LMFDB - Embedded newform 480.3.bg.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [480,3,Mod(97,480)]

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, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("480.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	480.bg (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:	$13.0790526893$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.443364212736.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 625 $ x^8 - x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.1
Root			$2.07011 - 0.845366i$ of defining polynomial
Character	$\chi$	$=$	480.193
Dual form			480.3.bg.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 1.22474i) q^{3} +(-0.915476 - 4.91548i) q^{5} +(-7.14143 + 7.14143i) q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 - 1.22474i) q^{3} +(-0.915476 - 4.91548i) q^{5} +(-7.14143 + 7.14143i) q^{7} +3.00000i q^{9} +12.2474 q^{11} +(-11.8310 - 11.8310i) q^{13} +(-4.89898 + 7.14143i) q^{15} +(-6.16905 + 6.16905i) q^{17} +19.1818i q^{19} +17.4929 q^{21} +(7.34847 + 7.34847i) q^{23} +(-23.3238 + 9.00000i) q^{25} +(3.67423 - 3.67423i) q^{27} +48.8167i q^{29} +19.5959 q^{31} +(-15.0000 - 15.0000i) q^{33} +(41.6413 + 28.5657i) q^{35} +(27.4929 - 27.4929i) q^{37} +28.9798i q^{39} +38.3381 q^{41} +(47.7476 + 47.7476i) q^{43} +(14.7464 - 2.74643i) q^{45} +(-36.3283 + 36.3283i) q^{47} -53.0000i q^{49} +15.1110 q^{51} +(-11.3238 - 11.3238i) q^{53} +(-11.2122 - 60.2020i) q^{55} +(23.4929 - 23.4929i) q^{57} +68.5507i q^{59} +16.9857 q^{61} +(-21.4243 - 21.4243i) q^{63} +(-47.3238 + 68.9857i) q^{65} +(-51.8184 + 51.8184i) q^{67} -18.0000i q^{69} -96.3233 q^{71} +(73.3095 + 73.3095i) q^{73} +(39.5884 + 17.5430i) q^{75} +(-87.4643 + 87.4643i) q^{77} +89.0098i q^{79} -9.00000 q^{81} +(-46.5403 - 46.5403i) q^{83} +(35.9714 + 24.6762i) q^{85} +(59.7880 - 59.7880i) q^{87} -20.6476i q^{89} +168.980 q^{91} +(-24.0000 - 24.0000i) q^{93} +(94.2879 - 17.5605i) q^{95} +(-21.6762 + 21.6762i) q^{97} +36.7423i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{5}+O(q^{10}) $ 8 * q + 16 * q^5	$ 8 q + 16 q^{5} - 48 q^{13} - 96 q^{17} - 120 q^{33} + 80 q^{37} + 400 q^{41} + 48 q^{45} + 96 q^{53} + 48 q^{57} - 144 q^{61} - 192 q^{65} + 120 q^{73} - 72 q^{81} - 272 q^{85} - 192 q^{93} - 360 q^{97}+O(q^{100}) $ 8 * q + 16 * q^5 - 48 * q^13 - 96 * q^17 - 120 * q^33 + 80 * q^37 + 400 * q^41 + 48 * q^45 + 96 * q^53 + 48 * q^57 - 144 * q^61 - 192 * q^65 + 120 * q^73 - 72 * q^81 - 272 * q^85 - 192 * q^93 - 360 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		0			0
$5$	−0.915476	−	4.91548i	−0.183095	−	0.983095i
$5$	−0.915476	−	4.91548i	−0.183095	−	0.983095i
$6$		0			0
$7$	−7.14143	+	7.14143i	−1.02020	+	1.02020i	−0.0204124	+	0.999792i	$0.506498\pi$
$7$	−7.14143	+	7.14143i	−1.02020	+	1.02020i	−0.999792	+	0.0204124i	$0.993502\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	12.2474			1.11340			0.556702	−	0.830712i	$-0.312066\pi$
$11$	12.2474			1.11340			0.556702	+	0.830712i	$0.312066\pi$
$12$		0			0
$13$	−11.8310	−	11.8310i	−0.910073	−	0.910073i	0.0862043	−	0.996277i	$-0.472526\pi$
$13$	−11.8310	−	11.8310i	−0.910073	−	0.910073i	−0.996277	+	0.0862043i	$0.972526\pi$
$14$		0			0
$15$	−4.89898	+	7.14143i	−0.326599	+	0.476095i
$16$		0			0
$17$	−6.16905	+	6.16905i	−0.362885	+	0.362885i	−0.864874	−	0.501989i	$-0.832602\pi$
$17$	−6.16905	+	6.16905i	−0.362885	+	0.362885i	0.501989	+	0.864874i	$0.332602\pi$
$18$		0			0
$19$			19.1818i			1.00957i	0.863245	+	0.504785i	$0.168428\pi$
$19$			19.1818i			1.00957i	−0.863245	+	0.504785i	$0.831572\pi$
$20$		0			0
$21$	17.4929			0.832993
$22$		0			0
$23$	7.34847	+	7.34847i	0.319499	+	0.319499i	0.848575	−	0.529076i	$-0.177461\pi$
$23$	7.34847	+	7.34847i	0.319499	+	0.319499i	−0.529076	+	0.848575i	$0.677461\pi$
$24$		0			0
$25$	−23.3238	+	9.00000i	−0.932952	+	0.360000i
$26$		0			0
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$		0			0
$29$			48.8167i			1.68333i	0.539998	+	0.841667i	$0.318425\pi$
$29$			48.8167i			1.68333i	−0.539998	+	0.841667i	$0.681575\pi$
$30$		0			0
$31$	19.5959			0.632126			0.316063	−	0.948738i	$-0.397639\pi$
$31$	19.5959			0.632126			0.316063	+	0.948738i	$0.397639\pi$
$32$		0			0
$33$	−15.0000	−	15.0000i	−0.454545	−	0.454545i
$34$		0			0
$35$	41.6413	+	28.5657i	1.18975	+	0.816163i
$36$		0			0
$37$	27.4929	−	27.4929i	0.743050	−	0.743050i	−0.230114	−	0.973164i	$-0.573910\pi$
$37$	27.4929	−	27.4929i	0.743050	−	0.743050i	0.973164	+	0.230114i	$0.0739098\pi$
$38$		0			0
$39$			28.9798i			0.743072i
$40$		0			0
$41$	38.3381			0.935076			0.467538	−	0.883973i	$-0.345141\pi$
$41$	38.3381			0.935076			0.467538	+	0.883973i	$0.345141\pi$
$42$		0			0
$43$	47.7476	+	47.7476i	1.11041	+	1.11041i	0.993095	+	0.117313i	$0.0374281\pi$
$43$	47.7476	+	47.7476i	1.11041	+	1.11041i	0.117313	+	0.993095i	$0.462572\pi$
$44$		0			0
$45$	14.7464	−	2.74643i	0.327698	−	0.0610317i
$46$		0			0
$47$	−36.3283	+	36.3283i	−0.772942	+	0.772942i	−0.978620	−	0.205678i	$-0.934060\pi$
$47$	−36.3283	+	36.3283i	−0.772942	+	0.772942i	0.205678	+	0.978620i	$0.434060\pi$
$48$		0			0
$49$		−	53.0000i		−	1.08163i
$50$		0			0
$51$	15.1110			0.296295
$52$		0			0
$53$	−11.3238	−	11.3238i	−0.213657	−	0.213657i	0.592162	−	0.805819i	$-0.298275\pi$
$53$	−11.3238	−	11.3238i	−0.213657	−	0.213657i	−0.805819	+	0.592162i	$0.798275\pi$
$54$		0			0
$55$	−11.2122	−	60.2020i	−0.203859	−	1.09458i
$56$		0			0
$57$	23.4929	−	23.4929i	0.412155	−	0.412155i
$58$		0			0
$59$			68.5507i			1.16188i	0.813948	+	0.580938i	$0.197314\pi$
$59$			68.5507i			1.16188i	−0.813948	+	0.580938i	$0.802686\pi$
$60$		0			0
$61$	16.9857			0.278454			0.139227	−	0.990260i	$-0.455538\pi$
$61$	16.9857			0.278454			0.139227	+	0.990260i	$0.455538\pi$
$62$		0			0
$63$	−21.4243	−	21.4243i	−0.340068	−	0.340068i
$64$		0			0
$65$	−47.3238	+	68.9857i	−0.728059	+	1.06132i
$66$		0			0
$67$	−51.8184	+	51.8184i	−0.773408	+	0.773408i	−0.978701	−	0.205292i	$-0.934186\pi$
$67$	−51.8184	+	51.8184i	−0.773408	+	0.773408i	0.205292	+	0.978701i	$0.434186\pi$
$68$		0			0
$69$		−	18.0000i		−	0.260870i
$70$		0			0
$71$	−96.3233			−1.35667			−0.678333	−	0.734755i	$-0.737297\pi$
$71$	−96.3233			−1.35667			−0.678333	+	0.734755i	$0.737297\pi$
$72$		0			0
$73$	73.3095	+	73.3095i	1.00424	+	1.00424i	0.999991	+	0.00424901i	$0.00135251\pi$
$73$	73.3095	+	73.3095i	1.00424	+	1.00424i	0.00424901	+	0.999991i	$0.498647\pi$
$74$		0			0
$75$	39.5884	+	17.5430i	0.527846	+	0.233907i
$76$		0			0
$77$	−87.4643	+	87.4643i	−1.13590	+	1.13590i
$78$		0			0
$79$			89.0098i			1.12671i	0.826216	+	0.563353i	$0.190489\pi$
$79$			89.0098i			1.12671i	−0.826216	+	0.563353i	$0.809511\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−46.5403	−	46.5403i	−0.560727	−	0.560727i	0.368787	−	0.929514i	$-0.379773\pi$
$83$	−46.5403	−	46.5403i	−0.560727	−	0.560727i	−0.929514	+	0.368787i	$0.879773\pi$
$84$		0			0
$85$	35.9714	+	24.6762i	0.423193	+	0.290308i
$86$		0			0
$87$	59.7880	−	59.7880i	0.687218	−	0.687218i
$88$		0			0
$89$		−	20.6476i		−	0.231996i	−0.993249	−	0.115998i	$-0.962993\pi$
$89$		−	20.6476i		−	0.231996i	0.993249	−	0.115998i	$-0.0370066\pi$
$90$		0			0
$91$	168.980			1.85692
$92$		0			0
$93$	−24.0000	−	24.0000i	−0.258065	−	0.258065i
$94$		0			0
$95$	94.2879	−	17.5605i	0.992504	−	0.184847i
$96$		0			0
$97$	−21.6762	+	21.6762i	−0.223466	+	0.223466i	−0.809956	−	0.586490i	$-0.800509\pi$
$97$	−21.6762	+	21.6762i	−0.223466	+	0.223466i	0.586490	+	0.809956i	$0.300509\pi$
$98$		0			0
$99$			36.7423i			0.371135i
$100$		0			0
$101$	−94.1119			−0.931801			−0.465900	−	0.884837i	$-0.654270\pi$
$101$	−94.1119			−0.931801			−0.465900	+	0.884837i	$0.654270\pi$
$102$		0			0
$103$	−134.101	−	134.101i	−1.30195	−	1.30195i	−0.927076	−	0.374874i	$-0.877686\pi$
$103$	−134.101	−	134.101i	−1.30195	−	1.30195i	−0.374874	−	0.927076i	$-0.622314\pi$
$104$		0			0
$105$	−16.0143	−	85.9857i	−0.152517	−	0.818912i
$106$		0			0
$107$	39.1568	−	39.1568i	0.365952	−	0.365952i	−0.500047	−	0.865998i	$-0.666684\pi$
$107$	39.1568	−	39.1568i	0.365952	−	0.365952i	0.865998	+	0.500047i	$0.166684\pi$
$108$		0			0
$109$		−	194.281i		−	1.78239i	−0.453617	−	0.891197i	$-0.649866\pi$
$109$		−	194.281i		−	1.78239i	0.453617	−	0.891197i	$-0.350134\pi$
$110$		0			0
$111$	−67.3435			−0.606698
$112$		0			0
$113$	4.50714	+	4.50714i	0.0398862	+	0.0398862i	0.726769	−	0.686882i	$-0.241021\pi$
$113$	4.50714	+	4.50714i	0.0398862	+	0.0398862i	−0.686882	+	0.726769i	$0.741021\pi$
$114$		0			0
$115$	29.3939	−	42.8486i	0.255599	−	0.372596i
$116$		0			0
$117$	35.4929	−	35.4929i	0.303358	−	0.303358i
$118$		0			0
$119$		−	88.1116i		−	0.740434i
$120$		0			0
$121$	29.0000			0.239669
$122$		0			0
$123$	−46.9544	−	46.9544i	−0.381743	−	0.381743i
$124$		0			0
$125$	65.5917	+	106.408i	0.524733	+	0.851267i
$126$		0			0
$127$	−129.616	+	129.616i	−1.02060	+	1.02060i	−0.0208144	+	0.999783i	$0.506626\pi$
$127$	−129.616	+	129.616i	−1.02060	+	1.02060i	−0.999783	+	0.0208144i	$0.993374\pi$
$128$		0			0
$129$		−	116.957i		−	0.906644i
$130$		0			0
$131$	186.954			1.42713			0.713566	−	0.700588i	$-0.247079\pi$
$131$	186.954			1.42713			0.713566	+	0.700588i	$0.247079\pi$
$132$		0			0
$133$	−136.986	−	136.986i	−1.02997	−	1.02997i
$134$		0			0
$135$	−21.4243	−	14.6969i	−0.158698	−	0.108866i
$136$		0			0
$137$	−120.450	+	120.450i	−0.879197	+	0.879197i	−0.993452	−	0.114255i	$-0.963552\pi$
$137$	−120.450	+	120.450i	−0.879197	+	0.879197i	0.114255	+	0.993452i	$0.463552\pi$
$138$		0			0
$139$		−	235.495i		−	1.69421i	−0.531426	−	0.847105i	$-0.678344\pi$
$139$		−	235.495i		−	1.69421i	0.531426	−	0.847105i	$-0.321656\pi$
$140$		0			0
$141$	88.9857			0.631104
$142$		0			0
$143$	−144.899	−	144.899i	−1.01328	−	1.01328i
$144$		0			0
$145$	239.957	−	44.6905i	1.65488	−	0.308210i
$146$		0			0
$147$	−64.9115	+	64.9115i	−0.441575	+	0.441575i
$148$		0			0
$149$			271.802i			1.82418i	0.409993	+	0.912089i	$0.365531\pi$
$149$			271.802i			1.82418i	−0.409993	+	0.912089i	$0.634469\pi$
$150$		0			0
$151$	−18.4237			−0.122011			−0.0610055	−	0.998137i	$-0.519431\pi$
$151$	−18.4237			−0.122011			−0.0610055	+	0.998137i	$0.519431\pi$
$152$		0			0
$153$	−18.5071	−	18.5071i	−0.120962	−	0.120962i
$154$		0			0
$155$	−17.9396	−	96.3233i	−0.115739	−	0.621440i
$156$		0			0
$157$	−11.5214	+	11.5214i	−0.0733849	+	0.0733849i	−0.742847	−	0.669462i	$-0.766525\pi$
$157$	−11.5214	+	11.5214i	−0.0733849	+	0.0733849i	0.669462	+	0.742847i	$0.266525\pi$
$158$		0			0
$159$			27.7376i			0.174450i
$160$		0			0
$161$	−104.957			−0.651908
$162$		0			0
$163$	−151.868	−	151.868i	−0.931708	−	0.931708i	0.0661049	−	0.997813i	$-0.478943\pi$
$163$	−151.868	−	151.868i	−0.931708	−	0.931708i	−0.997813	+	0.0661049i	$0.978943\pi$
$164$		0			0
$165$	−60.0000	+	87.4643i	−0.363636	+	0.530087i
$166$		0			0
$167$	35.0860	−	35.0860i	0.210096	−	0.210096i	−0.594212	−	0.804308i	$-0.702536\pi$
$167$	35.0860	−	35.0860i	0.210096	−	0.210096i	0.804308	+	0.594212i	$0.202536\pi$
$168$		0			0
$169$			110.943i			0.656467i
$170$		0			0
$171$	−57.5455			−0.336523
$172$		0			0
$173$	142.450	+	142.450i	0.823410	+	0.823410i	0.986595	−	0.163185i	$-0.0521768\pi$
$173$	142.450	+	142.450i	0.823410	+	0.823410i	−0.163185	+	0.986595i	$0.552177\pi$
$174$		0			0
$175$	102.292	−	230.838i	0.584528	−	1.31908i
$176$		0			0
$177$	83.9571	−	83.9571i	0.474334	−	0.474334i
$178$		0			0
$179$			240.843i			1.34549i	0.739873	+	0.672746i	$0.234885\pi$
$179$			240.843i			1.34549i	−0.739873	+	0.672746i	$0.765115\pi$
$180$		0			0
$181$	−92.3667			−0.510313			−0.255157	−	0.966900i	$-0.582127\pi$
$181$	−92.3667			−0.510313			−0.255157	+	0.966900i	$0.582127\pi$
$182$		0			0
$183$	−20.8032	−	20.8032i	−0.113678	−	0.113678i
$184$		0			0
$185$	−160.310	−	109.971i	−0.866538	−	0.594440i
$186$		0			0
$187$	−75.5551	+	75.5551i	−0.404038	+	0.404038i
$188$		0			0
$189$			52.4786i			0.277664i
$190$		0			0
$191$	−119.990			−0.628220			−0.314110	−	0.949387i	$-0.601706\pi$
$191$	−119.990			−0.628220			−0.314110	+	0.949387i	$0.601706\pi$
$192$		0			0
$193$	−21.9571	−	21.9571i	−0.113768	−	0.113768i	0.647931	−	0.761699i	$-0.275634\pi$
$193$	−21.9571	−	21.9571i	−0.113768	−	0.113768i	−0.761699	+	0.647931i	$0.775634\pi$
$194$		0			0
$195$	142.449	−	26.5303i	0.730510	−	0.136053i
$196$		0			0
$197$	197.971	−	197.971i	1.00493	−	1.00493i	0.00494330	−	0.999988i	$-0.498426\pi$
$197$	197.971	−	197.971i	1.00493	−	1.00493i	0.999988	−	0.00494330i	$-0.00157351\pi$
$198$		0			0
$199$			122.060i			0.613369i	0.951811	+	0.306684i	$0.0992196\pi$
$199$			122.060i			0.613369i	−0.951811	+	0.306684i	$0.900780\pi$
$200$		0			0
$201$	126.929			0.631485
$202$		0			0
$203$	−348.621	−	348.621i	−1.71734	−	1.71734i
$204$		0			0
$205$	−35.0976	−	188.450i	−0.171208	−	0.919268i
$206$		0			0
$207$	−22.0454	+	22.0454i	−0.106500	+	0.106500i
$208$		0			0
$209$			234.929i			1.12406i
$210$		0			0
$211$	−86.8694			−0.411703			−0.205852	−	0.978583i	$-0.565996\pi$
$211$	−86.8694			−0.411703			−0.205852	+	0.978583i	$0.565996\pi$
$212$		0			0
$213$	117.971	+	117.971i	0.553856	+	0.553856i
$214$		0			0
$215$	190.990	−	278.414i	0.888327	−	1.29495i
$216$		0			0
$217$	−139.943	+	139.943i	−0.644898	+	0.644898i
$218$		0			0
$219$		−	179.571i		−	0.819959i
$220$		0			0
$221$	145.971			0.660504
$222$		0			0
$223$	85.5251	+	85.5251i	0.383521	+	0.383521i	0.872369	−	0.488848i	$-0.162583\pi$
$223$	85.5251	+	85.5251i	0.383521	+	0.383521i	−0.488848	+	0.872369i	$0.662583\pi$
$224$		0			0
$225$	−27.0000	−	69.9714i	−0.120000	−	0.310984i
$226$		0			0
$227$	−155.939	+	155.939i	−0.686957	+	0.686957i	−0.961558	−	0.274601i	$-0.911454\pi$
$227$	−155.939	+	155.939i	−0.686957	+	0.686957i	0.274601	+	0.961558i	$0.411454\pi$
$228$		0			0
$229$		−	339.971i		−	1.48459i	−0.670072	−	0.742296i	$-0.733737\pi$
$229$		−	339.971i		−	1.48459i	0.670072	−	0.742296i	$-0.266263\pi$
$230$		0			0
$231$	214.243			0.927458
$232$		0			0
$233$	−14.1119	−	14.1119i	−0.0605661	−	0.0605661i	0.676175	−	0.736741i	$-0.263636\pi$
$233$	−14.1119	−	14.1119i	−0.0605661	−	0.0605661i	−0.736741	+	0.676175i	$0.763636\pi$
$234$		0			0
$235$	211.828	+	145.313i	0.901397	+	0.618353i
$236$		0			0
$237$	109.014	−	109.014i	0.459976	−	0.459976i
$238$		0			0
$239$			332.302i			1.39039i	0.718823	+	0.695193i	$0.244681\pi$
$239$			332.302i			1.39039i	−0.718823	+	0.695193i	$0.755319\pi$
$240$		0			0
$241$	69.9714			0.290338			0.145169	−	0.989407i	$-0.453627\pi$
$241$	69.9714			0.290338			0.145169	+	0.989407i	$0.453627\pi$
$242$		0			0
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−260.520	+	48.5202i	−1.06335	+	0.198042i
$246$		0			0
$247$	226.939	−	226.939i	0.918783	−	0.918783i
$248$		0			0
$249$			114.000i			0.457831i
$250$		0			0
$251$	341.237			1.35951			0.679755	−	0.733439i	$-0.262086\pi$
$251$	341.237			1.35951			0.679755	+	0.733439i	$0.262086\pi$
$252$		0			0
$253$	90.0000	+	90.0000i	0.355731	+	0.355731i
$254$		0			0
$255$	−13.8338	−	74.2779i	−0.0542501	−	0.291286i
$256$		0			0
$257$	96.4500	−	96.4500i	0.375292	−	0.375292i	−0.494108	−	0.869400i	$-0.664505\pi$
$257$	96.4500	−	96.4500i	0.375292	−	0.375292i	0.869400	+	0.494108i	$0.164505\pi$
$258$		0			0
$259$			392.677i			1.51613i
$260$		0			0
$261$	−146.450			−0.561111
$262$		0			0
$263$	257.885	+	257.885i	0.980550	+	0.980550i	0.999814	−	0.0192647i	$-0.00613251\pi$
$263$	257.885	+	257.885i	0.980550	+	0.980550i	−0.0192647	+	0.999814i	$0.506133\pi$
$264$		0			0
$265$	−45.2952	+	66.0286i	−0.170925	+	0.249164i
$266$		0			0
$267$	−25.2881	+	25.2881i	−0.0947118	+	0.0947118i
$268$		0			0
$269$			141.831i			0.527253i	0.964625	+	0.263626i	$0.0849186\pi$
$269$			141.831i			0.527253i	−0.964625	+	0.263626i	$0.915081\pi$
$270$		0			0
$271$	−9.31388			−0.0343686			−0.0171843	−	0.999852i	$-0.505470\pi$
$271$	−9.31388			−0.0343686			−0.0171843	+	0.999852i	$0.505470\pi$
$272$		0			0
$273$	−206.957	−	206.957i	−0.758085	−	0.758085i
$274$		0			0
$275$	−285.657	+	110.227i	−1.03875	+	0.400826i
$276$		0			0
$277$	196.055	−	196.055i	0.707779	−	0.707779i	−0.258289	−	0.966068i	$-0.583159\pi$
$277$	196.055	−	196.055i	0.707779	−	0.707779i	0.966068	+	0.258289i	$0.0831586\pi$
$278$		0			0
$279$			58.7878i			0.210709i
$280$		0			0
$281$	−6.39525			−0.0227589			−0.0113794	−	0.999935i	$-0.503622\pi$
$281$	−6.39525			−0.0227589			−0.0113794	+	0.999935i	$0.503622\pi$
$282$		0			0
$283$	−310.636	−	310.636i	−1.09765	−	1.09765i	−0.994685	−	0.102970i	$-0.967166\pi$
$283$	−310.636	−	310.636i	−1.09765	−	1.09765i	−0.102970	−	0.994685i	$-0.532834\pi$
$284$		0			0
$285$	−136.986	−	93.9714i	−0.480652	−	0.329724i
$286$		0			0
$287$	−273.789	+	273.789i	−0.953968	+	0.953968i
$288$		0			0
$289$			212.886i			0.736629i
$290$		0			0
$291$	53.0956			0.182459
$292$		0			0
$293$	−88.9571	−	88.9571i	−0.303608	−	0.303608i	0.538816	−	0.842424i	$-0.318872\pi$
$293$	−88.9571	−	88.9571i	−0.303608	−	0.303608i	−0.842424	+	0.538816i	$0.818872\pi$
$294$		0			0
$295$	336.959	−	62.7565i	1.14224	−	0.212734i
$296$		0			0
$297$	45.0000	−	45.0000i	0.151515	−	0.151515i
$298$		0			0
$299$		−	173.879i		−	0.581534i
$300$		0			0
$301$	−681.971			−2.26569
$302$		0			0
$303$	115.263	+	115.263i	0.380406	+	0.380406i
$304$		0			0
$305$	−15.5500	−	83.4929i	−0.0509836	−	0.273747i
$306$		0			0
$307$	−142.484	+	142.484i	−0.464119	+	0.464119i	−0.900003	−	0.435884i	$-0.856436\pi$
$307$	−142.484	+	142.484i	−0.464119	+	0.464119i	0.435884	+	0.900003i	$0.356436\pi$
$308$		0			0
$309$			328.479i			1.06304i
$310$		0			0
$311$	222.040			0.713956			0.356978	−	0.934113i	$-0.383807\pi$
$311$	222.040			0.713956			0.356978	+	0.934113i	$0.383807\pi$
$312$		0			0
$313$	275.929	+	275.929i	0.881561	+	0.881561i	0.993693	−	0.112132i	$-0.0357681\pi$
$313$	275.929	+	275.929i	0.881561	+	0.881561i	−0.112132	+	0.993693i	$0.535768\pi$
$314$		0			0
$315$	−85.6971	+	124.924i	−0.272054	+	0.396584i
$316$		0			0
$317$	−230.112	+	230.112i	−0.725905	+	0.725905i	−0.969801	−	0.243896i	$-0.921574\pi$
$317$	−230.112	+	230.112i	−0.725905	+	0.725905i	0.243896	+	0.969801i	$0.421574\pi$
$318$		0			0
$319$			597.880i			1.87423i
$320$		0			0
$321$	−95.9143			−0.298798
$322$		0			0
$323$	−118.334	−	118.334i	−0.366358	−	0.366358i
$324$		0			0
$325$	382.421	+	169.464i	1.17668	+	0.521429i
$326$		0			0
$327$	−237.945	+	237.945i	−0.727659	+	0.727659i
$328$		0			0
$329$		−	518.871i		−	1.57712i
$330$		0			0
$331$	−6.07122			−0.0183421			−0.00917103	−	0.999958i	$-0.502919\pi$
$331$	−6.07122			−0.0183421			−0.00917103	+	0.999958i	$0.502919\pi$
$332$		0			0
$333$	82.4786	+	82.4786i	0.247683	+	0.247683i
$334$		0			0
$335$	302.150	+	207.273i	0.901941	+	0.618727i
$336$		0			0
$337$	−190.605	+	190.605i	−0.565593	+	0.565593i	−0.930891	−	0.365298i	$-0.880967\pi$
$337$	−190.605	+	190.605i	−0.565593	+	0.565593i	0.365298	+	0.930891i	$0.380967\pi$
$338$		0			0
$339$		−	11.0402i		−	0.0325670i
$340$		0			0
$341$	240.000			0.703812
$342$		0			0
$343$	28.5657	+	28.5657i	0.0832820	+	0.0832820i
$344$		0			0
$345$	−88.4786	+	16.4786i	−0.256460	+	0.0477640i
$346$		0			0
$347$	−111.848	+	111.848i	−0.322330	+	0.322330i	−0.849660	−	0.527331i	$-0.823193\pi$
$347$	−111.848	+	111.848i	−0.322330	+	0.322330i	0.527331	+	0.849660i	$0.323193\pi$
$348$		0			0
$349$		−	250.900i		−	0.718911i	−0.933162	−	0.359456i	$-0.882962\pi$
$349$		−	250.900i		−	0.718911i	0.933162	−	0.359456i	$-0.117038\pi$
$350$		0			0
$351$	−86.9394			−0.247691
$352$		0			0
$353$	−162.845	−	162.845i	−0.461318	−	0.461318i	0.437769	−	0.899087i	$-0.355769\pi$
$353$	−162.845	−	162.845i	−0.461318	−	0.461318i	−0.899087	+	0.437769i	$0.855769\pi$
$354$		0			0
$355$	88.1816	+	473.475i	0.248399	+	1.33373i
$356$		0			0
$357$	−107.914	+	107.914i	−0.302281	+	0.302281i
$358$		0			0
$359$			359.142i			1.00040i	0.865911	+	0.500198i	$0.166739\pi$
$359$			359.142i			1.00040i	−0.865911	+	0.500198i	$0.833261\pi$
$360$		0			0
$361$	−6.94285			−0.0192323
$362$		0			0
$363$	−35.5176	−	35.5176i	−0.0978446	−	0.0978446i
$364$		0			0
$365$	293.238	−	427.464i	0.803392	−	1.17114i
$366$		0			0
$367$	116.161	−	116.161i	0.316516	−	0.316516i	−0.530912	−	0.847427i	$-0.678150\pi$
$367$	116.161	−	116.161i	0.316516	−	0.316516i	0.847427	+	0.530912i	$0.178150\pi$
$368$		0			0
$369$			115.014i			0.311692i
$370$		0			0
$371$	161.736			0.435947
$372$		0			0
$373$	298.507	+	298.507i	0.800287	+	0.800287i	0.983140	−	0.182853i	$-0.0585332\pi$
$373$	298.507	+	298.507i	0.800287	+	0.800287i	−0.182853	+	0.983140i	$0.558533\pi$
$374$		0			0
$375$	49.9900	−	210.656i	0.133307	−	0.561750i
$376$		0			0
$377$	577.548	−	577.548i	1.53196	−	1.53196i
$378$		0			0
$379$		−	269.030i		−	0.709841i	−0.934896	−	0.354921i	$-0.884508\pi$
$379$		−	269.030i		−	0.709841i	0.934896	−	0.354921i	$-0.115492\pi$
$380$		0			0
$381$	317.493			0.833315
$382$		0			0
$383$	243.742	+	243.742i	0.636401	+	0.636401i	0.949666	−	0.313265i	$-0.101423\pi$
$383$	243.742	+	243.742i	0.636401	+	0.636401i	−0.313265	+	0.949666i	$0.601423\pi$
$384$		0			0
$385$	510.000	+	349.857i	1.32468	+	0.908720i
$386$		0			0
$387$	−143.243	+	143.243i	−0.370136	+	0.370136i
$388$		0			0
$389$			40.1976i			0.103336i	0.998664	+	0.0516679i	$0.0164537\pi$
$389$			40.1976i			0.103336i	−0.998664	+	0.0516679i	$0.983546\pi$
$390$		0			0
$391$	−90.6661			−0.231883
$392$		0			0
$393$	−228.971	−	228.971i	−0.582624	−	0.582624i
$394$		0			0
$395$	437.526	−	81.4863i	1.10766	−	0.206294i
$396$		0			0
$397$	−345.436	+	345.436i	−0.870115	+	0.870115i	−0.992485	−	0.122369i	$-0.960951\pi$
$397$	−345.436	+	345.436i	−0.870115	+	0.870115i	0.122369	+	0.992485i	$0.460951\pi$
$398$		0			0
$399$			335.545i			0.840965i
$400$		0			0
$401$	0.647615			0.00161500			0.000807500	−	1.00000i	$-0.499743\pi$
$401$	0.647615			0.00161500			0.000807500		1.00000i	$0.499743\pi$
$402$		0			0
$403$	−231.838	−	231.838i	−0.575281	−	0.575281i
$404$		0			0
$405$	8.23928	+	44.2393i	0.0203439	+	0.109233i
$406$		0			0
$407$	336.717	−	336.717i	0.827315	−	0.827315i
$408$		0			0
$409$		−	554.533i		−	1.35583i	−0.735142	−	0.677914i	$-0.762884\pi$
$409$		−	554.533i		−	1.35583i	0.735142	−	0.677914i	$-0.237116\pi$
$410$		0			0
$411$	295.041			0.717861
$412$		0			0
$413$	−489.550	−	489.550i	−1.18535	−	1.18535i
$414$		0			0
$415$	−186.161	+	271.374i	−0.448581	+	0.653914i
$416$		0			0
$417$	−288.421	+	288.421i	−0.691658	+	0.691658i
$418$		0			0
$419$		−	271.065i		−	0.646934i	−0.946240	−	0.323467i	$-0.895152\pi$
$419$		−	271.065i		−	0.646934i	0.946240	−	0.323467i	$-0.104848\pi$
$420$		0			0
$421$	−145.943			−0.346658			−0.173329	−	0.984864i	$-0.555452\pi$
$421$	−145.943			−0.346658			−0.173329	+	0.984864i	$0.555452\pi$
$422$		0			0
$423$	−108.985	−	108.985i	−0.257647	−	0.257647i
$424$		0			0
$425$	88.3643	−	199.407i	0.207916	−	0.469193i
$426$		0			0
$427$	−121.302	+	121.302i	−0.284080	+	0.284080i
$428$		0			0
$429$			354.929i			0.827339i
$430$		0			0
$431$	−159.322			−0.369656			−0.184828	−	0.982771i	$-0.559173\pi$
$431$	−159.322			−0.369656			−0.184828	+	0.982771i	$0.559173\pi$
$432$		0			0
$433$	397.843	+	397.843i	0.918806	+	0.918806i	0.996943	−	0.0781370i	$-0.0248972\pi$
$433$	397.843	+	397.843i	0.918806	+	0.918806i	−0.0781370	+	0.996943i	$0.524897\pi$
$434$		0			0
$435$	−348.621	−	239.152i	−0.801427	−	0.549774i
$436$		0			0
$437$	−140.957	+	140.957i	−0.322556	+	0.322556i
$438$		0			0
$439$			137.656i			0.313566i	0.987633	+	0.156783i	$0.0501123\pi$
$439$			137.656i			0.313566i	−0.987633	+	0.156783i	$0.949888\pi$
$440$		0			0
$441$	159.000			0.360544
$442$		0			0
$443$	360.728	+	360.728i	0.814285	+	0.814285i	0.985273	−	0.170988i	$-0.0546960\pi$
$443$	360.728	+	360.728i	0.814285	+	0.814285i	−0.170988	+	0.985273i	$0.554696\pi$
$444$		0			0
$445$	−101.493	+	18.9024i	−0.228074	+	0.0424773i
$446$		0			0
$447$	332.889	−	332.889i	0.744717	−	0.744717i
$448$		0			0
$449$			153.776i			0.342486i	0.985229	+	0.171243i	$0.0547783\pi$
$449$			153.776i			0.342486i	−0.985229	+	0.171243i	$0.945222\pi$
$450$		0			0
$451$	469.544			1.04112
$452$		0			0
$453$	22.5643	+	22.5643i	0.0498108	+	0.0498108i
$454$		0			0
$455$	−154.697	−	830.616i	−0.339993	−	1.82553i
$456$		0			0
$457$	−626.238	+	626.238i	−1.37032	+	1.37032i	−0.510368	+	0.859956i	$0.670491\pi$
$457$	−626.238	+	626.238i	−1.37032	+	1.37032i	−0.859956	+	0.510368i	$0.829509\pi$
$458$		0			0
$459$			45.3331i			0.0987648i
$460$		0			0
$461$	566.731			1.22935			0.614676	−	0.788780i	$-0.289287\pi$
$461$	566.731			1.22935			0.614676	+	0.788780i	$0.289287\pi$
$462$		0			0
$463$	403.131	+	403.131i	0.870692	+	0.870692i	0.992548	−	0.121855i	$-0.0388844\pi$
$463$	403.131	+	403.131i	0.870692	+	0.870692i	−0.121855	+	0.992548i	$0.538884\pi$
$464$		0			0
$465$	−96.0000	+	139.943i	−0.206452	+	0.300952i
$466$		0			0
$467$	−465.298	+	465.298i	−0.996356	+	0.996356i	−0.999993	−	0.00363781i	$-0.998842\pi$
$467$	−465.298	+	465.298i	−0.996356	+	0.996356i	0.00363781	+	0.999993i	$0.498842\pi$
$468$		0			0
$469$		−	740.114i		−	1.57807i
$470$		0			0
$471$	28.2216			0.0599185
$472$		0			0
$473$	584.786	+	584.786i	1.23633	+	1.23633i
$474$		0			0
$475$	−172.637	−	447.393i	−0.363445	−	0.941881i
$476$		0			0
$477$	33.9714	−	33.9714i	0.0712189	−	0.0712189i
$478$		0			0
$479$		−	411.374i		−	0.858819i	−0.903110	−	0.429409i	$-0.858722\pi$
$479$		−	411.374i		−	0.858819i	0.903110	−	0.429409i	$-0.141278\pi$
$480$		0			0
$481$	−650.533			−1.35246
$482$		0			0
$483$	128.546	+	128.546i	0.266140	+	0.266140i
$484$		0			0
$485$	126.393	+	86.7048i	0.260604	+	0.178773i
$486$		0			0
$487$	356.141	−	356.141i	0.731296	−	0.731296i	−0.239580	−	0.970877i	$-0.577010\pi$
$487$	356.141	−	356.141i	0.731296	−	0.731296i	0.970877	+	0.239580i	$0.0770099\pi$
$488$		0			0
$489$			372.000i			0.760736i
$490$		0			0
$491$	−613.924			−1.25035			−0.625177	−	0.780483i	$-0.714973\pi$
$491$	−613.924			−1.25035			−0.625177	+	0.780483i	$0.714973\pi$
$492$		0			0
$493$	−301.152	−	301.152i	−0.610857	−	0.610857i
$494$		0			0
$495$	180.606	−	33.6367i	0.364861	−	0.0679530i
$496$		0			0
$497$	687.886	−	687.886i	1.38408	−	1.38408i
$498$		0			0
$499$			5.38306i			0.0107877i	0.999985	+	0.00539385i	$0.00171692\pi$
$499$			5.38306i			0.0107877i	−0.999985	+	0.00539385i	$0.998283\pi$
$500$		0			0
$501$	−85.9428			−0.171543
$502$		0			0
$503$	−333.440	−	333.440i	−0.662902	−	0.662902i	0.293161	−	0.956063i	$-0.405293\pi$
$503$	−333.440	−	333.440i	−0.662902	−	0.662902i	−0.956063	+	0.293161i	$0.905293\pi$
$504$		0			0
$505$	86.1572	+	462.605i	0.170608	+	0.916049i
$506$		0			0
$507$	135.877	−	135.877i	0.268001	−	0.268001i
$508$		0			0
$509$		−	107.802i		−	0.211792i	−0.994377	−	0.105896i	$-0.966229\pi$
$509$		−	107.802i		−	0.211792i	0.994377	−	0.105896i	$-0.0337711\pi$
$510$		0			0
$511$	−1047.07			−2.04906
$512$		0			0
$513$	70.4786	+	70.4786i	0.137385	+	0.137385i
$514$		0			0
$515$	−536.403	+	781.935i	−1.04156	+	1.51832i
$516$		0			0
$517$	−444.929	+	444.929i	−0.860597	+	0.860597i
$518$		0			0
$519$		−	348.930i		−	0.672312i
$520$		0			0
$521$	−213.776			−0.410319			−0.205160	−	0.978729i	$-0.565771\pi$
$521$	−213.776			−0.410319			−0.205160	+	0.978729i	$0.565771\pi$
$522$		0			0
$523$	−344.929	−	344.929i	−0.659520	−	0.659520i	0.295746	−	0.955266i	$-0.404432\pi$
$523$	−344.929	−	344.929i	−0.659520	−	0.659520i	−0.955266	+	0.295746i	$0.904432\pi$
$524$		0			0
$525$	−408.000	+	157.436i	−0.777143	+	0.299878i
$526$		0			0
$527$	−120.888	+	120.888i	−0.229389	+	0.229389i
$528$		0			0
$529$		−	421.000i		−	0.795841i
$530$		0			0
$531$	−205.652			−0.387292
$532$		0			0
$533$	−453.576	−	453.576i	−0.850987	−	0.850987i
$534$		0			0
$535$	−228.322	−	156.627i	−0.426769	−	0.292761i
$536$		0			0
$537$	294.971	−	294.971i	0.549295	−	0.549295i
$538$		0			0
$539$		−	649.115i		−	1.20429i
$540$		0			0
$541$	582.338			1.07641			0.538205	−	0.842814i	$-0.319103\pi$
$541$	582.338			1.07641			0.538205	+	0.842814i	$0.319103\pi$
$542$		0			0
$543$	113.126	+	113.126i	0.208334	+	0.208334i
$544$		0			0
$545$	−954.983	+	177.860i	−1.75226	+	0.326348i
$546$		0			0
$547$	483.757	−	483.757i	0.884382	−	0.884382i	−0.109595	−	0.993976i	$-0.534955\pi$
$547$	483.757	−	483.757i	0.884382	−	0.884382i	0.993976	+	0.109595i	$0.0349553\pi$
$548$		0			0
$549$			50.9571i			0.0928181i
$550$		0			0
$551$	−936.393			−1.69944
$552$		0			0
$553$	−635.657	−	635.657i	−1.14947	−	1.14947i
$554$		0			0
$555$	61.6513	+	331.025i	0.111083	+	0.596442i
$556$		0			0
$557$	608.448	−	608.448i	1.09237	−	1.09237i	0.0970899	−	0.995276i	$-0.469047\pi$
$557$	608.448	−	608.448i	1.09237	−	1.09237i	0.995276	−	0.0970899i	$-0.0309534\pi$
$558$		0			0
$559$		−	1129.80i		−	2.02111i
$560$		0			0
$561$	185.071			0.329896
$562$		0			0
$563$	−311.808	−	311.808i	−0.553834	−	0.553834i	0.373711	−	0.927545i	$-0.378085\pi$
$563$	−311.808	−	311.808i	−0.553834	−	0.553834i	−0.927545	+	0.373711i	$0.878085\pi$
$564$		0			0
$565$	18.0286	−	26.2809i	0.0319090	−	0.0465149i
$566$		0			0
$567$	64.2729	−	64.2729i	0.113356	−	0.113356i
$568$		0			0
$569$		−	585.324i		−	1.02869i	−0.857584	−	0.514344i	$-0.828035\pi$
$569$		−	585.324i		−	1.02869i	0.857584	−	0.514344i	$-0.171965\pi$
$570$		0			0
$571$	1050.86			1.84039			0.920193	−	0.391465i	$-0.128032\pi$
$571$	1050.86			1.84039			0.920193	+	0.391465i	$0.128032\pi$
$572$		0			0
$573$	146.957	+	146.957i	0.256470	+	0.256470i
$574$		0			0
$575$	−237.531	−	105.258i	−0.413097	−	0.183057i
$576$		0			0
$577$	424.829	−	424.829i	0.736271	−	0.736271i	−0.235583	−	0.971854i	$-0.575700\pi$
$577$	424.829	−	424.829i	0.736271	−	0.736271i	0.971854	+	0.235583i	$0.0756999\pi$
$578$		0			0
$579$			53.7838i			0.0928908i
$580$		0			0
$581$	664.729			1.14411
$582$		0			0
$583$	−138.688	−	138.688i	−0.237886	−	0.237886i
$584$		0			0
$585$	−206.957	−	141.971i	−0.353773	−	0.242686i
$586$		0			0
$587$	599.915	−	599.915i	1.02200	−	1.02200i	0.0222492	−	0.999752i	$-0.492917\pi$
$587$	599.915	−	599.915i	1.02200	−	1.02200i	0.999752	−	0.0222492i	$-0.00708273\pi$
$588$		0			0
$589$			375.886i			0.638176i
$590$		0			0
$591$	−484.929			−0.820523
$592$		0			0
$593$	−508.336	−	508.336i	−0.857227	−	0.857227i	0.133783	−	0.991011i	$-0.457287\pi$
$593$	−508.336	−	508.336i	−0.857227	−	0.857227i	−0.991011	+	0.133783i	$0.957287\pi$
$594$		0			0
$595$	−433.111	+	80.6641i	−0.727917	+	0.135570i
$596$		0			0
$597$	149.493	−	149.493i	0.250407	−	0.250407i
$598$		0			0
$599$			263.647i			0.440145i	0.975484	+	0.220072i	$0.0706294\pi$
$599$			263.647i			0.440145i	−0.975484	+	0.220072i	$0.929371\pi$
$600$		0			0
$601$	−1015.86			−1.69028			−0.845139	−	0.534547i	$-0.820482\pi$
$601$	−1015.86			−1.69028			−0.845139	+	0.534547i	$0.820482\pi$
$602$		0			0
$603$	−155.455	−	155.455i	−0.257803	−	0.257803i
$604$		0			0
$605$	−26.5488	−	142.549i	−0.0438823	−	0.235618i
$606$		0			0
$607$	−502.697	+	502.697i	−0.828166	+	0.828166i	−0.987263	−	0.159097i	$-0.949142\pi$
$607$	−502.697	+	502.697i	−0.828166	+	0.828166i	0.159097	+	0.987263i	$0.449142\pi$
$608$		0			0
$609$			853.943i			1.40221i
$610$		0			0
$611$	859.596			1.40687
$612$		0			0
$613$	835.236	+	835.236i	1.36254	+	1.36254i	0.870670	+	0.491868i	$0.163686\pi$
$613$	835.236	+	835.236i	1.36254	+	1.36254i	0.491868	+	0.870670i	$0.336314\pi$
$614$		0			0
$615$	−187.818	+	273.789i	−0.305394	+	0.445185i
$616$		0			0
$617$	33.8881	−	33.8881i	0.0549240	−	0.0549240i	−0.679111	−	0.734035i	$-0.737635\pi$
$617$	33.8881	−	33.8881i	0.0549240	−	0.0549240i	0.734035	+	0.679111i	$0.237635\pi$
$618$		0			0
$619$		−	626.725i		−	1.01248i	−0.862393	−	0.506240i	$-0.831035\pi$
$619$		−	626.725i		−	1.01248i	0.862393	−	0.506240i	$-0.168965\pi$
$620$		0			0
$621$	54.0000			0.0869565
$622$		0			0
$623$	147.453	+	147.453i	0.236683	+	0.236683i
$624$		0			0
$625$	463.000	−	419.829i	0.740800	−	0.671726i
$626$		0			0
$627$	287.728	−	287.728i	0.458896	−	0.458896i
$628$		0			0
$629$			339.209i			0.539284i
$630$		0			0
$631$	28.4257			0.0450487			0.0225243	−	0.999746i	$-0.492830\pi$
$631$	28.4257			0.0450487			0.0225243	+	0.999746i	$0.492830\pi$
$632$		0			0
$633$	106.393	+	106.393i	0.168077	+	0.168077i
$634$		0			0
$635$	755.784	+	518.464i	1.19021	+	0.816478i
$636$		0			0
$637$	−627.040	+	627.040i	−0.984365	+	0.984365i
$638$		0			0
$639$		−	288.970i		−	0.452222i
$640$		0			0
$641$	914.562			1.42677			0.713387	−	0.700770i	$-0.247160\pi$
$641$	914.562			1.42677			0.713387	+	0.700770i	$0.247160\pi$
$642$		0			0
$643$	670.950	+	670.950i	1.04347	+	1.04347i	0.999011	+	0.0444571i	$0.0141558\pi$
$643$	670.950	+	670.950i	1.04347	+	1.04347i	0.0444571	+	0.999011i	$0.485844\pi$
$644$		0			0
$645$	−574.900	+	107.071i	−0.891318	+	0.166002i
$646$		0			0
$647$	473.854	−	473.854i	0.732386	−	0.732386i	−0.238706	−	0.971092i	$-0.576723\pi$
$647$	473.854	−	473.854i	0.732386	−	0.732386i	0.971092	+	0.238706i	$0.0767232\pi$
$648$		0			0
$649$			839.571i			1.29364i
$650$		0			0
$651$	342.789			0.526557
$652$		0			0
$653$	−90.8452	−	90.8452i	−0.139120	−	0.139120i	0.634117	−	0.773237i	$-0.281364\pi$
$653$	−90.8452	−	90.8452i	−0.139120	−	0.139120i	−0.773237	+	0.634117i	$0.781364\pi$
$654$		0			0
$655$	−171.152	−	918.970i	−0.261301	−	1.40301i
$656$		0			0
$657$	−219.929	+	219.929i	−0.334747	+	0.334747i
$658$		0			0
$659$		−	961.471i		−	1.45899i	−0.683989	−	0.729493i	$-0.739756\pi$
$659$		−	961.471i		−	1.45899i	0.683989	−	0.729493i	$-0.260244\pi$
$660$		0			0
$661$	−183.129			−0.277048			−0.138524	−	0.990359i	$-0.544236\pi$
$661$	−183.129			−0.277048			−0.138524	+	0.990359i	$0.544236\pi$
$662$		0			0
$663$	−178.778	−	178.778i	−0.269650	−	0.269650i
$664$		0			0
$665$	−547.943	+	798.757i	−0.823974	+	1.20114i
$666$		0			0
$667$	−358.728	+	358.728i	−0.537823	+	0.537823i
$668$		0			0
$669$		−	209.493i		−	0.313143i
$670$		0			0
$671$	208.032			0.310032
$672$		0			0
$673$	−74.1286	−	74.1286i	−0.110147	−	0.110147i	0.649886	−	0.760032i	$-0.274817\pi$
$673$	−74.1286	−	74.1286i	−0.110147	−	0.110147i	−0.760032	+	0.649886i	$0.774817\pi$
$674$		0			0
$675$	−52.6290	+	118.765i	−0.0779689	+	0.175949i
$676$		0			0
$677$	−157.945	+	157.945i	−0.233302	+	0.233302i	−0.814069	−	0.580768i	$-0.802752\pi$
$677$	−157.945	+	157.945i	−0.233302	+	0.233302i	0.580768	+	0.814069i	$0.302752\pi$
$678$		0			0
$679$		−	309.598i		−	0.455962i
$680$		0			0
$681$	381.971			0.560898
$682$		0			0
$683$	143.762	+	143.762i	0.210486	+	0.210486i	0.804474	−	0.593988i	$-0.202447\pi$
$683$	143.762	+	143.762i	0.210486	+	0.210486i	−0.593988	+	0.804474i	$0.702447\pi$
$684$		0			0
$685$	702.338	+	481.800i	1.02531	+	0.703358i
$686$		0			0
$687$	−416.378	+	416.378i	−0.606082	+	0.606082i
$688$		0			0
$689$			267.943i			0.388887i
$690$		0			0
$691$	−624.171			−0.903286			−0.451643	−	0.892199i	$-0.649162\pi$
$691$	−624.171			−0.903286			−0.451643	+	0.892199i	$0.649162\pi$
$692$		0			0
$693$	−262.393	−	262.393i	−0.378633	−	0.378633i
$694$		0			0
$695$	−1157.57	+	215.590i	−1.66557	+	0.310202i
$696$		0			0
$697$	−236.510	+	236.510i	−0.339325	+	0.339325i
$698$		0			0
$699$			34.5669i			0.0494520i
$700$		0			0
$701$	151.298			0.215831			0.107916	−	0.994160i	$-0.465582\pi$
$701$	151.298			0.215831			0.107916	+	0.994160i	$0.465582\pi$
$702$		0			0
$703$	527.363	+	527.363i	0.750161	+	0.750161i
$704$		0			0
$705$	−81.4643	−	437.407i	−0.115552	−	0.620436i
$706$		0			0
$707$	672.093	−	672.093i	0.950627	−	0.950627i
$708$		0			0
$709$		−	731.914i		−	1.03232i	−0.856492	−	0.516160i	$-0.827361\pi$
$709$		−	731.914i		−	1.03232i	0.856492	−	0.516160i	$-0.172639\pi$
$710$		0			0
$711$	−267.029			−0.375569
$712$		0			0
$713$	144.000	+	144.000i	0.201964	+	0.201964i
$714$		0			0
$715$	−579.596	+	844.899i	−0.810624	+	1.18168i
$716$		0			0
$717$	406.986	−	406.986i	0.567623	−	0.567623i
$718$		0			0
$719$			263.577i			0.366588i	0.983058	+	0.183294i	$0.0586760\pi$
$719$			263.577i			0.366588i	−0.983058	+	0.183294i	$0.941324\pi$
$720$		0			0
$721$	1915.34			2.65651
$722$		0			0
$723$	−85.6971	−	85.6971i	−0.118530	−	0.118530i
$724$		0			0
$725$	−439.350	−	1138.59i	−0.606000	−	1.57047i
$726$		0			0
$727$	11.8363	−	11.8363i	0.0162811	−	0.0162811i	−0.698919	−	0.715200i	$-0.746335\pi$
$727$	11.8363	−	11.8363i	0.0162811	−	0.0162811i	0.715200	+	0.698919i	$0.246335\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−589.114			−0.805901
$732$		0			0
$733$	−172.055	−	172.055i	−0.234727	−	0.234727i	0.579936	−	0.814662i	$-0.303078\pi$
$733$	−172.055	−	172.055i	−0.234727	−	0.234727i	−0.814662	+	0.579936i	$0.803078\pi$
$734$		0			0
$735$	378.496	+	259.646i	0.514960	+	0.353260i
$736$		0			0
$737$	−634.643	+	634.643i	−0.861116	+	0.861116i
$738$		0			0
$739$			542.194i			0.733687i	0.930283	+	0.366843i	$0.119562\pi$
$739$			542.194i			0.733687i	−0.930283	+	0.366843i	$0.880438\pi$
$740$		0			0
$741$	−555.886			−0.750183
$742$		0			0
$743$	247.883	+	247.883i	0.333624	+	0.333624i	0.853961	−	0.520337i	$-0.174194\pi$
$743$	247.883	+	247.883i	0.333624	+	0.333624i	−0.520337	+	0.853961i	$0.674194\pi$
$744$		0			0
$745$	1336.04	−	248.829i	1.79334	−	0.333998i
$746$		0			0
$747$	139.621	−	139.621i	0.186909	−	0.186909i
$748$		0			0
$749$			559.271i			0.746691i
$750$		0			0
$751$	−958.264			−1.27598			−0.637992	−	0.770043i	$-0.720235\pi$
$751$	−958.264			−1.27598			−0.637992	+	0.770043i	$0.720235\pi$
$752$		0			0
$753$	−417.929	−	417.929i	−0.555018	−	0.555018i
$754$		0			0
$755$	16.8664	+	90.5611i	0.0223396	+	0.119949i
$756$		0			0
$757$	399.212	−	399.212i	0.527361	−	0.527361i	−0.392424	−	0.919784i	$-0.628363\pi$
$757$	399.212	−	399.212i	0.527361	−	0.527361i	0.919784	+	0.392424i	$0.128363\pi$
$758$		0			0
$759$		−	220.454i		−	0.290453i
$760$		0			0
$761$	−112.081			−0.147281			−0.0736405	−	0.997285i	$-0.523462\pi$
$761$	−112.081			−0.147281			−0.0736405	+	0.997285i	$0.523462\pi$
$762$		0			0
$763$	1387.44	+	1387.44i	1.81841	+	1.81841i
$764$		0			0
$765$	−74.0286	+	107.914i	−0.0967694	+	0.141064i
$766$		0			0
$767$	811.020	−	811.020i	1.05739	−	1.05739i
$768$		0			0
$769$		−	1367.57i		−	1.77838i	−0.457542	−	0.889188i	$-0.651270\pi$
$769$		−	1367.57i		−	1.77838i	0.457542	−	0.889188i	$-0.348730\pi$
$770$		0			0
$771$	−236.253			−0.306424
$772$		0			0
$773$	434.617	+	434.617i	0.562247	+	0.562247i	0.929945	−	0.367698i	$-0.119854\pi$
$773$	434.617	+	434.617i	0.562247	+	0.562247i	−0.367698	+	0.929945i	$0.619854\pi$
$774$		0			0
$775$	−457.051	+	176.363i	−0.589744	+	0.227565i
$776$		0			0
$777$	480.929	−	480.929i	0.618956	−	0.618956i
$778$		0			0
$779$			735.395i			0.944025i
$780$		0			0
$781$	−1179.71			−1.51052
$782$		0			0
$783$	179.364	+	179.364i	0.229073	+	0.229073i
$784$		0			0
$785$	67.1809	+	46.0857i	0.0855808	+	0.0587079i
$786$		0			0
$787$	161.322	−	161.322i	0.204984	−	0.204984i	−0.597148	−	0.802131i	$-0.703699\pi$
$787$	161.322	−	161.322i	0.204984	−	0.204984i	0.802131	+	0.597148i	$0.203699\pi$
$788$		0			0
$789$		−	631.686i		−	0.800616i
$790$		0			0
$791$	−64.3749			−0.0813842
$792$		0			0
$793$	−200.957	−	200.957i	−0.253414	−	0.253414i
$794$		0			0
$795$	136.343	−	25.3931i	0.171501	−	0.0319410i
$796$		0			0
$797$	341.436	−	341.436i	0.428401	−	0.428401i	−0.459682	−	0.888083i	$-0.652037\pi$
$797$	341.436	−	341.436i	0.428401	−	0.428401i	0.888083	+	0.459682i	$0.152037\pi$
$798$		0			0
$799$		−	448.222i		−	0.560978i
$800$		0			0
$801$	61.9428			0.0773319
$802$		0			0
$803$	897.855	+	897.855i	1.11813	+	1.11813i
$804$		0			0
$805$	96.0857	+	515.914i	0.119361	+	0.640887i
$806$		0			0
$807$	173.707	−	173.707i	0.215250	−	0.215250i
$808$		0			0
$809$			834.276i			1.03124i	0.856816	+	0.515622i	$0.172439\pi$
$809$			834.276i			1.03124i	−0.856816	+	0.515622i	$0.827561\pi$
$810$		0			0
$811$	−64.9290			−0.0800604			−0.0400302	−	0.999198i	$-0.512745\pi$
$811$	−64.9290			−0.0800604			−0.0400302	+	0.999198i	$0.512745\pi$
$812$		0			0
$813$	11.4071	+	11.4071i	0.0140309	+	0.0140309i
$814$		0			0
$815$	−607.473	+	885.537i	−0.745366	+	1.08655i
$816$		0			0
$817$	−915.886	+	915.886i	−1.12104	+	1.12104i
$818$		0			0
$819$			506.939i			0.618974i
$820$		0			0
$821$	−1153.32			−1.40477			−0.702385	−	0.711797i	$-0.747882\pi$
$821$	−1153.32			−1.40477			−0.702385	+	0.711797i	$0.747882\pi$
$822$		0			0
$823$	497.728	+	497.728i	0.604772	+	0.604772i	0.941575	−	0.336803i	$-0.109346\pi$
$823$	497.728	+	497.728i	0.604772	+	0.604772i	−0.336803	+	0.941575i	$0.609346\pi$
$824$		0			0
$825$	484.857	+	214.857i	0.587706	+	0.260433i
$826$		0			0
$827$	−612.921	+	612.921i	−0.741137	+	0.741137i	−0.972797	−	0.231660i	$-0.925584\pi$
$827$	−612.921	+	612.921i	−0.741137	+	0.741137i	0.231660	+	0.972797i	$0.425584\pi$
$828$		0			0
$829$			94.0523i			0.113453i	0.998390	+	0.0567264i	$0.0180663\pi$
$829$			94.0523i			0.113453i	−0.998390	+	0.0567264i	$0.981934\pi$
$830$		0			0
$831$	−480.234			−0.577899
$832$		0			0
$833$	326.960	+	326.960i	0.392508	+	0.392508i
$834$		0			0
$835$	−204.585	−	140.344i	−0.245012	−	0.168077i
$836$		0			0
$837$	72.0000	−	72.0000i	0.0860215	−	0.0860215i
$838$		0			0
$839$			853.869i			1.01772i	0.860849	+	0.508861i	$0.169933\pi$
$839$			853.869i			1.01772i	−0.860849	+	0.508861i	$0.830067\pi$
$840$		0			0
$841$	−1542.07			−1.83361
$842$		0			0
$843$	7.83255	+	7.83255i	0.00929128	+	0.00929128i
$844$		0			0
$845$	545.337	−	101.566i	0.645369	−	0.120196i
$846$		0			0
$847$	−207.101	+	207.101i	−0.244512	+	0.244512i
$848$		0			0
$849$			760.900i			0.896231i
$850$		0			0
$851$	404.061			0.474807
$852$		0			0
$853$	1130.34	+	1130.34i	1.32513	+	1.32513i	0.909562	+	0.415567i	$0.136417\pi$
$853$	1130.34	+	1130.34i	1.32513	+	1.32513i	0.415567	+	0.909562i	$0.363583\pi$
$854$		0			0
$855$	52.6815	+	282.864i	0.0616158	+	0.330835i
$856$		0			0
$857$	326.112	−	326.112i	0.380527	−	0.380527i	−0.490765	−	0.871292i	$-0.663283\pi$
$857$	326.112	−	326.112i	0.380527	−	0.380527i	0.871292	+	0.490765i	$0.163283\pi$
$858$		0			0
$859$		−	954.059i		−	1.11066i	−0.831629	−	0.555331i	$-0.812592\pi$
$859$		−	954.059i		−	1.11066i	0.831629	−	0.555331i	$-0.187408\pi$
$860$		0			0
$861$	670.643			0.778911
$862$		0			0
$863$	−118.987	−	118.987i	−0.137876	−	0.137876i	0.634800	−	0.772676i	$-0.281082\pi$
$863$	−118.987	−	118.987i	−0.137876	−	0.137876i	−0.772676	+	0.634800i	$0.781082\pi$
$864$		0			0
$865$	569.800	−	830.619i	0.658728	−	0.960253i
$866$		0			0
$867$	260.731	−	260.731i	0.300727	−	0.300727i
$868$		0			0
$869$			1090.14i			1.25448i
$870$		0			0
$871$	1226.12			1.40772
$872$		0			0
$873$	−65.0286	−	65.0286i	−0.0744886	−	0.0744886i
$874$		0			0
$875$	−1228.33	−	291.489i	−1.40380	−	0.333131i
$876$		0			0
$877$	−245.607	+	245.607i	−0.280054	+	0.280054i	−0.833130	−	0.553077i	$-0.813454\pi$
$877$	−245.607	+	245.607i	−0.280054	+	0.280054i	0.553077	+	0.833130i	$0.313454\pi$
$878$		0			0
$879$			217.900i			0.247895i
$880$		0			0
$881$	−1498.33			−1.70072			−0.850359	−	0.526202i	$-0.823615\pi$
$881$	−1498.33			−1.70072			−0.850359	+	0.526202i	$0.823615\pi$
$882$		0			0
$883$	−75.8292	−	75.8292i	−0.0858768	−	0.0858768i	0.662863	−	0.748740i	$-0.269341\pi$
$883$	−75.8292	−	75.8292i	−0.0858768	−	0.0858768i	−0.748740	+	0.662863i	$0.769341\pi$
$884$		0			0
$885$	−489.550	−	335.829i	−0.553164	−	0.379467i
$886$		0			0
$887$	−16.1783	+	16.1783i	−0.0182393	+	0.0182393i	−0.716168	−	0.697928i	$-0.754105\pi$
$887$	−16.1783	+	16.1783i	−0.0182393	+	0.0182393i	0.697928	+	0.716168i	$0.254105\pi$
$888$		0			0
$889$		−	1851.29i		−	2.08244i
$890$		0			0
$891$	−110.227			−0.123712
$892$		0			0
$893$	−696.843	−	696.843i	−0.780339	−	0.780339i
$894$		0			0
$895$	1183.86	−	220.486i	1.32275	−	0.246353i
$896$		0			0
$897$	−212.957	+	212.957i	−0.237410	+	0.237410i
$898$		0			0
$899$			956.607i			1.06408i
$900$		0			0
$901$	139.714			0.155066
$902$		0			0
$903$	835.241	+	835.241i	0.924962	+	0.924962i
$904$		0			0
$905$	84.5595	+	454.026i	0.0934359	+	0.501686i
$906$		0			0
$907$	−223.627	+	223.627i	−0.246556	+	0.246556i	−0.819556	−	0.572999i	$-0.805780\pi$
$907$	−223.627	+	223.627i	−0.246556	+	0.246556i	0.572999	+	0.819556i	$0.305780\pi$
$908$		0			0
$909$		−	282.336i		−	0.310600i
$910$		0			0
$911$	−500.594			−0.549500			−0.274750	−	0.961516i	$-0.588595\pi$
$911$	−500.594			−0.549500			−0.274750	+	0.961516i	$0.588595\pi$
$912$		0			0
$913$	−570.000	−	570.000i	−0.624315	−	0.624315i
$914$		0			0
$915$	−83.2127	+	121.302i	−0.0909428	+	0.132571i
$916$		0			0
$917$	−1335.12	+	1335.12i	−1.45597	+	1.45597i
$918$		0			0
$919$			698.688i			0.760270i	0.924931	+	0.380135i	$0.124122\pi$
$919$			698.688i			0.760270i	−0.924931	+	0.380135i	$0.875878\pi$
$920$		0			0
$921$	349.014			0.378951
$922$		0			0
$923$	1139.60	+	1139.60i	1.23467	+	1.23467i
$924$		0			0
$925$	−393.802	+	888.674i	−0.425732	+	0.960728i
$926$		0			0
$927$	402.302	−	402.302i	0.433983	−	0.433983i
$928$		0			0
$929$		−	439.576i		−	0.473171i	−0.971611	−	0.236586i	$-0.923972\pi$
$929$		−	439.576i		−	0.473171i	0.971611	−	0.236586i	$-0.0760284\pi$
$930$		0			0
$931$	1016.64			1.09198
$932$		0			0
$933$	−271.943	−	271.943i	−0.291471	−	0.291471i
$934$		0			0
$935$	440.558	+	302.220i	0.471185	+	0.323230i
$936$		0			0
$937$	397.114	−	397.114i	0.423815	−	0.423815i	−0.462700	−	0.886515i	$-0.653119\pi$
$937$	397.114	−	397.114i	0.423815	−	0.423815i	0.886515	+	0.462700i	$0.153119\pi$
$938$		0			0
$939$		−	675.884i		−	0.719791i
$940$		0			0
$941$	−1020.70			−1.08470			−0.542350	−	0.840153i	$-0.682465\pi$
$941$	−1020.70			−1.08470			−0.542350	+	0.840153i	$0.682465\pi$
$942$		0			0
$943$	281.726	+	281.726i	0.298755	+	0.298755i
$944$		0			0
$945$	257.957	−	48.0429i	0.272971	−	0.0508390i
$946$		0			0
$947$	−550.342	+	550.342i	−0.581143	+	0.581143i	−0.935217	−	0.354075i	$-0.884796\pi$
$947$	−550.342	+	550.342i	−0.581143	+	0.581143i	0.354075	+	0.935217i	$0.384796\pi$
$948$		0			0
$949$		−	1734.64i		−	1.82786i
$950$		0			0
$951$	563.657			0.592699
$952$		0			0
$953$	1238.48	+	1238.48i	1.29956	+	1.29956i	0.928683	+	0.370875i	$0.120942\pi$
$953$	1238.48	+	1238.48i	1.29956	+	1.29956i	0.370875	+	0.928683i	$0.379058\pi$
$954$		0			0
$955$	109.848	+	589.808i	0.115024	+	0.617600i
$956$		0			0
$957$	732.250	−	732.250i	0.765151	−	0.765151i
$958$		0			0
$959$		−	1720.37i		−	1.79392i
$960$		0			0
$961$	−577.000			−0.600416
$962$		0			0
$963$	117.471	+	117.471i	0.121984	+	0.121984i
$964$		0			0
$965$	−87.8285	+	128.031i	−0.0910140	+	0.132675i
$966$		0			0
$967$	−30.7382	+	30.7382i	−0.0317871	+	0.0317871i	−0.722822	−	0.691035i	$-0.757155\pi$
$967$	−30.7382	+	30.7382i	−0.0317871	+	0.0317871i	0.691035	+	0.722822i	$0.257155\pi$
$968$		0			0
$969$			289.857i			0.299130i
$970$		0			0
$971$	−1147.84			−1.18212			−0.591062	−	0.806626i	$-0.701291\pi$
$971$	−1147.84			−1.18212			−0.591062	+	0.806626i	$0.701291\pi$
$972$		0			0
$973$	1681.77	+	1681.77i	1.72844	+	1.72844i
$974$		0			0
$975$	−260.818	−	675.919i	−0.267506	−	0.693250i
$976$		0			0
$977$	−206.617	+	206.617i	−0.211481	+	0.211481i	−0.804896	−	0.593416i	$-0.797779\pi$
$977$	−206.617	+	206.617i	−0.211481	+	0.211481i	0.593416	+	0.804896i	$0.297779\pi$
$978$		0			0
$979$		−	252.881i		−	0.258305i
$980$		0			0
$981$	582.843			0.594131
$982$		0			0
$983$	1036.13	+	1036.13i	1.05405	+	1.05405i	0.998453	+	0.0555936i	$0.0177051\pi$
$983$	1036.13	+	1036.13i	1.05405	+	1.05405i	0.0555936	+	0.998453i	$0.482295\pi$
$984$		0			0
$985$	−1154.36	−	791.886i	−1.17194	−	0.803945i
$986$		0			0
$987$	−635.485	+	635.485i	−0.643855	+	0.643855i
$988$		0			0
$989$			701.743i			0.709548i
$990$		0			0
$991$	761.960			0.768880			0.384440	−	0.923150i	$-0.374395\pi$
$991$	761.960			0.768880			0.384440	+	0.923150i	$0.374395\pi$
$992$		0			0
$993$	7.43570	+	7.43570i	0.00748812	+	0.00748812i
$994$		0			0
$995$	599.985	−	111.743i	0.603000	−	0.112305i
$996$		0			0
$997$	1404.39	−	1404.39i	1.40862	−	1.40862i	0.641473	−	0.767145i	$-0.278323\pi$
$997$	1404.39	−	1404.39i	1.40862	−	1.40862i	0.767145	−	0.641473i	$-0.221677\pi$
$998$		0			0
$999$		−	202.030i		−	0.202233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	480.3.bg.b.193.1	yes	8
4.3	odd	2	inner	480.3.bg.b.193.3	yes	8
5.2	odd	4	inner	480.3.bg.b.97.1	✓	8
8.3	odd	2		960.3.bg.j.193.2		8
8.5	even	2		960.3.bg.j.193.4		8
20.7	even	4	inner	480.3.bg.b.97.3	yes	8
40.27	even	4		960.3.bg.j.577.2		8
40.37	odd	4		960.3.bg.j.577.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.3.bg.b.97.1	✓	8	5.2	odd	4	inner
480.3.bg.b.97.3	yes	8	20.7	even	4	inner
480.3.bg.b.193.1	yes	8	1.1	even	1	trivial
480.3.bg.b.193.3	yes	8	4.3	odd	2	inner
960.3.bg.j.193.2		8	8.3	odd	2
960.3.bg.j.193.4		8	8.5	even	2
960.3.bg.j.577.2		8	40.27	even	4
960.3.bg.j.577.4		8	40.37	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	480.bg (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 1.22474i) q^{3} +(-0.915476 - 4.91548i) q^{5} +(-7.14143 + 7.14143i) q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 - 1.22474i) q^{3} +(-0.915476 - 4.91548i) q^{5} +(-7.14143 + 7.14143i) q^{7} +3.00000i q^{9} +12.2474 q^{11} +(-11.8310 - 11.8310i) q^{13} +(-4.89898 + 7.14143i) q^{15} +(-6.16905 + 6.16905i) q^{17} +19.1818i q^{19} +17.4929 q^{21} +(7.34847 + 7.34847i) q^{23} +(-23.3238 + 9.00000i) q^{25} +(3.67423 - 3.67423i) q^{27} +48.8167i q^{29} +19.5959 q^{31} +(-15.0000 - 15.0000i) q^{33} +(41.6413 + 28.5657i) q^{35} +(27.4929 - 27.4929i) q^{37} +28.9798i q^{39} +38.3381 q^{41} +(47.7476 + 47.7476i) q^{43} +(14.7464 - 2.74643i) q^{45} +(-36.3283 + 36.3283i) q^{47} -53.0000i q^{49} +15.1110 q^{51} +(-11.3238 - 11.3238i) q^{53} +(-11.2122 - 60.2020i) q^{55} +(23.4929 - 23.4929i) q^{57} +68.5507i q^{59} +16.9857 q^{61} +(-21.4243 - 21.4243i) q^{63} +(-47.3238 + 68.9857i) q^{65} +(-51.8184 + 51.8184i) q^{67} -18.0000i q^{69} -96.3233 q^{71} +(73.3095 + 73.3095i) q^{73} +(39.5884 + 17.5430i) q^{75} +(-87.4643 + 87.4643i) q^{77} +89.0098i q^{79} -9.00000 q^{81} +(-46.5403 - 46.5403i) q^{83} +(35.9714 + 24.6762i) q^{85} +(59.7880 - 59.7880i) q^{87} -20.6476i q^{89} +168.980 q^{91} +(-24.0000 - 24.0000i) q^{93} +(94.2879 - 17.5605i) q^{95} +(-21.6762 + 21.6762i) q^{97} +36.7423i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{5}+O(q^{10}) \) 8 * q + 16 * q^5	\( 8 q + 16 q^{5} - 48 q^{13} - 96 q^{17} - 120 q^{33} + 80 q^{37} + 400 q^{41} + 48 q^{45} + 96 q^{53} + 48 q^{57} - 144 q^{61} - 192 q^{65} + 120 q^{73} - 72 q^{81} - 272 q^{85} - 192 q^{93} - 360 q^{97}+O(q^{100}) \) 8 * q + 16 * q^5 - 48 * q^13 - 96 * q^17 - 120 * q^33 + 80 * q^37 + 400 * q^41 + 48 * q^45 + 96 * q^53 + 48 * q^57 - 144 * q^61 - 192 * q^65 + 120 * q^73 - 72 * q^81 - 272 * q^85 - 192 * q^93 - 360 * q^97

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