LMFDB - Embedded newform 1110.2.ba.a.529.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.11
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.a.619.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.17865 - 0.503482i) q^{5} -1.00000i q^{6} +(-3.20005 - 1.84755i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.17865 - 0.503482i) q^{5} -1.00000i q^{6} +(-3.20005 - 1.84755i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.52535 - 1.63502i) q^{10} +4.44239 q^{11} +(-0.866025 + 0.500000i) q^{12} +(-3.09657 + 5.36341i) q^{13} +3.69510i q^{14} +(2.13851 + 0.653296i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.67263 + 2.89708i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.88936 + 2.82287i) q^{19} +(-0.653296 + 2.13851i) q^{20} +(-1.84755 - 3.20005i) q^{21} +(-2.22120 - 3.84723i) q^{22} +3.31793 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.49301 - 2.19382i) q^{25} +6.19314 q^{26} +1.00000i q^{27} +(3.20005 - 1.84755i) q^{28} -0.108323i q^{29} +(-0.503482 - 2.17865i) q^{30} -3.58380i q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.84723 + 2.22120i) q^{33} +(1.67263 - 2.89708i) q^{34} +(-7.90200 - 2.41400i) q^{35} -1.00000 q^{36} +(-1.62326 - 5.86217i) q^{37} -5.64574i q^{38} +(-5.36341 + 3.09657i) q^{39} +(2.17865 - 0.503482i) q^{40} +(0.667426 - 1.15602i) q^{41} +(-1.84755 + 3.20005i) q^{42} -1.49655 q^{43} +(-2.22120 + 3.84723i) q^{44} +(1.52535 + 1.63502i) q^{45} +(-1.65897 - 2.87341i) q^{46} -1.22763i q^{47} -1.00000i q^{48} +(3.32690 + 5.76236i) q^{49} +(-4.14641 - 2.79415i) q^{50} +3.34526i q^{51} +(-3.09657 - 5.36341i) q^{52} +(7.70341 - 4.44757i) q^{53} +(0.866025 - 0.500000i) q^{54} +(9.67841 - 2.23666i) q^{55} +(-3.20005 - 1.84755i) q^{56} +(2.82287 + 4.88936i) q^{57} +(-0.0938106 + 0.0541616i) q^{58} +(-0.292750 + 0.169019i) q^{59} +(-1.63502 + 1.52535i) q^{60} +(11.4397 + 6.60469i) q^{61} +(-3.10366 + 1.79190i) q^{62} -3.69510i q^{63} +1.00000 q^{64} +(-4.04595 + 13.2441i) q^{65} -4.44239i q^{66} +(12.7735 + 7.37478i) q^{67} -3.34526 q^{68} +(2.87341 + 1.65897i) q^{69} +(1.86042 + 8.05033i) q^{70} +(2.66182 - 4.61040i) q^{71} +(0.500000 + 0.866025i) q^{72} -2.67315i q^{73} +(-4.26515 + 4.33687i) q^{74} +(4.98797 + 0.346604i) q^{75} +(-4.88936 + 2.82287i) q^{76} +(-14.2159 - 8.20755i) q^{77} +(5.36341 + 3.09657i) q^{78} +(-4.87431 - 2.81418i) q^{79} +(-1.52535 - 1.63502i) q^{80} +(-0.500000 + 0.866025i) q^{81} -1.33485 q^{82} +(-5.20372 + 3.00437i) q^{83} +3.69510 q^{84} +(5.10271 + 5.46959i) q^{85} +(0.748273 + 1.29605i) q^{86} +(0.0541616 - 0.0938106i) q^{87} +4.44239 q^{88} +(-13.9095 + 8.03066i) q^{89} +(0.653296 - 2.13851i) q^{90} +(19.8184 - 11.4421i) q^{91} +(-1.65897 + 2.87341i) q^{92} +(1.79190 - 3.10366i) q^{93} +(-1.06316 + 0.613817i) q^{94} +(12.0735 + 3.68834i) q^{95} +(-0.866025 + 0.500000i) q^{96} -12.8116 q^{97} +(3.32690 - 5.76236i) q^{98} +(2.22120 + 3.84723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * 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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.17865	−	0.503482i	0.974321	−	0.225164i
$5$	2.17865	−	0.503482i	0.974321	−	0.225164i
$6$		−	1.00000i		−	0.408248i
$7$	−3.20005	−	1.84755i	−1.20951	−	0.698309i	−0.246855	−	0.969052i	$-0.579397\pi$
$7$	−3.20005	−	1.84755i	−1.20951	−	0.698309i	−0.962652	+	0.270743i	$0.912731\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.52535	−	1.63502i	−0.482359	−	0.517040i
$11$	4.44239			1.33943			0.669716	−	0.742617i	$-0.266416\pi$
$11$	4.44239			1.33943			0.669716	+	0.742617i	$0.266416\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−3.09657	+	5.36341i	−0.858833	+	1.48754i	0.0142091	+	0.999899i	$0.495477\pi$
$13$	−3.09657	+	5.36341i	−0.858833	+	1.48754i	−0.873043	+	0.487644i	$0.837856\pi$
$14$			3.69510i			0.987558i
$15$	2.13851	+	0.653296i	0.552160	+	0.168680i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.67263	+	2.89708i	0.405673	+	0.702646i	0.994400	−	0.105686i	$-0.0337039\pi$
$17$	1.67263	+	2.89708i	0.405673	+	0.702646i	−0.588727	+	0.808332i	$0.700371\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	4.88936	+	2.82287i	1.12170	+	0.647611i	0.941833	−	0.336081i	$-0.109101\pi$
$19$	4.88936	+	2.82287i	1.12170	+	0.647611i	0.179862	+	0.983692i	$0.442435\pi$
$20$	−0.653296	+	2.13851i	−0.146081	+	0.478184i
$21$	−1.84755	−	3.20005i	−0.403169	−	0.698309i
$22$	−2.22120	−	3.84723i	−0.473561	−	0.820231i
$23$	3.31793			0.691837			0.345918	−	0.938265i	$-0.387567\pi$
$23$	3.31793			0.691837			0.345918	+	0.938265i	$0.387567\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	4.49301	−	2.19382i	0.898602	−	0.438764i
$26$	6.19314			1.21457
$27$			1.00000i			0.192450i
$28$	3.20005	−	1.84755i	0.604753	−	0.349155i
$29$		−	0.108323i		−	0.0201151i	−0.999949	−	0.0100575i	$-0.996799\pi$
$29$		−	0.108323i		−	0.0201151i	0.999949	−	0.0100575i	$-0.00320147\pi$
$30$	−0.503482	−	2.17865i	−0.0919227	−	0.397765i
$31$		−	3.58380i		−	0.643670i	−0.946796	−	0.321835i	$-0.895700\pi$
$31$		−	3.58380i		−	0.643670i	0.946796	−	0.321835i	$-0.104300\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.84723	+	2.22120i	0.669716	+	0.386661i
$34$	1.67263	−	2.89708i	0.286854	−	0.496846i
$35$	−7.90200	−	2.41400i	−1.33568	−	0.408040i
$36$	−1.00000			−0.166667
$37$	−1.62326	−	5.86217i	−0.266863	−	0.963734i
$37$	−1.62326	−	5.86217i	−0.266863	−	0.963734i
$38$		−	5.64574i		−	0.915861i
$39$	−5.36341	+	3.09657i	−0.858833	+	0.495848i
$40$	2.17865	−	0.503482i	0.344474	−	0.0796074i
$41$	0.667426	−	1.15602i	0.104234	−	0.180539i	−0.809191	−	0.587546i	$-0.800094\pi$
$41$	0.667426	−	1.15602i	0.104234	−	0.180539i	0.913425	+	0.407007i	$0.133427\pi$
$42$	−1.84755	+	3.20005i	−0.285084	+	0.493779i
$43$	−1.49655			−0.228221			−0.114111	−	0.993468i	$-0.536402\pi$
$43$	−1.49655			−0.228221			−0.114111	+	0.993468i	$0.536402\pi$
$44$	−2.22120	+	3.84723i	−0.334858	+	0.579991i
$45$	1.52535	+	1.63502i	0.227386	+	0.243735i
$46$	−1.65897	−	2.87341i	−0.244601	−	0.423662i
$47$		−	1.22763i		−	0.179069i	−0.995984	−	0.0895343i	$-0.971462\pi$
$47$		−	1.22763i		−	0.179069i	0.995984	−	0.0895343i	$-0.0285379\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.32690	+	5.76236i	0.475271	+	0.823194i
$50$	−4.14641	−	2.79415i	−0.586391	−	0.395153i
$51$			3.34526i			0.468431i
$52$	−3.09657	−	5.36341i	−0.429417	−	0.743772i
$53$	7.70341	−	4.44757i	1.05814	−	0.610920i	0.133226	−	0.991086i	$-0.457466\pi$
$53$	7.70341	−	4.44757i	1.05814	−	0.610920i	0.924919	+	0.380165i	$0.124133\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	9.67841	−	2.23666i	1.30504	−	0.301592i
$56$	−3.20005	−	1.84755i	−0.427625	−	0.246890i
$57$	2.82287	+	4.88936i	0.373899	+	0.647611i
$58$	−0.0938106	+	0.0541616i	−0.0123179	+	0.00711176i
$59$	−0.292750	+	0.169019i	−0.0381128	+	0.0220044i	−0.518935	−	0.854814i	$-0.673671\pi$
$59$	−0.292750	+	0.169019i	−0.0381128	+	0.0220044i	0.480823	+	0.876818i	$0.340338\pi$
$60$	−1.63502	+	1.52535i	−0.211081	+	0.196922i
$61$	11.4397	+	6.60469i	1.46470	+	0.845644i	0.999223	−	0.0394160i	$-0.0125497\pi$
$61$	11.4397	+	6.60469i	1.46470	+	0.845644i	0.465476	+	0.885060i	$0.345883\pi$
$62$	−3.10366	+	1.79190i	−0.394166	+	0.227572i
$63$		−	3.69510i		−	0.465539i
$64$	1.00000			0.125000
$65$	−4.04595	+	13.2441i	−0.501838	+	1.64272i
$66$		−	4.44239i		−	0.546821i
$67$	12.7735	+	7.37478i	1.56053	+	0.900972i	0.997203	+	0.0747384i	$0.0238122\pi$
$67$	12.7735	+	7.37478i	1.56053	+	0.900972i	0.563327	+	0.826234i	$0.309521\pi$
$68$	−3.34526			−0.405673
$69$	2.87341	+	1.65897i	0.345918	+	0.199716i
$70$	1.86042	+	8.05033i	0.222362	+	0.962199i
$71$	2.66182	−	4.61040i	0.315899	−	0.547154i	−0.663729	−	0.747973i	$-0.731027\pi$
$71$	2.66182	−	4.61040i	0.315899	−	0.547154i	0.979628	+	0.200819i	$0.0643605\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$		−	2.67315i		−	0.312868i	−0.987688	−	0.156434i	$-0.950000\pi$
$73$		−	2.67315i		−	0.312868i	0.987688	−	0.156434i	$-0.0499999\pi$
$74$	−4.26515	+	4.33687i	−0.495814	+	0.504151i
$75$	4.98797	+	0.346604i	0.575961	+	0.0400224i
$76$	−4.88936	+	2.82287i	−0.560848	+	0.323806i
$77$	−14.2159	−	8.20755i	−1.62005	−	0.935338i
$78$	5.36341	+	3.09657i	0.607287	+	0.350617i
$79$	−4.87431	−	2.81418i	−0.548403	−	0.316620i	0.200075	−	0.979781i	$-0.435881\pi$
$79$	−4.87431	−	2.81418i	−0.548403	−	0.316620i	−0.748478	+	0.663160i	$0.769215\pi$
$80$	−1.52535	−	1.63502i	−0.170540	−	0.182801i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.33485			−0.147410
$83$	−5.20372	+	3.00437i	−0.571182	+	0.329772i	−0.757621	−	0.652694i	$-0.773639\pi$
$83$	−5.20372	+	3.00437i	−0.571182	+	0.329772i	0.186439	+	0.982466i	$0.440305\pi$
$84$	3.69510			0.403169
$85$	5.10271	+	5.46959i	0.553466	+	0.593260i
$86$	0.748273	+	1.29605i	0.0806884	+	0.139756i
$87$	0.0541616	−	0.0938106i	0.00580673	−	0.0100575i
$88$	4.44239			0.473561
$89$	−13.9095	+	8.03066i	−1.47440	+	0.851248i	−0.999584	−	0.0288348i	$-0.990820\pi$
$89$	−13.9095	+	8.03066i	−1.47440	+	0.851248i	−0.474820	+	0.880083i	$0.657487\pi$
$90$	0.653296	−	2.13851i	0.0688634	−	0.225418i
$91$	19.8184	−	11.4421i	2.07753	−	1.19946i
$92$	−1.65897	+	2.87341i	−0.172959	+	0.299574i
$93$	1.79190	−	3.10366i	0.185811	−	0.321835i
$94$	−1.06316	+	0.613817i	−0.109657	+	0.0633103i
$95$	12.0735	+	3.68834i	1.23871	+	0.378416i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−12.8116			−1.30082			−0.650410	−	0.759583i	$-0.725403\pi$
$97$	−12.8116			−1.30082			−0.650410	+	0.759583i	$0.725403\pi$
$98$	3.32690	−	5.76236i	0.336068	−	0.582086i
$99$	2.22120	+	3.84723i	0.223239	+	0.386661i
$100$	−0.346604	+	4.98797i	−0.0346604	+	0.498797i
$101$	−10.2462			−1.01953			−0.509766	−	0.860313i	$-0.670268\pi$
$101$	−10.2462			−1.01953			−0.509766	+	0.860313i	$0.670268\pi$
$102$	2.89708	−	1.67263i	0.286854	−	0.165615i
$103$	5.94305			0.585586			0.292793	−	0.956176i	$-0.405415\pi$
$103$	5.94305			0.585586			0.292793	+	0.956176i	$0.405415\pi$
$104$	−3.09657	+	5.36341i	−0.303643	+	0.525926i
$105$	−5.63633	−	6.04158i	−0.550050	−	0.589598i
$106$	−7.70341	−	4.44757i	−0.748221	−	0.431986i
$107$	9.10060	+	5.25423i	0.879788	+	0.507946i	0.870588	−	0.492012i	$-0.163738\pi$
$107$	9.10060	+	5.25423i	0.879788	+	0.507946i	0.00919937	+	0.999958i	$0.497072\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−1.27969	+	0.738832i	−0.122573	+	0.0707673i	−0.560033	−	0.828471i	$-0.689211\pi$
$109$	−1.27969	+	0.738832i	−0.122573	+	0.0707673i	0.437460	+	0.899238i	$0.355878\pi$
$110$	−6.77621	−	7.26342i	−0.646087	−	0.692540i
$111$	1.52530	−	5.88842i	0.144775	−	0.558904i
$112$			3.69510i			0.349155i
$113$	−3.19271	−	5.52994i	−0.300345	−	0.520213i	0.675869	−	0.737022i	$-0.263769\pi$
$113$	−3.19271	−	5.52994i	−0.300345	−	0.520213i	−0.976214	+	0.216809i	$0.930435\pi$
$114$	2.82287	−	4.88936i	0.264386	−	0.457930i
$115$	7.22861	−	1.67052i	0.674071	−	0.155777i
$116$	0.0938106	+	0.0541616i	0.00871009	+	0.00502877i
$117$	−6.19314			−0.572556
$118$	0.292750	+	0.169019i	0.0269498	+	0.0155595i
$119$		−	12.3611i		−	1.13314i
$120$	2.13851	+	0.653296i	0.195218	+	0.0596375i
$121$	8.73486			0.794078
$122$		−	13.2094i		−	1.19592i
$123$	1.15602	−	0.667426i	0.104234	−	0.0601797i
$124$	3.10366	+	1.79190i	0.278717	+	0.160917i
$125$	8.68414	−	7.04171i	0.776734	−	0.629829i
$126$	−3.20005	+	1.84755i	−0.285084	+	0.164593i
$127$	15.2469	−	8.80279i	1.35294	−	0.781122i	0.364282	−	0.931289i	$-0.381315\pi$
$127$	15.2469	−	8.80279i	1.35294	−	0.781122i	0.988661	+	0.150167i	$0.0479812\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.29605	−	0.748273i	−0.114111	−	0.0658818i
$130$	13.4927	−	3.11813i	1.18338	−	0.273478i
$131$	−18.6551	+	10.7705i	−1.62990	+	0.941025i	−0.645783	+	0.763521i	$0.723469\pi$
$131$	−18.6551	+	10.7705i	−1.62990	+	0.941025i	−0.984120	+	0.177504i	$0.943198\pi$
$132$	−3.84723	+	2.22120i	−0.334858	+	0.193330i
$133$	−10.4308	−	18.0667i	−0.904466	−	1.56658i
$134$		−	14.7496i		−	1.27417i
$135$	0.503482	+	2.17865i	0.0433328	+	0.187508i
$136$	1.67263	+	2.89708i	0.143427	+	0.248423i
$137$			10.1403i			0.866343i	0.901312	+	0.433171i	$0.142606\pi$
$137$			10.1403i			0.866343i	−0.901312	+	0.433171i	$0.857394\pi$
$138$		−	3.31793i		−	0.282441i
$139$	−3.23928	−	5.61060i	−0.274752	−	0.475885i	0.695320	−	0.718700i	$-0.255263\pi$
$139$	−3.23928	−	5.61060i	−0.274752	−	0.475885i	−0.970073	+	0.242815i	$0.921929\pi$
$140$	6.04158	−	5.63633i	0.510607	−	0.476357i
$141$	0.613817	−	1.06316i	0.0516927	−	0.0895343i
$142$	−5.32363			−0.446749
$143$	−13.7562	+	23.8264i	−1.15035	+	1.99246i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−0.0545387	−	0.235998i	−0.00452919	−	0.0195986i
$146$	−2.31501	+	1.33657i	−0.191592	+	0.110616i
$147$			6.65380i			0.548796i
$148$	5.88842	+	1.52530i	0.484025	+	0.125378i
$149$	1.79951			0.147421			0.0737107	−	0.997280i	$-0.476516\pi$
$149$	1.79951			0.147421			0.0737107	+	0.997280i	$0.476516\pi$
$150$	−2.19382	−	4.49301i	−0.179125	−	0.366853i
$151$	5.78284	−	10.0162i	0.470601	−	0.815104i	−0.528834	−	0.848725i	$-0.677371\pi$
$151$	5.78284	−	10.0162i	0.470601	−	0.815104i	0.999435	+	0.0336210i	$0.0107039\pi$
$152$	4.88936	+	2.82287i	0.396579	+	0.228965i
$153$	−1.67263	+	2.89708i	−0.135224	+	0.234215i
$154$			16.4151i			1.32277i
$155$	−1.80438	−	7.80784i	−0.144931	−	0.627141i
$156$		−	6.19314i		−	0.495848i
$157$	−17.0546	+	9.84650i	−1.36111	+	0.785836i	−0.989771	−	0.142662i	$-0.954434\pi$
$157$	−17.0546	+	9.84650i	−1.36111	+	0.785836i	−0.371337	+	0.928498i	$0.621101\pi$
$158$			5.62837i			0.447769i
$159$	8.89513			0.705430
$160$	−0.653296	+	2.13851i	−0.0516476	+	0.169064i
$161$	−10.6176	−	6.13005i	−0.836781	−	0.483116i
$162$	1.00000			0.0785674
$163$	8.25810	+	14.3034i	0.646824	+	1.12033i	0.983877	+	0.178847i	$0.0572366\pi$
$163$	8.25810	+	14.3034i	0.646824	+	1.12033i	−0.337053	+	0.941486i	$0.609430\pi$
$164$	0.667426	+	1.15602i	0.0521172	+	0.0902696i
$165$	9.50008	+	2.90220i	0.739580	+	0.225936i
$166$	5.20372	+	3.00437i	0.403887	+	0.233184i
$167$	5.60293	−	9.70456i	0.433568	−	0.750961i	−0.563610	−	0.826041i	$-0.690588\pi$
$167$	5.60293	−	9.70456i	0.433568	−	0.750961i	0.997178	+	0.0750799i	$0.0239212\pi$
$168$	−1.84755	−	3.20005i	−0.142542	−	0.246890i
$169$	−12.6775	−	21.9580i	−0.975190	−	1.68908i
$170$	2.18545	−	7.15387i	0.167616	−	0.548676i
$171$			5.64574i			0.431741i
$172$	0.748273	−	1.29605i	0.0570553	−	0.0988227i
$173$	12.4041	−	7.16151i	0.943066	−	0.544480i	0.0521462	−	0.998639i	$-0.483394\pi$
$173$	12.4041	−	7.16151i	0.943066	−	0.544480i	0.890920	+	0.454160i	$0.150060\pi$
$174$	−0.108323			−0.00821195
$175$	−18.4311	−	1.28074i	−1.39326	−	0.0968147i
$176$	−2.22120	−	3.84723i	−0.167429	−	0.289996i
$177$	−0.338038			−0.0254085
$178$	13.9095	+	8.03066i	1.04256	+	0.601923i
$179$			6.16211i			0.460578i	0.973122	+	0.230289i	$0.0739671\pi$
$179$			6.16211i			0.460578i	−0.973122	+	0.230289i	$0.926033\pi$
$180$	−2.17865	+	0.503482i	−0.162387	+	0.0375273i
$181$	−1.83239	+	3.17379i	−0.136200	+	0.235906i	−0.926055	−	0.377388i	$-0.876822\pi$
$181$	−1.83239	+	3.17379i	−0.136200	+	0.235906i	0.789855	+	0.613294i	$0.210156\pi$
$182$	−19.8184	−	11.4421i	−1.46904	−	0.848148i
$183$	6.60469	+	11.4397i	0.488233	+	0.845644i
$184$	3.31793			0.244601
$185$	−6.48802	−	11.9543i	−0.477008	−	0.878899i
$186$	−3.58380			−0.262777
$187$	7.43049	+	12.8700i	0.543371	+	0.941147i
$188$	1.06316	+	0.613817i	0.0775390	+	0.0447672i
$189$	1.84755	−	3.20005i	0.134390	−	0.232770i
$190$	−2.84253	−	12.3001i	−0.206219	−	0.892342i
$191$		−	17.0867i		−	1.23635i	−0.786040	−	0.618176i	$-0.787872\pi$
$191$		−	17.0867i		−	1.23635i	0.786040	−	0.618176i	$-0.212128\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−24.1866			−1.74099			−0.870495	−	0.492177i	$-0.836201\pi$
$193$	−24.1866			−1.74099			−0.870495	+	0.492177i	$0.836201\pi$
$194$	6.40580	+	11.0952i	0.459910	+	0.796587i
$195$	−10.1259	+	9.44671i	−0.725132	+	0.676493i
$196$	−6.65380			−0.475271
$197$	−8.50118	+	4.90816i	−0.605684	+	0.349692i	−0.771274	−	0.636503i	$-0.780380\pi$
$197$	−8.50118	+	4.90816i	−0.605684	+	0.349692i	0.165591	+	0.986195i	$0.447047\pi$
$198$	2.22120	−	3.84723i	0.157854	−	0.273410i
$199$		−	22.0251i		−	1.56132i	−0.624958	−	0.780659i	$-0.714884\pi$
$199$		−	22.0251i		−	1.56132i	0.624958	−	0.780659i	$-0.285116\pi$
$200$	4.49301	−	2.19382i	0.317704	−	0.155126i
$201$	7.37478	+	12.7735i	0.520177	+	0.900972i
$202$	5.12308	+	8.87344i	0.360459	+	0.624333i
$203$	−0.200133	+	0.346640i	−0.0140466	+	0.0243294i
$204$	−2.89708	−	1.67263i	−0.202836	−	0.117108i
$205$	0.872053	−	2.85459i	0.0609068	−	0.199373i
$206$	−2.97152	−	5.14683i	−0.207036	−	0.358597i
$207$	1.65897	+	2.87341i	0.115306	+	0.199716i
$208$	6.19314			0.429417
$209$	21.7205	+	12.5403i	1.50244	+	0.867431i
$210$	−2.41400	+	7.90200i	−0.166582	+	0.545290i
$211$	−7.17457			−0.493918			−0.246959	−	0.969026i	$-0.579431\pi$
$211$	−7.17457			−0.493918			−0.246959	+	0.969026i	$0.579431\pi$
$212$			8.89513i			0.610920i
$213$	4.61040	−	2.66182i	0.315899	−	0.182385i
$214$		−	10.5085i		−	0.718344i
$215$	−3.26045	+	0.753483i	−0.222361	+	0.0513871i
$216$			1.00000i			0.0680414i
$217$	−6.62126	+	11.4684i	−0.449481	+	0.778523i
$218$	1.27969	+	0.738832i	0.0866719	+	0.0500400i
$219$	1.33657	−	2.31501i	0.0903173	−	0.156434i
$220$	−2.90220	+	9.50008i	−0.195666	+	0.640495i
$221$	−20.7177			−1.39362
$222$	−5.86217	+	1.62326i	−0.393443	+	0.108946i
$223$		−	0.219842i		−	0.0147217i	−0.999973	−	0.00736087i	$-0.997657\pi$
$223$		−	0.219842i		−	0.0147217i	0.999973	−	0.00736087i	$-0.00234306\pi$
$224$	3.20005	−	1.84755i	0.213813	−	0.123445i
$225$	4.14641	+	2.79415i	0.276427	+	0.186277i
$226$	−3.19271	+	5.52994i	−0.212376	+	0.367846i
$227$	−12.3956	+	21.4699i	−0.822728	+	1.42501i	0.0809161	+	0.996721i	$0.474215\pi$
$227$	−12.3956	+	21.4699i	−0.822728	+	1.42501i	−0.903644	+	0.428285i	$0.859118\pi$
$228$	−5.64574			−0.373899
$229$	−5.65301	+	9.79129i	−0.373561	+	0.647027i	−0.990111	−	0.140289i	$-0.955197\pi$
$229$	−5.65301	+	9.79129i	−0.373561	+	0.647027i	0.616549	+	0.787316i	$0.288530\pi$
$230$	−5.06101	−	5.42490i	−0.333713	−	0.357707i
$231$	−8.20755	−	14.2159i	−0.540017	−	0.935338i
$232$		−	0.108323i		−	0.00711176i
$233$		−	14.3078i		−	0.937337i	−0.883374	−	0.468669i	$-0.844734\pi$
$233$		−	14.3078i		−	0.937337i	0.883374	−	0.468669i	$-0.155266\pi$
$234$	3.09657	+	5.36341i	0.202429	+	0.350617i
$235$	−0.618091	−	2.67458i	−0.0403198	−	0.174470i
$236$		−	0.338038i		−	0.0220044i
$237$	−2.81418	−	4.87431i	−0.182801	−	0.316620i
$238$	−10.7050	+	6.18055i	−0.693904	+	0.400626i
$239$	5.88745	−	3.39912i	0.380828	−	0.219871i	−0.297351	−	0.954768i	$-0.596103\pi$
$239$	5.88745	−	3.39912i	0.380828	−	0.219871i	0.678178	+	0.734897i	$0.262770\pi$
$240$	−0.503482	−	2.17865i	−0.0324996	−	0.140631i
$241$	−4.79812	−	2.77020i	−0.309074	−	0.178444i	0.337438	−	0.941348i	$-0.390440\pi$
$241$	−4.79812	−	2.77020i	−0.309074	−	0.178444i	−0.646512	+	0.762904i	$0.723773\pi$
$242$	−4.36743	−	7.56461i	−0.280749	−	0.486272i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−11.4397	+	6.60469i	−0.732350	+	0.422822i
$245$	10.1494	+	10.8791i	0.648420	+	0.695041i
$246$	−1.15602	−	0.667426i	−0.0737048	−	0.0425535i
$247$	−30.2805	+	17.4824i	−1.92670	+	1.11238i
$248$		−	3.58380i		−	0.227572i
$249$	−6.00873			−0.380788
$250$	−10.4404	−	3.99984i	−0.660307	−	0.252972i
$251$			30.0814i			1.89872i	0.314193	+	0.949359i	$0.398266\pi$
$251$			30.0814i			1.89872i	−0.314193	+	0.949359i	$0.601734\pi$
$252$	3.20005	+	1.84755i	0.201584	+	0.116385i
$253$	14.7396			0.926668
$254$	−15.2469	−	8.80279i	−0.956675	−	0.552336i
$255$	1.68428	+	7.28815i	0.105474	+	0.456402i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.7565	−	20.3629i	−0.733350	−	1.27020i	−0.955443	−	0.295174i	$-0.904622\pi$
$257$	−11.7565	−	20.3629i	−0.733350	−	1.27020i	0.222093	−	0.975025i	$-0.428711\pi$
$258$			1.49655i			0.0931709i
$259$	−5.63613	+	21.7583i	−0.350212	+	1.35200i
$260$	−9.44671	−	10.1259i	−0.585860	−	0.627983i
$261$	0.0938106	−	0.0541616i	0.00580673	−	0.00335252i
$262$	18.6551	+	10.7705i	1.15252	+	0.665405i
$263$	−23.8858	−	13.7905i	−1.47286	−	0.850357i	−0.473327	−	0.880887i	$-0.656947\pi$
$263$	−23.8858	−	13.7905i	−1.47286	−	0.850357i	−0.999534	+	0.0305303i	$0.990280\pi$
$264$	3.84723	+	2.22120i	0.236780	+	0.136705i
$265$	14.5438	−	13.5682i	0.893416	−	0.833488i
$266$	−10.4308	+	18.0667i	−0.639554	+	1.10774i
$267$	−16.0613			−0.982936
$268$	−12.7735	+	7.37478i	−0.780265	+	0.450486i
$269$	−13.5863			−0.828370			−0.414185	−	0.910193i	$-0.635933\pi$
$269$	−13.5863			−0.828370			−0.414185	+	0.910193i	$0.635933\pi$
$270$	1.63502	−	1.52535i	0.0995044	−	0.0928300i
$271$	4.97694	+	8.62031i	0.302327	+	0.523646i	0.976663	−	0.214779i	$-0.0689031\pi$
$271$	4.97694	+	8.62031i	0.302327	+	0.523646i	−0.674335	+	0.738425i	$0.735570\pi$
$272$	1.67263	−	2.89708i	0.101418	−	0.175662i
$273$	22.8843			1.38502
$274$	8.78174	−	5.07014i	0.530525	−	0.306299i
$275$	19.9597	−	9.74580i	1.20362	−	0.587694i
$276$	−2.87341	+	1.65897i	−0.172959	+	0.0998580i
$277$	−13.3467	+	23.1172i	−0.801926	+	1.38898i	0.116421	+	0.993200i	$0.462858\pi$
$277$	−13.3467	+	23.1172i	−0.801926	+	1.38898i	−0.918347	+	0.395777i	$0.870475\pi$
$278$	−3.23928	+	5.61060i	−0.194279	+	0.336502i
$279$	3.10366	−	1.79190i	0.185811	−	0.107278i
$280$	−7.90200	−	2.41400i	−0.472235	−	0.144264i
$281$	−0.674004	+	0.389137i	−0.0402077	+	0.0232139i	−0.519969	−	0.854185i	$-0.674057\pi$
$281$	−0.674004	+	0.389137i	−0.0402077	+	0.0232139i	0.479761	+	0.877399i	$0.340723\pi$
$282$	−1.22763			−0.0731045
$283$	5.81231	−	10.0672i	0.345506	−	0.598434i	−0.639940	−	0.768425i	$-0.721041\pi$
$283$	5.81231	−	10.0672i	0.345506	−	0.598434i	0.985446	+	0.169991i	$0.0543740\pi$
$284$	2.66182	+	4.61040i	0.157950	+	0.273577i
$285$	8.61175	+	9.23092i	0.510116	+	0.546793i
$286$	27.5123			1.62684
$287$	−4.27160	+	2.46621i	−0.252144	+	0.145576i
$288$	−1.00000			−0.0589256
$289$	2.90460	−	5.03092i	0.170859	−	0.295936i
$290$	−0.177111	+	0.165231i	−0.0104003	+	0.00970269i
$291$	−11.0952	−	6.40580i	−0.650410	−	0.375515i
$292$	2.31501	+	1.33657i	0.135476	+	0.0782170i
$293$	9.00934	+	5.20154i	0.526331	+	0.303877i	0.739521	−	0.673133i	$-0.235052\pi$
$293$	9.00934	+	5.20154i	0.526331	+	0.303877i	−0.213190	+	0.977011i	$0.568385\pi$
$294$	5.76236	−	3.32690i	0.336068	−	0.194029i
$295$	−0.552700	+	0.515627i	−0.0321795	+	0.0300210i
$296$	−1.62326	−	5.86217i	−0.0943504	−	0.340732i
$297$			4.44239i			0.257774i
$298$	−0.899754	−	1.55842i	−0.0521213	−	0.0902768i
$299$	−10.2742	+	17.7954i	−0.594173	+	1.02914i
$300$	−2.79415	+	4.14641i	−0.161321	+	0.239393i
$301$	4.78903	+	2.76495i	0.276035	+	0.159369i
$302$	−11.5657			−0.665530
$303$	−8.87344	−	5.12308i	−0.509766	−	0.294313i
$304$		−	5.64574i		−	0.323806i
$305$	28.2483	+	8.62964i	1.61750	+	0.494132i
$306$	3.34526			0.191236
$307$			18.4064i			1.05051i	0.850945	+	0.525254i	$0.176030\pi$
$307$			18.4064i			1.05051i	−0.850945	+	0.525254i	$0.823970\pi$
$308$	14.2159	−	8.20755i	0.810026	−	0.467669i
$309$	5.14683	+	2.97152i	0.292793	+	0.169044i
$310$	−5.85960	+	5.46656i	−0.332803	+	0.310480i
$311$	16.0430	−	9.26245i	0.909717	−	0.525225i	0.0293771	−	0.999568i	$-0.490648\pi$
$311$	16.0430	−	9.26245i	0.909717	−	0.525225i	0.880340	+	0.474343i	$0.157314\pi$
$312$	−5.36341	+	3.09657i	−0.303643	+	0.175309i
$313$	−10.9094	−	18.8956i	−0.616634	−	1.06804i	−0.990095	−	0.140396i	$-0.955162\pi$
$313$	−10.9094	−	18.8956i	−0.616634	−	1.06804i	0.373461	−	0.927646i	$-0.378171\pi$
$314$	17.0546	+	9.84650i	0.962449	+	0.555670i
$315$	−1.86042	−	8.05033i	−0.104823	−	0.453585i
$316$	4.87431	−	2.81418i	0.274201	−	0.158310i
$317$	−24.1836	+	13.9624i	−1.35829	+	0.784207i	−0.989393	−	0.145264i	$-0.953597\pi$
$317$	−24.1836	+	13.9624i	−1.35829	+	0.784207i	−0.368894	+	0.929472i	$0.620263\pi$
$318$	−4.44757	−	7.70341i	−0.249407	−	0.431986i
$319$		−	0.481214i		−	0.0269428i
$320$	2.17865	−	0.503482i	0.121790	−	0.0281455i
$321$	5.25423	+	9.10060i	0.293263	+	0.507946i
$322$			12.2601i			0.683229i
$323$			18.8865i			1.05087i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−2.14656	+	30.8912i	−0.119070	+	1.71353i
$326$	8.25810	−	14.3034i	0.457374	−	0.792195i
$327$	−1.47766			−0.0817150
$328$	0.667426	−	1.15602i	0.0368524	−	0.0638303i
$329$	−2.26812	+	3.92849i	−0.125045	+	0.216585i
$330$	−2.23666	−	9.67841i	−0.123124	−	0.532779i
$331$	28.7591	−	16.6041i	1.58074	−	0.912642i	0.585991	−	0.810318i	$-0.300706\pi$
$331$	28.7591	−	16.6041i	1.58074	−	0.912642i	0.994751	−	0.102324i	$-0.0326278\pi$
$332$		−	6.00873i		−	0.329772i
$333$	4.26515	−	4.33687i	0.233729	−	0.237659i
$334$	−11.2059			−0.613157
$335$	31.5420	+	9.63583i	1.72332	+	0.526461i
$336$	−1.84755	+	3.20005i	−0.100792	+	0.174577i
$337$	5.47768	+	3.16254i	0.298388	+	0.172275i	0.641719	−	0.766940i	$-0.278222\pi$
$337$	5.47768	+	3.16254i	0.298388	+	0.172275i	−0.343330	+	0.939215i	$0.611555\pi$
$338$	−12.6775	+	21.9580i	−0.689563	+	1.19436i
$339$		−	6.38543i		−	0.346809i
$340$	−7.28815	+	1.68428i	−0.395256	+	0.0913429i
$341$		−	15.9207i		−	0.862152i
$342$	4.88936	−	2.82287i	0.264386	−	0.152643i
$343$			1.27925i			0.0690733i
$344$	−1.49655			−0.0806884
$345$	7.09542	+	2.16759i	0.382004	+	0.116699i
$346$	−12.4041	−	7.16151i	−0.666849	−	0.385005i
$347$	26.7305			1.43497			0.717483	−	0.696576i	$-0.245294\pi$
$347$	26.7305			1.43497			0.717483	+	0.696576i	$0.245294\pi$
$348$	0.0541616	+	0.0938106i	0.00290336	+	0.00502877i
$349$	−9.72032	−	16.8361i	−0.520317	−	0.901215i	−0.999721	−	0.0236209i	$-0.992481\pi$
$349$	−9.72032	−	16.8361i	−0.520317	−	0.901215i	0.479404	−	0.877594i	$-0.340853\pi$
$350$	8.10639	+	16.6022i	0.433305	+	0.887422i
$351$	−5.36341	−	3.09657i	−0.286278	−	0.165283i
$352$	−2.22120	+	3.84723i	−0.118390	+	0.205058i
$353$	2.02075	+	3.50004i	0.107554	+	0.186288i	0.914779	−	0.403955i	$-0.132365\pi$
$353$	2.02075	+	3.50004i	0.107554	+	0.186288i	−0.807225	+	0.590244i	$0.799032\pi$
$354$	0.169019	+	0.292750i	0.00898326	+	0.0155595i
$355$	3.47791	−	11.3846i	0.184588	−	0.604232i
$356$		−	16.0613i		−	0.851248i
$357$	6.18055	−	10.7050i	0.327109	−	0.566570i
$358$	5.33654	−	3.08106i	0.282045	−	0.162839i
$359$	−0.449208			−0.0237083			−0.0118542	−	0.999930i	$-0.503773\pi$
$359$	−0.449208			−0.0237083			−0.0118542	+	0.999930i	$0.503773\pi$
$360$	1.52535	+	1.63502i	0.0803931	+	0.0861733i
$361$	6.43721	+	11.1496i	0.338801	+	0.586820i
$362$	3.66478			0.192617
$363$	7.56461	+	4.36743i	0.397039	+	0.229231i
$364$			22.8843i			1.19946i
$365$	−1.34588	−	5.82384i	−0.0704466	−	0.304834i
$366$	6.60469	−	11.4397i	0.345233	−	0.597961i
$367$	−28.8599	−	16.6623i	−1.50647	−	0.869763i	−0.999972	−	0.00752386i	$-0.997605\pi$
$367$	−28.8599	−	16.6623i	−1.50647	−	0.869763i	−0.506502	−	0.862239i	$-0.669062\pi$
$368$	−1.65897	−	2.87341i	−0.0864796	−	0.149787i
$369$	1.33485			0.0694896
$370$	−7.10873	+	11.5959i	−0.369565	+	0.602844i
$371$	−32.8684			−1.70644
$372$	1.79190	+	3.10366i	0.0929057	+	0.160917i
$373$	−0.921169	−	0.531837i	−0.0476963	−	0.0275375i	0.475962	−	0.879466i	$-0.342100\pi$
$373$	−0.921169	−	0.531837i	−0.0476963	−	0.0275375i	−0.523659	+	0.851928i	$0.675433\pi$
$374$	7.43049	−	12.8700i	0.384222	−	0.665491i
$375$	11.0415	−	1.75622i	0.570183	−	0.0906910i
$376$		−	1.22763i		−	0.0633103i
$377$	0.580982	+	0.335430i	0.0299221	+	0.0172755i
$378$	−3.69510			−0.190056
$379$	−11.9117	−	20.6317i	−0.611863	−	1.05978i	−0.990926	−	0.134407i	$-0.957087\pi$
$379$	−11.9117	−	20.6317i	−0.611863	−	1.05978i	0.379063	−	0.925371i	$-0.376246\pi$
$380$	−9.23092	+	8.61175i	−0.473536	+	0.441773i
$381$	17.6056			0.901962
$382$	−14.7975	+	8.54336i	−0.757107	+	0.437116i
$383$	−12.3247	+	21.3470i	−0.629762	+	1.09078i	0.357838	+	0.933784i	$0.383514\pi$
$383$	−12.3247	+	21.3470i	−0.629762	+	1.09078i	−0.987599	+	0.156995i	$0.949819\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−35.1038	−	10.7239i	−1.78906	−	0.546542i
$386$	12.0933	+	20.9462i	0.615533	+	1.06613i
$387$	−0.748273	−	1.29605i	−0.0380369	−	0.0658818i
$388$	6.40580	−	11.0952i	0.325205	−	0.563272i
$389$	3.99858	+	2.30858i	0.202736	+	0.117050i	0.597931	−	0.801548i	$-0.295990\pi$
$389$	3.99858	+	2.30858i	0.202736	+	0.117050i	−0.395195	+	0.918597i	$0.629323\pi$
$390$	13.2441	+	4.04595i	0.670639	+	0.204875i
$391$	5.54968	+	9.61233i	0.280659	+	0.486116i
$392$	3.32690	+	5.76236i	0.168034	+	0.291043i
$393$	−21.5410			−1.08660
$394$	8.50118	+	4.90816i	0.428283	+	0.247269i
$395$	−12.0363	−	3.67699i	−0.605612	−	0.185009i
$396$	−4.44239			−0.223239
$397$		−	11.6194i		−	0.583162i	−0.956546	−	0.291581i	$-0.905819\pi$
$397$		−	11.6194i		−	0.583162i	0.956546	−	0.291581i	$-0.0941813\pi$
$398$	−19.0743	+	11.0125i	−0.956108	+	0.552009i
$399$		−	20.8616i		−	1.04439i
$400$	−4.14641	−	2.79415i	−0.207320	−	0.139708i
$401$			6.31885i			0.315548i	0.987475	+	0.157774i	$0.0504318\pi$
$401$			6.31885i			0.315548i	−0.987475	+	0.157774i	$0.949568\pi$
$402$	7.37478	−	12.7735i	0.367820	−	0.637084i
$403$	19.2214	+	11.0975i	0.957487	+	0.552805i
$404$	5.12308	−	8.87344i	0.254883	−	0.441470i
$405$	−0.653296	+	2.13851i	−0.0324625	+	0.106263i
$406$	0.400265			0.0198648
$407$	−7.21118	−	26.0421i	−0.357445	−	1.29086i
$408$			3.34526i			0.165615i
$409$	−12.2422	+	7.06806i	−0.605340	+	0.349493i	−0.771139	−	0.636666i	$-0.780313\pi$
$409$	−12.2422	+	7.06806i	−0.605340	+	0.349493i	0.165799	+	0.986159i	$0.446980\pi$
$410$	−2.90817	+	0.672073i	−0.143624	+	0.0331913i
$411$	−5.07014	+	8.78174i	−0.250092	+	0.433171i
$412$	−2.97152	+	5.14683i	−0.146396	+	0.253566i
$413$	1.24909			0.0614635
$414$	1.65897	−	2.87341i	0.0815337	−	0.141221i
$415$	−9.82442	+	9.16543i	−0.482262	+	0.449913i
$416$	−3.09657	−	5.36341i	−0.151822	−	0.262963i
$417$		−	6.47856i		−	0.317257i
$418$		−	25.0806i		−	1.22673i
$419$	−19.8015	−	34.2972i	−0.967366	−	1.67553i	−0.703119	−	0.711073i	$-0.748210\pi$
$419$	−19.8015	−	34.2972i	−0.967366	−	1.67553i	−0.264248	−	0.964455i	$-0.585124\pi$
$420$	8.05033	−	1.86042i	0.392816	−	0.0907791i
$421$		−	7.95090i		−	0.387503i	−0.981051	−	0.193752i	$-0.937934\pi$
$421$		−	7.95090i		−	0.387503i	0.981051	−	0.193752i	$-0.0620656\pi$
$422$	3.58728	+	6.21336i	0.174626	+	0.302462i
$423$	1.06316	−	0.613817i	0.0516927	−	0.0298448i
$424$	7.70341	−	4.44757i	0.374111	−	0.215993i
$425$	13.8708	+	9.34718i	0.672834	+	0.453405i
$426$	−4.61040	−	2.66182i	−0.223375	−	0.128965i
$427$	−24.4050	−	42.2708i	−1.18104	−	2.04563i
$428$	−9.10060	+	5.25423i	−0.439894	+	0.253973i
$429$	−23.8264	+	13.7562i	−1.15035	+	0.664154i
$430$	2.28276	+	2.44689i	0.110084	+	0.117999i
$431$	9.99522	+	5.77074i	0.481453	+	0.277967i	0.721022	−	0.692912i	$-0.243673\pi$
$431$	9.99522	+	5.77074i	0.481453	+	0.277967i	−0.239569	+	0.970879i	$0.577006\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	14.0193i		−	0.673725i	−0.941554	−	0.336862i	$-0.890634\pi$
$433$		−	14.0193i		−	0.673725i	0.941554	−	0.336862i	$-0.109366\pi$
$434$	13.2425			0.635661
$435$	0.0707671	−	0.231650i	0.00339302	−	0.0111067i
$436$		−	1.47766i		−	0.0707673i
$437$	16.2226	+	9.36610i	0.776030	+	0.448041i
$438$	−2.67315			−0.127728
$439$	−20.7334	−	11.9704i	−0.989551	−	0.571317i	−0.0844108	−	0.996431i	$-0.526901\pi$
$439$	−20.7334	−	11.9704i	−0.989551	−	0.571317i	−0.905140	+	0.425114i	$0.860234\pi$
$440$	9.67841	−	2.23666i	0.461400	−	0.106629i
$441$	−3.32690	+	5.76236i	−0.158424	+	0.274398i
$442$	10.3588	+	17.9420i	0.492720	+	0.853416i
$443$		−	26.2329i		−	1.24636i	−0.782077	−	0.623182i	$-0.785840\pi$
$443$		−	26.2329i		−	1.24636i	0.782077	−	0.623182i	$-0.214160\pi$
$444$	4.33687	+	4.26515i	0.205819	+	0.202415i
$445$	−26.2606	+	24.4992i	−1.24487	+	1.16137i
$446$	−0.190389	+	0.109921i	−0.00901519	+	0.00520492i
$447$	1.55842	+	0.899754i	0.0737107	+	0.0425569i
$448$	−3.20005	−	1.84755i	−0.151188	−	0.0872886i
$449$	16.5697	+	9.56655i	0.781974	+	0.451473i	0.837130	−	0.547005i	$-0.184232\pi$
$449$	16.5697	+	9.56655i	0.781974	+	0.451473i	−0.0551551	+	0.998478i	$0.517565\pi$
$450$	0.346604	−	4.98797i	0.0163391	−	0.235135i
$451$	2.96497	−	5.13547i	0.139615	−	0.241820i
$452$	6.38543			0.300345
$453$	10.0162	−	5.78284i	0.470601	−	0.271701i
$454$	24.7913			1.16351
$455$	37.4163	−	34.9066i	1.75411	−	1.63645i
$456$	2.82287	+	4.88936i	0.132193	+	0.228965i
$457$	20.5198	−	35.5413i	0.959875	−	1.66255i	0.237081	−	0.971490i	$-0.423809\pi$
$457$	20.5198	−	35.5413i	0.959875	−	1.66255i	0.722794	−	0.691063i	$-0.242857\pi$
$458$	11.3060			0.528295
$459$	−2.89708	+	1.67263i	−0.135224	+	0.0780718i
$460$	−2.16759	+	7.09542i	−0.101065	+	0.330825i
$461$	−9.56724	+	5.52365i	−0.445591	+	0.257262i	−0.705966	−	0.708245i	$-0.749487\pi$
$461$	−9.56724	+	5.52365i	−0.445591	+	0.257262i	0.260375	+	0.965507i	$0.416154\pi$
$462$	−8.20755	+	14.2159i	−0.381850	+	0.661384i
$463$	4.02668	−	6.97442i	0.187136	−	0.324129i	−0.757158	−	0.653231i	$-0.773413\pi$
$463$	4.02668	−	6.97442i	0.187136	−	0.324129i	0.944294	+	0.329103i	$0.106746\pi$
$464$	−0.0938106	+	0.0541616i	−0.00435505	+	0.00251439i
$465$	2.34128	−	7.66398i	0.108574	−	0.355409i
$466$	−12.3909	+	7.15391i	−0.573999	+	0.331399i
$467$	9.63792			0.445990			0.222995	−	0.974820i	$-0.428417\pi$
$467$	9.63792			0.445990			0.222995	+	0.974820i	$0.428417\pi$
$468$	3.09657	−	5.36341i	0.143139	−	0.247924i
$469$	−27.2506	−	47.1994i	−1.25831	−	2.17946i
$470$	−2.00721	+	1.87257i	−0.0925856	+	0.0863753i
$471$	−19.6930			−0.907406
$472$	−0.292750	+	0.169019i	−0.0134749	+	0.00777973i
$473$	−6.64825			−0.305687
$474$	−2.81418	+	4.87431i	−0.129260	+	0.223884i
$475$	28.1608	+	1.95684i	1.29211	+	0.0897858i
$476$	10.7050	+	6.18055i	0.490664	+	0.283285i
$477$	7.70341	+	4.44757i	0.352715	+	0.203640i
$478$	−5.88745	−	3.39912i	−0.269286	−	0.155472i
$479$	−27.4842	+	15.8680i	−1.25578	+	0.725027i	−0.972252	−	0.233936i	$-0.924840\pi$
$479$	−27.4842	+	15.8680i	−1.25578	+	0.725027i	−0.283532	+	0.958963i	$0.591506\pi$
$480$	−1.63502	+	1.52535i	−0.0746283	+	0.0696225i
$481$	36.4678	+	9.44636i	1.66279	+	0.430717i
$482$			5.54039i			0.252358i
$483$	−6.13005	−	10.6176i	−0.278927	−	0.483116i
$484$	−4.36743	+	7.56461i	−0.198520	+	0.343846i
$485$	−27.9120	+	6.45041i	−1.26742	+	0.292898i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	4.48336			0.203161			0.101580	−	0.994827i	$-0.467610\pi$
$487$	4.48336			0.203161			0.101580	+	0.994827i	$0.467610\pi$
$488$	11.4397	+	6.60469i	0.517849	+	0.298980i
$489$			16.5162i			0.746888i
$490$	4.34690	−	14.2292i	0.196373	−	0.642809i
$491$	−8.90853			−0.402037			−0.201018	−	0.979587i	$-0.564425\pi$
$491$	−8.90853			−0.402037			−0.201018	+	0.979587i	$0.564425\pi$
$492$			1.33485i			0.0601797i
$493$	0.313821	−	0.181185i	0.0141338	−	0.00816015i
$494$	30.2805	+	17.4824i	1.36238	+	0.786572i
$495$	6.77621	+	7.26342i	0.304568	+	0.326466i
$496$	−3.10366	+	1.79190i	−0.139359	+	0.0804587i
$497$	−17.0359	+	9.83569i	−0.764165	+	0.441191i
$498$	3.00437	+	5.20372i	0.134629	+	0.233184i
$499$	31.6688	+	18.2840i	1.41769	+	0.818503i	0.996096	−	0.0882814i	$-0.0281375\pi$
$499$	31.6688	+	18.2840i	1.41769	+	0.818503i	0.421594	+	0.906785i	$0.361471\pi$
$500$	1.75622	+	11.0415i	0.0785408	+	0.493793i
$501$	9.70456	−	5.60293i	0.433568	−	0.250320i
$502$	26.0512	−	15.0407i	1.16272	−	0.671298i
$503$	4.13426	+	7.16075i	0.184338	+	0.319282i	0.943353	−	0.331790i	$-0.107653\pi$
$503$	4.13426	+	7.16075i	0.184338	+	0.319282i	−0.759016	+	0.651073i	$0.774319\pi$
$504$		−	3.69510i		−	0.164593i
$505$	−22.3228	+	5.15876i	−0.993351	+	0.229562i
$506$	−7.36978	−	12.7648i	−0.327627	−	0.567466i
$507$		−	25.3549i		−	1.12605i
$508$			17.6056i			0.781122i
$509$	−18.6383	−	32.2825i	−0.826129	−	1.43090i	−0.901053	−	0.433709i	$-0.857205\pi$
$509$	−18.6383	−	32.2825i	−0.826129	−	1.43090i	0.0749237	−	0.997189i	$-0.476129\pi$
$510$	5.46959	−	5.10271i	0.242197	−	0.225952i
$511$	−4.93878	+	8.55421i	−0.218479	+	0.378416i
$512$	1.00000			0.0441942
$513$	−2.82287	+	4.88936i	−0.124633	+	0.215870i
$514$	−11.7565	+	20.3629i	−0.518557	+	0.898167i
$515$	12.9478	−	2.99222i	0.570549	−	0.131853i
$516$	1.29605	−	0.748273i	0.0570553	−	0.0329409i
$517$		−	5.45363i		−	0.239850i
$518$	21.6613	−	5.99813i	0.951744	−	0.263543i
$519$	14.3230			0.628711
$520$	−4.04595	+	13.2441i	−0.177427	+	0.580790i
$521$	−2.11581	+	3.66469i	−0.0926953	+	0.160553i	−0.908644	−	0.417571i	$-0.862882\pi$
$521$	−2.11581	+	3.66469i	−0.0926953	+	0.160553i	0.815949	+	0.578124i	$0.196215\pi$
$522$	−0.0938106	−	0.0541616i	−0.00410598	−	0.00237059i
$523$	−6.66483	+	11.5438i	−0.291433	+	0.504776i	−0.974149	−	0.225908i	$-0.927465\pi$
$523$	−6.66483	+	11.5438i	−0.291433	+	0.504776i	0.682716	+	0.730684i	$0.260799\pi$
$524$		−	21.5410i		−	0.941025i
$525$	−15.3214	−	10.3247i	−0.668681	−	0.450606i
$526$			27.5809i			1.20259i
$527$	10.3826	−	5.99438i	0.452272	−	0.261119i
$528$		−	4.44239i		−	0.193330i
$529$	−11.9913			−0.521362
$530$	−19.0223	−	5.81115i	−0.826275	−	0.252420i
$531$	−0.292750	−	0.169019i	−0.0127043	−	0.00733480i
$532$	20.8616			0.904466
$533$	4.13346	+	7.15936i	0.179040	+	0.310106i
$534$	8.03066	+	13.9095i	0.347521	+	0.601923i
$535$	22.4724	+	6.86514i	0.971567	+	0.296806i
$536$	12.7735	+	7.37478i	0.551731	+	0.318542i
$537$	−3.08106	+	5.33654i	−0.132957	+	0.230289i
$538$	6.79314	+	11.7661i	0.292873	+	0.507271i
$539$	14.7794	+	25.5987i	0.636594	+	1.10261i
$540$	−2.13851	−	0.653296i	−0.0920266	−	0.0281134i
$541$			8.60984i			0.370166i	0.982723	+	0.185083i	$0.0592554\pi$
$541$			8.60984i			0.370166i	−0.982723	+	0.185083i	$0.940745\pi$
$542$	4.97694	−	8.62031i	0.213778	−	0.370274i
$543$	−3.17379	+	1.83239i	−0.136200	+	0.0786354i
$544$	−3.34526			−0.143427
$545$	−2.41602	+	2.25396i	−0.103491	+	0.0965489i
$546$	−11.4421	−	19.8184i	−0.489678	−	0.848148i
$547$	16.9211			0.723496			0.361748	−	0.932276i	$-0.382180\pi$
$547$	16.9211			0.723496			0.361748	+	0.932276i	$0.382180\pi$
$548$	−8.78174	−	5.07014i	−0.375138	−	0.216586i
$549$			13.2094i			0.563763i
$550$	−18.4200	−	12.4127i	−0.785431	−	0.529281i
$551$	0.305782	−	0.529631i	0.0130268	−	0.0225630i
$552$	2.87341	+	1.65897i	0.122301	+	0.0706103i
$553$	10.3987	+	18.0111i	0.442198	+	0.765909i
$554$	26.6934			1.13409
$555$	0.358370	−	13.5967i	0.0152120	−	0.577150i
$556$	6.47856			0.274752
$557$	17.5570	+	30.4096i	0.743914	+	1.28850i	0.950701	+	0.310110i	$0.100366\pi$
$557$	17.5570	+	30.4096i	0.743914	+	1.28850i	−0.206787	+	0.978386i	$0.566301\pi$
$558$	−3.10366	−	1.79190i	−0.131389	−	0.0758572i
$559$	4.63416	−	8.02659i	0.196004	−	0.339489i
$560$	1.86042	+	8.05033i	0.0786170	+	0.340189i
$561$			14.8610i			0.627431i
$562$	0.674004	+	0.389137i	0.0284312	+	0.0164147i
$563$	−13.6442			−0.575035			−0.287518	−	0.957775i	$-0.592830\pi$
$563$	−13.6442			−0.575035			−0.287518	+	0.957775i	$0.592830\pi$
$564$	0.613817	+	1.06316i	0.0258463	+	0.0447672i
$565$	−9.74003	−	10.4403i	−0.409766	−	0.439228i
$566$	−11.6246			−0.488619
$567$	3.20005	−	1.84755i	0.134390	−	0.0775899i
$568$	2.66182	−	4.61040i	0.111687	−	0.193448i
$569$		−	32.8741i		−	1.37815i	−0.724689	−	0.689076i	$-0.758016\pi$
$569$		−	32.8741i		−	1.37815i	0.724689	−	0.689076i	$-0.241984\pi$
$570$	3.68834	−	12.0735i	0.154488	−	0.505701i
$571$	15.5801	+	26.9856i	0.652008	+	1.12931i	0.982635	+	0.185550i	$0.0594066\pi$
$571$	15.5801	+	26.9856i	0.652008	+	1.12931i	−0.330627	+	0.943762i	$0.607260\pi$
$572$	−13.7562	−	23.8264i	−0.575175	−	0.996232i
$573$	8.54336	−	14.7975i	0.356904	−	0.618176i
$574$	4.27160	+	2.46621i	0.178293	+	0.102938i
$575$	14.9075	−	7.27894i	0.621686	−	0.303553i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−5.44050	−	9.42322i	−0.226491	−	0.392294i	0.730275	−	0.683154i	$-0.239392\pi$
$577$	−5.44050	−	9.42322i	−0.226491	−	0.392294i	−0.956766	+	0.290860i	$0.906059\pi$
$578$	−5.80920			−0.241631
$579$	−20.9462	−	12.0933i	−0.870495	−	0.502581i
$580$	0.231650	+	0.0707671i	0.00961872	+	0.00293844i
$581$	22.2029			0.921131
$582$			12.8116i			0.531058i
$583$	34.2216	−	19.7578i	1.41731	−	0.818286i
$584$		−	2.67315i		−	0.110616i
$585$	−13.4927	+	3.11813i	−0.557853	+	0.128919i
$586$		−	10.4031i		−	0.429748i
$587$	12.4630	−	21.5865i	0.514403	−	0.890971i	−0.485458	−	0.874260i	$-0.661347\pi$
$587$	12.4630	−	21.5865i	0.514403	−	0.890971i	0.999860	−	0.0167112i	$-0.00531960\pi$
$588$	−5.76236	−	3.32690i	−0.237636	−	0.137199i
$589$	10.1166	−	17.5225i	0.416848	−	0.722002i
$590$	0.722896	+	0.220839i	0.0297612	+	0.00909180i
$591$	−9.81631			−0.403789
$592$	−4.26515	+	4.33687i	−0.175297	+	0.178244i
$593$		−	14.2693i		−	0.585969i	−0.956117	−	0.292984i	$-0.905352\pi$
$593$		−	14.2693i		−	0.585969i	0.956117	−	0.292984i	$-0.0946484\pi$
$594$	3.84723	−	2.22120i	0.157854	−	0.0911368i
$595$	−6.22359	−	26.9305i	−0.255142	−	1.10404i
$596$	−0.899754	+	1.55842i	−0.0368554	+	0.0638354i
$597$	11.0125	−	19.0743i	0.450714	−	0.780659i
$598$	20.5484			0.840287
$599$	10.1315	−	17.5483i	0.413962	−	0.717003i	−0.581357	−	0.813648i	$-0.697478\pi$
$599$	10.1315	−	17.5483i	0.413962	−	0.717003i	0.995319	+	0.0966459i	$0.0308114\pi$
$600$	4.98797	+	0.346604i	0.203633	+	0.0141500i
$601$	−6.63186	−	11.4867i	−0.270519	−	0.468553i	0.698476	−	0.715634i	$-0.253862\pi$
$601$	−6.63186	−	11.4867i	−0.270519	−	0.468553i	−0.968995	+	0.247081i	$0.920529\pi$
$602$		−	5.52989i		−	0.225382i
$603$			14.7496i			0.600648i
$604$	5.78284	+	10.0162i	0.235300	+	0.407552i
$605$	19.0302	−	4.39784i	0.773687	−	0.178798i
$606$			10.2462i			0.416222i
$607$	−1.63728	−	2.83585i	−0.0664552	−	0.115104i	0.830883	−	0.556447i	$-0.187836\pi$
$607$	−1.63728	−	2.83585i	−0.0664552	−	0.115104i	−0.897339	+	0.441343i	$0.854502\pi$
$608$	−4.88936	+	2.82287i	−0.198290	+	0.114483i
$609$	−0.346640	+	0.200133i	−0.0140466	+	0.00810978i
$610$	−6.65068	−	28.7786i	−0.269278	−	1.16521i
$611$	6.58430	+	3.80145i	0.266372	+	0.153790i
$612$	−1.67263	−	2.89708i	−0.0676122	−	0.117108i
$613$	26.8039	−	15.4752i	1.08260	−	0.625039i	0.151003	−	0.988533i	$-0.451750\pi$
$613$	26.8039	−	15.4752i	1.08260	−	0.625039i	0.931597	+	0.363494i	$0.118416\pi$
$614$	15.9404	−	9.20320i	0.643302	−	0.371411i
$615$	2.18251	−	2.03612i	0.0880074	−	0.0821042i
$616$	−14.2159	−	8.20755i	−0.572775	−	0.330692i
$617$	−0.416548	+	0.240494i	−0.0167696	+	0.00968194i	−0.508361	−	0.861144i	$-0.669749\pi$
$617$	−0.416548	+	0.240494i	−0.0167696	+	0.00968194i	0.491592	+	0.870826i	$0.336415\pi$
$618$		−	5.94305i		−	0.239064i
$619$	−0.362624			−0.0145751			−0.00728754	−	0.999973i	$-0.502320\pi$
$619$	−0.362624			−0.0145751			−0.00728754	+	0.999973i	$0.502320\pi$
$620$	7.66398	+	2.34128i	0.307793	+	0.0940282i
$621$			3.31793i			0.133144i
$622$	−16.0430	−	9.26245i	−0.643267	−	0.371391i
$623$	59.3482			2.37774
$624$	5.36341	+	3.09657i	0.214708	+	0.123962i
$625$	15.3743	−	19.7137i	0.614973	−	0.788548i
$626$	−10.9094	+	18.8956i	−0.436026	+	0.755220i
$627$	12.5403	+	21.7205i	0.500812	+	0.867431i
$628$		−	19.6930i		−	0.785836i
$629$	14.2681	−	14.5080i	0.568905	−	0.578471i
$630$	−6.04158	+	5.63633i	−0.240702	+	0.224557i
$631$	−16.6855	+	9.63338i	−0.664239	+	0.383499i	−0.793890	−	0.608061i	$-0.791948\pi$
$631$	−16.6855	+	9.63338i	−0.664239	+	0.383499i	0.129651	+	0.991560i	$0.458614\pi$
$632$	−4.87431	−	2.81418i	−0.193890	−	0.111942i
$633$	−6.21336	−	3.58728i	−0.246959	−	0.142582i
$634$	24.1836	+	13.9624i	0.960454	+	0.554518i
$635$	28.7856	−	26.8547i	1.14232	−	1.06570i
$636$	−4.44757	+	7.70341i	−0.176357	+	0.305460i
$637$	−41.2079			−1.63272
$638$	−0.416744	+	0.240607i	−0.0164990	+	0.00952572i
$639$	5.32363			0.210600
$640$	−1.52535	−	1.63502i	−0.0602948	−	0.0646300i
$641$	−6.93767	−	12.0164i	−0.274021	−	0.474619i	0.695866	−	0.718171i	$-0.255021\pi$
$641$	−6.93767	−	12.0164i	−0.274021	−	0.474619i	−0.969888	+	0.243552i	$0.921687\pi$
$642$	5.25423	−	9.10060i	0.207368	−	0.359172i
$643$	32.7410			1.29118			0.645589	−	0.763685i	$-0.276612\pi$
$643$	32.7410			1.29118			0.645589	+	0.763685i	$0.276612\pi$
$644$	10.6176	−	6.13005i	0.418391	−	0.241558i
$645$	−3.20037	−	0.977688i	−0.126015	−	0.0384964i
$646$	16.3562	−	9.44325i	0.643526	−	0.371540i
$647$	−10.0075	+	17.3335i	−0.393435	+	0.681449i	−0.992900	−	0.118952i	$-0.962047\pi$
$647$	−10.0075	+	17.3335i	−0.393435	+	0.681449i	0.599465	+	0.800401i	$0.295380\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−1.30051	+	0.750849i	−0.0510495	+	0.0294734i
$650$	27.8258	−	13.5866i	1.09142	−	0.532911i
$651$	−11.4684	+	6.62126i	−0.449481	+	0.259508i
$652$	−16.5162			−0.646824
$653$	−12.6958	+	21.9898i	−0.496825	+	0.860526i	−0.999993	−	0.00366254i	$-0.998834\pi$
$653$	−12.6958	+	21.9898i	−0.496825	+	0.860526i	0.503168	+	0.864188i	$0.332168\pi$
$654$	0.738832	+	1.27969i	0.0288906	+	0.0500400i
$655$	−35.2201	+	32.8577i	−1.37616	+	1.28386i
$656$	−1.33485			−0.0521172
$657$	2.31501	−	1.33657i	0.0903173	−	0.0521447i
$658$	4.53623			0.176841
$659$	10.2268	−	17.7134i	0.398381	−	0.690016i	−0.595145	−	0.803618i	$-0.702906\pi$
$659$	10.2268	−	17.7134i	0.398381	−	0.690016i	0.993526	+	0.113602i	$0.0362388\pi$
$660$	−7.26342	+	6.77621i	−0.282728	+	0.263764i
$661$	0.419280	+	0.242071i	0.0163081	+	0.00941548i	0.508132	−	0.861279i	$-0.330336\pi$
$661$	0.419280	+	0.242071i	0.0163081	+	0.00941548i	−0.491824	+	0.870695i	$0.663670\pi$
$662$	−28.7591	−	16.6041i	−1.11775	−	0.645335i
$663$	−17.9420	−	10.3588i	−0.696811	−	0.402304i
$664$	−5.20372	+	3.00437i	−0.201943	+	0.116592i
$665$	−31.8213	−	34.1092i	−1.23398	−	1.32270i
$666$	−5.88842	−	1.52530i	−0.228172	−	0.0591040i
$667$		−	0.359409i		−	0.0139164i
$668$	5.60293	+	9.70456i	0.216784	+	0.375481i
$669$	0.109921	−	0.190389i	0.00424980	−	0.00736087i
$670$	−7.42613	−	32.1341i	−0.286896	−	1.24145i
$671$	50.8195	+	29.3407i	1.96187	+	1.13268i
$672$	3.69510			0.142542
$673$	35.6479	+	20.5813i	1.37413	+	0.793352i	0.991445	−	0.130529i	$-0.0416674\pi$
$673$	35.6479	+	20.5813i	1.37413	+	0.793352i	0.382681	+	0.923880i	$0.375001\pi$
$674$		−	6.32508i		−	0.243633i
$675$	2.19382	+	4.49301i	0.0844401	+	0.172936i
$676$	25.3549			0.975190
$677$			15.4030i			0.591984i	0.955190	+	0.295992i	$0.0956501\pi$
$677$			15.4030i			0.591984i	−0.955190	+	0.295992i	$0.904350\pi$
$678$	−5.52994	+	3.19271i	−0.212376	+	0.122615i
$679$	40.9978	+	23.6701i	1.57335	+	0.908375i
$680$	5.10271	+	5.46959i	0.195680	+	0.209749i
$681$	−21.4699	+	12.3956i	−0.822728	+	0.475002i
$682$	−13.7877	+	7.96033i	−0.527958	+	0.304817i
$683$	−7.89432	−	13.6734i	−0.302068	−	0.523197i	0.674536	−	0.738242i	$-0.264344\pi$
$683$	−7.89432	−	13.6734i	−0.302068	−	0.523197i	−0.976604	+	0.215045i	$0.931010\pi$
$684$	−4.88936	−	2.82287i	−0.186949	−	0.107935i
$685$	5.10545	+	22.0921i	0.195069	+	0.844096i
$686$	1.10787	−	0.639627i	0.0422986	−	0.0244211i
$687$	−9.79129	+	5.65301i	−0.373561	+	0.215676i
$688$	0.748273	+	1.29605i	0.0285276	+	0.0494113i
$689$			55.0888i			2.09871i
$690$	−1.67052	−	7.22861i	−0.0635955	−	0.275188i
$691$	13.8305	+	23.9551i	0.526137	+	0.911297i	0.999536	+	0.0304486i	$0.00969358\pi$
$691$	13.8305	+	23.9551i	0.526137	+	0.911297i	−0.473399	+	0.880848i	$0.656973\pi$
$692$			14.3230i			0.544480i
$693$		−	16.4151i		−	0.623558i
$694$	−13.3652	−	23.1493i	−0.507337	−	0.878734i
$695$	−9.88209	−	10.5926i	−0.374849	−	0.401800i
$696$	0.0541616	−	0.0938106i	0.00205299	−	0.00355588i
$697$	4.46543			0.169140
$698$	−9.72032	+	16.8361i	−0.367920	+	0.637255i
$699$	7.15391	−	12.3909i	0.270586	−	0.468669i
$700$	10.3247	−	15.3214i	0.390237	−	0.579095i
$701$	−10.6850	+	6.16897i	−0.403566	+	0.232999i	−0.688021	−	0.725690i	$-0.741521\pi$
$701$	−10.6850	+	6.16897i	−0.403566	+	0.232999i	0.284456	+	0.958689i	$0.408187\pi$
$702$			6.19314i			0.233745i
$703$	8.61143	−	33.2445i	0.324786	−	1.25384i
$704$	4.44239			0.167429
$705$	0.802008	−	2.62530i	0.0302054	−	0.0988745i
$706$	2.02075	−	3.50004i	0.0760519	−	0.131726i
$707$	32.7883	+	18.9303i	1.23313	+	0.711948i
$708$	0.169019	−	0.292750i	0.00635213	−	0.0110022i
$709$			40.5310i			1.52217i	0.648651	+	0.761086i	$0.275334\pi$
$709$			40.5310i			1.52217i	−0.648651	+	0.761086i	$0.724666\pi$
$710$	−11.5983	+	2.68035i	−0.435277	+	0.100592i
$711$		−	5.62837i		−	0.211080i
$712$	−13.9095	+	8.03066i	−0.521281	+	0.300962i
$713$		−	11.8908i		−	0.445314i
$714$	−12.3611			−0.462603
$715$	−17.9737	+	58.8353i	−0.672179	+	2.20032i
$716$	−5.33654	−	3.08106i	−0.199436	−	0.115144i
$717$	6.79825			0.253885
$718$	0.224604	+	0.389026i	0.00838216	+	0.0145183i
$719$	−2.47337	−	4.28400i	−0.0922412	−	0.159766i	0.816213	−	0.577752i	$-0.196070\pi$
$719$	−2.47337	−	4.28400i	−0.0922412	−	0.159766i	−0.908454	+	0.417985i	$0.862736\pi$
$720$	0.653296	−	2.13851i	0.0243469	−	0.0796974i
$721$	−19.0181	−	10.9801i	−0.708270	−	0.408920i
$722$	6.43721	−	11.1496i	0.239568	−	0.414944i
$723$	−2.77020	−	4.79812i	−0.103025	−	0.178444i
$724$	−1.83239	−	3.17379i	−0.0681002	−	0.117953i
$725$	−0.237641	−	0.486697i	−0.00882577	−	0.0180755i
$726$		−	8.73486i		−	0.324181i
$727$	17.2930	−	29.9524i	0.641363	−	1.11087i	−0.343766	−	0.939055i	$-0.611703\pi$
$727$	17.2930	−	29.9524i	0.641363	−	1.11087i	0.985129	−	0.171817i	$-0.0549639\pi$
$728$	19.8184	−	11.4421i	0.734518	−	0.424074i
$729$	−1.00000			−0.0370370
$730$	−4.37066	+	4.07749i	−0.161765	+	0.150915i
$731$	−2.50317	−	4.33562i	−0.0925831	−	0.160359i
$732$	−13.2094			−0.488233
$733$	−34.9113	−	20.1561i	−1.28948	−	0.744481i	−0.310917	−	0.950437i	$-0.600636\pi$
$733$	−34.9113	−	20.1561i	−1.28948	−	0.744481i	−0.978561	+	0.205956i	$0.933970\pi$
$734$			33.3245i			1.23003i
$735$	3.35006	+	14.4963i	0.123569	+	0.534703i
$736$	−1.65897	+	2.87341i	−0.0611503	+	0.105915i
$737$	56.7449	+	32.7617i	2.09022	+	1.20679i
$738$	−0.667426	−	1.15602i	−0.0245683	−	0.0425535i
$739$	−15.1392			−0.556904			−0.278452	−	0.960450i	$-0.589821\pi$
$739$	−15.1392			−0.556904			−0.278452	+	0.960450i	$0.589821\pi$
$740$	13.5967	+	0.358370i	0.499826	+	0.0131740i
$741$	−34.9649			−1.28447
$742$	16.4342	+	28.4649i	0.603319	+	1.04498i
$743$	−13.4411	−	7.76020i	−0.493105	−	0.284694i	0.232757	−	0.972535i	$-0.425225\pi$
$743$	−13.4411	−	7.76020i	−0.493105	−	0.284694i	−0.725862	+	0.687841i	$0.758559\pi$
$744$	1.79190	−	3.10366i	0.0656943	−	0.113786i
$745$	3.92049	−	0.906019i	0.143636	−	0.0331940i
$746$			1.06367i			0.0389439i
$747$	−5.20372	−	3.00437i	−0.190394	−	0.109924i
$748$	−14.8610			−0.543371
$749$	−19.4149	−	33.6277i	−0.709406	−	1.22873i
$750$	−7.04171	−	8.68414i	−0.257127	−	0.317100i
$751$	17.8620			0.651793			0.325896	−	0.945406i	$-0.394334\pi$
$751$	17.8620			0.651793			0.325896	+	0.945406i	$0.394334\pi$
$752$	−1.06316	+	0.613817i	−0.0387695	+	0.0223836i
$753$	−15.0407	+	26.0512i	−0.548113	+	0.949359i
$754$		−	0.670860i		−	0.0244313i
$755$	7.55581	−	24.7333i	0.274984	−	0.900135i
$756$	1.84755	+	3.20005i	0.0671948	+	0.116385i
$757$	−5.03804	−	8.72614i	−0.183111	−	0.317157i	0.759828	−	0.650125i	$-0.225283\pi$
$757$	−5.03804	−	8.72614i	−0.183111	−	0.317157i	−0.942938	+	0.332968i	$0.891950\pi$
$758$	−11.9117	+	20.6317i	−0.432652	+	0.749376i
$759$	12.7648	+	7.36978i	0.463334	+	0.267506i
$760$	12.0735	+	3.68834i	0.437950	+	0.133790i
$761$	14.5679	+	25.2324i	0.528086	+	0.914672i	0.999464	+	0.0327408i	$0.0104236\pi$
$761$	14.5679	+	25.2324i	0.528086	+	0.914672i	−0.471378	+	0.881931i	$0.656243\pi$
$762$	−8.80279	−	15.2469i	−0.318892	−	0.552336i
$763$	5.46012			0.197670
$764$	14.7975	+	8.54336i	0.535356	+	0.309088i
$765$	−2.18545	+	7.15387i	−0.0790150	+	0.258649i
$766$	24.6494			0.890617
$767$		−	2.09352i		−	0.0755925i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$			48.5732i			1.75160i	0.482678	+	0.875798i	$0.339664\pi$
$769$			48.5732i			1.75160i	−0.482678	+	0.875798i	$0.660336\pi$
$770$	8.26471	+	35.7627i	0.297839	+	1.28880i
$771$		−	23.5130i		−	0.846800i
$772$	12.0933	−	20.9462i	0.435248	−	0.753871i
$773$	24.3124	+	14.0368i	0.874458	+	0.504868i	0.868827	−	0.495116i	$-0.164874\pi$
$773$	24.3124	+	14.0368i	0.874458	+	0.504868i	0.00563072	+	0.999984i	$0.498208\pi$
$774$	−0.748273	+	1.29605i	−0.0268961	+	0.0465854i
$775$	−7.86221	−	16.1021i	−0.282419	−	0.578403i
$776$	−12.8116			−0.459910
$777$	−15.7602	+	16.0252i	−0.565394	+	0.574901i
$778$		−	4.61716i		−	0.165533i
$779$	6.52657	−	3.76811i	0.233838	−	0.135007i
$780$	−3.11813	−	13.4927i	−0.111647	−	0.483115i
$781$	11.8248	−	20.4812i	0.423126	−	0.732875i
$782$	5.54968	−	9.61233i	0.198456	−	0.343736i
$783$	0.108323			0.00387115
$784$	3.32690	−	5.76236i	0.118818	−	0.205798i
$785$	−32.1985	+	30.0388i	−1.14921	+	1.07213i
$786$	10.7705	+	18.6551i	0.384172	+	0.665405i
$787$		−	18.8436i		−	0.671702i	−0.941915	−	0.335851i	$-0.890976\pi$
$787$		−	18.8436i		−	0.671702i	0.941915	−	0.335851i	$-0.109024\pi$
$788$		−	9.81631i		−	0.349692i
$789$	−13.7905	−	23.8858i	−0.490954	−	0.850357i
$790$	2.83378	+	12.2622i	0.100821	+	0.436271i
$791$			23.5948i			0.838936i
$792$	2.22120	+	3.84723i	0.0789268	+	0.136705i
$793$	−70.8474	+	40.9038i	−2.51587	+	1.45254i
$794$	−10.0627	+	5.80971i	−0.357113	+	0.206179i
$795$	19.3794	−	4.47854i	0.687315	−	0.158837i
$796$	19.0743	+	11.0125i	0.676070	+	0.390329i
$797$	−14.8187	−	25.6667i	−0.524905	−	0.909163i	−0.999579	−	0.0290012i	$-0.990767\pi$
$797$	−14.8187	−	25.6667i	−0.524905	−	0.909163i	0.474674	−	0.880162i	$-0.342566\pi$
$798$	−18.0667	+	10.4308i	−0.639554	+	0.369247i
$799$	3.55656	−	2.05338i	0.125822	−	0.0726433i
$800$	−0.346604	+	4.98797i	−0.0122543	+	0.176351i
$801$	−13.9095	−	8.03066i	−0.491468	−	0.283749i
$802$	5.47228	−	3.15942i	0.193233	−	0.111563i
$803$		−	11.8752i		−	0.419066i
$804$	−14.7496			−0.520177
$805$	−26.2183	−	8.00948i	−0.924074	−	0.282297i
$806$		−	22.1950i		−	0.781785i
$807$	−11.7661	−	6.79314i	−0.414185	−	0.239130i
$808$	−10.2462			−0.360459
$809$	32.2806	+	18.6372i	1.13493	+	0.655251i	0.945169	−	0.326580i	$-0.105896\pi$
$809$	32.2806	+	18.6372i	1.13493	+	0.655251i	0.189758	+	0.981831i	$0.439230\pi$
$810$	2.17865	−	0.503482i	0.0765499	−	0.0176905i
$811$	8.33056	−	14.4289i	0.292525	−	0.506669i	−0.681881	−	0.731463i	$-0.738838\pi$
$811$	8.33056	−	14.4289i	0.292525	−	0.506669i	0.974406	+	0.224794i	$0.0721711\pi$
$812$	−0.200133	−	0.346640i	−0.00702328	−	0.0121647i
$813$			9.95387i			0.349098i
$814$	−18.9475	+	19.2661i	−0.664109	+	0.675276i
$815$	25.1930	+	27.0044i	0.882473	+	0.945922i
$816$	2.89708	−	1.67263i	0.101418	−	0.0585538i
$817$	−7.31715	−	4.22456i	−0.255995	−	0.147799i
$818$	12.2422	+	7.06806i	0.428040	+	0.247129i
$819$	19.8184	+	11.4421i	0.692510	+	0.399821i
$820$	2.03612	+	2.18251i	0.0711043	+	0.0762167i
$821$	−10.5880	+	18.3390i	−0.369525	+	0.640037i	−0.989491	−	0.144592i	$-0.953813\pi$
$821$	−10.5880	+	18.3390i	−0.369525	+	0.640037i	0.619966	+	0.784629i	$0.287146\pi$
$822$	10.1403			0.353683
$823$	−17.6753	+	10.2048i	−0.616121	+	0.355717i	−0.775357	−	0.631523i	$-0.782430\pi$
$823$	−17.6753	+	10.2048i	−0.616121	+	0.355717i	0.159236	+	0.987240i	$0.449097\pi$
$824$	5.94305			0.207036
$825$	22.1585	+	1.53975i	0.771461	+	0.0536072i
$826$	−0.624543	−	1.08174i	−0.0217306	−	0.0376386i
$827$	−9.94714	+	17.2290i	−0.345896	+	0.599110i	−0.985516	−	0.169582i	$-0.945758\pi$
$827$	−9.94714	+	17.2290i	−0.345896	+	0.599110i	0.639620	+	0.768691i	$0.279092\pi$
$828$	−3.31793			−0.115306
$829$	−33.0369	+	19.0739i	−1.14742	+	0.662463i	−0.948257	−	0.317503i	$-0.897156\pi$
$829$	−33.0369	+	19.0739i	−1.14742	+	0.662463i	−0.199163	+	0.979966i	$0.563822\pi$
$830$	12.8497	+	3.92548i	0.446020	+	0.136255i
$831$	−23.1172	+	13.3467i	−0.801926	+	0.462992i
$832$	−3.09657	+	5.36341i	−0.107354	+	0.185943i
$833$	−11.1294	+	19.2766i	−0.385609	+	0.667895i
$834$	−5.61060	+	3.23928i	−0.194279	+	0.112167i
$835$	7.32074	−	23.9638i	0.253345	−	0.829301i
$836$	−21.7205	+	12.5403i	−0.751218	+	0.433716i
$837$	3.58380			0.123874
$838$	−19.8015	+	34.2972i	−0.684031	+	1.18478i
$839$	−24.9103	−	43.1458i	−0.859998	−	1.48956i	−0.871930	−	0.489631i	$-0.837132\pi$
$839$	−24.9103	−	43.1458i	−0.859998	−	1.48956i	0.0119323	−	0.999929i	$-0.496202\pi$
$840$	−5.63633	−	6.04158i	−0.194472	−	0.208454i
$841$	28.9883			0.999595
$842$	−6.88568	+	3.97545i	−0.237296	+	0.137003i
$843$	−0.778273			−0.0268051
$844$	3.58728	−	6.21336i	0.123479	−	0.213873i
$845$	−38.6752	−	41.4559i	−1.33047	−	1.42613i
$846$	−1.06316	−	0.613817i	−0.0365522	−	0.0211034i
$847$	−27.9520	−	16.1381i	−0.960443	−	0.554512i
$848$	−7.70341	−	4.44757i	−0.264536	−	0.152730i
$849$	10.0672	−	5.81231i	0.345506	−	0.199478i
$850$	1.15948	−	16.6861i	0.0397699	−	0.572328i
$851$	−5.38588	−	19.4503i	−0.184626	−	0.666747i
$852$			5.32363i			0.182385i
$853$	−15.7852	−	27.3408i	−0.540475	−	0.936130i	−0.998877	−	0.0473848i	$-0.984911\pi$
$853$	−15.7852	−	27.3408i	−0.540475	−	0.936130i	0.458402	−	0.888745i	$-0.348422\pi$
$854$	−24.4050	+	42.2708i	−0.835123	+	1.44648i
$855$	2.84253	+	12.3001i	0.0972124	+	0.420654i
$856$	9.10060	+	5.25423i	0.311052	+	0.179586i
$857$	−51.4712			−1.75822			−0.879112	−	0.476615i	$-0.841863\pi$
$857$	−51.4712			−1.75822			−0.879112	+	0.476615i	$0.841863\pi$
$858$	23.8264	+	13.7562i	0.813420	+	0.469628i
$859$		−	8.76509i		−	0.299061i	−0.988757	−	0.149531i	$-0.952224\pi$
$859$		−	8.76509i		−	0.299061i	0.988757	−	0.149531i	$-0.0477762\pi$
$860$	0.977688	−	3.20037i	0.0333389	−	0.109132i
$861$	−4.93242			−0.168096
$862$		−	11.5415i		−	0.393104i
$863$	−42.3921	+	24.4751i	−1.44305	+	0.833143i	−0.998052	−	0.0623913i	$-0.980127\pi$
$863$	−42.3921	+	24.4751i	−1.44305	+	0.833143i	−0.444993	+	0.895534i	$0.646794\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	23.4185	−	21.8476i	0.796252	−	0.742842i
$866$	−12.1411	+	7.00965i	−0.412571	+	0.238198i
$867$	5.03092	−	2.90460i	0.170859	−	0.0986455i
$868$	−6.62126	−	11.4684i	−0.224740	−	0.389262i
$869$	−21.6536	−	12.5017i	−0.734548	−	0.424092i
$870$	−0.235998	+	0.0545387i	−0.00800108	+	0.00184904i
$871$	−79.1080	+	45.6730i	−2.68047	+	1.54757i
$872$	−1.27969	+	0.738832i	−0.0433359	+	0.0250200i
$873$	−6.40580	−	11.0952i	−0.216803	−	0.375515i
$874$		−	18.7322i		−	0.633626i
$875$	−40.7997	+	6.48943i	−1.37928	+	0.219383i
$876$	1.33657	+	2.31501i	0.0451586	+	0.0782170i
$877$			36.6528i			1.23768i	0.785518	+	0.618839i	$0.212397\pi$
$877$			36.6528i			1.23768i	−0.785518	+	0.618839i	$0.787603\pi$
$878$			23.9409i			0.807965i
$879$	5.20154	+	9.00934i	0.175444	+	0.303877i
$880$	−6.77621	−	7.26342i	−0.228426	−	0.244850i
$881$	13.2691	−	22.9828i	0.447048	−	0.774310i	−0.551144	−	0.834410i	$-0.685809\pi$
$881$	13.2691	−	22.9828i	0.447048	−	0.774310i	0.998192	+	0.0600998i	$0.0191419\pi$
$882$	6.65380			0.224045
$883$	19.8327	−	34.3512i	0.667422	−	1.15601i	−0.311201	−	0.950344i	$-0.600731\pi$
$883$	19.8327	−	34.3512i	0.667422	−	1.15601i	0.978623	−	0.205665i	$-0.0659356\pi$
$884$	10.3588	−	17.9420i	0.348405	−	0.603456i
$885$	−0.736466	+	0.170196i	−0.0247560	+	0.00572108i
$886$	−22.7184	+	13.1165i	−0.763239	+	0.440656i
$887$			0.635075i			0.0213237i	0.999943	+	0.0106619i	$0.00339384\pi$
$887$			0.635075i			0.0213237i	−0.999943	+	0.0106619i	$0.996606\pi$
$888$	1.52530	−	5.88842i	0.0511856	−	0.197602i
$889$	−65.0545			−2.18186
$890$	34.3472	+	10.4928i	1.15132	+	0.351719i
$891$	−2.22120	+	3.84723i	−0.0744129	+	0.128887i
$892$	0.190389	+	0.109921i	0.00637470	+	0.00368044i
$893$	3.46545	−	6.00234i	0.115967	−	0.200861i
$894$		−	1.79951i		−	0.0601845i
$895$	3.10251	+	13.4251i	0.103705	+	0.448751i
$896$			3.69510i			0.123445i
$897$	−17.7954	+	10.2742i	−0.594173	+	0.343046i
$898$		−	19.1331i		−	0.638479i
$899$	−0.388209			−0.0129475
$900$	−4.49301	+	2.19382i	−0.149767	+	0.0731273i
$901$	25.7699	+	14.8783i	0.858521	+	0.495668i
$902$	−5.92994			−0.197445
$903$	2.76495	+	4.78903i	0.0920117	+	0.159369i
$904$	−3.19271	−	5.52994i	−0.106188	−	0.183923i
$905$	−2.39419	+	7.83715i	−0.0795854	+	0.260516i
$906$	−10.0162	−	5.78284i	−0.332765	−	0.192122i
$907$	6.74363	−	11.6803i	0.223919	−	0.387838i	−0.732076	−	0.681223i	$-0.761448\pi$
$907$	6.74363	−	11.6803i	0.223919	−	0.387838i	0.955994	+	0.293385i	$0.0947817\pi$
$908$	−12.3956	−	21.4699i	−0.411364	−	0.712503i
$909$	−5.12308	−	8.87344i	−0.169922	−	0.294313i
$910$	−48.9382	−	14.9502i	−1.62228	−	0.495595i
$911$		−	1.13010i		−	0.0374418i	−0.999825	−	0.0187209i	$-0.994041\pi$
$911$		−	1.13010i		−	0.0374418i	0.999825	−	0.0187209i	$-0.00595939\pi$
$912$	2.82287	−	4.88936i	0.0934746	−	0.161903i
$913$	−23.1170	+	13.3466i	−0.765059	+	0.441707i
$914$	−41.0396			−1.35747
$915$	20.1490	+	21.5977i	0.666104	+	0.713997i
$916$	−5.65301	−	9.79129i	−0.186781	−	0.323513i
$917$	79.5964			2.62851
$918$	2.89708	+	1.67263i	0.0956180	+	0.0552051i
$919$		−	32.5408i		−	1.07342i	−0.843766	−	0.536712i	$-0.819666\pi$
$919$		−	32.5408i		−	1.07342i	0.843766	−	0.536712i	$-0.180334\pi$
$920$	7.22861	−	1.67052i	0.238320	−	0.0550753i
$921$	−9.20320	+	15.9404i	−0.303256	+	0.525254i
$922$	9.56724	+	5.52365i	0.315080	+	0.181912i
$923$	16.4850	+	28.5528i	0.542610	+	0.939828i
$924$	16.4151			0.540017
$925$	−20.1539	−	22.7776i	−0.662656	−	0.748924i
$926$	−8.05337			−0.264650
$927$	2.97152	+	5.14683i	0.0975976	+	0.169044i
$928$	0.0938106	+	0.0541616i	0.00307948	+	0.00177794i
$929$	0.825374	−	1.42959i	0.0270797	−	0.0469033i	−0.852168	−	0.523268i	$-0.824713\pi$
$929$	0.825374	−	1.42959i	0.0270797	−	0.0469033i	0.879248	+	0.476365i	$0.158046\pi$
$930$	−7.80784	+	1.80438i	−0.256029	+	0.0591679i
$931$			37.5656i			1.23116i
$932$	12.3909	+	7.15391i	0.405879	+	0.234334i
$933$	18.5249			0.606478
$934$	−4.81896	−	8.34668i	−0.157681	−	0.273112i
$935$	22.6682	+	24.2981i	0.741330	+	0.794631i
$936$	−6.19314			−0.202429
$937$	47.2940	−	27.3052i	1.54503	−	0.892022i	0.546517	−	0.837448i	$-0.315953\pi$
$937$	47.2940	−	27.3052i	1.54503	−	0.892022i	0.998510	−	0.0545738i	$-0.0173800\pi$
$938$	−27.2506	+	47.1994i	−0.889763	+	1.54111i
$939$		−	21.8188i		−	0.712028i
$940$	2.62530	+	0.802008i	0.0856278	+	0.0261586i
$941$	5.39829	+	9.35012i	0.175979	+	0.304805i	0.940500	−	0.339794i	$-0.110357\pi$
$941$	5.39829	+	9.35012i	0.175979	+	0.304805i	−0.764520	+	0.644599i	$0.777024\pi$
$942$	9.84650	+	17.0546i	0.320816	+	0.555670i
$943$	2.21447	−	3.83558i	0.0721132	−	0.124904i
$944$	0.292750	+	0.169019i	0.00952819	+	0.00550110i
$945$	2.41400	−	7.90200i	0.0785273	−	0.257052i
$946$	3.32412	+	5.75755i	0.108077	+	0.187194i
$947$	26.1293	+	45.2573i	0.849089	+	1.47067i	0.882022	+	0.471208i	$0.156182\pi$
$947$	26.1293	+	45.2573i	0.849089	+	1.47067i	−0.0329334	+	0.999458i	$0.510485\pi$
$948$	5.62837			0.182801
$949$	14.3372	+	8.27758i	0.465405	+	0.268702i
$950$	−12.3857	−	25.3664i	−0.401846	−	0.822995i
$951$	−27.9248			−0.905524
$952$		−	12.3611i		−	0.400626i
$953$	−44.8260	+	25.8803i	−1.45206	+	0.838345i	−0.998598	−	0.0529333i	$-0.983143\pi$
$953$	−44.8260	+	25.8803i	−1.45206	+	0.838345i	−0.453457	+	0.891278i	$0.649810\pi$
$954$		−	8.89513i		−	0.287991i
$955$	−8.60285	−	37.2259i	−0.278382	−	1.20460i
$956$			6.79825i			0.219871i
$957$	0.240607	−	0.416744i	0.00777772	−	0.0134714i
$958$	27.4842	+	15.8680i	0.887973	+	0.512672i
$959$	18.7347	−	32.4495i	0.604975	−	1.04785i
$960$	2.13851	+	0.653296i	0.0690200	+	0.0210850i
$961$	18.1564			0.585689
$962$	−10.0531	−	36.3052i	−0.324125	−	1.17053i
$963$			10.5085i			0.338630i
$964$	4.79812	−	2.77020i	0.154537	−	0.0892220i
$965$	−52.6941	+	12.1775i	−1.69628	+	0.392008i
$966$	−6.13005	+	10.6176i	−0.197231	+	0.341615i
$967$	6.57419	−	11.3868i	0.211412	−	0.366176i	−0.740745	−	0.671787i	$-0.765527\pi$
$967$	6.57419	−	11.3868i	0.211412	−	0.366176i	0.952157	+	0.305611i	$0.0988605\pi$
$968$	8.73486			0.280749
$969$	−9.44325	+	16.3562i	−0.303361	+	0.525437i
$970$	19.5422	+	20.9473i	0.627462	+	0.672576i
$971$	−15.3443	−	26.5771i	−0.492423	−	0.852901i	0.507539	−	0.861629i	$-0.330555\pi$
$971$	−15.3443	−	26.5771i	−0.492423	−	0.852901i	−0.999962	+	0.00872744i	$0.997222\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			23.9390i			0.767448i
$974$	−2.24168	−	3.88271i	−0.0718281	−	0.124410i
$975$	−17.3046	+	25.6793i	−0.554190	+	0.822395i
$976$		−	13.2094i		−	0.422822i
$977$	−2.65295	−	4.59505i	−0.0848755	−	0.147009i	0.820463	−	0.571700i	$-0.193716\pi$
$977$	−2.65295	−	4.59505i	−0.0848755	−	0.147009i	−0.905338	+	0.424691i	$0.860383\pi$
$978$	14.3034	−	8.25810i	0.457374	−	0.264065i
$979$	−61.7915	+	35.6753i	−1.97486	+	1.14019i
$980$	−14.4963	+	3.35006i	−0.463067	+	0.107014i
$981$	−1.27969	−	0.738832i	−0.0408575	−	0.0235891i
$982$	4.45427	+	7.71502i	0.142141	+	0.246196i
$983$	−6.62158	+	3.82297i	−0.211196	+	0.121934i	−0.601867	−	0.798596i	$-0.705576\pi$
$983$	−6.62158	+	3.82297i	−0.211196	+	0.121934i	0.390671	+	0.920530i	$0.372243\pi$
$984$	1.15602	−	0.667426i	0.0368524	−	0.0212768i
$985$	−16.0499	+	14.9733i	−0.511392	+	0.477090i
$986$	−0.313821	−	0.181185i	−0.00999410	−	0.00577010i
$987$	−3.92849	+	2.26812i	−0.125045	+	0.0721949i
$988$		−	34.9649i		−	1.11238i
$989$	−4.96544			−0.157892
$990$	2.90220	−	9.50008i	0.0922379	−	0.301932i
$991$		−	5.76561i		−	0.183151i	−0.995798	−	0.0915753i	$-0.970810\pi$
$991$		−	5.76561i		−	0.183151i	0.995798	−	0.0915753i	$-0.0291902\pi$
$992$	3.10366	+	1.79190i	0.0985414	+	0.0568929i
$993$	33.2081			1.05383
$994$	17.0359	+	9.83569i	0.540346	+	0.311969i
$995$	−11.0892	−	47.9849i	−0.351552	−	1.52122i
$996$	3.00437	−	5.20372i	0.0951970	−	0.164886i
$997$	8.96717	+	15.5316i	0.283993	+	0.491891i	0.972365	−	0.233468i	$-0.0750074\pi$
$997$	8.96717	+	15.5316i	0.283993	+	0.491891i	−0.688371	+	0.725358i	$0.741674\pi$
$998$		−	36.5680i		−	1.15754i
$999$	5.86217	−	1.62326i	0.185471	−	0.0513578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.529.11	✓	36
5.4	even	2		1110.2.ba.b.529.8	yes	36
37.27	even	6		1110.2.ba.b.619.8	yes	36
185.64	even	6	inner	1110.2.ba.a.619.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.11	✓	36	1.1	even	1	trivial
1110.2.ba.a.619.11	yes	36	185.64	even	6	inner
1110.2.ba.b.529.8	yes	36	5.4	even	2
1110.2.ba.b.619.8	yes	36	37.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.17865 - 0.503482i) q^{5} -1.00000i q^{6} +(-3.20005 - 1.84755i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.17865 - 0.503482i) q^{5} -1.00000i q^{6} +(-3.20005 - 1.84755i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.52535 - 1.63502i) q^{10} +4.44239 q^{11} +(-0.866025 + 0.500000i) q^{12} +(-3.09657 + 5.36341i) q^{13} +3.69510i q^{14} +(2.13851 + 0.653296i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.67263 + 2.89708i) q^{17} +(0.500000 - 0.866025i) q^{18} +(4.88936 + 2.82287i) q^{19} +(-0.653296 + 2.13851i) q^{20} +(-1.84755 - 3.20005i) q^{21} +(-2.22120 - 3.84723i) q^{22} +3.31793 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.49301 - 2.19382i) q^{25} +6.19314 q^{26} +1.00000i q^{27} +(3.20005 - 1.84755i) q^{28} -0.108323i q^{29} +(-0.503482 - 2.17865i) q^{30} -3.58380i q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.84723 + 2.22120i) q^{33} +(1.67263 - 2.89708i) q^{34} +(-7.90200 - 2.41400i) q^{35} -1.00000 q^{36} +(-1.62326 - 5.86217i) q^{37} -5.64574i q^{38} +(-5.36341 + 3.09657i) q^{39} +(2.17865 - 0.503482i) q^{40} +(0.667426 - 1.15602i) q^{41} +(-1.84755 + 3.20005i) q^{42} -1.49655 q^{43} +(-2.22120 + 3.84723i) q^{44} +(1.52535 + 1.63502i) q^{45} +(-1.65897 - 2.87341i) q^{46} -1.22763i q^{47} -1.00000i q^{48} +(3.32690 + 5.76236i) q^{49} +(-4.14641 - 2.79415i) q^{50} +3.34526i q^{51} +(-3.09657 - 5.36341i) q^{52} +(7.70341 - 4.44757i) q^{53} +(0.866025 - 0.500000i) q^{54} +(9.67841 - 2.23666i) q^{55} +(-3.20005 - 1.84755i) q^{56} +(2.82287 + 4.88936i) q^{57} +(-0.0938106 + 0.0541616i) q^{58} +(-0.292750 + 0.169019i) q^{59} +(-1.63502 + 1.52535i) q^{60} +(11.4397 + 6.60469i) q^{61} +(-3.10366 + 1.79190i) q^{62} -3.69510i q^{63} +1.00000 q^{64} +(-4.04595 + 13.2441i) q^{65} -4.44239i q^{66} +(12.7735 + 7.37478i) q^{67} -3.34526 q^{68} +(2.87341 + 1.65897i) q^{69} +(1.86042 + 8.05033i) q^{70} +(2.66182 - 4.61040i) q^{71} +(0.500000 + 0.866025i) q^{72} -2.67315i q^{73} +(-4.26515 + 4.33687i) q^{74} +(4.98797 + 0.346604i) q^{75} +(-4.88936 + 2.82287i) q^{76} +(-14.2159 - 8.20755i) q^{77} +(5.36341 + 3.09657i) q^{78} +(-4.87431 - 2.81418i) q^{79} +(-1.52535 - 1.63502i) q^{80} +(-0.500000 + 0.866025i) q^{81} -1.33485 q^{82} +(-5.20372 + 3.00437i) q^{83} +3.69510 q^{84} +(5.10271 + 5.46959i) q^{85} +(0.748273 + 1.29605i) q^{86} +(0.0541616 - 0.0938106i) q^{87} +4.44239 q^{88} +(-13.9095 + 8.03066i) q^{89} +(0.653296 - 2.13851i) q^{90} +(19.8184 - 11.4421i) q^{91} +(-1.65897 + 2.87341i) q^{92} +(1.79190 - 3.10366i) q^{93} +(-1.06316 + 0.613817i) q^{94} +(12.0735 + 3.68834i) q^{95} +(-0.866025 + 0.500000i) q^{96} -12.8116 q^{97} +(3.32690 - 5.76236i) q^{98} +(2.22120 + 3.84723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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