868452	+	0.501401i
$358$	−9.84088	−	17.0449i	−0.520107	−	0.900851i
$359$	−29.8646			−1.57619			−0.788096	−	0.615552i	$-0.788933\pi$
$359$	−29.8646			−1.57619			−0.788096	+	0.615552i	$0.788933\pi$
$360$	1.00000			0.0527046
$361$	7.78087	+	13.4769i	0.409519	+	0.709308i
$362$		−	24.2636i		−	1.27527i
$363$	−2.22068	+	3.84633i	−0.116556	+	0.201880i
$364$		−	16.9998i		−	0.891034i
$365$	−11.0484	−	6.37880i	−0.578300	−	0.333882i
$366$	6.58176	−	11.3999i	0.344034	−	0.595884i
$367$	−1.62227	+	2.80986i	−0.0846820	+	0.146674i	−0.905256	−	0.424867i	$-0.860321\pi$
$367$	−1.62227	+	2.80986i	−0.0846820	+	0.146674i	0.820574	+	0.571541i	$0.193654\pi$
$368$	−2.05285	+	1.18521i	−0.107012	+	0.0617835i
$369$	0.337747			0.0175824
$370$	−4.95102	−	3.53375i	−0.257391	−	0.183711i
$371$	32.5749			1.69120
$372$	−0.660217	+	0.381177i	−0.0342307	+	0.0197631i
$373$	−15.1303	+	26.2065i	−0.783418	+	1.35692i	0.146521	+	0.989208i	$0.453192\pi$
$373$	−15.1303	+	26.2065i	−0.783418	+	1.35692i	−0.929939	+	0.367713i	$0.880141\pi$
$374$	7.58092	−	13.1305i	0.392000	−	0.678964i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$		−	8.59819i		−	0.443418i
$377$	8.12084	−	14.0657i	0.418244	−	0.724420i
$378$		−	3.20040i		−	0.164611i
$379$	13.9061	+	24.0860i	0.714306	+	1.23721i	0.963227	+	0.268691i	$0.0865909\pi$
$379$	13.9061	+	24.0860i	0.714306	+	1.23721i	−0.248920	+	0.968524i	$0.580076\pi$
$380$	5.87892			0.301582
$381$	4.62316			0.236852
$382$	1.45353	+	2.51758i	0.0743690	+	0.128811i
$383$	3.20395	+	1.84980i	0.163714	+	0.0945205i	0.579619	−	0.814888i	$-0.303202\pi$
$383$	3.20395	+	1.84980i	0.163714	+	0.0945205i	−0.415904	+	0.909408i	$0.636535\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	7.09809	−	4.09809i	0.361752	−	0.208858i
$386$	0.0979723	+	0.169693i	0.00498666	+	0.00863714i
$387$	−8.42538	+	4.86439i	−0.428286	+	0.247271i
$388$	−12.1082	−	6.99065i	−0.614699	−	0.354896i
$389$	3.96635	+	2.28997i	0.201102	+	0.116106i	0.597169	−	0.802115i	$-0.296292\pi$
$389$	3.96635	+	2.28997i	0.201102	+	0.116106i	−0.396067	+	0.918221i	$0.629625\pi$
$390$	−4.60015	+	2.65590i	−0.232937	+	0.134486i
$391$	7.01683	+	12.1535i	0.354857	+	0.614630i
$392$	2.80814	−	1.62128i	0.141832	−	0.0818869i
$393$		−	9.72217i		−	0.490418i
$394$	17.7986	+	10.2760i	0.896679	+	0.517698i
$395$	7.80151	+	13.5126i	0.392537	+	0.679893i
$396$	−2.56098			−0.128694
$397$	1.42065			0.0713005			0.0356503	−	0.999364i	$-0.488650\pi$
$397$	1.42065			0.0713005			0.0356503	+	0.999364i	$0.488650\pi$
$398$	5.33416	+	9.23904i	0.267377	+	0.463111i
$399$		−	18.8149i		−	0.941923i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	25.4855i		−	1.27268i	−0.771408	−	0.636341i	$-0.780447\pi$
$401$		−	25.4855i		−	1.27268i	0.771408	−	0.636341i	$-0.219553\pi$
$402$	7.46693	+	4.31103i	0.372417	+	0.215015i
$403$	2.02473	−	3.50694i	0.100859	−	0.174693i
$404$	3.48877	−	6.04273i	0.173573	−	0.300637i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	9.78575			0.485659
$407$	12.6795	+	9.04988i	0.628498	+	0.448586i
$408$	−5.92032			−0.293099
$409$	−26.1866	+	15.1189i	−1.29485	+	0.747579i	−0.979509	−	0.201400i	$-0.935451\pi$
$409$	−26.1866	+	15.1189i	−1.29485	+	0.747579i	−0.315337	+	0.948980i	$0.602117\pi$
$410$	0.168873	−	0.292497i	0.00834006	−	0.0144454i
$411$	−11.1082	+	19.2400i	−0.547929	+	0.949040i
$412$	−3.73799	−	2.15813i	−0.184158	−	0.106323i
$413$		−	22.4878i		−	1.10655i
$414$	1.18521	−	2.05285i	0.0582500	−	0.100892i
$415$		−	0.171578i		−	0.00842245i
$416$	2.65590	+	4.60015i	0.130216	+	0.225541i
$417$	6.48068			0.317360
$418$	−15.0558			−0.736405
$419$	−7.33040	−	12.6966i	−0.358114	−	0.620271i	0.629532	−	0.776975i	$-0.283247\pi$
$419$	−7.33040	−	12.6966i	−0.358114	−	0.620271i	−0.987646	+	0.156703i	$0.949913\pi$
$420$	−2.77163	−	1.60020i	−0.135242	−	0.0780817i
$421$		−	1.90358i		−	0.0927748i	−0.998924	−	0.0463874i	$-0.985229\pi$
$421$		−	1.90358i		−	0.0927748i	0.998924	−	0.0463874i	$-0.0147709\pi$
$422$	10.2533	−	5.91976i	0.499124	−	0.288169i
$423$	4.29909	+	7.44625i	0.209029	+	0.362049i
$424$	−8.81474	+	5.08919i	−0.428081	+	0.247153i
$425$	−5.12715	−	2.96016i	−0.248703	−	0.143589i
$426$	−3.11050	−	1.79585i	−0.150704	−	0.0870090i
$427$	−36.4844	+	21.0643i	−1.76560	+	1.01937i
$428$	2.72950	+	4.72763i	0.131935	+	0.228518i
$429$	11.7809	−	6.80170i	0.568787	−	0.328389i
$430$			9.72879i			0.469164i
$431$	27.0252	+	15.6030i	1.30176	+	0.751571i	0.980706	−	0.195490i	$-0.0626297\pi$
$431$	27.0252	+	15.6030i	1.30176	+	0.751571i	0.321054	+	0.947061i	$0.395963\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	10.9840			0.527857			0.263929	−	0.964542i	$-0.414982\pi$
$433$	10.9840			0.527857			0.263929	+	0.964542i	$0.414982\pi$
$434$	2.43983			0.117116
$435$	−1.52883	−	2.64802i	−0.0733019	−	0.126963i
$436$		−	9.58662i		−	0.459116i
$437$	6.96777	−	12.0685i	0.333314	−	0.577316i
$438$		−	12.7576i		−	0.609582i
$439$	15.9583	+	9.21351i	0.761646	+	0.439737i	0.829887	−	0.557932i	$-0.188405\pi$
$439$	15.9583	+	9.21351i	0.761646	+	0.439737i	−0.0682402	+	0.997669i	$0.521738\pi$
$440$	−1.28049	+	2.21788i	−0.0610451	+	0.105733i
$441$	−1.62128	+	2.80814i	−0.0772037	+	0.133721i
$442$	27.2343	−	15.7237i	1.29540	−	0.747902i
$443$	41.3641			1.96527			0.982634	−	0.185552i	$-0.0594073\pi$
$443$	41.3641			1.96527			0.982634	+	0.185552i	$0.0594073\pi$
$444$	0.584810	−	6.05458i	0.0277538	−	0.287338i
$445$	7.91265			0.375096
$446$	18.4073	−	10.6275i	0.871610	−	0.503224i
$447$	11.0758	−	19.1838i	0.523866	−	0.907362i
$448$	−1.60020	+	2.77163i	−0.0756023	+	0.130947i
$449$	20.0419	+	11.5712i	0.945836	+	0.546079i	0.891785	−	0.452459i	$-0.149453\pi$
$449$	20.0419	+	11.5712i	0.945836	+	0.546079i	0.0540513	+	0.998538i	$0.482787\pi$
$450$			1.00000i			0.0471405i
$451$	−0.432482	+	0.749081i	−0.0203648	+	0.0352728i
$452$			5.41656i			0.254773i
$453$	4.29303	+	7.43575i	0.201704	+	0.349362i
$454$	−4.87772			−0.228923
$455$	16.9998			0.796965
$456$	2.93946	+	5.09130i	0.137653	+	0.238422i
$457$	24.4425	+	14.1119i	1.14337	+	0.660127i	0.947264	−	0.320455i	$-0.103836\pi$
$457$	24.4425	+	14.1119i	1.14337	+	0.660127i	0.196110	+	0.980582i	$0.437169\pi$
$458$			6.66987i			0.311663i
$459$	5.12715	−	2.96016i	0.239315	−	0.138168i
$460$	−1.18521	−	2.05285i	−0.0552608	−	0.0957145i
$461$	11.8459	−	6.83924i	0.551719	−	0.318535i	−0.198096	−	0.980183i	$-0.563476\pi$
$461$	11.8459	−	6.83924i	0.551719	−	0.318535i	0.749815	+	0.661647i	$0.230142\pi$
$462$	7.09809	+	4.09809i	0.330233	+	0.190660i
$463$	−18.0680	−	10.4316i	−0.839692	−	0.484796i	0.0174677	−	0.999847i	$-0.494440\pi$
$463$	−18.0680	−	10.4316i	−0.839692	−	0.484796i	−0.857159	+	0.515051i	$0.827773\pi$
$464$	−2.64802	+	1.52883i	−0.122931	+	0.0709743i
$465$	−0.381177	−	0.660217i	−0.0176766	−	0.0306168i
$466$	14.7133	−	8.49472i	0.681580	−	0.393510i
$467$			13.7152i			0.634663i	0.948315	+	0.317332i	$0.102787\pi$
$467$			13.7152i			0.634663i	−0.948315	+	0.317332i	$0.897213\pi$
$468$	−4.60015	−	2.65590i	−0.212642	−	0.122769i
$469$	−13.7970	−	23.8972i	−0.637087	−	1.10347i
$470$	8.59819			0.396605
$471$	3.68423			0.169760
$472$	3.51328	+	6.08519i	0.161712	+	0.280093i
$473$		−	24.9153i		−	1.14561i
$474$	−7.80151	+	13.5126i	−0.358335	+	0.620655i
$475$			5.87892i			0.269744i
$476$	16.4089	+	9.47369i	0.752101	+	0.434226i
$477$	5.08919	−	8.81474i	0.233018	−	0.403599i
$478$	6.37865	−	11.0481i	0.291752	−	0.505330i
$479$	−1.69786	+	0.980259i	−0.0775771	+	0.0447892i	−0.538287	−	0.842762i	$-0.680928\pi$
$479$	−1.69786	+	0.980259i	−0.0775771	+	0.0447892i	0.460710	+	0.887551i	$0.347595\pi$
$480$	1.00000			0.0456435
$481$	13.3901	+	29.4052i	0.610537	+	1.34076i
$482$	−19.2831			−0.878321
$483$	−6.56993	+	3.79315i	−0.298942	+	0.172594i
$484$	−2.22068	+	3.84633i	−0.100940	+	0.174833i
$485$	6.99065	−	12.1082i	0.317429	−	0.549803i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$			34.0268i			1.54190i	0.636894	+	0.770951i	$0.280219\pi$
$487$			34.0268i			1.54190i	−0.636894	+	0.770951i	$0.719781\pi$
$488$	6.58176	−	11.3999i	0.297942	−	0.516051i
$489$			5.24223i			0.237062i
$490$	1.62128	+	2.80814i	0.0732419	+	0.126859i
$491$	−6.26252			−0.282624			−0.141312	−	0.989965i	$-0.545132\pi$
$491$	−6.26252			−0.282624			−0.141312	+	0.989965i	$0.545132\pi$
$492$	0.337747			0.0152268
$493$	9.05117	+	15.6771i	0.407644	+	0.706061i
$494$	−27.0439	−	15.6138i	−1.21676	−	0.702498i
$495$		−	2.56098i		−	0.115108i
$496$	−0.660217	+	0.381177i	−0.0296446	+	0.0171153i
$497$	5.74742	+	9.95483i	0.257807	+	0.446535i
$498$	0.148591	−	0.0857892i	0.00665853	−	0.00384431i
$499$	11.6271	+	6.71293i	0.520502	+	0.300512i	0.737140	−	0.675740i	$-0.236176\pi$
$499$	11.6271	+	6.71293i	0.520502	+	0.300512i	−0.216638	+	0.976252i	$0.569509\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−17.4530	+	10.0765i	−0.779742	+	0.450184i
$502$	−4.16875	−	7.22049i	−0.186061	−	0.322266i
$503$	−7.80537	+	4.50643i	−0.348024	+	0.200932i	−0.663815	−	0.747897i	$-0.731064\pi$
$503$	−7.80537	+	4.50643i	−0.348024	+	0.200932i	0.315790	+	0.948829i	$0.397730\pi$
$504$		−	3.20040i		−	0.142557i
$505$	6.04273	+	3.48877i	0.268898	+	0.155248i
$506$	3.03531	+	5.25731i	0.134936	+	0.233716i
$507$	15.2151			0.675727
$508$	4.62316			0.205120
$509$	9.05612	+	15.6857i	0.401405	+	0.695255i	0.993896	−	0.110323i	$-0.0351885\pi$
$509$	9.05612	+	15.6857i	0.401405	+	0.695255i	−0.592490	+	0.805578i	$0.701855\pi$
$510$		−	5.92032i		−	0.262156i
$511$	−20.4147	+	35.3593i	−0.903094	+	1.56420i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.09130	−	2.93946i	−0.224786	−	0.129780i
$514$	−4.07228	+	7.05340i	−0.179621	+	0.311112i
$515$	2.15813	−	3.73799i	0.0950985	−	0.164716i
$516$	−8.42538	+	4.86439i	−0.370907	+	0.214143i
$517$	−22.0198			−0.968430
$518$	−11.3094	+	15.8452i	−0.496907	+	0.696200i
$519$	0.242977			0.0106655
$520$	−4.60015	+	2.65590i	−0.201730	+	0.116469i
$521$	13.5779	−	23.5176i	0.594858	−	1.03032i	−0.398709	−	0.917077i	$-0.630542\pi$
$521$	13.5779	−	23.5176i	0.594858	−	1.03032i	0.993567	−	0.113247i	$-0.0361250\pi$
$522$	1.52883	−	2.64802i	0.0669152	−	0.115900i
$523$	8.54070	+	4.93097i	0.373459	+	0.215616i	0.674968	−	0.737847i	$-0.264157\pi$
$523$	8.54070	+	4.93097i	0.373459	+	0.215616i	−0.301510	+	0.953463i	$0.597491\pi$
$524$		−	9.72217i		−	0.424715i
$525$	1.60020	−	2.77163i	0.0698384	−	0.120964i
$526$			4.99112i			0.217623i
$527$	2.25669	+	3.90870i	0.0983028	+	0.170265i
$528$	−2.56098			−0.111453
$529$	17.3811			0.755699
$530$	−5.08919	−	8.81474i	−0.221060	−	0.382888i
$531$	−6.08519	−	3.51328i	−0.264075	−	0.152464i
$532$		−	18.8149i		−	0.815729i
$533$	−1.55368	+	0.897020i	−0.0672975	+	0.0388542i
$534$	3.95633	+	6.85256i	0.171207	+	0.296539i
$535$	−4.72763	+	2.72950i	−0.204393	+	0.118006i
$536$	7.46693	+	4.31103i	0.322522	+	0.186208i
$537$	17.0449	+	9.84088i	0.735542	+	0.424665i
$538$	22.5436	−	13.0156i	0.971925	−	0.561141i
$539$	−4.15207	−	7.19159i	−0.178842	−	0.309764i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$		−	28.8621i		−	1.24088i	−0.784254	−	0.620440i	$-0.786954\pi$
$541$		−	28.8621i		−	1.24088i	0.784254	−	0.620440i	$-0.213046\pi$
$542$	0.221485	+	0.127875i	0.00951361	+	0.00549268i
$543$	12.1318	+	21.0129i	0.520626	+	0.901750i
$544$	−5.92032			−0.253832
$545$	9.58662			0.410646
$546$	8.49992	+	14.7223i	0.363763	+	0.630056i
$547$			39.5740i			1.69206i	0.533134	+	0.846031i	$0.321014\pi$
$547$			39.5740i			1.69206i	−0.533134	+	0.846031i	$0.678986\pi$
$548$	−11.1082	+	19.2400i	−0.474520	+	0.821893i
$549$			13.1635i			0.561805i
$550$	−2.21788	−	1.28049i	−0.0945706	−	0.0546004i
$551$	8.98789	−	15.5675i	0.382897	−	0.663197i
$552$	1.18521	−	2.05285i	0.0504460	−	0.0873750i
$553$	43.2458	−	24.9680i	1.83900	−	1.06175i
$554$	23.4566			0.996573
$555$	6.05458	+	0.584810i	0.257003	+	0.0248238i
$556$	6.48068			0.274842
$557$	−10.8221	+	6.24815i	−0.458548	+	0.264743i	−0.711433	−	0.702753i	$-0.751954\pi$
$557$	−10.8221	+	6.24815i	−0.458548	+	0.264743i	0.252886	+	0.967496i	$0.418620\pi$
$558$	0.381177	−	0.660217i	0.0161365	−	0.0279492i
$559$	25.8386	−	44.7538i	1.09286	−	1.89289i
$560$	−2.77163	−	1.60020i	−0.117123	−	0.0676208i
$561$			15.1618i			0.640133i
$562$	−1.10820	+	1.91946i	−0.0467467	+	0.0809677i
$563$		−	32.1882i		−	1.35657i	−0.734799	−	0.678284i	$-0.762724\pi$
$563$		−	32.1882i		−	1.35657i	0.734799	−	0.678284i	$-0.237276\pi$
$564$	4.29909	+	7.44625i	0.181024	+	0.313544i
$565$	−5.41656			−0.227876
$566$	−17.9373			−0.753962
$567$	1.60020	+	2.77163i	0.0672021	+	0.116397i
$568$	−3.11050	−	1.79585i	−0.130514	−	0.0753520i
$569$		−	13.8474i		−	0.580512i	−0.956949	−	0.290256i	$-0.906260\pi$
$569$		−	13.8474i		−	0.580512i	0.956949	−	0.290256i	$-0.0937404\pi$
$570$	−5.09130	+	2.93946i	−0.213251	+	0.123121i
$571$	−7.31580	−	12.6713i	−0.306157	−	0.530279i	0.671362	−	0.741130i	$-0.265710\pi$
$571$	−7.31580	−	12.6713i	−0.306157	−	0.530279i	−0.977518	+	0.210851i	$0.932376\pi$
$572$	11.7809	−	6.80170i	0.492584	−	0.284394i
$573$	−2.51758	−	1.45353i	−0.105174	−	0.0607220i
$574$	−0.936108	−	0.540462i	−0.0390724	−	0.0225585i
$575$	2.05285	−	1.18521i	0.0856097	−	0.0494268i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−12.1860	+	7.03556i	−0.507308	+	0.292894i	−0.731726	−	0.681599i	$-0.761285\pi$
$577$	−12.1860	+	7.03556i	−0.507308	+	0.292894i	0.224418	+	0.974493i	$0.427952\pi$
$578$			18.0502i			0.750787i
$579$	−0.169693	−	0.0979723i	−0.00705220	−	0.00407159i
$580$	−1.52883	−	2.64802i	−0.0634813	−	0.109953i
$581$	−0.549119			−0.0227813
$582$	13.9813			0.579544
$583$	13.0333	+	22.5744i	0.539786	+	0.934936i
$584$		−	12.7576i		−	0.527914i
$585$	2.65590	−	4.60015i	0.109808	−	0.190193i
$586$			16.9439i			0.699945i
$587$	−6.53912	−	3.77536i	−0.269898	−	0.155826i	0.358943	−	0.933359i	$-0.383137\pi$
$587$	−6.53912	−	3.77536i	−0.269898	−	0.155826i	−0.628841	+	0.777534i	$0.716471\pi$
$588$	−1.62128	+	2.80814i	−0.0668604	+	0.115806i
$589$	2.24091	−	3.88137i	0.0923350	−	0.159929i
$590$	−6.08519	+	3.51328i	−0.250523	+	0.144640i
$591$	−20.5520			−0.845397
$592$	0.584810	−	6.05458i	0.0240355	−	0.248842i
$593$	27.1127			1.11339			0.556693	−	0.830718i	$-0.312070\pi$
$593$	27.1127			1.11339			0.556693	+	0.830718i	$0.312070\pi$
$594$	2.21788	−	1.28049i	0.0910006	−	0.0525392i
$595$	−9.47369	+	16.4089i	−0.388383	+	0.672700i
$596$	11.0758	−	19.1838i	0.453681	−	0.785799i
$597$	−9.23904	−	5.33416i	−0.378129	−	0.218313i
$598$			12.5912i			0.514892i
$599$	11.0561	−	19.1497i	0.451740	−	0.782436i	−0.546755	−	0.837293i	$-0.684137\pi$
$599$	11.0561	−	19.1497i	0.451740	−	0.782436i	0.998494	+	0.0548569i	$0.0174703\pi$
$600$			1.00000i			0.0408248i
$601$	−13.7147	−	23.7545i	−0.559434	−	0.968968i	−0.997544	−	0.0700463i	$-0.977685\pi$
$601$	−13.7147	−	23.7545i	−0.559434	−	0.968968i	0.438110	−	0.898921i	$-0.355648\pi$
$602$	31.1360			1.26901
$603$	−8.62207			−0.351118
$604$	4.29303	+	7.43575i	0.174681	+	0.302557i
$605$	−3.84633	−	2.22068i	−0.156376	−	0.0902835i
$606$			6.97754i			0.283443i
$607$	16.7438	−	9.66704i	0.679610	−	0.392373i	−0.120098	−	0.992762i	$-0.538321\pi$
$607$	16.7438	−	9.66704i	0.679610	−	0.392373i	0.799708	+	0.600389i	$0.204988\pi$
$608$	2.93946	+	5.09130i	0.119211	+	0.206479i
$609$	−8.47471	+	4.89287i	−0.343412	+	0.198269i
$610$	11.3999	+	6.58176i	0.461570	+	0.266488i
$611$	−39.5529	−	22.8359i	−1.60014	−	0.923841i
$612$	5.12715	−	2.96016i	0.207253	−	0.119657i
$613$	−14.8099	−	25.6515i	−0.598166	−	1.03605i	−0.993092	−	0.117341i	$-0.962563\pi$
$613$	−14.8099	−	25.6515i	−0.598166	−	1.03605i	0.394926	−	0.918713i	$-0.370770\pi$
$614$	12.9203	−	7.45955i	0.521422	−	0.301043i
$615$			0.337747i			0.0136193i
$616$	7.09809	+	4.09809i	0.285990	+	0.165117i
$617$	−6.92112	−	11.9877i	−0.278634	−	0.482608i	0.692412	−	0.721503i	$-0.256548\pi$
$617$	−6.92112	−	11.9877i	−0.278634	−	0.482608i	−0.971045	+	0.238895i	$0.923215\pi$
$618$	4.31626			0.173625
$619$	8.35618			0.335863			0.167932	−	0.985799i	$-0.446291\pi$
$619$	8.35618			0.335863			0.167932	+	0.985799i	$0.446291\pi$
$620$	−0.381177	−	0.660217i	−0.0153084	−	0.0265150i
$621$			2.37042i			0.0951219i
$622$	16.2826	−	28.2023i	0.652873	−	1.13081i
$623$		−	25.3236i		−	1.01457i
$624$	−4.60015	−	2.65590i	−0.184153	−	0.106321i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.79211	−	10.0322i	0.231499	−	0.400968i
$627$	13.0387	−	7.52791i	0.520717	−	0.300636i
$628$	3.68423			0.147017
$629$	−35.8451	−	3.46226i	−1.42924	−	0.138049i
$630$	3.20040			0.127507
$631$	23.3008	−	13.4527i	0.927592	−	0.535545i	0.0415426	−	0.999137i	$-0.486773\pi$
$631$	23.3008	−	13.4527i	0.927592	−	0.535545i	0.886049	+	0.463591i	$0.153439\pi$
$632$	−7.80151	+	13.5126i	−0.310327	+	0.537503i
$633$	−5.91976	+	10.2533i	−0.235289	+	0.407533i
$634$	−17.8276	−	10.2928i	−0.708026	−	0.408779i
$635$			4.62316i			0.183464i
$636$	5.08919	−	8.81474i	0.201800	−	0.349527i
$637$		−	17.2238i		−	0.682431i
$638$	3.91531	+	6.78152i	0.155009	+	0.268483i
$639$	3.59169			0.142085
$640$	1.00000			0.0395285
$641$	3.96991	+	6.87608i	0.156802	+	0.271589i	0.933714	−	0.358021i	$-0.116548\pi$
$641$	3.96991	+	6.87608i	0.156802	+	0.271589i	−0.776912	+	0.629610i	$0.783215\pi$
$642$	−4.72763	−	2.72950i	−0.186585	−	0.107725i
$643$		−	22.8535i		−	0.901255i	−0.892712	−	0.450627i	$-0.851200\pi$
$643$		−	22.8535i		−	0.901255i	0.892712	−	0.450627i	$-0.148800\pi$
$644$	−6.56993	+	3.79315i	−0.258892	+	0.149471i
$645$	−4.86439	−	8.42538i	−0.191535	−	0.331749i
$646$	30.1421	−	17.4025i	1.18592	−	0.684694i
$647$	−0.695003	−	0.401260i	−0.0273234	−	0.0157752i	0.486276	−	0.873805i	$-0.338355\pi$
$647$	−0.695003	−	0.401260i	−0.0273234	−	0.0157752i	−0.513599	+	0.858030i	$0.671688\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	15.5841	−	8.99746i	0.611728	−	0.353181i
$650$	−2.65590	−	4.60015i	−0.104173	−	0.180433i
$651$	−2.11296	+	1.21992i	−0.0828134	+	0.0478123i
$652$			5.24223i			0.205302i
$653$	21.1850	+	12.2312i	0.829033	+	0.478642i	0.853521	−	0.521058i	$-0.174462\pi$
$653$	21.1850	+	12.2312i	0.829033	+	0.478642i	−0.0244886	+	0.999700i	$0.507796\pi$
$654$	4.79331	+	8.30226i	0.187433	+	0.324644i
$655$	9.72217			0.379876
$656$	0.337747			0.0131868
$657$	6.37880	+	11.0484i	0.248861	+	0.431040i
$658$		−	27.5176i		−	1.07275i
$659$	2.06372	−	3.57447i	0.0803912	−	0.139242i	−0.823027	−	0.568003i	$-0.807716\pi$
$659$	2.06372	−	3.57447i	0.0803912	−	0.139242i	0.903418	+	0.428761i	$0.141050\pi$
$660$		−	2.56098i		−	0.0996862i
$661$	11.3515	+	6.55381i	0.441523	+	0.254914i	0.704244	−	0.709958i	$-0.251286\pi$
$661$	11.3515	+	6.55381i	0.441523	+	0.254914i	−0.262720	+	0.964872i	$0.584620\pi$
$662$	2.12138	−	3.67434i	0.0824499	−	0.142807i
$663$	−15.7237	+	27.2343i	−0.610659	+	1.05769i
$664$	0.148591	−	0.0857892i	0.00576646	−	0.00332927i
$665$	18.8149			0.729611
$666$	2.52083	+	5.53583i	0.0976803	+	0.214509i
$667$	−7.24796			−0.280642
$668$	−17.4530	+	10.0765i	−0.675276	+	0.389871i
$669$	−10.6275	+	18.4073i	−0.410881	+	0.711667i
$670$	−4.31103	+	7.46693i	−0.166550	+	0.288473i
$671$	−29.1951	−	16.8558i	−1.12706	−	0.650710i
$672$		−	3.20040i		−	0.123458i
$673$	8.59306	−	14.8836i	0.331238	−	0.573721i	−0.651517	−	0.758634i	$-0.725867\pi$
$673$	8.59306	−	14.8836i	0.331238	−	0.573721i	0.982755	+	0.184913i	$0.0592003\pi$
$674$		−	29.3413i		−	1.13019i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	15.2151			0.585197
$677$	−20.8957			−0.803085			−0.401543	−	0.915840i	$-0.631526\pi$
$677$	−20.8957			−0.803085			−0.401543	+	0.915840i	$0.631526\pi$
$678$	−2.70828	−	4.69088i	−0.104011	−	0.180152i
$679$	−38.7510	−	22.3729i	−1.48712	−	0.858592i
$680$		−	5.92032i		−	0.227034i
$681$	4.22423	−	2.43886i	0.161873	−	0.0934573i
$682$	0.976187	+	1.69081i	0.0373801	+	0.0647443i
$683$	−5.59385	+	3.22961i	−0.214043	+	0.123578i	−0.603189	−	0.797598i	$-0.706103\pi$
$683$	−5.59385	+	3.22961i	−0.214043	+	0.123578i	0.389146	+	0.921176i	$0.372770\pi$
$684$	−5.09130	−	2.93946i	−0.194671	−	0.112393i
$685$	−19.2400	−	11.1082i	−0.735123	−	0.424424i
$686$	−10.4142	+	6.01266i	−0.397617	+	0.229564i
$687$	−3.33494	−	5.77628i	−0.127236	−	0.220379i
$688$	−8.42538	+	4.86439i	−0.321215	+	0.185453i
$689$			54.0654i			2.05973i
$690$	2.05285	+	1.18521i	0.0781506	+	0.0451203i
$691$	15.9830	+	27.6833i	0.608021	+	1.05312i	0.991566	+	0.129601i	$0.0413695\pi$
$691$	15.9830	+	27.6833i	0.608021	+	1.05312i	−0.383546	+	0.923522i	$0.625297\pi$
$692$	0.242977			0.00923659
$693$	−8.19617			−0.311347
$694$	−10.7440	−	18.6091i	−0.407835	−	0.706392i
$695$			6.48068i			0.245826i
$696$	1.52883	−	2.64802i	0.0579502	−	0.100373i
$697$		−	1.99957i		−	0.0757390i
$698$	28.7497	+	16.5986i	1.08819	+	0.628268i
$699$	−8.49472	+	14.7133i	−0.321300	+	0.556507i
$700$	1.60020	−	2.77163i	0.0604819	−	0.104758i
$701$	−34.4716	+	19.9022i	−1.30197	+	0.751694i	−0.980742	−	0.195307i	$-0.937430\pi$
$701$	−34.4716	+	19.9022i	−1.30197	+	0.751694i	−0.321231	+	0.947001i	$0.604096\pi$
$702$	5.31179			0.200481
$703$	14.8198	+	32.5447i	0.558939	+	1.22745i
$704$	−2.56098			−0.0965207
$705$	−7.44625	+	4.29909i	−0.280442	+	0.161913i
$706$	2.40711	−	4.16924i	0.0905929	−	0.156911i
$707$	11.1655	−	19.3391i	0.419920	−	0.727323i
$708$	−6.08519	−	3.51328i	−0.228695	−	0.132037i
$709$			47.1422i			1.77046i	0.465150	+	0.885232i	$0.346000\pi$
$709$			47.1422i			1.77046i	−0.465150	+	0.885232i	$0.654000\pi$
$710$	1.79585	−	3.11050i	0.0673969	−	0.116735i
$711$		−	15.6030i		−	0.585159i
$712$	3.95633	+	6.85256i	0.148270	+	0.256810i
$713$	−1.80710			−0.0676765
$714$	−18.9474			−0.709088
$715$	6.80170	+	11.7809i	0.254369	+	0.440581i
$716$	17.0449	+	9.84088i	0.636998	+	0.367771i
$717$			12.7573i			0.476430i
$718$	25.8635	−	14.9323i	0.965217	−	0.557268i
$719$	−21.2373	−	36.7840i	−0.792016	−	1.37181i	−0.924717	−	0.380656i	$-0.875698\pi$
$719$	−21.2373	−	36.7840i	−0.792016	−	1.37181i	0.132700	−	0.991156i	$-0.457635\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	−11.9631	−	6.90688i	−0.445528	−	0.257225i
$722$	−13.4769	−	7.78087i	−0.501557	−	0.289574i
$723$	16.6996	−	9.64155i	0.621067	−	0.358573i
$724$	12.1318	+	21.0129i	0.450875	+	0.780939i
$725$	2.64802	−	1.52883i	0.0983448	−	0.0567794i
$726$		−	4.44136i		−	0.164834i
$727$	6.08823	+	3.51504i	0.225800	+	0.130366i	0.608633	−	0.793452i	$-0.291718\pi$
$727$	6.08823	+	3.51504i	0.225800	+	0.130366i	−0.382833	+	0.923818i	$0.625052\pi$
$728$	8.49992	+	14.7223i	0.315028	+	0.545645i
$729$	1.00000			0.0370370
$730$	12.7576			0.472180
$731$	28.7988	+	49.8809i	1.06516	+	1.84491i
$732$			13.1635i			0.486538i
$733$	−16.8464	+	29.1789i	−0.622237	+	1.07775i	0.366831	+	0.930288i	$0.380443\pi$
$733$	−16.8464	+	29.1789i	−0.622237	+	1.07775i	−0.989068	+	0.147459i	$0.952891\pi$
$734$		−	3.24455i		−	0.119758i
$735$	−2.80814	−	1.62128i	−0.103580	−	0.0598017i
$736$	1.18521	−	2.05285i	0.0436875	−	0.0756690i
$737$	11.0405	−	19.1227i	0.406681	−	0.704393i
$738$	−0.292497	+	0.168873i	−0.0107670	+	0.00621631i
$739$	0.107770			0.00396437			0.00198218	−	0.999998i	$-0.499369\pi$
$739$	0.107770			0.00396437			0.00198218	+	0.999998i	$0.499369\pi$
$740$	6.05458	+	0.584810i	0.222571	+	0.0214980i
$741$	31.2276			1.14717
$742$	−28.2107	+	16.2874i	−1.03565	+	0.597931i
$743$	13.0389	−	22.5841i	0.478352	−	0.828529i	−0.521340	−	0.853349i	$-0.674568\pi$
$743$	13.0389	−	22.5841i	0.478352	−	0.828529i	0.999692	+	0.0248196i	$0.00790115\pi$
$744$	0.381177	−	0.660217i	0.0139746	−	0.0242047i
$745$	19.1838	+	11.0758i	0.702840	+	0.405785i
$746$		−	30.2606i		−	1.10792i
$747$	−0.0857892	+	0.148591i	−0.00313886	+	0.00543667i
$748$			15.1618i			0.554372i
$749$	8.73548	+	15.1303i	0.319187	+	0.552849i
$750$	−1.00000			−0.0365148
$751$	−47.3580			−1.72812			−0.864059	−	0.503391i	$-0.832086\pi$
$751$	−47.3580			−1.72812			−0.864059	+	0.503391i	$0.832086\pi$
$752$	4.29909	+	7.44625i	0.156772	+	0.271537i
$753$	7.22049	+	4.16875i	0.263129	+	0.151918i
$754$			16.2417i			0.591487i
$755$	−7.43575	+	4.29303i	−0.270615	+	0.156240i
$756$	1.60020	+	2.77163i	0.0581987	+	0.100803i
$757$	−14.1442	+	8.16618i	−0.514081	+	0.296805i	−0.734510	−	0.678598i	$-0.762588\pi$
$757$	−14.1442	+	8.16618i	−0.514081	+	0.296805i	0.220429	+	0.975403i	$0.429254\pi$
$758$	−24.0860	−	13.9061i	−0.874843	−	0.505091i
$759$	−5.25731	−	3.03531i	−0.190828	−	0.110175i
$760$	−5.09130	+	2.93946i	−0.184681	+	0.106625i
$761$	−8.05342	−	13.9489i	−0.291936	−	0.505648i	0.682331	−	0.731043i	$-0.260966\pi$
$761$	−8.05342	−	13.9489i	−0.291936	−	0.505648i	−0.974268	+	0.225395i	$0.927633\pi$
$762$	−4.00377	+	2.31158i	−0.145041	+	0.0837397i
$763$		−	30.6810i		−	1.11073i
$764$	−2.51758	−	1.45353i	−0.0910830	−	0.0525868i
$765$	2.96016	+	5.12715i	0.107025	+	0.185372i
$766$	−3.69961			−0.133672
$767$	37.3236			1.34768
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$		−	5.08139i		−	0.183240i	−0.995794	−	0.0916198i	$-0.970796\pi$
$769$		−	5.08139i		−	0.183240i	0.995794	−	0.0916198i	$-0.0292044\pi$
$770$	−4.09809	+	7.09809i	−0.147685	+	0.255797i
$771$		−	8.14456i		−	0.293319i
$772$	−0.169693	−	0.0979723i	−0.00610738	−	0.00352610i
$773$	−8.96749	+	15.5321i	−0.322538	+	0.558652i	−0.981011	−	0.193952i	$-0.937869\pi$
$773$	−8.96749	+	15.5321i	−0.322538	+	0.558652i	0.658473	+	0.752604i	$0.271203\pi$
$774$	4.86439	−	8.42538i	0.174847	−	0.302844i
$775$	0.660217	−	0.381177i	0.0237157	−	0.0136923i
$776$	13.9813			0.501899
$777$	1.87163	−	19.3771i	0.0671442	−	0.695149i
$778$	−4.57995			−0.164199
$779$	−1.71957	+	0.992794i	−0.0616100	+	0.0355705i
$780$	2.65590	−	4.60015i	0.0950963	−	0.164712i
$781$	−4.59913	+	7.96593i	−0.164570	+	0.285043i
$782$	−12.1535	−	7.01683i	−0.434609	−	0.250921i
$783$			3.05766i			0.109272i
$784$	−1.62128	+	2.80814i	−0.0579028	+	0.100291i
$785$			3.68423i			0.131496i
$786$	4.86108	+	8.41964i	0.173389	+	0.300319i
$787$	5.74145			0.204661			0.102330	−	0.994750i	$-0.467370\pi$
$787$	5.74145			0.204661			0.102330	+	0.994750i	$0.467370\pi$
$788$	−20.5520			−0.732135
$789$	−2.49556	−	4.32244i	−0.0888444	−	0.153883i
$790$	−13.5126	−	7.80151i	−0.480757	−	0.277565i
$791$			17.3351i			0.616367i
$792$	2.21788	−	1.28049i	0.0788088	−	0.0455003i
$793$	−34.9609	−	60.5541i	−1.24150	−	2.15034i
$794$	−1.23032	+	0.710326i	−0.0436625	+	0.0252085i
$795$	8.81474	+	5.08919i	0.312626	+	0.180495i
$796$	−9.23904	−	5.33416i	−0.327469	−	0.189064i
$797$	26.7065	−	15.4190i	0.945994	−	0.546170i	0.0541599	−	0.998532i	$-0.482752\pi$
$797$	26.7065	−	15.4190i	0.945994	−	0.546170i	0.891834	+	0.452362i	$0.149419\pi$
$798$	9.40745	+	16.2942i	0.333020	+	0.576808i
$799$	44.0841	−	25.4520i	1.55959	−	0.900427i
$800$			1.00000i			0.0353553i
$801$	−6.85256	−	3.95633i	−0.242123	−	0.139790i
$802$	12.7427	+	22.0710i	0.449961	+	0.779356i
$803$	−32.6720			−1.15297
$804$	−8.62207			−0.304077
$805$	−3.79315	−	6.56993i	−0.133691	−	0.231560i
$806$			4.04946i			0.142636i
$807$	−13.0156	+	22.5436i	−0.458170	+	0.793574i
$808$			6.97754i			0.245469i
$809$	−0.257036	−	0.148400i	−0.00903690	−	0.00521746i	0.495475	−	0.868622i	$-0.334994\pi$
$809$	−0.257036	−	0.148400i	−0.00903690	−	0.00521746i	−0.504512	+	0.863405i	$0.668327\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−19.5041	+	33.7821i	−0.684882	+	1.18625i	0.288592	+	0.957452i	$0.406813\pi$
$811$	−19.5041	+	33.7821i	−0.684882	+	1.18625i	−0.973474	+	0.228799i	$0.926520\pi$
$812$	−8.47471	+	4.89287i	−0.297404	+	0.171706i
$813$	−0.255749			−0.00896951
$814$	−15.5057	−	1.49769i	−0.543474	−	0.0524940i
$815$	−5.24223			−0.183627
$816$	5.12715	−	2.96016i	0.179486	−	0.103626i
$817$	28.5974	−	49.5321i	1.00050	−	1.73291i
$818$	15.1189	−	26.1866i	0.528619	−	0.915594i
$819$	−14.7223	−	8.49992i	−0.514439	−	0.297011i
$820$			0.337747i			0.0117946i
$821$	3.57886	−	6.19877i	0.124903	−	0.216339i	−0.796792	−	0.604254i	$-0.793471\pi$
$821$	3.57886	−	6.19877i	0.124903	−	0.216339i	0.921695	+	0.387915i	$0.126805\pi$
$822$		−	22.2165i		−	0.774888i
$823$	10.2169	+	17.6962i	0.356138	+	0.616849i	0.987312	−	0.158792i	$-0.0507600\pi$
$823$	10.2169	+	17.6962i	0.356138	+	0.616849i	−0.631174	+	0.775641i	$0.717427\pi$
$824$	4.31626			0.150364
$825$	2.56098			0.0891620
$826$	11.2439	+	19.4750i	0.391226	+	0.677623i
$827$	−15.5220	−	8.96162i	−0.539752	−	0.311626i	0.205226	−	0.978715i	$-0.434207\pi$
$827$	−15.5220	−	8.96162i	−0.539752	−	0.311626i	−0.744979	+	0.667088i	$0.767540\pi$
$828$			2.37042i			0.0823780i
$829$	−36.4043	+	21.0180i	−1.26437	+	0.729986i	−0.973917	−	0.226903i	$-0.927140\pi$
$829$	−36.4043	+	21.0180i	−1.26437	+	0.729986i	−0.290455	+	0.956889i	$0.593807\pi$
$830$	0.0857892	+	0.148591i	0.00297779	+	0.00515768i
$831$	−20.3140	+	11.7283i	−0.704684	+	0.406849i
$832$	−4.60015	−	2.65590i	−0.159481	−	0.0920766i
$833$	16.6251	+	9.59848i	0.576024	+	0.332568i
$834$	−5.61243	+	3.24034i	−0.194343	+	0.112204i
$835$	−10.0765	−	17.4530i	−0.348711	−	0.603985i
$836$	13.0387	−	7.52791i	0.450954	−	0.260358i
$837$			0.762353i			0.0263508i
$838$	12.6966	+	7.33040i	0.438598	+	0.253225i
$839$	−12.8686	−	22.2891i	−0.444273	−	0.769504i	0.553728	−	0.832698i	$-0.313205\pi$
$839$	−12.8686	−	22.2891i	−0.444273	−	0.769504i	−0.998001	+	0.0631937i	$0.979871\pi$
$840$	3.20040			0.110424
$841$	19.6507			0.677610
$842$	0.951790	+	1.64855i	0.0328008	+	0.0568127i
$843$		−	2.21641i		−	0.0763371i
$844$	−5.91976	+	10.2533i	−0.203766	+	0.352934i
$845$			15.2151i			0.523416i
$846$	−7.44625	−	4.29909i	−0.256007	−	0.147806i
$847$	−7.10707	+	12.3098i	−0.244202	+	0.422970i
$848$	5.08919	−	8.81474i	0.174764	−	0.302699i
$849$	15.5342	−	8.96867i	0.533132	−	0.307804i
$850$	5.92032			0.203065
$851$	8.37650	−	11.7360i	0.287143	−	0.402306i
$852$	3.59169			0.123049
$853$	28.0616	−	16.2014i	0.960812	−	0.554725i	0.0643889	−	0.997925i	$-0.479490\pi$
$853$	28.0616	−	16.2014i	0.960812	−	0.554725i	0.896423	+	0.443200i	$0.146157\pi$
$854$	21.0643	−	36.4844i	0.720804	−	1.24847i
$855$	2.93946	−	5.09130i	0.100527	−	0.174119i
$856$	−4.72763	−	2.72950i	−0.161587	−	0.0932923i
$857$		−	27.1496i		−	0.927412i	−0.885989	−	0.463706i	$-0.846519\pi$
$857$		−	27.1496i		−	0.927412i	0.885989	−	0.463706i	$-0.153481\pi$
$858$	−6.80170	+	11.7809i	−0.232206	+	0.402193i
$859$			23.3544i			0.796842i	0.917203	+	0.398421i	$0.130442\pi$
$859$			23.3544i			0.796842i	−0.917203	+	0.398421i	$0.869558\pi$
$860$	−4.86439	−	8.42538i	−0.165874	−	0.287303i
$861$	1.08092			0.0368378
$862$	−31.2060			−1.06288
$863$	19.4358	+	33.6638i	0.661602	+	1.14593i	0.980195	+	0.198037i	$0.0634566\pi$
$863$	19.4358	+	33.6638i	0.661602	+	1.14593i	−0.318592	+	0.947892i	$0.603210\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$			0.242977i			0.00826146i
$866$	−9.51242	+	5.49200i	−0.323245	+	0.186626i
$867$	−9.02508	−	15.6319i	−0.306508	−	0.530887i
$868$	−2.11296	+	1.21992i	−0.0717185	+	0.0414067i
$869$	34.6056	+	19.9795i	1.17391	+	0.677760i
$870$	2.64802	+	1.52883i	0.0897761	+	0.0518323i
$871$	39.6628	−	22.8993i	1.34392	−	0.775913i
$872$	4.79331	+	8.30226i	0.162322	+	0.281150i
$873$	−12.1082	+	6.99065i	−0.409799	+	0.236598i
$874$			13.9355i			0.471377i
$875$	2.77163	+	1.60020i	0.0936981	+	0.0540966i
$876$	6.37880	+	11.0484i	0.215520	+	0.373291i
$877$	−52.4367			−1.77066			−0.885332	−	0.464960i	$-0.846069\pi$
$877$	−52.4367			−1.77066			−0.885332	+	0.464960i	$0.846069\pi$
$878$	−18.4270			−0.621882
$879$	−8.47194	−	14.6738i	−0.285751	−	0.494936i
$880$		−	2.56098i		−	0.0863307i
$881$	−5.95488	+	10.3142i	−0.200625	+	0.347493i	−0.948730	−	0.316088i	$-0.897631\pi$
$881$	−5.95488	+	10.3142i	−0.200625	+	0.347493i	0.748105	+	0.663580i	$0.230964\pi$
$882$		−	3.24256i		−	0.109183i
$883$	43.2673	+	24.9804i	1.45606	+	0.840658i	0.998814	−	0.0486819i	$-0.0155021\pi$
$883$	43.2673	+	24.9804i	1.45606	+	0.840658i	0.457247	+	0.889340i	$0.348835\pi$
$884$	−15.7237	+	27.2343i	−0.528847	+	0.915989i
$885$	3.51328	−	6.08519i	0.118098	−	0.204551i
$886$	−35.8224	+	20.6821i	−1.20348	+	0.694827i
$887$	−45.5128			−1.52817			−0.764085	−	0.645116i	$-0.776809\pi$
$887$	−45.5128			−1.52817			−0.764085	+	0.645116i	$0.776809\pi$
$888$	2.52083	+	5.53583i	0.0845936	+	0.185770i
$889$	14.7960			0.496240
$890$	−6.85256	+	3.95633i	−0.229698	+	0.132616i
$891$	−1.28049	+	2.21788i	−0.0428981	+	0.0743017i
$892$	−10.6275	+	18.4073i	−0.355833	+	0.616321i
$893$	−43.7759	−	25.2740i	−1.46491	−	0.845763i
$894$			22.1515i			0.740858i
$895$	−9.84088	+	17.0449i	−0.328944	+	0.569748i
$896$		−	3.20040i		−	0.106918i
$897$	−6.29560	−	10.9043i	−0.210204	−	0.364084i
$898$	−23.1424			−0.772272
$899$	−2.33102			−0.0777439
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−52.1860	−	30.1296i	−1.73857	−	1.00376i
$902$		−	0.864964i		−	0.0288001i
$903$	−26.9646	+	15.5680i	−0.897325	+	0.518071i
$904$	−2.70828	−	4.69088i	−0.0900760	−	0.156016i
$905$	−21.0129	+	12.1318i	−0.698493	+	0.403275i
$906$	−7.43575	−	4.29303i	−0.247036	−	0.142627i
$907$	16.7499	+	9.67054i	0.556170	+	0.321105i	0.751607	−	0.659611i	$-0.229279\pi$
$907$	16.7499	+	9.67054i	0.556170	+	0.321105i	−0.195437	+	0.980716i	$0.562612\pi$
$908$	4.22423	−	2.43886i	0.140186	−	0.0809364i
$909$	−3.48877	−	6.04273i	−0.115715	−	0.200425i
$910$	−14.7223	+	8.49992i	−0.488040	+	0.281770i
$911$		−	9.01624i		−	0.298721i	−0.988783	−	0.149361i	$-0.952278\pi$
$911$		−	9.01624i		−	0.298721i	0.988783	−	0.149361i	$-0.0477216\pi$
$912$	−5.09130	−	2.93946i	−0.168590	−	0.0973353i
$913$	−0.219705	−	0.380540i	−0.00727116	−	0.0125940i
$914$	−28.2238			−0.933560
$915$	−13.1635			−0.435172
$916$	−3.33494	−	5.77628i	−0.110189	−	0.190854i
$917$		−	31.1148i		−	1.02750i
$918$	−2.96016	+	5.12715i	−0.0976998	+	0.169221i
$919$		−	21.4132i		−	0.706355i	−0.935556	−	0.353177i	$-0.885101\pi$
$919$		−	21.4132i		−	0.706355i	0.935556	−	0.353177i	$-0.114899\pi$
$920$	2.05285	+	1.18521i	0.0676804	+	0.0390753i
$921$	−7.45955	+	12.9203i	−0.245801	+	0.425739i
$922$	−6.83924	+	11.8459i	−0.225238	+	0.390124i
$923$	−16.5223	+	9.53916i	−0.543838	+	0.313985i
$924$	−8.19617			−0.269634
$925$	−0.584810	+	6.05458i	−0.0192284	+	0.199074i
$926$	20.8631			0.685605
$927$	−3.73799	+	2.15813i	−0.122772	+	0.0708823i
$928$	1.52883	−	2.64802i	0.0501864	−	0.0869254i
$929$	−13.9729	+	24.2017i	−0.458435	+	0.794033i	−0.998878	−	0.0473477i	$-0.984923\pi$
$929$	−13.9729	+	24.2017i	−0.458435	+	0.794033i	0.540444	+	0.841380i	$0.318256\pi$
$930$	0.660217	+	0.381177i	0.0216494	+	0.0124993i
$931$		−	19.0627i		−	0.624756i
$932$	−8.49472	+	14.7133i	−0.278254	+	0.481950i
$933$			32.5652i			1.06614i
$934$	−6.85759	−	11.8777i	−0.224387	−	0.388650i
$935$	−15.1618			−0.495845
$936$	5.31179			0.173621
$937$	−22.3173	−	38.6547i	−0.729075	−	1.26280i	−0.957274	−	0.289181i	$-0.906617\pi$
$937$	−22.3173	−	38.6547i	−0.729075	−	1.26280i	0.228199	−	0.973614i	$-0.426716\pi$
$938$	23.8972	+	13.7970i	0.780270	+	0.450489i
$939$			11.5842i			0.378037i
$940$	−7.44625	+	4.29909i	−0.242870	+	0.140221i
$941$	−15.7456	−	27.2722i	−0.513293	−	0.889050i	−0.999881	−	0.0154181i	$-0.995092\pi$
$941$	−15.7456	−	27.2722i	−0.513293	−	0.889050i	0.486588	−	0.873632i	$-0.338241\pi$
$942$	−3.19063	+	1.84211i	−0.103956	+	0.0600193i
$943$	0.693343	+	0.400302i	0.0225783	+	0.0130356i
$944$	−6.08519	−	3.51328i	−0.198056	−	0.114348i
$945$	−2.77163	+	1.60020i	−0.0901610	+	0.0520545i
$946$	12.4576	+	21.5773i	0.405033	+	0.701537i
$947$	36.2812	−	20.9470i	1.17898	−	0.680685i	0.223202	−	0.974772i	$-0.428349\pi$
$947$	36.2812	−	20.9470i	1.17898	−	0.680685i	0.955779	+	0.294087i	$0.0950156\pi$
$948$		−	15.6030i		−	0.506763i
$949$	−58.6869	−	33.8829i	−1.90506	−	1.09988i
$950$	−2.93946	−	5.09130i	−0.0953687	−	0.165183i
$951$	20.5856			0.667534
$952$	−18.9474			−0.614088
$953$	23.7035	+	41.0556i	0.767831	+	1.32992i	0.938737	+	0.344635i	$0.111997\pi$
$953$	23.7035	+	41.0556i	0.767831	+	1.32992i	−0.170906	+	0.985287i	$0.554669\pi$
$954$			10.1784i			0.329537i
$955$	1.45353	−	2.51758i	0.0470351	−	0.0814671i
$956$			12.7573i			0.412600i
$957$	−6.78152	−	3.91531i	−0.219216	−	0.126564i
$958$	0.980259	−	1.69786i	0.0316707	−	0.0548553i
$959$	−35.5508	+	61.5757i	−1.14799	+	1.98838i
$960$	−0.866025	+	0.500000i	−0.0279508	+	0.0161374i
$961$	30.4188			0.981252
$962$	−26.2988	−	18.7706i	−0.847907	−	0.605187i
$963$	5.45899			0.175914
$964$	16.6996	−	9.64155i	0.537859	−	0.310533i
$965$	0.0979723	−	0.169693i	0.00315384	−	0.00546261i
$966$	3.79315	−	6.56993i	0.122043	−	0.211384i
$967$	−10.9916	−	6.34599i	−0.353465	−	0.204073i	0.312745	−	0.949837i	$-0.398751\pi$
$967$	−10.9916	−	6.34599i	−0.353465	−	0.204073i	−0.666210	+	0.745764i	$0.732085\pi$
$968$		−	4.44136i		−	0.142751i
$969$	−17.4025	+	30.1421i	−0.559050	+	0.968304i
$970$			13.9813i			0.448912i
$971$	7.69952	+	13.3360i	0.247089	+	0.427971i	0.962717	−	0.270511i	$-0.0871926\pi$
$971$	7.69952	+	13.3360i	0.247089	+	0.427971i	−0.715628	+	0.698482i	$0.753859\pi$
$972$	1.00000			0.0320750
$973$	20.7408			0.664918
$974$	−17.0134	−	29.4681i	−0.545145	−	0.944219i
$975$	4.60015	+	2.65590i	0.147323	+	0.0850567i
$976$			13.1635i			0.421354i
$977$	44.5922	−	25.7453i	1.42663	−	0.823666i	0.429778	−	0.902934i	$-0.358592\pi$
$977$	44.5922	−	25.7453i	1.42663	−	0.823666i	0.996853	+	0.0792684i	$0.0252584\pi$
$978$	−2.62111	−	4.53990i	−0.0838140	−	0.145170i
$979$	17.5493	−	10.1321i	0.560878	−	0.323823i
$980$	−2.80814	−	1.62128i	−0.0897026	−	0.0517898i
$981$	−8.30226	−	4.79331i	−0.265071	−	0.153039i
$982$	5.42350	−	3.13126i	0.173071	−	0.0999225i
$983$	−11.1774	−	19.3599i	−0.356505	−	0.617485i	0.630869	−	0.775889i	$-0.282698\pi$
$983$	−11.1774	−	19.3599i	−0.356505	−	0.617485i	−0.987374	+	0.158404i	$0.949365\pi$
$984$	−0.292497	+	0.168873i	−0.00932447	+	0.00538349i
$985$		−	20.5520i		−	0.654842i
$986$	−15.6771	−	9.05117i	−0.499260	−	0.288248i
$987$	13.7588	+	23.8310i	0.437948	+	0.758548i
$988$	31.2276			0.993483
$989$	−23.0614			−0.733309
$990$	1.28049	+	2.21788i	0.0406967	+	0.0704888i
$991$		−	27.4930i		−	0.873344i	−0.899621	−	0.436672i	$-0.856157\pi$
$991$		−	27.4930i		−	0.873344i	0.899621	−	0.436672i	$-0.143843\pi$
$992$	0.381177	−	0.660217i	0.0121024	−	0.0209619i
$993$			4.24277i			0.134640i
$994$	−9.95483	−	5.74742i	−0.315748	−	0.182297i
$995$	5.33416	−	9.23904i	0.169104	−	0.292897i
$996$	−0.0857892	+	0.148591i	−0.00271833	+	0.00470829i
$997$	−21.2243	+	12.2539i	−0.672181	+	0.388084i	−0.796902	−	0.604108i	$-0.793529\pi$
$997$	−21.2243	+	12.2539i	−0.672181	+	0.388084i	0.124722	+	0.992192i	$0.460196\pi$
$998$	−13.4259			−0.424988
$999$	−4.95102	−	3.53375i	−0.156643	−	0.111803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.751.3	✓	16
37.27	even	6	inner	1110.2.x.e.841.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.3	✓	16	1.1	even	1	trivial
1110.2.x.e.841.3	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.60020 - 2.77163i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(1.60020 - 2.77163i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +2.56098 q^{11} +(-0.500000 - 0.866025i) q^{12} +(4.60015 + 2.65590i) q^{13} +3.20040i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.12715 + 2.96016i) q^{17} +(0.866025 + 0.500000i) q^{18} +(5.09130 + 2.93946i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.60020 - 2.77163i) q^{21} +(-2.21788 + 1.28049i) q^{22} -2.37042i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.31179 q^{26} -1.00000 q^{27} +(-1.60020 - 2.77163i) q^{28} -3.05766i q^{29} +(-0.500000 + 0.866025i) q^{30} -0.762353i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.28049 - 2.21788i) q^{33} +(2.96016 - 5.12715i) q^{34} +(2.77163 - 1.60020i) q^{35} -1.00000 q^{36} +(4.95102 + 3.53375i) q^{37} -5.87892 q^{38} +(4.60015 - 2.65590i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.168873 + 0.292497i) q^{41} +(2.77163 + 1.60020i) q^{42} -9.72879i q^{43} +(1.28049 - 2.21788i) q^{44} -1.00000i q^{45} +(1.18521 + 2.05285i) q^{46} -8.59819 q^{47} -1.00000 q^{48} +(-1.62128 - 2.80814i) q^{49} +(-0.866025 - 0.500000i) q^{50} +5.92032i q^{51} +(4.60015 - 2.65590i) q^{52} +(5.08919 + 8.81474i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.21788 + 1.28049i) q^{55} +(2.77163 + 1.60020i) q^{56} +(5.09130 - 2.93946i) q^{57} +(1.52883 + 2.64802i) q^{58} +(6.08519 - 3.51328i) q^{59} -1.00000i q^{60} +(-11.3999 - 6.58176i) q^{61} +(0.381177 + 0.660217i) q^{62} -3.20040 q^{63} -1.00000 q^{64} +(2.65590 + 4.60015i) q^{65} +2.56098i q^{66} +(4.31103 - 7.46693i) q^{67} +5.92032i q^{68} +(-2.05285 - 1.18521i) q^{69} +(-1.60020 + 2.77163i) q^{70} +(-1.79585 + 3.11050i) q^{71} +(0.866025 - 0.500000i) q^{72} -12.7576 q^{73} +(-6.05458 - 0.584810i) q^{74} +1.00000 q^{75} +(5.09130 - 2.93946i) q^{76} +(4.09809 - 7.09809i) q^{77} +(-2.65590 + 4.60015i) q^{78} +(13.5126 + 7.80151i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -0.337747i q^{82} +(-0.0857892 - 0.148591i) q^{83} -3.20040 q^{84} -5.92032 q^{85} +(4.86439 + 8.42538i) q^{86} +(-2.64802 - 1.52883i) q^{87} +2.56098i q^{88} +(6.85256 - 3.95633i) q^{89} +(0.500000 + 0.866025i) q^{90} +(14.7223 - 8.49992i) q^{91} +(-2.05285 - 1.18521i) q^{92} +(-0.660217 - 0.381177i) q^{93} +(7.44625 - 4.29909i) q^{94} +(2.93946 + 5.09130i) q^{95} +(0.866025 - 0.500000i) q^{96} -13.9813i q^{97} +(2.80814 + 1.62128i) q^{98} +(-1.28049 - 2.21788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more