LMFDB - Embedded newform 480.3.bg.b.97.3

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			97.3
Root			$0.845366 + 2.07011i$ of defining polynomial
Character	$\chi$	$=$	480.97
Dual form			480.3.bg.b.193.3

$q$-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 $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22474	−	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	0.999792	+	0.0204124i	$0.00649793\pi$
$7$	7.14143	+	7.14143i	1.02020	+	1.02020i	0.0204124	+	0.999792i	$0.493502\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−12.2474			−1.11340			−0.556702	−	0.830712i	$-0.687934\pi$
$11$	−12.2474			−1.11340			−0.556702	+	0.830712i	$0.687934\pi$
$12$		0			0
$13$	−11.8310	+	11.8310i	−0.910073	+	0.910073i	−0.996277	−	0.0862043i	$-0.972526\pi$
$13$	−11.8310	+	11.8310i	−0.910073	+	0.910073i	0.0862043	+	0.996277i	$0.472526\pi$
$14$		0			0
$15$	4.89898	+	7.14143i	0.326599	+	0.476095i
$16$		0			0
$17$	−6.16905	−	6.16905i	−0.362885	−	0.362885i	0.501989	−	0.864874i	$-0.332602\pi$
$17$	−6.16905	−	6.16905i	−0.362885	−	0.362885i	−0.864874	+	0.501989i	$0.832602\pi$
$18$		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	$-0.822539\pi$
$23$	−7.34847	+	7.34847i	−0.319499	+	0.319499i	0.529076	+	0.848575i	$0.322539\pi$
$24$		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	$-0.681575\pi$
$29$		−	48.8167i		−	1.68333i	0.539998	−	0.841667i	$-0.318425\pi$
$30$		0			0
$31$	−19.5959			−0.632126			−0.316063	−	0.948738i	$-0.602361\pi$
$31$	−19.5959			−0.632126			−0.316063	+	0.948738i	$0.602361\pi$
$32$		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	0.973164	−	0.230114i	$-0.0739098\pi$
$37$	27.4929	+	27.4929i	0.743050	+	0.743050i	−0.230114	+	0.973164i	$0.573910\pi$
$38$		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	−0.117313	+	0.993095i	$0.537428\pi$
$43$	−47.7476	+	47.7476i	−1.11041	+	1.11041i	−0.993095	+	0.117313i	$0.962572\pi$
$44$		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	$-0.0659399\pi$
$47$	36.3283	+	36.3283i	0.772942	+	0.772942i	−0.205678	+	0.978620i	$0.565940\pi$
$48$		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	−0.805819	−	0.592162i	$-0.798275\pi$
$53$	−11.3238	+	11.3238i	−0.213657	+	0.213657i	0.592162	+	0.805819i	$0.298275\pi$
$54$		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	$-0.0658145\pi$
$67$	51.8184	+	51.8184i	0.773408	+	0.773408i	−0.205292	+	0.978701i	$0.565814\pi$
$68$		0			0
$69$			18.0000i			0.260870i
$70$		0			0
$71$	96.3233			1.35667			0.678333	−	0.734755i	$-0.262703\pi$
$71$	96.3233			1.35667			0.678333	+	0.734755i	$0.262703\pi$
$72$		0			0
$73$	73.3095	−	73.3095i	1.00424	−	1.00424i	0.00424901	−	0.999991i	$-0.498647\pi$
$73$	73.3095	−	73.3095i	1.00424	−	1.00424i	0.999991	−	0.00424901i	$-0.00135251\pi$
$74$		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	$-0.620227\pi$
$83$	46.5403	−	46.5403i	0.560727	−	0.560727i	0.929514	+	0.368787i	$0.120227\pi$
$84$		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	$0.0370066\pi$
$89$			20.6476i			0.231996i	−0.993249	+	0.115998i	$0.962993\pi$
$90$		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	0.586490	−	0.809956i	$-0.300509\pi$
$97$	−21.6762	−	21.6762i	−0.223466	−	0.223466i	−0.809956	+	0.586490i	$0.800509\pi$
$98$		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	0.374874	−	0.927076i	$-0.377686\pi$
$103$	134.101	−	134.101i	1.30195	−	1.30195i	0.927076	−	0.374874i	$-0.122314\pi$
$104$		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	$-0.333316\pi$
$107$	−39.1568	−	39.1568i	−0.365952	−	0.365952i	−0.865998	+	0.500047i	$0.833316\pi$
$108$		0			0
$109$			194.281i			1.78239i	0.453617	+	0.891197i	$0.350134\pi$
$109$			194.281i			1.78239i	−0.453617	+	0.891197i	$0.649866\pi$
$110$		0			0
$111$	67.3435			0.606698
$112$		0			0
$113$	4.50714	−	4.50714i	0.0398862	−	0.0398862i	−0.686882	−	0.726769i	$-0.741021\pi$
$113$	4.50714	−	4.50714i	0.0398862	−	0.0398862i	0.726769	+	0.686882i	$0.241021\pi$
$114$		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	0.999783	+	0.0208144i	$0.00662591\pi$
$127$	129.616	+	129.616i	1.02060	+	1.02060i	0.0208144	+	0.999783i	$0.493374\pi$
$128$		0			0
$129$			116.957i			0.906644i
$130$		0			0
$131$	−186.954			−1.42713			−0.713566	−	0.700588i	$-0.752921\pi$
$131$	−186.954			−1.42713			−0.713566	+	0.700588i	$0.752921\pi$
$132$		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	0.114255	−	0.993452i	$-0.463552\pi$
$137$	−120.450	−	120.450i	−0.879197	−	0.879197i	−0.993452	+	0.114255i	$0.963552\pi$
$138$		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	$-0.634469\pi$
$149$		−	271.802i		−	1.82418i	0.409993	−	0.912089i	$-0.365531\pi$
$150$		0			0
$151$	18.4237			0.122011			0.0610055	−	0.998137i	$-0.480569\pi$
$151$	18.4237			0.122011			0.0610055	+	0.998137i	$0.480569\pi$
$152$		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	0.669462	−	0.742847i	$-0.266525\pi$
$157$	−11.5214	−	11.5214i	−0.0733849	−	0.0733849i	−0.742847	+	0.669462i	$0.766525\pi$
$158$		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	$-0.521057\pi$
$163$	151.868	−	151.868i	0.931708	−	0.931708i	0.997813	+	0.0661049i	$0.0210572\pi$
$164$		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	$-0.297464\pi$
$167$	−35.0860	−	35.0860i	−0.210096	−	0.210096i	−0.804308	+	0.594212i	$0.797464\pi$
$168$		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	−0.163185	−	0.986595i	$-0.552177\pi$
$173$	142.450	−	142.450i	0.823410	−	0.823410i	0.986595	+	0.163185i	$0.0521768\pi$
$174$		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	$-0.398294\pi$
$191$	119.990			0.628220			0.314110	+	0.949387i	$0.398294\pi$
$192$		0			0
$193$	−21.9571	+	21.9571i	−0.113768	+	0.113768i	−0.761699	−	0.647931i	$-0.775634\pi$
$193$	−21.9571	+	21.9571i	−0.113768	+	0.113768i	0.647931	+	0.761699i	$0.275634\pi$
$194$		0			0
$195$	−142.449	−	26.5303i	−0.730510	−	0.136053i
$196$		0			0
$197$	197.971	+	197.971i	1.00493	+	1.00493i	0.999988	+	0.00494330i	$0.00157351\pi$
$197$	197.971	+	197.971i	1.00493	+	1.00493i	0.00494330	+	0.999988i	$0.498426\pi$
$198$		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	$-0.434004\pi$
$211$	86.8694			0.411703			0.205852	+	0.978583i	$0.434004\pi$
$212$		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	$-0.837417\pi$
$223$	−85.5251	+	85.5251i	−0.383521	+	0.383521i	0.488848	+	0.872369i	$0.337417\pi$
$224$		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	$-0.0885459\pi$
$227$	155.939	+	155.939i	0.686957	+	0.686957i	−0.274601	+	0.961558i	$0.588546\pi$
$228$		0			0
$229$			339.971i			1.48459i	0.670072	+	0.742296i	$0.266263\pi$
$229$			339.971i			1.48459i	−0.670072	+	0.742296i	$0.733737\pi$
$230$		0			0
$231$	−214.243			−0.927458
$232$		0			0
$233$	−14.1119	+	14.1119i	−0.0605661	+	0.0605661i	−0.736741	−	0.676175i	$-0.763636\pi$
$233$	−14.1119	+	14.1119i	−0.0605661	+	0.0605661i	0.676175	+	0.736741i	$0.263636\pi$
$234$		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	$-0.737914\pi$
$251$	−341.237			−1.35951			−0.679755	+	0.733439i	$0.737914\pi$
$252$		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	0.869400	−	0.494108i	$-0.164505\pi$
$257$	96.4500	+	96.4500i	0.375292	+	0.375292i	−0.494108	+	0.869400i	$0.664505\pi$
$258$		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	$-0.993867\pi$
$263$	−257.885	+	257.885i	−0.980550	+	0.980550i	0.0192647	+	0.999814i	$0.493867\pi$
$264$		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	$-0.915081\pi$
$269$		−	141.831i		−	0.527253i	0.964625	−	0.263626i	$-0.0849186\pi$
$270$		0			0
$271$	9.31388			0.0343686			0.0171843	−	0.999852i	$-0.494530\pi$
$271$	9.31388			0.0343686			0.0171843	+	0.999852i	$0.494530\pi$
$272$		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	0.966068	−	0.258289i	$-0.0831586\pi$
$277$	196.055	+	196.055i	0.707779	+	0.707779i	−0.258289	+	0.966068i	$0.583159\pi$
$278$		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	0.102970	−	0.994685i	$-0.467166\pi$
$283$	310.636	−	310.636i	1.09765	−	1.09765i	0.994685	−	0.102970i	$-0.0328344\pi$
$284$		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	−0.842424	−	0.538816i	$-0.818872\pi$
$293$	−88.9571	+	88.9571i	−0.303608	+	0.303608i	0.538816	+	0.842424i	$0.318872\pi$
$294$		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	$-0.143564\pi$
$307$	142.484	+	142.484i	0.464119	+	0.464119i	−0.435884	+	0.900003i	$0.643564\pi$
$308$		0			0
$309$		−	328.479i		−	1.06304i
$310$		0			0
$311$	−222.040			−0.713956			−0.356978	−	0.934113i	$-0.616193\pi$
$311$	−222.040			−0.713956			−0.356978	+	0.934113i	$0.616193\pi$
$312$		0			0
$313$	275.929	−	275.929i	0.881561	−	0.881561i	−0.112132	−	0.993693i	$-0.535768\pi$
$313$	275.929	−	275.929i	0.881561	−	0.881561i	0.993693	+	0.112132i	$0.0357681\pi$
$314$		0			0
$315$	85.6971	+	124.924i	0.272054	+	0.396584i
$316$		0			0
$317$	−230.112	−	230.112i	−0.725905	−	0.725905i	0.243896	−	0.969801i	$-0.421574\pi$
$317$	−230.112	−	230.112i	−0.725905	−	0.725905i	−0.969801	+	0.243896i	$0.921574\pi$
$318$		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	$-0.497081\pi$
$331$	6.07122			0.0183421			0.00917103	+	0.999958i	$0.497081\pi$
$332$		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	0.365298	−	0.930891i	$-0.380967\pi$
$337$	−190.605	−	190.605i	−0.565593	−	0.565593i	−0.930891	+	0.365298i	$0.880967\pi$
$338$		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	$-0.176807\pi$
$347$	111.848	+	111.848i	0.322330	+	0.322330i	−0.527331	+	0.849660i	$0.676807\pi$
$348$		0			0
$349$			250.900i			0.718911i	0.933162	+	0.359456i	$0.117038\pi$
$349$			250.900i			0.718911i	−0.933162	+	0.359456i	$0.882962\pi$
$350$		0			0
$351$	86.9394			0.247691
$352$		0			0
$353$	−162.845	+	162.845i	−0.461318	+	0.461318i	−0.899087	−	0.437769i	$-0.855769\pi$
$353$	−162.845	+	162.845i	−0.461318	+	0.461318i	0.437769	+	0.899087i	$0.355769\pi$
$354$		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	$-0.321850\pi$
$367$	−116.161	−	116.161i	−0.316516	−	0.316516i	−0.847427	+	0.530912i	$0.821850\pi$
$368$		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	−0.182853	−	0.983140i	$-0.558533\pi$
$373$	298.507	−	298.507i	0.800287	−	0.800287i	0.983140	+	0.182853i	$0.0585332\pi$
$374$		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	$-0.898577\pi$
$383$	−243.742	+	243.742i	−0.636401	+	0.636401i	0.313265	+	0.949666i	$0.398577\pi$
$384$		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	$-0.983546\pi$
$389$		−	40.1976i		−	0.103336i	0.998664	−	0.0516679i	$-0.0164537\pi$
$390$		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	0.122369	−	0.992485i	$-0.460951\pi$
$397$	−345.436	−	345.436i	−0.870115	−	0.870115i	−0.992485	+	0.122369i	$0.960951\pi$
$398$		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	$0.237116\pi$
$409$			554.533i			1.35583i	−0.735142	+	0.677914i	$0.762884\pi$
$410$		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	$-0.440827\pi$
$431$	159.322			0.369656			0.184828	+	0.982771i	$0.440827\pi$
$432$		0			0
$433$	397.843	−	397.843i	0.918806	−	0.918806i	−0.0781370	−	0.996943i	$-0.524897\pi$
$433$	397.843	−	397.843i	0.918806	−	0.918806i	0.996943	+	0.0781370i	$0.0248972\pi$
$434$		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	$-0.945304\pi$
$443$	−360.728	+	360.728i	−0.814285	+	0.814285i	0.170988	+	0.985273i	$0.445304\pi$
$444$		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	$-0.945222\pi$
$449$		−	153.776i		−	0.342486i	0.985229	−	0.171243i	$-0.0547783\pi$
$450$		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	−0.859956	−	0.510368i	$-0.829509\pi$
$457$	−626.238	−	626.238i	−1.37032	−	1.37032i	−0.510368	−	0.859956i	$-0.670491\pi$
$458$		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	$-0.961116\pi$
$463$	−403.131	+	403.131i	−0.870692	+	0.870692i	0.121855	+	0.992548i	$0.461116\pi$
$464$		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	$-0.00115795\pi$
$467$	465.298	+	465.298i	0.996356	+	0.996356i	−0.00363781	+	0.999993i	$0.501158\pi$
$468$		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	$-0.422990\pi$
$487$	−356.141	−	356.141i	−0.731296	−	0.731296i	−0.970877	+	0.239580i	$0.922990\pi$
$488$		0			0
$489$		−	372.000i		−	0.760736i
$490$		0			0
$491$	613.924			1.25035			0.625177	−	0.780483i	$-0.285027\pi$
$491$	613.924			1.25035			0.625177	+	0.780483i	$0.285027\pi$
$492$		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	$-0.594707\pi$
$503$	333.440	−	333.440i	0.662902	−	0.662902i	0.956063	+	0.293161i	$0.0947072\pi$
$504$		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	$0.0337711\pi$
$509$			107.802i			0.211792i	−0.994377	+	0.105896i	$0.966229\pi$
$510$		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	$-0.595568\pi$
$523$	344.929	−	344.929i	0.659520	−	0.659520i	0.955266	+	0.295746i	$0.0955684\pi$
$524$		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	$-0.465045\pi$
$547$	−483.757	−	483.757i	−0.884382	−	0.884382i	−0.993976	+	0.109595i	$0.965045\pi$
$548$		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	0.995276	+	0.0970899i	$0.0309534\pi$
$557$	608.448	+	608.448i	1.09237	+	1.09237i	0.0970899	+	0.995276i	$0.469047\pi$
$558$		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	$-0.621915\pi$
$563$	311.808	−	311.808i	0.553834	−	0.553834i	0.927545	+	0.373711i	$0.121915\pi$
$564$		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	$0.171965\pi$
$569$			585.324i			1.02869i	−0.857584	+	0.514344i	$0.828035\pi$
$570$		0			0
$571$	−1050.86			−1.84039			−0.920193	−	0.391465i	$-0.871968\pi$
$571$	−1050.86			−1.84039			−0.920193	+	0.391465i	$0.871968\pi$
$572$		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	0.971854	−	0.235583i	$-0.0756999\pi$
$577$	424.829	+	424.829i	0.736271	+	0.736271i	−0.235583	+	0.971854i	$0.575700\pi$
$578$		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	−0.999752	−	0.0222492i	$-0.992917\pi$
$587$	−599.915	−	599.915i	−1.02200	−	1.02200i	−0.0222492	−	0.999752i	$-0.507083\pi$
$588$		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	−0.991011	−	0.133783i	$-0.957287\pi$
$593$	−508.336	+	508.336i	−0.857227	+	0.857227i	0.133783	+	0.991011i	$0.457287\pi$
$594$		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	$-0.0508584\pi$
$607$	502.697	+	502.697i	0.828166	+	0.828166i	−0.159097	+	0.987263i	$0.550858\pi$
$608$		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	0.491868	−	0.870670i	$-0.336314\pi$
$613$	835.236	−	835.236i	1.36254	−	1.36254i	0.870670	−	0.491868i	$-0.163686\pi$
$614$		0			0
$615$	187.818	+	273.789i	0.305394	+	0.445185i
$616$		0			0
$617$	33.8881	+	33.8881i	0.0549240	+	0.0549240i	0.734035	−	0.679111i	$-0.237635\pi$
$617$	33.8881	+	33.8881i	0.0549240	+	0.0549240i	−0.679111	+	0.734035i	$0.737635\pi$
$618$		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	$-0.507170\pi$
$631$	−28.4257			−0.0450487			−0.0225243	+	0.999746i	$0.507170\pi$
$632$		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	−0.0444571	+	0.999011i	$0.514156\pi$
$643$	−670.950	+	670.950i	−1.04347	+	1.04347i	−0.999011	+	0.0444571i	$0.985844\pi$
$644$		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	$-0.423277\pi$
$647$	−473.854	−	473.854i	−0.732386	−	0.732386i	−0.971092	+	0.238706i	$0.923277\pi$
$648$		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	−0.773237	−	0.634117i	$-0.781364\pi$
$653$	−90.8452	+	90.8452i	−0.139120	+	0.139120i	0.634117	+	0.773237i	$0.281364\pi$
$654$		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	−0.760032	−	0.649886i	$-0.774817\pi$
$673$	−74.1286	+	74.1286i	−0.110147	+	0.110147i	0.649886	+	0.760032i	$0.274817\pi$
$674$		0			0
$675$	52.6290	+	118.765i	0.0779689	+	0.175949i
$676$		0			0
$677$	−157.945	−	157.945i	−0.233302	−	0.233302i	0.580768	−	0.814069i	$-0.302752\pi$
$677$	−157.945	−	157.945i	−0.233302	−	0.233302i	−0.814069	+	0.580768i	$0.802752\pi$
$678$		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	$-0.797553\pi$
$683$	−143.762	+	143.762i	−0.210486	+	0.210486i	0.593988	+	0.804474i	$0.297553\pi$
$684$		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	$-0.350838\pi$
$691$	624.171			0.903286			0.451643	+	0.892199i	$0.350838\pi$
$692$		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	$0.172639\pi$
$709$			731.914i			1.03232i	−0.856492	+	0.516160i	$0.827361\pi$
$710$		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	$-0.253665\pi$
$727$	−11.8363	−	11.8363i	−0.0162811	−	0.0162811i	−0.715200	+	0.698919i	$0.753665\pi$
$728$		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	−0.814662	−	0.579936i	$-0.803078\pi$
$733$	−172.055	+	172.055i	−0.234727	+	0.234727i	0.579936	+	0.814662i	$0.303078\pi$
$734$		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	$-0.825806\pi$
$743$	−247.883	+	247.883i	−0.333624	+	0.333624i	0.520337	+	0.853961i	$0.325806\pi$
$744$		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	$-0.279765\pi$
$751$	958.264			1.27598			0.637992	+	0.770043i	$0.279765\pi$
$752$		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	0.919784	−	0.392424i	$-0.128363\pi$
$757$	399.212	+	399.212i	0.527361	+	0.527361i	−0.392424	+	0.919784i	$0.628363\pi$
$758$		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	$0.348730\pi$
$769$			1367.57i			1.77838i	−0.457542	+	0.889188i	$0.651270\pi$
$770$		0			0
$771$	236.253			0.306424
$772$		0			0
$773$	434.617	−	434.617i	0.562247	−	0.562247i	−0.367698	−	0.929945i	$-0.619854\pi$
$773$	434.617	−	434.617i	0.562247	−	0.562247i	0.929945	+	0.367698i	$0.119854\pi$
$774$		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	$-0.296301\pi$
$787$	−161.322	−	161.322i	−0.204984	−	0.204984i	−0.802131	+	0.597148i	$0.796301\pi$
$788$		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	0.888083	−	0.459682i	$-0.152037\pi$
$797$	341.436	+	341.436i	0.428401	+	0.428401i	−0.459682	+	0.888083i	$0.652037\pi$
$798$		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	$-0.827561\pi$
$809$		−	834.276i		−	1.03124i	0.856816	−	0.515622i	$-0.172439\pi$
$810$		0			0
$811$	64.9290			0.0800604			0.0400302	−	0.999198i	$-0.487255\pi$
$811$	64.9290			0.0800604			0.0400302	+	0.999198i	$0.487255\pi$
$812$		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	$-0.890654\pi$
$823$	−497.728	+	497.728i	−0.604772	+	0.604772i	0.336803	+	0.941575i	$0.390654\pi$
$824$		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	$-0.0744155\pi$
$827$	612.921	+	612.921i	0.741137	+	0.741137i	−0.231660	+	0.972797i	$0.574416\pi$
$828$		0			0
$829$		−	94.0523i		−	0.113453i	−0.998390	−	0.0567264i	$-0.981934\pi$
$829$		−	94.0523i		−	0.113453i	0.998390	−	0.0567264i	$-0.0180663\pi$
$830$		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	0.415567	−	0.909562i	$-0.363583\pi$
$853$	1130.34	−	1130.34i	1.32513	−	1.32513i	0.909562	−	0.415567i	$-0.136417\pi$
$854$		0			0
$855$	−52.6815	+	282.864i	−0.0616158	+	0.330835i
$856$		0			0
$857$	326.112	+	326.112i	0.380527	+	0.380527i	0.871292	−	0.490765i	$-0.163283\pi$
$857$	326.112	+	326.112i	0.380527	+	0.380527i	−0.490765	+	0.871292i	$0.663283\pi$
$858$		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	$-0.718918\pi$
$863$	118.987	−	118.987i	0.137876	−	0.137876i	0.772676	+	0.634800i	$0.218918\pi$
$864$		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	0.553077	−	0.833130i	$-0.313454\pi$
$877$	−245.607	−	245.607i	−0.280054	−	0.280054i	−0.833130	+	0.553077i	$0.813454\pi$
$878$		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	$-0.730659\pi$
$883$	75.8292	−	75.8292i	0.0858768	−	0.0858768i	0.748740	+	0.662863i	$0.230659\pi$
$884$		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	$-0.245895\pi$
$887$	16.1783	+	16.1783i	0.0182393	+	0.0182393i	−0.697928	+	0.716168i	$0.745895\pi$
$888$		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	$-0.194220\pi$
$907$	223.627	+	223.627i	0.246556	+	0.246556i	−0.572999	+	0.819556i	$0.694220\pi$
$908$		0			0
$909$			282.336i			0.310600i
$910$		0			0
$911$	500.594			0.549500			0.274750	−	0.961516i	$-0.411405\pi$
$911$	500.594			0.549500			0.274750	+	0.961516i	$0.411405\pi$
$912$		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	$0.0760284\pi$
$929$			439.576i			0.473171i	−0.971611	+	0.236586i	$0.923972\pi$
$930$		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	0.886515	−	0.462700i	$-0.153119\pi$
$937$	397.114	+	397.114i	0.423815	+	0.423815i	−0.462700	+	0.886515i	$0.653119\pi$
$938$		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	$-0.115204\pi$
$947$	550.342	+	550.342i	0.581143	+	0.581143i	−0.354075	+	0.935217i	$0.615204\pi$
$948$		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	0.370875	−	0.928683i	$-0.379058\pi$
$953$	1238.48	−	1238.48i	1.29956	−	1.29956i	0.928683	−	0.370875i	$-0.120942\pi$
$954$		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	$-0.242845\pi$
$967$	30.7382	+	30.7382i	0.0317871	+	0.0317871i	−0.691035	+	0.722822i	$0.742845\pi$
$968$		0			0
$969$		−	289.857i		−	0.299130i
$970$		0			0
$971$	1147.84			1.18212			0.591062	−	0.806626i	$-0.298709\pi$
$971$	1147.84			1.18212			0.591062	+	0.806626i	$0.298709\pi$
$972$		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	0.593416	−	0.804896i	$-0.297779\pi$
$977$	−206.617	−	206.617i	−0.211481	−	0.211481i	−0.804896	+	0.593416i	$0.797779\pi$
$978$		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	−0.0555936	+	0.998453i	$0.517705\pi$
$983$	−1036.13	+	1036.13i	−1.05405	+	1.05405i	−0.998453	+	0.0555936i	$0.982295\pi$
$984$		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	$-0.625605\pi$
$991$	−761.960			−0.768880			−0.384440	+	0.923150i	$0.625605\pi$
$992$		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	0.767145	+	0.641473i	$0.221677\pi$
$997$	1404.39	+	1404.39i	1.40862	+	1.40862i	0.641473	+	0.767145i	$0.278323\pi$
$998$		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.97.3	yes	8
4.3	odd	2	inner	480.3.bg.b.97.1	✓	8
5.3	odd	4	inner	480.3.bg.b.193.3	yes	8
8.3	odd	2		960.3.bg.j.577.4		8
8.5	even	2		960.3.bg.j.577.2		8
20.3	even	4	inner	480.3.bg.b.193.1	yes	8
40.3	even	4		960.3.bg.j.193.4		8
40.13	odd	4		960.3.bg.j.193.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.3.bg.b.97.1	✓	8	4.3	odd	2	inner
480.3.bg.b.97.3	yes	8	1.1	even	1	trivial
480.3.bg.b.193.1	yes	8	20.3	even	4	inner
480.3.bg.b.193.3	yes	8	5.3	odd	4	inner
960.3.bg.j.193.2		8	40.13	odd	4
960.3.bg.j.193.4		8	40.3	even	4
960.3.bg.j.577.2		8	8.5	even	2
960.3.bg.j.577.4		8	8.3	odd	2

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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