LMFDB - Embedded newform 324.3.d.c.163.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,3,Mod(163,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.163"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.c.163.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -4.00000 q^{5} -3.46410i q^{7} -8.00000 q^{8} +(-4.00000 + 6.92820i) q^{10} +12.1244i q^{11} -22.0000 q^{13} +(-6.00000 - 3.46410i) q^{14} +(-8.00000 + 13.8564i) q^{16} +11.0000 q^{17} -15.5885i q^{19} +(8.00000 + 13.8564i) q^{20} +(21.0000 + 12.1244i) q^{22} +24.2487i q^{23} -9.00000 q^{25} +(-22.0000 + 38.1051i) q^{26} +(-12.0000 + 6.92820i) q^{28} -34.0000 q^{29} -6.92820i q^{31} +(16.0000 + 27.7128i) q^{32} +(11.0000 - 19.0526i) q^{34} +13.8564i q^{35} -16.0000 q^{37} +(-27.0000 - 15.5885i) q^{38} +32.0000 q^{40} -13.0000 q^{41} -50.2295i q^{43} +(42.0000 - 24.2487i) q^{44} +(42.0000 + 24.2487i) q^{46} -3.46410i q^{47} +37.0000 q^{49} +(-9.00000 + 15.5885i) q^{50} +(44.0000 + 76.2102i) q^{52} -52.0000 q^{53} -48.4974i q^{55} +27.7128i q^{56} +(-34.0000 + 58.8897i) q^{58} -53.6936i q^{59} -16.0000 q^{61} +(-12.0000 - 6.92820i) q^{62} +64.0000 q^{64} +88.0000 q^{65} -116.047i q^{67} +(-22.0000 - 38.1051i) q^{68} +(24.0000 + 13.8564i) q^{70} -25.0000 q^{73} +(-16.0000 + 27.7128i) q^{74} +(-54.0000 + 31.1769i) q^{76} +42.0000 q^{77} +27.7128i q^{79} +(32.0000 - 55.4256i) q^{80} +(-13.0000 + 22.5167i) q^{82} -34.6410i q^{83} -44.0000 q^{85} +(-87.0000 - 50.2295i) q^{86} -96.9948i q^{88} +2.00000 q^{89} +76.2102i q^{91} +(84.0000 - 48.4974i) q^{92} +(-6.00000 - 3.46410i) q^{94} +62.3538i q^{95} -43.0000 q^{97} +(37.0000 - 64.0859i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 8 q^{5} - 16 q^{8} - 8 q^{10} - 44 q^{13} - 12 q^{14} - 16 q^{16} + 22 q^{17} + 16 q^{20} + 42 q^{22} - 18 q^{25} - 44 q^{26} - 24 q^{28} - 68 q^{29} + 32 q^{32} + 22 q^{34} - 32 q^{37}+ \cdots + 74 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 8 * q^5 - 16 * q^8 - 8 * q^10 - 44 * q^13 - 12 * q^14 - 16 * q^16 + 22 * q^17 + 16 * q^20 + 42 * q^22 - 18 * q^25 - 44 * q^26 - 24 * q^28 - 68 * q^29 + 32 * q^32 + 22 * q^34 - 32 * q^37 - 54 * q^38 + 64 * q^40 - 26 * q^41 + 84 * q^44 + 84 * q^46 + 74 * q^49 - 18 * q^50 + 88 * q^52 - 104 * q^53 - 68 * q^58 - 32 * q^61 - 24 * q^62 + 128 * q^64 + 176 * q^65 - 44 * q^68 + 48 * q^70 - 50 * q^73 - 32 * q^74 - 108 * q^76 + 84 * q^77 + 64 * q^80 - 26 * q^82 - 88 * q^85 - 174 * q^86 + 4 * q^89 + 168 * q^92 - 12 * q^94 - 86 * q^97 + 74 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000	−	1.73205i	0.500000	−	0.866025i
$2$	1.00000	−	1.73205i	0.500000	−	0.866025i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	−4.00000			−0.800000			−0.400000	−	0.916515i	$-0.630990\pi$
$5$	−4.00000			−0.800000			−0.400000	+	0.916515i	$0.630990\pi$
$6$		0			0
$7$		−	3.46410i		−	0.494872i	−0.968904	−	0.247436i	$-0.920412\pi$
$7$		−	3.46410i		−	0.494872i	0.968904	−	0.247436i	$-0.0795879\pi$
$8$	−8.00000			−1.00000
$9$		0			0
$10$	−4.00000	+	6.92820i	−0.400000	+	0.692820i
$11$			12.1244i			1.10221i	0.834435	+	0.551107i	$0.185794\pi$
$11$			12.1244i			1.10221i	−0.834435	+	0.551107i	$0.814206\pi$
$12$		0			0
$13$	−22.0000			−1.69231			−0.846154	−	0.532939i	$-0.821088\pi$
$13$	−22.0000			−1.69231			−0.846154	+	0.532939i	$0.821088\pi$
$14$	−6.00000	−	3.46410i	−0.428571	−	0.247436i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	11.0000			0.647059			0.323529	−	0.946218i	$-0.395131\pi$
$17$	11.0000			0.647059			0.323529	+	0.946218i	$0.395131\pi$
$18$		0			0
$19$		−	15.5885i		−	0.820445i	−0.911985	−	0.410223i	$-0.865451\pi$
$19$		−	15.5885i		−	0.820445i	0.911985	−	0.410223i	$-0.134549\pi$
$20$	8.00000	+	13.8564i	0.400000	+	0.692820i
$21$		0			0
$22$	21.0000	+	12.1244i	0.954545	+	0.551107i
$23$			24.2487i			1.05429i	0.849775	+	0.527146i	$0.176738\pi$
$23$			24.2487i			1.05429i	−0.849775	+	0.527146i	$0.823262\pi$
$24$		0			0
$25$	−9.00000			−0.360000
$26$	−22.0000	+	38.1051i	−0.846154	+	1.46558i
$27$		0			0
$28$	−12.0000	+	6.92820i	−0.428571	+	0.247436i
$29$	−34.0000			−1.17241			−0.586207	−	0.810161i	$-0.699379\pi$
$29$	−34.0000			−1.17241			−0.586207	+	0.810161i	$0.699379\pi$
$30$		0			0
$31$		−	6.92820i		−	0.223490i	−0.993737	−	0.111745i	$-0.964356\pi$
$31$		−	6.92820i		−	0.223490i	0.993737	−	0.111745i	$-0.0356441\pi$
$32$	16.0000	+	27.7128i	0.500000	+	0.866025i
$33$		0			0
$34$	11.0000	−	19.0526i	0.323529	−	0.560369i
$35$			13.8564i			0.395897i
$36$		0			0
$37$	−16.0000			−0.432432			−0.216216	−	0.976346i	$-0.569372\pi$
$37$	−16.0000			−0.432432			−0.216216	+	0.976346i	$0.569372\pi$
$38$	−27.0000	−	15.5885i	−0.710526	−	0.410223i
$39$		0			0
$40$	32.0000			0.800000
$41$	−13.0000			−0.317073			−0.158537	−	0.987353i	$-0.550678\pi$
$41$	−13.0000			−0.317073			−0.158537	+	0.987353i	$0.550678\pi$
$42$		0			0
$43$		−	50.2295i		−	1.16813i	−0.811708	−	0.584064i	$-0.801462\pi$
$43$		−	50.2295i		−	1.16813i	0.811708	−	0.584064i	$-0.198538\pi$
$44$	42.0000	−	24.2487i	0.954545	−	0.551107i
$45$		0			0
$46$	42.0000	+	24.2487i	0.913043	+	0.527146i
$47$		−	3.46410i		−	0.0737043i	−0.999321	−	0.0368521i	$-0.988267\pi$
$47$		−	3.46410i		−	0.0737043i	0.999321	−	0.0368521i	$-0.0117331\pi$
$48$		0			0
$49$	37.0000			0.755102
$50$	−9.00000	+	15.5885i	−0.180000	+	0.311769i
$51$		0			0
$52$	44.0000	+	76.2102i	0.846154	+	1.46558i
$53$	−52.0000			−0.981132			−0.490566	−	0.871404i	$-0.663210\pi$
$53$	−52.0000			−0.981132			−0.490566	+	0.871404i	$0.663210\pi$
$54$		0			0
$55$		−	48.4974i		−	0.881771i
$56$			27.7128i			0.494872i
$57$		0			0
$58$	−34.0000	+	58.8897i	−0.586207	+	1.01534i
$59$		−	53.6936i		−	0.910061i	−0.890476	−	0.455030i	$-0.849628\pi$
$59$		−	53.6936i		−	0.910061i	0.890476	−	0.455030i	$-0.150372\pi$
$60$		0			0
$61$	−16.0000			−0.262295			−0.131148	−	0.991363i	$-0.541866\pi$
$61$	−16.0000			−0.262295			−0.131148	+	0.991363i	$0.541866\pi$
$62$	−12.0000	−	6.92820i	−0.193548	−	0.111745i
$63$		0			0
$64$	64.0000			1.00000
$65$	88.0000			1.35385
$66$		0			0
$67$		−	116.047i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$67$		−	116.047i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$68$	−22.0000	−	38.1051i	−0.323529	−	0.560369i
$69$		0			0
$70$	24.0000	+	13.8564i	0.342857	+	0.197949i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−25.0000			−0.342466			−0.171233	−	0.985231i	$-0.554775\pi$
$73$	−25.0000			−0.342466			−0.171233	+	0.985231i	$0.554775\pi$
$74$	−16.0000	+	27.7128i	−0.216216	+	0.374497i
$75$		0			0
$76$	−54.0000	+	31.1769i	−0.710526	+	0.410223i
$77$	42.0000			0.545455
$78$		0			0
$79$			27.7128i			0.350795i	0.984498	+	0.175398i	$0.0561211\pi$
$79$			27.7128i			0.350795i	−0.984498	+	0.175398i	$0.943879\pi$
$80$	32.0000	−	55.4256i	0.400000	−	0.692820i
$81$		0			0
$82$	−13.0000	+	22.5167i	−0.158537	+	0.274593i
$83$		−	34.6410i		−	0.417362i	−0.977984	−	0.208681i	$-0.933083\pi$
$83$		−	34.6410i		−	0.417362i	0.977984	−	0.208681i	$-0.0669170\pi$
$84$		0			0
$85$	−44.0000			−0.517647
$86$	−87.0000	−	50.2295i	−1.01163	−	0.584064i
$87$		0			0
$88$		−	96.9948i		−	1.10221i
$89$	2.00000			0.0224719			0.0112360	−	0.999937i	$-0.496423\pi$
$89$	2.00000			0.0224719			0.0112360	+	0.999937i	$0.496423\pi$
$90$		0			0
$91$			76.2102i			0.837475i
$92$	84.0000	−	48.4974i	0.913043	−	0.527146i
$93$		0			0
$94$	−6.00000	−	3.46410i	−0.0638298	−	0.0368521i
$95$			62.3538i			0.656356i
$96$		0			0
$97$	−43.0000			−0.443299			−0.221649	−	0.975126i	$-0.571144\pi$
$97$	−43.0000			−0.443299			−0.221649	+	0.975126i	$0.571144\pi$
$98$	37.0000	−	64.0859i	0.377551	−	0.653938i
$99$		0			0
$100$	18.0000	+	31.1769i	0.180000	+	0.311769i
$101$	20.0000			0.198020			0.0990099	−	0.995086i	$-0.468432\pi$
$101$	20.0000			0.198020			0.0990099	+	0.995086i	$0.468432\pi$
$102$		0			0
$103$			24.2487i			0.235424i	0.993048	+	0.117712i	$0.0375560\pi$
$103$			24.2487i			0.235424i	−0.993048	+	0.117712i	$0.962444\pi$
$104$	176.000			1.69231
$105$		0			0
$106$	−52.0000	+	90.0666i	−0.490566	+	0.849685i
$107$			15.5885i			0.145687i	0.997343	+	0.0728433i	$0.0232073\pi$
$107$			15.5885i			0.145687i	−0.997343	+	0.0728433i	$0.976793\pi$
$108$		0			0
$109$	−88.0000			−0.807339			−0.403670	−	0.914905i	$-0.632266\pi$
$109$	−88.0000			−0.807339			−0.403670	+	0.914905i	$0.632266\pi$
$110$	−84.0000	−	48.4974i	−0.763636	−	0.440886i
$111$		0			0
$112$	48.0000	+	27.7128i	0.428571	+	0.247436i
$113$	50.0000			0.442478			0.221239	−	0.975220i	$-0.428990\pi$
$113$	50.0000			0.442478			0.221239	+	0.975220i	$0.428990\pi$
$114$		0			0
$115$		−	96.9948i		−	0.843433i
$116$	68.0000	+	117.779i	0.586207	+	1.01534i
$117$		0			0
$118$	−93.0000	−	53.6936i	−0.788136	−	0.455030i
$119$		−	38.1051i		−	0.320211i
$120$		0			0
$121$	−26.0000			−0.214876
$122$	−16.0000	+	27.7128i	−0.131148	+	0.227154i
$123$		0			0
$124$	−24.0000	+	13.8564i	−0.193548	+	0.111745i
$125$	136.000			1.08800
$126$		0			0
$127$		−	218.238i		−	1.71841i	−0.511629	−	0.859206i	$-0.670958\pi$
$127$		−	218.238i		−	1.71841i	0.511629	−	0.859206i	$-0.329042\pi$
$128$	64.0000	−	110.851i	0.500000	−	0.866025i
$129$		0			0
$130$	88.0000	−	152.420i	0.676923	−	1.17247i
$131$		−	193.990i		−	1.48084i	−0.672146	−	0.740419i	$-0.734627\pi$
$131$		−	193.990i		−	1.48084i	0.672146	−	0.740419i	$-0.265373\pi$
$132$		0			0
$133$	−54.0000			−0.406015
$134$	−201.000	−	116.047i	−1.50000	−	0.866025i
$135$		0			0
$136$	−88.0000			−0.647059
$137$	−169.000			−1.23358			−0.616788	−	0.787129i	$-0.711567\pi$
$137$	−169.000			−1.23358			−0.616788	+	0.787129i	$0.711567\pi$
$138$		0			0
$139$			195.722i			1.40807i	0.710165	+	0.704035i	$0.248620\pi$
$139$			195.722i			1.40807i	−0.710165	+	0.704035i	$0.751380\pi$
$140$	48.0000	−	27.7128i	0.342857	−	0.197949i
$141$		0			0
$142$		0			0
$143$		−	266.736i		−	1.86529i
$144$		0			0
$145$	136.000			0.937931
$146$	−25.0000	+	43.3013i	−0.171233	+	0.296584i
$147$		0			0
$148$	32.0000	+	55.4256i	0.216216	+	0.374497i
$149$	−130.000			−0.872483			−0.436242	−	0.899830i	$-0.643691\pi$
$149$	−130.000			−0.872483			−0.436242	+	0.899830i	$0.643691\pi$
$150$		0			0
$151$			121.244i			0.802937i	0.915873	+	0.401469i	$0.131500\pi$
$151$			121.244i			0.802937i	−0.915873	+	0.401469i	$0.868500\pi$
$152$			124.708i			0.820445i
$153$		0			0
$154$	42.0000	−	72.7461i	0.272727	−	0.472377i
$155$			27.7128i			0.178792i
$156$		0			0
$157$	−4.00000			−0.0254777			−0.0127389	−	0.999919i	$-0.504055\pi$
$157$	−4.00000			−0.0254777			−0.0127389	+	0.999919i	$0.504055\pi$
$158$	48.0000	+	27.7128i	0.303797	+	0.175398i
$159$		0			0
$160$	−64.0000	−	110.851i	−0.400000	−	0.692820i
$161$	84.0000			0.521739
$162$		0			0
$163$			311.769i			1.91269i	0.292233	+	0.956347i	$0.405602\pi$
$163$			311.769i			1.91269i	−0.292233	+	0.956347i	$0.594398\pi$
$164$	26.0000	+	45.0333i	0.158537	+	0.274593i
$165$		0			0
$166$	−60.0000	−	34.6410i	−0.361446	−	0.208681i
$167$			180.133i			1.07864i	0.842100	+	0.539321i	$0.181319\pi$
$167$			180.133i			1.07864i	−0.842100	+	0.539321i	$0.818681\pi$
$168$		0			0
$169$	315.000			1.86391
$170$	−44.0000	+	76.2102i	−0.258824	+	0.448296i
$171$		0			0
$172$	−174.000	+	100.459i	−1.01163	+	0.584064i
$173$	2.00000			0.0115607			0.00578035	−	0.999983i	$-0.498160\pi$
$173$	2.00000			0.0115607			0.00578035	+	0.999983i	$0.498160\pi$
$174$		0			0
$175$			31.1769i			0.178154i
$176$	−168.000	−	96.9948i	−0.954545	−	0.551107i
$177$		0			0
$178$	2.00000	−	3.46410i	0.0112360	−	0.0194612i
$179$			187.061i			1.04504i	0.852628	+	0.522518i	$0.175007\pi$
$179$			187.061i			1.04504i	−0.852628	+	0.522518i	$0.824993\pi$
$180$		0			0
$181$	254.000			1.40331			0.701657	−	0.712514i	$-0.252444\pi$
$181$	254.000			1.40331			0.701657	+	0.712514i	$0.252444\pi$
$182$	132.000	+	76.2102i	0.725275	+	0.418738i
$183$		0			0
$184$		−	193.990i		−	1.05429i
$185$	64.0000			0.345946
$186$		0			0
$187$			133.368i			0.713197i
$188$	−12.0000	+	6.92820i	−0.0638298	+	0.0368521i
$189$		0			0
$190$	108.000	+	62.3538i	0.568421	+	0.328178i
$191$		−	3.46410i		−	0.0181367i	−0.999959	−	0.00906833i	$-0.997113\pi$
$191$		−	3.46410i		−	0.0181367i	0.999959	−	0.00906833i	$-0.00288658\pi$
$192$		0			0
$193$	−67.0000			−0.347150			−0.173575	−	0.984821i	$-0.555532\pi$
$193$	−67.0000			−0.347150			−0.173575	+	0.984821i	$0.555532\pi$
$194$	−43.0000	+	74.4782i	−0.221649	+	0.383908i
$195$		0			0
$196$	−74.0000	−	128.172i	−0.377551	−	0.653938i
$197$	−268.000			−1.36041			−0.680203	−	0.733024i	$-0.738108\pi$
$197$	−268.000			−1.36041			−0.680203	+	0.733024i	$0.738108\pi$
$198$		0			0
$199$			31.1769i			0.156668i	0.996927	+	0.0783340i	$0.0249600\pi$
$199$			31.1769i			0.156668i	−0.996927	+	0.0783340i	$0.975040\pi$
$200$	72.0000			0.360000
$201$		0			0
$202$	20.0000	−	34.6410i	0.0990099	−	0.171490i
$203$			117.779i			0.580194i
$204$		0			0
$205$	52.0000			0.253659
$206$	42.0000	+	24.2487i	0.203883	+	0.117712i
$207$		0			0
$208$	176.000	−	304.841i	0.846154	−	1.46558i
$209$	189.000			0.904306
$210$		0			0
$211$		−	131.636i		−	0.623867i	−0.950104	−	0.311933i	$-0.899023\pi$
$211$		−	131.636i		−	0.623867i	0.950104	−	0.311933i	$-0.100977\pi$
$212$	104.000	+	180.133i	0.490566	+	0.849685i
$213$		0			0
$214$	27.0000	+	15.5885i	0.126168	+	0.0728433i
$215$			200.918i			0.934502i
$216$		0			0
$217$	−24.0000			−0.110599
$218$	−88.0000	+	152.420i	−0.403670	+	0.699176i
$219$		0			0
$220$	−168.000	+	96.9948i	−0.763636	+	0.440886i
$221$	−242.000			−1.09502
$222$		0			0
$223$			58.8897i			0.264079i	0.991244	+	0.132040i	$0.0421527\pi$
$223$			58.8897i			0.264079i	−0.991244	+	0.132040i	$0.957847\pi$
$224$	96.0000	−	55.4256i	0.428571	−	0.247436i
$225$		0			0
$226$	50.0000	−	86.6025i	0.221239	−	0.383197i
$227$			448.601i			1.97622i	0.153760	+	0.988108i	$0.450862\pi$
$227$			448.601i			1.97622i	−0.153760	+	0.988108i	$0.549138\pi$
$228$		0			0
$229$	410.000			1.79039			0.895197	−	0.445672i	$-0.147035\pi$
$229$	410.000			1.79039			0.895197	+	0.445672i	$0.147035\pi$
$230$	−168.000	−	96.9948i	−0.730435	−	0.421717i
$231$		0			0
$232$	272.000			1.17241
$233$	65.0000			0.278970			0.139485	−	0.990224i	$-0.455455\pi$
$233$	65.0000			0.278970			0.139485	+	0.990224i	$0.455455\pi$
$234$		0			0
$235$			13.8564i			0.0589634i
$236$	−186.000	+	107.387i	−0.788136	+	0.455030i
$237$		0			0
$238$	−66.0000	−	38.1051i	−0.277311	−	0.160106i
$239$		−	38.1051i		−	0.159436i	−0.996817	−	0.0797178i	$-0.974598\pi$
$239$		−	38.1051i		−	0.159436i	0.996817	−	0.0797178i	$-0.0254019\pi$
$240$		0			0
$241$	−223.000			−0.925311			−0.462656	−	0.886538i	$-0.653103\pi$
$241$	−223.000			−0.925311			−0.462656	+	0.886538i	$0.653103\pi$
$242$	−26.0000	+	45.0333i	−0.107438	+	0.186088i
$243$		0			0
$244$	32.0000	+	55.4256i	0.131148	+	0.227154i
$245$	−148.000			−0.604082
$246$		0			0
$247$			342.946i			1.38845i
$248$			55.4256i			0.223490i
$249$		0			0
$250$	136.000	−	235.559i	0.544000	−	0.942236i
$251$			109.119i			0.434738i	0.976090	+	0.217369i	$0.0697475\pi$
$251$			109.119i			0.434738i	−0.976090	+	0.217369i	$0.930253\pi$
$252$		0			0
$253$	−294.000			−1.16206
$254$	−378.000	−	218.238i	−1.48819	−	0.859206i
$255$		0			0
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	437.000			1.70039			0.850195	−	0.526469i	$-0.176484\pi$
$257$	437.000			1.70039			0.850195	+	0.526469i	$0.176484\pi$
$258$		0			0
$259$			55.4256i			0.213999i
$260$	−176.000	−	304.841i	−0.676923	−	1.17247i
$261$		0			0
$262$	−336.000	−	193.990i	−1.28244	−	0.740419i
$263$		−	315.233i		−	1.19861i	−0.800522	−	0.599303i	$-0.795445\pi$
$263$		−	315.233i		−	1.19861i	0.800522	−	0.599303i	$-0.204555\pi$
$264$		0			0
$265$	208.000			0.784906
$266$	−54.0000	+	93.5307i	−0.203008	+	0.351619i
$267$		0			0
$268$	−402.000	+	232.095i	−1.50000	+	0.866025i
$269$	−304.000			−1.13011			−0.565056	−	0.825053i	$-0.691145\pi$
$269$	−304.000			−1.13011			−0.565056	+	0.825053i	$0.691145\pi$
$270$		0			0
$271$			311.769i			1.15044i	0.817999	+	0.575220i	$0.195083\pi$
$271$			311.769i			1.15044i	−0.817999	+	0.575220i	$0.804917\pi$
$272$	−88.0000	+	152.420i	−0.323529	+	0.560369i
$273$		0			0
$274$	−169.000	+	292.717i	−0.616788	+	1.06831i
$275$		−	109.119i		−	0.396797i
$276$		0			0
$277$	−34.0000			−0.122744			−0.0613718	−	0.998115i	$-0.519548\pi$
$277$	−34.0000			−0.122744			−0.0613718	+	0.998115i	$0.519548\pi$
$278$	339.000	+	195.722i	1.21942	+	0.704035i
$279$		0			0
$280$		−	110.851i		−	0.395897i
$281$	218.000			0.775801			0.387900	−	0.921701i	$-0.373200\pi$
$281$	218.000			0.775801			0.387900	+	0.921701i	$0.373200\pi$
$282$		0			0
$283$		−	6.92820i		−	0.0244813i	−0.999925	−	0.0122406i	$-0.996104\pi$
$283$		−	6.92820i		−	0.0244813i	0.999925	−	0.0122406i	$-0.00389641\pi$
$284$		0			0
$285$		0			0
$286$	−462.000	−	266.736i	−1.61538	−	0.932643i
$287$			45.0333i			0.156911i
$288$		0			0
$289$	−168.000			−0.581315
$290$	136.000	−	235.559i	0.468966	−	0.812272i
$291$		0			0
$292$	50.0000	+	86.6025i	0.171233	+	0.296584i
$293$	−202.000			−0.689420			−0.344710	−	0.938709i	$-0.612023\pi$
$293$	−202.000			−0.689420			−0.344710	+	0.938709i	$0.612023\pi$
$294$		0			0
$295$			214.774i			0.728048i
$296$	128.000			0.432432
$297$		0			0
$298$	−130.000	+	225.167i	−0.436242	+	0.755593i
$299$		−	533.472i		−	1.78419i
$300$		0			0
$301$	−174.000			−0.578073
$302$	210.000	+	121.244i	0.695364	+	0.401469i
$303$		0			0
$304$	216.000	+	124.708i	0.710526	+	0.410223i
$305$	64.0000			0.209836
$306$		0			0
$307$		−	109.119i		−	0.355437i	−0.984081	−	0.177719i	$-0.943128\pi$
$307$		−	109.119i		−	0.355437i	0.984081	−	0.177719i	$-0.0568717\pi$
$308$	−84.0000	−	145.492i	−0.272727	−	0.472377i
$309$		0			0
$310$	48.0000	+	27.7128i	0.154839	+	0.0893962i
$311$			273.664i			0.879949i	0.898010	+	0.439974i	$0.145012\pi$
$311$			273.664i			0.879949i	−0.898010	+	0.439974i	$0.854988\pi$
$312$		0			0
$313$	−79.0000			−0.252396			−0.126198	−	0.992005i	$-0.540277\pi$
$313$	−79.0000			−0.252396			−0.126198	+	0.992005i	$0.540277\pi$
$314$	−4.00000	+	6.92820i	−0.0127389	+	0.0220643i
$315$		0			0
$316$	96.0000	−	55.4256i	0.303797	−	0.175398i
$317$	−502.000			−1.58360			−0.791798	−	0.610783i	$-0.790855\pi$
$317$	−502.000			−1.58360			−0.791798	+	0.610783i	$0.790855\pi$
$318$		0			0
$319$		−	412.228i		−	1.29225i
$320$	−256.000			−0.800000
$321$		0			0
$322$	84.0000	−	145.492i	0.260870	−	0.451839i
$323$		−	171.473i		−	0.530876i
$324$		0			0
$325$	198.000			0.609231
$326$	540.000	+	311.769i	1.65644	+	0.956347i
$327$		0			0
$328$	104.000			0.317073
$329$	−12.0000			−0.0364742
$330$		0			0
$331$		−	408.764i		−	1.23494i	−0.786596	−	0.617468i	$-0.788158\pi$
$331$		−	408.764i		−	1.23494i	0.786596	−	0.617468i	$-0.211842\pi$
$332$	−120.000	+	69.2820i	−0.361446	+	0.208681i
$333$		0			0
$334$	312.000	+	180.133i	0.934132	+	0.539321i
$335$			464.190i			1.38564i
$336$		0			0
$337$	−337.000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$337$	−337.000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$338$	315.000	−	545.596i	0.931953	−	1.61419i
$339$		0			0
$340$	88.0000	+	152.420i	0.258824	+	0.448296i
$341$	84.0000			0.246334
$342$		0			0
$343$		−	297.913i		−	0.868550i
$344$			401.836i			1.16813i
$345$		0			0
$346$	2.00000	−	3.46410i	0.00578035	−	0.0100119i
$347$		−	271.932i		−	0.783666i	−0.920036	−	0.391833i	$-0.871841\pi$
$347$		−	271.932i		−	0.783666i	0.920036	−	0.391833i	$-0.128159\pi$
$348$		0			0
$349$	272.000			0.779370			0.389685	−	0.920948i	$-0.372584\pi$
$349$	272.000			0.779370			0.389685	+	0.920948i	$0.372584\pi$
$350$	54.0000	+	31.1769i	0.154286	+	0.0890769i
$351$		0			0
$352$	−336.000	+	193.990i	−0.954545	+	0.551107i
$353$	461.000			1.30595			0.652975	−	0.757380i	$-0.273521\pi$
$353$	461.000			1.30595			0.652975	+	0.757380i	$0.273521\pi$
$354$		0			0
$355$		0			0
$356$	−4.00000	−	6.92820i	−0.0112360	−	0.0194612i
$357$		0			0
$358$	324.000	+	187.061i	0.905028	+	0.522518i
$359$		−	530.008i		−	1.47634i	−0.674612	−	0.738172i	$-0.735689\pi$
$359$		−	530.008i		−	1.47634i	0.674612	−	0.738172i	$-0.264311\pi$
$360$		0			0
$361$	118.000			0.326870
$362$	254.000	−	439.941i	0.701657	−	1.21531i
$363$		0			0
$364$	264.000	−	152.420i	0.725275	−	0.418738i
$365$	100.000			0.273973
$366$		0			0
$367$		−	96.9948i		−	0.264291i	−0.991230	−	0.132146i	$-0.957813\pi$
$367$		−	96.9948i		−	0.264291i	0.991230	−	0.132146i	$-0.0421866\pi$
$368$	−336.000	−	193.990i	−0.913043	−	0.527146i
$369$		0			0
$370$	64.0000	−	110.851i	0.172973	−	0.299598i
$371$			180.133i			0.485534i
$372$		0			0
$373$	−346.000			−0.927614			−0.463807	−	0.885936i	$-0.653517\pi$
$373$	−346.000			−0.927614			−0.463807	+	0.885936i	$0.653517\pi$
$374$	231.000	+	133.368i	0.617647	+	0.356599i
$375$		0			0
$376$			27.7128i			0.0737043i
$377$	748.000			1.98408
$378$		0			0
$379$		−	327.358i		−	0.863740i	−0.901936	−	0.431870i	$-0.857854\pi$
$379$		−	327.358i		−	0.863740i	0.901936	−	0.431870i	$-0.142146\pi$
$380$	216.000	−	124.708i	0.568421	−	0.328178i
$381$		0			0
$382$	−6.00000	−	3.46410i	−0.0157068	−	0.00906833i
$383$		−	630.466i		−	1.64613i	−0.567950	−	0.823063i	$-0.692263\pi$
$383$		−	630.466i		−	1.64613i	0.567950	−	0.823063i	$-0.307737\pi$
$384$		0			0
$385$	−168.000			−0.436364
$386$	−67.0000	+	116.047i	−0.173575	+	0.300641i
$387$		0			0
$388$	86.0000	+	148.956i	0.221649	+	0.383908i
$389$	146.000			0.375321			0.187661	−	0.982234i	$-0.439909\pi$
$389$	146.000			0.375321			0.187661	+	0.982234i	$0.439909\pi$
$390$		0			0
$391$			266.736i			0.682189i
$392$	−296.000			−0.755102
$393$		0			0
$394$	−268.000	+	464.190i	−0.680203	+	1.17815i
$395$		−	110.851i		−	0.280636i
$396$		0			0
$397$	488.000			1.22922			0.614610	−	0.788831i	$-0.289314\pi$
$397$	488.000			1.22922			0.614610	+	0.788831i	$0.289314\pi$
$398$	54.0000	+	31.1769i	0.135678	+	0.0783340i
$399$		0			0
$400$	72.0000	−	124.708i	0.180000	−	0.311769i
$401$	−445.000			−1.10973			−0.554863	−	0.831942i	$-0.687229\pi$
$401$	−445.000			−1.10973			−0.554863	+	0.831942i	$0.687229\pi$
$402$		0			0
$403$			152.420i			0.378215i
$404$	−40.0000	−	69.2820i	−0.0990099	−	0.171490i
$405$		0			0
$406$	204.000	+	117.779i	0.502463	+	0.290097i
$407$		−	193.990i		−	0.476633i
$408$		0			0
$409$	−67.0000			−0.163814			−0.0819071	−	0.996640i	$-0.526101\pi$
$409$	−67.0000			−0.163814			−0.0819071	+	0.996640i	$0.526101\pi$
$410$	52.0000	−	90.0666i	0.126829	−	0.219675i
$411$		0			0
$412$	84.0000	−	48.4974i	0.203883	−	0.117712i
$413$	−186.000			−0.450363
$414$		0			0
$415$			138.564i			0.333889i
$416$	−352.000	−	609.682i	−0.846154	−	1.46558i
$417$		0			0
$418$	189.000	−	327.358i	0.452153	−	0.783152i
$419$			616.610i			1.47162i	0.677186	+	0.735812i	$0.263199\pi$
$419$			616.610i			1.47162i	−0.677186	+	0.735812i	$0.736801\pi$
$420$		0			0
$421$	272.000			0.646081			0.323040	−	0.946385i	$-0.395295\pi$
$421$	272.000			0.646081			0.323040	+	0.946385i	$0.395295\pi$
$422$	−228.000	−	131.636i	−0.540284	−	0.311933i
$423$		0			0
$424$	416.000			0.981132
$425$	−99.0000			−0.232941
$426$		0			0
$427$			55.4256i			0.129802i
$428$	54.0000	−	31.1769i	0.126168	−	0.0728433i
$429$		0			0
$430$	348.000	+	200.918i	0.809302	+	0.467251i
$431$			405.300i			0.940371i	0.882568	+	0.470185i	$0.155813\pi$
$431$			405.300i			0.940371i	−0.882568	+	0.470185i	$0.844187\pi$
$432$		0			0
$433$	−439.000			−1.01386			−0.506928	−	0.861988i	$-0.669219\pi$
$433$	−439.000			−1.01386			−0.506928	+	0.861988i	$0.669219\pi$
$434$	−24.0000	+	41.5692i	−0.0552995	+	0.0957816i
$435$		0			0
$436$	176.000	+	304.841i	0.403670	+	0.699176i
$437$	378.000			0.864989
$438$		0			0
$439$		−	845.241i		−	1.92538i	−0.270611	−	0.962689i	$-0.587226\pi$
$439$		−	845.241i		−	1.92538i	0.270611	−	0.962689i	$-0.412774\pi$
$440$			387.979i			0.881771i
$441$		0			0
$442$	−242.000	+	419.156i	−0.547511	+	0.948317i
$443$		−	330.822i		−	0.746776i	−0.927675	−	0.373388i	$-0.878196\pi$
$443$		−	330.822i		−	0.746776i	0.927675	−	0.373388i	$-0.121804\pi$
$444$		0			0
$445$	−8.00000			−0.0179775
$446$	102.000	+	58.8897i	0.228700	+	0.132040i
$447$		0			0
$448$		−	221.703i		−	0.494872i
$449$	47.0000			0.104677			0.0523385	−	0.998629i	$-0.483333\pi$
$449$	47.0000			0.104677			0.0523385	+	0.998629i	$0.483333\pi$
$450$		0			0
$451$		−	157.617i		−	0.349483i
$452$	−100.000	−	173.205i	−0.221239	−	0.383197i
$453$		0			0
$454$	777.000	+	448.601i	1.71145	+	0.988108i
$455$		−	304.841i		−	0.669980i
$456$		0			0
$457$	−331.000			−0.724289			−0.362144	−	0.932122i	$-0.617955\pi$
$457$	−331.000			−0.724289			−0.362144	+	0.932122i	$0.617955\pi$
$458$	410.000	−	710.141i	0.895197	−	1.55053i
$459$		0			0
$460$	−336.000	+	193.990i	−0.730435	+	0.421717i
$461$	−538.000			−1.16703			−0.583514	−	0.812103i	$-0.698323\pi$
$461$	−538.000			−1.16703			−0.583514	+	0.812103i	$0.698323\pi$
$462$		0			0
$463$		−	568.113i		−	1.22703i	−0.789685	−	0.613513i	$-0.789756\pi$
$463$		−	568.113i		−	1.22703i	0.789685	−	0.613513i	$-0.210244\pi$
$464$	272.000	−	471.118i	0.586207	−	1.01534i
$465$		0			0
$466$	65.0000	−	112.583i	0.139485	−	0.241595i
$467$		−	639.127i		−	1.36858i	−0.729210	−	0.684290i	$-0.760112\pi$
$467$		−	639.127i		−	1.36858i	0.729210	−	0.684290i	$-0.239888\pi$
$468$		0			0
$469$	−402.000			−0.857143
$470$	24.0000	+	13.8564i	0.0510638	+	0.0294817i
$471$		0			0
$472$			429.549i			0.910061i
$473$	609.000			1.28753
$474$		0			0
$475$			140.296i			0.295360i
$476$	−132.000	+	76.2102i	−0.277311	+	0.160106i
$477$		0			0
$478$	−66.0000	−	38.1051i	−0.138075	−	0.0797178i
$479$			121.244i			0.253118i	0.991959	+	0.126559i	$0.0403933\pi$
$479$			121.244i			0.253118i	−0.991959	+	0.126559i	$0.959607\pi$
$480$		0			0
$481$	352.000			0.731809
$482$	−223.000	+	386.247i	−0.462656	+	0.801343i
$483$		0			0
$484$	52.0000	+	90.0666i	0.107438	+	0.186088i
$485$	172.000			0.354639
$486$		0			0
$487$		−	405.300i		−	0.832238i	−0.909310	−	0.416119i	$-0.863390\pi$
$487$		−	405.300i		−	0.832238i	0.909310	−	0.416119i	$-0.136610\pi$
$488$	128.000			0.262295
$489$		0			0
$490$	−148.000	+	256.344i	−0.302041	+	0.523150i
$491$			725.729i			1.47806i	0.673670	+	0.739032i	$0.264717\pi$
$491$			725.729i			1.47806i	−0.673670	+	0.739032i	$0.735283\pi$
$492$		0			0
$493$	−374.000			−0.758621
$494$	594.000	+	342.946i	1.20243	+	0.694223i
$495$		0			0
$496$	96.0000	+	55.4256i	0.193548	+	0.111745i
$497$		0			0
$498$		0			0
$499$		−	521.347i		−	1.04478i	−0.852705	−	0.522392i	$-0.825040\pi$
$499$		−	521.347i		−	1.04478i	0.852705	−	0.522392i	$-0.174960\pi$
$500$	−272.000	−	471.118i	−0.544000	−	0.942236i
$501$		0			0
$502$	189.000	+	109.119i	0.376494	+	0.217369i
$503$			872.954i			1.73549i	0.497006	+	0.867747i	$0.334433\pi$
$503$			872.954i			1.73549i	−0.497006	+	0.867747i	$0.665567\pi$
$504$		0			0
$505$	−80.0000			−0.158416
$506$	−294.000	+	509.223i	−0.581028	+	1.00637i
$507$		0			0
$508$	−756.000	+	436.477i	−1.48819	+	0.859206i
$509$	−760.000			−1.49312			−0.746562	−	0.665316i	$-0.768297\pi$
$509$	−760.000			−1.49312			−0.746562	+	0.665316i	$0.768297\pi$
$510$		0			0
$511$			86.6025i			0.169477i
$512$	−512.000			−1.00000
$513$		0			0
$514$	437.000	−	756.906i	0.850195	−	1.47258i
$515$		−	96.9948i		−	0.188340i
$516$		0			0
$517$	42.0000			0.0812379
$518$	96.0000	+	55.4256i	0.185328	+	0.106999i
$519$		0			0
$520$	−704.000			−1.35385
$521$	−745.000			−1.42994			−0.714971	−	0.699154i	$-0.753560\pi$
$521$	−745.000			−1.42994			−0.714971	+	0.699154i	$0.753560\pi$
$522$		0			0
$523$		−	561.184i		−	1.07301i	−0.843897	−	0.536505i	$-0.819744\pi$
$523$		−	561.184i		−	1.07301i	0.843897	−	0.536505i	$-0.180256\pi$
$524$	−672.000	+	387.979i	−1.28244	+	0.740419i
$525$		0			0
$526$	−546.000	−	315.233i	−1.03802	−	0.599303i
$527$		−	76.2102i		−	0.144611i
$528$		0			0
$529$	−59.0000			−0.111531
$530$	208.000	−	360.267i	0.392453	−	0.679748i
$531$		0			0
$532$	108.000	+	187.061i	0.203008	+	0.351619i
$533$	286.000			0.536585
$534$		0			0
$535$		−	62.3538i		−	0.116549i
$536$			928.379i			1.73205i
$537$		0			0
$538$	−304.000	+	526.543i	−0.565056	+	0.978705i
$539$			448.601i			0.832284i
$540$		0			0
$541$	−520.000			−0.961183			−0.480591	−	0.876945i	$-0.659578\pi$
$541$	−520.000			−0.961183			−0.480591	+	0.876945i	$0.659578\pi$
$542$	540.000	+	311.769i	0.996310	+	0.575220i
$543$		0			0
$544$	176.000	+	304.841i	0.323529	+	0.560369i
$545$	352.000			0.645872
$546$		0			0
$547$			386.247i			0.706119i	0.935601	+	0.353060i	$0.114859\pi$
$547$			386.247i			0.706119i	−0.935601	+	0.353060i	$0.885141\pi$
$548$	338.000	+	585.433i	0.616788	+	1.06831i
$549$		0			0
$550$	−189.000	−	109.119i	−0.343636	−	0.198399i
$551$			530.008i			0.961901i
$552$		0			0
$553$	96.0000			0.173599
$554$	−34.0000	+	58.8897i	−0.0613718	+	0.106299i
$555$		0			0
$556$	678.000	−	391.443i	1.21942	−	0.704035i
$557$	−934.000			−1.67684			−0.838420	−	0.545025i	$-0.816520\pi$
$557$	−934.000			−1.67684			−0.838420	+	0.545025i	$0.816520\pi$
$558$		0			0
$559$			1105.05i			1.97683i
$560$	−192.000	−	110.851i	−0.342857	−	0.197949i
$561$		0			0
$562$	218.000	−	377.587i	0.387900	−	0.671863i
$563$		−	708.409i		−	1.25827i	−0.777294	−	0.629137i	$-0.783408\pi$
$563$		−	708.409i		−	1.25827i	0.777294	−	0.629137i	$-0.216592\pi$
$564$		0			0
$565$	−200.000			−0.353982
$566$	−12.0000	−	6.92820i	−0.0212014	−	0.0122406i
$567$		0			0
$568$		0			0
$569$	695.000			1.22144			0.610721	−	0.791846i	$-0.290880\pi$
$569$	695.000			1.22144			0.610721	+	0.791846i	$0.290880\pi$
$570$		0			0
$571$			538.668i			0.943376i	0.881765	+	0.471688i	$0.156355\pi$
$571$			538.668i			0.943376i	−0.881765	+	0.471688i	$0.843645\pi$
$572$	−924.000	+	533.472i	−1.61538	+	0.932643i
$573$		0			0
$574$	78.0000	+	45.0333i	0.135889	+	0.0784553i
$575$		−	218.238i		−	0.379545i
$576$		0			0
$577$	227.000			0.393414			0.196707	−	0.980462i	$-0.436975\pi$
$577$	227.000			0.393414			0.196707	+	0.980462i	$0.436975\pi$
$578$	−168.000	+	290.985i	−0.290657	+	0.503433i
$579$		0			0
$580$	−272.000	−	471.118i	−0.468966	−	0.812272i
$581$	−120.000			−0.206540
$582$		0			0
$583$		−	630.466i		−	1.08142i
$584$	200.000			0.342466
$585$		0			0
$586$	−202.000	+	349.874i	−0.344710	+	0.597055i
$587$		−	143.760i		−	0.244907i	−0.992474	−	0.122453i	$-0.960924\pi$
$587$		−	143.760i		−	0.244907i	0.992474	−	0.122453i	$-0.0390762\pi$
$588$		0			0
$589$	−108.000			−0.183362
$590$	372.000	+	214.774i	0.630508	+	0.364024i
$591$		0			0
$592$	128.000	−	221.703i	0.216216	−	0.374497i
$593$	506.000			0.853288			0.426644	−	0.904420i	$-0.359696\pi$
$593$	506.000			0.853288			0.426644	+	0.904420i	$0.359696\pi$
$594$		0			0
$595$			152.420i			0.256169i
$596$	260.000	+	450.333i	0.436242	+	0.755593i
$597$		0			0
$598$	−924.000	−	533.472i	−1.54515	−	0.892093i
$599$			55.4256i			0.0925303i	0.998929	+	0.0462651i	$0.0147319\pi$
$599$			55.4256i			0.0925303i	−0.998929	+	0.0462651i	$0.985268\pi$
$600$		0			0
$601$	335.000			0.557404			0.278702	−	0.960378i	$-0.410096\pi$
$601$	335.000			0.557404			0.278702	+	0.960378i	$0.410096\pi$
$602$	−174.000	+	301.377i	−0.289037	+	0.500626i
$603$		0			0
$604$	420.000	−	242.487i	0.695364	−	0.401469i
$605$	104.000			0.171901
$606$		0			0
$607$		−	630.466i		−	1.03866i	−0.854574	−	0.519330i	$-0.826182\pi$
$607$		−	630.466i		−	1.03866i	0.854574	−	0.519330i	$-0.173818\pi$
$608$	432.000	−	249.415i	0.710526	−	0.410223i
$609$		0			0
$610$	64.0000	−	110.851i	0.104918	−	0.181723i
$611$			76.2102i			0.124730i
$612$		0			0
$613$	−340.000			−0.554649			−0.277325	−	0.960776i	$-0.589448\pi$
$613$	−340.000			−0.554649			−0.277325	+	0.960776i	$0.589448\pi$
$614$	−189.000	−	109.119i	−0.307818	−	0.177719i
$615$		0			0
$616$	−336.000			−0.545455
$617$	−391.000			−0.633712			−0.316856	−	0.948474i	$-0.602627\pi$
$617$	−391.000			−0.633712			−0.316856	+	0.948474i	$0.602627\pi$
$618$		0			0
$619$			12.1244i			0.0195870i	0.999952	+	0.00979350i	$0.00311742\pi$
$619$			12.1244i			0.0195870i	−0.999952	+	0.00979350i	$0.996883\pi$
$620$	96.0000	−	55.4256i	0.154839	−	0.0893962i
$621$		0			0
$622$	474.000	+	273.664i	0.762058	+	0.439974i
$623$		−	6.92820i		−	0.0111207i
$624$		0			0
$625$	−319.000			−0.510400
$626$	−79.0000	+	136.832i	−0.126198	+	0.218581i
$627$		0			0
$628$	8.00000	+	13.8564i	0.0127389	+	0.0220643i
$629$	−176.000			−0.279809
$630$		0			0
$631$			436.477i			0.691722i	0.938286	+	0.345861i	$0.112413\pi$
$631$			436.477i			0.691722i	−0.938286	+	0.345861i	$0.887587\pi$
$632$		−	221.703i		−	0.350795i
$633$		0			0
$634$	−502.000	+	869.490i	−0.791798	+	1.37143i
$635$			872.954i			1.37473i
$636$		0			0
$637$	−814.000			−1.27786
$638$	−714.000	−	412.228i	−1.11912	−	0.646126i
$639$		0			0
$640$	−256.000	+	443.405i	−0.400000	+	0.692820i
$641$	−421.000			−0.656786			−0.328393	−	0.944541i	$-0.606507\pi$
$641$	−421.000			−0.656786			−0.328393	+	0.944541i	$0.606507\pi$
$642$		0			0
$643$			413.960i			0.643795i	0.946775	+	0.321897i	$0.104321\pi$
$643$			413.960i			0.643795i	−0.946775	+	0.321897i	$0.895679\pi$
$644$	−168.000	−	290.985i	−0.260870	−	0.451839i
$645$		0			0
$646$	−297.000	−	171.473i	−0.459752	−	0.265438i
$647$			405.300i			0.626430i	0.949682	+	0.313215i	$0.101406\pi$
$647$			405.300i			0.626430i	−0.949682	+	0.313215i	$0.898594\pi$
$648$		0			0
$649$	651.000			1.00308
$650$	198.000	−	342.946i	0.304615	−	0.527609i
$651$		0			0
$652$	1080.00	−	623.538i	1.65644	−	0.956347i
$653$	−886.000			−1.35681			−0.678407	−	0.734686i	$-0.737330\pi$
$653$	−886.000			−1.35681			−0.678407	+	0.734686i	$0.737330\pi$
$654$		0			0
$655$			775.959i			1.18467i
$656$	104.000	−	180.133i	0.158537	−	0.274593i
$657$		0			0
$658$	−12.0000	+	20.7846i	−0.0182371	+	0.0315876i
$659$			838.313i			1.27210i	0.771649	+	0.636049i	$0.219432\pi$
$659$			838.313i			1.27210i	−0.771649	+	0.636049i	$0.780568\pi$
$660$		0			0
$661$	248.000			0.375189			0.187595	−	0.982247i	$-0.439931\pi$
$661$	248.000			0.375189			0.187595	+	0.982247i	$0.439931\pi$
$662$	−708.000	−	408.764i	−1.06949	−	0.617468i
$663$		0			0
$664$			277.128i			0.417362i
$665$	216.000			0.324812
$666$		0			0
$667$		−	824.456i		−	1.23607i
$668$	624.000	−	360.267i	0.934132	−	0.539321i
$669$		0			0
$670$	804.000	+	464.190i	1.20000	+	0.692820i
$671$		−	193.990i		−	0.289105i
$672$		0			0
$673$	1154.00			1.71471			0.857355	−	0.514725i	$-0.172106\pi$
$673$	1154.00			1.71471			0.857355	+	0.514725i	$0.172106\pi$
$674$	−337.000	+	583.701i	−0.500000	+	0.866025i
$675$		0			0
$676$	−630.000	−	1091.19i	−0.931953	−	1.61419i
$677$	−1132.00			−1.67208			−0.836041	−	0.548666i	$-0.815136\pi$
$677$	−1132.00			−1.67208			−0.836041	+	0.548666i	$0.815136\pi$
$678$		0			0
$679$			148.956i			0.219376i
$680$	352.000			0.517647
$681$		0			0
$682$	84.0000	−	145.492i	0.123167	−	0.213332i
$683$		−	795.011i		−	1.16400i	−0.813189	−	0.582000i	$-0.802271\pi$
$683$		−	795.011i		−	1.16400i	0.813189	−	0.582000i	$-0.197729\pi$
$684$		0			0
$685$	676.000			0.986861
$686$	−516.000	−	297.913i	−0.752187	−	0.434275i
$687$		0			0
$688$	696.000	+	401.836i	1.01163	+	0.584064i
$689$	1144.00			1.66038
$690$		0			0
$691$			900.666i			1.30342i	0.758466	+	0.651712i	$0.225949\pi$
$691$			900.666i			1.30342i	−0.758466	+	0.651712i	$0.774051\pi$
$692$	−4.00000	−	6.92820i	−0.00578035	−	0.0100119i
$693$		0			0
$694$	−471.000	−	271.932i	−0.678674	−	0.391833i
$695$		−	782.887i		−	1.12646i
$696$		0			0
$697$	−143.000			−0.205165
$698$	272.000	−	471.118i	0.389685	−	0.674954i
$699$		0			0
$700$	108.000	−	62.3538i	0.154286	−	0.0890769i
$701$	−142.000			−0.202568			−0.101284	−	0.994858i	$-0.532295\pi$
$701$	−142.000			−0.202568			−0.101284	+	0.994858i	$0.532295\pi$
$702$		0			0
$703$			249.415i			0.354787i
$704$			775.959i			1.10221i
$705$		0			0
$706$	461.000	−	798.475i	0.652975	−	1.13099i
$707$		−	69.2820i		−	0.0979944i
$708$		0			0
$709$	740.000			1.04372			0.521862	−	0.853030i	$-0.325238\pi$
$709$	740.000			1.04372			0.521862	+	0.853030i	$0.325238\pi$
$710$		0			0
$711$		0			0
$712$	−16.0000			−0.0224719
$713$	168.000			0.235624
$714$		0			0
$715$			1066.94i			1.49223i
$716$	648.000	−	374.123i	0.905028	−	0.522518i
$717$		0			0
$718$	−918.000	−	530.008i	−1.27855	−	0.738172i
$719$			124.708i			0.173446i	0.996232	+	0.0867230i	$0.0276395\pi$
$719$			124.708i			0.173446i	−0.996232	+	0.0867230i	$0.972360\pi$
$720$		0			0
$721$	84.0000			0.116505
$722$	118.000	−	204.382i	0.163435	−	0.283078i
$723$		0			0
$724$	−508.000	−	879.882i	−0.701657	−	1.21531i
$725$	306.000			0.422069
$726$		0			0
$727$		−	814.064i		−	1.11976i	−0.828574	−	0.559879i	$-0.810848\pi$
$727$		−	814.064i		−	1.11976i	0.828574	−	0.559879i	$-0.189152\pi$
$728$		−	609.682i		−	0.837475i
$729$		0			0
$730$	100.000	−	173.205i	0.136986	−	0.237267i
$731$		−	552.524i		−	0.755847i
$732$		0			0
$733$	914.000			1.24693			0.623465	−	0.781851i	$-0.285724\pi$
$733$	914.000			1.24693			0.623465	+	0.781851i	$0.285724\pi$
$734$	−168.000	−	96.9948i	−0.228883	−	0.132146i
$735$		0			0
$736$	−672.000	+	387.979i	−0.913043	+	0.527146i
$737$	1407.00			1.90909
$738$		0			0
$739$			358.535i			0.485162i	0.970131	+	0.242581i	$0.0779940\pi$
$739$			358.535i			0.485162i	−0.970131	+	0.242581i	$0.922006\pi$
$740$	−128.000	−	221.703i	−0.172973	−	0.299598i
$741$		0			0
$742$	312.000	+	180.133i	0.420485	+	0.242767i
$743$			398.372i			0.536166i	0.963396	+	0.268083i	$0.0863902\pi$
$743$			398.372i			0.536166i	−0.963396	+	0.268083i	$0.913610\pi$
$744$		0			0
$745$	520.000			0.697987
$746$	−346.000	+	599.290i	−0.463807	+	0.803337i
$747$		0			0
$748$	462.000	−	266.736i	0.617647	−	0.356599i
$749$	54.0000			0.0720961
$750$		0			0
$751$			1115.44i			1.48527i	0.669694	+	0.742637i	$0.266425\pi$
$751$			1115.44i			1.48527i	−0.669694	+	0.742637i	$0.733575\pi$
$752$	48.0000	+	27.7128i	0.0638298	+	0.0368521i
$753$		0			0
$754$	748.000	−	1295.57i	0.992042	−	1.71827i
$755$		−	484.974i		−	0.642350i
$756$		0			0
$757$	758.000			1.00132			0.500661	−	0.865644i	$-0.333091\pi$
$757$	758.000			1.00132			0.500661	+	0.865644i	$0.333091\pi$
$758$	−567.000	−	327.358i	−0.748021	−	0.431870i
$759$		0			0
$760$		−	498.831i		−	0.656356i
$761$	374.000			0.491459			0.245729	−	0.969338i	$-0.420973\pi$
$761$	374.000			0.491459			0.245729	+	0.969338i	$0.420973\pi$
$762$		0			0
$763$			304.841i			0.399529i
$764$	−12.0000	+	6.92820i	−0.0157068	+	0.00906833i
$765$		0			0
$766$	−1092.00	−	630.466i	−1.42559	−	0.823063i
$767$			1181.26i			1.54010i
$768$		0			0
$769$	−22.0000			−0.0286086			−0.0143043	−	0.999898i	$-0.504553\pi$
$769$	−22.0000			−0.0286086			−0.0143043	+	0.999898i	$0.504553\pi$
$770$	−168.000	+	290.985i	−0.218182	+	0.377902i
$771$		0			0
$772$	134.000	+	232.095i	0.173575	+	0.300641i
$773$	1334.00			1.72574			0.862872	−	0.505423i	$-0.168663\pi$
$773$	1334.00			1.72574			0.862872	+	0.505423i	$0.168663\pi$
$774$		0			0
$775$			62.3538i			0.0804566i
$776$	344.000			0.443299
$777$		0			0
$778$	146.000	−	252.879i	0.187661	−	0.325038i
$779$			202.650i			0.260141i
$780$		0			0
$781$		0			0
$782$	462.000	+	266.736i	0.590793	+	0.341094i
$783$		0			0
$784$	−296.000	+	512.687i	−0.377551	+	0.653938i
$785$	16.0000			0.0203822
$786$		0			0
$787$		−	879.882i		−	1.11802i	−0.829161	−	0.559010i	$-0.811181\pi$
$787$		−	879.882i		−	1.11802i	0.829161	−	0.559010i	$-0.188819\pi$
$788$	536.000	+	928.379i	0.680203	+	1.17815i
$789$		0			0
$790$	−192.000	−	110.851i	−0.243038	−	0.140318i
$791$		−	173.205i		−	0.218970i
$792$		0			0
$793$	352.000			0.443884
$794$	488.000	−	845.241i	0.614610	−	1.06454i
$795$		0			0
$796$	108.000	−	62.3538i	0.135678	−	0.0783340i
$797$	−832.000			−1.04391			−0.521957	−	0.852972i	$-0.674798\pi$
$797$	−832.000			−1.04391			−0.521957	+	0.852972i	$0.674798\pi$
$798$		0			0
$799$		−	38.1051i		−	0.0476910i
$800$	−144.000	−	249.415i	−0.180000	−	0.311769i
$801$		0			0
$802$	−445.000	+	770.763i	−0.554863	+	0.961051i
$803$		−	303.109i		−	0.377471i
$804$		0			0
$805$	−336.000			−0.417391
$806$	264.000	+	152.420i	0.327543	+	0.189107i
$807$		0			0
$808$	−160.000			−0.198020
$809$	−493.000			−0.609394			−0.304697	−	0.952449i	$-0.598555\pi$
$809$	−493.000			−0.609394			−0.304697	+	0.952449i	$0.598555\pi$
$810$		0			0
$811$			327.358i			0.403647i	0.979422	+	0.201823i	$0.0646867\pi$
$811$			327.358i			0.403647i	−0.979422	+	0.201823i	$0.935313\pi$
$812$	408.000	−	235.559i	0.502463	−	0.290097i
$813$		0			0
$814$	−336.000	−	193.990i	−0.412776	−	0.238317i
$815$		−	1247.08i		−	1.53016i
$816$		0			0
$817$	−783.000			−0.958384
$818$	−67.0000	+	116.047i	−0.0819071	+	0.141867i
$819$		0			0
$820$	−104.000	−	180.133i	−0.126829	−	0.219675i
$821$	758.000			0.923264			0.461632	−	0.887071i	$-0.347264\pi$
$821$	758.000			0.923264			0.461632	+	0.887071i	$0.347264\pi$
$822$		0			0
$823$			866.025i			1.05228i	0.850398	+	0.526139i	$0.176361\pi$
$823$			866.025i			1.05228i	−0.850398	+	0.526139i	$0.823639\pi$
$824$		−	193.990i		−	0.235424i
$825$		0			0
$826$	−186.000	+	322.161i	−0.225182	+	0.390026i
$827$			436.477i			0.527783i	0.964552	+	0.263892i	$0.0850061\pi$
$827$			436.477i			0.527783i	−0.964552	+	0.263892i	$0.914994\pi$
$828$		0			0
$829$	−718.000			−0.866104			−0.433052	−	0.901369i	$-0.642563\pi$
$829$	−718.000			−0.866104			−0.433052	+	0.901369i	$0.642563\pi$
$830$	240.000	+	138.564i	0.289157	+	0.166945i
$831$		0			0
$832$	−1408.00			−1.69231
$833$	407.000			0.488595
$834$		0			0
$835$		−	720.533i		−	0.862914i
$836$	−378.000	−	654.715i	−0.452153	−	0.783152i
$837$		0			0
$838$	1068.00	+	616.610i	1.27446	+	0.735812i
$839$		−	907.595i		−	1.08176i	−0.841101	−	0.540879i	$-0.818092\pi$
$839$		−	907.595i		−	1.08176i	0.841101	−	0.540879i	$-0.181908\pi$
$840$		0			0
$841$	315.000			0.374554
$842$	272.000	−	471.118i	0.323040	−	0.559522i
$843$		0			0
$844$	−456.000	+	263.272i	−0.540284	+	0.311933i
$845$	−1260.00			−1.49112
$846$		0			0
$847$			90.0666i			0.106336i
$848$	416.000	−	720.533i	0.490566	−	0.849685i
$849$		0			0
$850$	−99.0000	+	171.473i	−0.116471	+	0.201733i
$851$		−	387.979i		−	0.455910i
$852$		0			0
$853$	146.000			0.171161			0.0855803	−	0.996331i	$-0.472726\pi$
$853$	146.000			0.171161			0.0855803	+	0.996331i	$0.472726\pi$
$854$	96.0000	+	55.4256i	0.112412	+	0.0649012i
$855$		0			0
$856$		−	124.708i		−	0.145687i
$857$	146.000			0.170362			0.0851809	−	0.996366i	$-0.472853\pi$
$857$	146.000			0.170362			0.0851809	+	0.996366i	$0.472853\pi$
$858$		0			0
$859$		−	84.8705i		−	0.0988015i	−0.998779	−	0.0494008i	$-0.984269\pi$
$859$		−	84.8705i		−	0.0988015i	0.998779	−	0.0494008i	$-0.0157312\pi$
$860$	696.000	−	401.836i	0.809302	−	0.467251i
$861$		0			0
$862$	702.000	+	405.300i	0.814385	+	0.470185i
$863$		−	1184.72i		−	1.37280i	−0.727226	−	0.686398i	$-0.759191\pi$
$863$		−	1184.72i		−	1.37280i	0.727226	−	0.686398i	$-0.240809\pi$
$864$		0			0
$865$	−8.00000			−0.00924855
$866$	−439.000	+	760.370i	−0.506928	+	0.878026i
$867$		0			0
$868$	48.0000	+	83.1384i	0.0552995	+	0.0957816i
$869$	−336.000			−0.386651
$870$		0			0
$871$			2553.04i			2.93116i
$872$	704.000			0.807339
$873$		0			0
$874$	378.000	−	654.715i	0.432494	−	0.749102i
$875$		−	471.118i		−	0.538420i
$876$		0			0
$877$	−1480.00			−1.68757			−0.843786	−	0.536680i	$-0.819678\pi$
$877$	−1480.00			−1.68757			−0.843786	+	0.536680i	$0.819678\pi$
$878$	−1464.00	−	845.241i	−1.66743	−	0.962689i
$879$		0			0
$880$	672.000	+	387.979i	0.763636	+	0.440886i
$881$	−142.000			−0.161180			−0.0805902	−	0.996747i	$-0.525681\pi$
$881$	−142.000			−0.161180			−0.0805902	+	0.996747i	$0.525681\pi$
$882$		0			0
$883$			1200.31i			1.35936i	0.733511	+	0.679678i	$0.237880\pi$
$883$			1200.31i			1.35936i	−0.733511	+	0.679678i	$0.762120\pi$
$884$	484.000	+	838.313i	0.547511	+	0.948317i
$885$		0			0
$886$	−573.000	−	330.822i	−0.646727	−	0.373388i
$887$		−	630.466i		−	0.710785i	−0.934717	−	0.355393i	$-0.884347\pi$
$887$		−	630.466i		−	0.710785i	0.934717	−	0.355393i	$-0.115653\pi$
$888$		0			0
$889$	−756.000			−0.850394
$890$	−8.00000	+	13.8564i	−0.00898876	+	0.0155690i
$891$		0			0
$892$	204.000	−	117.779i	0.228700	−	0.132040i
$893$	−54.0000			−0.0604703
$894$		0			0
$895$		−	748.246i		−	0.836029i
$896$	−384.000	−	221.703i	−0.428571	−	0.247436i
$897$		0			0
$898$	47.0000	−	81.4064i	0.0523385	−	0.0906530i
$899$			235.559i			0.262023i
$900$		0			0
$901$	−572.000			−0.634850
$902$	−273.000	−	157.617i	−0.302661	−	0.174741i
$903$		0			0
$904$	−400.000			−0.442478
$905$	−1016.00			−1.12265
$906$		0			0
$907$		−	642.591i		−	0.708479i	−0.935155	−	0.354240i	$-0.884740\pi$
$907$		−	642.591i		−	0.708479i	0.935155	−	0.354240i	$-0.115260\pi$
$908$	1554.00	−	897.202i	1.71145	−	0.988108i
$909$		0			0
$910$	−528.000	−	304.841i	−0.580220	−	0.334990i
$911$			401.836i			0.441093i	0.975376	+	0.220547i	$0.0707841\pi$
$911$			401.836i			0.441093i	−0.975376	+	0.220547i	$0.929216\pi$
$912$		0			0
$913$	420.000			0.460022
$914$	−331.000	+	573.309i	−0.362144	+	0.627253i
$915$		0			0
$916$	−820.000	−	1420.28i	−0.895197	−	1.55053i
$917$	−672.000			−0.732824
$918$		0			0
$919$		−	779.423i		−	0.848121i	−0.905634	−	0.424060i	$-0.860604\pi$
$919$		−	779.423i		−	0.848121i	0.905634	−	0.424060i	$-0.139396\pi$
$920$			775.959i			0.843433i
$921$		0			0
$922$	−538.000	+	931.843i	−0.583514	+	1.01068i
$923$		0			0
$924$		0			0
$925$	144.000			0.155676
$926$	−984.000	−	568.113i	−1.06263	−	0.613513i
$927$		0			0
$928$	−544.000	−	942.236i	−0.586207	−	1.01534i
$929$	758.000			0.815931			0.407966	−	0.912997i	$-0.366238\pi$
$929$	758.000			0.815931			0.407966	+	0.912997i	$0.366238\pi$
$930$		0			0
$931$		−	576.773i		−	0.619520i
$932$	−130.000	−	225.167i	−0.139485	−	0.241595i
$933$		0			0
$934$	−1107.00	−	639.127i	−1.18522	−	0.684290i
$935$		−	533.472i		−	0.570558i
$936$		0			0
$937$	−754.000			−0.804696			−0.402348	−	0.915487i	$-0.631806\pi$
$937$	−754.000			−0.804696			−0.402348	+	0.915487i	$0.631806\pi$
$938$	−402.000	+	696.284i	−0.428571	+	0.742307i
$939$		0			0
$940$	48.0000	−	27.7128i	0.0510638	−	0.0294817i
$941$	1796.00			1.90861			0.954304	−	0.298838i	$-0.0965989\pi$
$941$	1796.00			1.90861			0.954304	+	0.298838i	$0.0965989\pi$
$942$		0			0
$943$		−	315.233i		−	0.334288i
$944$	744.000	+	429.549i	0.788136	+	0.455030i
$945$		0			0
$946$	609.000	−	1054.82i	0.643763	−	1.11503i
$947$			105.655i			0.111568i	0.998443	+	0.0557841i	$0.0177659\pi$
$947$			105.655i			0.111568i	−0.998443	+	0.0557841i	$0.982234\pi$
$948$		0			0
$949$	550.000			0.579557
$950$	243.000	+	140.296i	0.255789	+	0.147680i
$951$		0			0
$952$			304.841i			0.320211i
$953$	−1213.00			−1.27282			−0.636411	−	0.771350i	$-0.719582\pi$
$953$	−1213.00			−1.27282			−0.636411	+	0.771350i	$0.719582\pi$
$954$		0			0
$955$			13.8564i			0.0145093i
$956$	−132.000	+	76.2102i	−0.138075	+	0.0797178i
$957$		0			0
$958$	210.000	+	121.244i	0.219207	+	0.126559i
$959$			585.433i			0.610462i
$960$		0			0
$961$	913.000			0.950052
$962$	352.000	−	609.682i	0.365904	−	0.633765i
$963$		0			0
$964$	446.000	+	772.495i	0.462656	+	0.801343i
$965$	268.000			0.277720
$966$		0			0
$967$		−	349.874i		−	0.361814i	−0.983500	−	0.180907i	$-0.942097\pi$
$967$		−	349.874i		−	0.361814i	0.983500	−	0.180907i	$-0.0579033\pi$
$968$	208.000			0.214876
$969$		0			0
$970$	172.000	−	297.913i	0.177320	−	0.307127i
$971$			1434.14i			1.47697i	0.674270	+	0.738485i	$0.264458\pi$
$971$			1434.14i			1.47697i	−0.674270	+	0.738485i	$0.735542\pi$
$972$		0			0
$973$	678.000			0.696814
$974$	−702.000	−	405.300i	−0.720739	−	0.416119i
$975$		0			0
$976$	128.000	−	221.703i	0.131148	−	0.227154i
$977$	−157.000			−0.160696			−0.0803480	−	0.996767i	$-0.525603\pi$
$977$	−157.000			−0.160696			−0.0803480	+	0.996767i	$0.525603\pi$
$978$		0			0
$979$			24.2487i			0.0247689i
$980$	296.000	+	512.687i	0.302041	+	0.523150i
$981$		0			0
$982$	1257.00	+	725.729i	1.28004	+	0.739032i
$983$		−	1406.43i		−	1.43075i	−0.698742	−	0.715374i	$-0.746256\pi$
$983$		−	1406.43i		−	1.43075i	0.698742	−	0.715374i	$-0.253744\pi$
$984$		0			0
$985$	1072.00			1.08832
$986$	−374.000	+	647.787i	−0.379310	+	0.656985i
$987$		0			0
$988$	1188.00	−	685.892i	1.20243	−	0.694223i
$989$	1218.00			1.23155
$990$		0			0
$991$			249.415i			0.251680i	0.992051	+	0.125840i	$0.0401627\pi$
$991$			249.415i			0.251680i	−0.992051	+	0.125840i	$0.959837\pi$
$992$	192.000	−	110.851i	0.193548	−	0.111745i
$993$		0			0
$994$		0			0
$995$		−	124.708i		−	0.125334i
$996$		0			0
$997$	−412.000			−0.413240			−0.206620	−	0.978421i	$-0.566246\pi$
$997$	−412.000			−0.413240			−0.206620	+	0.978421i	$0.566246\pi$
$998$	−903.000	−	521.347i	−0.904810	−	0.522392i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.c.163.1		2
3.2	odd	2		324.3.d.b.163.2		2
4.3	odd	2	inner	324.3.d.c.163.2		2
9.2	odd	6		36.3.f.b.31.1	yes	2
9.4	even	3		108.3.f.b.19.1		2
9.5	odd	6		36.3.f.a.7.1	✓	2
9.7	even	3		108.3.f.a.91.1		2
12.11	even	2		324.3.d.b.163.1		2
36.7	odd	6		108.3.f.b.91.1		2
36.11	even	6		36.3.f.a.31.1	yes	2
36.23	even	6		36.3.f.b.7.1	yes	2
36.31	odd	6		108.3.f.a.19.1		2
72.5	odd	6		576.3.o.a.511.1		2
72.11	even	6		576.3.o.a.319.1		2
72.13	even	6		1728.3.o.b.127.1		2
72.29	odd	6		576.3.o.b.319.1		2
72.43	odd	6		1728.3.o.b.1279.1		2
72.59	even	6		576.3.o.b.511.1		2
72.61	even	6		1728.3.o.a.1279.1		2
72.67	odd	6		1728.3.o.a.127.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.a.7.1	✓	2	9.5	odd	6
36.3.f.a.31.1	yes	2	36.11	even	6
36.3.f.b.7.1	yes	2	36.23	even	6
36.3.f.b.31.1	yes	2	9.2	odd	6
108.3.f.a.19.1		2	36.31	odd	6
108.3.f.a.91.1		2	9.7	even	3
108.3.f.b.19.1		2	9.4	even	3
108.3.f.b.91.1		2	36.7	odd	6
324.3.d.b.163.1		2	12.11	even	2
324.3.d.b.163.2		2	3.2	odd	2
324.3.d.c.163.1		2	1.1	even	1	trivial
324.3.d.c.163.2		2	4.3	odd	2	inner
576.3.o.a.319.1		2	72.11	even	6
576.3.o.a.511.1		2	72.5	odd	6
576.3.o.b.319.1		2	72.29	odd	6
576.3.o.b.511.1		2	72.59	even	6
1728.3.o.a.127.1		2	72.67	odd	6
1728.3.o.a.1279.1		2	72.61	even	6
1728.3.o.b.127.1		2	72.13	even	6
1728.3.o.b.1279.1		2	72.43	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -4.00000 q^{5} -3.46410i q^{7} -8.00000 q^{8} +(-4.00000 + 6.92820i) q^{10} +12.1244i q^{11} -22.0000 q^{13} +(-6.00000 - 3.46410i) q^{14} +(-8.00000 + 13.8564i) q^{16} +11.0000 q^{17} -15.5885i q^{19} +(8.00000 + 13.8564i) q^{20} +(21.0000 + 12.1244i) q^{22} +24.2487i q^{23} -9.00000 q^{25} +(-22.0000 + 38.1051i) q^{26} +(-12.0000 + 6.92820i) q^{28} -34.0000 q^{29} -6.92820i q^{31} +(16.0000 + 27.7128i) q^{32} +(11.0000 - 19.0526i) q^{34} +13.8564i q^{35} -16.0000 q^{37} +(-27.0000 - 15.5885i) q^{38} +32.0000 q^{40} -13.0000 q^{41} -50.2295i q^{43} +(42.0000 - 24.2487i) q^{44} +(42.0000 + 24.2487i) q^{46} -3.46410i q^{47} +37.0000 q^{49} +(-9.00000 + 15.5885i) q^{50} +(44.0000 + 76.2102i) q^{52} -52.0000 q^{53} -48.4974i q^{55} +27.7128i q^{56} +(-34.0000 + 58.8897i) q^{58} -53.6936i q^{59} -16.0000 q^{61} +(-12.0000 - 6.92820i) q^{62} +64.0000 q^{64} +88.0000 q^{65} -116.047i q^{67} +(-22.0000 - 38.1051i) q^{68} +(24.0000 + 13.8564i) q^{70} -25.0000 q^{73} +(-16.0000 + 27.7128i) q^{74} +(-54.0000 + 31.1769i) q^{76} +42.0000 q^{77} +27.7128i q^{79} +(32.0000 - 55.4256i) q^{80} +(-13.0000 + 22.5167i) q^{82} -34.6410i q^{83} -44.0000 q^{85} +(-87.0000 - 50.2295i) q^{86} -96.9948i q^{88} +2.00000 q^{89} +76.2102i q^{91} +(84.0000 - 48.4974i) q^{92} +(-6.00000 - 3.46410i) q^{94} +62.3538i q^{95} -43.0000 q^{97} +(37.0000 - 64.0859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 8 q^{5} - 16 q^{8} - 8 q^{10} - 44 q^{13} - 12 q^{14} - 16 q^{16} + 22 q^{17} + 16 q^{20} + 42 q^{22} - 18 q^{25} - 44 q^{26} - 24 q^{28} - 68 q^{29} + 32 q^{32} + 22 q^{34} - 32 q^{37}+ \cdots + 74 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 8 * q^5 - 16 * q^8 - 8 * q^10 - 44 * q^13 - 12 * q^14 - 16 * q^16 + 22 * q^17 + 16 * q^20 + 42 * q^22 - 18 * q^25 - 44 * q^26 - 24 * q^28 - 68 * q^29 + 32 * q^32 + 22 * q^34 - 32 * q^37 - 54 * q^38 + 64 * q^40 - 26 * q^41 + 84 * q^44 + 84 * q^46 + 74 * q^49 - 18 * q^50 + 88 * q^52 - 104 * q^53 - 68 * q^58 - 32 * q^61 - 24 * q^62 + 128 * q^64 + 176 * q^65 - 44 * q^68 + 48 * q^70 - 50 * q^73 - 32 * q^74 - 108 * q^76 + 84 * q^77 + 64 * q^80 - 26 * q^82 - 88 * q^85 - 174 * q^86 + 4 * q^89 + 168 * q^92 - 12 * q^94 - 86 * q^97 + 74 * q^98

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