LMFDB - Embedded newform 273.2.bd.a.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (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:	$2.17991597518$
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} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.3
Root			$0.775848i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.671904 + 0.387924i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.699030 + 1.21076i) q^{4} -3.03444i q^{5} +(0.671904 + 0.387924i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.63638i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.671904 + 0.387924i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.699030 + 1.21076i) q^{4} -3.03444i q^{5} +(0.671904 + 0.387924i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.63638i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.17713 + 2.03885i) q^{10} +(-5.32050 + 3.07179i) q^{11} +1.39806 q^{12} +(-3.49183 - 0.898406i) q^{13} -0.775848 q^{14} +(-2.62790 + 1.51722i) q^{15} +(-0.375346 - 0.650117i) q^{16} +(3.22272 - 5.58191i) q^{17} -0.775848i q^{18} +(-3.74367 - 2.16141i) q^{19} +(3.67396 + 2.12116i) q^{20} -1.00000i q^{21} +(2.38324 - 4.12790i) q^{22} +(-4.46121 - 7.72705i) q^{23} +(-2.28317 + 1.31819i) q^{24} -4.20781 q^{25} +(2.69469 - 0.750922i) q^{26} +1.00000 q^{27} +(-1.21076 + 0.699030i) q^{28} +(1.22473 + 2.12129i) q^{29} +(1.17713 - 2.03885i) q^{30} +3.00419i q^{31} +(5.07073 + 2.92759i) q^{32} +(5.32050 + 3.07179i) q^{33} +5.00068i q^{34} +(1.51722 - 2.62790i) q^{35} +(-0.699030 - 1.21076i) q^{36} +(-2.06833 + 1.19415i) q^{37} +3.35385 q^{38} +(0.967872 + 3.47322i) q^{39} -7.99993 q^{40} +(-0.818443 + 0.472528i) q^{41} +(0.387924 + 0.671904i) q^{42} +(-2.64454 + 4.58049i) q^{43} -8.58910i q^{44} +(2.62790 + 1.51722i) q^{45} +(5.99501 + 3.46122i) q^{46} +0.212978i q^{47} +(-0.375346 + 0.650117i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.82725 - 1.63231i) q^{50} -6.44544 q^{51} +(3.52864 - 3.59974i) q^{52} +4.03626 q^{53} +(-0.671904 + 0.387924i) q^{54} +(9.32116 + 16.1447i) q^{55} +(1.31819 - 2.28317i) q^{56} +4.32282i q^{57} +(-1.64580 - 0.950203i) q^{58} +(1.49241 + 0.861641i) q^{59} -4.24233i q^{60} +(6.76645 - 11.7198i) q^{61} +(-1.16540 - 2.01853i) q^{62} +(-0.866025 + 0.500000i) q^{63} -3.04135 q^{64} +(-2.72616 + 10.5957i) q^{65} -4.76649 q^{66} +(5.50012 - 3.17550i) q^{67} +(4.50556 + 7.80385i) q^{68} +(-4.46121 + 7.72705i) q^{69} +2.35426i q^{70} +(-6.12027 - 3.53354i) q^{71} +(2.28317 + 1.31819i) q^{72} +1.75626i q^{73} +(0.926478 - 1.60471i) q^{74} +(2.10391 + 3.64407i) q^{75} +(5.23387 - 3.02178i) q^{76} -6.14359 q^{77} +(-1.99766 - 1.95821i) q^{78} +17.3116 q^{79} +(-1.97274 + 1.13896i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.366610 - 0.634988i) q^{82} +4.99898i q^{83} +(1.21076 + 0.699030i) q^{84} +(-16.9380 - 9.77914i) q^{85} -4.10353i q^{86} +(1.22473 - 2.12129i) q^{87} +(8.09841 + 14.0269i) q^{88} +(-3.08985 + 1.78393i) q^{89} -2.35426 q^{90} +(-2.57481 - 2.52396i) q^{91} +12.4741 q^{92} +(2.60171 - 1.50210i) q^{93} +(-0.0826195 - 0.143101i) q^{94} +(-6.55866 + 11.3599i) q^{95} -5.85518i q^{96} +(-1.36396 - 0.787482i) q^{97} +(-0.671904 - 0.387924i) q^{98} -6.14359i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.671904	+	0.387924i	−0.475108	+	0.274304i	−0.718376	−	0.695656i	$-0.755114\pi$
$2$	−0.671904	+	0.387924i	−0.475108	+	0.274304i	0.243268	+	0.969959i	$0.421781\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.699030	+	1.21076i	−0.349515	+	0.605378i
$5$		−	3.03444i		−	1.35704i	−0.734581	−	0.678521i	$-0.762621\pi$
$5$		−	3.03444i		−	1.35704i	0.734581	−	0.678521i	$-0.237379\pi$
$6$	0.671904	+	0.387924i	0.274304	+	0.158369i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	2.63638i		−	0.932100i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.17713	+	2.03885i	0.372242	+	0.644741i
$11$	−5.32050	+	3.07179i	−1.60419	+	0.926180i	−0.613555	+	0.789652i	$0.710261\pi$
$11$	−5.32050	+	3.07179i	−1.60419	+	0.926180i	−0.990636	+	0.136529i	$0.956405\pi$
$12$	1.39806			0.403585
$13$	−3.49183	−	0.898406i	−0.968459	−	0.249173i
$13$	−3.49183	−	0.898406i	−0.968459	−	0.249173i
$14$	−0.775848			−0.207354
$15$	−2.62790	+	1.51722i	−0.678521	+	0.391744i
$16$	−0.375346	−	0.650117i	−0.0938364	−	0.162529i
$17$	3.22272	−	5.58191i	0.781624	−	1.35381i	−0.149371	−	0.988781i	$-0.547725\pi$
$17$	3.22272	−	5.58191i	0.781624	−	1.35381i	0.930995	−	0.365032i	$-0.118942\pi$
$18$		−	0.775848i		−	0.182869i
$19$	−3.74367	−	2.16141i	−0.858857	−	0.495861i	0.00477253	−	0.999989i	$-0.498481\pi$
$19$	−3.74367	−	2.16141i	−0.858857	−	0.495861i	−0.863629	+	0.504127i	$0.831814\pi$
$20$	3.67396	+	2.12116i	0.821523	+	0.474306i
$21$		−	1.00000i		−	0.218218i
$22$	2.38324	−	4.12790i	0.508109	−	0.880071i
$23$	−4.46121	−	7.72705i	−0.930227	−	1.61120i	−0.782931	−	0.622108i	$-0.786276\pi$
$23$	−4.46121	−	7.72705i	−0.930227	−	1.61120i	−0.147296	−	0.989092i	$-0.547057\pi$
$24$	−2.28317	+	1.31819i	−0.466050	+	0.269074i
$25$	−4.20781			−0.841563
$26$	2.69469	−	0.750922i	0.528472	−	0.147268i
$27$	1.00000			0.192450
$28$	−1.21076	+	0.699030i	−0.228811	+	0.132104i
$29$	1.22473	+	2.12129i	0.227426	+	0.393914i	0.957045	−	0.289941i	$-0.0936356\pi$
$29$	1.22473	+	2.12129i	0.227426	+	0.393914i	−0.729618	+	0.683855i	$0.760302\pi$
$30$	1.17713	−	2.03885i	0.214914	−	0.372242i
$31$			3.00419i			0.539568i	0.962921	+	0.269784i	$0.0869524\pi$
$31$			3.00419i			0.539568i	−0.962921	+	0.269784i	$0.913048\pi$
$32$	5.07073	+	2.92759i	0.896387	+	0.517530i
$33$	5.32050	+	3.07179i	0.926180	+	0.534730i
$34$			5.00068i			0.857610i
$35$	1.51722	−	2.62790i	0.256457	−	0.444196i
$36$	−0.699030	−	1.21076i	−0.116505	−	0.201793i
$37$	−2.06833	+	1.19415i	−0.340031	+	0.196317i	−0.660286	−	0.751015i	$-0.729565\pi$
$37$	−2.06833	+	1.19415i	−0.340031	+	0.196317i	0.320255	+	0.947331i	$0.396231\pi$
$38$	3.35385			0.544066
$39$	0.967872	+	3.47322i	0.154984	+	0.556160i
$40$	−7.99993			−1.26490
$41$	−0.818443	+	0.472528i	−0.127819	+	0.0737966i	−0.562546	−	0.826766i	$-0.690178\pi$
$41$	−0.818443	+	0.472528i	−0.127819	+	0.0737966i	0.434727	+	0.900562i	$0.356845\pi$
$42$	0.387924	+	0.671904i	0.0598580	+	0.103677i
$43$	−2.64454	+	4.58049i	−0.403289	+	0.698518i	−0.994121	−	0.108278i	$-0.965466\pi$
$43$	−2.64454	+	4.58049i	−0.403289	+	0.698518i	0.590831	+	0.806795i	$0.298800\pi$
$44$		−	8.58910i		−	1.29486i
$45$	2.62790	+	1.51722i	0.391744	+	0.226174i
$46$	5.99501	+	3.46122i	0.883917	+	0.510330i
$47$			0.212978i			0.0310661i	0.999879	+	0.0155331i	$0.00494452\pi$
$47$			0.212978i			0.0310661i	−0.999879	+	0.0155331i	$0.995055\pi$
$48$	−0.375346	+	0.650117i	−0.0541765	+	0.0938364i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	2.82725	−	1.63231i	0.399833	−	0.230844i
$51$	−6.44544			−0.902542
$52$	3.52864	−	3.59974i	0.489335	−	0.499194i
$53$	4.03626			0.554422			0.277211	−	0.960809i	$-0.410590\pi$
$53$	4.03626			0.554422			0.277211	+	0.960809i	$0.410590\pi$
$54$	−0.671904	+	0.387924i	−0.0914346	+	0.0527898i
$55$	9.32116	+	16.1447i	1.25687	+	2.17695i
$56$	1.31819	−	2.28317i	0.176150	−	0.305101i
$57$			4.32282i			0.572571i
$58$	−1.64580	−	0.950203i	−0.216104	−	0.124768i
$59$	1.49241	+	0.861641i	0.194295	+	0.112176i	0.593991	−	0.804471i	$-0.297551\pi$
$59$	1.49241	+	0.861641i	0.194295	+	0.112176i	−0.399697	+	0.916647i	$0.630885\pi$
$60$		−	4.24233i		−	0.547682i
$61$	6.76645	−	11.7198i	0.866355	−	1.50057i	0.000660196	−	1.00000i	$-0.499790\pi$
$61$	6.76645	−	11.7198i	0.866355	−	1.50057i	0.865695	−	0.500572i	$-0.166877\pi$
$62$	−1.16540	−	2.01853i	−0.148006	−	0.256353i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	−3.04135			−0.380168
$65$	−2.72616	+	10.5957i	−0.338138	+	1.31424i
$66$	−4.76649			−0.586714
$67$	5.50012	−	3.17550i	0.671947	−	0.387949i	−0.124867	−	0.992173i	$-0.539850\pi$
$67$	5.50012	−	3.17550i	0.671947	−	0.387949i	0.796814	+	0.604225i	$0.206517\pi$
$68$	4.50556	+	7.80385i	0.546379	+	0.946356i
$69$	−4.46121	+	7.72705i	−0.537067	+	0.930227i
$70$			2.35426i			0.281388i
$71$	−6.12027	−	3.53354i	−0.726343	−	0.419354i	0.0907400	−	0.995875i	$-0.471077\pi$
$71$	−6.12027	−	3.53354i	−0.726343	−	0.419354i	−0.817083	+	0.576520i	$0.804410\pi$
$72$	2.28317	+	1.31819i	0.269074	+	0.155350i
$73$			1.75626i			0.205554i	0.994704	+	0.102777i	$0.0327729\pi$
$73$			1.75626i			0.205554i	−0.994704	+	0.102777i	$0.967227\pi$
$74$	0.926478	−	1.60471i	0.107701	−	0.186543i
$75$	2.10391	+	3.64407i	0.242938	+	0.420781i
$76$	5.23387	−	3.02178i	0.600367	−	0.346622i
$77$	−6.14359			−0.700127
$78$	−1.99766	−	1.95821i	−0.226191	−	0.221723i
$79$	17.3116			1.94771			0.973856	−	0.227168i	$-0.0729467\pi$
$79$	17.3116			1.94771			0.973856	+	0.227168i	$0.0729467\pi$
$80$	−1.97274	+	1.13896i	−0.220559	+	0.127340i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.366610	−	0.634988i	0.0404853	−	0.0701227i
$83$			4.99898i			0.548709i	0.961629	+	0.274355i	$0.0884642\pi$
$83$			4.99898i			0.548709i	−0.961629	+	0.274355i	$0.911536\pi$
$84$	1.21076	+	0.699030i	0.132104	+	0.0762704i
$85$	−16.9380	−	9.77914i	−1.83718	−	1.06070i
$86$		−	4.10353i		−	0.442495i
$87$	1.22473	−	2.12129i	0.131305	−	0.227426i
$88$	8.09841	+	14.0269i	0.863293	+	1.49527i
$89$	−3.08985	+	1.78393i	−0.327524	+	0.189096i	−0.654741	−	0.755853i	$-0.727222\pi$
$89$	−3.08985	+	1.78393i	−0.327524	+	0.189096i	0.327217	+	0.944949i	$0.393889\pi$
$90$	−2.35426			−0.248161
$91$	−2.57481	−	2.52396i	−0.269913	−	0.264583i
$92$	12.4741			1.30051
$93$	2.60171	−	1.50210i	0.269784	−	0.155760i
$94$	−0.0826195	−	0.143101i	−0.00852155	−	0.0147598i
$95$	−6.55866	+	11.3599i	−0.672904	+	1.16550i
$96$		−	5.85518i		−	0.597592i
$97$	−1.36396	−	0.787482i	−0.138489	−	0.0799567i	0.429155	−	0.903231i	$-0.358812\pi$
$97$	−1.36396	−	0.787482i	−0.138489	−	0.0799567i	−0.567644	+	0.823274i	$0.692145\pi$
$98$	−0.671904	−	0.387924i	−0.0678726	−	0.0391862i
$99$		−	6.14359i		−	0.617454i
$100$	2.94139	−	5.09463i	0.294139	−	0.509463i
$101$	−4.27311	−	7.40125i	−0.425191	−	0.736452i	0.571248	−	0.820778i	$-0.306460\pi$
$101$	−4.27311	−	7.40125i	−0.425191	−	0.736452i	−0.996438	+	0.0843260i	$0.973126\pi$
$102$	4.33072	−	2.50034i	0.428805	−	0.247571i
$103$	1.58051			0.155733			0.0778663	−	0.996964i	$-0.475189\pi$
$103$	1.58051			0.155733			0.0778663	+	0.996964i	$0.475189\pi$
$104$	−2.36854	+	9.20578i	−0.232254	+	0.902701i
$105$	−3.03444			−0.296131
$106$	−2.71198	+	1.56576i	−0.263410	+	0.152080i
$107$	1.83085	+	3.17112i	0.176994	+	0.306563i	0.940850	−	0.338824i	$-0.110029\pi$
$107$	1.83085	+	3.17112i	0.176994	+	0.306563i	−0.763855	+	0.645388i	$0.776696\pi$
$108$	−0.699030	+	1.21076i	−0.0672642	+	0.116505i
$109$			3.05967i			0.293063i	0.989206	+	0.146532i	$0.0468110\pi$
$109$			3.05967i			0.293063i	−0.989206	+	0.146532i	$0.953189\pi$
$110$	−12.5259	−	7.23181i	−1.19429	−	0.689526i
$111$	2.06833	+	1.19415i	0.196317	+	0.113344i
$112$		−	0.750691i		−	0.0709336i
$113$	5.88917	−	10.2003i	0.554007	−	0.959568i	−0.443973	−	0.896040i	$-0.646432\pi$
$113$	5.88917	−	10.2003i	0.554007	−	0.959568i	0.997980	−	0.0635278i	$-0.0202351\pi$
$114$	−1.67692	−	2.90452i	−0.157058	−	0.272033i
$115$	−23.4472	+	13.5373i	−2.18647	+	1.26236i
$116$	−3.42449			−0.317956
$117$	2.52396	−	2.57481i	0.233340	−	0.238041i
$118$	−1.33700			−0.123081
$119$	5.58191	−	3.22272i	0.511693	−	0.295426i
$120$	3.99996	+	6.92814i	0.365145	+	0.632450i
$121$	13.3718	−	23.1607i	1.21562	−	2.10552i
$122$			10.4995i			0.950578i
$123$	0.818443	+	0.472528i	0.0737966	+	0.0426065i
$124$	−3.63734	−	2.10002i	−0.326643	−	0.188587i
$125$		−	2.40384i		−	0.215006i
$126$	0.387924	−	0.671904i	0.0345590	−	0.0598580i
$127$	0.339937	+	0.588788i	0.0301645	+	0.0522465i	0.880714	−	0.473649i	$-0.157064\pi$
$127$	0.339937	+	0.588788i	0.0301645	+	0.0522465i	−0.850549	+	0.525896i	$0.823730\pi$
$128$	−8.09797	+	4.67537i	−0.715766	+	0.413248i
$129$	5.28909			0.465678
$130$	−2.27863	−	8.17686i	−0.199849	−	0.717158i
$131$	−14.3741			−1.25587			−0.627936	−	0.778265i	$-0.716100\pi$
$131$	−14.3741			−1.25587			−0.627936	+	0.778265i	$0.716100\pi$
$132$	−7.43838	+	4.29455i	−0.647428	+	0.373793i
$133$	−2.16141	−	3.74367i	−0.187418	−	0.324617i
$134$	−2.46370	+	4.26726i	−0.212832	+	0.368635i
$135$		−	3.03444i		−	0.261163i
$136$	−14.7160	−	8.49631i	−1.26189	−	0.728552i
$137$	−8.81724	−	5.09063i	−0.753307	−	0.434922i	0.0735803	−	0.997289i	$-0.476557\pi$
$137$	−8.81724	−	5.09063i	−0.753307	−	0.434922i	−0.826888	+	0.562367i	$0.809891\pi$
$138$		−	6.92245i		−	0.589278i
$139$	−6.17626	+	10.6976i	−0.523863	+	0.907358i	0.475751	+	0.879580i	$0.342176\pi$
$139$	−6.17626	+	10.6976i	−0.523863	+	0.907358i	−0.999614	+	0.0277776i	$0.991157\pi$
$140$	2.12116	+	3.67396i	0.179271	+	0.310506i
$141$	0.184445	−	0.106489i	0.0155331	−	0.00896801i
$142$	5.48298			0.460122
$143$	21.3380	−	5.94621i	1.78437	−	0.497247i
$144$	0.750691			0.0625576
$145$	6.43693	−	3.71636i	0.534558	−	0.308627i
$146$	−0.681295	−	1.18004i	−0.0563844	−	0.0976606i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	3.33898i		−	0.274463i
$149$	−10.3752	−	5.99014i	−0.849971	−	0.490731i	0.0106699	−	0.999943i	$-0.496604\pi$
$149$	−10.3752	−	5.99014i	−0.849971	−	0.490731i	−0.860641	+	0.509212i	$0.829937\pi$
$150$	−2.82725	−	1.63231i	−0.230844	−	0.133278i
$151$		−	16.0560i		−	1.30662i	−0.757092	−	0.653309i	$-0.773380\pi$
$151$		−	16.0560i		−	1.30662i	0.757092	−	0.653309i	$-0.226620\pi$
$152$	−5.69829	+	9.86973i	−0.462192	+	0.800541i
$153$	3.22272	+	5.58191i	0.260541	+	0.451271i
$154$	4.12790	−	2.38324i	0.332636	−	0.192047i
$155$	9.11603			0.732217
$156$	−4.88179	−	1.25602i	−0.390856	−	0.100562i
$157$	18.9571			1.51294			0.756470	−	0.654028i	$-0.226922\pi$
$157$	18.9571			1.51294			0.756470	+	0.654028i	$0.226922\pi$
$158$	−11.6318	+	6.71560i	−0.925373	+	0.534264i
$159$	−2.01813	−	3.49550i	−0.160048	−	0.277211i
$160$	8.88359	−	15.3868i	0.702309	−	1.21644i
$161$		−	8.92243i		−	0.703186i
$162$	0.671904	+	0.387924i	0.0527898	+	0.0304782i
$163$	−6.27493	−	3.62283i	−0.491491	−	0.283762i	0.233702	−	0.972308i	$-0.424916\pi$
$163$	−6.27493	−	3.62283i	−0.491491	−	0.283762i	−0.725193	+	0.688546i	$0.758249\pi$
$164$		−	1.32125i		−	0.103172i
$165$	9.32116	−	16.1447i	0.725652	−	1.25687i
$166$	−1.93922	−	3.35883i	−0.150513	−	0.260696i
$167$	9.59085	−	5.53728i	0.742162	−	0.428487i	−0.0806929	−	0.996739i	$-0.525713\pi$
$167$	9.59085	−	5.53728i	0.742162	−	0.428487i	0.822855	+	0.568252i	$0.192380\pi$
$168$	−2.63638			−0.203401
$169$	11.3857	+	6.27416i	0.875826	+	0.482627i
$170$	15.1743			1.16381
$171$	3.74367	−	2.16141i	0.286286	−	0.165287i
$172$	−3.69723	−	6.40379i	−0.281911	−	0.488285i
$173$	2.28825	−	3.96336i	0.173972	−	0.301329i	−0.765833	−	0.643040i	$-0.777673\pi$
$173$	2.28825	−	3.96336i	0.173972	−	0.301329i	0.939805	+	0.341711i	$0.111006\pi$
$174$			1.90041i			0.144069i
$175$	−3.64407	−	2.10391i	−0.275466	−	0.159040i
$176$	3.99405	+	2.30597i	0.301063	+	0.173819i
$177$		−	1.72328i		−	0.129530i
$178$	1.38406	−	2.39726i	0.103739	−	0.179682i
$179$	1.62818	+	2.82009i	0.121696	+	0.210784i	0.920437	−	0.390892i	$-0.127833\pi$
$179$	1.62818	+	2.82009i	0.121696	+	0.210784i	−0.798741	+	0.601675i	$0.794500\pi$
$180$	−3.67396	+	2.12116i	−0.273841	+	0.158102i
$181$	−20.2771			−1.50718			−0.753591	−	0.657343i	$-0.771680\pi$
$181$	−20.2771			−1.50718			−0.753591	+	0.657343i	$0.771680\pi$
$182$	2.70913	+	0.697026i	0.200814	+	0.0516670i
$183$	−13.5329			−1.00038
$184$	−20.3714	+	11.7614i	−1.50180	+	0.867065i
$185$	3.62357	+	6.27621i	0.266410	+	0.461436i
$186$	−1.16540	+	2.01853i	−0.0854511	+	0.148006i
$187$			39.5981i			2.89570i
$188$	−0.257865	−	0.148878i	−0.0188067	−	0.0108581i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	10.1770i		−	0.738321i
$191$	−11.9614	+	20.7178i	−0.865499	+	1.49909i	0.00105140	+	0.999999i	$0.499665\pi$
$191$	−11.9614	+	20.7178i	−0.865499	+	1.49909i	−0.866551	+	0.499089i	$0.833668\pi$
$192$	1.52067	+	2.63388i	0.109745	+	0.190084i
$193$	−7.30438	+	4.21718i	−0.525780	+	0.303559i	−0.739296	−	0.673380i	$-0.764842\pi$
$193$	−7.30438	+	4.21718i	−0.525780	+	0.303559i	0.213516	+	0.976940i	$0.431508\pi$
$194$	1.22193			0.0877297
$195$	10.5393	−	2.93695i	0.754732	−	0.210319i
$196$	−1.39806			−0.0998614
$197$	−20.7635	+	11.9878i	−1.47934	+	0.854096i	−0.999727	−	0.0233857i	$-0.992555\pi$
$197$	−20.7635	+	11.9878i	−1.47934	+	0.854096i	−0.479611	+	0.877481i	$0.659222\pi$
$198$	2.38324	+	4.12790i	0.169370	+	0.293357i
$199$	−5.20970	+	9.02347i	−0.369306	+	0.639657i	−0.989457	−	0.144825i	$-0.953738\pi$
$199$	−5.20970	+	9.02347i	−0.369306	+	0.639657i	0.620151	+	0.784482i	$0.287071\pi$
$200$			11.0934i			0.784421i
$201$	−5.50012	−	3.17550i	−0.387949	−	0.223982i
$202$	5.74224	+	3.31529i	0.404023	+	0.233263i
$203$			2.44946i			0.171918i
$204$	4.50556	−	7.80385i	0.315452	−	0.546379i
$205$	1.43386	+	2.48352i	0.100145	+	0.173456i
$206$	−1.06195	+	0.613119i	−0.0739898	+	0.0427180i
$207$	8.92243			0.620151
$208$	0.726573	+	2.60731i	0.0503788	+	0.180785i
$209$	26.5576			1.83703
$210$	2.03885	−	1.17713i	0.140694	−	0.0812298i
$211$	−4.09185	−	7.08728i	−0.281694	−	0.487909i	0.690108	−	0.723707i	$-0.257563\pi$
$211$	−4.09185	−	7.08728i	−0.281694	−	0.487909i	−0.971802	+	0.235798i	$0.924230\pi$
$212$	−2.82146	+	4.88692i	−0.193779	+	0.335635i
$213$			7.06708i			0.484228i
$214$	−2.46030	−	1.42046i	−0.168183	−	0.0971005i
$215$	13.8992	+	8.02471i	0.947917	+	0.547280i
$216$		−	2.63638i		−	0.179383i
$217$	−1.50210	+	2.60171i	−0.101969	+	0.176615i
$218$	−1.18692	−	2.05580i	−0.0803883	−	0.139237i
$219$	1.52096	−	0.878129i	0.102777	−	0.0593385i
$220$	−26.0631			−1.75717
$221$	−16.2680	+	16.5958i	−1.09430	+	1.11635i
$222$	−1.85296			−0.124362
$223$	6.60900	−	3.81571i	0.442572	−	0.255519i	−0.262116	−	0.965036i	$-0.584420\pi$
$223$	6.60900	−	3.81571i	0.442572	−	0.255519i	0.704688	+	0.709517i	$0.251087\pi$
$224$	2.92759	+	5.07073i	0.195608	+	0.338803i
$225$	2.10391	−	3.64407i	0.140260	−	0.242938i
$226$			9.13820i			0.607864i
$227$	−7.31264	−	4.22196i	−0.485357	−	0.280221i	0.237289	−	0.971439i	$-0.423741\pi$
$227$	−7.31264	−	4.22196i	−0.485357	−	0.280221i	−0.722646	+	0.691218i	$0.757074\pi$
$228$	−5.23387	−	3.02178i	−0.346622	−	0.200122i
$229$		−	19.3696i		−	1.27998i	−0.768382	−	0.639991i	$-0.778938\pi$
$229$		−	19.3696i		−	1.27998i	0.768382	−	0.639991i	$-0.221062\pi$
$230$	10.5029	−	18.1915i	0.692539	−	1.19951i
$231$	3.07179	+	5.32050i	0.202109	+	0.350063i
$232$	5.59253	−	3.22885i	0.367167	−	0.211984i
$233$	−3.12399			−0.204660			−0.102330	−	0.994751i	$-0.532630\pi$
$233$	−3.12399			−0.204660			−0.102330	+	0.994751i	$0.532630\pi$
$234$	−0.697026	+	2.70913i	−0.0455660	+	0.177101i
$235$	0.646270			0.0421580
$236$	−2.08647	+	1.20463i	−0.135818	+	0.0784144i
$237$	−8.65582	−	14.9923i	−0.562256	−	0.973856i
$238$	−2.50034	+	4.33072i	−0.162073	+	0.280719i
$239$		−	22.3164i		−	1.44353i	−0.692138	−	0.721765i	$-0.743331\pi$
$239$		−	22.3164i		−	1.44353i	0.692138	−	0.721765i	$-0.256669\pi$
$240$	1.97274	+	1.13896i	0.127340	+	0.0735197i
$241$	19.0473	+	10.9970i	1.22694	+	0.708376i	0.966389	−	0.257083i	$-0.0827613\pi$
$241$	19.0473	+	10.9970i	1.22694	+	0.708376i	0.260555	+	0.965459i	$0.416095\pi$
$242$			20.7490i			1.33380i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	9.45990	+	16.3850i	0.605608	+	1.04894i
$245$	2.62790	−	1.51722i	0.167890	−	0.0969316i
$246$	−0.733221			−0.0467484
$247$	11.1304	+	10.9106i	0.708212	+	0.694225i
$248$	7.92018			0.502932
$249$	4.32924	−	2.49949i	0.274355	−	0.158399i
$250$	0.932508	+	1.61515i	0.0589770	+	0.102151i
$251$	0.749917	−	1.29889i	0.0473344	−	0.0819855i	−0.841388	−	0.540432i	$-0.818261\pi$
$251$	0.749917	−	1.29889i	0.0473344	−	0.0819855i	0.888722	+	0.458447i	$0.151594\pi$
$252$		−	1.39806i		−	0.0880695i
$253$	47.4718	+	27.4078i	2.98453	+	1.72312i
$254$	−0.456810	−	0.263739i	−0.0286628	−	0.0165485i
$255$			19.5583i			1.22479i
$256$	6.66872	−	11.5506i	0.416795	−	0.721910i
$257$	−4.46695	−	7.73699i	−0.278641	−	0.482620i	0.692406	−	0.721508i	$-0.256551\pi$
$257$	−4.46695	−	7.73699i	−0.278641	−	0.482620i	−0.971047	+	0.238888i	$0.923217\pi$
$258$	−3.55376	+	2.05176i	−0.221247	+	0.127737i
$259$	−2.38830			−0.148402
$260$	−10.9232	−	10.7074i	−0.677427	−	0.664048i
$261$	−2.44946			−0.151618
$262$	9.65803	−	5.57607i	0.596675	−	0.344490i
$263$	5.23118	+	9.06067i	0.322568	+	0.558705i	0.981017	−	0.193921i	$-0.0621204\pi$
$263$	5.23118	+	9.06067i	0.322568	+	0.558705i	−0.658449	+	0.752625i	$0.728787\pi$
$264$	8.09841	−	14.0269i	0.498422	−	0.863293i
$265$		−	12.2478i		−	0.752374i
$266$	2.90452	+	1.67692i	0.178087	+	0.102819i
$267$	3.08985	+	1.78393i	0.189096	+	0.109175i
$268$			8.87907i			0.542376i
$269$	−1.45845	+	2.52611i	−0.0889232	+	0.154020i	−0.907056	−	0.421009i	$-0.861676\pi$
$269$	−1.45845	+	2.52611i	−0.0889232	+	0.154020i	0.818133	+	0.575029i	$0.195009\pi$
$270$	1.17713	+	2.03885i	0.0716379	+	0.124081i
$271$	19.6297	−	11.3332i	1.19242	−	0.688444i	0.233565	−	0.972341i	$-0.424961\pi$
$271$	19.6297	−	11.3332i	1.19242	−	0.688444i	0.958855	+	0.283897i	$0.0916274\pi$
$272$	−4.83853			−0.293379
$273$	−0.898406	+	3.49183i	−0.0543740	+	0.211335i
$274$	7.89912			0.477203
$275$	22.3877	−	12.9255i	1.35003	−	0.779439i
$276$	−6.23704	−	10.8029i	−0.375426	−	0.650257i
$277$	0.113802	−	0.197112i	0.00683773	−	0.0118433i	−0.862586	−	0.505910i	$-0.831157\pi$
$277$	0.113802	−	0.197112i	0.00683773	−	0.0118433i	0.869424	+	0.494067i	$0.164490\pi$
$278$		−	9.58367i		−	0.574790i
$279$	−2.60171	−	1.50210i	−0.155760	−	0.0899281i
$280$	−6.92814	−	3.99996i	−0.414035	−	0.239043i
$281$		−	11.1627i		−	0.665908i	−0.942943	−	0.332954i	$-0.891955\pi$
$281$		−	11.1627i		−	0.665908i	0.942943	−	0.332954i	$-0.108045\pi$
$282$	−0.0826195	+	0.143101i	−0.00491992	+	0.00852155i
$283$	−10.0339	−	17.3793i	−0.596456	−	1.03309i	−0.993340	−	0.115224i	$-0.963242\pi$
$283$	−10.0339	−	17.3793i	−0.596456	−	1.03309i	0.396883	−	0.917869i	$-0.370092\pi$
$284$	8.55651	−	4.94010i	0.507735	−	0.293141i
$285$	13.1173			0.777003
$286$	−12.0304	+	12.2728i	−0.711373	+	0.725706i
$287$	−0.945057			−0.0557850
$288$	−5.07073	+	2.92759i	−0.298796	+	0.172510i
$289$	−12.2718	−	21.2555i	−0.721873	−	1.25032i
$290$	−2.88333	+	4.99408i	−0.169315	+	0.293262i
$291$			1.57496i			0.0923260i
$292$	−2.12640	−	1.22768i	−0.124438	−	0.0718444i
$293$	−3.19399	−	1.84405i	−0.186595	−	0.107731i	0.403793	−	0.914851i	$-0.367692\pi$
$293$	−3.19399	−	1.84405i	−0.186595	−	0.107731i	−0.590388	+	0.807120i	$0.701025\pi$
$294$			0.775848i			0.0452484i
$295$	2.61459	−	4.52861i	0.152228	−	0.263666i
$296$	3.14823	+	5.45289i	0.182987	+	0.316943i
$297$	−5.32050	+	3.07179i	−0.308727	+	0.178243i
$298$	9.29487			0.538438
$299$	8.63577	+	30.9895i	0.499419	+	1.79217i
$300$	−5.88277			−0.339642
$301$	−4.58049	+	2.64454i	−0.264015	+	0.152429i
$302$	6.22850	+	10.7881i	0.358410	+	0.620784i
$303$	−4.27311	+	7.40125i	−0.245484	+	0.425191i
$304$			3.24510i			0.186119i
$305$	−35.5631	−	20.5324i	−2.03634	−	1.17568i
$306$	−4.33072	−	2.50034i	−0.247571	−	0.142935i
$307$		−	25.5280i		−	1.45696i	−0.685068	−	0.728479i	$-0.740228\pi$
$307$		−	25.5280i		−	1.45696i	0.685068	−	0.728479i	$-0.259772\pi$
$308$	4.29455	−	7.43838i	0.244705	−	0.423841i
$309$	−0.790256	−	1.36876i	−0.0449561	−	0.0778663i
$310$	−6.12510	+	3.53633i	−0.347882	+	0.200850i
$311$	15.7918			0.895469			0.447734	−	0.894167i	$-0.352231\pi$
$311$	15.7918			0.895469			0.447734	+	0.894167i	$0.352231\pi$
$312$	9.15671	−	2.55168i	0.518397	−	0.144460i
$313$	4.21208			0.238081			0.119041	−	0.992889i	$-0.462018\pi$
$313$	4.21208			0.238081			0.119041	+	0.992889i	$0.462018\pi$
$314$	−12.7373	+	7.35391i	−0.718810	+	0.415005i
$315$	1.51722	+	2.62790i	0.0854856	+	0.148065i
$316$	−12.1014	+	20.9602i	−0.680754	+	1.17910i
$317$			23.6448i			1.32802i	0.747723	+	0.664011i	$0.231147\pi$
$317$			23.6448i			1.32802i	−0.747723	+	0.664011i	$0.768853\pi$
$318$	2.71198	+	1.56576i	0.152080	+	0.0878035i
$319$	−13.0323	−	7.52422i	−0.729671	−	0.421276i
$320$			9.22878i			0.515904i
$321$	1.83085	−	3.17112i	0.102188	−	0.176994i
$322$	3.46122	+	5.99501i	0.192886	+	0.334089i
$323$	−24.1296	+	13.9312i	−1.34261	+	0.775154i
$324$	1.39806			0.0776700
$325$	14.6930	+	3.78032i	0.815019	+	0.209695i
$326$	5.62154			0.311348
$327$	2.64975	−	1.52983i	0.146532	−	0.0846001i
$328$	1.24576	+	2.15773i	0.0687858	+	0.119140i
$329$	−0.106489	+	0.184445i	−0.00587094	+	0.0101688i
$330$			14.4636i			0.796196i
$331$	3.07258	+	1.77396i	0.168884	+	0.0975055i	0.582060	−	0.813146i	$-0.302247\pi$
$331$	3.07258	+	1.77396i	0.168884	+	0.0975055i	−0.413175	+	0.910652i	$0.635580\pi$
$332$	−6.05254	−	3.49444i	−0.332176	−	0.191782i
$333$		−	2.38830i		−	0.130878i
$334$	−4.29609	+	7.44104i	−0.235071	+	0.407156i
$335$	−9.63585	−	16.6898i	−0.526463	−	0.911860i
$336$	−0.650117	+	0.375346i	−0.0354668	+	0.0204768i
$337$	−18.4037			−1.00251			−0.501256	−	0.865299i	$-0.667129\pi$
$337$	−18.4037			−1.00251			−0.501256	+	0.865299i	$0.667129\pi$
$338$	−10.0840	+	0.201169i	−0.548498	+	0.0109421i
$339$	−11.7783			−0.639712
$340$	23.6803	−	13.6718i	1.28424	−	0.741459i
$341$	−9.22825	−	15.9838i	−0.499738	−	0.865571i
$342$	−1.67692	+	2.90452i	−0.0906777	+	0.157058i
$343$			1.00000i			0.0539949i
$344$	12.0759	+	6.97202i	0.651088	+	0.375906i
$345$	23.4472	+	13.5373i	1.26236	+	0.728822i
$346$			3.55067i			0.190885i
$347$	10.4997	−	18.1859i	0.563651	−	0.976272i	−0.433523	−	0.901143i	$-0.642730\pi$
$347$	10.4997	−	18.1859i	0.563651	−	0.976272i	0.997174	−	0.0751294i	$-0.0239370\pi$
$348$	1.71224	+	2.96569i	0.0917859	+	0.158978i
$349$	−1.96091	+	1.13213i	−0.104965	+	0.0606016i	−0.551564	−	0.834133i	$-0.685969\pi$
$349$	−1.96091	+	1.13213i	−0.104965	+	0.0606016i	0.446598	+	0.894734i	$0.352635\pi$
$350$	3.26462			0.174501
$351$	−3.49183	−	0.898406i	−0.186380	−	0.0479533i
$352$	−35.9718			−1.91730
$353$	−1.60054	+	0.924074i	−0.0851883	+	0.0491835i	−0.541989	−	0.840386i	$-0.682329\pi$
$353$	−1.60054	+	0.924074i	−0.0851883	+	0.0491835i	0.456801	+	0.889569i	$0.348995\pi$
$354$	0.668502	+	1.15788i	0.0355305	+	0.0615406i
$355$	−10.7223	+	18.5716i	−0.569081	+	0.985677i
$356$		−	4.98808i		−	0.264367i
$357$	−5.58191	−	3.22272i	−0.295426	−	0.170564i
$358$	−2.18796	−	1.26322i	−0.115637	−	0.0667633i
$359$			10.1169i			0.533949i	0.963704	+	0.266974i	$0.0860239\pi$
$359$			10.1169i			0.533949i	−0.963704	+	0.266974i	$0.913976\pi$
$360$	3.99996	−	6.92814i	0.210817	−	0.365145i
$361$	−0.156625	−	0.271282i	−0.00824340	−	0.0142780i
$362$	13.6242	−	7.86596i	0.716074	−	0.413426i
$363$	−26.7436			−1.40368
$364$	4.85576	−	1.35314i	0.254511	−	0.0709240i
$365$	5.32926			0.278946
$366$	9.09281	−	5.24974i	0.475289	−	0.274408i
$367$	7.90389	+	13.6899i	0.412580	+	0.714609i	0.995171	−	0.0981561i	$-0.0312945\pi$
$367$	7.90389	+	13.6899i	0.412580	+	0.714609i	−0.582591	+	0.812765i	$0.697961\pi$
$368$	−3.34899	+	5.80063i	−0.174578	+	0.302378i
$369$		−	0.945057i		−	0.0491977i
$370$	−4.86938	−	2.81134i	−0.253147	−	0.146155i
$371$	3.49550	+	2.01813i	0.181477	+	0.104776i
$372$			4.20004i			0.217762i
$373$	5.59141	−	9.68461i	0.289512	−	0.501450i	−0.684181	−	0.729312i	$-0.739840\pi$
$373$	5.59141	−	9.68461i	0.289512	−	0.501450i	0.973693	+	0.227862i	$0.0731735\pi$
$374$	−15.3611	−	26.6061i	−0.794301	−	1.37577i
$375$	−2.08179	+	1.20192i	−0.107503	+	0.0620669i
$376$	0.561492			0.0289567
$377$	−2.37076	−	8.50749i	−0.122100	−	0.438158i
$378$	−0.775848			−0.0399053
$379$	−23.7453	+	13.7094i	−1.21971	+	0.704203i	−0.964857	−	0.262776i	$-0.915362\pi$
$379$	−23.7453	+	13.7094i	−1.21971	+	0.704203i	−0.254858	+	0.966979i	$0.582029\pi$
$380$	−9.16940	−	15.8819i	−0.470380	−	0.814723i
$381$	0.339937	−	0.588788i	0.0174155	−	0.0301645i
$382$		−	18.5605i		−	0.949639i
$383$	3.37784	+	1.95019i	0.172599	+	0.0996503i	0.583811	−	0.811890i	$-0.301561\pi$
$383$	3.37784	+	1.95019i	0.172599	+	0.0996503i	−0.411212	+	0.911540i	$0.634894\pi$
$384$	8.09797	+	4.67537i	0.413248	+	0.238589i
$385$			18.6423i			0.950101i
$386$	3.27189	−	5.66709i	0.166535	−	0.288447i
$387$	−2.64454	−	4.58049i	−0.134430	−	0.232839i
$388$	1.90690	−	1.10095i	0.0968080	−	0.0558921i
$389$	20.5060			1.03970			0.519848	−	0.854259i	$-0.325988\pi$
$389$	20.5060			1.03970			0.519848	+	0.854259i	$0.325988\pi$
$390$	−5.94206	+	6.06178i	−0.300888	+	0.306950i
$391$	−57.5090			−2.90835
$392$	2.28317	−	1.31819i	0.115318	−	0.0665786i
$393$	7.18706	+	12.4484i	0.362539	+	0.627936i
$394$	9.30071	−	16.1093i	0.468563	−	0.811575i
$395$		−	52.5311i		−	2.64313i
$396$	7.43838	+	4.29455i	0.373793	+	0.215809i
$397$	26.8427	+	15.4976i	1.34720	+	0.777804i	0.987852	−	0.155400i	$-0.0496667\pi$
$397$	26.8427	+	15.4976i	1.34720	+	0.777804i	0.359345	+	0.933205i	$0.383000\pi$
$398$		−	8.08388i		−	0.405208i
$399$	−2.16141	+	3.74367i	−0.108206	+	0.187418i
$400$	1.57938	+	2.73557i	0.0789692	+	0.136779i
$401$	13.4988	−	7.79356i	0.674100	−	0.389192i	−0.123528	−	0.992341i	$-0.539421\pi$
$401$	13.4988	−	7.79356i	0.674100	−	0.389192i	0.797628	+	0.603149i	$0.206088\pi$
$402$	4.92741			0.245757
$403$	2.69898	−	10.4901i	0.134446	−	0.522550i
$404$	11.9481			0.594442
$405$	−2.62790	+	1.51722i	−0.130581	+	0.0753912i
$406$	−0.950203	−	1.64580i	−0.0471578	−	0.0816797i
$407$	7.33635	−	12.7069i	0.363650	−	0.629859i
$408$			16.9926i			0.841260i
$409$	−16.6373	−	9.60553i	−0.822659	−	0.474963i	0.0286732	−	0.999589i	$-0.490872\pi$
$409$	−16.6373	−	9.60553i	−0.822659	−	0.474963i	−0.851333	+	0.524626i	$0.824205\pi$
$410$	−1.92683	−	1.11246i	−0.0951594	−	0.0549403i
$411$			10.1813i			0.502205i
$412$	−1.10483	+	1.91361i	−0.0544308	+	0.0942770i
$413$	0.861641	+	1.49241i	0.0423986	+	0.0734365i
$414$	−5.99501	+	3.46122i	−0.294639	+	0.170110i
$415$	15.1691			0.744621
$416$	−15.0760	−	14.7782i	−0.739160	−	0.724562i
$417$	12.3525			0.604905
$418$	−17.8442	+	10.3023i	−0.872786	+	0.503903i
$419$	−10.4250	−	18.0566i	−0.509294	−	0.882123i	−0.999942	−	0.0107651i	$-0.996573\pi$
$419$	−10.4250	−	18.0566i	−0.509294	−	0.882123i	0.490648	−	0.871358i	$-0.336760\pi$
$420$	2.12116	−	3.67396i	0.103502	−	0.179271i
$421$		−	3.31213i		−	0.161423i	−0.996737	−	0.0807116i	$-0.974281\pi$
$421$		−	3.31213i		−	0.161423i	0.996737	−	0.0807116i	$-0.0257193\pi$
$422$	5.49866	+	3.17465i	0.267670	+	0.154540i
$423$	−0.184445	−	0.106489i	−0.00896801	−	0.00517768i
$424$		−	10.6411i		−	0.516777i
$425$	−13.5606	+	23.4877i	−0.657786	+	1.13932i
$426$	−2.74149	−	4.74840i	−0.132826	−	0.230061i
$427$	11.7198	−	6.76645i	0.567163	−	0.327452i
$428$	−5.11926			−0.247449
$429$	−15.8186	−	15.5061i	−0.763727	−	0.748644i
$430$	−12.4519			−0.600484
$431$	−24.5755	+	14.1886i	−1.18376	+	0.683443i	−0.956881	−	0.290480i	$-0.906185\pi$
$431$	−24.5755	+	14.1886i	−1.18376	+	0.683443i	−0.226877	+	0.973923i	$0.572852\pi$
$432$	−0.375346	−	0.650117i	−0.0180588	−	0.0312788i
$433$	10.5977	−	18.3558i	0.509293	−	0.882121i	−0.490649	−	0.871357i	$-0.663240\pi$
$433$	10.5977	−	18.3558i	0.509293	−	0.882121i	0.999942	−	0.0107640i	$-0.00342637\pi$
$434$		−	2.33080i		−	0.111882i
$435$	−6.43693	−	3.71636i	−0.308627	−	0.178186i
$436$	−3.70451	−	2.13880i	−0.177414	−	0.102430i
$437$			38.5700i			1.84505i
$438$	−0.681295	+	1.18004i	−0.0325535	+	0.0563844i
$439$	6.28658	+	10.8887i	0.300042	+	0.519688i	0.976145	−	0.217119i	$-0.0696659\pi$
$439$	6.28658	+	10.8887i	0.300042	+	0.519688i	−0.676103	+	0.736807i	$0.736333\pi$
$440$	42.5636	−	24.5741i	2.02914	−	1.17152i
$441$	−1.00000			−0.0476190
$442$	4.49264	−	17.4615i	0.213693	−	0.830560i
$443$	10.7230			0.509465			0.254732	−	0.967012i	$-0.418013\pi$
$443$	10.7230			0.509465			0.254732	+	0.967012i	$0.418013\pi$
$444$	−2.89164	+	1.66949i	−0.137231	+	0.0792305i
$445$	5.41322	+	9.37597i	0.256611	+	0.444464i
$446$	−2.96041	+	5.12758i	−0.140180	+	0.242798i
$447$			11.9803i			0.566648i
$448$	−2.63388	−	1.52067i	−0.124439	−	0.0718451i
$449$	9.68677	+	5.59266i	0.457147	+	0.263934i	0.710844	−	0.703350i	$-0.248313\pi$
$449$	9.68677	+	5.59266i	0.457147	+	0.263934i	−0.253697	+	0.967284i	$0.581647\pi$
$450$			3.26462i			0.153896i
$451$	2.90302	−	5.02818i	0.136698	−	0.236768i
$452$	8.23341	+	14.2607i	0.387267	+	0.670767i
$453$	−13.9049	+	8.02799i	−0.653309	+	0.377188i
$454$	6.55119			0.307463
$455$	−7.65879	+	7.81310i	−0.359050	+	0.366284i
$456$	11.3966			0.533694
$457$	2.16642	−	1.25078i	0.101341	−	0.0585090i	−0.448473	−	0.893796i	$-0.648032\pi$
$457$	2.16642	−	1.25078i	0.101341	−	0.0585090i	0.549814	+	0.835287i	$0.314699\pi$
$458$	7.51395	+	13.0145i	0.351104	+	0.608130i
$459$	3.22272	−	5.58191i	0.150424	−	0.260541i
$460$		−	37.8518i		−	1.76485i
$461$	−7.56327	−	4.36666i	−0.352257	−	0.203375i	0.313422	−	0.949614i	$-0.398525\pi$
$461$	−7.56327	−	4.36666i	−0.352257	−	0.203375i	−0.665679	+	0.746238i	$0.731858\pi$
$462$	−4.12790	−	2.38324i	−0.192047	−	0.110879i
$463$			12.0840i			0.561591i	0.959768	+	0.280795i	$0.0905982\pi$
$463$			12.0840i			0.561591i	−0.959768	+	0.280795i	$0.909402\pi$
$464$	0.919393	−	1.59243i	0.0426817	−	0.0739269i
$465$	−4.55801	−	7.89471i	−0.211373	−	0.366109i
$466$	2.09902	−	1.21187i	0.0972354	−	0.0561389i
$467$	−3.44741			−0.159527			−0.0797635	−	0.996814i	$-0.525417\pi$
$467$	−3.44741			−0.159527			−0.0797635	+	0.996814i	$0.525417\pi$
$468$	1.35314	+	4.85576i	0.0625491	+	0.224458i
$469$	6.35099			0.293262
$470$	−0.434231	+	0.250704i	−0.0200296	+	0.0115641i
$471$	−9.47854	−	16.4173i	−0.436748	−	0.756470i
$472$	2.27161	−	3.93454i	0.104559	−	0.181102i
$473$		−	32.4940i		−	1.49407i
$474$	11.6318	+	6.71560i	0.534264	+	0.308458i
$475$	15.7527	+	9.09480i	0.722782	+	0.417298i
$476$			9.01111i			0.413024i
$477$	−2.01813	+	3.49550i	−0.0924037	+	0.160048i
$478$	8.65708	+	14.9945i	0.395966	+	0.685832i
$479$	10.9556	−	6.32520i	0.500573	−	0.289006i	−0.228377	−	0.973573i	$-0.573342\pi$
$479$	10.9556	−	6.32520i	0.500573	−	0.289006i	0.728950	+	0.684567i	$0.240009\pi$
$480$	−17.7672			−0.810957
$481$	8.29507	−	2.31157i	0.378223	−	0.105398i
$482$	−17.0639			−0.777241
$483$	−7.72705	+	4.46121i	−0.351593	+	0.202992i
$484$	18.6946	+	32.3800i	0.849755	+	1.47182i
$485$	−2.38957	+	4.13885i	−0.108505	+	0.187935i
$486$		−	0.775848i		−	0.0351932i
$487$	−6.68224	−	3.85800i	−0.302801	−	0.174822i	0.340899	−	0.940100i	$-0.389268\pi$
$487$	−6.68224	−	3.85800i	−0.302801	−	0.174822i	−0.643701	+	0.765277i	$0.722602\pi$
$488$	−30.8979	−	17.8389i	−1.39868	−	0.807530i
$489$			7.24567i			0.327660i
$490$	−1.17713	+	2.03885i	−0.0531774	+	0.0921059i
$491$	2.32807	+	4.03233i	0.105064	+	0.181977i	0.913764	−	0.406244i	$-0.133162\pi$
$491$	2.32807	+	4.03233i	0.105064	+	0.181977i	−0.808700	+	0.588221i	$0.799829\pi$
$492$	−1.14423	+	0.660623i	−0.0515860	+	0.0297832i
$493$	15.7878			0.711048
$494$	−11.7111	−	3.01312i	−0.526906	−	0.135567i
$495$	−18.6423			−0.837910
$496$	1.95308	−	1.12761i	0.0876957	−	0.0506312i
$497$	−3.53354	−	6.12027i	−0.158501	−	0.274532i
$498$	−1.93922	+	3.35883i	−0.0868987	+	0.150513i
$499$			32.4249i			1.45154i	0.687938	+	0.725769i	$0.258516\pi$
$499$			32.4249i			1.45154i	−0.687938	+	0.725769i	$0.741484\pi$
$500$	2.91046	+	1.68036i	0.130160	+	0.0751479i
$501$	−9.59085	−	5.53728i	−0.428487	−	0.247387i
$502$			1.16364i			0.0519359i
$503$	0.146303	−	0.253405i	0.00652335	−	0.0112988i	−0.862745	−	0.505639i	$-0.831257\pi$
$503$	0.146303	−	0.253405i	0.00652335	−	0.0112988i	0.869269	+	0.494340i	$0.164590\pi$
$504$	1.31819	+	2.28317i	0.0587168	+	0.101700i
$505$	−22.4586	+	12.9665i	−0.999396	+	0.577001i
$506$	−42.5286			−1.89063
$507$	−0.259289	−	12.9974i	−0.0115154	−	0.577235i
$508$	−0.950504			−0.0421718
$509$	4.18694	−	2.41733i	0.185583	−	0.107146i	−0.404330	−	0.914613i	$-0.632495\pi$
$509$	4.18694	−	2.41733i	0.185583	−	0.107146i	0.589913	+	0.807467i	$0.299162\pi$
$510$	−7.58713	−	13.1413i	−0.335964	−	0.581906i
$511$	−0.878129	+	1.52096i	−0.0388461	+	0.0672835i
$512$		−	8.35364i		−	0.369182i
$513$	−3.74367	−	2.16141i	−0.165287	−	0.0954285i
$514$	6.00273	+	3.46568i	0.264769	+	0.152864i
$515$		−	4.79597i		−	0.211336i
$516$	−3.69723	+	6.40379i	−0.162762	+	0.281911i
$517$	−0.654226	−	1.13315i	−0.0287728	−	0.0498360i
$518$	1.60471	−	0.926478i	0.0705068	−	0.0407071i
$519$	−4.57650			−0.200886
$520$	27.9344	+	7.18718i	1.22500	+	0.315179i
$521$	35.8024			1.56853			0.784265	−	0.620425i	$-0.213040\pi$
$521$	35.8024			1.56853			0.784265	+	0.620425i	$0.213040\pi$
$522$	1.64580	−	0.950203i	0.0720347	−	0.0415893i
$523$	−20.0259	−	34.6859i	−0.875673	−	1.51671i	−0.856044	−	0.516903i	$-0.827085\pi$
$523$	−20.0259	−	34.6859i	−0.875673	−	1.51671i	−0.0196295	−	0.999807i	$-0.506249\pi$
$524$	10.0479	−	17.4035i	0.438946	−	0.760277i
$525$			4.20781i			0.183644i
$526$	−7.02970	−	4.05860i	−0.306510	−	0.176963i
$527$	16.7691	+	9.68166i	0.730475	+	0.421740i
$528$		−	4.61193i		−	0.200709i
$529$	−28.3048	+	49.0254i	−1.23065	+	2.13154i
$530$	4.75120	+	8.22933i	0.206379	+	0.357459i
$531$	−1.49241	+	0.861641i	−0.0647649	+	0.0373920i
$532$	6.04356			0.262021
$533$	3.28239	−	0.914695i	0.142176	−	0.0396198i
$534$	−2.76811			−0.119788
$535$	9.62256	−	5.55559i	0.416019	−	0.240189i
$536$	−8.37181	−	14.5004i	−0.361607	−	0.626322i
$537$	1.62818	−	2.82009i	0.0702612	−	0.121696i
$538$		−	2.26307i		−	0.0975679i
$539$	−5.32050	−	3.07179i	−0.229170	−	0.132311i
$540$	3.67396	+	2.12116i	0.158102	+	0.0912803i
$541$			24.0781i			1.03520i	0.855623	+	0.517599i	$0.173174\pi$
$541$			24.0781i			1.03520i	−0.855623	+	0.517599i	$0.826826\pi$
$542$	−8.79286	+	15.2297i	−0.377686	+	0.654171i
$543$	10.1385	+	17.5605i	0.435086	+	0.753591i
$544$	32.6831	−	18.8696i	1.40128	−	0.809027i
$545$	9.28438			0.397699
$546$	−0.750922	−	2.69469i	−0.0321365	−	0.115322i
$547$	−30.4282			−1.30102			−0.650508	−	0.759500i	$-0.725444\pi$
$547$	−30.4282			−1.30102			−0.650508	+	0.759500i	$0.725444\pi$
$548$	12.3270	−	7.11701i	0.526584	−	0.304024i
$549$	6.76645	+	11.7198i	0.288785	+	0.500190i
$550$	−10.0282	+	17.3694i	−0.427606	+	0.740635i
$551$		−	10.5886i		−	0.451088i
$552$	20.3714	+	11.7614i	0.867065	+	0.500600i
$553$	14.9923	+	8.65582i	0.637538	+	0.368083i
$554$			0.176587i			0.00750246i
$555$	3.62357	−	6.27621i	0.153812	−	0.266410i
$556$	−8.63477	−	14.9559i	−0.366196	−	0.634270i
$557$	−24.0688	+	13.8961i	−1.01983	+	0.588797i	−0.914054	−	0.405593i	$-0.867065\pi$
$557$	−24.0688	+	13.8961i	−1.01983	+	0.588797i	−0.105773	+	0.994390i	$0.533732\pi$
$558$	2.33080			0.0986704
$559$	13.3494	−	13.6184i	0.564621	−	0.575997i
$560$	−2.27793			−0.0962599
$561$	34.2930	−	19.7991i	1.44785	−	0.835917i
$562$	4.33026	+	7.50024i	0.182661	+	0.316378i
$563$	23.2403	−	40.2533i	0.979461	−	1.69648i	0.315109	−	0.949056i	$-0.397959\pi$
$563$	23.2403	−	40.2533i	0.979461	−	1.69648i	0.664352	−	0.747420i	$-0.268708\pi$
$564$			0.297757i			0.0125378i
$565$	−30.9523	−	17.8703i	−1.30217	−	0.751810i
$566$	13.4837	+	7.78482i	0.566762	+	0.327220i
$567$		−	1.00000i		−	0.0419961i
$568$	−9.31575	+	16.1354i	−0.390880	+	0.677024i
$569$	6.21834	+	10.7705i	0.260686	+	0.451522i	0.966425	−	0.256951i	$-0.0827178\pi$
$569$	6.21834	+	10.7705i	0.260686	+	0.451522i	−0.705738	+	0.708473i	$0.749384\pi$
$570$	−8.81358	+	5.08852i	−0.369160	+	0.213135i
$571$	11.1120			0.465022			0.232511	−	0.972594i	$-0.425306\pi$
$571$	11.1120			0.465022			0.232511	+	0.972594i	$0.425306\pi$
$572$	−7.71650	+	29.9917i	−0.322643	+	1.25401i
$573$	23.9229			0.999392
$574$	0.634988	−	0.366610i	0.0265039	−	0.0153020i
$575$	18.7720	+	32.5140i	0.782844	+	1.35593i
$576$	1.52067	−	2.63388i	0.0633614	−	0.109745i
$577$			19.5793i			0.815097i	0.913183	+	0.407549i	$0.133616\pi$
$577$			19.5793i			0.815097i	−0.913183	+	0.407549i	$0.866384\pi$
$578$	16.4910	+	9.52109i	0.685936	+	0.396025i
$579$	7.30438	+	4.21718i	0.303559	+	0.175260i
$580$			10.3914i			0.431479i
$581$	−2.49949	+	4.32924i	−0.103696	+	0.179607i
$582$	−0.610966	−	1.05822i	−0.0253254	−	0.0438648i
$583$	−21.4749	+	12.3985i	−0.889400	+	0.513495i
$584$	4.63016			0.191597
$585$	−7.81310	−	7.65879i	−0.323032	−	0.316652i
$586$	2.86141			0.118204
$587$	7.19732	−	4.15537i	0.297065	−	0.171511i	−0.344059	−	0.938948i	$-0.611802\pi$
$587$	7.19732	−	4.15537i	0.297065	−	0.171511i	0.641124	+	0.767438i	$0.278469\pi$
$588$	0.699030	+	1.21076i	0.0288275	+	0.0499307i
$589$	6.49328	−	11.2467i	0.267551	−	0.463412i
$590$			4.05706i			0.167026i
$591$	20.7635	+	11.9878i	0.854096	+	0.493112i
$592$	1.55267	+	0.896436i	0.0638145	+	0.0368433i
$593$			0.319656i			0.0131267i	0.999978	+	0.00656336i	$0.00208920\pi$
$593$			0.319656i			0.0131267i	−0.999978	+	0.00656336i	$0.997911\pi$
$594$	2.38324	−	4.12790i	0.0977857	−	0.169370i
$595$	−9.77914	−	16.9380i	−0.400906	−	0.694389i
$596$	14.5052	−	8.37457i	0.594155	−	0.343036i
$597$	10.4194			0.426438
$598$	−17.8240	−	17.4720i	−0.728877	−	0.714481i
$599$	9.32910			0.381177			0.190588	−	0.981670i	$-0.438960\pi$
$599$	9.32910			0.381177			0.190588	+	0.981670i	$0.438960\pi$
$600$	9.60715	−	5.54669i	0.392210	−	0.226443i
$601$	−16.5174	−	28.6089i	−0.673757	−	1.16698i	−0.976830	−	0.214015i	$-0.931346\pi$
$601$	−16.5174	−	28.6089i	−0.673757	−	1.16698i	0.303073	−	0.952967i	$-0.401987\pi$
$602$	2.05176	−	3.55376i	0.0836237	−	0.144840i
$603$			6.35099i			0.258633i
$604$	19.4399	+	11.2236i	0.790997	+	0.456682i
$605$	−70.2796	−	40.5760i	−2.85727	−	1.64965i
$606$		−	6.63057i		−	0.269349i
$607$	−11.1301	+	19.2780i	−0.451759	+	0.782469i	−0.998495	−	0.0548354i	$-0.982537\pi$
$607$	−11.1301	+	19.2780i	−0.451759	+	0.782469i	0.546737	+	0.837305i	$0.315870\pi$
$608$	−12.6554	−	21.9199i	−0.513246	−	0.888967i
$609$	2.12129	−	1.22473i	0.0859591	−	0.0496285i
$610$	31.8600			1.28997
$611$	0.191341	−	0.743684i	0.00774083	−	0.0300862i
$612$	−9.01111			−0.364253
$613$	37.0963	−	21.4176i	1.49831	−	0.865048i	0.498309	−	0.867000i	$-0.333955\pi$
$613$	37.0963	−	21.4176i	1.49831	−	0.865048i	0.999998	+	0.00195170i	$0.000621246\pi$
$614$	9.90291	+	17.1523i	0.399649	+	0.692212i
$615$	1.43386	−	2.48352i	0.0578187	−	0.100145i
$616$			16.1968i			0.652588i
$617$	22.2996	+	12.8747i	0.897750	+	0.518316i	0.876469	−	0.481457i	$-0.159892\pi$
$617$	22.2996	+	12.8747i	0.897750	+	0.518316i	0.0212803	+	0.999774i	$0.493226\pi$
$618$	1.06195	+	0.613119i	0.0427180	+	0.0246633i
$619$		−	28.8141i		−	1.15814i	−0.815279	−	0.579068i	$-0.803417\pi$
$619$		−	28.8141i		−	1.15814i	0.815279	−	0.579068i	$-0.196583\pi$
$620$	−6.37238	+	11.0373i	−0.255921	+	0.443268i
$621$	−4.46121	−	7.72705i	−0.179022	−	0.310076i
$622$	−10.6105	+	6.12600i	−0.425444	+	0.245630i
$623$	−3.56786			−0.142943
$624$	1.89471	−	1.93289i	0.0758492	−	0.0773774i
$625$	−28.3334			−1.13333
$626$	−2.83012	+	1.63397i	−0.113114	+	0.0653065i
$627$	−13.2788	−	22.9996i	−0.530304	−	0.918514i
$628$	−13.2516	+	22.9524i	−0.528795	+	0.915900i
$629$			15.3936i			0.613784i
$630$	−2.03885	−	1.17713i	−0.0812298	−	0.0468980i
$631$	−13.6241	−	7.86586i	−0.542366	−	0.313135i	0.203671	−	0.979039i	$-0.434713\pi$
$631$	−13.6241	−	7.86586i	−0.542366	−	0.313135i	−0.746037	+	0.665904i	$0.768046\pi$
$632$		−	45.6400i		−	1.81546i
$633$	−4.09185	+	7.08728i	−0.162636	+	0.281694i
$634$	−9.17237	−	15.8870i	−0.364282	−	0.630954i
$635$	1.78664	−	1.03152i	0.0709007	−	0.0409345i
$636$	5.64293			0.223757
$637$	−0.967872	−	3.47322i	−0.0383485	−	0.137614i
$638$	11.6753			0.462230
$639$	6.12027	−	3.53354i	0.242114	−	0.139785i
$640$	14.1871	+	24.5728i	0.560795	+	0.971325i
$641$	−3.17860	+	5.50549i	−0.125547	+	0.217454i	−0.921947	−	0.387317i	$-0.873402\pi$
$641$	−3.17860	+	5.50549i	−0.125547	+	0.217454i	0.796400	+	0.604771i	$0.206735\pi$
$642$			2.84091i			0.112122i
$643$	22.1332	+	12.7786i	0.872850	+	0.503940i	0.868294	−	0.496050i	$-0.165217\pi$
$643$	22.1332	+	12.7786i	0.872850	+	0.503940i	0.00455542	+	0.999990i	$0.498550\pi$
$644$	10.8029	+	6.23704i	0.425693	+	0.245774i
$645$		−	16.0494i		−	0.631945i
$646$	10.8085	−	18.7209i	0.425255	−	0.736564i
$647$	22.7305	+	39.3705i	0.893630	+	1.54781i	0.835491	+	0.549504i	$0.185183\pi$
$647$	22.7305	+	39.3705i	0.893630	+	1.54781i	0.0581389	+	0.998309i	$0.481483\pi$
$648$	−2.28317	+	1.31819i	−0.0896914	+	0.0517834i
$649$	−10.5871			−0.415581
$650$	−11.3387	+	3.15974i	−0.444742	+	0.123935i
$651$	3.00419			0.117743
$652$	8.77273	−	5.06494i	0.343567	−	0.198358i
$653$	2.27104	+	3.93356i	0.0888727	+	0.153932i	0.907035	−	0.421055i	$-0.138340\pi$
$653$	2.27104	+	3.93356i	0.0888727	+	0.153932i	−0.818162	+	0.574988i	$0.805007\pi$
$654$	−1.18692	+	2.05580i	−0.0464122	+	0.0803883i
$655$			43.6174i			1.70427i
$656$	0.614398	+	0.354723i	0.0239882	+	0.0138496i
$657$	−1.52096	−	0.878129i	−0.0593385	−	0.0342591i
$658$		−	0.165239i		−	0.00644168i
$659$	−16.5764	+	28.7111i	−0.645724	+	1.11843i	0.338410	+	0.940999i	$0.390111\pi$
$659$	−16.5764	+	28.7111i	−0.645724	+	1.11843i	−0.984134	+	0.177428i	$0.943222\pi$
$660$	13.0315	+	22.5713i	0.507252	+	0.878587i
$661$	−0.847994	+	0.489590i	−0.0329832	+	0.0190428i	−0.516401	−	0.856347i	$-0.672729\pi$
$661$	−0.847994	+	0.489590i	−0.0329832	+	0.0190428i	0.483418	+	0.875390i	$0.339395\pi$
$662$	−2.75264			−0.106984
$663$	22.5064	+	5.79062i	0.874075	+	0.224889i
$664$	13.1792			0.511452
$665$	−11.3599	+	6.55866i	−0.440519	+	0.254334i
$666$	0.926478	+	1.60471i	0.0359003	+	0.0621811i
$667$	10.9275	−	18.9271i	0.423116	−	0.732859i
$668$			15.4829i			0.599051i
$669$	−6.60900	−	3.81571i	−0.255519	−	0.147524i
$670$	12.9487	+	7.47595i	0.500253	+	0.288821i
$671$			83.1405i			3.20961i
$672$	2.92759	−	5.07073i	0.112934	−	0.195608i
$673$	−11.8838	−	20.5834i	−0.458088	−	0.793432i	0.540772	−	0.841169i	$-0.318132\pi$
$673$	−11.8838	−	20.5834i	−0.458088	−	0.793432i	−0.998860	+	0.0477377i	$0.984799\pi$
$674$	12.3655	−	7.13923i	0.476302	−	0.274993i
$675$	−4.20781			−0.161959
$676$	−15.5554	+	9.39952i	−0.598286	+	0.361520i
$677$	7.86778			0.302383			0.151192	−	0.988504i	$-0.451689\pi$
$677$	7.86778			0.302383			0.151192	+	0.988504i	$0.451689\pi$
$678$	7.91392	−	4.56910i	0.303932	−	0.175475i
$679$	−0.787482	−	1.36396i	−0.0302208	−	0.0523439i
$680$	−25.7815	+	44.6549i	−0.988676	+	1.71244i
$681$			8.44391i			0.323571i
$682$	12.4010	+	7.15972i	0.474859	+	0.274160i
$683$	−28.2267	−	16.2967i	−1.08006	−	0.623576i	−0.149151	−	0.988814i	$-0.547654\pi$
$683$	−28.2267	−	16.2967i	−1.08006	−	0.623576i	−0.930914	+	0.365239i	$0.880987\pi$
$684$			6.04356i			0.231081i
$685$	−15.4472	+	26.7554i	−0.590208	+	1.02227i
$686$	−0.387924	−	0.671904i	−0.0148110	−	0.0256534i
$687$	−16.7746	+	9.68482i	−0.639991	+	0.369499i
$688$	3.97047			0.151373
$689$	−14.0939	−	3.62619i	−0.536935	−	0.138147i
$690$	−21.0057			−0.799675
$691$	3.51539	−	2.02961i	0.133732	−	0.0772100i	−0.431642	−	0.902045i	$-0.642065\pi$
$691$	3.51539	−	2.02961i	0.133732	−	0.0772100i	0.565373	+	0.824835i	$0.308732\pi$
$692$	3.19911	+	5.54102i	0.121612	+	0.210638i
$693$	3.07179	−	5.32050i	0.116688	−	0.202109i
$694$			16.2923i			0.618446i
$695$	32.4612	+	18.7415i	1.23132	+	0.710904i
$696$	−5.59253	−	3.22885i	−0.211984	−	0.122389i
$697$			6.09131i			0.230725i
$698$	0.878362	−	1.52137i	0.0332465	−	0.0575846i
$699$	1.56200	+	2.70546i	0.0590802	+	0.102330i
$700$	5.09463	−	2.94139i	0.192559	−	0.111174i
$701$	16.8527			0.636518			0.318259	−	0.948004i	$-0.396902\pi$
$701$	16.8527			0.636518			0.318259	+	0.948004i	$0.396902\pi$
$702$	2.69469	−	0.750922i	0.101704	−	0.0283417i
$703$	10.3242			0.389383
$704$	16.1815	−	9.34239i	0.609863	−	0.352104i
$705$	−0.323135	−	0.559686i	−0.0121700	−	0.0210790i
$706$	0.716941	−	1.24178i	0.0269824	−	0.0467350i
$707$		−	8.54623i		−	0.321414i
$708$	2.08647	+	1.20463i	0.0784144	+	0.0452726i
$709$	−22.5519	−	13.0204i	−0.846956	−	0.488990i	0.0126669	−	0.999920i	$-0.495968\pi$
$709$	−22.5519	−	13.0204i	−0.846956	−	0.488990i	−0.859622	+	0.510930i	$0.829301\pi$
$710$		−	16.6378i		−	0.624404i
$711$	−8.65582	+	14.9923i	−0.324619	+	0.562256i
$712$	4.70311	+	8.14602i	0.176256	+	0.305285i
$713$	23.2135	−	13.4023i	0.869353	−	0.501921i
$714$	5.00068			0.187146
$715$	−18.0434	−	64.7488i	−0.674785	−	2.42147i
$716$	−4.55259			−0.170138
$717$	−19.3266	+	11.1582i	−0.721765	+	0.416711i
$718$	−3.92458	−	6.79758i	−0.146464	−	0.253683i
$719$	−3.22839	+	5.59173i	−0.120399	+	0.208536i	−0.919925	−	0.392095i	$-0.871751\pi$
$719$	−3.22839	+	5.59173i	−0.120399	+	0.208536i	0.799526	+	0.600631i	$0.205084\pi$
$720$		−	2.27793i		−	0.0848933i
$721$	1.36876	+	0.790256i	0.0509754	+	0.0294307i
$722$	0.210473	+	0.121517i	0.00783301	+	0.00452239i
$723$		−	21.9939i		−	0.817963i
$724$	14.1743	−	24.5506i	0.526783	−	0.912414i
$725$	−5.15343	−	8.92600i	−0.191394	−	0.331503i
$726$	17.9692	−	10.3745i	0.666898	−	0.385034i
$727$	−6.77208			−0.251162			−0.125581	−	0.992083i	$-0.540080\pi$
$727$	−6.77208			−0.251162			−0.125581	+	0.992083i	$0.540080\pi$
$728$	−6.65410	+	6.78817i	−0.246617	+	0.251586i
$729$	1.00000			0.0370370
$730$	−3.58075	+	2.06735i	−0.132529	+	0.0765159i
$731$	17.0453	+	29.5232i	0.630441	+	1.09196i
$732$	9.45990	−	16.3850i	0.349648	−	0.605608i
$733$		−	14.1788i		−	0.523708i	−0.965108	−	0.261854i	$-0.915666\pi$
$733$		−	14.1788i		−	0.523708i	0.965108	−	0.261854i	$-0.0843338\pi$
$734$	−10.6213	−	6.13222i	−0.392040	−	0.226344i
$735$	−2.62790	−	1.51722i	−0.0969316	−	0.0559635i
$736$		−	52.2424i		−	1.92568i
$737$	−19.5089	+	33.7905i	−0.718621	+	1.24469i
$738$	0.366610	+	0.634988i	0.0134951	+	0.0233742i
$739$	16.7703	−	9.68236i	0.616907	−	0.356172i	−0.158757	−	0.987318i	$-0.550749\pi$
$739$	16.7703	−	9.68236i	0.616907	−	0.356172i	0.775664	+	0.631146i	$0.217415\pi$
$740$	−10.1319			−0.372457
$741$	3.88364	−	15.0945i	0.142669	−	0.554512i
$742$	−3.13152			−0.114962
$743$	22.2969	−	12.8731i	0.817992	−	0.472268i	−0.0317314	−	0.999496i	$-0.510102\pi$
$743$	22.2969	−	12.8731i	0.817992	−	0.472268i	0.849724	+	0.527228i	$0.176769\pi$
$744$	−3.96009	−	6.85908i	−0.145184	−	0.251466i
$745$	−18.1767	+	31.4830i	−0.665943	+	1.15345i
$746$			8.67617i			0.317657i
$747$	−4.32924	−	2.49949i	−0.158399	−	0.0914515i
$748$	−47.9436	−	27.6803i	−1.75299	−	1.01209i
$749$			3.66169i			0.133795i
$750$	0.932508	−	1.61515i	0.0340504	−	0.0589770i
$751$	−9.92820	−	17.1961i	−0.362285	−	0.627496i	0.626051	−	0.779782i	$-0.284670\pi$
$751$	−9.92820	−	17.1961i	−0.362285	−	0.627496i	−0.988337	+	0.152285i	$0.951337\pi$
$752$	0.138461	−	0.0799405i	0.00504915	−	0.00291513i
$753$	−1.49983			−0.0546570
$754$	4.89318	+	4.79654i	0.178199	+	0.174680i
$755$	−48.7209			−1.77313
$756$	−1.21076	+	0.699030i	−0.0440347	+	0.0254235i
$757$	14.9040	+	25.8144i	0.541694	+	0.938242i	0.998807	+	0.0488330i	$0.0155502\pi$
$757$	14.9040	+	25.8144i	0.541694	+	0.938242i	−0.457113	+	0.889409i	$0.651116\pi$
$758$	10.6364	−	18.4228i	0.386331	−	0.669145i
$759$		−	54.8157i		−	1.98968i
$760$	29.9491	+	17.2911i	1.08637	+	0.627214i
$761$	−9.49030	−	5.47923i	−0.344023	−	0.198622i	0.318027	−	0.948082i	$-0.396980\pi$
$761$	−9.49030	−	5.47923i	−0.344023	−	0.198622i	−0.662050	+	0.749460i	$0.730313\pi$
$762$			0.527479i			0.0191085i
$763$	−1.52983	+	2.64975i	−0.0553837	+	0.0959274i
$764$	−16.7228	−	28.9647i	−0.605010	−	1.04791i
$765$	16.9380	−	9.77914i	0.612394	−	0.353566i
$766$	−3.02611			−0.109338
$767$	−4.43712	−	4.34949i	−0.160215	−	0.157051i
$768$	−13.3374			−0.481273
$769$	7.01718	−	4.05137i	0.253046	−	0.146096i	−0.368112	−	0.929781i	$-0.619996\pi$
$769$	7.01718	−	4.05137i	0.253046	−	0.146096i	0.621158	+	0.783685i	$0.286662\pi$
$770$	−7.23181	−	12.5259i	−0.260616	−	0.451401i
$771$	−4.46695	+	7.73699i	−0.160873	+	0.278641i
$772$		−	11.7917i		−	0.424394i
$773$	17.7910	+	10.2716i	0.639898	+	0.369445i	0.784575	−	0.620034i	$-0.212881\pi$
$773$	17.7910	+	10.2716i	0.639898	+	0.369445i	−0.144677	+	0.989479i	$0.546214\pi$
$774$	3.55376	+	2.05176i	0.127737	+	0.0737492i
$775$		−	12.6411i		−	0.454081i
$776$	−2.07610	+	3.59591i	−0.0745277	+	0.129086i
$777$	1.19415	+	2.06833i	0.0428398	+	0.0742008i
$778$	−13.7781	+	7.95478i	−0.493968	+	0.285193i
$779$	4.08531			0.146371
$780$	−3.81133	+	14.8135i	−0.136467	+	0.530407i
$781$	43.4172			1.55359
$782$	38.6405	−	22.3091i	1.38178	−	0.797772i
$783$	1.22473	+	2.12129i	0.0437682	+	0.0758088i
$784$	0.375346	−	0.650117i	0.0134052	−	0.0232185i
$785$		−	57.5241i		−	2.05312i
$786$	−9.65803	−	5.57607i	−0.344490	−	0.198892i
$787$	29.9944	+	17.3173i	1.06919	+	0.617295i	0.927959	−	0.372683i	$-0.121562\pi$
$787$	29.9944	+	17.3173i	1.06919	+	0.617295i	0.141227	+	0.989977i	$0.454895\pi$
$788$		−	33.5193i		−	1.19408i
$789$	5.23118	−	9.06067i	0.186235	−	0.322568i
$790$	20.3781	+	35.2958i	0.725019	+	1.25577i
$791$	10.2003	−	5.88917i	0.362683	−	0.209395i
$792$	−16.1968			−0.575529
$793$	−34.1565	+	34.8446i	−1.21293	+	1.23737i
$794$	−24.0476			−0.853419
$795$	−10.6069	+	6.12388i	−0.376187	+	0.217192i
$796$	−7.28348	−	12.6154i	−0.258156	−	0.447139i
$797$	−19.5351	+	33.8358i	−0.691969	+	1.19853i	0.279223	+	0.960226i	$0.409923\pi$
$797$	−19.5351	+	33.8358i	−0.691969	+	1.19853i	−0.971192	+	0.238299i	$0.923410\pi$
$798$		−	3.35385i		−	0.118725i
$799$	1.18883	+	0.686370i	0.0420577	+	0.0242820i
$800$	−21.3367	−	12.3187i	−0.754366	−	0.435534i
$801$		−	3.56786i		−	0.126064i
$802$	−6.04662	+	10.4731i	−0.213514	+	0.369816i
$803$	−5.39486	−	9.34417i	−0.190381	−	0.329749i
$804$	7.68950	−	4.43954i	0.271188	−	0.156570i
$805$	−27.0745			−0.954252
$806$	2.25591	+	8.09535i	0.0794611	+	0.285147i
$807$	2.91690			0.102680
$808$	−19.5125	+	11.2655i	−0.686447	+	0.396320i
$809$	17.8454	+	30.9091i	0.627410	+	1.08671i	0.988070	+	0.154008i	$0.0492182\pi$
$809$	17.8454	+	30.9091i	0.627410	+	1.08671i	−0.360660	+	0.932697i	$0.617448\pi$
$810$	1.17713	−	2.03885i	0.0413602	−	0.0716379i
$811$		−	34.8691i		−	1.22442i	−0.790696	−	0.612209i	$-0.790281\pi$
$811$		−	34.8691i		−	1.22442i	0.790696	−	0.612209i	$-0.209719\pi$
$812$	−2.96569	−	1.71224i	−0.104075	−	0.0600880i
$813$	−19.6297	−	11.3332i	−0.688444	−	0.397473i
$814$			11.3838i			0.399002i
$815$	−10.9933	+	19.0409i	−0.385077	+	0.666973i
$816$	2.41927	+	4.19029i	0.0846913	+	0.146690i
$817$	19.8006	−	11.4319i	0.692735	−	0.399951i
$818$	14.9049			0.521136
$819$	3.47322	−	0.967872i	0.121364	−	0.0338202i
$820$	−4.00924			−0.140009
$821$	−36.0883	+	20.8356i	−1.25949	+	0.727166i	−0.972975	−	0.230910i	$-0.925830\pi$
$821$	−36.0883	+	20.8356i	−1.25949	+	0.727166i	−0.286514	+	0.958076i	$0.592496\pi$
$822$	−3.94956	−	6.84084i	−0.137757	−	0.238602i
$823$	7.61766	−	13.1942i	0.265535	−	0.459920i	−0.702169	−	0.712011i	$-0.747785\pi$
$823$	7.61766	−	13.1942i	0.265535	−	0.459920i	0.967704	+	0.252091i	$0.0811181\pi$
$824$		−	4.16683i		−	0.145158i
$825$	−22.3877	−	12.9255i	−0.779439	−	0.450009i
$826$	−1.15788	−	0.668502i	−0.0402878	−	0.0232602i
$827$		−	31.0121i		−	1.07839i	−0.842179	−	0.539197i	$-0.818728\pi$
$827$		−	31.0121i		−	1.07839i	0.842179	−	0.539197i	$-0.181272\pi$
$828$	−6.23704	+	10.8029i	−0.216752	+	0.375426i
$829$	−7.11262	−	12.3194i	−0.247031	−	0.427871i	0.715669	−	0.698439i	$-0.246122\pi$
$829$	−7.11262	−	12.3194i	−0.247031	−	0.427871i	−0.962701	+	0.270568i	$0.912788\pi$
$830$	−10.1922	+	5.88446i	−0.353776	+	0.204252i
$831$	−0.227605			−0.00789553
$832$	10.6199	+	2.73236i	0.368177	+	0.0947276i
$833$	6.44544			0.223321
$834$	−8.29970	+	4.79184i	−0.287395	+	0.165928i
$835$	−16.8025	−	29.1028i	−0.581475	−	1.00714i
$836$	−18.5646	+	32.1548i	−0.642069	+	1.11210i
$837$			3.00419i			0.103840i
$838$	14.0092	+	8.08820i	0.483939	+	0.279402i
$839$	11.7558	+	6.78723i	0.405856	+	0.234321i	0.689008	−	0.724754i	$-0.258047\pi$
$839$	11.7558	+	6.78723i	0.405856	+	0.234321i	−0.283151	+	0.959075i	$0.591380\pi$
$840$			7.99993i			0.276024i
$841$	11.5001	−	19.9187i	0.396554	−	0.686853i
$842$	1.28485	+	2.22543i	0.0442790	+	0.0766934i
$843$	−9.66715	+	5.58133i	−0.332954	+	0.192231i
$844$	11.4413			0.393825
$845$	19.0385	−	34.5493i	0.654946	−	1.18853i
$846$	0.165239			0.00568103
$847$	23.1607	−	13.3718i	0.795810	−	0.459461i
$848$	−1.51499	−	2.62404i	−0.0520250	−	0.0901099i
$849$	−10.0339	+	17.3793i	−0.344364	+	0.596456i
$850$		−	21.0419i		−	0.721732i
$851$	18.4545	+	10.6547i	0.632612	+	0.365238i
$852$	−8.55651	−	4.94010i	−0.293141	−	0.169245i
$853$			33.8621i			1.15942i	0.814824	+	0.579708i	$0.196833\pi$
$853$			33.8621i			1.15942i	−0.814824	+	0.579708i	$0.803167\pi$
$854$	−5.24974	+	9.09281i	−0.179642	+	0.311150i
$855$	−6.55866	−	11.3599i	−0.224301	−	0.388502i
$856$	8.36026	−	4.82680i	0.285748	−	0.164977i
$857$	−37.5517			−1.28274			−0.641370	−	0.767232i	$-0.721634\pi$
$857$	−37.5517			−1.28274			−0.641370	+	0.767232i	$0.721634\pi$
$858$	16.6438	+	4.28224i	0.568209	+	0.146193i
$859$	−23.9785			−0.818134			−0.409067	−	0.912504i	$-0.634146\pi$
$859$	−23.9785			−0.818134			−0.409067	+	0.912504i	$0.634146\pi$
$860$	−19.4319	+	11.2190i	−0.662623	+	0.382565i
$861$	0.472528	+	0.818443i	0.0161037	+	0.0278925i
$862$	11.0082	−	19.0668i	0.374942	−	0.649418i
$863$		−	45.2748i		−	1.54117i	−0.637337	−	0.770585i	$-0.719964\pi$
$863$		−	45.2748i		−	1.54117i	0.637337	−	0.770585i	$-0.280036\pi$
$864$	5.07073	+	2.92759i	0.172510	+	0.0995986i
$865$	−12.0266	−	6.94355i	−0.408916	−	0.236088i
$866$			16.4444i			0.558804i
$867$	−12.2718	+	21.2555i	−0.416774	+	0.721873i
$868$	−2.10002	−	3.63734i	−0.0712793	−	0.123459i
$869$	−92.1066	+	53.1778i	−3.12450	+	1.80393i
$870$	5.76667			0.195508
$871$	−22.0584	+	6.14695i	−0.747419	+	0.208282i
$872$	8.06645			0.273164
$873$	1.36396	−	0.787482i	0.0461630	−	0.0266522i
$874$	−14.9622	−	25.9154i	−0.506105	−	0.876600i
$875$	1.20192	−	2.08179i	0.0406323	−	0.0703773i
$876$			2.45535i			0.0829587i
$877$	−14.3496	−	8.28474i	−0.484551	−	0.279756i	0.237760	−	0.971324i	$-0.423587\pi$
$877$	−14.3496	−	8.28474i	−0.484551	−	0.279756i	−0.722311	+	0.691568i	$0.756920\pi$
$878$	−8.44796	−	4.87743i	−0.285105	−	0.164605i
$879$			3.68811i			0.124397i
$880$	6.99731	−	12.1197i	0.235879	−	0.408555i
$881$	2.05956	+	3.56726i	0.0693883	+	0.120184i	0.898632	−	0.438703i	$-0.144562\pi$
$881$	2.05956	+	3.56726i	0.0693883	+	0.120184i	−0.829244	+	0.558887i	$0.811229\pi$
$882$	0.671904	−	0.387924i	0.0226242	−	0.0130621i
$883$	57.7416			1.94316			0.971580	−	0.236710i	$-0.0760692\pi$
$883$	57.7416			1.94316			0.971580	+	0.236710i	$0.0760692\pi$
$884$	−8.72160	−	31.2975i	−0.293339	−	1.05265i
$885$	−5.22919			−0.175777
$886$	−7.20482	+	4.15971i	−0.242051	+	0.139748i
$887$	−25.4452	−	44.0725i	−0.854368	−	1.47981i	−0.877230	−	0.480070i	$-0.840611\pi$
$887$	−25.4452	−	44.0725i	−0.854368	−	1.47981i	0.0228627	−	0.999739i	$-0.492722\pi$
$888$	3.14823	−	5.45289i	0.105648	−	0.182987i
$889$			0.679874i			0.0228022i
$890$	−7.27433	−	4.19983i	−0.243836	−	0.140779i
$891$	5.32050	+	3.07179i	0.178243	+	0.102909i
$892$			10.6692i			0.357231i
$893$	0.460334	−	0.797321i	0.0154045	−	0.0266813i
$894$	−4.64744	−	8.04960i	−0.155434	−	0.269219i
$895$	8.55739	−	4.94061i	0.286042	−	0.165146i
$896$	−9.35073			−0.312386
$897$	22.5198	−	22.9735i	0.751915	−	0.767064i
$898$	−8.67811			−0.289592
$899$	−6.37276	+	3.67932i	−0.212544	+	0.122712i
$900$	2.94139	+	5.09463i	0.0980462	+	0.169821i
$901$	13.0077	−	22.5300i	0.433350	−	0.750584i
$902$			4.50460i			0.149987i
$903$	4.58049	+	2.64454i	0.152429	+	0.0880049i
$904$	−26.8920	−	15.5261i	−0.894413	−	0.516390i
$905$			61.5295i			2.04531i
$906$	6.22850	−	10.7881i	0.206928	−	0.358410i
$907$	−28.6763	−	49.6687i	−0.952179	−	1.64922i	−0.740695	−	0.671842i	$-0.765503\pi$
$907$	−28.6763	−	49.6687i	−0.952179	−	1.64922i	−0.211485	−	0.977381i	$-0.567830\pi$
$908$	10.2235	−	5.90255i	0.339279	−	0.195883i
$909$	8.54623			0.283460
$910$	2.11508	−	8.22068i	0.0701143	−	0.272513i
$911$	35.1349			1.16407			0.582036	−	0.813163i	$-0.302256\pi$
$911$	35.1349			1.16407			0.582036	+	0.813163i	$0.302256\pi$
$912$	2.81034	−	1.62255i	0.0930596	−	0.0537280i
$913$	−15.3558	−	26.5971i	−0.508204	−	0.880235i
$914$	−0.970416	+	1.68081i	−0.0320985	+	0.0555962i
$915$			41.0648i			1.35756i
$916$	23.4519	+	13.5400i	0.774873	+	0.447373i
$917$	−12.4484	−	7.18706i	−0.411081	−	0.237338i
$918$			5.00068i			0.165047i
$919$	−8.54835	+	14.8062i	−0.281984	+	0.488411i	−0.971873	−	0.235504i	$-0.924326\pi$
$919$	−8.54835	+	14.8062i	−0.281984	+	0.488411i	0.689889	+	0.723915i	$0.257659\pi$
$920$	35.6894	+	61.8158i	1.17664	+	2.03801i
$921$	−22.1079	+	12.7640i	−0.728479	+	0.420587i
$922$	6.77572			0.223147
$923$	18.1964	+	17.8370i	0.598941	+	0.587112i
$924$	−8.58910			−0.282561
$925$	8.70313	−	5.02475i	0.286157	−	0.165213i
$926$	−4.68767	−	8.11929i	−0.154046	−	0.266816i
$927$	−0.790256	+	1.36876i	−0.0259554	+	0.0449561i
$928$			14.3420i			0.470799i
$929$	−25.6752	−	14.8236i	−0.842376	−	0.486346i	0.0156953	−	0.999877i	$-0.495004\pi$
$929$	−25.6752	−	14.8236i	−0.842376	−	0.486346i	−0.858071	+	0.513531i	$0.828337\pi$
$930$	6.12510	+	3.53633i	0.200850	+	0.115961i
$931$		−	4.32282i		−	0.141675i
$932$	2.18377	−	3.78239i	0.0715316	−	0.123896i
$933$	−7.89588	−	13.6761i	−0.258500	−	0.447734i
$934$	2.31633	−	1.33733i	0.0757925	−	0.0437588i
$935$	120.158			3.92959
$936$	−6.78817	−	6.65410i	−0.221878	−	0.217496i
$937$	−6.82549			−0.222979			−0.111489	−	0.993766i	$-0.535562\pi$
$937$	−6.82549			−0.222979			−0.111489	+	0.993766i	$0.535562\pi$
$938$	−4.26726	+	2.46370i	−0.139331	+	0.0804428i
$939$	−2.10604	−	3.64777i	−0.0687281	−	0.119041i
$940$	−0.451762	+	0.782475i	−0.0147349	+	0.0255215i
$941$			44.6666i			1.45609i	0.685529	+	0.728045i	$0.259571\pi$
$941$			44.6666i			1.45609i	−0.685529	+	0.728045i	$0.740429\pi$
$942$	12.7373	+	7.35391i	0.415005	+	0.239603i
$943$	7.30250	+	4.21610i	0.237802	+	0.137295i
$944$		−	1.29365i		−	0.0421048i
$945$	1.51722	−	2.62790i	0.0493551	−	0.0854856i
$946$	12.6052	+	21.8328i	0.409830	+	0.709847i
$947$	47.7725	−	27.5815i	1.55240	−	0.896278i	0.554452	−	0.832215i	$-0.312928\pi$
$947$	47.7725	−	27.5815i	1.55240	−	0.896278i	0.997946	−	0.0640622i	$-0.0204056\pi$
$948$	24.2027			0.786067
$949$	1.57783	−	6.13255i	0.0512186	−	0.199071i
$950$	−14.1124			−0.457866
$951$	20.4770	−	11.8224i	0.664011	−	0.383367i
$952$	−8.49631	−	14.7160i	−0.275367	−	0.476950i
$953$	−14.6513	+	25.3768i	−0.474602	+	0.822035i	−0.999577	−	0.0290830i	$-0.990741\pi$
$953$	−14.6513	+	25.3768i	−0.474602	+	0.822035i	0.524975	+	0.851118i	$0.324075\pi$
$954$		−	3.13152i		−	0.101387i
$955$	62.8669	+	36.2962i	2.03433	+	1.17452i
$956$	27.0197	+	15.5998i	0.873881	+	0.504535i
$957$			15.0484i			0.486447i
$958$	−4.90740	+	8.49986i	−0.158551	+	0.274618i
$959$	−5.09063	−	8.81724i	−0.164385	−	0.284723i
$960$	7.99236	−	4.61439i	0.257952	−	0.148929i
$961$	21.9748			0.708866
$962$	−4.67678	+	4.77101i	−0.150785	+	0.153823i
$963$	−3.66169			−0.117996
$964$	−26.6293	+	15.3744i	−0.857671	+	0.495176i
$965$	12.7968	+	22.1647i	0.411943	+	0.713506i
$966$	3.46122	−	5.99501i	0.111363	−	0.192886i
$967$			7.07095i			0.227387i	0.993516	+	0.113693i	$0.0362681\pi$
$967$			7.07095i			0.227387i	−0.993516	+	0.113693i	$0.963732\pi$
$968$	−61.0603	−	35.2532i	−1.96255	−	1.13308i
$969$	24.1296	+	13.9312i	0.775154	+	0.447536i
$970$		−	3.70788i		−	0.119053i
$971$	−3.64851	+	6.31940i	−0.117086	+	0.202799i	−0.918612	−	0.395161i	$-0.870689\pi$
$971$	−3.64851	+	6.31940i	−0.117086	+	0.202799i	0.801526	+	0.597961i	$0.204022\pi$
$972$	−0.699030	−	1.21076i	−0.0224214	−	0.0388350i
$973$	−10.6976	+	6.17626i	−0.342949	+	0.198002i
$974$	5.98644			0.191818
$975$	−4.07263	−	14.6146i	−0.130428	−	0.468043i
$976$	−10.1590			−0.325183
$977$	15.2846	−	8.82457i	0.488998	−	0.282323i	−0.235161	−	0.971956i	$-0.575562\pi$
$977$	15.2846	−	8.82457i	0.488998	−	0.282323i	0.724159	+	0.689634i	$0.242228\pi$
$978$	−2.81077	−	4.86839i	−0.0898785	−	0.155674i
$979$	10.9597	−	18.9828i	0.350274	−	0.606692i
$980$			4.24233i			0.135516i
$981$	−2.64975	−	1.52983i	−0.0846001	−	0.0488439i
$982$	−3.12848	−	1.80623i	−0.0998337	−	0.0576390i
$983$		−	36.1510i		−	1.15304i	−0.817083	−	0.576520i	$-0.804410\pi$
$983$		−	36.1510i		−	1.15304i	0.817083	−	0.576520i	$-0.195590\pi$
$984$	1.24576	−	2.15773i	0.0397135	−	0.0687858i
$985$	36.3762	+	63.0055i	1.15904	+	2.00752i
$986$	−10.6079	+	6.12448i	−0.337825	+	0.195043i
$987$	0.212978			0.00677918
$988$	−20.9906	+	5.84939i	−0.667799	+	0.186094i
$989$	47.1915			1.50060
$990$	12.5259	−	7.23181i	0.398098	−	0.229842i
$991$	1.09938	+	1.90418i	0.0349230	+	0.0604884i	0.882959	−	0.469451i	$-0.155548\pi$
$991$	1.09938	+	1.90418i	0.0349230	+	0.0604884i	−0.848036	+	0.529939i	$0.822215\pi$
$992$	−8.79503	+	15.2334i	−0.279243	+	0.483662i
$993$		−	3.54791i		−	0.112590i
$994$	4.74840	+	2.74149i	0.150610	+	0.0869548i
$995$	27.3812	+	15.8085i	0.868041	+	0.501164i
$996$			6.98887i			0.221451i
$997$	18.2244	−	31.5655i	0.577171	−	0.999690i	−0.418631	−	0.908156i	$-0.637490\pi$
$997$	18.2244	−	31.5655i	0.577171	−	0.999690i	0.995802	−	0.0915332i	$-0.0291768\pi$
$998$	−12.5784	−	21.7864i	−0.398162	−	0.689638i
$999$	−2.06833	+	1.19415i	−0.0654389	+	0.0377812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.a.127.3	yes	16
3.2	odd	2		819.2.ct.b.127.6		16
13.2	odd	12		3549.2.a.bd.1.3		8
13.4	even	6	inner	273.2.bd.a.43.3	✓	16
13.11	odd	12		3549.2.a.bb.1.6		8
39.17	odd	6		819.2.ct.b.316.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.3	✓	16	13.4	even	6	inner
273.2.bd.a.127.3	yes	16	1.1	even	1	trivial
819.2.ct.b.127.6		16	3.2	odd	2
819.2.ct.b.316.6		16	39.17	odd	6
3549.2.a.bb.1.6		8	13.11	odd	12
3549.2.a.bd.1.3		8	13.2	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.671904 + 0.387924i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.699030 + 1.21076i) q^{4} -3.03444i q^{5} +(0.671904 + 0.387924i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.63638i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.671904 + 0.387924i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.699030 + 1.21076i) q^{4} -3.03444i q^{5} +(0.671904 + 0.387924i) q^{6} +(0.866025 + 0.500000i) q^{7} -2.63638i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.17713 + 2.03885i) q^{10} +(-5.32050 + 3.07179i) q^{11} +1.39806 q^{12} +(-3.49183 - 0.898406i) q^{13} -0.775848 q^{14} +(-2.62790 + 1.51722i) q^{15} +(-0.375346 - 0.650117i) q^{16} +(3.22272 - 5.58191i) q^{17} -0.775848i q^{18} +(-3.74367 - 2.16141i) q^{19} +(3.67396 + 2.12116i) q^{20} -1.00000i q^{21} +(2.38324 - 4.12790i) q^{22} +(-4.46121 - 7.72705i) q^{23} +(-2.28317 + 1.31819i) q^{24} -4.20781 q^{25} +(2.69469 - 0.750922i) q^{26} +1.00000 q^{27} +(-1.21076 + 0.699030i) q^{28} +(1.22473 + 2.12129i) q^{29} +(1.17713 - 2.03885i) q^{30} +3.00419i q^{31} +(5.07073 + 2.92759i) q^{32} +(5.32050 + 3.07179i) q^{33} +5.00068i q^{34} +(1.51722 - 2.62790i) q^{35} +(-0.699030 - 1.21076i) q^{36} +(-2.06833 + 1.19415i) q^{37} +3.35385 q^{38} +(0.967872 + 3.47322i) q^{39} -7.99993 q^{40} +(-0.818443 + 0.472528i) q^{41} +(0.387924 + 0.671904i) q^{42} +(-2.64454 + 4.58049i) q^{43} -8.58910i q^{44} +(2.62790 + 1.51722i) q^{45} +(5.99501 + 3.46122i) q^{46} +0.212978i q^{47} +(-0.375346 + 0.650117i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.82725 - 1.63231i) q^{50} -6.44544 q^{51} +(3.52864 - 3.59974i) q^{52} +4.03626 q^{53} +(-0.671904 + 0.387924i) q^{54} +(9.32116 + 16.1447i) q^{55} +(1.31819 - 2.28317i) q^{56} +4.32282i q^{57} +(-1.64580 - 0.950203i) q^{58} +(1.49241 + 0.861641i) q^{59} -4.24233i q^{60} +(6.76645 - 11.7198i) q^{61} +(-1.16540 - 2.01853i) q^{62} +(-0.866025 + 0.500000i) q^{63} -3.04135 q^{64} +(-2.72616 + 10.5957i) q^{65} -4.76649 q^{66} +(5.50012 - 3.17550i) q^{67} +(4.50556 + 7.80385i) q^{68} +(-4.46121 + 7.72705i) q^{69} +2.35426i q^{70} +(-6.12027 - 3.53354i) q^{71} +(2.28317 + 1.31819i) q^{72} +1.75626i q^{73} +(0.926478 - 1.60471i) q^{74} +(2.10391 + 3.64407i) q^{75} +(5.23387 - 3.02178i) q^{76} -6.14359 q^{77} +(-1.99766 - 1.95821i) q^{78} +17.3116 q^{79} +(-1.97274 + 1.13896i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.366610 - 0.634988i) q^{82} +4.99898i q^{83} +(1.21076 + 0.699030i) q^{84} +(-16.9380 - 9.77914i) q^{85} -4.10353i q^{86} +(1.22473 - 2.12129i) q^{87} +(8.09841 + 14.0269i) q^{88} +(-3.08985 + 1.78393i) q^{89} -2.35426 q^{90} +(-2.57481 - 2.52396i) q^{91} +12.4741 q^{92} +(2.60171 - 1.50210i) q^{93} +(-0.0826195 - 0.143101i) q^{94} +(-6.55866 + 11.3599i) q^{95} -5.85518i q^{96} +(-1.36396 - 0.787482i) q^{97} +(-0.671904 - 0.387924i) q^{98} -6.14359i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

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