LMFDB - Embedded newform 960.2.v.j.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(257,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("960.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.v (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:	$7.66563859404$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 480)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	960.257
Dual form			960.2.v.j.833.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70711 - 0.292893i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(2.82843 - 1.00000i) q^{9} -4.24264i q^{11} +(4.00000 - 4.00000i) q^{13} +(-0.585786 + 3.82843i) q^{15} +(-1.41421 + 1.41421i) q^{17} +(-6.00000 - 4.24264i) q^{21} +(-4.00000 - 3.00000i) q^{25} +(4.53553 - 2.53553i) q^{27} +4.24264 q^{29} -6.00000 q^{31} +(-1.24264 - 7.24264i) q^{33} +(8.48528 - 4.24264i) q^{35} +(2.00000 + 2.00000i) q^{37} +(5.65685 - 8.00000i) q^{39} +(6.00000 - 6.00000i) q^{43} +(0.121320 + 6.70711i) q^{45} +(8.48528 - 8.48528i) q^{47} +11.0000i q^{49} +(-2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(9.00000 + 3.00000i) q^{55} -4.24264 q^{59} +6.00000 q^{61} +(-11.4853 - 5.48528i) q^{63} +(5.65685 + 11.3137i) q^{65} +8.48528i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-7.70711 - 3.94975i) q^{75} +(-12.7279 + 12.7279i) q^{77} -6.00000i q^{79} +(7.00000 - 5.65685i) q^{81} +(8.48528 + 8.48528i) q^{83} +(-2.00000 - 4.00000i) q^{85} +(7.24264 - 1.24264i) q^{87} -8.48528 q^{89} -24.0000 q^{91} +(-10.2426 + 1.75736i) q^{93} +(-5.00000 - 5.00000i) q^{97} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 12 q^{7} + 16 q^{13} - 8 q^{15} - 24 q^{21} - 16 q^{25} + 4 q^{27} - 24 q^{31} + 12 q^{33} + 8 q^{37} + 24 q^{43} - 8 q^{45} - 8 q^{51} + 36 q^{55} + 24 q^{61} - 12 q^{63} - 20 q^{73} - 28 q^{75}+ \cdots - 20 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 - 12 * q^7 + 16 * q^13 - 8 * q^15 - 24 * q^21 - 16 * q^25 + 4 * q^27 - 24 * q^31 + 12 * q^33 + 8 * q^37 + 24 * q^43 - 8 * q^45 - 8 * q^51 + 36 * q^55 + 24 * q^61 - 12 * q^63 - 20 * q^73 - 28 * q^75 + 28 * q^81 - 8 * q^85 + 12 * q^87 - 96 * q^91 - 24 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70711	−	0.292893i	0.985599	−	0.169102i
$3$	1.70711	−	0.292893i	0.985599	−	0.169102i
$4$		0			0
$5$	−0.707107	+	2.12132i	−0.316228	+	0.948683i
$5$	−0.707107	+	2.12132i	−0.316228	+	0.948683i
$6$		0			0
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$		0			0
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$		0			0
$11$		−	4.24264i		−	1.27920i	−0.768706	−	0.639602i	$-0.779099\pi$
$11$		−	4.24264i		−	1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$12$		0			0
$13$	4.00000	−	4.00000i	1.10940	−	1.10940i	0.116171	−	0.993229i	$-0.462938\pi$
$13$	4.00000	−	4.00000i	1.10940	−	1.10940i	0.993229	−	0.116171i	$-0.0370621\pi$
$14$		0			0
$15$	−0.585786	+	3.82843i	−0.151249	+	0.988496i
$16$		0			0
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−6.00000	−	4.24264i	−1.30931	−	0.925820i
$22$		0			0
$23$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$23$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$24$		0			0
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$		0			0
$27$	4.53553	−	2.53553i	0.872864	−	0.487964i
$28$		0			0
$29$	4.24264			0.787839			0.393919	−	0.919145i	$-0.371119\pi$
$29$	4.24264			0.787839			0.393919	+	0.919145i	$0.371119\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$		0			0
$33$	−1.24264	−	7.24264i	−0.216316	−	1.26078i
$34$		0			0
$35$	8.48528	−	4.24264i	1.43427	−	0.717137i
$36$		0			0
$37$	2.00000	+	2.00000i	0.328798	+	0.328798i	0.852129	−	0.523331i	$-0.175311\pi$
$37$	2.00000	+	2.00000i	0.328798	+	0.328798i	−0.523331	+	0.852129i	$0.675311\pi$
$38$		0			0
$39$	5.65685	−	8.00000i	0.905822	−	1.28103i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	−0.0816682	−	0.996660i	$-0.526025\pi$
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	0.996660	+	0.0816682i	$0.0260248\pi$
$44$		0			0
$45$	0.121320	+	6.70711i	0.0180854	+	0.999836i
$46$		0			0
$47$	8.48528	−	8.48528i	1.23771	−	1.23771i	0.276769	−	0.960936i	$-0.410736\pi$
$47$	8.48528	−	8.48528i	1.23771	−	1.23771i	0.960936	−	0.276769i	$-0.0892637\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$		0			0
$51$	−2.00000	+	2.82843i	−0.280056	+	0.396059i
$52$		0			0
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	0.485643	−	0.874157i	$-0.338586\pi$
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	−0.874157	+	0.485643i	$0.838586\pi$
$54$		0			0
$55$	9.00000	+	3.00000i	1.21356	+	0.404520i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.24264			−0.552345			−0.276172	−	0.961108i	$-0.589066\pi$
$59$	−4.24264			−0.552345			−0.276172	+	0.961108i	$0.589066\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$		0			0
$63$	−11.4853	−	5.48528i	−1.44701	−	0.691080i
$64$		0			0
$65$	5.65685	+	11.3137i	0.701646	+	1.40329i
$66$		0			0
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			8.48528i			1.00702i	0.863990	+	0.503509i	$0.167958\pi$
$71$			8.48528i			1.00702i	−0.863990	+	0.503509i	$0.832042\pi$
$72$		0			0
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$		0			0
$75$	−7.70711	−	3.94975i	−0.889940	−	0.456078i
$76$		0			0
$77$	−12.7279	+	12.7279i	−1.45048	+	1.45048i
$78$		0			0
$79$		−	6.00000i		−	0.675053i	−0.941316	−	0.337526i	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$		0			0
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$		0			0
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$		0			0
$85$	−2.00000	−	4.00000i	−0.216930	−	0.433861i
$86$		0			0
$87$	7.24264	−	1.24264i	0.776493	−	0.133225i
$88$		0			0
$89$	−8.48528			−0.899438			−0.449719	−	0.893170i	$-0.648476\pi$
$89$	−8.48528			−0.899438			−0.449719	+	0.893170i	$0.648476\pi$
$90$		0			0
$91$	−24.0000			−2.51588
$92$		0			0
$93$	−10.2426	+	1.75736i	−1.06211	+	0.182230i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	0.406138	−	0.913812i	$-0.366875\pi$
$97$	−5.00000	−	5.00000i	−0.507673	−	0.507673i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$	−4.24264	−	12.0000i	−0.426401	−	1.20605i
$100$		0			0
$101$			9.89949i			0.985037i	0.870302	+	0.492518i	$0.163924\pi$
$101$			9.89949i			0.985037i	−0.870302	+	0.492518i	$0.836076\pi$
$102$		0			0
$103$	3.00000	−	3.00000i	0.295599	−	0.295599i	−0.543688	−	0.839287i	$-0.682973\pi$
$103$	3.00000	−	3.00000i	0.295599	−	0.295599i	0.839287	+	0.543688i	$0.182973\pi$
$104$		0			0
$105$	13.2426	−	9.72792i	1.29235	−	0.949348i
$106$		0			0
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	−0.986151	−	0.165848i	$-0.946964\pi$
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	0.165848	+	0.986151i	$0.446964\pi$
$108$		0			0
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	4.00000	+	2.82843i	0.379663	+	0.268462i
$112$		0			0
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	0.770490	−	0.637452i	$-0.220012\pi$
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	−0.637452	+	0.770490i	$0.720012\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	7.31371	−	15.3137i	0.676153	−	1.41575i
$118$		0			0
$119$	8.48528			0.777844
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.19239	−	6.36396i	0.822192	−	0.569210i
$126$		0			0
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	0.827570	−	0.561363i	$-0.189723\pi$
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	−0.561363	+	0.827570i	$0.689723\pi$
$128$		0			0
$129$	8.48528	−	12.0000i	0.747087	−	1.05654i
$130$		0			0
$131$			12.7279i			1.11204i	0.831168	+	0.556022i	$0.187673\pi$
$131$			12.7279i			1.11204i	−0.831168	+	0.556022i	$0.812327\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.17157	+	11.4142i	0.186899	+	0.982379i
$136$		0			0
$137$	−7.07107	+	7.07107i	−0.604122	+	0.604122i	−0.941404	−	0.337282i	$-0.890493\pi$
$137$	−7.07107	+	7.07107i	−0.604122	+	0.604122i	0.337282	+	0.941404i	$0.390493\pi$
$138$		0			0
$139$			12.0000i			1.01783i	0.860818	+	0.508913i	$0.169953\pi$
$139$			12.0000i			1.01783i	−0.860818	+	0.508913i	$0.830047\pi$
$140$		0			0
$141$	12.0000	−	16.9706i	1.01058	−	1.42918i
$142$		0			0
$143$	−16.9706	−	16.9706i	−1.41915	−	1.41915i
$144$		0			0
$145$	−3.00000	+	9.00000i	−0.249136	+	0.747409i
$146$		0			0
$147$	3.22183	+	18.7782i	0.265732	+	1.54880i
$148$		0			0
$149$	1.41421			0.115857			0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421			0.115857			0.0579284	+	0.998321i	$0.481550\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−2.58579	+	5.41421i	−0.209048	+	0.437713i
$154$		0			0
$155$	4.24264	−	12.7279i	0.340777	−	1.02233i
$156$		0			0
$157$	−8.00000	−	8.00000i	−0.638470	−	0.638470i	0.311708	−	0.950178i	$-0.399099\pi$
$157$	−8.00000	−	8.00000i	−0.638470	−	0.638470i	−0.950178	+	0.311708i	$0.899099\pi$
$158$		0			0
$159$	−5.65685	−	4.00000i	−0.448618	−	0.317221i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	12.0000	−	12.0000i	0.939913	−	0.939913i	−0.0583818	−	0.998294i	$-0.518594\pi$
$163$	12.0000	−	12.0000i	0.939913	−	0.939913i	0.998294	+	0.0583818i	$0.0185941\pi$
$164$		0			0
$165$	16.2426	+	2.48528i	1.26449	+	0.193479i
$166$		0			0
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	−0.954577	−	0.297966i	$-0.903692\pi$
$167$	−8.48528	+	8.48528i	−0.656611	+	0.656611i	0.297966	+	0.954577i	$0.403692\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.89949	+	9.89949i	0.752645	+	0.752645i	0.974972	−	0.222327i	$-0.0713654\pi$
$173$	9.89949	+	9.89949i	0.752645	+	0.752645i	−0.222327	+	0.974972i	$0.571365\pi$
$174$		0			0
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$		0			0
$177$	−7.24264	+	1.24264i	−0.544390	+	0.0934026i
$178$		0			0
$179$	−21.2132			−1.58555			−0.792775	−	0.609515i	$-0.791364\pi$
$179$	−21.2132			−1.58555			−0.792775	+	0.609515i	$0.791364\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	10.2426	−	1.75736i	0.757158	−	0.129908i
$184$		0			0
$185$	−5.65685	+	2.82843i	−0.415900	+	0.207950i
$186$		0			0
$187$	6.00000	+	6.00000i	0.438763	+	0.438763i
$188$		0			0
$189$	−21.2132	−	6.00000i	−1.54303	−	0.436436i
$190$		0			0
$191$			8.48528i			0.613973i	0.951714	+	0.306987i	$0.0993207\pi$
$191$			8.48528i			0.613973i	−0.951714	+	0.306987i	$0.900679\pi$
$192$		0			0
$193$	17.0000	−	17.0000i	1.22369	−	1.22369i	0.257375	−	0.966312i	$-0.417142\pi$
$193$	17.0000	−	17.0000i	1.22369	−	1.22369i	0.966312	−	0.257375i	$-0.0828576\pi$
$194$		0			0
$195$	12.9706	+	17.6569i	0.928841	+	1.26443i
$196$		0			0
$197$	−5.65685	+	5.65685i	−0.403034	+	0.403034i	−0.879301	−	0.476267i	$-0.841990\pi$
$197$	−5.65685	+	5.65685i	−0.403034	+	0.403034i	0.476267	+	0.879301i	$0.341990\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.7279	−	12.7279i	−0.893325	−	0.893325i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$		0			0
$213$	2.48528	+	14.4853i	0.170289	+	0.992515i
$214$		0			0
$215$	8.48528	+	16.9706i	0.578691	+	1.15738i
$216$		0			0
$217$	18.0000	+	18.0000i	1.22192	+	1.22192i
$218$		0			0
$219$	−7.07107	+	10.0000i	−0.477818	+	0.675737i
$220$		0			0
$221$			11.3137i			0.761042i
$222$		0			0
$223$	−3.00000	+	3.00000i	−0.200895	+	0.200895i	−0.800383	−	0.599489i	$-0.795371\pi$
$223$	−3.00000	+	3.00000i	−0.200895	+	0.200895i	0.599489	+	0.800383i	$0.295371\pi$
$224$		0			0
$225$	−14.3137	−	4.48528i	−0.954247	−	0.299019i
$226$		0			0
$227$	12.7279	−	12.7279i	0.844782	−	0.844782i	−0.144695	−	0.989476i	$-0.546220\pi$
$227$	12.7279	−	12.7279i	0.844782	−	0.844782i	0.989476	+	0.144695i	$0.0462199\pi$
$228$		0			0
$229$			6.00000i			0.396491i	0.980152	+	0.198246i	$0.0635244\pi$
$229$			6.00000i			0.396491i	−0.980152	+	0.198246i	$0.936476\pi$
$230$		0			0
$231$	−18.0000	+	25.4558i	−1.18431	+	1.67487i
$232$		0			0
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.972806	+	0.231621i	$0.0744028\pi$
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.231621	+	0.972806i	$0.425597\pi$
$234$		0			0
$235$	12.0000	+	24.0000i	0.782794	+	1.56559i
$236$		0			0
$237$	−1.75736	−	10.2426i	−0.114153	−	0.665331i
$238$		0			0
$239$	−25.4558			−1.64660			−0.823301	−	0.567605i	$-0.807870\pi$
$239$	−25.4558			−1.64660			−0.823301	+	0.567605i	$0.807870\pi$
$240$		0			0
$241$	−12.0000			−0.772988			−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000			−0.772988			−0.386494	+	0.922292i	$0.626314\pi$
$242$		0			0
$243$	10.2929	−	11.7071i	0.660289	−	0.751011i
$244$		0			0
$245$	−23.3345	−	7.77817i	−1.49079	−	0.496929i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	16.9706	+	12.0000i	1.07547	+	0.760469i
$250$		0			0
$251$			4.24264i			0.267793i	0.990995	+	0.133897i	$0.0427490\pi$
$251$			4.24264i			0.267793i	−0.990995	+	0.133897i	$0.957251\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−4.58579	−	6.24264i	−0.287173	−	0.390929i
$256$		0			0
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	−0.0291953	−	0.999574i	$-0.509294\pi$
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	0.999574	+	0.0291953i	$0.00929448\pi$
$258$		0			0
$259$		−	12.0000i		−	0.745644i
$260$		0			0
$261$	12.0000	−	4.24264i	0.742781	−	0.262613i
$262$		0			0
$263$	−8.48528	−	8.48528i	−0.523225	−	0.523225i	0.395319	−	0.918544i	$-0.370634\pi$
$263$	−8.48528	−	8.48528i	−0.523225	−	0.523225i	−0.918544	+	0.395319i	$0.870634\pi$
$264$		0			0
$265$	8.00000	−	4.00000i	0.491436	−	0.245718i
$266$		0			0
$267$	−14.4853	+	2.48528i	−0.886485	+	0.152097i
$268$		0			0
$269$	18.3848			1.12094			0.560470	−	0.828175i	$-0.310621\pi$
$269$	18.3848			1.12094			0.560470	+	0.828175i	$0.310621\pi$
$270$		0			0
$271$	−24.0000			−1.45790			−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000			−1.45790			−0.728948	+	0.684569i	$0.759990\pi$
$272$		0			0
$273$	−40.9706	+	7.02944i	−2.47965	+	0.425441i
$274$		0			0
$275$	−12.7279	+	16.9706i	−0.767523	+	1.02336i
$276$		0			0
$277$	22.0000	+	22.0000i	1.32185	+	1.32185i	0.912276	+	0.409576i	$0.134323\pi$
$277$	22.0000	+	22.0000i	1.32185	+	1.32185i	0.409576	+	0.912276i	$0.365677\pi$
$278$		0			0
$279$	−16.9706	+	6.00000i	−1.01600	+	0.359211i
$280$		0			0
$281$		−	8.48528i		−	0.506189i	−0.967442	−	0.253095i	$-0.918552\pi$
$281$		−	8.48528i		−	0.506189i	0.967442	−	0.253095i	$-0.0814484\pi$
$282$		0			0
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$			13.0000i			0.764706i
$290$		0			0
$291$	−10.0000	−	7.07107i	−0.586210	−	0.414513i
$292$		0			0
$293$	−22.6274	−	22.6274i	−1.32191	−	1.32191i	−0.912231	−	0.409677i	$-0.865641\pi$
$293$	−22.6274	−	22.6274i	−1.32191	−	1.32191i	−0.409677	−	0.912231i	$-0.634359\pi$
$294$		0			0
$295$	3.00000	−	9.00000i	0.174667	−	0.524000i
$296$		0			0
$297$	−10.7574	−	19.2426i	−0.624205	−	1.11657i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−36.0000			−2.07501
$302$		0			0
$303$	2.89949	+	16.8995i	0.166572	+	0.970851i
$304$		0			0
$305$	−4.24264	+	12.7279i	−0.242933	+	0.728799i
$306$		0			0
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.999616	+	0.0276979i	$0.00881765\pi$
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.0276979	+	0.999616i	$0.491182\pi$
$308$		0			0
$309$	4.24264	−	6.00000i	0.241355	−	0.341328i
$310$		0			0
$311$			8.48528i			0.481156i	0.970630	+	0.240578i	$0.0773370\pi$
$311$			8.48528i			0.481156i	−0.970630	+	0.240578i	$0.922663\pi$
$312$		0			0
$313$	17.0000	−	17.0000i	0.960897	−	0.960897i	−0.0383669	−	0.999264i	$-0.512216\pi$
$313$	17.0000	−	17.0000i	0.960897	−	0.960897i	0.999264	+	0.0383669i	$0.0122156\pi$
$314$		0			0
$315$	19.7574	−	20.4853i	1.11320	−	1.15421i
$316$		0			0
$317$	9.89949	−	9.89949i	0.556011	−	0.556011i	−0.372158	−	0.928169i	$-0.621382\pi$
$317$	9.89949	−	9.89949i	0.556011	−	0.556011i	0.928169	+	0.372158i	$0.121382\pi$
$318$		0			0
$319$		−	18.0000i		−	1.00781i
$320$		0			0
$321$	−12.0000	+	16.9706i	−0.669775	+	0.947204i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−28.0000	+	4.00000i	−1.55316	+	0.221880i
$326$		0			0
$327$	0.585786	+	3.41421i	0.0323941	+	0.188806i
$328$		0			0
$329$	−50.9117			−2.80685
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$	7.65685	+	3.65685i	0.419593	+	0.200394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.00000	+	7.00000i	0.381314	+	0.381314i	0.871576	−	0.490261i	$-0.163099\pi$
$337$	7.00000	+	7.00000i	0.381314	+	0.381314i	−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	2.82843	+	2.00000i	0.153619	+	0.108625i
$340$		0			0
$341$			25.4558i			1.37851i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.7279	−	12.7279i	0.683271	−	0.683271i	−0.277465	−	0.960736i	$-0.589494\pi$
$347$	12.7279	−	12.7279i	0.683271	−	0.683271i	0.960736	+	0.277465i	$0.0894943\pi$
$348$		0			0
$349$			18.0000i			0.963518i	0.876304	+	0.481759i	$0.160002\pi$
$349$			18.0000i			0.963518i	−0.876304	+	0.481759i	$0.839998\pi$
$350$		0			0
$351$	8.00000	−	28.2843i	0.427008	−	1.50970i
$352$		0			0
$353$	−1.41421	−	1.41421i	−0.0752710	−	0.0752710i	0.668469	−	0.743740i	$-0.266950\pi$
$353$	−1.41421	−	1.41421i	−0.0752710	−	0.0752710i	−0.743740	+	0.668469i	$0.766950\pi$
$354$		0			0
$355$	−18.0000	−	6.00000i	−0.955341	−	0.318447i
$356$		0			0
$357$	14.4853	−	2.48528i	0.766642	−	0.131535i
$358$		0			0
$359$	16.9706			0.895672			0.447836	−	0.894116i	$-0.352195\pi$
$359$	16.9706			0.895672			0.447836	+	0.894116i	$0.352195\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	−11.9497	+	2.05025i	−0.627199	+	0.107610i
$364$		0			0
$365$	−7.07107	−	14.1421i	−0.370117	−	0.740233i
$366$		0			0
$367$	15.0000	+	15.0000i	0.782994	+	0.782994i	0.980335	−	0.197341i	$-0.0632307\pi$
$367$	15.0000	+	15.0000i	0.782994	+	0.782994i	−0.197341	+	0.980335i	$0.563231\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$			16.9706i			0.881068i
$372$		0			0
$373$	20.0000	−	20.0000i	1.03556	−	1.03556i	0.0362168	−	0.999344i	$-0.488469\pi$
$373$	20.0000	−	20.0000i	1.03556	−	1.03556i	0.999344	−	0.0362168i	$-0.0115307\pi$
$374$		0			0
$375$	13.8284	−	13.5563i	0.714097	−	0.700047i
$376$		0			0
$377$	16.9706	−	16.9706i	0.874028	−	0.874028i
$378$		0			0
$379$		−	36.0000i		−	1.84920i	−0.380945	−	0.924598i	$-0.624401\pi$
$379$		−	36.0000i		−	1.84920i	0.380945	−	0.924598i	$-0.375599\pi$
$380$		0			0
$381$	6.00000	+	4.24264i	0.307389	+	0.217357i
$382$		0			0
$383$	25.4558	+	25.4558i	1.30073	+	1.30073i	0.927898	+	0.372835i	$0.121614\pi$
$383$	25.4558	+	25.4558i	1.30073	+	1.30073i	0.372835	+	0.927898i	$0.378386\pi$
$384$		0			0
$385$	−18.0000	−	36.0000i	−0.917365	−	1.83473i
$386$		0			0
$387$	10.9706	−	22.9706i	0.557665	−	1.16766i
$388$		0			0
$389$	15.5563			0.788738			0.394369	−	0.918952i	$-0.370963\pi$
$389$	15.5563			0.788738			0.394369	+	0.918952i	$0.370963\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	3.72792	+	21.7279i	0.188049	+	1.09603i
$394$		0			0
$395$	12.7279	+	4.24264i	0.640411	+	0.213470i
$396$		0			0
$397$	14.0000	+	14.0000i	0.702640	+	0.702640i	0.964976	−	0.262337i	$-0.0844931\pi$
$397$	14.0000	+	14.0000i	0.702640	+	0.702640i	−0.262337	+	0.964976i	$0.584493\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			14.1421i			0.706225i	0.935581	+	0.353112i	$0.114877\pi$
$401$			14.1421i			0.706225i	−0.935581	+	0.353112i	$0.885123\pi$
$402$		0			0
$403$	−24.0000	+	24.0000i	−1.19553	+	1.19553i
$404$		0			0
$405$	7.05025	+	18.8492i	0.350330	+	0.936626i
$406$		0			0
$407$	8.48528	−	8.48528i	0.420600	−	0.420600i
$408$		0			0
$409$			32.0000i			1.58230i	0.611623	+	0.791149i	$0.290517\pi$
$409$			32.0000i			1.58230i	−0.611623	+	0.791149i	$0.709483\pi$
$410$		0			0
$411$	−10.0000	+	14.1421i	−0.493264	+	0.697580i
$412$		0			0
$413$	12.7279	+	12.7279i	0.626300	+	0.626300i
$414$		0			0
$415$	−24.0000	+	12.0000i	−1.17811	+	0.589057i
$416$		0			0
$417$	3.51472	+	20.4853i	0.172117	+	1.00317i
$418$		0			0
$419$	29.6985			1.45087			0.725433	−	0.688293i	$-0.241640\pi$
$419$	29.6985			1.45087			0.725433	+	0.688293i	$0.241640\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$		0			0
$423$	15.5147	−	32.4853i	0.754351	−	1.57949i
$424$		0			0
$425$	9.89949	−	1.41421i	0.480196	−	0.0685994i
$426$		0			0
$427$	−18.0000	−	18.0000i	−0.871081	−	0.871081i
$428$		0			0
$429$	−33.9411	−	24.0000i	−1.63869	−	1.15873i
$430$		0			0
$431$		−	16.9706i		−	0.817443i	−0.912659	−	0.408722i	$-0.865975\pi$
$431$		−	16.9706i		−	0.817443i	0.912659	−	0.408722i	$-0.134025\pi$
$432$		0			0
$433$	7.00000	−	7.00000i	0.336399	−	0.336399i	−0.518611	−	0.855010i	$-0.673551\pi$
$433$	7.00000	−	7.00000i	0.336399	−	0.336399i	0.855010	+	0.518611i	$0.173551\pi$
$434$		0			0
$435$	−2.48528	+	16.2426i	−0.119160	+	0.778775i
$436$		0			0
$437$		0			0
$438$		0			0
$439$			24.0000i			1.14546i	0.819745	+	0.572729i	$0.194115\pi$
$439$			24.0000i			1.14546i	−0.819745	+	0.572729i	$0.805885\pi$
$440$		0			0
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$		0			0
$443$	−12.7279	−	12.7279i	−0.604722	−	0.604722i	0.336840	−	0.941562i	$-0.390642\pi$
$443$	−12.7279	−	12.7279i	−0.604722	−	0.604722i	−0.941562	+	0.336840i	$0.890642\pi$
$444$		0			0
$445$	6.00000	−	18.0000i	0.284427	−	0.853282i
$446$		0			0
$447$	2.41421	−	0.414214i	0.114188	−	0.0195916i
$448$		0			0
$449$	31.1127			1.46830			0.734150	−	0.678988i	$-0.237581\pi$
$449$	31.1127			1.46830			0.734150	+	0.678988i	$0.237581\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	16.9706	−	50.9117i	0.795592	−	2.38678i
$456$		0			0
$457$	−7.00000	−	7.00000i	−0.327446	−	0.327446i	0.524168	−	0.851615i	$-0.324376\pi$
$457$	−7.00000	−	7.00000i	−0.327446	−	0.327446i	−0.851615	+	0.524168i	$0.824376\pi$
$458$		0			0
$459$	−2.82843	+	10.0000i	−0.132020	+	0.466760i
$460$		0			0
$461$		−	15.5563i		−	0.724531i	−0.932075	−	0.362266i	$-0.882003\pi$
$461$		−	15.5563i		−	0.724531i	0.932075	−	0.362266i	$-0.117997\pi$
$462$		0			0
$463$	15.0000	−	15.0000i	0.697109	−	0.697109i	−0.266677	−	0.963786i	$-0.585926\pi$
$463$	15.0000	−	15.0000i	0.697109	−	0.697109i	0.963786	+	0.266677i	$0.0859256\pi$
$464$		0			0
$465$	3.51472	−	22.9706i	0.162991	−	1.06523i
$466$		0			0
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	−0.875632	−	0.482980i	$-0.839555\pi$
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	0.482980	+	0.875632i	$0.339555\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−16.0000	−	11.3137i	−0.737241	−	0.521308i
$472$		0			0
$473$	−25.4558	−	25.4558i	−1.17046	−	1.17046i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−10.8284	−	5.17157i	−0.495800	−	0.236790i
$478$		0			0
$479$	−8.48528			−0.387702			−0.193851	−	0.981031i	$-0.562098\pi$
$479$	−8.48528			−0.387702			−0.193851	+	0.981031i	$0.562098\pi$
$480$		0			0
$481$	16.0000			0.729537
$482$		0			0
$483$		0			0
$484$		0			0
$485$	14.1421	−	7.07107i	0.642161	−	0.321081i
$486$		0			0
$487$	3.00000	+	3.00000i	0.135943	+	0.135943i	0.771804	−	0.635861i	$-0.219355\pi$
$487$	3.00000	+	3.00000i	0.135943	+	0.135943i	−0.635861	+	0.771804i	$0.719355\pi$
$488$		0			0
$489$	16.9706	−	24.0000i	0.767435	−	1.08532i
$490$		0			0
$491$			12.7279i			0.574403i	0.957870	+	0.287202i	$0.0927249\pi$
$491$			12.7279i			0.574403i	−0.957870	+	0.287202i	$0.907275\pi$
$492$		0			0
$493$	−6.00000	+	6.00000i	−0.270226	+	0.270226i
$494$		0			0
$495$	28.4558	−	0.514719i	1.27900	−	0.0231349i
$496$		0			0
$497$	25.4558	−	25.4558i	1.14185	−	1.14185i
$498$		0			0
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$		0			0
$501$	−12.0000	+	16.9706i	−0.536120	+	0.758189i
$502$		0			0
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$	−21.0000	−	7.00000i	−0.934488	−	0.311496i
$506$		0			0
$507$	−5.56497	−	32.4350i	−0.247149	−	1.44049i
$508$		0			0
$509$	−12.7279			−0.564155			−0.282078	−	0.959392i	$-0.591024\pi$
$509$	−12.7279			−0.564155			−0.282078	+	0.959392i	$0.591024\pi$
$510$		0			0
$511$	30.0000			1.32712
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.24264	+	8.48528i	0.186953	+	0.373906i
$516$		0			0
$517$	−36.0000	−	36.0000i	−1.58328	−	1.58328i
$518$		0			0
$519$	19.7990	+	14.0000i	0.869079	+	0.614532i
$520$		0			0
$521$		−	31.1127i		−	1.36307i	−0.731785	−	0.681536i	$-0.761312\pi$
$521$		−	31.1127i		−	1.36307i	0.731785	−	0.681536i	$-0.238688\pi$
$522$		0			0
$523$	12.0000	−	12.0000i	0.524723	−	0.524723i	−0.394271	−	0.918994i	$-0.629003\pi$
$523$	12.0000	−	12.0000i	0.524723	−	0.524723i	0.918994	+	0.394271i	$0.129003\pi$
$524$		0			0
$525$	11.2721	+	34.9706i	0.491954	+	1.52624i
$526$		0			0
$527$	8.48528	−	8.48528i	0.369625	−	0.369625i
$528$		0			0
$529$		−	23.0000i		−	1.00000i
$530$		0			0
$531$	−12.0000	+	4.24264i	−0.520756	+	0.184115i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−12.0000	−	24.0000i	−0.518805	−	1.03761i
$536$		0			0
$537$	−36.2132	+	6.21320i	−1.56272	+	0.268120i
$538$		0			0
$539$	46.6690			2.01018
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		0			0
$543$	−3.41421	+	0.585786i	−0.146518	+	0.0251385i
$544$		0			0
$545$	−4.24264	−	1.41421i	−0.181735	−	0.0605783i
$546$		0			0
$547$	−18.0000	−	18.0000i	−0.769624	−	0.769624i	0.208416	−	0.978040i	$-0.433169\pi$
$547$	−18.0000	−	18.0000i	−0.769624	−	0.769624i	−0.978040	+	0.208416i	$0.933169\pi$
$548$		0			0
$549$	16.9706	−	6.00000i	0.724286	−	0.256074i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−18.0000	+	18.0000i	−0.765438	+	0.765438i
$554$		0			0
$555$	−8.82843	+	6.48528i	−0.374746	+	0.275285i
$556$		0			0
$557$	11.3137	−	11.3137i	0.479377	−	0.479377i	−0.425555	−	0.904932i	$-0.639921\pi$
$557$	11.3137	−	11.3137i	0.479377	−	0.479377i	0.904932	+	0.425555i	$0.139921\pi$
$558$		0			0
$559$		−	48.0000i		−	2.03018i
$560$		0			0
$561$	12.0000	+	8.48528i	0.506640	+	0.358249i
$562$		0			0
$563$	−21.2132	−	21.2132i	−0.894030	−	0.894030i	0.100870	−	0.994900i	$-0.467837\pi$
$563$	−21.2132	−	21.2132i	−0.894030	−	0.894030i	−0.994900	+	0.100870i	$0.967837\pi$
$564$		0			0
$565$	−4.00000	+	2.00000i	−0.168281	+	0.0841406i
$566$		0			0
$567$	−37.9706	−	4.02944i	−1.59461	−	0.169220i
$568$		0			0
$569$	−2.82843			−0.118574			−0.0592869	−	0.998241i	$-0.518883\pi$
$569$	−2.82843			−0.118574			−0.0592869	+	0.998241i	$0.518883\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		0			0
$573$	2.48528	+	14.4853i	0.103824	+	0.605131i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	5.00000	+	5.00000i	0.208153	+	0.208153i	0.803482	−	0.595329i	$-0.202978\pi$
$577$	5.00000	+	5.00000i	0.208153	+	0.208153i	−0.595329	+	0.803482i	$0.702978\pi$
$578$		0			0
$579$	24.0416	−	34.0000i	0.999136	−	1.41299i
$580$		0			0
$581$		−	50.9117i		−	2.11217i
$582$		0			0
$583$	−12.0000	+	12.0000i	−0.496989	+	0.496989i
$584$		0			0
$585$	27.3137	+	26.3431i	1.12928	+	1.08916i
$586$		0			0
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	−0.860193	−	0.509968i	$-0.829657\pi$
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	0.509968	+	0.860193i	$0.329657\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−8.00000	+	11.3137i	−0.329076	+	0.465384i
$592$		0			0
$593$	24.0416	+	24.0416i	0.987271	+	0.987271i	0.999920	−	0.0126486i	$-0.00402627\pi$
$593$	24.0416	+	24.0416i	0.987271	+	0.987271i	−0.0126486	+	0.999920i	$0.504026\pi$
$594$		0			0
$595$	−6.00000	+	18.0000i	−0.245976	+	0.737928i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.9706			−0.693398			−0.346699	−	0.937976i	$-0.612698\pi$
$599$	−16.9706			−0.693398			−0.346699	+	0.937976i	$0.612698\pi$
$600$		0			0
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.94975	−	14.8492i	0.201236	−	0.603708i
$606$		0			0
$607$	9.00000	+	9.00000i	0.365299	+	0.365299i	0.865759	−	0.500461i	$-0.166836\pi$
$607$	9.00000	+	9.00000i	0.365299	+	0.365299i	−0.500461	+	0.865759i	$0.666836\pi$
$608$		0			0
$609$	−25.4558	−	18.0000i	−1.03152	−	0.729397i
$610$		0			0
$611$		−	67.8823i		−	2.74622i
$612$		0			0
$613$	10.0000	−	10.0000i	0.403896	−	0.403896i	−0.475707	−	0.879604i	$-0.657808\pi$
$613$	10.0000	−	10.0000i	0.403896	−	0.403896i	0.879604	+	0.475707i	$0.157808\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.0854011	+	0.996347i	$0.527217\pi$
$617$	−26.8701	+	26.8701i	−1.08175	+	1.08175i	−0.996347	+	0.0854011i	$0.972783\pi$
$618$		0			0
$619$			36.0000i			1.44696i	0.690344	+	0.723481i	$0.257459\pi$
$619$			36.0000i			1.44696i	−0.690344	+	0.723481i	$0.742541\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	25.4558	+	25.4558i	1.01987	+	1.01987i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.65685			−0.225554
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$		0			0
$633$	20.4853	−	3.51472i	0.814217	−	0.139698i
$634$		0			0
$635$	−8.48528	+	4.24264i	−0.336728	+	0.168364i
$636$		0			0
$637$	44.0000	+	44.0000i	1.74334	+	1.74334i
$638$		0			0
$639$	8.48528	+	24.0000i	0.335673	+	0.949425i
$640$		0			0
$641$		−	16.9706i		−	0.670297i	−0.942165	−	0.335148i	$-0.891214\pi$
$641$		−	16.9706i		−	0.670297i	0.942165	−	0.335148i	$-0.108786\pi$
$642$		0			0
$643$	−24.0000	+	24.0000i	−0.946468	+	0.946468i	−0.998638	−	0.0521706i	$-0.983386\pi$
$643$	−24.0000	+	24.0000i	−0.946468	+	0.946468i	0.0521706	+	0.998638i	$0.483386\pi$
$644$		0			0
$645$	19.4558	+	26.4853i	0.766073	+	1.04286i
$646$		0			0
$647$	−16.9706	+	16.9706i	−0.667182	+	0.667182i	−0.957063	−	0.289881i	$-0.906384\pi$
$647$	−16.9706	+	16.9706i	−0.667182	+	0.667182i	0.289881	+	0.957063i	$0.406384\pi$
$648$		0			0
$649$			18.0000i			0.706562i
$650$		0			0
$651$	36.0000	+	25.4558i	1.41095	+	0.997693i
$652$		0			0
$653$	−7.07107	−	7.07107i	−0.276712	−	0.276712i	0.555083	−	0.831795i	$-0.312687\pi$
$653$	−7.07107	−	7.07107i	−0.276712	−	0.276712i	−0.831795	+	0.555083i	$0.812687\pi$
$654$		0			0
$655$	−27.0000	−	9.00000i	−1.05498	−	0.351659i
$656$		0			0
$657$	−9.14214	+	19.1421i	−0.356669	+	0.746806i
$658$		0			0
$659$	−38.1838			−1.48743			−0.743714	−	0.668498i	$-0.766938\pi$
$659$	−38.1838			−1.48743			−0.743714	+	0.668498i	$0.766938\pi$
$660$		0			0
$661$	30.0000			1.16686			0.583432	−	0.812162i	$-0.301709\pi$
$661$	30.0000			1.16686			0.583432	+	0.812162i	$0.301709\pi$
$662$		0			0
$663$	3.31371	+	19.3137i	0.128694	+	0.750082i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−4.24264	+	6.00000i	−0.164030	+	0.231973i
$670$		0			0
$671$		−	25.4558i		−	0.982712i
$672$		0			0
$673$	−11.0000	+	11.0000i	−0.424019	+	0.424019i	−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−11.0000	+	11.0000i	−0.424019	+	0.424019i	0.462566	+	0.886585i	$0.346929\pi$
$674$		0			0
$675$	−25.7487	−	3.46447i	−0.991069	−	0.133347i
$676$		0			0
$677$	−26.8701	+	26.8701i	−1.03270	+	1.03270i	−0.0332533	+	0.999447i	$0.510587\pi$
$677$	−26.8701	+	26.8701i	−1.03270	+	1.03270i	−0.999447	+	0.0332533i	$0.989413\pi$
$678$		0			0
$679$			30.0000i			1.15129i
$680$		0			0
$681$	18.0000	−	25.4558i	0.689761	−	0.975470i
$682$		0			0
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	0.850559	−	0.525879i	$-0.176264\pi$
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	−0.525879	+	0.850559i	$0.676264\pi$
$684$		0			0
$685$	−10.0000	−	20.0000i	−0.382080	−	0.764161i
$686$		0			0
$687$	1.75736	+	10.2426i	0.0670474	+	0.390781i
$688$		0			0
$689$	−22.6274			−0.862036
$690$		0			0
$691$	48.0000			1.82601			0.913003	−	0.407953i	$-0.133757\pi$
$691$	48.0000			1.82601			0.913003	+	0.407953i	$0.133757\pi$
$692$		0			0
$693$	−23.2721	+	48.7279i	−0.884033	+	1.85102i
$694$		0			0
$695$	−25.4558	−	8.48528i	−0.965595	−	0.321865i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	36.7696	+	26.0000i	1.39075	+	0.983410i
$700$		0			0
$701$			29.6985i			1.12170i	0.827919	+	0.560848i	$0.189525\pi$
$701$			29.6985i			1.12170i	−0.827919	+	0.560848i	$0.810475\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	27.5147	+	37.4558i	1.03626	+	1.41067i
$706$		0			0
$707$	29.6985	−	29.6985i	1.11693	−	1.11693i
$708$		0			0
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$		0			0
$711$	−6.00000	−	16.9706i	−0.225018	−	0.636446i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	48.0000	−	24.0000i	1.79510	−	0.897549i
$716$		0			0
$717$	−43.4558	+	7.45584i	−1.62289	+	0.278444i
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−18.0000			−0.670355
$722$		0			0
$723$	−20.4853	+	3.51472i	−0.761856	+	0.130714i
$724$		0			0
$725$	−16.9706	−	12.7279i	−0.630271	−	0.472703i
$726$		0			0
$727$	−33.0000	−	33.0000i	−1.22390	−	1.22390i	−0.966233	−	0.257669i	$-0.917046\pi$
$727$	−33.0000	−	33.0000i	−1.22390	−	1.22390i	−0.257669	−	0.966233i	$-0.582954\pi$
$728$		0			0
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$		0			0
$731$			16.9706i			0.627679i
$732$		0			0
$733$	2.00000	−	2.00000i	0.0738717	−	0.0738717i	−0.669206	−	0.743077i	$-0.733365\pi$
$733$	2.00000	−	2.00000i	0.0738717	−	0.0738717i	0.743077	+	0.669206i	$0.233365\pi$
$734$		0			0
$735$	−42.1127	−	6.44365i	−1.55335	−	0.237678i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.9706	+	16.9706i	0.622590	+	0.622590i	0.946193	−	0.323603i	$-0.104894\pi$
$743$	16.9706	+	16.9706i	0.622590	+	0.622590i	−0.323603	+	0.946193i	$0.604894\pi$
$744$		0			0
$745$	−1.00000	+	3.00000i	−0.0366372	+	0.109911i
$746$		0			0
$747$	32.4853	+	15.5147i	1.18857	+	0.567654i
$748$		0			0
$749$	50.9117			1.86027
$750$		0			0
$751$	6.00000			0.218943			0.109472	−	0.993990i	$-0.465084\pi$
$751$	6.00000			0.218943			0.109472	+	0.993990i	$0.465084\pi$
$752$		0			0
$753$	1.24264	+	7.24264i	0.0452843	+	0.263936i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−26.0000	−	26.0000i	−0.944986	−	0.944986i	0.0535776	−	0.998564i	$-0.482938\pi$
$757$	−26.0000	−	26.0000i	−0.944986	−	0.944986i	−0.998564	+	0.0535776i	$0.982938\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	36.7696i		−	1.33290i	−0.745552	−	0.666448i	$-0.767814\pi$
$761$		−	36.7696i		−	1.33290i	0.745552	−	0.666448i	$-0.232186\pi$
$762$		0			0
$763$	6.00000	−	6.00000i	0.217215	−	0.217215i
$764$		0			0
$765$	−9.65685	−	9.31371i	−0.349144	−	0.336738i
$766$		0			0
$767$	−16.9706	+	16.9706i	−0.612772	+	0.612772i
$768$		0			0
$769$			42.0000i			1.51456i	0.653091	+	0.757279i	$0.273472\pi$
$769$			42.0000i			1.51456i	−0.653091	+	0.757279i	$0.726528\pi$
$770$		0			0
$771$	22.0000	−	31.1127i	0.792311	−	1.12050i
$772$		0			0
$773$	−26.8701	−	26.8701i	−0.966449	−	0.966449i	0.0330063	−	0.999455i	$-0.489492\pi$
$773$	−26.8701	−	26.8701i	−0.966449	−	0.966449i	−0.999455	+	0.0330063i	$0.989492\pi$
$774$		0			0
$775$	24.0000	+	18.0000i	0.862105	+	0.646579i
$776$		0			0
$777$	−3.51472	−	20.4853i	−0.126090	−	0.734905i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$	19.2426	−	10.7574i	0.687676	−	0.384437i
$784$		0			0
$785$	22.6274	−	11.3137i	0.807607	−	0.403804i
$786$		0			0
$787$	24.0000	+	24.0000i	0.855508	+	0.855508i	0.990805	−	0.135297i	$-0.0431990\pi$
$787$	24.0000	+	24.0000i	0.855508	+	0.855508i	−0.135297	+	0.990805i	$0.543199\pi$
$788$		0			0
$789$	−16.9706	−	12.0000i	−0.604168	−	0.427211i
$790$		0			0
$791$		−	8.48528i		−	0.301702i
$792$		0			0
$793$	24.0000	−	24.0000i	0.852265	−	0.852265i
$794$		0			0
$795$	12.4853	−	9.17157i	0.442807	−	0.325282i
$796$		0			0
$797$	1.41421	−	1.41421i	0.0500940	−	0.0500940i	−0.681616	−	0.731710i	$-0.738723\pi$
$797$	1.41421	−	1.41421i	0.0500940	−	0.0500940i	0.731710	+	0.681616i	$0.238723\pi$
$798$		0			0
$799$			24.0000i			0.849059i
$800$		0			0
$801$	−24.0000	+	8.48528i	−0.847998	+	0.299813i
$802$		0			0
$803$	21.2132	+	21.2132i	0.748598	+	0.748598i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	31.3848	−	5.38478i	1.10480	−	0.189553i
$808$		0			0
$809$	33.9411			1.19331			0.596653	−	0.802499i	$-0.296497\pi$
$809$	33.9411			1.19331			0.596653	+	0.802499i	$0.296497\pi$
$810$		0			0
$811$	−24.0000			−0.842754			−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000			−0.842754			−0.421377	+	0.906886i	$0.638453\pi$
$812$		0			0
$813$	−40.9706	+	7.02944i	−1.43690	+	0.246533i
$814$		0			0
$815$	16.9706	+	33.9411i	0.594453	+	1.18891i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−67.8823	+	24.0000i	−2.37200	+	0.838628i
$820$		0			0
$821$		−	21.2132i		−	0.740346i	−0.928963	−	0.370173i	$-0.879298\pi$
$821$		−	21.2132i		−	0.740346i	0.928963	−	0.370173i	$-0.120702\pi$
$822$		0			0
$823$	−27.0000	+	27.0000i	−0.941161	+	0.941161i	−0.998363	−	0.0572018i	$-0.981782\pi$
$823$	−27.0000	+	27.0000i	−0.941161	+	0.941161i	0.0572018	+	0.998363i	$0.481782\pi$
$824$		0			0
$825$	−16.7574	+	32.6985i	−0.583416	+	1.13842i
$826$		0			0
$827$	−21.2132	+	21.2132i	−0.737655	+	0.737655i	−0.972124	−	0.234468i	$-0.924665\pi$
$827$	−21.2132	+	21.2132i	−0.737655	+	0.737655i	0.234468	+	0.972124i	$0.424665\pi$
$828$		0			0
$829$		−	38.0000i		−	1.31979i	−0.751356	−	0.659897i	$-0.770600\pi$
$829$		−	38.0000i		−	1.31979i	0.751356	−	0.659897i	$-0.229400\pi$
$830$		0			0
$831$	44.0000	+	31.1127i	1.52634	+	1.07929i
$832$		0			0
$833$	−15.5563	−	15.5563i	−0.538996	−	0.538996i
$834$		0			0
$835$	−12.0000	−	24.0000i	−0.415277	−	0.830554i
$836$		0			0
$837$	−27.2132	+	15.2132i	−0.940626	+	0.525845i
$838$		0			0
$839$	−33.9411			−1.17178			−0.585889	−	0.810391i	$-0.699255\pi$
$839$	−33.9411			−1.17178			−0.585889	+	0.810391i	$0.699255\pi$
$840$		0			0
$841$	−11.0000			−0.379310
$842$		0			0
$843$	−2.48528	−	14.4853i	−0.0855976	−	0.498900i
$844$		0			0
$845$	40.3051	+	13.4350i	1.38654	+	0.462179i
$846$		0			0
$847$	21.0000	+	21.0000i	0.721569	+	0.721569i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	22.0000	−	22.0000i	0.753266	−	0.753266i	−0.221822	−	0.975087i	$-0.571200\pi$
$853$	22.0000	−	22.0000i	0.753266	−	0.753266i	0.975087	+	0.221822i	$0.0712003\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.89949	−	9.89949i	0.338160	−	0.338160i	−0.517514	−	0.855675i	$-0.673143\pi$
$857$	9.89949	−	9.89949i	0.338160	−	0.338160i	0.855675	+	0.517514i	$0.173143\pi$
$858$		0			0
$859$			36.0000i			1.22830i	0.789188	+	0.614152i	$0.210502\pi$
$859$			36.0000i			1.22830i	−0.789188	+	0.614152i	$0.789498\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$		0			0
$865$	−28.0000	+	14.0000i	−0.952029	+	0.476014i
$866$		0			0
$867$	3.80761	+	22.1924i	0.129313	+	0.753693i
$868$		0			0
$869$	−25.4558			−0.863530
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−19.1421	−	9.14214i	−0.647863	−	0.309414i
$874$		0			0
$875$	−46.6690	−	8.48528i	−1.57770	−	0.286855i
$876$		0			0
$877$	4.00000	+	4.00000i	0.135070	+	0.135070i	0.771409	−	0.636339i	$-0.219552\pi$
$877$	4.00000	+	4.00000i	0.135070	+	0.135070i	−0.636339	+	0.771409i	$0.719552\pi$
$878$		0			0
$879$	−45.2548	−	32.0000i	−1.52641	−	1.07933i
$880$		0			0
$881$		−	25.4558i		−	0.857629i	−0.903393	−	0.428815i	$-0.858931\pi$
$881$		−	25.4558i		−	0.857629i	0.903393	−	0.428815i	$-0.141069\pi$
$882$		0			0
$883$	−12.0000	+	12.0000i	−0.403832	+	0.403832i	−0.879581	−	0.475749i	$-0.842177\pi$
$883$	−12.0000	+	12.0000i	−0.403832	+	0.403832i	0.475749	+	0.879581i	$0.342177\pi$
$884$		0			0
$885$	2.48528	−	16.2426i	0.0835418	−	0.545990i
$886$		0			0
$887$	−16.9706	+	16.9706i	−0.569816	+	0.569816i	−0.932077	−	0.362261i	$-0.882005\pi$
$887$	−16.9706	+	16.9706i	−0.569816	+	0.569816i	0.362261	+	0.932077i	$0.382005\pi$
$888$		0			0
$889$		−	18.0000i		−	0.603701i
$890$		0			0
$891$	−24.0000	−	29.6985i	−0.804030	−	0.994937i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	15.0000	−	45.0000i	0.501395	−	1.50418i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−25.4558			−0.849000
$900$		0			0
$901$	8.00000			0.266519
$902$		0			0
$903$	−61.4558	+	10.5442i	−2.04512	+	0.350888i
$904$		0			0
$905$	1.41421	−	4.24264i	0.0470100	−	0.141030i
$906$		0			0
$907$	−6.00000	−	6.00000i	−0.199227	−	0.199227i	0.600442	−	0.799668i	$-0.294991\pi$
$907$	−6.00000	−	6.00000i	−0.199227	−	0.199227i	−0.799668	+	0.600442i	$0.794991\pi$
$908$		0			0
$909$	9.89949	+	28.0000i	0.328346	+	0.928701i
$910$		0			0
$911$			33.9411i			1.12452i	0.826961	+	0.562260i	$0.190068\pi$
$911$			33.9411i			1.12452i	−0.826961	+	0.562260i	$0.809932\pi$
$912$		0			0
$913$	36.0000	−	36.0000i	1.19143	−	1.19143i
$914$		0			0
$915$	−3.51472	+	22.9706i	−0.116193	+	0.759383i
$916$		0			0
$917$	38.1838	−	38.1838i	1.26094	−	1.26094i
$918$		0			0
$919$			42.0000i			1.38545i	0.721201	+	0.692726i	$0.243591\pi$
$919$			42.0000i			1.38545i	−0.721201	+	0.692726i	$0.756409\pi$
$920$		0			0
$921$	36.0000	+	25.4558i	1.18624	+	0.838799i
$922$		0			0
$923$	33.9411	+	33.9411i	1.11719	+	1.11719i
$924$		0			0
$925$	−2.00000	−	14.0000i	−0.0657596	−	0.460317i
$926$		0			0
$927$	5.48528	−	11.4853i	0.180160	−	0.377226i
$928$		0			0
$929$	2.82843			0.0927977			0.0463988	−	0.998923i	$-0.485225\pi$
$929$	2.82843			0.0927977			0.0463988	+	0.998923i	$0.485225\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2.48528	+	14.4853i	0.0813645	+	0.474227i
$934$		0			0
$935$	−16.9706	+	8.48528i	−0.554997	+	0.277498i
$936$		0			0
$937$	11.0000	+	11.0000i	0.359354	+	0.359354i	0.863575	−	0.504221i	$-0.168220\pi$
$937$	11.0000	+	11.0000i	0.359354	+	0.359354i	−0.504221	+	0.863575i	$0.668220\pi$
$938$		0			0
$939$	24.0416	−	34.0000i	0.784569	−	1.10955i
$940$		0			0
$941$		−	1.41421i		−	0.0461020i	−0.999734	−	0.0230510i	$-0.992662\pi$
$941$		−	1.41421i		−	0.0461020i	0.999734	−	0.0230510i	$-0.00733802\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	27.7279	−	40.7574i	0.901989	−	1.32584i
$946$		0			0
$947$	−21.2132	+	21.2132i	−0.689336	+	0.689336i	−0.962085	−	0.272749i	$-0.912067\pi$
$947$	−21.2132	+	21.2132i	−0.689336	+	0.689336i	0.272749	+	0.962085i	$0.412067\pi$
$948$		0			0
$949$			40.0000i			1.29845i
$950$		0			0
$951$	14.0000	−	19.7990i	0.453981	−	0.642026i
$952$		0			0
$953$	−24.0416	−	24.0416i	−0.778785	−	0.778785i	0.200839	−	0.979624i	$-0.435633\pi$
$953$	−24.0416	−	24.0416i	−0.778785	−	0.778785i	−0.979624	+	0.200839i	$0.935633\pi$
$954$		0			0
$955$	−18.0000	−	6.00000i	−0.582466	−	0.194155i
$956$		0			0
$957$	−5.27208	−	30.7279i	−0.170422	−	0.993293i
$958$		0			0
$959$	42.4264			1.37002
$960$		0			0
$961$	5.00000			0.161290
$962$		0			0
$963$	−15.5147	+	32.4853i	−0.499955	+	1.04682i
$964$		0			0
$965$	24.0416	+	48.0833i	0.773927	+	1.54785i
$966$		0			0
$967$	−15.0000	−	15.0000i	−0.482367	−	0.482367i	0.423520	−	0.905887i	$-0.360795\pi$
$967$	−15.0000	−	15.0000i	−0.482367	−	0.482367i	−0.905887	+	0.423520i	$0.860795\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			46.6690i			1.49768i	0.662750	+	0.748841i	$0.269389\pi$
$971$			46.6690i			1.49768i	−0.662750	+	0.748841i	$0.730611\pi$
$972$		0			0
$973$	36.0000	−	36.0000i	1.15411	−	1.15411i
$974$		0			0
$975$	−46.6274	+	15.0294i	−1.49327	+	0.481327i
$976$		0			0
$977$	−32.5269	+	32.5269i	−1.04063	+	1.04063i	−0.0414892	+	0.999139i	$0.513210\pi$
$977$	−32.5269	+	32.5269i	−1.04063	+	1.04063i	−0.999139	+	0.0414892i	$0.986790\pi$
$978$		0			0
$979$			36.0000i			1.15056i
$980$		0			0
$981$	2.00000	+	5.65685i	0.0638551	+	0.180609i
$982$		0			0
$983$	−33.9411	−	33.9411i	−1.08255	−	1.08255i	−0.996271	−	0.0862831i	$-0.972501\pi$
$983$	−33.9411	−	33.9411i	−1.08255	−	1.08255i	−0.0862831	−	0.996271i	$-0.527499\pi$
$984$		0			0
$985$	−8.00000	−	16.0000i	−0.254901	−	0.509802i
$986$		0			0
$987$	−86.9117	+	14.9117i	−2.76643	+	0.474644i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	48.0000			1.52477			0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000			1.52477			0.762385	+	0.647124i	$0.224028\pi$
$992$		0			0
$993$	−20.4853	+	3.51472i	−0.650081	+	0.111536i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	28.0000	+	28.0000i	0.886769	+	0.886769i	0.994211	−	0.107442i	$-0.0342661\pi$
$997$	28.0000	+	28.0000i	0.886769	+	0.886769i	−0.107442	+	0.994211i	$0.534266\pi$
$998$		0			0
$999$	14.1421	+	4.00000i	0.447437	+	0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.v.j.257.2		4
3.2	odd	2	inner	960.2.v.j.257.1		4
4.3	odd	2		960.2.v.d.257.1		4
5.3	odd	4	inner	960.2.v.j.833.1		4
8.3	odd	2		480.2.v.b.257.2	yes	4
8.5	even	2		480.2.v.a.257.1	✓	4
12.11	even	2		960.2.v.d.257.2		4
15.8	even	4	inner	960.2.v.j.833.2		4
20.3	even	4		960.2.v.d.833.2		4
24.5	odd	2		480.2.v.a.257.2	yes	4
24.11	even	2		480.2.v.b.257.1	yes	4
40.3	even	4		480.2.v.b.353.1	yes	4
40.13	odd	4		480.2.v.a.353.2	yes	4
60.23	odd	4		960.2.v.d.833.1		4
120.53	even	4		480.2.v.a.353.1	yes	4
120.83	odd	4		480.2.v.b.353.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.v.a.257.1	✓	4	8.5	even	2
480.2.v.a.257.2	yes	4	24.5	odd	2
480.2.v.a.353.1	yes	4	120.53	even	4
480.2.v.a.353.2	yes	4	40.13	odd	4
480.2.v.b.257.1	yes	4	24.11	even	2
480.2.v.b.257.2	yes	4	8.3	odd	2
480.2.v.b.353.1	yes	4	40.3	even	4
480.2.v.b.353.2	yes	4	120.83	odd	4
960.2.v.d.257.1		4	4.3	odd	2
960.2.v.d.257.2		4	12.11	even	2
960.2.v.d.833.1		4	60.23	odd	4
960.2.v.d.833.2		4	20.3	even	4
960.2.v.j.257.1		4	3.2	odd	2	inner
960.2.v.j.257.2		4	1.1	even	1	trivial
960.2.v.j.833.1		4	5.3	odd	4	inner
960.2.v.j.833.2		4	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70711 - 0.292893i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(2.82843 - 1.00000i) q^{9} -4.24264i q^{11} +(4.00000 - 4.00000i) q^{13} +(-0.585786 + 3.82843i) q^{15} +(-1.41421 + 1.41421i) q^{17} +(-6.00000 - 4.24264i) q^{21} +(-4.00000 - 3.00000i) q^{25} +(4.53553 - 2.53553i) q^{27} +4.24264 q^{29} -6.00000 q^{31} +(-1.24264 - 7.24264i) q^{33} +(8.48528 - 4.24264i) q^{35} +(2.00000 + 2.00000i) q^{37} +(5.65685 - 8.00000i) q^{39} +(6.00000 - 6.00000i) q^{43} +(0.121320 + 6.70711i) q^{45} +(8.48528 - 8.48528i) q^{47} +11.0000i q^{49} +(-2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(9.00000 + 3.00000i) q^{55} -4.24264 q^{59} +6.00000 q^{61} +(-11.4853 - 5.48528i) q^{63} +(5.65685 + 11.3137i) q^{65} +8.48528i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-7.70711 - 3.94975i) q^{75} +(-12.7279 + 12.7279i) q^{77} -6.00000i q^{79} +(7.00000 - 5.65685i) q^{81} +(8.48528 + 8.48528i) q^{83} +(-2.00000 - 4.00000i) q^{85} +(7.24264 - 1.24264i) q^{87} -8.48528 q^{89} -24.0000 q^{91} +(-10.2426 + 1.75736i) q^{93} +(-5.00000 - 5.00000i) q^{97} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 12 q^{7} + 16 q^{13} - 8 q^{15} - 24 q^{21} - 16 q^{25} + 4 q^{27} - 24 q^{31} + 12 q^{33} + 8 q^{37} + 24 q^{43} - 8 q^{45} - 8 q^{51} + 36 q^{55} + 24 q^{61} - 12 q^{63} - 20 q^{73} - 28 q^{75}+ \cdots - 20 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 - 12 * q^7 + 16 * q^13 - 8 * q^15 - 24 * q^21 - 16 * q^25 + 4 * q^27 - 24 * q^31 + 12 * q^33 + 8 * q^37 + 24 * q^43 - 8 * q^45 - 8 * q^51 + 36 * q^55 + 24 * q^61 - 12 * q^63 - 20 * q^73 - 28 * q^75 + 28 * q^81 - 8 * q^85 + 12 * q^87 - 96 * q^91 - 24 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more