LMFDB - Embedded newform 960.2.v.j.833.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(257,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,4,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			833.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	960.833
Dual form			960.2.v.j.257.1

$q$-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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$		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	0.993229	+	0.116171i	$0.0370621\pi$
$13$	4.00000	+	4.00000i	1.10940	+	1.10940i	0.116171	+	0.993229i	$0.462938\pi$
$14$		0			0
$15$	−3.41421	+	1.82843i	−0.881546	+	0.472098i
$16$		0			0
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	0.857493	−	0.514496i	$-0.172021\pi$
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	−0.514496	+	0.857493i	$0.672021\pi$
$18$		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	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$		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	$-0.628881\pi$
$29$	−4.24264			−0.787839			−0.393919	+	0.919145i	$0.628881\pi$
$30$		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	$-0.675311\pi$
$37$	2.00000	−	2.00000i	0.328798	−	0.328798i	0.852129	+	0.523331i	$0.175311\pi$
$38$		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	$-0.0260248\pi$
$43$	6.00000	+	6.00000i	0.914991	+	0.914991i	−0.0816682	+	0.996660i	$0.526025\pi$
$44$		0			0
$45$	−4.12132	−	5.29289i	−0.614370	−	0.789018i
$46$		0			0
$47$	−8.48528	−	8.48528i	−1.23771	−	1.23771i	−0.960936	−	0.276769i	$-0.910736\pi$
$47$	−8.48528	−	8.48528i	−1.23771	−	1.23771i	−0.276769	−	0.960936i	$-0.589264\pi$
$48$		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	$-0.661414\pi$
$53$	2.82843	−	2.82843i	0.388514	−	0.388514i	0.874157	+	0.485643i	$0.161414\pi$
$54$		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	$-0.410934\pi$
$59$	4.24264			0.552345			0.276172	+	0.961108i	$0.410934\pi$
$60$		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
$63$	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	$-0.750000\pi$
$67$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$68$		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	0.351123	−	0.936329i	$-0.385800\pi$
$73$	−5.00000	−	5.00000i	−0.585206	−	0.585206i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		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	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$		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	$-0.978845\pi$
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	0.0664117	+	0.997792i	$0.478845\pi$
$84$		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	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−5.00000	+	5.00000i	−0.507673	+	0.507673i	0.406138	+	0.913812i	$0.366875\pi$
$98$		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	0.839287	−	0.543688i	$-0.182973\pi$
$103$	3.00000	+	3.00000i	0.295599	+	0.295599i	−0.543688	+	0.839287i	$0.682973\pi$
$104$		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	$-0.0530362\pi$
$107$	8.48528	+	8.48528i	0.820303	+	0.820303i	−0.165848	+	0.986151i	$0.553036\pi$
$108$		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	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$		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	−0.561363	−	0.827570i	$-0.689723\pi$
$127$	3.00000	−	3.00000i	0.266207	−	0.266207i	0.827570	+	0.561363i	$0.189723\pi$
$128$		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	0.941404	−	0.337282i	$-0.109507\pi$
$137$	7.07107	+	7.07107i	0.604122	+	0.604122i	−0.337282	+	0.941404i	$0.609507\pi$
$138$		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	$-0.518450\pi$
$149$	−1.41421			−0.115857			−0.0579284	+	0.998321i	$0.518450\pi$
$150$		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	$-0.899099\pi$
$157$	−8.00000	+	8.00000i	−0.638470	+	0.638470i	0.311708	+	0.950178i	$0.399099\pi$
$158$		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	$-0.0185941\pi$
$163$	12.0000	+	12.0000i	0.939913	+	0.939913i	−0.0583818	+	0.998294i	$0.518594\pi$
$164$		0			0
$165$	7.75736	+	14.4853i	0.603910	+	1.12768i
$166$		0			0
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$		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	$-0.928635\pi$
$173$	−9.89949	+	9.89949i	−0.752645	+	0.752645i	0.222327	+	0.974972i	$0.428635\pi$
$174$		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	$-0.208636\pi$
$179$	21.2132			1.58555			0.792775	+	0.609515i	$0.208636\pi$
$180$		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
$183$	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	$0.0993207\pi$
$191$			8.48528i			0.613973i	−0.951714	+	0.306987i	$0.900679\pi$
$192$		0			0
$193$	17.0000	+	17.0000i	1.22369	+	1.22369i	0.966312	+	0.257375i	$0.0828576\pi$
$193$	17.0000	+	17.0000i	1.22369	+	1.22369i	0.257375	+	0.966312i	$0.417142\pi$
$194$		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	$-0.158010\pi$
$197$	5.65685	+	5.65685i	0.403034	+	0.403034i	−0.476267	+	0.879301i	$0.658010\pi$
$198$		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
$213$	−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	0.599489	−	0.800383i	$-0.295371\pi$
$223$	−3.00000	−	3.00000i	−0.200895	−	0.200895i	−0.800383	+	0.599489i	$0.795371\pi$
$224$		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	$-0.453780\pi$
$227$	−12.7279	−	12.7279i	−0.844782	−	0.844782i	−0.989476	+	0.144695i	$0.953780\pi$
$228$		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	−0.231621	+	0.972806i	$0.574403\pi$
$233$	−18.3848	+	18.3848i	−1.20443	+	1.20443i	−0.972806	+	0.231621i	$0.925597\pi$
$234$		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	0.0291953	−	0.999574i	$-0.490706\pi$
$257$	−15.5563	−	15.5563i	−0.970378	−	0.970378i	−0.999574	+	0.0291953i	$0.990706\pi$
$258$		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	$-0.629366\pi$
$263$	8.48528	−	8.48528i	0.523225	−	0.523225i	0.918544	+	0.395319i	$0.129366\pi$
$264$		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	$-0.689379\pi$
$269$	−18.3848			−1.12094			−0.560470	+	0.828175i	$0.689379\pi$
$270$		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	0.409576	−	0.912276i	$-0.365677\pi$
$277$	22.0000	−	22.0000i	1.32185	−	1.32185i	0.912276	−	0.409576i	$-0.134323\pi$
$278$		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	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		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	0.409677	−	0.912231i	$-0.365641\pi$
$293$	22.6274	−	22.6274i	1.32191	−	1.32191i	0.912231	−	0.409677i	$-0.134359\pi$
$294$		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	0.0276979	−	0.999616i	$-0.491182\pi$
$307$	18.0000	−	18.0000i	1.02731	−	1.02731i	0.999616	−	0.0276979i	$-0.00881765\pi$
$308$		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	0.999264	−	0.0383669i	$-0.0122156\pi$
$313$	17.0000	+	17.0000i	0.960897	+	0.960897i	−0.0383669	+	0.999264i	$0.512216\pi$
$314$		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	$-0.378618\pi$
$317$	−9.89949	−	9.89949i	−0.556011	−	0.556011i	−0.928169	+	0.372158i	$0.878618\pi$
$318$		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	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		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	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	7.00000	−	7.00000i	0.381314	−	0.381314i	0.871576	+	0.490261i	$0.163099\pi$
$338$		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	$-0.410506\pi$
$347$	−12.7279	−	12.7279i	−0.683271	−	0.683271i	−0.960736	+	0.277465i	$0.910506\pi$
$348$		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	−0.668469	−	0.743740i	$-0.733050\pi$
$353$	1.41421	−	1.41421i	0.0752710	−	0.0752710i	0.743740	+	0.668469i	$0.233050\pi$
$354$		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	−0.197341	−	0.980335i	$-0.563231\pi$
$367$	15.0000	−	15.0000i	0.782994	−	0.782994i	0.980335	+	0.197341i	$0.0632307\pi$
$368$		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	0.999344	+	0.0362168i	$0.0115307\pi$
$373$	20.0000	+	20.0000i	1.03556	+	1.03556i	0.0362168	+	0.999344i	$0.488469\pi$
$374$		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	−0.372835	+	0.927898i	$0.621614\pi$
$383$	−25.4558	+	25.4558i	−1.30073	+	1.30073i	−0.927898	+	0.372835i	$0.878386\pi$
$384$		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	$-0.629037\pi$
$389$	−15.5563			−0.788738			−0.394369	+	0.918952i	$0.629037\pi$
$390$		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	$-0.584493\pi$
$397$	14.0000	−	14.0000i	0.702640	−	0.702640i	0.964976	+	0.262337i	$0.0844931\pi$
$398$		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
$405$	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	$-0.709483\pi$
$409$		−	32.0000i		−	1.58230i	0.611623	−	0.791149i	$-0.290517\pi$
$410$		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	$-0.758360\pi$
$419$	−29.6985			−1.45087			−0.725433	+	0.688293i	$0.758360\pi$
$420$		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
$423$	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	$-0.865975\pi$
$431$		−	16.9706i		−	0.817443i	0.912659	−	0.408722i	$-0.134025\pi$
$432$		0			0
$433$	7.00000	+	7.00000i	0.336399	+	0.336399i	0.855010	−	0.518611i	$-0.173551\pi$
$433$	7.00000	+	7.00000i	0.336399	+	0.336399i	−0.518611	+	0.855010i	$0.673551\pi$
$434$		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	$-0.805885\pi$
$439$		−	24.0000i		−	1.14546i	0.819745	−	0.572729i	$-0.194115\pi$
$440$		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	$-0.609358\pi$
$443$	12.7279	−	12.7279i	0.604722	−	0.604722i	0.941562	+	0.336840i	$0.109358\pi$
$444$		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	−0.851615	−	0.524168i	$-0.824376\pi$
$457$	−7.00000	+	7.00000i	−0.327446	+	0.327446i	0.524168	+	0.851615i	$0.324376\pi$
$458$		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	0.963786	−	0.266677i	$-0.0859256\pi$
$463$	15.0000	+	15.0000i	0.697109	+	0.697109i	−0.266677	+	0.963786i	$0.585926\pi$
$464$		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	$-0.160445\pi$
$467$	8.48528	+	8.48528i	0.392652	+	0.392652i	−0.482980	+	0.875632i	$0.660445\pi$
$468$		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	−0.635861	−	0.771804i	$-0.719355\pi$
$487$	3.00000	−	3.00000i	0.135943	−	0.135943i	0.771804	+	0.635861i	$0.219355\pi$
$488$		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	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		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	$-0.408976\pi$
$509$	12.7279			0.564155			0.282078	+	0.959392i	$0.408976\pi$
$510$		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	0.918994	−	0.394271i	$-0.129003\pi$
$523$	12.0000	+	12.0000i	0.524723	+	0.524723i	−0.394271	+	0.918994i	$0.629003\pi$
$524$		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	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		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	$-0.933169\pi$
$547$	−18.0000	+	18.0000i	−0.769624	+	0.769624i	0.208416	+	0.978040i	$0.433169\pi$
$548$		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	$-0.360079\pi$
$557$	−11.3137	−	11.3137i	−0.479377	−	0.479377i	−0.904932	+	0.425555i	$0.860079\pi$
$558$		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	$-0.532163\pi$
$563$	21.2132	−	21.2132i	0.894030	−	0.894030i	0.994900	+	0.100870i	$0.0321625\pi$
$564$		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	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		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	−0.595329	−	0.803482i	$-0.702978\pi$
$577$	5.00000	−	5.00000i	0.208153	−	0.208153i	0.803482	+	0.595329i	$0.202978\pi$
$578$		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	$-0.170343\pi$
$587$	8.48528	+	8.48528i	0.350225	+	0.350225i	−0.509968	+	0.860193i	$0.670343\pi$
$588$		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	$-0.995974\pi$
$593$	−24.0416	+	24.0416i	−0.987271	+	0.987271i	0.0126486	+	0.999920i	$0.495974\pi$
$594$		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	−0.500461	−	0.865759i	$-0.666836\pi$
$607$	9.00000	−	9.00000i	0.365299	−	0.365299i	0.865759	+	0.500461i	$0.166836\pi$
$608$		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	$-0.157808\pi$
$613$	10.0000	+	10.0000i	0.403896	+	0.403896i	−0.475707	+	0.879604i	$0.657808\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	26.8701	+	26.8701i	1.08175	+	1.08175i	0.996347	+	0.0854011i	$0.0272172\pi$
$617$	26.8701	+	26.8701i	1.08175	+	1.08175i	0.0854011	+	0.996347i	$0.472783\pi$
$618$		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	$-0.891214\pi$
$641$		−	16.9706i		−	0.670297i	0.942165	−	0.335148i	$-0.108786\pi$
$642$		0			0
$643$	−24.0000	−	24.0000i	−0.946468	−	0.946468i	0.0521706	−	0.998638i	$-0.483386\pi$
$643$	−24.0000	−	24.0000i	−0.946468	−	0.946468i	−0.998638	+	0.0521706i	$0.983386\pi$
$644$		0			0
$645$	−31.4558	−	9.51472i	−1.23857	−	0.374642i
$646$		0			0
$647$	16.9706	+	16.9706i	0.667182	+	0.667182i	0.957063	−	0.289881i	$-0.0936157\pi$
$647$	16.9706	+	16.9706i	0.667182	+	0.667182i	−0.289881	+	0.957063i	$0.593616\pi$
$648$		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	$-0.687313\pi$
$653$	7.07107	−	7.07107i	0.276712	−	0.276712i	0.831795	+	0.555083i	$0.187313\pi$
$654$		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	$-0.233062\pi$
$659$	38.1838			1.48743			0.743714	+	0.668498i	$0.233062\pi$
$660$		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
$663$	−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	0.462566	−	0.886585i	$-0.346929\pi$
$673$	−11.0000	−	11.0000i	−0.424019	−	0.424019i	−0.886585	+	0.462566i	$0.846929\pi$
$674$		0			0
$675$	23.7487	+	10.5355i	0.914089	+	0.405513i
$676$		0			0
$677$	26.8701	+	26.8701i	1.03270	+	1.03270i	0.999447	+	0.0332533i	$0.0105868\pi$
$677$	26.8701	+	26.8701i	1.03270	+	1.03270i	0.0332533	+	0.999447i	$0.489413\pi$
$678$		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	$-0.823736\pi$
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	0.525879	+	0.850559i	$0.323736\pi$
$684$		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	$-0.133757\pi$
$691$	48.0000			1.82601			0.913003	+	0.407953i	$0.133757\pi$
$692$		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	−0.257669	+	0.966233i	$0.582954\pi$
$727$	−33.0000	+	33.0000i	−1.22390	+	1.22390i	−0.966233	+	0.257669i	$0.917046\pi$
$728$		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	$-0.233365\pi$
$733$	2.00000	+	2.00000i	0.0738717	+	0.0738717i	−0.669206	+	0.743077i	$0.733365\pi$
$734$		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	−0.946193	−	0.323603i	$-0.895106\pi$
$743$	−16.9706	+	16.9706i	−0.622590	+	0.622590i	0.323603	+	0.946193i	$0.395106\pi$
$744$		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	$-0.982938\pi$
$757$	−26.0000	+	26.0000i	−0.944986	+	0.944986i	0.0535776	+	0.998564i	$0.482938\pi$
$758$		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
$765$	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	$-0.726528\pi$
$769$		−	42.0000i		−	1.51456i	0.653091	−	0.757279i	$-0.273472\pi$
$770$		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	$-0.510508\pi$
$773$	26.8701	−	26.8701i	0.966449	−	0.966449i	0.999455	+	0.0330063i	$0.0105082\pi$
$774$		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	$-0.543199\pi$
$787$	24.0000	−	24.0000i	0.855508	−	0.855508i	0.990805	+	0.135297i	$0.0431990\pi$
$788$		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	$-0.261277\pi$
$797$	−1.41421	−	1.41421i	−0.0500940	−	0.0500940i	−0.731710	+	0.681616i	$0.761277\pi$
$798$		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	$-0.638453\pi$
$811$	−24.0000			−0.842754			−0.421377	+	0.906886i	$0.638453\pi$
$812$		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	0.0572018	−	0.998363i	$-0.481782\pi$
$823$	−27.0000	−	27.0000i	−0.941161	−	0.941161i	−0.998363	+	0.0572018i	$0.981782\pi$
$824$		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	$-0.0753349\pi$
$827$	21.2132	+	21.2132i	0.737655	+	0.737655i	−0.234468	+	0.972124i	$0.575335\pi$
$828$		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	$-0.0712003\pi$
$853$	22.0000	+	22.0000i	0.753266	+	0.753266i	−0.221822	+	0.975087i	$0.571200\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.89949	−	9.89949i	−0.338160	−	0.338160i	0.517514	−	0.855675i	$-0.326857\pi$
$857$	−9.89949	−	9.89949i	−0.338160	−	0.338160i	−0.855675	+	0.517514i	$0.826857\pi$
$858$		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	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$		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	$-0.719552\pi$
$877$	4.00000	−	4.00000i	0.135070	−	0.135070i	0.771409	+	0.636339i	$0.219552\pi$
$878$		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	0.475749	−	0.879581i	$-0.342177\pi$
$883$	−12.0000	−	12.0000i	−0.403832	−	0.403832i	−0.879581	+	0.475749i	$0.842177\pi$
$884$		0			0
$885$	−14.4853	+	7.75736i	−0.486917	+	0.260761i
$886$		0			0
$887$	16.9706	+	16.9706i	0.569816	+	0.569816i	0.932077	−	0.362261i	$-0.117995\pi$
$887$	16.9706	+	16.9706i	0.569816	+	0.569816i	−0.362261	+	0.932077i	$0.617995\pi$
$888$		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	$-0.794991\pi$
$907$	−6.00000	+	6.00000i	−0.199227	+	0.199227i	0.600442	+	0.799668i	$0.294991\pi$
$908$		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
$915$	−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	$-0.756409\pi$
$919$		−	42.0000i		−	1.38545i	0.721201	−	0.692726i	$-0.243591\pi$
$920$		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	−0.504221	−	0.863575i	$-0.668220\pi$
$937$	11.0000	−	11.0000i	0.359354	−	0.359354i	0.863575	+	0.504221i	$0.168220\pi$
$938$		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	$-0.0879328\pi$
$947$	21.2132	+	21.2132i	0.689336	+	0.689336i	−0.272749	+	0.962085i	$0.587933\pi$
$948$		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	$-0.564367\pi$
$953$	24.0416	−	24.0416i	0.778785	−	0.778785i	0.979624	+	0.200839i	$0.0643669\pi$
$954$		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	−0.905887	−	0.423520i	$-0.860795\pi$
$967$	−15.0000	+	15.0000i	−0.482367	+	0.482367i	0.423520	+	0.905887i	$0.360795\pi$
$968$		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	0.999139	+	0.0414892i	$0.0132102\pi$
$977$	32.5269	+	32.5269i	1.04063	+	1.04063i	0.0414892	+	0.999139i	$0.486790\pi$
$978$		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	0.0862831	−	0.996271i	$-0.472501\pi$
$983$	33.9411	−	33.9411i	1.08255	−	1.08255i	0.996271	−	0.0862831i	$-0.0274990\pi$
$984$		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	$-0.534266\pi$
$997$	28.0000	−	28.0000i	0.886769	−	0.886769i	0.994211	+	0.107442i	$0.0342661\pi$
$998$		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.833.1		4
3.2	odd	2	inner	960.2.v.j.833.2		4
4.3	odd	2		960.2.v.d.833.2		4
5.2	odd	4	inner	960.2.v.j.257.2		4
8.3	odd	2		480.2.v.b.353.1	yes	4
8.5	even	2		480.2.v.a.353.2	yes	4
12.11	even	2		960.2.v.d.833.1		4
15.2	even	4	inner	960.2.v.j.257.1		4
20.7	even	4		960.2.v.d.257.1		4
24.5	odd	2		480.2.v.a.353.1	yes	4
24.11	even	2		480.2.v.b.353.2	yes	4
40.27	even	4		480.2.v.b.257.2	yes	4
40.37	odd	4		480.2.v.a.257.1	✓	4
60.47	odd	4		960.2.v.d.257.2		4
120.77	even	4		480.2.v.a.257.2	yes	4
120.107	odd	4		480.2.v.b.257.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.v.a.257.1	✓	4	40.37	odd	4
480.2.v.a.257.2	yes	4	120.77	even	4
480.2.v.a.353.1	yes	4	24.5	odd	2
480.2.v.a.353.2	yes	4	8.5	even	2
480.2.v.b.257.1	yes	4	120.107	odd	4
480.2.v.b.257.2	yes	4	40.27	even	4
480.2.v.b.353.1	yes	4	8.3	odd	2
480.2.v.b.353.2	yes	4	24.11	even	2
960.2.v.d.257.1		4	20.7	even	4
960.2.v.d.257.2		4	60.47	odd	4
960.2.v.d.833.1		4	12.11	even	2
960.2.v.d.833.2		4	4.3	odd	2
960.2.v.j.257.1		4	15.2	even	4	inner
960.2.v.j.257.2		4	5.2	odd	4	inner
960.2.v.j.833.1		4	1.1	even	1	trivial
960.2.v.j.833.2		4	3.2	odd	2	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 $\F_{q}$
Belyi maps

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more