LMFDB - Embedded newform 273.2.cg.a.115.6

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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.6
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.562494 - 0.150720i) q^{2} +1.00000i q^{3} +(-1.43837 + 0.830442i) q^{4} +(-0.672922 - 0.180309i) q^{5} +(0.150720 + 0.562494i) q^{6} +(-2.49458 + 0.881516i) q^{7} +(-1.50746 + 1.50746i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.562494 - 0.150720i) q^{2} +1.00000i q^{3} +(-1.43837 + 0.830442i) q^{4} +(-0.672922 - 0.180309i) q^{5} +(0.150720 + 0.562494i) q^{6} +(-2.49458 + 0.881516i) q^{7} +(-1.50746 + 1.50746i) q^{8} -1.00000 q^{9} -0.405691 q^{10} +(-0.628957 + 0.628957i) q^{11} +(-0.830442 - 1.43837i) q^{12} +(-0.659853 + 3.54466i) q^{13} +(-1.27033 + 0.871831i) q^{14} +(0.180309 - 0.672922i) q^{15} +(1.04015 - 1.80159i) q^{16} +(-0.0230331 - 0.0398944i) q^{17} +(-0.562494 + 0.150720i) q^{18} +(-0.617410 + 0.617410i) q^{19} +(1.11765 - 0.299472i) q^{20} +(-0.881516 - 2.49458i) q^{21} +(-0.258989 + 0.448581i) q^{22} +(2.76363 + 1.59558i) q^{23} +(-1.50746 - 1.50746i) q^{24} +(-3.90981 - 2.25733i) q^{25} +(0.163087 + 2.09330i) q^{26} -1.00000i q^{27} +(2.85607 - 3.33955i) q^{28} +(4.08244 + 7.07099i) q^{29} -0.405691i q^{30} +(1.04511 + 3.90039i) q^{31} +(1.41708 - 5.28861i) q^{32} +(-0.628957 - 0.628957i) q^{33} +(-0.0189689 - 0.0189689i) q^{34} +(1.83760 - 0.143397i) q^{35} +(1.43837 - 0.830442i) q^{36} +(-1.82246 - 6.80150i) q^{37} +(-0.254234 + 0.440346i) q^{38} +(-3.54466 - 0.659853i) q^{39} +(1.28621 - 0.742594i) q^{40} +(8.56284 + 2.29441i) q^{41} +(-0.871831 - 1.27033i) q^{42} +(1.29226 + 0.746085i) q^{43} +(0.382359 - 1.42698i) q^{44} +(0.672922 + 0.180309i) q^{45} +(1.79501 + 0.480971i) q^{46} +(-3.24985 + 12.1286i) q^{47} +(1.80159 + 1.04015i) q^{48} +(5.44586 - 4.39802i) q^{49} +(-2.53947 - 0.680450i) q^{50} +(0.0398944 - 0.0230331i) q^{51} +(-1.99452 - 5.64649i) q^{52} +(4.89224 - 8.47362i) q^{53} +(-0.150720 - 0.562494i) q^{54} +(0.536646 - 0.309833i) q^{55} +(2.43163 - 5.08932i) q^{56} +(-0.617410 - 0.617410i) q^{57} +(3.36209 + 3.36209i) q^{58} +(-2.28980 + 8.54567i) q^{59} +(0.299472 + 1.11765i) q^{60} -1.01326i q^{61} +(1.17573 + 2.03643i) q^{62} +(2.49458 - 0.881516i) q^{63} +0.972206i q^{64} +(1.08316 - 2.26630i) q^{65} +(-0.448581 - 0.258989i) q^{66} +(-1.77192 - 1.77192i) q^{67} +(0.0662600 + 0.0382552i) q^{68} +(-1.59558 + 2.76363i) q^{69} +(1.01203 - 0.357623i) q^{70} +(-0.798336 + 0.213913i) q^{71} +(1.50746 - 1.50746i) q^{72} +(-15.2725 + 4.09226i) q^{73} +(-2.05024 - 3.55112i) q^{74} +(2.25733 - 3.90981i) q^{75} +(0.375340 - 1.40079i) q^{76} +(1.01455 - 2.12342i) q^{77} +(-2.09330 + 0.163087i) q^{78} +(-4.73655 - 8.20394i) q^{79} +(-1.02478 + 1.02478i) q^{80} +1.00000 q^{81} +5.16236 q^{82} +(3.50364 - 3.50364i) q^{83} +(3.33955 + 2.85607i) q^{84} +(0.00830614 + 0.0309989i) q^{85} +(0.839337 + 0.224900i) q^{86} +(-7.07099 + 4.08244i) q^{87} -1.89625i q^{88} +(-5.05100 + 1.35341i) q^{89} +0.405691 q^{90} +(-1.47861 - 9.42410i) q^{91} -5.30014 q^{92} +(-3.90039 + 1.04511i) q^{93} +7.31209i q^{94} +(0.526794 - 0.304145i) q^{95} +(5.28861 + 1.41708i) q^{96} +(0.288642 + 1.07723i) q^{97} +(2.40040 - 3.29466i) q^{98} +(0.628957 - 0.628957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.562494	−	0.150720i	0.397744	−	0.106575i	−0.0544022	−	0.998519i	$-0.517325\pi$
$2$	0.562494	−	0.150720i	0.397744	−	0.106575i	0.452146	+	0.891944i	$0.350659\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.43837	+	0.830442i	−0.719184	+	0.415221i
$5$	−0.672922	−	0.180309i	−0.300940	−	0.0806367i	0.105189	−	0.994452i	$-0.466455\pi$
$5$	−0.672922	−	0.180309i	−0.300940	−	0.0806367i	−0.406129	+	0.913816i	$0.633122\pi$
$6$	0.150720	+	0.562494i	0.0615312	+	0.229637i
$7$	−2.49458	+	0.881516i	−0.942863	+	0.333182i
$7$	−2.49458	+	0.881516i	−0.942863	+	0.333182i
$8$	−1.50746	+	1.50746i	−0.532967	+	0.532967i
$9$	−1.00000			−0.333333
$10$	−0.405691			−0.128291
$11$	−0.628957	+	0.628957i	−0.189638	+	0.189638i	−0.795539	−	0.605902i	$-0.792812\pi$
$11$	−0.628957	+	0.628957i	−0.189638	+	0.189638i	0.605902	+	0.795539i	$0.292812\pi$
$12$	−0.830442	−	1.43837i	−0.239728	−	0.415221i
$13$	−0.659853	+	3.54466i	−0.183010	+	0.983111i
$13$	−0.659853	+	3.54466i	−0.183010	+	0.983111i
$14$	−1.27033	+	0.871831i	−0.339509	+	0.233007i
$15$	0.180309	−	0.672922i	0.0465556	−	0.173748i
$16$	1.04015	−	1.80159i	0.260038	−	0.450398i
$17$	−0.0230331	−	0.0398944i	−0.00558634	−	0.00967582i	0.863219	−	0.504830i	$-0.168445\pi$
$17$	−0.0230331	−	0.0398944i	−0.00558634	−	0.00967582i	−0.868805	+	0.495154i	$0.835112\pi$
$18$	−0.562494	+	0.150720i	−0.132581	+	0.0355250i
$19$	−0.617410	+	0.617410i	−0.141644	+	0.141644i	−0.774373	−	0.632729i	$-0.781935\pi$
$19$	−0.617410	+	0.617410i	−0.141644	+	0.141644i	0.632729	+	0.774373i	$0.281935\pi$
$20$	1.11765	−	0.299472i	0.249913	−	0.0669640i
$21$	−0.881516	−	2.49458i	−0.192363	−	0.544362i
$22$	−0.258989	+	0.448581i	−0.0552165	+	0.0956379i
$23$	2.76363	+	1.59558i	0.576256	+	0.332701i	0.759644	−	0.650339i	$-0.225373\pi$
$23$	2.76363	+	1.59558i	0.576256	+	0.332701i	−0.183388	+	0.983041i	$0.558707\pi$
$24$	−1.50746	−	1.50746i	−0.307709	−	0.307709i
$25$	−3.90981	−	2.25733i	−0.781963	−	0.451466i
$26$	0.163087	+	2.09330i	0.0319839	+	0.410530i
$27$		−	1.00000i		−	0.192450i
$28$	2.85607	−	3.33955i	0.539747	−	0.631115i
$29$	4.08244	+	7.07099i	0.758090	+	1.31305i	0.943824	+	0.330450i	$0.107200\pi$
$29$	4.08244	+	7.07099i	0.758090	+	1.31305i	−0.185734	+	0.982600i	$0.559466\pi$
$30$		−	0.405691i		−	0.0740688i
$31$	1.04511	+	3.90039i	0.187707	+	0.700531i	0.994035	+	0.109063i	$0.0347849\pi$
$31$	1.04511	+	3.90039i	0.187707	+	0.700531i	−0.806328	+	0.591468i	$0.798548\pi$
$32$	1.41708	−	5.28861i	0.250507	−	0.934903i
$33$	−0.628957	−	0.628957i	−0.109487	−	0.109487i
$34$	−0.0189689	−	0.0189689i	−0.00325313	−	0.00325313i
$35$	1.83760	−	0.143397i	0.310612	−	0.0242385i
$36$	1.43837	−	0.830442i	0.239728	−	0.138407i
$37$	−1.82246	−	6.80150i	−0.299610	−	1.11816i	−0.937487	−	0.348021i	$-0.886854\pi$
$37$	−1.82246	−	6.80150i	−0.299610	−	1.11816i	0.637877	−	0.770138i	$-0.279813\pi$
$38$	−0.254234	+	0.440346i	−0.0412422	+	0.0714335i
$39$	−3.54466	−	0.659853i	−0.567599	−	0.105661i
$40$	1.28621	−	0.742594i	0.203368	−	0.117414i
$41$	8.56284	+	2.29441i	1.33729	+	0.358326i	0.855429	−	0.517921i	$-0.173294\pi$
$41$	8.56284	+	2.29441i	1.33729	+	0.358326i	0.481863	+	0.876247i	$0.339960\pi$
$42$	−0.871831	−	1.27033i	−0.134526	−	0.196015i
$43$	1.29226	+	0.746085i	0.197067	+	0.113777i	0.595287	−	0.803513i	$-0.297038\pi$
$43$	1.29226	+	0.746085i	0.197067	+	0.113777i	−0.398219	+	0.917290i	$0.630372\pi$
$44$	0.382359	−	1.42698i	0.0576428	−	0.215126i
$45$	0.672922	+	0.180309i	0.100313	+	0.0268789i
$46$	1.79501	+	0.480971i	0.264660	+	0.0709154i
$47$	−3.24985	+	12.1286i	−0.474039	+	1.76914i	0.150987	+	0.988536i	$0.451755\pi$
$47$	−3.24985	+	12.1286i	−0.474039	+	1.76914i	−0.625026	+	0.780604i	$0.714912\pi$
$48$	1.80159	+	1.04015i	0.260038	+	0.150133i
$49$	5.44586	−	4.39802i	0.777980	−	0.628289i
$50$	−2.53947	−	0.680450i	−0.359136	−	0.0962301i
$51$	0.0398944	−	0.0230331i	0.00558634	−	0.00322527i
$52$	−1.99452	−	5.64649i	−0.276590	−	0.783027i
$53$	4.89224	−	8.47362i	0.672001	−	1.16394i	−0.305334	−	0.952245i	$-0.598768\pi$
$53$	4.89224	−	8.47362i	0.672001	−	1.16394i	0.977336	−	0.211695i	$-0.0678985\pi$
$54$	−0.150720	−	0.562494i	−0.0205104	−	0.0765458i
$55$	0.536646	−	0.309833i	0.0723613	−	0.0417778i
$56$	2.43163	−	5.08932i	0.324940	−	0.680090i
$57$	−0.617410	−	0.617410i	−0.0817780	−	0.0817780i
$58$	3.36209	+	3.36209i	0.441464	+	0.441464i
$59$	−2.28980	+	8.54567i	−0.298107	+	1.11255i	0.640611	+	0.767866i	$0.278681\pi$
$59$	−2.28980	+	8.54567i	−0.298107	+	1.11255i	−0.938718	+	0.344686i	$0.887986\pi$
$60$	0.299472	+	1.11765i	0.0386617	+	0.144287i
$61$		−	1.01326i		−	0.129734i	−0.997894	−	0.0648672i	$-0.979338\pi$
$61$		−	1.01326i		−	0.129734i	0.997894	−	0.0648672i	$-0.0206624\pi$
$62$	1.17573	+	2.03643i	0.149318	+	0.258627i
$63$	2.49458	−	0.881516i	0.314288	−	0.111061i
$64$			0.972206i			0.121526i
$65$	1.08316	−	2.26630i	0.134350	−	0.281100i
$66$	−0.448581	−	0.258989i	−0.0552165	−	0.0318793i
$67$	−1.77192	−	1.77192i	−0.216474	−	0.216474i	0.590537	−	0.807011i	$-0.298916\pi$
$67$	−1.77192	−	1.77192i	−0.216474	−	0.216474i	−0.807011	+	0.590537i	$0.798916\pi$
$68$	0.0662600	+	0.0382552i	0.00803521	+	0.00463913i
$69$	−1.59558	+	2.76363i	−0.192085	+	0.332701i
$70$	1.01203	−	0.357623i	0.120961	−	0.0427442i
$71$	−0.798336	+	0.213913i	−0.0947450	+	0.0253869i	−0.305880	−	0.952070i	$-0.598951\pi$
$71$	−0.798336	+	0.213913i	−0.0947450	+	0.0253869i	0.211135	+	0.977457i	$0.432284\pi$
$72$	1.50746	−	1.50746i	0.177656	−	0.177656i
$73$	−15.2725	+	4.09226i	−1.78751	+	0.478963i	−0.991920	−	0.126867i	$-0.959508\pi$
$73$	−15.2725	+	4.09226i	−1.78751	+	0.478963i	−0.795594	+	0.605830i	$0.792841\pi$
$74$	−2.05024	−	3.55112i	−0.238336	−	0.412810i
$75$	2.25733	−	3.90981i	0.260654	−	0.451466i
$76$	0.375340	−	1.40079i	0.0430544	−	0.160681i
$77$	1.01455	−	2.12342i	0.115618	−	0.241986i
$78$	−2.09330	+	0.163087i	−0.237020	+	0.0184659i
$79$	−4.73655	−	8.20394i	−0.532903	−	0.923016i	−0.999262	−	0.0384199i	$-0.987768\pi$
$79$	−4.73655	−	8.20394i	−0.532903	−	0.923016i	0.466358	−	0.884596i	$-0.345566\pi$
$80$	−1.02478	+	1.02478i	−0.114574	+	0.114574i
$81$	1.00000			0.111111
$82$	5.16236			0.570088
$83$	3.50364	−	3.50364i	0.384574	−	0.384574i	−0.488173	−	0.872747i	$-0.662336\pi$
$83$	3.50364	−	3.50364i	0.384574	−	0.384574i	0.872747	+	0.488173i	$0.162336\pi$
$84$	3.33955	+	2.85607i	0.364374	+	0.311623i
$85$	0.00830614	+	0.0309989i	0.000900927	+	0.00336231i
$86$	0.839337	+	0.224900i	0.0905081	+	0.0242516i
$87$	−7.07099	+	4.08244i	−0.758090	+	0.437683i
$88$		−	1.89625i		−	0.202141i
$89$	−5.05100	+	1.35341i	−0.535405	+	0.143461i	−0.516383	−	0.856358i	$-0.672722\pi$
$89$	−5.05100	+	1.35341i	−0.535405	+	0.143461i	−0.0190218	+	0.999819i	$0.506055\pi$
$90$	0.405691			0.0427636
$91$	−1.47861	−	9.42410i	−0.155001	−	0.987914i
$92$	−5.30014			−0.552578
$93$	−3.90039	+	1.04511i	−0.404452	+	0.108373i
$94$			7.31209i			0.754185i
$95$	0.526794	−	0.304145i	0.0540479	−	0.0312046i
$96$	5.28861	+	1.41708i	0.539767	+	0.144630i
$97$	0.288642	+	1.07723i	0.0293071	+	0.109376i	0.979030	−	0.203716i	$-0.0653019\pi$
$97$	0.288642	+	1.07723i	0.0293071	+	0.109376i	−0.949723	+	0.313092i	$0.898635\pi$
$98$	2.40040	−	3.29466i	0.242477	−	0.332811i
$99$	0.628957	−	0.628957i	0.0632126	−	0.0632126i
$100$	7.49833			0.749833
$101$	14.6075			1.45350			0.726752	−	0.686900i	$-0.241029\pi$
$101$	14.6075			1.45350			0.726752	+	0.686900i	$0.241029\pi$
$102$	0.0189689	−	0.0189689i	0.00187820	−	0.00187820i
$103$	6.34652	+	10.9925i	0.625342	+	1.08312i	0.988475	+	0.151386i	$0.0483737\pi$
$103$	6.34652	+	10.9925i	0.625342	+	1.08312i	−0.363133	+	0.931737i	$0.618293\pi$
$104$	−4.34872	−	6.33812i	−0.426427	−	0.621504i
$105$	0.143397	+	1.83760i	0.0139941	+	0.179332i
$106$	1.47472	−	5.50372i	0.143237	−	0.534569i
$107$	−5.89611	+	10.2124i	−0.569999	+	0.987267i	0.426566	+	0.904456i	$0.359723\pi$
$107$	−5.89611	+	10.2124i	−0.569999	+	0.987267i	−0.996565	+	0.0828108i	$0.973610\pi$
$108$	0.830442	+	1.43837i	0.0799093	+	0.138407i
$109$	−3.31627	+	0.888593i	−0.317641	+	0.0851118i	−0.414117	−	0.910224i	$-0.635910\pi$
$109$	−3.31627	+	0.888593i	−0.317641	+	0.0851118i	0.0964758	+	0.995335i	$0.469243\pi$
$110$	0.255162	−	0.255162i	0.0243288	−	0.0243288i
$111$	6.80150	−	1.82246i	0.645569	−	0.172980i
$112$	−1.00661	+	5.41113i	−0.0951152	+	0.511304i
$113$	7.53468	−	13.0504i	0.708803	−	1.22768i	−0.256498	−	0.966545i	$-0.582569\pi$
$113$	7.53468	−	13.0504i	0.708803	−	1.22768i	0.965301	−	0.261138i	$-0.0840978\pi$
$114$	−0.440346	−	0.254234i	−0.0412422	−	0.0238112i
$115$	−1.57201	−	1.57201i	−0.146591	−	0.146591i
$116$	−11.7441	−	6.78045i	−1.09041	−	0.629549i
$117$	0.659853	−	3.54466i	0.0610035	−	0.327704i
$118$			5.15201i			0.474281i
$119$	0.0926254	+	0.0792158i	0.00849096	+	0.00726170i
$120$	0.742594	+	1.28621i	0.0677893	+	0.117414i
$121$			10.2088i			0.928075i
$122$	−0.152718	−	0.569952i	−0.0138265	−	0.0516010i
$123$	−2.29441	+	8.56284i	−0.206880	+	0.772086i
$124$	−4.74230	−	4.74230i	−0.425871	−	0.425871i
$125$	4.68705	+	4.68705i	0.419223	+	0.419223i
$126$	1.27033	−	0.871831i	0.113170	−	0.0776689i
$127$	−6.17582	+	3.56561i	−0.548016	+	0.316397i	−0.748321	−	0.663337i	$-0.769140\pi$
$127$	−6.17582	+	3.56561i	−0.548016	+	0.316397i	0.200306	+	0.979733i	$0.435806\pi$
$128$	2.98069	+	11.1241i	0.263458	+	0.983239i
$129$	−0.746085	+	1.29226i	−0.0656891	+	0.113777i
$130$	0.267697	−	1.43804i	0.0234786	−	0.126124i
$131$	−11.8790	+	6.85837i	−1.03788	+	0.599219i	−0.919231	−	0.393718i	$-0.871189\pi$
$131$	−11.8790	+	6.85837i	−1.03788	+	0.599219i	−0.118646	+	0.992937i	$0.537855\pi$
$132$	1.42698	+	0.382359i	0.124203	+	0.0332801i
$133$	0.995922	−	2.08444i	0.0863574	−	0.180744i
$134$	−1.26376	−	0.729630i	−0.109172	−	0.0630304i
$135$	−0.180309	+	0.672922i	−0.0155185	+	0.0579159i
$136$	0.0948606	+	0.0254178i	0.00813423	+	0.00217956i
$137$	−11.2780	−	3.02192i	−0.963541	−	0.258180i	−0.257442	−	0.966294i	$-0.582880\pi$
$137$	−11.2780	−	3.02192i	−0.963541	−	0.258180i	−0.706098	+	0.708114i	$0.749546\pi$
$138$	−0.480971	+	1.79501i	−0.0409430	+	0.152801i
$139$	0.834941	+	0.482054i	0.0708188	+	0.0408873i	0.534991	−	0.844858i	$-0.320315\pi$
$139$	0.834941	+	0.482054i	0.0708188	+	0.0408873i	−0.464172	+	0.885745i	$0.653648\pi$
$140$	−2.52407	+	1.73228i	−0.213323	+	0.146404i
$141$	−12.1286	−	3.24985i	−1.02141	−	0.273687i
$142$	−0.416818	+	0.240650i	−0.0349786	+	0.0201949i
$143$	−1.81442	−	2.64446i	−0.151729	−	0.221141i
$144$	−1.04015	+	1.80159i	−0.0866792	+	0.150133i
$145$	−1.47220	−	5.49433i	−0.122260	−	0.456279i
$146$	−7.97393	+	4.60375i	−0.659927	+	0.381009i
$147$	4.39802	+	5.44586i	0.362743	+	0.449167i
$148$	8.26961	+	8.26961i	0.679757	+	0.679757i
$149$	1.64140	+	1.64140i	0.134469	+	0.134469i	0.771137	−	0.636669i	$-0.219688\pi$
$149$	1.64140	+	1.64140i	0.134469	+	0.134469i	−0.636669	+	0.771137i	$0.719688\pi$
$150$	0.680450	−	2.53947i	0.0555585	−	0.207347i
$151$	3.52700	+	13.1629i	0.287023	+	1.07118i	0.947348	+	0.320205i	$0.103752\pi$
$151$	3.52700	+	13.1629i	0.287023	+	1.07118i	−0.660325	+	0.750980i	$0.729582\pi$
$152$		−	1.86144i		−	0.150983i
$153$	0.0230331	+	0.0398944i	0.00186211	+	0.00322527i
$154$	0.250636	−	1.34732i	0.0201968	−	0.108570i
$155$		−	2.81310i		−	0.225954i
$156$	5.64649	−	1.99452i	0.452081	−	0.159689i
$157$	3.81144	+	2.20054i	0.304186	+	0.175622i	0.644322	−	0.764754i	$-0.277140\pi$
$157$	3.81144	+	2.20054i	0.304186	+	0.175622i	−0.340136	+	0.940376i	$0.610473\pi$
$158$	−3.90078	−	3.90078i	−0.310329	−	0.310329i
$159$	8.47362	+	4.89224i	0.672001	+	0.387980i
$160$	−1.90717	+	3.30331i	−0.150775	+	0.261150i
$161$	−8.30061	−	1.54412i	−0.654180	−	0.121694i
$162$	0.562494	−	0.150720i	0.0441937	−	0.0118417i
$163$	0.215757	−	0.215757i	0.0168994	−	0.0168994i	−0.698607	−	0.715506i	$-0.746196\pi$
$163$	0.215757	−	0.215757i	0.0168994	−	0.0168994i	0.715506	+	0.698607i	$0.246196\pi$
$164$	−14.2219	+	3.81074i	−1.11054	+	0.297569i
$165$	0.309833	+	0.536646i	0.0241204	+	0.0417778i
$166$	1.44271	−	2.49884i	0.111976	−	0.193948i
$167$	−0.106108	+	0.396000i	−0.00821087	+	0.0306434i	−0.969910	−	0.243465i	$-0.921716\pi$
$167$	−0.106108	+	0.396000i	−0.00821087	+	0.0306434i	0.961699	+	0.274108i	$0.0883826\pi$
$168$	5.08932	+	2.43163i	0.392650	+	0.187604i
$169$	−12.1292	−	4.67791i	−0.933014	−	0.359839i
$170$	0.00934431	+	0.0161848i	0.000716676	+	0.00124132i
$171$	0.617410	−	0.617410i	0.0472145	−	0.0472145i
$172$	−2.47832			−0.188970
$173$	−2.07593			−0.157830			−0.0789149	−	0.996881i	$-0.525146\pi$
$173$	−2.07593			−0.157830			−0.0789149	+	0.996881i	$0.525146\pi$
$174$	−3.36209	+	3.36209i	−0.254879	+	0.254879i
$175$	11.7432	+	2.18453i	0.887704	+	0.165135i
$176$	0.478915	+	1.78734i	0.0360996	+	0.134725i
$177$	−8.54567	−	2.28980i	−0.642332	−	0.172112i
$178$	−2.63717	+	1.52257i	−0.197664	+	0.114122i
$179$		−	13.4116i		−	1.00243i	−0.865322	−	0.501216i	$-0.832886\pi$
$179$		−	13.4116i		−	1.00243i	0.865322	−	0.501216i	$-0.167114\pi$
$180$	−1.11765	+	0.299472i	−0.0833044	+	0.0223213i
$181$	2.32661			0.172935			0.0864677	−	0.996255i	$-0.472442\pi$
$181$	2.32661			0.172935			0.0864677	+	0.996255i	$0.472442\pi$
$182$	−2.25211	−	5.07815i	−0.166938	−	0.376417i
$183$	1.01326			0.0749022
$184$	−6.57132	+	1.76078i	−0.484444	+	0.129806i
$185$			4.90548i			0.360658i
$186$	−2.03643	+	1.17573i	−0.149318	+	0.0862090i
$187$	0.0395787	+	0.0106051i	0.00289428	+	0.000775520i
$188$	−5.39762	−	20.1442i	−0.393662	−	1.46917i
$189$	0.881516	+	2.49458i	0.0641209	+	0.181454i
$190$	0.250478	−	0.250478i	0.0181716	−	0.0181716i
$191$	22.9951			1.66387			0.831934	−	0.554875i	$-0.187234\pi$
$191$	22.9951			1.66387			0.831934	+	0.554875i	$0.187234\pi$
$192$	−0.972206			−0.0701629
$193$	4.77121	−	4.77121i	0.343439	−	0.343439i	−0.514220	−	0.857659i	$-0.671918\pi$
$193$	4.77121	−	4.77121i	0.343439	−	0.343439i	0.857659	+	0.514220i	$0.171918\pi$
$194$	0.324719	+	0.562430i	0.0233135	+	0.0403801i
$195$	2.26630	+	1.08316i	0.162293	+	0.0775670i
$196$	−4.18084	+	10.8484i	−0.298632	+	0.774889i
$197$	3.30495	−	12.3342i	0.235468	−	0.878778i	−0.742470	−	0.669880i	$-0.766346\pi$
$197$	3.30495	−	12.3342i	0.235468	−	0.878778i	0.977937	−	0.208898i	$-0.0669876\pi$
$198$	0.258989	−	0.448581i	0.0184055	−	0.0318793i
$199$	0.415227	+	0.719195i	0.0294347	+	0.0509824i	0.880368	−	0.474292i	$-0.157296\pi$
$199$	0.415227	+	0.719195i	0.0294347	+	0.0509824i	−0.850933	+	0.525275i	$0.823963\pi$
$200$	9.29672	−	2.49105i	0.657377	−	0.176144i
$201$	1.77192	−	1.77192i	0.124981	−	0.124981i
$202$	8.21665	−	2.20165i	0.578122	−	0.154907i
$203$	−16.4172	−	14.0404i	−1.15226	−	0.985444i
$204$	−0.0382552	+	0.0662600i	−0.00267840	+	0.00463913i
$205$	−5.34843	−	3.08792i	−0.373550	−	0.215669i
$206$	5.22667	+	5.22667i	0.364160	+	0.364160i
$207$	−2.76363	−	1.59558i	−0.192085	−	0.110900i
$208$	5.69968	+	4.87576i	0.395202	+	0.338073i
$209$		−	0.776649i		−	0.0537220i
$210$	0.357623	+	1.01203i	0.0246784	+	0.0698367i
$211$	11.5683	+	20.0368i	0.796392	+	1.37939i	0.921952	+	0.387305i	$0.126594\pi$
$211$	11.5683	+	20.0368i	0.796392	+	1.37939i	−0.125560	+	0.992086i	$0.540073\pi$
$212$			16.2509i			1.11612i
$213$	−0.213913	−	0.798336i	−0.0146571	−	0.0547011i
$214$	−1.77732	+	6.63306i	−0.121495	+	0.453427i
$215$	−0.735063	−	0.735063i	−0.0501309	−	0.0501309i
$216$	1.50746	+	1.50746i	0.102570	+	0.102570i
$217$	−6.04536	−	8.80856i	−0.410386	−	0.597964i
$218$	−1.73146	+	0.999657i	−0.117269	+	0.0677053i
$219$	−4.09226	−	15.2725i	−0.276529	−	1.03202i
$220$	−0.514596	+	0.891307i	−0.0346941	+	0.0600919i
$221$	0.156611	−	0.0553198i	0.0105348	−	0.00372121i
$222$	3.55112	−	2.05024i	0.238336	−	0.137603i
$223$	13.8755	+	3.71792i	0.929171	+	0.248971i	0.691501	−	0.722375i	$-0.256950\pi$
$223$	13.8755	+	3.71792i	0.929171	+	0.248971i	0.237670	+	0.971346i	$0.423616\pi$
$224$	1.12698	+	14.4420i	0.0752994	+	0.964949i
$225$	3.90981	+	2.25733i	0.260654	+	0.150489i
$226$	2.27125	−	8.47643i	0.151081	−	0.563844i
$227$	−19.8561	−	5.32042i	−1.31789	−	0.353129i	−0.469705	−	0.882823i	$-0.655640\pi$
$227$	−19.8561	−	5.32042i	−1.31789	−	0.353129i	−0.848188	+	0.529695i	$0.822306\pi$
$228$	1.40079	+	0.375340i	0.0927693	+	0.0248575i
$229$	1.07018	−	3.99397i	0.0707196	−	0.263929i	−0.921509	−	0.388357i	$-0.873043\pi$
$229$	1.07018	−	3.99397i	0.0707196	−	0.263929i	0.992229	+	0.124428i	$0.0397095\pi$
$230$	−1.12118	−	0.647313i	−0.0739283	−	0.0426826i
$231$	2.12342	+	1.01455i	0.139711	+	0.0667524i
$232$	−16.8133	−	4.50512i	−1.10385	−	0.295775i
$233$	1.72269	−	0.994594i	0.112857	−	0.0651580i	−0.442509	−	0.896764i	$-0.645912\pi$
$233$	1.72269	−	0.994594i	0.112857	−	0.0651580i	0.555366	+	0.831606i	$0.312578\pi$
$234$	−0.163087	−	2.09330i	−0.0106613	−	0.136843i
$235$	4.37380	−	7.57564i	0.285315	−	0.494180i
$236$	−3.80310	−	14.1934i	−0.247561	−	0.923909i
$237$	8.20394	−	4.73655i	0.532903	−	0.307672i
$238$	0.0640407	+	0.0305980i	0.00415114	+	0.00198337i
$239$	10.1339	+	10.1339i	0.655510	+	0.655510i	0.954314	−	0.298805i	$-0.0965879\pi$
$239$	10.1339	+	10.1339i	0.655510	+	0.655510i	−0.298805	+	0.954314i	$0.596588\pi$
$240$	−1.02478	−	1.02478i	−0.0661495	−	0.0661495i
$241$	7.15869	−	26.7166i	0.461132	−	1.72097i	−0.208275	−	0.978070i	$-0.566785\pi$
$241$	7.15869	−	26.7166i	0.461132	−	1.72097i	0.669406	−	0.742896i	$-0.266549\pi$
$242$	1.53867	+	5.74241i	0.0989097	+	0.369136i
$243$			1.00000i			0.0641500i
$244$	0.841452	+	1.45744i	0.0538684	+	0.0933029i
$245$	−4.45764	+	1.97759i	−0.284788	+	0.126344i
$246$			5.16236i			0.329140i
$247$	−1.78111	−	2.59591i	−0.113329	−	0.165174i
$248$	−7.45513	−	4.30422i	−0.473401	−	0.273318i
$249$	3.50364	+	3.50364i	0.222034	+	0.222034i
$250$	3.34287	+	1.93001i	0.211422	+	0.122064i
$251$	3.92297	−	6.79478i	0.247616	−	0.428883i	−0.715248	−	0.698871i	$-0.753686\pi$
$251$	3.92297	−	6.79478i	0.247616	−	0.428883i	0.962864	+	0.269988i	$0.0870197\pi$
$252$	−2.85607	+	3.33955i	−0.179916	+	0.210372i
$253$	−2.74175	+	0.734651i	−0.172373	+	0.0461871i
$254$	−2.93646	+	2.93646i	−0.184250	+	0.184250i
$255$	−0.0309989	+	0.00830614i	−0.00194123	+	0.000520151i
$256$	2.38104	+	4.12408i	0.148815	+	0.257755i
$257$	−0.181903	+	0.315066i	−0.0113468	+	0.0196533i	−0.871643	−	0.490141i	$-0.836945\pi$
$257$	−0.181903	+	0.315066i	−0.0113468	+	0.0196533i	0.860296	+	0.509794i	$0.170279\pi$
$258$	−0.224900	+	0.839337i	−0.0140017	+	0.0522549i
$259$	10.5419	+	15.3604i	0.655041	+	0.954446i
$260$	0.324044	+	4.15928i	0.0200964	+	0.257948i
$261$	−4.08244	−	7.07099i	−0.252697	−	0.437683i
$262$	−5.64821	+	5.64821i	−0.348947	+	0.348947i
$263$	22.3462			1.37793			0.688963	−	0.724797i	$-0.258066\pi$
$263$	22.3462			1.37793			0.688963	+	0.724797i	$0.258066\pi$
$264$	1.89625			0.116706
$265$	−4.81997	+	4.81997i	−0.296088	+	0.296088i
$266$	0.246035	−	1.32259i	0.0150854	−	0.0810932i
$267$	−1.35341	−	5.05100i	−0.0828274	−	0.309116i
$268$	4.02014	+	1.07719i	0.245569	+	0.0658000i
$269$	22.7714	−	13.1471i	1.38839	−	0.801590i	0.395260	−	0.918569i	$-0.370654\pi$
$269$	22.7714	−	13.1471i	1.38839	−	0.801590i	0.993134	+	0.116979i	$0.0373210\pi$
$270$			0.405691i			0.0246896i
$271$	0.228195	−	0.0611447i	0.0138619	−	0.00371427i	−0.251881	−	0.967758i	$-0.581049\pi$
$271$	0.228195	−	0.0611447i	0.0138619	−	0.00371427i	0.265743	+	0.964044i	$0.414383\pi$
$272$	−0.0958314			−0.00581063
$273$	9.42410	−	1.47861i	0.570373	−	0.0894898i
$274$	−6.79925			−0.410758
$275$	3.87887	−	1.03934i	0.233905	−	0.0626746i
$276$		−	5.30014i		−	0.319031i
$277$	−1.63409	+	0.943444i	−0.0981831	+	0.0566860i	−0.548288	−	0.836290i	$-0.684720\pi$
$277$	−1.63409	+	0.943444i	−0.0981831	+	0.0566860i	0.450104	+	0.892976i	$0.351387\pi$
$278$	0.542305	+	0.145310i	0.0325253	+	0.00871513i
$279$	−1.04511	−	3.90039i	−0.0625689	−	0.233510i
$280$	−2.55395	+	2.98628i	−0.152628	+	0.178464i
$281$	14.2823	−	14.2823i	0.852011	−	0.852011i	−0.138370	−	0.990381i	$-0.544186\pi$
$281$	14.2823	−	14.2823i	0.852011	−	0.852011i	0.990381	+	0.138370i	$0.0441863\pi$
$282$	−7.31209			−0.435429
$283$	17.1254			1.01800			0.509001	−	0.860766i	$-0.330015\pi$
$283$	17.1254			1.01800			0.509001	+	0.860766i	$0.330015\pi$
$284$	0.970657	−	0.970657i	0.0575979	−	0.0575979i
$285$	0.304145	+	0.526794i	0.0180160	+	0.0312046i
$286$	−1.41917	−	1.21402i	−0.0839174	−	0.0717867i
$287$	−23.3833	+	1.82470i	−1.38027	+	0.107709i
$288$	−1.41708	+	5.28861i	−0.0835022	+	0.311634i
$289$	8.49894	−	14.7206i	0.499938	−	0.865917i
$290$	−1.65621	−	2.86864i	−0.0972560	−	0.168452i
$291$	−1.07723	+	0.288642i	−0.0631481	+	0.0169205i
$292$	18.5691	−	18.5691i	1.08668	−	1.08668i
$293$	0.0551536	−	0.0147783i	0.00322210	−	0.000863360i	−0.257208	−	0.966356i	$-0.582802\pi$
$293$	0.0551536	−	0.0147783i	0.00322210	−	0.000863360i	0.260430	+	0.965493i	$0.416136\pi$
$294$	3.29466	+	2.40040i	0.192149	+	0.139994i
$295$	3.08172	−	5.33770i	0.179425	−	0.310773i
$296$	13.0002	+	7.50570i	0.755624	+	0.436260i
$297$	0.628957	+	0.628957i	0.0364958	+	0.0364958i
$298$	1.17067	+	0.675886i	0.0678150	+	0.0391530i
$299$	−7.47937	+	8.74326i	−0.432543	+	0.505636i
$300$			7.49833i			0.432916i
$301$	−3.88133	−	0.722023i	−0.223716	−	0.0416167i
$302$	3.96783	+	6.87249i	0.228323	+	0.395467i
$303$			14.6075i			0.839181i
$304$	0.470123	+	1.75452i	0.0269634	+	0.100629i
$305$	−0.182700	+	0.681844i	−0.0104613	+	0.0390423i
$306$	0.0189689	+	0.0189689i	0.00108438	+	0.00108438i
$307$	−17.7169	−	17.7169i	−1.01116	−	1.01116i	−0.999937	−	0.0112203i	$-0.996428\pi$
$307$	−17.7169	−	17.7169i	−1.01116	−	1.01116i	−0.0112203	−	0.999937i	$-0.503572\pi$
$308$	0.304084	+	3.89678i	0.0173268	+	0.222040i
$309$	−10.9925	+	6.34652i	−0.625342	+	0.361041i
$310$	−0.423991	−	1.58235i	−0.0240811	−	0.0898717i
$311$	9.52232	−	16.4931i	0.539961	−	0.935240i	−0.458944	−	0.888465i	$-0.651772\pi$
$311$	9.52232	−	16.4931i	0.539961	−	0.935240i	0.998905	−	0.0467749i	$-0.0148944\pi$
$312$	6.33812	−	4.34872i	0.358826	−	0.246198i
$313$	−2.59097	+	1.49590i	−0.146450	+	0.0845530i	−0.571435	−	0.820648i	$-0.693613\pi$
$313$	−2.59097	+	1.49590i	−0.146450	+	0.0845530i	0.424984	+	0.905201i	$0.360280\pi$
$314$	2.47558	+	0.663329i	0.139705	+	0.0374338i
$315$	−1.83760	+	0.143397i	−0.103537	+	0.00807949i
$316$	13.6258	+	7.86686i	0.766511	+	0.442545i
$317$	−0.183258	+	0.683930i	−0.0102928	+	0.0384133i	−0.970881	−	0.239561i	$-0.922996\pi$
$317$	−0.183258	+	0.683930i	−0.0102928	+	0.0384133i	0.960588	+	0.277975i	$0.0896631\pi$
$318$	5.50372	+	1.47472i	0.308633	+	0.0826980i
$319$	−7.01503	−	1.87967i	−0.392766	−	0.105241i
$320$	0.175298	−	0.654219i	0.00979943	−	0.0365720i
$321$	−10.2124	−	5.89611i	−0.569999	−	0.329089i
$322$	−4.90178	+	0.382508i	−0.273165	+	0.0213164i
$323$	0.0388521	+	0.0104104i	0.00216179	+	0.000579249i
$324$	−1.43837	+	0.830442i	−0.0799093	+	0.0461357i
$325$	10.5814	−	12.3694i	0.586949	−	0.686133i
$326$	0.0888434	−	0.153881i	0.00492058	−	0.00852269i
$327$	−0.888593	−	3.31627i	−0.0491393	−	0.183390i
$328$	−16.3669	+	9.44941i	−0.903708	+	0.521756i
$329$	−2.58455	−	33.1206i	−0.142491	−	1.82600i
$330$	0.255162	+	0.255162i	0.0140462	+	0.0140462i
$331$	−6.71159	−	6.71159i	−0.368903	−	0.368903i	0.498174	−	0.867077i	$-0.334004\pi$
$331$	−6.71159	−	6.71159i	−0.368903	−	0.368903i	−0.867077	+	0.498174i	$0.834004\pi$
$332$	−2.12995	+	7.94908i	−0.116896	+	0.436263i
$333$	1.82246	+	6.80150i	0.0998699	+	0.372720i
$334$			0.238740i			0.0130633i
$335$	0.872869	+	1.51185i	0.0476899	+	0.0826014i
$336$	−5.41113	−	1.00661i	−0.295201	−	0.0549148i
$337$			28.3561i			1.54465i	0.635226	+	0.772327i	$0.280907\pi$
$337$			28.3561i			1.54465i	−0.635226	+	0.772327i	$0.719093\pi$
$338$	−7.52765	−	0.803187i	−0.409450	−	0.0436876i
$339$	13.0504	+	7.53468i	0.708803	+	0.409228i
$340$	−0.0376901	−	0.0376901i	−0.00204403	−	0.00204403i
$341$	−3.11051	−	1.79585i	−0.168443	−	0.0972508i
$342$	0.254234	−	0.440346i	0.0137474	−	0.0238112i
$343$	−9.70820	+	15.7718i	−0.524194	+	0.851599i
$344$	−3.07272	+	0.823332i	−0.165670	+	0.0443911i
$345$	1.57201	−	1.57201i	0.0846341	−	0.0846341i
$346$	−1.16770	+	0.312884i	−0.0627758	+	0.0168207i
$347$	11.1898	+	19.3814i	0.600702	+	1.04045i	0.992715	+	0.120487i	$0.0384455\pi$
$347$	11.1898	+	19.3814i	0.600702	+	1.04045i	−0.392013	+	0.919960i	$0.628221\pi$
$348$	6.78045	−	11.7441i	0.363470	−	0.629549i
$349$	2.36174	−	8.81412i	0.126421	−	0.471809i	−0.873465	−	0.486886i	$-0.838133\pi$
$349$	2.36174	−	8.81412i	0.126421	−	0.471809i	0.999886	+	0.0150770i	$0.00479935\pi$
$350$	6.93475	−	0.541150i	0.370678	−	0.0289257i
$351$	3.54466	+	0.659853i	0.189200	+	0.0352204i
$352$	2.43503	+	4.21759i	0.129787	+	0.224798i
$353$	−2.03241	+	2.03241i	−0.108174	+	0.108174i	−0.759122	−	0.650948i	$-0.774372\pi$
$353$	−2.03241	+	2.03241i	−0.108174	+	0.108174i	0.650948	+	0.759122i	$0.274372\pi$
$354$	−5.15201			−0.273826
$355$	0.575789			0.0305597
$356$	6.14126	−	6.14126i	0.325486	−	0.325486i
$357$	−0.0792158	+	0.0926254i	−0.00419255	+	0.00490226i
$358$	−2.02140	−	7.54396i	−0.106834	−	0.398711i
$359$	−7.79454	−	2.08854i	−0.411380	−	0.110229i	0.0471928	−	0.998886i	$-0.484972\pi$
$359$	−7.79454	−	2.08854i	−0.411380	−	0.110229i	−0.458573	+	0.888657i	$0.651639\pi$
$360$	−1.28621	+	0.742594i	−0.0677893	+	0.0391382i
$361$			18.2376i			0.959874i
$362$	1.30870	−	0.350666i	0.0687840	−	0.0184306i
$363$	−10.2088			−0.535824
$364$	9.95296	+	12.3274i	0.521677	+	0.646132i
$365$	11.0151			0.576557
$366$	0.569952	−	0.152718i	0.0297919	−	0.00798271i
$367$		−	1.67913i		−	0.0876497i	−0.999039	−	0.0438249i	$-0.986046\pi$
$367$		−	1.67913i		−	0.0876497i	0.999039	−	0.0438249i	$-0.0139544\pi$
$368$	5.74917	−	3.31929i	0.299696	−	0.173030i
$369$	−8.56284	−	2.29441i	−0.445764	−	0.119442i
$370$	0.739354	+	2.75931i	0.0384372	+	0.143450i
$371$	−4.73447	+	25.4507i	−0.245801	+	1.32133i
$372$	4.74230	−	4.74230i	0.245877	−	0.245877i
$373$	−32.2757			−1.67117			−0.835587	−	0.549358i	$-0.814872\pi$
$373$	−32.2757			−1.67117			−0.835587	+	0.549358i	$0.814872\pi$
$374$	0.0238612			0.00123383
$375$	−4.68705	+	4.68705i	−0.242038	+	0.242038i
$376$	−13.3844	−	23.1824i	−0.690246	−	1.19554i
$377$	−27.7580	+	9.80502i	−1.42961	+	0.504984i
$378$	0.871831	+	1.27033i	0.0448421	+	0.0653385i
$379$	5.38351	−	20.0915i	0.276532	−	1.03203i	−0.678276	−	0.734808i	$-0.737272\pi$
$379$	5.38351	−	20.0915i	0.276532	−	1.03203i	0.954808	−	0.297224i	$-0.0960609\pi$
$380$	−0.505149	+	0.874943i	−0.0259136	+	0.0448837i
$381$	−3.56561	−	6.17582i	−0.182672	−	0.316397i
$382$	12.9346	−	3.46582i	0.661793	−	0.177327i
$383$	−19.8878	+	19.8878i	−1.01622	+	1.01622i	−0.0163519	+	0.999866i	$0.505205\pi$
$383$	−19.8878	+	19.8878i	−1.01622	+	1.01622i	−0.999866	+	0.0163519i	$0.994795\pi$
$384$	−11.1241	+	2.98069i	−0.567673	+	0.152108i
$385$	−1.06558	+	1.24596i	−0.0543072	+	0.0635002i
$386$	1.96466	−	3.40289i	0.0999986	−	0.173203i
$387$	−1.29226	−	0.746085i	−0.0656891	−	0.0379256i
$388$	−1.30975	−	1.30975i	−0.0664923	−	0.0664923i
$389$	9.23904	+	5.33416i	0.468438	+	0.270453i	0.715586	−	0.698525i	$-0.246160\pi$
$389$	9.23904	+	5.33416i	0.468438	+	0.270453i	−0.247148	+	0.968978i	$0.579493\pi$
$390$	1.43804	+	0.267697i	0.0728178	+	0.0135554i
$391$		−	0.147004i		−	0.00743433i
$392$	−1.57957	+	14.8392i	−0.0797801	+	0.749495i
$393$	−6.85837	−	11.8790i	−0.345959	−	0.599219i
$394$		−	7.43606i		−	0.374623i
$395$	1.70809	+	6.37466i	0.0859431	+	0.320744i
$396$	−0.382359	+	1.42698i	−0.0192143	+	0.0717086i
$397$	1.67763	+	1.67763i	0.0841976	+	0.0841976i	0.747951	−	0.663754i	$-0.231038\pi$
$397$	1.67763	+	1.67763i	0.0841976	+	0.0841976i	−0.663754	+	0.747951i	$0.731038\pi$
$398$	0.341960	+	0.341960i	0.0171409	+	0.0171409i
$399$	2.08444	+	0.995922i	0.104352	+	0.0498585i
$400$	−8.13359	+	4.69593i	−0.406679	+	0.234797i
$401$	8.06712	+	30.1069i	0.402853	+	1.50347i	0.807982	+	0.589208i	$0.200560\pi$
$401$	8.06712	+	30.1069i	0.402853	+	1.50347i	−0.405129	+	0.914260i	$0.632773\pi$
$402$	0.729630	−	1.26376i	0.0363906	−	0.0630304i
$403$	−14.5152	+	1.13086i	−0.723052	+	0.0563321i
$404$	−21.0110	+	12.1307i	−1.04534	+	0.603525i
$405$	−0.672922	−	0.180309i	−0.0334378	−	0.00895963i
$406$	−11.3507	−	5.42326i	−0.563327	−	0.269152i
$407$	5.42410	+	3.13160i	0.268862	+	0.155228i
$408$	−0.0254178	+	0.0948606i	−0.00125837	+	0.00469630i
$409$	22.2302	+	5.95656i	1.09921	+	0.294533i	0.762444	−	0.647055i	$-0.223999\pi$
$409$	22.2302	+	5.95656i	1.09921	+	0.294533i	0.336768	+	0.941588i	$0.390666\pi$
$410$	−3.47387	−	0.930821i	−0.171562	−	0.0459700i
$411$	3.02192	−	11.2780i	0.149060	−	0.556300i
$412$	−18.2573	−	10.5408i	−0.899471	−	0.519310i
$413$	−1.82104	−	23.3364i	−0.0896076	−	1.14831i
$414$	−1.79501	−	0.480971i	−0.0882199	−	0.0236385i
$415$	−2.98941	+	1.72594i	−0.146745	+	0.0847230i
$416$	17.8112	+	8.51277i	0.873268	+	0.417373i
$417$	−0.482054	+	0.834941i	−0.0236063	+	0.0408873i
$418$	−0.117057	−	0.436861i	−0.00572542	−	0.0213676i
$419$	−15.0030	+	8.66198i	−0.732944	+	0.423166i	−0.819498	−	0.573082i	$-0.805748\pi$
$419$	−15.0030	+	8.66198i	−0.732944	+	0.423166i	0.0865540	+	0.996247i	$0.472414\pi$
$420$	−1.73228	−	2.52407i	−0.0845266	−	0.123162i
$421$	−28.4825	−	28.4825i	−1.38815	−	1.38815i	−0.829203	−	0.558947i	$-0.811206\pi$
$421$	−28.4825	−	28.4825i	−1.38815	−	1.38815i	−0.558947	−	0.829203i	$-0.688794\pi$
$422$	9.52703	+	9.52703i	0.463769	+	0.463769i
$423$	3.24985	−	12.1286i	0.158013	−	0.589713i
$424$	5.39877	+	20.1485i	0.262187	+	0.978497i
$425$			0.207973i			0.0100882i
$426$	−0.240650	−	0.416818i	−0.0116595	−	0.0201949i
$427$	0.893203	+	2.52765i	0.0432251	+	0.122322i
$428$		−	19.5855i		−	0.946702i
$429$	2.64446	−	1.81442i	0.127676	−	0.0876009i
$430$	−0.524258	−	0.302680i	−0.0252819	−	0.0145965i
$431$	23.9598	+	23.9598i	1.15410	+	1.15410i	0.985722	+	0.168381i	$0.0538539\pi$
$431$	23.9598	+	23.9598i	1.15410	+	1.15410i	0.168381	+	0.985722i	$0.446146\pi$
$432$	−1.80159	−	1.04015i	−0.0866792	−	0.0500443i
$433$	−15.2303	+	26.3796i	−0.731921	+	1.26772i	0.224141	+	0.974557i	$0.428042\pi$
$433$	−15.2303	+	26.3796i	−0.731921	+	1.26772i	−0.956061	+	0.293167i	$0.905291\pi$
$434$	−4.72811	−	4.04361i	−0.226956	−	0.194099i
$435$	5.49433	−	1.47220i	0.263433	−	0.0705866i
$436$	4.03210	−	4.03210i	0.193102	−	0.193102i
$437$	−2.69142	+	0.721163i	−0.128748	+	0.0344979i
$438$	−4.60375	−	7.97393i	−0.219976	−	0.381009i
$439$	−1.36285	+	2.36053i	−0.0650455	+	0.112662i	−0.896714	−	0.442610i	$-0.854053\pi$
$439$	−1.36285	+	2.36053i	−0.0650455	+	0.112662i	0.831669	+	0.555272i	$0.187386\pi$
$440$	−0.341912	+	1.27603i	−0.0163000	+	0.0608324i
$441$	−5.44586	+	4.39802i	−0.259327	+	0.209430i
$442$	0.0797547	−	0.0547214i	0.00379355	−	0.00260283i
$443$	−17.3901	−	30.1206i	−0.826229	−	1.43107i	−0.900976	−	0.433869i	$-0.857148\pi$
$443$	−17.3901	−	30.1206i	−0.826229	−	1.43107i	0.0747467	−	0.997203i	$-0.476185\pi$
$444$	−8.26961	+	8.26961i	−0.392458	+	0.392458i
$445$	3.64296			0.172693
$446$	8.36525			0.396106
$447$	−1.64140	+	1.64140i	−0.0776355	+	0.0776355i
$448$	−0.857015	−	2.42525i	−0.0404902	−	0.114582i
$449$	9.41298	+	35.1297i	0.444226	+	1.65787i	0.717972	+	0.696072i	$0.245070\pi$
$449$	9.41298	+	35.1297i	0.444226	+	1.65787i	−0.273746	+	0.961802i	$0.588263\pi$
$450$	2.53947	+	0.680450i	0.119712	+	0.0320767i
$451$	−6.82875	+	3.94258i	−0.321553	+	0.185649i
$452$			25.0284i			1.17724i
$453$	−13.1629	+	3.52700i	−0.618448	+	0.165713i
$454$	−11.9708			−0.561818
$455$	−0.704257	+	6.60830i	−0.0330161	+	0.309802i
$456$	1.86144			0.0871700
$457$	−30.7526	+	8.24014i	−1.43855	+	0.385457i	−0.892025	−	0.451987i	$-0.850715\pi$
$457$	−30.7526	+	8.24014i	−1.43855	+	0.385457i	−0.546522	+	0.837444i	$0.684049\pi$
$458$		−	2.40789i		−	0.112513i
$459$	−0.0398944	+	0.0230331i	−0.00186211	+	0.00107509i
$460$	3.56659	+	0.955664i	0.166293	+	0.0445581i
$461$	4.67038	+	17.4301i	0.217521	+	0.811800i	0.985264	+	0.171042i	$0.0547133\pi$
$461$	4.67038	+	17.4301i	0.217521	+	0.811800i	−0.767743	+	0.640758i	$0.778620\pi$
$462$	1.34732	+	0.250636i	0.0626832	+	0.0116606i
$463$	16.2446	−	16.2446i	0.754951	−	0.754951i	−0.220448	−	0.975399i	$-0.570752\pi$
$463$	16.2446	−	16.2446i	0.754951	−	0.754951i	0.975399	+	0.220448i	$0.0707518\pi$
$464$	16.9854			0.788527
$465$	2.81310			0.130455
$466$	0.819097	−	0.819097i	0.0379439	−	0.0379439i
$467$	18.7401	+	32.4588i	0.867188	+	1.50201i	0.864859	+	0.502016i	$0.167408\pi$
$467$	18.7401	+	32.4588i	0.867188	+	1.50201i	0.00232895	+	0.999997i	$0.499259\pi$
$468$	1.99452	+	5.64649i	0.0921967	+	0.261009i
$469$	5.98216	+	2.85821i	0.276230	+	0.131980i
$470$	1.31844	−	4.92047i	0.0608149	−	0.226964i
$471$	−2.20054	+	3.81144i	−0.101395	+	0.175622i
$472$	−9.43045	−	16.3340i	−0.434072	−	0.751834i
$473$	−1.28203	+	0.343519i	−0.0589478	+	0.0157950i
$474$	3.90078	−	3.90078i	0.179169	−	0.179169i
$475$	3.80766	−	1.02026i	0.174707	−	0.0468127i
$476$	−0.199013	−	0.0370215i	−0.00912177	−	0.00169688i
$477$	−4.89224	+	8.47362i	−0.224000	+	0.387980i
$478$	7.22767	+	4.17289i	0.330586	+	0.190864i
$479$	18.8991	+	18.8991i	0.863522	+	0.863522i	0.991745	−	0.128224i	$-0.0409275\pi$
$479$	18.8991	+	18.8991i	0.863522	+	0.863522i	−0.128224	+	0.991745i	$0.540928\pi$
$480$	−3.30331	−	1.90717i	−0.150775	−	0.0870499i
$481$	25.3115	−	1.97199i	1.15411	−	0.0899149i
$482$		−	16.1069i		−	0.733649i
$483$	1.54412	−	8.30061i	0.0702600	−	0.377691i
$484$	−8.47784	−	14.6840i	−0.385356	−	0.667456i
$485$		−	0.776935i		−	0.0352788i
$486$	0.150720	+	0.562494i	0.00683679	+	0.0255153i
$487$	−6.41427	+	23.9384i	−0.290658	+	1.08475i	0.653946	+	0.756541i	$0.273112\pi$
$487$	−6.41427	+	23.9384i	−0.290658	+	1.08475i	−0.944605	+	0.328210i	$0.893555\pi$
$488$	1.52744	+	1.52744i	0.0691442	+	0.0691442i
$489$	0.215757	+	0.215757i	0.00975689	+	0.00975689i
$490$	−2.20934	+	1.78424i	−0.0998077	+	0.0806038i
$491$	9.62086	−	5.55460i	0.434183	−	0.250676i	−0.266944	−	0.963712i	$-0.586014\pi$
$491$	9.62086	−	5.55460i	0.434183	−	0.250676i	0.701127	+	0.713036i	$0.252681\pi$
$492$	−3.81074	−	14.2219i	−0.171802	−	0.641172i
$493$	0.188062	−	0.325733i	0.00846989	−	0.0146703i
$494$	−1.39312	−	1.19174i	−0.0626794	−	0.0536187i
$495$	−0.536646	+	0.309833i	−0.0241204	+	0.0139259i
$496$	8.11399	+	2.17414i	0.364329	+	0.0976216i
$497$	1.80294	−	1.23737i	0.0808731	−	0.0555036i
$498$	2.49884	+	1.44271i	0.111976	+	0.0646493i
$499$	0.0481231	−	0.179598i	0.00215428	−	0.00803990i	−0.964840	−	0.262837i	$-0.915342\pi$
$499$	0.0481231	−	0.179598i	0.00215428	−	0.00803990i	0.966995	+	0.254797i	$0.0820086\pi$
$500$	−10.6340	−	2.84938i	−0.475568	−	0.127428i
$501$	−0.396000	−	0.106108i	−0.0176920	−	0.00474055i
$502$	1.18254	−	4.41330i	0.0527793	−	0.196975i
$503$	−0.488766	−	0.282189i	−0.0217930	−	0.0125822i	0.489064	−	0.872248i	$-0.337338\pi$
$503$	−0.488766	−	0.282189i	−0.0217930	−	0.0125822i	−0.510857	+	0.859666i	$0.670672\pi$
$504$	−2.43163	+	5.08932i	−0.108313	+	0.226697i
$505$	−9.82973	−	2.63387i	−0.437417	−	0.117206i
$506$	−1.43149	+	0.826474i	−0.0636377	+	0.0367412i
$507$	4.67791	−	12.1292i	0.207753	−	0.538676i
$508$	5.92207	−	10.2573i	0.262749	−	0.455095i
$509$	−5.90635	−	22.0428i	−0.261794	−	0.977029i	−0.964183	−	0.265236i	$-0.914550\pi$
$509$	−5.90635	−	22.0428i	−0.261794	−	0.977029i	0.702389	−	0.711793i	$-0.252117\pi$
$510$	−0.0161848	+	0.00934431i	−0.000716676	+	0.000413773i
$511$	34.4911	−	23.6714i	1.52580	−	1.04716i
$512$	−14.3259	−	14.3259i	−0.633121	−	0.633121i
$513$	0.617410	+	0.617410i	0.0272593	+	0.0272593i
$514$	−0.0548329	+	0.204639i	−0.00241858	+	0.00902625i
$515$	−2.28867	−	8.54144i	−0.100851	−	0.376381i
$516$		−	2.47832i		−	0.109102i
$517$	−5.58436	−	9.67239i	−0.245600	−	0.425391i
$518$	8.24486	+	7.05124i	0.362259	+	0.309814i
$519$		−	2.07593i		−	0.0911231i
$520$	1.78353	+	5.04918i	0.0782130	+	0.221421i
$521$	20.6918	+	11.9464i	0.906523	+	0.523381i	0.879311	−	0.476249i	$-0.158004\pi$
$521$	20.6918	+	11.9464i	0.906523	+	0.523381i	0.0272119	+	0.999630i	$0.491337\pi$
$522$	−3.36209	−	3.36209i	−0.147155	−	0.147155i
$523$	−28.3525	−	16.3694i	−1.23977	−	0.715782i	−0.270723	−	0.962657i	$-0.587263\pi$
$523$	−28.3525	−	16.3694i	−1.23977	−	0.715782i	−0.969047	+	0.246876i	$0.920596\pi$
$524$	11.3910	−	19.7297i	0.497616	−	0.861897i
$525$	−2.18453	+	11.7432i	−0.0953408	+	0.512516i
$526$	12.5696	−	3.36802i	0.548061	−	0.146853i
$527$	0.131532	−	0.131532i	0.00572962	−	0.00572962i
$528$	−1.78734	+	0.478915i	−0.0777838	+	0.0208421i
$529$	−6.40825	−	11.0994i	−0.278620	−	0.482583i
$530$	−1.98474	+	3.43767i	−0.0862116	+	0.149323i
$531$	2.28980	−	8.54567i	0.0993691	−	0.370850i
$532$	0.298501	+	3.82524i	0.0129417	+	0.165845i
$533$	−13.7831	+	28.8384i	−0.597013	+	1.24913i
$534$	−1.52257	−	2.63717i	−0.0658881	−	0.114122i
$535$	5.80901	−	5.80901i	0.251145	−	0.251145i
$536$	5.34218			0.230747
$537$	13.4116			0.578754
$538$	10.8272	−	10.8272i	0.466796	−	0.466796i
$539$	−0.659043	+	6.19138i	−0.0283870	+	0.266682i
$540$	−0.299472	−	1.11765i	−0.0128872	−	0.0480958i
$541$	17.0583	+	4.57076i	0.733394	+	0.196512i	0.606140	−	0.795358i	$-0.292717\pi$
$541$	17.0583	+	4.57076i	0.733394	+	0.196512i	0.127254	+	0.991870i	$0.459384\pi$
$542$	0.119143	−	0.0687871i	0.00511762	−	0.00295466i
$543$			2.32661i			0.0998443i
$544$	−0.243626	+	0.0652793i	−0.0104454	+	0.00279883i
$545$	2.39182			0.102454
$546$	5.07815	−	2.25211i	0.217325	−	0.0963815i
$547$	24.8672			1.06324			0.531621	−	0.846982i	$-0.321583\pi$
$547$	24.8672			1.06324			0.531621	+	0.846982i	$0.321583\pi$
$548$	18.7314	−	5.01905i	0.800164	−	0.214403i
$549$			1.01326i			0.0432448i
$550$	2.02519	−	1.16925i	0.0863546	−	0.0498568i
$551$	−6.88624	−	1.84516i	−0.293364	−	0.0786066i
$552$	−1.76078	−	6.57132i	−0.0749438	−	0.279694i
$553$	19.0476	+	16.2901i	0.809987	+	0.692723i
$554$	−0.776972	+	0.776972i	−0.0330104	+	0.0330104i
$555$	−4.90548			−0.208226
$556$	−1.60127			−0.0679090
$557$	25.7600	−	25.7600i	1.09148	−	1.09148i	0.0961140	−	0.995370i	$-0.469359\pi$
$557$	25.7600	−	25.7600i	1.09148	−	1.09148i	0.995370	−	0.0961140i	$-0.0306413\pi$
$558$	−1.17573	−	2.03643i	−0.0497728	−	0.0862090i
$559$	−3.49732	+	4.08830i	−0.147921	+	0.172917i
$560$	1.65304	−	3.45977i	0.0698538	−	0.146202i
$561$	−0.0106051	+	0.0395787i	−0.000447747	+	0.00167101i
$562$	5.88109	−	10.1863i	0.248079	−	0.429685i
$563$	−19.9769	−	34.6011i	−0.841928	−	1.45826i	−0.888263	−	0.459336i	$-0.848087\pi$
$563$	−19.9769	−	34.6011i	−0.841928	−	1.45826i	0.0463350	−	0.998926i	$-0.485246\pi$
$564$	20.1442	−	5.39762i	0.848224	−	0.227281i
$565$	−7.42337	+	7.42337i	−0.312303	+	0.312303i
$566$	9.63296	−	2.58114i	0.404904	−	0.108494i
$567$	−2.49458	+	0.881516i	−0.104763	+	0.0370202i
$568$	0.880992	−	1.52592i	0.0369656	−	0.0640263i
$569$	−22.6412	−	13.0719i	−0.949167	−	0.548002i	−0.0563450	−	0.998411i	$-0.517945\pi$
$569$	−22.6412	−	13.0719i	−0.949167	−	0.548002i	−0.892822	+	0.450409i	$0.851278\pi$
$570$	0.250478	+	0.250478i	0.0104914	+	0.0104914i
$571$	−20.3089	−	11.7254i	−0.849902	−	0.490691i	0.0107157	−	0.999943i	$-0.496589\pi$
$571$	−20.3089	−	11.7254i	−0.849902	−	0.490691i	−0.860618	+	0.509251i	$0.829922\pi$
$572$	4.80587	+	2.29693i	0.200943	+	0.0960396i
$573$			22.9951i			0.960634i
$574$	−12.8779	+	4.55071i	−0.537514	+	0.189943i
$575$	−7.20351	−	12.4768i	−0.300407	−	0.520320i
$576$		−	0.972206i		−	0.0405086i
$577$	4.20645	+	15.6987i	0.175117	+	0.653544i	0.996532	+	0.0832134i	$0.0265183\pi$
$577$	4.20645	+	15.6987i	0.175117	+	0.653544i	−0.821415	+	0.570331i	$0.806815\pi$
$578$	2.56192	−	9.56121i	0.106562	−	0.397694i
$579$	4.77121	+	4.77121i	0.198285	+	0.198285i
$580$	6.68028	+	6.68028i	0.277384	+	0.277384i
$581$	−5.65159	+	11.8286i	−0.234467	+	0.490734i
$582$	−0.562430	+	0.324719i	−0.0233135	+	0.0134600i
$583$	2.25253	+	8.40655i	0.0932902	+	0.348164i
$584$	16.8538	−	29.1916i	0.697415	−	1.20796i
$585$	−1.08316	+	2.26630i	−0.0447833	+	0.0937001i
$586$	0.0287962	−	0.0166255i	0.00118956	−	0.000686792i
$587$	−25.3256	−	6.78596i	−1.04530	−	0.280087i	−0.304991	−	0.952355i	$-0.598653\pi$
$587$	−25.3256	−	6.78596i	−1.04530	−	0.280087i	−0.740307	+	0.672269i	$0.765320\pi$
$588$	−10.8484	−	4.18084i	−0.447382	−	0.172415i
$589$	−3.05340	−	1.76288i	−0.125813	−	0.0726383i
$590$	0.928954	−	3.46690i	0.0382444	−	0.142730i
$591$	12.3342	+	3.30495i	0.507362	+	0.135947i
$592$	−14.1492	−	3.79126i	−0.581527	−	0.155820i
$593$	2.65816	−	9.92038i	0.109157	−	0.407381i	−0.889626	−	0.456690i	$-0.849035\pi$
$593$	2.65816	−	9.92038i	0.109157	−	0.407381i	0.998784	+	0.0493084i	$0.0157017\pi$
$594$	0.448581	+	0.258989i	0.0184055	+	0.0106264i
$595$	−0.0480464	−	0.0700073i	−0.00196971	−	0.00287002i
$596$	−3.72402	−	0.997848i	−0.152542	−	0.0408734i
$597$	−0.719195	+	0.415227i	−0.0294347	+	0.0169941i
$598$	−2.88932	+	6.04532i	−0.118153	+	0.247212i
$599$	9.56265	−	16.5630i	0.390719	−	0.676746i	−0.601825	−	0.798628i	$-0.705560\pi$
$599$	9.56265	−	16.5630i	0.390719	−	0.676746i	0.992545	+	0.121882i	$0.0388930\pi$
$600$	2.49105	+	9.29672i	0.101697	+	0.379537i
$601$	38.9868	−	22.5091i	1.59031	−	0.918164i	0.597052	−	0.802202i	$-0.296339\pi$
$601$	38.9868	−	22.5091i	1.59031	−	0.918164i	0.993254	−	0.115961i	$-0.0369948\pi$
$602$	−2.29205	+	0.178859i	−0.0934169	+	0.00728975i
$603$	1.77192	+	1.77192i	0.0721580	+	0.0721580i
$604$	−16.0042	−	16.0042i	−0.651200	−	0.651200i
$605$	1.84074	−	6.86975i	0.0748369	−	0.279295i
$606$	2.20165	+	8.21665i	0.0894357	+	0.333779i
$607$			47.3844i			1.92328i	0.274323	+	0.961638i	$0.411546\pi$
$607$			47.3844i			1.92328i	−0.274323	+	0.961638i	$0.588454\pi$
$608$	2.39032	+	4.14016i	0.0969404	+	0.167906i
$609$	14.0404	−	16.4172i	0.568946	−	0.665257i
$610$			0.411070i			0.0166437i
$611$	−40.8473	−	19.5227i	−1.65251	−	0.789804i
$612$	−0.0662600	−	0.0382552i	−0.00267840	−	0.00154638i
$613$	28.5133	+	28.5133i	1.15164	+	1.15164i	0.986223	+	0.165420i	$0.0528978\pi$
$613$	28.5133	+	28.5133i	1.15164	+	1.15164i	0.165420	+	0.986223i	$0.447102\pi$
$614$	−12.6360	−	7.29537i	−0.509946	−	0.294417i
$615$	3.08792	−	5.34843i	0.124517	−	0.215669i
$616$	1.67158	+	4.73036i	0.0673498	+	0.190591i
$617$	−12.1180	+	3.24702i	−0.487854	+	0.130720i	−0.494357	−	0.869259i	$-0.664596\pi$
$617$	−12.1180	+	3.24702i	−0.487854	+	0.130720i	0.00650361	+	0.999979i	$0.497930\pi$
$618$	−5.22667	+	5.22667i	−0.210248	+	0.210248i
$619$	−8.09314	+	2.16855i	−0.325291	+	0.0871614i	−0.417769	−	0.908553i	$-0.637188\pi$
$619$	−8.09314	+	2.16855i	−0.325291	+	0.0871614i	0.0924781	+	0.995715i	$0.470521\pi$
$620$	2.33612	+	4.04628i	0.0938208	+	0.162502i
$621$	1.59558	−	2.76363i	0.0640284	−	0.110900i
$622$	2.87041	−	10.7125i	0.115093	−	0.429532i
$623$	11.4071	−	7.82873i	0.457014	−	0.313651i
$624$	−4.87576	+	5.69968i	−0.195187	+	0.228170i
$625$	8.97776	+	15.5499i	0.359110	+	0.621997i
$626$	−1.23194	+	1.23194i	−0.0492383	+	0.0492383i
$627$	0.776649			0.0310164
$628$	−7.30967			−0.291688
$629$	−0.229365	+	0.229365i	−0.00914538	+	0.00914538i
$630$	−1.01203	+	0.357623i	−0.0403202	+	0.0142481i
$631$	3.60680	+	13.4608i	0.143584	+	0.535864i	0.999814	+	0.0192694i	$0.00613403\pi$
$631$	3.60680	+	13.4608i	0.143584	+	0.535864i	−0.856230	+	0.516595i	$0.827199\pi$
$632$	19.5073	+	5.22695i	0.775957	+	0.207917i
$633$	−20.0368	+	11.5683i	−0.796392	+	0.459797i
$634$			0.412327i			0.0163756i
$635$	4.79876	−	1.28582i	0.190433	−	0.0510264i
$636$	−16.2509			−0.644390
$637$	11.9960	+	22.2058i	0.475300	+	0.879824i
$638$	−4.22922			−0.167436
$639$	0.798336	−	0.213913i	0.0315817	−	0.00846228i
$640$		−	8.02309i		−	0.317140i
$641$	−41.8233	+	24.1467i	−1.65192	+	0.953736i	−0.675638	+	0.737234i	$0.736132\pi$
$641$	−41.8233	+	24.1467i	−1.65192	+	0.953736i	−0.976282	+	0.216503i	$0.930535\pi$
$642$	−6.63306	−	1.77732i	−0.261786	−	0.0701454i
$643$	−4.25643	−	15.8852i	−0.167857	−	0.626451i	−0.997658	−	0.0683924i	$-0.978213\pi$
$643$	−4.25643	−	15.8852i	−0.167857	−	0.626451i	0.829801	−	0.558059i	$-0.188454\pi$
$644$	13.2216	−	4.67216i	0.521005	−	0.184109i
$645$	0.735063	−	0.735063i	0.0289431	−	0.0289431i
$646$	0.0234231			0.000921571
$647$	−14.2020			−0.558336			−0.279168	−	0.960242i	$-0.590059\pi$
$647$	−14.2020			−0.558336			−0.279168	+	0.960242i	$0.590059\pi$
$648$	−1.50746	+	1.50746i	−0.0592186	+	0.0592186i
$649$	−3.93467	−	6.81505i	−0.154449	−	0.267514i
$650$	4.08764	−	8.55256i	0.160330	−	0.335459i
$651$	8.80856	−	6.04536i	0.345235	−	0.236936i
$652$	−0.131164	+	0.489512i	−0.00513680	+	0.0191708i
$653$	4.99313	−	8.64836i	0.195396	−	0.338436i	−0.751634	−	0.659580i	$-0.770734\pi$
$653$	4.99313	−	8.64836i	0.195396	−	0.338436i	0.947030	+	0.321144i	$0.104067\pi$
$654$	−0.999657	−	1.73146i	−0.0390897	−	0.0677053i
$655$	9.23031	−	2.47325i	0.360658	−	0.0966380i
$656$	13.0402	−	13.0402i	0.509136	−	0.509136i
$657$	15.2725	−	4.09226i	0.595838	−	0.159654i
$658$	−6.44573	−	18.2406i	−0.251281	−	0.711093i
$659$	12.1444	−	21.0347i	0.473079	−	0.819397i	−0.526446	−	0.850208i	$-0.676476\pi$
$659$	12.1444	−	21.0347i	0.473079	−	0.819397i	0.999525	+	0.0308117i	$0.00980923\pi$
$660$	−0.891307	−	0.514596i	−0.0346941	−	0.0200306i
$661$	17.0003	+	17.0003i	0.661233	+	0.661233i	0.955671	−	0.294437i	$-0.0951323\pi$
$661$	17.0003	+	17.0003i	0.661233	+	0.661233i	−0.294437	+	0.955671i	$0.595132\pi$
$662$	−4.78681	−	2.76366i	−0.186044	−	0.107413i
$663$	0.0553198	+	0.156611i	0.00214844	+	0.00608225i
$664$			10.5632i			0.409931i
$665$	−1.04602	+	1.22309i	−0.0405630	+	0.0474294i
$666$	2.05024	+	3.55112i	0.0794453	+	0.137603i
$667$			26.0554i			1.00887i
$668$	−0.176233	−	0.657709i	−0.00681865	−	0.0254475i
$669$	−3.71792	+	13.8755i	−0.143743	+	0.536457i
$670$	0.718851	+	0.718851i	0.0277716	+	0.0277716i
$671$	0.637296	+	0.637296i	0.0246025	+	0.0246025i
$672$	−14.4420	+	1.12698i	−0.557114	+	0.0434741i
$673$	−18.1748	+	10.4933i	−0.700589	+	0.404485i	−0.807567	−	0.589776i	$-0.799216\pi$
$673$	−18.1748	+	10.4933i	−0.700589	+	0.404485i	0.106978	+	0.994261i	$0.465883\pi$
$674$	4.27382	+	15.9501i	0.164622	+	0.614376i
$675$	−2.25733	+	3.90981i	−0.0868847	+	0.150489i
$676$	21.3310	−	3.34403i	0.820421	−	0.128617i
$677$	42.3269	−	24.4375i	1.62676	−	0.939208i	0.641705	−	0.766952i	$-0.278228\pi$
$677$	42.3269	−	24.4375i	1.62676	−	0.939208i	0.985052	−	0.172256i	$-0.0551058\pi$
$678$	8.47643	+	2.27125i	0.325535	+	0.0872269i
$679$	−1.66963	−	2.43278i	−0.0640746	−	0.0933617i
$680$	−0.0592508	−	0.0342084i	−0.00227216	−	0.00131183i
$681$	5.32042	−	19.8561i	0.203879	−	0.760886i
$682$	−2.02031	−	0.541341i	−0.0773618	−	0.0207290i
$683$	−39.3645	−	10.5477i	−1.50624	−	0.403596i	−0.591055	−	0.806631i	$-0.701288\pi$
$683$	−39.3645	−	10.5477i	−1.50624	−	0.403596i	−0.915184	+	0.403035i	$0.867955\pi$
$684$	−0.375340	+	1.40079i	−0.0143515	+	0.0535604i
$685$	7.04431	+	4.06703i	0.269149	+	0.155393i
$686$	−3.08368	+	10.3348i	−0.117735	+	0.394584i
$687$	3.99397	+	1.07018i	0.152380	+	0.0408300i
$688$	2.68828	−	1.55208i	0.102490	−	0.0591726i
$689$	26.8079	+	22.9327i	1.02130	+	0.873665i
$690$	0.647313	−	1.12118i	0.0246428	−	0.0426826i
$691$	−0.836048	−	3.12017i	−0.0318048	−	0.118697i	0.948198	−	0.317679i	$-0.102903\pi$
$691$	−0.836048	−	3.12017i	−0.0318048	−	0.118697i	−0.980003	+	0.198982i	$0.936237\pi$
$692$	2.98595	−	1.72394i	0.113509	−	0.0655342i
$693$	−1.01455	+	2.12342i	−0.0385395	+	0.0806620i
$694$	9.21538	+	9.21538i	0.349811	+	0.349811i
$695$	−0.474932	−	0.474932i	−0.0180152	−	0.0180152i
$696$	4.50512	−	16.8133i	0.170766	−	0.637307i
$697$	−0.105694	−	0.394457i	−0.00400346	−	0.0149411i
$698$		−	5.31385i		−	0.201132i
$699$	0.994594	+	1.72269i	0.0376190	+	0.0651580i
$700$	−18.7052	+	6.60990i	−0.706990	+	0.249831i
$701$			8.12097i			0.306725i	0.988170	+	0.153362i	$0.0490102\pi$
$701$			8.12097i			0.306725i	−0.988170	+	0.153362i	$0.950990\pi$
$702$	2.09330	−	0.163087i	0.0790066	−	0.00615531i
$703$	5.32452	+	3.07411i	0.200818	+	0.115942i
$704$	−0.611476	−	0.611476i	−0.0230459	−	0.0230459i
$705$	7.57564	+	4.37380i	0.285315	+	0.164727i
$706$	−0.836893	+	1.44954i	−0.0314969	+	0.0545542i
$707$	−36.4396	+	12.8768i	−1.37045	+	0.484281i
$708$	14.1934	−	3.80310i	0.533419	−	0.142929i
$709$	−9.64349	+	9.64349i	−0.362169	+	0.362169i	−0.864611	−	0.502442i	$-0.832435\pi$
$709$	−9.64349	+	9.64349i	−0.362169	+	0.362169i	0.502442	+	0.864611i	$0.332435\pi$
$710$	0.323878	−	0.0867828i	0.0121549	−	0.00325690i
$711$	4.73655	+	8.20394i	0.177634	+	0.307672i
$712$	5.57396	−	9.65438i	0.208893	−	0.361813i
$713$	−3.33510	+	12.4468i	−0.124901	+	0.466135i
$714$	−0.0305980	+	0.0640407i	−0.00114510	+	0.00239666i
$715$	0.744143	+	2.10667i	0.0278294	+	0.0787850i
$716$	11.1376	+	19.2908i	0.416230	+	0.720932i
$717$	−10.1339	+	10.1339i	−0.378459	+	0.378459i
$718$	−4.69917			−0.175371
$719$	−28.0584			−1.04640			−0.523200	−	0.852210i	$-0.675262\pi$
$719$	−28.0584			−1.04640			−0.523200	+	0.852210i	$0.675262\pi$
$720$	1.02478	−	1.02478i	0.0381915	−	0.0381915i
$721$	−25.5220	−	21.8271i	−0.950488	−	0.812884i
$722$	2.74877	+	10.2586i	0.102299	+	0.381784i
$723$	26.7166	+	7.15869i	0.993601	+	0.266234i
$724$	−3.34652	+	1.93211i	−0.124372	+	0.0718064i
$725$		−	36.8617i		−	1.36901i
$726$	−5.74241	+	1.53867i	−0.213121	+	0.0571055i
$727$	21.2410			0.787785			0.393893	−	0.919156i	$-0.371128\pi$
$727$	21.2410			0.787785			0.393893	+	0.919156i	$0.371128\pi$
$728$	16.4354	+	11.9775i	0.609136	+	0.443915i
$729$	−1.00000			−0.0370370
$730$	6.19593	−	1.66019i	0.229322	−	0.0614466i
$731$		−	0.0687385i		−	0.00254239i
$732$	−1.45744	+	0.841452i	−0.0538684	+	0.0311010i
$733$	−8.19585	−	2.19607i	−0.302721	−	0.0811138i	0.104261	−	0.994550i	$-0.466752\pi$
$733$	−8.19585	−	2.19607i	−0.302721	−	0.0811138i	−0.406982	+	0.913436i	$0.633419\pi$
$734$	−0.253078	−	0.944500i	−0.00934128	−	0.0348621i
$735$	−1.97759	−	4.45764i	−0.0729446	−	0.164423i
$736$	12.3547	−	12.3547i	0.455399	−	0.455399i
$737$	2.22892			0.0821032
$738$	−5.16236			−0.190029
$739$	15.6168	−	15.6168i	0.574475	−	0.574475i	−0.358901	−	0.933376i	$-0.616848\pi$
$739$	15.6168	−	15.6168i	0.574475	−	0.574475i	0.933376	+	0.358901i	$0.116848\pi$
$740$	−4.07372	−	7.05589i	−0.149753	−	0.259380i
$741$	2.59591	−	1.78111i	0.0953631	−	0.0654306i
$742$	1.17282	+	15.0295i	0.0430555	+	0.551749i
$743$	−7.10193	+	26.5048i	−0.260544	+	0.972365i	0.704377	+	0.709826i	$0.251226\pi$
$743$	−7.10193	+	26.5048i	−0.260544	+	0.972365i	−0.964921	+	0.262539i	$0.915440\pi$
$744$	4.30422	−	7.45513i	0.157800	−	0.273318i
$745$	−0.808575	−	1.40049i	−0.0296239	−	0.0513101i
$746$	−18.1549	+	4.86459i	−0.664699	+	0.178105i
$747$	−3.50364	+	3.50364i	−0.128191	+	0.128191i
$748$	−0.0657356	+	0.0176138i	−0.00240353	+	0.000644024i
$749$	5.70596	−	30.6731i	0.208491	−	1.12077i
$750$	−1.93001	+	3.34287i	−0.0704739	+	0.122064i
$751$	−7.00030	−	4.04163i	−0.255445	−	0.147481i	0.366810	−	0.930296i	$-0.380450\pi$
$751$	−7.00030	−	4.04163i	−0.255445	−	0.147481i	−0.622255	+	0.782815i	$0.713783\pi$
$752$	18.4705	+	18.4705i	0.673549	+	0.673549i
$753$	6.79478	+	3.92297i	0.247616	+	0.142961i
$754$	−14.1359	+	9.69896i	−0.514800	+	0.353215i
$755$		−	9.49358i		−	0.345507i
$756$	−3.33955	−	2.85607i	−0.121458	−	0.103874i
$757$	−15.2508	−	26.4151i	−0.554299	−	0.960074i	−0.997958	−	0.0638779i	$-0.979653\pi$
$757$	−15.2508	−	26.4151i	−0.554299	−	0.960074i	0.443659	−	0.896196i	$-0.353680\pi$
$758$		−	12.1128i		−	0.439956i
$759$	−0.734651	−	2.74175i	−0.0266661	−	0.0995194i
$760$	−0.335635	+	1.25261i	−0.0121747	+	0.0454368i
$761$	9.95454	+	9.95454i	0.360852	+	0.360852i	0.864126	−	0.503275i	$-0.167872\pi$
$761$	9.95454	+	9.95454i	0.360852	+	0.360852i	−0.503275	+	0.864126i	$0.667872\pi$
$762$	−2.93646	−	2.93646i	−0.106377	−	0.106377i
$763$	7.48940	−	5.14001i	0.271135	−	0.186081i
$764$	−33.0754	+	19.0961i	−1.19663	+	0.690872i
$765$	−0.00830614	−	0.0309989i	−0.000300309	−	0.00112077i
$766$	−8.18928	+	14.1843i	−0.295891	+	0.512498i
$767$	−28.7805	−	13.7555i	−1.03920	−	0.496681i
$768$	−4.12408	+	2.38104i	−0.148815	+	0.0859182i
$769$	3.42800	+	0.918529i	0.123617	+	0.0331230i	0.320097	−	0.947385i	$-0.396285\pi$
$769$	3.42800	+	0.918529i	0.123617	+	0.0331230i	−0.196480	+	0.980508i	$0.562951\pi$
$770$	−0.411593	+	0.861453i	−0.0148328	+	0.0310446i
$771$	−0.315066	−	0.181903i	−0.0113468	−	0.00655109i
$772$	−2.90054	+	10.8250i	−0.104393	+	0.389599i
$773$	−47.3633	−	12.6910i	−1.70354	−	0.456462i	−0.729712	−	0.683754i	$-0.760346\pi$
$773$	−47.3633	−	12.6910i	−1.70354	−	0.456462i	−0.973827	+	0.227293i	$0.927013\pi$
$774$	−0.839337	−	0.224900i	−0.0301694	−	0.00808386i
$775$	4.71831	−	17.6090i	0.169487	−	0.632532i
$776$	−2.05899	−	1.18876i	−0.0739134	−	0.0426739i
$777$	−15.3604	+	10.5419i	−0.551050	+	0.378188i
$778$	6.00087	+	1.60793i	0.215142	+	0.0576471i
$779$	−6.70338	+	3.87020i	−0.240173	+	0.138664i
$780$	−4.15928	+	0.324044i	−0.148926	+	0.0116026i
$781$	0.367577	−	0.636661i	0.0131529	−	0.0227815i
$782$	−0.0221565	−	0.0826891i	−0.000792314	−	0.00295696i
$783$	7.07099	−	4.08244i	0.252697	−	0.145894i
$784$	−2.25894	−	14.3858i	−0.0806764	−	0.513780i
$785$	−2.16803	−	2.16803i	−0.0773802	−	0.0773802i
$786$	−5.64821	−	5.64821i	−0.201465	−	0.201465i
$787$	7.94340	−	29.6452i	0.283152	−	1.05674i	−0.667028	−	0.745033i	$-0.732434\pi$
$787$	7.94340	−	29.6452i	0.283152	−	1.05674i	0.950179	−	0.311704i	$-0.100900\pi$
$788$	5.48913	+	20.4857i	0.195542	+	0.729774i
$789$			22.3462i			0.795546i
$790$	1.92158	+	3.32827i	0.0683666	+	0.118414i
$791$	−7.29168	+	39.1973i	−0.259262	+	1.39370i
$792$			1.89625i			0.0673804i
$793$	3.59165	+	0.668602i	0.127543	+	0.0237427i
$794$	1.19651	+	0.690804i	0.0424624	+	0.0245157i
$795$	−4.81997	−	4.81997i	−0.170947	−	0.170947i
$796$	−1.19450	−	0.689644i	−0.0423379	−	0.0244438i
$797$	−9.95011	+	17.2341i	−0.352451	+	0.610463i	−0.986678	−	0.162684i	$-0.947985\pi$
$797$	−9.95011	+	17.2341i	−0.352451	+	0.610463i	0.634227	+	0.773147i	$0.281318\pi$
$798$	1.32259	+	0.246035i	0.0468192	+	0.00870953i
$799$	0.558718	−	0.149708i	0.0197660	−	0.00529629i
$800$	−17.4787	+	17.4787i	−0.617964	+	0.617964i
$801$	5.05100	−	1.35341i	0.178468	−	0.0478204i
$802$	9.07542	+	15.7191i	0.320464	+	0.555060i
$803$	7.03191	−	12.1796i	0.248151	−	0.429809i
$804$	−1.07719	+	4.02014i	−0.0379897	+	0.141779i
$805$	5.30725	+	2.53575i	0.187056	+	0.0893734i
$806$	−7.99426	+	2.82383i	−0.281586	+	0.0994650i
$807$	13.1471	+	22.7714i	0.462798	+	0.801590i
$808$	−22.0202	+	22.0202i	−0.774669	+	0.774669i
$809$	−3.40755			−0.119803			−0.0599015	−	0.998204i	$-0.519079\pi$
$809$	−3.40755			−0.119803			−0.0599015	+	0.998204i	$0.519079\pi$
$810$	−0.405691			−0.0142545
$811$	−6.11425	+	6.11425i	−0.214700	+	0.214700i	−0.806261	−	0.591560i	$-0.798512\pi$
$811$	−6.11425	+	6.11425i	−0.214700	+	0.214700i	0.591560	+	0.806261i	$0.298512\pi$
$812$	35.2736	+	6.56178i	1.23786	+	0.230273i
$813$	0.0611447	+	0.228195i	0.00214444	+	0.00800315i
$814$	3.52302	+	0.943990i	0.123482	+	0.0330868i
$815$	−0.184091	+	0.106285i	−0.00644843	+	0.00372300i
$816$		−	0.0958314i		−	0.00335477i
$817$	−1.25849	+	0.337212i	−0.0440291	+	0.0117976i
$818$	13.4021			0.468594
$819$	1.47861	+	9.42410i	0.0516670	+	0.329305i
$820$	10.2573			0.358202
$821$	−14.5367	+	3.89511i	−0.507336	+	0.135940i	−0.503402	−	0.864052i	$-0.667919\pi$
$821$	−14.5367	+	3.89511i	−0.507336	+	0.135940i	−0.00393318	+	0.999992i	$0.501252\pi$
$822$		−	6.79925i		−	0.237151i
$823$	−40.2287	+	23.2260i	−1.40228	+	0.809608i	−0.994627	−	0.103527i	$-0.966987\pi$
$823$	−40.2287	+	23.2260i	−1.40228	+	0.809608i	−0.407656	+	0.913135i	$0.633654\pi$
$824$	−26.1379	−	7.00362i	−0.910556	−	0.243983i
$825$	1.03934	+	3.87887i	0.0361852	+	0.135045i
$826$	−4.54158	−	12.8521i	−0.158022	−	0.447182i
$827$	30.9402	−	30.9402i	1.07590	−	1.07590i	0.0790236	−	0.996873i	$-0.474820\pi$
$827$	30.9402	−	30.9402i	1.07590	−	1.07590i	0.996873	−	0.0790236i	$-0.0251802\pi$
$828$	5.30014			0.184193
$829$	−32.6864			−1.13525			−0.567623	−	0.823289i	$-0.692137\pi$
$829$	−32.6864			−1.13525			−0.567623	+	0.823289i	$0.692137\pi$
$830$	−1.42140	+	1.42140i	−0.0493373	+	0.0493373i
$831$	−0.943444	−	1.63409i	−0.0327277	−	0.0566860i
$832$	−3.44614	−	0.641513i	−0.119473	−	0.0222405i
$833$	−0.300891	−	0.115959i	−0.0104253	−	0.00401776i
$834$	−0.145310	+	0.542305i	−0.00503168	+	0.0187785i
$835$	0.142805	−	0.247345i	0.00494196	−	0.00855972i
$836$	0.644962	+	1.11711i	0.0223065	+	0.0386360i
$837$	3.90039	−	1.04511i	0.134817	−	0.0361242i
$838$	−7.13357	+	7.13357i	−0.246425	+	0.246425i
$839$	−25.2872	+	6.77567i	−0.873010	+	0.233922i	−0.667389	−	0.744710i	$-0.732588\pi$
$839$	−25.2872	+	6.77567i	−0.873010	+	0.233922i	−0.205621	+	0.978632i	$0.565921\pi$
$840$	−2.98628	−	2.55395i	−0.103036	−	0.0881196i
$841$	−18.8326	+	32.6190i	−0.649399	+	1.12479i
$842$	−20.3141	−	11.7284i	−0.700070	−	0.404186i
$843$	14.2823	+	14.2823i	0.491909	+	0.491909i
$844$	−33.2788	−	19.2135i	−1.14550	−	0.661357i
$845$	7.31853	+	5.33487i	0.251765	+	0.183525i
$846$		−	7.31209i		−	0.251395i
$847$	−8.99924	−	25.4667i	−0.309218	−	0.875047i
$848$	−10.1773	−	17.6277i	−0.349491	−	0.605337i
$849$			17.1254i			0.587743i
$850$	0.0313457	+	0.116984i	0.00107515	+	0.00401251i
$851$	5.81575	−	21.7047i	0.199361	−	0.744026i
$852$	0.970657	+	0.970657i	0.0332542	+	0.0332542i
$853$	26.6435	+	26.6435i	0.912255	+	0.912255i	0.996449	−	0.0841944i	$-0.0268317\pi$
$853$	26.6435	+	26.6435i	0.912255	+	0.912255i	−0.0841944	+	0.996449i	$0.526832\pi$
$854$	0.883390	+	1.28717i	0.0302290	+	0.0440460i
$855$	−0.526794	+	0.304145i	−0.0180160	+	0.0104015i
$856$	−6.50658	−	24.2829i	−0.222390	−	0.829971i
$857$	14.1671	−	24.5382i	0.483940	−	0.838208i	−0.515890	−	0.856655i	$-0.672539\pi$
$857$	14.1671	−	24.5382i	0.483940	−	0.838208i	0.999830	+	0.0184467i	$0.00587210\pi$
$858$	1.21402	−	1.41917i	0.0414461	−	0.0484497i
$859$	−10.1518	+	5.86113i	−0.346374	+	0.199979i	−0.663087	−	0.748542i	$-0.730754\pi$
$859$	−10.1518	+	5.86113i	−0.346374	+	0.199979i	0.316713	+	0.948521i	$0.397421\pi$
$860$	1.66772	+	0.446864i	0.0568687	+	0.0152379i
$861$	−1.82470	−	23.3833i	−0.0621857	−	0.796899i
$862$	17.0885	+	9.86603i	0.582036	+	0.336038i
$863$	11.1245	−	41.5172i	0.378682	−	1.41326i	−0.469207	−	0.883088i	$-0.655460\pi$
$863$	11.1245	−	41.5172i	0.378682	−	1.41326i	0.847889	−	0.530174i	$-0.177873\pi$
$864$	−5.28861	−	1.41708i	−0.179922	−	0.0482100i
$865$	1.39694	+	0.374308i	0.0474973	+	0.0127269i
$866$	−4.59101	+	17.1339i	−0.156009	+	0.582233i
$867$	14.7206	+	8.49894i	0.499938	+	0.288639i
$868$	16.0104	+	7.64963i	0.543430	+	0.259645i
$869$	8.13902	+	2.18084i	0.276097	+	0.0739800i
$870$	2.86864	−	1.65621i	0.0972560	−	0.0561508i
$871$	7.45004	−	5.11163i	0.252435	−	0.173201i
$872$	3.65963	−	6.33866i	0.123931	−	0.214654i
$873$	−0.288642	−	1.07723i	−0.00976905	−	0.0364586i
$874$	−1.40521	+	0.811301i	−0.0475321	+	0.0274427i
$875$	−15.8239	−	7.56051i	−0.534947	−	0.255592i
$876$	18.5691	+	18.5691i	0.627392	+	0.627392i
$877$	20.3159	+	20.3159i	0.686021	+	0.686021i	0.961350	−	0.275329i	$-0.0887869\pi$
$877$	20.3159	+	20.3159i	0.686021	+	0.686021i	−0.275329	+	0.961350i	$0.588787\pi$
$878$	−0.410818	+	1.53320i	−0.0138644	+	0.0517428i
$879$	0.0147783	+	0.0551536i	0.000498461	+	0.00186028i
$880$		−	1.28909i		−	0.0434552i
$881$	20.6648	+	35.7924i	0.696213	+	1.20588i	0.969770	+	0.244021i	$0.0784665\pi$
$881$	20.6648	+	35.7924i	0.696213	+	1.20588i	−0.273557	+	0.961856i	$0.588200\pi$
$882$	−2.40040	+	3.29466i	−0.0808255	+	0.110937i
$883$		−	14.7746i		−	0.497205i	−0.968606	−	0.248603i	$-0.920029\pi$
$883$		−	14.7746i		−	0.497205i	0.968606	−	0.248603i	$-0.0799713\pi$
$884$	−0.179324	+	0.209626i	−0.00603130	+	0.00705049i
$885$	5.33770	+	3.08172i	0.179425	+	0.103591i
$886$	−14.3216	−	14.3216i	−0.481144	−	0.481144i
$887$	−13.9020	−	8.02631i	−0.466783	−	0.269497i	0.248109	−	0.968732i	$-0.420191\pi$
$887$	−13.9020	−	8.02631i	−0.466783	−	0.269497i	−0.714892	+	0.699235i	$0.753524\pi$
$888$	−7.50570	+	13.0002i	−0.251875	+	0.436260i
$889$	12.2629	−	14.3388i	0.411286	−	0.480908i
$890$	2.04915	−	0.549067i	0.0686875	−	0.0184048i
$891$	−0.628957	+	0.628957i	−0.0210709	+	0.0210709i
$892$	−23.0456	+	6.17504i	−0.771622	+	0.206756i
$893$	−5.48184	−	9.49482i	−0.183443	−	0.317732i
$894$	−0.675886	+	1.17067i	−0.0226050	+	0.0391530i
$895$	−2.41824	+	9.02498i	−0.0808327	+	0.301672i
$896$	−17.2416	−	25.1224i	−0.576002	−	0.839280i
$897$	−8.74326	−	7.47937i	−0.291929	−	0.249729i
$898$	10.5895	+	18.3415i	0.353376	+	0.612065i
$899$	−23.3130	+	23.3130i	−0.777533	+	0.777533i
$900$	−7.49833			−0.249944
$901$	−0.450733			−0.0150161
$902$	−3.24691	+	3.24691i	−0.108110	+	0.108110i
$903$	0.722023	−	3.88133i	0.0240274	−	0.129162i
$904$	8.31479	+	31.0312i	0.276546	+	1.03208i
$905$	−1.56563	−	0.419509i	−0.0520432	−	0.0139449i
$906$	−6.87249	+	3.96783i	−0.228323	+	0.131822i
$907$		−	15.4903i		−	0.514346i	−0.966365	−	0.257173i	$-0.917209\pi$
$907$		−	15.4903i		−	0.514346i	0.966365	−	0.257173i	$-0.0827911\pi$
$908$	32.9786	−	8.83659i	1.09443	−	0.293253i
$909$	−14.6075			−0.484501
$910$	0.599861	+	3.82328i	0.0198852	+	0.126740i
$911$	−28.0514			−0.929383			−0.464691	−	0.885473i	$-0.653835\pi$
$911$	−28.0514			−0.929383			−0.464691	+	0.885473i	$0.653835\pi$
$912$	−1.75452	+	0.470123i	−0.0580980	+	0.0155673i
$913$			4.40728i			0.145860i
$914$	−16.0562	+	9.27007i	−0.531093	+	0.306627i
$915$	−0.681844	−	0.182700i	−0.0225411	−	0.00603986i
$916$	1.77745	+	6.63353i	0.0587285	+	0.219178i
$917$	23.5875	−	27.5803i	0.778927	−	0.910783i
$918$	−0.0189689	+	0.0189689i	−0.000626065	+	0.000626065i
$919$	35.1125			1.15825			0.579127	−	0.815237i	$-0.303394\pi$
$919$	35.1125			1.15825			0.579127	+	0.815237i	$0.303394\pi$
$920$	4.73947			0.156256
$921$	17.7169	−	17.7169i	0.583792	−	0.583792i
$922$	5.25412	+	9.10041i	0.173035	+	0.299706i
$923$	−0.231465	−	2.97098i	−0.00761877	−	0.0977909i
$924$	−3.89678	+	0.304084i	−0.128195	+	0.0100036i
$925$	−8.22777	+	30.7065i	−0.270527	+	1.00962i
$926$	6.68912	−	11.5859i	0.219818	−	0.380736i
$927$	−6.34652	−	10.9925i	−0.208447	−	0.361041i
$928$	43.1808	−	11.5703i	1.41748	−	0.379813i
$929$	4.96042	−	4.96042i	0.162746	−	0.162746i	−0.621036	−	0.783782i	$-0.713288\pi$
$929$	4.96042	−	4.96042i	0.162746	−	0.162746i	0.783782	+	0.621036i	$0.213288\pi$
$930$	1.58235	−	0.423991i	0.0518875	−	0.0139032i
$931$	−0.646944	+	6.07772i	−0.0212027	+	0.199189i
$932$	−1.65190	+	2.86118i	−0.0541099	+	0.0937211i
$933$	16.4931	+	9.52232i	0.539961	+	0.311747i
$934$	15.4334	+	15.4334i	0.504995	+	0.504995i
$935$	−0.0247212	−	0.0142728i	−0.000808470	−	0.000466770i
$936$	4.34872	+	6.33812i	0.142142	+	0.207168i
$937$		−	40.3619i		−	1.31857i	−0.751894	−	0.659284i	$-0.770860\pi$
$937$		−	40.3619i		−	1.31857i	0.751894	−	0.659284i	$-0.229140\pi$
$938$	3.79572	+	0.706099i	0.123935	+	0.0230549i
$939$	−1.49590	−	2.59097i	−0.0488167	−	0.0845530i
$940$			14.5287i			0.473875i
$941$	7.16434	+	26.7377i	0.233551	+	0.871624i	0.978797	+	0.204834i	$0.0656655\pi$
$941$	7.16434	+	26.7377i	0.233551	+	0.871624i	−0.745246	+	0.666790i	$0.767668\pi$
$942$	−0.663329	+	2.47558i	−0.0216124	+	0.0806587i
$943$	20.0036	+	20.0036i	0.651406	+	0.651406i
$944$	13.0141	+	13.0141i	0.423572	+	0.423572i
$945$	−0.143397	−	1.83760i	−0.00466469	−	0.0597773i
$946$	−0.669360	+	0.386455i	−0.0217628	+	0.0125647i
$947$	2.00930	+	7.49880i	0.0652934	+	0.243678i	0.990857	−	0.134913i	$-0.0430754\pi$
$947$	2.00930	+	7.49880i	0.0652934	+	0.243678i	−0.925564	+	0.378591i	$0.876409\pi$
$948$	−7.86686	+	13.6258i	−0.255504	+	0.442545i
$949$	−4.42803	−	56.8362i	−0.143740	−	1.84498i
$950$	1.98801	−	1.14778i	0.0644997	−	0.0372389i
$951$	−0.683930	−	0.183258i	−0.0221779	−	0.00594256i
$952$	−0.259044	+	0.0202144i	−0.00839565	+	0.000655151i
$953$	19.1100	+	11.0332i	0.619034	+	0.357400i	0.776493	−	0.630126i	$-0.216997\pi$
$953$	19.1100	+	11.0332i	0.619034	+	0.357400i	−0.157459	+	0.987526i	$0.550330\pi$
$954$	−1.47472	+	5.50372i	−0.0477457	+	0.178190i
$955$	−15.4739	−	4.14623i	−0.500724	−	0.134169i
$956$	−22.9920	−	6.16068i	−0.743613	−	0.199250i
$957$	1.87967	−	7.01503i	0.0607611	−	0.226764i
$958$	13.4791	+	7.78217i	0.435490	+	0.251430i
$959$	30.7976	−	2.40328i	0.994507	−	0.0776059i
$960$	0.654219	+	0.175298i	0.0211148	+	0.00565770i
$961$	12.7260	−	7.34735i	0.410516	−	0.237011i
$962$	13.9404	−	4.92418i	0.449456	−	0.158762i
$963$	5.89611	−	10.2124i	0.190000	−	0.329089i
$964$	11.8897	+	44.3731i	0.382943	+	1.42916i
$965$	−4.07094	+	2.35036i	−0.131048	+	0.0756608i
$966$	−0.382508	−	4.90178i	−0.0123070	−	0.157712i
$967$	−38.9477	−	38.9477i	−1.25248	−	1.25248i	−0.954607	−	0.297868i	$-0.903724\pi$
$967$	−38.9477	−	38.9477i	−1.25248	−	1.25248i	−0.297868	−	0.954607i	$-0.596276\pi$
$968$	−15.3894	−	15.3894i	−0.494633	−	0.494633i
$969$	−0.0104104	+	0.0388521i	−0.000334430	+	0.00124811i
$970$	−0.117100	−	0.437021i	−0.00375984	−	0.0140319i
$971$		−	25.4616i		−	0.817101i	−0.912736	−	0.408551i	$-0.866034\pi$
$971$		−	25.4616i		−	0.817101i	0.912736	−	0.408551i	$-0.133966\pi$
$972$	−0.830442	−	1.43837i	−0.0266364	−	0.0461357i
$973$	−2.50777	−	0.466507i	−0.0803953	−	0.0149555i
$974$			14.4320i			0.462430i
$975$	12.3694	+	10.5814i	0.396139	+	0.338875i
$976$	−1.82548	−	1.05394i	−0.0584322	−	0.0337358i
$977$	22.0852	+	22.0852i	0.706569	+	0.706569i	0.965812	−	0.259243i	$-0.0834731\pi$
$977$	22.0852	+	22.0852i	0.706569	+	0.706569i	−0.259243	+	0.965812i	$0.583473\pi$
$978$	0.153881	+	0.0888434i	0.00492058	+	0.00284090i
$979$	2.32562	−	4.02810i	0.0743273	−	0.128739i
$980$	4.76945	−	6.54632i	0.152355	−	0.209114i
$981$	3.31627	−	0.888593i	0.105880	−	0.0283706i
$982$	4.57449	−	4.57449i	0.145978	−	0.145978i
$983$	−42.1212	+	11.2863i	−1.34346	+	0.359978i	−0.857715	−	0.514125i	$-0.828117\pi$
$983$	−42.1212	+	11.2863i	−1.34346	+	0.359978i	−0.485741	+	0.874103i	$0.661450\pi$
$984$	−9.44941	−	16.3669i	−0.301236	−	0.521756i
$985$	−4.44795	+	7.70407i	−0.141723	+	0.245472i
$986$	0.0566894	−	0.211568i	0.00180536	−	0.00673769i
$987$	33.1206	−	2.58455i	1.05424	−	0.0822671i
$988$	4.71764	+	2.25476i	0.150088	+	0.0717336i
$989$	2.38088	+	4.12380i	0.0757075	+	0.131129i
$990$	−0.255162	+	0.255162i	−0.00810960	+	0.00810960i
$991$	−14.5030			−0.460701			−0.230351	−	0.973108i	$-0.573987\pi$
$991$	−14.5030			−0.460701			−0.230351	+	0.973108i	$0.573987\pi$
$992$	22.1087			0.701950
$993$	6.71159	−	6.71159i	0.212986	−	0.212986i
$994$	0.827650	−	0.967753i	0.0262515	−	0.0306953i
$995$	−0.149738	−	0.558832i	−0.00474703	−	0.0177162i
$996$	−7.94908	−	2.12995i	−0.251876	−	0.0674901i
$997$	−42.3984	+	24.4787i	−1.34277	+	0.775249i	−0.987213	−	0.159405i	$-0.949042\pi$
$997$	−42.3984	+	24.4787i	−1.34277	+	0.775249i	−0.355558	+	0.934654i	$0.615709\pi$
$998$		−	0.108276i		−	0.00342741i
$999$	−6.80150	+	1.82246i	−0.215190	+	0.0576599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.115.6	yes	36
3.2	odd	2		819.2.gh.c.388.4		36
7.5	odd	6		273.2.bt.a.271.4	yes	36
13.6	odd	12		273.2.bt.a.136.4	✓	36
21.5	even	6		819.2.et.c.271.6		36
39.32	even	12		819.2.et.c.136.6		36
91.19	even	12	inner	273.2.cg.a.19.6	yes	36
273.110	odd	12		819.2.gh.c.19.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.4	✓	36	13.6	odd	12
273.2.bt.a.271.4	yes	36	7.5	odd	6
273.2.cg.a.19.6	yes	36	91.19	even	12	inner
273.2.cg.a.115.6	yes	36	1.1	even	1	trivial
819.2.et.c.136.6		36	39.32	even	12
819.2.et.c.271.6		36	21.5	even	6
819.2.gh.c.19.4		36	273.110	odd	12
819.2.gh.c.388.4		36	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.562494 - 0.150720i) q^{2} +1.00000i q^{3} +(-1.43837 + 0.830442i) q^{4} +(-0.672922 - 0.180309i) q^{5} +(0.150720 + 0.562494i) q^{6} +(-2.49458 + 0.881516i) q^{7} +(-1.50746 + 1.50746i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.562494 - 0.150720i) q^{2} +1.00000i q^{3} +(-1.43837 + 0.830442i) q^{4} +(-0.672922 - 0.180309i) q^{5} +(0.150720 + 0.562494i) q^{6} +(-2.49458 + 0.881516i) q^{7} +(-1.50746 + 1.50746i) q^{8} -1.00000 q^{9} -0.405691 q^{10} +(-0.628957 + 0.628957i) q^{11} +(-0.830442 - 1.43837i) q^{12} +(-0.659853 + 3.54466i) q^{13} +(-1.27033 + 0.871831i) q^{14} +(0.180309 - 0.672922i) q^{15} +(1.04015 - 1.80159i) q^{16} +(-0.0230331 - 0.0398944i) q^{17} +(-0.562494 + 0.150720i) q^{18} +(-0.617410 + 0.617410i) q^{19} +(1.11765 - 0.299472i) q^{20} +(-0.881516 - 2.49458i) q^{21} +(-0.258989 + 0.448581i) q^{22} +(2.76363 + 1.59558i) q^{23} +(-1.50746 - 1.50746i) q^{24} +(-3.90981 - 2.25733i) q^{25} +(0.163087 + 2.09330i) q^{26} -1.00000i q^{27} +(2.85607 - 3.33955i) q^{28} +(4.08244 + 7.07099i) q^{29} -0.405691i q^{30} +(1.04511 + 3.90039i) q^{31} +(1.41708 - 5.28861i) q^{32} +(-0.628957 - 0.628957i) q^{33} +(-0.0189689 - 0.0189689i) q^{34} +(1.83760 - 0.143397i) q^{35} +(1.43837 - 0.830442i) q^{36} +(-1.82246 - 6.80150i) q^{37} +(-0.254234 + 0.440346i) q^{38} +(-3.54466 - 0.659853i) q^{39} +(1.28621 - 0.742594i) q^{40} +(8.56284 + 2.29441i) q^{41} +(-0.871831 - 1.27033i) q^{42} +(1.29226 + 0.746085i) q^{43} +(0.382359 - 1.42698i) q^{44} +(0.672922 + 0.180309i) q^{45} +(1.79501 + 0.480971i) q^{46} +(-3.24985 + 12.1286i) q^{47} +(1.80159 + 1.04015i) q^{48} +(5.44586 - 4.39802i) q^{49} +(-2.53947 - 0.680450i) q^{50} +(0.0398944 - 0.0230331i) q^{51} +(-1.99452 - 5.64649i) q^{52} +(4.89224 - 8.47362i) q^{53} +(-0.150720 - 0.562494i) q^{54} +(0.536646 - 0.309833i) q^{55} +(2.43163 - 5.08932i) q^{56} +(-0.617410 - 0.617410i) q^{57} +(3.36209 + 3.36209i) q^{58} +(-2.28980 + 8.54567i) q^{59} +(0.299472 + 1.11765i) q^{60} -1.01326i q^{61} +(1.17573 + 2.03643i) q^{62} +(2.49458 - 0.881516i) q^{63} +0.972206i q^{64} +(1.08316 - 2.26630i) q^{65} +(-0.448581 - 0.258989i) q^{66} +(-1.77192 - 1.77192i) q^{67} +(0.0662600 + 0.0382552i) q^{68} +(-1.59558 + 2.76363i) q^{69} +(1.01203 - 0.357623i) q^{70} +(-0.798336 + 0.213913i) q^{71} +(1.50746 - 1.50746i) q^{72} +(-15.2725 + 4.09226i) q^{73} +(-2.05024 - 3.55112i) q^{74} +(2.25733 - 3.90981i) q^{75} +(0.375340 - 1.40079i) q^{76} +(1.01455 - 2.12342i) q^{77} +(-2.09330 + 0.163087i) q^{78} +(-4.73655 - 8.20394i) q^{79} +(-1.02478 + 1.02478i) q^{80} +1.00000 q^{81} +5.16236 q^{82} +(3.50364 - 3.50364i) q^{83} +(3.33955 + 2.85607i) q^{84} +(0.00830614 + 0.0309989i) q^{85} +(0.839337 + 0.224900i) q^{86} +(-7.07099 + 4.08244i) q^{87} -1.89625i q^{88} +(-5.05100 + 1.35341i) q^{89} +0.405691 q^{90} +(-1.47861 - 9.42410i) q^{91} -5.30014 q^{92} +(-3.90039 + 1.04511i) q^{93} +7.31209i q^{94} +(0.526794 - 0.304145i) q^{95} +(5.28861 + 1.41708i) q^{96} +(0.288642 + 1.07723i) q^{97} +(2.40040 - 3.29466i) q^{98} +(0.628957 - 0.628957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more