LMFDB - Embedded newform 720.2.t.d.541.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.8
Root			$-1.04932 + 0.948122i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.d.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04932 + 0.948122i) q^{2} +(0.202128 + 1.98976i) q^{4} +(0.707107 - 0.707107i) q^{5} +0.740019i q^{7} +(-1.67444 + 2.27953i) q^{8} +O(q^{10})$	\(q+(1.04932 + 0.948122i) q^{2} +(0.202128 + 1.98976i) q^{4} +(0.707107 - 0.707107i) q^{5} +0.740019i q^{7} +(-1.67444 + 2.27953i) q^{8} +(1.41240 - 0.0715547i) q^{10} +(3.83476 - 3.83476i) q^{11} +(3.31314 + 3.31314i) q^{13} +(-0.701629 + 0.776514i) q^{14} +(-3.91829 + 0.804372i) q^{16} -2.93893 q^{17} +(5.02789 + 5.02789i) q^{19} +(1.54990 + 1.26405i) q^{20} +(7.65970 - 0.388053i) q^{22} +5.45159i q^{23} -1.00000i q^{25} +(0.335268 + 6.61779i) q^{26} +(-1.47246 + 0.149579i) q^{28} +(-2.64012 - 2.64012i) q^{29} -5.94837 q^{31} +(-4.87417 - 2.87098i) q^{32} +(-3.08387 - 2.78647i) q^{34} +(0.523272 + 0.523272i) q^{35} +(-0.479352 + 0.479352i) q^{37} +(0.508791 + 10.0429i) q^{38} +(0.427863 + 2.79588i) q^{40} -10.1918i q^{41} +(-4.93728 + 4.93728i) q^{43} +(8.40537 + 6.85514i) q^{44} +(-5.16877 + 5.72044i) q^{46} +8.15706 q^{47} +6.45237 q^{49} +(0.948122 - 1.04932i) q^{50} +(-5.92267 + 7.26203i) q^{52} +(5.05247 - 5.05247i) q^{53} -5.42317i q^{55} +(-1.68689 - 1.23912i) q^{56} +(-0.267163 - 5.27348i) q^{58} +(-3.83709 + 3.83709i) q^{59} +(-4.87697 - 4.87697i) q^{61} +(-6.24172 - 5.63978i) q^{62} +(-2.39250 - 7.63387i) q^{64} +4.68548 q^{65} +(-3.99222 - 3.99222i) q^{67} +(-0.594040 - 5.84777i) q^{68} +(0.0529518 + 1.04520i) q^{70} +3.55343i q^{71} -11.1655i q^{73} +(-0.957475 + 0.0485073i) q^{74} +(-8.98803 + 11.0206i) q^{76} +(2.83780 + 2.83780i) q^{77} +10.7776 q^{79} +(-2.20187 + 3.33943i) q^{80} +(9.66309 - 10.6944i) q^{82} +(-4.61002 - 4.61002i) q^{83} +(-2.07814 + 2.07814i) q^{85} +(-9.86192 + 0.499621i) q^{86} +(2.32037 + 15.1625i) q^{88} -2.62476i q^{89} +(-2.45179 + 2.45179i) q^{91} +(-10.8473 + 1.10192i) q^{92} +(8.55934 + 7.73389i) q^{94} +7.11052 q^{95} +1.67846 q^{97} +(6.77058 + 6.11764i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} - 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 - 12 * q^8	$ 20 q + 4 q^{4} - 12 q^{8} - 8 q^{11} + 4 q^{14} - 20 q^{16} + 24 q^{17} - 4 q^{19} + 8 q^{20} + 8 q^{22} - 28 q^{26} - 8 q^{28} - 16 q^{29} + 40 q^{32} - 44 q^{34} + 16 q^{37} + 8 q^{38} + 12 q^{40} - 8 q^{43} - 24 q^{44} - 12 q^{46} - 52 q^{49} - 4 q^{50} - 56 q^{52} + 16 q^{53} - 64 q^{56} + 72 q^{58} + 16 q^{59} - 4 q^{61} + 44 q^{62} - 56 q^{64} - 8 q^{67} + 32 q^{68} + 20 q^{70} - 60 q^{74} + 28 q^{76} + 40 q^{77} + 56 q^{79} + 16 q^{80} - 24 q^{82} + 48 q^{83} + 4 q^{85} - 64 q^{86} + 40 q^{88} - 8 q^{91} - 88 q^{92} - 20 q^{94} + 56 q^{97} + 48 q^{98}+O(q^{100}) $ 20 * q + 4 * q^4 - 12 * q^8 - 8 * q^11 + 4 * q^14 - 20 * q^16 + 24 * q^17 - 4 * q^19 + 8 * q^20 + 8 * q^22 - 28 * q^26 - 8 * q^28 - 16 * q^29 + 40 * q^32 - 44 * q^34 + 16 * q^37 + 8 * q^38 + 12 * q^40 - 8 * q^43 - 24 * q^44 - 12 * q^46 - 52 * q^49 - 4 * q^50 - 56 * q^52 + 16 * q^53 - 64 * q^56 + 72 * q^58 + 16 * q^59 - 4 * q^61 + 44 * q^62 - 56 * q^64 - 8 * q^67 + 32 * q^68 + 20 * q^70 - 60 * q^74 + 28 * q^76 + 40 * q^77 + 56 * q^79 + 16 * q^80 - 24 * q^82 + 48 * q^83 + 4 * q^85 - 64 * q^86 + 40 * q^88 - 8 * q^91 - 88 * q^92 - 20 * q^94 + 56 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.04932	+	0.948122i	0.741978	+	0.670424i
$2$	1.04932	+	0.948122i	0.741978	+	0.670424i
$3$		0			0
$3$		0			0
$4$	0.202128	+	1.98976i	0.101064	+	0.994880i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			0.740019i			0.279701i	0.990173	+	0.139850i	$0.0446622\pi$
$7$			0.740019i			0.279701i	−0.990173	+	0.139850i	$0.955338\pi$
$8$	−1.67444	+	2.27953i	−0.592004	+	0.805935i
$9$		0			0
$10$	1.41240	−	0.0715547i	0.446641	−	0.0226276i
$11$	3.83476	−	3.83476i	1.15622	−	1.15622i	0.170943	−	0.985281i	$-0.445318\pi$
$11$	3.83476	−	3.83476i	1.15622	−	1.15622i	0.985281	−	0.170943i	$-0.0546815\pi$
$12$		0			0
$13$	3.31314	+	3.31314i	0.918899	+	0.918899i	0.996949	−	0.0780503i	$-0.0248695\pi$
$13$	3.31314	+	3.31314i	0.918899	+	0.918899i	−0.0780503	+	0.996949i	$0.524869\pi$
$14$	−0.701629	+	0.776514i	−0.187518	+	0.207532i
$15$		0			0
$16$	−3.91829	+	0.804372i	−0.979572	+	0.201093i
$17$	−2.93893			−0.712796			−0.356398	−	0.934334i	$-0.615995\pi$
$17$	−2.93893			−0.712796			−0.356398	+	0.934334i	$0.615995\pi$
$18$		0			0
$19$	5.02789	+	5.02789i	1.15348	+	1.15348i	0.985850	+	0.167628i	$0.0536107\pi$
$19$	5.02789	+	5.02789i	1.15348	+	1.15348i	0.167628	+	0.985850i	$0.446389\pi$
$20$	1.54990	+	1.26405i	0.346568	+	0.282649i
$21$		0			0
$22$	7.65970	−	0.388053i	1.63305	−	0.0827332i
$23$			5.45159i			1.13673i	0.822775	+	0.568367i	$0.192425\pi$
$23$			5.45159i			1.13673i	−0.822775	+	0.568367i	$0.807575\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	0.335268	+	6.61779i	0.0657515	+	1.29786i
$27$		0			0
$28$	−1.47246	+	0.149579i	−0.278269	+	0.0282677i
$29$	−2.64012	−	2.64012i	−0.490258	−	0.490258i	0.418129	−	0.908388i	$-0.362686\pi$
$29$	−2.64012	−	2.64012i	−0.490258	−	0.490258i	−0.908388	+	0.418129i	$0.862686\pi$
$30$		0			0
$31$	−5.94837			−1.06836			−0.534179	−	0.845371i	$-0.679379\pi$
$31$	−5.94837			−1.06836			−0.534179	+	0.845371i	$0.679379\pi$
$32$	−4.87417	−	2.87098i	−0.861639	−	0.507522i
$33$		0			0
$34$	−3.08387	−	2.78647i	−0.528879	−	0.477875i
$35$	0.523272	+	0.523272i	0.0884492	+	0.0884492i
$36$		0			0
$37$	−0.479352	+	0.479352i	−0.0788049	+	0.0788049i	−0.745411	−	0.666606i	$-0.767747\pi$
$37$	−0.479352	+	0.479352i	−0.0788049	+	0.0788049i	0.666606	+	0.745411i	$0.267747\pi$
$38$	0.508791	+	10.0429i	0.0825368	+	1.62918i
$39$		0			0
$40$	0.427863	+	2.79588i	0.0676510	+	0.442067i
$41$		−	10.1918i		−	1.59169i	−0.605497	−	0.795847i	$-0.707026\pi$
$41$		−	10.1918i		−	1.59169i	0.605497	−	0.795847i	$-0.292974\pi$
$42$		0			0
$43$	−4.93728	+	4.93728i	−0.752929	+	0.752929i	−0.975025	−	0.222096i	$-0.928710\pi$
$43$	−4.93728	+	4.93728i	−0.752929	+	0.752929i	0.222096	+	0.975025i	$0.428710\pi$
$44$	8.40537	+	6.85514i	1.26716	+	1.03345i
$45$		0			0
$46$	−5.16877	+	5.72044i	−0.762094	+	0.843432i
$47$	8.15706			1.18983			0.594915	−	0.803789i	$-0.297186\pi$
$47$	8.15706			1.18983			0.594915	+	0.803789i	$0.297186\pi$
$48$		0			0
$49$	6.45237			0.921767
$50$	0.948122	−	1.04932i	0.134085	−	0.148396i
$51$		0			0
$52$	−5.92267	+	7.26203i	−0.821327	+	1.00706i
$53$	5.05247	−	5.05247i	0.694010	−	0.694010i	−0.269102	−	0.963112i	$-0.586727\pi$
$53$	5.05247	−	5.05247i	0.694010	−	0.694010i	0.963112	+	0.269102i	$0.0867267\pi$
$54$		0			0
$55$		−	5.42317i		−	0.731260i
$56$	−1.68689	−	1.23912i	−0.225421	−	0.165584i
$57$		0			0
$58$	−0.267163	−	5.27348i	−0.0350803	−	0.692442i
$59$	−3.83709	+	3.83709i	−0.499547	+	0.499547i	−0.911297	−	0.411750i	$-0.864918\pi$
$59$	−3.83709	+	3.83709i	−0.499547	+	0.499547i	0.411750	+	0.911297i	$0.364918\pi$
$60$		0			0
$61$	−4.87697	−	4.87697i	−0.624432	−	0.624432i	0.322229	−	0.946662i	$-0.395568\pi$
$61$	−4.87697	−	4.87697i	−0.624432	−	0.624432i	−0.946662	+	0.322229i	$0.895568\pi$
$62$	−6.24172	−	5.63978i	−0.792699	−	0.716253i
$63$		0			0
$64$	−2.39250	−	7.63387i	−0.299063	−	0.954233i
$65$	4.68548			0.581163
$66$		0			0
$67$	−3.99222	−	3.99222i	−0.487728	−	0.487728i	0.419861	−	0.907588i	$-0.362079\pi$
$67$	−3.99222	−	3.99222i	−0.487728	−	0.487728i	−0.907588	+	0.419861i	$0.862079\pi$
$68$	−0.594040	−	5.84777i	−0.0720379	−	0.709146i
$69$		0			0
$70$	0.0529518	+	1.04520i	0.00632895	+	0.124926i
$71$			3.55343i			0.421715i	0.977517	+	0.210857i	$0.0676255\pi$
$71$			3.55343i			0.421715i	−0.977517	+	0.210857i	$0.932374\pi$
$72$		0			0
$73$		−	11.1655i		−	1.30683i	−0.757002	−	0.653413i	$-0.773337\pi$
$73$		−	11.1655i		−	1.30683i	0.757002	−	0.653413i	$-0.226663\pi$
$74$	−0.957475	+	0.0485073i	−0.111304	+	0.00563886i
$75$		0			0
$76$	−8.98803	+	11.0206i	−1.03100	+	1.26415i
$77$	2.83780	+	2.83780i	0.323397	+	0.323397i
$78$		0			0
$79$	10.7776			1.21258			0.606288	−	0.795245i	$-0.292658\pi$
$79$	10.7776			1.21258			0.606288	+	0.795245i	$0.292658\pi$
$80$	−2.20187	+	3.33943i	−0.246177	+	0.373359i
$81$		0			0
$82$	9.66309	−	10.6944i	1.06711	−	1.18100i
$83$	−4.61002	−	4.61002i	−0.506016	−	0.506016i	0.407285	−	0.913301i	$-0.366475\pi$
$83$	−4.61002	−	4.61002i	−0.506016	−	0.506016i	−0.913301	+	0.407285i	$0.866475\pi$
$84$		0			0
$85$	−2.07814	+	2.07814i	−0.225406	+	0.225406i
$86$	−9.86192	+	0.499621i	−1.06344	+	0.0538756i
$87$		0			0
$88$	2.32037	+	15.1625i	0.247353	+	1.61633i
$89$		−	2.62476i		−	0.278224i	−0.990277	−	0.139112i	$-0.955575\pi$
$89$		−	2.62476i		−	0.278224i	0.990277	−	0.139112i	$-0.0444247\pi$
$90$		0			0
$91$	−2.45179	+	2.45179i	−0.257017	+	0.257017i
$92$	−10.8473	+	1.10192i	−1.13091	+	0.114883i
$93$		0			0
$94$	8.55934	+	7.73389i	0.882828	+	0.797690i
$95$	7.11052			0.729524
$96$		0			0
$97$	1.67846			0.170422			0.0852108	−	0.996363i	$-0.472844\pi$
$97$	1.67846			0.170422			0.0852108	+	0.996363i	$0.472844\pi$
$98$	6.77058	+	6.11764i	0.683932	+	0.617975i
$99$		0			0
$100$	1.98976	−	0.202128i	0.198976	−	0.0202128i
$101$	−6.52161	+	6.52161i	−0.648925	+	0.648925i	−0.952733	−	0.303808i	$-0.901742\pi$
$101$	−6.52161	+	6.52161i	−0.648925	+	0.648925i	0.303808	+	0.952733i	$0.401742\pi$
$102$		0			0
$103$		−	0.302418i		−	0.0297981i	−0.999889	−	0.0148991i	$-0.995257\pi$
$103$		−	0.302418i		−	0.0297981i	0.999889	−	0.0148991i	$-0.00474269\pi$
$104$	−13.1000	+	2.00474i	−1.28456	+	0.196581i
$105$		0			0
$106$	10.0920	−	0.511278i	0.980222	−	0.0496597i
$107$	1.20078	−	1.20078i	0.116084	−	0.116084i	−0.646679	−	0.762762i	$-0.723843\pi$
$107$	1.20078	−	1.20078i	0.116084	−	0.116084i	0.762762	+	0.646679i	$0.223843\pi$
$108$		0			0
$109$	−6.99992	−	6.99992i	−0.670471	−	0.670471i	0.287353	−	0.957825i	$-0.407225\pi$
$109$	−6.99992	−	6.99992i	−0.670471	−	0.670471i	−0.957825	+	0.287353i	$0.907225\pi$
$110$	5.14183	−	5.69062i	0.490254	−	0.542579i
$111$		0			0
$112$	−0.595251	−	2.89961i	−0.0562459	−	0.273987i
$113$	−15.1350			−1.42378			−0.711892	−	0.702289i	$-0.752161\pi$
$113$	−15.1350			−1.42378			−0.711892	+	0.702289i	$0.752161\pi$
$114$		0			0
$115$	3.85485	+	3.85485i	0.359467	+	0.359467i
$116$	4.71957	−	5.78685i	0.438201	−	0.537296i
$117$		0			0
$118$	−7.66436	+	0.388289i	−0.705561	+	0.0357449i
$119$		−	2.17486i		−	0.199370i
$120$		0			0
$121$		−	18.4108i		−	1.67371i
$122$	−0.493518	−	9.74145i	−0.0446811	−	0.881950i
$123$		0			0
$124$	−1.20233	−	11.8358i	−0.107973	−	1.06289i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	8.94547			0.793782			0.396891	−	0.917866i	$-0.370089\pi$
$127$	8.94547			0.793782			0.396891	+	0.917866i	$0.370089\pi$
$128$	4.72735	−	10.2787i	0.417843	−	0.908519i
$129$		0			0
$130$	4.91655	+	4.44241i	0.431210	+	0.389625i
$131$	−9.63786	−	9.63786i	−0.842064	−	0.842064i	0.147063	−	0.989127i	$-0.453018\pi$
$131$	−9.63786	−	9.63786i	−0.842064	−	0.842064i	−0.989127	+	0.147063i	$0.953018\pi$
$132$		0			0
$133$	−3.72074	+	3.72074i	−0.322629	+	0.322629i
$134$	−0.403987	−	7.97422i	−0.0348992	−	0.688867i
$135$		0			0
$136$	4.92106	−	6.69938i	0.421978	−	0.574467i
$137$		−	6.92180i		−	0.591370i	−0.955286	−	0.295685i	$-0.904452\pi$
$137$		−	6.92180i		−	0.591370i	0.955286	−	0.295685i	$-0.0955478\pi$
$138$		0			0
$139$	6.50393	−	6.50393i	0.551657	−	0.551657i	−0.375262	−	0.926919i	$-0.622447\pi$
$139$	6.50393	−	6.50393i	0.551657	−	0.551657i	0.926919	+	0.375262i	$0.122447\pi$
$140$	−0.935419	+	1.14695i	−0.0790573	+	0.0969353i
$141$		0			0
$142$	−3.36909	+	3.72867i	−0.282728	+	0.312903i
$143$	25.4102			2.12491
$144$		0			0
$145$	−3.73370			−0.310067
$146$	10.5863	−	11.7162i	0.876127	−	0.969636i
$147$		0			0
$148$	−1.05068	−	0.856904i	−0.0863658	−	0.0704371i
$149$	5.75043	−	5.75043i	0.471094	−	0.471094i	−0.431175	−	0.902268i	$-0.641901\pi$
$149$	5.75043	−	5.75043i	0.471094	−	0.471094i	0.902268	+	0.431175i	$0.141901\pi$
$150$		0			0
$151$		−	0.185782i		−	0.0151187i	−0.999971	−	0.00755935i	$-0.997594\pi$
$151$		−	0.185782i		−	0.0151187i	0.999971	−	0.00755935i	$-0.00240624\pi$
$152$	−19.8801	+	3.04232i	−1.61249	+	0.246765i
$153$		0			0
$154$	0.287167	+	5.66832i	0.0231406	+	0.456767i
$155$	−4.20613	+	4.20613i	−0.337845	+	0.337845i
$156$		0			0
$157$	−11.8717	−	11.8717i	−0.947462	−	0.947462i	0.0512256	−	0.998687i	$-0.483687\pi$
$157$	−11.8717	−	11.8717i	−0.947462	−	0.947462i	−0.998687	+	0.0512256i	$0.983687\pi$
$158$	11.3091	+	10.2185i	0.899705	+	0.812940i
$159$		0			0
$160$	−5.47664	+	1.41647i	−0.432967	+	0.111982i
$161$	−4.03428			−0.317946
$162$		0			0
$163$	11.3813	+	11.3813i	0.891454	+	0.891454i	0.994660	−	0.103206i	$-0.0329101\pi$
$163$	11.3813	+	11.3813i	0.891454	+	0.891454i	−0.103206	+	0.994660i	$0.532910\pi$
$164$	20.2793	−	2.06005i	1.58354	−	0.160863i
$165$		0			0
$166$	−0.466505	−	9.20823i	−0.0362078	−	0.714698i
$167$			12.8924i			0.997644i	0.866705	+	0.498822i	$0.166234\pi$
$167$			12.8924i			0.997644i	−0.866705	+	0.498822i	$0.833766\pi$
$168$		0			0
$169$			8.95377i			0.688751i
$170$	−4.15095	+	0.210294i	−0.318364	+	0.0161288i
$171$		0			0
$172$	−10.8220	−	8.82604i	−0.825167	−	0.672980i
$173$	12.1023	+	12.1023i	0.920122	+	0.920122i	0.997038	−	0.0769156i	$-0.0245072\pi$
$173$	12.1023	+	12.1023i	0.920122	+	0.920122i	−0.0769156	+	0.997038i	$0.524507\pi$
$174$		0			0
$175$	0.740019			0.0559402
$176$	−11.9411	+	18.1103i	−0.900096	+	1.36511i
$177$		0			0
$178$	2.48859	−	2.75420i	0.186528	−	0.206436i
$179$	−15.5558	−	15.5558i	−1.16269	−	1.16269i	−0.983884	−	0.178809i	$-0.942776\pi$
$179$	−15.5558	−	15.5558i	−1.16269	−	1.16269i	−0.178809	−	0.983884i	$-0.557224\pi$
$180$		0			0
$181$	10.5970	−	10.5970i	0.787670	−	0.787670i	−0.193442	−	0.981112i	$-0.561965\pi$
$181$	10.5970	−	10.5970i	0.787670	−	0.787670i	0.981112	+	0.193442i	$0.0619651\pi$
$182$	−4.89729	+	0.248105i	−0.363011	+	0.0183908i
$183$		0			0
$184$	−12.4270	−	9.12835i	−0.916134	−	0.672951i
$185$			0.677905i			0.0498406i
$186$		0			0
$187$	−11.2701	+	11.2701i	−0.824151	+	0.824151i
$188$	1.64877	+	16.2306i	0.120249	+	1.18374i
$189$		0			0
$190$	7.46118	+	6.74164i	0.541291	+	0.489090i
$191$	−8.84439			−0.639958			−0.319979	−	0.947425i	$-0.603676\pi$
$191$	−8.84439			−0.639958			−0.319979	+	0.947425i	$0.603676\pi$
$192$		0			0
$193$	14.0714			1.01289			0.506443	−	0.862274i	$-0.330960\pi$
$193$	14.0714			1.01289			0.506443	+	0.862274i	$0.330960\pi$
$194$	1.76123	+	1.59138i	0.126449	+	0.114255i
$195$		0			0
$196$	1.30420	+	12.8387i	0.0931575	+	0.917048i
$197$	−8.15230	+	8.15230i	−0.580827	+	0.580827i	−0.935131	−	0.354303i	$-0.884718\pi$
$197$	−8.15230	+	8.15230i	−0.580827	+	0.580827i	0.354303	+	0.935131i	$0.384718\pi$
$198$		0			0
$199$			11.3466i			0.804340i	0.915565	+	0.402170i	$0.131744\pi$
$199$			11.3466i			0.804340i	−0.915565	+	0.402170i	$0.868256\pi$
$200$	2.27953	+	1.67444i	0.161187	+	0.118401i
$201$		0			0
$202$	−13.0265	+	0.659945i	−0.916543	+	0.0464336i
$203$	1.95374	−	1.95374i	0.137126	−	0.137126i
$204$		0			0
$205$	−7.20670	−	7.20670i	−0.503338	−	0.503338i
$206$	0.286729	−	0.317332i	0.0199774	−	0.0221096i
$207$		0			0
$208$	−15.6468	−	10.3168i	−1.08491	−	0.715344i
$209$	38.5616			2.66736
$210$		0			0
$211$	−15.6416	−	15.6416i	−1.07681	−	1.07681i	−0.996793	−	0.0800209i	$-0.974501\pi$
$211$	−15.6416	−	15.6416i	−1.07681	−	1.07681i	−0.0800209	−	0.996793i	$-0.525499\pi$
$212$	11.0744	+	9.03196i	0.760596	+	0.620317i
$213$		0			0
$214$	2.39848	−	0.121511i	0.163957	−	0.00830632i
$215$			6.98237i			0.476194i
$216$		0			0
$217$		−	4.40191i		−	0.298821i
$218$	−0.708347	−	13.9819i	−0.0479753	−	0.946975i
$219$		0			0
$220$	10.7908	−	1.09617i	0.727516	−	0.0739041i
$221$	−9.73708	−	9.73708i	−0.654987	−	0.654987i
$222$		0			0
$223$	−10.2773			−0.688219			−0.344110	−	0.938929i	$-0.611819\pi$
$223$	−10.2773			−0.688219			−0.344110	+	0.938929i	$0.611819\pi$
$224$	2.12458	−	3.60698i	0.141954	−	0.241001i
$225$		0			0
$226$	−15.8814	−	14.3499i	−1.05642	−	0.954539i
$227$	13.8323	+	13.8323i	0.918082	+	0.918082i	0.996890	−	0.0788077i	$-0.0251113\pi$
$227$	13.8323	+	13.8323i	0.918082	+	0.918082i	−0.0788077	+	0.996890i	$0.525111\pi$
$228$		0			0
$229$	−11.3025	+	11.3025i	−0.746890	+	0.746890i	−0.973894	−	0.227004i	$-0.927107\pi$
$229$	−11.3025	+	11.3025i	−0.746890	+	0.746890i	0.227004	+	0.973894i	$0.427107\pi$
$230$	0.390086	+	7.69983i	0.0257215	+	0.507712i
$231$		0			0
$232$	10.4390	−	1.59751i	0.685351	−	0.104882i
$233$			0.638284i			0.0418154i	0.999781	+	0.0209077i	$0.00665561\pi$
$233$			0.638284i			0.0418154i	−0.999781	+	0.0209077i	$0.993344\pi$
$234$		0			0
$235$	5.76791	−	5.76791i	0.376257	−	0.376257i
$236$	−8.41048	−	6.85931i	−0.547475	−	0.446503i
$237$		0			0
$238$	2.06204	−	2.28212i	0.133662	−	0.147928i
$239$	−27.2255			−1.76107			−0.880534	−	0.473983i	$-0.842816\pi$
$239$	−27.2255			−1.76107			−0.880534	+	0.473983i	$0.842816\pi$
$240$		0			0
$241$	−14.0821			−0.907106			−0.453553	−	0.891229i	$-0.649844\pi$
$241$	−14.0821			−0.907106			−0.453553	+	0.891229i	$0.649844\pi$
$242$	17.4557	−	19.3187i	1.12209	−	1.24186i
$243$		0			0
$244$	8.71823	−	10.6898i	0.558128	−	0.684343i
$245$	4.56252	−	4.56252i	0.291488	−	0.291488i
$246$		0			0
$247$			33.3162i			2.11986i
$248$	9.96019	−	13.5595i	0.632473	−	0.861028i
$249$		0			0
$250$	−0.0715547	−	1.41240i	−0.00452551	−	0.0893282i
$251$	−1.61761	+	1.61761i	−0.102103	+	0.102103i	−0.756313	−	0.654210i	$-0.773001\pi$
$251$	−1.61761	+	1.61761i	−0.102103	+	0.102103i	0.654210	+	0.756313i	$0.273001\pi$
$252$		0			0
$253$	20.9055	+	20.9055i	1.31432	+	1.31432i
$254$	9.38663	+	8.48140i	0.588969	+	0.532170i
$255$		0			0
$256$	14.7060	−	6.30352i	0.919123	−	0.393970i
$257$	−4.53176			−0.282683			−0.141342	−	0.989961i	$-0.545142\pi$
$257$	−4.53176			−0.282683			−0.141342	+	0.989961i	$0.545142\pi$
$258$		0			0
$259$	−0.354729	−	0.354729i	−0.0220418	−	0.0220418i
$260$	0.947067	+	9.32299i	0.0587346	+	0.578187i
$261$		0			0
$262$	−0.975289	−	19.2510i	−0.0602536	−	1.18933i
$263$			8.25620i			0.509099i	0.967060	+	0.254550i	$0.0819272\pi$
$263$			8.25620i			0.509099i	−0.967060	+	0.254550i	$0.918073\pi$
$264$		0			0
$265$		−	7.14527i		−	0.438931i
$266$	−7.43194	+	0.376515i	−0.455682	+	0.0230856i
$267$		0			0
$268$	7.13662	−	8.75050i	0.435939	−	0.534522i
$269$	14.8352	+	14.8352i	0.904520	+	0.904520i	0.995823	−	0.0913029i	$-0.0291031\pi$
$269$	14.8352	+	14.8352i	0.904520	+	0.904520i	−0.0913029	+	0.995823i	$0.529103\pi$
$270$		0			0
$271$	32.0786			1.94864			0.974319	−	0.225172i	$-0.0722944\pi$
$271$	32.0786			1.94864			0.974319	+	0.225172i	$0.0722944\pi$
$272$	11.5156	−	2.36399i	0.698235	−	0.143338i
$273$		0			0
$274$	6.56272	−	7.26316i	0.396468	−	0.438784i
$275$	−3.83476	−	3.83476i	−0.231245	−	0.231245i
$276$		0			0
$277$	−14.6755	+	14.6755i	−0.881763	+	0.881763i	−0.993714	−	0.111951i	$-0.964290\pi$
$277$	−14.6755	+	14.6755i	−0.881763	+	0.881763i	0.111951	+	0.993714i	$0.464290\pi$
$278$	12.9912	−	0.658156i	0.779161	−	0.0394736i
$279$		0			0
$280$	−2.06900	+	0.316626i	−0.123647	+	0.0189220i
$281$		−	24.6456i		−	1.47023i	−0.677942	−	0.735116i	$-0.737128\pi$
$281$		−	24.6456i		−	1.47023i	0.677942	−	0.735116i	$-0.262872\pi$
$282$		0			0
$283$	−0.116449	+	0.116449i	−0.00692219	+	0.00692219i	−0.710559	−	0.703637i	$-0.751558\pi$
$283$	−0.116449	+	0.116449i	−0.00692219	+	0.00692219i	0.703637	+	0.710559i	$0.251558\pi$
$284$	−7.07047	+	0.718248i	−0.419555	+	0.0426202i
$285$		0			0
$286$	26.6633	+	24.0920i	1.57664	+	1.42459i
$287$	7.54214			0.445198
$288$		0			0
$289$	−8.36268			−0.491923
$290$	−3.91783	−	3.54000i	−0.230063	−	0.207876i
$291$		0			0
$292$	22.2167	−	2.25686i	1.30013	−	0.132073i
$293$	−21.5697	+	21.5697i	−1.26012	+	1.26012i	−0.309079	+	0.951036i	$0.600021\pi$
$293$	−21.5697	+	21.5697i	−1.26012	+	1.26012i	−0.951036	+	0.309079i	$0.899979\pi$
$294$		0			0
$295$			5.42647i			0.315941i
$296$	−0.290050	−	1.89534i	−0.0168588	−	0.110164i
$297$		0			0
$298$	11.4861	−	0.581907i	0.665374	−	0.0337090i
$299$	−18.0619	+	18.0619i	−1.04454	+	1.04454i
$300$		0			0
$301$	−3.65368	−	3.65368i	−0.210595	−	0.210595i
$302$	0.176144	−	0.194944i	0.0101359	−	0.0112177i
$303$		0			0
$304$	−23.7450	−	15.6564i	−1.36187	−	0.897959i
$305$	−6.89708			−0.394926
$306$		0			0
$307$	11.7544	+	11.7544i	0.670856	+	0.670856i	0.957913	−	0.287057i	$-0.0926770\pi$
$307$	11.7544	+	11.7544i	0.670856	+	0.670856i	−0.287057	+	0.957913i	$0.592677\pi$
$308$	−5.07294	+	6.22013i	−0.289057	+	0.354425i
$309$		0			0
$310$	−8.40149	+	0.425634i	−0.477173	+	0.0241744i
$311$		−	15.8798i		−	0.900462i	−0.892912	−	0.450231i	$-0.851342\pi$
$311$		−	15.8798i		−	0.900462i	0.892912	−	0.450231i	$-0.148658\pi$
$312$		0			0
$313$		−	32.5435i		−	1.83947i	−0.392542	−	0.919734i	$-0.628404\pi$
$313$		−	32.5435i		−	1.83947i	0.392542	−	0.919734i	$-0.371596\pi$
$314$	−1.20134	−	23.7129i	−0.0677953	−	1.33820i
$315$		0			0
$316$	2.17846	+	21.4449i	0.122548	+	1.20637i
$317$	−13.8078	−	13.8078i	−0.775523	−	0.775523i	0.203543	−	0.979066i	$-0.434754\pi$
$317$	−13.8078	−	13.8078i	−0.775523	−	0.775523i	−0.979066	+	0.203543i	$0.934754\pi$
$318$		0			0
$319$	−20.2485			−1.13370
$320$	−7.08971	−	3.70620i	−0.396327	−	0.207183i
$321$		0			0
$322$	−4.23323	−	3.82499i	−0.235909	−	0.213158i
$323$	−14.7766	−	14.7766i	−0.822194	−	0.822194i
$324$		0			0
$325$	3.31314	−	3.31314i	0.183780	−	0.183780i
$326$	1.15172	+	22.7335i	0.0637877	+	1.25909i
$327$		0			0
$328$	23.2325	+	17.0656i	1.28280	+	0.942289i
$329$			6.03638i			0.332796i
$330$		0			0
$331$	−5.85148	+	5.85148i	−0.321627	+	0.321627i	−0.849391	−	0.527764i	$-0.823030\pi$
$331$	−5.85148	+	5.85148i	−0.321627	+	0.321627i	0.527764	+	0.849391i	$0.323030\pi$
$332$	8.24102	−	10.1047i	0.452285	−	0.554565i
$333$		0			0
$334$	−12.2236	+	13.5282i	−0.668844	+	0.740230i
$335$	−5.64585			−0.308466
$336$		0			0
$337$	−19.3223			−1.05255			−0.526276	−	0.850314i	$-0.676412\pi$
$337$	−19.3223			−1.05255			−0.526276	+	0.850314i	$0.676412\pi$
$338$	−8.48927	+	9.39533i	−0.461755	+	0.511039i
$339$		0			0
$340$	−4.55505	−	3.71495i	−0.247032	−	0.201471i
$341$	−22.8106	+	22.8106i	−1.23526	+	1.23526i
$342$		0			0
$343$			9.95501i			0.537520i
$344$	−2.98750	−	19.5219i	−0.161075	−	1.05255i
$345$		0			0
$346$	1.22468	+	24.1736i	0.0658390	+	1.29958i
$347$	−6.92151	+	6.92151i	−0.371566	+	0.371566i	−0.868047	−	0.496481i	$-0.834625\pi$
$347$	−6.92151	+	6.92151i	−0.371566	+	0.371566i	0.496481	+	0.868047i	$0.334625\pi$
$348$		0			0
$349$	13.2497	+	13.2497i	0.709241	+	0.709241i	0.966376	−	0.257135i	$-0.0827784\pi$
$349$	13.2497	+	13.2497i	0.709241	+	0.709241i	−0.257135	+	0.966376i	$0.582778\pi$
$350$	0.776514	+	0.701629i	0.0415064	+	0.0375036i
$351$		0			0
$352$	−29.7008	+	7.68175i	−1.58306	+	0.409439i
$353$	21.8789			1.16450			0.582249	−	0.813010i	$-0.302173\pi$
$353$	21.8789			1.16450			0.582249	+	0.813010i	$0.302173\pi$
$354$		0			0
$355$	2.51265	+	2.51265i	0.133358	+	0.133358i
$356$	5.22263	−	0.530537i	0.276799	−	0.0281184i
$357$		0			0
$358$	−1.57414	−	31.0717i	−0.0831961	−	1.64219i
$359$			6.94782i			0.366692i	0.983048	+	0.183346i	$0.0586928\pi$
$359$			6.94782i			0.366692i	−0.983048	+	0.183346i	$0.941307\pi$
$360$		0			0
$361$			31.5595i			1.66102i
$362$	21.1669	−	1.07235i	1.11251	−	0.0563615i
$363$		0			0
$364$	−5.37404	−	4.38289i	−0.281676	−	0.229726i
$365$	−7.89522	−	7.89522i	−0.413254	−	0.413254i
$366$		0			0
$367$	17.0448			0.889730			0.444865	−	0.895598i	$-0.353252\pi$
$367$	17.0448			0.889730			0.444865	+	0.895598i	$0.353252\pi$
$368$	−4.38510	−	21.3609i	−0.228589	−	1.11351i
$369$		0			0
$370$	−0.642737	+	0.711337i	−0.0334143	+	0.0369807i
$371$	3.73892	+	3.73892i	0.194115	+	0.194115i
$372$		0			0
$373$	−14.3704	+	14.3704i	−0.744071	+	0.744071i	−0.973359	−	0.229287i	$-0.926360\pi$
$373$	−14.3704	+	14.3704i	−0.744071	+	0.744071i	0.229287	+	0.973359i	$0.426360\pi$
$374$	−22.5113	+	1.14046i	−1.16403	+	0.0589719i
$375$		0			0
$376$	−13.6585	+	18.5943i	−0.704384	+	0.958926i
$377$		−	17.4942i		−	0.900996i
$378$		0			0
$379$	2.97499	−	2.97499i	0.152815	−	0.152815i	−0.626559	−	0.779374i	$-0.715537\pi$
$379$	2.97499	−	2.97499i	0.152815	−	0.152815i	0.779374	+	0.626559i	$0.215537\pi$
$380$	1.43723	+	14.1482i	0.0737286	+	0.725788i
$381$		0			0
$382$	−9.28056	−	8.38557i	−0.474835	−	0.429043i
$383$	20.4810			1.04653			0.523266	−	0.852170i	$-0.324714\pi$
$383$	20.4810			1.04653			0.523266	+	0.852170i	$0.324714\pi$
$384$		0			0
$385$	4.01325			0.204534
$386$	14.7654	+	13.3415i	0.751539	+	0.679062i
$387$		0			0
$388$	0.339263	+	3.33973i	0.0172235	+	0.169549i
$389$	−11.8703	+	11.8703i	−0.601848	+	0.601848i	−0.940803	−	0.338955i	$-0.889927\pi$
$389$	−11.8703	+	11.8703i	−0.601848	+	0.601848i	0.338955	+	0.940803i	$0.389927\pi$
$390$		0			0
$391$		−	16.0218i		−	0.810259i
$392$	−10.8041	+	14.7084i	−0.545690	+	0.742885i
$393$		0			0
$394$	−16.2837	+	0.824960i	−0.820361	+	0.0415609i
$395$	7.62092	−	7.62092i	0.383450	−	0.383450i
$396$		0			0
$397$	19.1282	+	19.1282i	0.960019	+	0.960019i	0.999231	−	0.0392118i	$-0.0124847\pi$
$397$	19.1282	+	19.1282i	0.960019	+	0.960019i	−0.0392118	+	0.999231i	$0.512485\pi$
$398$	−10.7580	+	11.9062i	−0.539249	+	0.596803i
$399$		0			0
$400$	0.804372	+	3.91829i	0.0402186	+	0.195914i
$401$	16.0874			0.803368			0.401684	−	0.915778i	$-0.368425\pi$
$401$	16.0874			0.803368			0.401684	+	0.915778i	$0.368425\pi$
$402$		0			0
$403$	−19.7078	−	19.7078i	−0.981714	−	0.981714i
$404$	−14.2946	−	11.6582i	−0.711185	−	0.580019i
$405$		0			0
$406$	3.90248	−	0.197706i	0.193677	−	0.00981198i
$407$			3.67640i			0.182232i
$408$		0			0
$409$			23.4524i			1.15964i	0.814743	+	0.579822i	$0.196878\pi$
$409$			23.4524i			1.15964i	−0.814743	+	0.579822i	$0.803122\pi$
$410$	−0.729272	−	14.3949i	−0.0360162	−	0.710916i
$411$		0			0
$412$	0.601739	−	0.0611271i	0.0296456	−	0.00301152i
$413$	−2.83952	−	2.83952i	−0.139724	−	0.139724i
$414$		0			0
$415$	−6.51956			−0.320032
$416$	−6.63684	−	25.6607i	−0.325398	−	1.25812i
$417$		0			0
$418$	40.4633	+	36.5611i	1.97912	+	1.78826i
$419$	14.1654	+	14.1654i	0.692027	+	0.692027i	0.962678	−	0.270651i	$-0.0872388\pi$
$419$	14.1654	+	14.1654i	0.692027	+	0.692027i	−0.270651	+	0.962678i	$0.587239\pi$
$420$		0			0
$421$	21.2978	−	21.2978i	1.03799	−	1.03799i	0.0387434	−	0.999249i	$-0.487665\pi$
$421$	21.2978	−	21.2978i	1.03799	−	1.03799i	0.999249	−	0.0387434i	$-0.0123355\pi$
$422$	−1.58283	−	31.2432i	−0.0770511	−	1.52089i
$423$		0			0
$424$	3.05719	+	19.9773i	0.148470	+	0.970184i
$425$			2.93893i			0.142559i
$426$		0			0
$427$	3.60905	−	3.60905i	0.174654	−	0.174654i
$428$	2.63197	+	2.14655i	0.127221	+	0.103757i
$429$		0			0
$430$	−6.62014	+	7.32671i	−0.319252	+	0.353326i
$431$	21.0148			1.01225			0.506123	−	0.862462i	$-0.331078\pi$
$431$	21.0148			1.01225			0.506123	+	0.862462i	$0.331078\pi$
$432$		0			0
$433$	16.2253			0.779738			0.389869	−	0.920870i	$-0.372520\pi$
$433$	16.2253			0.779738			0.389869	+	0.920870i	$0.372520\pi$
$434$	4.17355	−	4.61899i	0.200337	−	0.221719i
$435$		0			0
$436$	12.5133	−	15.3430i	0.599278	−	0.734799i
$437$	−27.4100	+	27.4100i	−1.31120	+	1.31120i
$438$		0			0
$439$		−	3.33967i		−	0.159394i	−0.996819	−	0.0796970i	$-0.974605\pi$
$439$		−	3.33967i		−	0.159394i	0.996819	−	0.0796970i	$-0.0253953\pi$
$440$	12.3623	+	9.08078i	0.589348	+	0.432909i
$441$		0			0
$442$	−0.985330	−	19.4492i	−0.0468674	−	0.925105i
$443$	−13.4671	+	13.4671i	−0.639841	+	0.639841i	−0.950516	−	0.310675i	$-0.899445\pi$
$443$	−13.4671	+	13.4671i	−0.639841	+	0.639841i	0.310675	+	0.950516i	$0.399445\pi$
$444$		0			0
$445$	−1.85598	−	1.85598i	−0.0879820	−	0.0879820i
$446$	−10.7841	−	9.74415i	−0.510644	−	0.461399i
$447$		0			0
$448$	5.64921	−	1.77050i	0.266900	−	0.0836482i
$449$	−19.2995			−0.910799			−0.455400	−	0.890287i	$-0.650504\pi$
$449$	−19.2995			−0.910799			−0.455400	+	0.890287i	$0.650504\pi$
$450$		0			0
$451$	−39.0832	−	39.0832i	−1.84036	−	1.84036i
$452$	−3.05921	−	30.1151i	−0.143893	−	1.41649i
$453$		0			0
$454$	1.39974	+	27.6292i	0.0656931	+	1.29670i
$455$			3.46735i			0.162552i
$456$		0			0
$457$			21.0222i			0.983377i	0.870771	+	0.491688i	$0.163620\pi$
$457$			21.0222i			0.983377i	−0.870771	+	0.491688i	$0.836380\pi$
$458$	−22.5760	+	1.14374i	−1.05491	+	0.0534434i
$459$		0			0
$460$	−6.89106	+	8.44941i	−0.321297	+	0.393956i
$461$	23.3056	+	23.3056i	1.08545	+	1.08545i	0.995990	+	0.0894616i	$0.0285146\pi$
$461$	23.3056	+	23.3056i	1.08545	+	1.08545i	0.0894616	+	0.995990i	$0.471485\pi$
$462$		0			0
$463$	−1.65187			−0.0767687			−0.0383844	−	0.999263i	$-0.512221\pi$
$463$	−1.65187			−0.0767687			−0.0383844	+	0.999263i	$0.512221\pi$
$464$	12.4684	+	8.22112i	0.578831	+	0.381656i
$465$		0			0
$466$	−0.605171	+	0.669762i	−0.0280340	+	0.0310261i
$467$	14.4723	+	14.4723i	0.669699	+	0.669699i	0.957646	−	0.287948i	$-0.0929729\pi$
$467$	14.4723	+	14.4723i	0.669699	+	0.669699i	−0.287948	+	0.957646i	$0.592973\pi$
$468$		0			0
$469$	2.95432	−	2.95432i	0.136418	−	0.136418i
$470$	11.5211	−	0.583676i	0.531427	−	0.0269230i
$471$		0			0
$472$	−2.32178	−	15.1717i	−0.106869	−	0.698336i
$473$			37.8666i			1.74111i
$474$		0			0
$475$	5.02789	−	5.02789i	0.230696	−	0.230696i
$476$	4.32746	−	0.439601i	0.198349	−	0.0201491i
$477$		0			0
$478$	−28.5681	−	25.8131i	−1.30667	−	1.18066i
$479$	−6.07727			−0.277678			−0.138839	−	0.990315i	$-0.544337\pi$
$479$	−6.07727			−0.277678			−0.138839	+	0.990315i	$0.544337\pi$
$480$		0			0
$481$	−3.17632			−0.144828
$482$	−14.7765	−	13.3515i	−0.673053	−	0.608145i
$483$		0			0
$484$	36.6331	−	3.72134i	1.66514	−	0.169152i
$485$	1.18685	−	1.18685i	0.0538921	−	0.0538921i
$486$		0			0
$487$		−	10.1863i		−	0.461586i	−0.973003	−	0.230793i	$-0.925868\pi$
$487$		−	10.1863i		−	0.461586i	0.973003	−	0.230793i	$-0.0741320\pi$
$488$	19.2834	−	2.95100i	0.872918	−	0.133586i
$489$		0			0
$490$	9.11334	−	0.461697i	0.411699	−	0.0208574i
$491$	−8.75035	+	8.75035i	−0.394898	+	0.394898i	−0.876429	−	0.481531i	$-0.840081\pi$
$491$	−8.75035	+	8.75035i	−0.394898	+	0.394898i	0.481531	+	0.876429i	$0.340081\pi$
$492$		0			0
$493$	7.75914	+	7.75914i	0.349454	+	0.349454i
$494$	−31.5879	+	34.9592i	−1.42120	+	1.57289i
$495$		0			0
$496$	23.3074	−	4.78470i	1.04653	−	0.214840i
$497$	−2.62961			−0.117954
$498$		0			0
$499$	−23.8260	−	23.8260i	−1.06660	−	1.06660i	−0.997618	−	0.0689808i	$-0.978025\pi$
$499$	−23.8260	−	23.8260i	−1.06660	−	1.06660i	−0.0689808	−	0.997618i	$-0.521975\pi$
$500$	1.26405	−	1.54990i	0.0565299	−	0.0693136i
$501$		0			0
$502$	−3.23108	+	0.163692i	−0.144210	+	0.00730592i
$503$		−	9.42267i		−	0.420136i	−0.977687	−	0.210068i	$-0.932631\pi$
$503$		−	9.42267i		−	0.420136i	0.977687	−	0.210068i	$-0.0673685\pi$
$504$		0			0
$505$			9.22295i			0.410416i
$506$	2.11551	+	41.7575i	0.0940457	+	1.85635i
$507$		0			0
$508$	1.80813	+	17.7993i	0.0802228	+	0.789718i
$509$	16.3129	+	16.3129i	0.723055	+	0.723055i	0.969226	−	0.246172i	$-0.0791727\pi$
$509$	16.3129	+	16.3129i	0.723055	+	0.723055i	−0.246172	+	0.969226i	$0.579173\pi$
$510$		0			0
$511$	8.26270			0.365520
$512$	21.4077	+	7.32867i	0.946097	+	0.323885i
$513$		0			0
$514$	−4.75525	−	4.29666i	−0.209745	−	0.189518i
$515$	−0.213842	−	0.213842i	−0.00942299	−	0.00942299i
$516$		0			0
$517$	31.2804	−	31.2804i	1.37571	−	1.37571i
$518$	−0.0358963	−	0.708550i	−0.00157719	−	0.0311319i
$519$		0			0
$520$	−7.84556	+	10.6807i	−0.344051	+	0.468380i
$521$		−	10.7287i		−	0.470033i	−0.971991	−	0.235016i	$-0.924486\pi$
$521$		−	10.7287i		−	0.470033i	0.971991	−	0.235016i	$-0.0755144\pi$
$522$		0			0
$523$	−16.3868	+	16.3868i	−0.716546	+	0.716546i	−0.967896	−	0.251351i	$-0.919125\pi$
$523$	−16.3868	+	16.3868i	−0.716546	+	0.716546i	0.251351	+	0.967896i	$0.419125\pi$
$524$	17.2289	−	21.1251i	0.752650	−	0.922855i
$525$		0			0
$526$	−7.82789	+	8.66337i	−0.341312	+	0.377741i
$527$	17.4819			0.761521
$528$		0			0
$529$	−6.71979			−0.292165
$530$	6.77459	−	7.49765i	0.294269	−	0.325677i
$531$		0			0
$532$	−8.15544	−	6.65131i	−0.353583	−	0.288371i
$533$	33.7669	−	33.7669i	1.46261	−	1.46261i
$534$		0			0
$535$		−	1.69816i		−	0.0734177i
$536$	15.7851	−	2.41565i	0.681813	−	0.104340i
$537$		0			0
$538$	1.50123	+	29.6325i	0.0647227	+	1.27755i
$539$	24.7433	−	24.7433i	1.06577	−	1.06577i
$540$		0			0
$541$	11.4471	+	11.4471i	0.492148	+	0.492148i	0.908983	−	0.416834i	$-0.136860\pi$
$541$	11.4471	+	11.4471i	0.492148	+	0.492148i	−0.416834	+	0.908983i	$0.636860\pi$
$542$	33.6606	+	30.4145i	1.44585	+	1.30641i
$543$		0			0
$544$	14.3248	+	8.43760i	0.614172	+	0.361759i
$545$	−9.89939			−0.424043
$546$		0			0
$547$	9.67749	+	9.67749i	0.413780	+	0.413780i	0.883053	−	0.469273i	$-0.155484\pi$
$547$	9.67749	+	9.67749i	0.413780	+	0.413780i	−0.469273	+	0.883053i	$0.655484\pi$
$548$	13.7727	−	1.39909i	0.588342	−	0.0597662i
$549$		0			0
$550$	−0.388053	−	7.65970i	−0.0165466	−	0.326611i
$551$		−	26.5485i		−	1.13100i
$552$		0			0
$553$			7.97564i			0.339159i
$554$	−29.3133	+	1.48506i	−1.24540	+	0.0630942i
$555$		0			0
$556$	14.2559	+	11.6266i	0.604585	+	0.493079i
$557$	−10.0484	−	10.0484i	−0.425762	−	0.425762i	0.461420	−	0.887182i	$-0.347340\pi$
$557$	−10.0484	−	10.0484i	−0.425762	−	0.425762i	−0.887182	+	0.461420i	$0.847340\pi$
$558$		0			0
$559$	−32.7158			−1.38373
$560$	−2.47124	−	1.62943i	−0.104429	−	0.0688558i
$561$		0			0
$562$	23.3670	−	25.8610i	0.985678	−	1.09088i
$563$	−8.44120	−	8.44120i	−0.355754	−	0.355754i	0.506491	−	0.862245i	$-0.330942\pi$
$563$	−8.44120	−	8.44120i	−0.355754	−	0.355754i	−0.862245	+	0.506491i	$0.830942\pi$
$564$		0			0
$565$	−10.7021	+	10.7021i	−0.450240	+	0.450240i
$566$	−0.232600	+	0.0117839i	−0.00977692	+	0.000495315i
$567$		0			0
$568$	−8.10015	−	5.95001i	−0.339875	−	0.249657i
$569$			7.27300i			0.304900i	0.988311	+	0.152450i	$0.0487163\pi$
$569$			7.27300i			0.304900i	−0.988311	+	0.152450i	$0.951284\pi$
$570$		0			0
$571$	−5.28045	+	5.28045i	−0.220980	+	0.220980i	−0.808911	−	0.587931i	$-0.799943\pi$
$571$	−5.28045	+	5.28045i	−0.220980	+	0.220980i	0.587931	+	0.808911i	$0.299943\pi$
$572$	5.13611	+	50.5602i	0.214752	+	2.11403i
$573$		0			0
$574$	7.91409	+	7.15087i	0.330328	+	0.298472i
$575$	5.45159			0.227347
$576$		0			0
$577$	27.0550			1.12631			0.563157	−	0.826350i	$-0.309587\pi$
$577$	27.0550			1.12631			0.563157	+	0.826350i	$0.309587\pi$
$578$	−8.77510	−	7.92885i	−0.364996	−	0.329797i
$579$		0			0
$580$	−0.754684	−	7.42916i	−0.0313366	−	0.308479i
$581$	3.41150	−	3.41150i	0.141533	−	0.141533i
$582$		0			0
$583$		−	38.7500i		−	1.60486i
$584$	25.4521	+	18.6960i	1.05322	+	0.773646i
$585$		0			0
$586$	−43.0841	+	2.18272i	−1.77979	+	0.0901671i
$587$	6.62135	−	6.62135i	0.273292	−	0.273292i	−0.557132	−	0.830424i	$-0.688098\pi$
$587$	6.62135	−	6.62135i	0.273292	−	0.273292i	0.830424	+	0.557132i	$0.188098\pi$
$588$		0			0
$589$	−29.9078	−	29.9078i	−1.23233	−	1.23233i
$590$	−5.14496	+	5.69408i	−0.211815	+	0.234422i
$591$		0			0
$592$	1.49266	−	2.26381i	0.0613480	−	0.0930422i
$593$	9.02017			0.370414			0.185207	−	0.982700i	$-0.440704\pi$
$593$	9.02017			0.370414			0.185207	+	0.982700i	$0.440704\pi$
$594$		0			0
$595$	−1.53786	−	1.53786i	−0.0630462	−	0.0630462i
$596$	12.6043	+	10.2797i	0.516292	+	0.421071i
$597$		0			0
$598$	−36.0774	+	1.82774i	−1.47532	+	0.0747420i
$599$			7.68375i			0.313950i	0.987603	+	0.156975i	$0.0501742\pi$
$599$			7.68375i			0.313950i	−0.987603	+	0.156975i	$0.949826\pi$
$600$		0			0
$601$		−	31.7822i		−	1.29642i	−0.761460	−	0.648212i	$-0.775517\pi$
$601$		−	31.7822i		−	1.29642i	0.761460	−	0.648212i	$-0.224483\pi$
$602$	−0.369729	−	7.29801i	−0.0150690	−	0.297445i
$603$		0			0
$604$	0.369661	−	0.0375517i	0.0150413	−	0.00152796i
$605$	−13.0184	−	13.0184i	−0.529273	−	0.529273i
$606$		0			0
$607$	25.7518			1.04524			0.522618	−	0.852567i	$-0.324956\pi$
$607$	25.7518			1.04524			0.522618	+	0.852567i	$0.324956\pi$
$608$	−10.0718	−	38.9418i	−0.408466	−	1.57930i
$609$		0			0
$610$	−7.23722	−	6.53928i	−0.293026	−	0.264768i
$611$	27.0255	+	27.0255i	1.09333	+	1.09333i
$612$		0			0
$613$	−10.4967	+	10.4967i	−0.423956	+	0.423956i	−0.886563	−	0.462607i	$-0.846914\pi$
$613$	−10.4967	+	10.4967i	−0.423956	+	0.423956i	0.462607	+	0.886563i	$0.346914\pi$
$614$	1.18947	+	23.4786i	0.0480029	+	0.947519i
$615$		0			0
$616$	−11.2206	+	1.71712i	−0.452089	+	0.0691847i
$617$		−	29.2461i		−	1.17740i	−0.808351	−	0.588701i	$-0.799640\pi$
$617$		−	29.2461i		−	1.17740i	0.808351	−	0.588701i	$-0.200360\pi$
$618$		0			0
$619$	21.9641	−	21.9641i	0.882814	−	0.882814i	−0.111006	−	0.993820i	$-0.535407\pi$
$619$	21.9641	−	21.9641i	0.882814	−	0.882814i	0.993820	+	0.111006i	$0.0354073\pi$
$620$	−9.21937	−	7.51902i	−0.370259	−	0.301971i
$621$		0			0
$622$	15.0560	−	16.6629i	0.603691	−	0.668123i
$623$	1.94237			0.0778194
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	30.8552	−	34.1484i	1.23322	−	1.36485i
$627$		0			0
$628$	21.2222	−	26.0213i	0.846856	−	1.03836i
$629$	1.40878	−	1.40878i	0.0561718	−	0.0561718i
$630$		0			0
$631$			6.46257i			0.257271i	0.991692	+	0.128635i	$0.0410597\pi$
$631$			6.46257i			0.257271i	−0.991692	+	0.128635i	$0.958940\pi$
$632$	−18.0465	+	24.5679i	−0.717850	+	0.977257i
$633$		0			0
$634$	−1.39726	−	27.5802i	−0.0554923	−	1.09535i
$635$	6.32540	−	6.32540i	0.251016	−	0.251016i
$636$		0			0
$637$	21.3776	+	21.3776i	0.847011	+	0.847011i
$638$	−21.2471	−	19.1980i	−0.841179	−	0.760058i
$639$		0			0
$640$	−3.92542	−	10.6109i	−0.155166	−	0.419432i
$641$	5.56318			0.219732			0.109866	−	0.993946i	$-0.464958\pi$
$641$	5.56318			0.219732			0.109866	+	0.993946i	$0.464958\pi$
$642$		0			0
$643$	2.91681	+	2.91681i	0.115028	+	0.115028i	0.762278	−	0.647250i	$-0.224081\pi$
$643$	2.91681	+	2.91681i	0.115028	+	0.115028i	−0.647250	+	0.762278i	$0.724081\pi$
$644$	−0.815440	−	8.02724i	−0.0321328	−	0.316318i
$645$		0			0
$646$	−1.49530	−	29.5154i	−0.0588318	−	1.16127i
$647$		−	22.9740i		−	0.903201i	−0.892220	−	0.451601i	$-0.850853\pi$
$647$		−	22.9740i		−	0.903201i	0.892220	−	0.451601i	$-0.149147\pi$
$648$		0			0
$649$			29.4287i			1.15518i
$650$	6.61779	−	0.335268i	0.259571	−	0.0131503i
$651$		0			0
$652$	−20.3456	+	24.9466i	−0.796796	+	0.976984i
$653$	−25.9783	−	25.9783i	−1.01661	−	1.01661i	−0.999860	−	0.0167495i	$-0.994668\pi$
$653$	−25.9783	−	25.9783i	−1.01661	−	1.01661i	−0.0167495	−	0.999860i	$-0.505332\pi$
$654$		0			0
$655$	−13.6300			−0.532568
$656$	8.19801	+	39.9345i	0.320079	+	1.55918i
$657$		0			0
$658$	−5.72323	+	6.33407i	−0.223115	+	0.246928i
$659$	−28.1599	−	28.1599i	−1.09695	−	1.09695i	−0.994765	−	0.102189i	$-0.967415\pi$
$659$	−28.1599	−	28.1599i	−1.09695	−	1.09695i	−0.102189	−	0.994765i	$-0.532585\pi$
$660$		0			0
$661$	−24.8805	+	24.8805i	−0.967741	+	0.967741i	−0.999496	−	0.0317548i	$-0.989890\pi$
$661$	−24.8805	+	24.8805i	−0.967741	+	0.967741i	0.0317548	+	0.999496i	$0.489890\pi$
$662$	−11.6880	+	0.592133i	−0.454266	+	0.0230139i
$663$		0			0
$664$	18.2279	−	2.78947i	0.707379	−	0.108253i
$665$			5.26192i			0.204048i
$666$		0			0
$667$	14.3929	−	14.3929i	0.557294	−	0.557294i
$668$	−25.6528	+	2.60591i	−0.992536	+	0.100826i
$669$		0			0
$670$	−5.92429	−	5.35296i	−0.228875	−	0.206803i
$671$	−37.4041			−1.44397
$672$		0			0
$673$	−4.37152			−0.168510			−0.0842548	−	0.996444i	$-0.526851\pi$
$673$	−4.37152			−0.168510			−0.0842548	+	0.996444i	$0.526851\pi$
$674$	−20.2752	−	18.3199i	−0.780970	−	0.705655i
$675$		0			0
$676$	−17.8158	+	1.80981i	−0.685225	+	0.0696079i
$677$	7.19018	−	7.19018i	0.276341	−	0.276341i	−0.555305	−	0.831646i	$-0.687399\pi$
$677$	7.19018	−	7.19018i	0.276341	−	0.276341i	0.831646	+	0.555305i	$0.187399\pi$
$678$		0			0
$679$			1.24209i			0.0476671i
$680$	−1.25746	−	8.21689i	−0.0482213	−	0.315103i
$681$		0			0
$682$	−45.5627	+	2.30828i	−1.74469	+	0.0883888i
$683$	−27.3182	+	27.3182i	−1.04530	+	1.04530i	−0.0463792	+	0.998924i	$0.514768\pi$
$683$	−27.3182	+	27.3182i	−1.04530	+	1.04530i	−0.998924	+	0.0463792i	$0.985232\pi$
$684$		0			0
$685$	−4.89445	−	4.89445i	−0.187007	−	0.187007i
$686$	−9.43857	+	10.4460i	−0.360366	+	0.398828i
$687$		0			0
$688$	15.3743	−	23.3171i	0.586139	−	0.888957i
$689$	33.4791			1.27545
$690$		0			0
$691$	10.7859	+	10.7859i	0.410316	+	0.410316i	0.881849	−	0.471533i	$-0.156299\pi$
$691$	10.7859	+	10.7859i	0.410316	+	0.410316i	−0.471533	+	0.881849i	$0.656299\pi$
$692$	−21.6345	+	26.5269i	−0.822420	+	1.00840i
$693$		0			0
$694$	−13.8253	+	0.700412i	−0.524801	+	0.0265873i
$695$		−	9.19795i		−	0.348898i
$696$		0			0
$697$			29.9530i			1.13455i
$698$	1.34079	+	26.4655i	0.0507495	+	1.00173i
$699$		0			0
$700$	0.149579	+	1.47246i	0.00565354	+	0.0556538i
$701$	7.34496	+	7.34496i	0.277415	+	0.277415i	0.832076	−	0.554661i	$-0.187152\pi$
$701$	7.34496	+	7.34496i	0.277415	+	0.277415i	−0.554661	+	0.832076i	$0.687152\pi$
$702$		0			0
$703$	−4.82026			−0.181799
$704$	−38.4487	−	20.0994i	−1.44909	−	0.757524i
$705$		0			0
$706$	22.9579	+	20.7439i	0.864033	+	0.780707i
$707$	−4.82612	−	4.82612i	−0.181505	−	0.181505i
$708$		0			0
$709$	36.8251	−	36.8251i	1.38299	−	1.38299i	0.543740	−	0.839254i	$-0.317008\pi$
$709$	36.8251	−	36.8251i	1.38299	−	1.38299i	0.839254	−	0.543740i	$-0.182992\pi$
$710$	0.254265	+	5.01887i	0.00954238	+	0.188355i
$711$		0			0
$712$	5.98321	+	4.39500i	0.224230	+	0.164709i
$713$		−	32.4281i		−	1.21444i
$714$		0			0
$715$	17.9677	−	17.9677i	0.671955	−	0.671955i
$716$	27.8080	−	34.0965i	1.03923	−	1.27425i
$717$		0			0
$718$	−6.58738	+	7.29046i	−0.245839	+	0.272077i
$719$	−15.1515			−0.565055			−0.282527	−	0.959259i	$-0.591173\pi$
$719$	−15.1515			−0.565055			−0.282527	+	0.959259i	$0.591173\pi$
$720$		0			0
$721$	0.223795			0.00833456
$722$	−29.9222	+	33.1158i	−1.11359	+	1.23244i
$723$		0			0
$724$	23.2275	+	18.9436i	0.863242	+	0.704032i
$725$	−2.64012	+	2.64012i	−0.0980517	+	0.0980517i
$726$		0			0
$727$		−	18.4900i		−	0.685756i	−0.939380	−	0.342878i	$-0.888598\pi$
$727$		−	18.4900i		−	0.685756i	0.939380	−	0.342878i	$-0.111402\pi$
$728$	−1.48355	−	9.69428i	−0.0549840	−	0.359294i
$729$		0			0
$730$	−0.798945	−	15.7702i	−0.0295703	−	0.583682i
$731$	14.5103	−	14.5103i	0.536684	−	0.536684i
$732$		0			0
$733$	−10.2992	−	10.2992i	−0.380409	−	0.380409i	0.490840	−	0.871250i	$-0.336690\pi$
$733$	−10.2992	−	10.2992i	−0.380409	−	0.380409i	−0.871250	+	0.490840i	$0.836690\pi$
$734$	17.8854	+	16.1605i	0.660161	+	0.596496i
$735$		0			0
$736$	15.6514	−	26.5719i	0.576917	−	0.979455i
$737$	−30.6184			−1.12784
$738$		0			0
$739$	25.4615	+	25.4615i	0.936618	+	0.936618i	0.998108	−	0.0614897i	$-0.0195851\pi$
$739$	25.4615	+	25.4615i	0.936618	+	0.936618i	−0.0614897	+	0.998108i	$0.519585\pi$
$740$	−1.34887	+	0.137024i	−0.0495854	+	0.00503709i
$741$		0			0
$742$	0.378355	+	7.46827i	0.0138899	+	0.274169i
$743$		−	46.0798i		−	1.69050i	−0.534368	−	0.845252i	$-0.679450\pi$
$743$		−	46.0798i		−	1.69050i	0.534368	−	0.845252i	$-0.320550\pi$
$744$		0			0
$745$		−	8.13234i		−	0.297946i
$746$	−28.7040	+	1.45419i	−1.05093	+	0.0532418i
$747$		0			0
$748$	−24.7028	−	20.1468i	−0.903224	−	0.736640i
$749$	0.888598	+	0.888598i	0.0324687	+	0.0324687i
$750$		0			0
$751$	−16.4699			−0.600997			−0.300498	−	0.953782i	$-0.597153\pi$
$751$	−16.4699			−0.600997			−0.300498	+	0.953782i	$0.597153\pi$
$752$	−31.9617	+	6.56131i	−1.16552	+	0.239266i
$753$		0			0
$754$	16.5866	−	18.3569i	0.604049	−	0.668520i
$755$	−0.131367	−	0.131367i	−0.00478095	−	0.00478095i
$756$		0			0
$757$	−21.4819	+	21.4819i	−0.780772	+	0.780772i	−0.979961	−	0.199189i	$-0.936169\pi$
$757$	−21.4819	+	21.4819i	−0.780772	+	0.780772i	0.199189	+	0.979961i	$0.436169\pi$
$758$	5.94235	−	0.301050i	0.215836	−	0.0109346i
$759$		0			0
$760$	−11.9061	+	16.2086i	−0.431881	+	0.587949i
$761$			10.1316i			0.367270i	0.982994	+	0.183635i	$0.0587865\pi$
$761$			10.1316i			0.367270i	−0.982994	+	0.183635i	$0.941214\pi$
$762$		0			0
$763$	5.18008	−	5.18008i	0.187531	−	0.187531i
$764$	−1.78770	−	17.5982i	−0.0646767	−	0.636681i
$765$		0			0
$766$	21.4911	+	19.4185i	0.776504	+	0.701619i
$767$	−25.4256			−0.918067
$768$		0			0
$769$	33.2758			1.19996			0.599979	−	0.800016i	$-0.295176\pi$
$769$	33.2758			1.19996			0.599979	+	0.800016i	$0.295176\pi$
$770$	4.21117	+	3.80505i	0.151760	+	0.137125i
$771$		0			0
$772$	2.84423	+	27.9988i	0.102366	+	1.00770i
$773$	−6.50648	+	6.50648i	−0.234022	+	0.234022i	−0.814369	−	0.580347i	$-0.802917\pi$
$773$	−6.50648	+	6.50648i	−0.234022	+	0.234022i	0.580347	+	0.814369i	$0.302917\pi$
$774$		0			0
$775$			5.94837i			0.213672i
$776$	−2.81048	+	3.82609i	−0.100890	+	0.137349i
$777$		0			0
$778$	−23.7102	+	1.20120i	−0.850052	+	0.0430651i
$779$	51.2434	−	51.2434i	1.83598	−	1.83598i
$780$		0			0
$781$	13.6266	+	13.6266i	0.487597	+	0.487597i
$782$	15.1907	−	16.8120i	0.543217	−	0.601195i
$783$		0			0
$784$	−25.2823	+	5.19011i	−0.902938	+	0.185361i
$785$	−16.7891			−0.599227
$786$		0			0
$787$	−25.9368	−	25.9368i	−0.924547	−	0.924547i	0.0727995	−	0.997347i	$-0.476807\pi$
$787$	−25.9368	−	25.9368i	−0.924547	−	0.924547i	−0.997347	+	0.0727995i	$0.976807\pi$
$788$	−17.8689	−	14.5733i	−0.636554	−	0.519153i
$789$		0			0
$790$	15.2223	−	0.771188i	0.541586	−	0.0274376i
$791$		−	11.2002i		−	0.398234i
$792$		0			0
$793$		−	32.3162i		−	1.14758i
$794$	1.93566	+	38.2075i	0.0686938	+	1.35593i
$795$		0			0
$796$	−22.5770	+	2.29347i	−0.800222	+	0.0812898i
$797$	1.54315	+	1.54315i	0.0546611	+	0.0546611i	0.733909	−	0.679248i	$-0.237694\pi$
$797$	1.54315	+	1.54315i	0.0546611	+	0.0546611i	−0.679248	+	0.733909i	$0.737694\pi$
$798$		0			0
$799$	−23.9730			−0.848105
$800$	−2.87098	+	4.87417i	−0.101504	+	0.172328i
$801$		0			0
$802$	16.8808	+	15.2529i	0.596082	+	0.538597i
$803$	−42.8171	−	42.8171i	−1.51098	−	1.51098i
$804$		0			0
$805$	−2.85266	+	2.85266i	−0.100543	+	0.100543i
$806$	−1.99430	−	39.3651i	−0.0702462	−	1.38658i
$807$		0			0
$808$	−3.94616	−	25.7863i	−0.138825	−	0.907157i
$809$			25.5155i			0.897076i	0.893764	+	0.448538i	$0.148055\pi$
$809$			25.5155i			0.897076i	−0.893764	+	0.448538i	$0.851945\pi$
$810$		0			0
$811$	10.6605	−	10.6605i	0.374342	−	0.374342i	−0.494714	−	0.869056i	$-0.664727\pi$
$811$	10.6605	−	10.6605i	0.374342	−	0.374342i	0.869056	+	0.494714i	$0.164727\pi$
$812$	4.28238	+	3.49257i	0.150282	+	0.122565i
$813$		0			0
$814$	−3.48568	+	3.85770i	−0.122173	+	0.135212i
$815$	16.0956			0.563805
$816$		0			0
$817$	−49.6483			−1.73697
$818$	−22.2357	+	24.6089i	−0.777453	+	0.860431i
$819$		0			0
$820$	12.8829	−	15.7963i	0.449892	−	0.551630i
$821$	34.9507	−	34.9507i	1.21979	−	1.21979i	0.252081	−	0.967706i	$-0.418885\pi$
$821$	34.9507	−	34.9507i	1.21979	−	1.21979i	0.967706	−	0.252081i	$-0.0811148\pi$
$822$		0			0
$823$		−	35.6125i		−	1.24137i	−0.784059	−	0.620686i	$-0.786854\pi$
$823$		−	35.6125i		−	1.24137i	0.784059	−	0.620686i	$-0.213146\pi$
$824$	0.689370	+	0.506381i	0.0240154	+	0.0176406i
$825$		0			0
$826$	−0.287341	−	5.67177i	−0.00999789	−	0.197346i
$827$	15.2133	−	15.2133i	0.529019	−	0.529019i	−0.391261	−	0.920280i	$-0.627961\pi$
$827$	15.2133	−	15.2133i	0.529019	−	0.529019i	0.920280	+	0.391261i	$0.127961\pi$
$828$		0			0
$829$	24.4188	+	24.4188i	0.848101	+	0.848101i	0.989896	−	0.141795i	$-0.0452874\pi$
$829$	24.4188	+	24.4188i	0.848101	+	0.848101i	−0.141795	+	0.989896i	$0.545287\pi$
$830$	−6.84107	−	6.18134i	−0.237457	−	0.214557i
$831$		0			0
$832$	17.3654	−	33.2187i	0.602036	−	1.15165i
$833$	−18.9631			−0.657032
$834$		0			0
$835$	9.11630	+	9.11630i	0.315483	+	0.315483i
$836$	7.79437	+	76.7282i	0.269574	+	2.65370i
$837$		0			0
$838$	1.43345	+	28.2946i	0.0495178	+	0.977420i
$839$			1.78206i			0.0615236i	0.999527	+	0.0307618i	$0.00979333\pi$
$839$			1.78206i			0.0615236i	−0.999527	+	0.0307618i	$0.990207\pi$
$840$		0			0
$841$		−	15.0595i		−	0.519293i
$842$	42.5411	−	2.15520i	1.46606	−	0.0742732i
$843$		0			0
$844$	27.9615	−	34.2847i	0.962474	−	1.18013i
$845$	6.33127	+	6.33127i	0.217802	+	0.217802i
$846$		0			0
$847$	13.6243			0.468138
$848$	−15.7330	+	23.8611i	−0.540272	+	0.819394i
$849$		0			0
$850$	−2.78647	+	3.08387i	−0.0955750	+	0.105776i
$851$	−2.61323	−	2.61323i	−0.0895802	−	0.0895802i
$852$		0			0
$853$	−20.1759	+	20.1759i	−0.690809	+	0.690809i	−0.962410	−	0.271601i	$-0.912447\pi$
$853$	−20.1759	+	20.1759i	−0.690809	+	0.690809i	0.271601	+	0.962410i	$0.412447\pi$
$854$	7.20886	−	0.365213i	0.246682	−	0.0124973i
$855$		0			0
$856$	0.726577	+	4.74784i	0.0248339	+	0.162278i
$857$			40.0844i			1.36926i	0.728893	+	0.684628i	$0.240035\pi$
$857$			40.0844i			1.36926i	−0.728893	+	0.684628i	$0.759965\pi$
$858$		0			0
$859$	−3.09121	+	3.09121i	−0.105471	+	0.105471i	−0.757873	−	0.652402i	$-0.773761\pi$
$859$	−3.09121	+	3.09121i	−0.105471	+	0.105471i	0.652402	+	0.757873i	$0.273761\pi$
$860$	−13.8932	+	1.41133i	−0.473756	+	0.0481260i
$861$		0			0
$862$	22.0511	+	19.9246i	0.751064	+	0.678633i
$863$	−13.8844			−0.472630			−0.236315	−	0.971676i	$-0.575940\pi$
$863$	−13.8844			−0.472630			−0.236315	+	0.971676i	$0.575940\pi$
$864$		0			0
$865$	17.1153			0.581936
$866$	17.0255	+	15.3836i	0.578549	+	0.522755i
$867$		0			0
$868$	8.75874	−	0.889748i	0.297291	−	0.0302000i
$869$	41.3296	−	41.3296i	1.40201	−	1.40201i
$870$		0			0
$871$		−	26.4536i		−	0.896345i
$872$	27.6775	−	4.23558i	0.937278	−	0.143435i
$873$		0			0
$874$	−54.7498	+	2.77372i	−1.85194	+	0.0938224i
$875$	0.523272	−	0.523272i	0.0176898	−	0.0176898i
$876$		0			0
$877$	−21.3550	−	21.3550i	−0.721107	−	0.721107i	0.247724	−	0.968831i	$-0.420317\pi$
$877$	−21.3550	−	21.3550i	−0.721107	−	0.721107i	−0.968831	+	0.247724i	$0.920317\pi$
$878$	3.16642	−	3.50437i	0.106861	−	0.118267i
$879$		0			0
$880$	4.36225	+	21.2496i	0.147051	+	0.716322i
$881$	25.1815			0.848387			0.424193	−	0.905572i	$-0.360558\pi$
$881$	25.1815			0.848387			0.424193	+	0.905572i	$0.360558\pi$
$882$		0			0
$883$	4.36865	+	4.36865i	0.147017	+	0.147017i	0.776784	−	0.629767i	$-0.216850\pi$
$883$	4.36865	+	4.36865i	0.147017	+	0.147017i	−0.629767	+	0.776784i	$0.716850\pi$
$884$	17.4063	−	21.3426i	0.585438	−	0.717829i
$885$		0			0
$886$	−26.8997	+	1.36278i	−0.903713	+	0.0457836i
$887$			36.7638i			1.23441i	0.786803	+	0.617204i	$0.211735\pi$
$887$			36.7638i			1.23441i	−0.786803	+	0.617204i	$0.788265\pi$
$888$		0			0
$889$			6.61982i			0.222022i
$890$	−0.187814	−	3.70721i	−0.00629552	−	0.124266i
$891$		0			0
$892$	−2.07733	−	20.4494i	−0.0695542	−	0.684696i
$893$	41.0129	+	41.0129i	1.37244	+	1.37244i
$894$		0			0
$895$	−21.9992			−0.735351
$896$	7.60645	+	3.49833i	0.254114	+	0.116871i
$897$		0			0
$898$	−20.2513	−	18.2983i	−0.675793	−	0.610622i
$899$	15.7044	+	15.7044i	0.523772	+	0.523772i
$900$		0			0
$901$	−14.8489	+	14.8489i	−0.494687	+	0.494687i
$902$	−3.95497	−	78.0663i	−0.131686	−	2.59932i
$903$		0			0
$904$	25.3427	−	34.5007i	0.842886	−	1.14748i
$905$		−	14.9864i		−	0.498166i
$906$		0			0
$907$	−24.5327	+	24.5327i	−0.814594	+	0.814594i	−0.985319	−	0.170725i	$-0.945389\pi$
$907$	−24.5327	+	24.5327i	−0.814594	+	0.814594i	0.170725	+	0.985319i	$0.445389\pi$
$908$	−24.7271	+	30.3189i	−0.820596	+	1.00617i
$909$		0			0
$910$	−3.28747	+	3.63834i	−0.108979	+	0.120610i
$911$	0.221626			0.00734279			0.00367139	−	0.999993i	$-0.498831\pi$
$911$	0.221626			0.00734279			0.00367139	+	0.999993i	$0.498831\pi$
$912$		0			0
$913$	−35.3567			−1.17014
$914$	−19.9316	+	22.0589i	−0.659279	+	0.729644i
$915$		0			0
$916$	−24.7738	−	20.2047i	−0.818549	−	0.667582i
$917$	7.13220	−	7.13220i	0.235526	−	0.235526i
$918$		0			0
$919$			22.8234i			0.752874i	0.926442	+	0.376437i	$0.122851\pi$
$919$			22.8234i			0.752874i	−0.926442	+	0.376437i	$0.877149\pi$
$920$	−15.2420	+	2.33253i	−0.502513	+	0.0769012i
$921$		0			0
$922$	2.35838	+	46.5516i	0.0776692	+	1.53309i
$923$	−11.7730	+	11.7730i	−0.387513	+	0.387513i
$924$		0			0
$925$	0.479352	+	0.479352i	0.0157610	+	0.0157610i
$926$	−1.73333	−	1.56617i	−0.0569607	−	0.0514676i
$927$		0			0
$928$	5.28866	+	20.4481i	0.173609	+	0.671243i
$929$	−12.9959			−0.426383			−0.213191	−	0.977010i	$-0.568386\pi$
$929$	−12.9959			−0.426383			−0.213191	+	0.977010i	$0.568386\pi$
$930$		0			0
$931$	32.4418	+	32.4418i	1.06324	+	1.06324i
$932$	−1.27003	+	0.129015i	−0.0416013	+	0.00422603i
$933$		0			0
$934$	1.46450	+	28.9075i	0.0479201	+	0.945884i
$935$			15.9383i			0.521239i
$936$		0			0
$937$		−	51.7244i		−	1.68976i	−0.534954	−	0.844881i	$-0.679671\pi$
$937$		−	51.7244i		−	1.68976i	0.534954	−	0.844881i	$-0.320329\pi$
$938$	5.90107	−	0.298958i	0.192677	−	0.00976133i
$939$		0			0
$940$	12.6426	+	10.3109i	0.412357	+	0.336305i
$941$	11.9700	+	11.9700i	0.390210	+	0.390210i	0.874762	−	0.484552i	$-0.161017\pi$
$941$	11.9700	+	11.9700i	0.390210	+	0.390210i	−0.484552	+	0.874762i	$0.661017\pi$
$942$		0			0
$943$	55.5616			1.80933
$944$	11.9484	−	18.1213i	0.388887	−	0.589798i
$945$		0			0
$946$	−35.9022	+	39.7340i	−1.16728	+	1.29186i
$947$	−3.97492	−	3.97492i	−0.129168	−	0.129168i	0.639567	−	0.768735i	$-0.279113\pi$
$947$	−3.97492	−	3.97492i	−0.129168	−	0.129168i	−0.768735	+	0.639567i	$0.779113\pi$
$948$		0			0
$949$	36.9929	−	36.9929i	1.20084	−	1.20084i
$950$	10.0429	−	0.508791i	0.325835	−	0.0165074i
$951$		0			0
$952$	4.95767	+	3.64168i	0.160679	+	0.118028i
$953$			13.1913i			0.427308i	0.976909	+	0.213654i	$0.0685365\pi$
$953$			13.1913i			0.427308i	−0.976909	+	0.213654i	$0.931463\pi$
$954$		0			0
$955$	−6.25393	+	6.25393i	−0.202372	+	0.202372i
$956$	−5.50303	−	54.1721i	−0.177981	−	1.75205i
$957$		0			0
$958$	−6.37698	−	5.76200i	−0.206031	−	0.186162i
$959$	5.12227			0.165407
$960$		0			0
$961$	4.38311			0.141391
$962$	−3.33296	−	3.01154i	−0.107459	−	0.0970958i
$963$		0			0
$964$	−2.84638	−	28.0199i	−0.0916757	−	0.902461i
$965$	9.95002	−	9.95002i	0.320302	−	0.320302i
$966$		0			0
$967$			5.07109i			0.163075i	0.996670	+	0.0815376i	$0.0259831\pi$
$967$			5.07109i			0.163075i	−0.996670	+	0.0815376i	$0.974017\pi$
$968$	41.9679	+	30.8278i	1.34890	+	0.990842i
$969$		0			0
$970$	2.37066	−	0.120102i	0.0761173	−	0.00385623i
$971$	−2.07041	+	2.07041i	−0.0664427	+	0.0664427i	−0.739547	−	0.673105i	$-0.764960\pi$
$971$	−2.07041	+	2.07041i	−0.0664427	+	0.0664427i	0.673105	+	0.739547i	$0.264960\pi$
$972$		0			0
$973$	4.81304	+	4.81304i	0.154299	+	0.154299i
$974$	9.65787	−	10.6887i	0.309458	−	0.342487i
$975$		0			0
$976$	23.0323	+	15.1865i	0.737246	+	0.486108i
$977$	6.93371			0.221829			0.110914	−	0.993830i	$-0.464622\pi$
$977$	6.93371			0.221829			0.110914	+	0.993830i	$0.464622\pi$
$978$		0			0
$979$	−10.0653	−	10.0653i	−0.321689	−	0.321689i
$980$	10.0005	+	8.15610i	0.319455	+	0.260537i
$981$		0			0
$982$	−17.4783	+	0.885479i	−0.557754	+	0.0282568i
$983$			49.6290i			1.58292i	0.611221	+	0.791460i	$0.290679\pi$
$983$			49.6290i			1.58292i	−0.611221	+	0.791460i	$0.709321\pi$
$984$		0			0
$985$			11.5291i			0.367347i
$986$	0.785175	+	15.4984i	0.0250051	+	0.493570i
$987$		0			0
$988$	−66.2913	+	6.73414i	−2.10901	+	0.214241i
$989$	−26.9160	−	26.9160i	−0.855880	−	0.855880i
$990$		0			0
$991$	47.6664			1.51417			0.757086	−	0.653315i	$-0.226622\pi$
$991$	47.6664			1.51417			0.757086	+	0.653315i	$0.226622\pi$
$992$	28.9933	+	17.0776i	0.920540	+	0.542215i
$993$		0			0
$994$	−2.75929	−	2.49319i	−0.0875193	−	0.0790791i
$995$	8.02327	+	8.02327i	0.254355	+	0.254355i
$996$		0			0
$997$	4.46020	−	4.46020i	0.141256	−	0.141256i	−0.632943	−	0.774199i	$-0.718153\pi$
$997$	4.46020	−	4.46020i	0.141256	−	0.141256i	0.774199	+	0.632943i	$0.218153\pi$
$998$	−2.41104	−	47.5910i	−0.0763201	−	1.50647i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.d.541.8		20
3.2	odd	2		240.2.s.c.61.3	✓	20
4.3	odd	2		2880.2.t.d.721.8		20
12.11	even	2		960.2.s.c.721.8		20
16.5	even	4	inner	720.2.t.d.181.8		20
16.11	odd	4		2880.2.t.d.2161.8		20
24.5	odd	2		1920.2.s.e.1441.8		20
24.11	even	2		1920.2.s.f.1441.3		20
48.5	odd	4		240.2.s.c.181.3	yes	20
48.11	even	4		960.2.s.c.241.8		20
48.29	odd	4		1920.2.s.e.481.8		20
48.35	even	4		1920.2.s.f.481.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.3	✓	20	3.2	odd	2
240.2.s.c.181.3	yes	20	48.5	odd	4
720.2.t.d.181.8		20	16.5	even	4	inner
720.2.t.d.541.8		20	1.1	even	1	trivial
960.2.s.c.241.8		20	48.11	even	4
960.2.s.c.721.8		20	12.11	even	2
1920.2.s.e.481.8		20	48.29	odd	4
1920.2.s.e.1441.8		20	24.5	odd	2
1920.2.s.f.481.3		20	48.35	even	4
1920.2.s.f.1441.3		20	24.11	even	2
2880.2.t.d.721.8		20	4.3	odd	2
2880.2.t.d.2161.8		20	16.11	odd	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04932 + 0.948122i) q^{2} +(0.202128 + 1.98976i) q^{4} +(0.707107 - 0.707107i) q^{5} +0.740019i q^{7} +(-1.67444 + 2.27953i) q^{8} +O(q^{10})\)	\(q+(1.04932 + 0.948122i) q^{2} +(0.202128 + 1.98976i) q^{4} +(0.707107 - 0.707107i) q^{5} +0.740019i q^{7} +(-1.67444 + 2.27953i) q^{8} +(1.41240 - 0.0715547i) q^{10} +(3.83476 - 3.83476i) q^{11} +(3.31314 + 3.31314i) q^{13} +(-0.701629 + 0.776514i) q^{14} +(-3.91829 + 0.804372i) q^{16} -2.93893 q^{17} +(5.02789 + 5.02789i) q^{19} +(1.54990 + 1.26405i) q^{20} +(7.65970 - 0.388053i) q^{22} +5.45159i q^{23} -1.00000i q^{25} +(0.335268 + 6.61779i) q^{26} +(-1.47246 + 0.149579i) q^{28} +(-2.64012 - 2.64012i) q^{29} -5.94837 q^{31} +(-4.87417 - 2.87098i) q^{32} +(-3.08387 - 2.78647i) q^{34} +(0.523272 + 0.523272i) q^{35} +(-0.479352 + 0.479352i) q^{37} +(0.508791 + 10.0429i) q^{38} +(0.427863 + 2.79588i) q^{40} -10.1918i q^{41} +(-4.93728 + 4.93728i) q^{43} +(8.40537 + 6.85514i) q^{44} +(-5.16877 + 5.72044i) q^{46} +8.15706 q^{47} +6.45237 q^{49} +(0.948122 - 1.04932i) q^{50} +(-5.92267 + 7.26203i) q^{52} +(5.05247 - 5.05247i) q^{53} -5.42317i q^{55} +(-1.68689 - 1.23912i) q^{56} +(-0.267163 - 5.27348i) q^{58} +(-3.83709 + 3.83709i) q^{59} +(-4.87697 - 4.87697i) q^{61} +(-6.24172 - 5.63978i) q^{62} +(-2.39250 - 7.63387i) q^{64} +4.68548 q^{65} +(-3.99222 - 3.99222i) q^{67} +(-0.594040 - 5.84777i) q^{68} +(0.0529518 + 1.04520i) q^{70} +3.55343i q^{71} -11.1655i q^{73} +(-0.957475 + 0.0485073i) q^{74} +(-8.98803 + 11.0206i) q^{76} +(2.83780 + 2.83780i) q^{77} +10.7776 q^{79} +(-2.20187 + 3.33943i) q^{80} +(9.66309 - 10.6944i) q^{82} +(-4.61002 - 4.61002i) q^{83} +(-2.07814 + 2.07814i) q^{85} +(-9.86192 + 0.499621i) q^{86} +(2.32037 + 15.1625i) q^{88} -2.62476i q^{89} +(-2.45179 + 2.45179i) q^{91} +(-10.8473 + 1.10192i) q^{92} +(8.55934 + 7.73389i) q^{94} +7.11052 q^{95} +1.67846 q^{97} +(6.77058 + 6.11764i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 - 12 * q^8	\( 20 q + 4 q^{4} - 12 q^{8} - 8 q^{11} + 4 q^{14} - 20 q^{16} + 24 q^{17} - 4 q^{19} + 8 q^{20} + 8 q^{22} - 28 q^{26} - 8 q^{28} - 16 q^{29} + 40 q^{32} - 44 q^{34} + 16 q^{37} + 8 q^{38} + 12 q^{40} - 8 q^{43} - 24 q^{44} - 12 q^{46} - 52 q^{49} - 4 q^{50} - 56 q^{52} + 16 q^{53} - 64 q^{56} + 72 q^{58} + 16 q^{59} - 4 q^{61} + 44 q^{62} - 56 q^{64} - 8 q^{67} + 32 q^{68} + 20 q^{70} - 60 q^{74} + 28 q^{76} + 40 q^{77} + 56 q^{79} + 16 q^{80} - 24 q^{82} + 48 q^{83} + 4 q^{85} - 64 q^{86} + 40 q^{88} - 8 q^{91} - 88 q^{92} - 20 q^{94} + 56 q^{97} + 48 q^{98}+O(q^{100}) \) 20 * q + 4 * q^4 - 12 * q^8 - 8 * q^11 + 4 * q^14 - 20 * q^16 + 24 * q^17 - 4 * q^19 + 8 * q^20 + 8 * q^22 - 28 * q^26 - 8 * q^28 - 16 * q^29 + 40 * q^32 - 44 * q^34 + 16 * q^37 + 8 * q^38 + 12 * q^40 - 8 * q^43 - 24 * q^44 - 12 * q^46 - 52 * q^49 - 4 * q^50 - 56 * q^52 + 16 * q^53 - 64 * q^56 + 72 * q^58 + 16 * q^59 - 4 * q^61 + 44 * q^62 - 56 * q^64 - 8 * q^67 + 32 * q^68 + 20 * q^70 - 60 * q^74 + 28 * q^76 + 40 * q^77 + 56 * q^79 + 16 * q^80 - 24 * q^82 + 48 * q^83 + 4 * q^85 - 64 * q^86 + 40 * q^88 - 8 * q^91 - 88 * q^92 - 20 * q^94 + 56 * q^97 + 48 * q^98

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