LMFDB - Embedded newform 728.2.s.b.393.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(113,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("728.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	728.393
Dual form			728.2.s.b.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 1.40126i) q^{3} +3.61803 q^{5} +(0.500000 - 0.866025i) q^{7} +(0.190983 - 0.330792i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 1.40126i) q^{3} +3.61803 q^{5} +(0.500000 - 0.866025i) q^{7} +(0.190983 - 0.330792i) q^{9} +(3.04508 + 5.27424i) q^{11} +(2.50000 + 2.59808i) q^{13} +(-2.92705 - 5.06980i) q^{15} +(0.500000 - 0.866025i) q^{17} +(-1.42705 + 2.47172i) q^{19} -1.61803 q^{21} +(-1.00000 - 1.73205i) q^{23} +8.09017 q^{25} -5.47214 q^{27} +(4.04508 + 7.00629i) q^{29} -5.47214 q^{31} +(4.92705 - 8.53390i) q^{33} +(1.80902 - 3.13331i) q^{35} +(-4.47214 - 7.74597i) q^{37} +(1.61803 - 5.60503i) q^{39} +(1.38197 + 2.39364i) q^{41} +(3.54508 - 6.14027i) q^{43} +(0.690983 - 1.19682i) q^{45} -3.00000 q^{47} +(-0.500000 - 0.866025i) q^{49} -1.61803 q^{51} -4.70820 q^{53} +(11.0172 + 19.0824i) q^{55} +4.61803 q^{57} +(4.73607 - 8.20311i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-0.190983 - 0.330792i) q^{63} +(9.04508 + 9.39993i) q^{65} +(-2.73607 - 4.73901i) q^{67} +(-1.61803 + 2.80252i) q^{69} +(0.381966 - 0.661585i) q^{71} -14.9443 q^{73} +(-6.54508 - 11.3364i) q^{75} +6.09017 q^{77} +8.94427 q^{79} +(3.85410 + 6.67550i) q^{81} +3.47214 q^{83} +(1.80902 - 3.13331i) q^{85} +(6.54508 - 11.3364i) q^{87} +(-7.66312 - 13.2729i) q^{89} +(3.50000 - 0.866025i) q^{91} +(4.42705 + 7.66788i) q^{93} +(-5.16312 + 8.94278i) q^{95} +(1.78115 - 3.08505i) q^{97} +2.32624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 10 q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 4 * q - q^3 + 10 * q^5 + 2 * q^7 + 3 * q^9	$ 4 q - q^{3} + 10 q^{5} + 2 q^{7} + 3 q^{9} + q^{11} + 10 q^{13} - 5 q^{15} + 2 q^{17} + q^{19} - 2 q^{21} - 4 q^{23} + 10 q^{25} - 4 q^{27} + 5 q^{29} - 4 q^{31} + 13 q^{33} + 5 q^{35} + 2 q^{39} + 10 q^{41} + 3 q^{43} + 5 q^{45} - 12 q^{47} - 2 q^{49} - 2 q^{51} + 8 q^{53} + 15 q^{55} + 14 q^{57} + 10 q^{59} + 12 q^{61} - 3 q^{63} + 25 q^{65} - 2 q^{67} - 2 q^{69} + 6 q^{71} - 24 q^{73} - 15 q^{75} + 2 q^{77} + 2 q^{81} - 4 q^{83} + 5 q^{85} + 15 q^{87} - 15 q^{89} + 14 q^{91} + 11 q^{93} - 5 q^{95} - 13 q^{97} - 22 q^{99}+O(q^{100}) $ 4 * q - q^3 + 10 * q^5 + 2 * q^7 + 3 * q^9 + q^11 + 10 * q^13 - 5 * q^15 + 2 * q^17 + q^19 - 2 * q^21 - 4 * q^23 + 10 * q^25 - 4 * q^27 + 5 * q^29 - 4 * q^31 + 13 * q^33 + 5 * q^35 + 2 * q^39 + 10 * q^41 + 3 * q^43 + 5 * q^45 - 12 * q^47 - 2 * q^49 - 2 * q^51 + 8 * q^53 + 15 * q^55 + 14 * q^57 + 10 * q^59 + 12 * q^61 - 3 * q^63 + 25 * q^65 - 2 * q^67 - 2 * q^69 + 6 * q^71 - 24 * q^73 - 15 * q^75 + 2 * q^77 + 2 * q^81 - 4 * q^83 + 5 * q^85 + 15 * q^87 - 15 * q^89 + 14 * q^91 + 11 * q^93 - 5 * q^95 - 13 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.809017	−	1.40126i	−0.467086	−	0.809017i	0.532207	−	0.846614i	$-0.321363\pi$
$3$	−0.809017	−	1.40126i	−0.467086	−	0.809017i	−0.999293	+	0.0375974i	$0.988030\pi$
$4$		0			0
$5$	3.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$5$	3.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	0.190983	−	0.330792i	0.0636610	−	0.110264i
$10$		0			0
$11$	3.04508	+	5.27424i	0.918128	+	1.59024i	0.802256	+	0.596980i	$0.203633\pi$
$11$	3.04508	+	5.27424i	0.918128	+	1.59024i	0.115871	+	0.993264i	$0.463034\pi$
$12$		0			0
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$		0			0
$15$	−2.92705	−	5.06980i	−0.755761	−	1.30902i
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$	−1.42705	+	2.47172i	−0.327388	+	0.567053i	−0.981993	−	0.188919i	$-0.939502\pi$
$19$	−1.42705	+	2.47172i	−0.327388	+	0.567053i	0.654605	+	0.755971i	$0.272835\pi$
$20$		0			0
$21$	−1.61803			−0.353084
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$	8.09017			1.61803
$26$		0			0
$27$	−5.47214			−1.05311
$28$		0			0
$29$	4.04508	+	7.00629i	0.751153	+	1.30104i	0.947264	+	0.320454i	$0.103835\pi$
$29$	4.04508	+	7.00629i	0.751153	+	1.30104i	−0.196111	+	0.980582i	$0.562831\pi$
$30$		0			0
$31$	−5.47214			−0.982825			−0.491412	−	0.870927i	$-0.663519\pi$
$31$	−5.47214			−0.982825			−0.491412	+	0.870927i	$0.663519\pi$
$32$		0			0
$33$	4.92705	−	8.53390i	0.857689	−	1.48556i
$34$		0			0
$35$	1.80902	−	3.13331i	0.305780	−	0.529626i
$36$		0			0
$37$	−4.47214	−	7.74597i	−0.735215	−	1.27343i	−0.954629	−	0.297797i	$-0.903748\pi$
$37$	−4.47214	−	7.74597i	−0.735215	−	1.27343i	0.219414	−	0.975632i	$-0.429585\pi$
$38$		0			0
$39$	1.61803	−	5.60503i	0.259093	−	0.897524i
$40$		0			0
$41$	1.38197	+	2.39364i	0.215827	+	0.373823i	0.953528	−	0.301304i	$-0.0974220\pi$
$41$	1.38197	+	2.39364i	0.215827	+	0.373823i	−0.737701	+	0.675127i	$0.764089\pi$
$42$		0			0
$43$	3.54508	−	6.14027i	0.540620	−	0.936382i	−0.458248	−	0.888824i	$-0.651523\pi$
$43$	3.54508	−	6.14027i	0.540620	−	0.936382i	0.998868	−	0.0475577i	$-0.0151438\pi$
$44$		0			0
$45$	0.690983	−	1.19682i	0.103006	−	0.178411i
$46$		0			0
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−1.61803			−0.226570
$52$		0			0
$53$	−4.70820			−0.646722			−0.323361	−	0.946276i	$-0.604813\pi$
$53$	−4.70820			−0.646722			−0.323361	+	0.946276i	$0.604813\pi$
$54$		0			0
$55$	11.0172	+	19.0824i	1.48556	+	2.57307i
$56$		0			0
$57$	4.61803			0.611674
$58$		0			0
$59$	4.73607	−	8.20311i	0.616584	−	1.06795i	−0.373521	−	0.927622i	$-0.621850\pi$
$59$	4.73607	−	8.20311i	0.616584	−	1.06795i	0.990104	−	0.140332i	$-0.0448171\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$		0			0
$63$	−0.190983	−	0.330792i	−0.0240616	−	0.0416759i
$64$		0			0
$65$	9.04508	+	9.39993i	1.12190	+	1.16592i
$66$		0			0
$67$	−2.73607	−	4.73901i	−0.334264	−	0.578962i	0.649079	−	0.760721i	$-0.275154\pi$
$67$	−2.73607	−	4.73901i	−0.334264	−	0.578962i	−0.983343	+	0.181759i	$0.941821\pi$
$68$		0			0
$69$	−1.61803	+	2.80252i	−0.194788	+	0.337383i
$70$		0			0
$71$	0.381966	−	0.661585i	0.0453310	−	0.0785156i	−0.842470	−	0.538744i	$-0.818899\pi$
$71$	0.381966	−	0.661585i	0.0453310	−	0.0785156i	0.887801	+	0.460228i	$0.152232\pi$
$72$		0			0
$73$	−14.9443			−1.74909			−0.874547	−	0.484940i	$-0.838841\pi$
$73$	−14.9443			−1.74909			−0.874547	+	0.484940i	$0.838841\pi$
$74$		0			0
$75$	−6.54508	−	11.3364i	−0.755761	−	1.30902i
$76$		0			0
$77$	6.09017			0.694039
$78$		0			0
$79$	8.94427			1.00631			0.503155	−	0.864196i	$-0.332173\pi$
$79$	8.94427			1.00631			0.503155	+	0.864196i	$0.332173\pi$
$80$		0			0
$81$	3.85410	+	6.67550i	0.428234	+	0.741722i
$82$		0			0
$83$	3.47214			0.381116			0.190558	−	0.981676i	$-0.438970\pi$
$83$	3.47214			0.381116			0.190558	+	0.981676i	$0.438970\pi$
$84$		0			0
$85$	1.80902	−	3.13331i	0.196215	−	0.339855i
$86$		0			0
$87$	6.54508	−	11.3364i	0.701707	−	1.21539i
$88$		0			0
$89$	−7.66312	−	13.2729i	−0.812289	−	1.40693i	−0.911258	−	0.411835i	$-0.864888\pi$
$89$	−7.66312	−	13.2729i	−0.812289	−	1.40693i	0.0989693	−	0.995090i	$-0.468445\pi$
$90$		0			0
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$		0			0
$93$	4.42705	+	7.66788i	0.459064	+	0.795122i
$94$		0			0
$95$	−5.16312	+	8.94278i	−0.529725	+	0.917510i
$96$		0			0
$97$	1.78115	−	3.08505i	0.180849	−	0.313239i	−0.761321	−	0.648375i	$-0.775449\pi$
$97$	1.78115	−	3.08505i	0.180849	−	0.313239i	0.942170	+	0.335136i	$0.108782\pi$
$98$		0			0
$99$	2.32624			0.233796
$100$		0			0
$101$	−0.190983	−	0.330792i	−0.0190035	−	0.0329151i	0.856367	−	0.516367i	$-0.172716\pi$
$101$	−0.190983	−	0.330792i	−0.0190035	−	0.0329151i	−0.875371	+	0.483452i	$0.839383\pi$
$102$		0			0
$103$	−13.4721			−1.32745			−0.663724	−	0.747977i	$-0.731025\pi$
$103$	−13.4721			−1.32745			−0.663724	+	0.747977i	$0.731025\pi$
$104$		0			0
$105$	−5.85410			−0.571302
$106$		0			0
$107$	−0.281153	−	0.486971i	−0.0271801	−	0.0470773i	0.852115	−	0.523354i	$-0.175319\pi$
$107$	−0.281153	−	0.486971i	−0.0271801	−	0.0470773i	−0.879295	+	0.476277i	$0.841986\pi$
$108$		0			0
$109$	−11.1803			−1.07088			−0.535441	−	0.844573i	$-0.679855\pi$
$109$	−11.1803			−1.07088			−0.535441	+	0.844573i	$0.679855\pi$
$110$		0			0
$111$	−7.23607	+	12.5332i	−0.686817	+	1.18960i
$112$		0			0
$113$	−4.73607	+	8.20311i	−0.445532	+	0.771684i	−0.998089	−	0.0617912i	$-0.980319\pi$
$113$	−4.73607	+	8.20311i	−0.445532	+	0.771684i	0.552557	+	0.833475i	$0.313652\pi$
$114$		0			0
$115$	−3.61803	−	6.26662i	−0.337383	−	0.584365i
$116$		0			0
$117$	1.33688	−	0.330792i	0.123595	−	0.0305818i
$118$		0			0
$119$	−0.500000	−	0.866025i	−0.0458349	−	0.0793884i
$120$		0			0
$121$	−13.0451	+	22.5947i	−1.18592	+	2.05407i
$122$		0			0
$123$	2.23607	−	3.87298i	0.201619	−	0.349215i
$124$		0			0
$125$	11.1803			1.00000
$126$		0			0
$127$	9.78115	+	16.9415i	0.867937	+	1.50331i	0.864101	+	0.503318i	$0.167888\pi$
$127$	9.78115	+	16.9415i	0.867937	+	1.50331i	0.00383588	+	0.999993i	$0.498779\pi$
$128$		0			0
$129$	−11.4721			−1.01007
$130$		0			0
$131$	−13.3820			−1.16919			−0.584594	−	0.811326i	$-0.698746\pi$
$131$	−13.3820			−1.16919			−0.584594	+	0.811326i	$0.698746\pi$
$132$		0			0
$133$	1.42705	+	2.47172i	0.123741	+	0.214326i
$134$		0			0
$135$	−19.7984			−1.70397
$136$		0			0
$137$	1.42705	−	2.47172i	0.121921	−	0.211174i	−0.798604	−	0.601857i	$-0.794428\pi$
$137$	1.42705	−	2.47172i	0.121921	−	0.211174i	0.920525	+	0.390683i	$0.127761\pi$
$138$		0			0
$139$	−0.309017	+	0.535233i	−0.0262105	+	0.0453979i	−0.878833	−	0.477129i	$-0.841677\pi$
$139$	−0.309017	+	0.535233i	−0.0262105	+	0.0453979i	0.852623	+	0.522527i	$0.175011\pi$
$140$		0			0
$141$	2.42705	+	4.20378i	0.204395	+	0.354022i
$142$		0			0
$143$	−6.09017	+	21.0970i	−0.509286	+	1.76422i
$144$		0			0
$145$	14.6353	+	25.3490i	1.21539	+	2.10512i
$146$		0			0
$147$	−0.809017	+	1.40126i	−0.0667266	+	0.115574i
$148$		0			0
$149$	−9.28115	+	16.0754i	−0.760342	+	1.31695i	0.182333	+	0.983237i	$0.441635\pi$
$149$	−9.28115	+	16.0754i	−0.760342	+	1.31695i	−0.942675	+	0.333714i	$0.891698\pi$
$150$		0			0
$151$	−6.52786			−0.531230			−0.265615	−	0.964079i	$-0.585575\pi$
$151$	−6.52786			−0.531230			−0.265615	+	0.964079i	$0.585575\pi$
$152$		0			0
$153$	−0.190983	−	0.330792i	−0.0154401	−	0.0267430i
$154$		0			0
$155$	−19.7984			−1.59024
$156$		0			0
$157$	21.7426			1.73525			0.867626	−	0.497217i	$-0.165645\pi$
$157$	21.7426			1.73525			0.867626	+	0.497217i	$0.165645\pi$
$158$		0			0
$159$	3.80902	+	6.59741i	0.302075	+	0.523209i
$160$		0			0
$161$	−2.00000			−0.157622
$162$		0			0
$163$	−8.38197	+	14.5180i	−0.656526	+	1.13714i	0.324983	+	0.945720i	$0.394642\pi$
$163$	−8.38197	+	14.5180i	−0.656526	+	1.13714i	−0.981509	+	0.191417i	$0.938692\pi$
$164$		0			0
$165$	17.8262	−	30.8759i	1.38777	−	2.40369i
$166$		0			0
$167$	−5.97214	−	10.3440i	−0.462138	−	0.800446i	0.536930	−	0.843627i	$-0.319584\pi$
$167$	−5.97214	−	10.3440i	−0.462138	−	0.800446i	−0.999067	+	0.0431810i	$0.986251\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	0.545085	+	0.944115i	0.0416837	+	0.0721983i
$172$		0			0
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	−0.701751	−	0.712422i	$-0.747598\pi$
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	0.967851	+	0.251523i	$0.0809315\pi$
$174$		0			0
$175$	4.04508	−	7.00629i	0.305780	−	0.529626i
$176$		0			0
$177$	−15.3262			−1.15199
$178$		0			0
$179$	−1.88197	−	3.25966i	−0.140665	−	0.243638i	0.787082	−	0.616848i	$-0.211591\pi$
$179$	−1.88197	−	3.25966i	−0.140665	−	0.243638i	−0.927747	+	0.373209i	$0.878257\pi$
$180$		0			0
$181$	−16.6525			−1.23777			−0.618884	−	0.785482i	$-0.712415\pi$
$181$	−16.6525			−1.23777			−0.618884	+	0.785482i	$0.712415\pi$
$182$		0			0
$183$	−9.70820			−0.717651
$184$		0			0
$185$	−16.1803	−	28.0252i	−1.18960	−	2.06045i
$186$		0			0
$187$	6.09017			0.445357
$188$		0			0
$189$	−2.73607	+	4.73901i	−0.199020	+	0.344712i
$190$		0			0
$191$	9.75329	−	16.8932i	0.705723	−	1.22235i	−0.260707	−	0.965418i	$-0.583956\pi$
$191$	9.75329	−	16.8932i	0.705723	−	1.22235i	0.966430	−	0.256930i	$-0.0827111\pi$
$192$		0			0
$193$	−0.527864	−	0.914287i	−0.0379965	−	0.0658118i	0.846402	−	0.532545i	$-0.178764\pi$
$193$	−0.527864	−	0.914287i	−0.0379965	−	0.0658118i	−0.884398	+	0.466733i	$0.845431\pi$
$194$		0			0
$195$	5.85410	−	20.2792i	0.419221	−	1.45222i
$196$		0			0
$197$	−7.89919	−	13.6818i	−0.562794	−	0.974787i	−0.997251	−	0.0740950i	$-0.976393\pi$
$197$	−7.89919	−	13.6818i	−0.562794	−	0.974787i	0.434457	−	0.900692i	$-0.356940\pi$
$198$		0			0
$199$	11.5902	−	20.0748i	0.821605	−	1.42306i	−0.0828809	−	0.996559i	$-0.526412\pi$
$199$	11.5902	−	20.0748i	0.821605	−	1.42306i	0.904486	−	0.426503i	$-0.140255\pi$
$200$		0			0
$201$	−4.42705	+	7.66788i	−0.312260	+	0.540850i
$202$		0			0
$203$	8.09017			0.567819
$204$		0			0
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$		0			0
$207$	−0.763932			−0.0530969
$208$		0			0
$209$	−17.3820			−1.20234
$210$		0			0
$211$	12.7361	+	22.0595i	0.876787	+	1.51864i	0.854847	+	0.518880i	$0.173651\pi$
$211$	12.7361	+	22.0595i	0.876787	+	1.51864i	0.0219403	+	0.999759i	$0.493016\pi$
$212$		0			0
$213$	−1.23607			−0.0846940
$214$		0			0
$215$	12.8262	−	22.2157i	0.874742	−	1.51510i
$216$		0			0
$217$	−2.73607	+	4.73901i	−0.185736	+	0.321705i
$218$		0			0
$219$	12.0902	+	20.9408i	0.816978	+	1.41505i
$220$		0			0
$221$	3.50000	−	0.866025i	0.235435	−	0.0582552i
$222$		0			0
$223$	10.0729	+	17.4469i	0.674535	+	1.16833i	0.976605	+	0.215042i	$0.0689890\pi$
$223$	10.0729	+	17.4469i	0.674535	+	1.16833i	−0.302070	+	0.953286i	$0.597678\pi$
$224$		0			0
$225$	1.54508	−	2.67617i	0.103006	−	0.178411i
$226$		0			0
$227$	3.40983	−	5.90600i	0.226318	−	0.391995i	−0.730396	−	0.683024i	$-0.760664\pi$
$227$	3.40983	−	5.90600i	0.226318	−	0.391995i	0.956714	+	0.291029i	$0.0939977\pi$
$228$		0			0
$229$	9.23607			0.610337			0.305168	−	0.952298i	$-0.401287\pi$
$229$	9.23607			0.610337			0.305168	+	0.952298i	$0.401287\pi$
$230$		0			0
$231$	−4.92705	−	8.53390i	−0.324176	−	0.561490i
$232$		0			0
$233$	20.7426			1.35890			0.679448	−	0.733724i	$-0.262219\pi$
$233$	20.7426			1.35890			0.679448	+	0.733724i	$0.262219\pi$
$234$		0			0
$235$	−10.8541			−0.708044
$236$		0			0
$237$	−7.23607	−	12.5332i	−0.470033	−	0.814121i
$238$		0			0
$239$	11.0000			0.711531			0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000			0.711531			0.355765	+	0.934575i	$0.384220\pi$
$240$		0			0
$241$	−4.83688	+	8.37772i	−0.311571	+	0.539657i	−0.978703	−	0.205283i	$-0.934188\pi$
$241$	−4.83688	+	8.37772i	−0.311571	+	0.539657i	0.667132	+	0.744940i	$0.267522\pi$
$242$		0			0
$243$	−1.97214	+	3.41584i	−0.126513	+	0.219126i
$244$		0			0
$245$	−1.80902	−	3.13331i	−0.115574	−	0.200180i
$246$		0			0
$247$	−9.98936	+	2.47172i	−0.635608	+	0.157272i
$248$		0			0
$249$	−2.80902	−	4.86536i	−0.178014	−	0.308330i
$250$		0			0
$251$	0.909830	−	1.57587i	0.0574280	−	0.0994682i	−0.835882	−	0.548909i	$-0.815043\pi$
$251$	0.909830	−	1.57587i	0.0574280	−	0.0994682i	0.893310	+	0.449441i	$0.148377\pi$
$252$		0			0
$253$	6.09017	−	10.5485i	0.382886	−	0.663177i
$254$		0			0
$255$	−5.85410			−0.366598
$256$		0			0
$257$	−4.21885	−	7.30726i	−0.263164	−	0.455814i	0.703917	−	0.710283i	$-0.251433\pi$
$257$	−4.21885	−	7.30726i	−0.263164	−	0.455814i	−0.967081	+	0.254468i	$0.918100\pi$
$258$		0			0
$259$	−8.94427			−0.555770
$260$		0			0
$261$	3.09017			0.191277
$262$		0			0
$263$	7.59017	+	13.1466i	0.468030	+	0.810652i	0.999333	−	0.0365305i	$-0.0116306\pi$
$263$	7.59017	+	13.1466i	0.468030	+	0.810652i	−0.531303	+	0.847182i	$0.678297\pi$
$264$		0			0
$265$	−17.0344			−1.04642
$266$		0			0
$267$	−12.3992	+	21.4760i	−0.758818	+	1.31431i
$268$		0			0
$269$	−1.01722	+	1.76188i	−0.0620211	+	0.107424i	−0.895369	−	0.445326i	$-0.853088\pi$
$269$	−1.01722	+	1.76188i	−0.0620211	+	0.107424i	0.833348	+	0.552749i	$0.186421\pi$
$270$		0			0
$271$	0.645898	+	1.11873i	0.0392355	+	0.0679579i	0.884976	−	0.465636i	$-0.154174\pi$
$271$	0.645898	+	1.11873i	0.0392355	+	0.0679579i	−0.845741	+	0.533594i	$0.820841\pi$
$272$		0			0
$273$	−4.04508	−	4.20378i	−0.244820	−	0.254424i
$274$		0			0
$275$	24.6353	+	42.6695i	1.48556	+	2.57307i
$276$		0			0
$277$	13.7361	−	23.7916i	0.825320	−	1.42950i	−0.0763539	−	0.997081i	$-0.524328\pi$
$277$	13.7361	−	23.7916i	0.825320	−	1.42950i	0.901674	−	0.432416i	$-0.142339\pi$
$278$		0			0
$279$	−1.04508	+	1.81014i	−0.0625676	+	0.108370i
$280$		0			0
$281$	−26.7639			−1.59660			−0.798301	−	0.602258i	$-0.794268\pi$
$281$	−26.7639			−1.59660			−0.798301	+	0.602258i	$0.794268\pi$
$282$		0			0
$283$	−11.9443	−	20.6881i	−0.710013	−	1.22978i	−0.964852	−	0.262795i	$-0.915356\pi$
$283$	−11.9443	−	20.6881i	−0.710013	−	1.22978i	0.254838	−	0.966984i	$-0.417978\pi$
$284$		0			0
$285$	16.7082			0.989709
$286$		0			0
$287$	2.76393			0.163150
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$	−5.76393			−0.337888
$292$		0			0
$293$	10.5623	−	18.2945i	0.617056	−	1.06877i	−0.372963	−	0.927846i	$-0.621658\pi$
$293$	10.5623	−	18.2945i	0.617056	−	1.06877i	0.990020	−	0.140927i	$-0.0450083\pi$
$294$		0			0
$295$	17.1353	−	29.6791i	0.997653	−	1.72799i
$296$		0			0
$297$	−16.6631	−	28.8614i	−0.966892	−	1.67471i
$298$		0			0
$299$	2.00000	−	6.92820i	0.115663	−	0.400668i
$300$		0			0
$301$	−3.54508	−	6.14027i	−0.204335	−	0.353919i
$302$		0			0
$303$	−0.309017	+	0.535233i	−0.0177526	+	0.0307483i
$304$		0			0
$305$	10.8541	−	18.7999i	0.621504	−	1.07648i
$306$		0			0
$307$	7.20163			0.411019			0.205509	−	0.978655i	$-0.434115\pi$
$307$	7.20163			0.411019			0.205509	+	0.978655i	$0.434115\pi$
$308$		0			0
$309$	10.8992	+	18.8779i	0.620033	+	1.07393i
$310$		0			0
$311$	20.7984			1.17937			0.589684	−	0.807634i	$-0.299252\pi$
$311$	20.7984			1.17937			0.589684	+	0.807634i	$0.299252\pi$
$312$		0			0
$313$	−26.1803			−1.47980			−0.739900	−	0.672717i	$-0.765127\pi$
$313$	−26.1803			−1.47980			−0.739900	+	0.672717i	$0.765127\pi$
$314$		0			0
$315$	−0.690983	−	1.19682i	−0.0389325	−	0.0674330i
$316$		0			0
$317$	18.7082			1.05076			0.525379	−	0.850869i	$-0.323924\pi$
$317$	18.7082			1.05076			0.525379	+	0.850869i	$0.323924\pi$
$318$		0			0
$319$	−24.6353	+	42.6695i	−1.37931	+	2.38903i
$320$		0			0
$321$	−0.454915	+	0.787936i	−0.0253909	+	0.0439783i
$322$		0			0
$323$	1.42705	+	2.47172i	0.0794032	+	0.137530i
$324$		0			0
$325$	20.2254	+	21.0189i	1.12190	+	1.16592i
$326$		0			0
$327$	9.04508	+	15.6665i	0.500194	+	0.866362i
$328$		0			0
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		0			0
$331$	−13.4271	+	23.2563i	−0.738017	+	1.27828i	0.215369	+	0.976533i	$0.430904\pi$
$331$	−13.4271	+	23.2563i	−0.738017	+	1.27828i	−0.953387	+	0.301751i	$0.902429\pi$
$332$		0			0
$333$	−3.41641			−0.187218
$334$		0			0
$335$	−9.89919	−	17.1459i	−0.540850	−	0.936780i
$336$		0			0
$337$	−6.85410			−0.373367			−0.186683	−	0.982420i	$-0.559774\pi$
$337$	−6.85410			−0.373367			−0.186683	+	0.982420i	$0.559774\pi$
$338$		0			0
$339$	15.3262			0.832407
$340$		0			0
$341$	−16.6631	−	28.8614i	−0.902358	−	1.56293i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−5.85410	+	10.1396i	−0.315174	+	0.545898i
$346$		0			0
$347$	10.8541	−	18.7999i	0.582679	−	1.00923i	−0.412482	−	0.910966i	$-0.635338\pi$
$347$	10.8541	−	18.7999i	0.582679	−	1.00923i	0.995160	−	0.0982633i	$-0.0313287\pi$
$348$		0			0
$349$	3.35410	+	5.80948i	0.179541	+	0.310974i	0.941723	−	0.336388i	$-0.109205\pi$
$349$	3.35410	+	5.80948i	0.179541	+	0.310974i	−0.762182	+	0.647362i	$0.775872\pi$
$350$		0			0
$351$	−13.6803	−	14.2170i	−0.730203	−	0.758849i
$352$		0			0
$353$	3.66312	+	6.34471i	0.194968	+	0.337695i	0.946890	−	0.321557i	$-0.104206\pi$
$353$	3.66312	+	6.34471i	0.194968	+	0.337695i	−0.751922	+	0.659252i	$0.770873\pi$
$354$		0			0
$355$	1.38197	−	2.39364i	0.0733471	−	0.127041i
$356$		0			0
$357$	−0.809017	+	1.40126i	−0.0428177	+	0.0741625i
$358$		0			0
$359$	8.61803			0.454842			0.227421	−	0.973796i	$-0.426971\pi$
$359$	8.61803			0.454842			0.227421	+	0.973796i	$0.426971\pi$
$360$		0			0
$361$	5.42705	+	9.39993i	0.285634	+	0.494733i
$362$		0			0
$363$	42.2148			2.21570
$364$		0			0
$365$	−54.0689			−2.83009
$366$		0			0
$367$	17.9443	+	31.0804i	0.936683	+	1.62238i	0.771604	+	0.636103i	$0.219455\pi$
$367$	17.9443	+	31.0804i	0.936683	+	1.62238i	0.165079	+	0.986280i	$0.447212\pi$
$368$		0			0
$369$	1.05573			0.0549590
$370$		0			0
$371$	−2.35410	+	4.07742i	−0.122219	+	0.211689i
$372$		0			0
$373$	−2.25329	+	3.90281i	−0.116671	+	0.202080i	−0.918446	−	0.395545i	$-0.870556\pi$
$373$	−2.25329	+	3.90281i	−0.116671	+	0.202080i	0.801776	+	0.597625i	$0.203889\pi$
$374$		0			0
$375$	−9.04508	−	15.6665i	−0.467086	−	0.809017i
$376$		0			0
$377$	−8.09017	+	28.0252i	−0.416665	+	1.44337i
$378$		0			0
$379$	11.8090	+	20.4538i	0.606588	+	1.05064i	0.991798	+	0.127813i	$0.0407957\pi$
$379$	11.8090	+	20.4538i	0.606588	+	1.05064i	−0.385210	+	0.922829i	$0.625871\pi$
$380$		0			0
$381$	15.8262	−	27.4118i	0.810803	−	1.40435i
$382$		0			0
$383$	0.836881	−	1.44952i	0.0427626	−	0.0740670i	−0.843852	−	0.536576i	$-0.819717\pi$
$383$	0.836881	−	1.44952i	0.0427626	−	0.0740670i	0.886615	+	0.462509i	$0.153051\pi$
$384$		0			0
$385$	22.0344			1.12298
$386$		0			0
$387$	−1.35410	−	2.34537i	−0.0688329	−	0.119222i
$388$		0			0
$389$	5.05573			0.256336			0.128168	−	0.991752i	$-0.459090\pi$
$389$	5.05573			0.256336			0.128168	+	0.991752i	$0.459090\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$		0			0
$393$	10.8262	+	18.7516i	0.546111	+	0.945893i
$394$		0			0
$395$	32.3607			1.62824
$396$		0			0
$397$	3.76393	−	6.51932i	0.188906	−	0.327195i	−0.755980	−	0.654595i	$-0.772839\pi$
$397$	3.76393	−	6.51932i	0.188906	−	0.327195i	0.944886	+	0.327400i	$0.106172\pi$
$398$		0			0
$399$	2.30902	−	3.99933i	0.115595	−	0.200217i
$400$		0			0
$401$	−7.66312	−	13.2729i	−0.382678	−	0.662818i	0.608766	−	0.793350i	$-0.291665\pi$
$401$	−7.66312	−	13.2729i	−0.382678	−	0.662818i	−0.991444	+	0.130532i	$0.958331\pi$
$402$		0			0
$403$	−13.6803	−	14.2170i	−0.681466	−	0.708201i
$404$		0			0
$405$	13.9443	+	24.1522i	0.692896	+	1.20013i
$406$		0			0
$407$	27.2361	−	47.1743i	1.35004	−	2.33834i
$408$		0			0
$409$	−11.3713	+	19.6957i	−0.562276	+	0.973890i	0.435022	+	0.900420i	$0.356741\pi$
$409$	−11.3713	+	19.6957i	−0.562276	+	0.973890i	−0.997297	+	0.0734702i	$0.976593\pi$
$410$		0			0
$411$	−4.61803			−0.227791
$412$		0			0
$413$	−4.73607	−	8.20311i	−0.233047	−	0.403649i
$414$		0			0
$415$	12.5623			0.616659
$416$		0			0
$417$	1.00000			0.0489702
$418$		0			0
$419$	−7.11803	−	12.3288i	−0.347739	−	0.602301i	0.638109	−	0.769946i	$-0.279717\pi$
$419$	−7.11803	−	12.3288i	−0.347739	−	0.602301i	−0.985847	+	0.167645i	$0.946384\pi$
$420$		0			0
$421$	20.4721			0.997751			0.498875	−	0.866674i	$-0.333747\pi$
$421$	20.4721			0.997751			0.498875	+	0.866674i	$0.333747\pi$
$422$		0			0
$423$	−0.572949	+	0.992377i	−0.0278577	+	0.0482510i
$424$		0			0
$425$	4.04508	−	7.00629i	0.196215	−	0.339855i
$426$		0			0
$427$	−3.00000	−	5.19615i	−0.145180	−	0.251459i
$428$		0			0
$429$	34.4894	−	8.53390i	1.66516	−	0.412021i
$430$		0			0
$431$	−4.48936	−	7.77579i	−0.216245	−	0.374547i	0.737412	−	0.675443i	$-0.236048\pi$
$431$	−4.48936	−	7.77579i	−0.216245	−	0.374547i	−0.953657	+	0.300896i	$0.902714\pi$
$432$		0			0
$433$	−8.26393	+	14.3136i	−0.397139	+	0.687865i	−0.993372	−	0.114947i	$-0.963330\pi$
$433$	−8.26393	+	14.3136i	−0.397139	+	0.687865i	0.596232	+	0.802812i	$0.296664\pi$
$434$		0			0
$435$	23.6803	−	41.0156i	1.13539	−	1.96655i
$436$		0			0
$437$	5.70820			0.273060
$438$		0			0
$439$	−1.98278	−	3.43427i	−0.0946329	−	0.163909i	0.814822	−	0.579711i	$-0.196834\pi$
$439$	−1.98278	−	3.43427i	−0.0946329	−	0.163909i	−0.909455	+	0.415802i	$0.863501\pi$
$440$		0			0
$441$	−0.381966			−0.0181889
$442$		0			0
$443$	−14.6525			−0.696160			−0.348080	−	0.937465i	$-0.613166\pi$
$443$	−14.6525			−0.696160			−0.348080	+	0.937465i	$0.613166\pi$
$444$		0			0
$445$	−27.7254	−	48.0218i	−1.31431	−	2.27645i
$446$		0			0
$447$	30.0344			1.42058
$448$		0			0
$449$	−10.7082	+	18.5472i	−0.505351	+	0.875294i	0.494629	+	0.869104i	$0.335304\pi$
$449$	−10.7082	+	18.5472i	−0.505351	+	0.875294i	−0.999981	+	0.00619031i	$0.998030\pi$
$450$		0			0
$451$	−8.41641	+	14.5776i	−0.396313	+	0.686435i
$452$		0			0
$453$	5.28115	+	9.14723i	0.248130	+	0.429774i
$454$		0			0
$455$	12.6631	−	3.13331i	0.593656	−	0.146892i
$456$		0			0
$457$	−18.6525	−	32.3070i	−0.872526	−	1.51126i	−0.859375	−	0.511346i	$-0.829147\pi$
$457$	−18.6525	−	32.3070i	−0.872526	−	1.51126i	−0.0131510	−	0.999914i	$-0.504186\pi$
$458$		0			0
$459$	−2.73607	+	4.73901i	−0.127709	+	0.221198i
$460$		0			0
$461$	−13.8090	+	23.9179i	−0.643150	+	1.11397i	0.341575	+	0.939854i	$0.389040\pi$
$461$	−13.8090	+	23.9179i	−0.643150	+	1.11397i	−0.984725	+	0.174114i	$0.944294\pi$
$462$		0			0
$463$	−10.5279			−0.489271			−0.244636	−	0.969615i	$-0.578668\pi$
$463$	−10.5279			−0.489271			−0.244636	+	0.969615i	$0.578668\pi$
$464$		0			0
$465$	16.0172	+	27.7426i	0.742781	+	1.28653i
$466$		0			0
$467$	25.9443			1.20056			0.600279	−	0.799791i	$-0.295056\pi$
$467$	25.9443			1.20056			0.600279	+	0.799791i	$0.295056\pi$
$468$		0			0
$469$	−5.47214			−0.252680
$470$		0			0
$471$	−17.5902	−	30.4671i	−0.810512	−	1.40385i
$472$		0			0
$473$	43.1803			1.98543
$474$		0			0
$475$	−11.5451	+	19.9967i	−0.529725	+	0.917510i
$476$		0			0
$477$	−0.899187	+	1.55744i	−0.0411709	+	0.0713102i
$478$		0			0
$479$	−13.6074	−	23.5687i	−0.621738	−	1.07688i	−0.989162	−	0.146828i	$-0.953094\pi$
$479$	−13.6074	−	23.5687i	−0.621738	−	1.07688i	0.367425	−	0.930053i	$-0.380240\pi$
$480$		0			0
$481$	8.94427	−	30.9839i	0.407824	−	1.41274i
$482$		0			0
$483$	1.61803	+	2.80252i	0.0736231	+	0.127519i
$484$		0			0
$485$	6.44427	−	11.1618i	0.292619	−	0.506832i
$486$		0			0
$487$	−11.9271	+	20.6583i	−0.540466	+	0.936115i	0.458411	+	0.888740i	$0.348419\pi$
$487$	−11.9271	+	20.6583i	−0.540466	+	0.936115i	−0.998877	+	0.0473747i	$0.984915\pi$
$488$		0			0
$489$	27.1246			1.22662
$490$		0			0
$491$	−0.309017	−	0.535233i	−0.0139457	−	0.0241547i	0.858968	−	0.512029i	$-0.171106\pi$
$491$	−0.309017	−	0.535233i	−0.0139457	−	0.0241547i	−0.872914	+	0.487874i	$0.837773\pi$
$492$		0			0
$493$	8.09017			0.364363
$494$		0			0
$495$	8.41641			0.378289
$496$		0			0
$497$	−0.381966	−	0.661585i	−0.0171335	−	0.0296761i
$498$		0			0
$499$	6.50658			0.291274			0.145637	−	0.989338i	$-0.453477\pi$
$499$	6.50658			0.291274			0.145637	+	0.989338i	$0.453477\pi$
$500$		0			0
$501$	−9.66312	+	16.7370i	−0.431716	+	0.747755i
$502$		0			0
$503$	−18.3156	+	31.7235i	−0.816652	+	1.41448i	0.0914836	+	0.995807i	$0.470839\pi$
$503$	−18.3156	+	31.7235i	−0.816652	+	1.41448i	−0.908136	+	0.418676i	$0.862494\pi$
$504$		0			0
$505$	−0.690983	−	1.19682i	−0.0307483	−	0.0532577i
$506$		0			0
$507$	18.6074	−	9.80881i	0.826383	−	0.435625i
$508$		0			0
$509$	−6.29837	−	10.9091i	−0.279171	−	0.483538i	0.692008	−	0.721890i	$-0.256726\pi$
$509$	−6.29837	−	10.9091i	−0.279171	−	0.483538i	−0.971179	+	0.238352i	$0.923393\pi$
$510$		0			0
$511$	−7.47214	+	12.9421i	−0.330548	+	0.572526i
$512$		0			0
$513$	7.80902	−	13.5256i	0.344777	−	0.597170i
$514$		0			0
$515$	−48.7426			−2.14786
$516$		0			0
$517$	−9.13525	−	15.8227i	−0.401768	−	0.695883i
$518$		0			0
$519$	−11.3262			−0.497167
$520$		0			0
$521$	−13.8197			−0.605450			−0.302725	−	0.953078i	$-0.597896\pi$
$521$	−13.8197			−0.605450			−0.302725	+	0.953078i	$0.597896\pi$
$522$		0			0
$523$	−10.7984	−	18.7033i	−0.472180	−	0.817840i	0.527313	−	0.849671i	$-0.323199\pi$
$523$	−10.7984	−	18.7033i	−0.472180	−	0.817840i	−0.999493	+	0.0318313i	$0.989866\pi$
$524$		0			0
$525$	−13.0902			−0.571302
$526$		0			0
$527$	−2.73607	+	4.73901i	−0.119185	+	0.206434i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	−1.80902	−	3.13331i	−0.0785047	−	0.135974i
$532$		0			0
$533$	−2.76393	+	9.57454i	−0.119719	+	0.414719i
$534$		0			0
$535$	−1.01722	−	1.76188i	−0.0439783	−	0.0761726i
$536$		0			0
$537$	−3.04508	+	5.27424i	−0.131405	+	0.227600i
$538$		0			0
$539$	3.04508	−	5.27424i	0.131161	−	0.227178i
$540$		0			0
$541$	23.0344			0.990328			0.495164	−	0.868800i	$-0.335108\pi$
$541$	23.0344			0.990328			0.495164	+	0.868800i	$0.335108\pi$
$542$		0			0
$543$	13.4721	+	23.3344i	0.578145	+	1.00138i
$544$		0			0
$545$	−40.4508			−1.73272
$546$		0			0
$547$	17.1803			0.734578			0.367289	−	0.930107i	$-0.380286\pi$
$547$	17.1803			0.734578			0.367289	+	0.930107i	$0.380286\pi$
$548$		0			0
$549$	−1.14590	−	1.98475i	−0.0489057	−	0.0847072i
$550$		0			0
$551$	−23.0902			−0.983674
$552$		0			0
$553$	4.47214	−	7.74597i	0.190175	−	0.329392i
$554$		0			0
$555$	−26.1803	+	45.3457i	−1.11129	+	1.92482i
$556$		0			0
$557$	21.3435	+	36.9680i	0.904351	+	1.56638i	0.821786	+	0.569797i	$0.192978\pi$
$557$	21.3435	+	36.9680i	0.904351	+	1.56638i	0.0825658	+	0.996586i	$0.473689\pi$
$558$		0			0
$559$	24.8156	−	6.14027i	1.04959	−	0.259706i
$560$		0			0
$561$	−4.92705	−	8.53390i	−0.208020	−	0.360302i
$562$		0			0
$563$	12.2361	−	21.1935i	0.515689	−	0.893199i	−0.484145	−	0.874988i	$-0.660869\pi$
$563$	12.2361	−	21.1935i	0.515689	−	0.893199i	0.999834	−	0.0182116i	$-0.00579725\pi$
$564$		0			0
$565$	−17.1353	+	29.6791i	−0.720886	+	1.24861i
$566$		0			0
$567$	7.70820			0.323714
$568$		0			0
$569$	−13.4721	−	23.3344i	−0.564781	−	0.978230i	−0.997070	−	0.0764947i	$-0.975627\pi$
$569$	−13.4721	−	23.3344i	−0.564781	−	0.978230i	0.432289	−	0.901735i	$-0.357706\pi$
$570$		0			0
$571$	−20.2016			−0.845412			−0.422706	−	0.906267i	$-0.638920\pi$
$571$	−20.2016			−0.845412			−0.422706	+	0.906267i	$0.638920\pi$
$572$		0			0
$573$	−31.5623			−1.31853
$574$		0			0
$575$	−8.09017	−	14.0126i	−0.337383	−	0.584365i
$576$		0			0
$577$	27.4721			1.14368			0.571840	−	0.820365i	$-0.306230\pi$
$577$	27.4721			1.14368			0.571840	+	0.820365i	$0.306230\pi$
$578$		0			0
$579$	−0.854102	+	1.47935i	−0.0354953	+	0.0614796i
$580$		0			0
$581$	1.73607	−	3.00696i	0.0720242	−	0.124750i
$582$		0			0
$583$	−14.3369	−	24.8322i	−0.593773	−	1.02844i
$584$		0			0
$585$	4.83688	−	1.19682i	0.199980	−	0.0494823i
$586$		0			0
$587$	−4.72542	−	8.18468i	−0.195039	−	0.337818i	0.751874	−	0.659307i	$-0.229150\pi$
$587$	−4.72542	−	8.18468i	−0.195039	−	0.337818i	−0.946913	+	0.321489i	$0.895817\pi$
$588$		0			0
$589$	7.80902	−	13.5256i	0.321765	−	0.557313i
$590$		0			0
$591$	−12.7812	+	22.1376i	−0.525746	+	0.910619i
$592$		0			0
$593$	−28.5066			−1.17062			−0.585312	−	0.810808i	$-0.699028\pi$
$593$	−28.5066			−1.17062			−0.585312	+	0.810808i	$0.699028\pi$
$594$		0			0
$595$	−1.80902	−	3.13331i	−0.0741625	−	0.128453i
$596$		0			0
$597$	−37.5066			−1.53504
$598$		0			0
$599$	24.3262			0.993943			0.496972	−	0.867767i	$-0.334445\pi$
$599$	24.3262			0.993943			0.496972	+	0.867767i	$0.334445\pi$
$600$		0			0
$601$	13.6631	+	23.6652i	0.557330	+	0.965324i	0.997718	+	0.0675167i	$0.0215076\pi$
$601$	13.6631	+	23.6652i	0.557330	+	0.965324i	−0.440388	+	0.897808i	$0.645159\pi$
$602$		0			0
$603$	−2.09017			−0.0851183
$604$		0			0
$605$	−47.1976	+	81.7486i	−1.91885	+	3.32355i
$606$		0			0
$607$	11.5344	−	19.9782i	0.468169	−	0.810892i	−0.531170	−	0.847265i	$-0.678247\pi$
$607$	11.5344	−	19.9782i	0.468169	−	0.810892i	0.999338	+	0.0363737i	$0.0115807\pi$
$608$		0			0
$609$	−6.54508	−	11.3364i	−0.265220	−	0.459375i
$610$		0			0
$611$	−7.50000	−	7.79423i	−0.303418	−	0.315321i
$612$		0			0
$613$	12.9615	+	22.4500i	0.523510	+	0.906746i	0.999626	+	0.0273629i	$0.00871097\pi$
$613$	12.9615	+	22.4500i	0.523510	+	0.906746i	−0.476116	+	0.879383i	$0.657956\pi$
$614$		0			0
$615$	8.09017	−	14.0126i	0.326227	−	0.565042i
$616$		0			0
$617$	16.4443	−	28.4823i	0.662021	−	1.14665i	−0.318062	−	0.948070i	$-0.603032\pi$
$617$	16.4443	−	28.4823i	0.662021	−	1.14665i	0.980084	−	0.198585i	$-0.0636346\pi$
$618$		0			0
$619$	−39.8885			−1.60326			−0.801628	−	0.597823i	$-0.796032\pi$
$619$	−39.8885			−1.60326			−0.801628	+	0.597823i	$0.796032\pi$
$620$		0			0
$621$	5.47214	+	9.47802i	0.219589	+	0.380340i
$622$		0			0
$623$	−15.3262			−0.614033
$624$		0			0
$625$		0			0
$626$		0			0
$627$	14.0623	+	24.3566i	0.561594	+	0.972710i
$628$		0			0
$629$	−8.94427			−0.356631
$630$		0			0
$631$	−17.2812	+	29.9318i	−0.687952	+	1.19157i	0.284548	+	0.958662i	$0.408157\pi$
$631$	−17.2812	+	29.9318i	−0.687952	+	1.19157i	−0.972499	+	0.232906i	$0.925177\pi$
$632$		0			0
$633$	20.6074	−	35.6930i	0.819070	−	1.41867i
$634$		0			0
$635$	35.3885	+	61.2948i	1.40435	+	2.43241i
$636$		0			0
$637$	1.00000	−	3.46410i	0.0396214	−	0.137253i
$638$		0			0
$639$	−0.145898	−	0.252703i	−0.00577164	−	0.00999677i
$640$		0			0
$641$	−23.2533	+	40.2759i	−0.918450	+	1.59080i	−0.116679	+	0.993170i	$0.537225\pi$
$641$	−23.2533	+	40.2759i	−0.918450	+	1.59080i	−0.801771	+	0.597632i	$0.796108\pi$
$642$		0			0
$643$	−9.59017	+	16.6107i	−0.378199	+	0.655061i	−0.990800	−	0.135332i	$-0.956790\pi$
$643$	−9.59017	+	16.6107i	−0.378199	+	0.655061i	0.612601	+	0.790392i	$0.290123\pi$
$644$		0			0
$645$	−41.5066			−1.63432
$646$		0			0
$647$	1.85410	+	3.21140i	0.0728923	+	0.126253i	0.900168	−	0.435543i	$-0.143444\pi$
$647$	1.85410	+	3.21140i	0.0728923	+	0.126253i	−0.827275	+	0.561796i	$0.810110\pi$
$648$		0			0
$649$	57.6869			2.26441
$650$		0			0
$651$	8.85410			0.347020
$652$		0			0
$653$	18.2533	+	31.6156i	0.714306	+	1.23721i	0.963226	+	0.268691i	$0.0865910\pi$
$653$	18.2533	+	31.6156i	0.714306	+	1.23721i	−0.248920	+	0.968524i	$0.580076\pi$
$654$		0			0
$655$	−48.4164			−1.89179
$656$		0			0
$657$	−2.85410	+	4.94345i	−0.111349	+	0.192862i
$658$		0			0
$659$	10.7082	−	18.5472i	0.417132	−	0.722495i	−0.578517	−	0.815670i	$-0.696368\pi$
$659$	10.7082	−	18.5472i	0.417132	−	0.722495i	0.995650	+	0.0931756i	$0.0297018\pi$
$660$		0			0
$661$	−18.7984	−	32.5597i	−0.731172	−	1.26643i	−0.956383	−	0.292117i	$-0.905640\pi$
$661$	−18.7984	−	32.5597i	−0.731172	−	1.26643i	0.225211	−	0.974310i	$-0.427693\pi$
$662$		0			0
$663$	−4.04508	−	4.20378i	−0.157098	−	0.163261i
$664$		0			0
$665$	5.16312	+	8.94278i	0.200217	+	0.346786i
$666$		0			0
$667$	8.09017	−	14.0126i	0.313253	−	0.542569i
$668$		0			0
$669$	16.2984	−	28.2296i	0.630132	−	1.09142i
$670$		0			0
$671$	36.5410			1.41065
$672$		0			0
$673$	−9.68034	−	16.7668i	−0.373150	−	0.646314i	0.616899	−	0.787043i	$-0.288389\pi$
$673$	−9.68034	−	16.7668i	−0.373150	−	0.646314i	−0.990048	+	0.140728i	$0.955056\pi$
$674$		0			0
$675$	−44.2705			−1.70397
$676$		0			0
$677$	−35.1459			−1.35077			−0.675383	−	0.737467i	$-0.736022\pi$
$677$	−35.1459			−1.35077			−0.675383	+	0.737467i	$0.736022\pi$
$678$		0			0
$679$	−1.78115	−	3.08505i	−0.0683544	−	0.118393i
$680$		0			0
$681$	−11.0344			−0.422841
$682$		0			0
$683$	12.7705	−	22.1192i	0.488650	−	0.846367i	−0.511265	−	0.859423i	$-0.670823\pi$
$683$	12.7705	−	22.1192i	0.488650	−	0.846367i	0.999915	+	0.0130567i	$0.00415618\pi$
$684$		0			0
$685$	5.16312	−	8.94278i	0.197273	−	0.341686i
$686$		0			0
$687$	−7.47214	−	12.9421i	−0.285080	−	0.493773i
$688$		0			0
$689$	−11.7705	−	12.2323i	−0.448421	−	0.466012i
$690$		0			0
$691$	13.5172	+	23.4125i	0.514219	+	0.890654i	0.999864	+	0.0164976i	$0.00525160\pi$
$691$	13.5172	+	23.4125i	0.514219	+	0.890654i	−0.485645	+	0.874156i	$0.661415\pi$
$692$		0			0
$693$	1.16312	−	2.01458i	0.0441832	−	0.0765276i
$694$		0			0
$695$	−1.11803	+	1.93649i	−0.0424094	+	0.0734553i
$696$		0			0
$697$	2.76393			0.104691
$698$		0			0
$699$	−16.7812	−	29.0658i	−0.634721	−	1.09937i
$700$		0			0
$701$	−1.81966			−0.0687276			−0.0343638	−	0.999409i	$-0.510940\pi$
$701$	−1.81966			−0.0687276			−0.0343638	+	0.999409i	$0.510940\pi$
$702$		0			0
$703$	25.5279			0.962802
$704$		0			0
$705$	8.78115	+	15.2094i	0.330717	+	0.572819i
$706$		0			0
$707$	−0.381966			−0.0143653
$708$		0			0
$709$	19.2254	−	33.2994i	0.722026	−	1.25059i	−0.238160	−	0.971226i	$-0.576544\pi$
$709$	19.2254	−	33.2994i	0.722026	−	1.25059i	0.960186	−	0.279360i	$-0.0901222\pi$
$710$		0			0
$711$	1.70820	−	2.95870i	0.0640627	−	0.110960i
$712$		0			0
$713$	5.47214	+	9.47802i	0.204933	+	0.354955i
$714$		0			0
$715$	−22.0344	+	76.3295i	−0.824041	+	2.85456i
$716$		0			0
$717$	−8.89919	−	15.4138i	−0.332346	−	0.575641i
$718$		0			0
$719$	−16.4443	+	28.4823i	−0.613268	+	1.06221i	0.377418	+	0.926043i	$0.376812\pi$
$719$	−16.4443	+	28.4823i	−0.613268	+	1.06221i	−0.990686	+	0.136168i	$0.956521\pi$
$720$		0			0
$721$	−6.73607	+	11.6672i	−0.250864	+	0.434510i
$722$		0			0
$723$	15.6525			0.582122
$724$		0			0
$725$	32.7254	+	56.6821i	1.21539	+	2.10512i
$726$		0			0
$727$	−19.8328			−0.735558			−0.367779	−	0.929913i	$-0.619882\pi$
$727$	−19.8328			−0.735558			−0.367779	+	0.929913i	$0.619882\pi$
$728$		0			0
$729$	29.5066			1.09284
$730$		0			0
$731$	−3.54508	−	6.14027i	−0.131120	−	0.227106i
$732$		0			0
$733$	16.6180			0.613801			0.306901	−	0.951742i	$-0.400708\pi$
$733$	16.6180			0.613801			0.306901	+	0.951742i	$0.400708\pi$
$734$		0			0
$735$	−2.92705	+	5.06980i	−0.107966	+	0.187002i
$736$		0			0
$737$	16.6631	−	28.8614i	0.613794	−	1.06312i
$738$		0			0
$739$	−14.1459	−	24.5014i	−0.520365	−	0.901299i	−0.999720	−	0.0236777i	$-0.992462\pi$
$739$	−14.1459	−	24.5014i	−0.520365	−	0.901299i	0.479354	−	0.877621i	$-0.340871\pi$
$740$		0			0
$741$	11.5451	+	11.9980i	0.424119	+	0.440758i
$742$		0			0
$743$	11.3435	+	19.6474i	0.416151	+	0.720795i	0.995549	−	0.0942503i	$-0.0300454\pi$
$743$	11.3435	+	19.6474i	0.416151	+	0.720795i	−0.579397	+	0.815045i	$0.696712\pi$
$744$		0			0
$745$	−33.5795	+	58.1614i	−1.23026	+	2.13087i
$746$		0			0
$747$	0.663119	−	1.14856i	0.0242623	−	0.0420235i
$748$		0			0
$749$	−0.562306			−0.0205462
$750$		0			0
$751$	−1.79180	−	3.10348i	−0.0653836	−	0.113248i	0.831481	−	0.555554i	$-0.187494\pi$
$751$	−1.79180	−	3.10348i	−0.0653836	−	0.113248i	−0.896864	+	0.442306i	$0.854160\pi$
$752$		0			0
$753$	−2.94427			−0.107295
$754$		0			0
$755$	−23.6180			−0.859548
$756$		0			0
$757$	−17.4164	−	30.1661i	−0.633010	−	1.09641i	−0.986933	−	0.161131i	$-0.948486\pi$
$757$	−17.4164	−	30.1661i	−0.633010	−	1.09641i	0.353923	−	0.935275i	$-0.384848\pi$
$758$		0			0
$759$	−19.7082			−0.715362
$760$		0			0
$761$	−2.01722	+	3.49393i	−0.0731242	+	0.126655i	−0.900269	−	0.435334i	$-0.856630\pi$
$761$	−2.01722	+	3.49393i	−0.0731242	+	0.126655i	0.827145	+	0.561989i	$0.189964\pi$
$762$		0			0
$763$	−5.59017	+	9.68246i	−0.202378	+	0.350529i
$764$		0			0
$765$	−0.690983	−	1.19682i	−0.0249825	−	0.0432710i
$766$		0			0
$767$	33.1525	−	8.20311i	1.19707	−	0.296197i
$768$		0			0
$769$	20.8607	+	36.1318i	0.752255	+	1.30294i	0.946727	+	0.322036i	$0.104367\pi$
$769$	20.8607	+	36.1318i	0.752255	+	1.30294i	−0.194472	+	0.980908i	$0.562299\pi$
$770$		0			0
$771$	−6.82624	+	11.8234i	−0.245841	+	0.425809i
$772$		0			0
$773$	13.6246	−	23.5985i	0.490043	−	0.848780i	−0.509891	−	0.860239i	$-0.670314\pi$
$773$	13.6246	−	23.5985i	0.490043	−	0.848780i	0.999934	+	0.0114592i	$0.00364765\pi$
$774$		0			0
$775$	−44.2705			−1.59024
$776$		0			0
$777$	7.23607	+	12.5332i	0.259592	+	0.449627i
$778$		0			0
$779$	−7.88854			−0.282636
$780$		0			0
$781$	4.65248			0.166479
$782$		0			0
$783$	−22.1353	−	38.3394i	−0.791049	−	1.37014i
$784$		0			0
$785$	78.6656			2.80770
$786$		0			0
$787$	21.4721	−	37.1908i	0.765399	−	1.32571i	−0.174636	−	0.984633i	$-0.555875\pi$
$787$	21.4721	−	37.1908i	0.765399	−	1.32571i	0.940035	−	0.341077i	$-0.110792\pi$
$788$		0			0
$789$	12.2812	−	21.2716i	0.437221	−	0.757288i
$790$		0			0
$791$	4.73607	+	8.20311i	0.168395	+	0.291669i
$792$		0			0
$793$	21.0000	−	5.19615i	0.745732	−	0.184521i
$794$		0			0
$795$	13.7812	+	23.8697i	0.488767	+	0.846569i
$796$		0			0
$797$	−20.0344	+	34.7007i	−0.709656	+	1.22916i	0.255328	+	0.966854i	$0.417816\pi$
$797$	−20.0344	+	34.7007i	−0.709656	+	1.22916i	−0.964985	+	0.262306i	$0.915517\pi$
$798$		0			0
$799$	−1.50000	+	2.59808i	−0.0530662	+	0.0919133i
$800$		0			0
$801$	−5.85410			−0.206845
$802$		0			0
$803$	−45.5066	−	78.8197i	−1.60589	−	2.78149i
$804$		0			0
$805$	−7.23607			−0.255038
$806$		0			0
$807$	3.29180			0.115877
$808$		0			0
$809$	−5.68034	−	9.83864i	−0.199710	−	0.345908i	0.748724	−	0.662882i	$-0.230667\pi$
$809$	−5.68034	−	9.83864i	−0.199710	−	0.345908i	−0.948434	+	0.316973i	$0.897333\pi$
$810$		0			0
$811$	−6.38197			−0.224101			−0.112051	−	0.993703i	$-0.535742\pi$
$811$	−6.38197			−0.224101			−0.112051	+	0.993703i	$0.535742\pi$
$812$		0			0
$813$	1.04508	−	1.81014i	0.0366527	−	0.0634844i
$814$		0			0
$815$	−30.3262	+	52.5266i	−1.06228	+	1.83993i
$816$		0			0
$817$	10.1180	+	17.5249i	0.353985	+	0.613120i
$818$		0			0
$819$	0.381966	−	1.32317i	0.0133470	−	0.0462353i
$820$		0			0
$821$	19.3885	+	33.5819i	0.676665	+	1.17202i	0.975979	+	0.217863i	$0.0699087\pi$
$821$	19.3885	+	33.5819i	0.676665	+	1.17202i	−0.299314	+	0.954155i	$0.596758\pi$
$822$		0			0
$823$	−3.64590	+	6.31488i	−0.127088	+	0.220123i	−0.922547	−	0.385884i	$-0.873896\pi$
$823$	−3.64590	+	6.31488i	−0.127088	+	0.220123i	0.795459	+	0.606007i	$0.207230\pi$
$824$		0			0
$825$	39.8607	−	69.0407i	1.38777	−	2.40369i
$826$		0			0
$827$	−33.5623			−1.16708			−0.583538	−	0.812086i	$-0.698332\pi$
$827$	−33.5623			−1.16708			−0.583538	+	0.812086i	$0.698332\pi$
$828$		0			0
$829$	12.4828	+	21.6208i	0.433545	+	0.750922i	0.997176	−	0.0751052i	$-0.0239292\pi$
$829$	12.4828	+	21.6208i	0.433545	+	0.750922i	−0.563631	+	0.826027i	$0.690596\pi$
$830$		0			0
$831$	−44.4508			−1.54198
$832$		0			0
$833$	−1.00000			−0.0346479
$834$		0			0
$835$	−21.6074	−	37.4251i	−0.747755	−	1.29515i
$836$		0			0
$837$	29.9443			1.03503
$838$		0			0
$839$	11.1910	−	19.3834i	0.386356	−	0.669188i	−0.605601	−	0.795769i	$-0.707067\pi$
$839$	11.1910	−	19.3834i	0.386356	−	0.669188i	0.991956	+	0.126581i	$0.0404004\pi$
$840$		0			0
$841$	−18.2254	+	31.5674i	−0.628463	+	1.08853i
$842$		0			0
$843$	21.6525	+	37.5032i	0.745751	+	1.29168i
$844$		0			0
$845$	−1.80902	+	46.9996i	−0.0622321	+	1.61684i
$846$		0			0
$847$	13.0451	+	22.5947i	0.448234	+	0.776365i
$848$		0			0
$849$	−19.3262	+	33.4740i	−0.663275	+	1.14883i
$850$		0			0
$851$	−8.94427	+	15.4919i	−0.306606	+	0.531057i
$852$		0			0
$853$	0.819660			0.0280646			0.0140323	−	0.999902i	$-0.495533\pi$
$853$	0.819660			0.0280646			0.0140323	+	0.999902i	$0.495533\pi$
$854$		0			0
$855$	1.97214	+	3.41584i	0.0674456	+	0.116819i
$856$		0			0
$857$	−25.0902			−0.857064			−0.428532	−	0.903527i	$-0.640969\pi$
$857$	−25.0902			−0.857064			−0.428532	+	0.903527i	$0.640969\pi$
$858$		0			0
$859$	−17.0557			−0.581934			−0.290967	−	0.956733i	$-0.593977\pi$
$859$	−17.0557			−0.581934			−0.290967	+	0.956733i	$0.593977\pi$
$860$		0			0
$861$	−2.23607	−	3.87298i	−0.0762050	−	0.131991i
$862$		0			0
$863$	4.47214			0.152233			0.0761166	−	0.997099i	$-0.475748\pi$
$863$	4.47214			0.152233			0.0761166	+	0.997099i	$0.475748\pi$
$864$		0			0
$865$	12.6631	−	21.9332i	0.430559	−	0.745750i
$866$		0			0
$867$	12.9443	−	22.4201i	0.439611	−	0.761428i
$868$		0			0
$869$	27.2361	+	47.1743i	0.923920	+	1.60028i
$870$		0			0
$871$	5.47214	−	18.9560i	0.185416	−	0.642301i
$872$		0			0
$873$	−0.680340	−	1.17838i	−0.0230260	−	0.0398822i
$874$		0			0
$875$	5.59017	−	9.68246i	0.188982	−	0.327327i
$876$		0			0
$877$	1.40983	−	2.44190i	0.0476066	−	0.0824570i	−0.841240	−	0.540662i	$-0.818174\pi$
$877$	1.40983	−	2.44190i	0.0476066	−	0.0824570i	0.888847	+	0.458205i	$0.151507\pi$
$878$		0			0
$879$	−34.1803			−1.15287
$880$		0			0
$881$	−21.1180	−	36.5775i	−0.711485	−	1.23233i	−0.964300	−	0.264813i	$-0.914690\pi$
$881$	−21.1180	−	36.5775i	−0.711485	−	1.23233i	0.252815	−	0.967515i	$-0.418644\pi$
$882$		0			0
$883$	8.23607			0.277166			0.138583	−	0.990351i	$-0.455745\pi$
$883$	8.23607			0.277166			0.138583	+	0.990351i	$0.455745\pi$
$884$		0			0
$885$	−55.4508			−1.86396
$886$		0			0
$887$	4.43769	+	7.68631i	0.149003	+	0.258081i	0.930859	−	0.365378i	$-0.119060\pi$
$887$	4.43769	+	7.68631i	0.149003	+	0.258081i	−0.781856	+	0.623459i	$0.785727\pi$
$888$		0			0
$889$	19.5623			0.656099
$890$		0			0
$891$	−23.4721	+	40.6549i	−0.786346	+	1.36199i
$892$		0			0
$893$	4.28115	−	7.41517i	0.143263	−	0.248139i
$894$		0			0
$895$	−6.80902	−	11.7936i	−0.227600	−	0.394215i
$896$		0			0
$897$	−11.3262	+	2.80252i	−0.378172	+	0.0935733i
$898$		0			0
$899$	−22.1353	−	38.3394i	−0.738252	−	1.27869i
$900$		0			0
$901$	−2.35410	+	4.07742i	−0.0784265	+	0.135839i
$902$		0			0
$903$	−5.73607	+	9.93516i	−0.190884	+	0.330621i
$904$		0			0
$905$	−60.2492			−2.00275
$906$		0			0
$907$	12.9443	+	22.4201i	0.429807	+	0.744448i	0.996856	−	0.0792361i	$-0.0252481\pi$
$907$	12.9443	+	22.4201i	0.429807	+	0.744448i	−0.567048	+	0.823684i	$0.691915\pi$
$908$		0			0
$909$	−0.145898			−0.00483913
$910$		0			0
$911$	27.8673			0.923283			0.461642	−	0.887066i	$-0.347261\pi$
$911$	27.8673			0.923283			0.461642	+	0.887066i	$0.347261\pi$
$912$		0			0
$913$	10.5729	+	18.3129i	0.349914	+	0.606068i
$914$		0			0
$915$	−35.1246			−1.16118
$916$		0			0
$917$	−6.69098	+	11.5891i	−0.220956	+	0.382707i
$918$		0			0
$919$	28.2361	−	48.9063i	0.931422	−	1.61327i	0.150529	−	0.988606i	$-0.451902\pi$
$919$	28.2361	−	48.9063i	0.931422	−	1.61327i	0.780893	−	0.624664i	$-0.214764\pi$
$920$		0			0
$921$	−5.82624	−	10.0913i	−0.191981	−	0.332521i
$922$		0			0
$923$	2.67376	−	0.661585i	0.0880080	−	0.0217763i
$924$		0			0
$925$	−36.1803	−	62.6662i	−1.18960	−	2.06045i
$926$		0			0
$927$	−2.57295	+	4.45648i	−0.0845067	+	0.146370i
$928$		0			0
$929$	7.88197	−	13.6520i	0.258599	−	0.447906i	−0.707268	−	0.706946i	$-0.750073\pi$
$929$	7.88197	−	13.6520i	0.258599	−	0.447906i	0.965867	+	0.259039i	$0.0834059\pi$
$930$		0			0
$931$	2.85410			0.0935394
$932$		0			0
$933$	−16.8262	−	29.1439i	−0.550866	−	0.954128i
$934$		0			0
$935$	22.0344			0.720603
$936$		0			0
$937$	40.1246			1.31081			0.655407	−	0.755276i	$-0.272497\pi$
$937$	40.1246			1.31081			0.655407	+	0.755276i	$0.272497\pi$
$938$		0			0
$939$	21.1803	+	36.6854i	0.691194	+	1.19718i
$940$		0			0
$941$	37.6525			1.22744			0.613718	−	0.789525i	$-0.289673\pi$
$941$	37.6525			1.22744			0.613718	+	0.789525i	$0.289673\pi$
$942$		0			0
$943$	2.76393	−	4.78727i	0.0900060	−	0.155895i
$944$		0			0
$945$	−9.89919	+	17.1459i	−0.322021	+	0.557756i
$946$		0			0
$947$	−7.19098	−	12.4551i	−0.233676	−	0.404738i	0.725211	−	0.688526i	$-0.241742\pi$
$947$	−7.19098	−	12.4551i	−0.233676	−	0.404738i	−0.958887	+	0.283788i	$0.908409\pi$
$948$		0			0
$949$	−37.3607	−	38.8264i	−1.21278	−	1.26036i
$950$		0			0
$951$	−15.1353	−	26.2150i	−0.490794	−	0.850081i
$952$		0			0
$953$	11.9164	−	20.6398i	0.386010	−	0.668589i	−0.605898	−	0.795542i	$-0.707186\pi$
$953$	11.9164	−	20.6398i	0.386010	−	0.668589i	0.991909	+	0.126952i	$0.0405196\pi$
$954$		0			0
$955$	35.2877	−	61.1201i	1.14188	−	1.97780i
$956$		0			0
$957$	79.7214			2.57703
$958$		0			0
$959$	−1.42705	−	2.47172i	−0.0460819	−	0.0798162i
$960$		0			0
$961$	−1.05573			−0.0340557
$962$		0			0
$963$	−0.214782			−0.00692124
$964$		0			0
$965$	−1.90983	−	3.30792i	−0.0614796	−	0.106486i
$966$		0			0
$967$	−2.23607			−0.0719071			−0.0359535	−	0.999353i	$-0.511447\pi$
$967$	−2.23607			−0.0719071			−0.0359535	+	0.999353i	$0.511447\pi$
$968$		0			0
$969$	2.30902	−	3.99933i	0.0741763	−	0.128477i
$970$		0			0
$971$	−22.1180	+	38.3096i	−0.709801	+	1.22941i	0.255129	+	0.966907i	$0.417882\pi$
$971$	−22.1180	+	38.3096i	−0.709801	+	1.22941i	−0.964931	+	0.262505i	$0.915451\pi$
$972$		0			0
$973$	0.309017	+	0.535233i	0.00990663	+	0.0171588i
$974$		0			0
$975$	13.0902	−	45.3457i	0.419221	−	1.45222i
$976$		0			0
$977$	−10.7361	−	18.5954i	−0.343477	−	0.594920i	0.641599	−	0.767041i	$-0.278271\pi$
$977$	−10.7361	−	18.5954i	−0.343477	−	0.594920i	−0.985076	+	0.172120i	$0.944938\pi$
$978$		0			0
$979$	46.6697	−	80.8343i	1.49157	−	2.58347i
$980$		0			0
$981$	−2.13525	+	3.69837i	−0.0681734	+	0.118080i
$982$		0			0
$983$	24.2148			0.772332			0.386166	−	0.922429i	$-0.373799\pi$
$983$	24.2148			0.772332			0.386166	+	0.922429i	$0.373799\pi$
$984$		0			0
$985$	−28.5795	−	49.5012i	−0.910619	−	1.57724i
$986$		0			0
$987$	4.85410			0.154508
$988$		0			0
$989$	−14.1803			−0.450909
$990$		0			0
$991$	−3.37132	−	5.83930i	−0.107094	−	0.185492i	0.807498	−	0.589870i	$-0.200821\pi$
$991$	−3.37132	−	5.83930i	−0.107094	−	0.185492i	−0.914592	+	0.404379i	$0.867488\pi$
$992$		0			0
$993$	43.4508			1.37887
$994$		0			0
$995$	41.9336	−	72.6312i	1.32939	−	2.30256i
$996$		0			0
$997$	−11.3885	+	19.7255i	−0.360679	+	0.624714i	−0.988073	−	0.153988i	$-0.950788\pi$
$997$	−11.3885	+	19.7255i	−0.360679	+	0.624714i	0.627394	+	0.778702i	$0.284122\pi$
$998$		0			0
$999$	24.4721	+	42.3870i	0.774264	+	1.34106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.s.b.393.1	yes	4
4.3	odd	2		1456.2.s.n.1121.2		4
13.3	even	3		9464.2.a.s.1.2		2
13.9	even	3	inner	728.2.s.b.113.1	✓	4
13.10	even	6		9464.2.a.q.1.2		2
52.35	odd	6		1456.2.s.n.113.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.s.b.113.1	✓	4	13.9	even	3	inner
728.2.s.b.393.1	yes	4	1.1	even	1	trivial
1456.2.s.n.113.2		4	52.35	odd	6
1456.2.s.n.1121.2		4	4.3	odd	2
9464.2.a.q.1.2		2	13.10	even	6
9464.2.a.s.1.2		2	13.3	even	3

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 1.40126i) q^{3} +3.61803 q^{5} +(0.500000 - 0.866025i) q^{7} +(0.190983 - 0.330792i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 1.40126i) q^{3} +3.61803 q^{5} +(0.500000 - 0.866025i) q^{7} +(0.190983 - 0.330792i) q^{9} +(3.04508 + 5.27424i) q^{11} +(2.50000 + 2.59808i) q^{13} +(-2.92705 - 5.06980i) q^{15} +(0.500000 - 0.866025i) q^{17} +(-1.42705 + 2.47172i) q^{19} -1.61803 q^{21} +(-1.00000 - 1.73205i) q^{23} +8.09017 q^{25} -5.47214 q^{27} +(4.04508 + 7.00629i) q^{29} -5.47214 q^{31} +(4.92705 - 8.53390i) q^{33} +(1.80902 - 3.13331i) q^{35} +(-4.47214 - 7.74597i) q^{37} +(1.61803 - 5.60503i) q^{39} +(1.38197 + 2.39364i) q^{41} +(3.54508 - 6.14027i) q^{43} +(0.690983 - 1.19682i) q^{45} -3.00000 q^{47} +(-0.500000 - 0.866025i) q^{49} -1.61803 q^{51} -4.70820 q^{53} +(11.0172 + 19.0824i) q^{55} +4.61803 q^{57} +(4.73607 - 8.20311i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-0.190983 - 0.330792i) q^{63} +(9.04508 + 9.39993i) q^{65} +(-2.73607 - 4.73901i) q^{67} +(-1.61803 + 2.80252i) q^{69} +(0.381966 - 0.661585i) q^{71} -14.9443 q^{73} +(-6.54508 - 11.3364i) q^{75} +6.09017 q^{77} +8.94427 q^{79} +(3.85410 + 6.67550i) q^{81} +3.47214 q^{83} +(1.80902 - 3.13331i) q^{85} +(6.54508 - 11.3364i) q^{87} +(-7.66312 - 13.2729i) q^{89} +(3.50000 - 0.866025i) q^{91} +(4.42705 + 7.66788i) q^{93} +(-5.16312 + 8.94278i) q^{95} +(1.78115 - 3.08505i) q^{97} +2.32624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 10 q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 4 * q - q^3 + 10 * q^5 + 2 * q^7 + 3 * q^9	\( 4 q - q^{3} + 10 q^{5} + 2 q^{7} + 3 q^{9} + q^{11} + 10 q^{13} - 5 q^{15} + 2 q^{17} + q^{19} - 2 q^{21} - 4 q^{23} + 10 q^{25} - 4 q^{27} + 5 q^{29} - 4 q^{31} + 13 q^{33} + 5 q^{35} + 2 q^{39} + 10 q^{41} + 3 q^{43} + 5 q^{45} - 12 q^{47} - 2 q^{49} - 2 q^{51} + 8 q^{53} + 15 q^{55} + 14 q^{57} + 10 q^{59} + 12 q^{61} - 3 q^{63} + 25 q^{65} - 2 q^{67} - 2 q^{69} + 6 q^{71} - 24 q^{73} - 15 q^{75} + 2 q^{77} + 2 q^{81} - 4 q^{83} + 5 q^{85} + 15 q^{87} - 15 q^{89} + 14 q^{91} + 11 q^{93} - 5 q^{95} - 13 q^{97} - 22 q^{99}+O(q^{100}) \) 4 * q - q^3 + 10 * q^5 + 2 * q^7 + 3 * q^9 + q^11 + 10 * q^13 - 5 * q^15 + 2 * q^17 + q^19 - 2 * q^21 - 4 * q^23 + 10 * q^25 - 4 * q^27 + 5 * q^29 - 4 * q^31 + 13 * q^33 + 5 * q^35 + 2 * q^39 + 10 * q^41 + 3 * q^43 + 5 * q^45 - 12 * q^47 - 2 * q^49 - 2 * q^51 + 8 * q^53 + 15 * q^55 + 14 * q^57 + 10 * q^59 + 12 * q^61 - 3 * q^63 + 25 * q^65 - 2 * q^67 - 2 * q^69 + 6 * q^71 - 24 * q^73 - 15 * q^75 + 2 * q^77 + 2 * q^81 - 4 * q^83 + 5 * q^85 + 15 * q^87 - 15 * q^89 + 14 * q^91 + 11 * q^93 - 5 * q^95 - 13 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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