LMFDB - Embedded newform 1920.2.s.e.1441.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(481,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1920.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1441.9
Root			$-0.0861743 - 1.41159i$ of defining polynomial
Character	$\chi$	$=$	1920.1441
Dual form			1920.2.s.e.481.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +2.76462i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +2.76462i q^{7} +1.00000i q^{9} +(3.51009 - 3.51009i) q^{11} +(4.55960 + 4.55960i) q^{13} +1.00000 q^{15} -5.00550 q^{17} +(0.812949 + 0.812949i) q^{19} +(-1.95488 + 1.95488i) q^{21} +7.48205i q^{23} -1.00000i q^{25} +(-0.707107 + 0.707107i) q^{27} +(-6.03354 - 6.03354i) q^{29} +7.58233 q^{31} +4.96402 q^{33} +(1.95488 + 1.95488i) q^{35} +(-1.08674 + 1.08674i) q^{37} +6.44825i q^{39} -3.15671i q^{41} +(3.10932 - 3.10932i) q^{43} +(0.707107 + 0.707107i) q^{45} -2.76008 q^{47} -0.643123 q^{49} +(-3.53942 - 3.53942i) q^{51} +(-6.41096 + 6.41096i) q^{53} -4.96402i q^{55} +1.14968i q^{57} +(5.13756 - 5.13756i) q^{59} +(2.49234 + 2.49234i) q^{61} -2.76462 q^{63} +6.44825 q^{65} +(3.14625 + 3.14625i) q^{67} +(-5.29061 + 5.29061i) q^{69} +3.50237i q^{71} +14.6145i q^{73} +(0.707107 - 0.707107i) q^{75} +(9.70408 + 9.70408i) q^{77} +8.95325 q^{79} -1.00000 q^{81} +(2.86293 + 2.86293i) q^{83} +(-3.53942 + 3.53942i) q^{85} -8.53271i q^{87} +7.23560i q^{89} +(-12.6056 + 12.6056i) q^{91} +(5.36151 + 5.36151i) q^{93} +1.14968 q^{95} -8.24056 q^{97} +(3.51009 + 3.51009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 8 q^{11} + 20 q^{15} - 24 q^{17} + 4 q^{19} - 16 q^{29} + 16 q^{33} - 16 q^{37} + 8 q^{43} - 52 q^{49} - 4 q^{51} + 16 q^{53} + 16 q^{59} + 4 q^{61} - 8 q^{63} + 8 q^{67} + 4 q^{69} + 40 q^{77} + 56 q^{79} - 20 q^{81} + 48 q^{83} - 4 q^{85} + 8 q^{91} - 16 q^{93} + 56 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 8 * q^11 + 20 * q^15 - 24 * q^17 + 4 * q^19 - 16 * q^29 + 16 * q^33 - 16 * q^37 + 8 * q^43 - 52 * q^49 - 4 * q^51 + 16 * q^53 + 16 * q^59 + 4 * q^61 - 8 * q^63 + 8 * q^67 + 4 * q^69 + 40 * q^77 + 56 * q^79 - 20 * q^81 + 48 * q^83 - 4 * q^85 + 8 * q^91 - 16 * q^93 + 56 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			2.76462i			1.04493i	0.852661	+	0.522464i	$0.174987\pi$
$7$			2.76462i			1.04493i	−0.852661	+	0.522464i	$0.825013\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	3.51009	−	3.51009i	1.05833	−	1.05833i	0.0601437	−	0.998190i	$-0.480844\pi$
$11$	3.51009	−	3.51009i	1.05833	−	1.05833i	0.998190	−	0.0601437i	$-0.0191559\pi$
$12$		0			0
$13$	4.55960	+	4.55960i	1.26461	+	1.26461i	0.948835	+	0.315771i	$0.102263\pi$
$13$	4.55960	+	4.55960i	1.26461	+	1.26461i	0.315771	+	0.948835i	$0.397737\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−5.00550			−1.21401			−0.607006	−	0.794697i	$-0.707630\pi$
$17$	−5.00550			−1.21401			−0.607006	+	0.794697i	$0.707630\pi$
$18$		0			0
$19$	0.812949	+	0.812949i	0.186503	+	0.186503i	0.794183	−	0.607679i	$-0.207899\pi$
$19$	0.812949	+	0.812949i	0.186503	+	0.186503i	−0.607679	+	0.794183i	$0.707899\pi$
$20$		0			0
$21$	−1.95488	+	1.95488i	−0.426590	+	0.426590i
$22$		0			0
$23$			7.48205i			1.56011i	0.625708	+	0.780057i	$0.284810\pi$
$23$			7.48205i			1.56011i	−0.625708	+	0.780057i	$0.715190\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	−6.03354	−	6.03354i	−1.12040	−	1.12040i	−0.991681	−	0.128719i	$-0.958913\pi$
$29$	−6.03354	−	6.03354i	−1.12040	−	1.12040i	−0.128719	−	0.991681i	$-0.541087\pi$
$30$		0			0
$31$	7.58233			1.36183			0.680913	−	0.732364i	$-0.261583\pi$
$31$	7.58233			1.36183			0.680913	+	0.732364i	$0.261583\pi$
$32$		0			0
$33$	4.96402			0.864126
$34$		0			0
$35$	1.95488	+	1.95488i	0.330435	+	0.330435i
$36$		0			0
$37$	−1.08674	+	1.08674i	−0.178659	+	0.178659i	−0.790771	−	0.612112i	$-0.790320\pi$
$37$	−1.08674	+	1.08674i	−0.178659	+	0.178659i	0.612112	+	0.790771i	$0.290320\pi$
$38$		0			0
$39$			6.44825i			1.03255i
$40$		0			0
$41$		−	3.15671i		−	0.492995i	−0.969143	−	0.246497i	$-0.920720\pi$
$41$		−	3.15671i		−	0.492995i	0.969143	−	0.246497i	$-0.0792797\pi$
$42$		0			0
$43$	3.10932	−	3.10932i	0.474166	−	0.474166i	−0.429094	−	0.903260i	$-0.641167\pi$
$43$	3.10932	−	3.10932i	0.474166	−	0.474166i	0.903260	+	0.429094i	$0.141167\pi$
$44$		0			0
$45$	0.707107	+	0.707107i	0.105409	+	0.105409i
$46$		0			0
$47$	−2.76008			−0.402599			−0.201299	−	0.979530i	$-0.564516\pi$
$47$	−2.76008			−0.402599			−0.201299	+	0.979530i	$0.564516\pi$
$48$		0			0
$49$	−0.643123			−0.0918747
$50$		0			0
$51$	−3.53942	−	3.53942i	−0.495618	−	0.495618i
$52$		0			0
$53$	−6.41096	+	6.41096i	−0.880613	+	0.880613i	−0.993597	−	0.112983i	$-0.963959\pi$
$53$	−6.41096	+	6.41096i	−0.880613	+	0.880613i	0.112983	+	0.993597i	$0.463959\pi$
$54$		0			0
$55$		−	4.96402i		−	0.669349i
$56$		0			0
$57$			1.14968i			0.152279i
$58$		0			0
$59$	5.13756	−	5.13756i	0.668854	−	0.668854i	−0.288597	−	0.957451i	$-0.593189\pi$
$59$	5.13756	−	5.13756i	0.668854	−	0.668854i	0.957451	+	0.288597i	$0.0931888\pi$
$60$		0			0
$61$	2.49234	+	2.49234i	0.319111	+	0.319111i	0.848426	−	0.529314i	$-0.177551\pi$
$61$	2.49234	+	2.49234i	0.319111	+	0.319111i	−0.529314	+	0.848426i	$0.677551\pi$
$62$		0			0
$63$	−2.76462			−0.348309
$64$		0			0
$65$	6.44825			0.799807
$66$		0			0
$67$	3.14625	+	3.14625i	0.384376	+	0.384376i	0.872676	−	0.488300i	$-0.162383\pi$
$67$	3.14625	+	3.14625i	0.384376	+	0.384376i	−0.488300	+	0.872676i	$0.662383\pi$
$68$		0			0
$69$	−5.29061	+	5.29061i	−0.636914	+	0.636914i
$70$		0			0
$71$			3.50237i			0.415655i	0.978166	+	0.207827i	$0.0666392\pi$
$71$			3.50237i			0.415655i	−0.978166	+	0.207827i	$0.933361\pi$
$72$		0			0
$73$			14.6145i			1.71050i	0.518217	+	0.855249i	$0.326596\pi$
$73$			14.6145i			1.71050i	−0.518217	+	0.855249i	$0.673404\pi$
$74$		0			0
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$		0			0
$77$	9.70408	+	9.70408i	1.10588	+	1.10588i
$78$		0			0
$79$	8.95325			1.00732			0.503660	−	0.863902i	$-0.331987\pi$
$79$	8.95325			1.00732			0.503660	+	0.863902i	$0.331987\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	2.86293	+	2.86293i	0.314247	+	0.314247i	0.846553	−	0.532305i	$-0.178674\pi$
$83$	2.86293	+	2.86293i	0.314247	+	0.314247i	−0.532305	+	0.846553i	$0.678674\pi$
$84$		0			0
$85$	−3.53942	+	3.53942i	−0.383904	+	0.383904i
$86$		0			0
$87$		−	8.53271i		−	0.914803i
$88$		0			0
$89$			7.23560i			0.766972i	0.923547	+	0.383486i	$0.125277\pi$
$89$			7.23560i			0.766972i	−0.923547	+	0.383486i	$0.874723\pi$
$90$		0			0
$91$	−12.6056	+	12.6056i	−1.32142	+	1.32142i
$92$		0			0
$93$	5.36151	+	5.36151i	0.555963	+	0.555963i
$94$		0			0
$95$	1.14968			0.117955
$96$		0			0
$97$	−8.24056			−0.836702			−0.418351	−	0.908285i	$-0.637392\pi$
$97$	−8.24056			−0.836702			−0.418351	+	0.908285i	$0.637392\pi$
$98$		0			0
$99$	3.51009	+	3.51009i	0.352778	+	0.352778i
$100$		0			0
$101$	−1.07326	+	1.07326i	−0.106794	+	0.106794i	−0.758485	−	0.651691i	$-0.774060\pi$
$101$	−1.07326	+	1.07326i	−0.106794	+	0.106794i	0.651691	+	0.758485i	$0.274060\pi$
$102$		0			0
$103$		−	1.66763i		−	0.164316i	−0.996619	−	0.0821582i	$-0.973819\pi$
$103$		−	1.66763i		−	0.164316i	0.996619	−	0.0821582i	$-0.0261813\pi$
$104$		0			0
$105$			2.76462i			0.269799i
$106$		0			0
$107$	6.08860	−	6.08860i	0.588607	−	0.588607i	−0.348647	−	0.937254i	$-0.613359\pi$
$107$	6.08860	−	6.08860i	0.588607	−	0.588607i	0.937254	+	0.348647i	$0.113359\pi$
$108$		0			0
$109$	−2.92136	−	2.92136i	−0.279816	−	0.279816i	0.553220	−	0.833035i	$-0.313399\pi$
$109$	−2.92136	−	2.92136i	−0.279816	−	0.279816i	−0.833035	+	0.553220i	$0.813399\pi$
$110$		0			0
$111$	−1.53688			−0.145874
$112$		0			0
$113$	−2.84395			−0.267536			−0.133768	−	0.991013i	$-0.542708\pi$
$113$	−2.84395			−0.267536			−0.133768	+	0.991013i	$0.542708\pi$
$114$		0			0
$115$	5.29061	+	5.29061i	0.493352	+	0.493352i
$116$		0			0
$117$	−4.55960	+	4.55960i	−0.421535	+	0.421535i
$118$		0			0
$119$		−	13.8383i		−	1.26856i
$120$		0			0
$121$		−	13.6415i		−	1.24014i
$122$		0			0
$123$	2.23213	−	2.23213i	0.201264	−	0.201264i
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−6.61073			−0.586607			−0.293304	−	0.956019i	$-0.594755\pi$
$127$	−6.61073			−0.586607			−0.293304	+	0.956019i	$0.594755\pi$
$128$		0			0
$129$	4.39724			0.387155
$130$		0			0
$131$	6.70125	+	6.70125i	0.585491	+	0.585491i	0.936407	−	0.350916i	$-0.114130\pi$
$131$	6.70125	+	6.70125i	0.585491	+	0.585491i	−0.350916	+	0.936407i	$0.614130\pi$
$132$		0			0
$133$	−2.24749	+	2.24749i	−0.194883	+	0.194883i
$134$		0			0
$135$			1.00000i			0.0860663i
$136$		0			0
$137$		−	14.3908i		−	1.22949i	−0.788725	−	0.614746i	$-0.789258\pi$
$137$		−	14.3908i		−	1.22949i	0.788725	−	0.614746i	$-0.210742\pi$
$138$		0			0
$139$	−0.292743	+	0.292743i	−0.0248302	+	0.0248302i	−0.719413	−	0.694583i	$-0.755589\pi$
$139$	−0.292743	+	0.292743i	−0.0248302	+	0.0248302i	0.694583	+	0.719413i	$0.255589\pi$
$140$		0			0
$141$	−1.95167	−	1.95167i	−0.164360	−	0.164360i
$142$		0			0
$143$	32.0093			2.67675
$144$		0			0
$145$	−8.53271			−0.708603
$146$		0			0
$147$	−0.454757	−	0.454757i	−0.0375077	−	0.0375077i
$148$		0			0
$149$	10.9363	−	10.9363i	0.895934	−	0.895934i	−0.0991393	−	0.995074i	$-0.531609\pi$
$149$	10.9363	−	10.9363i	0.895934	−	0.895934i	0.995074	+	0.0991393i	$0.0316089\pi$
$150$		0			0
$151$			13.5225i			1.10045i	0.835017	+	0.550223i	$0.185457\pi$
$151$			13.5225i			1.10045i	−0.835017	+	0.550223i	$0.814543\pi$
$152$		0			0
$153$		−	5.00550i		−	0.404671i
$154$		0			0
$155$	5.36151	−	5.36151i	0.430647	−	0.430647i
$156$		0			0
$157$	−2.76487	−	2.76487i	−0.220661	−	0.220661i	0.588116	−	0.808777i	$-0.299870\pi$
$157$	−2.76487	−	2.76487i	−0.220661	−	0.220661i	−0.808777	+	0.588116i	$0.799870\pi$
$158$		0			0
$159$	−9.06647			−0.719018
$160$		0			0
$161$	−20.6850			−1.63021
$162$		0			0
$163$	−15.4942	−	15.4942i	−1.21360	−	1.21360i	−0.969834	−	0.243767i	$-0.921617\pi$
$163$	−15.4942	−	15.4942i	−1.21360	−	1.21360i	−0.243767	−	0.969834i	$-0.578383\pi$
$164$		0			0
$165$	3.51009	−	3.51009i	0.273261	−	0.273261i
$166$		0			0
$167$		−	1.76898i		−	0.136888i	−0.997655	−	0.0684439i	$-0.978197\pi$
$167$		−	1.76898i		−	0.136888i	0.997655	−	0.0684439i	$-0.0218034\pi$
$168$		0			0
$169$			28.5800i			2.19846i
$170$		0			0
$171$	−0.812949	+	0.812949i	−0.0621678	+	0.0621678i
$172$		0			0
$173$	−4.01351	−	4.01351i	−0.305142	−	0.305142i	0.537880	−	0.843022i	$-0.319225\pi$
$173$	−4.01351	−	4.01351i	−0.305142	−	0.305142i	−0.843022	+	0.537880i	$0.819225\pi$
$174$		0			0
$175$	2.76462			0.208986
$176$		0			0
$177$	7.26561			0.546117
$178$		0			0
$179$	5.31340	+	5.31340i	0.397142	+	0.397142i	0.877224	−	0.480082i	$-0.159393\pi$
$179$	5.31340	+	5.31340i	0.397142	+	0.397142i	−0.480082	+	0.877224i	$0.659393\pi$
$180$		0			0
$181$	8.74918	−	8.74918i	0.650321	−	0.650321i	−0.302749	−	0.953070i	$-0.597904\pi$
$181$	8.74918	−	8.74918i	0.650321	−	0.650321i	0.953070	+	0.302749i	$0.0979044\pi$
$182$		0			0
$183$			3.52470i			0.260553i
$184$		0			0
$185$			1.53688i			0.112994i
$186$		0			0
$187$	−17.5698	+	17.5698i	−1.28483	+	1.28483i
$188$		0			0
$189$	−1.95488	−	1.95488i	−0.142197	−	0.142197i
$190$		0			0
$191$	−4.03787			−0.292170			−0.146085	−	0.989272i	$-0.546667\pi$
$191$	−4.03787			−0.292170			−0.146085	+	0.989272i	$0.546667\pi$
$192$		0			0
$193$	0.437111			0.0314639			0.0157320	−	0.999876i	$-0.494992\pi$
$193$	0.437111			0.0314639			0.0157320	+	0.999876i	$0.494992\pi$
$194$		0			0
$195$	4.55960	+	4.55960i	0.326520	+	0.326520i
$196$		0			0
$197$	−11.6836	+	11.6836i	−0.832424	+	0.832424i	−0.987848	−	0.155424i	$-0.950326\pi$
$197$	−11.6836	+	11.6836i	−0.832424	+	0.832424i	0.155424	+	0.987848i	$0.450326\pi$
$198$		0			0
$199$		−	15.7412i		−	1.11587i	−0.829886	−	0.557933i	$-0.811595\pi$
$199$		−	15.7412i		−	1.11587i	0.829886	−	0.557933i	$-0.188405\pi$
$200$		0			0
$201$			4.44947i			0.313842i
$202$		0			0
$203$	16.6804	−	16.6804i	1.17074	−	1.17074i
$204$		0			0
$205$	−2.23213	−	2.23213i	−0.155899	−	0.155899i
$206$		0			0
$207$	−7.48205			−0.520038
$208$		0			0
$209$	5.70706			0.394765
$210$		0			0
$211$	2.13765	+	2.13765i	0.147162	+	0.147162i	0.776849	−	0.629687i	$-0.216817\pi$
$211$	2.13765	+	2.13765i	0.147162	+	0.147162i	−0.629687	+	0.776849i	$0.716817\pi$
$212$		0			0
$213$	−2.47655	+	2.47655i	−0.169690	+	0.169690i
$214$		0			0
$215$		−	4.39724i		−	0.299889i
$216$		0			0
$217$			20.9622i			1.42301i
$218$		0			0
$219$	−10.3340	+	10.3340i	−0.698308	+	0.698308i
$220$		0			0
$221$	−22.8231	−	22.8231i	−1.53525	−	1.53525i
$222$		0			0
$223$	13.4768			0.902476			0.451238	−	0.892404i	$-0.350983\pi$
$223$	13.4768			0.902476			0.451238	+	0.892404i	$0.350983\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	2.70567	+	2.70567i	0.179582	+	0.179582i	0.791174	−	0.611592i	$-0.209470\pi$
$227$	2.70567	+	2.70567i	0.179582	+	0.179582i	−0.611592	+	0.791174i	$0.709470\pi$
$228$		0			0
$229$	−0.507051	+	0.507051i	−0.0335069	+	0.0335069i	−0.723662	−	0.690155i	$-0.757542\pi$
$229$	−0.507051	+	0.507051i	−0.0335069	+	0.0335069i	0.690155	+	0.723662i	$0.257542\pi$
$230$		0			0
$231$			13.7236i			0.902949i
$232$		0			0
$233$			8.16109i			0.534651i	0.963606	+	0.267325i	$0.0861399\pi$
$233$			8.16109i			0.534651i	−0.963606	+	0.267325i	$0.913860\pi$
$234$		0			0
$235$	−1.95167	+	1.95167i	−0.127313	+	0.127313i
$236$		0			0
$237$	6.33090	+	6.33090i	0.411236	+	0.411236i
$238$		0			0
$239$	−2.46397			−0.159381			−0.0796905	−	0.996820i	$-0.525393\pi$
$239$	−2.46397			−0.159381			−0.0796905	+	0.996820i	$0.525393\pi$
$240$		0			0
$241$	7.38073			0.475434			0.237717	−	0.971334i	$-0.423601\pi$
$241$	7.38073			0.475434			0.237717	+	0.971334i	$0.423601\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.454757	+	0.454757i	−0.0290533	+	0.0290533i
$246$		0			0
$247$			7.41345i			0.471707i
$248$		0			0
$249$			4.04880i			0.256582i
$250$		0			0
$251$	5.15322	−	5.15322i	0.325268	−	0.325268i	−0.525516	−	0.850784i	$-0.676128\pi$
$251$	5.15322	−	5.15322i	0.325268	−	0.325268i	0.850784	+	0.525516i	$0.176128\pi$
$252$		0			0
$253$	26.2627	+	26.2627i	1.65112	+	1.65112i
$254$		0			0
$255$	−5.00550			−0.313457
$256$		0			0
$257$	9.84129			0.613883			0.306942	−	0.951728i	$-0.400694\pi$
$257$	9.84129			0.613883			0.306942	+	0.951728i	$0.400694\pi$
$258$		0			0
$259$	−3.00442	−	3.00442i	−0.186686	−	0.186686i
$260$		0			0
$261$	6.03354	−	6.03354i	0.373467	−	0.373467i
$262$		0			0
$263$		−	27.5027i		−	1.69589i	−0.530086	−	0.847944i	$-0.677840\pi$
$263$		−	27.5027i		−	1.69589i	0.530086	−	0.847944i	$-0.322160\pi$
$264$		0			0
$265$			9.06647i			0.556949i
$266$		0			0
$267$	−5.11634	+	5.11634i	−0.313115	+	0.313115i
$268$		0			0
$269$	−7.35280	−	7.35280i	−0.448308	−	0.448308i	0.446484	−	0.894792i	$-0.352676\pi$
$269$	−7.35280	−	7.35280i	−0.448308	−	0.448308i	−0.894792	+	0.446484i	$0.852676\pi$
$270$		0			0
$271$	−16.1826			−0.983023			−0.491511	−	0.870871i	$-0.663555\pi$
$271$	−16.1826			−0.983023			−0.491511	+	0.870871i	$0.663555\pi$
$272$		0			0
$273$	−17.8270			−1.07894
$274$		0			0
$275$	−3.51009	−	3.51009i	−0.211667	−	0.211667i
$276$		0			0
$277$	19.3725	−	19.3725i	1.16398	−	1.16398i	0.180381	−	0.983597i	$-0.442267\pi$
$277$	19.3725	−	19.3725i	1.16398	−	1.16398i	0.983597	−	0.180381i	$-0.0577331\pi$
$278$		0			0
$279$			7.58233i			0.453942i
$280$		0			0
$281$		−	18.1786i		−	1.08445i	−0.840235	−	0.542223i	$-0.817583\pi$
$281$		−	18.1786i		−	1.08445i	0.840235	−	0.542223i	$-0.182417\pi$
$282$		0			0
$283$	7.74925	−	7.74925i	0.460645	−	0.460645i	−0.438222	−	0.898867i	$-0.644391\pi$
$283$	7.74925	−	7.74925i	0.460645	−	0.460645i	0.898867	+	0.438222i	$0.144391\pi$
$284$		0			0
$285$	0.812949	+	0.812949i	0.0481549	+	0.0481549i
$286$		0			0
$287$	8.72709			0.515144
$288$		0			0
$289$	8.05503			0.473825
$290$		0			0
$291$	−5.82695	−	5.82695i	−0.341582	−	0.341582i
$292$		0			0
$293$	1.24572	−	1.24572i	0.0727760	−	0.0727760i	−0.669782	−	0.742558i	$-0.733612\pi$
$293$	1.24572	−	1.24572i	0.0727760	−	0.0727760i	0.742558	+	0.669782i	$0.233612\pi$
$294$		0			0
$295$		−	7.26561i		−	0.423020i
$296$		0			0
$297$			4.96402i			0.288042i
$298$		0			0
$299$	−34.1152	+	34.1152i	−1.97293	+	1.97293i
$300$		0			0
$301$	8.59608	+	8.59608i	0.495470	+	0.495470i
$302$		0			0
$303$	−1.51782			−0.0871966
$304$		0			0
$305$	3.52470			0.201824
$306$		0			0
$307$	−13.5042	−	13.5042i	−0.770727	−	0.770727i	0.207506	−	0.978234i	$-0.433465\pi$
$307$	−13.5042	−	13.5042i	−0.770727	−	0.770727i	−0.978234	+	0.207506i	$0.933465\pi$
$308$		0			0
$309$	1.17919	−	1.17919i	0.0670819	−	0.0670819i
$310$		0			0
$311$			11.9549i			0.677901i	0.940804	+	0.338951i	$0.110072\pi$
$311$			11.9549i			0.677901i	−0.940804	+	0.338951i	$0.889928\pi$
$312$		0			0
$313$		−	15.2385i		−	0.861333i	−0.902511	−	0.430667i	$-0.858279\pi$
$313$		−	15.2385i		−	0.861333i	0.902511	−	0.430667i	$-0.141721\pi$
$314$		0			0
$315$	−1.95488	+	1.95488i	−0.110145	+	0.110145i
$316$		0			0
$317$	−22.4062	−	22.4062i	−1.25846	−	1.25846i	−0.951830	−	0.306625i	$-0.900800\pi$
$317$	−22.4062	−	22.4062i	−1.25846	−	1.25846i	−0.306625	−	0.951830i	$-0.599200\pi$
$318$		0			0
$319$	−42.3566			−2.37151
$320$		0			0
$321$	8.61058			0.480595
$322$		0			0
$323$	−4.06922	−	4.06922i	−0.226417	−	0.226417i
$324$		0			0
$325$	4.55960	−	4.55960i	0.252921	−	0.252921i
$326$		0			0
$327$		−	4.13143i		−	0.228469i
$328$		0			0
$329$		−	7.63057i		−	0.420687i
$330$		0			0
$331$	−8.11650	+	8.11650i	−0.446123	+	0.446123i	−0.894063	−	0.447940i	$-0.852158\pi$
$331$	−8.11650	+	8.11650i	−0.446123	+	0.446123i	0.447940	+	0.894063i	$0.352158\pi$
$332$		0			0
$333$	−1.08674	−	1.08674i	−0.0595529	−	0.0595529i
$334$		0			0
$335$	4.44947			0.243101
$336$		0			0
$337$	−19.1995			−1.04587			−0.522933	−	0.852374i	$-0.675162\pi$
$337$	−19.1995			−1.04587			−0.522933	+	0.852374i	$0.675162\pi$
$338$		0			0
$339$	−2.01097	−	2.01097i	−0.109221	−	0.109221i
$340$		0			0
$341$	26.6147	−	26.6147i	1.44127	−	1.44127i
$342$		0			0
$343$			17.5743i			0.948926i
$344$		0			0
$345$			7.48205i			0.402820i
$346$		0			0
$347$	3.64968	−	3.64968i	0.195925	−	0.195925i	−0.602325	−	0.798251i	$-0.705759\pi$
$347$	3.64968	−	3.64968i	0.195925	−	0.195925i	0.798251	+	0.602325i	$0.205759\pi$
$348$		0			0
$349$	−16.7180	−	16.7180i	−0.894896	−	0.894896i	0.100083	−	0.994979i	$-0.468089\pi$
$349$	−16.7180	−	16.7180i	−0.894896	−	0.894896i	−0.994979	+	0.100083i	$0.968089\pi$
$350$		0			0
$351$	−6.44825			−0.344182
$352$		0			0
$353$	9.42887			0.501848			0.250924	−	0.968007i	$-0.419266\pi$
$353$	9.42887			0.501848			0.250924	+	0.968007i	$0.419266\pi$
$354$		0			0
$355$	2.47655	+	2.47655i	0.131442	+	0.131442i
$356$		0			0
$357$	9.78516	−	9.78516i	0.517886	−	0.517886i
$358$		0			0
$359$		−	1.12135i		−	0.0591826i	−0.999562	−	0.0295913i	$-0.990579\pi$
$359$		−	1.12135i		−	0.0591826i	0.999562	−	0.0295913i	$-0.00942059\pi$
$360$		0			0
$361$		−	17.6782i		−	0.930433i
$362$		0			0
$363$	9.64602	−	9.64602i	0.506285	−	0.506285i
$364$		0			0
$365$	10.3340	+	10.3340i	0.540907	+	0.540907i
$366$		0			0
$367$	−7.22666			−0.377228			−0.188614	−	0.982051i	$-0.560400\pi$
$367$	−7.22666			−0.377228			−0.188614	+	0.982051i	$0.560400\pi$
$368$		0			0
$369$	3.15671			0.164332
$370$		0			0
$371$	−17.7239	−	17.7239i	−0.920178	−	0.920178i
$372$		0			0
$373$	8.83590	−	8.83590i	0.457506	−	0.457506i	−0.440330	−	0.897836i	$-0.645139\pi$
$373$	8.83590	−	8.83590i	0.457506	−	0.457506i	0.897836	+	0.440330i	$0.145139\pi$
$374$		0			0
$375$		−	1.00000i		−	0.0516398i
$376$		0			0
$377$		−	55.0211i		−	2.83373i
$378$		0			0
$379$	26.2339	−	26.2339i	1.34754	−	1.34754i	0.459223	−	0.888321i	$-0.348128\pi$
$379$	26.2339	−	26.2339i	1.34754	−	1.34754i	0.888321	−	0.459223i	$-0.151872\pi$
$380$		0			0
$381$	−4.67449	−	4.67449i	−0.239481	−	0.239481i
$382$		0			0
$383$	14.3557			0.733544			0.366772	−	0.930311i	$-0.380463\pi$
$383$	14.3557			0.733544			0.366772	+	0.930311i	$0.380463\pi$
$384$		0			0
$385$	13.7236			0.699421
$386$		0			0
$387$	3.10932	+	3.10932i	0.158055	+	0.158055i
$388$		0			0
$389$	1.07721	−	1.07721i	0.0546168	−	0.0546168i	−0.679271	−	0.733888i	$-0.737704\pi$
$389$	1.07721	−	1.07721i	0.0546168	−	0.0546168i	0.733888	+	0.679271i	$0.237704\pi$
$390$		0			0
$391$		−	37.4514i		−	1.89400i
$392$		0			0
$393$			9.47700i			0.478052i
$394$		0			0
$395$	6.33090	−	6.33090i	0.318542	−	0.318542i
$396$		0			0
$397$	−16.8838	−	16.8838i	−0.847376	−	0.847376i	0.142429	−	0.989805i	$-0.454509\pi$
$397$	−16.8838	−	16.8838i	−0.847376	−	0.847376i	−0.989805	+	0.142429i	$0.954509\pi$
$398$		0			0
$399$	−3.17844			−0.159121
$400$		0			0
$401$	−0.406306			−0.0202900			−0.0101450	−	0.999949i	$-0.503229\pi$
$401$	−0.406306			−0.0202900			−0.0101450	+	0.999949i	$0.503229\pi$
$402$		0			0
$403$	34.5724	+	34.5724i	1.72217	+	1.72217i
$404$		0			0
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$		0			0
$407$			7.62911i			0.378161i
$408$		0			0
$409$		−	38.0171i		−	1.87983i	−0.341413	−	0.939913i	$-0.610906\pi$
$409$		−	38.0171i		−	1.87983i	0.341413	−	0.939913i	$-0.389094\pi$
$410$		0			0
$411$	10.1759	−	10.1759i	0.501938	−	0.501938i
$412$		0			0
$413$	14.2034	+	14.2034i	0.698904	+	0.698904i
$414$		0			0
$415$	4.04880			0.198748
$416$		0			0
$417$	−0.414002			−0.0202737
$418$		0			0
$419$	23.2302	+	23.2302i	1.13487	+	1.13487i	0.989357	+	0.145512i	$0.0464829\pi$
$419$	23.2302	+	23.2302i	1.13487	+	1.13487i	0.145512	+	0.989357i	$0.453517\pi$
$420$		0			0
$421$	−26.7883	+	26.7883i	−1.30558	+	1.30558i	−0.381009	+	0.924572i	$0.624423\pi$
$421$	−26.7883	+	26.7883i	−1.30558	+	1.30558i	−0.924572	+	0.381009i	$0.875577\pi$
$422$		0			0
$423$		−	2.76008i		−	0.134200i
$424$		0			0
$425$			5.00550i			0.242802i
$426$		0			0
$427$	−6.89037	+	6.89037i	−0.333448	+	0.333448i
$428$		0			0
$429$	22.6340	+	22.6340i	1.09278	+	1.09278i
$430$		0			0
$431$	−9.17509			−0.441949			−0.220974	−	0.975280i	$-0.570924\pi$
$431$	−9.17509			−0.441949			−0.220974	+	0.975280i	$0.570924\pi$
$432$		0			0
$433$	36.5762			1.75774			0.878869	−	0.477063i	$-0.158299\pi$
$433$	36.5762			1.75774			0.878869	+	0.477063i	$0.158299\pi$
$434$		0			0
$435$	−6.03354	−	6.03354i	−0.289286	−	0.289286i
$436$		0			0
$437$	−6.08252	+	6.08252i	−0.290967	+	0.290967i
$438$		0			0
$439$			6.96346i			0.332348i	0.986096	+	0.166174i	$0.0531413\pi$
$439$			6.96346i			0.332348i	−0.986096	+	0.166174i	$0.946859\pi$
$440$		0			0
$441$		−	0.643123i		−	0.0306249i
$442$		0			0
$443$	−2.15777	+	2.15777i	−0.102519	+	0.102519i	−0.756506	−	0.653987i	$-0.773095\pi$
$443$	−2.15777	+	2.15777i	−0.102519	+	0.102519i	0.653987	+	0.756506i	$0.273095\pi$
$444$		0			0
$445$	5.11634	+	5.11634i	0.242538	+	0.242538i
$446$		0			0
$447$	15.4662			0.731527
$448$		0			0
$449$	13.1720			0.621627			0.310814	−	0.950471i	$-0.399398\pi$
$449$	13.1720			0.621627			0.310814	+	0.950471i	$0.399398\pi$
$450$		0			0
$451$	−11.0803	−	11.0803i	−0.521753	−	0.521753i
$452$		0			0
$453$	−9.56186	+	9.56186i	−0.449256	+	0.449256i
$454$		0			0
$455$			17.8270i			0.835741i
$456$		0			0
$457$		−	10.0012i		−	0.467834i	−0.972257	−	0.233917i	$-0.924846\pi$
$457$		−	10.0012i		−	0.467834i	0.972257	−	0.233917i	$-0.0751545\pi$
$458$		0			0
$459$	3.53942	−	3.53942i	0.165206	−	0.165206i
$460$		0			0
$461$	1.79443	+	1.79443i	0.0835750	+	0.0835750i	0.747658	−	0.664083i	$-0.231178\pi$
$461$	1.79443	+	1.79443i	0.0835750	+	0.0835750i	−0.664083	+	0.747658i	$0.731178\pi$
$462$		0			0
$463$	−2.58325			−0.120054			−0.0600269	−	0.998197i	$-0.519119\pi$
$463$	−2.58325			−0.120054			−0.0600269	+	0.998197i	$0.519119\pi$
$464$		0			0
$465$	7.58233			0.351622
$466$		0			0
$467$	−24.6809	−	24.6809i	−1.14210	−	1.14210i	−0.988066	−	0.154029i	$-0.950775\pi$
$467$	−24.6809	−	24.6809i	−1.14210	−	1.14210i	−0.154029	−	0.988066i	$-0.549225\pi$
$468$		0			0
$469$	−8.69819	+	8.69819i	−0.401645	+	0.401645i
$470$		0			0
$471$		−	3.91012i		−	0.180169i
$472$		0			0
$473$		−	21.8280i		−	1.00365i
$474$		0			0
$475$	0.812949	−	0.812949i	0.0373007	−	0.0373007i
$476$		0			0
$477$	−6.41096	−	6.41096i	−0.293538	−	0.293538i
$478$		0			0
$479$	1.39344			0.0636679			0.0318339	−	0.999493i	$-0.489865\pi$
$479$	1.39344			0.0636679			0.0318339	+	0.999493i	$0.489865\pi$
$480$		0			0
$481$	−9.91020			−0.451866
$482$		0			0
$483$	−14.6265	−	14.6265i	−0.665530	−	0.665530i
$484$		0			0
$485$	−5.82695	+	5.82695i	−0.264588	+	0.264588i
$486$		0			0
$487$			26.7044i			1.21009i	0.796191	+	0.605045i	$0.206845\pi$
$487$			26.7044i			1.21009i	−0.796191	+	0.605045i	$0.793155\pi$
$488$		0			0
$489$		−	21.9121i		−	0.990901i
$490$		0			0
$491$	−16.3259	+	16.3259i	−0.736775	+	0.736775i	−0.971953	−	0.235177i	$-0.924433\pi$
$491$	−16.3259	+	16.3259i	−0.736775	+	0.736775i	0.235177	+	0.971953i	$0.424433\pi$
$492$		0			0
$493$	30.2009	+	30.2009i	1.36018	+	1.36018i
$494$		0			0
$495$	4.96402			0.223116
$496$		0			0
$497$	−9.68272			−0.434329
$498$		0			0
$499$	−26.4923	−	26.4923i	−1.18596	−	1.18596i	−0.978175	−	0.207783i	$-0.933375\pi$
$499$	−26.4923	−	26.4923i	−1.18596	−	1.18596i	−0.207783	−	0.978175i	$-0.566625\pi$
$500$		0			0
$501$	1.25086	−	1.25086i	0.0558842	−	0.0558842i
$502$		0			0
$503$		−	14.2132i		−	0.633737i	−0.948470	−	0.316868i	$-0.897369\pi$
$503$		−	14.2132i		−	0.633737i	0.948470	−	0.316868i	$-0.102631\pi$
$504$		0			0
$505$			1.51782i			0.0675422i
$506$		0			0
$507$	−20.2091	+	20.2091i	−0.897517	+	0.897517i
$508$		0			0
$509$	−4.26128	−	4.26128i	−0.188878	−	0.188878i	0.606333	−	0.795211i	$-0.292640\pi$
$509$	−4.26128	−	4.26128i	−0.188878	−	0.188878i	−0.795211	+	0.606333i	$0.792640\pi$
$510$		0			0
$511$	−40.4036			−1.78735
$512$		0			0
$513$	−1.14968			−0.0507598
$514$		0			0
$515$	−1.17919	−	1.17919i	−0.0519614	−	0.0519614i
$516$		0			0
$517$	−9.68814	+	9.68814i	−0.426084	+	0.426084i
$518$		0			0
$519$		−	5.67597i		−	0.249147i
$520$		0			0
$521$		−	31.9522i		−	1.39985i	−0.714215	−	0.699926i	$-0.753216\pi$
$521$		−	31.9522i		−	1.39985i	0.714215	−	0.699926i	$-0.246784\pi$
$522$		0			0
$523$	−12.3608	+	12.3608i	−0.540498	+	0.540498i	−0.923675	−	0.383177i	$-0.874830\pi$
$523$	−12.3608	+	12.3608i	−0.540498	+	0.540498i	0.383177	+	0.923675i	$0.374830\pi$
$524$		0			0
$525$	1.95488	+	1.95488i	0.0853180	+	0.0853180i
$526$		0			0
$527$	−37.9533			−1.65327
$528$		0			0
$529$	−32.9810			−1.43396
$530$		0			0
$531$	5.13756	+	5.13756i	0.222951	+	0.222951i
$532$		0			0
$533$	14.3933	−	14.3933i	0.623444	−	0.623444i
$534$		0			0
$535$		−	8.61058i		−	0.372268i
$536$		0			0
$537$			7.51428i			0.324265i
$538$		0			0
$539$	−2.25742	+	2.25742i	−0.0972341	+	0.0972341i
$540$		0			0
$541$	−25.6126	−	25.6126i	−1.10117	−	1.10117i	−0.994270	−	0.106902i	$-0.965907\pi$
$541$	−25.6126	−	25.6126i	−1.10117	−	1.10117i	−0.106902	−	0.994270i	$-0.534093\pi$
$542$		0			0
$543$	12.3732			0.530985
$544$		0			0
$545$	−4.13143			−0.176971
$546$		0			0
$547$	−1.56643	−	1.56643i	−0.0669759	−	0.0669759i	0.672825	−	0.739801i	$-0.265081\pi$
$547$	−1.56643	−	1.56643i	−0.0669759	−	0.0669759i	−0.739801	+	0.672825i	$0.765081\pi$
$548$		0			0
$549$	−2.49234	+	2.49234i	−0.106370	+	0.106370i
$550$		0			0
$551$		−	9.80992i		−	0.417917i
$552$		0			0
$553$			24.7523i			1.05258i
$554$		0			0
$555$	−1.08674	+	1.08674i	−0.0461295	+	0.0461295i
$556$		0			0
$557$	−3.96707	−	3.96707i	−0.168090	−	0.168090i	0.618049	−	0.786139i	$-0.287923\pi$
$557$	−3.96707	−	3.96707i	−0.168090	−	0.168090i	−0.786139	+	0.618049i	$0.787923\pi$
$558$		0			0
$559$	28.3545			1.19927
$560$		0			0
$561$	−24.8474			−1.04906
$562$		0			0
$563$	−23.0565	−	23.0565i	−0.971715	−	0.971715i	0.0278956	−	0.999611i	$-0.491119\pi$
$563$	−23.0565	−	23.0565i	−0.971715	−	0.971715i	−0.999611	+	0.0278956i	$0.991119\pi$
$564$		0			0
$565$	−2.01097	+	2.01097i	−0.0846023	+	0.0846023i
$566$		0			0
$567$		−	2.76462i		−	0.116103i
$568$		0			0
$569$			32.6228i			1.36762i	0.729660	+	0.683810i	$0.239678\pi$
$569$			32.6228i			1.36762i	−0.729660	+	0.683810i	$0.760322\pi$
$570$		0			0
$571$	−13.3559	+	13.3559i	−0.558926	+	0.558926i	−0.929002	−	0.370076i	$-0.879332\pi$
$571$	−13.3559	+	13.3559i	−0.558926	+	0.558926i	0.370076	+	0.929002i	$0.379332\pi$
$572$		0			0
$573$	−2.85521	−	2.85521i	−0.119278	−	0.119278i
$574$		0			0
$575$	7.48205			0.312023
$576$		0			0
$577$	46.5999			1.93998			0.969989	−	0.243147i	$-0.0781798\pi$
$577$	46.5999			1.93998			0.969989	+	0.243147i	$0.0781798\pi$
$578$		0			0
$579$	0.309084	+	0.309084i	0.0128451	+	0.0128451i
$580$		0			0
$581$	−7.91492	+	7.91492i	−0.328366	+	0.328366i
$582$		0			0
$583$			45.0062i			1.86397i
$584$		0			0
$585$			6.44825i			0.266602i
$586$		0			0
$587$	29.5590	−	29.5590i	1.22003	−	1.22003i	0.252408	−	0.967621i	$-0.418778\pi$
$587$	29.5590	−	29.5590i	1.22003	−	1.22003i	0.967621	−	0.252408i	$-0.0812224\pi$
$588$		0			0
$589$	6.16404	+	6.16404i	0.253985	+	0.253985i
$590$		0			0
$591$	−16.5231			−0.679671
$592$		0			0
$593$	−35.4555			−1.45598			−0.727991	−	0.685587i	$-0.759546\pi$
$593$	−35.4555			−1.45598			−0.727991	+	0.685587i	$0.759546\pi$
$594$		0			0
$595$	−9.78516	−	9.78516i	−0.401152	−	0.401152i
$596$		0			0
$597$	11.1307	−	11.1307i	0.455551	−	0.455551i
$598$		0			0
$599$		−	22.8571i		−	0.933915i	−0.884280	−	0.466958i	$-0.845350\pi$
$599$		−	22.8571i		−	0.933915i	0.884280	−	0.466958i	$-0.154650\pi$
$600$		0			0
$601$		−	19.4253i		−	0.792374i	−0.918170	−	0.396187i	$-0.870333\pi$
$601$		−	19.4253i		−	0.792374i	0.918170	−	0.396187i	$-0.129667\pi$
$602$		0			0
$603$	−3.14625	+	3.14625i	−0.128125	+	0.128125i
$604$		0			0
$605$	−9.64602	−	9.64602i	−0.392166	−	0.392166i
$606$		0			0
$607$	−19.2455			−0.781149			−0.390574	−	0.920571i	$-0.627724\pi$
$607$	−19.2455			−0.781149			−0.390574	+	0.920571i	$0.627724\pi$
$608$		0			0
$609$	23.5897			0.955903
$610$		0			0
$611$	−12.5849	−	12.5849i	−0.509129	−	0.509129i
$612$		0			0
$613$	−17.3922	+	17.3922i	−0.702465	+	0.702465i	−0.964939	−	0.262474i	$-0.915462\pi$
$613$	−17.3922	+	17.3922i	−0.702465	+	0.702465i	0.262474	+	0.964939i	$0.415462\pi$
$614$		0			0
$615$		−	3.15671i		−	0.127291i
$616$		0			0
$617$			29.7863i			1.19915i	0.800318	+	0.599576i	$0.204664\pi$
$617$			29.7863i			1.19915i	−0.800318	+	0.599576i	$0.795336\pi$
$618$		0			0
$619$	10.6404	−	10.6404i	0.427673	−	0.427673i	−0.460162	−	0.887835i	$-0.652209\pi$
$619$	10.6404	−	10.6404i	0.427673	−	0.427673i	0.887835	+	0.460162i	$0.152209\pi$
$620$		0			0
$621$	−5.29061	−	5.29061i	−0.212305	−	0.212305i
$622$		0			0
$623$	−20.0037			−0.801430
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	4.03550	+	4.03550i	0.161162	+	0.161162i
$628$		0			0
$629$	5.43967	−	5.43967i	0.216894	−	0.216894i
$630$		0			0
$631$			38.7660i			1.54325i	0.636078	+	0.771625i	$0.280556\pi$
$631$			38.7660i			1.54325i	−0.636078	+	0.771625i	$0.719444\pi$
$632$		0			0
$633$			3.02309i			0.120157i
$634$		0			0
$635$	−4.67449	+	4.67449i	−0.185502	+	0.185502i
$636$		0			0
$637$	−2.93239	−	2.93239i	−0.116185	−	0.116185i
$638$		0			0
$639$	−3.50237			−0.138552
$640$		0			0
$641$	3.84117			0.151717			0.0758585	−	0.997119i	$-0.475830\pi$
$641$	3.84117			0.151717			0.0758585	+	0.997119i	$0.475830\pi$
$642$		0			0
$643$	4.00729	+	4.00729i	0.158032	+	0.158032i	0.781694	−	0.623662i	$-0.214356\pi$
$643$	4.00729	+	4.00729i	0.158032	+	0.158032i	−0.623662	+	0.781694i	$0.714356\pi$
$644$		0			0
$645$	3.10932	−	3.10932i	0.122429	−	0.122429i
$646$		0			0
$647$			25.3385i			0.996158i	0.867132	+	0.498079i	$0.165961\pi$
$647$			25.3385i			0.996158i	−0.867132	+	0.498079i	$0.834039\pi$
$648$		0			0
$649$		−	36.0667i		−	1.41574i
$650$		0			0
$651$	−14.8225	+	14.8225i	−0.580941	+	0.580941i
$652$		0			0
$653$	−0.690132	−	0.690132i	−0.0270069	−	0.0270069i	0.693474	−	0.720481i	$-0.256079\pi$
$653$	−0.690132	−	0.690132i	−0.0270069	−	0.0270069i	−0.720481	+	0.693474i	$0.756079\pi$
$654$		0			0
$655$	9.47700			0.370297
$656$		0			0
$657$	−14.6145			−0.570166
$658$		0			0
$659$	27.4031	+	27.4031i	1.06747	+	1.06747i	0.997552	+	0.0699222i	$0.0222751\pi$
$659$	27.4031	+	27.4031i	1.06747	+	1.06747i	0.0699222	+	0.997552i	$0.477725\pi$
$660$		0			0
$661$	−14.4586	+	14.4586i	−0.562373	+	0.562373i	−0.929981	−	0.367608i	$-0.880177\pi$
$661$	−14.4586	+	14.4586i	−0.562373	+	0.562373i	0.367608	+	0.929981i	$0.380177\pi$
$662$		0			0
$663$		−	32.2767i		−	1.25352i
$664$		0			0
$665$			3.17844i			0.123255i
$666$		0			0
$667$	45.1432	−	45.1432i	1.74795	−	1.74795i
$668$		0			0
$669$	9.52957	+	9.52957i	0.368434	+	0.368434i
$670$		0			0
$671$	17.4967			0.675452
$672$		0			0
$673$	38.4496			1.48212			0.741061	−	0.671438i	$-0.234323\pi$
$673$	38.4496			1.48212			0.741061	+	0.671438i	$0.234323\pi$
$674$		0			0
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$		0			0
$677$	15.2625	−	15.2625i	0.586586	−	0.586586i	−0.350119	−	0.936705i	$-0.613859\pi$
$677$	15.2625	−	15.2625i	0.586586	−	0.586586i	0.936705	+	0.350119i	$0.113859\pi$
$678$		0			0
$679$		−	22.7820i		−	0.874293i
$680$		0			0
$681$			3.82640i			0.146628i
$682$		0			0
$683$	31.6516	−	31.6516i	1.21111	−	1.21111i	0.240453	−	0.970661i	$-0.422704\pi$
$683$	31.6516	−	31.6516i	1.21111	−	1.21111i	0.970661	−	0.240453i	$-0.0772959\pi$
$684$		0			0
$685$	−10.1759	−	10.1759i	−0.388800	−	0.388800i
$686$		0			0
$687$	−0.717078			−0.0273582
$688$		0			0
$689$	−58.4629			−2.22726
$690$		0			0
$691$	12.0010	+	12.0010i	0.456539	+	0.456539i	0.897518	−	0.440979i	$-0.145369\pi$
$691$	12.0010	+	12.0010i	0.456539	+	0.456539i	−0.440979	+	0.897518i	$0.645369\pi$
$692$		0			0
$693$	−9.70408	+	9.70408i	−0.368627	+	0.368627i
$694$		0			0
$695$			0.414002i			0.0157040i
$696$		0			0
$697$			15.8009i			0.598502i
$698$		0			0
$699$	−5.77076	+	5.77076i	−0.218270	+	0.218270i
$700$		0			0
$701$	0.298277	+	0.298277i	0.0112658	+	0.0112658i	0.712717	−	0.701451i	$-0.247464\pi$
$701$	0.298277	+	0.298277i	0.0112658	+	0.0112658i	−0.701451	+	0.712717i	$0.747464\pi$
$702$		0			0
$703$	−1.76693			−0.0666409
$704$		0			0
$705$	−2.76008			−0.103951
$706$		0			0
$707$	−2.96716	−	2.96716i	−0.111592	−	0.111592i
$708$		0			0
$709$	11.6489	−	11.6489i	0.437485	−	0.437485i	−0.453680	−	0.891165i	$-0.649889\pi$
$709$	11.6489	−	11.6489i	0.437485	−	0.437485i	0.891165	+	0.453680i	$0.149889\pi$
$710$		0			0
$711$			8.95325i			0.335773i
$712$		0			0
$713$			56.7313i			2.12460i
$714$		0			0
$715$	22.6340	−	22.6340i	0.846463	−	0.846463i
$716$		0			0
$717$	−1.74229	−	1.74229i	−0.0650670	−	0.0650670i
$718$		0			0
$719$	1.69024			0.0630353			0.0315177	−	0.999503i	$-0.489966\pi$
$719$	1.69024			0.0630353			0.0315177	+	0.999503i	$0.489966\pi$
$720$		0			0
$721$	4.61036			0.171699
$722$		0			0
$723$	5.21896	+	5.21896i	0.194095	+	0.194095i
$724$		0			0
$725$	−6.03354	+	6.03354i	−0.224080	+	0.224080i
$726$		0			0
$727$		−	27.2221i		−	1.00961i	−0.863233	−	0.504805i	$-0.831564\pi$
$727$		−	27.2221i		−	1.00961i	0.863233	−	0.504805i	$-0.168436\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−15.5637	+	15.5637i	−0.575644	+	0.575644i
$732$		0			0
$733$	−20.9172	−	20.9172i	−0.772596	−	0.772596i	0.205963	−	0.978560i	$-0.433967\pi$
$733$	−20.9172	−	20.9172i	−0.772596	−	0.772596i	−0.978560	+	0.205963i	$0.933967\pi$
$734$		0			0
$735$	−0.643123			−0.0237219
$736$		0			0
$737$	22.0873			0.813596
$738$		0			0
$739$	3.53634	+	3.53634i	0.130086	+	0.130086i	0.769152	−	0.639066i	$-0.220679\pi$
$739$	3.53634	+	3.53634i	0.130086	+	0.130086i	−0.639066	+	0.769152i	$0.720679\pi$
$740$		0			0
$741$	−5.24210	+	5.24210i	−0.192573	+	0.192573i
$742$		0			0
$743$		−	38.5438i		−	1.41403i	−0.707196	−	0.707017i	$-0.750040\pi$
$743$		−	38.5438i		−	1.41403i	0.707196	−	0.707017i	$-0.249960\pi$
$744$		0			0
$745$		−	15.4662i		−	0.566639i
$746$		0			0
$747$	−2.86293	+	2.86293i	−0.104749	+	0.104749i
$748$		0			0
$749$	16.8327	+	16.8327i	0.615052	+	0.615052i
$750$		0			0
$751$	−7.07646			−0.258224			−0.129112	−	0.991630i	$-0.541213\pi$
$751$	−7.07646			−0.258224			−0.129112	+	0.991630i	$0.541213\pi$
$752$		0			0
$753$	7.28775			0.265580
$754$		0			0
$755$	9.56186	+	9.56186i	0.347992	+	0.347992i
$756$		0			0
$757$	32.5233	−	32.5233i	1.18208	−	1.18208i	0.202873	−	0.979205i	$-0.434972\pi$
$757$	32.5233	−	32.5233i	1.18208	−	1.18208i	0.979205	−	0.202873i	$-0.0650280\pi$
$758$		0			0
$759$			37.1411i			1.34814i
$760$		0			0
$761$			43.1903i			1.56565i	0.622243	+	0.782824i	$0.286222\pi$
$761$			43.1903i			1.56565i	−0.622243	+	0.782824i	$0.713778\pi$
$762$		0			0
$763$	8.07645	−	8.07645i	0.292387	−	0.292387i
$764$		0			0
$765$	−3.53942	−	3.53942i	−0.127968	−	0.127968i
$766$		0			0
$767$	46.8505			1.69167
$768$		0			0
$769$	−31.1675			−1.12393			−0.561965	−	0.827161i	$-0.689955\pi$
$769$	−31.1675			−1.12393			−0.561965	+	0.827161i	$0.689955\pi$
$770$		0			0
$771$	6.95885	+	6.95885i	0.250617	+	0.250617i
$772$		0			0
$773$	−11.7904	+	11.7904i	−0.424072	+	0.424072i	−0.886603	−	0.462531i	$-0.846941\pi$
$773$	−11.7904	+	11.7904i	−0.424072	+	0.424072i	0.462531	+	0.886603i	$0.346941\pi$
$774$		0			0
$775$		−	7.58233i		−	0.272365i
$776$		0			0
$777$		−	4.24889i		−	0.152428i
$778$		0			0
$779$	2.56624	−	2.56624i	0.0919452	−	0.0919452i
$780$		0			0
$781$	12.2936	+	12.2936i	0.439901	+	0.439901i
$782$		0			0
$783$	8.53271			0.304934
$784$		0			0
$785$	−3.91012			−0.139558
$786$		0			0
$787$	3.50469	+	3.50469i	0.124929	+	0.124929i	0.766807	−	0.641878i	$-0.221844\pi$
$787$	3.50469	+	3.50469i	0.124929	+	0.124929i	−0.641878	+	0.766807i	$0.721844\pi$
$788$		0			0
$789$	19.4473	−	19.4473i	0.692343	−	0.692343i
$790$		0			0
$791$		−	7.86243i		−	0.279556i
$792$		0			0
$793$			22.7282i			0.807100i
$794$		0			0
$795$	−6.41096	+	6.41096i	−0.227373	+	0.227373i
$796$		0			0
$797$	34.1882	+	34.1882i	1.21101	+	1.21101i	0.970696	+	0.240312i	$0.0772497\pi$
$797$	34.1882	+	34.1882i	1.21101	+	1.21101i	0.240312	+	0.970696i	$0.422750\pi$
$798$		0			0
$799$	13.8156			0.488760
$800$		0			0
$801$	−7.23560			−0.255657
$802$		0			0
$803$	51.2983	+	51.2983i	1.81028	+	1.81028i
$804$		0			0
$805$	−14.6265	+	14.6265i	−0.515517	+	0.515517i
$806$		0			0
$807$		−	10.3984i		−	0.366042i
$808$		0			0
$809$		−	0.637755i		−	0.0224223i	−0.999937	−	0.0112111i	$-0.996431\pi$
$809$		−	0.637755i		−	0.0224223i	0.999937	−	0.0112111i	$-0.00356869\pi$
$810$		0			0
$811$	−30.6724	+	30.6724i	−1.07705	+	1.07705i	−0.0802798	+	0.996772i	$0.525581\pi$
$811$	−30.6724	+	30.6724i	−1.07705	+	1.07705i	−0.996772	+	0.0802798i	$0.974419\pi$
$812$		0			0
$813$	−11.4428	−	11.4428i	−0.401317	−	0.401317i
$814$		0			0
$815$	−21.9121			−0.767549
$816$		0			0
$817$	5.05543			0.176867
$818$		0			0
$819$	−12.6056	−	12.6056i	−0.440474	−	0.440474i
$820$		0			0
$821$	−2.40778	+	2.40778i	−0.0840320	+	0.0840320i	−0.747873	−	0.663841i	$-0.768925\pi$
$821$	−2.40778	+	2.40778i	−0.0840320	+	0.0840320i	0.663841	+	0.747873i	$0.268925\pi$
$822$		0			0
$823$		−	32.4455i		−	1.13098i	−0.824755	−	0.565490i	$-0.808687\pi$
$823$		−	32.4455i		−	1.13098i	0.824755	−	0.565490i	$-0.191313\pi$
$824$		0			0
$825$		−	4.96402i		−	0.172825i
$826$		0			0
$827$	−32.2278	+	32.2278i	−1.12067	+	1.12067i	−0.129028	+	0.991641i	$0.541186\pi$
$827$	−32.2278	+	32.2278i	−1.12067	+	1.12067i	−0.991641	+	0.129028i	$0.958814\pi$
$828$		0			0
$829$	−29.6767	−	29.6767i	−1.03072	−	1.03072i	−0.999513	−	0.0312027i	$-0.990066\pi$
$829$	−29.6767	−	29.6767i	−1.03072	−	1.03072i	−0.0312027	−	0.999513i	$-0.509934\pi$
$830$		0			0
$831$	27.3968			0.950384
$832$		0			0
$833$	3.21915			0.111537
$834$		0			0
$835$	−1.25086	−	1.25086i	−0.0432877	−	0.0432877i
$836$		0			0
$837$	−5.36151	+	5.36151i	−0.185321	+	0.185321i
$838$		0			0
$839$			42.4417i			1.46525i	0.680632	+	0.732625i	$0.261705\pi$
$839$			42.4417i			1.46525i	−0.680632	+	0.732625i	$0.738295\pi$
$840$		0			0
$841$			43.8072i			1.51059i
$842$		0			0
$843$	12.8542	−	12.8542i	0.442723	−	0.442723i
$844$		0			0
$845$	20.2091	+	20.2091i	0.695214	+	0.695214i
$846$		0			0
$847$	37.7136			1.29586
$848$		0			0
$849$	10.9591			0.376115
$850$		0			0
$851$	−8.13103	−	8.13103i	−0.278728	−	0.278728i
$852$		0			0
$853$	16.7844	−	16.7844i	0.574686	−	0.574686i	−0.358748	−	0.933434i	$-0.616796\pi$
$853$	16.7844	−	16.7844i	0.574686	−	0.574686i	0.933434	+	0.358748i	$0.116796\pi$
$854$		0			0
$855$			1.14968i			0.0393183i
$856$		0			0
$857$		−	31.0924i		−	1.06210i	−0.847341	−	0.531049i	$-0.821798\pi$
$857$		−	31.0924i		−	1.06210i	0.847341	−	0.531049i	$-0.178202\pi$
$858$		0			0
$859$	16.2508	−	16.2508i	0.554469	−	0.554469i	−0.373258	−	0.927727i	$-0.621759\pi$
$859$	16.2508	−	16.2508i	0.554469	−	0.554469i	0.927727	+	0.373258i	$0.121759\pi$
$860$		0			0
$861$	6.17099	+	6.17099i	0.210307	+	0.210307i
$862$		0			0
$863$	−22.4656			−0.764739			−0.382369	−	0.924010i	$-0.624892\pi$
$863$	−22.4656			−0.764739			−0.382369	+	0.924010i	$0.624892\pi$
$864$		0			0
$865$	−5.67597			−0.192989
$866$		0			0
$867$	5.69577	+	5.69577i	0.193438	+	0.193438i
$868$		0			0
$869$	31.4268	−	31.4268i	1.06608	−	1.06608i
$870$		0			0
$871$			28.6913i			0.972169i
$872$		0			0
$873$		−	8.24056i		−	0.278901i
$874$		0			0
$875$	1.95488	−	1.95488i	0.0660871	−	0.0660871i
$876$		0			0
$877$	−1.46527	−	1.46527i	−0.0494785	−	0.0494785i	0.681935	−	0.731413i	$-0.261139\pi$
$877$	−1.46527	−	1.46527i	−0.0494785	−	0.0494785i	−0.731413	+	0.681935i	$0.761139\pi$
$878$		0			0
$879$	1.76172			0.0594213
$880$		0			0
$881$	0.578022			0.0194740			0.00973702	−	0.999953i	$-0.496901\pi$
$881$	0.578022			0.0194740			0.00973702	+	0.999953i	$0.496901\pi$
$882$		0			0
$883$	10.1372	+	10.1372i	0.341144	+	0.341144i	0.856797	−	0.515653i	$-0.172451\pi$
$883$	10.1372	+	10.1372i	0.341144	+	0.341144i	−0.515653	+	0.856797i	$0.672451\pi$
$884$		0			0
$885$	5.13756	−	5.13756i	0.172697	−	0.172697i
$886$		0			0
$887$			56.0202i			1.88097i	0.339831	+	0.940487i	$0.389630\pi$
$887$			56.0202i			1.88097i	−0.339831	+	0.940487i	$0.610370\pi$
$888$		0			0
$889$		−	18.2762i		−	0.612962i
$890$		0			0
$891$	−3.51009	+	3.51009i	−0.117593	+	0.117593i
$892$		0			0
$893$	−2.24380	−	2.24380i	−0.0750860	−	0.0750860i
$894$		0			0
$895$	7.51428			0.251175
$896$		0			0
$897$	−48.2461			−1.61089
$898$		0			0
$899$	−45.7483	−	45.7483i	−1.52579	−	1.52579i
$900$		0			0
$901$	32.0901	−	32.0901i	1.06908	−	1.06908i
$902$		0			0
$903$			12.1567i			0.404549i
$904$		0			0
$905$		−	12.3732i		−	0.411299i
$906$		0			0
$907$	−31.3292	+	31.3292i	−1.04027	+	1.04027i	−0.0411133	+	0.999154i	$0.513090\pi$
$907$	−31.3292	+	31.3292i	−1.04027	+	1.04027i	−0.999154	+	0.0411133i	$0.986910\pi$
$908$		0			0
$909$	−1.07326	−	1.07326i	−0.0355979	−	0.0355979i
$910$		0			0
$911$	−24.7701			−0.820670			−0.410335	−	0.911935i	$-0.634588\pi$
$911$	−24.7701			−0.820670			−0.410335	+	0.911935i	$0.634588\pi$
$912$		0			0
$913$	20.0983			0.665157
$914$		0			0
$915$	2.49234	+	2.49234i	0.0823942	+	0.0823942i
$916$		0			0
$917$	−18.5264	+	18.5264i	−0.611796	+	0.611796i
$918$		0			0
$919$			7.82495i			0.258121i	0.991637	+	0.129061i	$0.0411962\pi$
$919$			7.82495i			0.258121i	−0.991637	+	0.129061i	$0.958804\pi$
$920$		0			0
$921$		−	19.0979i		−	0.629296i
$922$		0			0
$923$	−15.9694	+	15.9694i	−0.525640	+	0.525640i
$924$		0			0
$925$	1.08674	+	1.08674i	0.0357318	+	0.0357318i
$926$		0			0
$927$	1.66763			0.0547721
$928$		0			0
$929$	54.8650			1.80006			0.900031	−	0.435826i	$-0.143544\pi$
$929$	54.8650			1.80006			0.900031	+	0.435826i	$0.143544\pi$
$930$		0			0
$931$	−0.522826	−	0.522826i	−0.0171349	−	0.0171349i
$932$		0			0
$933$	−8.45340	+	8.45340i	−0.276752	+	0.276752i
$934$		0			0
$935$			24.8474i			0.812598i
$936$		0			0
$937$			19.3306i			0.631504i	0.948842	+	0.315752i	$0.102257\pi$
$937$			19.3306i			0.631504i	−0.948842	+	0.315752i	$0.897743\pi$
$938$		0			0
$939$	10.7753	−	10.7753i	0.351638	−	0.351638i
$940$		0			0
$941$	−11.4226	−	11.4226i	−0.372365	−	0.372365i	0.495973	−	0.868338i	$-0.334812\pi$
$941$	−11.4226	−	11.4226i	−0.372365	−	0.372365i	−0.868338	+	0.495973i	$0.834812\pi$
$942$		0			0
$943$	23.6186			0.769129
$944$		0			0
$945$	−2.76462			−0.0899331
$946$		0			0
$947$	26.8761	+	26.8761i	0.873357	+	0.873357i	0.992837	−	0.119480i	$-0.0381227\pi$
$947$	26.8761	+	26.8761i	0.873357	+	0.873357i	−0.119480	+	0.992837i	$0.538123\pi$
$948$		0			0
$949$	−66.6364	+	66.6364i	−2.16311	+	2.16311i
$950$		0			0
$951$		−	31.6871i		−	1.02752i
$952$		0			0
$953$			36.6661i			1.18773i	0.804564	+	0.593866i	$0.202399\pi$
$953$			36.6661i			1.18773i	−0.804564	+	0.593866i	$0.797601\pi$
$954$		0			0
$955$	−2.85521	+	2.85521i	−0.0923923	+	0.0923923i
$956$		0			0
$957$	−29.9506	−	29.9506i	−0.968167	−	0.968167i
$958$		0			0
$959$	39.7852			1.28473
$960$		0			0
$961$	26.4917			0.854570
$962$		0			0
$963$	6.08860	+	6.08860i	0.196202	+	0.196202i
$964$		0			0
$965$	0.309084	−	0.309084i	0.00994976	−	0.00994976i
$966$		0			0
$967$		−	43.0462i		−	1.38427i	−0.721767	−	0.692136i	$-0.756670\pi$
$967$		−	43.0462i		−	1.38427i	0.721767	−	0.692136i	$-0.243330\pi$
$968$		0			0
$969$		−	5.75474i		−	0.184869i
$970$		0			0
$971$	3.26831	−	3.26831i	0.104885	−	0.104885i	−0.652717	−	0.757602i	$-0.726371\pi$
$971$	3.26831	−	3.26831i	0.104885	−	0.104885i	0.757602	+	0.652717i	$0.226371\pi$
$972$		0			0
$973$	−0.809324	−	0.809324i	−0.0259457	−	0.0259457i
$974$		0			0
$975$	6.44825			0.206509
$976$		0			0
$977$	1.62437			0.0519681			0.0259840	−	0.999662i	$-0.491728\pi$
$977$	1.62437			0.0519681			0.0259840	+	0.999662i	$0.491728\pi$
$978$		0			0
$979$	25.3976	+	25.3976i	0.811712	+	0.811712i
$980$		0			0
$981$	2.92136	−	2.92136i	0.0932719	−	0.0932719i
$982$		0			0
$983$		−	45.7756i		−	1.46001i	−0.683439	−	0.730007i	$-0.739517\pi$
$983$		−	45.7756i		−	1.46001i	0.683439	−	0.730007i	$-0.260483\pi$
$984$		0			0
$985$			16.5231i			0.526471i
$986$		0			0
$987$	5.39563	−	5.39563i	0.171745	−	0.171745i
$988$		0			0
$989$	23.2641	+	23.2641i	0.739754	+	0.739754i
$990$		0			0
$991$	11.0608			0.351357			0.175679	−	0.984448i	$-0.443788\pi$
$991$	11.0608			0.351357			0.175679	+	0.984448i	$0.443788\pi$
$992$		0			0
$993$	−11.4785			−0.364258
$994$		0			0
$995$	−11.1307	−	11.1307i	−0.352868	−	0.352868i
$996$		0			0
$997$	−21.9716	+	21.9716i	−0.695848	+	0.695848i	−0.963512	−	0.267664i	$-0.913748\pi$
$997$	−21.9716	+	21.9716i	−0.695848	+	0.695848i	0.267664	+	0.963512i	$0.413748\pi$
$998$		0			0
$999$		−	1.53688i		−	0.0486248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.s.e.1441.9		20
4.3	odd	2		1920.2.s.f.1441.2		20
8.3	odd	2		960.2.s.c.721.7		20
8.5	even	2		240.2.s.c.61.6	✓	20
16.3	odd	4		960.2.s.c.241.9		20
16.5	even	4	inner	1920.2.s.e.481.7		20
16.11	odd	4		1920.2.s.f.481.4		20
16.13	even	4		240.2.s.c.181.6	yes	20
24.5	odd	2		720.2.t.d.541.5		20
24.11	even	2		2880.2.t.d.721.7		20
48.29	odd	4		720.2.t.d.181.5		20
48.35	even	4		2880.2.t.d.2161.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.6	✓	20	8.5	even	2
240.2.s.c.181.6	yes	20	16.13	even	4
720.2.t.d.181.5		20	48.29	odd	4
720.2.t.d.541.5		20	24.5	odd	2
960.2.s.c.241.9		20	16.3	odd	4
960.2.s.c.721.7		20	8.3	odd	2
1920.2.s.e.481.7		20	16.5	even	4	inner
1920.2.s.e.1441.9		20	1.1	even	1	trivial
1920.2.s.f.481.4		20	16.11	odd	4
1920.2.s.f.1441.2		20	4.3	odd	2
2880.2.t.d.721.7		20	24.11	even	2
2880.2.t.d.2161.9		20	48.35	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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +2.76462i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +2.76462i q^{7} +1.00000i q^{9} +(3.51009 - 3.51009i) q^{11} +(4.55960 + 4.55960i) q^{13} +1.00000 q^{15} -5.00550 q^{17} +(0.812949 + 0.812949i) q^{19} +(-1.95488 + 1.95488i) q^{21} +7.48205i q^{23} -1.00000i q^{25} +(-0.707107 + 0.707107i) q^{27} +(-6.03354 - 6.03354i) q^{29} +7.58233 q^{31} +4.96402 q^{33} +(1.95488 + 1.95488i) q^{35} +(-1.08674 + 1.08674i) q^{37} +6.44825i q^{39} -3.15671i q^{41} +(3.10932 - 3.10932i) q^{43} +(0.707107 + 0.707107i) q^{45} -2.76008 q^{47} -0.643123 q^{49} +(-3.53942 - 3.53942i) q^{51} +(-6.41096 + 6.41096i) q^{53} -4.96402i q^{55} +1.14968i q^{57} +(5.13756 - 5.13756i) q^{59} +(2.49234 + 2.49234i) q^{61} -2.76462 q^{63} +6.44825 q^{65} +(3.14625 + 3.14625i) q^{67} +(-5.29061 + 5.29061i) q^{69} +3.50237i q^{71} +14.6145i q^{73} +(0.707107 - 0.707107i) q^{75} +(9.70408 + 9.70408i) q^{77} +8.95325 q^{79} -1.00000 q^{81} +(2.86293 + 2.86293i) q^{83} +(-3.53942 + 3.53942i) q^{85} -8.53271i q^{87} +7.23560i q^{89} +(-12.6056 + 12.6056i) q^{91} +(5.36151 + 5.36151i) q^{93} +1.14968 q^{95} -8.24056 q^{97} +(3.51009 + 3.51009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 8 q^{11} + 20 q^{15} - 24 q^{17} + 4 q^{19} - 16 q^{29} + 16 q^{33} - 16 q^{37} + 8 q^{43} - 52 q^{49} - 4 q^{51} + 16 q^{53} + 16 q^{59} + 4 q^{61} - 8 q^{63} + 8 q^{67} + 4 q^{69} + 40 q^{77} + 56 q^{79} - 20 q^{81} + 48 q^{83} - 4 q^{85} + 8 q^{91} - 16 q^{93} + 56 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 8 * q^11 + 20 * q^15 - 24 * q^17 + 4 * q^19 - 16 * q^29 + 16 * q^33 - 16 * q^37 + 8 * q^43 - 52 * q^49 - 4 * q^51 + 16 * q^53 + 16 * q^59 + 4 * q^61 - 8 * q^63 + 8 * q^67 + 4 * q^69 + 40 * q^77 + 56 * q^79 - 20 * q^81 + 48 * q^83 - 4 * q^85 + 8 * q^91 - 16 * q^93 + 56 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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