LMFDB - Embedded newform 1920.2.s.a.1441.2

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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1441.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1920.1441
Dual form			1920.2.s.a.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +1.00000i q^{9} +(-1.41421 + 1.41421i) q^{11} +(0.585786 + 0.585786i) q^{13} -1.00000 q^{15} +5.41421 q^{17} +(-3.82843 - 3.82843i) q^{19} +(-3.41421 + 3.41421i) q^{21} +5.41421i q^{23} -1.00000i q^{25} +(-0.707107 + 0.707107i) q^{27} +(0.585786 + 0.585786i) q^{29} +3.65685 q^{31} -2.00000 q^{33} +(-3.41421 - 3.41421i) q^{35} +(-4.58579 + 4.58579i) q^{37} +0.828427i q^{39} -4.82843i q^{41} +(-3.65685 + 3.65685i) q^{43} +(-0.707107 - 0.707107i) q^{45} -7.07107 q^{47} -16.3137 q^{49} +(3.82843 + 3.82843i) q^{51} +(4.00000 - 4.00000i) q^{53} -2.00000i q^{55} -5.41421i q^{57} +(7.41421 - 7.41421i) q^{59} +(-9.48528 - 9.48528i) q^{61} -4.82843 q^{63} -0.828427 q^{65} +(7.65685 + 7.65685i) q^{67} +(-3.82843 + 3.82843i) q^{69} +8.00000i q^{71} -3.17157i q^{73} +(0.707107 - 0.707107i) q^{75} +(-6.82843 - 6.82843i) q^{77} -13.6569 q^{79} -1.00000 q^{81} +(3.07107 + 3.07107i) q^{83} +(-3.82843 + 3.82843i) q^{85} +0.828427i q^{87} -3.65685i q^{89} +(-2.82843 + 2.82843i) q^{91} +(2.58579 + 2.58579i) q^{93} +5.41421 q^{95} -13.3137 q^{97} +(-1.41421 - 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 8 q^{13} - 4 q^{15} + 16 q^{17} - 4 q^{19} - 8 q^{21} + 8 q^{29} - 8 q^{31} - 8 q^{33} - 8 q^{35} - 24 q^{37} + 8 q^{43} - 20 q^{49} + 4 q^{51} + 16 q^{53} + 24 q^{59} - 4 q^{61} - 8 q^{63} + 8 q^{65} + 8 q^{67} - 4 q^{69} - 16 q^{77} - 32 q^{79} - 4 q^{81} - 16 q^{83} - 4 q^{85} + 16 q^{93} + 16 q^{95} - 8 q^{97}+O(q^{100}) $ 4 * q + 8 * q^13 - 4 * q^15 + 16 * q^17 - 4 * q^19 - 8 * q^21 + 8 * q^29 - 8 * q^31 - 8 * q^33 - 8 * q^35 - 24 * q^37 + 8 * q^43 - 20 * q^49 + 4 * q^51 + 16 * q^53 + 24 * q^59 - 4 * q^61 - 8 * q^63 + 8 * q^65 + 8 * q^67 - 4 * q^69 - 16 * q^77 - 32 * q^79 - 4 * q^81 - 16 * q^83 - 4 * q^85 + 16 * q^93 + 16 * q^95 - 8 * q^97

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
$7$			4.82843i			1.82497i	0.409106	+	0.912487i	$0.365841\pi$
$7$			4.82843i			1.82497i	−0.409106	+	0.912487i	$0.634159\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	−0.887401	−	0.460999i	$-0.847491\pi$
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	0.460999	+	0.887401i	$0.347491\pi$
$12$		0			0
$13$	0.585786	+	0.585786i	0.162468	+	0.162468i	0.783659	−	0.621191i	$-0.213351\pi$
$13$	0.585786	+	0.585786i	0.162468	+	0.162468i	−0.621191	+	0.783659i	$0.713351\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	5.41421			1.31314			0.656570	−	0.754265i	$-0.272007\pi$
$17$	5.41421			1.31314			0.656570	+	0.754265i	$0.272007\pi$
$18$		0			0
$19$	−3.82843	−	3.82843i	−0.878301	−	0.878301i	0.115057	−	0.993359i	$-0.463295\pi$
$19$	−3.82843	−	3.82843i	−0.878301	−	0.878301i	−0.993359	+	0.115057i	$0.963295\pi$
$20$		0			0
$21$	−3.41421	+	3.41421i	−0.745042	+	0.745042i
$22$		0			0
$23$			5.41421i			1.12894i	0.825453	+	0.564471i	$0.190920\pi$
$23$			5.41421i			1.12894i	−0.825453	+	0.564471i	$0.809080\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	0.585786	+	0.585786i	0.108778	+	0.108778i	0.759401	−	0.650623i	$-0.225492\pi$
$29$	0.585786	+	0.585786i	0.108778	+	0.108778i	−0.650623	+	0.759401i	$0.725492\pi$
$30$		0			0
$31$	3.65685			0.656790			0.328395	−	0.944540i	$-0.393492\pi$
$31$	3.65685			0.656790			0.328395	+	0.944540i	$0.393492\pi$
$32$		0			0
$33$	−2.00000			−0.348155
$34$		0			0
$35$	−3.41421	−	3.41421i	−0.577107	−	0.577107i
$36$		0			0
$37$	−4.58579	+	4.58579i	−0.753899	+	0.753899i	−0.975204	−	0.221306i	$-0.928968\pi$
$37$	−4.58579	+	4.58579i	−0.753899	+	0.753899i	0.221306	+	0.975204i	$0.428968\pi$
$38$		0			0
$39$			0.828427i			0.132655i
$40$		0			0
$41$		−	4.82843i		−	0.754074i	−0.926198	−	0.377037i	$-0.876943\pi$
$41$		−	4.82843i		−	0.754074i	0.926198	−	0.377037i	$-0.123057\pi$
$42$		0			0
$43$	−3.65685	+	3.65685i	−0.557665	+	0.557665i	−0.928642	−	0.370977i	$-0.879023\pi$
$43$	−3.65685	+	3.65685i	−0.557665	+	0.557665i	0.370977	+	0.928642i	$0.379023\pi$
$44$		0			0
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$		0			0
$47$	−7.07107			−1.03142			−0.515711	−	0.856763i	$-0.672472\pi$
$47$	−7.07107			−1.03142			−0.515711	+	0.856763i	$0.672472\pi$
$48$		0			0
$49$	−16.3137			−2.33053
$50$		0			0
$51$	3.82843	+	3.82843i	0.536087	+	0.536087i
$52$		0			0
$53$	4.00000	−	4.00000i	0.549442	−	0.549442i	−0.376837	−	0.926279i	$-0.622988\pi$
$53$	4.00000	−	4.00000i	0.549442	−	0.549442i	0.926279	+	0.376837i	$0.122988\pi$
$54$		0			0
$55$		−	2.00000i		−	0.269680i
$56$		0			0
$57$		−	5.41421i		−	0.717130i
$58$		0			0
$59$	7.41421	−	7.41421i	0.965248	−	0.965248i	−0.0341677	−	0.999416i	$-0.510878\pi$
$59$	7.41421	−	7.41421i	0.965248	−	0.965248i	0.999416	+	0.0341677i	$0.0108780\pi$
$60$		0			0
$61$	−9.48528	−	9.48528i	−1.21447	−	1.21447i	−0.969542	−	0.244923i	$-0.921237\pi$
$61$	−9.48528	−	9.48528i	−1.21447	−	1.21447i	−0.244923	−	0.969542i	$-0.578763\pi$
$62$		0			0
$63$	−4.82843			−0.608325
$64$		0			0
$65$	−0.828427			−0.102754
$66$		0			0
$67$	7.65685	+	7.65685i	0.935434	+	0.935434i	0.998038	−	0.0626048i	$-0.0199408\pi$
$67$	7.65685	+	7.65685i	0.935434	+	0.935434i	−0.0626048	+	0.998038i	$0.519941\pi$
$68$		0			0
$69$	−3.82843	+	3.82843i	−0.460888	+	0.460888i
$70$		0			0
$71$			8.00000i			0.949425i	0.880141	+	0.474713i	$0.157448\pi$
$71$			8.00000i			0.949425i	−0.880141	+	0.474713i	$0.842552\pi$
$72$		0			0
$73$		−	3.17157i		−	0.371205i	−0.982625	−	0.185602i	$-0.940576\pi$
$73$		−	3.17157i		−	0.371205i	0.982625	−	0.185602i	$-0.0594236\pi$
$74$		0			0
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$		0			0
$77$	−6.82843	−	6.82843i	−0.778171	−	0.778171i
$78$		0			0
$79$	−13.6569			−1.53652			−0.768258	−	0.640140i	$-0.778876\pi$
$79$	−13.6569			−1.53652			−0.768258	+	0.640140i	$0.778876\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	3.07107	+	3.07107i	0.337093	+	0.337093i	0.855272	−	0.518179i	$-0.173390\pi$
$83$	3.07107	+	3.07107i	0.337093	+	0.337093i	−0.518179	+	0.855272i	$0.673390\pi$
$84$		0			0
$85$	−3.82843	+	3.82843i	−0.415251	+	0.415251i
$86$		0			0
$87$			0.828427i			0.0888167i
$88$		0			0
$89$		−	3.65685i		−	0.387626i	−0.981039	−	0.193813i	$-0.937915\pi$
$89$		−	3.65685i		−	0.387626i	0.981039	−	0.193813i	$-0.0620855\pi$
$90$		0			0
$91$	−2.82843	+	2.82843i	−0.296500	+	0.296500i
$92$		0			0
$93$	2.58579	+	2.58579i	0.268134	+	0.268134i
$94$		0			0
$95$	5.41421			0.555487
$96$		0			0
$97$	−13.3137			−1.35180			−0.675901	−	0.736992i	$-0.736245\pi$
$97$	−13.3137			−1.35180			−0.675901	+	0.736992i	$0.736245\pi$
$98$		0			0
$99$	−1.41421	−	1.41421i	−0.142134	−	0.142134i
$100$		0			0
$101$	0.585786	−	0.585786i	0.0582879	−	0.0582879i	−0.677362	−	0.735650i	$-0.736877\pi$
$101$	0.585786	−	0.585786i	0.0582879	−	0.0582879i	0.735650	+	0.677362i	$0.236877\pi$
$102$		0			0
$103$		−	10.0000i		−	0.985329i	−0.870219	−	0.492665i	$-0.836023\pi$
$103$		−	10.0000i		−	0.985329i	0.870219	−	0.492665i	$-0.163977\pi$
$104$		0			0
$105$		−	4.82843i		−	0.471206i
$106$		0			0
$107$	−12.2426	+	12.2426i	−1.18354	+	1.18354i	−0.204720	+	0.978821i	$0.565628\pi$
$107$	−12.2426	+	12.2426i	−1.18354	+	1.18354i	−0.978821	+	0.204720i	$0.934372\pi$
$108$		0			0
$109$	5.48528	+	5.48528i	0.525395	+	0.525395i	0.919196	−	0.393801i	$-0.128840\pi$
$109$	5.48528	+	5.48528i	0.525395	+	0.525395i	−0.393801	+	0.919196i	$0.628840\pi$
$110$		0			0
$111$	−6.48528			−0.615556
$112$		0			0
$113$	17.4142			1.63819			0.819096	−	0.573657i	$-0.194476\pi$
$113$	17.4142			1.63819			0.819096	+	0.573657i	$0.194476\pi$
$114$		0			0
$115$	−3.82843	−	3.82843i	−0.357003	−	0.357003i
$116$		0			0
$117$	−0.585786	+	0.585786i	−0.0541560	+	0.0541560i
$118$		0			0
$119$			26.1421i			2.39645i
$120$		0			0
$121$			7.00000i			0.636364i
$122$		0			0
$123$	3.41421	−	3.41421i	0.307849	−	0.307849i
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	19.6569			1.74426			0.872132	−	0.489271i	$-0.162737\pi$
$127$	19.6569			1.74426			0.872132	+	0.489271i	$0.162737\pi$
$128$		0			0
$129$	−5.17157			−0.455332
$130$		0			0
$131$	13.4142	+	13.4142i	1.17201	+	1.17201i	0.981731	+	0.190274i	$0.0609377\pi$
$131$	13.4142	+	13.4142i	1.17201	+	1.17201i	0.190274	+	0.981731i	$0.439062\pi$
$132$		0			0
$133$	18.4853	−	18.4853i	1.60288	−	1.60288i
$134$		0			0
$135$		−	1.00000i		−	0.0860663i
$136$		0			0
$137$			4.24264i			0.362473i	0.983440	+	0.181237i	$0.0580100\pi$
$137$			4.24264i			0.362473i	−0.983440	+	0.181237i	$0.941990\pi$
$138$		0			0
$139$	−6.65685	+	6.65685i	−0.564627	+	0.564627i	−0.930618	−	0.365991i	$-0.880730\pi$
$139$	−6.65685	+	6.65685i	−0.564627	+	0.564627i	0.365991	+	0.930618i	$0.380730\pi$
$140$		0			0
$141$	−5.00000	−	5.00000i	−0.421076	−	0.421076i
$142$		0			0
$143$	−1.65685			−0.138553
$144$		0			0
$145$	−0.828427			−0.0687971
$146$		0			0
$147$	−11.5355	−	11.5355i	−0.951435	−	0.951435i
$148$		0			0
$149$	−7.07107	+	7.07107i	−0.579284	+	0.579284i	−0.934706	−	0.355422i	$-0.884337\pi$
$149$	−7.07107	+	7.07107i	−0.579284	+	0.579284i	0.355422	+	0.934706i	$0.384337\pi$
$150$		0			0
$151$		−	3.65685i		−	0.297591i	−0.988868	−	0.148795i	$-0.952460\pi$
$151$		−	3.65685i		−	0.297591i	0.988868	−	0.148795i	$-0.0475395\pi$
$152$		0			0
$153$			5.41421i			0.437713i
$154$		0			0
$155$	−2.58579	+	2.58579i	−0.207695	+	0.207695i
$156$		0			0
$157$	7.07107	+	7.07107i	0.564333	+	0.564333i	0.930535	−	0.366203i	$-0.119342\pi$
$157$	7.07107	+	7.07107i	0.564333	+	0.564333i	−0.366203	+	0.930535i	$0.619342\pi$
$158$		0			0
$159$	5.65685			0.448618
$160$		0			0
$161$	−26.1421			−2.06029
$162$		0			0
$163$	−2.34315	−	2.34315i	−0.183529	−	0.183529i	0.609362	−	0.792892i	$-0.291425\pi$
$163$	−2.34315	−	2.34315i	−0.183529	−	0.183529i	−0.792892	+	0.609362i	$0.791425\pi$
$164$		0			0
$165$	1.41421	−	1.41421i	0.110096	−	0.110096i
$166$		0			0
$167$			3.07107i			0.237646i	0.992915	+	0.118823i	$0.0379122\pi$
$167$			3.07107i			0.237646i	−0.992915	+	0.118823i	$0.962088\pi$
$168$		0			0
$169$		−	12.3137i		−	0.947208i
$170$		0			0
$171$	3.82843	−	3.82843i	0.292767	−	0.292767i
$172$		0			0
$173$	−11.3137	−	11.3137i	−0.860165	−	0.860165i	0.131192	−	0.991357i	$-0.458120\pi$
$173$	−11.3137	−	11.3137i	−0.860165	−	0.860165i	−0.991357	+	0.131192i	$0.958120\pi$
$174$		0			0
$175$	4.82843			0.364995
$176$		0			0
$177$	10.4853			0.788122
$178$		0			0
$179$	10.5858	+	10.5858i	0.791219	+	0.791219i	0.981692	−	0.190474i	$-0.0610023\pi$
$179$	10.5858	+	10.5858i	0.791219	+	0.791219i	−0.190474	+	0.981692i	$0.561002\pi$
$180$		0			0
$181$	−8.17157	+	8.17157i	−0.607388	+	0.607388i	−0.942263	−	0.334875i	$-0.891306\pi$
$181$	−8.17157	+	8.17157i	−0.607388	+	0.607388i	0.334875	+	0.942263i	$0.391306\pi$
$182$		0			0
$183$		−	13.4142i		−	0.991607i
$184$		0			0
$185$		−	6.48528i		−	0.476807i
$186$		0			0
$187$	−7.65685	+	7.65685i	−0.559925	+	0.559925i
$188$		0			0
$189$	−3.41421	−	3.41421i	−0.248347	−	0.248347i
$190$		0			0
$191$	−4.48528			−0.324544			−0.162272	−	0.986746i	$-0.551882\pi$
$191$	−4.48528			−0.324544			−0.162272	+	0.986746i	$0.551882\pi$
$192$		0			0
$193$	0.828427			0.0596315			0.0298157	−	0.999555i	$-0.490508\pi$
$193$	0.828427			0.0596315			0.0298157	+	0.999555i	$0.490508\pi$
$194$		0			0
$195$	−0.585786	−	0.585786i	−0.0419490	−	0.0419490i
$196$		0			0
$197$	7.75736	−	7.75736i	0.552689	−	0.552689i	−0.374527	−	0.927216i	$-0.622195\pi$
$197$	7.75736	−	7.75736i	0.552689	−	0.552689i	0.927216	+	0.374527i	$0.122195\pi$
$198$		0			0
$199$		−	6.34315i		−	0.449654i	−0.974399	−	0.224827i	$-0.927818\pi$
$199$		−	6.34315i		−	0.449654i	0.974399	−	0.224827i	$-0.0721816\pi$
$200$		0			0
$201$			10.8284i			0.763778i
$202$		0			0
$203$	−2.82843	+	2.82843i	−0.198517	+	0.198517i
$204$		0			0
$205$	3.41421	+	3.41421i	0.238459	+	0.238459i
$206$		0			0
$207$	−5.41421			−0.376314
$208$		0			0
$209$	10.8284			0.749018
$210$		0			0
$211$	−2.65685	−	2.65685i	−0.182905	−	0.182905i	0.609715	−	0.792621i	$-0.291284\pi$
$211$	−2.65685	−	2.65685i	−0.182905	−	0.182905i	−0.792621	+	0.609715i	$0.791284\pi$
$212$		0			0
$213$	−5.65685	+	5.65685i	−0.387601	+	0.387601i
$214$		0			0
$215$		−	5.17157i		−	0.352698i
$216$		0			0
$217$			17.6569i			1.19863i
$218$		0			0
$219$	2.24264	−	2.24264i	0.151544	−	0.151544i
$220$		0			0
$221$	3.17157	+	3.17157i	0.213343	+	0.213343i
$222$		0			0
$223$	−15.1716			−1.01596			−0.507982	−	0.861368i	$-0.669608\pi$
$223$	−15.1716			−1.01596			−0.507982	+	0.861368i	$0.669608\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	14.5858	+	14.5858i	0.968093	+	0.968093i	0.999506	−	0.0314138i	$-0.0100010\pi$
$227$	14.5858	+	14.5858i	0.968093	+	0.968093i	−0.0314138	+	0.999506i	$0.510001\pi$
$228$		0			0
$229$	13.0000	−	13.0000i	0.859064	−	0.859064i	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	13.0000	−	13.0000i	0.859064	−	0.859064i	0.991228	+	0.132164i	$0.0421925\pi$
$230$		0			0
$231$		−	9.65685i		−	0.635374i
$232$		0			0
$233$			3.55635i			0.232984i	0.993192	+	0.116492i	$0.0371650\pi$
$233$			3.55635i			0.232984i	−0.993192	+	0.116492i	$0.962835\pi$
$234$		0			0
$235$	5.00000	−	5.00000i	0.326164	−	0.326164i
$236$		0			0
$237$	−9.65685	−	9.65685i	−0.627280	−	0.627280i
$238$		0			0
$239$	20.9706			1.35647			0.678236	−	0.734844i	$-0.262745\pi$
$239$	20.9706			1.35647			0.678236	+	0.734844i	$0.262745\pi$
$240$		0			0
$241$	−10.3431			−0.666261			−0.333130	−	0.942881i	$-0.608105\pi$
$241$	−10.3431			−0.666261			−0.333130	+	0.942881i	$0.608105\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	11.5355	−	11.5355i	0.736978	−	0.736978i
$246$		0			0
$247$		−	4.48528i		−	0.285392i
$248$		0			0
$249$			4.34315i			0.275236i
$250$		0			0
$251$	3.89949	−	3.89949i	0.246134	−	0.246134i	−0.573248	−	0.819382i	$-0.694317\pi$
$251$	3.89949	−	3.89949i	0.246134	−	0.246134i	0.819382	+	0.573248i	$0.194317\pi$
$252$		0			0
$253$	−7.65685	−	7.65685i	−0.481382	−	0.481382i
$254$		0			0
$255$	−5.41421			−0.339051
$256$		0			0
$257$	10.3848			0.647785			0.323892	−	0.946094i	$-0.395008\pi$
$257$	10.3848			0.647785			0.323892	+	0.946094i	$0.395008\pi$
$258$		0			0
$259$	−22.1421	−	22.1421i	−1.37585	−	1.37585i
$260$		0			0
$261$	−0.585786	+	0.585786i	−0.0362593	+	0.0362593i
$262$		0			0
$263$		−	22.3848i		−	1.38030i	−0.723664	−	0.690152i	$-0.757544\pi$
$263$		−	22.3848i		−	1.38030i	0.723664	−	0.690152i	$-0.242456\pi$
$264$		0			0
$265$			5.65685i			0.347498i
$266$		0			0
$267$	2.58579	−	2.58579i	0.158248	−	0.158248i
$268$		0			0
$269$	18.7279	+	18.7279i	1.14186	+	1.14186i	0.988109	+	0.153752i	$0.0491357\pi$
$269$	18.7279	+	18.7279i	1.14186	+	1.14186i	0.153752	+	0.988109i	$0.450864\pi$
$270$		0			0
$271$	23.3137			1.41621			0.708103	−	0.706109i	$-0.249551\pi$
$271$	23.3137			1.41621			0.708103	+	0.706109i	$0.249551\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$		0			0
$275$	1.41421	+	1.41421i	0.0852803	+	0.0852803i
$276$		0			0
$277$	−16.5858	+	16.5858i	−0.996543	+	0.996543i	−0.999994	−	0.00345072i	$-0.998902\pi$
$277$	−16.5858	+	16.5858i	−0.996543	+	0.996543i	0.00345072	+	0.999994i	$0.498902\pi$
$278$		0			0
$279$			3.65685i			0.218930i
$280$		0			0
$281$			16.1421i			0.962959i	0.876457	+	0.481480i	$0.159900\pi$
$281$			16.1421i			0.962959i	−0.876457	+	0.481480i	$0.840100\pi$
$282$		0			0
$283$	11.6569	−	11.6569i	0.692928	−	0.692928i	−0.269947	−	0.962875i	$-0.587006\pi$
$283$	11.6569	−	11.6569i	0.692928	−	0.692928i	0.962875	+	0.269947i	$0.0870062\pi$
$284$		0			0
$285$	3.82843	+	3.82843i	0.226776	+	0.226776i
$286$		0			0
$287$	23.3137			1.37616
$288$		0			0
$289$	12.3137			0.724336
$290$		0			0
$291$	−9.41421	−	9.41421i	−0.551871	−	0.551871i
$292$		0			0
$293$	2.34315	−	2.34315i	0.136888	−	0.136888i	−0.635342	−	0.772231i	$-0.719141\pi$
$293$	2.34315	−	2.34315i	0.136888	−	0.136888i	0.772231	+	0.635342i	$0.219141\pi$
$294$		0			0
$295$			10.4853i			0.610477i
$296$		0			0
$297$		−	2.00000i		−	0.116052i
$298$		0			0
$299$	−3.17157	+	3.17157i	−0.183417	+	0.183417i
$300$		0			0
$301$	−17.6569	−	17.6569i	−1.01772	−	1.01772i
$302$		0			0
$303$	0.828427			0.0475919
$304$		0			0
$305$	13.4142			0.768096
$306$		0			0
$307$	3.65685	+	3.65685i	0.208708	+	0.208708i	0.803718	−	0.595010i	$-0.202852\pi$
$307$	3.65685	+	3.65685i	0.208708	+	0.208708i	−0.595010	+	0.803718i	$0.702852\pi$
$308$		0			0
$309$	7.07107	−	7.07107i	0.402259	−	0.402259i
$310$		0			0
$311$		−	0.970563i		−	0.0550356i	−0.999621	−	0.0275178i	$-0.991240\pi$
$311$		−	0.970563i		−	0.0550356i	0.999621	−	0.0275178i	$-0.00876029\pi$
$312$		0			0
$313$			11.1716i			0.631455i	0.948850	+	0.315727i	$0.102248\pi$
$313$			11.1716i			0.631455i	−0.948850	+	0.315727i	$0.897752\pi$
$314$		0			0
$315$	3.41421	−	3.41421i	0.192369	−	0.192369i
$316$		0			0
$317$	6.58579	+	6.58579i	0.369895	+	0.369895i	0.867439	−	0.497544i	$-0.165765\pi$
$317$	6.58579	+	6.58579i	0.369895	+	0.369895i	−0.497544	+	0.867439i	$0.665765\pi$
$318$		0			0
$319$	−1.65685			−0.0927660
$320$		0			0
$321$	−17.3137			−0.966357
$322$		0			0
$323$	−20.7279	−	20.7279i	−1.15333	−	1.15333i
$324$		0			0
$325$	0.585786	−	0.585786i	0.0324936	−	0.0324936i
$326$		0			0
$327$			7.75736i			0.428983i
$328$		0			0
$329$		−	34.1421i		−	1.88232i
$330$		0			0
$331$	−10.1716	+	10.1716i	−0.559080	+	0.559080i	−0.929046	−	0.369965i	$-0.879370\pi$
$331$	−10.1716	+	10.1716i	−0.559080	+	0.559080i	0.369965	+	0.929046i	$0.379370\pi$
$332$		0			0
$333$	−4.58579	−	4.58579i	−0.251300	−	0.251300i
$334$		0			0
$335$	−10.8284			−0.591620
$336$		0			0
$337$	2.48528			0.135382			0.0676910	−	0.997706i	$-0.478437\pi$
$337$	2.48528			0.135382			0.0676910	+	0.997706i	$0.478437\pi$
$338$		0			0
$339$	12.3137	+	12.3137i	0.668789	+	0.668789i
$340$		0			0
$341$	−5.17157	+	5.17157i	−0.280056	+	0.280056i
$342$		0			0
$343$		−	44.9706i		−	2.42818i
$344$		0			0
$345$		−	5.41421i		−	0.291491i
$346$		0			0
$347$	−9.17157	+	9.17157i	−0.492356	+	0.492356i	−0.909048	−	0.416692i	$-0.863189\pi$
$347$	−9.17157	+	9.17157i	−0.492356	+	0.492356i	0.416692	+	0.909048i	$0.363189\pi$
$348$		0			0
$349$	7.48528	+	7.48528i	0.400678	+	0.400678i	0.878472	−	0.477794i	$-0.158563\pi$
$349$	7.48528	+	7.48528i	0.400678	+	0.400678i	−0.477794	+	0.878472i	$0.658563\pi$
$350$		0			0
$351$	−0.828427			−0.0442182
$352$		0			0
$353$	21.4142			1.13976			0.569882	−	0.821727i	$-0.306989\pi$
$353$	21.4142			1.13976			0.569882	+	0.821727i	$0.306989\pi$
$354$		0			0
$355$	−5.65685	−	5.65685i	−0.300235	−	0.300235i
$356$		0			0
$357$	−18.4853	+	18.4853i	−0.978345	+	0.978345i
$358$		0			0
$359$			18.8284i			0.993726i	0.867829	+	0.496863i	$0.165515\pi$
$359$			18.8284i			0.993726i	−0.867829	+	0.496863i	$0.834485\pi$
$360$		0			0
$361$			10.3137i			0.542827i
$362$		0			0
$363$	−4.94975	+	4.94975i	−0.259794	+	0.259794i
$364$		0			0
$365$	2.24264	+	2.24264i	0.117385	+	0.117385i
$366$		0			0
$367$	−34.9706			−1.82545			−0.912724	−	0.408576i	$-0.866025\pi$
$367$	−34.9706			−1.82545			−0.912724	+	0.408576i	$0.866025\pi$
$368$		0			0
$369$	4.82843			0.251358
$370$		0			0
$371$	19.3137	+	19.3137i	1.00272	+	1.00272i
$372$		0			0
$373$	11.0711	−	11.0711i	0.573238	−	0.573238i	−0.359794	−	0.933032i	$-0.617153\pi$
$373$	11.0711	−	11.0711i	0.573238	−	0.573238i	0.933032	+	0.359794i	$0.117153\pi$
$374$		0			0
$375$			1.00000i			0.0516398i
$376$		0			0
$377$			0.686292i			0.0353458i
$378$		0			0
$379$	−5.34315	+	5.34315i	−0.274459	+	0.274459i	−0.830892	−	0.556433i	$-0.812169\pi$
$379$	−5.34315	+	5.34315i	−0.274459	+	0.274459i	0.556433	+	0.830892i	$0.312169\pi$
$380$		0			0
$381$	13.8995	+	13.8995i	0.712093	+	0.712093i
$382$		0			0
$383$	−23.0711			−1.17888			−0.589438	−	0.807813i	$-0.700651\pi$
$383$	−23.0711			−1.17888			−0.589438	+	0.807813i	$0.700651\pi$
$384$		0			0
$385$	9.65685			0.492159
$386$		0			0
$387$	−3.65685	−	3.65685i	−0.185888	−	0.185888i
$388$		0			0
$389$	10.3848	−	10.3848i	0.526529	−	0.526529i	−0.393007	−	0.919536i	$-0.628565\pi$
$389$	10.3848	−	10.3848i	0.526529	−	0.526529i	0.919536	+	0.393007i	$0.128565\pi$
$390$		0			0
$391$			29.3137i			1.48246i
$392$		0			0
$393$			18.9706i			0.956938i
$394$		0			0
$395$	9.65685	−	9.65685i	0.485889	−	0.485889i
$396$		0			0
$397$	9.89949	+	9.89949i	0.496841	+	0.496841i	0.910453	−	0.413612i	$-0.135733\pi$
$397$	9.89949	+	9.89949i	0.496841	+	0.496841i	−0.413612	+	0.910453i	$0.635733\pi$
$398$		0			0
$399$	26.1421			1.30874
$400$		0			0
$401$	26.9706			1.34685			0.673423	−	0.739258i	$-0.264823\pi$
$401$	26.9706			1.34685			0.673423	+	0.739258i	$0.264823\pi$
$402$		0			0
$403$	2.14214	+	2.14214i	0.106707	+	0.106707i
$404$		0			0
$405$	0.707107	−	0.707107i	0.0351364	−	0.0351364i
$406$		0			0
$407$		−	12.9706i		−	0.642927i
$408$		0			0
$409$			30.6274i			1.51443i	0.653167	+	0.757214i	$0.273440\pi$
$409$			30.6274i			1.51443i	−0.653167	+	0.757214i	$0.726560\pi$
$410$		0			0
$411$	−3.00000	+	3.00000i	−0.147979	+	0.147979i
$412$		0			0
$413$	35.7990	+	35.7990i	1.76155	+	1.76155i
$414$		0			0
$415$	−4.34315			−0.213197
$416$		0			0
$417$	−9.41421			−0.461016
$418$		0			0
$419$	−10.2426	−	10.2426i	−0.500386	−	0.500386i	0.411172	−	0.911558i	$-0.365120\pi$
$419$	−10.2426	−	10.2426i	−0.500386	−	0.500386i	−0.911558	+	0.411172i	$0.865120\pi$
$420$		0			0
$421$	−3.00000	+	3.00000i	−0.146211	+	0.146211i	−0.776423	−	0.630212i	$-0.782968\pi$
$421$	−3.00000	+	3.00000i	−0.146211	+	0.146211i	0.630212	+	0.776423i	$0.282968\pi$
$422$		0			0
$423$		−	7.07107i		−	0.343807i
$424$		0			0
$425$		−	5.41421i		−	0.262628i
$426$		0			0
$427$	45.7990	−	45.7990i	2.21637	−	2.21637i
$428$		0			0
$429$	−1.17157	−	1.17157i	−0.0565641	−	0.0565641i
$430$		0			0
$431$	−12.4853			−0.601395			−0.300697	−	0.953720i	$-0.597219\pi$
$431$	−12.4853			−0.601395			−0.300697	+	0.953720i	$0.597219\pi$
$432$		0			0
$433$	36.8284			1.76986			0.884931	−	0.465723i	$-0.154206\pi$
$433$	36.8284			1.76986			0.884931	+	0.465723i	$0.154206\pi$
$434$		0			0
$435$	−0.585786	−	0.585786i	−0.0280863	−	0.0280863i
$436$		0			0
$437$	20.7279	−	20.7279i	0.991551	−	0.991551i
$438$		0			0
$439$			6.34315i			0.302742i	0.988477	+	0.151371i	$0.0483688\pi$
$439$			6.34315i			0.302742i	−0.988477	+	0.151371i	$0.951631\pi$
$440$		0			0
$441$		−	16.3137i		−	0.776843i
$442$		0			0
$443$	10.5858	−	10.5858i	0.502946	−	0.502946i	−0.409406	−	0.912352i	$-0.634264\pi$
$443$	10.5858	−	10.5858i	0.502946	−	0.502946i	0.912352	+	0.409406i	$0.134264\pi$
$444$		0			0
$445$	2.58579	+	2.58579i	0.122578	+	0.122578i
$446$		0			0
$447$	−10.0000			−0.472984
$448$		0			0
$449$	8.82843			0.416639			0.208320	−	0.978061i	$-0.433201\pi$
$449$	8.82843			0.416639			0.208320	+	0.978061i	$0.433201\pi$
$450$		0			0
$451$	6.82843	+	6.82843i	0.321538	+	0.321538i
$452$		0			0
$453$	2.58579	−	2.58579i	0.121491	−	0.121491i
$454$		0			0
$455$		−	4.00000i		−	0.187523i
$456$		0			0
$457$		−	23.6569i		−	1.10662i	−0.832975	−	0.553310i	$-0.813364\pi$
$457$		−	23.6569i		−	1.10662i	0.832975	−	0.553310i	$-0.186636\pi$
$458$		0			0
$459$	−3.82843	+	3.82843i	−0.178696	+	0.178696i
$460$		0			0
$461$	8.72792	+	8.72792i	0.406500	+	0.406500i	0.880516	−	0.474016i	$-0.157196\pi$
$461$	8.72792	+	8.72792i	0.406500	+	0.406500i	−0.474016	+	0.880516i	$0.657196\pi$
$462$		0			0
$463$	11.6569			0.541740			0.270870	−	0.962616i	$-0.412689\pi$
$463$	11.6569			0.541740			0.270870	+	0.962616i	$0.412689\pi$
$464$		0			0
$465$	−3.65685			−0.169583
$466$		0			0
$467$	−7.31371	−	7.31371i	−0.338438	−	0.338438i	0.517341	−	0.855779i	$-0.326922\pi$
$467$	−7.31371	−	7.31371i	−0.338438	−	0.338438i	−0.855779	+	0.517341i	$0.826922\pi$
$468$		0			0
$469$	−36.9706	+	36.9706i	−1.70714	+	1.70714i
$470$		0			0
$471$			10.0000i			0.460776i
$472$		0			0
$473$		−	10.3431i		−	0.475578i
$474$		0			0
$475$	−3.82843	+	3.82843i	−0.175660	+	0.175660i
$476$		0			0
$477$	4.00000	+	4.00000i	0.183147	+	0.183147i
$478$		0			0
$479$	−4.00000			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$480$		0			0
$481$	−5.37258			−0.244969
$482$		0			0
$483$	−18.4853	−	18.4853i	−0.841109	−	0.841109i
$484$		0			0
$485$	9.41421	−	9.41421i	0.427477	−	0.427477i
$486$		0			0
$487$			26.0000i			1.17817i	0.808070	+	0.589086i	$0.200512\pi$
$487$			26.0000i			1.17817i	−0.808070	+	0.589086i	$0.799488\pi$
$488$		0			0
$489$		−	3.31371i		−	0.149851i
$490$		0			0
$491$	−2.24264	+	2.24264i	−0.101209	+	0.101209i	−0.755898	−	0.654689i	$-0.772800\pi$
$491$	−2.24264	+	2.24264i	−0.101209	+	0.101209i	0.654689	+	0.755898i	$0.272800\pi$
$492$		0			0
$493$	3.17157	+	3.17157i	0.142840	+	0.142840i
$494$		0			0
$495$	2.00000			0.0898933
$496$		0			0
$497$	−38.6274			−1.73268
$498$		0			0
$499$	4.51472	+	4.51472i	0.202107	+	0.202107i	0.800902	−	0.598795i	$-0.204354\pi$
$499$	4.51472	+	4.51472i	0.202107	+	0.202107i	−0.598795	+	0.800902i	$0.704354\pi$
$500$		0			0
$501$	−2.17157	+	2.17157i	−0.0970187	+	0.0970187i
$502$		0			0
$503$		−	20.2426i		−	0.902575i	−0.892379	−	0.451287i	$-0.850965\pi$
$503$		−	20.2426i		−	0.902575i	0.892379	−	0.451287i	$-0.149035\pi$
$504$		0			0
$505$			0.828427i			0.0368645i
$506$		0			0
$507$	8.70711	−	8.70711i	0.386696	−	0.386696i
$508$		0			0
$509$	8.58579	+	8.58579i	0.380558	+	0.380558i	0.871303	−	0.490745i	$-0.163275\pi$
$509$	8.58579	+	8.58579i	0.380558	+	0.380558i	−0.490745	+	0.871303i	$0.663275\pi$
$510$		0			0
$511$	15.3137			0.677439
$512$		0			0
$513$	5.41421			0.239043
$514$		0			0
$515$	7.07107	+	7.07107i	0.311588	+	0.311588i
$516$		0			0
$517$	10.0000	−	10.0000i	0.439799	−	0.439799i
$518$		0			0
$519$		−	16.0000i		−	0.702322i
$520$		0			0
$521$		−	18.4853i		−	0.809855i	−0.914349	−	0.404927i	$-0.867297\pi$
$521$		−	18.4853i		−	0.809855i	0.914349	−	0.404927i	$-0.132703\pi$
$522$		0			0
$523$	16.6274	−	16.6274i	0.727066	−	0.727066i	−0.242968	−	0.970034i	$-0.578121\pi$
$523$	16.6274	−	16.6274i	0.727066	−	0.727066i	0.970034	+	0.242968i	$0.0781210\pi$
$524$		0			0
$525$	3.41421	+	3.41421i	0.149008	+	0.149008i
$526$		0			0
$527$	19.7990			0.862458
$528$		0			0
$529$	−6.31371			−0.274509
$530$		0			0
$531$	7.41421	+	7.41421i	0.321749	+	0.321749i
$532$		0			0
$533$	2.82843	−	2.82843i	0.122513	−	0.122513i
$534$		0			0
$535$		−	17.3137i		−	0.748537i
$536$		0			0
$537$			14.9706i			0.646027i
$538$		0			0
$539$	23.0711	−	23.0711i	0.993741	−	0.993741i
$540$		0			0
$541$	17.4853	+	17.4853i	0.751751	+	0.751751i	0.974806	−	0.223055i	$-0.0716029\pi$
$541$	17.4853	+	17.4853i	0.751751	+	0.751751i	−0.223055	+	0.974806i	$0.571603\pi$
$542$		0			0
$543$	−11.5563			−0.495930
$544$		0			0
$545$	−7.75736			−0.332289
$546$		0			0
$547$	14.4853	+	14.4853i	0.619346	+	0.619346i	0.945364	−	0.326018i	$-0.105707\pi$
$547$	14.4853	+	14.4853i	0.619346	+	0.619346i	−0.326018	+	0.945364i	$0.605707\pi$
$548$		0			0
$549$	9.48528	−	9.48528i	0.404822	−	0.404822i
$550$		0			0
$551$		−	4.48528i		−	0.191079i
$552$		0			0
$553$		−	65.9411i		−	2.80410i
$554$		0			0
$555$	4.58579	−	4.58579i	0.194656	−	0.194656i
$556$		0			0
$557$	−13.1716	−	13.1716i	−0.558097	−	0.558097i	0.370668	−	0.928765i	$-0.379129\pi$
$557$	−13.1716	−	13.1716i	−0.558097	−	0.558097i	−0.928765	+	0.370668i	$0.879129\pi$
$558$		0			0
$559$	−4.28427			−0.181205
$560$		0			0
$561$	−10.8284			−0.457177
$562$		0			0
$563$	−8.48528	−	8.48528i	−0.357612	−	0.357612i	0.505320	−	0.862932i	$-0.331374\pi$
$563$	−8.48528	−	8.48528i	−0.357612	−	0.357612i	−0.862932	+	0.505320i	$0.831374\pi$
$564$		0			0
$565$	−12.3137	+	12.3137i	−0.518042	+	0.518042i
$566$		0			0
$567$		−	4.82843i		−	0.202775i
$568$		0			0
$569$		−	10.6863i		−	0.447993i	−0.974590	−	0.223996i	$-0.928090\pi$
$569$		−	10.6863i		−	0.447993i	0.974590	−	0.223996i	$-0.0719104\pi$
$570$		0			0
$571$	18.1716	−	18.1716i	0.760457	−	0.760457i	−0.215948	−	0.976405i	$-0.569284\pi$
$571$	18.1716	−	18.1716i	0.760457	−	0.760457i	0.976405	+	0.215948i	$0.0692842\pi$
$572$		0			0
$573$	−3.17157	−	3.17157i	−0.132494	−	0.132494i
$574$		0			0
$575$	5.41421			0.225788
$576$		0			0
$577$	−27.6569			−1.15137			−0.575685	−	0.817672i	$-0.695265\pi$
$577$	−27.6569			−1.15137			−0.575685	+	0.817672i	$0.695265\pi$
$578$		0			0
$579$	0.585786	+	0.585786i	0.0243445	+	0.0243445i
$580$		0			0
$581$	−14.8284	+	14.8284i	−0.615187	+	0.615187i
$582$		0			0
$583$			11.3137i			0.468566i
$584$		0			0
$585$		−	0.828427i		−	0.0342512i
$586$		0			0
$587$	3.07107	−	3.07107i	0.126757	−	0.126757i	−0.640882	−	0.767639i	$-0.721431\pi$
$587$	3.07107	−	3.07107i	0.126757	−	0.126757i	0.767639	+	0.640882i	$0.221431\pi$
$588$		0			0
$589$	−14.0000	−	14.0000i	−0.576860	−	0.576860i
$590$		0			0
$591$	10.9706			0.451269
$592$		0			0
$593$	33.8995			1.39209			0.696043	−	0.718000i	$-0.254942\pi$
$593$	33.8995			1.39209			0.696043	+	0.718000i	$0.254942\pi$
$594$		0			0
$595$	−18.4853	−	18.4853i	−0.757823	−	0.757823i
$596$		0			0
$597$	4.48528	−	4.48528i	0.183570	−	0.183570i
$598$		0			0
$599$			1.85786i			0.0759103i	0.999279	+	0.0379551i	$0.0120844\pi$
$599$			1.85786i			0.0759103i	−0.999279	+	0.0379551i	$0.987916\pi$
$600$		0			0
$601$		−	4.97056i		−	0.202753i	−0.994848	−	0.101377i	$-0.967675\pi$
$601$		−	4.97056i		−	0.202753i	0.994848	−	0.101377i	$-0.0323247\pi$
$602$		0			0
$603$	−7.65685	+	7.65685i	−0.311811	+	0.311811i
$604$		0			0
$605$	−4.94975	−	4.94975i	−0.201236	−	0.201236i
$606$		0			0
$607$	−18.4853			−0.750294			−0.375147	−	0.926965i	$-0.622408\pi$
$607$	−18.4853			−0.750294			−0.375147	+	0.926965i	$0.622408\pi$
$608$		0			0
$609$	−4.00000			−0.162088
$610$		0			0
$611$	−4.14214	−	4.14214i	−0.167573	−	0.167573i
$612$		0			0
$613$	1.41421	−	1.41421i	0.0571195	−	0.0571195i	−0.677970	−	0.735090i	$-0.737140\pi$
$613$	1.41421	−	1.41421i	0.0571195	−	0.0571195i	0.735090	+	0.677970i	$0.237140\pi$
$614$		0			0
$615$			4.82843i			0.194701i
$616$		0			0
$617$			40.7279i			1.63964i	0.572618	+	0.819822i	$0.305928\pi$
$617$			40.7279i			1.63964i	−0.572618	+	0.819822i	$0.694072\pi$
$618$		0			0
$619$	16.3137	−	16.3137i	0.655703	−	0.655703i	−0.298657	−	0.954360i	$-0.596539\pi$
$619$	16.3137	−	16.3137i	0.655703	−	0.655703i	0.954360	+	0.298657i	$0.0965387\pi$
$620$		0			0
$621$	−3.82843	−	3.82843i	−0.153629	−	0.153629i
$622$		0			0
$623$	17.6569			0.707407
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	7.65685	+	7.65685i	0.305785	+	0.305785i
$628$		0			0
$629$	−24.8284	+	24.8284i	−0.989974	+	0.989974i
$630$		0			0
$631$			11.3137i			0.450392i	0.974314	+	0.225196i	$0.0723022\pi$
$631$			11.3137i			0.450392i	−0.974314	+	0.225196i	$0.927698\pi$
$632$		0			0
$633$		−	3.75736i		−	0.149342i
$634$		0			0
$635$	−13.8995	+	13.8995i	−0.551585	+	0.551585i
$636$		0			0
$637$	−9.55635	−	9.55635i	−0.378636	−	0.378636i
$638$		0			0
$639$	−8.00000			−0.316475
$640$		0			0
$641$	9.31371			0.367869			0.183935	−	0.982938i	$-0.441117\pi$
$641$	9.31371			0.367869			0.183935	+	0.982938i	$0.441117\pi$
$642$		0			0
$643$	0.970563	+	0.970563i	0.0382753	+	0.0382753i	0.725985	−	0.687710i	$-0.241384\pi$
$643$	0.970563	+	0.970563i	0.0382753	+	0.0382753i	−0.687710	+	0.725985i	$0.741384\pi$
$644$		0			0
$645$	3.65685	−	3.65685i	0.143988	−	0.143988i
$646$		0			0
$647$			7.07107i			0.277992i	0.990293	+	0.138996i	$0.0443876\pi$
$647$			7.07107i			0.277992i	−0.990293	+	0.138996i	$0.955612\pi$
$648$		0			0
$649$			20.9706i			0.823167i
$650$		0			0
$651$	−12.4853	+	12.4853i	−0.489337	+	0.489337i
$652$		0			0
$653$	−9.65685	−	9.65685i	−0.377902	−	0.377902i	0.492443	−	0.870345i	$-0.336104\pi$
$653$	−9.65685	−	9.65685i	−0.377902	−	0.377902i	−0.870345	+	0.492443i	$0.836104\pi$
$654$		0			0
$655$	−18.9706			−0.741241
$656$		0			0
$657$	3.17157			0.123735
$658$		0			0
$659$	−9.27208	−	9.27208i	−0.361189	−	0.361189i	0.503062	−	0.864251i	$-0.332207\pi$
$659$	−9.27208	−	9.27208i	−0.361189	−	0.361189i	−0.864251	+	0.503062i	$0.832207\pi$
$660$		0			0
$661$	−11.8284	+	11.8284i	−0.460072	+	0.460072i	−0.898679	−	0.438607i	$-0.855472\pi$
$661$	−11.8284	+	11.8284i	−0.460072	+	0.460072i	0.438607	+	0.898679i	$0.355472\pi$
$662$		0			0
$663$			4.48528i			0.174194i
$664$		0			0
$665$			26.1421i			1.01375i
$666$		0			0
$667$	−3.17157	+	3.17157i	−0.122804	+	0.122804i
$668$		0			0
$669$	−10.7279	−	10.7279i	−0.414765	−	0.414765i
$670$		0			0
$671$	26.8284			1.03570
$672$		0			0
$673$	25.7990			0.994478			0.497239	−	0.867614i	$-0.334347\pi$
$673$	25.7990			0.994478			0.497239	+	0.867614i	$0.334347\pi$
$674$		0			0
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$		0			0
$677$	20.0000	−	20.0000i	0.768662	−	0.768662i	−0.209209	−	0.977871i	$-0.567089\pi$
$677$	20.0000	−	20.0000i	0.768662	−	0.768662i	0.977871	+	0.209209i	$0.0670888\pi$
$678$		0			0
$679$		−	64.2843i		−	2.46700i
$680$		0			0
$681$			20.6274i			0.790444i
$682$		0			0
$683$	14.3431	−	14.3431i	0.548825	−	0.548825i	−0.377276	−	0.926101i	$-0.623139\pi$
$683$	14.3431	−	14.3431i	0.548825	−	0.548825i	0.926101	+	0.377276i	$0.123139\pi$
$684$		0			0
$685$	−3.00000	−	3.00000i	−0.114624	−	0.114624i
$686$		0			0
$687$	18.3848			0.701423
$688$		0			0
$689$	4.68629			0.178533
$690$		0			0
$691$	4.17157	+	4.17157i	0.158694	+	0.158694i	0.781988	−	0.623294i	$-0.214206\pi$
$691$	4.17157	+	4.17157i	0.158694	+	0.158694i	−0.623294	+	0.781988i	$0.714206\pi$
$692$		0			0
$693$	6.82843	−	6.82843i	0.259390	−	0.259390i
$694$		0			0
$695$		−	9.41421i		−	0.357101i
$696$		0			0
$697$		−	26.1421i		−	0.990204i
$698$		0			0
$699$	−2.51472	+	2.51472i	−0.0951154	+	0.0951154i
$700$		0			0
$701$	−29.0711	−	29.0711i	−1.09800	−	1.09800i	−0.994645	−	0.103354i	$-0.967042\pi$
$701$	−29.0711	−	29.0711i	−1.09800	−	1.09800i	−0.103354	−	0.994645i	$-0.532958\pi$
$702$		0			0
$703$	35.1127			1.32430
$704$		0			0
$705$	7.07107			0.266312
$706$		0			0
$707$	2.82843	+	2.82843i	0.106374	+	0.106374i
$708$		0			0
$709$	−29.2843	+	29.2843i	−1.09979	+	1.09979i	−0.105360	+	0.994434i	$0.533599\pi$
$709$	−29.2843	+	29.2843i	−1.09979	+	1.09979i	−0.994434	+	0.105360i	$0.966401\pi$
$710$		0			0
$711$		−	13.6569i		−	0.512172i
$712$		0			0
$713$			19.7990i			0.741478i
$714$		0			0
$715$	1.17157	−	1.17157i	0.0438143	−	0.0438143i
$716$		0			0
$717$	14.8284	+	14.8284i	0.553778	+	0.553778i
$718$		0			0
$719$	8.97056			0.334546			0.167273	−	0.985911i	$-0.446504\pi$
$719$	8.97056			0.334546			0.167273	+	0.985911i	$0.446504\pi$
$720$		0			0
$721$	48.2843			1.79820
$722$		0			0
$723$	−7.31371	−	7.31371i	−0.272000	−	0.272000i
$724$		0			0
$725$	0.585786	−	0.585786i	0.0217556	−	0.0217556i
$726$		0			0
$727$		−	17.3137i		−	0.642130i	−0.947057	−	0.321065i	$-0.895959\pi$
$727$		−	17.3137i		−	0.642130i	0.947057	−	0.321065i	$-0.104041\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−19.7990	+	19.7990i	−0.732292	+	0.732292i
$732$		0			0
$733$	7.41421	+	7.41421i	0.273850	+	0.273850i	0.830648	−	0.556798i	$-0.187970\pi$
$733$	7.41421	+	7.41421i	0.273850	+	0.273850i	−0.556798	+	0.830648i	$0.687970\pi$
$734$		0			0
$735$	16.3137			0.601740
$736$		0			0
$737$	−21.6569			−0.797740
$738$		0			0
$739$	7.82843	+	7.82843i	0.287973	+	0.287973i	0.836278	−	0.548305i	$-0.184727\pi$
$739$	7.82843	+	7.82843i	0.287973	+	0.287973i	−0.548305	+	0.836278i	$0.684727\pi$
$740$		0			0
$741$	3.17157	−	3.17157i	0.116511	−	0.116511i
$742$		0			0
$743$			46.1838i			1.69432i	0.531339	+	0.847159i	$0.321689\pi$
$743$			46.1838i			1.69432i	−0.531339	+	0.847159i	$0.678311\pi$
$744$		0			0
$745$		−	10.0000i		−	0.366372i
$746$		0			0
$747$	−3.07107	+	3.07107i	−0.112364	+	0.112364i
$748$		0			0
$749$	−59.1127	−	59.1127i	−2.15993	−	2.15993i
$750$		0			0
$751$	−11.6569			−0.425365			−0.212682	−	0.977121i	$-0.568220\pi$
$751$	−11.6569			−0.425365			−0.212682	+	0.977121i	$0.568220\pi$
$752$		0			0
$753$	5.51472			0.200968
$754$		0			0
$755$	2.58579	+	2.58579i	0.0941064	+	0.0941064i
$756$		0			0
$757$	4.58579	−	4.58579i	0.166673	−	0.166673i	−0.618842	−	0.785515i	$-0.712398\pi$
$757$	4.58579	−	4.58579i	0.166673	−	0.166673i	0.785515	+	0.618842i	$0.212398\pi$
$758$		0			0
$759$		−	10.8284i		−	0.393047i
$760$		0			0
$761$			44.8284i			1.62503i	0.582941	+	0.812515i	$0.301902\pi$
$761$			44.8284i			1.62503i	−0.582941	+	0.812515i	$0.698098\pi$
$762$		0			0
$763$	−26.4853	+	26.4853i	−0.958832	+	0.958832i
$764$		0			0
$765$	−3.82843	−	3.82843i	−0.138417	−	0.138417i
$766$		0			0
$767$	8.68629			0.313644
$768$		0			0
$769$	−40.9706			−1.47744			−0.738718	−	0.674014i	$-0.764569\pi$
$769$	−40.9706			−1.47744			−0.738718	+	0.674014i	$0.764569\pi$
$770$		0			0
$771$	7.34315	+	7.34315i	0.264457	+	0.264457i
$772$		0			0
$773$	3.27208	−	3.27208i	0.117688	−	0.117688i	−0.645810	−	0.763498i	$-0.723480\pi$
$773$	3.27208	−	3.27208i	0.117688	−	0.117688i	0.763498	+	0.645810i	$0.223480\pi$
$774$		0			0
$775$		−	3.65685i		−	0.131358i
$776$		0			0
$777$		−	31.3137i		−	1.12337i
$778$		0			0
$779$	−18.4853	+	18.4853i	−0.662304	+	0.662304i
$780$		0			0
$781$	−11.3137	−	11.3137i	−0.404836	−	0.404836i
$782$		0			0
$783$	−0.828427			−0.0296056
$784$		0			0
$785$	−10.0000			−0.356915
$786$		0			0
$787$	−16.1421	−	16.1421i	−0.575405	−	0.575405i	0.358229	−	0.933634i	$-0.383381\pi$
$787$	−16.1421	−	16.1421i	−0.575405	−	0.575405i	−0.933634	+	0.358229i	$0.883381\pi$
$788$		0			0
$789$	15.8284	−	15.8284i	0.563507	−	0.563507i
$790$		0			0
$791$			84.0833i			2.98966i
$792$		0			0
$793$		−	11.1127i		−	0.394623i
$794$		0			0
$795$	−4.00000	+	4.00000i	−0.141865	+	0.141865i
$796$		0			0
$797$	9.89949	+	9.89949i	0.350658	+	0.350658i	0.860354	−	0.509696i	$-0.170242\pi$
$797$	9.89949	+	9.89949i	0.350658	+	0.350658i	−0.509696	+	0.860354i	$0.670242\pi$
$798$		0			0
$799$	−38.2843			−1.35440
$800$		0			0
$801$	3.65685			0.129209
$802$		0			0
$803$	4.48528	+	4.48528i	0.158282	+	0.158282i
$804$		0			0
$805$	18.4853	−	18.4853i	0.651521	−	0.651521i
$806$		0			0
$807$			26.4853i			0.932326i
$808$		0			0
$809$		−	22.9706i		−	0.807602i	−0.914847	−	0.403801i	$-0.867689\pi$
$809$		−	22.9706i		−	0.807602i	0.914847	−	0.403801i	$-0.132311\pi$
$810$		0			0
$811$	−21.0000	+	21.0000i	−0.737410	+	0.737410i	−0.972076	−	0.234666i	$-0.924600\pi$
$811$	−21.0000	+	21.0000i	−0.737410	+	0.737410i	0.234666	+	0.972076i	$0.424600\pi$
$812$		0			0
$813$	16.4853	+	16.4853i	0.578164	+	0.578164i
$814$		0			0
$815$	3.31371			0.116074
$816$		0			0
$817$	28.0000			0.979596
$818$		0			0
$819$	−2.82843	−	2.82843i	−0.0988332	−	0.0988332i
$820$		0			0
$821$	−2.92893	+	2.92893i	−0.102220	+	0.102220i	−0.756367	−	0.654147i	$-0.773028\pi$
$821$	−2.92893	+	2.92893i	−0.102220	+	0.102220i	0.654147	+	0.756367i	$0.273028\pi$
$822$		0			0
$823$			54.0833i			1.88522i	0.333890	+	0.942612i	$0.391639\pi$
$823$			54.0833i			1.88522i	−0.333890	+	0.942612i	$0.608361\pi$
$824$		0			0
$825$			2.00000i			0.0696311i
$826$		0			0
$827$	−26.1421	+	26.1421i	−0.909051	+	0.909051i	−0.996196	−	0.0871446i	$-0.972226\pi$
$827$	−26.1421	+	26.1421i	−0.909051	+	0.909051i	0.0871446	+	0.996196i	$0.472226\pi$
$828$		0			0
$829$	12.5147	+	12.5147i	0.434654	+	0.434654i	0.890208	−	0.455554i	$-0.150559\pi$
$829$	12.5147	+	12.5147i	0.434654	+	0.434654i	−0.455554	+	0.890208i	$0.650559\pi$
$830$		0			0
$831$	−23.4558			−0.813674
$832$		0			0
$833$	−88.3259			−3.06031
$834$		0			0
$835$	−2.17157	−	2.17157i	−0.0751504	−	0.0751504i
$836$		0			0
$837$	−2.58579	+	2.58579i	−0.0893779	+	0.0893779i
$838$		0			0
$839$		−	15.7990i		−	0.545442i	−0.962093	−	0.272721i	$-0.912076\pi$
$839$		−	15.7990i		−	0.545442i	0.962093	−	0.272721i	$-0.0879235\pi$
$840$		0			0
$841$		−	28.3137i		−	0.976335i
$842$		0			0
$843$	−11.4142	+	11.4142i	−0.393126	+	0.393126i
$844$		0			0
$845$	8.70711	+	8.70711i	0.299534	+	0.299534i
$846$		0			0
$847$	−33.7990			−1.16135
$848$		0			0
$849$	16.4853			0.565773
$850$		0			0
$851$	−24.8284	−	24.8284i	−0.851108	−	0.851108i
$852$		0			0
$853$	40.0416	−	40.0416i	1.37100	−	1.37100i	0.512034	−	0.858965i	$-0.328892\pi$
$853$	40.0416	−	40.0416i	1.37100	−	1.37100i	0.858965	−	0.512034i	$-0.171108\pi$
$854$		0			0
$855$			5.41421i			0.185162i
$856$		0			0
$857$			51.5563i			1.76113i	0.473924	+	0.880566i	$0.342837\pi$
$857$			51.5563i			1.76113i	−0.473924	+	0.880566i	$0.657163\pi$
$858$		0			0
$859$	−29.2843	+	29.2843i	−0.999166	+	0.999166i	−1.00000		0.000833212i	$-0.999735\pi$
$859$	−29.2843	+	29.2843i	−0.999166	+	0.999166i	0.000833212		1.00000i	$0.499735\pi$
$860$		0			0
$861$	16.4853	+	16.4853i	0.561817	+	0.561817i
$862$		0			0
$863$	−29.4142			−1.00127			−0.500636	−	0.865658i	$-0.666900\pi$
$863$	−29.4142			−1.00127			−0.500636	+	0.865658i	$0.666900\pi$
$864$		0			0
$865$	16.0000			0.544016
$866$		0			0
$867$	8.70711	+	8.70711i	0.295709	+	0.295709i
$868$		0			0
$869$	19.3137	−	19.3137i	0.655173	−	0.655173i
$870$		0			0
$871$			8.97056i			0.303956i
$872$		0			0
$873$		−	13.3137i		−	0.450601i
$874$		0			0
$875$	−3.41421	+	3.41421i	−0.115421	+	0.115421i
$876$		0			0
$877$	−19.0711	−	19.0711i	−0.643984	−	0.643984i	0.307548	−	0.951532i	$-0.400491\pi$
$877$	−19.0711	−	19.0711i	−0.643984	−	0.643984i	−0.951532	+	0.307548i	$0.900491\pi$
$878$		0			0
$879$	3.31371			0.111769
$880$		0			0
$881$	−39.9411			−1.34565			−0.672825	−	0.739801i	$-0.734919\pi$
$881$	−39.9411			−1.34565			−0.672825	+	0.739801i	$0.734919\pi$
$882$		0			0
$883$	19.5147	+	19.5147i	0.656723	+	0.656723i	0.954603	−	0.297881i	$-0.0962797\pi$
$883$	19.5147	+	19.5147i	0.656723	+	0.656723i	−0.297881	+	0.954603i	$0.596280\pi$
$884$		0			0
$885$	−7.41421	+	7.41421i	−0.249226	+	0.249226i
$886$		0			0
$887$		−	14.7868i		−	0.496492i	−0.968697	−	0.248246i	$-0.920146\pi$
$887$		−	14.7868i		−	0.496492i	0.968697	−	0.248246i	$-0.0798541\pi$
$888$		0			0
$889$			94.9117i			3.18324i
$890$		0			0
$891$	1.41421	−	1.41421i	0.0473779	−	0.0473779i
$892$		0			0
$893$	27.0711	+	27.0711i	0.905899	+	0.905899i
$894$		0			0
$895$	−14.9706			−0.500411
$896$		0			0
$897$	−4.48528			−0.149759
$898$		0			0
$899$	2.14214	+	2.14214i	0.0714442	+	0.0714442i
$900$		0			0
$901$	21.6569	−	21.6569i	0.721494	−	0.721494i
$902$		0			0
$903$		−	24.9706i		−	0.830968i
$904$		0			0
$905$		−	11.5563i		−	0.384146i
$906$		0			0
$907$	−25.1716	+	25.1716i	−0.835808	+	0.835808i	−0.988304	−	0.152496i	$-0.951269\pi$
$907$	−25.1716	+	25.1716i	−0.835808	+	0.835808i	0.152496	+	0.988304i	$0.451269\pi$
$908$		0			0
$909$	0.585786	+	0.585786i	0.0194293	+	0.0194293i
$910$		0			0
$911$	6.82843			0.226236			0.113118	−	0.993582i	$-0.463916\pi$
$911$	6.82843			0.226236			0.113118	+	0.993582i	$0.463916\pi$
$912$		0			0
$913$	−8.68629			−0.287474
$914$		0			0
$915$	9.48528	+	9.48528i	0.313574	+	0.313574i
$916$		0			0
$917$	−64.7696	+	64.7696i	−2.13888	+	2.13888i
$918$		0			0
$919$		−	16.6274i		−	0.548488i	−0.961660	−	0.274244i	$-0.911572\pi$
$919$		−	16.6274i		−	0.548488i	0.961660	−	0.274244i	$-0.0884276\pi$
$920$		0			0
$921$			5.17157i			0.170409i
$922$		0			0
$923$	−4.68629	+	4.68629i	−0.154251	+	0.154251i
$924$		0			0
$925$	4.58579	+	4.58579i	0.150780	+	0.150780i
$926$		0			0
$927$	10.0000			0.328443
$928$		0			0
$929$	3.45584			0.113383			0.0566913	−	0.998392i	$-0.481945\pi$
$929$	3.45584			0.113383			0.0566913	+	0.998392i	$0.481945\pi$
$930$		0			0
$931$	62.4558	+	62.4558i	2.04691	+	2.04691i
$932$		0			0
$933$	0.686292	−	0.686292i	0.0224682	−	0.0224682i
$934$		0			0
$935$		−	10.8284i		−	0.354127i
$936$		0			0
$937$		−	36.6274i		−	1.19657i	−0.801285	−	0.598283i	$-0.795850\pi$
$937$		−	36.6274i		−	1.19657i	0.801285	−	0.598283i	$-0.204150\pi$
$938$		0			0
$939$	−7.89949	+	7.89949i	−0.257790	+	0.257790i
$940$		0			0
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	0.962569	−	0.271038i	$-0.0873669\pi$
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	−0.271038	+	0.962569i	$0.587367\pi$
$942$		0			0
$943$	26.1421			0.851305
$944$		0			0
$945$	4.82843			0.157069
$946$		0			0
$947$	11.0711	+	11.0711i	0.359761	+	0.359761i	0.863725	−	0.503964i	$-0.168125\pi$
$947$	11.0711	+	11.0711i	0.359761	+	0.359761i	−0.503964	+	0.863725i	$0.668125\pi$
$948$		0			0
$949$	1.85786	−	1.85786i	0.0603088	−	0.0603088i
$950$		0			0
$951$			9.31371i			0.302018i
$952$		0			0
$953$		−	57.9828i		−	1.87825i	−0.343582	−	0.939123i	$-0.611640\pi$
$953$		−	57.9828i		−	1.87825i	0.343582	−	0.939123i	$-0.388360\pi$
$954$		0			0
$955$	3.17157	−	3.17157i	0.102630	−	0.102630i
$956$		0			0
$957$	−1.17157	−	1.17157i	−0.0378716	−	0.0378716i
$958$		0			0
$959$	−20.4853			−0.661504
$960$		0			0
$961$	−17.6274			−0.568626
$962$		0			0
$963$	−12.2426	−	12.2426i	−0.394514	−	0.394514i
$964$		0			0
$965$	−0.585786	+	0.585786i	−0.0188571	+	0.0188571i
$966$		0			0
$967$			19.4558i			0.625658i	0.949810	+	0.312829i	$0.101277\pi$
$967$			19.4558i			0.625658i	−0.949810	+	0.312829i	$0.898723\pi$
$968$		0			0
$969$		−	29.3137i		−	0.941692i
$970$		0			0
$971$	−22.2426	+	22.2426i	−0.713800	+	0.713800i	−0.967328	−	0.253528i	$-0.918409\pi$
$971$	−22.2426	+	22.2426i	−0.713800	+	0.713800i	0.253528	+	0.967328i	$0.418409\pi$
$972$		0			0
$973$	−32.1421	−	32.1421i	−1.03043	−	1.03043i
$974$		0			0
$975$	0.828427			0.0265309
$976$		0			0
$977$	−11.5563			−0.369720			−0.184860	−	0.982765i	$-0.559183\pi$
$977$	−11.5563			−0.369720			−0.184860	+	0.982765i	$0.559183\pi$
$978$		0			0
$979$	5.17157	+	5.17157i	0.165284	+	0.165284i
$980$		0			0
$981$	−5.48528	+	5.48528i	−0.175132	+	0.175132i
$982$		0			0
$983$		−	20.7279i		−	0.661118i	−0.943785	−	0.330559i	$-0.892763\pi$
$983$		−	20.7279i		−	0.661118i	0.943785	−	0.330559i	$-0.107237\pi$
$984$		0			0
$985$			10.9706i			0.349551i
$986$		0			0
$987$	24.1421	−	24.1421i	0.768453	−	0.768453i
$988$		0			0
$989$	−19.7990	−	19.7990i	−0.629571	−	0.629571i
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$	−14.3848			−0.456487
$994$		0			0
$995$	4.48528	+	4.48528i	0.142193	+	0.142193i
$996$		0			0
$997$	−9.75736	+	9.75736i	−0.309019	+	0.309019i	−0.844529	−	0.535510i	$-0.820119\pi$
$997$	−9.75736	+	9.75736i	−0.309019	+	0.309019i	0.535510	+	0.844529i	$0.320119\pi$
$998$		0			0
$999$		−	6.48528i		−	0.205185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.s.a.1441.2		4
4.3	odd	2		1920.2.s.b.1441.1		4
8.3	odd	2		960.2.s.a.721.2		4
8.5	even	2		240.2.s.a.61.1	✓	4
16.3	odd	4		960.2.s.a.241.2		4
16.5	even	4	inner	1920.2.s.a.481.2		4
16.11	odd	4		1920.2.s.b.481.1		4
16.13	even	4		240.2.s.a.181.1	yes	4
24.5	odd	2		720.2.t.a.541.2		4
24.11	even	2		2880.2.t.a.721.1		4
48.29	odd	4		720.2.t.a.181.2		4
48.35	even	4		2880.2.t.a.2161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.a.61.1	✓	4	8.5	even	2
240.2.s.a.181.1	yes	4	16.13	even	4
720.2.t.a.181.2		4	48.29	odd	4
720.2.t.a.541.2		4	24.5	odd	2
960.2.s.a.241.2		4	16.3	odd	4
960.2.s.a.721.2		4	8.3	odd	2
1920.2.s.a.481.2		4	16.5	even	4	inner
1920.2.s.a.1441.2		4	1.1	even	1	trivial
1920.2.s.b.481.1		4	16.11	odd	4
1920.2.s.b.1441.1		4	4.3	odd	2
2880.2.t.a.721.1		4	24.11	even	2
2880.2.t.a.2161.1		4	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-0.707107 + 0.707107i) q^{5} +4.82843i q^{7} +1.00000i q^{9} +(-1.41421 + 1.41421i) q^{11} +(0.585786 + 0.585786i) q^{13} -1.00000 q^{15} +5.41421 q^{17} +(-3.82843 - 3.82843i) q^{19} +(-3.41421 + 3.41421i) q^{21} +5.41421i q^{23} -1.00000i q^{25} +(-0.707107 + 0.707107i) q^{27} +(0.585786 + 0.585786i) q^{29} +3.65685 q^{31} -2.00000 q^{33} +(-3.41421 - 3.41421i) q^{35} +(-4.58579 + 4.58579i) q^{37} +0.828427i q^{39} -4.82843i q^{41} +(-3.65685 + 3.65685i) q^{43} +(-0.707107 - 0.707107i) q^{45} -7.07107 q^{47} -16.3137 q^{49} +(3.82843 + 3.82843i) q^{51} +(4.00000 - 4.00000i) q^{53} -2.00000i q^{55} -5.41421i q^{57} +(7.41421 - 7.41421i) q^{59} +(-9.48528 - 9.48528i) q^{61} -4.82843 q^{63} -0.828427 q^{65} +(7.65685 + 7.65685i) q^{67} +(-3.82843 + 3.82843i) q^{69} +8.00000i q^{71} -3.17157i q^{73} +(0.707107 - 0.707107i) q^{75} +(-6.82843 - 6.82843i) q^{77} -13.6569 q^{79} -1.00000 q^{81} +(3.07107 + 3.07107i) q^{83} +(-3.82843 + 3.82843i) q^{85} +0.828427i q^{87} -3.65685i q^{89} +(-2.82843 + 2.82843i) q^{91} +(2.58579 + 2.58579i) q^{93} +5.41421 q^{95} -13.3137 q^{97} +(-1.41421 - 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 8 q^{13} - 4 q^{15} + 16 q^{17} - 4 q^{19} - 8 q^{21} + 8 q^{29} - 8 q^{31} - 8 q^{33} - 8 q^{35} - 24 q^{37} + 8 q^{43} - 20 q^{49} + 4 q^{51} + 16 q^{53} + 24 q^{59} - 4 q^{61} - 8 q^{63} + 8 q^{65} + 8 q^{67} - 4 q^{69} - 16 q^{77} - 32 q^{79} - 4 q^{81} - 16 q^{83} - 4 q^{85} + 16 q^{93} + 16 q^{95} - 8 q^{97}+O(q^{100}) \) 4 * q + 8 * q^13 - 4 * q^15 + 16 * q^17 - 4 * q^19 - 8 * q^21 + 8 * q^29 - 8 * q^31 - 8 * q^33 - 8 * q^35 - 24 * q^37 + 8 * q^43 - 20 * q^49 + 4 * q^51 + 16 * q^53 + 24 * q^59 - 4 * q^61 - 8 * q^63 + 8 * q^65 + 8 * q^67 - 4 * q^69 - 16 * q^77 - 32 * q^79 - 4 * q^81 - 16 * q^83 - 4 * q^85 + 16 * q^93 + 16 * q^95 - 8 * q^97

Introduction

L-functions

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