LMFDB - Embedded newform 1458.2.c.h.487.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1458,2,Mod(487,1458)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1458, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1458.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1458 = 2 \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1458.c (of order $3$, degree $2$, not 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:	$11.6421886147$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.5
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	1458.487
Dual form			1458.2.c.h.973.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.53967 + 2.66679i) q^{5} +(0.127119 - 0.220177i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.53967 + 2.66679i) q^{5} +(0.127119 - 0.220177i) q^{7} -1.00000 q^{8} +3.07935 q^{10} +(1.72685 - 2.99099i) q^{11} +(-2.81997 - 4.88434i) q^{13} +(-0.127119 - 0.220177i) q^{14} +(-0.500000 + 0.866025i) q^{16} +5.01396 q^{17} -0.904786 q^{19} +(1.53967 - 2.66679i) q^{20} +(-1.72685 - 2.99099i) q^{22} +(-2.82492 - 4.89291i) q^{23} +(-2.24119 + 3.88185i) q^{25} -5.63995 q^{26} -0.254239 q^{28} +(0.883384 - 1.53007i) q^{29} +(5.32933 + 9.23068i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50698 - 4.34222i) q^{34} +0.782889 q^{35} +8.83464 q^{37} +(-0.452393 + 0.783568i) q^{38} +(-1.53967 - 2.66679i) q^{40} +(2.85708 + 4.94860i) q^{41} +(4.28287 - 7.41815i) q^{43} -3.45369 q^{44} -5.64985 q^{46} +(6.26544 - 10.8521i) q^{47} +(3.46768 + 6.00620i) q^{49} +(2.24119 + 3.88185i) q^{50} +(-2.81997 + 4.88434i) q^{52} +2.65282 q^{53} +10.6351 q^{55} +(-0.127119 + 0.220177i) q^{56} +(-0.883384 - 1.53007i) q^{58} +(-1.85069 - 3.20549i) q^{59} +(1.88942 - 3.27257i) q^{61} +10.6587 q^{62} +1.00000 q^{64} +(8.68367 - 15.0406i) q^{65} +(3.79302 + 6.56970i) q^{67} +(-2.50698 - 4.34222i) q^{68} +(0.391444 - 0.678002i) q^{70} -8.42685 q^{71} -6.99035 q^{73} +(4.41732 - 7.65102i) q^{74} +(0.452393 + 0.783568i) q^{76} +(-0.439031 - 0.760424i) q^{77} +(-6.55453 + 11.3528i) q^{79} -3.07935 q^{80} +5.71415 q^{82} +(3.46219 - 5.99669i) q^{83} +(7.71986 + 13.3712i) q^{85} +(-4.28287 - 7.41815i) q^{86} +(-1.72685 + 2.99099i) q^{88} -6.80373 q^{89} -1.43389 q^{91} +(-2.82492 + 4.89291i) q^{92} +(-6.26544 - 10.8521i) q^{94} +(-1.39308 - 2.41288i) q^{95} +(-4.31305 + 7.47042i) q^{97} +6.93536 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^8	$ 12 q + 6 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 6 q^{16} - 24 q^{17} + 12 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} - 6 q^{25} - 12 q^{26} + 6 q^{29} + 6 q^{31} + 6 q^{32} - 12 q^{34} - 24 q^{35} + 6 q^{38} - 6 q^{40} + 24 q^{41} + 6 q^{43} - 12 q^{44} + 24 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} - 6 q^{52} - 48 q^{53} - 36 q^{55} - 6 q^{58} + 12 q^{59} + 6 q^{61} + 12 q^{62} + 12 q^{64} + 12 q^{65} + 24 q^{67} + 12 q^{68} - 12 q^{70} + 12 q^{71} - 48 q^{73} - 6 q^{76} + 12 q^{77} + 12 q^{79} - 12 q^{80} + 48 q^{82} + 18 q^{83} - 6 q^{86} - 6 q^{88} - 24 q^{89} - 60 q^{91} + 12 q^{92} - 18 q^{94} - 6 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 6 * q^16 - 24 * q^17 + 12 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 - 6 * q^25 - 12 * q^26 + 6 * q^29 + 6 * q^31 + 6 * q^32 - 12 * q^34 - 24 * q^35 + 6 * q^38 - 6 * q^40 + 24 * q^41 + 6 * q^43 - 12 * q^44 + 24 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 - 6 * q^52 - 48 * q^53 - 36 * q^55 - 6 * q^58 + 12 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^64 + 12 * q^65 + 24 * q^67 + 12 * q^68 - 12 * q^70 + 12 * q^71 - 48 * q^73 - 6 * q^76 + 12 * q^77 + 12 * q^79 - 12 * q^80 + 48 * q^82 + 18 * q^83 - 6 * q^86 - 6 * q^88 - 24 * q^89 - 60 * q^91 + 12 * q^92 - 18 * q^94 - 6 * q^95 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times$.

$n$	$731$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.53967	+	2.66679i	0.688563	+	1.19263i	0.972303	+	0.233725i	$0.0750915\pi$
$5$	1.53967	+	2.66679i	0.688563	+	1.19263i	−0.283740	+	0.958901i	$0.591575\pi$
$6$		0			0
$7$	0.127119	−	0.220177i	0.0480466	−	0.0832191i	−0.841002	−	0.541032i	$-0.818034\pi$
$7$	0.127119	−	0.220177i	0.0480466	−	0.0832191i	0.889049	+	0.457813i	$0.151367\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	3.07935			0.973775
$11$	1.72685	−	2.99099i	0.520664	−	0.901816i	−0.479047	−	0.877789i	$-0.659018\pi$
$11$	1.72685	−	2.99099i	0.520664	−	0.901816i	0.999711	−	0.0240273i	$-0.00764888\pi$
$12$		0			0
$13$	−2.81997	−	4.88434i	−0.782120	−	1.35467i	−0.930705	−	0.365771i	$-0.880805\pi$
$13$	−2.81997	−	4.88434i	−0.782120	−	1.35467i	0.148585	−	0.988900i	$-0.452528\pi$
$14$	−0.127119	−	0.220177i	−0.0339741	−	0.0588448i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.01396			1.21606			0.608032	−	0.793912i	$-0.291959\pi$
$17$	5.01396			1.21606			0.608032	+	0.793912i	$0.291959\pi$
$18$		0			0
$19$	−0.904786			−0.207572			−0.103786	−	0.994600i	$-0.533096\pi$
$19$	−0.904786			−0.207572			−0.103786	+	0.994600i	$0.533096\pi$
$20$	1.53967	−	2.66679i	0.344281	−	0.596313i
$21$		0			0
$22$	−1.72685	−	2.99099i	−0.368165	−	0.637680i
$23$	−2.82492	−	4.89291i	−0.589037	−	1.02024i	−0.994359	−	0.106068i	$-0.966174\pi$
$23$	−2.82492	−	4.89291i	−0.589037	−	1.02024i	0.405322	−	0.914174i	$-0.367160\pi$
$24$		0			0
$25$	−2.24119	+	3.88185i	−0.448238	+	0.776371i
$26$	−5.63995			−1.10608
$27$		0			0
$28$	−0.254239			−0.0480466
$29$	0.883384	−	1.53007i	0.164040	−	0.284126i	−0.772274	−	0.635290i	$-0.780881\pi$
$29$	0.883384	−	1.53007i	0.164040	−	0.284126i	0.936314	+	0.351164i	$0.114214\pi$
$30$		0			0
$31$	5.32933	+	9.23068i	0.957177	+	1.65788i	0.729307	+	0.684187i	$0.239843\pi$
$31$	5.32933	+	9.23068i	0.957177	+	1.65788i	0.227870	+	0.973692i	$0.426824\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.50698	−	4.34222i	0.429944	−	0.744684i
$35$	0.782889			0.132332
$36$		0			0
$37$	8.83464			1.45241			0.726203	−	0.687481i	$-0.241283\pi$
$37$	8.83464			1.45241			0.726203	+	0.687481i	$0.241283\pi$
$38$	−0.452393	+	0.783568i	−0.0733879	+	0.127112i
$39$		0			0
$40$	−1.53967	−	2.66679i	−0.243444	−	0.421657i
$41$	2.85708	+	4.94860i	0.446200	+	0.772842i	0.998135	−	0.0610457i	$-0.0194435\pi$
$41$	2.85708	+	4.94860i	0.446200	+	0.772842i	−0.551935	+	0.833887i	$0.686110\pi$
$42$		0			0
$43$	4.28287	−	7.41815i	0.653131	−	1.13126i	−0.329227	−	0.944251i	$-0.606788\pi$
$43$	4.28287	−	7.41815i	0.653131	−	1.13126i	0.982359	−	0.187006i	$-0.0598784\pi$
$44$	−3.45369			−0.520664
$45$		0			0
$46$	−5.64985			−0.833024
$47$	6.26544	−	10.8521i	0.913908	−	1.58294i	0.105417	−	0.994428i	$-0.466382\pi$
$47$	6.26544	−	10.8521i	0.913908	−	1.58294i	0.808492	−	0.588508i	$-0.200284\pi$
$48$		0			0
$49$	3.46768	+	6.00620i	0.495383	+	0.858029i
$50$	2.24119	+	3.88185i	0.316952	+	0.548977i
$51$		0			0
$52$	−2.81997	+	4.88434i	−0.391060	+	0.677336i
$53$	2.65282			0.364393			0.182196	−	0.983262i	$-0.441679\pi$
$53$	2.65282			0.364393			0.182196	+	0.983262i	$0.441679\pi$
$54$		0			0
$55$	10.6351			1.43404
$56$	−0.127119	+	0.220177i	−0.0169870	+	0.0294224i
$57$		0			0
$58$	−0.883384	−	1.53007i	−0.115994	−	0.200907i
$59$	−1.85069	−	3.20549i	−0.240939	−	0.417319i	0.720043	−	0.693930i	$-0.244122\pi$
$59$	−1.85069	−	3.20549i	−0.240939	−	0.417319i	−0.960982	+	0.276610i	$0.910789\pi$
$60$		0			0
$61$	1.88942	−	3.27257i	0.241915	−	0.419010i	−0.719345	−	0.694653i	$-0.755558\pi$
$61$	1.88942	−	3.27257i	0.241915	−	0.419010i	0.961260	+	0.275644i	$0.0888911\pi$
$62$	10.6587			1.35365
$63$		0			0
$64$	1.00000			0.125000
$65$	8.68367	−	15.0406i	1.07708	−	1.86555i
$66$		0			0
$67$	3.79302	+	6.56970i	0.463391	+	0.802616i	0.999127	−	0.0417688i	$-0.0132993\pi$
$67$	3.79302	+	6.56970i	0.463391	+	0.802616i	−0.535736	+	0.844385i	$0.679966\pi$
$68$	−2.50698	−	4.34222i	−0.304016	−	0.526571i
$69$		0			0
$70$	0.391444	−	0.678002i	0.0467866	−	0.0810367i
$71$	−8.42685			−1.00008			−0.500041	−	0.866002i	$-0.666682\pi$
$71$	−8.42685			−1.00008			−0.500041	+	0.866002i	$0.666682\pi$
$72$		0			0
$73$	−6.99035			−0.818159			−0.409080	−	0.912499i	$-0.634150\pi$
$73$	−6.99035			−0.818159			−0.409080	+	0.912499i	$0.634150\pi$
$74$	4.41732	−	7.65102i	0.513503	−	0.889413i
$75$		0			0
$76$	0.452393	+	0.783568i	0.0518931	+	0.0898814i
$77$	−0.439031	−	0.760424i	−0.0500322	−	0.0866584i
$78$		0			0
$79$	−6.55453	+	11.3528i	−0.737442	+	1.27729i	0.216201	+	0.976349i	$0.430633\pi$
$79$	−6.55453	+	11.3528i	−0.737442	+	1.27729i	−0.953644	+	0.300939i	$0.902700\pi$
$80$	−3.07935			−0.344281
$81$		0			0
$82$	5.71415			0.631023
$83$	3.46219	−	5.99669i	0.380025	−	0.658222i	−0.611041	−	0.791599i	$-0.709249\pi$
$83$	3.46219	−	5.99669i	0.380025	−	0.658222i	0.991065	+	0.133377i	$0.0425821\pi$
$84$		0			0
$85$	7.71986	+	13.3712i	0.837337	+	1.45031i
$86$	−4.28287	−	7.41815i	−0.461834	−	0.799919i
$87$		0			0
$88$	−1.72685	+	2.99099i	−0.184083	+	0.318840i
$89$	−6.80373			−0.721194			−0.360597	−	0.932722i	$-0.617427\pi$
$89$	−6.80373			−0.721194			−0.360597	+	0.932722i	$0.617427\pi$
$90$		0			0
$91$	−1.43389			−0.150313
$92$	−2.82492	+	4.89291i	−0.294519	+	0.510121i
$93$		0			0
$94$	−6.26544	−	10.8521i	−0.646231	−	1.11930i
$95$	−1.39308	−	2.41288i	−0.142927	−	0.247556i
$96$		0			0
$97$	−4.31305	+	7.47042i	−0.437924	+	0.758506i	−0.997529	−	0.0702531i	$-0.977619\pi$
$97$	−4.31305	+	7.47042i	−0.437924	+	0.758506i	0.559606	+	0.828759i	$0.310953\pi$
$98$	6.93536			0.700577
$99$		0			0
$100$	4.48238			0.448238
$101$	−1.24409	+	2.15483i	−0.123792	+	0.214413i	−0.921260	−	0.388947i	$-0.872839\pi$
$101$	−1.24409	+	2.15483i	−0.123792	+	0.214413i	0.797468	+	0.603361i	$0.206172\pi$
$102$		0			0
$103$	−0.514312	−	0.890814i	−0.0506767	−	0.0877746i	0.839574	−	0.543245i	$-0.182804\pi$
$103$	−0.514312	−	0.890814i	−0.0506767	−	0.0877746i	−0.890251	+	0.455470i	$0.849471\pi$
$104$	2.81997	+	4.88434i	0.276521	+	0.478949i
$105$		0			0
$106$	1.32641	−	2.29741i	0.128832	−	0.223144i
$107$	7.61531			0.736199			0.368100	−	0.929786i	$-0.380009\pi$
$107$	7.61531			0.736199			0.368100	+	0.929786i	$0.380009\pi$
$108$		0			0
$109$	−14.6099			−1.39937			−0.699687	−	0.714449i	$-0.746677\pi$
$109$	−14.6099			−1.39937			−0.699687	+	0.714449i	$0.746677\pi$
$110$	5.31756	−	9.21029i	0.507010	−	0.878166i
$111$		0			0
$112$	0.127119	+	0.220177i	0.0120116	+	0.0208048i
$113$	2.29356	+	3.97256i	0.215760	+	0.373707i	0.953507	−	0.301370i	$-0.0974439\pi$
$113$	2.29356	+	3.97256i	0.215760	+	0.373707i	−0.737748	+	0.675077i	$0.764111\pi$
$114$		0			0
$115$	8.69892	−	15.0670i	0.811178	−	1.40500i
$116$	−1.76677			−0.164040
$117$		0			0
$118$	−3.70138			−0.340740
$119$	0.637371	−	1.10396i	0.0584277	−	0.101200i
$120$		0			0
$121$	−0.464001	−	0.803673i	−0.0421819	−	0.0730612i
$122$	−1.88942	−	3.27257i	−0.171060	−	0.296284i
$123$		0			0
$124$	5.32933	−	9.23068i	0.478588	−	0.828939i
$125$	1.59393			0.142566
$126$		0			0
$127$	−21.0106			−1.86439			−0.932195	−	0.361958i	$-0.882108\pi$
$127$	−21.0106			−1.86439			−0.932195	+	0.361958i	$0.882108\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.68367	−	15.0406i	−0.761609	−	1.31914i
$131$	−8.72909	−	15.1192i	−0.762664	−	1.32097i	−0.941473	−	0.337089i	$-0.890558\pi$
$131$	−8.72909	−	15.1192i	−0.762664	−	1.32097i	0.178809	−	0.983884i	$-0.442776\pi$
$132$		0			0
$133$	−0.115016	+	0.199213i	−0.00997314	+	0.0172740i
$134$	7.58603			0.655334
$135$		0			0
$136$	−5.01396			−0.429944
$137$	−0.131175	+	0.227202i	−0.0112070	+	0.0194112i	−0.871575	−	0.490263i	$-0.836901\pi$
$137$	−0.131175	+	0.227202i	−0.0112070	+	0.0194112i	0.860367	+	0.509674i	$0.170234\pi$
$138$		0			0
$139$	−5.90557	−	10.2287i	−0.500904	−	0.867591i	−0.999999	−	0.00104415i	$-0.999668\pi$
$139$	−5.90557	−	10.2287i	−0.500904	−	0.867591i	0.499095	−	0.866547i	$-0.333666\pi$
$140$	−0.391444	−	0.678002i	−0.0330831	−	0.0573016i
$141$		0			0
$142$	−4.21342	+	7.29786i	−0.353583	+	0.612423i
$143$	−19.4786			−1.62889
$144$		0			0
$145$	5.44049			0.451808
$146$	−3.49518	+	6.05382i	−0.289263	+	0.501018i
$147$		0			0
$148$	−4.41732	−	7.65102i	−0.363101	−	0.628910i
$149$	2.31705	+	4.01325i	0.189820	+	0.328778i	0.945190	−	0.326520i	$-0.105876\pi$
$149$	2.31705	+	4.01325i	0.189820	+	0.328778i	−0.755370	+	0.655299i	$0.772543\pi$
$150$		0			0
$151$	3.65600	−	6.33237i	0.297521	−	0.515321i	−0.678047	−	0.735018i	$-0.737174\pi$
$151$	3.65600	−	6.33237i	0.297521	−	0.515321i	0.975568	+	0.219697i	$0.0705069\pi$
$152$	0.904786			0.0733879
$153$		0			0
$154$	−0.878062			−0.0707563
$155$	−16.4109	+	28.4245i	−1.31815	+	2.28311i
$156$		0			0
$157$	1.66679	+	2.88697i	0.133025	+	0.230405i	0.924841	−	0.380354i	$-0.124198\pi$
$157$	1.66679	+	2.88697i	0.133025	+	0.230405i	−0.791817	+	0.610759i	$0.790864\pi$
$158$	6.55453	+	11.3528i	0.521450	+	0.903179i
$159$		0			0
$160$	−1.53967	+	2.66679i	−0.121722	+	0.210828i
$161$	−1.43641			−0.113205
$162$		0			0
$163$	−2.00066			−0.156704			−0.0783519	−	0.996926i	$-0.524966\pi$
$163$	−2.00066			−0.156704			−0.0783519	+	0.996926i	$0.524966\pi$
$164$	2.85708	−	4.94860i	0.223100	−	0.386421i
$165$		0			0
$166$	−3.46219	−	5.99669i	−0.268718	−	0.465433i
$167$	6.93756	+	12.0162i	0.536844	+	0.929842i	0.999072	+	0.0430803i	$0.0137171\pi$
$167$	6.93756	+	12.0162i	0.536844	+	0.929842i	−0.462227	+	0.886762i	$0.652950\pi$
$168$		0			0
$169$	−9.40449	+	16.2891i	−0.723422	+	1.25300i
$170$	15.4397			1.18417
$171$		0			0
$172$	−8.56574			−0.653131
$173$	4.81055	−	8.33212i	0.365740	−	0.633480i	−0.623155	−	0.782098i	$-0.714149\pi$
$173$	4.81055	−	8.33212i	0.365740	−	0.633480i	0.988895	+	0.148619i	$0.0474827\pi$
$174$		0			0
$175$	0.569797	+	0.986917i	0.0430726	+	0.0746039i
$176$	1.72685	+	2.99099i	0.130166	+	0.225454i
$177$		0			0
$178$	−3.40187	+	5.89220i	−0.254981	+	0.441639i
$179$	0.0919653			0.00687381			0.00343691	−	0.999994i	$-0.498906\pi$
$179$	0.0919653			0.00687381			0.00343691	+	0.999994i	$0.498906\pi$
$180$		0			0
$181$	4.70338			0.349599			0.174800	−	0.984604i	$-0.444072\pi$
$181$	4.70338			0.349599			0.174800	+	0.984604i	$0.444072\pi$
$182$	−0.716946	+	1.24179i	−0.0531436	+	0.0920473i
$183$		0			0
$184$	2.82492	+	4.89291i	0.208256	+	0.360710i
$185$	13.6025	+	23.5602i	1.00007	+	1.73218i
$186$		0			0
$187$	8.65834	−	14.9967i	0.633161	−	1.09667i
$188$	−12.5309			−0.913908
$189$		0			0
$190$	−2.78615			−0.202129
$191$	5.64826	−	9.78307i	0.408694	−	0.707878i	−0.586050	−	0.810275i	$-0.699318\pi$
$191$	5.64826	−	9.78307i	0.408694	−	0.707878i	0.994744	+	0.102397i	$0.0326512\pi$
$192$		0			0
$193$	−0.115536	−	0.200115i	−0.00831648	−	0.0144046i	0.861837	−	0.507185i	$-0.169314\pi$
$193$	−0.115536	−	0.200115i	−0.00831648	−	0.0144046i	−0.870154	+	0.492780i	$0.835981\pi$
$194$	4.31305	+	7.47042i	0.309659	+	0.536345i
$195$		0			0
$196$	3.46768	−	6.00620i	0.247692	−	0.429014i
$197$	−12.2292			−0.871295			−0.435647	−	0.900117i	$-0.643481\pi$
$197$	−12.2292			−0.871295			−0.435647	+	0.900117i	$0.643481\pi$
$198$		0			0
$199$	−8.31187			−0.589213			−0.294606	−	0.955619i	$-0.595189\pi$
$199$	−8.31187			−0.589213			−0.294606	+	0.955619i	$0.595189\pi$
$200$	2.24119	−	3.88185i	0.158476	−	0.274489i
$201$		0			0
$202$	1.24409	+	2.15483i	0.0875339	+	0.151613i
$203$	−0.224590	−	0.389002i	−0.0157631	−	0.0273026i
$204$		0			0
$205$	−8.79793	+	15.2385i	−0.614474	+	1.06430i
$206$	−1.02862			−0.0716676
$207$		0			0
$208$	5.63995			0.391060
$209$	−1.56243	+	2.70620i	−0.108075	+	0.187192i
$210$		0			0
$211$	4.36976	+	7.56865i	0.300827	+	0.521048i	0.976324	−	0.216316i	$-0.0694040\pi$
$211$	4.36976	+	7.56865i	0.300827	+	0.521048i	−0.675497	+	0.737363i	$0.736071\pi$
$212$	−1.32641	−	2.29741i	−0.0910982	−	0.157787i
$213$		0			0
$214$	3.80765	−	6.59505i	0.260286	−	0.450828i
$215$	26.3769			1.79889
$216$		0			0
$217$	2.70984			0.183956
$218$	−7.30495	+	12.6525i	−0.494754	+	0.856938i
$219$		0			0
$220$	−5.31756	−	9.21029i	−0.358510	−	0.620957i
$221$	−14.1392	−	24.4899i	−0.951108	−	1.64737i
$222$		0			0
$223$	2.74267	−	4.75045i	0.183663	−	0.318113i	−0.759462	−	0.650551i	$-0.774538\pi$
$223$	2.74267	−	4.75045i	0.183663	−	0.318113i	0.943125	+	0.332438i	$0.107871\pi$
$224$	0.254239			0.0169870
$225$		0			0
$226$	4.58711			0.305130
$227$	−6.99375	+	12.1135i	−0.464191	+	0.804003i	−0.999165	−	0.0408661i	$-0.986988\pi$
$227$	−6.99375	+	12.1135i	−0.464191	+	0.804003i	0.534973	+	0.844869i	$0.320322\pi$
$228$		0			0
$229$	8.20460	+	14.2108i	0.542175	+	0.939075i	0.998779	+	0.0494047i	$0.0157324\pi$
$229$	8.20460	+	14.2108i	0.542175	+	0.939075i	−0.456604	+	0.889670i	$0.650934\pi$
$230$	−8.69892	−	15.0670i	−0.573590	−	0.993487i
$231$		0			0
$232$	−0.883384	+	1.53007i	−0.0579970	+	0.100454i
$233$	−7.02588			−0.460281			−0.230140	−	0.973157i	$-0.573919\pi$
$233$	−7.02588			−0.460281			−0.230140	+	0.973157i	$0.573919\pi$
$234$		0			0
$235$	38.5869			2.51713
$236$	−1.85069	+	3.20549i	−0.120470	+	0.208660i
$237$		0			0
$238$	−0.637371	−	1.10396i	−0.0413146	−	0.0715591i
$239$	−8.96503	−	15.5279i	−0.579900	−	1.00442i	−0.995490	−	0.0948641i	$-0.969758\pi$
$239$	−8.96503	−	15.5279i	−0.579900	−	1.00442i	0.415590	−	0.909552i	$-0.363575\pi$
$240$		0			0
$241$	5.27769	−	9.14124i	0.339966	−	0.588839i	−0.644460	−	0.764638i	$-0.722918\pi$
$241$	5.27769	−	9.14124i	0.339966	−	0.588839i	0.984426	+	0.175799i	$0.0562510\pi$
$242$	−0.928001			−0.0596542
$243$		0			0
$244$	−3.77884			−0.241915
$245$	−10.6782	+	18.4952i	−0.682205	+	1.18161i
$246$		0			0
$247$	2.55147	+	4.41928i	0.162346	+	0.281192i
$248$	−5.32933	−	9.23068i	−0.338413	−	0.586149i
$249$		0			0
$250$	0.796967	−	1.38039i	0.0504046	−	0.0873034i
$251$	25.9705			1.63924			0.819622	−	0.572905i	$-0.194184\pi$
$251$	25.9705			1.63924			0.819622	+	0.572905i	$0.194184\pi$
$252$		0			0
$253$	−19.5128			−1.22676
$254$	−10.5053	+	18.1957i	−0.659161	+	1.14170i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.94087	+	13.7540i	0.495338	+	0.857950i	0.999986	−	0.00537537i	$-0.00171104\pi$
$257$	7.94087	+	13.7540i	0.495338	+	0.857950i	−0.504648	+	0.863325i	$0.668378\pi$
$258$		0			0
$259$	1.12305	−	1.94518i	0.0697831	−	0.120868i
$260$	−17.3673			−1.07708
$261$		0			0
$262$	−17.4582			−1.07857
$263$	10.4246	−	18.0560i	0.642809	−	1.11338i	−0.341993	−	0.939702i	$-0.611102\pi$
$263$	10.4246	−	18.0560i	0.642809	−	1.11338i	0.984803	−	0.173676i	$-0.0555646\pi$
$264$		0			0
$265$	4.08447	+	7.07452i	0.250907	+	0.434584i
$266$	0.115016	+	0.199213i	0.00705207	+	0.0122145i
$267$		0			0
$268$	3.79302	−	6.56970i	0.231695	−	0.401308i
$269$	−12.0416			−0.734187			−0.367094	−	0.930184i	$-0.619647\pi$
$269$	−12.0416			−0.734187			−0.367094	+	0.930184i	$0.619647\pi$
$270$		0			0
$271$	−21.5767			−1.31069			−0.655346	−	0.755329i	$-0.727477\pi$
$271$	−21.5767			−1.31069			−0.655346	+	0.755329i	$0.727477\pi$
$272$	−2.50698	+	4.34222i	−0.152008	+	0.263286i
$273$		0			0
$274$	0.131175	+	0.227202i	0.00792458	+	0.0137258i
$275$	7.74038	+	13.4067i	0.466763	+	0.808457i
$276$		0			0
$277$	−13.5773	+	23.5166i	−0.815783	+	1.41298i	0.0929809	+	0.995668i	$0.470360\pi$
$277$	−13.5773	+	23.5166i	−0.815783	+	1.41298i	−0.908764	+	0.417310i	$0.862973\pi$
$278$	−11.8111			−0.708385
$279$		0			0
$280$	−0.782889			−0.0467866
$281$	−7.75719	+	13.4358i	−0.462755	+	0.801515i	−0.999097	−	0.0424854i	$-0.986472\pi$
$281$	−7.75719	+	13.4358i	−0.462755	+	0.801515i	0.536342	+	0.844001i	$0.319806\pi$
$282$		0			0
$283$	10.1081	+	17.5078i	0.600866	+	1.04073i	0.992690	+	0.120690i	$0.0385108\pi$
$283$	10.1081	+	17.5078i	0.600866	+	1.04073i	−0.391824	+	0.920040i	$0.628156\pi$
$284$	4.21342	+	7.29786i	0.250021	+	0.433048i
$285$		0			0
$286$	−9.73932	+	16.8690i	−0.575898	+	0.997485i
$287$	1.45276			0.0857536
$288$		0			0
$289$	8.13981			0.478812
$290$	2.72024	−	4.71160i	0.159738	−	0.276675i
$291$		0			0
$292$	3.49518	+	6.05382i	0.204540	+	0.354273i
$293$	−1.40689	−	2.43681i	−0.0821917	−	0.142360i	0.821999	−	0.569488i	$-0.192859\pi$
$293$	−1.40689	−	2.43681i	−0.0821917	−	0.142360i	−0.904191	+	0.427128i	$0.859525\pi$
$294$		0			0
$295$	5.69892	−	9.87082i	0.331804	−	0.574701i
$296$	−8.83464			−0.513503
$297$		0			0
$298$	4.63410			0.268446
$299$	−15.9324	+	27.5957i	−0.921395	+	1.59590i
$300$		0			0
$301$	−1.08887	−	1.88598i	−0.0627614	−	0.108706i
$302$	−3.65600	−	6.33237i	−0.210379	−	0.364387i
$303$		0			0
$304$	0.452393	−	0.783568i	0.0259465	−	0.0449407i
$305$	11.6364			0.666296
$306$		0			0
$307$	−7.23426			−0.412881			−0.206440	−	0.978459i	$-0.566188\pi$
$307$	−7.23426			−0.412881			−0.206440	+	0.978459i	$0.566188\pi$
$308$	−0.439031	+	0.760424i	−0.0250161	+	0.0433292i
$309$		0			0
$310$	16.4109	+	28.4245i	0.932075	+	1.61440i
$311$	−2.92848	−	5.07227i	−0.166059	−	0.287622i	0.770972	−	0.636869i	$-0.219771\pi$
$311$	−2.92848	−	5.07227i	−0.166059	−	0.287622i	−0.937031	+	0.349247i	$0.886437\pi$
$312$		0			0
$313$	6.42324	−	11.1254i	0.363063	−	0.628844i	−0.625400	−	0.780304i	$-0.715064\pi$
$313$	6.42324	−	11.1254i	0.363063	−	0.628844i	0.988463	+	0.151461i	$0.0483976\pi$
$314$	3.33359			0.188125
$315$		0			0
$316$	13.1091			0.737442
$317$	−11.7853	+	20.4128i	−0.661931	+	1.14650i	0.318176	+	0.948031i	$0.396930\pi$
$317$	−11.7853	+	20.4128i	−0.661931	+	1.14650i	−0.980108	+	0.198467i	$0.936404\pi$
$318$		0			0
$319$	−3.05094	−	5.28438i	−0.170820	−	0.295868i
$320$	1.53967	+	2.66679i	0.0860704	+	0.149078i
$321$		0			0
$322$	−0.718204	+	1.24397i	−0.0400240	+	0.0693235i
$323$	−4.53656			−0.252421
$324$		0			0
$325$	25.2804			1.40230
$326$	−1.00033	+	1.73262i	−0.0554032	+	0.0959611i
$327$		0			0
$328$	−2.85708	−	4.94860i	−0.157756	−	0.273241i
$329$	−1.59292	−	2.75901i	−0.0878203	−	0.152109i
$330$		0			0
$331$	−7.58324	+	13.1346i	−0.416813	+	0.721941i	−0.995617	−	0.0935258i	$-0.970186\pi$
$331$	−7.58324	+	13.1346i	−0.416813	+	0.721941i	0.578804	+	0.815467i	$0.303520\pi$
$332$	−6.92438			−0.380025
$333$		0			0
$334$	13.8751			0.759213
$335$	−11.6800	+	20.2304i	−0.638148	+	1.10530i
$336$		0			0
$337$	7.18113	+	12.4381i	0.391181	+	0.677546i	0.992606	−	0.121384i	$-0.0387332\pi$
$337$	7.18113	+	12.4381i	0.391181	+	0.677546i	−0.601424	+	0.798930i	$0.705400\pi$
$338$	9.40449	+	16.2891i	0.511537	+	0.886008i
$339$		0			0
$340$	7.71986	−	13.3712i	0.418668	−	0.725155i
$341$	36.8118			1.99347
$342$		0			0
$343$	3.54291			0.191299
$344$	−4.28287	+	7.41815i	−0.230917	+	0.399960i
$345$		0			0
$346$	−4.81055	−	8.33212i	−0.258617	−	0.447938i
$347$	5.55207	+	9.61647i	0.298051	+	0.516239i	0.975690	−	0.219155i	$-0.0703302\pi$
$347$	5.55207	+	9.61647i	0.298051	+	0.516239i	−0.677639	+	0.735395i	$0.736997\pi$
$348$		0			0
$349$	−7.16912	+	12.4173i	−0.383754	+	0.664682i	−0.991596	−	0.129377i	$-0.958702\pi$
$349$	−7.16912	+	12.4173i	−0.383754	+	0.664682i	0.607841	+	0.794058i	$0.292036\pi$
$350$	1.13959			0.0609138
$351$		0			0
$352$	3.45369			0.184083
$353$	−16.0290	+	27.7631i	−0.853139	+	1.47768i	0.0252214	+	0.999682i	$0.491971\pi$
$353$	−16.0290	+	27.7631i	−0.853139	+	1.47768i	−0.878361	+	0.477999i	$0.841362\pi$
$354$		0			0
$355$	−12.9746	−	22.4727i	−0.688620	−	1.19272i
$356$	3.40187	+	5.89220i	0.180299	+	0.312286i
$357$		0			0
$358$	0.0459827	−	0.0796443i	0.00243026	−	0.00420933i
$359$	7.89430			0.416645			0.208323	−	0.978060i	$-0.433200\pi$
$359$	7.89430			0.416645			0.208323	+	0.978060i	$0.433200\pi$
$360$		0			0
$361$	−18.1814			−0.956914
$362$	2.35169	−	4.07325i	0.123602	−	0.214085i
$363$		0			0
$364$	0.716946	+	1.24179i	0.0375782	+	0.0650873i
$365$	−10.7629	−	18.6418i	−0.563354	−	0.975758i
$366$		0			0
$367$	4.80325	−	8.31947i	0.250728	−	0.434273i	−0.712999	−	0.701165i	$-0.752663\pi$
$367$	4.80325	−	8.31947i	0.250728	−	0.434273i	0.963726	+	0.266892i	$0.0859968\pi$
$368$	5.64985			0.294519
$369$		0			0
$370$	27.2049			1.41432
$371$	0.337224	−	0.584090i	0.0175078	−	0.0303244i
$372$		0			0
$373$	−1.18530	−	2.05300i	−0.0613726	−	0.106300i	0.833707	−	0.552208i	$-0.186214\pi$
$373$	−1.18530	−	2.05300i	−0.0613726	−	0.106300i	−0.895079	+	0.445907i	$0.852881\pi$
$374$	−8.65834	−	14.9967i	−0.447712	−	0.775460i
$375$		0			0
$376$	−6.26544	+	10.8521i	−0.323115	+	0.559652i
$377$	−9.96447			−0.513196
$378$		0			0
$379$	12.1691			0.625087			0.312543	−	0.949904i	$-0.398819\pi$
$379$	12.1691			0.625087			0.312543	+	0.949904i	$0.398819\pi$
$380$	−1.39308	+	2.41288i	−0.0714633	+	0.123778i
$381$		0			0
$382$	−5.64826	−	9.78307i	−0.288990	−	0.500545i
$383$	3.34239	+	5.78918i	0.170788	+	0.295813i	0.938696	−	0.344747i	$-0.112035\pi$
$383$	3.34239	+	5.78918i	0.170788	+	0.295813i	−0.767908	+	0.640561i	$0.778702\pi$
$384$		0			0
$385$	1.35193	−	2.34161i	0.0689007	−	0.119339i
$386$	−0.231072			−0.0117613
$387$		0			0
$388$	8.62609			0.437924
$389$	10.7113	−	18.5525i	0.543084	−	0.940649i	−0.455641	−	0.890164i	$-0.650590\pi$
$389$	10.7113	−	18.5525i	0.543084	−	0.940649i	0.998725	−	0.0504854i	$-0.0160768\pi$
$390$		0			0
$391$	−14.1641	−	24.5329i	−0.716307	−	1.24068i
$392$	−3.46768	−	6.00620i	−0.175144	−	0.303359i
$393$		0			0
$394$	−6.11460	+	10.5908i	−0.308049	+	0.533557i
$395$	−40.3673			−2.03110
$396$		0			0
$397$	21.1756			1.06277			0.531387	−	0.847129i	$-0.321671\pi$
$397$	21.1756			1.06277			0.531387	+	0.847129i	$0.321671\pi$
$398$	−4.15593	+	7.19829i	−0.208318	+	0.360818i
$399$		0			0
$400$	−2.24119	−	3.88185i	−0.112059	−	0.194093i
$401$	−17.4698	−	30.2586i	−0.872402	−	1.51104i	−0.859505	−	0.511128i	$-0.829228\pi$
$401$	−17.4698	−	30.2586i	−0.872402	−	1.51104i	−0.0128975	−	0.999917i	$-0.504106\pi$
$402$		0			0
$403$	30.0572	−	52.0605i	1.49725	−	2.59332i
$404$	2.48818			0.123792
$405$		0			0
$406$	−0.449180			−0.0222924
$407$	15.2561	−	26.4243i	0.756215	−	1.30980i
$408$		0			0
$409$	−14.1132	−	24.4448i	−0.697854	−	1.20872i	−0.969209	−	0.246239i	$-0.920805\pi$
$409$	−14.1132	−	24.4448i	−0.697854	−	1.20872i	0.271355	−	0.962479i	$-0.412528\pi$
$410$	8.79793	+	15.2385i	0.434499	+	0.752574i
$411$		0			0
$412$	−0.514312	+	0.890814i	−0.0253383	+	0.0438873i
$413$	−0.941034			−0.0463053
$414$		0			0
$415$	21.3226			1.04668
$416$	2.81997	−	4.88434i	0.138261	−	0.239474i
$417$		0			0
$418$	1.56243	+	2.70620i	0.0764208	+	0.132365i
$419$	4.28257	+	7.41762i	0.209217	+	0.362374i	0.951468	−	0.307747i	$-0.0995752\pi$
$419$	4.28257	+	7.41762i	0.209217	+	0.362374i	−0.742251	+	0.670122i	$0.766242\pi$
$420$		0			0
$421$	−18.4922	+	32.0295i	−0.901256	+	1.56102i	−0.0753895	+	0.997154i	$0.524020\pi$
$421$	−18.4922	+	32.0295i	−0.901256	+	1.56102i	−0.825866	+	0.563866i	$0.809313\pi$
$422$	8.73953			0.425434
$423$		0			0
$424$	−2.65282			−0.128832
$425$	−11.2372	+	19.4635i	−0.545086	+	0.944117i
$426$		0			0
$427$	−0.480363	−	0.832013i	−0.0232464	−	0.0402639i
$428$	−3.80765	−	6.59505i	−0.184050	−	0.318784i
$429$		0			0
$430$	13.1884	−	22.8430i	0.636003	−	1.10159i
$431$	−17.1539			−0.826273			−0.413137	−	0.910669i	$-0.635567\pi$
$431$	−17.1539			−0.826273			−0.413137	+	0.910669i	$0.635567\pi$
$432$		0			0
$433$	5.42645			0.260779			0.130389	−	0.991463i	$-0.458377\pi$
$433$	5.42645			0.260779			0.130389	+	0.991463i	$0.458377\pi$
$434$	1.35492	−	2.34679i	0.0650384	−	0.112650i
$435$		0			0
$436$	7.30495	+	12.6525i	0.349844	+	0.605947i
$437$	2.55595	+	4.42704i	0.122268	+	0.211774i
$438$		0			0
$439$	9.64110	−	16.6989i	0.460145	−	0.796994i	−0.538823	−	0.842419i	$-0.681131\pi$
$439$	9.64110	−	16.6989i	0.460145	−	0.796994i	0.998968	+	0.0454251i	$0.0144642\pi$
$440$	−10.6351			−0.507010
$441$		0			0
$442$	−28.2785			−1.34507
$443$	−18.1084	+	31.3647i	−0.860356	+	1.49018i	0.0112303	+	0.999937i	$0.496425\pi$
$443$	−18.1084	+	31.3647i	−0.860356	+	1.49018i	−0.871586	+	0.490243i	$0.836908\pi$
$444$		0			0
$445$	−10.4755	−	18.1441i	−0.496588	−	0.860115i
$446$	−2.74267	−	4.75045i	−0.129869	−	0.224940i
$447$		0			0
$448$	0.127119	−	0.220177i	0.00600582	−	0.0104024i
$449$	37.4745			1.76853			0.884266	−	0.466983i	$-0.154659\pi$
$449$	37.4745			1.76853			0.884266	+	0.466983i	$0.154659\pi$
$450$		0			0
$451$	19.7349			0.929282
$452$	2.29356	−	3.97256i	0.107880	−	0.186853i
$453$		0			0
$454$	6.99375	+	12.1135i	0.328233	+	0.568516i
$455$	−2.20773	−	3.82389i	−0.103500	−	0.179267i
$456$		0			0
$457$	−20.0347	+	34.7011i	−0.937183	+	1.62325i	−0.166490	+	0.986043i	$0.553243\pi$
$457$	−20.0347	+	34.7011i	−0.937183	+	1.62325i	−0.770694	+	0.637206i	$0.780090\pi$
$458$	16.4092			0.766751
$459$		0			0
$460$	−17.3978			−0.811178
$461$	1.39325	−	2.41319i	0.0648903	−	0.112393i	−0.831755	−	0.555143i	$-0.812664\pi$
$461$	1.39325	−	2.41319i	0.0648903	−	0.112393i	0.896645	+	0.442750i	$0.145997\pi$
$462$		0			0
$463$	2.63361	+	4.56154i	0.122394	+	0.211993i	0.920711	−	0.390244i	$-0.127609\pi$
$463$	2.63361	+	4.56154i	0.122394	+	0.211993i	−0.798317	+	0.602237i	$0.794276\pi$
$464$	0.883384	+	1.53007i	0.0410101	+	0.0710315i
$465$		0			0
$466$	−3.51294	+	6.08459i	−0.162734	+	0.281863i
$467$	−5.17863			−0.239639			−0.119819	−	0.992796i	$-0.538232\pi$
$467$	−5.17863			−0.239639			−0.119819	+	0.992796i	$0.538232\pi$
$468$		0			0
$469$	1.92866			0.0890574
$470$	19.2935	−	33.4173i	0.889941	−	1.54142i
$471$		0			0
$472$	1.85069	+	3.20549i	0.0851849	+	0.147545i
$473$	−14.7917	−	25.6200i	−0.680124	−	1.17801i
$474$		0			0
$475$	2.02780	−	3.51225i	0.0930417	−	0.161153i
$476$	−1.27474			−0.0584277
$477$		0			0
$478$	−17.9301			−0.820102
$479$	10.1446	−	17.5710i	0.463519	−	0.802839i	−0.535614	−	0.844463i	$-0.679920\pi$
$479$	10.1446	−	17.5710i	0.463519	−	0.802839i	0.999133	+	0.0416238i	$0.0132531\pi$
$480$		0			0
$481$	−24.9134	−	43.1513i	−1.13596	−	1.96753i
$482$	−5.27769	−	9.14124i	−0.240392	−	0.416372i
$483$		0			0
$484$	−0.464001	+	0.803673i	−0.0210909	+	0.0365306i
$485$	−26.5627			−1.20615
$486$		0			0
$487$	−11.0515			−0.500791			−0.250396	−	0.968144i	$-0.580561\pi$
$487$	−11.0515			−0.500791			−0.250396	+	0.968144i	$0.580561\pi$
$488$	−1.88942	+	3.27257i	−0.0855300	+	0.148142i
$489$		0			0
$490$	10.6782	+	18.4952i	0.482392	+	0.835527i
$491$	12.6906	+	21.9807i	0.572717	+	0.991975i	0.996286	+	0.0861113i	$0.0274441\pi$
$491$	12.6906	+	21.9807i	0.572717	+	0.991975i	−0.423568	+	0.905864i	$0.639223\pi$
$492$		0			0
$493$	4.42925	−	7.67169i	0.199483	−	0.345515i
$494$	5.10295			0.229592
$495$		0			0
$496$	−10.6587			−0.478588
$497$	−1.07121	+	1.85540i	−0.0480505	+	0.0832260i
$498$		0			0
$499$	6.36108	+	11.0177i	0.284761	+	0.493221i	0.972551	−	0.232689i	$-0.0747524\pi$
$499$	6.36108	+	11.0177i	0.284761	+	0.493221i	−0.687790	+	0.725910i	$0.741419\pi$
$500$	−0.796967	−	1.38039i	−0.0356415	−	0.0617328i
$501$		0			0
$502$	12.9852	−	22.4911i	0.579560	−	1.00383i
$503$	10.5666			0.471143			0.235572	−	0.971857i	$-0.424304\pi$
$503$	10.5666			0.471143			0.235572	+	0.971857i	$0.424304\pi$
$504$		0			0
$505$	−7.66197			−0.340953
$506$	−9.75642	+	16.8986i	−0.433726	+	0.751235i
$507$		0			0
$508$	10.5053	+	18.1957i	0.466097	+	0.807304i
$509$	20.0055	+	34.6506i	0.886728	+	1.53586i	0.843720	+	0.536784i	$0.180361\pi$
$509$	20.0055	+	34.6506i	0.886728	+	1.53586i	0.0430087	+	0.999075i	$0.486306\pi$
$510$		0			0
$511$	−0.888609	+	1.53912i	−0.0393097	+	0.0680865i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	15.8817			0.700513
$515$	1.58375	−	2.74313i	0.0697881	−	0.120877i
$516$		0			0
$517$	−21.6389	−	37.4797i	−0.951678	−	1.64836i
$518$	−1.12305	−	1.94518i	−0.0493441	−	0.0854665i
$519$		0			0
$520$	−8.68367	+	15.0406i	−0.380804	+	0.659572i
$521$	−29.9472			−1.31201			−0.656006	−	0.754756i	$-0.727755\pi$
$521$	−29.9472			−1.31201			−0.656006	+	0.754756i	$0.727755\pi$
$522$		0			0
$523$	17.9761			0.786040			0.393020	−	0.919530i	$-0.371430\pi$
$523$	17.9761			0.786040			0.393020	+	0.919530i	$0.371430\pi$
$524$	−8.72909	+	15.1192i	−0.381332	+	0.660487i
$525$		0			0
$526$	−10.4246	−	18.0560i	−0.454535	−	0.787278i
$527$	26.7211	+	46.2823i	1.16399	+	2.01609i
$528$		0			0
$529$	−4.46038	+	7.72561i	−0.193930	+	0.335896i
$530$	8.16895			0.354836
$531$		0			0
$532$	0.230032			0.00997314
$533$	16.1138	−	27.9098i	0.697964	−	1.20891i
$534$		0			0
$535$	11.7251	+	20.3084i	0.506920	+	0.878011i
$536$	−3.79302	−	6.56970i	−0.163833	−	0.283768i
$537$		0			0
$538$	−6.02078	+	10.4283i	−0.259574	+	0.449596i
$539$	23.9526			1.03171
$540$		0			0
$541$	−25.6164			−1.10134			−0.550668	−	0.834724i	$-0.685627\pi$
$541$	−25.6164			−1.10134			−0.550668	+	0.834724i	$0.685627\pi$
$542$	−10.7884	+	18.6860i	−0.463399	+	0.802631i
$543$		0			0
$544$	2.50698	+	4.34222i	0.107486	+	0.186171i
$545$	−22.4945	−	38.9616i	−0.963557	−	1.66893i
$546$		0			0
$547$	−5.24035	+	9.07655i	−0.224061	+	0.388085i	−0.956037	−	0.293245i	$-0.905265\pi$
$547$	−5.24035	+	9.07655i	−0.224061	+	0.388085i	0.731976	+	0.681330i	$0.238598\pi$
$548$	0.262350			0.0112070
$549$		0			0
$550$	15.4808			0.660102
$551$	−0.799274	+	1.38438i	−0.0340502	+	0.0589767i
$552$		0			0
$553$	1.66641	+	2.88631i	0.0708631	+	0.122739i
$554$	13.5773	+	23.5166i	0.576846	+	0.999126i
$555$		0			0
$556$	−5.90557	+	10.2287i	−0.250452	+	0.433796i
$557$	−20.6161			−0.873534			−0.436767	−	0.899575i	$-0.643877\pi$
$557$	−20.6161			−0.873534			−0.436767	+	0.899575i	$0.643877\pi$
$558$		0			0
$559$	−48.3103			−2.04331
$560$	−0.391444	+	0.678002i	−0.0165415	+	0.0286508i
$561$		0			0
$562$	7.75719	+	13.4358i	0.327217	+	0.566757i
$563$	18.6354	+	32.2775i	0.785390	+	1.36034i	0.928766	+	0.370667i	$0.120871\pi$
$563$	18.6354	+	32.2775i	0.785390	+	1.36034i	−0.143376	+	0.989668i	$0.545796\pi$
$564$		0			0
$565$	−7.06266	+	12.2329i	−0.297128	+	0.514641i
$566$	20.2163			0.849753
$567$		0			0
$568$	8.42685			0.353583
$569$	12.2314	−	21.1855i	0.512768	−	0.888141i	−0.487122	−	0.873334i	$-0.661953\pi$
$569$	12.2314	−	21.1855i	0.512768	−	0.888141i	0.999890	−	0.0148071i	$-0.00471341\pi$
$570$		0			0
$571$	20.9439	+	36.2760i	0.876477	+	1.51810i	0.855182	+	0.518329i	$0.173446\pi$
$571$	20.9439	+	36.2760i	0.876477	+	1.51810i	0.0212950	+	0.999773i	$0.493221\pi$
$572$	9.73932	+	16.8690i	0.407222	+	0.705328i
$573$		0			0
$574$	0.726379	−	1.25813i	0.0303185	−	0.0525131i
$575$	25.3248			1.05612
$576$		0			0
$577$	22.2497			0.926267			0.463134	−	0.886288i	$-0.346725\pi$
$577$	22.2497			0.926267			0.463134	+	0.886288i	$0.346725\pi$
$578$	4.06990	−	7.04928i	0.169286	−	0.293211i
$579$		0			0
$580$	−2.72024	−	4.71160i	−0.112952	−	0.195639i
$581$	−0.880223	−	1.52459i	−0.0365178	−	0.0632507i
$582$		0			0
$583$	4.58101	−	7.93454i	0.189726	−	0.328615i
$584$	6.99035			0.289263
$585$		0			0
$586$	−2.81379			−0.116237
$587$	3.78620	−	6.55789i	0.156273	−	0.270673i	−0.777249	−	0.629193i	$-0.783385\pi$
$587$	3.78620	−	6.55789i	0.156273	−	0.270673i	0.933522	+	0.358520i	$0.116719\pi$
$588$		0			0
$589$	−4.82191	−	8.35179i	−0.198683	−	0.344130i
$590$	−5.69892	−	9.87082i	−0.234621	−	0.406375i
$591$		0			0
$592$	−4.41732	+	7.65102i	−0.181551	+	0.314455i
$593$	−11.2028			−0.460045			−0.230022	−	0.973185i	$-0.573880\pi$
$593$	−11.2028			−0.460045			−0.230022	+	0.973185i	$0.573880\pi$
$594$		0			0
$595$	3.92537			0.160925
$596$	2.31705	−	4.01325i	0.0949102	−	0.164389i
$597$		0			0
$598$	15.9324	+	27.5957i	0.651525	+	1.12847i
$599$	4.10562	+	7.11115i	0.167751	+	0.290554i	0.937629	−	0.347638i	$-0.113016\pi$
$599$	4.10562	+	7.11115i	0.167751	+	0.290554i	−0.769878	+	0.638192i	$0.779683\pi$
$600$		0			0
$601$	−6.11229	+	10.5868i	−0.249325	+	0.431844i	−0.963339	−	0.268288i	$-0.913542\pi$
$601$	−6.11229	+	10.5868i	−0.249325	+	0.431844i	0.714013	+	0.700132i	$0.246876\pi$
$602$	−2.17774			−0.0887581
$603$		0			0
$604$	−7.31199			−0.297521
$605$	1.42882	−	2.47479i	0.0580898	−	0.100614i
$606$		0			0
$607$	−13.6343	−	23.6153i	−0.553398	−	0.958514i	−0.998026	−	0.0627988i	$-0.979997\pi$
$607$	−13.6343	−	23.6153i	−0.553398	−	0.958514i	0.444628	−	0.895715i	$-0.353336\pi$
$608$	−0.452393	−	0.783568i	−0.0183470	−	0.0317779i
$609$		0			0
$610$	5.81818	−	10.0774i	0.235571	−	0.408021i
$611$	−70.6735			−2.85914
$612$		0			0
$613$	−32.6777			−1.31984			−0.659920	−	0.751336i	$-0.729410\pi$
$613$	−32.6777			−1.31984			−0.659920	+	0.751336i	$0.729410\pi$
$614$	−3.61713	+	6.26505i	−0.145975	+	0.252837i
$615$		0			0
$616$	0.439031	+	0.760424i	0.0176891	+	0.0306384i
$617$	16.0230	+	27.7527i	0.645063	+	1.11728i	0.984287	+	0.176577i	$0.0565024\pi$
$617$	16.0230	+	27.7527i	0.645063	+	1.11728i	−0.339223	+	0.940706i	$0.610164\pi$
$618$		0			0
$619$	6.56235	−	11.3663i	0.263763	−	0.456851i	−0.703476	−	0.710719i	$-0.748370\pi$
$619$	6.56235	−	11.3663i	0.263763	−	0.456851i	0.967239	+	0.253868i	$0.0817029\pi$
$620$	32.8217			1.31815
$621$		0			0
$622$	−5.85695			−0.234842
$623$	−0.864886	+	1.49803i	−0.0346509	+	0.0600171i
$624$		0			0
$625$	13.6601	+	23.6600i	0.546403	+	0.946399i
$626$	−6.42324	−	11.1254i	−0.256724	−	0.444660i
$627$		0			0
$628$	1.66679	−	2.88697i	0.0665123	−	0.115203i
$629$	44.2965			1.76622
$630$		0			0
$631$	−1.88376			−0.0749913			−0.0374957	−	0.999297i	$-0.511938\pi$
$631$	−1.88376			−0.0749913			−0.0374957	+	0.999297i	$0.511938\pi$
$632$	6.55453	−	11.3528i	0.260725	−	0.451589i
$633$		0			0
$634$	11.7853	+	20.4128i	0.468056	+	0.810697i
$635$	−32.3495	−	56.0309i	−1.28375	−	2.22352i
$636$		0			0
$637$	19.5575	−	33.8746i	0.774898	−	1.34216i
$638$	−6.10187			−0.241575
$639$		0			0
$640$	3.07935			0.121722
$641$	8.30489	−	14.3845i	0.328024	−	0.568154i	−0.654096	−	0.756412i	$-0.726951\pi$
$641$	8.30489	−	14.3845i	0.328024	−	0.568154i	0.982120	+	0.188258i	$0.0602841\pi$
$642$		0			0
$643$	−8.07208	−	13.9813i	−0.318332	−	0.551367i	0.661808	−	0.749673i	$-0.269789\pi$
$643$	−8.07208	−	13.9813i	−0.318332	−	0.551367i	−0.980140	+	0.198306i	$0.936456\pi$
$644$	0.718204	+	1.24397i	0.0283012	+	0.0490192i
$645$		0			0
$646$	−2.26828	+	3.92878i	−0.0892444	+	0.154576i
$647$	−25.3119			−0.995114			−0.497557	−	0.867431i	$-0.665769\pi$
$647$	−25.3119			−0.995114			−0.497557	+	0.867431i	$0.665769\pi$
$648$		0			0
$649$	−12.7834			−0.501794
$650$	12.6402	−	21.8934i	0.495789	−	0.858732i
$651$		0			0
$652$	1.00033	+	1.73262i	0.0391760	+	0.0678548i
$653$	−19.4627	−	33.7103i	−0.761633	−	1.31919i	−0.942009	−	0.335589i	$-0.891065\pi$
$653$	−19.4627	−	33.7103i	−0.761633	−	1.31919i	0.180376	−	0.983598i	$-0.442268\pi$
$654$		0			0
$655$	26.8799	−	46.5574i	1.05028	−	1.81915i
$656$	−5.71415			−0.223100
$657$		0			0
$658$	−3.18583			−0.124197
$659$	0.267263	−	0.462914i	0.0104111	−	0.0180326i	−0.860773	−	0.508989i	$-0.830019\pi$
$659$	0.267263	−	0.462914i	0.0104111	−	0.0180326i	0.871184	+	0.490957i	$0.163353\pi$
$660$		0			0
$661$	9.20936	+	15.9511i	0.358202	+	0.620425i	0.987661	−	0.156610i	$-0.0500564\pi$
$661$	9.20936	+	15.9511i	0.358202	+	0.620425i	−0.629458	+	0.777034i	$0.716723\pi$
$662$	7.58324	+	13.1346i	0.294731	+	0.510489i
$663$		0			0
$664$	−3.46219	+	5.99669i	−0.134359	+	0.232717i
$665$	−0.708347			−0.0274685
$666$		0			0
$667$	−9.98196			−0.386503
$668$	6.93756	−	12.0162i	0.268422	−	0.464921i
$669$		0			0
$670$	11.6800	+	20.2304i	0.451238	+	0.781568i
$671$	−6.52547	−	11.3025i	−0.251913	−	0.436326i
$672$		0			0
$673$	−15.8736	+	27.4939i	−0.611882	+	1.05981i	0.379041	+	0.925380i	$0.376254\pi$
$673$	−15.8736	+	27.4939i	−0.611882	+	1.05981i	−0.990923	+	0.134431i	$0.957079\pi$
$674$	14.3623			0.553214
$675$		0			0
$676$	18.8090			0.723422
$677$	13.5528	−	23.4741i	0.520877	−	0.902185i	−0.478829	−	0.877908i	$-0.658939\pi$
$677$	13.5528	−	23.4741i	0.520877	−	0.902185i	0.999705	−	0.0242763i	$-0.00772815\pi$
$678$		0			0
$679$	1.09654	+	1.89927i	0.0420815	+	0.0728872i
$680$	−7.71986	−	13.3712i	−0.296043	−	0.512762i
$681$		0			0
$682$	18.4059	−	31.8799i	0.704798	−	1.22075i
$683$	−9.36887			−0.358490			−0.179245	−	0.983804i	$-0.557365\pi$
$683$	−9.36887			−0.358490			−0.179245	+	0.983804i	$0.557365\pi$
$684$		0			0
$685$	−0.807867			−0.0308670
$686$	1.77145	−	3.06825i	0.0676344	−	0.117146i
$687$		0			0
$688$	4.28287	+	7.41815i	0.163283	+	0.282814i
$689$	−7.48088	−	12.9573i	−0.284999	−	0.493632i
$690$		0			0
$691$	−20.0548	+	34.7359i	−0.762920	+	1.32142i	0.178419	+	0.983955i	$0.442902\pi$
$691$	−20.0548	+	34.7359i	−0.762920	+	1.32142i	−0.941339	+	0.337462i	$0.890432\pi$
$692$	−9.62111			−0.365740
$693$		0			0
$694$	11.1041			0.421508
$695$	18.1853	−	31.4979i	0.689808	−	1.19478i
$696$		0			0
$697$	14.3253	+	24.8121i	0.542608	+	0.939825i
$698$	7.16912	+	12.4173i	0.271355	+	0.470001i
$699$		0			0
$700$	0.569797	−	0.986917i	0.0215363	−	0.0373020i
$701$	10.7919			0.407605			0.203803	−	0.979012i	$-0.434670\pi$
$701$	10.7919			0.407605			0.203803	+	0.979012i	$0.434670\pi$
$702$		0			0
$703$	−7.99346			−0.301479
$704$	1.72685	−	2.99099i	0.0650830	−	0.112727i
$705$		0			0
$706$	16.0290	+	27.7631i	0.603261	+	1.04488i
$707$	0.316296	+	0.547840i	0.0118955	+	0.0206036i
$708$		0			0
$709$	3.15687	−	5.46785i	0.118559	−	0.205349i	−0.800638	−	0.599148i	$-0.795506\pi$
$709$	3.15687	−	5.46785i	0.118559	−	0.205349i	0.919197	+	0.393799i	$0.128839\pi$
$710$	−25.9492			−0.973855
$711$		0			0
$712$	6.80373			0.254981
$713$	30.1099	−	52.1519i	1.12763	−	1.95310i
$714$		0			0
$715$	−29.9908	−	51.9455i	−1.12159	−	1.94265i
$716$	−0.0459827	−	0.0796443i	−0.00171845	−	0.00297645i
$717$		0			0
$718$	3.94715	−	6.83667i	0.147306	−	0.255142i
$719$	11.0750			0.413027			0.206513	−	0.978444i	$-0.433788\pi$
$719$	11.0750			0.413027			0.206513	+	0.978444i	$0.433788\pi$
$720$		0			0
$721$	−0.261516			−0.00973936
$722$	−9.09068	+	15.7455i	−0.338320	+	0.585988i
$723$		0			0
$724$	−2.35169	−	4.07325i	−0.0873998	−	0.151381i
$725$	3.95966	+	6.85833i	0.147058	+	0.254712i
$726$		0			0
$727$	−6.89280	+	11.9387i	−0.255640	+	0.442781i	−0.965069	−	0.261995i	$-0.915619\pi$
$727$	−6.89280	+	11.9387i	−0.255640	+	0.442781i	0.709429	+	0.704777i	$0.248953\pi$
$728$	1.43389			0.0531436
$729$		0			0
$730$	−21.5257			−0.796703
$731$	21.4741	−	37.1943i	0.794250	−	1.37568i
$732$		0			0
$733$	4.28134	+	7.41550i	0.158135	+	0.273898i	0.934196	−	0.356760i	$-0.116119\pi$
$733$	4.28134	+	7.41550i	0.158135	+	0.273898i	−0.776061	+	0.630658i	$0.782785\pi$
$734$	−4.80325	−	8.31947i	−0.177291	−	0.307077i
$735$		0			0
$736$	2.82492	−	4.89291i	0.104128	−	0.180355i
$737$	26.1998			0.965084
$738$		0			0
$739$	−11.8089			−0.434398			−0.217199	−	0.976127i	$-0.569692\pi$
$739$	−11.8089			−0.434398			−0.217199	+	0.976127i	$0.569692\pi$
$740$	13.6025	−	23.5602i	0.500036	−	0.866088i
$741$		0			0
$742$	−0.337224	−	0.584090i	−0.0123799	−	0.0214426i
$743$	10.2552	+	17.7625i	0.376226	+	0.651642i	0.990510	−	0.137443i	$-0.0438884\pi$
$743$	10.2552	+	17.7625i	0.376226	+	0.651642i	−0.614284	+	0.789085i	$0.710555\pi$
$744$		0			0
$745$	−7.13501	+	12.3582i	−0.261406	+	0.452769i
$746$	−2.37060			−0.0867939
$747$		0			0
$748$	−17.3167			−0.633161
$749$	0.968052	−	1.67672i	0.0353719	−	0.0612659i
$750$		0			0
$751$	−10.9711	−	19.0025i	−0.400341	−	0.693411i	0.593426	−	0.804889i	$-0.297775\pi$
$751$	−10.9711	−	19.0025i	−0.400341	−	0.693411i	−0.993767	+	0.111477i	$0.964442\pi$
$752$	6.26544	+	10.8521i	0.228477	+	0.395734i
$753$		0			0
$754$	−4.98224	+	8.62948i	−0.181442	+	0.314267i
$755$	22.5162			0.819447
$756$		0			0
$757$	38.7972			1.41011			0.705054	−	0.709153i	$-0.250923\pi$
$757$	38.7972			1.41011			0.705054	+	0.709153i	$0.250923\pi$
$758$	6.08457	−	10.5388i	0.221001	−	0.382786i
$759$		0			0
$760$	1.39308	+	2.41288i	0.0505322	+	0.0875243i
$761$	−11.8919	−	20.5974i	−0.431082	−	0.746656i	0.565885	−	0.824484i	$-0.308535\pi$
$761$	−11.8919	−	20.5974i	−0.431082	−	0.746656i	−0.996967	+	0.0778286i	$0.975201\pi$
$762$		0			0
$763$	−1.85720	+	3.21676i	−0.0672351	+	0.116455i
$764$	−11.2965			−0.408694
$765$		0			0
$766$	6.68477			0.241531
$767$	−10.4378	+	18.0788i	−0.376887	+	0.652787i
$768$		0			0
$769$	−13.7106	−	23.7475i	−0.494417	−	0.856355i	0.505562	−	0.862790i	$-0.331285\pi$
$769$	−13.7106	−	23.7475i	−0.494417	−	0.856355i	−0.999979	+	0.00643491i	$0.997952\pi$
$770$	−1.35193	−	2.34161i	−0.0487201	−	0.0843858i
$771$		0			0
$772$	−0.115536	+	0.200115i	−0.00415824	+	0.00720228i
$773$	32.0681			1.15341			0.576705	−	0.816952i	$-0.304338\pi$
$773$	32.0681			1.15341			0.576705	+	0.816952i	$0.304338\pi$
$774$		0			0
$775$	−47.7762			−1.71617
$776$	4.31305	−	7.47042i	0.154829	−	0.268172i
$777$		0			0
$778$	−10.7113	−	18.5525i	−0.384018	−	0.665139i
$779$	−2.58504	−	4.47743i	−0.0926188	−	0.160420i
$780$		0			0
$781$	−14.5519	+	25.2046i	−0.520707	+	0.901891i
$782$	−28.3281			−1.01301
$783$		0			0
$784$	−6.93536			−0.247692
$785$	−5.13263	+	8.88998i	−0.183192	+	0.317297i
$786$		0			0
$787$	−15.0431	−	26.0555i	−0.536230	−	0.928777i	−0.999103	−	0.0423523i	$-0.986515\pi$
$787$	−15.0431	−	26.0555i	−0.536230	−	0.928777i	0.462873	−	0.886425i	$-0.346819\pi$
$788$	6.11460	+	10.5908i	0.217824	+	0.377282i
$789$		0			0
$790$	−20.1837	+	34.9591i	−0.718103	+	1.24379i
$791$	1.16622			0.0414661
$792$		0			0
$793$	−21.3124			−0.756827
$794$	10.5878	−	18.3386i	0.375748	−	0.650814i
$795$		0			0
$796$	4.15593	+	7.19829i	0.147303	+	0.255137i
$797$	13.8741	+	24.0307i	0.491446	+	0.851210i	0.999951	−	0.00984880i	$-0.00313502\pi$
$797$	13.8741	+	24.0307i	0.491446	+	0.851210i	−0.508505	+	0.861059i	$0.669802\pi$
$798$		0			0
$799$	31.4147	−	54.4118i	1.11137	−	1.92495i
$800$	−4.48238			−0.158476
$801$		0			0
$802$	−34.9397			−1.23376
$803$	−12.0713	+	20.9081i	−0.425986	+	0.737829i
$804$		0			0
$805$	−2.21160	−	3.83060i	−0.0779487	−	0.135011i
$806$	−30.0572	−	52.0605i	−1.05872	−	1.83375i
$807$		0			0
$808$	1.24409	−	2.15483i	0.0437669	−	0.0758065i
$809$	−5.28719			−0.185888			−0.0929439	−	0.995671i	$-0.529628\pi$
$809$	−5.28719			−0.185888			−0.0929439	+	0.995671i	$0.529628\pi$
$810$		0			0
$811$	1.82768			0.0641785			0.0320893	−	0.999485i	$-0.489784\pi$
$811$	1.82768			0.0641785			0.0320893	+	0.999485i	$0.489784\pi$
$812$	−0.224590	+	0.389002i	−0.00788157	+	0.0136513i
$813$		0			0
$814$	−15.2561	−	26.4243i	−0.534725	−	0.926171i
$815$	−3.08037	−	5.33535i	−0.107900	−	0.186889i
$816$		0			0
$817$	−3.87508	+	6.71184i	−0.135572	+	0.234817i
$818$	−28.2265			−0.986915
$819$		0			0
$820$	17.5959			0.614474
$821$	−11.3987	+	19.7432i	−0.397819	+	0.689043i	−0.993457	−	0.114211i	$-0.963566\pi$
$821$	−11.3987	+	19.7432i	−0.397819	+	0.689043i	0.595638	+	0.803253i	$0.296899\pi$
$822$		0			0
$823$	−11.0866	−	19.2025i	−0.386453	−	0.669356i	0.605517	−	0.795833i	$-0.292966\pi$
$823$	−11.0866	−	19.2025i	−0.386453	−	0.669356i	−0.991970	+	0.126477i	$0.959633\pi$
$824$	0.514312	+	0.890814i	0.0179169	+	0.0310330i
$825$		0			0
$826$	−0.470517	+	0.814959i	−0.0163714	+	0.0283561i
$827$	16.3304			0.567863			0.283931	−	0.958845i	$-0.408361\pi$
$827$	16.3304			0.567863			0.283931	+	0.958845i	$0.408361\pi$
$828$		0			0
$829$	−26.3084			−0.913729			−0.456865	−	0.889536i	$-0.651028\pi$
$829$	−26.3084			−0.913729			−0.456865	+	0.889536i	$0.651028\pi$
$830$	10.6613	−	18.4659i	0.370059	−	0.640961i
$831$		0			0
$832$	−2.81997	−	4.88434i	−0.0977650	−	0.169334i
$833$	17.3868	+	30.1149i	0.602418	+	1.04342i
$834$		0			0
$835$	−21.3632	+	37.0021i	−0.739302	+	1.28051i
$836$	3.12486			0.108075
$837$		0			0
$838$	8.56513			0.295878
$839$	28.5119	−	49.3841i	0.984341	−	1.70493i	0.339513	−	0.940601i	$-0.389738\pi$
$839$	28.5119	−	49.3841i	0.984341	−	1.70493i	0.644828	−	0.764328i	$-0.276929\pi$
$840$		0			0
$841$	12.9393	+	22.4115i	0.446182	+	0.772809i
$842$	18.4922	+	32.0295i	0.637284	+	1.10381i
$843$		0			0
$844$	4.36976	−	7.56865i	0.150413	−	0.260524i
$845$	−57.9194			−1.99249
$846$		0			0
$847$	−0.235934			−0.00810678
$848$	−1.32641	+	2.29741i	−0.0455491	+	0.0788933i
$849$		0			0
$850$	11.2372	+	19.4635i	0.385434	+	0.667591i
$851$	−24.9572	−	43.2271i	−0.855521	−	1.48181i
$852$		0			0
$853$	15.9156	−	27.5667i	0.544941	−	0.943866i	−0.453670	−	0.891170i	$-0.649885\pi$
$853$	15.9156	−	27.5667i	0.544941	−	0.943866i	0.998611	−	0.0526956i	$-0.0167813\pi$
$854$	−0.960726			−0.0328754
$855$		0			0
$856$	−7.61531			−0.260286
$857$	6.47793	−	11.2201i	0.221282	−	0.383272i	−0.733916	−	0.679241i	$-0.762309\pi$
$857$	6.47793	−	11.2201i	0.221282	−	0.383272i	0.955198	+	0.295969i	$0.0956425\pi$
$858$		0			0
$859$	−12.7428	−	22.0711i	−0.434778	−	0.753058i	0.562499	−	0.826798i	$-0.309840\pi$
$859$	−12.7428	−	22.0711i	−0.434778	−	0.753058i	−0.997278	+	0.0737399i	$0.976507\pi$
$860$	−13.1884	−	22.8430i	−0.449722	−	0.778941i
$861$		0			0
$862$	−8.57694	+	14.8557i	−0.292132	+	0.505987i
$863$	16.1395			0.549396			0.274698	−	0.961531i	$-0.411422\pi$
$863$	16.1395			0.549396			0.274698	+	0.961531i	$0.411422\pi$
$864$		0			0
$865$	29.6267			1.00734
$866$	2.71323	−	4.69945i	0.0921992	−	0.159694i
$867$		0			0
$868$	−1.35492	−	2.34679i	−0.0459891	−	0.0796554i
$869$	22.6373	+	39.2090i	0.767919	+	1.33007i
$870$		0			0
$871$	21.3924	−	37.0527i	0.724854	−	1.25548i
$872$	14.6099			0.494754
$873$		0			0
$874$	5.11190			0.172913
$875$	0.202620	−	0.350948i	0.00684980	−	0.0118642i
$876$		0			0
$877$	−10.5831	−	18.3304i	−0.357364	−	0.618973i	0.630155	−	0.776469i	$-0.282991\pi$
$877$	−10.5831	−	18.3304i	−0.357364	−	0.618973i	−0.987520	+	0.157496i	$0.949658\pi$
$878$	−9.64110	−	16.6989i	−0.325371	−	0.563560i
$879$		0			0
$880$	−5.31756	+	9.21029i	−0.179255	+	0.310479i
$881$	4.52441			0.152431			0.0762157	−	0.997091i	$-0.475716\pi$
$881$	4.52441			0.152431			0.0762157	+	0.997091i	$0.475716\pi$
$882$		0			0
$883$	30.5817			1.02916			0.514578	−	0.857444i	$-0.327949\pi$
$883$	30.5817			1.02916			0.514578	+	0.857444i	$0.327949\pi$
$884$	−14.1392	+	24.4899i	−0.475554	+	0.823683i
$885$		0			0
$886$	18.1084	+	31.3647i	0.608363	+	1.05372i
$887$	−11.1914	−	19.3840i	−0.375769	−	0.650851i	0.614673	−	0.788782i	$-0.289288\pi$
$887$	−11.1914	−	19.3840i	−0.375769	−	0.650851i	−0.990442	+	0.137931i	$0.955955\pi$
$888$		0			0
$889$	−2.67085	+	4.62605i	−0.0895775	+	0.155153i
$890$	−20.9511			−0.702281
$891$		0			0
$892$	−5.48534			−0.183663
$893$	−5.66889	+	9.81880i	−0.189702	+	0.328574i
$894$		0			0
$895$	0.141597	+	0.245253i	0.00473305	+	0.00819789i
$896$	−0.127119	−	0.220177i	−0.00424676	−	0.00735560i
$897$		0			0
$898$	18.7373	−	32.4539i	0.625271	−	1.08300i
$899$	18.8314			0.628062
$900$		0			0
$901$	13.3011			0.443125
$902$	9.86747	−	17.0910i	0.328551	−	0.569067i
$903$		0			0
$904$	−2.29356	−	3.97256i	−0.0762826	−	0.132125i
$905$	7.24167	+	12.5429i	0.240721	+	0.416941i
$906$		0			0
$907$	20.5258	−	35.5517i	0.681547	−	1.18047i	−0.292961	−	0.956124i	$-0.594641\pi$
$907$	20.5258	−	35.5517i	0.681547	−	1.18047i	0.974509	−	0.224350i	$-0.0720259\pi$
$908$	13.9875			0.464191
$909$		0			0
$910$	−4.41545			−0.146371
$911$	4.82856	−	8.36332i	0.159977	−	0.277089i	−0.774883	−	0.632105i	$-0.782191\pi$
$911$	4.82856	−	8.36332i	0.159977	−	0.277089i	0.934860	+	0.355016i	$0.115525\pi$
$912$		0			0
$913$	−11.9573	−	20.7107i	−0.395730	−	0.685425i
$914$	20.0347	+	34.7011i	0.662689	+	1.14781i
$915$		0			0
$916$	8.20460	−	14.2108i	0.271088	−	0.469537i
$917$	−4.43854			−0.146574
$918$		0			0
$919$	−17.8488			−0.588776			−0.294388	−	0.955686i	$-0.595116\pi$
$919$	−17.8488			−0.588776			−0.294388	+	0.955686i	$0.595116\pi$
$920$	−8.69892	+	15.0670i	−0.286795	+	0.496743i
$921$		0			0
$922$	−1.39325	−	2.41319i	−0.0458844	−	0.0794741i
$923$	23.7635	+	41.1595i	0.782184	+	1.35478i
$924$		0			0
$925$	−19.8001	+	34.2948i	−0.651023	+	1.12761i
$926$	5.26722			0.173091
$927$		0			0
$928$	1.76677			0.0579970
$929$	4.96387	−	8.59767i	0.162859	−	0.282080i	−0.773034	−	0.634365i	$-0.781262\pi$
$929$	4.96387	−	8.59767i	0.162859	−	0.282080i	0.935893	+	0.352284i	$0.114595\pi$
$930$		0			0
$931$	−3.13751	−	5.43433i	−0.102828	−	0.178103i
$932$	3.51294	+	6.08459i	0.115070	+	0.199307i
$933$		0			0
$934$	−2.58932	+	4.48483i	−0.0847250	+	0.146748i
$935$	53.3241			1.74388
$936$		0			0
$937$	14.9391			0.488041			0.244020	−	0.969770i	$-0.421534\pi$
$937$	14.9391			0.488041			0.244020	+	0.969770i	$0.421534\pi$
$938$	0.964331	−	1.67027i	0.0314865	−	0.0545363i
$939$		0			0
$940$	−19.2935	−	33.4173i	−0.629283	−	1.08995i
$941$	−12.8627	−	22.2789i	−0.419313	−	0.726272i	0.576557	−	0.817057i	$-0.304396\pi$
$941$	−12.8627	−	22.2789i	−0.419313	−	0.726272i	−0.995871	+	0.0907847i	$0.971062\pi$
$942$		0			0
$943$	16.1420	−	27.9588i	0.525657	−	0.910465i
$944$	3.70138			0.120470
$945$		0			0
$946$	−29.5834			−0.961840
$947$	−2.36392	+	4.09443i	−0.0768171	+	0.133051i	−0.901875	−	0.431997i	$-0.857809\pi$
$947$	−2.36392	+	4.09443i	−0.0768171	+	0.133051i	0.825058	+	0.565048i	$0.191142\pi$
$948$		0			0
$949$	19.7126	+	34.1432i	0.639898	+	1.10834i
$950$	−2.02780	−	3.51225i	−0.0657904	−	0.113952i
$951$		0			0
$952$	−0.637371	+	1.10396i	−0.0206573	+	0.0357795i
$953$	10.9627			0.355118			0.177559	−	0.984110i	$-0.443180\pi$
$953$	10.9627			0.355118			0.177559	+	0.984110i	$0.443180\pi$
$954$		0			0
$955$	34.7859			1.12564
$956$	−8.96503	+	15.5279i	−0.289950	+	0.502208i
$957$		0			0
$958$	−10.1446	−	17.5710i	−0.327758	−	0.567693i
$959$	0.0333498	+	0.0577635i	0.00107692	+	0.00186528i
$960$		0			0
$961$	−41.3036	+	71.5399i	−1.33237	+	2.30774i
$962$	−49.8269			−1.60648
$963$		0			0
$964$	−10.5554			−0.339966
$965$	0.355776	−	0.616222i	0.0114528	−	0.0198369i
$966$		0			0
$967$	−3.57739	−	6.19623i	−0.115041	−	0.199257i	0.802755	−	0.596309i	$-0.203367\pi$
$967$	−3.57739	−	6.19623i	−0.115041	−	0.199257i	−0.917796	+	0.397052i	$0.870033\pi$
$968$	0.464001	+	0.803673i	0.0149135	+	0.0258310i
$969$		0			0
$970$	−13.2814	+	23.0040i	−0.426439	+	0.738614i
$971$	9.66743			0.310243			0.155121	−	0.987895i	$-0.450423\pi$
$971$	9.66743			0.310243			0.155121	+	0.987895i	$0.450423\pi$
$972$		0			0
$973$	−3.00285			−0.0962669
$974$	−5.52575	+	9.57088i	−0.177056	+	0.306671i
$975$		0			0
$976$	1.88942	+	3.27257i	0.0604788	+	0.104752i
$977$	−5.29634	−	9.17353i	−0.169445	−	0.293487i	0.768780	−	0.639514i	$-0.220864\pi$
$977$	−5.29634	−	9.17353i	−0.169445	−	0.293487i	−0.938225	+	0.346026i	$0.887531\pi$
$978$		0			0
$979$	−11.7490	+	20.3499i	−0.375500	+	0.650385i
$980$	21.3564			0.682205
$981$		0			0
$982$	25.3811			0.809945
$983$	5.10176	−	8.83652i	0.162721	−	0.281841i	−0.773123	−	0.634257i	$-0.781306\pi$
$983$	5.10176	−	8.83652i	0.162721	−	0.281841i	0.935844	+	0.352416i	$0.114640\pi$
$984$		0			0
$985$	−18.8290	−	32.6128i	−0.599941	−	1.03913i
$986$	−4.42925	−	7.67169i	−0.141056	−	0.244316i
$987$		0			0
$988$	2.55147	−	4.41928i	0.0811732	−	0.140596i
$989$	−48.3951			−1.53887
$990$		0			0
$991$	55.3945			1.75966			0.879832	−	0.475285i	$-0.157655\pi$
$991$	55.3945			1.75966			0.879832	+	0.475285i	$0.157655\pi$
$992$	−5.32933	+	9.23068i	−0.169207	+	0.293074i
$993$		0			0
$994$	1.07121	+	1.85540i	0.0339769	+	0.0588497i
$995$	−12.7976	−	22.1660i	−0.405710	−	0.702711i
$996$		0			0
$997$	8.88537	−	15.3899i	0.281402	−	0.487403i	−0.690328	−	0.723497i	$-0.742534\pi$
$997$	8.88537	−	15.3899i	0.281402	−	0.487403i	0.971730	+	0.236093i	$0.0758671\pi$
$998$	12.7222			0.402713
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1458.2.c.h.487.5		12
3.2	odd	2		1458.2.c.e.487.2		12
9.2	odd	6		1458.2.a.h.1.5	yes	6
9.4	even	3	inner	1458.2.c.h.973.5		12
9.5	odd	6		1458.2.c.e.973.2		12
9.7	even	3		1458.2.a.e.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1458.2.a.e.1.2	✓	6	9.7	even	3
1458.2.a.h.1.5	yes	6	9.2	odd	6
1458.2.c.e.487.2		12	3.2	odd	2
1458.2.c.e.973.2		12	9.5	odd	6
1458.2.c.h.487.5		12	1.1	even	1	trivial
1458.2.c.h.973.5		12	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1458.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.53967 + 2.66679i) q^{5} +(0.127119 - 0.220177i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.53967 + 2.66679i) q^{5} +(0.127119 - 0.220177i) q^{7} -1.00000 q^{8} +3.07935 q^{10} +(1.72685 - 2.99099i) q^{11} +(-2.81997 - 4.88434i) q^{13} +(-0.127119 - 0.220177i) q^{14} +(-0.500000 + 0.866025i) q^{16} +5.01396 q^{17} -0.904786 q^{19} +(1.53967 - 2.66679i) q^{20} +(-1.72685 - 2.99099i) q^{22} +(-2.82492 - 4.89291i) q^{23} +(-2.24119 + 3.88185i) q^{25} -5.63995 q^{26} -0.254239 q^{28} +(0.883384 - 1.53007i) q^{29} +(5.32933 + 9.23068i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50698 - 4.34222i) q^{34} +0.782889 q^{35} +8.83464 q^{37} +(-0.452393 + 0.783568i) q^{38} +(-1.53967 - 2.66679i) q^{40} +(2.85708 + 4.94860i) q^{41} +(4.28287 - 7.41815i) q^{43} -3.45369 q^{44} -5.64985 q^{46} +(6.26544 - 10.8521i) q^{47} +(3.46768 + 6.00620i) q^{49} +(2.24119 + 3.88185i) q^{50} +(-2.81997 + 4.88434i) q^{52} +2.65282 q^{53} +10.6351 q^{55} +(-0.127119 + 0.220177i) q^{56} +(-0.883384 - 1.53007i) q^{58} +(-1.85069 - 3.20549i) q^{59} +(1.88942 - 3.27257i) q^{61} +10.6587 q^{62} +1.00000 q^{64} +(8.68367 - 15.0406i) q^{65} +(3.79302 + 6.56970i) q^{67} +(-2.50698 - 4.34222i) q^{68} +(0.391444 - 0.678002i) q^{70} -8.42685 q^{71} -6.99035 q^{73} +(4.41732 - 7.65102i) q^{74} +(0.452393 + 0.783568i) q^{76} +(-0.439031 - 0.760424i) q^{77} +(-6.55453 + 11.3528i) q^{79} -3.07935 q^{80} +5.71415 q^{82} +(3.46219 - 5.99669i) q^{83} +(7.71986 + 13.3712i) q^{85} +(-4.28287 - 7.41815i) q^{86} +(-1.72685 + 2.99099i) q^{88} -6.80373 q^{89} -1.43389 q^{91} +(-2.82492 + 4.89291i) q^{92} +(-6.26544 - 10.8521i) q^{94} +(-1.39308 - 2.41288i) q^{95} +(-4.31305 + 7.47042i) q^{97} +6.93536 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^8	\( 12 q + 6 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 6 q^{16} - 24 q^{17} + 12 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} - 6 q^{25} - 12 q^{26} + 6 q^{29} + 6 q^{31} + 6 q^{32} - 12 q^{34} - 24 q^{35} + 6 q^{38} - 6 q^{40} + 24 q^{41} + 6 q^{43} - 12 q^{44} + 24 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} - 6 q^{52} - 48 q^{53} - 36 q^{55} - 6 q^{58} + 12 q^{59} + 6 q^{61} + 12 q^{62} + 12 q^{64} + 12 q^{65} + 24 q^{67} + 12 q^{68} - 12 q^{70} + 12 q^{71} - 48 q^{73} - 6 q^{76} + 12 q^{77} + 12 q^{79} - 12 q^{80} + 48 q^{82} + 18 q^{83} - 6 q^{86} - 6 q^{88} - 24 q^{89} - 60 q^{91} + 12 q^{92} - 18 q^{94} - 6 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 6 * q^16 - 24 * q^17 + 12 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 - 6 * q^25 - 12 * q^26 + 6 * q^29 + 6 * q^31 + 6 * q^32 - 12 * q^34 - 24 * q^35 + 6 * q^38 - 6 * q^40 + 24 * q^41 + 6 * q^43 - 12 * q^44 + 24 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 - 6 * q^52 - 48 * q^53 - 36 * q^55 - 6 * q^58 + 12 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^64 + 12 * q^65 + 24 * q^67 + 12 * q^68 - 12 * q^70 + 12 * q^71 - 48 * q^73 - 6 * q^76 + 12 * q^77 + 12 * q^79 - 12 * q^80 + 48 * q^82 + 18 * q^83 - 6 * q^86 - 6 * q^88 - 24 * q^89 - 60 * q^91 + 12 * q^92 - 18 * q^94 - 6 * q^95 - 6 * q^97 - 12 * q^98

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