LMFDB - Embedded newform 1078.2.c.b.1077.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(1077,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1078.1077");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.c (of order $2$, degree $1$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1077.15
Root			$0.601150 + 2.24352i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.b.1077.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.59518i q^{3} -1.00000 q^{4} +3.53900i q^{5} -2.59518 q^{6} -1.00000i q^{8} -3.73495 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.59518i q^{3} -1.00000 q^{4} +3.53900i q^{5} -2.59518 q^{6} -1.00000i q^{8} -3.73495 q^{9} -3.53900 q^{10} +(-2.29457 - 2.39477i) q^{11} -2.59518i q^{12} +5.01680 q^{13} -9.18432 q^{15} +1.00000 q^{16} -3.89362 q^{17} -3.73495i q^{18} -4.65637 q^{19} -3.53900i q^{20} +(2.39477 - 2.29457i) q^{22} -1.55962 q^{23} +2.59518 q^{24} -7.52450 q^{25} +5.01680i q^{26} -1.90732i q^{27} +0.100205i q^{29} -9.18432i q^{30} -0.279729i q^{31} +1.00000i q^{32} +(6.21487 - 5.95482i) q^{33} -3.89362i q^{34} +3.73495 q^{36} +0.705430 q^{37} -4.65637i q^{38} +13.0195i q^{39} +3.53900 q^{40} -2.94809 q^{41} +9.03556i q^{43} +(2.29457 + 2.39477i) q^{44} -13.2180i q^{45} -1.55962i q^{46} -6.56949i q^{47} +2.59518i q^{48} -7.52450i q^{50} -10.1046i q^{51} -5.01680 q^{52} +5.54058 q^{53} +1.90732 q^{54} +(8.47510 - 8.12048i) q^{55} -12.0841i q^{57} -0.100205 q^{58} +14.5344i q^{59} +9.18432 q^{60} +11.1272 q^{61} +0.279729 q^{62} -1.00000 q^{64} +17.7544i q^{65} +(5.95482 + 6.21487i) q^{66} +3.98392 q^{67} +3.89362 q^{68} -4.04750i q^{69} -8.45381 q^{71} +3.73495i q^{72} +3.89771 q^{73} +0.705430i q^{74} -19.5274i q^{75} +4.65637 q^{76} -13.0195 q^{78} +7.69982i q^{79} +3.53900i q^{80} -6.25501 q^{81} -2.94809i q^{82} -2.87320 q^{83} -13.7795i q^{85} -9.03556 q^{86} -0.260049 q^{87} +(-2.39477 + 2.29457i) q^{88} +5.94902i q^{89} +13.2180 q^{90} +1.55962 q^{92} +0.725946 q^{93} +6.56949 q^{94} -16.4789i q^{95} -2.59518 q^{96} +16.7587i q^{97} +(8.57010 + 8.94436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 32 * q^9	$ 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 32 * q^9 - 16 * q^11 - 8 * q^15 + 16 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 32 * q^37 + 16 * q^44 + 56 * q^53 + 24 * q^58 + 8 * q^60 - 16 * q^64 - 24 * q^67 + 8 * q^71 - 16 * q^78 + 16 * q^81 - 40 * q^86 + 8 * q^88 + 32 * q^92 + 88 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			2.59518i			1.49833i	0.662385	+	0.749163i	$0.269544\pi$
$3$			2.59518i			1.49833i	−0.662385	+	0.749163i	$0.730456\pi$
$4$	−1.00000			−0.500000
$5$			3.53900i			1.58269i	0.611372	+	0.791344i	$0.290618\pi$
$5$			3.53900i			1.58269i	−0.611372	+	0.791344i	$0.709382\pi$
$6$	−2.59518			−1.05948
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−3.73495			−1.24498
$10$	−3.53900			−1.11913
$11$	−2.29457	−	2.39477i	−0.691839	−	0.722052i
$11$	−2.29457	−	2.39477i	−0.691839	−	0.722052i
$12$		−	2.59518i		−	0.749163i
$13$	5.01680			1.39141			0.695704	−	0.718328i	$-0.255092\pi$
$13$	5.01680			1.39141			0.695704	+	0.718328i	$0.255092\pi$
$14$		0			0
$15$	−9.18432			−2.37138
$16$	1.00000			0.250000
$17$	−3.89362			−0.944342			−0.472171	−	0.881507i	$-0.656529\pi$
$17$	−3.89362			−0.944342			−0.472171	+	0.881507i	$0.656529\pi$
$18$		−	3.73495i		−	0.880335i
$19$	−4.65637			−1.06825			−0.534123	−	0.845407i	$-0.679358\pi$
$19$	−4.65637			−1.06825			−0.534123	+	0.845407i	$0.679358\pi$
$20$		−	3.53900i		−	0.791344i
$21$		0			0
$22$	2.39477	−	2.29457i	0.510568	−	0.489204i
$23$	−1.55962			−0.325204			−0.162602	−	0.986692i	$-0.551989\pi$
$23$	−1.55962			−0.325204			−0.162602	+	0.986692i	$0.551989\pi$
$24$	2.59518			0.529738
$25$	−7.52450			−1.50490
$26$			5.01680i			0.983875i
$27$		−	1.90732i		−	0.367064i
$28$		0			0
$29$			0.100205i			0.0186075i	0.999957	+	0.00930376i	$0.00296152\pi$
$29$			0.100205i			0.0186075i	−0.999957	+	0.00930376i	$0.997038\pi$
$30$		−	9.18432i		−	1.67682i
$31$		−	0.279729i		−	0.0502408i	−0.999684	−	0.0251204i	$-0.992003\pi$
$31$		−	0.279729i		−	0.0502408i	0.999684	−	0.0251204i	$-0.00799691\pi$
$32$			1.00000i			0.176777i
$33$	6.21487	−	5.95482i	1.08187	−	1.03660i
$34$		−	3.89362i		−	0.667750i
$35$		0			0
$36$	3.73495			0.622491
$37$	0.705430			0.115972			0.0579860	−	0.998317i	$-0.481532\pi$
$37$	0.705430			0.115972			0.0579860	+	0.998317i	$0.481532\pi$
$38$		−	4.65637i		−	0.755364i
$39$			13.0195i			2.08478i
$40$	3.53900			0.559564
$41$	−2.94809			−0.460415			−0.230207	−	0.973142i	$-0.573940\pi$
$41$	−2.94809			−0.460415			−0.230207	+	0.973142i	$0.573940\pi$
$42$		0			0
$43$			9.03556i			1.37791i	0.724804	+	0.688955i	$0.241930\pi$
$43$			9.03556i			1.37791i	−0.724804	+	0.688955i	$0.758070\pi$
$44$	2.29457	+	2.39477i	0.345919	+	0.361026i
$45$		−	13.2180i		−	1.97042i
$46$		−	1.55962i		−	0.229954i
$47$		−	6.56949i		−	0.958259i	−0.877744	−	0.479129i	$-0.840952\pi$
$47$		−	6.56949i		−	0.958259i	0.877744	−	0.479129i	$-0.159048\pi$
$48$			2.59518i			0.374582i
$49$		0			0
$50$		−	7.52450i		−	1.06412i
$51$		−	10.1046i		−	1.41493i
$52$	−5.01680			−0.695704
$53$	5.54058			0.761057			0.380529	−	0.924769i	$-0.375742\pi$
$53$	5.54058			0.761057			0.380529	+	0.924769i	$0.375742\pi$
$54$	1.90732			0.259553
$55$	8.47510	−	8.12048i	1.14278	−	1.09496i
$56$		0			0
$57$		−	12.0841i		−	1.60058i
$58$	−0.100205			−0.0131575
$59$			14.5344i			1.89222i	0.323853	+	0.946108i	$0.395022\pi$
$59$			14.5344i			1.89222i	−0.323853	+	0.946108i	$0.604978\pi$
$60$	9.18432			1.18569
$61$	11.1272			1.42469			0.712346	−	0.701828i	$-0.247633\pi$
$61$	11.1272			1.42469			0.712346	+	0.701828i	$0.247633\pi$
$62$	0.279729			0.0355256
$63$		0			0
$64$	−1.00000			−0.125000
$65$			17.7544i			2.20217i
$66$	5.95482	+	6.21487i	0.732987	+	0.764997i
$67$	3.98392			0.486713			0.243356	−	0.969937i	$-0.421752\pi$
$67$	3.98392			0.486713			0.243356	+	0.969937i	$0.421752\pi$
$68$	3.89362			0.472171
$69$		−	4.04750i		−	0.487262i
$70$		0			0
$71$	−8.45381			−1.00328			−0.501641	−	0.865076i	$-0.667270\pi$
$71$	−8.45381			−1.00328			−0.501641	+	0.865076i	$0.667270\pi$
$72$			3.73495i			0.440168i
$73$	3.89771			0.456192			0.228096	−	0.973639i	$-0.426750\pi$
$73$	3.89771			0.456192			0.228096	+	0.973639i	$0.426750\pi$
$74$			0.705430i			0.0820045i
$75$		−	19.5274i		−	2.25483i
$76$	4.65637			0.534123
$77$		0			0
$78$	−13.0195			−1.47417
$79$			7.69982i			0.866297i	0.901322	+	0.433149i	$0.142598\pi$
$79$			7.69982i			0.866297i	−0.901322	+	0.433149i	$0.857402\pi$
$80$			3.53900i			0.395672i
$81$	−6.25501			−0.695001
$82$		−	2.94809i		−	0.325562i
$83$	−2.87320			−0.315375			−0.157687	−	0.987489i	$-0.550404\pi$
$83$	−2.87320			−0.315375			−0.157687	+	0.987489i	$0.550404\pi$
$84$		0			0
$85$		−	13.7795i		−	1.49460i
$86$	−9.03556			−0.974330
$87$	−0.260049			−0.0278801
$88$	−2.39477	+	2.29457i	−0.255284	+	0.244602i
$89$			5.94902i			0.630595i	0.948993	+	0.315297i	$0.102104\pi$
$89$			5.94902i			0.630595i	−0.948993	+	0.315297i	$0.897896\pi$
$90$	13.2180			1.39330
$91$		0			0
$92$	1.55962			0.162602
$93$	0.725946			0.0752771
$94$	6.56949			0.677591
$95$		−	16.4789i		−	1.69070i
$96$	−2.59518			−0.264869
$97$			16.7587i			1.70159i	0.525502	+	0.850793i	$0.323878\pi$
$97$			16.7587i			1.70159i	−0.525502	+	0.850793i	$0.676122\pi$
$98$		0			0
$99$	8.57010	+	8.94436i	0.861327	+	0.898942i
$100$	7.52450			0.752450
$101$	1.40290			0.139594			0.0697971	−	0.997561i	$-0.477765\pi$
$101$	1.40290			0.139594			0.0697971	+	0.997561i	$0.477765\pi$
$102$	10.1046			1.00051
$103$		−	2.06291i		−	0.203264i	−0.994822	−	0.101632i	$-0.967594\pi$
$103$		−	2.06291i		−	0.203264i	0.994822	−	0.101632i	$-0.0324064\pi$
$104$		−	5.01680i		−	0.491937i
$105$		0			0
$106$			5.54058i			0.538149i
$107$		−	12.2655i		−	1.18575i	−0.805295	−	0.592875i	$-0.797993\pi$
$107$		−	12.2655i		−	1.18575i	0.805295	−	0.592875i	$-0.202007\pi$
$108$			1.90732i			0.183532i
$109$		−	6.72491i		−	0.644129i	−0.946718	−	0.322065i	$-0.895623\pi$
$109$		−	6.72491i		−	0.644129i	0.946718	−	0.322065i	$-0.104377\pi$
$110$	8.12048	+	8.47510i	0.774257	+	0.808069i
$111$			1.83072i			0.173764i
$112$		0			0
$113$	−11.9900			−1.12792			−0.563960	−	0.825802i	$-0.690723\pi$
$113$	−11.9900			−1.12792			−0.563960	+	0.825802i	$0.690723\pi$
$114$	12.0841			1.13178
$115$		−	5.51950i		−	0.514696i
$116$		−	0.100205i		−	0.00930376i
$117$	−18.7375			−1.73228
$118$	−14.5344			−1.33800
$119$		0			0
$120$			9.18432i			0.838410i
$121$	−0.469894	+	10.9900i	−0.0427176	+	0.999087i
$122$			11.1272i			1.00741i
$123$		−	7.65083i		−	0.689852i
$124$			0.279729i			0.0251204i
$125$		−	8.93419i		−	0.799098i
$126$		0			0
$127$		−	13.2199i		−	1.17308i	−0.809922	−	0.586538i	$-0.800491\pi$
$127$		−	13.2199i		−	1.17308i	0.809922	−	0.586538i	$-0.199509\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−23.4489			−2.06456
$130$	−17.7544			−1.55717
$131$	−16.4986			−1.44149			−0.720746	−	0.693200i	$-0.756200\pi$
$131$	−16.4986			−1.44149			−0.720746	+	0.693200i	$0.756200\pi$
$132$	−6.21487	+	5.95482i	−0.540935	+	0.518300i
$133$		0			0
$134$			3.98392i			0.344158i
$135$	6.74999			0.580947
$136$			3.89362i			0.333875i
$137$	6.64374			0.567613			0.283807	−	0.958882i	$-0.408403\pi$
$137$	6.64374			0.567613			0.283807	+	0.958882i	$0.408403\pi$
$138$	4.04750			0.344546
$139$	14.3533			1.21743			0.608716	−	0.793388i	$-0.291685\pi$
$139$	14.3533			1.21743			0.608716	+	0.793388i	$0.291685\pi$
$140$		0			0
$141$	17.0490			1.43578
$142$		−	8.45381i		−	0.709428i
$143$	−11.5114	−	12.0141i	−0.962631	−	1.00467i
$144$	−3.73495			−0.311246
$145$	−0.354624			−0.0294499
$146$			3.89771i			0.322577i
$147$		0			0
$148$	−0.705430			−0.0579860
$149$		−	2.66587i		−	0.218397i	−0.994020	−	0.109198i	$-0.965172\pi$
$149$		−	2.66587i		−	0.218397i	0.994020	−	0.109198i	$-0.0348284\pi$
$150$	19.5274			1.59441
$151$			10.3903i			0.845554i	0.906234	+	0.422777i	$0.138945\pi$
$151$			10.3903i			0.845554i	−0.906234	+	0.422777i	$0.861055\pi$
$152$			4.65637i			0.377682i
$153$	14.5425			1.17569
$154$		0			0
$155$	0.989959			0.0795154
$156$		−	13.0195i		−	1.04239i
$157$			8.37473i			0.668376i	0.942506	+	0.334188i	$0.108462\pi$
$157$			8.37473i			0.668376i	−0.942506	+	0.334188i	$0.891538\pi$
$158$	−7.69982			−0.612565
$159$			14.3788i			1.14031i
$160$	−3.53900			−0.279782
$161$		0			0
$162$		−	6.25501i		−	0.491440i
$163$	3.06508			0.240075			0.120038	−	0.992769i	$-0.461698\pi$
$163$	3.06508			0.240075			0.120038	+	0.992769i	$0.461698\pi$
$164$	2.94809			0.230207
$165$	21.0741	+	21.9944i	1.64061	+	1.71226i
$166$		−	2.87320i		−	0.223003i
$167$	−10.0731			−0.779482			−0.389741	−	0.920925i	$-0.627435\pi$
$167$	−10.0731			−0.779482			−0.389741	+	0.920925i	$0.627435\pi$
$168$		0			0
$169$	12.1682			0.936018
$170$	13.7795			1.05684
$171$	17.3913			1.32995
$172$		−	9.03556i		−	0.688955i
$173$	−0.0766026			−0.00582399			−0.00291200	−	0.999996i	$-0.500927\pi$
$173$	−0.0766026			−0.00582399			−0.00291200	+	0.999996i	$0.500927\pi$
$174$		−	0.260049i		−	0.0197142i
$175$		0			0
$176$	−2.29457	−	2.39477i	−0.172960	−	0.180513i
$177$	−37.7193			−2.83516
$178$	−5.94902			−0.445898
$179$	−8.97491			−0.670817			−0.335408	−	0.942073i	$-0.608874\pi$
$179$	−8.97491			−0.670817			−0.335408	+	0.942073i	$0.608874\pi$
$180$			13.2180i			0.985209i
$181$			15.1450i			1.12572i	0.826554	+	0.562858i	$0.190298\pi$
$181$			15.1450i			1.12572i	−0.826554	+	0.562858i	$0.809702\pi$
$182$		0			0
$183$			28.8771i			2.13465i
$184$			1.55962i			0.114977i
$185$			2.49651i			0.183547i
$186$			0.725946i			0.0532289i
$187$	8.93419	+	9.32434i	0.653332	+	0.681864i
$188$			6.56949i			0.479129i
$189$		0			0
$190$	16.4789			1.19550
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$		−	2.59518i		−	0.187291i
$193$		−	14.8281i		−	1.06735i	−0.845690	−	0.533674i	$-0.820811\pi$
$193$		−	14.8281i		−	1.06735i	0.845690	−	0.533674i	$-0.179189\pi$
$194$	−16.7587			−1.20320
$195$	−46.0759			−3.29956
$196$		0			0
$197$			14.4745i			1.03126i	0.856811	+	0.515631i	$0.172443\pi$
$197$			14.4745i			1.03126i	−0.856811	+	0.515631i	$0.827557\pi$
$198$	−8.94436	+	8.57010i	−0.635648	+	0.609050i
$199$		−	11.2259i		−	0.795780i	−0.917433	−	0.397890i	$-0.869742\pi$
$199$		−	11.2259i		−	0.795780i	0.917433	−	0.397890i	$-0.130258\pi$
$200$			7.52450i			0.532062i
$201$			10.3390i			0.729255i
$202$			1.40290i			0.0987080i
$203$		0			0
$204$			10.1046i			0.707466i
$205$		−	10.4333i		−	0.728693i
$206$	2.06291			0.143729
$207$	5.82511			0.404873
$208$	5.01680			0.347852
$209$	10.6844	+	11.1510i	0.739054	+	0.771329i
$210$		0			0
$211$		−	6.44038i		−	0.443374i	−0.975118	−	0.221687i	$-0.928844\pi$
$211$		−	6.44038i		−	0.443374i	0.975118	−	0.221687i	$-0.0711563\pi$
$212$	−5.54058			−0.380529
$213$		−	21.9391i		−	1.50324i
$214$	12.2655			0.838451
$215$	−31.9768			−2.18080
$216$	−1.90732			−0.129777
$217$		0			0
$218$	6.72491			0.455468
$219$			10.1152i			0.683525i
$220$	−8.47510	+	8.12048i	−0.571391	+	0.547482i
$221$	−19.5335			−1.31397
$222$	−1.83072			−0.122870
$223$			4.01793i			0.269061i	0.990909	+	0.134530i	$0.0429526\pi$
$223$			4.01793i			0.269061i	−0.990909	+	0.134530i	$0.957047\pi$
$224$		0			0
$225$	28.1036			1.87357
$226$		−	11.9900i		−	0.797560i
$227$	−12.7293			−0.844874			−0.422437	−	0.906392i	$-0.638825\pi$
$227$	−12.7293			−0.844874			−0.422437	+	0.906392i	$0.638825\pi$
$228$			12.0841i			0.800290i
$229$			6.01345i			0.397380i	0.980062	+	0.198690i	$0.0636687\pi$
$229$			6.01345i			0.397380i	−0.980062	+	0.198690i	$0.936331\pi$
$230$	5.51950			0.363945
$231$		0			0
$232$	0.100205			0.00657875
$233$		−	6.46694i		−	0.423663i	−0.977306	−	0.211832i	$-0.932057\pi$
$233$		−	6.46694i		−	0.423663i	0.977306	−	0.211832i	$-0.0679428\pi$
$234$		−	18.7375i		−	1.22491i
$235$	23.2494			1.51662
$236$		−	14.5344i		−	0.946108i
$237$	−19.9824			−1.29800
$238$		0			0
$239$			15.5775i			1.00762i	0.863813	+	0.503812i	$0.168070\pi$
$239$			15.5775i			1.00762i	−0.863813	+	0.503812i	$0.831930\pi$
$240$	−9.18432			−0.592846
$241$	23.4762			1.51224			0.756119	−	0.654434i	$-0.227093\pi$
$241$	23.4762			1.51224			0.756119	+	0.654434i	$0.227093\pi$
$242$	−10.9900	−	0.469894i	−0.706461	−	0.0302059i
$243$		−	21.9548i		−	1.40840i
$244$	−11.1272			−0.712346
$245$		0			0
$246$	7.65083			0.487799
$247$	−23.3601			−1.48637
$248$	−0.279729			−0.0177628
$249$		−	7.45646i		−	0.472534i
$250$	8.93419			0.565048
$251$		−	18.2818i		−	1.15394i	−0.816766	−	0.576968i	$-0.804236\pi$
$251$		−	18.2818i		−	1.15394i	0.816766	−	0.576968i	$-0.195764\pi$
$252$		0			0
$253$	3.57867	+	3.73495i	0.224989	+	0.234814i
$254$	13.2199			0.829489
$255$	35.7603			2.23940
$256$	1.00000			0.0625000
$257$			9.61966i			0.600058i	0.953930	+	0.300029i	$0.0969964\pi$
$257$			9.61966i			0.600058i	−0.953930	+	0.300029i	$0.903004\pi$
$258$		−	23.4489i		−	1.45986i
$259$		0			0
$260$		−	17.7544i		−	1.10108i
$261$		−	0.374259i		−	0.0231660i
$262$		−	16.4986i		−	1.01929i
$263$			0.578666i			0.0356820i	0.999841	+	0.0178410i	$0.00567928\pi$
$263$			0.578666i			0.0356820i	−0.999841	+	0.0178410i	$0.994321\pi$
$264$	−5.95482	−	6.21487i	−0.366494	−	0.382499i
$265$			19.6081i			1.20452i
$266$		0			0
$267$	−15.4388			−0.944837
$268$	−3.98392			−0.243356
$269$			22.0896i			1.34683i	0.739266	+	0.673413i	$0.235173\pi$
$269$			22.0896i			1.34683i	−0.739266	+	0.673413i	$0.764827\pi$
$270$			6.74999i			0.410791i
$271$	−4.26222			−0.258911			−0.129456	−	0.991585i	$-0.541323\pi$
$271$	−4.26222			−0.258911			−0.129456	+	0.991585i	$0.541323\pi$
$272$	−3.89362			−0.236085
$273$		0			0
$274$			6.64374i			0.401363i
$275$	17.2655	+	18.0195i	1.04115	+	1.08662i
$276$			4.04750i			0.243631i
$277$		−	18.3653i		−	1.10346i	−0.834022	−	0.551731i	$-0.813968\pi$
$277$		−	18.3653i		−	1.10346i	0.834022	−	0.551731i	$-0.186032\pi$
$278$			14.3533i			0.860855i
$279$			1.04477i			0.0625489i
$280$		0			0
$281$			3.72890i			0.222448i	0.993795	+	0.111224i	$0.0354771\pi$
$281$			3.72890i			0.222448i	−0.993795	+	0.111224i	$0.964523\pi$
$282$			17.0490i			1.01525i
$283$	−12.7315			−0.756811			−0.378405	−	0.925640i	$-0.623527\pi$
$283$	−12.7315			−0.756811			−0.378405	+	0.925640i	$0.623527\pi$
$284$	8.45381			0.501641
$285$	42.7657			2.53322
$286$	12.0141	−	11.5114i	0.710408	−	0.680683i
$287$		0			0
$288$		−	3.73495i		−	0.220084i
$289$	−1.83972			−0.108219
$290$		−	0.354624i		−	0.0208242i
$291$	−43.4917			−2.54953
$292$	−3.89771			−0.228096
$293$	26.2251			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$293$	26.2251			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$294$		0			0
$295$	−51.4371			−2.99478
$296$		−	0.705430i		−	0.0410023i
$297$	−4.56760	+	4.37648i	−0.265039	+	0.253949i
$298$	2.66587			0.154430
$299$	−7.82431			−0.452492
$300$			19.5274i			1.12742i
$301$		0			0
$302$	−10.3903			−0.597897
$303$			3.64079i			0.209158i
$304$	−4.65637			−0.267061
$305$			39.3791i			2.25484i
$306$			14.5425i			0.831337i
$307$	−25.5942			−1.46074			−0.730369	−	0.683053i	$-0.760652\pi$
$307$	−25.5942			−1.46074			−0.730369	+	0.683053i	$0.760652\pi$
$308$		0			0
$309$	5.35360			0.304556
$310$			0.989959i			0.0562259i
$311$		−	1.90970i		−	0.108289i	−0.998533	−	0.0541446i	$-0.982757\pi$
$311$		−	1.90970i		−	0.108289i	0.998533	−	0.0541446i	$-0.0172432\pi$
$312$	13.0195			0.737083
$313$			30.4503i			1.72115i	0.509323	+	0.860576i	$0.329896\pi$
$313$			30.4503i			1.72115i	−0.509323	+	0.860576i	$0.670104\pi$
$314$	−8.37473			−0.472613
$315$		0			0
$316$		−	7.69982i		−	0.433149i
$317$	34.3942			1.93177			0.965885	−	0.258973i	$-0.0833841\pi$
$317$	34.3942			1.93177			0.965885	+	0.258973i	$0.0833841\pi$
$318$	−14.3788			−0.806323
$319$	0.239967	−	0.229926i	0.0134356	−	0.0128734i
$320$		−	3.53900i		−	0.197836i
$321$	31.8311			1.77664
$322$		0			0
$323$	18.1302			1.00879
$324$	6.25501			0.347501
$325$	−37.7489			−2.09393
$326$			3.06508i			0.169759i
$327$	17.4523			0.965116
$328$			2.94809i			0.162781i
$329$		0			0
$330$	−21.9944	+	21.0741i	−1.21075	+	1.16009i
$331$	15.5128			0.852663			0.426332	−	0.904567i	$-0.359806\pi$
$331$	15.5128			0.852663			0.426332	+	0.904567i	$0.359806\pi$
$332$	2.87320			0.157687
$333$	−2.63474			−0.144383
$334$		−	10.0731i		−	0.551177i
$335$			14.0991i			0.770314i
$336$		0			0
$337$		−	7.70882i		−	0.419926i	−0.977709	−	0.209963i	$-0.932666\pi$
$337$		−	7.70882i		−	0.419926i	0.977709	−	0.209963i	$-0.0673344\pi$
$338$			12.1682i			0.661865i
$339$		−	31.1161i		−	1.68999i
$340$			13.7795i			0.747299i
$341$	−0.669887	+	0.641857i	−0.0362764	+	0.0347585i
$342$			17.3913i			0.940415i
$343$		0			0
$344$	9.03556			0.487165
$345$	14.3241			0.771183
$346$		−	0.0766026i		−	0.00411818i
$347$			21.7413i			1.16713i	0.812065	+	0.583567i	$0.198343\pi$
$347$			21.7413i			1.16713i	−0.812065	+	0.583567i	$0.801657\pi$
$348$	0.260049			0.0139401
$349$	−13.4565			−0.720307			−0.360154	−	0.932893i	$-0.617276\pi$
$349$	−13.4565			−0.720307			−0.360154	+	0.932893i	$0.617276\pi$
$350$		0			0
$351$		−	9.56862i		−	0.510735i
$352$	2.39477	−	2.29457i	0.127642	−	0.122301i
$353$			6.70769i			0.357014i	0.983939	+	0.178507i	$0.0571267\pi$
$353$			6.70769i			0.357014i	−0.983939	+	0.178507i	$0.942873\pi$
$354$		−	37.7193i		−	2.00476i
$355$		−	29.9180i		−	1.58788i
$356$		−	5.94902i		−	0.315297i
$357$		0			0
$358$		−	8.97491i		−	0.474339i
$359$			31.0463i			1.63856i	0.573391	+	0.819282i	$0.305627\pi$
$359$			31.0463i			1.63856i	−0.573391	+	0.819282i	$0.694373\pi$
$360$	−13.2180			−0.696648
$361$	2.68183			0.141149
$362$	−15.1450			−0.796002
$363$	−28.5209	−	1.21946i	−1.49696	−	0.0640050i
$364$		0			0
$365$			13.7940i			0.722010i
$366$	−28.8771			−1.50943
$367$			29.6492i			1.54768i	0.633384	+	0.773838i	$0.281665\pi$
$367$			29.6492i			1.54768i	−0.633384	+	0.773838i	$0.718335\pi$
$368$	−1.55962			−0.0813010
$369$	11.0110			0.573208
$370$	−2.49651			−0.129788
$371$		0			0
$372$	−0.725946			−0.0376385
$373$		−	8.78055i		−	0.454640i	−0.973820	−	0.227320i	$-0.927004\pi$
$373$		−	8.78055i		−	0.454640i	0.973820	−	0.227320i	$-0.0729963\pi$
$374$	−9.32434	+	8.93419i	−0.482150	+	0.461976i
$375$	23.1858			1.19731
$376$	−6.56949			−0.338796
$377$			0.502706i			0.0258907i
$378$		0			0
$379$	30.8135			1.58278			0.791391	−	0.611311i	$-0.209358\pi$
$379$	30.8135			1.58278			0.791391	+	0.611311i	$0.209358\pi$
$380$			16.4789i			0.845349i
$381$	34.3080			1.75765
$382$			6.00000i			0.306987i
$383$		−	5.29482i		−	0.270553i	−0.990808	−	0.135276i	$-0.956808\pi$
$383$		−	5.29482i		−	0.270553i	0.990808	−	0.135276i	$-0.0431922\pi$
$384$	2.59518			0.132435
$385$		0			0
$386$	14.8281			0.754729
$387$		−	33.7473i		−	1.71547i
$388$		−	16.7587i		−	0.850793i
$389$	0.860237			0.0436158			0.0218079	−	0.999762i	$-0.493058\pi$
$389$	0.860237			0.0436158			0.0218079	+	0.999762i	$0.493058\pi$
$390$		−	46.0759i		−	2.33314i
$391$	6.07258			0.307104
$392$		0			0
$393$		−	42.8168i		−	2.15982i
$394$	−14.4745			−0.729213
$395$	−27.2496			−1.37108
$396$	−8.57010	−	8.94436i	−0.430664	−	0.449471i
$397$		−	12.3473i		−	0.619695i	−0.950786	−	0.309847i	$-0.899722\pi$
$397$		−	12.3473i		−	0.619695i	0.950786	−	0.309847i	$-0.100278\pi$
$398$	11.2259			0.562702
$399$		0			0
$400$	−7.52450			−0.376225
$401$	33.7252			1.68416			0.842078	−	0.539355i	$-0.181332\pi$
$401$	33.7252			1.68416			0.842078	+	0.539355i	$0.181332\pi$
$402$	−10.3390			−0.515661
$403$		−	1.40334i		−	0.0699054i
$404$	−1.40290			−0.0697971
$405$		−	22.1365i		−	1.09997i
$406$		0			0
$407$	−1.61866	−	1.68935i	−0.0802339	−	0.0837377i
$408$	−10.1046			−0.500254
$409$	38.3692			1.89723			0.948616	−	0.316428i	$-0.102484\pi$
$409$	38.3692			1.89723			0.948616	+	0.316428i	$0.102484\pi$
$410$	10.4333			0.515264
$411$			17.2417i			0.850470i
$412$			2.06291i			0.101632i
$413$		0			0
$414$			5.82511i			0.286289i
$415$		−	10.1682i		−	0.499139i
$416$			5.01680i			0.245969i
$417$			37.2494i			1.82411i
$418$	−11.1510	+	10.6844i	−0.545412	+	0.522590i
$419$		−	33.5023i		−	1.63670i	−0.574723	−	0.818348i	$-0.694890\pi$
$419$		−	33.5023i		−	1.63670i	0.574723	−	0.818348i	$-0.305110\pi$
$420$		0			0
$421$	−23.0155			−1.12171			−0.560853	−	0.827915i	$-0.689527\pi$
$421$	−23.0155			−1.12171			−0.560853	+	0.827915i	$0.689527\pi$
$422$	6.44038			0.313513
$423$			24.5367i			1.19302i
$424$		−	5.54058i		−	0.269074i
$425$	29.2975			1.42114
$426$	21.9391			1.06295
$427$		0			0
$428$			12.2655i			0.592875i
$429$	31.1787	−	29.8741i	1.50532	−	1.44234i
$430$		−	31.9768i		−	1.54206i
$431$		−	26.8381i		−	1.29275i	−0.763021	−	0.646373i	$-0.776285\pi$
$431$		−	26.8381i		−	1.29275i	0.763021	−	0.646373i	$-0.223715\pi$
$432$		−	1.90732i		−	0.0917659i
$433$		−	30.6912i		−	1.47493i	−0.675387	−	0.737463i	$-0.736024\pi$
$433$		−	30.6912i		−	1.47493i	0.675387	−	0.737463i	$-0.263976\pi$
$434$		0			0
$435$		−	0.920312i		−	0.0441256i
$436$			6.72491i			0.322065i
$437$	7.26219			0.347398
$438$	−10.1152			−0.483325
$439$	16.8452			0.803976			0.401988	−	0.915645i	$-0.368319\pi$
$439$	16.8452			0.803976			0.401988	+	0.915645i	$0.368319\pi$
$440$	−8.12048	−	8.47510i	−0.387129	−	0.404035i
$441$		0			0
$442$		−	19.5335i		−	0.929114i
$443$	−0.790590			−0.0375620			−0.0187810	−	0.999824i	$-0.505979\pi$
$443$	−0.790590			−0.0375620			−0.0187810	+	0.999824i	$0.505979\pi$
$444$		−	1.83072i		−	0.0868819i
$445$	−21.0536			−0.998035
$446$	−4.01793			−0.190255
$447$	6.91841			0.327230
$448$		0			0
$449$	15.9734			0.753833			0.376917	−	0.926247i	$-0.376984\pi$
$449$	15.9734			0.753833			0.376917	+	0.926247i	$0.376984\pi$
$450$			28.1036i			1.32482i
$451$	6.76461	+	7.06002i	0.318533	+	0.332443i
$452$	11.9900			0.563960
$453$	−26.9648			−1.26692
$454$		−	12.7293i		−	0.597416i
$455$		0			0
$456$	−12.0841			−0.565891
$457$		−	34.9331i		−	1.63410i	−0.576564	−	0.817052i	$-0.695607\pi$
$457$		−	34.9331i		−	1.63410i	0.576564	−	0.817052i	$-0.304393\pi$
$458$	−6.01345			−0.280990
$459$			7.42637i			0.346633i
$460$			5.51950i			0.257348i
$461$	−20.8346			−0.970364			−0.485182	−	0.874413i	$-0.661247\pi$
$461$	−20.8346			−0.970364			−0.485182	+	0.874413i	$0.661247\pi$
$462$		0			0
$463$	13.1724			0.612172			0.306086	−	0.952004i	$-0.400981\pi$
$463$	13.1724			0.612172			0.306086	+	0.952004i	$0.400981\pi$
$464$			0.100205i			0.00465188i
$465$			2.56912i			0.119140i
$466$	6.46694			0.299575
$467$			16.8184i			0.778262i	0.921182	+	0.389131i	$0.127225\pi$
$467$			16.8184i			0.778262i	−0.921182	+	0.389131i	$0.872775\pi$
$468$	18.7375			0.866140
$469$		0			0
$470$			23.2494i			1.07241i
$471$	−21.7339			−1.00145
$472$	14.5344			0.668999
$473$	21.6381	−	20.7327i	0.994922	−	0.953292i
$474$		−	19.9824i		−	0.917822i
$475$	35.0369			1.60760
$476$		0			0
$477$	−20.6938			−0.947503
$478$	−15.5775			−0.712498
$479$	22.8582			1.04442			0.522208	−	0.852818i	$-0.325109\pi$
$479$	22.8582			1.04442			0.522208	+	0.852818i	$0.325109\pi$
$480$		−	9.18432i		−	0.419205i
$481$	3.53900			0.161364
$482$			23.4762i			1.06931i
$483$		0			0
$484$	0.469894	−	10.9900i	0.0213588	−	0.499544i
$485$	−59.3089			−2.69308
$486$	21.9548			0.995891
$487$	31.2628			1.41665			0.708327	−	0.705884i	$-0.249450\pi$
$487$	31.2628			1.41665			0.708327	+	0.705884i	$0.249450\pi$
$488$		−	11.1272i		−	0.503705i
$489$			7.95442i			0.359711i
$490$		0			0
$491$		−	22.4979i		−	1.01532i	−0.861558	−	0.507659i	$-0.830511\pi$
$491$		−	22.4979i		−	1.01532i	0.861558	−	0.507659i	$-0.169489\pi$
$492$			7.65083i			0.344926i
$493$		−	0.390159i		−	0.0175719i
$494$		−	23.3601i		−	1.05102i
$495$	−31.6541	+	30.3295i	−1.42274	+	1.36321i
$496$		−	0.279729i		−	0.0125602i
$497$		0			0
$498$	7.45646			0.334132
$499$	−31.9097			−1.42847			−0.714236	−	0.699905i	$-0.753226\pi$
$499$	−31.9097			−1.42847			−0.714236	+	0.699905i	$0.753226\pi$
$500$			8.93419i			0.399549i
$501$		−	26.1415i		−	1.16792i
$502$	18.2818			0.815957
$503$	30.2687			1.34962			0.674808	−	0.737994i	$-0.264227\pi$
$503$	30.2687			1.34962			0.674808	+	0.737994i	$0.264227\pi$
$504$		0			0
$505$			4.96487i			0.220934i
$506$	−3.73495	+	3.57867i	−0.166039	+	0.159091i
$507$			31.5787i			1.40246i
$508$			13.2199i			0.586538i
$509$			23.0542i			1.02186i	0.859622	+	0.510930i	$0.170699\pi$
$509$			23.0542i			1.02186i	−0.859622	+	0.510930i	$0.829301\pi$
$510$			35.7603i			1.58349i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			8.88119i			0.392114i
$514$	−9.61966			−0.424305
$515$	7.30061			0.321703
$516$	23.4489			1.03228
$517$	−15.7325	+	15.0742i	−0.691912	+	0.662961i
$518$		0			0
$519$		−	0.198797i		−	0.00872624i
$520$	17.7544			0.778583
$521$		−	7.98303i		−	0.349743i	−0.984591	−	0.174872i	$-0.944049\pi$
$521$		−	7.98303i		−	0.349743i	0.984591	−	0.174872i	$-0.0559510\pi$
$522$	0.374259			0.0163809
$523$	−5.58280			−0.244119			−0.122059	−	0.992523i	$-0.538950\pi$
$523$	−5.58280			−0.244119			−0.122059	+	0.992523i	$0.538950\pi$
$524$	16.4986			0.720746
$525$		0			0
$526$	−0.578666			−0.0252310
$527$			1.08916i			0.0474444i
$528$	6.21487	−	5.95482i	0.270467	−	0.259150i
$529$	−20.5676			−0.894242
$530$	−19.6081			−0.851721
$531$		−	54.2851i		−	2.35577i
$532$		0			0
$533$	−14.7900			−0.640625
$534$		−	15.4388i		−	0.668101i
$535$	43.4075			1.87667
$536$		−	3.98392i		−	0.172079i
$537$		−	23.2915i		−	1.00510i
$538$	−22.0896			−0.952350
$539$		0			0
$540$	−6.74999			−0.290473
$541$		−	13.4022i		−	0.576204i	−0.957600	−	0.288102i	$-0.906976\pi$
$541$		−	13.4022i		−	0.576204i	0.957600	−	0.288102i	$-0.0930242\pi$
$542$		−	4.26222i		−	0.183078i
$543$	−39.3039			−1.68669
$544$		−	3.89362i		−	0.166938i
$545$	23.7994			1.01946
$546$		0			0
$547$			24.5161i			1.04823i	0.851647	+	0.524116i	$0.175604\pi$
$547$			24.5161i			1.04823i	−0.851647	+	0.524116i	$0.824396\pi$
$548$	−6.64374			−0.283807
$549$	−41.5595			−1.77372
$550$	−18.0195	+	17.2655i	−0.768353	+	0.736203i
$551$		−	0.466590i		−	0.0198774i
$552$	−4.04750			−0.172273
$553$		0			0
$554$	18.3653			0.780265
$555$	−6.47890			−0.275014
$556$	−14.3533			−0.608716
$557$			3.61157i			0.153027i	0.997069	+	0.0765137i	$0.0243789\pi$
$557$			3.61157i			0.153027i	−0.997069	+	0.0765137i	$0.975621\pi$
$558$	−1.04477			−0.0442287
$559$			45.3296i			1.91724i
$560$		0			0
$561$	−24.1983	+	23.1858i	−1.02165	+	0.978905i
$562$	−3.72890			−0.157294
$563$	−5.85803			−0.246887			−0.123443	−	0.992352i	$-0.539394\pi$
$563$	−5.85803			−0.246887			−0.123443	+	0.992352i	$0.539394\pi$
$564$	−17.0490			−0.717892
$565$		−	42.4324i		−	1.78515i
$566$		−	12.7315i		−	0.535146i
$567$		0			0
$568$			8.45381i			0.354714i
$569$			34.6147i			1.45112i	0.688158	+	0.725561i	$0.258420\pi$
$569$			34.6147i			1.45112i	−0.688158	+	0.725561i	$0.741580\pi$
$570$			42.7657i			1.79126i
$571$		−	7.96636i		−	0.333382i	−0.986009	−	0.166691i	$-0.946692\pi$
$571$		−	7.96636i		−	0.333382i	0.986009	−	0.166691i	$-0.0533082\pi$
$572$	11.5114	+	12.0141i	0.481315	+	0.502335i
$573$			15.5711i			0.650491i
$574$		0			0
$575$	11.7354			0.489399
$576$	3.73495			0.155623
$577$			18.3764i			0.765018i	0.923952	+	0.382509i	$0.124940\pi$
$577$			18.3764i			0.765018i	−0.923952	+	0.382509i	$0.875060\pi$
$578$		−	1.83972i		−	0.0765223i
$579$	38.4815			1.59924
$580$	0.354624			0.0147249
$581$		0			0
$582$		−	43.4917i		−	1.80279i
$583$	−12.7133	−	13.2684i	−0.526529	−	0.549523i
$584$		−	3.89771i		−	0.161288i
$585$		−	66.3118i		−	2.74166i
$586$			26.2251i			1.08335i
$587$			17.2267i			0.711021i	0.934672	+	0.355511i	$0.115693\pi$
$587$			17.2267i			0.711021i	−0.934672	+	0.355511i	$0.884307\pi$
$588$		0			0
$589$			1.30252i			0.0536695i
$590$		−	51.4371i		−	2.11763i
$591$	−37.5638			−1.54517
$592$	0.705430			0.0289930
$593$	−41.2427			−1.69363			−0.846817	−	0.531884i	$-0.821484\pi$
$593$	−41.2427			−1.69363			−0.846817	+	0.531884i	$0.821484\pi$
$594$	−4.37648	−	4.56760i	−0.179569	−	0.187411i
$595$		0			0
$596$			2.66587i			0.109198i
$597$	29.1331			1.19234
$598$		−	7.82431i		−	0.319960i
$599$	9.95440			0.406726			0.203363	−	0.979103i	$-0.434813\pi$
$599$	9.95440			0.406726			0.203363	+	0.979103i	$0.434813\pi$
$600$	−19.5274			−0.797203
$601$	4.76767			0.194477			0.0972386	−	0.995261i	$-0.468999\pi$
$601$	4.76767			0.194477			0.0972386	+	0.995261i	$0.468999\pi$
$602$		0			0
$603$	−14.8797			−0.605949
$604$		−	10.3903i		−	0.422777i
$605$	−38.8934	−	1.66295i	−1.58124	−	0.0676087i
$606$	−3.64079			−0.147897
$607$	4.55345			0.184819			0.0924094	−	0.995721i	$-0.470543\pi$
$607$	4.55345			0.184819			0.0924094	+	0.995721i	$0.470543\pi$
$608$		−	4.65637i		−	0.188841i
$609$		0			0
$610$	−39.3791			−1.59441
$611$		−	32.9578i		−	1.33333i
$612$	−14.5425			−0.587844
$613$			1.44894i			0.0585223i	0.999572	+	0.0292611i	$0.00931544\pi$
$613$			1.44894i			0.0585223i	−0.999572	+	0.0292611i	$0.990685\pi$
$614$		−	25.5942i		−	1.03290i
$615$	27.0762			1.09182
$616$		0			0
$617$	−2.96752			−0.119468			−0.0597340	−	0.998214i	$-0.519025\pi$
$617$	−2.96752			−0.119468			−0.0597340	+	0.998214i	$0.519025\pi$
$618$			5.35360i			0.215354i
$619$		−	11.5475i		−	0.464133i	−0.972700	−	0.232067i	$-0.925451\pi$
$619$		−	11.5475i		−	0.464133i	0.972700	−	0.232067i	$-0.0745488\pi$
$620$	−0.989959			−0.0397577
$621$			2.97470i			0.119371i
$622$	1.90970			0.0765720
$623$		0			0
$624$			13.0195i			0.521196i
$625$	−6.00443			−0.240177
$626$	−30.4503			−1.21704
$627$	−28.9387	+	27.7279i	−1.15570	+	1.10734i
$628$		−	8.37473i		−	0.334188i
$629$	−2.74668			−0.109517
$630$		0			0
$631$	−27.5215			−1.09562			−0.547808	−	0.836604i	$-0.684537\pi$
$631$	−27.5215			−1.09562			−0.547808	+	0.836604i	$0.684537\pi$
$632$	7.69982			0.306282
$633$	16.7139			0.664319
$634$			34.3942i			1.36597i
$635$	46.7851			1.85661
$636$		−	14.3788i		−	0.570156i
$637$		0			0
$638$	0.229926	+	0.239967i	0.00910288	+	0.00950040i
$639$	31.5745			1.24907
$640$	3.53900			0.139891
$641$	33.6547			1.32928			0.664639	−	0.747164i	$-0.268585\pi$
$641$	33.6547			1.32928			0.664639	+	0.747164i	$0.268585\pi$
$642$			31.8311i			1.25627i
$643$		−	5.95261i		−	0.234748i	−0.993088	−	0.117374i	$-0.962552\pi$
$643$		−	5.95261i		−	0.234748i	0.993088	−	0.117374i	$-0.0374476\pi$
$644$		0			0
$645$		−	82.9855i		−	3.26755i
$646$			18.1302i			0.713321i
$647$			11.7737i			0.462873i	0.972850	+	0.231437i	$0.0743426\pi$
$647$			11.7737i			0.462873i	−0.972850	+	0.231437i	$0.925657\pi$
$648$			6.25501i			0.245720i
$649$	34.8066	−	33.3502i	1.36628	−	1.30911i
$650$		−	37.7489i		−	1.48063i
$651$		0			0
$652$	−3.06508			−0.120038
$653$	28.8670			1.12965			0.564827	−	0.825209i	$-0.308943\pi$
$653$	28.8670			1.12965			0.564827	+	0.825209i	$0.308943\pi$
$654$			17.4523i			0.682440i
$655$		−	58.3886i		−	2.28143i
$656$	−2.94809			−0.115104
$657$	−14.5577			−0.567952
$658$		0			0
$659$		−	44.6812i		−	1.74053i	−0.492581	−	0.870266i	$-0.663947\pi$
$659$		−	44.6812i		−	1.74053i	0.492581	−	0.870266i	$-0.336053\pi$
$660$	−21.0741	−	21.9944i	−0.820307	−	0.856130i
$661$		−	39.6341i		−	1.54159i	−0.637084	−	0.770794i	$-0.719860\pi$
$661$		−	39.6341i		−	1.54159i	0.637084	−	0.770794i	$-0.280140\pi$
$662$			15.5128i			0.602924i
$663$		−	50.6929i		−	1.96875i
$664$			2.87320i			0.111502i
$665$		0			0
$666$		−	2.63474i		−	0.102094i
$667$		−	0.156281i		−	0.00605124i
$668$	10.0731			0.389741
$669$	−10.4272			−0.403141
$670$	−14.0991			−0.544694
$671$	−25.5321	−	26.6471i	−0.985657	−	1.02870i
$672$		0			0
$673$			2.71886i			0.104804i	0.998626	+	0.0524022i	$0.0166878\pi$
$673$			2.71886i			0.104804i	−0.998626	+	0.0524022i	$0.983312\pi$
$674$	7.70882			0.296933
$675$			14.3516i			0.552394i
$676$	−12.1682			−0.468009
$677$	6.05945			0.232884			0.116442	−	0.993198i	$-0.462851\pi$
$677$	6.05945			0.232884			0.116442	+	0.993198i	$0.462851\pi$
$678$	31.1161			1.19501
$679$		0			0
$680$	−13.7795			−0.528420
$681$		−	33.0348i		−	1.26590i
$682$	−0.641857	−	0.669887i	−0.0245780	−	0.0256513i
$683$	−6.03409			−0.230888			−0.115444	−	0.993314i	$-0.536829\pi$
$683$	−6.03409			−0.230888			−0.115444	+	0.993314i	$0.536829\pi$
$684$	−17.3913			−0.664973
$685$			23.5122i			0.898354i
$686$		0			0
$687$	−15.6060			−0.595405
$688$			9.03556i			0.344478i
$689$	27.7960			1.05894
$690$			14.3241i			0.545309i
$691$			19.8053i			0.753427i	0.926330	+	0.376714i	$0.122946\pi$
$691$			19.8053i			0.753427i	−0.926330	+	0.376714i	$0.877054\pi$
$692$	0.0766026			0.00291200
$693$		0			0
$694$	−21.7413			−0.825288
$695$			50.7963i			1.92681i
$696$			0.260049i			0.00985712i
$697$	11.4788			0.434789
$698$		−	13.4565i		−	0.509334i
$699$	16.7828			0.634786
$700$		0			0
$701$			26.0155i			0.982591i	0.870993	+	0.491296i	$0.163476\pi$
$701$			26.0155i			0.982591i	−0.870993	+	0.491296i	$0.836524\pi$
$702$	9.56862			0.361144
$703$	−3.28475			−0.123887
$704$	2.29457	+	2.39477i	0.0864799	+	0.0902565i
$705$			60.3363i			2.27240i
$706$	−6.70769			−0.252447
$707$		0			0
$708$	37.7193			1.41758
$709$	−24.8917			−0.934826			−0.467413	−	0.884039i	$-0.654814\pi$
$709$	−24.8917			−0.934826			−0.467413	+	0.884039i	$0.654814\pi$
$710$	29.9180			1.12280
$711$		−	28.7584i		−	1.07853i
$712$	5.94902			0.222949
$713$			0.436271i			0.0163385i
$714$		0			0
$715$	42.5178	−	40.7388i	1.59008	−	1.52354i
$716$	8.97491			0.335408
$717$	−40.4263			−1.50975
$718$	−31.0463			−1.15864
$719$			13.2970i			0.495895i	0.968773	+	0.247948i	$0.0797561\pi$
$719$			13.2970i			0.495895i	−0.968773	+	0.247948i	$0.920244\pi$
$720$		−	13.2180i		−	0.492604i
$721$		0			0
$722$			2.68183i			0.0998073i
$723$			60.9250i			2.26583i
$724$		−	15.1450i		−	0.562858i
$725$		−	0.753989i		−	0.0280025i
$726$	1.21946	−	28.5209i	0.0452583	−	1.05851i
$727$		−	5.67083i		−	0.210319i	−0.994455	−	0.105160i	$-0.966465\pi$
$727$		−	5.67083i		−	0.210319i	0.994455	−	0.105160i	$-0.0335354\pi$
$728$		0			0
$729$	38.2116			1.41525
$730$	−13.7940			−0.510538
$731$		−	35.1810i		−	1.30122i
$732$		−	28.8771i		−	1.06733i
$733$	−41.3759			−1.52825			−0.764127	−	0.645066i	$-0.776830\pi$
$733$	−41.3759			−1.52825			−0.764127	+	0.645066i	$0.776830\pi$
$734$	−29.6492			−1.09437
$735$		0			0
$736$		−	1.55962i		−	0.0574885i
$737$	−9.14137	−	9.54058i	−0.336727	−	0.351432i
$738$			11.0110i			0.405320i
$739$			41.5403i			1.52808i	0.645167	+	0.764042i	$0.276788\pi$
$739$			41.5403i			1.52808i	−0.645167	+	0.764042i	$0.723212\pi$
$740$		−	2.49651i		−	0.0917736i
$741$		−	60.6236i		−	2.22706i
$742$		0			0
$743$			39.7404i			1.45793i	0.684549	+	0.728967i	$0.259999\pi$
$743$			39.7404i			1.45793i	−0.684549	+	0.728967i	$0.740001\pi$
$744$		−	0.725946i		−	0.0266145i
$745$	9.43451			0.345654
$746$	8.78055			0.321479
$747$	10.7312			0.392636
$748$	−8.93419	−	9.32434i	−0.326666	−	0.340932i
$749$		0			0
$750$			23.1858i			0.846626i
$751$	5.36526			0.195781			0.0978905	−	0.995197i	$-0.468791\pi$
$751$	5.36526			0.195781			0.0978905	+	0.995197i	$0.468791\pi$
$752$		−	6.56949i		−	0.239565i
$753$	47.4445			1.72897
$754$	−0.502706			−0.0183075
$755$	−36.7714			−1.33825
$756$		0			0
$757$	25.8962			0.941215			0.470607	−	0.882343i	$-0.344035\pi$
$757$	25.8962			0.941215			0.470607	+	0.882343i	$0.344035\pi$
$758$			30.8135i			1.11920i
$759$	−9.69285	+	9.28727i	−0.351828	+	0.337107i
$760$	−16.4789			−0.597752
$761$	15.2206			0.551747			0.275873	−	0.961194i	$-0.411033\pi$
$761$	15.2206			0.551747			0.275873	+	0.961194i	$0.411033\pi$
$762$			34.3080i			1.24285i
$763$		0			0
$764$	−6.00000			−0.217072
$765$			51.4657i			1.86075i
$766$	5.29482			0.191310
$767$			72.9160i			2.63284i
$768$			2.59518i			0.0936454i
$769$	22.5146			0.811898			0.405949	−	0.913896i	$-0.366941\pi$
$769$	22.5146			0.811898			0.405949	+	0.913896i	$0.366941\pi$
$770$		0			0
$771$	−24.9647			−0.899083
$772$			14.8281i			0.533674i
$773$			28.0333i			1.00829i	0.863619	+	0.504144i	$0.168192\pi$
$773$			28.0333i			1.00829i	−0.863619	+	0.504144i	$0.831808\pi$
$774$	33.7473			1.21302
$775$			2.10482i			0.0756073i
$776$	16.7587			0.601601
$777$		0			0
$778$			0.860237i			0.0308410i
$779$	13.7274			0.491836
$780$	46.0759			1.64978
$781$	19.3979	+	20.2450i	0.694110	+	0.724422i
$782$			6.07258i			0.217155i
$783$	0.191122			0.00683014
$784$		0			0
$785$	−29.6381			−1.05783
$786$	42.8168			1.52723
$787$	12.7432			0.454246			0.227123	−	0.973866i	$-0.427068\pi$
$787$	12.7432			0.454246			0.227123	+	0.973866i	$0.427068\pi$
$788$		−	14.4745i		−	0.515631i
$789$	−1.50174			−0.0534634
$790$		−	27.2496i		−	0.969499i
$791$		0			0
$792$	8.94436	−	8.57010i	0.317824	−	0.304525i
$793$	55.8229			1.98233
$794$	12.3473			0.438190
$795$	−50.8865			−1.80476
$796$			11.2259i			0.397890i
$797$		−	5.63488i		−	0.199598i	−0.995008	−	0.0997989i	$-0.968180\pi$
$797$		−	5.63488i		−	0.199598i	0.995008	−	0.0997989i	$-0.0318199\pi$
$798$		0			0
$799$			25.5791i			0.904923i
$800$		−	7.52450i		−	0.266031i
$801$		−	22.2193i		−	0.785080i
$802$			33.7252i			1.19088i
$803$	−8.94357	−	9.33414i	−0.315612	−	0.329395i
$804$		−	10.3390i		−	0.364627i
$805$		0			0
$806$	1.40334			0.0494306
$807$	−57.3264			−2.01799
$808$		−	1.40290i		−	0.0493540i
$809$		−	17.0401i		−	0.599099i	−0.954081	−	0.299550i	$-0.903164\pi$
$809$		−	17.0401i		−	0.599099i	0.954081	−	0.299550i	$-0.0968364\pi$
$810$	22.1365			0.777796
$811$	0.332109			0.0116619			0.00583097	−	0.999983i	$-0.498144\pi$
$811$	0.332109			0.0116619			0.00583097	+	0.999983i	$0.498144\pi$
$812$		0			0
$813$		−	11.0612i		−	0.387934i
$814$	1.68935	−	1.61866i	0.0592115	−	0.0567339i
$815$			10.8473i			0.379964i
$816$		−	10.1046i		−	0.353733i
$817$		−	42.0730i		−	1.47195i
$818$			38.3692i			1.34155i
$819$		0			0
$820$			10.4333i			0.364346i
$821$			2.28292i			0.0796744i	0.999206	+	0.0398372i	$0.0126839\pi$
$821$			2.28292i			0.0796744i	−0.999206	+	0.0398372i	$0.987316\pi$
$822$	−17.2417			−0.601373
$823$	10.0846			0.351525			0.175763	−	0.984433i	$-0.443761\pi$
$823$	10.0846			0.351525			0.175763	+	0.984433i	$0.443761\pi$
$824$	−2.06291			−0.0718647
$825$	−46.7637	+	44.8070i	−1.62810	+	1.55998i
$826$		0			0
$827$			10.9337i			0.380204i	0.981764	+	0.190102i	$0.0608818\pi$
$827$			10.9337i			0.380204i	−0.981764	+	0.190102i	$0.939118\pi$
$828$	−5.82511			−0.202437
$829$		−	11.6257i		−	0.403779i	−0.979408	−	0.201889i	$-0.935292\pi$
$829$		−	11.6257i		−	0.403779i	0.979408	−	0.201889i	$-0.0647081\pi$
$830$	10.1682			0.352945
$831$	47.6611			1.65335
$832$	−5.01680			−0.173926
$833$		0			0
$834$	−37.2494			−1.28984
$835$		−	35.6487i		−	1.23368i
$836$	−10.6844	−	11.1510i	−0.369527	−	0.385664i
$837$	−0.533532			−0.0184416
$838$	33.5023			1.15732
$839$		−	23.4571i		−	0.809828i	−0.914355	−	0.404914i	$-0.867301\pi$
$839$		−	23.4571i		−	0.809828i	0.914355	−	0.404914i	$-0.132699\pi$
$840$		0			0
$841$	28.9900			0.999654
$842$		−	23.0155i		−	0.793166i
$843$	−9.67717			−0.333299
$844$			6.44038i			0.221687i
$845$			43.0634i			1.48142i
$846$	−24.5367			−0.843589
$847$		0			0
$848$	5.54058			0.190264
$849$		−	33.0406i		−	1.13395i
$850$			29.2975i			1.00490i
$851$	−1.10020			−0.0377145
$852$			21.9391i			0.751622i
$853$	38.5870			1.32119			0.660597	−	0.750741i	$-0.270303\pi$
$853$	38.5870			1.32119			0.660597	+	0.750741i	$0.270303\pi$
$854$		0			0
$855$			61.5478i			2.10489i
$856$	−12.2655			−0.419226
$857$	−42.6013			−1.45523			−0.727617	−	0.685984i	$-0.759372\pi$
$857$	−42.6013			−1.45523			−0.727617	+	0.685984i	$0.759372\pi$
$858$	29.8741	+	31.1787i	1.01989	+	1.06442i
$859$		−	12.3950i		−	0.422913i	−0.977387	−	0.211457i	$-0.932179\pi$
$859$		−	12.3950i		−	0.422913i	0.977387	−	0.211457i	$-0.0678207\pi$
$860$	31.9768			1.09040
$861$		0			0
$862$	26.8381			0.914110
$863$	−39.2748			−1.33693			−0.668465	−	0.743744i	$-0.733048\pi$
$863$	−39.2748			−1.33693			−0.668465	+	0.743744i	$0.733048\pi$
$864$	1.90732			0.0648883
$865$		−	0.271096i		−	0.00921756i
$866$	30.6912			1.04293
$867$		−	4.77440i		−	0.162147i
$868$		0			0
$869$	18.4393	−	17.6678i	0.625512	−	0.599338i
$870$	0.920312			0.0312015
$871$	19.9865			0.677216
$872$	−6.72491			−0.227734
$873$		−	62.5927i		−	2.11844i
$874$			7.26219i			0.245647i
$875$		0			0
$876$		−	10.1152i		−	0.341763i
$877$			46.1191i			1.55733i	0.627440	+	0.778665i	$0.284103\pi$
$877$			46.1191i			1.55733i	−0.627440	+	0.778665i	$0.715897\pi$
$878$			16.8452i			0.568497i
$879$			68.0589i			2.29557i
$880$	8.47510	−	8.12048i	0.285696	−	0.273741i
$881$			14.9583i			0.503957i	0.967733	+	0.251978i	$0.0810812\pi$
$881$			14.9583i			0.503957i	−0.967733	+	0.251978i	$0.918919\pi$
$882$		0			0
$883$	−8.42386			−0.283485			−0.141743	−	0.989904i	$-0.545271\pi$
$883$	−8.42386			−0.283485			−0.141743	+	0.989904i	$0.545271\pi$
$884$	19.5335			0.656983
$885$		−	133.488i		−	4.48717i
$886$		−	0.790590i		−	0.0265604i
$887$	−11.3204			−0.380103			−0.190052	−	0.981774i	$-0.560866\pi$
$887$	−11.3204			−0.380103			−0.190052	+	0.981774i	$0.560866\pi$
$888$	1.83072			0.0614348
$889$		0			0
$890$		−	21.0536i		−	0.705717i
$891$	14.3526	+	14.9793i	0.480829	+	0.501827i
$892$		−	4.01793i		−	0.134530i
$893$			30.5900i			1.02366i
$894$			6.91841i			0.231386i
$895$		−	31.7622i		−	1.06169i
$896$		0			0
$897$		−	20.3055i		−	0.677980i
$898$			15.9734i			0.533041i
$899$	0.0280301			0.000934856
$900$	−28.1036			−0.936787
$901$	−21.5729			−0.718698
$902$	−7.06002	+	6.76461i	−0.235073	+	0.225237i
$903$		0			0
$904$			11.9900i			0.398780i
$905$	−53.5980			−1.78166
$906$		−	26.9648i		−	0.895845i
$907$	54.8065			1.81982			0.909910	−	0.414805i	$-0.136150\pi$
$907$	54.8065			1.81982			0.909910	+	0.414805i	$0.136150\pi$
$908$	12.7293			0.422437
$909$	−5.23977			−0.173792
$910$		0			0
$911$	46.5914			1.54364			0.771820	−	0.635841i	$-0.219347\pi$
$911$	46.5914			1.54364			0.771820	+	0.635841i	$0.219347\pi$
$912$		−	12.0841i		−	0.400145i
$913$	6.59276	+	6.88066i	0.218188	+	0.227717i
$914$	34.9331			1.15549
$915$	−102.196			−3.37849
$916$		−	6.01345i		−	0.198690i
$917$		0			0
$918$	−7.42637			−0.245107
$919$			54.3073i			1.79143i	0.444627	+	0.895716i	$0.353336\pi$
$919$			54.3073i			1.79143i	−0.444627	+	0.895716i	$0.646664\pi$
$920$	−5.51950			−0.181973
$921$		−	66.4215i		−	2.18866i
$922$		−	20.8346i		−	0.686151i
$923$	−42.4110			−1.39598
$924$		0			0
$925$	−5.30800			−0.174526
$926$			13.1724i			0.432871i
$927$			7.70484i			0.253060i
$928$	−0.100205			−0.00328938
$929$			21.5409i			0.706734i	0.935485	+	0.353367i	$0.114963\pi$
$929$			21.5409i			0.706734i	−0.935485	+	0.353367i	$0.885037\pi$
$930$	−2.56912			−0.0842447
$931$		0			0
$932$			6.46694i			0.211832i
$933$	4.95601			0.162252
$934$	−16.8184			−0.550314
$935$	−32.9988	+	31.6181i	−1.07918	+	1.03402i
$936$			18.7375i			0.612453i
$937$	−15.2663			−0.498729			−0.249364	−	0.968410i	$-0.580222\pi$
$937$	−15.2663			−0.498729			−0.249364	+	0.968410i	$0.580222\pi$
$938$		0			0
$939$	−79.0239			−2.57885
$940$	−23.2494			−0.758312
$941$	36.1889			1.17973			0.589863	−	0.807503i	$-0.299182\pi$
$941$	36.1889			1.17973			0.589863	+	0.807503i	$0.299182\pi$
$942$		−	21.7339i		−	0.708129i
$943$	4.59792			0.149729
$944$			14.5344i			0.473054i
$945$		0			0
$946$	20.7327	+	21.6381i	0.674079	+	0.703516i
$947$	39.9218			1.29728			0.648641	−	0.761094i	$-0.275338\pi$
$947$	39.9218			1.29728			0.648641	+	0.761094i	$0.275338\pi$
$948$	19.9824			0.648998
$949$	19.5540			0.634750
$950$			35.0369i			1.13675i
$951$			89.2590i			2.89442i
$952$		0			0
$953$			8.97831i			0.290836i	0.989370	+	0.145418i	$0.0464527\pi$
$953$			8.97831i			0.290836i	−0.989370	+	0.145418i	$0.953547\pi$
$954$		−	20.6938i		−	0.669986i
$955$			21.2340i			0.687115i
$956$		−	15.5775i		−	0.503812i
$957$	0.596700	+	0.622758i	0.0192886	+	0.0201309i
$958$			22.8582i			0.738513i
$959$		0			0
$960$	9.18432			0.296423
$961$	30.9218			0.997476
$962$			3.53900i			0.114102i
$963$			45.8109i			1.47624i
$964$	−23.4762			−0.756119
$965$	52.4765			1.68928
$966$		0			0
$967$			51.5738i			1.65850i	0.558877	+	0.829251i	$0.311232\pi$
$967$			51.5738i			1.65850i	−0.558877	+	0.829251i	$0.688768\pi$
$968$	10.9900	+	0.469894i	0.353231	+	0.0151030i
$969$			47.0510i			1.51150i
$970$		−	59.3089i		−	1.90429i
$971$			33.5695i			1.07730i	0.842530	+	0.538649i	$0.181065\pi$
$971$			33.5695i			1.07730i	−0.842530	+	0.538649i	$0.818935\pi$
$972$			21.9548i			0.704201i
$973$		0			0
$974$			31.2628i			1.00173i
$975$		−	97.9650i		−	3.13739i
$976$	11.1272			0.356173
$977$	−1.15259			−0.0368746			−0.0184373	−	0.999830i	$-0.505869\pi$
$977$	−1.15259			−0.0368746			−0.0184373	+	0.999830i	$0.505869\pi$
$978$	−7.95442			−0.254354
$979$	14.2466	−	13.6504i	0.455322	−	0.436270i
$980$		0			0
$981$			25.1172i			0.801929i
$982$	22.4979			0.717938
$983$		−	16.6099i		−	0.529774i	−0.964279	−	0.264887i	$-0.914665\pi$
$983$		−	16.6099i		−	0.529774i	0.964279	−	0.264887i	$-0.0853346\pi$
$984$	−7.65083			−0.243899
$985$	−51.2251			−1.63217
$986$	0.390159			0.0124252
$987$		0			0
$988$	23.3601			0.743183
$989$		−	14.0921i		−	0.448102i
$990$	−30.3295	−	31.6541i	−0.963936	−	1.00603i
$991$	−18.4914			−0.587399			−0.293700	−	0.955898i	$-0.594887\pi$
$991$	−18.4914			−0.587399			−0.293700	+	0.955898i	$0.594887\pi$
$992$	0.279729			0.00888140
$993$			40.2586i			1.27757i
$994$		0			0
$995$	39.7283			1.25947
$996$			7.45646i			0.236267i
$997$	−21.1730			−0.670555			−0.335277	−	0.942119i	$-0.608830\pi$
$997$	−21.1730			−0.670555			−0.335277	+	0.942119i	$0.608830\pi$
$998$		−	31.9097i		−	1.01008i
$999$		−	1.34548i		−	0.0425691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.b.1077.15		16
7.2	even	3		1078.2.i.c.1011.5		16
7.3	odd	6		1078.2.i.c.901.1		16
7.4	even	3		154.2.i.a.131.4	yes	16
7.5	odd	6		154.2.i.a.87.8	yes	16
7.6	odd	2	inner	1078.2.c.b.1077.10		16
11.10	odd	2	inner	1078.2.c.b.1077.7		16
21.5	even	6		1386.2.bk.c.703.4		16
21.11	odd	6		1386.2.bk.c.901.8		16
28.11	odd	6		1232.2.bn.b.593.2		16
28.19	even	6		1232.2.bn.b.241.1		16
77.10	even	6		1078.2.i.c.901.5		16
77.32	odd	6		154.2.i.a.131.8	yes	16
77.54	even	6		154.2.i.a.87.4	✓	16
77.65	odd	6		1078.2.i.c.1011.1		16
77.76	even	2	inner	1078.2.c.b.1077.2		16
231.32	even	6		1386.2.bk.c.901.4		16
231.131	odd	6		1386.2.bk.c.703.8		16
308.131	odd	6		1232.2.bn.b.241.2		16
308.263	even	6		1232.2.bn.b.593.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.4	✓	16	77.54	even	6
154.2.i.a.87.8	yes	16	7.5	odd	6
154.2.i.a.131.4	yes	16	7.4	even	3
154.2.i.a.131.8	yes	16	77.32	odd	6
1078.2.c.b.1077.2		16	77.76	even	2	inner
1078.2.c.b.1077.7		16	11.10	odd	2	inner
1078.2.c.b.1077.10		16	7.6	odd	2	inner
1078.2.c.b.1077.15		16	1.1	even	1	trivial
1078.2.i.c.901.1		16	7.3	odd	6
1078.2.i.c.901.5		16	77.10	even	6
1078.2.i.c.1011.1		16	77.65	odd	6
1078.2.i.c.1011.5		16	7.2	even	3
1232.2.bn.b.241.1		16	28.19	even	6
1232.2.bn.b.241.2		16	308.131	odd	6
1232.2.bn.b.593.1		16	308.263	even	6
1232.2.bn.b.593.2		16	28.11	odd	6
1386.2.bk.c.703.4		16	21.5	even	6
1386.2.bk.c.703.8		16	231.131	odd	6
1386.2.bk.c.901.4		16	231.32	even	6
1386.2.bk.c.901.8		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.59518i q^{3} -1.00000 q^{4} +3.53900i q^{5} -2.59518 q^{6} -1.00000i q^{8} -3.73495 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.59518i q^{3} -1.00000 q^{4} +3.53900i q^{5} -2.59518 q^{6} -1.00000i q^{8} -3.73495 q^{9} -3.53900 q^{10} +(-2.29457 - 2.39477i) q^{11} -2.59518i q^{12} +5.01680 q^{13} -9.18432 q^{15} +1.00000 q^{16} -3.89362 q^{17} -3.73495i q^{18} -4.65637 q^{19} -3.53900i q^{20} +(2.39477 - 2.29457i) q^{22} -1.55962 q^{23} +2.59518 q^{24} -7.52450 q^{25} +5.01680i q^{26} -1.90732i q^{27} +0.100205i q^{29} -9.18432i q^{30} -0.279729i q^{31} +1.00000i q^{32} +(6.21487 - 5.95482i) q^{33} -3.89362i q^{34} +3.73495 q^{36} +0.705430 q^{37} -4.65637i q^{38} +13.0195i q^{39} +3.53900 q^{40} -2.94809 q^{41} +9.03556i q^{43} +(2.29457 + 2.39477i) q^{44} -13.2180i q^{45} -1.55962i q^{46} -6.56949i q^{47} +2.59518i q^{48} -7.52450i q^{50} -10.1046i q^{51} -5.01680 q^{52} +5.54058 q^{53} +1.90732 q^{54} +(8.47510 - 8.12048i) q^{55} -12.0841i q^{57} -0.100205 q^{58} +14.5344i q^{59} +9.18432 q^{60} +11.1272 q^{61} +0.279729 q^{62} -1.00000 q^{64} +17.7544i q^{65} +(5.95482 + 6.21487i) q^{66} +3.98392 q^{67} +3.89362 q^{68} -4.04750i q^{69} -8.45381 q^{71} +3.73495i q^{72} +3.89771 q^{73} +0.705430i q^{74} -19.5274i q^{75} +4.65637 q^{76} -13.0195 q^{78} +7.69982i q^{79} +3.53900i q^{80} -6.25501 q^{81} -2.94809i q^{82} -2.87320 q^{83} -13.7795i q^{85} -9.03556 q^{86} -0.260049 q^{87} +(-2.39477 + 2.29457i) q^{88} +5.94902i q^{89} +13.2180 q^{90} +1.55962 q^{92} +0.725946 q^{93} +6.56949 q^{94} -16.4789i q^{95} -2.59518 q^{96} +16.7587i q^{97} +(8.57010 + 8.94436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 32 * q^9	\( 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 32 * q^9 - 16 * q^11 - 8 * q^15 + 16 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 32 * q^37 + 16 * q^44 + 56 * q^53 + 24 * q^58 + 8 * q^60 - 16 * q^64 - 24 * q^67 + 8 * q^71 - 16 * q^78 + 16 * q^81 - 40 * q^86 + 8 * q^88 + 32 * q^92 + 88 * q^93 + 56 * q^99

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