LMFDB - Embedded newform 360.2.w.c.307.4

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			307.4
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	360.307
Dual form			360.2.w.c.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39680 + 0.221232i) q^{2} +(1.90211 + 0.618034i) q^{4} +(-1.17557 + 1.90211i) q^{5} +(-1.90211 + 1.90211i) q^{7} +(2.52015 + 1.28408i) q^{8} +(-2.06285 + 2.39680i) q^{10} +3.23607 q^{11} +(0.726543 + 0.726543i) q^{13} +(-3.07768 + 2.23607i) q^{14} +(3.23607 + 2.35114i) q^{16} +(1.00000 + 1.00000i) q^{17} -2.00000i q^{19} +(-3.41164 + 2.89149i) q^{20} +(4.52015 + 0.715921i) q^{22} +(-4.25325 - 4.25325i) q^{23} +(-2.23607 - 4.47214i) q^{25} +(0.854102 + 1.17557i) q^{26} +(-4.79360 + 2.44246i) q^{28} +6.15537 q^{29} -8.50651i q^{31} +(4.00000 + 4.00000i) q^{32} +(1.17557 + 1.61803i) q^{34} +(-1.38197 - 5.85410i) q^{35} +(-0.726543 + 0.726543i) q^{37} +(0.442463 - 2.79360i) q^{38} +(-5.40507 + 3.28408i) q^{40} -5.70820 q^{41} +(4.61803 - 4.61803i) q^{43} +(6.15537 + 2.00000i) q^{44} +(-5.00000 - 6.88191i) q^{46} +(-3.35520 + 3.35520i) q^{47} -0.236068i q^{49} +(-2.13397 - 6.74138i) q^{50} +(0.932938 + 1.83099i) q^{52} +(3.07768 + 3.07768i) q^{53} +(-3.80423 + 6.15537i) q^{55} +(-7.23607 + 2.35114i) q^{56} +(8.59783 + 1.36176i) q^{58} +0.472136i q^{59} +0.898056i q^{61} +(1.88191 - 11.8819i) q^{62} +(4.70228 + 6.47214i) q^{64} +(-2.23607 + 0.527864i) q^{65} +(-4.61803 - 4.61803i) q^{67} +(1.28408 + 2.52015i) q^{68} +(-0.635220 - 8.48276i) q^{70} -11.4127i q^{71} +(-4.70820 + 4.70820i) q^{73} +(-1.17557 + 0.854102i) q^{74} +(1.23607 - 3.80423i) q^{76} +(-6.15537 + 6.15537i) q^{77} +2.90617 q^{79} +(-8.27636 + 3.39144i) q^{80} +(-7.97323 - 1.26284i) q^{82} +(6.61803 - 6.61803i) q^{83} +(-3.07768 + 0.726543i) q^{85} +(7.47214 - 5.42882i) q^{86} +(8.15537 + 4.15537i) q^{88} -2.47214i q^{89} -2.76393 q^{91} +(-5.46151 - 10.7188i) q^{92} +(-5.42882 + 3.94427i) q^{94} +(3.80423 + 2.35114i) q^{95} +(4.23607 + 4.23607i) q^{97} +(0.0522257 - 0.329740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	1.39680	+	0.221232i	0.987688	+	0.156434i
$2$	1.39680	+	0.221232i	0.987688	+	0.156434i
$3$		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	−0.968386	−	0.249455i	$-0.919748\pi$
$7$	−1.90211	+	1.90211i	−0.718931	+	0.718931i	0.249455	+	0.968386i	$0.419748\pi$
$8$	2.52015	+	1.28408i	0.891007	+	0.453990i
$9$		0			0
$10$	−2.06285	+	2.39680i	−0.652330	+	0.757935i
$11$	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	0.800645	−	0.599139i	$-0.204490\pi$
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	−0.599139	+	0.800645i	$0.704490\pi$
$14$	−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	$-0.0736815\pi$
$20$	−3.41164	+	2.89149i	−0.762866	+	0.646557i
$21$		0			0
$22$	4.52015	+	0.715921i	0.963699	+	0.152635i
$23$	−4.25325	−	4.25325i	−0.886865	−	0.886865i	0.107356	−	0.994221i	$-0.465762\pi$
$23$	−4.25325	−	4.25325i	−0.886865	−	0.886865i	−0.994221	+	0.107356i	$0.965762\pi$
$24$		0			0
$25$	−2.23607	−	4.47214i	−0.447214	−	0.894427i
$26$	0.854102	+	1.17557i	0.167503	+	0.230548i
$27$		0			0
$28$	−4.79360	+	2.44246i	−0.905906	+	0.461582i
$29$	6.15537			1.14302			0.571511	−	0.820594i	$-0.306357\pi$
$29$	6.15537			1.14302			0.571511	+	0.820594i	$0.306357\pi$
$30$		0			0
$31$		−	8.50651i		−	1.52781i	−0.645326	−	0.763907i	$-0.723279\pi$
$31$		−	8.50651i		−	1.52781i	0.645326	−	0.763907i	$-0.276721\pi$
$32$	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	−0.764302	−	0.644859i	$-0.776916\pi$
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	0.644859	+	0.764302i	$0.276916\pi$
$38$	0.442463	−	2.79360i	0.0717771	−	0.453182i
$39$		0			0
$40$	−5.40507	+	3.28408i	−0.854617	+	0.519258i
$41$	−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	−0.908119	−	0.418713i	$-0.862481\pi$
$47$	−3.35520	+	3.35520i	−0.489406	+	0.489406i	0.418713	+	0.908119i	$0.362481\pi$
$48$		0			0
$49$		−	0.236068i		−	0.0337240i
$50$	−2.13397	−	6.74138i	−0.301788	−	0.953375i
$51$		0			0
$52$	0.932938	+	1.83099i	0.129375	+	0.253913i
$53$	3.07768	+	3.07768i	0.422752	+	0.422752i	0.886150	−	0.463398i	$-0.153370\pi$
$53$	3.07768	+	3.07768i	0.422752	+	0.422752i	−0.463398	+	0.886150i	$0.653370\pi$
$54$		0			0
$55$	−3.80423	+	6.15537i	−0.512962	+	0.829990i
$56$	−7.23607	+	2.35114i	−0.966960	+	0.314184i
$57$		0			0
$58$	8.59783	+	1.36176i	1.12895	+	0.178808i
$59$			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	$0.0183104\pi$
$61$			0.898056i			0.114984i	−0.998346	+	0.0574921i	$0.981690\pi$
$62$	1.88191	−	11.8819i	0.239003	−	1.50900i
$63$		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	$0.880621\pi$
$68$	1.28408	+	2.52015i	0.155717	+	0.305613i
$69$		0			0
$70$	−0.635220	−	8.48276i	−0.0759233	−	1.01388i
$71$		−	11.4127i		−	1.35444i	−0.735783	−	0.677218i	$-0.763185\pi$
$71$		−	11.4127i		−	1.35444i	0.735783	−	0.677218i	$-0.236815\pi$
$72$		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	$-0.447727\pi$
$79$	2.90617			0.326970			0.163485	+	0.986546i	$0.447727\pi$
$80$	−8.27636	+	3.39144i	−0.925325	+	0.379174i
$81$		0			0
$82$	−7.97323	−	1.26284i	−0.880496	−	0.139457i
$83$	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
$88$	8.15537	+	4.15537i	0.869365	+	0.442964i
$89$		−	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
$92$	−5.46151	−	10.7188i	−0.569402	−	1.11751i
$93$		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	$0.651634\pi$
$98$	0.0522257	−	0.329740i	0.00527560	−	0.0333088i
$99$		0			0
$100$	−1.48932	−	9.88847i	−0.148932	−	0.988847i
$101$		−	2.90617i		−	0.289175i	−0.989492	−	0.144587i	$-0.953815\pi$
$101$		−	2.90617i		−	0.289175i	0.989492	−	0.144587i	$-0.0461855\pi$
$102$		0			0
$103$	−3.35520	−	3.35520i	−0.330597	−	0.330597i	0.522216	−	0.852813i	$-0.325106\pi$
$103$	−3.35520	−	3.35520i	−0.330597	−	0.330597i	−0.852813	+	0.522216i	$0.825106\pi$
$104$	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	$-0.252212\pi$
$109$	14.6619			1.40435			0.702176	+	0.712003i	$0.252212\pi$
$110$	−6.67551	+	7.75621i	−0.636485	+	0.739526i
$111$		0			0
$112$	−10.6275	+	1.68323i	−1.00420	+	0.159050i
$113$	−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
$118$	−0.104451	+	0.659481i	−0.00961554	+	0.0607101i
$119$	−3.80423			−0.348733
$120$		0			0
$121$	−0.527864			−0.0479876
$122$	−0.198678	+	1.25441i	−0.0179875	+	0.113569i
$123$		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	−0.571870	−	0.820344i	$-0.693782\pi$
$127$	2.80017	−	2.80017i	0.248475	−	0.248475i	0.820344	+	0.571870i	$0.193782\pi$
$128$	5.13632	+	10.0806i	0.453990	+	0.891007i
$129$		0			0
$130$	−3.24013	+	0.242632i	−0.284178	+	0.0212803i
$131$	−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	$0.637413\pi$
$140$	0.989378	−	11.9893i	0.0836177	−	1.01328i
$141$		0			0
$142$	2.52485	−	15.9413i	0.211880	−	1.33776i
$143$	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
$148$	−1.83099	+	0.932938i	−0.150507	+	0.0766870i
$149$	12.8658			1.05400			0.527002	−	0.849864i	$-0.323316\pi$
$149$	12.8658			1.05400			0.527002	+	0.849864i	$0.323316\pi$
$150$		0			0
$151$		−	6.71040i		−	0.546084i	−0.962002	−	0.273042i	$-0.911970\pi$
$151$		−	6.71040i		−	0.546084i	0.962002	−	0.273042i	$-0.0880298\pi$
$152$	2.56816	−	5.04029i	0.208305	−	0.408822i
$153$		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	$0.538066\pi$
$157$	−13.9353	+	13.9353i	−1.11216	+	1.11216i	−0.992858	+	0.119303i	$0.961934\pi$
$158$	4.05934	+	0.642937i	0.322944	+	0.0511493i
$159$		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	−0.946426	−	0.322920i	$-0.895336\pi$
$167$	−8.05748	+	8.05748i	−0.623507	+	0.623507i	0.322920	+	0.946426i	$0.395336\pi$
$168$		0			0
$169$		−	11.9443i		−	0.918790i
$170$	−4.45965	+	0.333955i	−0.342040	+	0.0256132i
$171$		0			0
$172$	11.6381	−	5.92992i	0.887399	−	0.452152i
$173$	−14.4904	−	14.4904i	−1.10168	−	1.10168i	−0.994208	−	0.107474i	$-0.965724\pi$
$173$	−14.4904	−	14.4904i	−1.10168	−	1.10168i	−0.107474	−	0.994208i	$-0.534276\pi$
$174$		0			0
$175$	12.7598	+	4.25325i	0.964547	+	0.321516i
$176$	10.4721	+	7.60845i	0.789367	+	0.573509i
$177$		0			0
$178$	0.546915	−	3.45309i	0.0409930	−	0.258820i
$179$			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	$-0.808671\pi$
$181$		−	15.2169i		−	1.13106i	0.824726	−	0.565532i	$-0.191329\pi$
$182$	−3.86067	−	0.611469i	−0.286172	−	0.0453251i
$183$		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
$188$	−8.45559	+	4.30834i	−0.616687	+	0.314218i
$189$		0			0
$190$	4.79360	+	4.12569i	0.347765	+	0.299309i
$191$		−	13.2088i		−	0.955755i	−0.878427	−	0.477877i	$-0.841406\pi$
$191$		−	13.2088i		−	0.955755i	0.878427	−	0.477877i	$-0.158594\pi$
$192$		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	−0.954866	−	0.297038i	$-0.904001\pi$
$197$	−9.23305	+	9.23305i	−0.657828	+	0.657828i	0.297038	+	0.954866i	$0.404001\pi$
$198$		0			0
$199$	−21.7153			−1.53936			−0.769678	−	0.638432i	$-0.779583\pi$
$199$	−21.7153			−1.53936			−0.769678	+	0.638432i	$0.779583\pi$
$200$	0.107356	−	14.1417i	0.00759122	−	0.999971i
$201$		0			0
$202$	0.642937	−	4.05934i	0.0452369	−	0.285615i
$203$	−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
$208$	0.642937	+	4.05934i	0.0445797	+	0.281465i
$209$		−	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	$0.474863\pi$
$212$	3.95199	+	7.75621i	0.271424	+	0.532699i
$213$		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
$218$	20.4797	+	3.24367i	1.38706	+	0.219689i
$219$		0			0
$220$	−11.0403	+	9.35706i	−0.744336	+	0.630853i
$221$			1.45309i			0.0977451i
$222$		0			0
$223$	14.2128	+	14.2128i	0.951763	+	0.951763i	0.998889	−	0.0471263i	$-0.0150063\pi$
$223$	14.2128	+	14.2128i	0.951763	+	0.951763i	−0.0471263	+	0.998889i	$0.515006\pi$
$224$	−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	$-0.415379\pi$
$229$	7.95148			0.525449			0.262724	+	0.964871i	$0.415379\pi$
$230$	18.9680	−	1.42040i	1.25071	−	0.0936581i
$231$		0			0
$232$	15.5124	+	7.90398i	1.01844	+	0.518922i
$233$	−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
$238$	−5.31375	−	0.841616i	−0.344439	−	0.0545538i
$239$	13.4208			0.868119			0.434059	−	0.900884i	$-0.357081\pi$
$239$	13.4208			0.868119			0.434059	+	0.900884i	$0.357081\pi$
$240$		0			0
$241$	11.2361			0.723779			0.361889	−	0.932221i	$-0.382132\pi$
$241$	11.2361			0.723779			0.361889	+	0.932221i	$0.382132\pi$
$242$	−0.737322	−	0.116780i	−0.0473968	−	0.00750692i
$243$		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
$248$	10.9230	−	21.4377i	0.693613	−	1.36129i
$249$		0			0
$250$	15.3315	+	3.86592i	0.969649	+	0.244502i
$251$	−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
$260$	−4.57949	−	0.377909i	−0.284008	−	0.0234369i
$261$		0			0
$262$	−19.1477	−	3.03269i	−1.18295	−	0.187360i
$263$	7.50245	+	7.50245i	0.462621	+	0.462621i	0.899514	−	0.436893i	$-0.143921\pi$
$263$	7.50245	+	7.50245i	0.462621	+	0.462621i	−0.436893	+	0.899514i	$0.643921\pi$
$264$		0			0
$265$	−9.47214	+	2.23607i	−0.581869	+	0.137361i
$266$	4.47214	+	6.15537i	0.274204	+	0.377410i
$267$		0			0
$268$	−5.92992	−	11.6381i	−0.362228	−	0.710912i
$269$	−20.4742			−1.24833			−0.624167	−	0.781291i	$-0.714562\pi$
$269$	−20.4742			−1.24833			−0.624167	+	0.781291i	$0.714562\pi$
$270$		0			0
$271$			17.2250i			1.04635i	0.852227	+	0.523173i	$0.175252\pi$
$271$			17.2250i			1.04635i	−0.852227	+	0.523173i	$0.824748\pi$
$272$	0.884927	+	5.58721i	0.0536566	+	0.338774i
$273$		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	−0.927811	−	0.373051i	$-0.878312\pi$
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	0.373051	+	0.927811i	$0.378312\pi$
$278$	−4.73799	+	29.9145i	−0.284166	+	1.79415i
$279$		0			0
$280$	4.03437	−	16.5278i	0.241100	−	0.987722i
$281$	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
$290$	−12.6976	+	14.7532i	−0.745628	+	0.866338i
$291$		0			0
$292$	−11.8654	+	6.04571i	−0.694368	+	0.353798i
$293$	−3.07768	−	3.07768i	−0.179800	−	0.179800i	0.611469	−	0.791269i	$-0.290579\pi$
$293$	−3.07768	−	3.07768i	−0.179800	−	0.179800i	−0.791269	+	0.611469i	$0.790579\pi$
$294$		0			0
$295$	−0.898056	−	0.555029i	−0.0522868	−	0.0323150i
$296$	−2.76393	+	0.898056i	−0.160650	+	0.0521984i
$297$		0			0
$298$	17.9709	+	2.84632i	1.04103	+	0.164883i
$299$		−	6.18034i		−	0.357418i
$300$		0			0
$301$			17.5680i			1.01261i
$302$	1.48455	−	9.37310i	0.0854264	−	0.539361i
$303$		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	$0.934356\pi$
$308$	−15.5124	+	7.90398i	−0.883903	+	0.450371i
$309$		0			0
$310$	20.3884	+	17.5476i	1.15798	+	0.996638i
$311$			20.8172i			1.18044i	0.807243	+	0.590219i	$0.200959\pi$
$311$			20.8172i			1.18044i	−0.807243	+	0.590219i	$0.799041\pi$
$312$		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	−0.586587	−	0.809886i	$-0.699529\pi$
$317$	3.97574	−	3.97574i	0.223300	−	0.223300i	0.809886	+	0.586587i	$0.199529\pi$
$318$		0			0
$319$	19.9192			1.11526
$320$	−17.8386	+	1.33582i	−0.997208	+	0.0746746i
$321$		0			0
$322$	22.6007	+	3.57960i	1.25949	+	0.199484i
$323$	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
$328$	−14.3855	−	7.32979i	−0.794307	−	0.404720i
$329$		−	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	$0.809597\pi$
$332$	16.6784	−	8.49808i	0.915347	−	0.466393i
$333$		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	$-0.528860\pi$
$338$	2.64245	−	16.6838i	0.143730	−	0.907478i
$339$		0			0
$340$	−6.30313	−	0.520147i	−0.341835	−	0.0282089i
$341$		−	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	$-0.647209\pi$
$349$	−16.6700			−0.892324			−0.446162	+	0.894952i	$0.647209\pi$
$350$	16.8819	+	8.76382i	0.902376	+	0.468446i
$351$		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
$358$	−1.66540	+	10.5149i	−0.0880193	+	0.555732i
$359$	−19.9192			−1.05129			−0.525647	−	0.850703i	$-0.676177\pi$
$359$	−19.9192			−1.05129			−0.525647	+	0.850703i	$0.676177\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	3.36646	−	21.2550i	0.176937	−	1.11714i
$363$		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	−0.312753	−	0.949835i	$-0.601251\pi$
$367$	12.2047	−	12.2047i	0.637082	−	0.637082i	0.949835	+	0.312753i	$0.101251\pi$
$368$	−3.76382	−	23.7638i	−0.196203	−	1.23877i
$369$		0			0
$370$	−0.242632	−	3.24013i	−0.0126139	−	0.168446i
$371$	−11.7082			−0.607860
$372$		0			0
$373$	−22.4418	−	22.4418i	−1.16199	−	1.16199i	−0.984038	−	0.177956i	$-0.943052\pi$
$373$	−22.4418	−	22.4418i	−1.16199	−	1.16199i	−0.177956	−	0.984038i	$-0.556948\pi$
$374$	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	$0.999089\pi$
$380$	5.78298	+	6.82328i	0.296661	+	0.350027i
$381$		0			0
$382$	2.92220	−	18.4501i	0.149513	−	0.943988i
$383$	1.00406	+	1.00406i	0.0513049	+	0.0513049i	0.732294	−	0.680989i	$-0.238450\pi$
$383$	1.00406	+	1.00406i	0.0513049	+	0.0513049i	−0.680989	+	0.732294i	$0.738450\pi$
$384$		0			0
$385$	−4.47214	−	18.9443i	−0.227921	−	0.965489i
$386$	2.38197	−	1.73060i	0.121239	−	0.0880852i
$387$		0			0
$388$	5.43945	+	10.6755i	0.276146	+	0.541967i
$389$	4.14725			0.210274			0.105137	−	0.994458i	$-0.466472\pi$
$389$	4.14725			0.210274			0.105137	+	0.994458i	$0.466472\pi$
$390$		0			0
$391$		−	8.50651i		−	0.430193i
$392$	0.303130	−	0.594926i	0.0153104	−	0.0300483i
$393$		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	$-0.415600\pi$
$397$	24.4500	−	24.4500i	1.22711	−	1.22711i	0.965053	−	0.262055i	$-0.0844002\pi$
$398$	−30.3320	−	4.80411i	−1.52040	−	0.240808i
$399$		0			0
$400$	3.27855	−	19.7294i	0.163928	−	0.986472i
$401$	−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	$-0.179291\pi$
$410$	11.7752	−	13.6814i	0.581533	−	0.675678i
$411$		0			0
$412$	−4.30834	−	8.45559i	−0.212257	−	0.416577i
$413$	−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
$418$	1.43184	−	9.04029i	0.0700337	−	0.442175i
$419$			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	$0.243575\pi$
$421$			28.4257i			1.38538i	−0.721234	+	0.692692i	$0.756425\pi$
$422$	3.20119	+	0.507018i	0.155831	+	0.0246813i
$423$		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
$428$	−1.16829	−	2.29291i	−0.0564716	−	0.110832i
$429$		0			0
$430$	1.54222	+	20.5948i	0.0743722	+	0.993170i
$431$			19.0211i			0.916216i	0.888897	+	0.458108i	$0.151473\pi$
$431$			19.0211i			0.916216i	−0.888897	+	0.458108i	$0.848527\pi$
$432$		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	$-0.816554\pi$
$439$	−35.1361			−1.67695			−0.838477	+	0.544937i	$0.816554\pi$
$440$	−17.4912	+	10.6275i	−0.833860	+	0.506646i
$441$		0			0
$442$	−0.321469	+	2.02967i	−0.0152907	+	0.0965417i
$443$	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
$448$	−21.2550	−	3.36646i	−1.00420	−	0.159050i
$449$		−	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
$452$	−21.9460	+	11.1820i	−1.03225	+	0.525958i
$453$		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	$0.646560\pi$
$458$	11.1066	+	1.75912i	0.518979	+	0.0821983i
$459$		0			0
$460$	26.8088	+	2.21232i	1.24997	+	0.103150i
$461$			27.5276i			1.28209i	0.767503	+	0.641045i	$0.221499\pi$
$461$			27.5276i			1.28209i	−0.767503	+	0.641045i	$0.778501\pi$
$462$		0			0
$463$	2.45714	+	2.45714i	0.114193	+	0.114193i	0.761894	−	0.647701i	$-0.224270\pi$
$463$	2.45714	+	2.45714i	0.114193	+	0.114193i	−0.647701	+	0.761894i	$0.724270\pi$
$464$	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
$470$	−1.12048	−	14.9630i	−0.0516841	−	0.690192i
$471$		0			0
$472$	−0.606260	+	1.18985i	−0.0279054	+	0.0547674i
$473$	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
$478$	18.7462	+	2.96911i	0.857431	+	0.135804i
$479$	4.70228			0.214853			0.107426	−	0.994213i	$-0.465739\pi$
$479$	4.70228			0.214853			0.107426	+	0.994213i	$0.465739\pi$
$480$		0			0
$481$	−1.05573			−0.0481371
$482$	15.6946	+	2.48577i	0.714868	+	0.113224i
$483$		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	−0.990999	−	0.133872i	$-0.957259\pi$
$487$	−18.9151	+	18.9151i	−0.857126	+	0.857126i	0.133872	+	0.990999i	$0.457259\pi$
$488$	−1.15317	+	2.26323i	−0.0522018	+	0.102452i
$489$		0			0
$490$	0.565808	+	0.486972i	0.0255606	+	0.0219992i
$491$	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	$0.914264\pi$
$500$	20.5598	+	8.79174i	0.919462	+	0.393179i
$501$		0			0
$502$	−0.251899	−	0.0398969i	−0.0112428	−	0.00178069i
$503$	−16.5640	−	16.5640i	−0.738552	−	0.738552i	0.233746	−	0.972298i	$-0.424902\pi$
$503$	−16.5640	−	16.5640i	−0.738552	−	0.738552i	−0.972298	+	0.233746i	$0.924902\pi$
$504$		0			0
$505$	5.52786	+	3.41641i	0.245987	+	0.152028i
$506$	−16.1803	−	22.2703i	−0.719304	−	0.990037i
$507$		0			0
$508$	7.05684	−	3.59564i	0.313097	−	0.159531i
$509$	10.8576			0.481257			0.240628	−	0.970617i	$-0.422646\pi$
$509$	10.8576			0.481257			0.240628	+	0.970617i	$0.422646\pi$
$510$		0			0
$511$		−	17.9111i		−	0.792339i
$512$	3.53971	+	22.3488i	0.156434	+	0.987688i
$513$		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
$518$	0.611469	−	3.86067i	0.0268664	−	0.169628i
$519$		0			0
$520$	−6.31304	−	1.54099i	−0.276845	−	0.0675770i
$521$	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
$530$	−13.7254	+	1.02781i	−0.596193	+	0.0446451i
$531$		0			0
$532$	4.88493	+	9.58721i	0.211788	+	0.415658i
$533$	−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
$538$	−28.5984	−	4.52955i	−1.23297	−	0.195283i
$539$		−	0.763932i		−	0.0329049i
$540$		0			0
$541$			12.3107i			0.529280i	0.964347	+	0.264640i	$0.0852531\pi$
$541$			12.3107i			0.529280i	−0.964347	+	0.264640i	$0.914747\pi$
$542$	−3.81072	+	24.0599i	−0.163684	+	1.03346i
$543$		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	$0.636327\pi$
$548$	7.02666	+	13.7906i	0.300164	+	0.589105i
$549$		0			0
$550$	−6.90566	−	21.8156i	−0.294458	−	0.930219i
$551$		−	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	−0.00207187	−	0.999998i	$-0.500659\pi$
$557$	23.5519	−	23.5519i	0.997926	−	0.997926i	0.999998	+	0.00207187i	$0.000659497\pi$
$558$		0			0
$559$	6.71040			0.283820
$560$	9.29168	−	22.1935i	0.392645	−	0.937845i
$561$		0			0
$562$	13.5604	+	2.14776i	0.572013	+	0.0905979i
$563$	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
$568$	14.6548	−	28.7616i	0.614901	−	1.20681i
$569$			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	$0.342814\pi$
$572$	3.01905	+	5.92522i	0.126233	+	0.247746i
$573$		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	$0.469097\pi$
$578$	3.31848	−	20.9520i	0.138030	−	0.871490i
$579$		0			0
$580$	−20.9999	+	17.7982i	−0.871973	+	0.739030i
$581$			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
$590$	−1.13162	−	0.973944i	−0.0465879	−	0.0400967i
$591$		0			0
$592$	−4.05934	+	0.642937i	−0.166838	+	0.0264246i
$593$	−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
$598$	1.36729	−	8.63271i	0.0559125	−	0.353018i
$599$	−6.49839			−0.265517			−0.132759	−	0.991148i	$-0.542383\pi$
$599$	−6.49839			−0.265517			−0.132759	+	0.991148i	$0.542383\pi$
$600$		0			0
$601$	−17.7082			−0.722333			−0.361166	−	0.932501i	$-0.617621\pi$
$601$	−17.7082			−0.722333			−0.361166	+	0.932501i	$0.617621\pi$
$602$	−3.88661	+	24.5391i	−0.158406	+	1.00014i
$603$		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	$-0.362763\pi$
$607$	32.6789	−	32.6789i	1.32640	−	1.32640i	0.908489	−	0.417908i	$-0.137237\pi$
$608$	8.00000	−	8.00000i	0.324443	−	0.324443i
$609$		0			0
$610$	−2.15246	−	1.85255i	−0.0871507	−	0.0750077i
$611$	−4.87539			−0.197237
$612$		0			0
$613$	19.5357	+	19.5357i	0.789038	+	0.789038i	0.981337	−	0.192298i	$-0.0615941\pi$
$613$	19.5357	+	19.5357i	0.789038	+	0.789038i	−0.192298	+	0.981337i	$0.561594\pi$
$614$	−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	$0.748915\pi$
$620$	24.5965	+	29.0211i	0.987819	+	1.16552i
$621$		0			0
$622$	−4.60543	+	29.0776i	−0.184661	+	1.16590i
$623$	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
$628$	−35.1191	+	17.8941i	−1.40140	+	0.714051i
$629$	−1.45309			−0.0579383
$630$		0			0
$631$			22.6134i			0.900223i	0.892972	+	0.450112i	$0.148616\pi$
$631$			22.6134i			0.900223i	−0.892972	+	0.450112i	$0.851384\pi$
$632$	7.32398	+	3.73175i	0.291332	+	0.148441i
$633$		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
$638$	27.8232	+	4.40676i	1.10153	+	0.174465i
$639$		0			0
$640$	−25.2125	−	2.08059i	−0.996612	−	0.0822425i
$641$	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	−0.193775	−	0.981046i	$-0.562073\pi$
$647$	20.0252	−	20.0252i	0.787271	−	0.787271i	0.981046	+	0.193775i	$0.0620731\pi$
$648$		0			0
$649$			1.52786i			0.0599739i
$650$	3.34748	−	6.44832i	0.131299	−	0.252924i
$651$		0			0
$652$	−34.9144	+	17.7898i	−1.36735	+	0.696701i
$653$	20.0907	+	20.0907i	0.786210	+	0.786210i	0.980871	−	0.194661i	$-0.0623606\pi$
$653$	20.0907	+	20.0907i	0.786210	+	0.786210i	−0.194661	+	0.980871i	$0.562361\pi$
$654$		0			0
$655$	16.1150	−	26.0746i	0.629664	−	1.01882i
$656$	−18.4721	−	13.4208i	−0.721216	−	0.523994i
$657$		0			0
$658$	2.82379	−	17.8287i	0.110083	−	0.695035i
$659$		−	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	$-0.976429\pi$
$661$		−	3.80423i		−	0.147967i	0.997259	−	0.0739836i	$-0.0235713\pi$
$662$	−42.0003	−	6.65219i	−1.63239	−	0.258545i
$663$		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
$668$	−20.3060	+	10.3464i	−0.785664	+	0.400316i
$669$		0			0
$670$	20.5948	−	1.54222i	0.795647	−	0.0595810i
$671$			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	−0.541617	−	0.840625i	$-0.682188\pi$
$677$	7.77997	−	7.77997i	0.299008	−	0.299008i	0.840625	+	0.541617i	$0.182188\pi$
$678$		0			0
$679$	−16.1150			−0.618435
$680$	−8.68915	−	2.12099i	−0.333214	−	0.0813364i
$681$		0			0
$682$	6.08999	−	38.4507i	0.233198	−	1.47235i
$683$	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
$688$	25.8019	−	4.08662i	0.983689	−	0.155801i
$689$			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	$0.444473\pi$
$692$	−18.6068	−	36.5178i	−0.707323	−	1.38820i
$693$		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
$698$	−23.2847	−	3.68793i	−0.881338	−	0.139590i
$699$		0			0
$700$	21.6419	+	15.9761i	0.817985	+	0.603841i
$701$			19.7072i			0.744330i	0.928167	+	0.372165i	$0.121384\pi$
$701$			19.7072i			0.744330i	−0.928167	+	0.372165i	$0.878616\pi$
$702$		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	$-0.480567\pi$
$709$	3.24920			0.122026			0.0610131	+	0.998137i	$0.480567\pi$
$710$	27.3539	+	23.5426i	1.02657	+	0.883539i
$711$		0			0
$712$	3.17442	−	6.23015i	0.118966	−	0.233485i
$713$	−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
$718$	−27.8232	−	4.40676i	−1.03835	−	0.164459i
$719$	−4.01623			−0.149780			−0.0748900	−	0.997192i	$-0.523861\pi$
$719$	−4.01623			−0.149780			−0.0748900	+	0.997192i	$0.523861\pi$
$720$		0			0
$721$	12.7639			0.475354
$722$	20.9520	+	3.31848i	0.779754	+	0.123501i
$723$		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	−0.861123	−	0.508396i	$-0.830239\pi$
$727$	−9.51057	+	9.51057i	−0.352727	+	0.352727i	0.508396	+	0.861123i	$0.330239\pi$
$728$	−6.96552	−	3.54911i	−0.258159	−	0.131539i
$729$		0			0
$730$	−1.57233	−	20.9969i	−0.0581945	−	0.777132i
$731$	9.23607			0.341608
$732$		0			0
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	0.966303	−	0.257407i	$-0.0828680\pi$
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	−0.257407	+	0.966303i	$0.582868\pi$
$734$	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	$-0.0554088\pi$
$740$	0.377909	−	4.57949i	0.0138922	−	0.168345i
$741$		0			0
$742$	−16.3540	−	2.59023i	−0.600376	−	0.0950902i
$743$	−4.80828	−	4.80828i	−0.176399	−	0.176399i	0.613385	−	0.789784i	$-0.289807\pi$
$743$	−4.80828	−	4.80828i	−0.176399	−	0.176399i	−0.789784	+	0.613385i	$0.789807\pi$
$744$		0			0
$745$	−15.1246	+	24.4721i	−0.554123	+	0.896590i
$746$	−26.3820	−	36.3117i	−0.965912	−	1.32946i
$747$		0			0
$748$	4.15537	+	8.15537i	0.151935	+	0.298190i
$749$	3.46120			0.126469
$750$		0			0
$751$		−	11.4127i		−	0.416455i	−0.978080	−	0.208227i	$-0.933231\pi$
$751$		−	11.4127i		−	0.416455i	0.978080	−	0.208227i	$-0.0667694\pi$
$752$	−18.7462	+	2.96911i	−0.683603	+	0.108272i
$753$		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	$-0.446686\pi$
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.986006	−	0.166709i	$-0.0533140\pi$
$758$	−0.0246576	+	0.155682i	−0.000895606	+	0.00565463i
$759$		0			0
$760$	6.56816	+	10.8101i	0.238252	+	0.392125i
$761$	−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	$-0.0372302\pi$
$770$	−2.05562	−	27.4508i	−0.0740792	−	0.989257i
$771$		0			0
$772$	3.71000	−	1.89034i	0.133526	−	0.0680348i
$773$	31.5034	+	31.5034i	1.13310	+	1.13310i	0.989659	+	0.143439i	$0.0458159\pi$
$773$	31.5034	+	31.5034i	1.13310	+	1.13310i	0.143439	+	0.989659i	$0.454184\pi$
$774$		0			0
$775$	−38.0423	+	19.0211i	−1.36652	+	0.683259i
$776$	5.23607	+	16.1150i	0.187964	+	0.578493i
$777$		0			0
$778$	5.79289	+	0.917504i	0.207685	+	0.0328941i
$779$			11.4164i			0.409035i
$780$		0			0
$781$		−	36.9322i		−	1.32154i
$782$	1.88191	−	11.8819i	0.0672969	−	0.424896i
$783$		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	$0.601415\pi$
$788$	−23.2686	+	11.8560i	−0.828911	+	0.422351i
$789$		0			0
$790$	−5.99499	+	6.96552i	−0.213292	+	0.247822i
$791$		−	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	−0.919205	−	0.393779i	$-0.871167\pi$
$797$	−14.8334	+	14.8334i	−0.525426	+	0.525426i	0.393779	+	0.919205i	$0.371167\pi$
$798$		0			0
$799$	−6.71040			−0.237397
$800$	8.94427	−	26.8328i	0.316228	−	0.948683i
$801$		0			0
$802$	−44.5420	−	7.05476i	−1.57283	−	0.249112i
$803$	−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
$808$	3.73175	−	7.32398i	0.131283	−	0.257657i
$809$			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	$0.348673\pi$
$812$	−29.5064	+	15.0343i	−1.03547	+	0.527599i
$813$		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
$818$	4.77789	−	30.1664i	0.167055	−	1.05474i
$819$		0			0
$820$	19.4743	−	16.5052i	0.680073	−	0.576387i
$821$			17.9111i			0.625101i	0.949901	+	0.312550i	$0.101183\pi$
$821$			17.9111i			0.625101i	−0.949901	+	0.312550i	$0.898817\pi$
$822$		0			0
$823$	−13.8698	−	13.8698i	−0.483472	−	0.483472i	0.422767	−	0.906238i	$-0.361059\pi$
$823$	−13.8698	−	13.8698i	−0.483472	−	0.483472i	−0.906238	+	0.422767i	$0.861059\pi$
$824$	−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	$-0.104655\pi$
$829$	54.5002			1.89287			0.946436	+	0.322892i	$0.104655\pi$
$830$	2.21013	+	29.5141i	0.0767146	+	1.02445i
$831$		0			0
$832$	−1.28587	+	8.11869i	−0.0445797	+	0.281465i
$833$	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
$838$	−6.37873	+	40.2737i	−0.220350	+	1.39123i
$839$	−15.2169			−0.525346			−0.262673	−	0.964885i	$-0.584604\pi$
$839$	−15.2169			−0.525346			−0.262673	+	0.964885i	$0.584604\pi$
$840$		0			0
$841$	8.88854			0.306502
$842$	−6.28867	+	39.7051i	−0.216722	+	1.36833i
$843$		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
$848$	2.72353	+	17.1957i	0.0935262	+	0.590501i
$849$		0			0
$850$	4.60741	−	8.87535i	0.158033	−	0.304422i
$851$	6.18034			0.211859
$852$		0			0
$853$	18.8496	+	18.8496i	0.645399	+	0.645399i	0.951877	−	0.306479i	$-0.0991509\pi$
$853$	18.8496	+	18.8496i	0.645399	+	0.645399i	−0.306479	+	0.951877i	$0.599151\pi$
$854$	−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	$-0.0906697\pi$
$860$	−2.40206	+	29.1081i	−0.0819095	+	0.992577i
$861$		0			0
$862$	−4.20808	+	26.5688i	−0.143328	+	0.904935i
$863$	35.5851	+	35.5851i	1.21133	+	1.21133i	0.970589	+	0.240743i	$0.0773909\pi$
$863$	35.5851	+	35.5851i	1.21133	+	1.21133i	0.240743	+	0.970589i	$0.422609\pi$
$864$		0			0
$865$	44.5967	−	10.5279i	1.51633	−	0.357958i
$866$	1.32624	−	0.963568i	0.0450674	−	0.0327434i
$867$		0			0
$868$	20.7768	+	40.7768i	0.705212	+	1.38406i
$869$	9.40456			0.319028
$870$		0			0
$871$		−	6.71040i		−	0.227373i
$872$	36.9501	+	18.8270i	1.25129	+	0.637563i
$873$		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	−0.970118	−	0.242636i	$-0.921988\pi$
$877$	−21.5438	+	21.5438i	−0.727482	+	0.727482i	0.242636	+	0.970118i	$0.421988\pi$
$878$	−49.0782	−	7.77322i	−1.65631	−	0.262333i
$879$		0			0
$880$	−26.7829	+	10.9749i	−0.902850	+	0.369964i
$881$	−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	−0.873530	−	0.486770i	$-0.838175\pi$
$887$	−11.5187	+	11.5187i	−0.386759	+	0.386759i	0.486770	+	0.873530i	$0.338175\pi$
$888$		0			0
$889$			10.6525i			0.357273i
$890$	5.92522	+	5.09964i	0.198614	+	0.170940i
$891$		0			0
$892$	18.2504	+	35.8185i	0.611069	+	1.19929i
$893$	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
$898$	3.89296	−	24.5792i	0.129910	−	0.820218i
$899$		−	52.3607i		−	1.74633i
$900$		0			0
$901$			6.15537i			0.205065i
$902$	−25.8019	−	4.08662i	−0.859110	−	0.136070i
$903$		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	$0.807666\pi$
$908$	12.0472	+	23.6439i	0.399800	+	0.784651i
$909$		0			0
$910$	5.70157	−	6.62460i	0.189005	−	0.219603i
$911$		−	10.3026i		−	0.341341i	−0.985328	−	0.170671i	$-0.945407\pi$
$911$		−	10.3026i		−	0.341341i	0.985328	−	0.170671i	$-0.0545934\pi$
$912$		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	$-0.403376\pi$
$919$	18.1231			0.597825			0.298913	+	0.954281i	$0.403376\pi$
$920$	36.9572	+	9.02113i	1.21844	+	0.297418i
$921$		0			0
$922$	−6.08999	+	38.4507i	−0.200563	+	1.26631i
$923$	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
$932$	−13.7906	+	7.02666i	−0.451726	+	0.230166i
$933$		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	$-0.681975\pi$
$938$	24.5391	+	3.88661i	0.801230	+	0.126902i
$939$		0			0
$940$	1.74520	−	21.1482i	0.0569220	−	0.689780i
$941$		−	37.6183i		−	1.22632i	−0.789959	−	0.613160i	$-0.789898\pi$
$941$		−	37.6183i		−	1.22632i	0.789959	−	0.613160i	$-0.210102\pi$
$942$		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
$950$	−13.4828	+	4.26793i	−0.437438	+	0.138470i
$951$		0			0
$952$	−9.58721	−	4.88493i	−0.310723	−	0.158321i
$953$	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
$958$	6.56816	+	1.04029i	0.212208	+	0.0336104i
$959$	−20.8172			−0.672224
$960$		0			0
$961$	−41.3607			−1.33422
$962$	−1.47464	−	0.233561i	−0.0475444	−	0.00753029i
$963$		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	−0.508497	−	0.861064i	$-0.669799\pi$
$967$	10.9637	−	10.9637i	0.352567	−	0.352567i	0.861064	+	0.508497i	$0.169799\pi$
$968$	−1.33030	−	0.677819i	−0.0427573	−	0.0217859i
$969$		0			0
$970$	−18.8914	+	1.41466i	−0.606566	+	0.0454219i
$971$	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
$980$	0.682589	+	0.805379i	0.0218045	+	0.0257269i
$981$		0			0
$982$	21.2818	+	3.37070i	0.679129	+	0.107563i
$983$	18.0171	+	18.0171i	0.574655	+	0.574655i	0.933426	−	0.358770i	$-0.116804\pi$
$983$	18.0171	+	18.0171i	0.574655	+	0.574655i	−0.358770	+	0.933426i	$0.616804\pi$
$984$		0			0
$985$	−6.70820	−	28.4164i	−0.213741	−	0.905422i
$986$	7.23607	+	9.95959i	0.230443	+	0.317178i
$987$		0			0
$988$	3.66199	−	1.86588i	0.116503	−	0.0593614i
$989$	−39.2833			−1.24914
$990$		0			0
$991$			14.3188i			0.454853i	0.973795	+	0.227427i	$0.0730312\pi$
$991$			14.3188i			0.454853i	−0.973795	+	0.227427i	$0.926969\pi$
$992$	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	−0.993934	−	0.109979i	$-0.964922\pi$
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	0.109979	+	0.993934i	$0.464922\pi$
$998$	−2.63012	+	16.6059i	−0.0832551	+	0.525652i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.39680 + 0.221232i) q^{2} +(1.90211 + 0.618034i) q^{4} +(-1.17557 + 1.90211i) q^{5} +(-1.90211 + 1.90211i) q^{7} +(2.52015 + 1.28408i) q^{8} +(-2.06285 + 2.39680i) q^{10} +3.23607 q^{11} +(0.726543 + 0.726543i) q^{13} +(-3.07768 + 2.23607i) q^{14} +(3.23607 + 2.35114i) q^{16} +(1.00000 + 1.00000i) q^{17} -2.00000i q^{19} +(-3.41164 + 2.89149i) q^{20} +(4.52015 + 0.715921i) q^{22} +(-4.25325 - 4.25325i) q^{23} +(-2.23607 - 4.47214i) q^{25} +(0.854102 + 1.17557i) q^{26} +(-4.79360 + 2.44246i) q^{28} +6.15537 q^{29} -8.50651i q^{31} +(4.00000 + 4.00000i) q^{32} +(1.17557 + 1.61803i) q^{34} +(-1.38197 - 5.85410i) q^{35} +(-0.726543 + 0.726543i) q^{37} +(0.442463 - 2.79360i) q^{38} +(-5.40507 + 3.28408i) q^{40} -5.70820 q^{41} +(4.61803 - 4.61803i) q^{43} +(6.15537 + 2.00000i) q^{44} +(-5.00000 - 6.88191i) q^{46} +(-3.35520 + 3.35520i) q^{47} -0.236068i q^{49} +(-2.13397 - 6.74138i) q^{50} +(0.932938 + 1.83099i) q^{52} +(3.07768 + 3.07768i) q^{53} +(-3.80423 + 6.15537i) q^{55} +(-7.23607 + 2.35114i) q^{56} +(8.59783 + 1.36176i) q^{58} +0.472136i q^{59} +0.898056i q^{61} +(1.88191 - 11.8819i) q^{62} +(4.70228 + 6.47214i) q^{64} +(-2.23607 + 0.527864i) q^{65} +(-4.61803 - 4.61803i) q^{67} +(1.28408 + 2.52015i) q^{68} +(-0.635220 - 8.48276i) q^{70} -11.4127i q^{71} +(-4.70820 + 4.70820i) q^{73} +(-1.17557 + 0.854102i) q^{74} +(1.23607 - 3.80423i) q^{76} +(-6.15537 + 6.15537i) q^{77} +2.90617 q^{79} +(-8.27636 + 3.39144i) q^{80} +(-7.97323 - 1.26284i) q^{82} +(6.61803 - 6.61803i) q^{83} +(-3.07768 + 0.726543i) q^{85} +(7.47214 - 5.42882i) q^{86} +(8.15537 + 4.15537i) q^{88} -2.47214i q^{89} -2.76393 q^{91} +(-5.46151 - 10.7188i) q^{92} +(-5.42882 + 3.94427i) q^{94} +(3.80423 + 2.35114i) q^{95} +(4.23607 + 4.23607i) q^{97} +(0.0522257 - 0.329740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{8} - 10 q^{10} + 8 q^{11} + 8 q^{16} + 8 q^{17} + 12 q^{22} - 20 q^{26} - 20 q^{28} + 32 q^{32} - 20 q^{35} + 4 q^{38} - 20 q^{40} + 8 q^{41} + 28 q^{43} - 40 q^{46} + 10 q^{50} + 20 q^{52}+ \cdots + 6 q^{98}+O(q^{100}) \) 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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