LMFDB - Embedded newform 222.2.c.a.73.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,2,Mod(73,222)] 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("222.73"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	222.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.77267892487$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	222.73
Dual form			222.2.c.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +3.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} -2.00000 q^{10} -3.00000 q^{11} -1.00000 q^{12} +1.00000i q^{13} +3.00000i q^{14} +2.00000i q^{15} +1.00000 q^{16} +3.00000i q^{17} +1.00000i q^{18} -1.00000i q^{19} -2.00000i q^{20} +3.00000 q^{21} -3.00000i q^{22} +1.00000i q^{23} -1.00000i q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -3.00000 q^{28} -6.00000i q^{29} -2.00000 q^{30} -10.0000i q^{31} +1.00000i q^{32} -3.00000 q^{33} -3.00000 q^{34} +6.00000i q^{35} -1.00000 q^{36} +(-6.00000 - 1.00000i) q^{37} +1.00000 q^{38} +1.00000i q^{39} +2.00000 q^{40} +2.00000 q^{41} +3.00000i q^{42} -4.00000i q^{43} +3.00000 q^{44} +2.00000i q^{45} -1.00000 q^{46} +8.00000 q^{47} +1.00000 q^{48} +2.00000 q^{49} +1.00000i q^{50} +3.00000i q^{51} -1.00000i q^{52} -11.0000 q^{53} +1.00000i q^{54} -6.00000i q^{55} -3.00000i q^{56} -1.00000i q^{57} +6.00000 q^{58} -6.00000i q^{59} -2.00000i q^{60} -10.0000i q^{61} +10.0000 q^{62} +3.00000 q^{63} -1.00000 q^{64} -2.00000 q^{65} -3.00000i q^{66} +8.00000 q^{67} -3.00000i q^{68} +1.00000i q^{69} -6.00000 q^{70} +2.00000 q^{71} -1.00000i q^{72} -1.00000 q^{73} +(1.00000 - 6.00000i) q^{74} +1.00000 q^{75} +1.00000i q^{76} -9.00000 q^{77} -1.00000 q^{78} +14.0000i q^{79} +2.00000i q^{80} +1.00000 q^{81} +2.00000i q^{82} -1.00000 q^{83} -3.00000 q^{84} -6.00000 q^{85} +4.00000 q^{86} -6.00000i q^{87} +3.00000i q^{88} +9.00000i q^{89} -2.00000 q^{90} +3.00000i q^{91} -1.00000i q^{92} -10.0000i q^{93} +8.00000i q^{94} +2.00000 q^{95} +1.00000i q^{96} +8.00000i q^{97} +2.00000i q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 2 q^{4} + 6 q^{7} + 2 q^{9} - 4 q^{10} - 6 q^{11} - 2 q^{12} + 2 q^{16} + 6 q^{21} + 2 q^{25} - 2 q^{26} + 2 q^{27} - 6 q^{28} - 4 q^{30} - 6 q^{33} - 6 q^{34} - 2 q^{36} - 12 q^{37} + 2 q^{38}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^4 + 6 * q^7 + 2 * q^9 - 4 * q^10 - 6 * q^11 - 2 * q^12 + 2 * q^16 + 6 * q^21 + 2 * q^25 - 2 * q^26 + 2 * q^27 - 6 * q^28 - 4 * q^30 - 6 * q^33 - 6 * q^34 - 2 * q^36 - 12 * q^37 + 2 * q^38 + 4 * q^40 + 4 * q^41 + 6 * q^44 - 2 * q^46 + 16 * q^47 + 2 * q^48 + 4 * q^49 - 22 * q^53 + 12 * q^58 + 20 * q^62 + 6 * q^63 - 2 * q^64 - 4 * q^65 + 16 * q^67 - 12 * q^70 + 4 * q^71 - 2 * q^73 + 2 * q^74 + 2 * q^75 - 18 * q^77 - 2 * q^78 + 2 * q^81 - 2 * q^83 - 6 * q^84 - 12 * q^85 + 8 * q^86 - 4 * q^90 + 4 * q^95 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$-1$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$			2.00000i			0.894427i	0.894427	+	0.447214i	$0.147584\pi$
$5$			2.00000i			0.894427i	−0.894427	+	0.447214i	$0.852416\pi$
$6$			1.00000i			0.408248i
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−2.00000			−0.632456
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000			−0.288675
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$			3.00000i			0.801784i
$15$			2.00000i			0.516398i
$16$	1.00000			0.250000
$17$			3.00000i			0.727607i	0.931476	+	0.363803i	$0.118522\pi$
$17$			3.00000i			0.727607i	−0.931476	+	0.363803i	$0.881478\pi$
$18$			1.00000i			0.235702i
$19$		−	1.00000i		−	0.229416i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$		−	1.00000i		−	0.229416i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$		−	2.00000i		−	0.447214i
$21$	3.00000			0.654654
$22$		−	3.00000i		−	0.639602i
$23$			1.00000i			0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$			1.00000i			0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$		−	1.00000i		−	0.204124i
$25$	1.00000			0.200000
$26$	−1.00000			−0.196116
$27$	1.00000			0.192450
$28$	−3.00000			−0.566947
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$	−2.00000			−0.365148
$31$		−	10.0000i		−	1.79605i	−0.439941	−	0.898027i	$-0.645001\pi$
$31$		−	10.0000i		−	1.79605i	0.439941	−	0.898027i	$-0.354999\pi$
$32$			1.00000i			0.176777i
$33$	−3.00000			−0.522233
$34$	−3.00000			−0.514496
$35$			6.00000i			1.01419i
$36$	−1.00000			−0.166667
$37$	−6.00000	−	1.00000i	−0.986394	−	0.164399i
$37$	−6.00000	−	1.00000i	−0.986394	−	0.164399i
$38$	1.00000			0.162221
$39$			1.00000i			0.160128i
$40$	2.00000			0.316228
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$			3.00000i			0.462910i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	3.00000			0.452267
$45$			2.00000i			0.298142i
$46$	−1.00000			−0.147442
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$	1.00000			0.144338
$49$	2.00000			0.285714
$50$			1.00000i			0.141421i
$51$			3.00000i			0.420084i
$52$		−	1.00000i		−	0.138675i
$53$	−11.0000			−1.51097			−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000			−1.51097			−0.755483	+	0.655168i	$0.772598\pi$
$54$			1.00000i			0.136083i
$55$		−	6.00000i		−	0.809040i
$56$		−	3.00000i		−	0.400892i
$57$		−	1.00000i		−	0.132453i
$58$	6.00000			0.787839
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		−	2.00000i		−	0.258199i
$61$		−	10.0000i		−	1.28037i	−0.768221	−	0.640184i	$-0.778858\pi$
$61$		−	10.0000i		−	1.28037i	0.768221	−	0.640184i	$-0.221142\pi$
$62$	10.0000			1.27000
$63$	3.00000			0.377964
$64$	−1.00000			−0.125000
$65$	−2.00000			−0.248069
$66$		−	3.00000i		−	0.369274i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$		−	3.00000i		−	0.363803i
$69$			1.00000i			0.120386i
$70$	−6.00000			−0.717137
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	1.00000	−	6.00000i	0.116248	−	0.697486i
$75$	1.00000			0.115470
$76$			1.00000i			0.114708i
$77$	−9.00000			−1.02565
$78$	−1.00000			−0.113228
$79$			14.0000i			1.57512i	0.616236	+	0.787562i	$0.288657\pi$
$79$			14.0000i			1.57512i	−0.616236	+	0.787562i	$0.711343\pi$
$80$			2.00000i			0.223607i
$81$	1.00000			0.111111
$82$			2.00000i			0.220863i
$83$	−1.00000			−0.109764			−0.0548821	−	0.998493i	$-0.517478\pi$
$83$	−1.00000			−0.109764			−0.0548821	+	0.998493i	$0.517478\pi$
$84$	−3.00000			−0.327327
$85$	−6.00000			−0.650791
$86$	4.00000			0.431331
$87$		−	6.00000i		−	0.643268i
$88$			3.00000i			0.319801i
$89$			9.00000i			0.953998i	0.878904	+	0.476999i	$0.158275\pi$
$89$			9.00000i			0.953998i	−0.878904	+	0.476999i	$0.841725\pi$
$90$	−2.00000			−0.210819
$91$			3.00000i			0.314485i
$92$		−	1.00000i		−	0.104257i
$93$		−	10.0000i		−	1.03695i
$94$			8.00000i			0.825137i
$95$	2.00000			0.205196
$96$			1.00000i			0.102062i
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$			2.00000i			0.202031i
$99$	−3.00000			−0.301511
$100$	−1.00000			−0.100000
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$	−3.00000			−0.297044
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$	1.00000			0.0980581
$105$			6.00000i			0.585540i
$106$		−	11.0000i		−	1.06841i
$107$	13.0000			1.25676			0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000			1.25676			0.628379	+	0.777908i	$0.283719\pi$
$108$	−1.00000			−0.0962250
$109$			19.0000i			1.81987i	0.414751	+	0.909935i	$0.363869\pi$
$109$			19.0000i			1.81987i	−0.414751	+	0.909935i	$0.636131\pi$
$110$	6.00000			0.572078
$111$	−6.00000	−	1.00000i	−0.569495	−	0.0949158i
$112$	3.00000			0.283473
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	1.00000			0.0936586
$115$	−2.00000			−0.186501
$116$			6.00000i			0.557086i
$117$			1.00000i			0.0924500i
$118$	6.00000			0.552345
$119$			9.00000i			0.825029i
$120$	2.00000			0.182574
$121$	−2.00000			−0.181818
$122$	10.0000			0.905357
$123$	2.00000			0.180334
$124$			10.0000i			0.898027i
$125$			12.0000i			1.07331i
$126$			3.00000i			0.267261i
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		−	4.00000i		−	0.352180i
$130$		−	2.00000i		−	0.175412i
$131$		−	10.0000i		−	0.873704i	−0.899533	−	0.436852i	$-0.856093\pi$
$131$		−	10.0000i		−	0.873704i	0.899533	−	0.436852i	$-0.143907\pi$
$132$	3.00000			0.261116
$133$		−	3.00000i		−	0.260133i
$134$			8.00000i			0.691095i
$135$			2.00000i			0.172133i
$136$	3.00000			0.257248
$137$	−12.0000			−1.02523			−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000			−1.02523			−0.512615	+	0.858619i	$0.671323\pi$
$138$	−1.00000			−0.0851257
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		−	6.00000i		−	0.507093i
$141$	8.00000			0.673722
$142$			2.00000i			0.167836i
$143$		−	3.00000i		−	0.250873i
$144$	1.00000			0.0833333
$145$	12.0000			0.996546
$146$		−	1.00000i		−	0.0827606i
$147$	2.00000			0.164957
$148$	6.00000	+	1.00000i	0.493197	+	0.0821995i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$			1.00000i			0.0816497i
$151$	−13.0000			−1.05792			−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000			−1.05792			−0.528962	+	0.848645i	$0.677419\pi$
$152$	−1.00000			−0.0811107
$153$			3.00000i			0.242536i
$154$		−	9.00000i		−	0.725241i
$155$	20.0000			1.60644
$156$		−	1.00000i		−	0.0800641i
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	−14.0000			−1.11378
$159$	−11.0000			−0.872357
$160$	−2.00000			−0.158114
$161$			3.00000i			0.236433i
$162$			1.00000i			0.0785674i
$163$		−	9.00000i		−	0.704934i	−0.935824	−	0.352467i	$-0.885343\pi$
$163$		−	9.00000i		−	0.704934i	0.935824	−	0.352467i	$-0.114657\pi$
$164$	−2.00000			−0.156174
$165$		−	6.00000i		−	0.467099i
$166$		−	1.00000i		−	0.0776151i
$167$		−	17.0000i		−	1.31550i	−0.753237	−	0.657750i	$-0.771508\pi$
$167$		−	17.0000i		−	1.31550i	0.753237	−	0.657750i	$-0.228492\pi$
$168$		−	3.00000i		−	0.231455i
$169$	12.0000			0.923077
$170$		−	6.00000i		−	0.460179i
$171$		−	1.00000i		−	0.0764719i
$172$			4.00000i			0.304997i
$173$	9.00000			0.684257			0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000			0.684257			0.342129	+	0.939653i	$0.388852\pi$
$174$	6.00000			0.454859
$175$	3.00000			0.226779
$176$	−3.00000			−0.226134
$177$		−	6.00000i		−	0.450988i
$178$	−9.00000			−0.674579
$179$			24.0000i			1.79384i	0.442189	+	0.896922i	$0.354202\pi$
$179$			24.0000i			1.79384i	−0.442189	+	0.896922i	$0.645798\pi$
$180$		−	2.00000i		−	0.149071i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−3.00000			−0.222375
$183$		−	10.0000i		−	0.739221i
$184$	1.00000			0.0737210
$185$	2.00000	−	12.0000i	0.147043	−	0.882258i
$186$	10.0000			0.733236
$187$		−	9.00000i		−	0.658145i
$188$	−8.00000			−0.583460
$189$	3.00000			0.218218
$190$			2.00000i			0.145095i
$191$		−	15.0000i		−	1.08536i	−0.839939	−	0.542681i	$-0.817409\pi$
$191$		−	15.0000i		−	1.08536i	0.839939	−	0.542681i	$-0.182591\pi$
$192$	−1.00000			−0.0721688
$193$			16.0000i			1.15171i	0.817554	+	0.575853i	$0.195330\pi$
$193$			16.0000i			1.15171i	−0.817554	+	0.575853i	$0.804670\pi$
$194$	−8.00000			−0.574367
$195$	−2.00000			−0.143223
$196$	−2.00000			−0.142857
$197$	−17.0000			−1.21120			−0.605600	−	0.795769i	$-0.707067\pi$
$197$	−17.0000			−1.21120			−0.605600	+	0.795769i	$0.707067\pi$
$198$		−	3.00000i		−	0.213201i
$199$			14.0000i			0.992434i	0.868199	+	0.496217i	$0.165278\pi$
$199$			14.0000i			0.992434i	−0.868199	+	0.496217i	$0.834722\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	8.00000			0.564276
$202$		−	18.0000i		−	1.26648i
$203$		−	18.0000i		−	1.26335i
$204$		−	3.00000i		−	0.210042i
$205$			4.00000i			0.279372i
$206$	−16.0000			−1.11477
$207$			1.00000i			0.0695048i
$208$			1.00000i			0.0693375i
$209$			3.00000i			0.207514i
$210$	−6.00000			−0.414039
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$	11.0000			0.755483
$213$	2.00000			0.137038
$214$			13.0000i			0.888662i
$215$	8.00000			0.545595
$216$		−	1.00000i		−	0.0680414i
$217$		−	30.0000i		−	2.03653i
$218$	−19.0000			−1.28684
$219$	−1.00000			−0.0675737
$220$			6.00000i			0.404520i
$221$	−3.00000			−0.201802
$222$	1.00000	−	6.00000i	0.0671156	−	0.402694i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$			3.00000i			0.200446i
$225$	1.00000			0.0666667
$226$	14.0000			0.931266
$227$			8.00000i			0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$227$			8.00000i			0.530979i	−0.964114	+	0.265489i	$0.914466\pi$
$228$			1.00000i			0.0662266i
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$		−	2.00000i		−	0.131876i
$231$	−9.00000			−0.592157
$232$	−6.00000			−0.393919
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−1.00000			−0.0653720
$235$			16.0000i			1.04372i
$236$			6.00000i			0.390567i
$237$			14.0000i			0.909398i
$238$	−9.00000			−0.583383
$239$		−	16.0000i		−	1.03495i	−0.855697	−	0.517477i	$-0.826871\pi$
$239$		−	16.0000i		−	1.03495i	0.855697	−	0.517477i	$-0.173129\pi$
$240$			2.00000i			0.129099i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$		−	2.00000i		−	0.128565i
$243$	1.00000			0.0641500
$244$			10.0000i			0.640184i
$245$			4.00000i			0.255551i
$246$			2.00000i			0.127515i
$247$	1.00000			0.0636285
$248$	−10.0000			−0.635001
$249$	−1.00000			−0.0633724
$250$	−12.0000			−0.758947
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	−3.00000			−0.188982
$253$		−	3.00000i		−	0.188608i
$254$		−	7.00000i		−	0.439219i
$255$	−6.00000			−0.375735
$256$	1.00000			0.0625000
$257$			3.00000i			0.187135i	0.995613	+	0.0935674i	$0.0298271\pi$
$257$			3.00000i			0.187135i	−0.995613	+	0.0935674i	$0.970173\pi$
$258$	4.00000			0.249029
$259$	−18.0000	−	3.00000i	−1.11847	−	0.186411i
$260$	2.00000			0.124035
$261$		−	6.00000i		−	0.371391i
$262$	10.0000			0.617802
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$			3.00000i			0.184637i
$265$		−	22.0000i		−	1.35145i
$266$	3.00000			0.183942
$267$			9.00000i			0.550791i
$268$	−8.00000			−0.488678
$269$	−5.00000			−0.304855			−0.152428	−	0.988315i	$-0.548709\pi$
$269$	−5.00000			−0.304855			−0.152428	+	0.988315i	$0.548709\pi$
$270$	−2.00000			−0.121716
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$			3.00000i			0.181902i
$273$			3.00000i			0.181568i
$274$		−	12.0000i		−	0.724947i
$275$	−3.00000			−0.180907
$276$		−	1.00000i		−	0.0601929i
$277$		−	7.00000i		−	0.420589i	−0.977638	−	0.210295i	$-0.932558\pi$
$277$		−	7.00000i		−	0.420589i	0.977638	−	0.210295i	$-0.0674423\pi$
$278$		0			0
$279$		−	10.0000i		−	0.598684i
$280$	6.00000			0.358569
$281$			15.0000i			0.894825i	0.894328	+	0.447412i	$0.147654\pi$
$281$			15.0000i			0.894825i	−0.894328	+	0.447412i	$0.852346\pi$
$282$			8.00000i			0.476393i
$283$		−	29.0000i		−	1.72387i	−0.507018	−	0.861936i	$-0.669252\pi$
$283$		−	29.0000i		−	1.72387i	0.507018	−	0.861936i	$-0.330748\pi$
$284$	−2.00000			−0.118678
$285$	2.00000			0.118470
$286$	3.00000			0.177394
$287$	6.00000			0.354169
$288$			1.00000i			0.0589256i
$289$	8.00000			0.470588
$290$			12.0000i			0.704664i
$291$			8.00000i			0.468968i
$292$	1.00000			0.0585206
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$			2.00000i			0.116642i
$295$	12.0000			0.698667
$296$	−1.00000	+	6.00000i	−0.0581238	+	0.348743i
$297$	−3.00000			−0.174078
$298$		−	10.0000i		−	0.579284i
$299$	−1.00000			−0.0578315
$300$	−1.00000			−0.0577350
$301$		−	12.0000i		−	0.691669i
$302$		−	13.0000i		−	0.748066i
$303$	−18.0000			−1.03407
$304$		−	1.00000i		−	0.0573539i
$305$	20.0000			1.14520
$306$	−3.00000			−0.171499
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	9.00000			0.512823
$309$			16.0000i			0.910208i
$310$			20.0000i			1.13592i
$311$			20.0000i			1.13410i	0.823685	+	0.567048i	$0.191915\pi$
$311$			20.0000i			1.13410i	−0.823685	+	0.567048i	$0.808085\pi$
$312$	1.00000			0.0566139
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$			8.00000i			0.451466i
$315$			6.00000i			0.338062i
$316$		−	14.0000i		−	0.787562i
$317$	−2.00000			−0.112331			−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000			−0.112331			−0.0561656	+	0.998421i	$0.517887\pi$
$318$		−	11.0000i		−	0.616849i
$319$			18.0000i			1.00781i
$320$		−	2.00000i		−	0.111803i
$321$	13.0000			0.725589
$322$	−3.00000			−0.167183
$323$	3.00000			0.166924
$324$	−1.00000			−0.0555556
$325$			1.00000i			0.0554700i
$326$	9.00000			0.498464
$327$			19.0000i			1.05070i
$328$		−	2.00000i		−	0.110432i
$329$	24.0000			1.32316
$330$	6.00000			0.330289
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$	1.00000			0.0548821
$333$	−6.00000	−	1.00000i	−0.328798	−	0.0547997i
$334$	17.0000			0.930199
$335$			16.0000i			0.874173i
$336$	3.00000			0.163663
$337$	3.00000			0.163420			0.0817102	−	0.996656i	$-0.473962\pi$
$337$	3.00000			0.163420			0.0817102	+	0.996656i	$0.473962\pi$
$338$			12.0000i			0.652714i
$339$		−	14.0000i		−	0.760376i
$340$	6.00000			0.325396
$341$			30.0000i			1.62459i
$342$	1.00000			0.0540738
$343$	−15.0000			−0.809924
$344$	−4.00000			−0.215666
$345$	−2.00000			−0.107676
$346$			9.00000i			0.483843i
$347$			18.0000i			0.966291i	0.875540	+	0.483145i	$0.160506\pi$
$347$			18.0000i			0.966291i	−0.875540	+	0.483145i	$0.839494\pi$
$348$			6.00000i			0.321634i
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$			3.00000i			0.160357i
$351$			1.00000i			0.0533761i
$352$		−	3.00000i		−	0.159901i
$353$		−	34.0000i		−	1.80964i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$		−	34.0000i		−	1.80964i	0.425797	−	0.904819i	$-0.359994\pi$
$354$	6.00000			0.318896
$355$			4.00000i			0.212298i
$356$		−	9.00000i		−	0.476999i
$357$			9.00000i			0.476331i
$358$	−24.0000			−1.26844
$359$	10.0000			0.527780			0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000			0.527780			0.263890	+	0.964553i	$0.414994\pi$
$360$	2.00000			0.105409
$361$	18.0000			0.947368
$362$			2.00000i			0.105118i
$363$	−2.00000			−0.104973
$364$		−	3.00000i		−	0.157243i
$365$		−	2.00000i		−	0.104685i
$366$	10.0000			0.522708
$367$	−17.0000			−0.887393			−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000			−0.887393			−0.443696	+	0.896177i	$0.646333\pi$
$368$			1.00000i			0.0521286i
$369$	2.00000			0.104116
$370$	12.0000	+	2.00000i	0.623850	+	0.103975i
$371$	−33.0000			−1.71327
$372$			10.0000i			0.518476i
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$	9.00000			0.465379
$375$			12.0000i			0.619677i
$376$		−	8.00000i		−	0.412568i
$377$	6.00000			0.309016
$378$			3.00000i			0.154303i
$379$	−30.0000			−1.54100			−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000			−1.54100			−0.770498	+	0.637442i	$0.779993\pi$
$380$	−2.00000			−0.102598
$381$	−7.00000			−0.358621
$382$	15.0000			0.767467
$383$			11.0000i			0.562074i	0.959697	+	0.281037i	$0.0906783\pi$
$383$			11.0000i			0.562074i	−0.959697	+	0.281037i	$0.909322\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		−	18.0000i		−	0.917365i
$386$	−16.0000			−0.814379
$387$		−	4.00000i		−	0.203331i
$388$		−	8.00000i		−	0.406138i
$389$			4.00000i			0.202808i	0.994845	+	0.101404i	$0.0323335\pi$
$389$			4.00000i			0.202808i	−0.994845	+	0.101404i	$0.967667\pi$
$390$		−	2.00000i		−	0.101274i
$391$	−3.00000			−0.151717
$392$		−	2.00000i		−	0.101015i
$393$		−	10.0000i		−	0.504433i
$394$		−	17.0000i		−	0.856448i
$395$	−28.0000			−1.40883
$396$	3.00000			0.150756
$397$	−32.0000			−1.60603			−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000			−1.60603			−0.803017	+	0.595956i	$0.796773\pi$
$398$	−14.0000			−0.701757
$399$		−	3.00000i		−	0.150188i
$400$	1.00000			0.0500000
$401$		−	15.0000i		−	0.749064i	−0.927214	−	0.374532i	$-0.877803\pi$
$401$		−	15.0000i		−	0.749064i	0.927214	−	0.374532i	$-0.122197\pi$
$402$			8.00000i			0.399004i
$403$	10.0000			0.498135
$404$	18.0000			0.895533
$405$			2.00000i			0.0993808i
$406$	18.0000			0.893325
$407$	18.0000	+	3.00000i	0.892227	+	0.148704i
$408$	3.00000			0.148522
$409$			24.0000i			1.18672i	0.804936	+	0.593362i	$0.202200\pi$
$409$			24.0000i			1.18672i	−0.804936	+	0.593362i	$0.797800\pi$
$410$	−4.00000			−0.197546
$411$	−12.0000			−0.591916
$412$		−	16.0000i		−	0.788263i
$413$		−	18.0000i		−	0.885722i
$414$	−1.00000			−0.0491473
$415$		−	2.00000i		−	0.0981761i
$416$	−1.00000			−0.0490290
$417$		0			0
$418$	−3.00000			−0.146735
$419$	−35.0000			−1.70986			−0.854931	−	0.518742i	$-0.826401\pi$
$419$	−35.0000			−1.70986			−0.854931	+	0.518742i	$0.826401\pi$
$420$		−	6.00000i		−	0.292770i
$421$			10.0000i			0.487370i	0.969854	+	0.243685i	$0.0783563\pi$
$421$			10.0000i			0.487370i	−0.969854	+	0.243685i	$0.921644\pi$
$422$			22.0000i			1.07094i
$423$	8.00000			0.388973
$424$			11.0000i			0.534207i
$425$			3.00000i			0.145521i
$426$			2.00000i			0.0969003i
$427$		−	30.0000i		−	1.45180i
$428$	−13.0000			−0.628379
$429$		−	3.00000i		−	0.144841i
$430$			8.00000i			0.385794i
$431$		−	15.0000i		−	0.722525i	−0.932464	−	0.361262i	$-0.882346\pi$
$431$		−	15.0000i		−	0.722525i	0.932464	−	0.361262i	$-0.117654\pi$
$432$	1.00000			0.0481125
$433$	−1.00000			−0.0480569			−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000			−0.0480569			−0.0240285	+	0.999711i	$0.507649\pi$
$434$	30.0000			1.44005
$435$	12.0000			0.575356
$436$		−	19.0000i		−	0.909935i
$437$	1.00000			0.0478365
$438$		−	1.00000i		−	0.0477818i
$439$		−	26.0000i		−	1.24091i	−0.784241	−	0.620456i	$-0.786947\pi$
$439$		−	26.0000i		−	1.24091i	0.784241	−	0.620456i	$-0.213053\pi$
$440$	−6.00000			−0.286039
$441$	2.00000			0.0952381
$442$		−	3.00000i		−	0.142695i
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$	6.00000	+	1.00000i	0.284747	+	0.0474579i
$445$	−18.0000			−0.853282
$446$			4.00000i			0.189405i
$447$	−10.0000			−0.472984
$448$	−3.00000			−0.141737
$449$			34.0000i			1.60456i	0.596948	+	0.802280i	$0.296380\pi$
$449$			34.0000i			1.60456i	−0.596948	+	0.802280i	$0.703620\pi$
$450$			1.00000i			0.0471405i
$451$	−6.00000			−0.282529
$452$			14.0000i			0.658505i
$453$	−13.0000			−0.610793
$454$	−8.00000			−0.375459
$455$	−6.00000			−0.281284
$456$	−1.00000			−0.0468293
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$		−	20.0000i		−	0.934539i
$459$			3.00000i			0.140028i
$460$	2.00000			0.0932505
$461$		−	40.0000i		−	1.86299i	−0.363760	−	0.931493i	$-0.618507\pi$
$461$		−	40.0000i		−	1.86299i	0.363760	−	0.931493i	$-0.381493\pi$
$462$		−	9.00000i		−	0.418718i
$463$		−	34.0000i		−	1.58011i	−0.613033	−	0.790057i	$-0.710051\pi$
$463$		−	34.0000i		−	1.58011i	0.613033	−	0.790057i	$-0.289949\pi$
$464$		−	6.00000i		−	0.278543i
$465$	20.0000			0.927478
$466$			24.0000i			1.11178i
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$		−	1.00000i		−	0.0462250i
$469$	24.0000			1.10822
$470$	−16.0000			−0.738025
$471$	8.00000			0.368621
$472$	−6.00000			−0.276172
$473$			12.0000i			0.551761i
$474$	−14.0000			−0.643041
$475$		−	1.00000i		−	0.0458831i
$476$		−	9.00000i		−	0.412514i
$477$	−11.0000			−0.503655
$478$	16.0000			0.731823
$479$		−	21.0000i		−	0.959514i	−0.877401	−	0.479757i	$-0.840725\pi$
$479$		−	21.0000i		−	0.959514i	0.877401	−	0.479757i	$-0.159275\pi$
$480$	−2.00000			−0.0912871
$481$	1.00000	−	6.00000i	0.0455961	−	0.273576i
$482$		0			0
$483$			3.00000i			0.136505i
$484$	2.00000			0.0909091
$485$	−16.0000			−0.726523
$486$			1.00000i			0.0453609i
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$	−10.0000			−0.452679
$489$		−	9.00000i		−	0.406994i
$490$	−4.00000			−0.180702
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$	−2.00000			−0.0901670
$493$	18.0000			0.810679
$494$			1.00000i			0.0449921i
$495$		−	6.00000i		−	0.269680i
$496$		−	10.0000i		−	0.449013i
$497$	6.00000			0.269137
$498$		−	1.00000i		−	0.0448111i
$499$			39.0000i			1.74588i	0.487828	+	0.872940i	$0.337789\pi$
$499$			39.0000i			1.74588i	−0.487828	+	0.872940i	$0.662211\pi$
$500$		−	12.0000i		−	0.536656i
$501$		−	17.0000i		−	0.759504i
$502$		0			0
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$		−	3.00000i		−	0.133631i
$505$		−	36.0000i		−	1.60198i
$506$	3.00000			0.133366
$507$	12.0000			0.532939
$508$	7.00000			0.310575
$509$	−5.00000			−0.221621			−0.110811	−	0.993842i	$-0.535345\pi$
$509$	−5.00000			−0.221621			−0.110811	+	0.993842i	$0.535345\pi$
$510$		−	6.00000i		−	0.265684i
$511$	−3.00000			−0.132712
$512$			1.00000i			0.0441942i
$513$		−	1.00000i		−	0.0441511i
$514$	−3.00000			−0.132324
$515$	−32.0000			−1.41009
$516$			4.00000i			0.176090i
$517$	−24.0000			−1.05552
$518$	3.00000	−	18.0000i	0.131812	−	0.790875i
$519$	9.00000			0.395056
$520$			2.00000i			0.0877058i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	6.00000			0.262613
$523$		−	4.00000i		−	0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$		−	4.00000i		−	0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$			10.0000i			0.436852i
$525$	3.00000			0.130931
$526$			24.0000i			1.04645i
$527$	30.0000			1.30682
$528$	−3.00000			−0.130558
$529$	22.0000			0.956522
$530$	22.0000			0.955619
$531$		−	6.00000i		−	0.260378i
$532$			3.00000i			0.130066i
$533$			2.00000i			0.0866296i
$534$	−9.00000			−0.389468
$535$			26.0000i			1.12408i
$536$		−	8.00000i		−	0.345547i
$537$			24.0000i			1.03568i
$538$		−	5.00000i		−	0.215565i
$539$	−6.00000			−0.258438
$540$		−	2.00000i		−	0.0860663i
$541$			45.0000i			1.93470i	0.253442	+	0.967351i	$0.418437\pi$
$541$			45.0000i			1.93470i	−0.253442	+	0.967351i	$0.581563\pi$
$542$		−	28.0000i		−	1.20270i
$543$	2.00000			0.0858282
$544$	−3.00000			−0.128624
$545$	−38.0000			−1.62774
$546$	−3.00000			−0.128388
$547$		−	17.0000i		−	0.726868i	−0.931620	−	0.363434i	$-0.881604\pi$
$547$		−	17.0000i		−	0.726868i	0.931620	−	0.363434i	$-0.118396\pi$
$548$	12.0000			0.512615
$549$		−	10.0000i		−	0.426790i
$550$		−	3.00000i		−	0.127920i
$551$	−6.00000			−0.255609
$552$	1.00000			0.0425628
$553$			42.0000i			1.78602i
$554$	7.00000			0.297402
$555$	2.00000	−	12.0000i	0.0848953	−	0.509372i
$556$		0			0
$557$			38.0000i			1.61011i	0.593199	+	0.805056i	$0.297865\pi$
$557$			38.0000i			1.61011i	−0.593199	+	0.805056i	$0.702135\pi$
$558$	10.0000			0.423334
$559$	4.00000			0.169182
$560$			6.00000i			0.253546i
$561$		−	9.00000i		−	0.379980i
$562$	−15.0000			−0.632737
$563$		−	14.0000i		−	0.590030i	−0.955493	−	0.295015i	$-0.904675\pi$
$563$		−	14.0000i		−	0.590030i	0.955493	−	0.295015i	$-0.0953246\pi$
$564$	−8.00000			−0.336861
$565$	28.0000			1.17797
$566$	29.0000			1.21896
$567$	3.00000			0.125988
$568$		−	2.00000i		−	0.0839181i
$569$		−	21.0000i		−	0.880366i	−0.897908	−	0.440183i	$-0.854914\pi$
$569$		−	21.0000i		−	0.880366i	0.897908	−	0.440183i	$-0.145086\pi$
$570$			2.00000i			0.0837708i
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$			3.00000i			0.125436i
$573$		−	15.0000i		−	0.626634i
$574$			6.00000i			0.250435i
$575$			1.00000i			0.0417029i
$576$	−1.00000			−0.0416667
$577$			8.00000i			0.333044i	0.986038	+	0.166522i	$0.0532537\pi$
$577$			8.00000i			0.333044i	−0.986038	+	0.166522i	$0.946746\pi$
$578$			8.00000i			0.332756i
$579$			16.0000i			0.664937i
$580$	−12.0000			−0.498273
$581$	−3.00000			−0.124461
$582$	−8.00000			−0.331611
$583$	33.0000			1.36672
$584$			1.00000i			0.0413803i
$585$	−2.00000			−0.0826898
$586$			9.00000i			0.371787i
$587$		−	2.00000i		−	0.0825488i	−0.999148	−	0.0412744i	$-0.986858\pi$
$587$		−	2.00000i		−	0.0825488i	0.999148	−	0.0412744i	$-0.0131418\pi$
$588$	−2.00000			−0.0824786
$589$	−10.0000			−0.412043
$590$			12.0000i			0.494032i
$591$	−17.0000			−0.699287
$592$	−6.00000	−	1.00000i	−0.246598	−	0.0410997i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		−	3.00000i		−	0.123091i
$595$	−18.0000			−0.737928
$596$	10.0000			0.409616
$597$			14.0000i			0.572982i
$598$		−	1.00000i		−	0.0408930i
$599$	10.0000			0.408589			0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000			0.408589			0.204294	+	0.978909i	$0.434510\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	12.0000			0.489083
$603$	8.00000			0.325785
$604$	13.0000			0.528962
$605$		−	4.00000i		−	0.162623i
$606$		−	18.0000i		−	0.731200i
$607$		−	12.0000i		−	0.487065i	−0.969893	−	0.243532i	$-0.921694\pi$
$607$		−	12.0000i		−	0.487065i	0.969893	−	0.243532i	$-0.0783062\pi$
$608$	1.00000			0.0405554
$609$		−	18.0000i		−	0.729397i
$610$			20.0000i			0.809776i
$611$			8.00000i			0.323645i
$612$		−	3.00000i		−	0.121268i
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$		−	12.0000i		−	0.484281i
$615$			4.00000i			0.161296i
$616$			9.00000i			0.362620i
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−16.0000			−0.643614
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$	−20.0000			−0.803219
$621$			1.00000i			0.0401286i
$622$	−20.0000			−0.801927
$623$			27.0000i			1.08173i
$624$			1.00000i			0.0400320i
$625$	−19.0000			−0.760000
$626$	−6.00000			−0.239808
$627$			3.00000i			0.119808i
$628$	−8.00000			−0.319235
$629$	3.00000	−	18.0000i	0.119618	−	0.717707i
$630$	−6.00000			−0.239046
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	14.0000			0.556890
$633$	22.0000			0.874421
$634$		−	2.00000i		−	0.0794301i
$635$		−	14.0000i		−	0.555573i
$636$	11.0000			0.436178
$637$			2.00000i			0.0792429i
$638$	−18.0000			−0.712627
$639$	2.00000			0.0791188
$640$	2.00000			0.0790569
$641$	−8.00000			−0.315981			−0.157991	−	0.987441i	$-0.550502\pi$
$641$	−8.00000			−0.315981			−0.157991	+	0.987441i	$0.550502\pi$
$642$			13.0000i			0.513069i
$643$			21.0000i			0.828159i	0.910241	+	0.414080i	$0.135896\pi$
$643$			21.0000i			0.828159i	−0.910241	+	0.414080i	$0.864104\pi$
$644$		−	3.00000i		−	0.118217i
$645$	8.00000			0.315000
$646$			3.00000i			0.118033i
$647$			3.00000i			0.117942i	0.998260	+	0.0589711i	$0.0187820\pi$
$647$			3.00000i			0.117942i	−0.998260	+	0.0589711i	$0.981218\pi$
$648$		−	1.00000i		−	0.0392837i
$649$			18.0000i			0.706562i
$650$	−1.00000			−0.0392232
$651$		−	30.0000i		−	1.17579i
$652$			9.00000i			0.352467i
$653$			6.00000i			0.234798i	0.993085	+	0.117399i	$0.0374557\pi$
$653$			6.00000i			0.234798i	−0.993085	+	0.117399i	$0.962544\pi$
$654$	−19.0000			−0.742959
$655$	20.0000			0.781465
$656$	2.00000			0.0780869
$657$	−1.00000			−0.0390137
$658$			24.0000i			0.935617i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$			6.00000i			0.233550i
$661$		−	25.0000i		−	0.972387i	−0.873851	−	0.486194i	$-0.838385\pi$
$661$		−	25.0000i		−	0.972387i	0.873851	−	0.486194i	$-0.161615\pi$
$662$	−20.0000			−0.777322
$663$	−3.00000			−0.116510
$664$			1.00000i			0.0388075i
$665$	6.00000			0.232670
$666$	1.00000	−	6.00000i	0.0387492	−	0.232495i
$667$	6.00000			0.232321
$668$			17.0000i			0.657750i
$669$	4.00000			0.154649
$670$	−16.0000			−0.618134
$671$			30.0000i			1.15814i
$672$			3.00000i			0.115728i
$673$	29.0000			1.11787			0.558934	−	0.829212i	$-0.311211\pi$
$673$	29.0000			1.11787			0.558934	+	0.829212i	$0.311211\pi$
$674$			3.00000i			0.115556i
$675$	1.00000			0.0384900
$676$	−12.0000			−0.461538
$677$	−7.00000			−0.269032			−0.134516	−	0.990911i	$-0.542948\pi$
$677$	−7.00000			−0.269032			−0.134516	+	0.990911i	$0.542948\pi$
$678$	14.0000			0.537667
$679$			24.0000i			0.921035i
$680$			6.00000i			0.230089i
$681$			8.00000i			0.306561i
$682$	−30.0000			−1.14876
$683$			16.0000i			0.612223i	0.951996	+	0.306111i	$0.0990280\pi$
$683$			16.0000i			0.612223i	−0.951996	+	0.306111i	$0.900972\pi$
$684$			1.00000i			0.0382360i
$685$		−	24.0000i		−	0.916993i
$686$		−	15.0000i		−	0.572703i
$687$	−20.0000			−0.763048
$688$		−	4.00000i		−	0.152499i
$689$		−	11.0000i		−	0.419067i
$690$		−	2.00000i		−	0.0761387i
$691$	2.00000			0.0760836			0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000			0.0760836			0.0380418	+	0.999276i	$0.487888\pi$
$692$	−9.00000			−0.342129
$693$	−9.00000			−0.341882
$694$	−18.0000			−0.683271
$695$		0			0
$696$	−6.00000			−0.227429
$697$			6.00000i			0.227266i
$698$			30.0000i			1.13552i
$699$	24.0000			0.907763
$700$	−3.00000			−0.113389
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−1.00000			−0.0377426
$703$	−1.00000	+	6.00000i	−0.0377157	+	0.226294i
$704$	3.00000			0.113067
$705$			16.0000i			0.602595i
$706$	34.0000			1.27961
$707$	−54.0000			−2.03088
$708$			6.00000i			0.225494i
$709$			49.0000i			1.84023i	0.391644	+	0.920117i	$0.371906\pi$
$709$			49.0000i			1.84023i	−0.391644	+	0.920117i	$0.628094\pi$
$710$	−4.00000			−0.150117
$711$			14.0000i			0.525041i
$712$	9.00000			0.337289
$713$	10.0000			0.374503
$714$	−9.00000			−0.336817
$715$	6.00000			0.224387
$716$		−	24.0000i		−	0.896922i
$717$		−	16.0000i		−	0.597531i
$718$			10.0000i			0.373197i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$			2.00000i			0.0745356i
$721$			48.0000i			1.78761i
$722$			18.0000i			0.669891i
$723$		0			0
$724$	−2.00000			−0.0743294
$725$		−	6.00000i		−	0.222834i
$726$		−	2.00000i		−	0.0742270i
$727$		−	42.0000i		−	1.55769i	−0.627214	−	0.778847i	$-0.715805\pi$
$727$		−	42.0000i		−	1.55769i	0.627214	−	0.778847i	$-0.284195\pi$
$728$	3.00000			0.111187
$729$	1.00000			0.0370370
$730$	2.00000			0.0740233
$731$	12.0000			0.443836
$732$			10.0000i			0.369611i
$733$	−26.0000			−0.960332			−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000			−0.960332			−0.480166	+	0.877178i	$0.659424\pi$
$734$		−	17.0000i		−	0.627481i
$735$			4.00000i			0.147542i
$736$	−1.00000			−0.0368605
$737$	−24.0000			−0.884051
$738$			2.00000i			0.0736210i
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	−2.00000	+	12.0000i	−0.0735215	+	0.441129i
$741$	1.00000			0.0367359
$742$		−	33.0000i		−	1.21147i
$743$	34.0000			1.24734			0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000			1.24734			0.623670	+	0.781688i	$0.285641\pi$
$744$	−10.0000			−0.366618
$745$		−	20.0000i		−	0.732743i
$746$			4.00000i			0.146450i
$747$	−1.00000			−0.0365881
$748$			9.00000i			0.329073i
$749$	39.0000			1.42503
$750$	−12.0000			−0.438178
$751$	−48.0000			−1.75154			−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000			−1.75154			−0.875772	+	0.482724i	$0.839647\pi$
$752$	8.00000			0.291730
$753$		0			0
$754$			6.00000i			0.218507i
$755$		−	26.0000i		−	0.946237i
$756$	−3.00000			−0.109109
$757$		−	17.0000i		−	0.617876i	−0.951082	−	0.308938i	$-0.900027\pi$
$757$		−	17.0000i		−	0.617876i	0.951082	−	0.308938i	$-0.0999735\pi$
$758$		−	30.0000i		−	1.08965i
$759$		−	3.00000i		−	0.108893i
$760$		−	2.00000i		−	0.0725476i
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$		−	7.00000i		−	0.253583i
$763$			57.0000i			2.06354i
$764$			15.0000i			0.542681i
$765$	−6.00000			−0.216930
$766$	−11.0000			−0.397446
$767$	6.00000			0.216647
$768$	1.00000			0.0360844
$769$		−	26.0000i		−	0.937584i	−0.883309	−	0.468792i	$-0.844689\pi$
$769$		−	26.0000i		−	0.937584i	0.883309	−	0.468792i	$-0.155311\pi$
$770$	18.0000			0.648675
$771$			3.00000i			0.108042i
$772$		−	16.0000i		−	0.575853i
$773$	39.0000			1.40273			0.701366	−	0.712801i	$-0.252574\pi$
$773$	39.0000			1.40273			0.701366	+	0.712801i	$0.252574\pi$
$774$	4.00000			0.143777
$775$		−	10.0000i		−	0.359211i
$776$	8.00000			0.287183
$777$	−18.0000	−	3.00000i	−0.645746	−	0.107624i
$778$	−4.00000			−0.143407
$779$		−	2.00000i		−	0.0716574i
$780$	2.00000			0.0716115
$781$	−6.00000			−0.214697
$782$		−	3.00000i		−	0.107280i
$783$		−	6.00000i		−	0.214423i
$784$	2.00000			0.0714286
$785$			16.0000i			0.571064i
$786$	10.0000			0.356688
$787$	38.0000			1.35455			0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000			1.35455			0.677277	+	0.735728i	$0.263160\pi$
$788$	17.0000			0.605600
$789$	24.0000			0.854423
$790$		−	28.0000i		−	0.996195i
$791$		−	42.0000i		−	1.49335i
$792$			3.00000i			0.106600i
$793$	10.0000			0.355110
$794$		−	32.0000i		−	1.13564i
$795$		−	22.0000i		−	0.780260i
$796$		−	14.0000i		−	0.496217i
$797$			8.00000i			0.283375i	0.989911	+	0.141687i	$0.0452527\pi$
$797$			8.00000i			0.283375i	−0.989911	+	0.141687i	$0.954747\pi$
$798$	3.00000			0.106199
$799$			24.0000i			0.849059i
$800$			1.00000i			0.0353553i
$801$			9.00000i			0.317999i
$802$	15.0000			0.529668
$803$	3.00000			0.105868
$804$	−8.00000			−0.282138
$805$	−6.00000			−0.211472
$806$			10.0000i			0.352235i
$807$	−5.00000			−0.176008
$808$			18.0000i			0.633238i
$809$		−	31.0000i		−	1.08990i	−0.838468	−	0.544951i	$-0.816548\pi$
$809$		−	31.0000i		−	1.08990i	0.838468	−	0.544951i	$-0.183452\pi$
$810$	−2.00000			−0.0702728
$811$	22.0000			0.772524			0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000			0.772524			0.386262	+	0.922389i	$0.373766\pi$
$812$			18.0000i			0.631676i
$813$	−28.0000			−0.982003
$814$	−3.00000	+	18.0000i	−0.105150	+	0.630900i
$815$	18.0000			0.630512
$816$			3.00000i			0.105021i
$817$	−4.00000			−0.139942
$818$	−24.0000			−0.839140
$819$			3.00000i			0.104828i
$820$		−	4.00000i		−	0.139686i
$821$	−3.00000			−0.104701			−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000			−0.104701			−0.0523504	+	0.998629i	$0.516671\pi$
$822$		−	12.0000i		−	0.418548i
$823$	29.0000			1.01088			0.505438	−	0.862863i	$-0.331331\pi$
$823$	29.0000			1.01088			0.505438	+	0.862863i	$0.331331\pi$
$824$	16.0000			0.557386
$825$	−3.00000			−0.104447
$826$	18.0000			0.626300
$827$		−	2.00000i		−	0.0695468i	−0.999395	−	0.0347734i	$-0.988929\pi$
$827$		−	2.00000i		−	0.0695468i	0.999395	−	0.0347734i	$-0.0110710\pi$
$828$		−	1.00000i		−	0.0347524i
$829$		−	11.0000i		−	0.382046i	−0.981586	−	0.191023i	$-0.938820\pi$
$829$		−	11.0000i		−	0.382046i	0.981586	−	0.191023i	$-0.0611805\pi$
$830$	2.00000			0.0694210
$831$		−	7.00000i		−	0.242827i
$832$		−	1.00000i		−	0.0346688i
$833$			6.00000i			0.207888i
$834$		0			0
$835$	34.0000			1.17662
$836$		−	3.00000i		−	0.103757i
$837$		−	10.0000i		−	0.345651i
$838$		−	35.0000i		−	1.20905i
$839$	−20.0000			−0.690477			−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$	6.00000			0.207020
$841$	−7.00000			−0.241379
$842$	−10.0000			−0.344623
$843$			15.0000i			0.516627i
$844$	−22.0000			−0.757271
$845$			24.0000i			0.825625i
$846$			8.00000i			0.275046i
$847$	−6.00000			−0.206162
$848$	−11.0000			−0.377742
$849$		−	29.0000i		−	0.995277i
$850$	−3.00000			−0.102899
$851$	1.00000	−	6.00000i	0.0342796	−	0.205677i
$852$	−2.00000			−0.0685189
$853$		−	49.0000i		−	1.67773i	−0.544341	−	0.838864i	$-0.683220\pi$
$853$		−	49.0000i		−	1.67773i	0.544341	−	0.838864i	$-0.316780\pi$
$854$	30.0000			1.02658
$855$	2.00000			0.0683986
$856$		−	13.0000i		−	0.444331i
$857$			13.0000i			0.444072i	0.975039	+	0.222036i	$0.0712702\pi$
$857$			13.0000i			0.444072i	−0.975039	+	0.222036i	$0.928730\pi$
$858$	3.00000			0.102418
$859$		−	31.0000i		−	1.05771i	−0.848713	−	0.528853i	$-0.822622\pi$
$859$		−	31.0000i		−	1.05771i	0.848713	−	0.528853i	$-0.177378\pi$
$860$	−8.00000			−0.272798
$861$	6.00000			0.204479
$862$	15.0000			0.510902
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$			1.00000i			0.0340207i
$865$			18.0000i			0.612018i
$866$		−	1.00000i		−	0.0339814i
$867$	8.00000			0.271694
$868$			30.0000i			1.01827i
$869$		−	42.0000i		−	1.42475i
$870$			12.0000i			0.406838i
$871$			8.00000i			0.271070i
$872$	19.0000			0.643421
$873$			8.00000i			0.270759i
$874$			1.00000i			0.0338255i
$875$			36.0000i			1.21702i
$876$	1.00000			0.0337869
$877$	−32.0000			−1.08056			−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000			−1.08056			−0.540282	+	0.841484i	$0.681682\pi$
$878$	26.0000			0.877457
$879$	9.00000			0.303562
$880$		−	6.00000i		−	0.202260i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$			2.00000i			0.0673435i
$883$			11.0000i			0.370179i	0.982722	+	0.185090i	$0.0592576\pi$
$883$			11.0000i			0.370179i	−0.982722	+	0.185090i	$0.940742\pi$
$884$	3.00000			0.100901
$885$	12.0000			0.403376
$886$			4.00000i			0.134383i
$887$	28.0000			0.940148			0.470074	−	0.882627i	$-0.344227\pi$
$887$	28.0000			0.940148			0.470074	+	0.882627i	$0.344227\pi$
$888$	−1.00000	+	6.00000i	−0.0335578	+	0.201347i
$889$	−21.0000			−0.704317
$890$		−	18.0000i		−	0.603361i
$891$	−3.00000			−0.100504
$892$	−4.00000			−0.133930
$893$		−	8.00000i		−	0.267710i
$894$		−	10.0000i		−	0.334450i
$895$	−48.0000			−1.60446
$896$		−	3.00000i		−	0.100223i
$897$	−1.00000			−0.0333890
$898$	−34.0000			−1.13459
$899$	−60.0000			−2.00111
$900$	−1.00000			−0.0333333
$901$		−	33.0000i		−	1.09939i
$902$		−	6.00000i		−	0.199778i
$903$		−	12.0000i		−	0.399335i
$904$	−14.0000			−0.465633
$905$			4.00000i			0.132964i
$906$		−	13.0000i		−	0.431896i
$907$		−	7.00000i		−	0.232431i	−0.993224	−	0.116216i	$-0.962924\pi$
$907$		−	7.00000i		−	0.232431i	0.993224	−	0.116216i	$-0.0370764\pi$
$908$		−	8.00000i		−	0.265489i
$909$	−18.0000			−0.597022
$910$		−	6.00000i		−	0.198898i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		−	1.00000i		−	0.0331133i
$913$	3.00000			0.0992855
$914$	2.00000			0.0661541
$915$	20.0000			0.661180
$916$	20.0000			0.660819
$917$		−	30.0000i		−	0.990687i
$918$	−3.00000			−0.0990148
$919$		−	36.0000i		−	1.18753i	−0.804638	−	0.593765i	$-0.797641\pi$
$919$		−	36.0000i		−	1.18753i	0.804638	−	0.593765i	$-0.202359\pi$
$920$			2.00000i			0.0659380i
$921$	−12.0000			−0.395413
$922$	40.0000			1.31733
$923$			2.00000i			0.0658308i
$924$	9.00000			0.296078
$925$	−6.00000	−	1.00000i	−0.197279	−	0.0328798i
$926$	34.0000			1.11731
$927$			16.0000i			0.525509i
$928$	6.00000			0.196960
$929$	−60.0000			−1.96854			−0.984268	−	0.176682i	$-0.943464\pi$
$929$	−60.0000			−1.96854			−0.984268	+	0.176682i	$0.943464\pi$
$930$			20.0000i			0.655826i
$931$		−	2.00000i		−	0.0655474i
$932$	−24.0000			−0.786146
$933$			20.0000i			0.654771i
$934$	−8.00000			−0.261768
$935$	18.0000			0.588663
$936$	1.00000			0.0326860
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$			24.0000i			0.783628i
$939$			6.00000i			0.195803i
$940$		−	16.0000i		−	0.521862i
$941$	−38.0000			−1.23876			−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000			−1.23876			−0.619382	+	0.785090i	$0.712617\pi$
$942$			8.00000i			0.260654i
$943$			2.00000i			0.0651290i
$944$		−	6.00000i		−	0.195283i
$945$			6.00000i			0.195180i
$946$	−12.0000			−0.390154
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$		−	14.0000i		−	0.454699i
$949$		−	1.00000i		−	0.0324614i
$950$	1.00000			0.0324443
$951$	−2.00000			−0.0648544
$952$	9.00000			0.291692
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$		−	11.0000i		−	0.356138i
$955$	30.0000			0.970777
$956$			16.0000i			0.517477i
$957$			18.0000i			0.581857i
$958$	21.0000			0.678479
$959$	−36.0000			−1.16250
$960$		−	2.00000i		−	0.0645497i
$961$	−69.0000			−2.22581
$962$	6.00000	+	1.00000i	0.193448	+	0.0322413i
$963$	13.0000			0.418919
$964$		0			0
$965$	−32.0000			−1.03012
$966$	−3.00000			−0.0965234
$967$		−	52.0000i		−	1.67221i	−0.548572	−	0.836104i	$-0.684828\pi$
$967$		−	52.0000i		−	1.67221i	0.548572	−	0.836104i	$-0.315172\pi$
$968$			2.00000i			0.0642824i
$969$	3.00000			0.0963739
$970$		−	16.0000i		−	0.513729i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−8.00000			−0.256337
$975$			1.00000i			0.0320256i
$976$		−	10.0000i		−	0.320092i
$977$			53.0000i			1.69562i	0.530300	+	0.847810i	$0.322079\pi$
$977$			53.0000i			1.69562i	−0.530300	+	0.847810i	$0.677921\pi$
$978$	9.00000			0.287788
$979$		−	27.0000i		−	0.862924i
$980$		−	4.00000i		−	0.127775i
$981$			19.0000i			0.606623i
$982$			27.0000i			0.861605i
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		−	2.00000i		−	0.0637577i
$985$		−	34.0000i		−	1.08333i
$986$			18.0000i			0.573237i
$987$	24.0000			0.763928
$988$	−1.00000			−0.0318142
$989$	4.00000			0.127193
$990$	6.00000			0.190693
$991$		−	10.0000i		−	0.317660i	−0.987306	−	0.158830i	$-0.949228\pi$
$991$		−	10.0000i		−	0.317660i	0.987306	−	0.158830i	$-0.0507723\pi$
$992$	10.0000			0.317500
$993$			20.0000i			0.634681i
$994$			6.00000i			0.190308i
$995$	−28.0000			−0.887660
$996$	1.00000			0.0316862
$997$		−	17.0000i		−	0.538395i	−0.963085	−	0.269198i	$-0.913241\pi$
$997$		−	17.0000i		−	0.538395i	0.963085	−	0.269198i	$-0.0867585\pi$
$998$	−39.0000			−1.23452
$999$	−6.00000	−	1.00000i	−0.189832	−	0.0316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.2.c.a.73.2	yes	2
3.2	odd	2		666.2.c.a.73.1		2
4.3	odd	2		1776.2.h.a.961.2		2
12.11	even	2		5328.2.h.b.2737.1		2
37.6	odd	4		8214.2.a.g.1.1		1
37.31	odd	4		8214.2.a.c.1.1		1
37.36	even	2	inner	222.2.c.a.73.1	✓	2
111.110	odd	2		666.2.c.a.73.2		2
148.147	odd	2		1776.2.h.a.961.1		2
444.443	even	2		5328.2.h.b.2737.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.c.a.73.1	✓	2	37.36	even	2	inner
222.2.c.a.73.2	yes	2	1.1	even	1	trivial
666.2.c.a.73.1		2	3.2	odd	2
666.2.c.a.73.2		2	111.110	odd	2
1776.2.h.a.961.1		2	148.147	odd	2
1776.2.h.a.961.2		2	4.3	odd	2
5328.2.h.b.2737.1		2	12.11	even	2
5328.2.h.b.2737.2		2	444.443	even	2
8214.2.a.c.1.1		1	37.31	odd	4
8214.2.a.g.1.1		1	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +3.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} -2.00000 q^{10} -3.00000 q^{11} -1.00000 q^{12} +1.00000i q^{13} +3.00000i q^{14} +2.00000i q^{15} +1.00000 q^{16} +3.00000i q^{17} +1.00000i q^{18} -1.00000i q^{19} -2.00000i q^{20} +3.00000 q^{21} -3.00000i q^{22} +1.00000i q^{23} -1.00000i q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -3.00000 q^{28} -6.00000i q^{29} -2.00000 q^{30} -10.0000i q^{31} +1.00000i q^{32} -3.00000 q^{33} -3.00000 q^{34} +6.00000i q^{35} -1.00000 q^{36} +(-6.00000 - 1.00000i) q^{37} +1.00000 q^{38} +1.00000i q^{39} +2.00000 q^{40} +2.00000 q^{41} +3.00000i q^{42} -4.00000i q^{43} +3.00000 q^{44} +2.00000i q^{45} -1.00000 q^{46} +8.00000 q^{47} +1.00000 q^{48} +2.00000 q^{49} +1.00000i q^{50} +3.00000i q^{51} -1.00000i q^{52} -11.0000 q^{53} +1.00000i q^{54} -6.00000i q^{55} -3.00000i q^{56} -1.00000i q^{57} +6.00000 q^{58} -6.00000i q^{59} -2.00000i q^{60} -10.0000i q^{61} +10.0000 q^{62} +3.00000 q^{63} -1.00000 q^{64} -2.00000 q^{65} -3.00000i q^{66} +8.00000 q^{67} -3.00000i q^{68} +1.00000i q^{69} -6.00000 q^{70} +2.00000 q^{71} -1.00000i q^{72} -1.00000 q^{73} +(1.00000 - 6.00000i) q^{74} +1.00000 q^{75} +1.00000i q^{76} -9.00000 q^{77} -1.00000 q^{78} +14.0000i q^{79} +2.00000i q^{80} +1.00000 q^{81} +2.00000i q^{82} -1.00000 q^{83} -3.00000 q^{84} -6.00000 q^{85} +4.00000 q^{86} -6.00000i q^{87} +3.00000i q^{88} +9.00000i q^{89} -2.00000 q^{90} +3.00000i q^{91} -1.00000i q^{92} -10.0000i q^{93} +8.00000i q^{94} +2.00000 q^{95} +1.00000i q^{96} +8.00000i q^{97} +2.00000i q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} + 6 q^{7} + 2 q^{9} - 4 q^{10} - 6 q^{11} - 2 q^{12} + 2 q^{16} + 6 q^{21} + 2 q^{25} - 2 q^{26} + 2 q^{27} - 6 q^{28} - 4 q^{30} - 6 q^{33} - 6 q^{34} - 2 q^{36} - 12 q^{37} + 2 q^{38}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^4 + 6 * q^7 + 2 * q^9 - 4 * q^10 - 6 * q^11 - 2 * q^12 + 2 * q^16 + 6 * q^21 + 2 * q^25 - 2 * q^26 + 2 * q^27 - 6 * q^28 - 4 * q^30 - 6 * q^33 - 6 * q^34 - 2 * q^36 - 12 * q^37 + 2 * q^38 + 4 * q^40 + 4 * q^41 + 6 * q^44 - 2 * q^46 + 16 * q^47 + 2 * q^48 + 4 * q^49 - 22 * q^53 + 12 * q^58 + 20 * q^62 + 6 * q^63 - 2 * q^64 - 4 * q^65 + 16 * q^67 - 12 * q^70 + 4 * q^71 - 2 * q^73 + 2 * q^74 + 2 * q^75 - 18 * q^77 - 2 * q^78 + 2 * q^81 - 2 * q^83 - 6 * q^84 - 12 * q^85 + 8 * q^86 - 4 * q^90 + 4 * q^95 - 6 * q^99

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