LMFDB - Embedded newform 1470.2.b.c.881.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 $ x^16 - 16x^13 + 2x^12 + 96x^10 - 80x^9 + 2x^8 - 240x^7 + 864x^6 + 162x^4 - 3888*x^3 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.13
Root			$1.73191 + 0.0223575i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.c.881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.683428 + 1.59152i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.59152 - 0.683428i) q^{6} -1.00000i q^{8} +(-2.06585 - 2.17537i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.683428 + 1.59152i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.59152 - 0.683428i) q^{6} -1.00000i q^{8} +(-2.06585 - 2.17537i) q^{9} -1.00000i q^{10} -2.78371i q^{11} +(0.683428 - 1.59152i) q^{12} +3.85040i q^{13} +(0.683428 - 1.59152i) q^{15} +1.00000 q^{16} +6.13320 q^{17} +(2.17537 - 2.06585i) q^{18} -7.77395i q^{19} +1.00000 q^{20} +2.78371 q^{22} -5.94960i q^{23} +(1.59152 + 0.683428i) q^{24} +1.00000 q^{25} -3.85040 q^{26} +(4.87401 - 1.80113i) q^{27} +0.293914i q^{29} +(1.59152 + 0.683428i) q^{30} +9.46905i q^{31} +1.00000i q^{32} +(4.43033 + 1.90247i) q^{33} +6.13320i q^{34} +(2.06585 + 2.17537i) q^{36} -5.38970 q^{37} +7.77395 q^{38} +(-6.12798 - 2.63147i) q^{39} +1.00000i q^{40} +2.06179 q^{41} +5.99125 q^{43} +2.78371i q^{44} +(2.06585 + 2.17537i) q^{45} +5.94960 q^{46} +4.88979 q^{47} +(-0.683428 + 1.59152i) q^{48} +1.00000i q^{50} +(-4.19160 + 9.76110i) q^{51} -3.85040i q^{52} -0.393343i q^{53} +(1.80113 + 4.87401i) q^{54} +2.78371i q^{55} +(12.3724 + 5.31293i) q^{57} -0.293914 q^{58} +2.81048 q^{59} +(-0.683428 + 1.59152i) q^{60} -0.167612i q^{61} -9.46905 q^{62} -1.00000 q^{64} -3.85040i q^{65} +(-1.90247 + 4.43033i) q^{66} +9.00242 q^{67} -6.13320 q^{68} +(9.46889 + 4.06612i) q^{69} -8.46969i q^{71} +(-2.17537 + 2.06585i) q^{72} -9.46753i q^{73} -5.38970i q^{74} +(-0.683428 + 1.59152i) q^{75} +7.77395i q^{76} +(2.63147 - 6.12798i) q^{78} -0.358168 q^{79} -1.00000 q^{80} +(-0.464498 + 8.98801i) q^{81} +2.06179i q^{82} +7.38866 q^{83} -6.13320 q^{85} +5.99125i q^{86} +(-0.467769 - 0.200869i) q^{87} -2.78371 q^{88} -0.493908 q^{89} +(-2.17537 + 2.06585i) q^{90} +5.94960i q^{92} +(-15.0702 - 6.47141i) q^{93} +4.88979i q^{94} +7.77395i q^{95} +(-1.59152 - 0.683428i) q^{96} +18.4958i q^{97} +(-6.05561 + 5.75074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	$ 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.683428	+	1.59152i	−0.394577	+	0.918863i
$3$	−0.683428	+	1.59152i	−0.394577	+	0.918863i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.59152	−	0.683428i	−0.649734	−	0.279008i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.06585	−	2.17537i	−0.688618	−	0.725124i
$10$		−	1.00000i		−	0.316228i
$11$		−	2.78371i		−	0.839321i	−0.907681	−	0.419660i	$-0.862149\pi$
$11$		−	2.78371i		−	0.839321i	0.907681	−	0.419660i	$-0.137851\pi$
$12$	0.683428	−	1.59152i	0.197289	−	0.459431i
$13$			3.85040i			1.06791i	0.845513	+	0.533955i	$0.179295\pi$
$13$			3.85040i			1.06791i	−0.845513	+	0.533955i	$0.820705\pi$
$14$		0			0
$15$	0.683428	−	1.59152i	0.176460	−	0.410928i
$16$	1.00000			0.250000
$17$	6.13320			1.48752			0.743760	−	0.668446i	$-0.233040\pi$
$17$	6.13320			1.48752			0.743760	+	0.668446i	$0.233040\pi$
$18$	2.17537	−	2.06585i	0.512740	−	0.486926i
$19$		−	7.77395i		−	1.78347i	−0.452560	−	0.891734i	$-0.649489\pi$
$19$		−	7.77395i		−	1.78347i	0.452560	−	0.891734i	$-0.350511\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	2.78371			0.593489
$23$		−	5.94960i		−	1.24058i	−0.784373	−	0.620289i	$-0.787015\pi$
$23$		−	5.94960i		−	1.24058i	0.784373	−	0.620289i	$-0.212985\pi$
$24$	1.59152	+	0.683428i	0.324867	+	0.139504i
$25$	1.00000			0.200000
$26$	−3.85040			−0.755126
$27$	4.87401	−	1.80113i	0.938003	−	0.346628i
$28$		0			0
$29$			0.293914i			0.0545784i	0.999628	+	0.0272892i	$0.00868750\pi$
$29$			0.293914i			0.0545784i	−0.999628	+	0.0272892i	$0.991312\pi$
$30$	1.59152	+	0.683428i	0.290570	+	0.124776i
$31$			9.46905i			1.70069i	0.526225	+	0.850346i	$0.323607\pi$
$31$			9.46905i			1.70069i	−0.526225	+	0.850346i	$0.676393\pi$
$32$			1.00000i			0.176777i
$33$	4.43033	+	1.90247i	0.771221	+	0.331177i
$34$			6.13320i			1.05184i
$35$		0			0
$36$	2.06585	+	2.17537i	0.344309	+	0.362562i
$37$	−5.38970			−0.886062			−0.443031	−	0.896506i	$-0.646097\pi$
$37$	−5.38970			−0.886062			−0.443031	+	0.896506i	$0.646097\pi$
$38$	7.77395			1.26110
$39$	−6.12798	−	2.63147i	−0.981262	−	0.421373i
$40$			1.00000i			0.158114i
$41$	2.06179			0.321998			0.160999	−	0.986955i	$-0.448528\pi$
$41$	2.06179			0.321998			0.160999	+	0.986955i	$0.448528\pi$
$42$		0			0
$43$	5.99125			0.913657			0.456828	−	0.889555i	$-0.348985\pi$
$43$	5.99125			0.913657			0.456828	+	0.889555i	$0.348985\pi$
$44$			2.78371i			0.419660i
$45$	2.06585	+	2.17537i	0.307959	+	0.324286i
$46$	5.94960			0.877221
$47$	4.88979			0.713250			0.356625	−	0.934248i	$-0.383927\pi$
$47$	4.88979			0.713250			0.356625	+	0.934248i	$0.383927\pi$
$48$	−0.683428	+	1.59152i	−0.0986443	+	0.229716i
$49$		0			0
$50$			1.00000i			0.141421i
$51$	−4.19160	+	9.76110i	−0.586942	+	1.36683i
$52$		−	3.85040i		−	0.533955i
$53$		−	0.393343i		−	0.0540298i	−0.999635	−	0.0270149i	$-0.991400\pi$
$53$		−	0.393343i		−	0.0540298i	0.999635	−	0.0270149i	$-0.00860015\pi$
$54$	1.80113	+	4.87401i	0.245103	+	0.663268i
$55$			2.78371i			0.375356i
$56$		0			0
$57$	12.3724	+	5.31293i	1.63876	+	0.703715i
$58$	−0.293914			−0.0385928
$59$	2.81048			0.365894			0.182947	−	0.983123i	$-0.441436\pi$
$59$	2.81048			0.365894			0.182947	+	0.983123i	$0.441436\pi$
$60$	−0.683428	+	1.59152i	−0.0882301	+	0.205464i
$61$		−	0.167612i		−	0.0214605i	−0.999942	−	0.0107303i	$-0.996584\pi$
$61$		−	0.167612i		−	0.0214605i	0.999942	−	0.0107303i	$-0.00341561\pi$
$62$	−9.46905			−1.20257
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.85040i		−	0.477584i
$66$	−1.90247	+	4.43033i	−0.234177	+	0.545335i
$67$	9.00242			1.09982			0.549911	−	0.835224i	$-0.314662\pi$
$67$	9.00242			1.09982			0.549911	+	0.835224i	$0.314662\pi$
$68$	−6.13320			−0.743760
$69$	9.46889	+	4.06612i	1.13992	+	0.489504i
$70$		0			0
$71$		−	8.46969i		−	1.00517i	−0.864529	−	0.502584i	$-0.832383\pi$
$71$		−	8.46969i		−	1.00517i	0.864529	−	0.502584i	$-0.167617\pi$
$72$	−2.17537	+	2.06585i	−0.256370	+	0.243463i
$73$		−	9.46753i		−	1.10809i	−0.832487	−	0.554045i	$-0.813084\pi$
$73$		−	9.46753i		−	1.10809i	0.832487	−	0.554045i	$-0.186916\pi$
$74$		−	5.38970i		−	0.626540i
$75$	−0.683428	+	1.59152i	−0.0789154	+	0.183773i
$76$			7.77395i			0.891734i
$77$		0			0
$78$	2.63147	−	6.12798i	0.297955	−	0.693857i
$79$	−0.358168			−0.0402970			−0.0201485	−	0.999797i	$-0.506414\pi$
$79$	−0.358168			−0.0402970			−0.0201485	+	0.999797i	$0.506414\pi$
$80$	−1.00000			−0.111803
$81$	−0.464498	+	8.98801i	−0.0516109	+	0.998667i
$82$			2.06179i			0.227687i
$83$	7.38866			0.811011			0.405505	−	0.914093i	$-0.367096\pi$
$83$	7.38866			0.811011			0.405505	+	0.914093i	$0.367096\pi$
$84$		0			0
$85$	−6.13320			−0.665239
$86$			5.99125i			0.646053i
$87$	−0.467769	−	0.200869i	−0.0501501	−	0.0215354i
$88$	−2.78371			−0.296745
$89$	−0.493908			−0.0523542			−0.0261771	−	0.999657i	$-0.508333\pi$
$89$	−0.493908			−0.0523542			−0.0261771	+	0.999657i	$0.508333\pi$
$90$	−2.17537	+	2.06585i	−0.229304	+	0.217760i
$91$		0			0
$92$			5.94960i			0.620289i
$93$	−15.0702	−	6.47141i	−1.56270	−	0.671054i
$94$			4.88979i			0.504344i
$95$			7.77395i			0.797591i
$96$	−1.59152	−	0.683428i	−0.162434	−	0.0697520i
$97$			18.4958i			1.87796i	0.343971	+	0.938980i	$0.388228\pi$
$97$			18.4958i			1.87796i	−0.343971	+	0.938980i	$0.611772\pi$
$98$		0			0
$99$	−6.05561	+	5.75074i	−0.608612	+	0.577971i
$100$	−1.00000			−0.100000
$101$	−17.4482			−1.73616			−0.868082	−	0.496421i	$-0.834647\pi$
$101$	−17.4482			−1.73616			−0.868082	+	0.496421i	$0.834647\pi$
$102$	−9.76110	−	4.19160i	−0.966493	−	0.415030i
$103$			10.7400i			1.05825i	0.848544	+	0.529124i	$0.177479\pi$
$103$			10.7400i			1.05825i	−0.848544	+	0.529124i	$0.822521\pi$
$104$	3.85040			0.377563
$105$		0			0
$106$	0.393343			0.0382048
$107$			10.8236i			1.04636i	0.852222	+	0.523180i	$0.175254\pi$
$107$			10.8236i			1.04636i	−0.852222	+	0.523180i	$0.824746\pi$
$108$	−4.87401	+	1.80113i	−0.469001	+	0.173314i
$109$	1.80838			0.173211			0.0866055	−	0.996243i	$-0.472398\pi$
$109$	1.80838			0.173211			0.0866055	+	0.996243i	$0.472398\pi$
$110$	−2.78371			−0.265417
$111$	3.68347	−	8.57781i	0.349620	−	0.814169i
$112$		0			0
$113$		−	17.3261i		−	1.62991i	−0.579527	−	0.814953i	$-0.696763\pi$
$113$		−	17.3261i		−	1.62991i	0.579527	−	0.814953i	$-0.303237\pi$
$114$	−5.31293	+	12.3724i	−0.497602	+	1.15878i
$115$			5.94960i			0.554803i
$116$		−	0.293914i		−	0.0272892i
$117$	8.37606	−	7.95437i	0.774367	−	0.735382i
$118$			2.81048i			0.258726i
$119$		0			0
$120$	−1.59152	−	0.683428i	−0.145285	−	0.0623881i
$121$	3.25095			0.295541
$122$	0.167612			0.0151749
$123$	−1.40909	+	3.28138i	−0.127053	+	0.295872i
$124$		−	9.46905i		−	0.850346i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.53139			−0.135888			−0.0679442	−	0.997689i	$-0.521644\pi$
$127$	−1.53139			−0.135888			−0.0679442	+	0.997689i	$0.521644\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.09458	+	9.53517i	−0.360508	+	0.839525i
$130$	3.85040			0.337703
$131$	20.9082			1.82676			0.913379	−	0.407110i	$-0.133463\pi$
$131$	20.9082			1.82676			0.913379	+	0.407110i	$0.133463\pi$
$132$	−4.43033	−	1.90247i	−0.385610	−	0.165588i
$133$		0			0
$134$			9.00242i			0.777691i
$135$	−4.87401	+	1.80113i	−0.419488	+	0.155017i
$136$		−	6.13320i		−	0.525918i
$137$		−	9.79136i		−	0.836533i	−0.908324	−	0.418266i	$-0.862638\pi$
$137$		−	9.79136i		−	0.836533i	0.908324	−	0.418266i	$-0.137362\pi$
$138$	−4.06612	+	9.46889i	−0.346131	+	0.806046i
$139$			6.86505i			0.582286i	0.956680	+	0.291143i	$0.0940355\pi$
$139$			6.86505i			0.582286i	−0.956680	+	0.291143i	$0.905965\pi$
$140$		0			0
$141$	−3.34182	+	7.78219i	−0.281432	+	0.655379i
$142$	8.46969			0.710761
$143$	10.7184			0.896319
$144$	−2.06585	−	2.17537i	−0.172154	−	0.181281i
$145$		−	0.293914i		−	0.0244082i
$146$	9.46753			0.783538
$147$		0			0
$148$	5.38970			0.443031
$149$		−	20.1309i		−	1.64919i	−0.565725	−	0.824594i	$-0.691404\pi$
$149$		−	20.1309i		−	1.64919i	0.565725	−	0.824594i	$-0.308596\pi$
$150$	−1.59152	−	0.683428i	−0.129947	−	0.0558016i
$151$	17.6661			1.43764			0.718822	−	0.695194i	$-0.244681\pi$
$151$	17.6661			1.43764			0.718822	+	0.695194i	$0.244681\pi$
$152$	−7.77395			−0.630551
$153$	−12.6703	−	13.3420i	−1.02433	−	1.07864i
$154$		0			0
$155$		−	9.46905i		−	0.760572i
$156$	6.12798	+	2.63147i	0.490631	+	0.210686i
$157$		−	4.57340i		−	0.364997i	−0.983206	−	0.182499i	$-0.941582\pi$
$157$		−	4.57340i		−	0.364997i	0.983206	−	0.182499i	$-0.0584185\pi$
$158$		−	0.358168i		−	0.0284943i
$159$	0.626012	+	0.268821i	0.0496460	+	0.0213189i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−8.98801	−	0.464498i	−0.706164	−	0.0364944i
$163$	0.531368			0.0416200			0.0208100	−	0.999783i	$-0.493376\pi$
$163$	0.531368			0.0416200			0.0208100	+	0.999783i	$0.493376\pi$
$164$	−2.06179			−0.160999
$165$	−4.43033	−	1.90247i	−0.344900	−	0.148107i
$166$			7.38866i			0.573471i
$167$	11.5050			0.890284			0.445142	−	0.895460i	$-0.353153\pi$
$167$	11.5050			0.890284			0.445142	+	0.895460i	$0.353153\pi$
$168$		0			0
$169$	−1.82560			−0.140431
$170$		−	6.13320i		−	0.470395i
$171$	−16.9113	+	16.0599i	−1.29324	+	1.22813i
$172$	−5.99125			−0.456828
$173$	−12.1901			−0.926797			−0.463398	−	0.886150i	$-0.653370\pi$
$173$	−12.1901			−0.926797			−0.463398	+	0.886150i	$0.653370\pi$
$174$	0.200869	−	0.467769i	0.0152278	−	0.0354615i
$175$		0			0
$176$		−	2.78371i		−	0.209830i
$177$	−1.92076	+	4.47293i	−0.144373	+	0.336206i
$178$		−	0.493908i		−	0.0370200i
$179$			10.6691i			0.797450i	0.917071	+	0.398725i	$0.130547\pi$
$179$			10.6691i			0.797450i	−0.917071	+	0.398725i	$0.869453\pi$
$180$	−2.06585	−	2.17537i	−0.153980	−	0.162143i
$181$		−	6.89007i		−	0.512135i	−0.966659	−	0.256068i	$-0.917573\pi$
$181$		−	6.89007i		−	0.512135i	0.966659	−	0.256068i	$-0.0824269\pi$
$182$		0			0
$183$	0.266757	+	0.114551i	0.0197193	+	0.00846783i
$184$	−5.94960			−0.438610
$185$	5.38970			0.396259
$186$	6.47141	−	15.0702i	0.474507	−	1.10500i
$187$		−	17.0731i		−	1.24851i
$188$	−4.88979			−0.356625
$189$		0			0
$190$	−7.77395			−0.563982
$191$			15.8451i			1.14651i	0.819377	+	0.573255i	$0.194320\pi$
$191$			15.8451i			1.14651i	−0.819377	+	0.573255i	$0.805680\pi$
$192$	0.683428	−	1.59152i	0.0493221	−	0.114858i
$193$	24.6498			1.77433			0.887167	−	0.461448i	$-0.152670\pi$
$193$	24.6498			1.77433			0.887167	+	0.461448i	$0.152670\pi$
$194$	−18.4958			−1.32792
$195$	6.12798	+	2.63147i	0.438834	+	0.188444i
$196$		0			0
$197$		−	8.86995i		−	0.631958i	−0.948766	−	0.315979i	$-0.897667\pi$
$197$		−	8.86995i		−	0.631958i	0.948766	−	0.315979i	$-0.102333\pi$
$198$	−5.75074	−	6.05561i	−0.408687	−	0.430354i
$199$		−	24.9844i		−	1.77110i	−0.464547	−	0.885548i	$-0.653783\pi$
$199$		−	24.9844i		−	1.77110i	0.464547	−	0.885548i	$-0.346217\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−6.15250	+	14.3275i	−0.433964	+	1.01058i
$202$		−	17.4482i		−	1.22765i
$203$		0			0
$204$	4.19160	−	9.76110i	0.293471	−	0.683414i
$205$	−2.06179			−0.144002
$206$	−10.7400			−0.748295
$207$	−12.9426	+	12.2910i	−0.899573	+	0.854284i
$208$			3.85040i			0.266977i
$209$	−21.6405			−1.49690
$210$		0			0
$211$	9.99057			0.687779			0.343890	−	0.939010i	$-0.388255\pi$
$211$	9.99057			0.687779			0.343890	+	0.939010i	$0.388255\pi$
$212$			0.393343i			0.0270149i
$213$	13.4797	+	5.78842i	0.923611	+	0.396616i
$214$	−10.8236			−0.739888
$215$	−5.99125			−0.408600
$216$	−1.80113	−	4.87401i	−0.122551	−	0.331634i
$217$		0			0
$218$			1.80838i			0.122479i
$219$	15.0677	+	6.47037i	1.01818	+	0.437227i
$220$		−	2.78371i		−	0.187678i
$221$			23.6153i			1.58854i
$222$	8.57781	+	3.68347i	0.575705	+	0.247219i
$223$		−	15.9961i		−	1.07118i	−0.844479	−	0.535589i	$-0.820090\pi$
$223$		−	15.9961i		−	1.07118i	0.844479	−	0.535589i	$-0.179910\pi$
$224$		0			0
$225$	−2.06585	−	2.17537i	−0.137724	−	0.145025i
$226$	17.3261			1.15252
$227$	−3.88632			−0.257944			−0.128972	−	0.991648i	$-0.541168\pi$
$227$	−3.88632			−0.257944			−0.128972	+	0.991648i	$0.541168\pi$
$228$	−12.3724	−	5.31293i	−0.819381	−	0.351858i
$229$		−	10.0440i		−	0.663728i	−0.943327	−	0.331864i	$-0.892323\pi$
$229$		−	10.0440i		−	0.663728i	0.943327	−	0.331864i	$-0.107677\pi$
$230$	−5.94960			−0.392305
$231$		0			0
$232$	0.293914			0.0192964
$233$		−	25.0949i		−	1.64402i	−0.569470	−	0.822012i	$-0.692851\pi$
$233$		−	25.0949i		−	1.64402i	0.569470	−	0.822012i	$-0.307149\pi$
$234$	7.95437	+	8.37606i	0.519993	+	0.547560i
$235$	−4.88979			−0.318975
$236$	−2.81048			−0.182947
$237$	0.244782	−	0.570030i	0.0159003	−	0.0370275i
$238$		0			0
$239$			19.4568i			1.25856i	0.777180	+	0.629279i	$0.216650\pi$
$239$			19.4568i			1.25856i	−0.777180	+	0.629279i	$0.783350\pi$
$240$	0.683428	−	1.59152i	0.0441151	−	0.102732i
$241$			0.752125i			0.0484486i	0.999707	+	0.0242243i	$0.00771159\pi$
$241$			0.752125i			0.0484486i	−0.999707	+	0.0242243i	$0.992288\pi$
$242$			3.25095i			0.208979i
$243$	−13.9871	−	6.88191i	−0.897274	−	0.441475i
$244$			0.167612i			0.0107303i
$245$		0			0
$246$	−3.28138	−	1.40909i	−0.209213	−	0.0898401i
$247$	29.9329			1.90458
$248$	9.46905			0.601285
$249$	−5.04961	+	11.7592i	−0.320006	+	0.745208i
$250$		−	1.00000i		−	0.0632456i
$251$	3.30554			0.208644			0.104322	−	0.994544i	$-0.466733\pi$
$251$	3.30554			0.208644			0.104322	+	0.994544i	$0.466733\pi$
$252$		0			0
$253$	−16.5620			−1.04124
$254$		−	1.53139i		−	0.0960877i
$255$	4.19160	−	9.76110i	0.262488	−	0.611264i
$256$	1.00000			0.0625000
$257$	13.4708			0.840288			0.420144	−	0.907457i	$-0.361979\pi$
$257$	13.4708			0.840288			0.420144	+	0.907457i	$0.361979\pi$
$258$	−9.53517	−	4.09458i	−0.593634	−	0.254918i
$259$		0			0
$260$			3.85040i			0.238792i
$261$	0.639372	−	0.607183i	0.0395762	−	0.0375837i
$262$			20.9082i			1.29171i
$263$		−	5.03279i		−	0.310335i	−0.987888	−	0.155167i	$-0.950408\pi$
$263$		−	5.03279i		−	0.310335i	0.987888	−	0.155167i	$-0.0495917\pi$
$264$	1.90247	−	4.43033i	0.117089	−	0.272668i
$265$			0.393343i			0.0241629i
$266$		0			0
$267$	0.337550	−	0.786063i	0.0206577	−	0.0481063i
$268$	−9.00242			−0.549911
$269$	−24.4184			−1.48882			−0.744409	−	0.667724i	$-0.767268\pi$
$269$	−24.4184			−1.48882			−0.744409	+	0.667724i	$0.767268\pi$
$270$	−1.80113	−	4.87401i	−0.109613	−	0.296623i
$271$		−	8.93330i		−	0.542659i	−0.962486	−	0.271330i	$-0.912537\pi$
$271$		−	8.93330i		−	0.542659i	0.962486	−	0.271330i	$-0.0874634\pi$
$272$	6.13320			0.371880
$273$		0			0
$274$	9.79136			0.591518
$275$		−	2.78371i		−	0.167864i
$276$	−9.46889	−	4.06612i	−0.569960	−	0.244752i
$277$	22.7119			1.36462			0.682311	−	0.731062i	$-0.260975\pi$
$277$	22.7119			1.36462			0.682311	+	0.731062i	$0.260975\pi$
$278$	−6.86505			−0.411738
$279$	20.5987	−	19.5617i	1.23321	−	1.17113i
$280$		0			0
$281$			21.8213i			1.30175i	0.759186	+	0.650874i	$0.225597\pi$
$281$			21.8213i			1.30175i	−0.759186	+	0.650874i	$0.774403\pi$
$282$	−7.78219	−	3.34182i	−0.463423	−	0.199003i
$283$		−	31.4471i		−	1.86934i	−0.355522	−	0.934668i	$-0.615697\pi$
$283$		−	31.4471i		−	1.86934i	0.355522	−	0.934668i	$-0.384303\pi$
$284$			8.46969i			0.502584i
$285$	−12.3724	−	5.31293i	−0.732877	−	0.314711i
$286$			10.7184i			0.633793i
$287$		0			0
$288$	2.17537	−	2.06585i	0.128185	−	0.121732i
$289$	20.6162			1.21272
$290$	0.293914			0.0172592
$291$	−29.4363	−	12.6405i	−1.72559	−	0.741000i
$292$			9.46753i			0.554045i
$293$	−26.8031			−1.56585			−0.782927	−	0.622114i	$-0.786274\pi$
$293$	−26.8031			−1.56585			−0.782927	+	0.622114i	$0.786274\pi$
$294$		0			0
$295$	−2.81048			−0.163633
$296$			5.38970i			0.313270i
$297$	−5.01383	−	13.5678i	−0.290932	−	0.787285i
$298$	20.1309			1.16615
$299$	22.9084			1.32482
$300$	0.683428	−	1.59152i	0.0394577	−	0.0918863i
$301$		0			0
$302$			17.6661i			1.01657i
$303$	11.9246	−	27.7692i	0.685050	−	1.59530i
$304$		−	7.77395i		−	0.445867i
$305$			0.167612i			0.00959744i
$306$	13.3420	−	12.6703i	0.762712	−	0.724313i
$307$		−	4.12520i		−	0.235438i	−0.993047	−	0.117719i	$-0.962442\pi$
$307$		−	4.12520i		−	0.235438i	0.993047	−	0.117719i	$-0.0375582\pi$
$308$		0			0
$309$	−17.0930	−	7.34005i	−0.972385	−	0.417561i
$310$	9.46905			0.537806
$311$	21.6262			1.22631			0.613156	−	0.789962i	$-0.289900\pi$
$311$	21.6262			1.22631			0.613156	+	0.789962i	$0.289900\pi$
$312$	−2.63147	+	6.12798i	−0.148978	+	0.346929i
$313$			8.40584i			0.475126i	0.971372	+	0.237563i	$0.0763487\pi$
$313$			8.40584i			0.475126i	−0.971372	+	0.237563i	$0.923651\pi$
$314$	4.57340			0.258092
$315$		0			0
$316$	0.358168			0.0201485
$317$		−	11.6893i		−	0.656537i	−0.944584	−	0.328269i	$-0.893535\pi$
$317$		−	11.6893i		−	0.656537i	0.944584	−	0.328269i	$-0.106465\pi$
$318$	−0.268821	+	0.626012i	−0.0150747	+	0.0351050i
$319$	0.818171			0.0458088
$320$	1.00000			0.0559017
$321$	−17.2260	−	7.39716i	−0.961461	−	0.412869i
$322$		0			0
$323$		−	47.6793i		−	2.65294i
$324$	0.464498	−	8.98801i	0.0258055	−	0.499334i
$325$			3.85040i			0.213582i
$326$			0.531368i			0.0294298i
$327$	−1.23589	+	2.87806i	−0.0683451	+	0.159157i
$328$		−	2.06179i		−	0.113843i
$329$		0			0
$330$	1.90247	−	4.43033i	0.104727	−	0.243881i
$331$	18.2140			1.00113			0.500566	−	0.865698i	$-0.333125\pi$
$331$	18.2140			1.00113			0.500566	+	0.865698i	$0.333125\pi$
$332$	−7.38866			−0.405505
$333$	11.1343	+	11.7246i	0.610158	+	0.642505i
$334$			11.5050i			0.629526i
$335$	−9.00242			−0.491855
$336$		0			0
$337$	5.63587			0.307005			0.153503	−	0.988148i	$-0.450945\pi$
$337$	5.63587			0.307005			0.153503	+	0.988148i	$0.450945\pi$
$338$		−	1.82560i		−	0.0992995i
$339$	27.5749	+	11.8412i	1.49766	+	0.643124i
$340$	6.13320			0.332620
$341$	26.3591			1.42743
$342$	−16.0599	−	16.9113i	−0.868417	−	0.914456i
$343$		0			0
$344$		−	5.99125i		−	0.323026i
$345$	−9.46889	−	4.06612i	−0.509788	−	0.218913i
$346$		−	12.1901i		−	0.655344i
$347$		−	24.1270i		−	1.29520i	−0.761979	−	0.647601i	$-0.775772\pi$
$347$		−	24.1270i		−	1.29520i	0.761979	−	0.647601i	$-0.224228\pi$
$348$	0.467769	+	0.200869i	0.0250750	+	0.0107677i
$349$			1.85774i			0.0994423i	0.998763	+	0.0497211i	$0.0158333\pi$
$349$			1.85774i			0.0994423i	−0.998763	+	0.0497211i	$0.984167\pi$
$350$		0			0
$351$	6.93508	+	18.7669i	0.370167	+	1.00170i
$352$	2.78371			0.148372
$353$	18.0834			0.962480			0.481240	−	0.876589i	$-0.340186\pi$
$353$	18.0834			0.962480			0.481240	+	0.876589i	$0.340186\pi$
$354$	−4.47293	−	1.92076i	−0.237734	−	0.102087i
$355$			8.46969i			0.449524i
$356$	0.493908			0.0261771
$357$		0			0
$358$	−10.6691			−0.563882
$359$			18.7873i			0.991558i	0.868449	+	0.495779i	$0.165117\pi$
$359$			18.7873i			0.991558i	−0.868449	+	0.495779i	$0.834883\pi$
$360$	2.17537	−	2.06585i	0.114652	−	0.108880i
$361$	−41.4344			−2.18076
$362$	6.89007			0.362134
$363$	−2.22179	+	5.17394i	−0.116614	+	0.271561i
$364$		0			0
$365$			9.46753i			0.495553i
$366$	−0.114551	+	0.266757i	−0.00598766	+	0.0139436i
$367$			8.07247i			0.421379i	0.977553	+	0.210690i	$0.0675710\pi$
$367$			8.07247i			0.421379i	−0.977553	+	0.210690i	$0.932429\pi$
$368$		−	5.94960i		−	0.310144i
$369$	−4.25936	−	4.48517i	−0.221734	−	0.233489i
$370$			5.38970i			0.280197i
$371$		0			0
$372$	15.0702	+	6.47141i	0.781351	+	0.335527i
$373$	−4.49811			−0.232903			−0.116452	−	0.993196i	$-0.537152\pi$
$373$	−4.49811			−0.232903			−0.116452	+	0.993196i	$0.537152\pi$
$374$	17.0731			0.882828
$375$	0.683428	−	1.59152i	0.0352920	−	0.0821856i
$376$		−	4.88979i		−	0.252172i
$377$	−1.13169			−0.0582848
$378$		0			0
$379$	−38.5761			−1.98152			−0.990759	−	0.135632i	$-0.956694\pi$
$379$	−38.5761			−1.98152			−0.990759	+	0.135632i	$0.956694\pi$
$380$		−	7.77395i		−	0.398795i
$381$	1.04659	−	2.43723i	0.0536185	−	0.124863i
$382$	−15.8451			−0.810705
$383$	−15.8225			−0.808491			−0.404245	−	0.914651i	$-0.632466\pi$
$383$	−15.8225			−0.808491			−0.404245	+	0.914651i	$0.632466\pi$
$384$	1.59152	+	0.683428i	0.0812168	+	0.0348760i
$385$		0			0
$386$			24.6498i			1.25464i
$387$	−12.3770	−	13.0332i	−0.629160	−	0.662515i
$388$		−	18.4958i		−	0.938980i
$389$		−	22.3710i		−	1.13426i	−0.823629	−	0.567129i	$-0.808054\pi$
$389$		−	22.3710i		−	1.13426i	0.823629	−	0.567129i	$-0.191946\pi$
$390$	−2.63147	+	6.12798i	−0.133250	+	0.310302i
$391$		−	36.4901i		−	1.84538i
$392$		0			0
$393$	−14.2892	+	33.2758i	−0.720797	+	1.67854i
$394$	8.86995			0.446862
$395$	0.358168			0.0180214
$396$	6.05561	−	5.75074i	0.304306	−	0.288986i
$397$			21.9759i			1.10294i	0.834195	+	0.551470i	$0.185933\pi$
$397$			21.9759i			1.10294i	−0.834195	+	0.551470i	$0.814067\pi$
$398$	24.9844			1.25235
$399$		0			0
$400$	1.00000			0.0500000
$401$			32.2802i			1.61199i	0.591919	+	0.805997i	$0.298371\pi$
$401$			32.2802i			1.61199i	−0.591919	+	0.805997i	$0.701629\pi$
$402$	−14.3275	−	6.15250i	−0.714591	−	0.306859i
$403$	−36.4596			−1.81618
$404$	17.4482			0.868082
$405$	0.464498	−	8.98801i	0.0230811	−	0.446618i
$406$		0			0
$407$			15.0034i			0.743690i
$408$	9.76110	+	4.19160i	0.483246	+	0.207515i
$409$		−	15.1770i		−	0.750456i	−0.926933	−	0.375228i	$-0.877564\pi$
$409$		−	15.1770i		−	0.750456i	0.926933	−	0.375228i	$-0.122436\pi$
$410$		−	2.06179i		−	0.101825i
$411$	15.5831	+	6.69169i	0.768659	+	0.330077i
$412$		−	10.7400i		−	0.529124i
$413$		0			0
$414$	−12.2910	−	12.9426i	−0.604070	−	0.636094i
$415$	−7.38866			−0.362695
$416$	−3.85040			−0.188782
$417$	−10.9258	−	4.69176i	−0.535041	−	0.229757i
$418$		−	21.6405i		−	1.05847i
$419$	−20.4574			−0.999408			−0.499704	−	0.866196i	$-0.666558\pi$
$419$	−20.4574			−0.999408			−0.499704	+	0.866196i	$0.666558\pi$
$420$		0			0
$421$	7.50916			0.365974			0.182987	−	0.983115i	$-0.441423\pi$
$421$	7.50916			0.365974			0.182987	+	0.983115i	$0.441423\pi$
$422$			9.99057i			0.486333i
$423$	−10.1016	−	10.6371i	−0.491157	−	0.517195i
$424$	−0.393343			−0.0191024
$425$	6.13320			0.297504
$426$	−5.78842	+	13.4797i	−0.280450	+	0.653092i
$427$		0			0
$428$		−	10.8236i		−	0.523180i
$429$	−7.32526	+	17.0585i	−0.353667	+	0.823594i
$430$		−	5.99125i		−	0.288924i
$431$		−	17.1954i		−	0.828275i	−0.910214	−	0.414138i	$-0.864083\pi$
$431$		−	17.1954i		−	0.828275i	0.910214	−	0.414138i	$-0.135917\pi$
$432$	4.87401	−	1.80113i	0.234501	−	0.0866570i
$433$			30.1155i			1.44726i	0.690189	+	0.723629i	$0.257527\pi$
$433$			30.1155i			1.44726i	−0.690189	+	0.723629i	$0.742473\pi$
$434$		0			0
$435$	0.467769	+	0.200869i	0.0224278	+	0.00963092i
$436$	−1.80838			−0.0866055
$437$	−46.2519			−2.21253
$438$	−6.47037	+	15.0677i	−0.309166	+	0.719964i
$439$		−	0.474648i		−	0.0226537i	−0.999936	−	0.0113269i	$-0.996394\pi$
$439$		−	0.474648i		−	0.0226537i	0.999936	−	0.0113269i	$-0.00360553\pi$
$440$	2.78371			0.132708
$441$		0			0
$442$	−23.6153			−1.12327
$443$			2.43255i			0.115574i	0.998329	+	0.0577870i	$0.0184044\pi$
$443$			2.43255i			0.115574i	−0.998329	+	0.0577870i	$0.981596\pi$
$444$	−3.68347	+	8.57781i	−0.174810	+	0.407085i
$445$	0.493908			0.0234135
$446$	15.9961			0.757438
$447$	32.0387	+	13.7580i	1.51538	+	0.650732i
$448$		0			0
$449$			26.5286i			1.25196i	0.779839	+	0.625980i	$0.215301\pi$
$449$			26.5286i			1.25196i	−0.779839	+	0.625980i	$0.784699\pi$
$450$	2.17537	−	2.06585i	0.102548	−	0.0973853i
$451$		−	5.73944i		−	0.270260i
$452$			17.3261i			0.814953i
$453$	−12.0735	+	28.1159i	−0.567262	+	1.32100i
$454$		−	3.88632i		−	0.182394i
$455$		0			0
$456$	5.31293	−	12.3724i	0.248801	−	0.579390i
$457$	2.75380			0.128817			0.0644087	−	0.997924i	$-0.479484\pi$
$457$	2.75380			0.128817			0.0644087	+	0.997924i	$0.479484\pi$
$458$	10.0440			0.469326
$459$	29.8933	−	11.0467i	1.39530	−	0.515616i
$460$		−	5.94960i		−	0.277402i
$461$	14.6562			0.682605			0.341303	−	0.939953i	$-0.389132\pi$
$461$	14.6562			0.682605			0.341303	+	0.939953i	$0.389132\pi$
$462$		0			0
$463$	14.0090			0.651054			0.325527	−	0.945533i	$-0.394458\pi$
$463$	14.0090			0.651054			0.325527	+	0.945533i	$0.394458\pi$
$464$			0.293914i			0.0136446i
$465$	15.0702	+	6.47141i	0.698861	+	0.300104i
$466$	25.0949			1.16250
$467$	−20.7897			−0.962030			−0.481015	−	0.876712i	$-0.659732\pi$
$467$	−20.7897			−0.962030			−0.481015	+	0.876712i	$0.659732\pi$
$468$	−8.37606	+	7.95437i	−0.387184	+	0.367691i
$469$		0			0
$470$		−	4.88979i		−	0.225549i
$471$	7.27864	+	3.12559i	0.335382	+	0.144019i
$472$		−	2.81048i		−	0.129363i
$473$		−	16.6779i		−	0.766851i
$474$	0.570030	+	0.244782i	0.0261824	+	0.0112432i
$475$		−	7.77395i		−	0.356693i
$476$		0			0
$477$	−0.855667	+	0.812588i	−0.0391783	+	0.0372059i
$478$	−19.4568			−0.889934
$479$	−39.2796			−1.79473			−0.897366	−	0.441287i	$-0.854522\pi$
$479$	−39.2796			−1.79473			−0.897366	+	0.441287i	$0.854522\pi$
$480$	1.59152	+	0.683428i	0.0726425	+	0.0311941i
$481$		−	20.7525i		−	0.946234i
$482$	−0.752125			−0.0342583
$483$		0			0
$484$	−3.25095			−0.147770
$485$		−	18.4958i		−	0.839849i
$486$	6.88191	−	13.9871i	0.312170	−	0.634468i
$487$	39.2914			1.78046			0.890231	−	0.455509i	$-0.150543\pi$
$487$	39.2914			1.78046			0.890231	+	0.455509i	$0.150543\pi$
$488$	−0.167612			−0.00758744
$489$	−0.363152	+	0.845681i	−0.0164223	+	0.0382430i
$490$		0			0
$491$			0.166656i			0.00752107i	0.999993	+	0.00376053i	$0.00119702\pi$
$491$			0.166656i			0.00752107i	−0.999993	+	0.00376053i	$0.998803\pi$
$492$	1.40909	−	3.28138i	0.0635265	−	0.147936i
$493$			1.80263i			0.0811865i
$494$			29.9329i			1.34674i
$495$	6.05561	−	5.75074i	0.272180	−	0.258477i
$496$			9.46905i			0.425173i
$497$		0			0
$498$	−11.7592	−	5.04961i	−0.526941	−	0.226279i
$499$	−5.94056			−0.265936			−0.132968	−	0.991120i	$-0.542451\pi$
$499$	−5.94056			−0.265936			−0.132968	+	0.991120i	$0.542451\pi$
$500$	1.00000			0.0447214
$501$	−7.86284	+	18.3104i	−0.351286	+	0.818049i
$502$			3.30554i			0.147533i
$503$	6.73800			0.300433			0.150216	−	0.988653i	$-0.452003\pi$
$503$	6.73800			0.300433			0.150216	+	0.988653i	$0.452003\pi$
$504$		0			0
$505$	17.4482			0.776436
$506$		−	16.5620i		−	0.736270i
$507$	1.24767	−	2.90547i	0.0554107	−	0.129037i
$508$	1.53139			0.0679442
$509$	−13.3753			−0.592851			−0.296425	−	0.955056i	$-0.595795\pi$
$509$	−13.3753			−0.592851			−0.296425	+	0.955056i	$0.595795\pi$
$510$	9.76110	+	4.19160i	0.432229	+	0.185607i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−14.0019	−	37.8903i	−0.618200	−	1.67290i
$514$			13.4708i			0.594174i
$515$		−	10.7400i		−	0.473263i
$516$	4.09458	−	9.53517i	0.180254	−	0.419763i
$517$		−	13.6118i		−	0.598645i
$518$		0			0
$519$	8.33106	−	19.4008i	0.365693	−	0.851599i
$520$	−3.85040			−0.168851
$521$	−16.7915			−0.735649			−0.367825	−	0.929895i	$-0.619897\pi$
$521$	−16.7915			−0.735649			−0.367825	+	0.929895i	$0.619897\pi$
$522$	0.607183	+	0.639372i	0.0265757	+	0.0279846i
$523$		−	17.2665i		−	0.755009i	−0.926008	−	0.377505i	$-0.876782\pi$
$523$		−	17.2665i		−	0.755009i	0.926008	−	0.377505i	$-0.123218\pi$
$524$	−20.9082			−0.913379
$525$		0			0
$526$	5.03279			0.219440
$527$			58.0756i			2.52981i
$528$	4.43033	+	1.90247i	0.192805	+	0.0827942i
$529$	−12.3978			−0.539033
$530$	−0.393343			−0.0170857
$531$	−5.80605	−	6.11385i	−0.251961	−	0.265319i
$532$		0			0
$533$			7.93873i			0.343865i
$534$	0.786063	+	0.337550i	0.0340163	+	0.0146072i
$535$		−	10.8236i		−	0.467946i
$536$		−	9.00242i		−	0.388845i
$537$	−16.9801	−	7.29159i	−0.732747	−	0.314655i
$538$		−	24.4184i		−	1.05275i
$539$		0			0
$540$	4.87401	−	1.80113i	0.209744	−	0.0775083i
$541$	−45.2367			−1.94488			−0.972438	−	0.233162i	$-0.925093\pi$
$541$	−45.2367			−1.94488			−0.972438	+	0.233162i	$0.925093\pi$
$542$	8.93330			0.383718
$543$	10.9657	+	4.70887i	0.470582	+	0.202077i
$544$			6.13320i			0.262959i
$545$	−1.80838			−0.0774623
$546$		0			0
$547$	−28.1188			−1.20227			−0.601137	−	0.799146i	$-0.705285\pi$
$547$	−28.1188			−1.20227			−0.601137	+	0.799146i	$0.705285\pi$
$548$			9.79136i			0.418266i
$549$	−0.364619	+	0.346262i	−0.0155615	+	0.0147781i
$550$	2.78371			0.118698
$551$	2.28487			0.0973388
$552$	4.06612	−	9.46889i	0.173066	−	0.403023i
$553$		0			0
$554$			22.7119i			0.964934i
$555$	−3.68347	+	8.57781i	−0.156355	+	0.364108i
$556$		−	6.86505i		−	0.291143i
$557$			6.80533i			0.288351i	0.989552	+	0.144175i	$0.0460530\pi$
$557$			6.80533i			0.288351i	−0.989552	+	0.144175i	$0.953947\pi$
$558$	19.5617	+	20.5987i	0.828111	+	0.872013i
$559$			23.0687i			0.975703i
$560$		0			0
$561$	27.1721	+	11.6682i	1.14721	+	0.492632i
$562$	−21.8213			−0.920475
$563$	26.8020			1.12957			0.564785	−	0.825238i	$-0.308959\pi$
$563$	26.8020			1.12957			0.564785	+	0.825238i	$0.308959\pi$
$564$	3.34182	−	7.78219i	0.140716	−	0.327689i
$565$			17.3261i			0.728916i
$566$	31.4471			1.32182
$567$		0			0
$568$	−8.46969			−0.355380
$569$		−	23.9413i		−	1.00367i	−0.864963	−	0.501835i	$-0.832658\pi$
$569$		−	23.9413i		−	1.00367i	0.864963	−	0.501835i	$-0.167342\pi$
$570$	5.31293	−	12.3724i	0.222534	−	0.518222i
$571$	−10.8703			−0.454908			−0.227454	−	0.973789i	$-0.573040\pi$
$571$	−10.8703			−0.454908			−0.227454	+	0.973789i	$0.573040\pi$
$572$	−10.7184			−0.448159
$573$	−25.2177	−	10.8290i	−1.05349	−	0.452387i
$574$		0			0
$575$		−	5.94960i		−	0.248116i
$576$	2.06585	+	2.17537i	0.0860772	+	0.0906406i
$577$			33.3481i			1.38830i	0.719831	+	0.694149i	$0.244219\pi$
$577$			33.3481i			1.38830i	−0.719831	+	0.694149i	$0.755781\pi$
$578$			20.6162i			0.857521i
$579$	−16.8464	+	39.2306i	−0.700112	+	1.63037i
$580$			0.293914i			0.0122041i
$581$		0			0
$582$	12.6405	−	29.4363i	0.523966	−	1.22018i
$583$	−1.09495			−0.0453483
$584$	−9.46753			−0.391769
$585$	−8.37606	+	7.95437i	−0.346308	+	0.328873i
$586$		−	26.8031i		−	1.10723i
$587$	4.22893			0.174547			0.0872733	−	0.996184i	$-0.472185\pi$
$587$	4.22893			0.174547			0.0872733	+	0.996184i	$0.472185\pi$
$588$		0			0
$589$	73.6119			3.03313
$590$		−	2.81048i		−	0.115706i
$591$	14.1167	+	6.06197i	0.580683	+	0.249356i
$592$	−5.38970			−0.221516
$593$	11.5449			0.474091			0.237045	−	0.971499i	$-0.423821\pi$
$593$	11.5449			0.474091			0.237045	+	0.971499i	$0.423821\pi$
$594$	13.5678	−	5.01383i	0.556695	−	0.205720i
$595$		0			0
$596$			20.1309i			0.824594i
$597$	39.7631	+	17.0750i	1.62739	+	0.698834i
$598$			22.9084i			0.936793i
$599$			12.0033i			0.490441i	0.969467	+	0.245220i	$0.0788604\pi$
$599$			12.0033i			0.490441i	−0.969467	+	0.245220i	$0.921140\pi$
$600$	1.59152	+	0.683428i	0.0649734	+	0.0279008i
$601$			10.4868i			0.427765i	0.976859	+	0.213883i	$0.0686110\pi$
$601$			10.4868i			0.427765i	−0.976859	+	0.213883i	$0.931389\pi$
$602$		0			0
$603$	−18.5977	−	19.5836i	−0.757356	−	0.797507i
$604$	−17.6661			−0.718822
$605$	−3.25095			−0.132170
$606$	27.7692	+	11.9246i	1.12804	+	0.484404i
$607$			29.4090i			1.19368i	0.802362	+	0.596838i	$0.203576\pi$
$607$			29.4090i			1.19368i	−0.802362	+	0.596838i	$0.796424\pi$
$608$	7.77395			0.315275
$609$		0			0
$610$	−0.167612			−0.00678641
$611$			18.8277i			0.761686i
$612$	12.6703	+	13.3420i	0.512167	+	0.539319i
$613$	−18.3574			−0.741448			−0.370724	−	0.928743i	$-0.620890\pi$
$613$	−18.3574			−0.741448			−0.370724	+	0.928743i	$0.620890\pi$
$614$	4.12520			0.166480
$615$	1.40909	−	3.28138i	0.0568198	−	0.132318i
$616$		0			0
$617$		−	5.60377i		−	0.225599i	−0.993618	−	0.112800i	$-0.964018\pi$
$617$		−	5.60377i		−	0.225599i	0.993618	−	0.112800i	$-0.0359818\pi$
$618$	7.34005	−	17.0930i	0.295260	−	0.687580i
$619$			3.06232i			0.123085i	0.998104	+	0.0615426i	$0.0196020\pi$
$619$			3.06232i			0.123085i	−0.998104	+	0.0615426i	$0.980398\pi$
$620$			9.46905i			0.380286i
$621$	−10.7160	−	28.9984i	−0.430019	−	1.16367i
$622$			21.6262i			0.867133i
$623$		0			0
$624$	−6.12798	−	2.63147i	−0.245316	−	0.105343i
$625$	1.00000			0.0400000
$626$	−8.40584			−0.335965
$627$	14.7897	−	34.4411i	0.590643	−	1.37545i
$628$			4.57340i			0.182499i
$629$	−33.0562			−1.31804
$630$		0			0
$631$	−18.1666			−0.723202			−0.361601	−	0.932333i	$-0.617770\pi$
$631$	−18.1666			−0.723202			−0.361601	+	0.932333i	$0.617770\pi$
$632$			0.358168i			0.0142472i
$633$	−6.82783	+	15.9002i	−0.271382	+	0.631975i
$634$	11.6893			0.464242
$635$	1.53139			0.0607712
$636$	−0.626012	−	0.268821i	−0.0248230	−	0.0106595i
$637$		0			0
$638$			0.818171i			0.0323917i
$639$	−18.4247	+	17.4971i	−0.728871	+	0.692176i
$640$			1.00000i			0.0395285i
$641$		−	50.2132i		−	1.98330i	−0.128944	−	0.991652i	$-0.541159\pi$
$641$		−	50.2132i		−	1.98330i	0.128944	−	0.991652i	$-0.458841\pi$
$642$	7.39716	−	17.2260i	0.291943	−	0.679855i
$643$			20.7242i			0.817284i	0.912695	+	0.408642i	$0.133998\pi$
$643$			20.7242i			0.817284i	−0.912695	+	0.408642i	$0.866002\pi$
$644$		0			0
$645$	4.09458	−	9.53517i	0.161224	−	0.375447i
$646$	47.6793			1.87592
$647$	21.1120			0.829997			0.414999	−	0.909822i	$-0.363782\pi$
$647$	21.1120			0.829997			0.414999	+	0.909822i	$0.363782\pi$
$648$	8.98801	+	0.464498i	0.353082	+	0.0182472i
$649$		−	7.82358i		−	0.307102i
$650$	−3.85040			−0.151025
$651$		0			0
$652$	−0.531368			−0.0208100
$653$			30.7211i			1.20221i	0.799171	+	0.601104i	$0.205272\pi$
$653$			30.7211i			1.20221i	−0.799171	+	0.601104i	$0.794728\pi$
$654$	−2.87806	−	1.23589i	−0.112541	−	0.0483273i
$655$	−20.9082			−0.816951
$656$	2.06179			0.0804995
$657$	−20.5954	+	19.5585i	−0.803503	+	0.763051i
$658$		0			0
$659$		−	35.3152i		−	1.37568i	−0.725860	−	0.687842i	$-0.758558\pi$
$659$		−	35.3152i		−	1.37568i	0.725860	−	0.687842i	$-0.241442\pi$
$660$	4.43033	+	1.90247i	0.172450	+	0.0740534i
$661$			27.8271i			1.08235i	0.840910	+	0.541175i	$0.182020\pi$
$661$			27.8271i			1.08235i	−0.840910	+	0.541175i	$0.817980\pi$
$662$			18.2140i			0.707908i
$663$	−37.5842	−	16.1394i	−1.45965	−	0.626800i
$664$		−	7.38866i		−	0.286736i
$665$		0			0
$666$	−11.7246	+	11.1343i	−0.454320	+	0.431447i
$667$	1.74867			0.0677088
$668$	−11.5050			−0.445142
$669$	25.4581	+	10.9322i	0.984266	+	0.422663i
$670$		−	9.00242i		−	0.347794i
$671$	−0.466584			−0.0180123
$672$		0			0
$673$	−17.8863			−0.689468			−0.344734	−	0.938700i	$-0.612031\pi$
$673$	−17.8863			−0.689468			−0.344734	+	0.938700i	$0.612031\pi$
$674$			5.63587i			0.217086i
$675$	4.87401	−	1.80113i	0.187601	−	0.0693256i
$676$	1.82560			0.0702154
$677$	−13.7137			−0.527059			−0.263530	−	0.964651i	$-0.584887\pi$
$677$	−13.7137			−0.527059			−0.263530	+	0.964651i	$0.584887\pi$
$678$	−11.8412	+	27.5749i	−0.454757	+	1.05901i
$679$		0			0
$680$			6.13320i			0.235198i
$681$	2.65602	−	6.18514i	0.101779	−	0.237015i
$682$			26.3591i			1.00934i
$683$			26.1896i			1.00212i	0.865413	+	0.501059i	$0.167056\pi$
$683$			26.1896i			1.00212i	−0.865413	+	0.501059i	$0.832944\pi$
$684$	16.9113	−	16.0599i	0.646618	−	0.614064i
$685$			9.79136i			0.374109i
$686$		0			0
$687$	15.9852	+	6.86436i	0.609875	+	0.261892i
$688$	5.99125			0.228414
$689$	1.51453			0.0576989
$690$	4.06612	−	9.46889i	0.154795	−	0.360475i
$691$		−	5.99364i		−	0.228009i	−0.993480	−	0.114004i	$-0.963632\pi$
$691$		−	5.99364i		−	0.228009i	0.993480	−	0.114004i	$-0.0363678\pi$
$692$	12.1901			0.463398
$693$		0			0
$694$	24.1270			0.915847
$695$		−	6.86505i		−	0.260406i
$696$	−0.200869	+	0.467769i	−0.00761391	+	0.0177307i
$697$	12.6454			0.478979
$698$	−1.85774			−0.0703163
$699$	39.9390	+	17.1506i	1.51063	+	0.648694i
$700$		0			0
$701$		−	12.7225i		−	0.480521i	−0.970708	−	0.240260i	$-0.922767\pi$
$701$		−	12.7225i		−	0.480521i	0.970708	−	0.240260i	$-0.0772328\pi$
$702$	−18.7669	+	6.93508i	−0.708310	+	0.261748i
$703$			41.8993i			1.58026i
$704$			2.78371i			0.104915i
$705$	3.34182	−	7.78219i	0.125860	−	0.293094i
$706$			18.0834i			0.680576i
$707$		0			0
$708$	1.92076	−	4.47293i	0.0721867	−	0.168103i
$709$	16.9474			0.636474			0.318237	−	0.948011i	$-0.396909\pi$
$709$	16.9474			0.636474			0.318237	+	0.948011i	$0.396909\pi$
$710$	−8.46969			−0.317862
$711$	0.739922	+	0.779149i	0.0277493	+	0.0292204i
$712$			0.493908i			0.0185100i
$713$	56.3371			2.10984
$714$		0			0
$715$	−10.7184			−0.400846
$716$		−	10.6691i		−	0.398725i
$717$	−30.9659	−	13.2973i	−1.15644	−	0.496598i
$718$	−18.7873			−0.701138
$719$	−25.8737			−0.964926			−0.482463	−	0.875916i	$-0.660258\pi$
$719$	−25.8737			−0.964926			−0.482463	+	0.875916i	$0.660258\pi$
$720$	2.06585	+	2.17537i	0.0769898	+	0.0810714i
$721$		0			0
$722$		−	41.4344i		−	1.54203i
$723$	−1.19702	−	0.514023i	−0.0445176	−	0.0191167i
$724$			6.89007i			0.256068i
$725$			0.293914i			0.0109157i
$726$	−5.17394	−	2.22179i	−0.192023	−	0.0824582i
$727$			18.5163i			0.686730i	0.939202	+	0.343365i	$0.111567\pi$
$727$			18.5163i			0.686730i	−0.939202	+	0.343365i	$0.888433\pi$
$728$		0			0
$729$	20.5119	−	17.5574i	0.759698	−	0.650276i
$730$	−9.46753			−0.350409
$731$	36.7455			1.35908
$732$	−0.266757	−	0.114551i	−0.00985964	−	0.00423391i
$733$			36.2139i			1.33759i	0.743447	+	0.668795i	$0.233190\pi$
$733$			36.2139i			1.33759i	−0.743447	+	0.668795i	$0.766810\pi$
$734$	−8.07247			−0.297960
$735$		0			0
$736$	5.94960			0.219305
$737$		−	25.0602i		−	0.923103i
$738$	4.48517	−	4.25936i	0.165101	−	0.156789i
$739$	3.21995			0.118448			0.0592239	−	0.998245i	$-0.481137\pi$
$739$	3.21995			0.118448			0.0592239	+	0.998245i	$0.481137\pi$
$740$	−5.38970			−0.198129
$741$	−20.4569	+	47.6386i	−0.751504	+	1.75005i
$742$		0			0
$743$		−	33.2983i		−	1.22159i	−0.791787	−	0.610797i	$-0.790849\pi$
$743$		−	33.2983i		−	1.22159i	0.791787	−	0.610797i	$-0.209151\pi$
$744$	−6.47141	+	15.0702i	−0.237253	+	0.552499i
$745$			20.1309i			0.737539i
$746$		−	4.49811i		−	0.164687i
$747$	−15.2639	−	16.0731i	−0.558476	−	0.588084i
$748$			17.0731i			0.624253i
$749$		0			0
$750$	1.59152	+	0.683428i	0.0581140	+	0.0249552i
$751$	−31.0257			−1.13214			−0.566072	−	0.824356i	$-0.691538\pi$
$751$	−31.0257			−1.13214			−0.566072	+	0.824356i	$0.691538\pi$
$752$	4.88979			0.178312
$753$	−2.25910	+	5.26082i	−0.0823261	+	0.191715i
$754$		−	1.13169i		−	0.0412136i
$755$	−17.6661			−0.642934
$756$		0			0
$757$	−21.0541			−0.765224			−0.382612	−	0.923909i	$-0.624975\pi$
$757$	−21.0541			−0.765224			−0.382612	+	0.923909i	$0.624975\pi$
$758$		−	38.5761i		−	1.40115i
$759$	11.3189	−	26.3587i	0.410850	−	0.956759i
$760$	7.77395			0.281991
$761$	−16.1321			−0.584788			−0.292394	−	0.956298i	$-0.594452\pi$
$761$	−16.1321			−0.584788			−0.292394	+	0.956298i	$0.594452\pi$
$762$	2.43723	+	1.04659i	0.0882914	+	0.0379140i
$763$		0			0
$764$		−	15.8451i		−	0.573255i
$765$	12.6703	+	13.3420i	0.458096	+	0.482381i
$766$		−	15.8225i		−	0.571689i
$767$			10.8215i			0.390742i
$768$	−0.683428	+	1.59152i	−0.0246611	+	0.0574289i
$769$		−	40.3343i		−	1.45449i	−0.686377	−	0.727246i	$-0.740800\pi$
$769$		−	40.3343i		−	1.45449i	0.686377	−	0.727246i	$-0.259200\pi$
$770$		0			0
$771$	−9.20635	+	21.4391i	−0.331559	+	0.772110i
$772$	−24.6498			−0.887167
$773$	19.0192			0.684073			0.342036	−	0.939687i	$-0.388883\pi$
$773$	19.0192			0.684073			0.342036	+	0.939687i	$0.388883\pi$
$774$	13.0332	−	12.3770i	0.468469	−	0.444883i
$775$			9.46905i			0.340138i
$776$	18.4958			0.663959
$777$		0			0
$778$	22.3710			0.802041
$779$		−	16.0283i		−	0.574273i
$780$	−6.12798	−	2.63147i	−0.219417	−	0.0942218i
$781$	−23.5772			−0.843658
$782$	36.4901			1.30488
$783$	0.529377	+	1.43254i	0.0189184	+	0.0511947i
$784$		0			0
$785$			4.57340i			0.163232i
$786$	−33.2758	−	14.2892i	−1.18691	−	0.509681i
$787$			6.86357i			0.244660i	0.992489	+	0.122330i	$0.0390366\pi$
$787$			6.86357i			0.244660i	−0.992489	+	0.122330i	$0.960963\pi$
$788$			8.86995i			0.315979i
$789$	8.00977	+	3.43954i	0.285155	+	0.122451i
$790$			0.358168i			0.0127430i
$791$		0			0
$792$	5.75074	+	6.05561i	0.204344	+	0.215177i
$793$	0.645374			0.0229179
$794$	−21.9759			−0.779896
$795$	−0.626012	−	0.268821i	−0.0222023	−	0.00953411i
$796$			24.9844i			0.885548i
$797$	−15.5317			−0.550161			−0.275081	−	0.961421i	$-0.588705\pi$
$797$	−15.5317			−0.550161			−0.275081	+	0.961421i	$0.588705\pi$
$798$		0			0
$799$	29.9901			1.06097
$800$			1.00000i			0.0353553i
$801$	1.02034	+	1.07443i	0.0360520	+	0.0379633i
$802$	−32.2802			−1.13985
$803$	−26.3549			−0.930043
$804$	6.15250	−	14.3275i	0.216982	−	0.505292i
$805$		0			0
$806$		−	36.4596i		−	1.28424i
$807$	16.6882	−	38.8623i	0.587453	−	1.36802i
$808$			17.4482i			0.613826i
$809$		−	12.6903i		−	0.446166i	−0.974799	−	0.223083i	$-0.928388\pi$
$809$		−	12.6903i		−	0.446166i	0.974799	−	0.223083i	$-0.0716121\pi$
$810$	8.98801	+	0.464498i	0.315806	+	0.0163208i
$811$		−	7.97232i		−	0.279946i	−0.990155	−	0.139973i	$-0.955298\pi$
$811$		−	7.97232i		−	0.279946i	0.990155	−	0.139973i	$-0.0447016\pi$
$812$		0			0
$813$	14.2175	+	6.10526i	0.498629	+	0.214121i
$814$	−15.0034			−0.525868
$815$	−0.531368			−0.0186130
$816$	−4.19160	+	9.76110i	−0.146735	+	0.341707i
$817$		−	46.5757i		−	1.62948i
$818$	15.1770			0.530652
$819$		0			0
$820$	2.06179			0.0720009
$821$			35.8082i			1.24971i	0.780739	+	0.624857i	$0.214843\pi$
$821$			35.8082i			1.24971i	−0.780739	+	0.624857i	$0.785157\pi$
$822$	−6.69169	+	15.5831i	−0.233399	+	0.543524i
$823$	6.29054			0.219274			0.109637	−	0.993972i	$-0.465031\pi$
$823$	6.29054			0.219274			0.109637	+	0.993972i	$0.465031\pi$
$824$	10.7400			0.374147
$825$	4.43033	+	1.90247i	0.154244	+	0.0662354i
$826$		0			0
$827$		−	21.1900i		−	0.736849i	−0.929658	−	0.368424i	$-0.879897\pi$
$827$		−	21.1900i		−	0.736849i	0.929658	−	0.368424i	$-0.120103\pi$
$828$	12.9426	−	12.2910i	0.449787	−	0.427142i
$829$			38.9232i			1.35186i	0.736967	+	0.675929i	$0.236257\pi$
$829$			38.9232i			1.35186i	−0.736967	+	0.675929i	$0.763743\pi$
$830$		−	7.38866i		−	0.256464i
$831$	−15.5219	+	36.1463i	−0.538449	+	1.25390i
$832$		−	3.85040i		−	0.133489i
$833$		0			0
$834$	4.69176	−	10.9258i	0.162462	−	0.378331i
$835$	−11.5050			−0.398147
$836$	21.6405			0.748451
$837$	17.0550	+	46.1522i	0.589507	+	1.59525i
$838$		−	20.4574i		−	0.706688i
$839$	22.5255			0.777667			0.388834	−	0.921308i	$-0.372878\pi$
$839$	22.5255			0.777667			0.388834	+	0.921308i	$0.372878\pi$
$840$		0			0
$841$	28.9136			0.997021
$842$			7.50916i			0.258783i
$843$	−34.7289	−	14.9133i	−1.19613	−	0.513640i
$844$	−9.99057			−0.343890
$845$	1.82560			0.0628025
$846$	10.6371	−	10.1016i	0.365712	−	0.347300i
$847$		0			0
$848$		−	0.393343i		−	0.0135074i
$849$	50.0486	+	21.4918i	1.71766	+	0.737597i
$850$			6.13320i			0.210367i
$851$			32.0666i			1.09923i
$852$	−13.4797	−	5.78842i	−0.461805	−	0.198308i
$853$			39.7678i			1.36162i	0.732459	+	0.680811i	$0.238372\pi$
$853$			39.7678i			1.36162i	−0.732459	+	0.680811i	$0.761628\pi$
$854$		0			0
$855$	16.9113	−	16.0599i	0.578353	−	0.549235i
$856$	10.8236			0.369944
$857$	−20.2994			−0.693413			−0.346707	−	0.937974i	$-0.612700\pi$
$857$	−20.2994			−0.693413			−0.346707	+	0.937974i	$0.612700\pi$
$858$	−17.0585	−	7.32526i	−0.582369	−	0.250080i
$859$			32.9034i			1.12265i	0.827595	+	0.561325i	$0.189708\pi$
$859$			32.9034i			1.12265i	−0.827595	+	0.561325i	$0.810292\pi$
$860$	5.99125			0.204300
$861$		0			0
$862$	17.1954			0.585679
$863$			44.3330i			1.50911i	0.656235	+	0.754556i	$0.272148\pi$
$863$			44.3330i			1.50911i	−0.656235	+	0.754556i	$0.727852\pi$
$864$	1.80113	+	4.87401i	0.0612757	+	0.165817i
$865$	12.1901			0.414476
$866$	−30.1155			−1.02337
$867$	−14.0897	+	32.8110i	−0.478511	+	1.11432i
$868$		0			0
$869$			0.997036i			0.0338221i
$870$	−0.200869	+	0.467769i	−0.00681009	+	0.0158589i
$871$			34.6630i			1.17451i
$872$		−	1.80838i		−	0.0612393i
$873$	40.2352	−	38.2095i	1.36176	−	1.29320i
$874$		−	46.2519i		−	1.56449i
$875$		0			0
$876$	−15.0677	−	6.47037i	−0.509091	−	0.218613i
$877$	−0.0566044			−0.00191140			−0.000955698	−	1.00000i	$-0.500304\pi$
$877$	−0.0566044			−0.00191140			−0.000955698		1.00000i	$0.500304\pi$
$878$	0.474648			0.0160186
$879$	18.3180	−	42.6576i	0.617850	−	1.43880i
$880$			2.78371i			0.0938389i
$881$	−38.3286			−1.29132			−0.645662	−	0.763623i	$-0.723419\pi$
$881$	−38.3286			−1.29132			−0.645662	+	0.763623i	$0.723419\pi$
$882$		0			0
$883$	30.3205			1.02037			0.510183	−	0.860066i	$-0.329578\pi$
$883$	30.3205			1.02037			0.510183	+	0.860066i	$0.329578\pi$
$884$		−	23.6153i		−	0.794269i
$885$	1.92076	−	4.47293i	0.0645657	−	0.150356i
$886$	−2.43255			−0.0817231
$887$	36.9582			1.24093			0.620467	−	0.784233i	$-0.286943\pi$
$887$	36.9582			1.24093			0.620467	+	0.784233i	$0.286943\pi$
$888$	−8.57781	−	3.68347i	−0.287852	−	0.123609i
$889$		0			0
$890$			0.493908i			0.0165558i
$891$	25.0200	+	1.29303i	0.838202	+	0.0433181i
$892$			15.9961i			0.535589i
$893$		−	38.0130i		−	1.27206i
$894$	−13.7580	+	32.0387i	−0.460137	+	1.07153i
$895$		−	10.6691i		−	0.356630i
$896$		0			0
$897$	−15.6562	+	36.4590i	−0.522745	+	1.21733i
$898$	−26.5286			−0.885270
$899$	−2.78308			−0.0928210
$900$	2.06585	+	2.17537i	0.0688618	+	0.0725124i
$901$		−	2.41245i		−	0.0803704i
$902$	5.73944			0.191102
$903$		0			0
$904$	−17.3261			−0.576259
$905$			6.89007i			0.229034i
$906$	−28.1159	−	12.0735i	−0.934087	−	0.401115i
$907$	−13.2978			−0.441546			−0.220773	−	0.975325i	$-0.570858\pi$
$907$	−13.2978			−0.441546			−0.220773	+	0.975325i	$0.570858\pi$
$908$	3.88632			0.128972
$909$	36.0455	+	37.9564i	1.19555	+	1.25893i
$910$		0			0
$911$		−	17.4268i		−	0.577375i	−0.957423	−	0.288688i	$-0.906781\pi$
$911$		−	17.4268i		−	0.577375i	0.957423	−	0.288688i	$-0.0932189\pi$
$912$	12.3724	+	5.31293i	0.409690	+	0.175929i
$913$		−	20.5679i		−	0.680698i
$914$			2.75380i			0.0910876i
$915$	−0.266757	−	0.114551i	−0.00881873	−	0.00378693i
$916$			10.0440i			0.331864i
$917$		0			0
$918$	11.0467	+	29.8933i	0.364596	+	0.986625i
$919$	−47.0079			−1.55065			−0.775323	−	0.631565i	$-0.782413\pi$
$919$	−47.0079			−1.55065			−0.775323	+	0.631565i	$0.782413\pi$
$920$	5.94960			0.196153
$921$	6.56533	+	2.81928i	0.216335	+	0.0928984i
$922$			14.6562i			0.482675i
$923$	32.6117			1.07343
$924$		0			0
$925$	−5.38970			−0.177212
$926$			14.0090i			0.460365i
$927$	23.3636	−	22.1874i	0.767362	−	0.728729i
$928$	−0.293914			−0.00964819
$929$	20.7411			0.680494			0.340247	−	0.940336i	$-0.389489\pi$
$929$	20.7411			0.680494			0.340247	+	0.940336i	$0.389489\pi$
$930$	−6.47141	+	15.0702i	−0.212206	+	0.494170i
$931$		0			0
$932$			25.0949i			0.822012i
$933$	−14.7800	+	34.4185i	−0.483874	+	1.12681i
$934$		−	20.7897i		−	0.680258i
$935$			17.0731i			0.558349i
$936$	−7.95437	−	8.37606i	−0.259997	−	0.273780i
$937$			19.3478i			0.632064i	0.948748	+	0.316032i	$0.102351\pi$
$937$			19.3478i			0.632064i	−0.948748	+	0.316032i	$0.897649\pi$
$938$		0			0
$939$	−13.3780	−	5.74478i	−0.436576	−	0.187474i
$940$	4.88979			0.159488
$941$	−28.0179			−0.913356			−0.456678	−	0.889632i	$-0.650961\pi$
$941$	−28.0179			−0.913356			−0.456678	+	0.889632i	$0.650961\pi$
$942$	−3.12559	+	7.27864i	−0.101837	+	0.237151i
$943$		−	12.2668i		−	0.399464i
$944$	2.81048			0.0914735
$945$		0			0
$946$	16.6779			0.542246
$947$		−	35.5161i		−	1.15412i	−0.816702	−	0.577060i	$-0.804200\pi$
$947$		−	35.5161i		−	1.15412i	0.816702	−	0.577060i	$-0.195800\pi$
$948$	−0.244782	+	0.570030i	−0.00795014	+	0.0185137i
$949$	36.4538			1.18334
$950$	7.77395			0.252220
$951$	18.6037	+	7.98880i	0.603267	+	0.259054i
$952$		0			0
$953$			55.9509i			1.81243i	0.422821	+	0.906213i	$0.361040\pi$
$953$			55.9509i			1.81243i	−0.422821	+	0.906213i	$0.638960\pi$
$954$	−0.812588	−	0.855667i	−0.0263085	−	0.0277033i
$955$		−	15.8451i		−	0.512735i
$956$		−	19.4568i		−	0.629279i
$957$	−0.559161	+	1.30213i	−0.0180751	+	0.0420920i
$958$		−	39.2796i		−	1.26907i
$959$		0			0
$960$	−0.683428	+	1.59152i	−0.0220575	+	0.0513660i
$961$	−58.6629			−1.89235
$962$	20.7525			0.669089
$963$	23.5454	−	22.3600i	0.758741	−	0.720542i
$964$		−	0.752125i		−	0.0242243i
$965$	−24.6498			−0.793507
$966$		0			0
$967$	17.0168			0.547224			0.273612	−	0.961840i	$-0.411782\pi$
$967$	17.0168			0.547224			0.273612	+	0.961840i	$0.411782\pi$
$968$		−	3.25095i		−	0.104489i
$969$	75.8823	+	32.5853i	2.43769	+	1.04679i
$970$	18.4958			0.593863
$971$	−6.44121			−0.206708			−0.103354	−	0.994645i	$-0.532958\pi$
$971$	−6.44121			−0.206708			−0.103354	+	0.994645i	$0.532958\pi$
$972$	13.9871	+	6.88191i	0.448637	+	0.220737i
$973$		0			0
$974$			39.2914i			1.25898i
$975$	−6.12798	−	2.63147i	−0.196252	−	0.0842745i
$976$		−	0.167612i		−	0.00536513i
$977$		−	7.52742i		−	0.240824i	−0.992724	−	0.120412i	$-0.961578\pi$
$977$		−	7.52742i		−	0.240824i	0.992724	−	0.120412i	$-0.0384215\pi$
$978$	−0.845681	−	0.363152i	−0.0270419	−	0.0116123i
$979$			1.37490i			0.0439419i
$980$		0			0
$981$	−3.73584	−	3.93389i	−0.119276	−	0.125600i
$982$	−0.166656			−0.00531820
$983$	12.5064			0.398894			0.199447	−	0.979909i	$-0.436085\pi$
$983$	12.5064			0.398894			0.199447	+	0.979909i	$0.436085\pi$
$984$	3.28138	+	1.40909i	0.104607	+	0.0449200i
$985$			8.86995i			0.282620i
$986$	−1.80263			−0.0574075
$987$		0			0
$988$	−29.9329			−0.952291
$989$		−	35.6455i		−	1.13346i
$990$	5.75074	+	6.05561i	0.182771	+	0.192460i
$991$	−44.8402			−1.42440			−0.712198	−	0.701978i	$-0.752300\pi$
$991$	−44.8402			−1.42440			−0.712198	+	0.701978i	$0.752300\pi$
$992$	−9.46905			−0.300643
$993$	−12.4480	+	28.9879i	−0.395024	+	0.919904i
$994$		0			0
$995$			24.9844i			0.792058i
$996$	5.04961	−	11.7592i	0.160003	−	0.372604i
$997$		−	30.8806i		−	0.977999i	−0.872284	−	0.488999i	$-0.837362\pi$
$997$		−	30.8806i		−	0.977999i	0.872284	−	0.488999i	$-0.162638\pi$
$998$		−	5.94056i		−	0.188045i
$999$	−26.2694	+	9.70757i	−0.831129	+	0.307134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.c.881.13	yes	16
3.2	odd	2		1470.2.b.d.881.4	yes	16
7.6	odd	2		1470.2.b.d.881.12	yes	16
21.20	even	2	inner	1470.2.b.c.881.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.b.c.881.5	✓	16	21.20	even	2	inner
1470.2.b.c.881.13	yes	16	1.1	even	1	trivial
1470.2.b.d.881.4	yes	16	3.2	odd	2
1470.2.b.d.881.12	yes	16	7.6	odd	2

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.683428 + 1.59152i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.59152 - 0.683428i) q^{6} -1.00000i q^{8} +(-2.06585 - 2.17537i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.683428 + 1.59152i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.59152 - 0.683428i) q^{6} -1.00000i q^{8} +(-2.06585 - 2.17537i) q^{9} -1.00000i q^{10} -2.78371i q^{11} +(0.683428 - 1.59152i) q^{12} +3.85040i q^{13} +(0.683428 - 1.59152i) q^{15} +1.00000 q^{16} +6.13320 q^{17} +(2.17537 - 2.06585i) q^{18} -7.77395i q^{19} +1.00000 q^{20} +2.78371 q^{22} -5.94960i q^{23} +(1.59152 + 0.683428i) q^{24} +1.00000 q^{25} -3.85040 q^{26} +(4.87401 - 1.80113i) q^{27} +0.293914i q^{29} +(1.59152 + 0.683428i) q^{30} +9.46905i q^{31} +1.00000i q^{32} +(4.43033 + 1.90247i) q^{33} +6.13320i q^{34} +(2.06585 + 2.17537i) q^{36} -5.38970 q^{37} +7.77395 q^{38} +(-6.12798 - 2.63147i) q^{39} +1.00000i q^{40} +2.06179 q^{41} +5.99125 q^{43} +2.78371i q^{44} +(2.06585 + 2.17537i) q^{45} +5.94960 q^{46} +4.88979 q^{47} +(-0.683428 + 1.59152i) q^{48} +1.00000i q^{50} +(-4.19160 + 9.76110i) q^{51} -3.85040i q^{52} -0.393343i q^{53} +(1.80113 + 4.87401i) q^{54} +2.78371i q^{55} +(12.3724 + 5.31293i) q^{57} -0.293914 q^{58} +2.81048 q^{59} +(-0.683428 + 1.59152i) q^{60} -0.167612i q^{61} -9.46905 q^{62} -1.00000 q^{64} -3.85040i q^{65} +(-1.90247 + 4.43033i) q^{66} +9.00242 q^{67} -6.13320 q^{68} +(9.46889 + 4.06612i) q^{69} -8.46969i q^{71} +(-2.17537 + 2.06585i) q^{72} -9.46753i q^{73} -5.38970i q^{74} +(-0.683428 + 1.59152i) q^{75} +7.77395i q^{76} +(2.63147 - 6.12798i) q^{78} -0.358168 q^{79} -1.00000 q^{80} +(-0.464498 + 8.98801i) q^{81} +2.06179i q^{82} +7.38866 q^{83} -6.13320 q^{85} +5.99125i q^{86} +(-0.467769 - 0.200869i) q^{87} -2.78371 q^{88} -0.493908 q^{89} +(-2.17537 + 2.06585i) q^{90} +5.94960i q^{92} +(-15.0702 - 6.47141i) q^{93} +4.88979i q^{94} +7.77395i q^{95} +(-1.59152 - 0.683428i) q^{96} +18.4958i q^{97} +(-6.05561 + 5.75074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9	\( 16 q - 8 q^{3} - 16 q^{4} - 16 q^{5} + 8 q^{9} + 8 q^{12} + 8 q^{15} + 16 q^{16} + 48 q^{17} + 16 q^{20} + 16 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{36} + 16 q^{41} + 16 q^{43} - 8 q^{45} - 16 q^{46} + 32 q^{47} - 8 q^{48} + 16 q^{51} + 32 q^{57} + 16 q^{58} + 32 q^{59} - 8 q^{60} + 16 q^{62} - 16 q^{64} + 16 q^{67} - 48 q^{68} - 8 q^{75} - 32 q^{78} - 48 q^{79} - 16 q^{80} + 8 q^{81} + 48 q^{83} - 48 q^{85} + 16 q^{89} - 64 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 16 * q^4 - 16 * q^5 + 8 * q^9 + 8 * q^12 + 8 * q^15 + 16 * q^16 + 48 * q^17 + 16 * q^20 + 16 * q^25 - 16 * q^26 - 8 * q^27 - 8 * q^36 + 16 * q^41 + 16 * q^43 - 8 * q^45 - 16 * q^46 + 32 * q^47 - 8 * q^48 + 16 * q^51 + 32 * q^57 + 16 * q^58 + 32 * q^59 - 8 * q^60 + 16 * q^62 - 16 * q^64 + 16 * q^67 - 48 * q^68 - 8 * q^75 - 32 * q^78 - 48 * q^79 - 16 * q^80 + 8 * q^81 + 48 * q^83 - 48 * q^85 + 16 * q^89 - 64 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more