LMFDB - Embedded newform 360.2.w.c.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	360.307
Dual form			360.2.w.c.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 + 1.39680i) q^{2} +(-1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(1.90211 - 1.90211i) q^{7} +(-1.28408 - 2.52015i) q^{8} +O(q^{10})$	\(q+(0.221232 + 1.39680i) q^{2} +(-1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(1.90211 - 1.90211i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(2.91695 + 1.22123i) q^{10} +3.23607 q^{11} +(-0.726543 - 0.726543i) q^{13} +(3.07768 + 2.23607i) q^{14} +(3.23607 - 2.35114i) q^{16} +(1.00000 + 1.00000i) q^{17} -2.00000i q^{19} +(-1.06050 + 4.34458i) q^{20} +(0.715921 + 4.52015i) q^{22} +(4.25325 + 4.25325i) q^{23} +(-2.23607 - 4.47214i) q^{25} +(0.854102 - 1.17557i) q^{26} +(-2.44246 + 4.79360i) q^{28} -6.15537 q^{29} +8.50651i q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.17557 + 1.61803i) q^{34} +(-1.38197 - 5.85410i) q^{35} +(0.726543 - 0.726543i) q^{37} +(2.79360 - 0.442463i) q^{38} +(-6.30313 - 0.520147i) q^{40} -5.70820 q^{41} +(4.61803 - 4.61803i) q^{43} +(-6.15537 + 2.00000i) q^{44} +(-5.00000 + 6.88191i) q^{46} +(3.35520 - 3.35520i) q^{47} -0.236068i q^{49} +(5.75200 - 4.11272i) q^{50} +(1.83099 + 0.932938i) q^{52} +(-3.07768 - 3.07768i) q^{53} +(3.80423 - 6.15537i) q^{55} +(-7.23607 - 2.35114i) q^{56} +(-1.36176 - 8.59783i) q^{58} +0.472136i q^{59} -0.898056i q^{61} +(-11.8819 + 1.88191i) q^{62} +(-4.70228 + 6.47214i) q^{64} +(-2.23607 + 0.527864i) q^{65} +(-4.61803 - 4.61803i) q^{67} +(-2.52015 - 1.28408i) q^{68} +(7.87129 - 3.22545i) q^{70} +11.4127i q^{71} +(-4.70820 + 4.70820i) q^{73} +(1.17557 + 0.854102i) q^{74} +(1.23607 + 3.80423i) q^{76} +(6.15537 - 6.15537i) q^{77} -2.90617 q^{79} +(-0.667910 - 8.91930i) q^{80} +(-1.26284 - 7.97323i) q^{82} +(6.61803 - 6.61803i) q^{83} +(3.07768 - 0.726543i) q^{85} +(7.47214 + 5.42882i) q^{86} +(-4.15537 - 8.15537i) q^{88} -2.47214i q^{89} -2.76393 q^{91} +(-10.7188 - 5.46151i) q^{92} +(5.42882 + 3.94427i) q^{94} +(-3.80423 - 2.35114i) q^{95} +(4.23607 + 4.23607i) q^{97} +(0.329740 - 0.0522257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^8	$ 8 q + 2 q^{2} - 4 q^{8} - 10 q^{10} + 8 q^{11} + 8 q^{16} + 8 q^{17} + 12 q^{22} - 20 q^{26} - 20 q^{28} + 32 q^{32} - 20 q^{35} + 4 q^{38} - 20 q^{40} + 8 q^{41} + 28 q^{43} - 40 q^{46} + 10 q^{50} + 20 q^{52} - 40 q^{56} + 20 q^{58} - 40 q^{62} - 28 q^{67} + 4 q^{68} + 20 q^{70} + 16 q^{73} - 8 q^{76} - 28 q^{82} + 44 q^{83} + 24 q^{86} + 16 q^{88} - 40 q^{91} - 20 q^{92} + 16 q^{97} + 6 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^8 - 10 * q^10 + 8 * q^11 + 8 * q^16 + 8 * q^17 + 12 * q^22 - 20 * q^26 - 20 * q^28 + 32 * q^32 - 20 * q^35 + 4 * q^38 - 20 * q^40 + 8 * q^41 + 28 * q^43 - 40 * q^46 + 10 * q^50 + 20 * q^52 - 40 * q^56 + 20 * q^58 - 40 * q^62 - 28 * q^67 + 4 * q^68 + 20 * q^70 + 16 * q^73 - 8 * q^76 - 28 * q^82 + 44 * q^83 + 24 * q^86 + 16 * q^88 - 40 * q^91 - 20 * q^92 + 16 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$3$		0			0
$3$		0			0
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$	1.17557	−	1.90211i	0.525731	−	0.850651i
$5$	1.17557	−	1.90211i	0.525731	−	0.850651i
$6$		0			0
$7$	1.90211	−	1.90211i	0.718931	−	0.718931i	−0.249455	−	0.968386i	$-0.580252\pi$
$7$	1.90211	−	1.90211i	0.718931	−	0.718931i	0.968386	+	0.249455i	$0.0802515\pi$
$8$	−1.28408	−	2.52015i	−0.453990	−	0.891007i
$9$		0			0
$10$	2.91695	+	1.22123i	0.922420	+	0.386187i
$11$	3.23607			0.975711			0.487856	−	0.872924i	$-0.337779\pi$
$11$	3.23607			0.975711			0.487856	+	0.872924i	$0.337779\pi$
$12$		0			0
$13$	−0.726543	−	0.726543i	−0.201507	−	0.201507i	0.599139	−	0.800645i	$-0.295510\pi$
$13$	−0.726543	−	0.726543i	−0.201507	−	0.201507i	−0.800645	+	0.599139i	$0.795510\pi$
$14$	3.07768	+	2.23607i	0.822546	+	0.597614i
$15$		0			0
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$		0			0
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$	−1.06050	+	4.34458i	−0.237134	+	0.971477i
$21$		0			0
$22$	0.715921	+	4.52015i	0.152635	+	0.963699i
$23$	4.25325	+	4.25325i	0.886865	+	0.886865i	0.994221	−	0.107356i	$-0.0342384\pi$
$23$	4.25325	+	4.25325i	0.886865	+	0.886865i	−0.107356	+	0.994221i	$0.534238\pi$
$24$		0			0
$25$	−2.23607	−	4.47214i	−0.447214	−	0.894427i
$26$	0.854102	−	1.17557i	0.167503	−	0.230548i
$27$		0			0
$28$	−2.44246	+	4.79360i	−0.461582	+	0.905906i
$29$	−6.15537			−1.14302			−0.571511	−	0.820594i	$-0.693643\pi$
$29$	−6.15537			−1.14302			−0.571511	+	0.820594i	$0.693643\pi$
$30$		0			0
$31$			8.50651i			1.52781i	0.645326	+	0.763907i	$0.276721\pi$
$31$			8.50651i			1.52781i	−0.645326	+	0.763907i	$0.723279\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		0			0
$34$	−1.17557	+	1.61803i	−0.201609	+	0.277491i
$35$	−1.38197	−	5.85410i	−0.233595	−	0.989524i
$36$		0			0
$37$	0.726543	−	0.726543i	0.119443	−	0.119443i	−0.644859	−	0.764302i	$-0.723084\pi$
$37$	0.726543	−	0.726543i	0.119443	−	0.119443i	0.764302	+	0.644859i	$0.223084\pi$
$38$	2.79360	−	0.442463i	0.453182	−	0.0717771i
$39$		0			0
$40$	−6.30313	−	0.520147i	−0.996612	−	0.0822425i
$41$	−5.70820			−0.891472			−0.445736	−	0.895165i	$-0.647058\pi$
$41$	−5.70820			−0.891472			−0.445736	+	0.895165i	$0.647058\pi$
$42$		0			0
$43$	4.61803	−	4.61803i	0.704244	−	0.704244i	−0.261075	−	0.965319i	$-0.584077\pi$
$43$	4.61803	−	4.61803i	0.704244	−	0.704244i	0.965319	+	0.261075i	$0.0840770\pi$
$44$	−6.15537	+	2.00000i	−0.927957	+	0.301511i
$45$		0			0
$46$	−5.00000	+	6.88191i	−0.737210	+	1.01468i
$47$	3.35520	−	3.35520i	0.489406	−	0.489406i	−0.418713	−	0.908119i	$-0.637519\pi$
$47$	3.35520	−	3.35520i	0.489406	−	0.489406i	0.908119	+	0.418713i	$0.137519\pi$
$48$		0			0
$49$		−	0.236068i		−	0.0337240i
$50$	5.75200	−	4.11272i	0.813456	−	0.581627i
$51$		0			0
$52$	1.83099	+	0.932938i	0.253913	+	0.129375i
$53$	−3.07768	−	3.07768i	−0.422752	−	0.422752i	0.463398	−	0.886150i	$-0.346630\pi$
$53$	−3.07768	−	3.07768i	−0.422752	−	0.422752i	−0.886150	+	0.463398i	$0.846630\pi$
$54$		0			0
$55$	3.80423	−	6.15537i	0.512962	−	0.829990i
$56$	−7.23607	−	2.35114i	−0.966960	−	0.314184i
$57$		0			0
$58$	−1.36176	−	8.59783i	−0.178808	−	1.12895i
$59$			0.472136i			0.0614669i	0.999528	+	0.0307334i	$0.00978430\pi$
$59$			0.472136i			0.0614669i	−0.999528	+	0.0307334i	$0.990216\pi$
$60$		0			0
$61$		−	0.898056i		−	0.114984i	−0.998346	−	0.0574921i	$-0.981690\pi$
$61$		−	0.898056i		−	0.114984i	0.998346	−	0.0574921i	$-0.0183104\pi$
$62$	−11.8819	+	1.88191i	−1.50900	+	0.239003i
$63$		0			0
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$	−2.23607	+	0.527864i	−0.277350	+	0.0654735i
$66$		0			0
$67$	−4.61803	−	4.61803i	−0.564183	−	0.564183i	0.366310	−	0.930493i	$-0.380621\pi$
$67$	−4.61803	−	4.61803i	−0.564183	−	0.564183i	−0.930493	+	0.366310i	$0.880621\pi$
$68$	−2.52015	−	1.28408i	−0.305613	−	0.155717i
$69$		0			0
$70$	7.87129	−	3.22545i	0.940799	−	0.385515i
$71$			11.4127i			1.35444i	0.735783	+	0.677218i	$0.236815\pi$
$71$			11.4127i			1.35444i	−0.735783	+	0.677218i	$0.763185\pi$
$72$		0			0
$73$	−4.70820	+	4.70820i	−0.551054	+	0.551054i	−0.926745	−	0.375691i	$-0.877405\pi$
$73$	−4.70820	+	4.70820i	−0.551054	+	0.551054i	0.375691	+	0.926745i	$0.377405\pi$
$74$	1.17557	+	0.854102i	0.136657	+	0.0992873i
$75$		0			0
$76$	1.23607	+	3.80423i	0.141787	+	0.436375i
$77$	6.15537	−	6.15537i	0.701469	−	0.701469i
$78$		0			0
$79$	−2.90617			−0.326970			−0.163485	−	0.986546i	$-0.552273\pi$
$79$	−2.90617			−0.326970			−0.163485	+	0.986546i	$0.552273\pi$
$80$	−0.667910	−	8.91930i	−0.0746746	−	0.997208i
$81$		0			0
$82$	−1.26284	−	7.97323i	−0.139457	−	0.880496i
$83$	6.61803	−	6.61803i	0.726424	−	0.726424i	−0.243482	−	0.969905i	$-0.578290\pi$
$83$	6.61803	−	6.61803i	0.726424	−	0.726424i	0.969905	+	0.243482i	$0.0782896\pi$
$84$		0			0
$85$	3.07768	−	0.726543i	0.333822	−	0.0788046i
$86$	7.47214	+	5.42882i	0.805741	+	0.585405i
$87$		0			0
$88$	−4.15537	−	8.15537i	−0.442964	−	0.869365i
$89$		−	2.47214i		−	0.262046i	−0.991379	−	0.131023i	$-0.958174\pi$
$89$		−	2.47214i		−	0.262046i	0.991379	−	0.131023i	$-0.0418262\pi$
$90$		0			0
$91$	−2.76393			−0.289739
$92$	−10.7188	−	5.46151i	−1.11751	−	0.569402i
$93$		0			0
$94$	5.42882	+	3.94427i	0.559940	+	0.406821i
$95$	−3.80423	−	2.35114i	−0.390305	−	0.241222i
$96$		0			0
$97$	4.23607	+	4.23607i	0.430108	+	0.430108i	0.888665	−	0.458557i	$-0.151634\pi$
$97$	4.23607	+	4.23607i	0.430108	+	0.430108i	−0.458557	+	0.888665i	$0.651634\pi$
$98$	0.329740	−	0.0522257i	0.0333088	−	0.00527560i
$99$		0			0
$100$	7.01719	+	7.12454i	0.701719	+	0.712454i
$101$			2.90617i			0.289175i	0.989492	+	0.144587i	$0.0461855\pi$
$101$			2.90617i			0.289175i	−0.989492	+	0.144587i	$0.953815\pi$
$102$		0			0
$103$	3.35520	+	3.35520i	0.330597	+	0.330597i	0.852813	−	0.522216i	$-0.174894\pi$
$103$	3.35520	+	3.35520i	0.330597	+	0.330597i	−0.522216	+	0.852813i	$0.674894\pi$
$104$	−0.898056	+	2.76393i	−0.0880616	+	0.271026i
$105$		0			0
$106$	3.61803	−	4.97980i	0.351415	−	0.483681i
$107$	−0.909830	−	0.909830i	−0.0879566	−	0.0879566i	0.661760	−	0.749716i	$-0.269810\pi$
$107$	−0.909830	−	0.909830i	−0.0879566	−	0.0879566i	−0.749716	+	0.661760i	$0.769810\pi$
$108$		0			0
$109$	−14.6619			−1.40435			−0.702176	−	0.712003i	$-0.747788\pi$
$109$	−14.6619			−1.40435			−0.702176	+	0.712003i	$0.747788\pi$
$110$	9.43945	+	3.95199i	0.900016	+	0.376807i
$111$		0			0
$112$	1.68323	−	10.6275i	0.159050	−	1.00420i
$113$	−8.70820	+	8.70820i	−0.819199	+	0.819199i	−0.985992	−	0.166793i	$-0.946659\pi$
$113$	−8.70820	+	8.70820i	−0.819199	+	0.819199i	0.166793	+	0.985992i	$0.446659\pi$
$114$		0			0
$115$	13.0902	−	3.09017i	1.22066	−	0.288160i
$116$	11.7082	−	3.80423i	1.08708	−	0.353214i
$117$		0			0
$118$	−0.659481	+	0.104451i	−0.0607101	+	0.00961554i
$119$	3.80423			0.348733
$120$		0			0
$121$	−0.527864			−0.0479876
$122$	1.25441	−	0.198678i	0.113569	−	0.0179875i
$123$		0			0
$124$	−5.25731	−	16.1803i	−0.472120	−	1.45304i
$125$	−11.1352	−	1.00406i	−0.995959	−	0.0898056i
$126$		0			0
$127$	−2.80017	+	2.80017i	−0.248475	+	0.248475i	−0.820344	−	0.571870i	$-0.806218\pi$
$127$	−2.80017	+	2.80017i	−0.248475	+	0.248475i	0.571870	+	0.820344i	$0.306218\pi$
$128$	−10.0806	−	5.13632i	−0.891007	−	0.453990i
$129$		0			0
$130$	−1.23201	−	3.00656i	−0.108055	−	0.263693i
$131$	−13.7082			−1.19769			−0.598846	−	0.800864i	$-0.704374\pi$
$131$	−13.7082			−1.19769			−0.598846	+	0.800864i	$0.704374\pi$
$132$		0			0
$133$	−3.80423	−	3.80423i	−0.329868	−	0.329868i
$134$	5.42882	−	7.47214i	0.468979	−	0.645494i
$135$		0			0
$136$	1.23607	−	3.80423i	0.105992	−	0.326210i
$137$	5.47214	+	5.47214i	0.467516	+	0.467516i	0.901109	−	0.433593i	$-0.142754\pi$
$137$	5.47214	+	5.47214i	0.467516	+	0.467516i	−0.433593	+	0.901109i	$0.642754\pi$
$138$		0			0
$139$			21.4164i			1.81652i	0.418411	+	0.908258i	$0.362587\pi$
$139$			21.4164i			1.81652i	−0.418411	+	0.908258i	$0.637413\pi$
$140$	6.24669	+	10.2811i	0.527942	+	0.868908i
$141$		0			0
$142$	−15.9413	+	2.52485i	−1.33776	+	0.211880i
$143$	−2.35114	−	2.35114i	−0.196612	−	0.196612i
$144$		0			0
$145$	−7.23607	+	11.7082i	−0.600923	+	0.972313i
$146$	−7.61803	−	5.53483i	−0.630473	−	0.458065i
$147$		0			0
$148$	−0.932938	+	1.83099i	−0.0766870	+	0.150507i
$149$	−12.8658			−1.05400			−0.527002	−	0.849864i	$-0.676684\pi$
$149$	−12.8658			−1.05400			−0.527002	+	0.849864i	$0.676684\pi$
$150$		0			0
$151$			6.71040i			0.546084i	0.962002	+	0.273042i	$0.0880298\pi$
$151$			6.71040i			0.546084i	−0.962002	+	0.273042i	$0.911970\pi$
$152$	−5.04029	+	2.56816i	−0.408822	+	0.208305i
$153$		0			0
$154$	9.95959	+	7.23607i	0.802567	+	0.583099i
$155$	16.1803	+	10.0000i	1.29964	+	0.803219i
$156$		0			0
$157$	13.9353	−	13.9353i	1.11216	−	1.11216i	0.119303	−	0.992858i	$-0.461934\pi$
$157$	13.9353	−	13.9353i	1.11216	−	1.11216i	0.992858	−	0.119303i	$-0.0380659\pi$
$158$	−0.642937	−	4.05934i	−0.0511493	−	0.322944i
$159$		0			0
$160$	12.3107	−	2.90617i	0.973249	−	0.229753i
$161$	16.1803			1.27519
$162$		0			0
$163$	−13.8541	+	13.8541i	−1.08514	+	1.08514i	−0.0891157	+	0.996021i	$0.528404\pi$
$163$	−13.8541	+	13.8541i	−1.08514	+	1.08514i	−0.996021	+	0.0891157i	$0.971596\pi$
$164$	10.8576	−	3.52786i	0.847840	−	0.275480i
$165$		0			0
$166$	10.7082	+	7.77997i	0.831118	+	0.603842i
$167$	8.05748	−	8.05748i	0.623507	−	0.623507i	−0.322920	−	0.946426i	$-0.604664\pi$
$167$	8.05748	−	8.05748i	0.623507	−	0.623507i	0.946426	+	0.322920i	$0.104664\pi$
$168$		0			0
$169$		−	11.9443i		−	0.918790i
$170$	1.69572	+	4.13818i	0.130056	+	0.317384i
$171$		0			0
$172$	−5.92992	+	11.6381i	−0.452152	+	0.887399i
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.994208	+	0.107474i	$0.0342762\pi$
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.107474	+	0.994208i	$0.465724\pi$
$174$		0			0
$175$	−12.7598	−	4.25325i	−0.964547	−	0.321516i
$176$	10.4721	−	7.60845i	0.789367	−	0.573509i
$177$		0			0
$178$	3.45309	−	0.546915i	0.258820	−	0.0409930i
$179$			7.52786i			0.562659i	0.959611	+	0.281329i	$0.0907754\pi$
$179$			7.52786i			0.562659i	−0.959611	+	0.281329i	$0.909225\pi$
$180$		0			0
$181$			15.2169i			1.13106i	0.824726	+	0.565532i	$0.191329\pi$
$181$			15.2169i			1.13106i	−0.824726	+	0.565532i	$0.808671\pi$
$182$	−0.611469	−	3.86067i	−0.0453251	−	0.286172i
$183$		0			0
$184$	5.25731	−	16.1803i	0.387574	−	1.19283i
$185$	−0.527864	−	2.23607i	−0.0388093	−	0.164399i
$186$		0			0
$187$	3.23607	+	3.23607i	0.236645	+	0.236645i
$188$	−4.30834	+	8.45559i	−0.314218	+	0.616687i
$189$		0			0
$190$	2.44246	−	5.83390i	0.177195	−	0.423235i
$191$			13.2088i			0.955755i	0.878427	+	0.477877i	$0.158594\pi$
$191$			13.2088i			0.955755i	−0.878427	+	0.477877i	$0.841406\pi$
$192$		0			0
$193$	1.47214	−	1.47214i	0.105967	−	0.105967i	−0.652136	−	0.758102i	$-0.726127\pi$
$193$	1.47214	−	1.47214i	0.105967	−	0.105967i	0.758102	+	0.652136i	$0.226127\pi$
$194$	−4.97980	+	6.85410i	−0.357529	+	0.492096i
$195$		0			0
$196$	0.145898	+	0.449028i	0.0104213	+	0.0320734i
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	−0.297038	−	0.954866i	$-0.595999\pi$
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	0.954866	+	0.297038i	$0.0959988\pi$
$198$		0			0
$199$	21.7153			1.53936			0.769678	−	0.638432i	$-0.220417\pi$
$199$	21.7153			1.53936			0.769678	+	0.638432i	$0.220417\pi$
$200$	−8.39915	+	11.3778i	−0.593910	+	0.804532i
$201$		0			0
$202$	−4.05934	+	0.642937i	−0.285615	+	0.0452369i
$203$	−11.7082	+	11.7082i	−0.821755	+	0.821755i
$204$		0			0
$205$	−6.71040	+	10.8576i	−0.468674	+	0.758331i
$206$	−3.94427	+	5.42882i	−0.274810	+	0.378244i
$207$		0			0
$208$	−4.05934	−	0.642937i	−0.281465	−	0.0445797i
$209$		−	6.47214i		−	0.447687i
$210$		0			0
$211$	2.29180			0.157774			0.0788869	−	0.996884i	$-0.474863\pi$
$211$	2.29180			0.157774			0.0788869	+	0.996884i	$0.474863\pi$
$212$	7.75621	+	3.95199i	0.532699	+	0.271424i
$213$		0			0
$214$	1.06957	−	1.47214i	0.0731143	−	0.100633i
$215$	−3.35520	−	14.2128i	−0.228823	−	0.969308i
$216$		0			0
$217$	16.1803	+	16.1803i	1.09839	+	1.09839i
$218$	−3.24367	−	20.4797i	−0.219689	−	1.38706i
$219$		0			0
$220$	−3.43184	+	14.0593i	−0.231375	+	0.947881i
$221$		−	1.45309i		−	0.0977451i
$222$		0			0
$223$	−14.2128	−	14.2128i	−0.951763	−	0.951763i	0.0471263	−	0.998889i	$-0.484994\pi$
$223$	−14.2128	−	14.2128i	−0.951763	−	0.951763i	−0.998889	+	0.0471263i	$0.984994\pi$
$224$	15.2169			1.01672
$225$		0			0
$226$	−14.0902	−	10.2371i	−0.937264	−	0.680962i
$227$	9.38197	+	9.38197i	0.622703	+	0.622703i	0.946222	−	0.323519i	$-0.104866\pi$
$227$	9.38197	+	9.38197i	0.622703	+	0.622703i	−0.323519	+	0.946222i	$0.604866\pi$
$228$		0			0
$229$	−7.95148			−0.525449			−0.262724	−	0.964871i	$-0.584621\pi$
$229$	−7.95148			−0.525449			−0.262724	+	0.964871i	$0.584621\pi$
$230$	7.21232	+	17.6007i	0.475566	+	1.16056i
$231$		0			0
$232$	7.90398	+	15.5124i	0.518922	+	1.01844i
$233$	−5.47214	+	5.47214i	−0.358492	+	0.358492i	−0.863257	−	0.504765i	$-0.831579\pi$
$233$	−5.47214	+	5.47214i	−0.358492	+	0.358492i	0.504765	+	0.863257i	$0.331579\pi$
$234$		0			0
$235$	−2.43769	−	10.3262i	−0.159018	−	0.673609i
$236$	−0.291796	−	0.898056i	−0.0189943	−	0.0584585i
$237$		0			0
$238$	0.841616	+	5.31375i	0.0545538	+	0.344439i
$239$	−13.4208			−0.868119			−0.434059	−	0.900884i	$-0.642919\pi$
$239$	−13.4208			−0.868119			−0.434059	+	0.900884i	$0.642919\pi$
$240$		0			0
$241$	11.2361			0.723779			0.361889	−	0.932221i	$-0.382132\pi$
$241$	11.2361			0.723779			0.361889	+	0.932221i	$0.382132\pi$
$242$	−0.116780	−	0.737322i	−0.00750692	−	0.0473968i
$243$		0			0
$244$	0.555029	+	1.70820i	0.0355321	+	0.109357i
$245$	−0.449028	−	0.277515i	−0.0286873	−	0.0177298i
$246$		0			0
$247$	−1.45309	+	1.45309i	−0.0924576	+	0.0924576i
$248$	21.4377	−	10.9230i	1.36129	−	0.693613i
$249$		0			0
$250$	−1.06098	−	15.7758i	−0.0671024	−	0.997746i
$251$	−0.180340			−0.0113830			−0.00569148	−	0.999984i	$-0.501812\pi$
$251$	−0.180340			−0.0113830			−0.00569148	+	0.999984i	$0.501812\pi$
$252$		0			0
$253$	13.7638	+	13.7638i	0.865324	+	0.865324i
$254$	−4.53077	−	3.29180i	−0.284286	−	0.206546i
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−5.29180	−	5.29180i	−0.330093	−	0.330093i	0.522529	−	0.852622i	$-0.324989\pi$
$257$	−5.29180	−	5.29180i	−0.330093	−	0.330093i	−0.852622	+	0.522529i	$0.824989\pi$
$258$		0			0
$259$		−	2.76393i		−	0.171742i
$260$	3.92702	−	2.38602i	0.243543	−	0.147975i
$261$		0			0
$262$	−3.03269	−	19.1477i	−0.187360	−	1.18295i
$263$	−7.50245	−	7.50245i	−0.462621	−	0.462621i	0.436893	−	0.899514i	$-0.356079\pi$
$263$	−7.50245	−	7.50245i	−0.462621	−	0.462621i	−0.899514	+	0.436893i	$0.856079\pi$
$264$		0			0
$265$	−9.47214	+	2.23607i	−0.581869	+	0.137361i
$266$	4.47214	−	6.15537i	0.274204	−	0.377410i
$267$		0			0
$268$	11.6381	+	5.92992i	0.710912	+	0.362228i
$269$	20.4742			1.24833			0.624167	−	0.781291i	$-0.285438\pi$
$269$	20.4742			1.24833			0.624167	+	0.781291i	$0.285438\pi$
$270$		0			0
$271$		−	17.2250i		−	1.04635i	−0.852227	−	0.523173i	$-0.824748\pi$
$271$		−	17.2250i		−	1.04635i	0.852227	−	0.523173i	$-0.175252\pi$
$272$	5.58721	+	0.884927i	0.338774	+	0.0536566i
$273$		0			0
$274$	−6.43288	+	8.85410i	−0.388625	+	0.534896i
$275$	−7.23607	−	14.4721i	−0.436351	−	0.872703i
$276$		0			0
$277$	9.23305	−	9.23305i	0.554760	−	0.554760i	−0.373051	−	0.927811i	$-0.621688\pi$
$277$	9.23305	−	9.23305i	0.554760	−	0.554760i	0.927811	+	0.373051i	$0.121688\pi$
$278$	−29.9145	+	4.73799i	−1.79415	+	0.284166i
$279$		0			0
$280$	−12.9786	+	10.9999i	−0.775622	+	0.657369i
$281$	9.70820			0.579143			0.289571	−	0.957156i	$-0.406487\pi$
$281$	9.70820			0.579143			0.289571	+	0.957156i	$0.406487\pi$
$282$		0			0
$283$	13.3820	−	13.3820i	0.795475	−	0.795475i	−0.186903	−	0.982378i	$-0.559845\pi$
$283$	13.3820	−	13.3820i	0.795475	−	0.795475i	0.982378	+	0.186903i	$0.0598450\pi$
$284$	−7.05342	−	21.7082i	−0.418544	−	1.28814i
$285$		0			0
$286$	2.76393	−	3.80423i	0.163435	−	0.224949i
$287$	−10.8576	+	10.8576i	−0.640907	+	0.640907i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$	−17.9549	−	7.51713i	−1.05435	−	0.441421i
$291$		0			0
$292$	6.04571	−	11.8654i	0.353798	−	0.694368i
$293$	3.07768	+	3.07768i	0.179800	+	0.179800i	0.791269	−	0.611469i	$-0.209421\pi$
$293$	3.07768	+	3.07768i	0.179800	+	0.179800i	−0.611469	+	0.791269i	$0.709421\pi$
$294$		0			0
$295$	0.898056	+	0.555029i	0.0522868	+	0.0323150i
$296$	−2.76393	−	0.898056i	−0.160650	−	0.0521984i
$297$		0			0
$298$	−2.84632	−	17.9709i	−0.164883	−	1.04103i
$299$		−	6.18034i		−	0.357418i
$300$		0			0
$301$		−	17.5680i		−	1.01261i
$302$	−9.37310	+	1.48455i	−0.539361	+	0.0854264i
$303$		0			0
$304$	−4.70228	−	6.47214i	−0.269694	−	0.371202i
$305$	−1.70820	−	1.05573i	−0.0978115	−	0.0604508i
$306$		0			0
$307$	−13.5623	−	13.5623i	−0.774042	−	0.774042i	0.204769	−	0.978810i	$-0.434356\pi$
$307$	−13.5623	−	13.5623i	−0.774042	−	0.774042i	−0.978810	+	0.204769i	$0.934356\pi$
$308$	−7.90398	+	15.5124i	−0.450371	+	0.883903i
$309$		0			0
$310$	−10.3884	+	24.8131i	−0.590022	+	1.40929i
$311$		−	20.8172i		−	1.18044i	−0.807243	−	0.590219i	$-0.799041\pi$
$311$		−	20.8172i		−	1.18044i	0.807243	−	0.590219i	$-0.200959\pi$
$312$		0			0
$313$	−1.76393	+	1.76393i	−0.0997033	+	0.0997033i	−0.755199	−	0.655496i	$-0.772460\pi$
$313$	−1.76393	+	1.76393i	−0.0997033	+	0.0997033i	0.655496	+	0.755199i	$0.272460\pi$
$314$	22.5478	+	16.3820i	1.27245	+	0.924488i
$315$		0			0
$316$	5.52786	−	1.79611i	0.310967	−	0.101039i
$317$	−3.97574	+	3.97574i	−0.223300	+	0.223300i	−0.809886	−	0.586587i	$-0.800471\pi$
$317$	−3.97574	+	3.97574i	−0.223300	+	0.223300i	0.586587	+	0.809886i	$0.300471\pi$
$318$		0			0
$319$	−19.9192			−1.11526
$320$	6.78287	+	16.5527i	0.379174	+	0.925325i
$321$		0			0
$322$	3.57960	+	22.6007i	0.199484	+	1.25949i
$323$	2.00000	−	2.00000i	0.111283	−	0.111283i
$324$		0			0
$325$	−1.62460	+	4.87380i	−0.0901165	+	0.270350i
$326$	−22.4164	−	16.2865i	−1.24153	−	0.902024i
$327$		0			0
$328$	7.32979	+	14.3855i	0.404720	+	0.794307i
$329$		−	12.7639i		−	0.703698i
$330$		0			0
$331$	−30.0689			−1.65274			−0.826368	−	0.563131i	$-0.809597\pi$
$331$	−30.0689			−1.65274			−0.826368	+	0.563131i	$0.809597\pi$
$332$	−8.49808	+	16.6784i	−0.466393	+	0.915347i
$333$		0			0
$334$	13.0373	+	9.47214i	0.713368	+	0.518292i
$335$	−14.2128	+	3.35520i	−0.776531	+	0.183314i
$336$		0			0
$337$	−19.9443	−	19.9443i	−1.08643	−	1.08643i	−0.995893	−	0.0905410i	$-0.971140\pi$
$337$	−19.9443	−	19.9443i	−1.08643	−	1.08643i	−0.0905410	−	0.995893i	$-0.528860\pi$
$338$	16.6838	−	2.64245i	0.907478	−	0.143730i
$339$		0			0
$340$	−5.40507	+	3.28408i	−0.293131	+	0.178104i
$341$			27.5276i			1.49071i
$342$		0			0
$343$	12.8658	+	12.8658i	0.694686	+	0.694686i
$344$	−17.5680	−	5.70820i	−0.947206	−	0.307766i
$345$		0			0
$346$	−17.0344	+	23.4459i	−0.915777	+	1.26046i
$347$	−26.0344	−	26.0344i	−1.39760	−	1.39760i	−0.806862	−	0.590740i	$-0.798836\pi$
$347$	−26.0344	−	26.0344i	−1.39760	−	1.39760i	−0.590740	−	0.806862i	$-0.701164\pi$
$348$		0			0
$349$	16.6700			0.892324			0.446162	−	0.894952i	$-0.352791\pi$
$349$	16.6700			0.892324			0.446162	+	0.894952i	$0.352791\pi$
$350$	3.11809	−	18.7638i	0.166669	−	1.00297i
$351$		0			0
$352$	12.9443	+	12.9443i	0.689932	+	0.689932i
$353$	22.4164	−	22.4164i	1.19311	−	1.19311i	0.216914	−	0.976191i	$-0.430401\pi$
$353$	22.4164	−	22.4164i	1.19311	−	1.19311i	0.976191	−	0.216914i	$-0.0695992\pi$
$354$		0			0
$355$	21.7082	+	13.4164i	1.15215	+	0.712069i
$356$	1.52786	+	4.70228i	0.0809766	+	0.249220i
$357$		0			0
$358$	−10.5149	+	1.66540i	−0.555732	+	0.0880193i
$359$	19.9192			1.05129			0.525647	−	0.850703i	$-0.323823\pi$
$359$	19.9192			1.05129			0.525647	+	0.850703i	$0.323823\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	−21.2550	+	3.36646i	−1.11714	+	0.176937i
$363$		0			0
$364$	5.25731	−	1.70820i	0.275558	−	0.0895342i
$365$	3.42071	+	14.4904i	0.179048	+	0.758460i
$366$		0			0
$367$	−12.2047	+	12.2047i	−0.637082	+	0.637082i	−0.949835	−	0.312753i	$-0.898749\pi$
$367$	−12.2047	+	12.2047i	−0.637082	+	0.637082i	0.312753	+	0.949835i	$0.398749\pi$
$368$	23.7638	+	3.76382i	1.23877	+	0.196203i
$369$		0			0
$370$	3.00656	−	1.23201i	0.156304	−	0.0640492i
$371$	−11.7082			−0.607860
$372$		0			0
$373$	22.4418	+	22.4418i	1.16199	+	1.16199i	0.984038	+	0.177956i	$0.0569485\pi$
$373$	22.4418	+	22.4418i	1.16199	+	1.16199i	0.177956	+	0.984038i	$0.443052\pi$
$374$	−3.80423	+	5.23607i	−0.196712	+	0.270751i
$375$		0			0
$376$	−12.7639	−	4.14725i	−0.658250	−	0.213878i
$377$	4.47214	+	4.47214i	0.230327	+	0.230327i
$378$		0			0
$379$			0.111456i			0.00572512i	0.999996	+	0.00286256i	$0.000911182\pi$
$379$			0.111456i			0.00572512i	−0.999996	+	0.00286256i	$0.999089\pi$
$380$	8.68915	+	2.12099i	0.445744	+	0.108805i
$381$		0			0
$382$	−18.4501	+	2.92220i	−0.943988	+	0.149513i
$383$	−1.00406	−	1.00406i	−0.0513049	−	0.0513049i	0.680989	−	0.732294i	$-0.261550\pi$
$383$	−1.00406	−	1.00406i	−0.0513049	−	0.0513049i	−0.732294	+	0.680989i	$0.761550\pi$
$384$		0			0
$385$	−4.47214	−	18.9443i	−0.227921	−	0.965489i
$386$	2.38197	+	1.73060i	0.121239	+	0.0880852i
$387$		0			0
$388$	−10.6755	−	5.43945i	−0.541967	−	0.276146i
$389$	−4.14725			−0.210274			−0.105137	−	0.994458i	$-0.533528\pi$
$389$	−4.14725			−0.210274			−0.105137	+	0.994458i	$0.533528\pi$
$390$		0			0
$391$			8.50651i			0.430193i
$392$	−0.594926	+	0.303130i	−0.0300483	+	0.0153104i
$393$		0			0
$394$	14.9394	+	10.8541i	0.752636	+	0.546822i
$395$	−3.41641	+	5.52786i	−0.171898	+	0.278137i
$396$		0			0
$397$	−24.4500	+	24.4500i	−1.22711	+	1.22711i	−0.262055	+	0.965053i	$0.584400\pi$
$397$	−24.4500	+	24.4500i	−1.22711	+	1.22711i	−0.965053	+	0.262055i	$0.915600\pi$
$398$	4.80411	+	30.3320i	0.240808	+	1.52040i
$399$		0			0
$400$	−17.7507	−	9.21482i	−0.887535	−	0.460741i
$401$	−31.8885			−1.59244			−0.796219	−	0.605009i	$-0.793170\pi$
$401$	−31.8885			−1.59244			−0.796219	+	0.605009i	$0.793170\pi$
$402$		0			0
$403$	6.18034	−	6.18034i	0.307865	−	0.307865i
$404$	−1.79611	−	5.52786i	−0.0893599	−	0.275022i
$405$		0			0
$406$	−18.9443	−	13.7638i	−0.940188	−	0.683087i
$407$	2.35114	−	2.35114i	0.116542	−	0.116542i
$408$		0			0
$409$		−	21.5967i		−	1.06789i	−0.845519	−	0.533945i	$-0.820709\pi$
$409$		−	21.5967i		−	1.06789i	0.845519	−	0.533945i	$-0.179291\pi$
$410$	−16.6505	−	6.97104i	−0.822312	−	0.344275i
$411$		0			0
$412$	−8.45559	−	4.30834i	−0.416577	−	0.212257i
$413$	0.898056	+	0.898056i	0.0441904	+	0.0441904i
$414$		0			0
$415$	−4.80828	−	20.3682i	−0.236029	−	0.999836i
$416$		−	5.81234i		−	0.284973i
$417$		0			0
$418$	9.04029	−	1.43184i	0.442175	−	0.0700337i
$419$			28.8328i			1.40858i	0.709915	+	0.704288i	$0.248733\pi$
$419$			28.8328i			1.40858i	−0.709915	+	0.704288i	$0.751267\pi$
$420$		0			0
$421$		−	28.4257i		−	1.38538i	−0.721234	−	0.692692i	$-0.756425\pi$
$421$		−	28.4257i		−	1.38538i	0.721234	−	0.692692i	$-0.243575\pi$
$422$	0.507018	+	3.20119i	0.0246813	+	0.155831i
$423$		0			0
$424$	−3.80423	+	11.7082i	−0.184750	+	0.568601i
$425$	2.23607	−	6.70820i	0.108465	−	0.325396i
$426$		0			0
$427$	−1.70820	−	1.70820i	−0.0826658	−	0.0826658i
$428$	2.29291	+	1.16829i	0.110832	+	0.0564716i
$429$		0			0
$430$	19.1103	−	7.83088i	0.921579	−	0.377639i
$431$		−	19.0211i		−	0.916216i	−0.888897	−	0.458108i	$-0.848527\pi$
$431$		−	19.0211i		−	0.916216i	0.888897	−	0.458108i	$-0.151473\pi$
$432$		0			0
$433$	0.819660	−	0.819660i	0.0393904	−	0.0393904i	−0.687137	−	0.726528i	$-0.741133\pi$
$433$	0.819660	−	0.819660i	0.0393904	−	0.0393904i	0.726528	+	0.687137i	$0.241133\pi$
$434$	−19.0211	+	26.1803i	−0.913043	+	1.25670i
$435$		0			0
$436$	27.8885	−	9.06154i	1.33562	−	0.433969i
$437$	8.50651	−	8.50651i	0.406921	−	0.406921i
$438$		0			0
$439$	35.1361			1.67695			0.838477	−	0.544937i	$-0.183446\pi$
$439$	35.1361			1.67695			0.838477	+	0.544937i	$0.183446\pi$
$440$	−20.3974	−	1.68323i	−0.972406	−	0.0802449i
$441$		0			0
$442$	2.02967	−	0.321469i	0.0965417	−	0.0152907i
$443$	1.09017	−	1.09017i	0.0517955	−	0.0517955i	−0.680735	−	0.732530i	$-0.738339\pi$
$443$	1.09017	−	1.09017i	0.0517955	−	0.0517955i	0.732530	+	0.680735i	$0.238339\pi$
$444$		0			0
$445$	−4.70228	−	2.90617i	−0.222910	−	0.137766i
$446$	16.7082	−	22.9969i	0.791156	−	1.08893i
$447$		0			0
$448$	3.36646	+	21.2550i	0.159050	+	1.00420i
$449$		−	17.5967i		−	0.830442i	−0.909721	−	0.415221i	$-0.863704\pi$
$449$		−	17.5967i		−	0.830442i	0.909721	−	0.415221i	$-0.136296\pi$
$450$		0			0
$451$	−18.4721			−0.869819
$452$	11.1820	−	21.9460i	0.525958	−	1.03225i
$453$		0			0
$454$	−11.0292	+	15.1803i	−0.517624	+	0.712449i
$455$	−3.24920	+	5.25731i	−0.152325	+	0.246467i
$456$		0			0
$457$	9.65248	+	9.65248i	0.451524	+	0.451524i	0.895860	−	0.444336i	$-0.146560\pi$
$457$	9.65248	+	9.65248i	0.451524	+	0.451524i	−0.444336	+	0.895860i	$0.646560\pi$
$458$	−1.75912	−	11.1066i	−0.0821983	−	0.518979i
$459$		0			0
$460$	−22.9892	+	13.9680i	−1.07187	+	0.651262i
$461$		−	27.5276i		−	1.28209i	−0.767503	−	0.641045i	$-0.778501\pi$
$461$		−	27.5276i		−	1.28209i	0.767503	−	0.641045i	$-0.221499\pi$
$462$		0			0
$463$	−2.45714	−	2.45714i	−0.114193	−	0.114193i	0.647701	−	0.761894i	$-0.275730\pi$
$463$	−2.45714	−	2.45714i	−0.114193	−	0.114193i	−0.761894	+	0.647701i	$0.775730\pi$
$464$	−19.9192	+	14.4721i	−0.924725	+	0.671852i
$465$		0			0
$466$	−8.85410	−	6.43288i	−0.410158	−	0.297997i
$467$	18.3262	+	18.3262i	0.848037	+	0.848037i	0.989888	−	0.141851i	$-0.0453054\pi$
$467$	18.3262	+	18.3262i	0.848037	+	0.848037i	−0.141851	+	0.989888i	$0.545305\pi$
$468$		0			0
$469$	−17.5680			−0.811217
$470$	13.8844	−	5.68947i	0.640440	−	0.262436i
$471$		0			0
$472$	1.18985	−	0.606260i	0.0547674	−	0.0279054i
$473$	14.9443	−	14.9443i	0.687138	−	0.687138i
$474$		0			0
$475$	−8.94427	+	4.47214i	−0.410391	+	0.205196i
$476$	−7.23607	+	2.35114i	−0.331665	+	0.107764i
$477$		0			0
$478$	−2.96911	−	18.7462i	−0.135804	−	0.857431i
$479$	−4.70228			−0.214853			−0.107426	−	0.994213i	$-0.534261\pi$
$479$	−4.70228			−0.214853			−0.107426	+	0.994213i	$0.534261\pi$
$480$		0			0
$481$	−1.05573			−0.0481371
$482$	2.48577	+	15.6946i	0.113224	+	0.714868i
$483$		0			0
$484$	1.00406	−	0.326238i	0.0456390	−	0.0148290i
$485$	13.0373	−	3.07768i	0.591992	−	0.139750i
$486$		0			0
$487$	18.9151	−	18.9151i	0.857126	−	0.857126i	−0.133872	−	0.990999i	$-0.542741\pi$
$487$	18.9151	−	18.9151i	0.857126	−	0.857126i	0.990999	+	0.133872i	$0.0427412\pi$
$488$	−2.26323	+	1.15317i	−0.102452	+	0.0522018i
$489$		0			0
$490$	0.288294	−	0.688598i	0.0130238	−	0.0311077i
$491$	15.2361			0.687594			0.343797	−	0.939044i	$-0.388287\pi$
$491$	15.2361			0.687594			0.343797	+	0.939044i	$0.388287\pi$
$492$		0			0
$493$	−6.15537	−	6.15537i	−0.277224	−	0.277224i
$494$	−2.35114	−	1.70820i	−0.105783	−	0.0768557i
$495$		0			0
$496$	20.0000	+	27.5276i	0.898027	+	1.23603i
$497$	21.7082	+	21.7082i	0.973746	+	0.973746i
$498$		0			0
$499$			11.8885i			0.532204i	0.963945	+	0.266102i	$0.0857359\pi$
$499$			11.8885i			0.532204i	−0.963945	+	0.266102i	$0.914264\pi$
$500$	21.8009	−	4.97208i	0.974965	−	0.222358i
$501$		0			0
$502$	−0.0398969	−	0.251899i	−0.00178069	−	0.0112428i
$503$	16.5640	+	16.5640i	0.738552	+	0.738552i	0.972298	−	0.233746i	$-0.0750984\pi$
$503$	16.5640	+	16.5640i	0.738552	+	0.738552i	−0.233746	+	0.972298i	$0.575098\pi$
$504$		0			0
$505$	5.52786	+	3.41641i	0.245987	+	0.152028i
$506$	−16.1803	+	22.2703i	−0.719304	+	0.990037i
$507$		0			0
$508$	3.59564	−	7.05684i	0.159531	−	0.313097i
$509$	−10.8576			−0.481257			−0.240628	−	0.970617i	$-0.577354\pi$
$509$	−10.8576			−0.481257			−0.240628	+	0.970617i	$0.577354\pi$
$510$		0			0
$511$			17.9111i			0.792339i
$512$	22.3488	+	3.53971i	0.987688	+	0.156434i
$513$		0			0
$514$	6.22088	−	8.56231i	0.274391	−	0.377667i
$515$	10.3262	−	2.43769i	0.455028	−	0.107418i
$516$		0			0
$517$	10.8576	−	10.8576i	0.477519	−	0.477519i
$518$	3.86067	−	0.611469i	0.169628	−	0.0268664i
$519$		0			0
$520$	4.20158	+	4.95740i	0.184252	+	0.217396i
$521$	0.472136			0.0206847			0.0103423	−	0.999947i	$-0.496708\pi$
$521$	0.472136			0.0206847			0.0103423	+	0.999947i	$0.496708\pi$
$522$		0			0
$523$	25.7426	−	25.7426i	1.12565	−	1.12565i	0.134770	−	0.990877i	$-0.456970\pi$
$523$	25.7426	−	25.7426i	1.12565	−	1.12565i	0.990877	−	0.134770i	$-0.0430297\pi$
$524$	26.0746	−	8.47214i	1.13907	−	0.370107i
$525$		0			0
$526$	8.81966	−	12.1392i	0.384555	−	0.529295i
$527$	−8.50651	+	8.50651i	−0.370549	+	0.370549i
$528$		0			0
$529$			13.1803i			0.573058i
$530$	−5.21888	−	12.7360i	−0.226694	−	0.553217i
$531$		0			0
$532$	9.58721	+	4.88493i	0.415658	+	0.211788i
$533$	4.14725	+	4.14725i	0.179637	+	0.179637i
$534$		0			0
$535$	−2.80017	+	0.661030i	−0.121062	+	0.0285788i
$536$	−5.70820	+	17.5680i	−0.246557	+	0.758824i
$537$		0			0
$538$	4.52955	+	28.5984i	0.195283	+	1.23297i
$539$		−	0.763932i		−	0.0329049i
$540$		0			0
$541$		−	12.3107i		−	0.529280i	−0.964347	−	0.264640i	$-0.914747\pi$
$541$		−	12.3107i		−	0.529280i	0.964347	−	0.264640i	$-0.0852531\pi$
$542$	24.0599	−	3.81072i	1.03346	−	0.163684i
$543$		0			0
$544$			8.00000i			0.342997i
$545$	−17.2361	+	27.8885i	−0.738312	+	1.19461i
$546$		0			0
$547$	11.5623	+	11.5623i	0.494369	+	0.494369i	0.909679	−	0.415311i	$-0.136327\pi$
$547$	11.5623	+	11.5623i	0.494369	+	0.494369i	−0.415311	+	0.909679i	$0.636327\pi$
$548$	−13.7906	−	7.02666i	−0.589105	−	0.300164i
$549$		0			0
$550$	18.6139	−	13.3091i	0.793698	−	0.567500i
$551$			12.3107i			0.524455i
$552$		0			0
$553$	−5.52786	+	5.52786i	−0.235069	+	0.235069i
$554$	14.9394	+	10.8541i	0.634714	+	0.461147i
$555$		0			0
$556$	−13.2361	−	40.7364i	−0.561334	−	1.72761i
$557$	−23.5519	+	23.5519i	−0.997926	+	0.997926i	−0.999998	−	0.00207187i	$-0.999341\pi$
$557$	−23.5519	+	23.5519i	−0.997926	+	0.997926i	0.00207187	+	0.999998i	$0.499341\pi$
$558$		0			0
$559$	−6.71040			−0.283820
$560$	−18.2360	−	15.6951i	−0.770610	−	0.663238i
$561$		0			0
$562$	2.14776	+	13.5604i	0.0905979	+	0.572013i
$563$	4.32624	−	4.32624i	0.182329	−	0.182329i	−0.610041	−	0.792370i	$-0.708847\pi$
$563$	4.32624	−	4.32624i	0.182329	−	0.182329i	0.792370	+	0.610041i	$0.208847\pi$
$564$		0			0
$565$	6.32688	+	26.8011i	0.266174	+	1.12753i
$566$	21.6525	+	15.7314i	0.910121	+	0.661242i
$567$		0			0
$568$	28.7616	−	14.6548i	1.20681	−	0.614901i
$569$			27.1246i			1.13712i	0.822641	+	0.568561i	$0.192500\pi$
$569$			27.1246i			1.13712i	−0.822641	+	0.568561i	$0.807500\pi$
$570$		0			0
$571$	22.6525			0.947977			0.473988	−	0.880531i	$-0.342814\pi$
$571$	22.6525			0.947977			0.473988	+	0.880531i	$0.342814\pi$
$572$	5.92522	+	3.01905i	0.247746	+	0.126233i
$573$		0			0
$574$	−17.5680	−	12.7639i	−0.733276	−	0.532756i
$575$	9.51057	−	28.5317i	0.396618	−	1.18985i
$576$		0			0
$577$	26.2361	+	26.2361i	1.09222	+	1.09222i	0.995291	+	0.0969307i	$0.0309025\pi$
$577$	26.2361	+	26.2361i	1.09222	+	1.09222i	0.0969307	+	0.995291i	$0.469097\pi$
$578$	20.9520	−	3.31848i	0.871490	−	0.138030i
$579$		0			0
$580$	6.52775	−	26.7425i	0.271050	−	1.11042i
$581$		−	25.1765i		−	1.04450i
$582$		0			0
$583$	−9.95959	−	9.95959i	−0.412484	−	0.412484i
$584$	17.9111	+	5.81966i	0.741165	+	0.240819i
$585$		0			0
$586$	−3.61803	+	4.97980i	−0.149460	+	0.205714i
$587$	−17.0902	−	17.0902i	−0.705387	−	0.705387i	0.260175	−	0.965562i	$-0.416220\pi$
$587$	−17.0902	−	17.0902i	−0.705387	−	0.705387i	−0.965562	+	0.260175i	$0.916220\pi$
$588$		0			0
$589$	17.0130			0.701009
$590$	−0.576587	+	1.37720i	−0.0237377	+	0.0566983i
$591$		0			0
$592$	0.642937	−	4.05934i	0.0264246	−	0.166838i
$593$	−20.4164	+	20.4164i	−0.838401	+	0.838401i	−0.988648	−	0.150247i	$-0.951993\pi$
$593$	−20.4164	+	20.4164i	−0.838401	+	0.838401i	0.150247	+	0.988648i	$0.451993\pi$
$594$		0			0
$595$	4.47214	−	7.23607i	0.183340	−	0.296650i
$596$	24.4721	−	7.95148i	1.00242	−	0.325705i
$597$		0			0
$598$	8.63271	−	1.36729i	0.353018	−	0.0559125i
$599$	6.49839			0.265517			0.132759	−	0.991148i	$-0.457617\pi$
$599$	6.49839			0.265517			0.132759	+	0.991148i	$0.457617\pi$
$600$		0			0
$601$	−17.7082			−0.722333			−0.361166	−	0.932501i	$-0.617621\pi$
$601$	−17.7082			−0.722333			−0.361166	+	0.932501i	$0.617621\pi$
$602$	24.5391	−	3.88661i	1.00014	−	0.158406i
$603$		0			0
$604$	−4.14725	−	12.7639i	−0.168749	−	0.519357i
$605$	−0.620541	+	1.00406i	−0.0252286	+	0.0408207i
$606$		0			0
$607$	−32.6789	+	32.6789i	−1.32640	+	1.32640i	−0.417908	+	0.908489i	$0.637237\pi$
$607$	−32.6789	+	32.6789i	−1.32640	+	1.32640i	−0.908489	+	0.417908i	$0.862763\pi$
$608$	8.00000	−	8.00000i	0.324443	−	0.324443i
$609$		0			0
$610$	1.09673	−	2.61958i	0.0444055	−	0.106064i
$611$	−4.87539			−0.197237
$612$		0			0
$613$	−19.5357	−	19.5357i	−0.789038	−	0.789038i	0.192298	−	0.981337i	$-0.438406\pi$
$613$	−19.5357	−	19.5357i	−0.789038	−	0.789038i	−0.981337	+	0.192298i	$0.938406\pi$
$614$	15.9434	−	21.9443i	0.643425	−	0.885599i
$615$		0			0
$616$	−23.4164	−	7.60845i	−0.943474	−	0.306553i
$617$	−4.88854	−	4.88854i	−0.196805	−	0.196805i	0.601824	−	0.798629i	$-0.294441\pi$
$617$	−4.88854	−	4.88854i	−0.196805	−	0.196805i	−0.798629	+	0.601824i	$0.794441\pi$
$618$		0			0
$619$			35.3050i			1.41903i	0.704692	+	0.709513i	$0.251085\pi$
$619$			35.3050i			1.41903i	−0.704692	+	0.709513i	$0.748915\pi$
$620$	−36.9572	−	9.02113i	−1.48424	−	0.362297i
$621$		0			0
$622$	29.0776	−	4.60543i	1.16590	−	0.184661i
$623$	−4.70228	−	4.70228i	−0.188393	−	0.188393i
$624$		0			0
$625$	−15.0000	+	20.0000i	−0.600000	+	0.800000i
$626$	−2.85410	−	2.07363i	−0.114073	−	0.0828788i
$627$		0			0
$628$	−17.8941	+	35.1191i	−0.714051	+	1.40140i
$629$	1.45309			0.0579383
$630$		0			0
$631$		−	22.6134i		−	0.900223i	−0.892972	−	0.450112i	$-0.851384\pi$
$631$		−	22.6134i		−	0.900223i	0.892972	−	0.450112i	$-0.148616\pi$
$632$	3.73175	+	7.32398i	0.148441	+	0.291332i
$633$		0			0
$634$	−6.43288	−	4.67376i	−0.255482	−	0.185619i
$635$	2.03444	+	8.61803i	0.0807344	+	0.341996i
$636$		0			0
$637$	−0.171513	+	0.171513i	−0.00679561	+	0.00679561i
$638$	−4.40676	−	27.8232i	−0.174465	−	1.10153i
$639$		0			0
$640$	−21.6203	+	13.1363i	−0.854617	+	0.519258i
$641$	38.6525			1.52668			0.763341	−	0.645996i	$-0.223558\pi$
$641$	38.6525			1.52668			0.763341	+	0.645996i	$0.223558\pi$
$642$		0			0
$643$	−11.5623	+	11.5623i	−0.455973	+	0.455973i	−0.897331	−	0.441358i	$-0.854497\pi$
$643$	−11.5623	+	11.5623i	−0.455973	+	0.455973i	0.441358	+	0.897331i	$0.354497\pi$
$644$	−30.7768	+	10.0000i	−1.21278	+	0.394055i
$645$		0			0
$646$	3.23607	+	2.35114i	0.127321	+	0.0925044i
$647$	−20.0252	+	20.0252i	−0.787271	+	0.787271i	−0.981046	−	0.193775i	$-0.937927\pi$
$647$	−20.0252	+	20.0252i	−0.787271	+	0.787271i	0.193775	+	0.981046i	$0.437927\pi$
$648$		0			0
$649$			1.52786i			0.0599739i
$650$	−7.16714	−	1.19100i	−0.281118	−	0.0467150i
$651$		0			0
$652$	17.7898	−	34.9144i	0.696701	−	1.36735i
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	0.194661	−	0.980871i	$-0.437639\pi$
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	−0.980871	+	0.194661i	$0.937639\pi$
$654$		0			0
$655$	−16.1150	+	26.0746i	−0.629664	+	1.01882i
$656$	−18.4721	+	13.4208i	−0.721216	+	0.523994i
$657$		0			0
$658$	17.8287	−	2.82379i	0.695035	−	0.110083i
$659$		−	18.0000i		−	0.701180i	−0.936529	−	0.350590i	$-0.885981\pi$
$659$		−	18.0000i		−	0.701180i	0.936529	−	0.350590i	$-0.114019\pi$
$660$		0			0
$661$			3.80423i			0.147967i	0.997259	+	0.0739836i	$0.0235713\pi$
$661$			3.80423i			0.147967i	−0.997259	+	0.0739836i	$0.976429\pi$
$662$	−6.65219	−	42.0003i	−0.258545	−	1.63239i
$663$		0			0
$664$	−25.1765	−	8.18034i	−0.977038	−	0.317459i
$665$	−11.7082	+	2.76393i	−0.454025	+	0.107181i
$666$		0			0
$667$	−26.1803	−	26.1803i	−1.01371	−	1.01371i
$668$	−10.3464	+	20.3060i	−0.400316	+	0.785664i
$669$		0			0
$670$	−7.83088	−	19.1103i	−0.302533	−	0.738294i
$671$		−	2.90617i		−	0.112191i
$672$		0			0
$673$	−17.2918	+	17.2918i	−0.666550	+	0.666550i	−0.956916	−	0.290366i	$-0.906223\pi$
$673$	−17.2918	+	17.2918i	−0.666550	+	0.666550i	0.290366	+	0.956916i	$0.406223\pi$
$674$	23.4459	−	32.2705i	0.903102	−	1.24301i
$675$		0			0
$676$	7.38197	+	22.7194i	0.283922	+	0.873821i
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	−0.840625	−	0.541617i	$-0.817812\pi$
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	0.541617	+	0.840625i	$0.317812\pi$
$678$		0			0
$679$	16.1150			0.618435
$680$	−5.78298	−	6.82328i	−0.221767	−	0.261661i
$681$		0			0
$682$	−38.4507	+	6.08999i	−1.47235	+	0.233198i
$683$	22.7984	−	22.7984i	0.872356	−	0.872356i	−0.120373	−	0.992729i	$-0.538409\pi$
$683$	22.7984	−	22.7984i	0.872356	−	0.872356i	0.992729	+	0.120373i	$0.0384091\pi$
$684$		0			0
$685$	16.8415	−	3.97574i	0.643481	−	0.151905i
$686$	−15.1246	+	20.8172i	−0.577460	+	0.794806i
$687$		0			0
$688$	4.08662	−	25.8019i	0.155801	−	0.983689i
$689$			4.47214i			0.170375i
$690$		0			0
$691$	9.12461			0.347117			0.173558	−	0.984824i	$-0.444473\pi$
$691$	9.12461			0.347117			0.173558	+	0.984824i	$0.444473\pi$
$692$	−36.5178	−	18.6068i	−1.38820	−	0.707323i
$693$		0			0
$694$	30.6053	−	42.1246i	1.16176	−	1.59903i
$695$	40.7364	+	25.1765i	1.54522	+	0.954999i
$696$		0			0
$697$	−5.70820	−	5.70820i	−0.216214	−	0.216214i
$698$	3.68793	+	23.2847i	0.139590	+	0.881338i
$699$		0			0
$700$	26.8992	+	0.204203i	1.01669	+	0.00771816i
$701$		−	19.7072i		−	0.744330i	−0.928167	−	0.372165i	$-0.878616\pi$
$701$		−	19.7072i		−	0.744330i	0.928167	−	0.372165i	$-0.121384\pi$
$702$		0			0
$703$	−1.45309	−	1.45309i	−0.0548041	−	0.0548041i
$704$	−15.2169	+	20.9443i	−0.573509	+	0.789367i
$705$		0			0
$706$	36.2705	+	26.3521i	1.36506	+	0.991773i
$707$	5.52786	+	5.52786i	0.207897	+	0.207897i
$708$		0			0
$709$	−3.24920			−0.122026			−0.0610131	−	0.998137i	$-0.519433\pi$
$709$	−3.24920			−0.122026			−0.0610131	+	0.998137i	$0.519433\pi$
$710$	−13.9375	+	33.2902i	−0.523066	+	1.24936i
$711$		0			0
$712$	−6.23015	+	3.17442i	−0.233485	+	0.118966i
$713$	−36.1803	+	36.1803i	−1.35496	+	1.35496i
$714$		0			0
$715$	−7.23607	+	1.70820i	−0.270614	+	0.0638832i
$716$	−4.65248	−	14.3188i	−0.173871	−	0.535120i
$717$		0			0
$718$	4.40676	+	27.8232i	0.164459	+	1.03835i
$719$	4.01623			0.149780			0.0748900	−	0.997192i	$-0.476139\pi$
$719$	4.01623			0.149780			0.0748900	+	0.997192i	$0.476139\pi$
$720$		0			0
$721$	12.7639			0.475354
$722$	3.31848	+	20.9520i	0.123501	+	0.779754i
$723$		0			0
$724$	−9.40456	−	28.9443i	−0.349518	−	1.07571i
$725$	13.7638	+	27.5276i	0.511175	+	1.02235i
$726$		0			0
$727$	9.51057	−	9.51057i	0.352727	−	0.352727i	−0.508396	−	0.861123i	$-0.669761\pi$
$727$	9.51057	−	9.51057i	0.352727	−	0.352727i	0.861123	+	0.508396i	$0.169761\pi$
$728$	3.54911	+	6.96552i	0.131539	+	0.258159i
$729$		0			0
$730$	−19.4834	+	7.98378i	−0.721113	+	0.295493i
$731$	9.23607			0.341608
$732$		0			0
$733$	−19.1926	−	19.1926i	−0.708896	−	0.708896i	0.257407	−	0.966303i	$-0.417132\pi$
$733$	−19.1926	−	19.1926i	−0.708896	−	0.708896i	−0.966303	+	0.257407i	$0.917132\pi$
$734$	−19.7477	−	14.3475i	−0.728900	−	0.529577i
$735$		0			0
$736$			34.0260i			1.25422i
$737$	−14.9443	−	14.9443i	−0.550479	−	0.550479i
$738$		0			0
$739$		−	9.41641i		−	0.346388i	−0.984888	−	0.173194i	$-0.944591\pi$
$739$		−	9.41641i		−	0.346388i	0.984888	−	0.173194i	$-0.0554088\pi$
$740$	2.38602	+	3.92702i	0.0877120	+	0.144360i
$741$		0			0
$742$	−2.59023	−	16.3540i	−0.0950902	−	0.600376i
$743$	4.80828	+	4.80828i	0.176399	+	0.176399i	0.789784	−	0.613385i	$-0.210193\pi$
$743$	4.80828	+	4.80828i	0.176399	+	0.176399i	−0.613385	+	0.789784i	$0.710193\pi$
$744$		0			0
$745$	−15.1246	+	24.4721i	−0.554123	+	0.896590i
$746$	−26.3820	+	36.3117i	−0.965912	+	1.32946i
$747$		0			0
$748$	−8.15537	−	4.15537i	−0.298190	−	0.151935i
$749$	−3.46120			−0.126469
$750$		0			0
$751$			11.4127i			0.416455i	0.978080	+	0.208227i	$0.0667694\pi$
$751$			11.4127i			0.416455i	−0.978080	+	0.208227i	$0.933231\pi$
$752$	2.96911	−	18.7462i	0.108272	−	0.683603i
$753$		0			0
$754$	−5.25731	+	7.23607i	−0.191460	+	0.263522i
$755$	12.7639	+	7.88854i	0.464527	+	0.287094i
$756$		0			0
$757$	−31.7154	+	31.7154i	−1.15272	+	1.15272i	−0.166709	+	0.986006i	$0.553314\pi$
$757$	−31.7154	+	31.7154i	−1.15272	+	1.15272i	−0.986006	+	0.166709i	$0.946686\pi$
$758$	−0.155682	+	0.0246576i	−0.00565463	+	0.000895606i
$759$		0			0
$760$	−1.04029	+	12.6063i	−0.0377354	+	0.457277i
$761$	−2.94427			−0.106730			−0.0533649	−	0.998575i	$-0.516995\pi$
$761$	−2.94427			−0.106730			−0.0533649	+	0.998575i	$0.516995\pi$
$762$		0			0
$763$	−27.8885	+	27.8885i	−1.00963	+	1.00963i
$764$	−8.16348	−	25.1246i	−0.295344	−	0.908977i
$765$		0			0
$766$	1.18034	−	1.62460i	0.0426474	−	0.0586991i
$767$	0.343027	−	0.343027i	0.0123860	−	0.0123860i
$768$		0			0
$769$		−	6.47214i		−	0.233391i	−0.993168	−	0.116696i	$-0.962770\pi$
$769$		−	6.47214i		−	0.233391i	0.993168	−	0.116696i	$-0.0372302\pi$
$770$	25.4720	−	10.4378i	0.917948	−	0.376151i
$771$		0			0
$772$	−1.89034	+	3.71000i	−0.0680348	+	0.133526i
$773$	−31.5034	−	31.5034i	−1.13310	−	1.13310i	−0.989659	−	0.143439i	$-0.954184\pi$
$773$	−31.5034	−	31.5034i	−1.13310	−	1.13310i	−0.143439	−	0.989659i	$-0.545816\pi$
$774$		0			0
$775$	38.0423	−	19.0211i	1.36652	−	0.683259i
$776$	5.23607	−	16.1150i	0.187964	−	0.578493i
$777$		0			0
$778$	−0.917504	−	5.79289i	−0.0328941	−	0.207685i
$779$			11.4164i			0.409035i
$780$		0			0
$781$			36.9322i			1.32154i
$782$	−11.8819	+	1.88191i	−0.424896	+	0.0672969i
$783$		0			0
$784$	−0.555029	−	0.763932i	−0.0198225	−	0.0272833i
$785$	−10.1246	−	42.8885i	−0.361363	−	1.53076i
$786$		0			0
$787$	17.8541	+	17.8541i	0.636430	+	0.636430i	0.949673	−	0.313243i	$-0.101415\pi$
$787$	17.8541	+	17.8541i	0.636430	+	0.636430i	−0.313243	+	0.949673i	$0.601415\pi$
$788$	−11.8560	+	23.2686i	−0.422351	+	0.828911i
$789$		0			0
$790$	−8.47715	−	3.54911i	−0.301603	−	0.126272i
$791$			33.1280i			1.17790i
$792$		0			0
$793$	−0.652476	+	0.652476i	−0.0231701	+	0.0231701i
$794$	−39.5609	−	28.7426i	−1.40396	−	1.02004i
$795$		0			0
$796$	−41.3050	+	13.4208i	−1.46402	+	0.475687i
$797$	14.8334	−	14.8334i	0.525426	−	0.525426i	−0.393779	−	0.919205i	$-0.628833\pi$
$797$	14.8334	−	14.8334i	0.525426	−	0.525426i	0.919205	+	0.393779i	$0.128833\pi$
$798$		0			0
$799$	6.71040			0.237397
$800$	8.94427	−	26.8328i	0.316228	−	0.948683i
$801$		0			0
$802$	−7.05476	−	44.5420i	−0.249112	−	1.57283i
$803$	−15.2361	+	15.2361i	−0.537669	+	0.537669i
$804$		0			0
$805$	19.0211	−	30.7768i	0.670407	−	1.08474i
$806$	10.0000	+	7.26543i	0.352235	+	0.255914i
$807$		0			0
$808$	7.32398	−	3.73175i	0.257657	−	0.131283i
$809$			4.94427i			0.173831i	0.996216	+	0.0869157i	$0.0277011\pi$
$809$			4.94427i			0.173831i	−0.996216	+	0.0869157i	$0.972299\pi$
$810$		0			0
$811$	26.0689			0.915402			0.457701	−	0.889106i	$-0.348673\pi$
$811$	26.0689			0.915402			0.457701	+	0.889106i	$0.348673\pi$
$812$	15.0343	−	29.5064i	0.527599	−	1.03547i
$813$		0			0
$814$	3.80423	+	2.76393i	0.133338	+	0.0968758i
$815$	10.0656	+	42.6385i	0.352582	+	1.49356i
$816$		0			0
$817$	−9.23607	−	9.23607i	−0.323129	−	0.323129i
$818$	30.1664	−	4.77789i	1.05474	−	0.167055i
$819$		0			0
$820$	6.05354	−	24.7997i	0.211399	−	0.866044i
$821$		−	17.9111i		−	0.625101i	−0.949901	−	0.312550i	$-0.898817\pi$
$821$		−	17.9111i		−	0.625101i	0.949901	−	0.312550i	$-0.101183\pi$
$822$		0			0
$823$	13.8698	+	13.8698i	0.483472	+	0.483472i	0.906238	−	0.422767i	$-0.138941\pi$
$823$	13.8698	+	13.8698i	0.483472	+	0.483472i	−0.422767	+	0.906238i	$0.638941\pi$
$824$	4.14725	−	12.7639i	0.144476	−	0.444653i
$825$		0			0
$826$	−1.05573	+	1.45309i	−0.0367335	+	0.0505593i
$827$	−8.14590	−	8.14590i	−0.283261	−	0.283261i	0.551147	−	0.834408i	$-0.314190\pi$
$827$	−8.14590	−	8.14590i	−0.283261	−	0.283261i	−0.834408	+	0.551147i	$0.814190\pi$
$828$		0			0
$829$	−54.5002			−1.89287			−0.946436	−	0.322892i	$-0.895345\pi$
$829$	−54.5002			−1.89287			−0.946436	+	0.322892i	$0.895345\pi$
$830$	27.3866	−	11.2223i	0.950604	−	0.389532i
$831$		0			0
$832$	8.11869	−	1.28587i	0.281465	−	0.0445797i
$833$	0.236068	−	0.236068i	0.00817927	−	0.00817927i
$834$		0			0
$835$	−5.85410	−	24.7984i	−0.202590	−	0.858183i
$836$	4.00000	+	12.3107i	0.138343	+	0.425776i
$837$		0			0
$838$	−40.2737	+	6.37873i	−1.39123	+	0.220350i
$839$	15.2169			0.525346			0.262673	−	0.964885i	$-0.415396\pi$
$839$	15.2169			0.525346			0.262673	+	0.964885i	$0.415396\pi$
$840$		0			0
$841$	8.88854			0.306502
$842$	39.7051	−	6.28867i	1.36833	−	0.216722i
$843$		0			0
$844$	−4.35926	+	1.41641i	−0.150052	+	0.0487548i
$845$	−22.7194	−	14.0413i	−0.781570	−	0.483037i
$846$		0			0
$847$	−1.00406	+	1.00406i	−0.0344998	+	0.0344998i
$848$	−17.1957	−	2.72353i	−0.590501	−	0.0935262i
$849$		0			0
$850$	9.86472	+	1.63928i	0.338357	+	0.0562267i
$851$	6.18034			0.211859
$852$		0			0
$853$	−18.8496	−	18.8496i	−0.645399	−	0.645399i	0.306479	−	0.951877i	$-0.400849\pi$
$853$	−18.8496	−	18.8496i	−0.645399	−	0.645399i	−0.951877	+	0.306479i	$0.900849\pi$
$854$	2.00811	−	2.76393i	0.0687163	−	0.0945798i
$855$		0			0
$856$	−1.12461	+	3.46120i	−0.0384384	+	0.118301i
$857$	−35.8328	−	35.8328i	−1.22403	−	1.22403i	−0.966188	−	0.257837i	$-0.916990\pi$
$857$	−35.8328	−	35.8328i	−1.22403	−	1.22403i	−0.257837	−	0.966188i	$-0.583010\pi$
$858$		0			0
$859$		−	16.4721i		−	0.562022i	−0.959705	−	0.281011i	$-0.909330\pi$
$859$		−	16.4721i		−	0.562022i	0.959705	−	0.281011i	$-0.0906697\pi$
$860$	15.1660	+	24.9608i	0.517156	+	0.851157i
$861$		0			0
$862$	26.5688	−	4.20808i	0.904935	−	0.143328i
$863$	−35.5851	−	35.5851i	−1.21133	−	1.21133i	−0.970589	−	0.240743i	$-0.922609\pi$
$863$	−35.5851	−	35.5851i	−1.21133	−	1.21133i	−0.240743	−	0.970589i	$-0.577391\pi$
$864$		0			0
$865$	44.5967	−	10.5279i	1.51633	−	0.357958i
$866$	1.32624	+	0.963568i	0.0450674	+	0.0327434i
$867$		0			0
$868$	−40.7768	−	20.7768i	−1.38406	−	0.705212i
$869$	−9.40456			−0.319028
$870$		0			0
$871$			6.71040i			0.227373i
$872$	18.8270	+	36.9501i	0.637563	+	1.25129i
$873$		0			0
$874$	13.7638	+	10.0000i	0.465568	+	0.338255i
$875$	−23.0902	+	19.2705i	−0.780590	+	0.651462i
$876$		0			0
$877$	21.5438	−	21.5438i	0.727482	−	0.727482i	−0.242636	−	0.970118i	$-0.578012\pi$
$877$	21.5438	−	21.5438i	0.727482	−	0.727482i	0.970118	+	0.242636i	$0.0780119\pi$
$878$	7.77322	+	49.0782i	0.262333	+	1.65631i
$879$		0			0
$880$	−2.16140	−	28.8635i	−0.0728608	−	0.972987i
$881$	−6.87539			−0.231638			−0.115819	−	0.993270i	$-0.536949\pi$
$881$	−6.87539			−0.231638			−0.115819	+	0.993270i	$0.536949\pi$
$882$		0			0
$883$	−2.79837	+	2.79837i	−0.0941728	+	0.0941728i	−0.752624	−	0.658451i	$-0.771212\pi$
$883$	−2.79837	+	2.79837i	−0.0941728	+	0.0941728i	0.658451	+	0.752624i	$0.271212\pi$
$884$	0.898056	+	2.76393i	0.0302049	+	0.0929611i
$885$		0			0
$886$	1.76393	+	1.28157i	0.0592605	+	0.0430552i
$887$	11.5187	−	11.5187i	0.386759	−	0.386759i	−0.486770	−	0.873530i	$-0.661825\pi$
$887$	11.5187	−	11.5187i	0.386759	−	0.386759i	0.873530	+	0.486770i	$0.161825\pi$
$888$		0			0
$889$			10.6525i			0.357273i
$890$	3.01905	−	7.21110i	0.101199	−	0.241716i
$891$		0			0
$892$	35.8185	+	18.2504i	1.19929	+	0.611069i
$893$	−6.71040	−	6.71040i	−0.224555	−	0.224555i
$894$		0			0
$895$	14.3188	+	8.84953i	0.478626	+	0.295807i
$896$	−28.9443	+	9.40456i	−0.966960	+	0.314184i
$897$		0			0
$898$	24.5792	−	3.89296i	0.820218	−	0.129910i
$899$		−	52.3607i		−	1.74633i
$900$		0			0
$901$		−	6.15537i		−	0.205065i
$902$	−4.08662	−	25.8019i	−0.136070	−	0.859110i
$903$		0			0
$904$	33.1280	+	10.7639i	1.10182	+	0.358003i
$905$	28.9443	+	17.8885i	0.962140	+	0.594635i
$906$		0			0
$907$	−7.67376	−	7.67376i	−0.254803	−	0.254803i	0.568133	−	0.822936i	$-0.307666\pi$
$907$	−7.67376	−	7.67376i	−0.254803	−	0.254803i	−0.822936	+	0.568133i	$0.807666\pi$
$908$	−23.6439	−	12.0472i	−0.784651	−	0.399800i
$909$		0			0
$910$	−8.06225	−	3.37540i	−0.267261	−	0.111893i
$911$			10.3026i			0.341341i	0.985328	+	0.170671i	$0.0545934\pi$
$911$			10.3026i			0.341341i	−0.985328	+	0.170671i	$0.945407\pi$
$912$		0			0
$913$	21.4164	−	21.4164i	0.708780	−	0.708780i
$914$	−11.3472	+	15.6180i	−0.375331	+	0.516599i
$915$		0			0
$916$	15.1246	−	4.91428i	0.499731	−	0.162373i
$917$	−26.0746	+	26.0746i	−0.861058	+	0.861058i
$918$		0			0
$919$	−18.1231			−0.597825			−0.298913	−	0.954281i	$-0.596624\pi$
$919$	−18.1231			−0.597825			−0.298913	+	0.954281i	$0.596624\pi$
$920$	−24.5965	−	29.0211i	−0.810922	−	0.956798i
$921$		0			0
$922$	38.4507	−	6.08999i	1.26631	−	0.200563i
$923$	8.29180	−	8.29180i	0.272928	−	0.272928i
$924$		0			0
$925$	−4.87380	−	1.62460i	−0.160249	−	0.0534165i
$926$	2.88854	−	3.97574i	0.0949234	−	0.130651i
$927$		0			0
$928$	−24.6215	−	24.6215i	−0.808239	−	0.808239i
$929$			36.6525i			1.20253i	0.799050	+	0.601264i	$0.205336\pi$
$929$			36.6525i			1.20253i	−0.799050	+	0.601264i	$0.794664\pi$
$930$		0			0
$931$	−0.472136			−0.0154736
$932$	7.02666	−	13.7906i	0.230166	−	0.451726i
$933$		0			0
$934$	−21.5438	+	29.6525i	−0.704934	+	0.970259i
$935$	9.95959	−	2.35114i	0.325714	−	0.0768905i
$936$		0			0
$937$	−42.3050	−	42.3050i	−1.38204	−	1.38204i	−0.840987	−	0.541056i	$-0.818025\pi$
$937$	−42.3050	−	42.3050i	−1.38204	−	1.38204i	−0.541056	−	0.840987i	$-0.681975\pi$
$938$	−3.88661	−	24.5391i	−0.126902	−	0.801230i
$939$		0			0
$940$	11.0187	+	18.1351i	0.359392	+	0.591502i
$941$			37.6183i			1.22632i	0.789959	+	0.613160i	$0.210102\pi$
$941$			37.6183i			1.22632i	−0.789959	+	0.613160i	$0.789898\pi$
$942$		0			0
$943$	−24.2784	−	24.2784i	−0.790615	−	0.790615i
$944$	1.11006	+	1.52786i	0.0361293	+	0.0497277i
$945$		0			0
$946$	24.1803	+	17.5680i	0.786171	+	0.571186i
$947$	2.14590	+	2.14590i	0.0697323	+	0.0697323i	0.741113	−	0.671381i	$-0.234298\pi$
$947$	2.14590	+	2.14590i	0.0697323	+	0.0697323i	−0.671381	+	0.741113i	$0.734298\pi$
$948$		0			0
$949$	6.84142			0.222082
$950$	−8.22545	−	11.5040i	−0.266869	−	0.373239i
$951$		0			0
$952$	−4.88493	−	9.58721i	−0.158321	−	0.310723i
$953$	29.1803	−	29.1803i	0.945244	−	0.945244i	−0.0533329	−	0.998577i	$-0.516984\pi$
$953$	29.1803	−	29.1803i	0.945244	−	0.945244i	0.998577	+	0.0533329i	$0.0169844\pi$
$954$		0			0
$955$	25.1246	+	15.5279i	0.813013	+	0.502470i
$956$	25.5279	−	8.29451i	0.825630	−	0.268263i
$957$		0			0
$958$	−1.04029	−	6.56816i	−0.0336104	−	0.212208i
$959$	20.8172			0.672224
$960$		0			0
$961$	−41.3607			−1.33422
$962$	−0.233561	−	1.47464i	−0.00753029	−	0.0475444i
$963$		0			0
$964$	−21.3723	+	6.94427i	−0.688355	+	0.223660i
$965$	−1.06957	−	4.53077i	−0.0344307	−	0.145851i
$966$		0			0
$967$	−10.9637	+	10.9637i	−0.352567	+	0.352567i	−0.861064	−	0.508497i	$-0.830201\pi$
$967$	−10.9637	+	10.9637i	−0.352567	+	0.352567i	0.508497	+	0.861064i	$0.330201\pi$
$968$	0.677819	+	1.33030i	0.0217859	+	0.0427573i
$969$		0			0
$970$	7.18317	+	17.5296i	0.230638	+	0.562842i
$971$	15.5967			0.500523			0.250262	−	0.968178i	$-0.419483\pi$
$971$	15.5967			0.500523			0.250262	+	0.968178i	$0.419483\pi$
$972$		0			0
$973$	40.7364	+	40.7364i	1.30595	+	1.30595i
$974$	30.6053	+	22.2361i	0.980658	+	0.712490i
$975$		0			0
$976$	−2.11146	−	2.90617i	−0.0675861	−	0.0930242i
$977$	23.7639	+	23.7639i	0.760276	+	0.760276i	0.976372	−	0.216096i	$-0.0693326\pi$
$977$	23.7639	+	23.7639i	0.760276	+	0.760276i	−0.216096	+	0.976372i	$0.569333\pi$
$978$		0			0
$979$		−	8.00000i		−	0.255681i
$980$	1.02562	+	0.250349i	0.0327621	+	0.00799712i
$981$		0			0
$982$	3.37070	+	21.2818i	0.107563	+	0.679129i
$983$	−18.0171	−	18.0171i	−0.574655	−	0.574655i	0.358770	−	0.933426i	$-0.383196\pi$
$983$	−18.0171	−	18.0171i	−0.574655	−	0.574655i	−0.933426	+	0.358770i	$0.883196\pi$
$984$		0			0
$985$	−6.70820	−	28.4164i	−0.213741	−	0.905422i
$986$	7.23607	−	9.95959i	0.230443	−	0.317178i
$987$		0			0
$988$	1.86588	−	3.66199i	0.0593614	−	0.116503i
$989$	39.2833			1.24914
$990$		0			0
$991$		−	14.3188i		−	0.454853i	−0.973795	−	0.227427i	$-0.926969\pi$
$991$		−	14.3188i		−	0.454853i	0.973795	−	0.227427i	$-0.0730312\pi$
$992$	−34.0260	+	34.0260i	−1.08033	+	1.08033i
$993$		0			0
$994$	−25.5195	+	35.1246i	−0.809430	+	1.11409i
$995$	25.5279	−	41.3050i	0.809288	−	1.30945i
$996$		0			0
$997$	27.9112	−	27.9112i	0.883955	−	0.883955i	−0.109979	−	0.993934i	$-0.535078\pi$
$997$	27.9112	−	27.9112i	0.883955	−	0.883955i	0.993934	+	0.109979i	$0.0350783\pi$
$998$	−16.6059	+	2.63012i	−0.525652	+	0.0832551i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.c.307.2		8
3.2	odd	2		40.2.k.a.27.3	yes	8
4.3	odd	2		1440.2.bi.c.847.3		8
5.3	odd	4	inner	360.2.w.c.163.4		8
8.3	odd	2	inner	360.2.w.c.307.4		8
8.5	even	2		1440.2.bi.c.847.2		8
12.11	even	2		160.2.o.a.47.1		8
15.2	even	4		200.2.k.h.43.4		8
15.8	even	4		40.2.k.a.3.1	✓	8
15.14	odd	2		200.2.k.h.107.2		8
20.3	even	4		1440.2.bi.c.1423.2		8
24.5	odd	2		160.2.o.a.47.2		8
24.11	even	2		40.2.k.a.27.1	yes	8
40.3	even	4	inner	360.2.w.c.163.2		8
40.13	odd	4		1440.2.bi.c.1423.3		8
48.5	odd	4		1280.2.n.q.767.1		8
48.11	even	4		1280.2.n.m.767.3		8
48.29	odd	4		1280.2.n.m.767.4		8
48.35	even	4		1280.2.n.q.767.2		8
60.23	odd	4		160.2.o.a.143.2		8
60.47	odd	4		800.2.o.g.143.3		8
60.59	even	2		800.2.o.g.207.4		8
120.29	odd	2		800.2.o.g.207.3		8
120.53	even	4		160.2.o.a.143.1		8
120.59	even	2		200.2.k.h.107.4		8
120.77	even	4		800.2.o.g.143.4		8
120.83	odd	4		40.2.k.a.3.3	yes	8
120.107	odd	4		200.2.k.h.43.2		8
240.53	even	4		1280.2.n.m.1023.3		8
240.83	odd	4		1280.2.n.m.1023.4		8
240.173	even	4		1280.2.n.q.1023.2		8
240.203	odd	4		1280.2.n.q.1023.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.1	✓	8	15.8	even	4
40.2.k.a.3.3	yes	8	120.83	odd	4
40.2.k.a.27.1	yes	8	24.11	even	2
40.2.k.a.27.3	yes	8	3.2	odd	2
160.2.o.a.47.1		8	12.11	even	2
160.2.o.a.47.2		8	24.5	odd	2
160.2.o.a.143.1		8	120.53	even	4
160.2.o.a.143.2		8	60.23	odd	4
200.2.k.h.43.2		8	120.107	odd	4
200.2.k.h.43.4		8	15.2	even	4
200.2.k.h.107.2		8	15.14	odd	2
200.2.k.h.107.4		8	120.59	even	2
360.2.w.c.163.2		8	40.3	even	4	inner
360.2.w.c.163.4		8	5.3	odd	4	inner
360.2.w.c.307.2		8	1.1	even	1	trivial
360.2.w.c.307.4		8	8.3	odd	2	inner
800.2.o.g.143.3		8	60.47	odd	4
800.2.o.g.143.4		8	120.77	even	4
800.2.o.g.207.3		8	120.29	odd	2
800.2.o.g.207.4		8	60.59	even	2
1280.2.n.m.767.3		8	48.11	even	4
1280.2.n.m.767.4		8	48.29	odd	4
1280.2.n.m.1023.3		8	240.53	even	4
1280.2.n.m.1023.4		8	240.83	odd	4
1280.2.n.q.767.1		8	48.5	odd	4
1280.2.n.q.767.2		8	48.35	even	4
1280.2.n.q.1023.1		8	240.203	odd	4
1280.2.n.q.1023.2		8	240.173	even	4
1440.2.bi.c.847.2		8	8.5	even	2
1440.2.bi.c.847.3		8	4.3	odd	2
1440.2.bi.c.1423.2		8	20.3	even	4
1440.2.bi.c.1423.3		8	40.13	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} +(-1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(1.90211 - 1.90211i) q^{7} +(-1.28408 - 2.52015i) q^{8} +O(q^{10})\)	\(q+(0.221232 + 1.39680i) q^{2} +(-1.90211 + 0.618034i) q^{4} +(1.17557 - 1.90211i) q^{5} +(1.90211 - 1.90211i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(2.91695 + 1.22123i) q^{10} +3.23607 q^{11} +(-0.726543 - 0.726543i) q^{13} +(3.07768 + 2.23607i) q^{14} +(3.23607 - 2.35114i) q^{16} +(1.00000 + 1.00000i) q^{17} -2.00000i q^{19} +(-1.06050 + 4.34458i) q^{20} +(0.715921 + 4.52015i) q^{22} +(4.25325 + 4.25325i) q^{23} +(-2.23607 - 4.47214i) q^{25} +(0.854102 - 1.17557i) q^{26} +(-2.44246 + 4.79360i) q^{28} -6.15537 q^{29} +8.50651i q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.17557 + 1.61803i) q^{34} +(-1.38197 - 5.85410i) q^{35} +(0.726543 - 0.726543i) q^{37} +(2.79360 - 0.442463i) q^{38} +(-6.30313 - 0.520147i) q^{40} -5.70820 q^{41} +(4.61803 - 4.61803i) q^{43} +(-6.15537 + 2.00000i) q^{44} +(-5.00000 + 6.88191i) q^{46} +(3.35520 - 3.35520i) q^{47} -0.236068i q^{49} +(5.75200 - 4.11272i) q^{50} +(1.83099 + 0.932938i) q^{52} +(-3.07768 - 3.07768i) q^{53} +(3.80423 - 6.15537i) q^{55} +(-7.23607 - 2.35114i) q^{56} +(-1.36176 - 8.59783i) q^{58} +0.472136i q^{59} -0.898056i q^{61} +(-11.8819 + 1.88191i) q^{62} +(-4.70228 + 6.47214i) q^{64} +(-2.23607 + 0.527864i) q^{65} +(-4.61803 - 4.61803i) q^{67} +(-2.52015 - 1.28408i) q^{68} +(7.87129 - 3.22545i) q^{70} +11.4127i q^{71} +(-4.70820 + 4.70820i) q^{73} +(1.17557 + 0.854102i) q^{74} +(1.23607 + 3.80423i) q^{76} +(6.15537 - 6.15537i) q^{77} -2.90617 q^{79} +(-0.667910 - 8.91930i) q^{80} +(-1.26284 - 7.97323i) q^{82} +(6.61803 - 6.61803i) q^{83} +(3.07768 - 0.726543i) q^{85} +(7.47214 + 5.42882i) q^{86} +(-4.15537 - 8.15537i) q^{88} -2.47214i q^{89} -2.76393 q^{91} +(-10.7188 - 5.46151i) q^{92} +(5.42882 + 3.94427i) q^{94} +(-3.80423 - 2.35114i) q^{95} +(4.23607 + 4.23607i) q^{97} +(0.329740 - 0.0522257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^8	\( 8 q + 2 q^{2} - 4 q^{8} - 10 q^{10} + 8 q^{11} + 8 q^{16} + 8 q^{17} + 12 q^{22} - 20 q^{26} - 20 q^{28} + 32 q^{32} - 20 q^{35} + 4 q^{38} - 20 q^{40} + 8 q^{41} + 28 q^{43} - 40 q^{46} + 10 q^{50} + 20 q^{52} - 40 q^{56} + 20 q^{58} - 40 q^{62} - 28 q^{67} + 4 q^{68} + 20 q^{70} + 16 q^{73} - 8 q^{76} - 28 q^{82} + 44 q^{83} + 24 q^{86} + 16 q^{88} - 40 q^{91} - 20 q^{92} + 16 q^{97} + 6 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^8 - 10 * q^10 + 8 * q^11 + 8 * q^16 + 8 * q^17 + 12 * q^22 - 20 * q^26 - 20 * q^28 + 32 * q^32 - 20 * q^35 + 4 * q^38 - 20 * q^40 + 8 * q^41 + 28 * q^43 - 40 * q^46 + 10 * q^50 + 20 * q^52 - 40 * q^56 + 20 * q^58 - 40 * q^62 - 28 * q^67 + 4 * q^68 + 20 * q^70 + 16 * q^73 - 8 * q^76 - 28 * q^82 + 44 * q^83 + 24 * q^86 + 16 * q^88 - 40 * q^91 - 20 * q^92 + 16 * q^97 + 6 * q^98

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