LMFDB - Embedded newform 480.2.v.a.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [480,2,Mod(257,480)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(480, 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("480.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	480.v (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.83281929702$
Analytic rank:	$1$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	480.257
Dual form			480.2.v.a.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.292893 + 1.70711i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.82843 - 1.00000i) q^{9} -4.24264i q^{11} +(-4.00000 + 4.00000i) q^{13} +(-3.41421 - 1.82843i) q^{15} +(1.41421 - 1.41421i) q^{17} +(6.00000 - 4.24264i) q^{21} +(-4.00000 - 3.00000i) q^{25} +(2.53553 - 4.53553i) q^{27} +4.24264 q^{29} -6.00000 q^{31} +(7.24264 + 1.24264i) q^{33} +(8.48528 - 4.24264i) q^{35} +(-2.00000 - 2.00000i) q^{37} +(-5.65685 - 8.00000i) q^{39} +(-6.00000 + 6.00000i) q^{43} +(4.12132 - 5.29289i) q^{45} +(-8.48528 + 8.48528i) q^{47} +11.0000i q^{49} +(2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(9.00000 + 3.00000i) q^{55} -4.24264 q^{59} -6.00000 q^{61} +(5.48528 + 11.4853i) q^{63} +(-5.65685 - 11.3137i) q^{65} -8.48528i q^{71} +(-5.00000 + 5.00000i) q^{73} +(6.29289 - 5.94975i) q^{75} +(-12.7279 + 12.7279i) q^{77} -6.00000i q^{79} +(7.00000 + 5.65685i) q^{81} +(8.48528 + 8.48528i) q^{83} +(2.00000 + 4.00000i) q^{85} +(-1.24264 + 7.24264i) q^{87} +8.48528 q^{89} +24.0000 q^{91} +(1.75736 - 10.2426i) q^{93} +(-5.00000 - 5.00000i) q^{97} +(-4.24264 + 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$4$		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	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$		0			0
$15$	−3.41421	−	1.82843i	−0.881546	−	0.472098i
$16$		0			0
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	−0.514496	−	0.857493i	$-0.672021\pi$
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	0.857493	+	0.514496i	$0.172021\pi$
$18$		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
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$		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
$33$	7.24264	+	1.24264i	1.26078	+	0.216316i
$34$		0			0
$35$	8.48528	−	4.24264i	1.43427	−	0.717137i
$36$		0			0
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$		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	−0.996660	−	0.0816682i	$-0.973975\pi$
$43$	−6.00000	+	6.00000i	−0.914991	+	0.914991i	0.0816682	+	0.996660i	$0.473975\pi$
$44$		0			0
$45$	4.12132	−	5.29289i	0.614370	−	0.789018i
$46$		0			0
$47$	−8.48528	+	8.48528i	−1.23771	+	1.23771i	−0.276769	+	0.960936i	$0.589264\pi$
$47$	−8.48528	+	8.48528i	−1.23771	+	1.23771i	−0.960936	+	0.276769i	$0.910736\pi$
$48$		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	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$		0			0
$63$	5.48528	+	11.4853i	0.691080	+	1.44701i
$64$		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	$-0.832042\pi$
$71$		−	8.48528i		−	1.00702i	0.863990	−	0.503509i	$-0.167958\pi$
$72$		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
$75$	6.29289	−	5.94975i	0.726641	−	0.687018i
$76$		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
$87$	−1.24264	+	7.24264i	−0.133225	+	0.776493i
$88$		0			0
$89$	8.48528			0.899438			0.449719	−	0.893170i	$-0.351524\pi$
$89$	8.48528			0.899438			0.449719	+	0.893170i	$0.351524\pi$
$90$		0			0
$91$	24.0000			2.51588
$92$		0			0
$93$	1.75736	−	10.2426i	0.182230	−	1.06211i
$94$		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
$105$	4.75736	+	15.7279i	0.464271	+	1.53489i
$106$		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	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$	4.00000	−	2.82843i	0.379663	−	0.268462i
$112$		0			0
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	0.637452	−	0.770490i	$-0.279988\pi$
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	−0.770490	+	0.637452i	$0.779988\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	15.3137	−	7.31371i	1.41575	−	0.676153i
$118$		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
$135$	7.82843	+	8.58579i	0.673764	+	0.738947i
$136$		0			0
$137$	7.07107	−	7.07107i	0.604122	−	0.604122i	−0.337282	−	0.941404i	$-0.609507\pi$
$137$	7.07107	−	7.07107i	0.604122	−	0.604122i	0.941404	+	0.337282i	$0.109507\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		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
$147$	−18.7782	−	3.22183i	−1.54880	−	0.265732i
$148$		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
$153$	−5.41421	+	2.58579i	−0.437713	+	0.209048i
$154$		0			0
$155$	4.24264	−	12.7279i	0.340777	−	1.02233i
$156$		0			0
$157$	8.00000	+	8.00000i	0.638470	+	0.638470i	0.950178	−	0.311708i	$-0.100901\pi$
$157$	8.00000	+	8.00000i	0.638470	+	0.638470i	−0.311708	+	0.950178i	$0.600901\pi$
$158$		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	−0.998294	−	0.0583818i	$-0.981406\pi$
$163$	−12.0000	+	12.0000i	−0.939913	+	0.939913i	0.0583818	+	0.998294i	$0.481406\pi$
$164$		0			0
$165$	−7.75736	+	14.4853i	−0.603910	+	1.12768i
$166$		0			0
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	−0.297966	−	0.954577i	$-0.596308\pi$
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	0.954577	+	0.297966i	$0.0963081\pi$
$168$		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
$177$	1.24264	−	7.24264i	0.0934026	−	0.544390i
$178$		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	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	1.75736	−	10.2426i	0.129908	−	0.757158i
$184$		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	$-0.900679\pi$
$191$		−	8.48528i		−	0.613973i	0.951714	−	0.306987i	$-0.0993207\pi$
$192$		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
$195$	20.9706	−	6.34315i	1.50173	−	0.454242i
$196$		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	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$	14.4853	+	2.48528i	0.992515	+	0.170289i
$214$		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
$225$	8.31371	+	12.4853i	0.554247	+	0.832352i
$226$		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	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		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	$-0.925597\pi$
$233$	−18.3848	−	18.3848i	−1.20443	−	1.20443i	−0.231621	−	0.972806i	$-0.574403\pi$
$234$		0			0
$235$	−12.0000	−	24.0000i	−0.782794	−	1.56559i
$236$		0			0
$237$	10.2426	+	1.75736i	0.665331	+	0.114153i
$238$		0			0
$239$	25.4558			1.64660			0.823301	−	0.567605i	$-0.192130\pi$
$239$	25.4558			1.64660			0.823301	+	0.567605i	$0.192130\pi$
$240$		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
$243$	−11.7071	+	10.2929i	−0.751011	+	0.660289i
$244$		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
$255$	−7.41421	+	2.24264i	−0.464296	+	0.140440i
$256$		0			0
$257$	−15.5563	+	15.5563i	−0.970378	+	0.970378i	−0.999574	−	0.0291953i	$-0.990706\pi$
$257$	−15.5563	+	15.5563i	−0.970378	+	0.970378i	0.0291953	+	0.999574i	$0.490706\pi$
$258$		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	0.918544	−	0.395319i	$-0.129366\pi$
$263$	8.48528	+	8.48528i	0.523225	+	0.523225i	−0.395319	+	0.918544i	$0.629366\pi$
$264$		0			0
$265$	8.00000	−	4.00000i	0.491436	−	0.245718i
$266$		0			0
$267$	−2.48528	+	14.4853i	−0.152097	+	0.886485i
$268$		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
$273$	−7.02944	+	40.9706i	−0.425441	+	2.47965i
$274$		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	$-0.865677\pi$
$277$	−22.0000	−	22.0000i	−1.32185	−	1.32185i	−0.409576	−	0.912276i	$-0.634323\pi$
$278$		0			0
$279$	16.9706	+	6.00000i	1.01600	+	0.359211i
$280$		0			0
$281$			8.48528i			0.506189i	0.967442	+	0.253095i	$0.0814484\pi$
$281$			8.48528i			0.506189i	−0.967442	+	0.253095i	$0.918552\pi$
$282$		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
$297$	−19.2426	−	10.7574i	−1.11657	−	0.624205i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	36.0000			2.07501
$302$		0			0
$303$	−16.8995	−	2.89949i	−0.970851	−	0.166572i
$304$		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	$-0.991182\pi$
$307$	−18.0000	−	18.0000i	−1.02731	−	1.02731i	−0.0276979	−	0.999616i	$-0.508818\pi$
$308$		0			0
$309$	4.24264	+	6.00000i	0.241355	+	0.341328i
$310$		0			0
$311$		−	8.48528i		−	0.481156i	−0.970630	−	0.240578i	$-0.922663\pi$
$311$		−	8.48528i		−	0.481156i	0.970630	−	0.240578i	$-0.0773370\pi$
$312$		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
$315$	−28.2426	+	3.51472i	−1.59129	+	0.198032i
$316$		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
$327$	3.41421	+	0.585786i	0.188806	+	0.0323941i
$328$		0			0
$329$	50.9117			2.80685
$330$		0			0
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$		0			0
$333$	3.65685	+	7.65685i	0.200394	+	0.419593i
$334$		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	$-0.839998\pi$
$349$		−	18.0000i		−	0.963518i	0.876304	−	0.481759i	$-0.160002\pi$
$350$		0			0
$351$	8.00000	+	28.2843i	0.427008	+	1.50970i
$352$		0			0
$353$	1.41421	+	1.41421i	0.0752710	+	0.0752710i	0.743740	−	0.668469i	$-0.233050\pi$
$353$	1.41421	+	1.41421i	0.0752710	+	0.0752710i	−0.668469	+	0.743740i	$0.733050\pi$
$354$		0			0
$355$	18.0000	+	6.00000i	0.955341	+	0.318447i
$356$		0			0
$357$	2.48528	−	14.4853i	0.131535	−	0.766642i
$358$		0			0
$359$	−16.9706			−0.895672			−0.447836	−	0.894116i	$-0.647805\pi$
$359$	−16.9706			−0.895672			−0.447836	+	0.894116i	$0.647805\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$		0			0
$363$	2.05025	−	11.9497i	0.107610	−	0.627199i
$364$		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	$0.511531\pi$
$373$	−20.0000	+	20.0000i	−1.03556	+	1.03556i	−0.999344	+	0.0362168i	$0.988469\pi$
$374$		0			0
$375$	8.17157	+	17.5563i	0.421978	+	0.906606i
$376$		0			0
$377$	−16.9706	+	16.9706i	−0.874028	+	0.874028i
$378$		0			0
$379$			36.0000i			1.84920i	0.380945	+	0.924598i	$0.375599\pi$
$379$			36.0000i			1.84920i	−0.380945	+	0.924598i	$0.624401\pi$
$380$		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	$-0.878386\pi$
$383$	−25.4558	−	25.4558i	−1.30073	−	1.30073i	−0.372835	−	0.927898i	$-0.621614\pi$
$384$		0			0
$385$	−18.0000	−	36.0000i	−0.917365	−	1.83473i
$386$		0			0
$387$	22.9706	−	10.9706i	1.16766	−	0.557665i
$388$		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
$393$	−21.7279	−	3.72792i	−1.09603	−	0.188049i
$394$		0			0
$395$	12.7279	+	4.24264i	0.640411	+	0.213470i
$396$		0			0
$397$	−14.0000	−	14.0000i	−0.702640	−	0.702640i	0.262337	−	0.964976i	$-0.415507\pi$
$397$	−14.0000	−	14.0000i	−0.702640	−	0.702640i	−0.964976	+	0.262337i	$0.915507\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	14.1421i		−	0.706225i	−0.935581	−	0.353112i	$-0.885123\pi$
$401$		−	14.1421i		−	0.706225i	0.935581	−	0.353112i	$-0.114877\pi$
$402$		0			0
$403$	24.0000	−	24.0000i	1.19553	−	1.19553i
$404$		0			0
$405$	−16.9497	+	10.8492i	−0.842240	+	0.539103i
$406$		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
$417$	20.4853	+	3.51472i	1.00317	+	0.172117i
$418$		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	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$		0			0
$423$	32.4853	−	15.5147i	1.57949	−	0.754351i
$424$		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	$0.134025\pi$
$431$			16.9706i			0.817443i	−0.912659	+	0.408722i	$0.865975\pi$
$432$		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
$435$	−14.4853	−	7.75736i	−0.694516	−	0.371937i
$436$		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
$447$	−0.414214	+	2.41421i	−0.0195916	+	0.114188i
$448$		0			0
$449$	−31.1127			−1.46830			−0.734150	−	0.678988i	$-0.762419\pi$
$449$	−31.1127			−1.46830			−0.734150	+	0.678988i	$0.762419\pi$
$450$		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
$465$	20.4853	+	10.9706i	0.949982	+	0.508748i
$466$		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
$477$	5.17157	+	10.8284i	0.236790	+	0.495800i
$478$		0			0
$479$	8.48528			0.387702			0.193851	−	0.981031i	$-0.437902\pi$
$479$	8.48528			0.387702			0.193851	+	0.981031i	$0.437902\pi$
$480$		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
$495$	−22.4558	−	17.4853i	−1.00932	−	0.785905i
$496$		0			0
$497$	−25.4558	+	25.4558i	−1.14185	+	1.14185i
$498$		0			0
$499$			24.0000i			1.07439i	0.843459	+	0.537194i	$0.180516\pi$
$499$			24.0000i			1.07439i	−0.843459	+	0.537194i	$0.819484\pi$
$500$		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
$507$	32.4350	+	5.56497i	1.44049	+	0.247149i
$508$		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	$0.238688\pi$
$521$			31.1127i			1.36307i	−0.731785	+	0.681536i	$0.761312\pi$
$522$		0			0
$523$	−12.0000	+	12.0000i	−0.524723	+	0.524723i	−0.918994	−	0.394271i	$-0.870997\pi$
$523$	−12.0000	+	12.0000i	−0.524723	+	0.524723i	0.394271	+	0.918994i	$0.370997\pi$
$524$		0			0
$525$	−36.7279	−	1.02944i	−1.60294	−	0.0449283i
$526$		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
$537$	6.21320	−	36.2132i	0.268120	−	1.56272i
$538$		0			0
$539$	46.6690			2.01018
$540$		0			0
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$	−0.585786	+	3.41421i	−0.0251385	+	0.146518i
$544$		0			0
$545$	4.24264	+	1.41421i	0.181735	+	0.0605783i
$546$		0			0
$547$	18.0000	+	18.0000i	0.769624	+	0.769624i	0.978040	−	0.208416i	$-0.0668307\pi$
$547$	18.0000	+	18.0000i	0.769624	+	0.769624i	−0.208416	+	0.978040i	$0.566831\pi$
$548$		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
$555$	3.17157	+	10.4853i	0.134626	+	0.445075i
$556$		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
$567$	−4.02944	−	37.9706i	−0.169220	−	1.59461i
$568$		0			0
$569$	2.82843			0.118574			0.0592869	−	0.998241i	$-0.481117\pi$
$569$	2.82843			0.118574			0.0592869	+	0.998241i	$0.481117\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$		0			0
$573$	14.4853	+	2.48528i	0.605131	+	0.103824i
$574$		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
$585$	4.68629	+	37.6569i	0.193754	+	1.55692i
$586$		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	0.0126486	−	0.999920i	$-0.495974\pi$
$593$	−24.0416	−	24.0416i	−0.987271	−	0.987271i	−0.999920	+	0.0126486i	$0.995974\pi$
$594$		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	$-0.387302\pi$
$599$	16.9706			0.693398			0.346699	+	0.937976i	$0.387302\pi$
$600$		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	−0.879604	−	0.475707i	$-0.842192\pi$
$613$	−10.0000	+	10.0000i	−0.403896	+	0.403896i	0.475707	+	0.879604i	$0.342192\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	26.8701	−	26.8701i	1.08175	−	1.08175i	0.0854011	−	0.996347i	$-0.472783\pi$
$617$	26.8701	−	26.8701i	1.08175	−	1.08175i	0.996347	−	0.0854011i	$-0.0272172\pi$
$618$		0			0
$619$		−	36.0000i		−	1.44696i	−0.690344	−	0.723481i	$-0.742541\pi$
$619$		−	36.0000i		−	1.44696i	0.690344	−	0.723481i	$-0.257459\pi$
$620$		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
$633$	3.51472	−	20.4853i	0.139698	−	0.814217i
$634$		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	$0.108786\pi$
$641$			16.9706i			0.670297i	−0.942165	+	0.335148i	$0.891214\pi$
$642$		0			0
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	−0.0521706	−	0.998638i	$-0.516614\pi$
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	0.998638	+	0.0521706i	$0.0166140\pi$
$644$		0			0
$645$	31.4558	−	9.51472i	1.23857	−	0.374642i
$646$		0			0
$647$	16.9706	−	16.9706i	0.667182	−	0.667182i	−0.289881	−	0.957063i	$-0.593616\pi$
$647$	16.9706	−	16.9706i	0.667182	−	0.667182i	0.957063	+	0.289881i	$0.0936157\pi$
$648$		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
$657$	19.1421	−	9.14214i	0.746806	−	0.356669i
$658$		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	$-0.698291\pi$
$661$	−30.0000			−1.16686			−0.583432	+	0.812162i	$0.698291\pi$
$662$		0			0
$663$	−19.3137	−	3.31371i	−0.750082	−	0.128694i
$664$		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
$675$	−23.7487	+	10.5355i	−0.914089	+	0.405513i
$676$		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
$687$	10.2426	+	1.75736i	0.390781	+	0.0670474i
$688$		0			0
$689$	22.6274			0.862036
$690$		0			0
$691$	−48.0000			−1.82601			−0.913003	−	0.407953i	$-0.866243\pi$
$691$	−48.0000			−1.82601			−0.913003	+	0.407953i	$0.866243\pi$
$692$		0			0
$693$	48.7279	−	23.2721i	1.85102	−	0.884033i
$694$		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
$705$	44.4853	−	13.4558i	1.67541	−	0.506776i
$706$		0			0
$707$	29.6985	−	29.6985i	1.11693	−	1.11693i
$708$		0			0
$709$		−	30.0000i		−	1.12667i	−0.826227	−	0.563337i	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$		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
$717$	−7.45584	+	43.4558i	−0.278444	+	1.62289i
$718$		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
$723$	3.51472	−	20.4853i	0.130714	−	0.761856i
$724$		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	−0.743077	−	0.669206i	$-0.766635\pi$
$733$	−2.00000	+	2.00000i	−0.0738717	+	0.0738717i	0.669206	+	0.743077i	$0.266635\pi$
$734$		0			0
$735$	20.1127	−	37.5563i	0.741868	−	1.38529i
$736$		0			0
$737$		0			0
$738$		0			0
$739$			12.0000i			0.441427i	0.975339	+	0.220714i	$0.0708386\pi$
$739$			12.0000i			0.441427i	−0.975339	+	0.220714i	$0.929161\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.9706	−	16.9706i	−0.622590	−	0.622590i	0.323603	−	0.946193i	$-0.395106\pi$
$743$	−16.9706	−	16.9706i	−0.622590	−	0.622590i	−0.946193	+	0.323603i	$0.895106\pi$
$744$		0			0
$745$	−1.00000	+	3.00000i	−0.0366372	+	0.109911i
$746$		0			0
$747$	−15.5147	−	32.4853i	−0.567654	−	1.18857i
$748$		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
$753$	−7.24264	−	1.24264i	−0.263936	−	0.0452843i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	26.0000	+	26.0000i	0.944986	+	0.944986i	0.998564	−	0.0535776i	$-0.0170625\pi$
$757$	26.0000	+	26.0000i	0.944986	+	0.944986i	−0.0535776	+	0.998564i	$0.517062\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			36.7696i			1.33290i	0.745552	+	0.666448i	$0.232186\pi$
$761$			36.7696i			1.33290i	−0.745552	+	0.666448i	$0.767814\pi$
$762$		0			0
$763$	−6.00000	+	6.00000i	−0.217215	+	0.217215i
$764$		0			0
$765$	−1.65685	−	13.3137i	−0.0599037	−	0.481358i
$766$		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
$777$	−20.4853	−	3.51472i	−0.734905	−	0.126090i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−36.0000			−1.28818
$782$		0			0
$783$	10.7574	−	19.2426i	0.384437	−	0.687676i
$784$		0			0
$785$	−22.6274	+	11.3137i	−0.807607	+	0.403804i
$786$		0			0
$787$	−24.0000	−	24.0000i	−0.855508	−	0.855508i	0.135297	−	0.990805i	$-0.456801\pi$
$787$	−24.0000	−	24.0000i	−0.855508	−	0.855508i	−0.990805	+	0.135297i	$0.956801\pi$
$788$		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
$795$	4.48528	+	14.8284i	0.159077	+	0.525910i
$796$		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
$807$	−5.38478	+	31.3848i	−0.189553	+	1.10480i
$808$		0			0
$809$	−33.9411			−1.19331			−0.596653	−	0.802499i	$-0.703503\pi$
$809$	−33.9411			−1.19331			−0.596653	+	0.802499i	$0.703503\pi$
$810$		0			0
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$		0			0
$813$	7.02944	−	40.9706i	0.246533	−	1.43690i
$814$		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
$825$	−25.2426	−	26.6985i	−0.878836	−	0.929522i
$826$		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	$0.229400\pi$
$829$			38.0000i			1.31979i	−0.751356	+	0.659897i	$0.770600\pi$
$830$		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
$837$	−15.2132	+	27.2132i	−0.525845	+	0.940626i
$838$		0			0
$839$	33.9411			1.17178			0.585889	−	0.810391i	$-0.300745\pi$
$839$	33.9411			1.17178			0.585889	+	0.810391i	$0.300745\pi$
$840$		0			0
$841$	−11.0000			−0.379310
$842$		0			0
$843$	−14.4853	−	2.48528i	−0.498900	−	0.0855976i
$844$		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	−0.975087	−	0.221822i	$-0.928800\pi$
$853$	−22.0000	+	22.0000i	−0.753266	+	0.753266i	0.221822	+	0.975087i	$0.428800\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	−0.855675	−	0.517514i	$-0.826857\pi$
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	0.517514	+	0.855675i	$0.326857\pi$
$858$		0			0
$859$		−	36.0000i		−	1.22830i	−0.789188	−	0.614152i	$-0.789498\pi$
$859$		−	36.0000i		−	1.22830i	0.789188	−	0.614152i	$-0.210502\pi$
$860$		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
$867$	−22.1924	−	3.80761i	−0.753693	−	0.129313i
$868$		0			0
$869$	−25.4558			−0.863530
$870$		0			0
$871$		0			0
$872$		0			0
$873$	9.14214	+	19.1421i	0.309414	+	0.647863i
$874$		0			0
$875$	−46.6690	−	8.48528i	−1.57770	−	0.286855i
$876$		0			0
$877$	−4.00000	−	4.00000i	−0.135070	−	0.135070i	0.636339	−	0.771409i	$-0.280448\pi$
$877$	−4.00000	−	4.00000i	−0.135070	−	0.135070i	−0.771409	+	0.636339i	$0.780448\pi$
$878$		0			0
$879$	45.2548	−	32.0000i	1.52641	−	1.07933i
$880$		0			0
$881$			25.4558i			0.857629i	0.903393	+	0.428815i	$0.141069\pi$
$881$			25.4558i			0.857629i	−0.903393	+	0.428815i	$0.858931\pi$
$882$		0			0
$883$	12.0000	−	12.0000i	0.403832	−	0.403832i	−0.475749	−	0.879581i	$-0.657823\pi$
$883$	12.0000	−	12.0000i	0.403832	−	0.403832i	0.879581	+	0.475749i	$0.157823\pi$
$884$		0			0
$885$	14.4853	+	7.75736i	0.486917	+	0.260761i
$886$		0			0
$887$	16.9706	−	16.9706i	0.569816	−	0.569816i	−0.362261	−	0.932077i	$-0.617995\pi$
$887$	16.9706	−	16.9706i	0.569816	−	0.569816i	0.932077	+	0.362261i	$0.117995\pi$
$888$		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
$903$	−10.5442	+	61.4558i	−0.350888	+	2.04512i
$904$		0			0
$905$	−1.41421	+	4.24264i	−0.0470100	+	0.141030i
$906$		0			0
$907$	6.00000	+	6.00000i	0.199227	+	0.199227i	0.799668	−	0.600442i	$-0.205009\pi$
$907$	6.00000	+	6.00000i	0.199227	+	0.199227i	−0.600442	+	0.799668i	$0.705009\pi$
$908$		0			0
$909$	9.89949	−	28.0000i	0.328346	−	0.928701i
$910$		0			0
$911$		−	33.9411i		−	1.12452i	−0.826961	−	0.562260i	$-0.809932\pi$
$911$		−	33.9411i		−	1.12452i	0.826961	−	0.562260i	$-0.190068\pi$
$912$		0			0
$913$	36.0000	−	36.0000i	1.19143	−	1.19143i
$914$		0			0
$915$	20.4853	+	10.9706i	0.677223	+	0.362676i
$916$		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
$927$	−11.4853	+	5.48528i	−0.377226	+	0.180160i
$928$		0			0
$929$	−2.82843			−0.0927977			−0.0463988	−	0.998923i	$-0.514775\pi$
$929$	−2.82843			−0.0927977			−0.0463988	+	0.998923i	$0.514775\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	14.4853	+	2.48528i	0.474227	+	0.0813645i
$934$		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
$945$	2.27208	−	49.2426i	0.0739107	−	1.60186i
$946$		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	0.979624	−	0.200839i	$-0.0643669\pi$
$953$	24.0416	+	24.0416i	0.778785	+	0.778785i	−0.200839	+	0.979624i	$0.564367\pi$
$954$		0			0
$955$	18.0000	+	6.00000i	0.582466	+	0.194155i
$956$		0			0
$957$	30.7279	+	5.27208i	0.993293	+	0.170422i
$958$		0			0
$959$	−42.4264			−1.37002
$960$		0			0
$961$	5.00000			0.161290
$962$		0			0
$963$	32.4853	−	15.5147i	1.04682	−	0.499955i
$964$		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
$975$	−1.37258	+	48.9706i	−0.0439578	+	1.56831i
$976$		0			0
$977$	32.5269	−	32.5269i	1.04063	−	1.04063i	0.0414892	−	0.999139i	$-0.486790\pi$
$977$	32.5269	−	32.5269i	1.04063	−	1.04063i	0.999139	−	0.0414892i	$-0.0132102\pi$
$978$		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	$0.0274990\pi$
$983$	33.9411	+	33.9411i	1.08255	+	1.08255i	0.0862831	+	0.996271i	$0.472501\pi$
$984$		0			0
$985$	−8.00000	−	16.0000i	−0.254901	−	0.509802i
$986$		0			0
$987$	−14.9117	+	86.9117i	−0.474644	+	2.76643i
$988$		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
$993$	−3.51472	+	20.4853i	−0.111536	+	0.650081i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−28.0000	−	28.0000i	−0.886769	−	0.886769i	0.107442	−	0.994211i	$-0.465734\pi$
$997$	−28.0000	−	28.0000i	−0.886769	−	0.886769i	−0.994211	+	0.107442i	$0.965734\pi$
$998$		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	480.2.v.a.257.2	yes	4
3.2	odd	2	inner	480.2.v.a.257.1	✓	4
4.3	odd	2		480.2.v.b.257.1	yes	4
5.3	odd	4	inner	480.2.v.a.353.1	yes	4
8.3	odd	2		960.2.v.d.257.2		4
8.5	even	2		960.2.v.j.257.1		4
12.11	even	2		480.2.v.b.257.2	yes	4
15.8	even	4	inner	480.2.v.a.353.2	yes	4
20.3	even	4		480.2.v.b.353.2	yes	4
24.5	odd	2		960.2.v.j.257.2		4
24.11	even	2		960.2.v.d.257.1		4
40.3	even	4		960.2.v.d.833.1		4
40.13	odd	4		960.2.v.j.833.2		4
60.23	odd	4		480.2.v.b.353.1	yes	4
120.53	even	4		960.2.v.j.833.1		4
120.83	odd	4		960.2.v.d.833.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.v.a.257.1	✓	4	3.2	odd	2	inner
480.2.v.a.257.2	yes	4	1.1	even	1	trivial
480.2.v.a.353.1	yes	4	5.3	odd	4	inner
480.2.v.a.353.2	yes	4	15.8	even	4	inner
480.2.v.b.257.1	yes	4	4.3	odd	2
480.2.v.b.257.2	yes	4	12.11	even	2
480.2.v.b.353.1	yes	4	60.23	odd	4
480.2.v.b.353.2	yes	4	20.3	even	4
960.2.v.d.257.1		4	24.11	even	2
960.2.v.d.257.2		4	8.3	odd	2
960.2.v.d.833.1		4	40.3	even	4
960.2.v.d.833.2		4	120.83	odd	4
960.2.v.j.257.1		4	8.5	even	2
960.2.v.j.257.2		4	24.5	odd	2
960.2.v.j.833.1		4	120.53	even	4
960.2.v.j.833.2		4	40.13	odd	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:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 + 1.70711i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.82843 - 1.00000i) q^{9} -4.24264i q^{11} +(-4.00000 + 4.00000i) q^{13} +(-3.41421 - 1.82843i) q^{15} +(1.41421 - 1.41421i) q^{17} +(6.00000 - 4.24264i) q^{21} +(-4.00000 - 3.00000i) q^{25} +(2.53553 - 4.53553i) q^{27} +4.24264 q^{29} -6.00000 q^{31} +(7.24264 + 1.24264i) q^{33} +(8.48528 - 4.24264i) q^{35} +(-2.00000 - 2.00000i) q^{37} +(-5.65685 - 8.00000i) q^{39} +(-6.00000 + 6.00000i) q^{43} +(4.12132 - 5.29289i) q^{45} +(-8.48528 + 8.48528i) q^{47} +11.0000i q^{49} +(2.00000 + 2.82843i) q^{51} +(-2.82843 - 2.82843i) q^{53} +(9.00000 + 3.00000i) q^{55} -4.24264 q^{59} -6.00000 q^{61} +(5.48528 + 11.4853i) q^{63} +(-5.65685 - 11.3137i) q^{65} -8.48528i q^{71} +(-5.00000 + 5.00000i) q^{73} +(6.29289 - 5.94975i) q^{75} +(-12.7279 + 12.7279i) q^{77} -6.00000i q^{79} +(7.00000 + 5.65685i) q^{81} +(8.48528 + 8.48528i) q^{83} +(2.00000 + 4.00000i) q^{85} +(-1.24264 + 7.24264i) q^{87} +8.48528 q^{89} +24.0000 q^{91} +(1.75736 - 10.2426i) q^{93} +(-5.00000 - 5.00000i) q^{97} +(-4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 12 q^{7} - 16 q^{13} - 8 q^{15} + 24 q^{21} - 16 q^{25} - 4 q^{27} - 24 q^{31} + 12 q^{33} - 8 q^{37} - 24 q^{43} + 8 q^{45} + 8 q^{51} + 36 q^{55} - 24 q^{61} - 12 q^{63} - 20 q^{73} + 28 q^{75}+ \cdots - 20 q^{97}+O(q^{100}) \) 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

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