LMFDB - Embedded newform 273.2.cg.b.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	273.19
Dual form			273.2.cg.b.115.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18205 + 0.584679i) q^{2} +1.00000i q^{3} +(2.68745 + 1.55160i) q^{4} +(2.27456 - 0.609466i) q^{5} +(-0.584679 + 2.18205i) q^{6} +(-2.33957 + 1.23548i) q^{7} +(1.76223 + 1.76223i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(2.18205 + 0.584679i) q^{2} +1.00000i q^{3} +(2.68745 + 1.55160i) q^{4} +(2.27456 - 0.609466i) q^{5} +(-0.584679 + 2.18205i) q^{6} +(-2.33957 + 1.23548i) q^{7} +(1.76223 + 1.76223i) q^{8} -1.00000 q^{9} +5.31955 q^{10} +(-3.57017 - 3.57017i) q^{11} +(-1.55160 + 2.68745i) q^{12} +(1.62322 - 3.21950i) q^{13} +(-5.82743 + 1.32798i) q^{14} +(0.609466 + 2.27456i) q^{15} +(-0.288264 - 0.499288i) q^{16} +(-2.64387 + 4.57931i) q^{17} +(-2.18205 - 0.584679i) q^{18} +(2.98754 + 2.98754i) q^{19} +(7.05842 + 1.89130i) q^{20} +(-1.23548 - 2.33957i) q^{21} +(-5.70290 - 9.87771i) q^{22} +(3.44956 - 1.99161i) q^{23} +(-1.76223 + 1.76223i) q^{24} +(0.472034 - 0.272529i) q^{25} +(5.42433 - 6.07604i) q^{26} -1.00000i q^{27} +(-8.20446 - 0.309797i) q^{28} +(0.565030 - 0.978660i) q^{29} +5.31955i q^{30} +(-1.40198 + 5.23228i) q^{31} +(-1.62713 - 6.07252i) q^{32} +(3.57017 - 3.57017i) q^{33} +(-8.44649 + 8.44649i) q^{34} +(-4.56851 + 4.23605i) q^{35} +(-2.68745 - 1.55160i) q^{36} +(1.37587 - 5.13480i) q^{37} +(4.77222 + 8.26572i) q^{38} +(3.21950 + 1.62322i) q^{39} +(5.08231 + 2.93428i) q^{40} +(5.61474 - 1.50446i) q^{41} +(-1.32798 - 5.82743i) q^{42} +(-9.65143 + 5.57225i) q^{43} +(-4.05519 - 15.1342i) q^{44} +(-2.27456 + 0.609466i) q^{45} +(8.69158 - 2.32890i) q^{46} +(1.95174 + 7.28399i) q^{47} +(0.499288 - 0.288264i) q^{48} +(3.94719 - 5.78098i) q^{49} +(1.18935 - 0.318684i) q^{50} +(-4.57931 - 2.64387i) q^{51} +(9.35771 - 6.13365i) q^{52} +(-0.538076 - 0.931975i) q^{53} +(0.584679 - 2.18205i) q^{54} +(-10.2965 - 5.94466i) q^{55} +(-6.30006 - 1.94567i) q^{56} +(-2.98754 + 2.98754i) q^{57} +(1.80513 - 1.80513i) q^{58} +(-2.18873 - 8.16845i) q^{59} +(-1.89130 + 7.05842i) q^{60} -3.15666i q^{61} +(-6.11841 + 10.5974i) q^{62} +(2.33957 - 1.23548i) q^{63} -13.0488i q^{64} +(1.72994 - 8.31222i) q^{65} +(9.87771 - 5.70290i) q^{66} +(-3.75730 + 3.75730i) q^{67} +(-14.2105 + 8.20446i) q^{68} +(1.99161 + 3.44956i) q^{69} +(-12.4455 + 6.57218i) q^{70} +(12.9802 + 3.47804i) q^{71} +(-1.76223 - 1.76223i) q^{72} +(1.56120 + 0.418321i) q^{73} +(6.00443 - 10.4000i) q^{74} +(0.272529 + 0.472034i) q^{75} +(3.39340 + 12.6644i) q^{76} +(12.7635 + 3.94181i) q^{77} +(6.07604 + 5.42433i) q^{78} +(-6.31940 + 10.9455i) q^{79} +(-0.959971 - 0.959971i) q^{80} +1.00000 q^{81} +13.1313 q^{82} +(-7.21679 - 7.21679i) q^{83} +(0.309797 - 8.20446i) q^{84} +(-3.22269 + 12.0273i) q^{85} +(-24.3179 + 6.51596i) q^{86} +(0.978660 + 0.565030i) q^{87} -12.5829i q^{88} +(8.63520 + 2.31379i) q^{89} -5.31955 q^{90} +(0.179969 + 9.53769i) q^{91} +12.3607 q^{92} +(-5.23228 - 1.40198i) q^{93} +17.0352i q^{94} +(8.61613 + 4.97453i) q^{95} +(6.07252 - 1.62713i) q^{96} +(-4.32019 + 16.1232i) q^{97} +(11.9930 - 10.3066i) q^{98} +(3.57017 + 3.57017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.18205	+	0.584679i	1.54294	+	0.413431i	0.927216	−	0.374528i	$-0.122195\pi$
$2$	2.18205	+	0.584679i	1.54294	+	0.413431i	0.615729	+	0.787958i	$0.288862\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	2.68745	+	1.55160i	1.34373	+	0.775801i
$5$	2.27456	−	0.609466i	1.01721	−	0.272561i	0.288573	−	0.957458i	$-0.406819\pi$
$5$	2.27456	−	0.609466i	1.01721	−	0.272561i	0.728640	+	0.684897i	$0.240153\pi$
$6$	−0.584679	+	2.18205i	−0.238694	+	0.890819i
$7$	−2.33957	+	1.23548i	−0.884275	+	0.466967i
$7$	−2.33957	+	1.23548i	−0.884275	+	0.466967i
$8$	1.76223	+	1.76223i	0.623043	+	0.623043i
$9$	−1.00000			−0.333333
$10$	5.31955			1.68219
$11$	−3.57017	−	3.57017i	−1.07645	−	1.07645i	−0.996825	−	0.0796226i	$-0.974628\pi$
$11$	−3.57017	−	3.57017i	−1.07645	−	1.07645i	−0.0796226	−	0.996825i	$-0.525372\pi$
$12$	−1.55160	+	2.68745i	−0.447909	+	0.775801i
$13$	1.62322	−	3.21950i	0.450201	−	0.892927i
$13$	1.62322	−	3.21950i	0.450201	−	0.892927i
$14$	−5.82743	+	1.32798i	−1.55745	+	0.354917i
$15$	0.609466	+	2.27456i	0.157363	+	0.587288i
$16$	−0.288264	−	0.499288i	−0.0720660	−	0.124822i
$17$	−2.64387	+	4.57931i	−0.641232	+	1.11065i	0.343926	+	0.938997i	$0.388243\pi$
$17$	−2.64387	+	4.57931i	−0.641232	+	1.11065i	−0.985158	+	0.171650i	$0.945090\pi$
$18$	−2.18205	−	0.584679i	−0.514315	−	0.137810i
$19$	2.98754	+	2.98754i	0.685389	+	0.685389i	0.961209	−	0.275820i	$-0.0889495\pi$
$19$	2.98754	+	2.98754i	0.685389	+	0.685389i	−0.275820	+	0.961209i	$0.588950\pi$
$20$	7.05842	+	1.89130i	1.57831	+	0.422907i
$21$	−1.23548	−	2.33957i	−0.269603	−	0.510536i
$22$	−5.70290	−	9.87771i	−1.21586	−	2.10594i
$23$	3.44956	−	1.99161i	0.719283	−	0.415278i	−0.0952055	−	0.995458i	$-0.530351\pi$
$23$	3.44956	−	1.99161i	0.719283	−	0.415278i	0.814489	+	0.580179i	$0.197017\pi$
$24$	−1.76223	+	1.76223i	−0.359714	+	0.359714i
$25$	0.472034	−	0.272529i	0.0944069	−	0.0545058i
$26$	5.42433	−	6.07604i	1.06380	−	1.19161i
$27$		−	1.00000i		−	0.192450i
$28$	−8.20446	−	0.309797i	−1.55050	−	0.0585460i
$29$	0.565030	−	0.978660i	0.104923	−	0.181733i	−0.808784	−	0.588106i	$-0.799874\pi$
$29$	0.565030	−	0.978660i	0.104923	−	0.181733i	0.913707	+	0.406374i	$0.133207\pi$
$30$			5.31955i			0.971212i
$31$	−1.40198	+	5.23228i	−0.251804	+	0.939745i	0.718037	+	0.696005i	$0.245041\pi$
$31$	−1.40198	+	5.23228i	−0.251804	+	0.939745i	−0.969841	+	0.243740i	$0.921626\pi$
$32$	−1.62713	−	6.07252i	−0.287638	−	1.07348i
$33$	3.57017	−	3.57017i	0.621487	−	0.621487i
$34$	−8.44649	+	8.44649i	−1.44856	+	1.44856i
$35$	−4.56851	+	4.23605i	−0.772219	+	0.716024i
$36$	−2.68745	−	1.55160i	−0.447909	−	0.258600i
$37$	1.37587	−	5.13480i	0.226191	−	0.844156i	−0.755733	−	0.654880i	$-0.772719\pi$
$37$	1.37587	−	5.13480i	0.226191	−	0.844156i	0.981924	−	0.189276i	$-0.0606142\pi$
$38$	4.77222	+	8.26572i	0.774156	+	1.34088i
$39$	3.21950	+	1.62322i	0.515532	+	0.259924i
$40$	5.08231	+	2.93428i	0.803584	+	0.463950i
$41$	5.61474	−	1.50446i	0.876875	−	0.234958i	0.207817	−	0.978168i	$-0.433364\pi$
$41$	5.61474	−	1.50446i	0.876875	−	0.234958i	0.669058	+	0.743210i	$0.266698\pi$
$42$	−1.32798	−	5.82743i	−0.204911	−	0.899192i
$43$	−9.65143	+	5.57225i	−1.47183	+	0.849761i	−0.999499	−	0.0316610i	$-0.989920\pi$
$43$	−9.65143	+	5.57225i	−1.47183	+	0.849761i	−0.472330	+	0.881422i	$0.656587\pi$
$44$	−4.05519	−	15.1342i	−0.611343	−	2.28156i
$45$	−2.27456	+	0.609466i	−0.339071	+	0.0908538i
$46$	8.69158	−	2.32890i	1.28150	−	0.343378i
$47$	1.95174	+	7.28399i	0.284691	+	1.06248i	0.949065	+	0.315080i	$0.102031\pi$
$47$	1.95174	+	7.28399i	0.284691	+	1.06248i	−0.664375	+	0.747400i	$0.731302\pi$
$48$	0.499288	−	0.288264i	0.0720660	−	0.0416073i
$49$	3.94719	−	5.78098i	0.563885	−	0.825854i
$50$	1.18935	−	0.318684i	0.168199	−	0.0450688i
$51$	−4.57931	−	2.64387i	−0.641232	−	0.370215i
$52$	9.35771	−	6.13365i	1.29768	−	0.850584i
$53$	−0.538076	−	0.931975i	−0.0739104	−	0.128017i	0.826702	−	0.562641i	$-0.190215\pi$
$53$	−0.538076	−	0.931975i	−0.0739104	−	0.128017i	−0.900612	+	0.434624i	$0.856881\pi$
$54$	0.584679	−	2.18205i	0.0795648	−	0.296940i
$55$	−10.2965	−	5.94466i	−1.38837	−	0.801578i
$56$	−6.30006	−	1.94567i	−0.841881	−	0.260001i
$57$	−2.98754	+	2.98754i	−0.395709	+	0.395709i
$58$	1.80513	−	1.80513i	0.237025	−	0.237025i
$59$	−2.18873	−	8.16845i	−0.284948	−	1.06344i	−0.948877	−	0.315645i	$-0.897779\pi$
$59$	−2.18873	−	8.16845i	−0.284948	−	1.06344i	0.663929	−	0.747796i	$-0.268888\pi$
$60$	−1.89130	+	7.05842i	−0.244165	+	0.911238i
$61$		−	3.15666i		−	0.404169i	−0.979368	−	0.202085i	$-0.935228\pi$
$61$		−	3.15666i		−	0.404169i	0.979368	−	0.202085i	$-0.0647716\pi$
$62$	−6.11841	+	10.5974i	−0.777039	+	1.34587i
$63$	2.33957	−	1.23548i	0.294758	−	0.155656i
$64$		−	13.0488i		−	1.63111i
$65$	1.72994	−	8.31222i	0.214573	−	1.03100i
$66$	9.87771	−	5.70290i	1.21586	−	0.701979i
$67$	−3.75730	+	3.75730i	−0.459027	+	0.459027i	−0.898336	−	0.439309i	$-0.855223\pi$
$67$	−3.75730	+	3.75730i	−0.459027	+	0.459027i	0.439309	+	0.898336i	$0.355223\pi$
$68$	−14.2105	+	8.20446i	−1.72328	+	0.994937i
$69$	1.99161	+	3.44956i	0.239761	+	0.415278i
$70$	−12.4455	+	6.57218i	−1.48752	+	0.785526i
$71$	12.9802	+	3.47804i	1.54047	+	0.412767i	0.926417	−	0.376498i	$-0.122872\pi$
$71$	12.9802	+	3.47804i	1.54047	+	0.412767i	0.614052	+	0.789266i	$0.289539\pi$
$72$	−1.76223	−	1.76223i	−0.207681	−	0.207681i
$73$	1.56120	+	0.418321i	0.182724	+	0.0489608i	0.349021	−	0.937115i	$-0.386514\pi$
$73$	1.56120	+	0.418321i	0.182724	+	0.0489608i	−0.166297	+	0.986076i	$0.553181\pi$
$74$	6.00443	−	10.4000i	0.698000	−	1.20897i
$75$	0.272529	+	0.472034i	0.0314690	+	0.0545058i
$76$	3.39340	+	12.6644i	0.389250	+	1.45270i
$77$	12.7635	+	3.94181i	1.45454	+	0.449211i
$78$	6.07604	+	5.42433i	0.687977	+	0.614184i
$79$	−6.31940	+	10.9455i	−0.710988	+	1.23147i	0.253498	+	0.967336i	$0.418419\pi$
$79$	−6.31940	+	10.9455i	−0.710988	+	1.23147i	−0.964486	+	0.264132i	$0.914914\pi$
$80$	−0.959971	−	0.959971i	−0.107328	−	0.107328i
$81$	1.00000			0.111111
$82$	13.1313			1.45011
$83$	−7.21679	−	7.21679i	−0.792145	−	0.792145i	0.189697	−	0.981843i	$-0.439249\pi$
$83$	−7.21679	−	7.21679i	−0.792145	−	0.792145i	−0.981843	+	0.189697i	$0.939249\pi$
$84$	0.309797	−	8.20446i	0.0338016	−	0.895180i
$85$	−3.22269	+	12.0273i	−0.349550	+	1.30454i
$86$	−24.3179	+	6.51596i	−2.62227	+	0.702634i
$87$	0.978660	+	0.565030i	0.104923	+	0.0605776i
$88$		−	12.5829i		−	1.34135i
$89$	8.63520	+	2.31379i	0.915329	+	0.245262i	0.685588	−	0.727990i	$-0.259545\pi$
$89$	8.63520	+	2.31379i	0.915329	+	0.245262i	0.229741	+	0.973252i	$0.426212\pi$
$90$	−5.31955			−0.560729
$91$	0.179969	+	9.53769i	0.0188658	+	0.999822i
$92$	12.3607			1.28869
$93$	−5.23228	−	1.40198i	−0.542562	−	0.145379i
$94$			17.0352i			1.75705i
$95$	8.61613	+	4.97453i	0.883997	+	0.510376i
$96$	6.07252	−	1.62713i	0.619774	−	0.166068i
$97$	−4.32019	+	16.1232i	−0.438649	+	1.63706i	0.293531	+	0.955950i	$0.405170\pi$
$97$	−4.32019	+	16.1232i	−0.438649	+	1.63706i	−0.732180	+	0.681111i	$0.761497\pi$
$98$	11.9930	−	10.3066i	1.21148	−	1.04112i
$99$	3.57017	+	3.57017i	0.358816	+	0.358816i
$100$	1.69143			0.169143
$101$	0.765232			0.0761434			0.0380717	−	0.999275i	$-0.487878\pi$
$101$	0.765232			0.0761434			0.0380717	+	0.999275i	$0.487878\pi$
$102$	−8.44649	−	8.44649i	−0.836327	−	0.836327i
$103$	2.76861	−	4.79537i	0.272799	−	0.472502i	−0.696778	−	0.717287i	$-0.745384\pi$
$103$	2.76861	−	4.79537i	0.272799	−	0.472502i	0.969578	+	0.244784i	$0.0787172\pi$
$104$	8.53399	−	2.81300i	0.836826	−	0.275838i
$105$	−4.23605	−	4.56851i	−0.413396	−	0.445841i
$106$	−0.629204	−	2.34822i	−0.0611137	−	0.228079i
$107$	3.87296	+	6.70816i	0.374413	+	0.648502i	0.990239	−	0.139380i	$-0.0445110\pi$
$107$	3.87296	+	6.70816i	0.374413	+	0.648502i	−0.615826	+	0.787882i	$0.711178\pi$
$108$	1.55160	−	2.68745i	0.149303	−	0.258600i
$109$	−10.8053	−	2.89526i	−1.03496	−	0.277316i	−0.298935	−	0.954273i	$-0.596631\pi$
$109$	−10.8053	−	2.89526i	−1.03496	−	0.277316i	−0.736022	+	0.676958i	$0.763298\pi$
$110$	−18.9917	−	18.9917i	−1.81079	−	1.81079i
$111$	5.13480	+	1.37587i	0.487374	+	0.130591i
$112$	1.29127	+	0.811976i	0.122014	+	0.0767245i
$113$	4.62961	+	8.01871i	0.435517	+	0.754337i	0.997338	−	0.0729218i	$-0.0232324\pi$
$113$	4.62961	+	8.01871i	0.435517	+	0.754337i	−0.561821	+	0.827259i	$0.689899\pi$
$114$	−8.26572	+	4.77222i	−0.774156	+	0.446959i
$115$	6.63241	−	6.63241i	0.618475	−	0.618475i
$116$	3.03698	−	1.75340i	0.281977	−	0.162799i
$117$	−1.62322	+	3.21950i	−0.150067	+	0.297642i
$118$		−	19.1037i		−	1.75864i
$119$	0.527881	−	13.9801i	0.0483907	−	1.28155i
$120$	−2.93428	+	5.08231i	−0.267861	+	0.463950i
$121$			14.4923i			1.31748i
$122$	1.84564	−	6.88801i	0.167096	−	0.623611i
$123$	1.50446	+	5.61474i	0.135653	+	0.506264i
$124$	−11.8862	+	11.8862i	−1.06741	+	1.06741i
$125$	−7.41788	+	7.41788i	−0.663476	+	0.663476i
$126$	5.82743	−	1.32798i	0.519149	−	0.118306i
$127$	−0.963214	−	0.556112i	−0.0854714	−	0.0493470i	0.456655	−	0.889644i	$-0.349047\pi$
$127$	−0.963214	−	0.556112i	−0.0854714	−	0.0493470i	−0.542127	+	0.840297i	$0.682381\pi$
$128$	4.37514	−	16.3282i	0.386711	−	1.44323i
$129$	−5.57225	−	9.65143i	−0.490610	−	0.849761i
$130$	8.63481	−	17.1263i	0.757323	−	1.50207i
$131$	−1.01316	−	0.584948i	−0.0885201	−	0.0511071i	0.455087	−	0.890447i	$-0.349608\pi$
$131$	−1.01316	−	0.584948i	−0.0885201	−	0.0511071i	−0.543607	+	0.839340i	$0.682942\pi$
$132$	15.1342	−	4.05519i	1.31726	−	0.352959i
$133$	−10.6806	−	3.29853i	−0.926126	−	0.286019i
$134$	−10.3954	+	6.00180i	−0.898028	+	0.518477i
$135$	−0.609466	−	2.27456i	−0.0524545	−	0.195763i
$136$	−12.7289	+	3.41070i	−1.09150	+	0.292465i
$137$	11.8263	−	3.16885i	1.01039	−	0.270733i	0.284597	−	0.958647i	$-0.408140\pi$
$137$	11.8263	−	3.16885i	1.01039	−	0.270733i	0.725792	+	0.687914i	$0.241473\pi$
$138$	2.32890	+	8.69158i	0.198249	+	0.739876i
$139$	−17.4448	+	10.0718i	−1.47965	+	0.854276i	−0.999735	−	0.0230384i	$-0.992666\pi$
$139$	−17.4448	+	10.0718i	−1.47965	+	0.854276i	−0.479915	+	0.877315i	$0.659333\pi$
$140$	−18.8503	+	4.29569i	−1.59314	+	0.363052i
$141$	−7.28399	+	1.95174i	−0.613423	+	0.164366i
$142$	26.2900	+	15.1785i	2.20621	+	1.27375i
$143$	−17.2893	+	5.69897i	−1.44581	+	0.476572i
$144$	0.288264	+	0.499288i	0.0240220	+	0.0416073i
$145$	0.688733	−	2.57039i	0.0571961	−	0.213459i
$146$	3.16203	+	1.82560i	0.261691	+	0.151088i
$147$	5.78098	+	3.94719i	0.476807	+	0.325559i
$148$	11.6648	−	11.6648i	0.958837	−	0.958837i
$149$	11.1605	−	11.1605i	0.914302	−	0.914302i	−0.0823053	−	0.996607i	$-0.526228\pi$
$149$	11.1605	−	11.1605i	0.914302	−	0.914302i	0.996607	+	0.0823053i	$0.0262283\pi$
$150$	0.318684	+	1.18935i	0.0260205	+	0.0971097i
$151$	4.18906	−	15.6338i	0.340901	−	1.27226i	−0.556428	−	0.830896i	$-0.687828\pi$
$151$	4.18906	−	15.6338i	0.340901	−	1.27226i	0.897329	−	0.441363i	$-0.145505\pi$
$152$			10.5295i			0.854053i
$153$	2.64387	−	4.57931i	0.213744	−	0.370215i
$154$	25.5460	+	16.0638i	2.05856	+	1.29446i
$155$			12.7556i			1.02455i
$156$	6.13365	+	9.35771i	0.491085	+	0.749217i
$157$	7.65145	−	4.41757i	0.610652	−	0.352560i	−0.162568	−	0.986697i	$-0.551978\pi$
$157$	7.65145	−	4.41757i	0.610652	−	0.352560i	0.773221	+	0.634137i	$0.218645\pi$
$158$	−20.1889	+	20.1889i	−1.60614	+	1.60614i
$159$	0.931975	−	0.538076i	0.0739104	−	0.0426722i
$160$	−7.40198	−	12.8206i	−0.585178	−	1.01356i
$161$	−5.60991	+	8.92136i	−0.442123	+	0.703102i
$162$	2.18205	+	0.584679i	0.171438	+	0.0459367i
$163$	−5.61466	−	5.61466i	−0.439774	−	0.439774i	0.452162	−	0.891936i	$-0.350653\pi$
$163$	−5.61466	−	5.61466i	−0.439774	−	0.439774i	−0.891936	+	0.452162i	$0.850653\pi$
$164$	17.4237	+	4.66866i	1.36056	+	0.364561i
$165$	5.94466	−	10.2965i	0.462791	−	0.801578i
$166$	−11.5279	−	19.9669i	−0.894739	−	1.54973i
$167$	2.54898	+	9.51291i	0.197246	+	0.736131i	0.991674	+	0.128773i	$0.0411040\pi$
$167$	2.54898	+	9.51291i	0.197246	+	0.736131i	−0.794428	+	0.607358i	$0.792229\pi$
$168$	1.94567	−	6.30006i	0.150112	−	0.486060i
$169$	−7.73030	−	10.4519i	−0.594638	−	0.803993i
$170$	−14.0642	+	24.3599i	−1.07867	+	1.86832i
$171$	−2.98754	−	2.98754i	−0.228463	−	0.228463i
$172$	−34.5837			−2.63698
$173$	3.39025			0.257756			0.128878	−	0.991660i	$-0.458862\pi$
$173$	3.39025			0.257756			0.128878	+	0.991660i	$0.458862\pi$
$174$	1.80513	+	1.80513i	0.136846	+	0.136846i
$175$	−0.767655	+	1.22079i	−0.0580292	+	0.0922830i
$176$	−0.753391	+	2.81170i	−0.0567890	+	0.211939i
$177$	8.16845	−	2.18873i	0.613978	−	0.164515i
$178$	17.4896	+	10.0976i	1.31090	+	0.756850i
$179$		−	6.78191i		−	0.506904i	−0.967348	−	0.253452i	$-0.918434\pi$
$179$		−	6.78191i		−	0.506904i	0.967348	−	0.253452i	$-0.0815659\pi$
$180$	−7.05842	−	1.89130i	−0.526103	−	0.140969i
$181$	10.9124			0.811109			0.405554	−	0.914071i	$-0.367078\pi$
$181$	10.9124			0.811109			0.405554	+	0.914071i	$0.367078\pi$
$182$	−5.18379	+	20.9170i	−0.384248	+	1.55047i
$183$	3.15666			0.233347
$184$	9.58859	+	2.56926i	0.706880	+	0.189408i
$185$		−	12.5179i		−	0.920338i
$186$	−10.5974	−	6.11841i	−0.777039	−	0.448624i
$187$	25.7880	−	6.90987i	1.88581	−	0.505300i
$188$	−6.05665	+	22.6037i	−0.441727	+	1.64855i
$189$	1.23548	+	2.33957i	0.0898677	+	0.170179i
$190$	15.8924	+	15.8924i	1.15295	+	1.15295i
$191$	−1.04515			−0.0756246			−0.0378123	−	0.999285i	$-0.512039\pi$
$191$	−1.04515			−0.0756246			−0.0378123	+	0.999285i	$0.512039\pi$
$192$	13.0488			0.941720
$193$	6.96641	+	6.96641i	0.501453	+	0.501453i	0.911889	−	0.410436i	$-0.134624\pi$
$193$	6.96641	+	6.96641i	0.501453	+	0.501453i	−0.410436	+	0.911889i	$0.634624\pi$
$194$	−18.8538	+	32.6557i	−1.35362	+	2.34454i
$195$	8.31222	+	1.72994i	0.595251	+	0.123884i
$196$	19.5777	−	9.41164i	1.39841	−	0.672260i
$197$	−1.53092	−	5.71348i	−0.109074	−	0.407069i	0.889702	−	0.456542i	$-0.150912\pi$
$197$	−1.53092	−	5.71348i	−0.109074	−	0.407069i	−0.998775	+	0.0494737i	$0.984246\pi$
$198$	5.70290	+	9.87771i	0.405287	+	0.701979i
$199$	2.65808	−	4.60393i	0.188426	−	0.326364i	−0.756299	−	0.654226i	$-0.772995\pi$
$199$	2.65808	−	4.60393i	0.188426	−	0.326364i	0.944726	+	0.327862i	$0.106328\pi$
$200$	1.31209	+	0.351574i	0.0927790	+	0.0248601i
$201$	−3.75730	−	3.75730i	−0.265019	−	0.265019i
$202$	1.66978	+	0.447415i	0.117485	+	0.0314800i
$203$	−0.112815	+	2.98773i	−0.00791807	+	0.209697i
$204$	−8.20446	−	14.2105i	−0.574427	−	0.994937i
$205$	11.8541	−	6.84398i	0.827928	−	0.478004i
$206$	8.84501	−	8.84501i	0.616261	−	0.616261i
$207$	−3.44956	+	1.99161i	−0.239761	+	0.138426i
$208$	−2.07537	+	0.117609i	−0.143901	+	0.00815474i
$209$		−	21.3321i		−	1.47557i
$210$	−6.57218	−	12.4455i	−0.453523	−	0.858818i
$211$	8.76315	−	15.1782i	0.603280	−	1.04491i	−0.389041	−	0.921221i	$-0.627193\pi$
$211$	8.76315	−	15.1782i	0.603280	−	1.04491i	0.992321	−	0.123691i	$-0.0394732\pi$
$212$		−	3.33952i		−	0.229359i
$213$	−3.47804	+	12.9802i	−0.238311	+	0.889390i
$214$	4.52888	+	16.9020i	0.309588	+	1.15540i
$215$	−18.5566	+	18.5566i	−1.26555	+	1.26555i
$216$	1.76223	−	1.76223i	0.119905	−	0.119905i
$217$	−3.18432	−	13.9734i	−0.216166	−	0.948577i
$218$	−21.8849	−	12.6352i	−1.48223	−	0.855766i
$219$	−0.418321	+	1.56120i	−0.0282675	+	0.105496i
$220$	−18.4475	−	31.9520i	−1.24373	−	2.15421i
$221$	10.4515	+	15.9452i	0.703043	+	1.07259i
$222$	10.4000	+	6.00443i	0.698000	+	0.402991i
$223$	−12.8318	+	3.43827i	−0.859282	+	0.230244i	−0.661447	−	0.749992i	$-0.730057\pi$
$223$	−12.8318	+	3.43827i	−0.859282	+	0.230244i	−0.197834	+	0.980235i	$0.563391\pi$
$224$	11.3092	+	12.1968i	0.755630	+	0.814934i
$225$	−0.472034	+	0.272529i	−0.0314690	+	0.0181686i
$226$	5.41367	+	20.2041i	0.360112	+	1.34396i
$227$	19.2938	−	5.16977i	1.28058	−	0.343130i	0.446503	−	0.894782i	$-0.352669\pi$
$227$	19.2938	−	5.16977i	1.28058	−	0.343130i	0.834074	+	0.551652i	$0.186003\pi$
$228$	−12.6644	+	3.39340i	−0.838717	+	0.224734i
$229$	−0.350071	−	1.30648i	−0.0231333	−	0.0863347i	0.953394	−	0.301728i	$-0.0975634\pi$
$229$	−0.350071	−	1.30648i	−0.0231333	−	0.0863347i	−0.976527	+	0.215393i	$0.930897\pi$
$230$	18.3501	−	10.5944i	1.20997	−	0.698576i
$231$	−3.94181	+	12.7635i	−0.259352	+	0.839780i
$232$	2.72034	−	0.728913i	0.178599	−	0.0478555i
$233$	−18.9116	−	10.9186i	−1.23894	−	0.715301i	−0.270061	−	0.962843i	$-0.587044\pi$
$233$	−18.9116	−	10.9186i	−1.23894	−	0.715301i	−0.968877	+	0.247542i	$0.920377\pi$
$234$	−5.42433	+	6.07604i	−0.354599	+	0.397203i
$235$	8.87869	+	15.3783i	0.579182	+	1.00317i
$236$	6.79207	−	25.3484i	0.442126	−	1.65004i
$237$	−10.9455	−	6.31940i	−0.710988	−	0.410489i
$238$	9.32572	−	30.1966i	0.604497	−	1.95736i
$239$	2.43660	−	2.43660i	0.157611	−	0.157611i	−0.623896	−	0.781507i	$-0.714451\pi$
$239$	2.43660	−	2.43660i	0.157611	−	0.157611i	0.781507	+	0.623896i	$0.214451\pi$
$240$	0.959971	−	0.959971i	0.0619659	−	0.0619659i
$241$	1.24212	+	4.63565i	0.0800120	+	0.298609i	0.994323	−	0.106404i	$-0.0339337\pi$
$241$	1.24212	+	4.63565i	0.0800120	+	0.298609i	−0.914311	+	0.405013i	$0.867267\pi$
$242$	−8.47333	+	31.6229i	−0.544686	+	2.03280i
$243$			1.00000i			0.0641500i
$244$	4.89789	−	8.48339i	0.313555	−	0.543094i
$245$	5.45481	−	15.5548i	0.348495	−	0.993762i
$246$			13.1313i			0.837220i
$247$	14.4678	−	4.76893i	0.920565	−	0.303440i
$248$	−11.6911	+	6.74986i	−0.742386	+	0.428617i
$249$	7.21679	−	7.21679i	0.457345	−	0.457345i
$250$	−20.5233	+	11.8491i	−1.29801	+	0.749405i
$251$	−8.94953	−	15.5010i	−0.564890	−	0.978417i	−0.997060	−	0.0766255i	$-0.975585\pi$
$251$	−8.94953	−	15.5010i	−0.564890	−	0.978417i	0.432170	−	0.901792i	$-0.357748\pi$
$252$	8.20446	+	0.309797i	0.516833	+	0.0195153i
$253$	−19.4259	−	5.20516i	−1.22130	−	0.327245i
$254$	−1.77664	−	1.77664i	−0.111476	−	0.111476i
$255$	−12.0273	−	3.22269i	−0.753176	−	0.201813i
$256$	6.04472	−	10.4698i	0.377795	−	0.654361i
$257$	−3.20380	−	5.54914i	−0.199847	−	0.346146i	0.748631	−	0.662986i	$-0.230711\pi$
$257$	−3.20380	−	5.54914i	−0.199847	−	0.346146i	−0.948479	+	0.316841i	$0.897378\pi$
$258$	−6.51596	−	24.3179i	−0.405666	−	1.51397i
$259$	3.12499	+	13.7131i	0.194178	+	0.852090i
$260$	17.5464	−	19.6545i	1.08818	−	1.21892i
$261$	−0.565030	+	0.978660i	−0.0349745	+	0.0605776i
$262$	−1.86876	−	1.86876i	−0.115452	−	0.115452i
$263$	2.42997			0.149838			0.0749191	−	0.997190i	$-0.476130\pi$
$263$	2.42997			0.149838			0.0749191	+	0.997190i	$0.476130\pi$
$264$	12.5829			0.774426
$265$	−1.79189	−	1.79189i	−0.110075	−	0.110075i
$266$	−21.3771	−	13.4423i	−1.31071	−	0.824200i
$267$	−2.31379	+	8.63520i	−0.141602	+	0.528465i
$268$	−15.9274	+	4.26773i	−0.972920	+	0.260693i
$269$	−13.7556	−	7.94178i	−0.838691	−	0.484219i	0.0181279	−	0.999836i	$-0.494229\pi$
$269$	−13.7556	−	7.94178i	−0.838691	−	0.484219i	−0.856819	+	0.515617i	$0.827563\pi$
$270$		−	5.31955i		−	0.323737i
$271$	−8.61532	−	2.30847i	−0.523344	−	0.140230i	−0.0125308	−	0.999921i	$-0.503989\pi$
$271$	−8.61532	−	2.30847i	−0.523344	−	0.140230i	−0.510813	+	0.859692i	$0.670655\pi$
$272$	3.04853			0.184844
$273$	−9.53769	+	0.179969i	−0.577248	+	0.0108922i
$274$	27.6584			1.67090
$275$	−2.65822	−	0.712268i	−0.160297	−	0.0429514i
$276$			12.3607i			0.744028i
$277$	−19.5494	−	11.2868i	−1.17461	−	0.678160i	−0.219846	−	0.975535i	$-0.570555\pi$
$277$	−19.5494	−	11.2868i	−1.17461	−	0.678160i	−0.954761	+	0.297375i	$0.903889\pi$
$278$	−43.9543	+	11.7775i	−2.63620	+	0.706368i
$279$	1.40198	−	5.23228i	0.0839346	−	0.313248i
$280$	−15.5157	−	0.585864i	−0.927239	−	0.0350121i
$281$	−2.03059	−	2.03059i	−0.121135	−	0.121135i	0.643941	−	0.765075i	$-0.277298\pi$
$281$	−2.03059	−	2.03059i	−0.121135	−	0.121135i	−0.765075	+	0.643941i	$0.777298\pi$
$282$	−17.0352			−1.01443
$283$	−7.12281			−0.423407			−0.211704	−	0.977334i	$-0.567901\pi$
$283$	−7.12281			−0.423407			−0.211704	+	0.977334i	$0.567901\pi$
$284$	29.4872	+	29.4872i	1.74974	+	1.74974i
$285$	−4.97453	+	8.61613i	−0.294666	+	0.510376i
$286$	−41.0583	+	2.32674i	−2.42783	+	0.137583i
$287$	−11.2774	+	10.4567i	−0.665681	+	0.617239i
$288$	1.62713	+	6.07252i	0.0958793	+	0.357827i
$289$	−5.48007	−	9.49176i	−0.322357	−	0.558339i
$290$	3.00570	−	5.20603i	0.176501	−	0.305709i
$291$	−16.1232	−	4.32019i	−0.945158	−	0.253254i
$292$	3.54657	+	3.54657i	0.207548	+	0.207548i
$293$	8.65417	+	2.31888i	0.505582	+	0.135470i	0.502589	−	0.864525i	$-0.332381\pi$
$293$	8.65417	+	2.31888i	0.505582	+	0.135470i	0.00299266	+	0.999996i	$0.499047\pi$
$294$	10.3066	+	11.9930i	0.601090	+	0.699446i
$295$	−9.95678	−	17.2456i	−0.579706	−	1.00408i
$296$	11.4733	−	6.62411i	0.666872	−	0.385019i
$297$	−3.57017	+	3.57017i	−0.207162	+	0.207162i
$298$	30.8781	−	17.8275i	1.78872	−	1.03272i
$299$	−0.812559	−	14.3387i	−0.0469915	−	0.829226i
$300$			1.69143i			0.0976546i
$301$	15.6958	−	24.9608i	0.904692	−	1.43872i
$302$	18.2815	−	31.6645i	1.05198	−	1.82209i
$303$			0.765232i			0.0439614i
$304$	0.630442	−	2.35284i	0.0361583	−	0.134945i
$305$	−1.92388	−	7.18001i	−0.110161	−	0.411126i
$306$	8.44649	−	8.44649i	0.482854	−	0.482854i
$307$	16.8943	−	16.8943i	0.964206	−	0.964206i	−0.0351747	−	0.999381i	$-0.511199\pi$
$307$	16.8943	−	16.8943i	0.964206	−	0.964206i	0.999381	+	0.0351747i	$0.0111988\pi$
$308$	28.1853	+	30.3974i	1.60601	+	1.73205i
$309$	4.79537	+	2.76861i	0.272799	+	0.157501i
$310$	−7.45792	+	27.8333i	−0.423582	+	1.58083i
$311$	−8.73808	−	15.1348i	−0.495491	−	0.858215i	0.504496	−	0.863414i	$-0.331678\pi$
$311$	−8.73808	−	15.1348i	−0.495491	−	0.858215i	−0.999986	+	0.00519889i	$0.998345\pi$
$312$	2.81300	+	8.53399i	0.159255	+	0.483142i
$313$	−5.69274	−	3.28670i	−0.321773	−	0.185775i	0.330410	−	0.943838i	$-0.392813\pi$
$313$	−5.69274	−	3.28670i	−0.321773	−	0.185775i	−0.652182	+	0.758062i	$0.726146\pi$
$314$	19.2787	−	5.16572i	1.08796	−	0.291518i
$315$	4.56851	−	4.23605i	0.257406	−	0.238675i
$316$	−33.9662	+	19.6104i	−1.91075	+	1.10317i
$317$	8.34364	+	31.1389i	0.468626	+	1.74894i	0.644580	+	0.764537i	$0.277032\pi$
$317$	8.34364	+	31.1389i	0.468626	+	1.74894i	−0.175954	+	0.984398i	$0.556301\pi$
$318$	2.34822	−	0.629204i	0.131682	−	0.0352840i
$319$	−5.51124	+	1.47673i	−0.308570	+	0.0826812i
$320$	−7.95283	−	29.6804i	−0.444577	−	1.65918i
$321$	−6.70816	+	3.87296i	−0.374413	+	0.216167i
$322$	−17.4573	+	16.1869i	−0.972855	+	0.902059i
$323$	−21.5795	+	5.78222i	−1.20072	+	0.321731i
$324$	2.68745	+	1.55160i	0.149303	+	0.0862001i
$325$	−0.111190	−	1.96209i	−0.00616770	−	0.108837i
$326$	−8.96870	−	15.5343i	−0.496731	−	0.860363i
$327$	2.89526	−	10.8053i	0.160108	−	0.597533i
$328$	12.5457	+	7.24325i	0.692719	+	0.399942i
$329$	−13.5654	−	14.6301i	−0.747887	−	0.806583i
$330$	18.9917	−	18.9917i	1.04546	−	1.04546i
$331$	19.1496	−	19.1496i	1.05256	−	1.05256i	0.0540185	−	0.998540i	$-0.482797\pi$
$331$	19.1496	−	19.1496i	1.05256	−	1.05256i	0.998540	−	0.0540185i	$-0.0172030\pi$
$332$	−8.19720	−	30.5924i	−0.449880	−	1.67897i
$333$	−1.37587	+	5.13480i	−0.0753970	+	0.281385i
$334$			22.2480i			1.21736i
$335$	−6.25624	+	10.8361i	−0.341815	+	0.592041i
$336$	−0.811976	+	1.29127i	−0.0442969	+	0.0704447i
$337$		−	9.62356i		−	0.524229i	−0.965037	−	0.262114i	$-0.915580\pi$
$337$		−	9.62356i		−	0.524229i	0.965037	−	0.262114i	$-0.0844197\pi$
$338$	−10.7569	−	27.3264i	−0.585099	−	1.48636i
$339$	−8.01871	+	4.62961i	−0.435517	+	0.251446i
$340$	−27.3224	+	27.3224i	−1.48176	+	1.48176i
$341$	23.6855	−	13.6748i	1.28264	−	0.740533i
$342$	−4.77222	−	8.26572i	−0.258052	−	0.446959i
$343$	−2.09247	+	18.4017i	−0.112983	+	0.993597i
$344$	−26.8276	−	7.18844i	−1.44645	−	0.387575i
$345$	6.63241	+	6.63241i	0.357077	+	0.357077i
$346$	7.39771	+	1.98221i	0.397703	+	0.106564i
$347$	1.14751	−	1.98755i	0.0616016	−	0.106697i	−0.833580	−	0.552399i	$-0.813713\pi$
$347$	1.14751	−	1.98755i	0.0616016	−	0.106697i	0.895181	+	0.445702i	$0.147046\pi$
$348$	1.75340	+	3.03698i	0.0939923	+	0.162799i
$349$	5.06133	+	18.8891i	0.270927	+	1.01111i	0.958522	+	0.285019i	$0.0919998\pi$
$349$	5.06133	+	18.8891i	0.270927	+	1.01111i	−0.687595	+	0.726094i	$0.741334\pi$
$350$	−2.38883	+	2.21499i	−0.127689	+	0.118396i
$351$	−3.21950	−	1.62322i	−0.171844	−	0.0866412i
$352$	−15.8708	+	27.4891i	−0.845918	+	1.46517i
$353$	11.7665	+	11.7665i	0.626267	+	0.626267i	0.947127	−	0.320860i	$-0.103972\pi$
$353$	11.7665	+	11.7665i	0.626267	+	0.626267i	−0.320860	+	0.947127i	$0.603972\pi$
$354$	19.1037			1.01535
$355$	31.6440			1.67949
$356$	19.6166	+	19.6166i	1.03968	+	1.03968i
$357$	13.9801	+	0.527881i	0.739904	+	0.0279384i
$358$	3.96524	−	14.7985i	0.209570	−	0.782124i
$359$	22.5333	−	6.03777i	1.18926	−	0.318661i	0.390667	−	0.920532i	$-0.372244\pi$
$359$	22.5333	−	6.03777i	1.18926	−	0.318661i	0.798594	+	0.601870i	$0.205578\pi$
$360$	−5.08231	−	2.93428i	−0.267861	−	0.154650i
$361$		−	1.14920i		−	0.0604845i
$362$	23.8113	+	6.38023i	1.25150	+	0.335337i
$363$	−14.4923			−0.760647
$364$	−14.3151	+	25.9114i	−0.750313	+	1.35812i
$365$	3.80598			0.199214
$366$	6.88801	+	1.84564i	0.360042	+	0.0964730i
$367$			23.9471i			1.25003i	0.780613	+	0.625014i	$0.214907\pi$
$367$			23.9471i			1.25003i	−0.780613	+	0.625014i	$0.785093\pi$
$368$	−1.98877	−	1.14822i	−0.103672	−	0.0598549i
$369$	−5.61474	+	1.50446i	−0.292292	+	0.0783193i
$370$	7.31898	−	27.3148i	0.380496	−	1.42003i
$371$	2.41030	+	1.51564i	0.125137	+	0.0786882i
$372$	−11.8862	−	11.8862i	−0.616270	−	0.616270i
$373$	−19.5555			−1.01254			−0.506272	−	0.862374i	$-0.668977\pi$
$373$	−19.5555			−1.01254			−0.506272	+	0.862374i	$0.668977\pi$
$374$	60.3108			3.11860
$375$	−7.41788	−	7.41788i	−0.383058	−	0.383058i
$376$	−9.39666	+	16.2755i	−0.484596	+	0.839345i
$377$	−2.23362	−	3.40769i	−0.115037	−	0.175505i
$378$	1.32798	+	5.82743i	0.0683038	+	0.299731i
$379$	9.94478	+	37.1144i	0.510829	+	1.90644i	0.411572	+	0.911377i	$0.364980\pi$
$379$	9.94478	+	37.1144i	0.510829	+	1.90644i	0.0992573	+	0.995062i	$0.468353\pi$
$380$	15.4370	+	26.7376i	0.791900	+	1.37161i
$381$	0.556112	−	0.963214i	0.0284905	−	0.0493470i
$382$	−2.28058	−	0.611079i	−0.116684	−	0.0312655i
$383$	4.26748	+	4.26748i	0.218058	+	0.218058i	0.807680	−	0.589622i	$-0.200723\pi$
$383$	4.26748	+	4.26748i	0.218058	+	0.218058i	−0.589622	+	0.807680i	$0.700723\pi$
$384$	16.3282	+	4.37514i	0.833247	+	0.223268i
$385$	31.4338	+	1.18693i	1.60202	+	0.0604913i
$386$	11.1280	+	19.2742i	0.566398	+	0.981031i
$387$	9.65143	−	5.57225i	0.490610	−	0.283254i
$388$	−36.6271	+	36.6271i	−1.85946	+	1.85946i
$389$	−19.6532	+	11.3468i	−0.996456	+	0.575304i	−0.907198	−	0.420705i	$-0.861783\pi$
$389$	−19.6532	+	11.3468i	−0.996456	+	0.575304i	−0.0892580	+	0.996009i	$0.528450\pi$
$390$	17.1263	+	8.63481i	0.867222	+	0.437240i
$391$			21.0622i			1.06516i
$392$	17.1433	−	3.23155i	0.865866	−	0.163218i
$393$	0.584948	−	1.01316i	0.0295067	−	0.0511071i
$394$		−	13.3622i		−	0.673179i
$395$	−7.70292	+	28.7477i	−0.387576	+	1.44645i
$396$	4.05519	+	15.1342i	0.203781	+	0.760521i
$397$	−21.6586	+	21.6586i	−1.08702	+	1.08702i	−0.0911808	+	0.995834i	$0.529064\pi$
$397$	−21.6586	+	21.6586i	−1.08702	+	1.08702i	−0.995834	+	0.0911808i	$0.970936\pi$
$398$	8.49190	−	8.49190i	0.425660	−	0.425660i
$399$	3.29853	−	10.6806i	0.165133	−	0.534699i
$400$	−0.272141	−	0.157121i	−0.0136070	−	0.00785603i
$401$	3.78423	−	14.1230i	0.188976	−	0.705267i	−0.804769	−	0.593588i	$-0.797711\pi$
$401$	3.78423	−	14.1230i	0.188976	−	0.705267i	0.993744	−	0.111678i	$-0.0356226\pi$
$402$	−6.00180	−	10.3954i	−0.299343	−	0.518477i
$403$	14.5696	+	13.0068i	0.725762	+	0.647916i
$404$	2.05653	+	1.18734i	0.102316	+	0.0590721i
$405$	2.27456	−	0.609466i	0.113024	−	0.0302846i
$406$	−1.99303	+	6.45342i	−0.0989125	+	0.320278i
$407$	−23.2442	+	13.4201i	−1.15217	+	0.665207i
$408$	−3.41070	−	12.7289i	−0.168855	−	0.630175i
$409$	0.688306	−	0.184431i	0.0340346	−	0.00911953i	−0.241762	−	0.970336i	$-0.577725\pi$
$409$	0.688306	−	0.184431i	0.0340346	−	0.00911953i	0.275796	+	0.961216i	$0.411059\pi$
$410$	29.8679	−	8.00307i	1.47507	−	0.395243i
$411$	3.16885	+	11.8263i	0.156308	+	0.583348i
$412$	14.8810	−	8.59157i	0.733136	−	0.423276i
$413$	15.2126	+	16.4065i	0.748564	+	0.807313i
$414$	−8.69158	+	2.32890i	−0.427168	+	0.114459i
$415$	−20.8134	−	12.0166i	−1.02169	−	0.589872i
$416$	−22.1916	−	4.61852i	−1.08803	−	0.226442i
$417$	−10.0718	−	17.4448i	−0.493217	−	0.854276i
$418$	12.4724	−	46.5477i	0.610046	−	2.27672i
$419$	−30.2738	−	17.4786i	−1.47897	−	0.853886i	−0.479257	−	0.877675i	$-0.659094\pi$
$419$	−30.2738	−	17.4786i	−1.47897	−	0.853886i	−0.999717	+	0.0237891i	$0.992427\pi$
$420$	−4.29569	−	18.8503i	−0.209608	−	0.919802i
$421$	9.56456	−	9.56456i	0.466148	−	0.466148i	−0.434516	−	0.900664i	$-0.643081\pi$
$421$	9.56456	−	9.56456i	0.466148	−	0.466148i	0.900664	+	0.434516i	$0.143081\pi$
$422$	27.9960	−	27.9960i	1.36283	−	1.36283i
$423$	−1.95174	−	7.28399i	−0.0948969	−	0.354160i
$424$	0.694141	−	2.59057i	0.0337105	−	0.125809i
$425$			2.88212i			0.139804i
$426$	−15.1785	+	26.2900i	−0.735403	+	1.27375i
$427$	3.89999	+	7.38524i	0.188734	+	0.357397i
$428$			24.0372i			1.16188i
$429$	−5.69897	−	17.2893i	−0.275149	−	0.834737i
$430$	−51.3412	+	29.6419i	−2.47589	+	1.42946i
$431$	−6.95507	+	6.95507i	−0.335014	+	0.335014i	−0.854487	−	0.519473i	$-0.826128\pi$
$431$	−6.95507	+	6.95507i	−0.335014	+	0.335014i	0.519473	+	0.854487i	$0.326128\pi$
$432$	−0.499288	+	0.288264i	−0.0240220	+	0.0138691i
$433$	6.68014	+	11.5703i	0.321027	+	0.556035i	0.980700	−	0.195517i	$-0.0626386\pi$
$433$	6.68014	+	11.5703i	0.321027	+	0.556035i	−0.659673	+	0.751553i	$0.729305\pi$
$434$	1.22162	−	32.3525i	0.0586394	−	1.55297i
$435$	2.57039	+	0.688733i	0.123241	+	0.0330222i
$436$	−24.5464	−	24.5464i	−1.17556	−	1.17556i
$437$	16.2557	+	4.35570i	0.777616	+	0.208362i
$438$	−1.82560	+	3.16203i	−0.0872304	+	0.151088i
$439$	0.272532	+	0.472039i	0.0130072	+	0.0225292i	0.872456	−	0.488693i	$-0.162526\pi$
$439$	0.272532	+	0.472039i	0.0130072	+	0.0225292i	−0.859449	+	0.511222i	$0.829193\pi$
$440$	−7.66887	−	28.6206i	−0.365599	−	1.36443i
$441$	−3.94719	+	5.78098i	−0.187962	+	0.275285i
$442$	13.4829	+	40.9040i	0.641316	+	1.94560i
$443$	20.9929	−	36.3608i	0.997402	−	1.72755i	0.436319	−	0.899792i	$-0.356282\pi$
$443$	20.9929	−	36.3608i	0.997402	−	1.72755i	0.561083	−	0.827760i	$-0.310385\pi$
$444$	11.6648	+	11.6648i	0.553585	+	0.553585i
$445$	21.0514			0.997933
$446$	−30.0100			−1.42101
$447$	11.1605	+	11.1605i	0.527872	+	0.527872i
$448$	16.1216	+	30.5287i	0.761672	+	1.44235i
$449$	9.43152	−	35.1989i	0.445101	−	1.66114i	−0.270570	−	0.962700i	$-0.587212\pi$
$449$	9.43152	−	35.1989i	0.445101	−	1.66114i	0.715670	−	0.698438i	$-0.246121\pi$
$450$	−1.18935	+	0.318684i	−0.0560663	+	0.0150229i
$451$	−25.4168	−	14.6744i	−1.19683	−	0.690990i
$452$			28.7332i			1.35150i
$453$	15.6338	+	4.18906i	0.734539	+	0.196819i
$454$	45.1228			2.11772
$455$	6.22225	+	21.5843i	0.291703	+	1.01189i
$456$	−10.5295			−0.493088
$457$	0.735237	+	0.197006i	0.0343930	+	0.00921556i	0.275975	−	0.961165i	$-0.410999\pi$
$457$	0.735237	+	0.197006i	0.0343930	+	0.00921556i	−0.241582	+	0.970381i	$0.577666\pi$
$458$		−	3.05549i		−	0.142774i
$459$	4.57931	+	2.64387i	0.213744	+	0.123405i
$460$	28.1152	−	7.53344i	1.31088	−	0.351248i
$461$	−8.56724	+	31.9734i	−0.399016	+	1.48915i	0.415814	+	0.909450i	$0.363497\pi$
$461$	−8.56724	+	31.9734i	−0.399016	+	1.48915i	−0.814830	+	0.579700i	$0.803170\pi$
$462$	−16.0638	+	25.5460i	−0.747356	+	1.18851i
$463$	−5.33423	−	5.33423i	−0.247902	−	0.247902i	0.572207	−	0.820109i	$-0.306087\pi$
$463$	−5.33423	−	5.33423i	−0.247902	−	0.247902i	−0.820109	+	0.572207i	$0.806087\pi$
$464$	−0.651511			−0.0302456
$465$	−12.7556			−0.591526
$466$	−34.8822	−	34.8822i	−1.61588	−	1.61588i
$467$	5.83331	−	10.1036i	0.269933	−	0.467538i	−0.698911	−	0.715209i	$-0.746332\pi$
$467$	5.83331	−	10.1036i	0.269933	−	0.467538i	0.968844	+	0.247670i	$0.0796650\pi$
$468$	−9.35771	+	6.13365i	−0.432560	+	0.283528i
$469$	4.14841	−	13.4325i	0.191556	−	0.620256i
$470$	10.3824	+	38.7475i	0.478903	+	1.78729i
$471$	4.41757	+	7.65145i	0.203551	+	0.352560i
$472$	10.5376	−	18.2517i	0.485034	−	0.840104i
$473$	54.3512	+	14.5634i	2.49907	+	0.669624i
$474$	−20.1889	−	20.1889i	−0.927307	−	0.927307i
$475$	2.22441	+	0.596030i	0.102063	+	0.0273477i
$476$	23.1102	−	36.7517i	1.05925	−	1.68451i
$477$	0.538076	+	0.931975i	0.0246368	+	0.0426722i
$478$	6.74143	−	3.89217i	0.308346	−	0.178024i
$479$	−6.06425	+	6.06425i	−0.277083	+	0.277083i	−0.831943	−	0.554861i	$-0.812772\pi$
$479$	−6.06425	+	6.06425i	−0.277083	+	0.277083i	0.554861	+	0.831943i	$0.312772\pi$
$480$	12.8206	−	7.40198i	0.585178	−	0.337853i
$481$	−14.2981	−	12.7645i	−0.651939	−	0.582012i
$482$			10.8415i			0.493816i
$483$	−8.92136	−	5.60991i	−0.405936	−	0.255260i
$484$	−22.4862	+	38.9473i	−1.02210	+	1.77033i
$485$			39.3061i			1.78480i
$486$	−0.584679	+	2.18205i	−0.0265216	+	0.0989799i
$487$	10.9821	+	40.9858i	0.497647	+	1.85724i	0.514672	+	0.857387i	$0.327914\pi$
$487$	10.9821	+	40.9858i	0.497647	+	1.85724i	−0.0170255	+	0.999855i	$0.505420\pi$
$488$	5.56277	−	5.56277i	0.251815	−	0.251815i
$489$	5.61466	−	5.61466i	0.253904	−	0.253904i
$490$	20.9973	−	30.7522i	0.948560	−	1.38924i
$491$	20.0110	+	11.5533i	0.903082	+	0.521394i	0.878199	−	0.478296i	$-0.158745\pi$
$491$	20.0110	+	11.5533i	0.903082	+	0.521394i	0.0248830	+	0.999690i	$0.492079\pi$
$492$	−4.66866	+	17.4237i	−0.210480	+	0.785520i
$493$	2.98773	+	5.17490i	0.134560	+	0.233066i
$494$	34.3578	−	1.94703i	1.54583	−	0.0876009i
$495$	10.2965	+	5.94466i	0.462791	+	0.267193i
$496$	3.01655	−	0.808283i	0.135447	−	0.0362930i
$497$	−34.6652	+	7.89965i	−1.55495	+	0.354348i
$498$	19.9669	−	11.5279i	0.894739	−	0.516578i
$499$	−8.91242	−	33.2616i	−0.398975	−	1.48899i	−0.814904	−	0.579596i	$-0.803210\pi$
$499$	−8.91242	−	33.2616i	−0.398975	−	1.48899i	0.415929	−	0.909397i	$-0.363456\pi$
$500$	−31.4448	+	8.42562i	−1.40626	+	0.376805i
$501$	−9.51291	+	2.54898i	−0.425006	+	0.113880i
$502$	−10.4652	−	39.0567i	−0.467085	−	1.74319i
$503$	−1.49019	+	0.860359i	−0.0664441	+	0.0383615i	−0.532854	−	0.846207i	$-0.678881\pi$
$503$	−1.49019	+	0.860359i	−0.0664441	+	0.0383615i	0.466410	+	0.884569i	$0.345547\pi$
$504$	6.30006	+	1.94567i	0.280627	+	0.0866670i
$505$	1.74056	−	0.466382i	0.0774540	−	0.0207537i
$506$	−39.3450	−	22.7159i	−1.74910	−	1.00984i
$507$	10.4519	−	7.73030i	0.464186	−	0.343315i
$508$	−1.72573	−	2.98905i	−0.0765669	−	0.132618i
$509$	4.08516	−	15.2460i	0.181071	−	0.675768i	−0.814366	−	0.580352i	$-0.802915\pi$
$509$	4.08516	−	15.2460i	0.181071	−	0.675768i	0.995437	−	0.0954162i	$-0.0304182\pi$
$510$	−24.3599	−	14.0642i	−1.07867	−	0.622772i
$511$	−4.16935	+	0.950129i	−0.184441	+	0.0420312i
$512$	−4.59484	+	4.59484i	−0.203065	+	0.203065i
$513$	2.98754	−	2.98754i	0.131903	−	0.131903i
$514$	−3.74639	−	13.9817i	−0.165246	−	0.616707i
$515$	3.37475	−	12.5947i	0.148709	−	0.554990i
$516$		−	34.5837i		−	1.52246i
$517$	19.0371	−	32.9732i	0.837249	−	1.45016i
$518$	−1.19886	+	31.7498i	−0.0526748	+	1.39501i
$519$			3.39025i			0.148816i
$520$	17.6966	−	11.5995i	0.776048	−	0.508672i
$521$	−23.8356	+	13.7615i	−1.04426	+	0.602902i	−0.921036	−	0.389477i	$-0.872656\pi$
$521$	−23.8356	+	13.7615i	−1.04426	+	0.602902i	−0.123221	+	0.992379i	$0.539323\pi$
$522$	−1.80513	+	1.80513i	−0.0790083	+	0.0790083i
$523$	24.8550	−	14.3500i	1.08683	−	0.627484i	0.154102	−	0.988055i	$-0.450752\pi$
$523$	24.8550	−	14.3500i	1.08683	−	0.627484i	0.932732	+	0.360571i	$0.117418\pi$
$524$	−1.81521	−	3.14404i	−0.0792979	−	0.137348i
$525$	−1.22079	−	0.767655i	−0.0532796	−	0.0335032i
$526$	5.30232	+	1.42075i	0.231192	+	0.0619477i
$527$	−20.2536	−	20.2536i	−0.882260	−	0.882260i
$528$	−2.81170	−	0.753391i	−0.122363	−	0.0327872i
$529$	−3.56702	+	6.17825i	−0.155088	+	0.268620i
$530$	−2.86232	−	4.95768i	−0.124331	−	0.215348i
$531$	2.18873	+	8.16845i	0.0949827	+	0.354480i
$532$	−23.5856	−	25.4367i	−1.02257	−	1.10282i
$533$	4.27035	−	20.5187i	0.184969	−	0.888764i
$534$	−10.0976	+	17.4896i	−0.436968	+	0.756850i
$535$	12.8977	+	12.8977i	0.557614	+	0.557614i
$536$	−13.2424			−0.571986
$537$	6.78191			0.292661
$538$	−25.3720	−	25.3720i	−1.09386	−	1.09386i
$539$	−34.7312	+	6.54693i	−1.49598	+	0.281996i
$540$	1.89130	−	7.05842i	0.0813885	−	0.303746i
$541$	−12.5009	+	3.34960i	−0.537454	+	0.144010i	−0.517328	−	0.855787i	$-0.673073\pi$
$541$	−12.5009	+	3.34960i	−0.537454	+	0.144010i	−0.0201258	+	0.999797i	$0.506407\pi$
$542$	−17.4494	−	10.0744i	−0.749515	−	0.432733i
$543$			10.9124i			0.468294i
$544$	32.1099	+	8.60381i	1.37670	+	0.368885i
$545$	−26.3418			−1.12836
$546$	−20.9170	−	5.18379i	−0.895164	−	0.221846i
$547$	9.86784			0.421918			0.210959	−	0.977495i	$-0.432341\pi$
$547$	9.86784			0.421918			0.210959	+	0.977495i	$0.432341\pi$
$548$	36.6994	+	9.83359i	1.56772	+	0.420070i
$549$			3.15666i			0.134723i
$550$	−5.38393	−	3.10841i	−0.229572	−	0.132543i
$551$	4.61184	−	1.23574i	0.196471	−	0.0526442i
$552$	−2.56926	+	9.58859i	−0.109355	+	0.408118i
$553$	1.26175	−	33.4153i	0.0536549	−	1.42096i
$554$	−36.0586	−	36.0586i	−1.53198	−	1.53198i
$555$	12.5179			0.531357
$556$	−62.5095			−2.65099
$557$	−23.4101	−	23.4101i	−0.991919	−	0.991919i	0.00804826	−	0.999968i	$-0.497438\pi$
$557$	−23.4101	−	23.4101i	−0.991919	−	0.991919i	−0.999968	+	0.00804826i	$0.997438\pi$
$558$	6.11841	−	10.5974i	0.259013	−	0.448624i
$559$	2.27343	+	40.1177i	0.0961560	+	1.69680i
$560$	3.43194	+	1.05990i	0.145026	+	0.0447889i
$561$	6.90987	+	25.7880i	0.291735	+	1.08877i
$562$	−3.24361	−	5.61810i	−0.136823	−	0.236985i
$563$	−19.0236	+	32.9499i	−0.801750	+	1.38867i	0.116714	+	0.993166i	$0.462764\pi$
$563$	−19.0236	+	32.9499i	−0.801750	+	1.38867i	−0.918464	+	0.395505i	$0.870569\pi$
$564$	−22.6037	−	6.05665i	−0.951789	−	0.255031i
$565$	15.4174	+	15.4174i	0.648616	+	0.648616i
$566$	−15.5424	−	4.16456i	−0.653294	−	0.175050i
$567$	−2.33957	+	1.23548i	−0.0982528	+	0.0518852i
$568$	16.7450	+	29.0033i	0.702606	+	1.21695i
$569$	−15.4440	+	8.91660i	−0.647446	+	0.373803i	−0.787477	−	0.616344i	$-0.788613\pi$
$569$	−15.4440	+	8.91660i	−0.647446	+	0.373803i	0.140031	+	0.990147i	$0.455280\pi$
$570$	−15.8924	+	15.8924i	−0.665658	+	0.665658i
$571$	−35.0123	+	20.2143i	−1.46522	+	0.845944i	−0.999245	−	0.0388557i	$-0.987629\pi$
$571$	−35.0123	+	20.2143i	−1.46522	+	0.845944i	−0.465972	+	0.884799i	$0.654295\pi$
$572$	−55.3069	−	11.5105i	−2.31250	−	0.481276i
$573$		−	1.04515i		−	0.0436619i
$574$	−30.7216	+	16.2234i	−1.28229	+	0.677152i
$575$	1.08554	−	1.88021i	0.0452702	−	0.0784103i
$576$			13.0488i			0.543702i
$577$	−0.274766	+	1.02544i	−0.0114387	+	0.0426897i	−0.971409	−	0.237411i	$-0.923701\pi$
$577$	−0.274766	+	1.02544i	−0.0114387	+	0.0426897i	0.959971	+	0.280101i	$0.0903679\pi$
$578$	−6.40816	−	23.9156i	−0.266545	−	0.994758i
$579$	−6.96641	+	6.96641i	−0.289514	+	0.289514i
$580$	5.83915	−	5.83915i	0.242458	−	0.242458i
$581$	25.8004	+	7.96801i	1.07038	+	0.330569i
$582$	−32.6557	−	18.8538i	−1.35362	−	0.781514i
$583$	−1.40629	+	5.24834i	−0.0582425	+	0.217364i
$584$	2.01401	+	3.48837i	0.0833403	+	0.144350i
$585$	−1.72994	+	8.31222i	−0.0715242	+	0.343668i
$586$	17.5281	+	10.1198i	0.724078	+	0.418046i
$587$	24.5244	−	6.57129i	1.01223	−	0.271226i	0.285669	−	0.958328i	$-0.407784\pi$
$587$	24.5244	−	6.57129i	1.01223	−	0.271226i	0.726561	+	0.687102i	$0.241118\pi$
$588$	9.41164	+	19.5777i	0.388129	+	0.807370i
$589$	−19.8201	+	11.4432i	−0.816674	+	0.471507i
$590$	−11.6430	−	43.4524i	−0.479336	−	1.78891i
$591$	5.71348	−	1.53092i	0.235021	−	0.0629737i
$592$	−2.96036	+	0.793225i	−0.121670	+	0.0326013i
$593$	3.58927	+	13.3953i	0.147394	+	0.550081i	0.999637	+	0.0269353i	$0.00857481\pi$
$593$	3.58927	+	13.3953i	0.147394	+	0.550081i	−0.852244	+	0.523145i	$0.824759\pi$
$594$	−9.87771	+	5.70290i	−0.405287	+	0.233993i
$595$	−7.31968	−	32.1202i	−0.300078	−	1.31680i
$596$	47.3099	−	12.6766i	1.93789	−	0.519256i
$597$	4.60393	+	2.65808i	0.188426	+	0.108788i
$598$	6.61047	−	31.7628i	0.270322	−	1.29888i
$599$	−15.3267	−	26.5466i	−0.626232	−	1.08467i	−0.988301	−	0.152515i	$-0.951263\pi$
$599$	−15.3267	−	26.5466i	−0.626232	−	1.08467i	0.362069	−	0.932151i	$-0.382070\pi$
$600$	−0.351574	+	1.31209i	−0.0143530	+	0.0535660i
$601$	8.40143	+	4.85057i	0.342701	+	0.197859i	0.661466	−	0.749975i	$-0.269935\pi$
$601$	8.40143	+	4.85057i	0.342701	+	0.197859i	−0.318765	+	0.947834i	$0.603268\pi$
$602$	48.8432	−	45.2888i	1.99070	−	1.84583i
$603$	3.75730	−	3.75730i	0.153009	−	0.153009i
$604$	35.5153	−	35.5153i	1.44510	−	1.44510i
$605$	8.83254	+	32.9635i	0.359094	+	1.34016i
$606$	−0.447415	+	1.66978i	−0.0181750	+	0.0678300i
$607$			14.6956i			0.596475i	0.954492	+	0.298238i	$0.0963988\pi$
$607$			14.6956i			0.596475i	−0.954492	+	0.298238i	$0.903601\pi$
$608$	13.2808	−	23.0030i	0.538607	−	0.932895i
$609$	−2.98773	−	0.112815i	−0.121069	−	0.00457150i
$610$		−	16.7920i		−	0.679889i
$611$	26.6189	+	5.53992i	1.07689	+	0.224121i
$612$	14.2105	−	8.20446i	0.574427	−	0.331646i
$613$	−25.7393	+	25.7393i	−1.03960	+	1.03960i	−0.0404173	+	0.999183i	$0.512869\pi$
$613$	−25.7393	+	25.7393i	−1.03960	+	1.03960i	−0.999183	+	0.0404173i	$0.987131\pi$
$614$	46.7419	−	26.9864i	1.88635	−	1.08908i
$615$	6.84398	+	11.8541i	0.275976	+	0.478004i
$616$	15.5459	+	29.4387i	0.626364	+	1.18612i
$617$	11.0647	+	2.96476i	0.445446	+	0.119357i	0.474568	−	0.880219i	$-0.342604\pi$
$617$	11.0647	+	2.96476i	0.445446	+	0.119357i	−0.0291217	+	0.999576i	$0.509271\pi$
$618$	8.84501	+	8.84501i	0.355798	+	0.355798i
$619$	42.1253	+	11.2874i	1.69316	+	0.453681i	0.971202	−	0.238257i	$-0.0765761\pi$
$619$	42.1253	+	11.2874i	1.69316	+	0.453681i	0.721957	+	0.691938i	$0.243243\pi$
$620$	−19.7916	+	34.2800i	−0.794849	+	1.37672i
$621$	−1.99161	−	3.44956i	−0.0799204	−	0.138426i
$622$	−10.2179	−	38.1339i	−0.409702	−	1.52903i
$623$	−23.0613	+	5.25530i	−0.923932	+	0.210549i
$624$	−0.117609	−	2.07537i	−0.00470814	−	0.0830813i
$625$	−13.7141	+	23.7535i	−0.548564	+	0.950141i
$626$	−10.5002	−	10.5002i	−0.419672	−	0.419672i
$627$	21.3321			0.851921
$628$	27.4172			1.09407
$629$	19.8763	+	19.8763i	0.792518	+	0.792518i
$630$	12.4455	−	6.57218i	0.495839	−	0.261842i
$631$	−0.0773405	+	0.288639i	−0.00307888	+	0.0114905i	−0.967448	−	0.253069i	$-0.918560\pi$
$631$	−0.0773405	+	0.288639i	−0.00307888	+	0.0114905i	0.964369	+	0.264560i	$0.0852266\pi$
$632$	−30.4248	+	8.15230i	−1.21023	+	0.324281i
$633$	15.1782	+	8.76315i	0.603280	+	0.348304i
$634$			72.8251i			2.89225i
$635$	−2.52982	−	0.677862i	−0.100393	−	0.0269001i
$636$	3.33952			0.132421
$637$	−12.2047	−	22.0918i	−0.483566	−	0.875308i
$638$	−12.8892			−0.510290
$639$	−12.9802	−	3.47804i	−0.513490	−	0.137589i
$640$		−	39.8060i		−	1.57347i
$641$	4.23982	+	2.44786i	0.167463	+	0.0966847i	0.581389	−	0.813626i	$-0.302509\pi$
$641$	4.23982	+	2.44786i	0.167463	+	0.0966847i	−0.413926	+	0.910310i	$0.635843\pi$
$642$	−16.9020	+	4.52888i	−0.667068	+	0.178740i
$643$	11.4094	−	42.5806i	0.449944	−	1.67921i	−0.252598	−	0.967571i	$-0.581285\pi$
$643$	11.4094	−	42.5806i	0.449944	−	1.67921i	0.702542	−	0.711643i	$-0.252048\pi$
$644$	−28.9188	+	15.2714i	−1.13956	+	0.601777i
$645$	−18.5566	−	18.5566i	−0.730666	−	0.730666i
$646$	−50.4684			−1.98565
$647$	−2.94231			−0.115674			−0.0578370	−	0.998326i	$-0.518420\pi$
$647$	−2.94231			−0.115674			−0.0578370	+	0.998326i	$0.518420\pi$
$648$	1.76223	+	1.76223i	0.0692270	+	0.0692270i
$649$	−21.3486	+	36.9769i	−0.838007	+	1.45147i
$650$	0.904570	−	4.34639i	0.0354802	−	0.170479i
$651$	13.9734	−	3.18432i	0.547661	−	0.124803i
$652$	−6.37742	−	23.8009i	−0.249759	−	0.932113i
$653$	−3.97706	−	6.88846i	−0.155634	−	0.269566i	0.777656	−	0.628691i	$-0.216409\pi$
$653$	−3.97706	−	6.88846i	−0.155634	−	0.269566i	−0.933290	+	0.359124i	$0.883075\pi$
$654$	12.6352	−	21.8849i	0.494077	−	0.855766i
$655$	−2.66099	−	0.713011i	−0.103974	−	0.0278596i
$656$	−2.36969	−	2.36969i	−0.0925207	−	0.0925207i
$657$	−1.56120	−	0.418321i	−0.0609080	−	0.0163203i
$658$	−21.0466	−	39.8551i	−0.820482	−	1.55371i
$659$	1.30483	+	2.26004i	0.0508291	+	0.0880385i	0.890320	−	0.455334i	$-0.150480\pi$
$659$	1.30483	+	2.26004i	0.0508291	+	0.0880385i	−0.839491	+	0.543373i	$0.817147\pi$
$660$	31.9520	−	18.4475i	1.24373	−	0.718068i
$661$	20.7944	−	20.7944i	0.808808	−	0.808808i	−0.175646	−	0.984453i	$-0.556201\pi$
$661$	20.7944	−	20.7944i	0.808808	−	0.808808i	0.984453	+	0.175646i	$0.0562013\pi$
$662$	52.9819	−	30.5891i	2.05920	−	1.18888i
$663$	−15.9452	+	10.4515i	−0.619259	+	0.405902i
$664$		−	25.4353i		−	0.987081i
$665$	−26.3040	−	0.993226i	−1.02002	−	0.0385156i
$666$	−6.00443	+	10.4000i	−0.232667	+	0.402991i
$667$		−	4.50127i		−	0.174290i
$668$	−7.91000	+	29.5205i	−0.306047	+	1.14218i
$669$	−3.43827	−	12.8318i	−0.132931	−	0.496106i
$670$	−19.9871	+	19.9871i	−0.772169	+	0.772169i
$671$	−11.2698	+	11.2698i	−0.435067	+	0.435067i
$672$	−12.1968	+	11.3092i	−0.470502	+	0.436263i
$673$	16.3940	+	9.46510i	0.631943	+	0.364853i	0.781504	−	0.623900i	$-0.214453\pi$
$673$	16.3940	+	9.46510i	0.631943	+	0.364853i	−0.149561	+	0.988753i	$0.547786\pi$
$674$	5.62669	−	20.9991i	0.216732	−	0.808855i
$675$	−0.272529	−	0.472034i	−0.0104897	−	0.0181686i
$676$	−4.55761	−	40.0834i	−0.175293	−	1.54167i
$677$	42.4727	+	24.5216i	1.63236	+	0.942443i	0.983363	+	0.181650i	$0.0581438\pi$
$677$	42.4727	+	24.5216i	1.63236	+	0.942443i	0.648995	+	0.760793i	$0.275190\pi$
$678$	−20.2041	+	5.41367i	−0.775933	+	0.207911i
$679$	−9.81242	−	43.0588i	−0.376566	−	1.65245i
$680$	−26.8739	+	15.5157i	−1.03057	+	0.594999i
$681$	5.16977	+	19.2938i	0.198106	+	0.739342i
$682$	59.6783	−	15.9908i	2.28520	−	0.612318i
$683$	31.9962	−	8.57335i	1.22430	−	0.328050i	0.411942	−	0.911210i	$-0.364851\pi$
$683$	31.9962	−	8.57335i	1.22430	−	0.328050i	0.812357	+	0.583160i	$0.198184\pi$
$684$	−3.39340	−	12.6644i	−0.129750	−	0.484234i
$685$	24.9683	−	14.4155i	0.953990	−	0.550786i
$686$	−15.3250	+	38.9300i	−0.585110	+	1.48635i
$687$	1.30648	−	0.350071i	0.0498454	−	0.0133560i
$688$	5.56431	+	3.21256i	0.212138	+	0.122478i
$689$	−3.87391	+	0.219531i	−0.147584	+	0.00836345i
$690$	10.5944	+	18.3501i	0.403323	+	0.698576i
$691$	−1.36491	+	5.09390i	−0.0519235	+	0.193781i	−0.987016	−	0.160623i	$-0.948650\pi$
$691$	−1.36491	+	5.09390i	−0.0519235	+	0.193781i	0.935092	+	0.354404i	$0.115316\pi$
$692$	9.11115	+	5.26032i	0.346354	+	0.199968i
$693$	−12.7635	−	3.94181i	−0.484847	−	0.149737i
$694$	3.66600	−	3.66600i	0.139160	−	0.139160i
$695$	−33.5408	+	33.5408i	−1.27228	+	1.27228i
$696$	0.728913	+	2.72034i	0.0276294	+	0.103114i
$697$	−7.95521	+	29.6892i	−0.301325	+	1.12456i
$698$			44.1764i			1.67210i
$699$	10.9186	−	18.9116i	0.412979	−	0.715301i
$700$	−3.95722	+	2.08972i	−0.149569	+	0.0789840i
$701$		−	16.2025i		−	0.611960i	−0.952038	−	0.305980i	$-0.901016\pi$
$701$		−	16.2025i		−	0.611960i	0.952038	−	0.305980i	$-0.0989841\pi$
$702$	−6.07604	−	5.42433i	−0.229326	−	0.204728i
$703$	19.4509	−	11.2300i	0.733604	−	0.423546i
$704$	−46.5867	+	46.5867i	−1.75580	+	1.75580i
$705$	−15.3783	+	8.87869i	−0.579182	+	0.334391i
$706$	18.7955	+	32.5547i	0.707377	+	1.22521i
$707$	−1.79031	+	0.945426i	−0.0673317	+	0.0355564i
$708$	25.3484	+	6.79207i	0.952650	+	0.255262i
$709$	18.4817	+	18.4817i	0.694096	+	0.694096i	0.963131	−	0.269034i	$-0.0867045\pi$
$709$	18.4817	+	18.4817i	0.694096	+	0.694096i	−0.269034	+	0.963131i	$0.586704\pi$
$710$	69.0489	+	18.5016i	2.59136	+	0.694353i
$711$	6.31940	−	10.9455i	0.236996	−	0.410489i
$712$	11.1398	+	19.2947i	0.417481	+	0.723098i
$713$	5.58440	+	20.8413i	0.209137	+	0.780512i
$714$	30.1966	+	9.32572i	1.13008	+	0.349006i
$715$	−35.8523	+	23.4999i	−1.34080	+	0.878846i
$716$	10.5228	−	18.2261i	0.393256	−	0.681140i
$717$	2.43660	+	2.43660i	0.0909966	+	0.0909966i
$718$	52.6990			1.96671
$719$	12.7257			0.474588			0.237294	−	0.971438i	$-0.423740\pi$
$719$	12.7257			0.474588			0.237294	+	0.971438i	$0.423740\pi$
$720$	0.959971	+	0.959971i	0.0357760	+	0.0357760i
$721$	−0.552787	+	14.6397i	−0.0205869	+	0.545210i
$722$	0.671916	−	2.50763i	0.0250061	−	0.0933242i
$723$	−4.63565	+	1.24212i	−0.172402	+	0.0461949i
$724$	29.3265	+	16.9316i	1.08991	+	0.629259i
$725$		−	0.615948i		−	0.0228758i
$726$	−31.6229	−	8.47333i	−1.17364	−	0.314475i
$727$	43.5266			1.61431			0.807157	−	0.590337i	$-0.201005\pi$
$727$	43.5266			1.61431			0.807157	+	0.590337i	$0.201005\pi$
$728$	−16.4905	+	17.1248i	−0.611178	+	0.634686i
$729$	−1.00000			−0.0370370
$730$	8.30485	+	2.22528i	0.307376	+	0.0823612i
$731$		−	58.9292i		−	2.17958i
$732$	8.48339	+	4.89789i	0.313555	+	0.181031i
$733$	−33.2097	+	8.89851i	−1.22663	+	0.328674i	−0.813265	−	0.581893i	$-0.802312\pi$
$733$	−33.2097	+	8.89851i	−1.22663	+	0.328674i	−0.413362	+	0.910567i	$0.635646\pi$
$734$	−14.0014	+	52.2538i	−0.516800	+	1.92872i
$735$	15.5548	+	5.45481i	0.573749	+	0.201204i
$736$	−17.7069	−	17.7069i	−0.652686	−	0.652686i
$737$	26.8284			0.988236
$738$	−13.1313			−0.483369
$739$	−11.8263	−	11.8263i	−0.435038	−	0.435038i	0.455300	−	0.890338i	$-0.349532\pi$
$739$	−11.8263	−	11.8263i	−0.435038	−	0.435038i	−0.890338	+	0.455300i	$0.849532\pi$
$740$	19.4229	−	33.6414i	0.713999	−	1.23668i
$741$	4.76893	+	14.4678i	0.175191	+	0.531488i
$742$	4.37324	+	4.71646i	0.160547	+	0.173147i
$743$	−5.21828	−	19.4749i	−0.191440	−	0.714465i	−0.993160	−	0.116764i	$-0.962748\pi$
$743$	−5.21828	−	19.4749i	−0.191440	−	0.714465i	0.801719	−	0.597700i	$-0.203919\pi$
$744$	−6.74986	−	11.6911i	−0.247462	−	0.428617i
$745$	18.5832	−	32.1871i	0.680836	−	1.17924i
$746$	−42.6711	−	11.4337i	−1.56230	−	0.418617i
$747$	7.21679	+	7.21679i	0.264048	+	0.264048i
$748$	80.0255	+	21.4428i	2.92602	+	0.784025i
$749$	−17.3488	−	10.9093i	−0.633913	−	0.398616i
$750$	−11.8491	−	20.5233i	−0.432669	−	0.749405i
$751$	16.8568	−	9.73227i	0.615113	−	0.355136i	−0.159851	−	0.987141i	$-0.551101\pi$
$751$	16.8568	−	9.73227i	0.615113	−	0.355136i	0.774964	+	0.632006i	$0.217768\pi$
$752$	3.07419	−	3.07419i	0.112104	−	0.112104i
$753$	15.5010	−	8.94953i	0.564890	−	0.326139i
$754$	−2.88148	−	8.74172i	−0.104937	−	0.318355i
$755$		−	38.1130i		−	1.38707i
$756$	−0.309797	+	8.20446i	−0.0112672	+	0.298393i
$757$	6.53791	−	11.3240i	0.237624	−	0.411577i	−0.722408	−	0.691467i	$-0.756965\pi$
$757$	6.53791	−	11.3240i	0.237624	−	0.411577i	0.960032	+	0.279890i	$0.0902980\pi$
$758$			86.8001i			3.15272i
$759$	5.20516	−	19.4259i	0.188935	−	0.705116i
$760$	6.41735	+	23.9499i	0.232782	+	0.868754i
$761$	−31.1657	+	31.1657i	−1.12975	+	1.12975i	−0.139537	+	0.990217i	$0.544562\pi$
$761$	−31.1657	+	31.1657i	−1.12975	+	1.12975i	−0.990217	+	0.139537i	$0.955438\pi$
$762$	1.77664	−	1.77664i	0.0643608	−	0.0643608i
$763$	28.8567	−	6.57599i	1.04468	−	0.238067i
$764$	−2.80880	−	1.62166i	−0.101619	−	0.0586696i
$765$	3.22269	−	12.0273i	0.116517	−	0.434846i
$766$	6.81676	+	11.8070i	0.246299	+	0.426603i
$767$	−29.8511	−	6.21260i	−1.07786	−	0.224324i
$768$	10.4698	+	6.04472i	0.377795	+	0.218120i
$769$	−12.8186	+	3.43473i	−0.462250	+	0.123860i	−0.482426	−	0.875937i	$-0.660244\pi$
$769$	−12.8186	+	3.43473i	−0.462250	+	0.123860i	0.0201755	+	0.999796i	$0.493578\pi$
$770$	67.8963	+	20.9686i	2.44681	+	0.755657i
$771$	5.54914	−	3.20380i	0.199847	−	0.115382i
$772$	7.91281	+	29.5310i	0.284788	+	1.06284i
$773$	−16.4501	+	4.40779i	−0.591669	+	0.158537i	−0.542216	−	0.840239i	$-0.682415\pi$
$773$	−16.4501	+	4.40779i	−0.591669	+	0.158537i	−0.0494533	+	0.998776i	$0.515748\pi$
$774$	24.3179	−	6.51596i	0.874089	−	0.234211i
$775$	0.764163	+	2.85190i	0.0274496	+	0.102443i
$776$	−36.0259	+	20.7996i	−1.29326	+	0.746662i
$777$	−13.7131	+	3.12499i	−0.491954	+	0.112109i
$778$	−49.5185	+	13.2684i	−1.77532	+	0.475697i
$779$	21.2689	+	12.2796i	0.762038	+	0.439963i
$780$	19.6545	+	17.5464i	0.703746	+	0.628262i
$781$	−33.9244	−	58.7589i	−1.21391	−	2.10256i
$782$	−12.3146	+	45.9588i	−0.440370	+	1.64348i
$783$	−0.978660	−	0.565030i	−0.0349745	−	0.0201925i
$784$	−4.02420	−	0.304338i	−0.143722	−	0.0108692i
$785$	14.7113	−	14.7113i	0.525069	−	0.525069i
$786$	1.86876	−	1.86876i	0.0666565	−	0.0666565i
$787$	4.78972	+	17.8755i	0.170735	+	0.637192i	0.997239	+	0.0742610i	$0.0236598\pi$
$787$	4.78972	+	17.8755i	0.170735	+	0.637192i	−0.826504	+	0.562931i	$0.809674\pi$
$788$	4.75077	−	17.7301i	0.169239	−	0.631609i
$789$			2.42997i			0.0865091i
$790$	−33.6164	+	58.2252i	−1.19602	+	2.07156i
$791$	−20.7382	−	13.0406i	−0.737367	−	0.463670i
$792$			12.5829i			0.447115i
$793$	−10.1629	−	5.12397i	−0.360894	−	0.181957i
$794$	−59.9236	+	34.5969i	−2.12661	+	1.22780i
$795$	1.79189	−	1.79189i	0.0635518	−	0.0635518i
$796$	14.2869	−	8.24857i	0.506387	−	0.292363i
$797$	−0.826191	−	1.43100i	−0.0292652	−	0.0506888i	0.851022	−	0.525130i	$-0.175983\pi$
$797$	−0.826191	−	1.43100i	−0.0292652	−	0.0506888i	−0.880287	+	0.474441i	$0.842650\pi$
$798$	13.4423	−	21.3771i	0.475852	−	0.756740i
$799$	−38.5158	−	10.3203i	−1.36259	−	0.365105i
$800$	−2.42300	−	2.42300i	−0.0856659	−	0.0856659i
$801$	−8.63520	−	2.31379i	−0.305110	−	0.0817539i
$802$	16.5148	−	28.6045i	0.583158	−	1.01006i
$803$	−4.08026	−	7.06722i	−0.143989	−	0.249397i
$804$	−4.26773	−	15.9274i	−0.150511	−	0.561716i
$805$	−7.32281	+	23.7112i	−0.258095	+	0.835710i
$806$	24.1867	+	36.9001i	0.851941	+	1.29975i
$807$	7.94178	−	13.7556i	0.279564	−	0.484219i
$808$	1.34851	+	1.34851i	0.0474406	+	0.0474406i
$809$	−39.0959			−1.37454			−0.687270	−	0.726402i	$-0.741191\pi$
$809$	−39.0959			−1.37454			−0.687270	+	0.726402i	$0.741191\pi$
$810$	5.31955			0.186910
$811$	−13.7840	−	13.7840i	−0.484023	−	0.484023i	0.422391	−	0.906414i	$-0.361191\pi$
$811$	−13.7840	−	13.7840i	−0.484023	−	0.484023i	−0.906414	+	0.422391i	$0.861191\pi$
$812$	−4.93895	+	7.85434i	−0.173323	+	0.275633i
$813$	2.30847	−	8.61532i	0.0809615	−	0.302153i
$814$	−58.5665	+	15.6929i	−2.05276	+	0.550034i
$815$	−16.1928	−	9.34892i	−0.567209	−	0.327478i
$816$			3.04853i			0.106720i
$817$	−45.4814	−	12.1867i	−1.59119	−	0.426358i
$818$	1.60975			0.0562837
$819$	−0.179969	−	9.53769i	−0.00628861	−	0.333274i
$820$	42.4766			1.48335
$821$	−8.58998	−	2.30168i	−0.299792	−	0.0803291i	0.105787	−	0.994389i	$-0.466264\pi$
$821$	−8.58998	−	2.30168i	−0.299792	−	0.0803291i	−0.405580	+	0.914060i	$0.632930\pi$
$822$			27.6584i			0.964697i
$823$	33.8210	+	19.5266i	1.17893	+	0.680654i	0.955766	−	0.294128i	$-0.0950292\pi$
$823$	33.8210	+	19.5266i	1.17893	+	0.680654i	0.223161	+	0.974782i	$0.428362\pi$
$824$	13.3295	−	3.57163i	0.464355	−	0.124423i
$825$	0.712268	−	2.65822i	0.0247980	−	0.0925474i
$826$	23.6022	+	44.6944i	0.821224	+	1.55512i
$827$	−23.1975	−	23.1975i	−0.806658	−	0.806658i	0.177469	−	0.984126i	$-0.443209\pi$
$827$	−23.1975	−	23.1975i	−0.806658	−	0.806658i	−0.984126	+	0.177469i	$0.943209\pi$
$828$	−12.3607			−0.429565
$829$	−22.8221			−0.792644			−0.396322	−	0.918112i	$-0.629714\pi$
$829$	−22.8221			−0.792644			−0.396322	+	0.918112i	$0.629714\pi$
$830$	−38.3900	−	38.3900i	−1.33254	−	1.33254i
$831$	11.2868	−	19.5494i	0.391536	−	0.678160i
$832$	−42.0107	−	21.1812i	−1.45646	−	0.734325i
$833$	16.0370	+	33.3596i	0.555651	+	1.15584i
$834$	−11.7775	−	43.9543i	−0.407822	−	1.52201i
$835$	11.5956	+	20.0841i	0.401282	+	0.695041i
$836$	33.0989	−	57.3290i	1.14475	−	1.98276i
$837$	5.23228	+	1.40198i	0.180854	+	0.0484597i
$838$	−55.8397	−	55.8397i	−1.92895	−	1.92895i
$839$	5.67692	+	1.52113i	0.195989	+	0.0525151i	0.355478	−	0.934685i	$-0.384318\pi$
$839$	5.67692	+	1.52113i	0.195989	+	0.0525151i	−0.159489	+	0.987200i	$0.550985\pi$
$840$	0.585864	−	15.5157i	0.0202142	−	0.535341i
$841$	13.8615	+	24.0088i	0.477982	+	0.827889i
$842$	26.4626	−	15.2782i	0.911960	−	0.526520i
$843$	2.03059	−	2.03059i	0.0699372	−	0.0699372i
$844$	47.1011	−	27.1939i	1.62129	−	0.936051i
$845$	−23.9531	−	19.0621i	−0.824011	−	0.655757i
$846$		−	17.0352i		−	0.585682i
$847$	−17.9049	−	33.9057i	−0.615219	−	1.16501i
$848$	−0.310216	+	0.537309i	−0.0106529	+	0.0184513i
$849$		−	7.12281i		−	0.244454i
$850$	−1.68512	+	6.28895i	−0.0577991	+	0.215709i
$851$	−5.48036	−	20.4530i	−0.187864	−	0.701120i
$852$	−29.4872	+	29.4872i	−1.01022	+	1.01022i
$853$	−19.3964	+	19.3964i	−0.664121	+	0.664121i	−0.956349	−	0.292228i	$-0.905603\pi$
$853$	−19.3964	+	19.3964i	−0.664121	+	0.664121i	0.292228	+	0.956349i	$0.405603\pi$
$854$	4.19198	+	18.3952i	0.143447	+	0.629472i
$855$	−8.61613	−	4.97453i	−0.294666	−	0.170125i
$856$	−4.99628	+	18.6464i	−0.170769	+	0.637320i
$857$	2.06684	+	3.57986i	0.0706017	+	0.122286i	0.899165	−	0.437609i	$-0.144175\pi$
$857$	2.06684	+	3.57986i	0.0706017	+	0.122286i	−0.828563	+	0.559895i	$0.810841\pi$
$858$	−2.32674	−	41.0583i	−0.0794335	−	1.40171i
$859$	−36.1933	−	20.8962i	−1.23490	−	0.712969i	−0.266851	−	0.963738i	$-0.585983\pi$
$859$	−36.1933	−	20.8962i	−1.23490	−	0.712969i	−0.968047	+	0.250769i	$0.919317\pi$
$860$	−78.6626	+	21.0776i	−2.68237	+	0.718739i
$861$	−10.4567	−	11.2774i	−0.356363	−	0.384331i
$862$	−19.2428	+	11.1099i	−0.655413	+	0.378403i
$863$	−0.399033	−	1.48921i	−0.0135832	−	0.0506933i	0.958802	−	0.284077i	$-0.0916870\pi$
$863$	−0.399033	−	1.48921i	−0.0135832	−	0.0506933i	−0.972385	+	0.233383i	$0.925020\pi$
$864$	−6.07252	+	1.62713i	−0.206591	+	0.0553560i
$865$	7.71132	−	2.06624i	0.262193	−	0.0702544i
$866$	7.81148	+	29.1529i	0.265445	+	0.990654i
$867$	9.49176	−	5.48007i	0.322357	−	0.186113i
$868$	13.1235	−	42.4937i	0.445440	−	1.44233i
$869$	61.6388	−	16.5161i	2.09095	−	0.560269i
$870$	5.20603	+	3.00570i	0.176501	+	0.101903i
$871$	5.99767	+	18.1955i	0.203223	+	0.616532i
$872$	−13.9393	−	24.1435i	−0.472043	−	0.817602i
$873$	4.32019	−	16.1232i	0.146216	−	0.545687i
$874$	32.9241	+	19.0088i	1.11368	+	0.642981i
$875$	8.19005	−	26.5193i	0.276874	−	0.896516i
$876$	−3.54657	+	3.54657i	−0.119828	+	0.119828i
$877$	−37.8335	+	37.8335i	−1.27755	+	1.27755i	−0.335511	+	0.942036i	$0.608909\pi$
$877$	−37.8335	+	37.8335i	−1.27755	+	1.27755i	−0.942036	+	0.335511i	$0.891091\pi$
$878$	0.318687	+	1.18936i	0.0107552	+	0.0401389i
$879$	−2.31888	+	8.65417i	−0.0782138	+	0.291898i
$880$			6.85453i			0.231066i
$881$	10.7817	−	18.6745i	0.363246	−	0.629160i	−0.625247	−	0.780427i	$-0.715002\pi$
$881$	10.7817	−	18.6745i	0.363246	−	0.629160i	0.988493	+	0.151266i	$0.0483351\pi$
$882$	−11.9930	+	10.3066i	−0.403825	+	0.347040i
$883$		−	28.6771i		−	0.965061i	−0.875879	−	0.482530i	$-0.839718\pi$
$883$		−	28.6771i		−	0.965061i	0.875879	−	0.482530i	$-0.160282\pi$
$884$	3.34735	+	59.0685i	0.112584	+	1.98669i
$885$	17.2456	−	9.95678i	0.579706	−	0.334693i
$886$	67.0670	−	67.0670i	2.25316	−	2.25316i
$887$	−21.9875	+	12.6945i	−0.738269	+	0.426240i	−0.821440	−	0.570295i	$-0.806829\pi$
$887$	−21.9875	+	12.6945i	−0.738269	+	0.426240i	0.0831704	+	0.996535i	$0.473495\pi$
$888$	6.62411	+	11.4733i	0.222291	+	0.385019i
$889$	2.94057	+	0.111035i	0.0986236	+	0.00372398i
$890$	45.9353	+	12.3083i	1.53976	+	0.412576i
$891$	−3.57017	−	3.57017i	−0.119605	−	0.119605i
$892$	−39.8197	−	10.6697i	−1.33326	−	0.357247i
$893$	−15.9303	+	27.5921i	−0.533088	+	0.923335i
$894$	17.8275	+	30.8781i	0.596239	+	1.03272i
$895$	−4.13334	−	15.4258i	−0.138162	−	0.515629i
$896$	9.93722	+	43.6065i	0.331979	+	1.45679i
$897$	14.3387	−	0.812559i	0.478754	−	0.0271306i
$898$	41.1601	−	71.2914i	1.37353	−	2.37903i
$899$	4.32846	+	4.32846i	0.144362	+	0.144362i
$900$	−1.69143			−0.0563809
$901$	5.69041			0.189575
$902$	−46.8810	−	46.8810i	−1.56097	−	1.56097i
$903$	24.9608	+	15.6958i	0.830644	+	0.522324i
$904$	−5.97239	+	22.2893i	−0.198639	+	0.741330i
$905$	24.8208	−	6.65070i	0.825070	−	0.221077i
$906$	31.6645	+	18.2815i	1.05198	+	0.607362i
$907$			19.4640i			0.646293i	0.946349	+	0.323146i	$0.104741\pi$
$907$			19.4640i			0.646293i	−0.946349	+	0.323146i	$0.895259\pi$
$908$	59.8727	+	16.0429i	1.98695	+	0.532401i
$909$	−0.765232			−0.0253811
$910$	0.957351	+	50.7362i	0.0317359	+	1.68189i
$911$	−50.4080			−1.67009			−0.835046	−	0.550180i	$-0.814559\pi$
$911$	−50.4080			−1.67009			−0.835046	+	0.550180i	$0.814559\pi$
$912$	2.35284	+	0.630442i	0.0779104	+	0.0208760i
$913$			51.5304i			1.70541i
$914$	1.48914	+	0.859756i	0.0492564	+	0.0284382i
$915$	7.18001	−	1.92388i	0.237364	−	0.0636015i
$916$	1.08634	−	4.05428i	0.0358937	−	0.133957i
$917$	3.09305	+	0.116792i	0.102141	+	0.00385681i
$918$	8.44649	+	8.44649i	0.278776	+	0.278776i
$919$	−56.5934			−1.86684			−0.933422	−	0.358781i	$-0.883193\pi$
$919$	−56.5934			−1.86684			−0.933422	+	0.358781i	$0.883193\pi$
$920$	23.3757			0.770673
$921$	16.8943	+	16.8943i	0.556685	+	0.556685i
$922$	−37.3884	+	64.7585i	−1.23132	+	2.13271i
$923$	32.2673	−	36.1441i	1.06209	−	1.18970i
$924$	−30.3974	+	28.1853i	−1.00000	+	0.927229i
$925$	−0.749927	−	2.79877i	−0.0246575	−	0.0920229i
$926$	−8.52075	−	14.7584i	−0.280009	−	0.484990i
$927$	−2.76861	+	4.79537i	−0.0909331	+	0.157501i
$928$	−6.86231	−	1.83875i	−0.225266	−	0.0603599i
$929$	−2.62133	−	2.62133i	−0.0860029	−	0.0860029i	0.662797	−	0.748799i	$-0.269369\pi$
$929$	−2.62133	−	2.62133i	−0.0860029	−	0.0860029i	−0.748799	+	0.662797i	$0.769369\pi$
$930$	−27.8333	−	7.45792i	−0.912691	−	0.244555i
$931$	29.0633	−	5.47850i	0.952511	−	0.179551i
$932$	−33.8826	−	58.6865i	−1.10986	−	1.92234i
$933$	15.1348	−	8.73808i	0.495491	−	0.286072i
$934$	18.6359	−	18.6359i	0.609787	−	0.609787i
$935$	54.4449	−	31.4338i	1.78054	−	1.02800i
$936$	−8.53399	+	2.81300i	−0.278942	+	0.0919458i
$937$			24.1869i			0.790151i	0.918649	+	0.395076i	$0.129282\pi$
$937$			24.1869i			0.790151i	−0.918649	+	0.395076i	$0.870718\pi$
$938$	16.9058	−	26.8850i	0.551993	−	0.877825i
$939$	3.28670	−	5.69274i	0.107258	−	0.185775i
$940$			55.1048i			1.79732i
$941$	−5.44880	+	20.3352i	−0.177626	+	0.662909i	0.818464	+	0.574558i	$0.194826\pi$
$941$	−5.44880	+	20.3352i	−0.177626	+	0.662909i	−0.996089	+	0.0883504i	$0.971840\pi$
$942$	5.16572	+	19.2787i	0.168308	+	0.628135i
$943$	16.3721	−	16.3721i	0.533149	−	0.533149i
$944$	−3.44747	+	3.44747i	−0.112206	+	0.112206i
$945$	4.23605	+	4.56851i	0.137799	+	0.148614i
$946$	110.082	+	63.5560i	3.57908	+	2.06638i
$947$	−8.82979	+	32.9532i	−0.286930	+	1.07084i	0.660488	+	0.750836i	$0.270349\pi$
$947$	−8.82979	+	32.9532i	−0.286930	+	1.07084i	−0.947418	+	0.319999i	$0.896317\pi$
$948$	−19.6104	−	33.9662i	−0.636916	−	1.10317i
$949$	3.88095	−	4.34723i	0.125981	−	0.141117i
$950$	4.50530	+	2.60114i	0.146171	+	0.0843920i
$951$	−31.1389	+	8.34364i	−1.00975	+	0.270561i
$952$	25.5664	−	23.7059i	0.828610	−	0.768311i
$953$	42.0367	−	24.2699i	1.36170	−	0.786180i	0.371853	−	0.928292i	$-0.378722\pi$
$953$	42.0367	−	24.2699i	1.36170	−	0.786180i	0.989851	+	0.142111i	$0.0453891\pi$
$954$	0.629204	+	2.34822i	0.0203712	+	0.0760264i
$955$	−2.37726	+	0.636984i	−0.0769263	+	0.0206123i
$956$	10.3289	−	2.76762i	0.334061	−	0.0895113i
$957$	−1.47673	−	5.51124i	−0.0477360	−	0.178153i
$958$	−16.7782	+	9.68687i	−0.542078	+	0.312969i
$959$	−23.7534	+	22.0249i	−0.767039	+	0.711220i
$960$	29.6804	−	7.95283i	0.957929	−	0.256676i
$961$	1.43561	+	0.828853i	0.0463102	+	0.0267372i
$962$	−23.7361	−	36.2127i	−0.765284	−	1.16754i
$963$	−3.87296	−	6.70816i	−0.124804	−	0.216167i
$964$	−3.85455	+	14.3854i	−0.124147	+	0.463322i
$965$	20.0913	+	11.5997i	0.646761	+	0.373408i
$966$	−16.1869	−	17.4573i	−0.520804	−	0.561678i
$967$	5.80997	−	5.80997i	0.186836	−	0.186836i	−0.607491	−	0.794327i	$-0.707824\pi$
$967$	5.80997	−	5.80997i	0.186836	−	0.186836i	0.794327	+	0.607491i	$0.207824\pi$
$968$	−25.5387	+	25.5387i	−0.820846	+	0.820846i
$969$	−5.78222	−	21.5795i	−0.185752	−	0.693235i
$970$	−22.9815	+	85.7680i	−0.737890	+	2.75384i
$971$			13.1439i			0.421806i	0.977507	+	0.210903i	$0.0676405\pi$
$971$			13.1439i			0.421806i	−0.977507	+	0.210903i	$0.932360\pi$
$972$	−1.55160	+	2.68745i	−0.0497677	+	0.0862001i
$973$	28.3700	−	45.1163i	0.909499	−	1.44636i
$974$			95.8541i			3.07136i
$975$	1.96209	−	0.111190i	0.0628371	−	0.00356092i
$976$	−1.57608	+	0.909952i	−0.0504492	+	0.0291269i
$977$	−6.93033	+	6.93033i	−0.221721	+	0.221721i	−0.809223	−	0.587502i	$-0.800111\pi$
$977$	−6.93033	+	6.93033i	−0.221721	+	0.221721i	0.587502	+	0.809223i	$0.300111\pi$
$978$	15.5343	−	8.96870i	0.496731	−	0.286788i
$979$	−22.5685	−	39.0898i	−0.721292	−	1.24932i
$980$	38.7945	−	33.3392i	1.23924	−	1.06498i
$981$	10.8053	+	2.89526i	0.344986	+	0.0924386i
$982$	36.9100	+	36.9100i	1.17784	+	1.17784i
$983$	−52.1268	−	13.9673i	−1.66259	−	0.445489i	−0.699490	−	0.714643i	$-0.746589\pi$
$983$	−52.1268	−	13.9673i	−1.66259	−	0.445489i	−0.963097	+	0.269154i	$0.913256\pi$
$984$	−7.24325	+	12.5457i	−0.230906	+	0.399942i
$985$	−6.96434	−	12.0626i	−0.221902	−	0.384346i
$986$	3.49373	+	13.0388i	0.111263	+	0.415239i
$987$	14.6301	−	13.5654i	0.465681	−	0.431793i
$988$	46.2811	+	9.63201i	1.47240	+	0.306435i
$989$	−22.1955	+	38.4437i	−0.705775	+	1.22244i
$990$	18.9917	+	18.9917i	0.603596	+	0.603596i
$991$	−45.8226			−1.45560			−0.727801	−	0.685789i	$-0.759457\pi$
$991$	−45.8226			−1.45560			−0.727801	+	0.685789i	$0.759457\pi$
$992$	34.0543			1.08123
$993$	19.1496	+	19.1496i	0.607695	+	0.607695i
$994$	−80.2601	−	3.03058i	−2.54569	−	0.0961242i
$995$	3.24002	−	12.0919i	0.102716	−	0.383339i
$996$	30.5924	−	8.19720i	0.969356	−	0.259738i
$997$	−14.5145	−	8.37997i	−0.459680	−	0.265396i	0.252230	−	0.967667i	$-0.418836\pi$
$997$	−14.5145	−	8.37997i	−0.459680	−	0.265396i	−0.711910	+	0.702271i	$0.752170\pi$
$998$		−	77.7895i		−	2.46238i
$999$	−5.13480	−	1.37587i	−0.162458	−	0.0435305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.19.9	yes	40
3.2	odd	2		819.2.gh.d.19.2		40
7.3	odd	6		273.2.bt.b.136.2	✓	40
13.11	odd	12		273.2.bt.b.271.2	yes	40
21.17	even	6		819.2.et.d.136.9		40
39.11	even	12		819.2.et.d.271.9		40
91.24	even	12	inner	273.2.cg.b.115.9	yes	40
273.206	odd	12		819.2.gh.d.388.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.2	✓	40	7.3	odd	6
273.2.bt.b.271.2	yes	40	13.11	odd	12
273.2.cg.b.19.9	yes	40	1.1	even	1	trivial
273.2.cg.b.115.9	yes	40	91.24	even	12	inner
819.2.et.d.136.9		40	21.17	even	6
819.2.et.d.271.9		40	39.11	even	12
819.2.gh.d.19.2		40	3.2	odd	2
819.2.gh.d.388.2		40	273.206	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.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.18205 + 0.584679i) q^{2} +1.00000i q^{3} +(2.68745 + 1.55160i) q^{4} +(2.27456 - 0.609466i) q^{5} +(-0.584679 + 2.18205i) q^{6} +(-2.33957 + 1.23548i) q^{7} +(1.76223 + 1.76223i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(2.18205 + 0.584679i) q^{2} +1.00000i q^{3} +(2.68745 + 1.55160i) q^{4} +(2.27456 - 0.609466i) q^{5} +(-0.584679 + 2.18205i) q^{6} +(-2.33957 + 1.23548i) q^{7} +(1.76223 + 1.76223i) q^{8} -1.00000 q^{9} +5.31955 q^{10} +(-3.57017 - 3.57017i) q^{11} +(-1.55160 + 2.68745i) q^{12} +(1.62322 - 3.21950i) q^{13} +(-5.82743 + 1.32798i) q^{14} +(0.609466 + 2.27456i) q^{15} +(-0.288264 - 0.499288i) q^{16} +(-2.64387 + 4.57931i) q^{17} +(-2.18205 - 0.584679i) q^{18} +(2.98754 + 2.98754i) q^{19} +(7.05842 + 1.89130i) q^{20} +(-1.23548 - 2.33957i) q^{21} +(-5.70290 - 9.87771i) q^{22} +(3.44956 - 1.99161i) q^{23} +(-1.76223 + 1.76223i) q^{24} +(0.472034 - 0.272529i) q^{25} +(5.42433 - 6.07604i) q^{26} -1.00000i q^{27} +(-8.20446 - 0.309797i) q^{28} +(0.565030 - 0.978660i) q^{29} +5.31955i q^{30} +(-1.40198 + 5.23228i) q^{31} +(-1.62713 - 6.07252i) q^{32} +(3.57017 - 3.57017i) q^{33} +(-8.44649 + 8.44649i) q^{34} +(-4.56851 + 4.23605i) q^{35} +(-2.68745 - 1.55160i) q^{36} +(1.37587 - 5.13480i) q^{37} +(4.77222 + 8.26572i) q^{38} +(3.21950 + 1.62322i) q^{39} +(5.08231 + 2.93428i) q^{40} +(5.61474 - 1.50446i) q^{41} +(-1.32798 - 5.82743i) q^{42} +(-9.65143 + 5.57225i) q^{43} +(-4.05519 - 15.1342i) q^{44} +(-2.27456 + 0.609466i) q^{45} +(8.69158 - 2.32890i) q^{46} +(1.95174 + 7.28399i) q^{47} +(0.499288 - 0.288264i) q^{48} +(3.94719 - 5.78098i) q^{49} +(1.18935 - 0.318684i) q^{50} +(-4.57931 - 2.64387i) q^{51} +(9.35771 - 6.13365i) q^{52} +(-0.538076 - 0.931975i) q^{53} +(0.584679 - 2.18205i) q^{54} +(-10.2965 - 5.94466i) q^{55} +(-6.30006 - 1.94567i) q^{56} +(-2.98754 + 2.98754i) q^{57} +(1.80513 - 1.80513i) q^{58} +(-2.18873 - 8.16845i) q^{59} +(-1.89130 + 7.05842i) q^{60} -3.15666i q^{61} +(-6.11841 + 10.5974i) q^{62} +(2.33957 - 1.23548i) q^{63} -13.0488i q^{64} +(1.72994 - 8.31222i) q^{65} +(9.87771 - 5.70290i) q^{66} +(-3.75730 + 3.75730i) q^{67} +(-14.2105 + 8.20446i) q^{68} +(1.99161 + 3.44956i) q^{69} +(-12.4455 + 6.57218i) q^{70} +(12.9802 + 3.47804i) q^{71} +(-1.76223 - 1.76223i) q^{72} +(1.56120 + 0.418321i) q^{73} +(6.00443 - 10.4000i) q^{74} +(0.272529 + 0.472034i) q^{75} +(3.39340 + 12.6644i) q^{76} +(12.7635 + 3.94181i) q^{77} +(6.07604 + 5.42433i) q^{78} +(-6.31940 + 10.9455i) q^{79} +(-0.959971 - 0.959971i) q^{80} +1.00000 q^{81} +13.1313 q^{82} +(-7.21679 - 7.21679i) q^{83} +(0.309797 - 8.20446i) q^{84} +(-3.22269 + 12.0273i) q^{85} +(-24.3179 + 6.51596i) q^{86} +(0.978660 + 0.565030i) q^{87} -12.5829i q^{88} +(8.63520 + 2.31379i) q^{89} -5.31955 q^{90} +(0.179969 + 9.53769i) q^{91} +12.3607 q^{92} +(-5.23228 - 1.40198i) q^{93} +17.0352i q^{94} +(8.61613 + 4.97453i) q^{95} +(6.07252 - 1.62713i) q^{96} +(-4.32019 + 16.1232i) q^{97} +(11.9930 - 10.3066i) q^{98} +(3.57017 + 3.57017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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