LMFDB - Embedded newform 221.2.c.a.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [221,2,Mod(103,221)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(221, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("221.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.76469388467$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			103.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	221.103
Dual form			221.2.c.a.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{2} +2.00000 q^{3} -1.00000 q^{4} -3.46410i q^{5} -3.46410i q^{6} +3.46410i q^{7} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.73205i q^{2} +2.00000 q^{3} -1.00000 q^{4} -3.46410i q^{5} -3.46410i q^{6} +3.46410i q^{7} -1.73205i q^{8} +1.00000 q^{9} -6.00000 q^{10} +3.46410i q^{11} -2.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +6.00000 q^{14} -6.92820i q^{15} -5.00000 q^{16} +1.00000 q^{17} -1.73205i q^{18} -3.46410i q^{19} +3.46410i q^{20} +6.92820i q^{21} +6.00000 q^{22} +6.00000 q^{23} -3.46410i q^{24} -7.00000 q^{25} +(6.00000 + 1.73205i) q^{26} -4.00000 q^{27} -3.46410i q^{28} -6.00000 q^{29} -12.0000 q^{30} +3.46410i q^{31} +5.19615i q^{32} +6.92820i q^{33} -1.73205i q^{34} +12.0000 q^{35} -1.00000 q^{36} -3.46410i q^{37} -6.00000 q^{38} +(-2.00000 + 6.92820i) q^{39} -6.00000 q^{40} +3.46410i q^{41} +12.0000 q^{42} +8.00000 q^{43} -3.46410i q^{44} -3.46410i q^{45} -10.3923i q^{46} -10.3923i q^{47} -10.0000 q^{48} -5.00000 q^{49} +12.1244i q^{50} +2.00000 q^{51} +(1.00000 - 3.46410i) q^{52} -6.00000 q^{53} +6.92820i q^{54} +12.0000 q^{55} +6.00000 q^{56} -6.92820i q^{57} +10.3923i q^{58} +10.3923i q^{59} +6.92820i q^{60} +10.0000 q^{61} +6.00000 q^{62} +3.46410i q^{63} -1.00000 q^{64} +(12.0000 + 3.46410i) q^{65} +12.0000 q^{66} +3.46410i q^{67} -1.00000 q^{68} +12.0000 q^{69} -20.7846i q^{70} -10.3923i q^{71} -1.73205i q^{72} +10.3923i q^{73} -6.00000 q^{74} -14.0000 q^{75} +3.46410i q^{76} -12.0000 q^{77} +(12.0000 + 3.46410i) q^{78} -2.00000 q^{79} +17.3205i q^{80} -11.0000 q^{81} +6.00000 q^{82} +3.46410i q^{83} -6.92820i q^{84} -3.46410i q^{85} -13.8564i q^{86} -12.0000 q^{87} +6.00000 q^{88} -13.8564i q^{89} -6.00000 q^{90} +(-12.0000 - 3.46410i) q^{91} -6.00000 q^{92} +6.92820i q^{93} -18.0000 q^{94} -12.0000 q^{95} +10.3923i q^{96} -3.46410i q^{97} +8.66025i q^{98} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9	$ 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9} - 12 q^{10} - 4 q^{12} - 2 q^{13} + 12 q^{14} - 10 q^{16} + 2 q^{17} + 12 q^{22} + 12 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{27} - 12 q^{29} - 24 q^{30} + 24 q^{35} - 2 q^{36} - 12 q^{38} - 4 q^{39} - 12 q^{40} + 24 q^{42} + 16 q^{43} - 20 q^{48} - 10 q^{49} + 4 q^{51} + 2 q^{52} - 12 q^{53} + 24 q^{55} + 12 q^{56} + 20 q^{61} + 12 q^{62} - 2 q^{64} + 24 q^{65} + 24 q^{66} - 2 q^{68} + 24 q^{69} - 12 q^{74} - 28 q^{75} - 24 q^{77} + 24 q^{78} - 4 q^{79} - 22 q^{81} + 12 q^{82} - 24 q^{87} + 12 q^{88} - 12 q^{90} - 24 q^{91} - 12 q^{92} - 36 q^{94} - 24 q^{95}+O(q^{100}) $ 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9 - 12 * q^10 - 4 * q^12 - 2 * q^13 + 12 * q^14 - 10 * q^16 + 2 * q^17 + 12 * q^22 + 12 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^27 - 12 * q^29 - 24 * q^30 + 24 * q^35 - 2 * q^36 - 12 * q^38 - 4 * q^39 - 12 * q^40 + 24 * q^42 + 16 * q^43 - 20 * q^48 - 10 * q^49 + 4 * q^51 + 2 * q^52 - 12 * q^53 + 24 * q^55 + 12 * q^56 + 20 * q^61 + 12 * q^62 - 2 * q^64 + 24 * q^65 + 24 * q^66 - 2 * q^68 + 24 * q^69 - 12 * q^74 - 28 * q^75 - 24 * q^77 + 24 * q^78 - 4 * q^79 - 22 * q^81 + 12 * q^82 - 24 * q^87 + 12 * q^88 - 12 * q^90 - 24 * q^91 - 12 * q^92 - 36 * q^94 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/221\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.73205i		−	1.22474i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$		−	1.73205i		−	1.22474i	0.790569	−	0.612372i	$-0.209785\pi$
$3$	2.00000			1.15470			0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000			1.15470			0.577350	+	0.816497i	$0.304087\pi$
$4$	−1.00000			−0.500000
$5$		−	3.46410i		−	1.54919i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$		−	3.46410i		−	1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$		−	3.46410i		−	1.41421i
$7$			3.46410i			1.30931i	0.755929	+	0.654654i	$0.227186\pi$
$7$			3.46410i			1.30931i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		−	1.73205i		−	0.612372i
$9$	1.00000			0.333333
$10$	−6.00000			−1.89737
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	−2.00000			−0.577350
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	6.00000			1.60357
$15$		−	6.92820i		−	1.78885i
$16$	−5.00000			−1.25000
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$		−	1.73205i		−	0.408248i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$			3.46410i			0.774597i
$21$			6.92820i			1.51186i
$22$	6.00000			1.27920
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		−	3.46410i		−	0.707107i
$25$	−7.00000			−1.40000
$26$	6.00000	+	1.73205i	1.17670	+	0.339683i
$27$	−4.00000			−0.769800
$28$		−	3.46410i		−	0.654654i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−12.0000			−2.19089
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$			5.19615i			0.918559i
$33$			6.92820i			1.20605i
$34$		−	1.73205i		−	0.297044i
$35$	12.0000			2.02837
$36$	−1.00000			−0.166667
$37$		−	3.46410i		−	0.569495i	−0.958603	−	0.284747i	$-0.908090\pi$
$37$		−	3.46410i		−	0.569495i	0.958603	−	0.284747i	$-0.0919097\pi$
$38$	−6.00000			−0.973329
$39$	−2.00000	+	6.92820i	−0.320256	+	1.10940i
$40$	−6.00000			−0.948683
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$	12.0000			1.85164
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		−	3.46410i		−	0.522233i
$45$		−	3.46410i		−	0.516398i
$46$		−	10.3923i		−	1.53226i
$47$		−	10.3923i		−	1.51587i	−0.652328	−	0.757937i	$-0.726208\pi$
$47$		−	10.3923i		−	1.51587i	0.652328	−	0.757937i	$-0.273792\pi$
$48$	−10.0000			−1.44338
$49$	−5.00000			−0.714286
$50$			12.1244i			1.71464i
$51$	2.00000			0.280056
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$			6.92820i			0.942809i
$55$	12.0000			1.61808
$56$	6.00000			0.801784
$57$		−	6.92820i		−	0.917663i
$58$			10.3923i			1.36458i
$59$			10.3923i			1.35296i	0.736460	+	0.676481i	$0.236496\pi$
$59$			10.3923i			1.35296i	−0.736460	+	0.676481i	$0.763504\pi$
$60$			6.92820i			0.894427i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	6.00000			0.762001
$63$			3.46410i			0.436436i
$64$	−1.00000			−0.125000
$65$	12.0000	+	3.46410i	1.48842	+	0.429669i
$66$	12.0000			1.47710
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−1.00000			−0.121268
$69$	12.0000			1.44463
$70$		−	20.7846i		−	2.48424i
$71$		−	10.3923i		−	1.23334i	−0.787222	−	0.616670i	$-0.788481\pi$
$71$		−	10.3923i		−	1.23334i	0.787222	−	0.616670i	$-0.211519\pi$
$72$		−	1.73205i		−	0.204124i
$73$			10.3923i			1.21633i	0.793812	+	0.608164i	$0.208094\pi$
$73$			10.3923i			1.21633i	−0.793812	+	0.608164i	$0.791906\pi$
$74$	−6.00000			−0.697486
$75$	−14.0000			−1.61658
$76$			3.46410i			0.397360i
$77$	−12.0000			−1.36753
$78$	12.0000	+	3.46410i	1.35873	+	0.392232i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$			17.3205i			1.93649i
$81$	−11.0000			−1.22222
$82$	6.00000			0.662589
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		−	6.92820i		−	0.755929i
$85$		−	3.46410i		−	0.375735i
$86$		−	13.8564i		−	1.49417i
$87$	−12.0000			−1.28654
$88$	6.00000			0.639602
$89$		−	13.8564i		−	1.46878i	−0.678730	−	0.734388i	$-0.737469\pi$
$89$		−	13.8564i		−	1.46878i	0.678730	−	0.734388i	$-0.262531\pi$
$90$	−6.00000			−0.632456
$91$	−12.0000	−	3.46410i	−1.25794	−	0.363137i
$92$	−6.00000			−0.625543
$93$			6.92820i			0.718421i
$94$	−18.0000			−1.85656
$95$	−12.0000			−1.23117
$96$			10.3923i			1.06066i
$97$		−	3.46410i		−	0.351726i	−0.984415	−	0.175863i	$-0.943728\pi$
$97$		−	3.46410i		−	0.351726i	0.984415	−	0.175863i	$-0.0562716\pi$
$98$			8.66025i			0.874818i
$99$			3.46410i			0.348155i
$100$	7.00000			0.700000
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		−	3.46410i		−	0.342997i
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$	6.00000	+	1.73205i	0.588348	+	0.169842i
$105$	24.0000			2.34216
$106$			10.3923i			1.00939i
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$	4.00000			0.384900
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		−	20.7846i		−	1.98173i
$111$		−	6.92820i		−	0.657596i
$112$		−	17.3205i		−	1.63663i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−12.0000			−1.12390
$115$		−	20.7846i		−	1.93817i
$116$	6.00000			0.557086
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	18.0000			1.65703
$119$			3.46410i			0.317554i
$120$	−12.0000			−1.09545
$121$	−1.00000			−0.0909091
$122$		−	17.3205i		−	1.56813i
$123$			6.92820i			0.624695i
$124$		−	3.46410i		−	0.311086i
$125$			6.92820i			0.619677i
$126$	6.00000			0.534522
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$			12.1244i			1.07165i
$129$	16.0000			1.40872
$130$	6.00000	−	20.7846i	0.526235	−	1.82293i
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$		−	6.92820i		−	0.603023i
$133$	12.0000			1.04053
$134$	6.00000			0.518321
$135$			13.8564i			1.19257i
$136$		−	1.73205i		−	0.148522i
$137$			13.8564i			1.18383i	0.805999	+	0.591916i	$0.201628\pi$
$137$			13.8564i			1.18383i	−0.805999	+	0.591916i	$0.798372\pi$
$138$		−	20.7846i		−	1.76930i
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$	−12.0000			−1.01419
$141$		−	20.7846i		−	1.75038i
$142$	−18.0000			−1.51053
$143$	−12.0000	−	3.46410i	−1.00349	−	0.289683i
$144$	−5.00000			−0.416667
$145$			20.7846i			1.72607i
$146$	18.0000			1.48969
$147$	−10.0000			−0.824786
$148$			3.46410i			0.284747i
$149$			6.92820i			0.567581i	0.958886	+	0.283790i	$0.0915919\pi$
$149$			6.92820i			0.567581i	−0.958886	+	0.283790i	$0.908408\pi$
$150$			24.2487i			1.97990i
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$	−6.00000			−0.486664
$153$	1.00000			0.0808452
$154$			20.7846i			1.67487i
$155$	12.0000			0.963863
$156$	2.00000	−	6.92820i	0.160128	−	0.554700i
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$			3.46410i			0.275589i
$159$	−12.0000			−0.951662
$160$	18.0000			1.42302
$161$			20.7846i			1.63806i
$162$			19.0526i			1.49691i
$163$		−	10.3923i		−	0.813988i	−0.913431	−	0.406994i	$-0.866577\pi$
$163$		−	10.3923i		−	0.813988i	0.913431	−	0.406994i	$-0.133423\pi$
$164$		−	3.46410i		−	0.270501i
$165$	24.0000			1.86840
$166$	6.00000			0.465690
$167$		−	10.3923i		−	0.804181i	−0.915600	−	0.402090i	$-0.868284\pi$
$167$		−	10.3923i		−	0.804181i	0.915600	−	0.402090i	$-0.131716\pi$
$168$	12.0000			0.925820
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	−6.00000			−0.460179
$171$		−	3.46410i		−	0.264906i
$172$	−8.00000			−0.609994
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$			20.7846i			1.57568i
$175$		−	24.2487i		−	1.83303i
$176$		−	17.3205i		−	1.30558i
$177$			20.7846i			1.56227i
$178$	−24.0000			−1.79888
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$			3.46410i			0.258199i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−6.00000	+	20.7846i	−0.444750	+	1.54066i
$183$	20.0000			1.47844
$184$		−	10.3923i		−	0.766131i
$185$	−12.0000			−0.882258
$186$	12.0000			0.879883
$187$			3.46410i			0.253320i
$188$			10.3923i			0.757937i
$189$		−	13.8564i		−	1.00791i
$190$			20.7846i			1.50787i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−2.00000			−0.144338
$193$			3.46410i			0.249351i	0.992198	+	0.124676i	$0.0397891\pi$
$193$			3.46410i			0.249351i	−0.992198	+	0.124676i	$0.960211\pi$
$194$	−6.00000			−0.430775
$195$	24.0000	+	6.92820i	1.71868	+	0.496139i
$196$	5.00000			0.357143
$197$		−	24.2487i		−	1.72765i	−0.503793	−	0.863825i	$-0.668062\pi$
$197$		−	24.2487i		−	1.72765i	0.503793	−	0.863825i	$-0.331938\pi$
$198$	6.00000			0.426401
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$			12.1244i			0.857321i
$201$			6.92820i			0.488678i
$202$			10.3923i			0.731200i
$203$		−	20.7846i		−	1.45879i
$204$	−2.00000			−0.140028
$205$	12.0000			0.838116
$206$			27.7128i			1.93084i
$207$	6.00000			0.417029
$208$	5.00000	−	17.3205i	0.346688	−	1.20096i
$209$	12.0000			0.830057
$210$		−	41.5692i		−	2.86855i
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$	6.00000			0.412082
$213$		−	20.7846i		−	1.42414i
$214$			10.3923i			0.710403i
$215$		−	27.7128i		−	1.89000i
$216$			6.92820i			0.471405i
$217$	−12.0000			−0.814613
$218$	−18.0000			−1.21911
$219$			20.7846i			1.40449i
$220$	−12.0000			−0.809040
$221$	−1.00000	+	3.46410i	−0.0672673	+	0.233021i
$222$	−12.0000			−0.805387
$223$			10.3923i			0.695920i	0.937509	+	0.347960i	$0.113126\pi$
$223$			10.3923i			0.695920i	−0.937509	+	0.347960i	$0.886874\pi$
$224$	−18.0000			−1.20268
$225$	−7.00000			−0.466667
$226$			10.3923i			0.691286i
$227$		−	10.3923i		−	0.689761i	−0.938647	−	0.344881i	$-0.887919\pi$
$227$		−	10.3923i		−	0.689761i	0.938647	−	0.344881i	$-0.112081\pi$
$228$			6.92820i			0.458831i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−36.0000			−2.37377
$231$	−24.0000			−1.57908
$232$			10.3923i			0.682288i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	6.00000	+	1.73205i	0.392232	+	0.113228i
$235$	−36.0000			−2.34838
$236$		−	10.3923i		−	0.676481i
$237$	−4.00000			−0.259828
$238$	6.00000			0.388922
$239$		−	3.46410i		−	0.224074i	−0.993704	−	0.112037i	$-0.964262\pi$
$239$		−	3.46410i		−	0.224074i	0.993704	−	0.112037i	$-0.0357375\pi$
$240$			34.6410i			2.23607i
$241$			10.3923i			0.669427i	0.942320	+	0.334714i	$0.108640\pi$
$241$			10.3923i			0.669427i	−0.942320	+	0.334714i	$0.891360\pi$
$242$			1.73205i			0.111340i
$243$	−10.0000			−0.641500
$244$	−10.0000			−0.640184
$245$			17.3205i			1.10657i
$246$	12.0000			0.765092
$247$	12.0000	+	3.46410i	0.763542	+	0.220416i
$248$	6.00000			0.381000
$249$			6.92820i			0.439057i
$250$	12.0000			0.758947
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		−	3.46410i		−	0.218218i
$253$			20.7846i			1.30672i
$254$			34.6410i			2.17357i
$255$		−	6.92820i		−	0.433861i
$256$	19.0000			1.18750
$257$	−30.0000			−1.87135			−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000			−1.87135			−0.935674	+	0.352865i	$0.885208\pi$
$258$		−	27.7128i		−	1.72532i
$259$	12.0000			0.745644
$260$	−12.0000	−	3.46410i	−0.744208	−	0.214834i
$261$	−6.00000			−0.371391
$262$		−	31.1769i		−	1.92612i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$	12.0000			0.738549
$265$			20.7846i			1.27679i
$266$		−	20.7846i		−	1.27439i
$267$		−	27.7128i		−	1.69600i
$268$		−	3.46410i		−	0.211604i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$	24.0000			1.46059
$271$		−	3.46410i		−	0.210429i	−0.994450	−	0.105215i	$-0.966447\pi$
$271$		−	3.46410i		−	0.210429i	0.994450	−	0.105215i	$-0.0335529\pi$
$272$	−5.00000			−0.303170
$273$	−24.0000	−	6.92820i	−1.45255	−	0.419314i
$274$	24.0000			1.44989
$275$		−	24.2487i		−	1.46225i
$276$	−12.0000			−0.722315
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$		−	3.46410i		−	0.207763i
$279$			3.46410i			0.207390i
$280$		−	20.7846i		−	1.24212i
$281$			20.7846i			1.23991i	0.784639	+	0.619953i	$0.212848\pi$
$281$			20.7846i			1.23991i	−0.784639	+	0.619953i	$0.787152\pi$
$282$	−36.0000			−2.14377
$283$	−2.00000			−0.118888			−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000			−0.118888			−0.0594438	+	0.998232i	$0.518933\pi$
$284$			10.3923i			0.616670i
$285$	−24.0000			−1.42164
$286$	−6.00000	+	20.7846i	−0.354787	+	1.22902i
$287$	−12.0000			−0.708338
$288$			5.19615i			0.306186i
$289$	1.00000			0.0588235
$290$	36.0000			2.11399
$291$		−	6.92820i		−	0.406138i
$292$		−	10.3923i		−	0.608164i
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$			17.3205i			1.01015i
$295$	36.0000			2.09600
$296$	−6.00000			−0.348743
$297$		−	13.8564i		−	0.804030i
$298$	12.0000			0.695141
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	14.0000			0.808290
$301$			27.7128i			1.59734i
$302$	−6.00000			−0.345261
$303$	−12.0000			−0.689382
$304$			17.3205i			0.993399i
$305$		−	34.6410i		−	1.98354i
$306$		−	1.73205i		−	0.0990148i
$307$			10.3923i			0.593120i	0.955014	+	0.296560i	$0.0958395\pi$
$307$			10.3923i			0.593120i	−0.955014	+	0.296560i	$0.904160\pi$
$308$	12.0000			0.683763
$309$	−32.0000			−1.82042
$310$		−	20.7846i		−	1.18049i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$	12.0000	+	3.46410i	0.679366	+	0.196116i
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$		−	3.46410i		−	0.195491i
$315$	12.0000			0.676123
$316$	2.00000			0.112509
$317$		−	10.3923i		−	0.583690i	−0.956466	−	0.291845i	$-0.905731\pi$
$317$		−	10.3923i		−	0.583690i	0.956466	−	0.291845i	$-0.0942691\pi$
$318$			20.7846i			1.16554i
$319$		−	20.7846i		−	1.16371i
$320$			3.46410i			0.193649i
$321$	−12.0000			−0.669775
$322$	36.0000			2.00620
$323$		−	3.46410i		−	0.192748i
$324$	11.0000			0.611111
$325$	7.00000	−	24.2487i	0.388290	−	1.34508i
$326$	−18.0000			−0.996928
$327$		−	20.7846i		−	1.14939i
$328$	6.00000			0.331295
$329$	36.0000			1.98474
$330$		−	41.5692i		−	2.28831i
$331$			17.3205i			0.952021i	0.879440	+	0.476011i	$0.157918\pi$
$331$			17.3205i			0.952021i	−0.879440	+	0.476011i	$0.842082\pi$
$332$		−	3.46410i		−	0.190117i
$333$		−	3.46410i		−	0.189832i
$334$	−18.0000			−0.984916
$335$	12.0000			0.655630
$336$		−	34.6410i		−	1.88982i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−12.0000	+	19.0526i	−0.652714	+	1.03632i
$339$	−12.0000			−0.651751
$340$			3.46410i			0.187867i
$341$	−12.0000			−0.649836
$342$	−6.00000			−0.324443
$343$			6.92820i			0.374088i
$344$		−	13.8564i		−	0.747087i
$345$		−	41.5692i		−	2.23801i
$346$			10.3923i			0.558694i
$347$	6.00000			0.322097			0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000			0.322097			0.161048	+	0.986947i	$0.448512\pi$
$348$	12.0000			0.643268
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	−42.0000			−2.24499
$351$	4.00000	−	13.8564i	0.213504	−	0.739600i
$352$	−18.0000			−0.959403
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	36.0000			1.91338
$355$	−36.0000			−1.91068
$356$			13.8564i			0.734388i
$357$			6.92820i			0.366679i
$358$		−	41.5692i		−	2.19700i
$359$		−	24.2487i		−	1.27980i	−0.768459	−	0.639899i	$-0.778976\pi$
$359$		−	24.2487i		−	1.27980i	0.768459	−	0.639899i	$-0.221024\pi$
$360$	−6.00000			−0.316228
$361$	7.00000			0.368421
$362$		−	3.46410i		−	0.182069i
$363$	−2.00000			−0.104973
$364$	12.0000	+	3.46410i	0.628971	+	0.181568i
$365$	36.0000			1.88433
$366$		−	34.6410i		−	1.81071i
$367$	14.0000			0.730794			0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000			0.730794			0.365397	+	0.930852i	$0.380933\pi$
$368$	−30.0000			−1.56386
$369$			3.46410i			0.180334i
$370$			20.7846i			1.08054i
$371$		−	20.7846i		−	1.07908i
$372$		−	6.92820i		−	0.359211i
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	6.00000			0.310253
$375$			13.8564i			0.715542i
$376$	−18.0000			−0.928279
$377$	6.00000	−	20.7846i	0.309016	−	1.07046i
$378$	−24.0000			−1.23443
$379$			17.3205i			0.889695i	0.895606	+	0.444847i	$0.146742\pi$
$379$			17.3205i			0.889695i	−0.895606	+	0.444847i	$0.853258\pi$
$380$	12.0000			0.615587
$381$	−40.0000			−2.04926
$382$		0			0
$383$			17.3205i			0.885037i	0.896759	+	0.442518i	$0.145915\pi$
$383$			17.3205i			0.885037i	−0.896759	+	0.442518i	$0.854085\pi$
$384$			24.2487i			1.23744i
$385$			41.5692i			2.11856i
$386$	6.00000			0.305392
$387$	8.00000			0.406663
$388$			3.46410i			0.175863i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$	12.0000	−	41.5692i	0.607644	−	2.10494i
$391$	6.00000			0.303433
$392$			8.66025i			0.437409i
$393$	36.0000			1.81596
$394$	−42.0000			−2.11593
$395$			6.92820i			0.348596i
$396$		−	3.46410i		−	0.174078i
$397$			31.1769i			1.56472i	0.622824	+	0.782362i	$0.285985\pi$
$397$			31.1769i			1.56472i	−0.622824	+	0.782362i	$0.714015\pi$
$398$			24.2487i			1.21548i
$399$	24.0000			1.20150
$400$	35.0000			1.75000
$401$		−	10.3923i		−	0.518967i	−0.965748	−	0.259483i	$-0.916448\pi$
$401$		−	10.3923i		−	0.518967i	0.965748	−	0.259483i	$-0.0835523\pi$
$402$	12.0000			0.598506
$403$	−12.0000	−	3.46410i	−0.597763	−	0.172559i
$404$	6.00000			0.298511
$405$			38.1051i			1.89346i
$406$	−36.0000			−1.78665
$407$	12.0000			0.594818
$408$		−	3.46410i		−	0.171499i
$409$			27.7128i			1.37031i	0.728397	+	0.685155i	$0.240266\pi$
$409$			27.7128i			1.37031i	−0.728397	+	0.685155i	$0.759734\pi$
$410$		−	20.7846i		−	1.02648i
$411$			27.7128i			1.36697i
$412$	16.0000			0.788263
$413$	−36.0000			−1.77144
$414$		−	10.3923i		−	0.510754i
$415$	12.0000			0.589057
$416$	−18.0000	−	5.19615i	−0.882523	−	0.254762i
$417$	4.00000			0.195881
$418$		−	20.7846i		−	1.01661i
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$	−24.0000			−1.17108
$421$			6.92820i			0.337660i	0.985645	+	0.168830i	$0.0539989\pi$
$421$			6.92820i			0.337660i	−0.985645	+	0.168830i	$0.946001\pi$
$422$		−	38.1051i		−	1.85493i
$423$		−	10.3923i		−	0.505291i
$424$			10.3923i			0.504695i
$425$	−7.00000			−0.339550
$426$	−36.0000			−1.74421
$427$			34.6410i			1.67640i
$428$	6.00000			0.290021
$429$	−24.0000	−	6.92820i	−1.15873	−	0.334497i
$430$	−48.0000			−2.31477
$431$			3.46410i			0.166860i	0.996514	+	0.0834300i	$0.0265875\pi$
$431$			3.46410i			0.166860i	−0.996514	+	0.0834300i	$0.973413\pi$
$432$	20.0000			0.962250
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$			20.7846i			0.997693i
$435$			41.5692i			1.99309i
$436$			10.3923i			0.497701i
$437$		−	20.7846i		−	0.994263i
$438$	36.0000			1.72015
$439$	26.0000			1.24091			0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000			1.24091			0.620456	+	0.784241i	$0.286947\pi$
$440$		−	20.7846i		−	0.990867i
$441$	−5.00000			−0.238095
$442$	6.00000	+	1.73205i	0.285391	+	0.0823853i
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$			6.92820i			0.328798i
$445$	−48.0000			−2.27542
$446$	18.0000			0.852325
$447$			13.8564i			0.655386i
$448$		−	3.46410i		−	0.163663i
$449$		−	10.3923i		−	0.490443i	−0.969467	−	0.245222i	$-0.921139\pi$
$449$		−	10.3923i		−	0.490443i	0.969467	−	0.245222i	$-0.0788607\pi$
$450$			12.1244i			0.571548i
$451$	−12.0000			−0.565058
$452$	6.00000			0.282216
$453$		−	6.92820i		−	0.325515i
$454$	−18.0000			−0.844782
$455$	−12.0000	+	41.5692i	−0.562569	+	1.94880i
$456$	−12.0000			−0.561951
$457$		−	20.7846i		−	0.972263i	−0.873886	−	0.486132i	$-0.838408\pi$
$457$		−	20.7846i		−	0.972263i	0.873886	−	0.486132i	$-0.161592\pi$
$458$		0			0
$459$	−4.00000			−0.186704
$460$			20.7846i			0.969087i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$			41.5692i			1.93398i
$463$		−	38.1051i		−	1.77090i	−0.464739	−	0.885448i	$-0.653852\pi$
$463$		−	38.1051i		−	1.77090i	0.464739	−	0.885448i	$-0.346148\pi$
$464$	30.0000			1.39272
$465$	24.0000			1.11297
$466$		−	31.1769i		−	1.44424i
$467$	24.0000			1.11059			0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000			1.11059			0.555294	+	0.831654i	$0.312606\pi$
$468$	1.00000	−	3.46410i	0.0462250	−	0.160128i
$469$	−12.0000			−0.554109
$470$			62.3538i			2.87617i
$471$	4.00000			0.184310
$472$	18.0000			0.828517
$473$			27.7128i			1.27424i
$474$			6.92820i			0.318223i
$475$			24.2487i			1.11261i
$476$		−	3.46410i		−	0.158777i
$477$	−6.00000			−0.274721
$478$	−6.00000			−0.274434
$479$			17.3205i			0.791394i	0.918381	+	0.395697i	$0.129497\pi$
$479$			17.3205i			0.791394i	−0.918381	+	0.395697i	$0.870503\pi$
$480$	36.0000			1.64317
$481$	12.0000	+	3.46410i	0.547153	+	0.157949i
$482$	18.0000			0.819878
$483$			41.5692i			1.89146i
$484$	1.00000			0.0454545
$485$	−12.0000			−0.544892
$486$			17.3205i			0.785674i
$487$		−	24.2487i		−	1.09881i	−0.835555	−	0.549407i	$-0.814854\pi$
$487$		−	24.2487i		−	1.09881i	0.835555	−	0.549407i	$-0.185146\pi$
$488$		−	17.3205i		−	0.784063i
$489$		−	20.7846i		−	0.939913i
$490$	30.0000			1.35526
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$		−	6.92820i		−	0.312348i
$493$	−6.00000			−0.270226
$494$	6.00000	−	20.7846i	0.269953	−	0.935144i
$495$	12.0000			0.539360
$496$		−	17.3205i		−	0.777714i
$497$	36.0000			1.61482
$498$	12.0000			0.537733
$499$		−	24.2487i		−	1.08552i	−0.839887	−	0.542761i	$-0.817379\pi$
$499$		−	24.2487i		−	1.08552i	0.839887	−	0.542761i	$-0.182621\pi$
$500$		−	6.92820i		−	0.309839i
$501$		−	20.7846i		−	0.928588i
$502$		−	20.7846i		−	0.927663i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	6.00000			0.267261
$505$			20.7846i			0.924903i
$506$	36.0000			1.60040
$507$	−22.0000	−	13.8564i	−0.977054	−	0.615385i
$508$	20.0000			0.887357
$509$		−	6.92820i		−	0.307087i	−0.988142	−	0.153544i	$-0.950931\pi$
$509$		−	6.92820i		−	0.307087i	0.988142	−	0.153544i	$-0.0490686\pi$
$510$	−12.0000			−0.531369
$511$	−36.0000			−1.59255
$512$		−	8.66025i		−	0.382733i
$513$			13.8564i			0.611775i
$514$			51.9615i			2.29192i
$515$			55.4256i			2.44234i
$516$	−16.0000			−0.704361
$517$	36.0000			1.58328
$518$		−	20.7846i		−	0.913223i
$519$	−12.0000			−0.526742
$520$	6.00000	−	20.7846i	0.263117	−	0.911465i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$			10.3923i			0.454859i
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−18.0000			−0.786334
$525$		−	48.4974i		−	2.11660i
$526$			20.7846i			0.906252i
$527$			3.46410i			0.150899i
$528$		−	34.6410i		−	1.50756i
$529$	13.0000			0.565217
$530$	36.0000			1.56374
$531$			10.3923i			0.450988i
$532$	−12.0000			−0.520266
$533$	−12.0000	−	3.46410i	−0.519778	−	0.150047i
$534$	−48.0000			−2.07716
$535$			20.7846i			0.898597i
$536$	6.00000			0.259161
$537$	48.0000			2.07135
$538$		−	31.1769i		−	1.34413i
$539$		−	17.3205i		−	0.746047i
$540$		−	13.8564i		−	0.596285i
$541$		−	31.1769i		−	1.34040i	−0.742180	−	0.670200i	$-0.766208\pi$
$541$		−	31.1769i		−	1.34040i	0.742180	−	0.670200i	$-0.233792\pi$
$542$	−6.00000			−0.257722
$543$	4.00000			0.171656
$544$			5.19615i			0.222783i
$545$	−36.0000			−1.54207
$546$	−12.0000	+	41.5692i	−0.513553	+	1.77900i
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$		−	13.8564i		−	0.591916i
$549$	10.0000			0.426790
$550$	−42.0000			−1.79089
$551$			20.7846i			0.885454i
$552$		−	20.7846i		−	0.884652i
$553$		−	6.92820i		−	0.294617i
$554$		−	45.0333i		−	1.91328i
$555$	−24.0000			−1.01874
$556$	−2.00000			−0.0848189
$557$			6.92820i			0.293557i	0.989169	+	0.146779i	$0.0468905\pi$
$557$			6.92820i			0.293557i	−0.989169	+	0.146779i	$0.953109\pi$
$558$	6.00000			0.254000
$559$	−8.00000	+	27.7128i	−0.338364	+	1.17213i
$560$	−60.0000			−2.53546
$561$			6.92820i			0.292509i
$562$	36.0000			1.51857
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$			20.7846i			0.875190i
$565$			20.7846i			0.874415i
$566$			3.46410i			0.145607i
$567$		−	38.1051i		−	1.60026i
$568$	−18.0000			−0.755263
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$			41.5692i			1.74114i
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$	12.0000	+	3.46410i	0.501745	+	0.144841i
$573$		0			0
$574$			20.7846i			0.867533i
$575$	−42.0000			−1.75152
$576$	−1.00000			−0.0416667
$577$			27.7128i			1.15370i	0.816850	+	0.576850i	$0.195718\pi$
$577$			27.7128i			1.15370i	−0.816850	+	0.576850i	$0.804282\pi$
$578$		−	1.73205i		−	0.0720438i
$579$			6.92820i			0.287926i
$580$		−	20.7846i		−	0.863034i
$581$	−12.0000			−0.497844
$582$	−12.0000			−0.497416
$583$		−	20.7846i		−	0.860811i
$584$	18.0000			0.744845
$585$	12.0000	+	3.46410i	0.496139	+	0.143223i
$586$	36.0000			1.48715
$587$		−	45.0333i		−	1.85872i	−0.369170	−	0.929362i	$-0.620358\pi$
$587$		−	45.0333i		−	1.85872i	0.369170	−	0.929362i	$-0.379642\pi$
$588$	10.0000			0.412393
$589$	12.0000			0.494451
$590$		−	62.3538i		−	2.56707i
$591$		−	48.4974i		−	1.99492i
$592$			17.3205i			0.711868i
$593$		−	20.7846i		−	0.853522i	−0.904365	−	0.426761i	$-0.859655\pi$
$593$		−	20.7846i		−	0.853522i	0.904365	−	0.426761i	$-0.140345\pi$
$594$	−24.0000			−0.984732
$595$	12.0000			0.491952
$596$		−	6.92820i		−	0.283790i
$597$	−28.0000			−1.14596
$598$	36.0000	+	10.3923i	1.47215	+	0.424973i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$			24.2487i			0.989949i
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$	48.0000			1.95633
$603$			3.46410i			0.141069i
$604$			3.46410i			0.140952i
$605$			3.46410i			0.140836i
$606$			20.7846i			0.844317i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	18.0000			0.729996
$609$		−	41.5692i		−	1.68447i
$610$	−60.0000			−2.42933
$611$	36.0000	+	10.3923i	1.45640	+	0.420428i
$612$	−1.00000			−0.0404226
$613$			34.6410i			1.39914i	0.714565	+	0.699569i	$0.246625\pi$
$613$			34.6410i			1.39914i	−0.714565	+	0.699569i	$0.753375\pi$
$614$	18.0000			0.726421
$615$	24.0000			0.967773
$616$			20.7846i			0.837436i
$617$		−	31.1769i		−	1.25514i	−0.778562	−	0.627568i	$-0.784051\pi$
$617$		−	31.1769i		−	1.25514i	0.778562	−	0.627568i	$-0.215949\pi$
$618$			55.4256i			2.22955i
$619$			31.1769i			1.25311i	0.779379	+	0.626553i	$0.215535\pi$
$619$			31.1769i			1.25311i	−0.779379	+	0.626553i	$0.784465\pi$
$620$	−12.0000			−0.481932
$621$	−24.0000			−0.963087
$622$			10.3923i			0.416693i
$623$	48.0000			1.92308
$624$	10.0000	−	34.6410i	0.400320	−	1.38675i
$625$	−11.0000			−0.440000
$626$		−	17.3205i		−	0.692267i
$627$	24.0000			0.958468
$628$	−2.00000			−0.0798087
$629$		−	3.46410i		−	0.138123i
$630$		−	20.7846i		−	0.828079i
$631$			3.46410i			0.137904i	0.997620	+	0.0689519i	$0.0219655\pi$
$631$			3.46410i			0.137904i	−0.997620	+	0.0689519i	$0.978035\pi$
$632$			3.46410i			0.137795i
$633$	44.0000			1.74884
$634$	−18.0000			−0.714871
$635$			69.2820i			2.74937i
$636$	12.0000			0.475831
$637$	5.00000	−	17.3205i	0.198107	−	0.686264i
$638$	−36.0000			−1.42525
$639$		−	10.3923i		−	0.411113i
$640$	42.0000			1.66020
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$			20.7846i			0.820303i
$643$			3.46410i			0.136611i	0.997664	+	0.0683054i	$0.0217592\pi$
$643$			3.46410i			0.136611i	−0.997664	+	0.0683054i	$0.978241\pi$
$644$		−	20.7846i		−	0.819028i
$645$		−	55.4256i		−	2.18238i
$646$	−6.00000			−0.236067
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$			19.0526i			0.748455i
$649$	−36.0000			−1.41312
$650$	−42.0000	−	12.1244i	−1.64738	−	0.475556i
$651$	−24.0000			−0.940634
$652$			10.3923i			0.406994i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	−36.0000			−1.40771
$655$		−	62.3538i		−	2.43637i
$656$		−	17.3205i		−	0.676252i
$657$			10.3923i			0.405442i
$658$		−	62.3538i		−	2.43081i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$	−24.0000			−0.934199
$661$		−	13.8564i		−	0.538952i	−0.963007	−	0.269476i	$-0.913150\pi$
$661$		−	13.8564i		−	0.538952i	0.963007	−	0.269476i	$-0.0868504\pi$
$662$	30.0000			1.16598
$663$	−2.00000	+	6.92820i	−0.0776736	+	0.269069i
$664$	6.00000			0.232845
$665$		−	41.5692i		−	1.61199i
$666$	−6.00000			−0.232495
$667$	−36.0000			−1.39393
$668$			10.3923i			0.402090i
$669$			20.7846i			0.803579i
$670$		−	20.7846i		−	0.802980i
$671$			34.6410i			1.33730i
$672$	−36.0000			−1.38873
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$			24.2487i			0.934025i
$675$	28.0000			1.07772
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$			20.7846i			0.798228i
$679$	12.0000			0.460518
$680$	−6.00000			−0.230089
$681$		−	20.7846i		−	0.796468i
$682$			20.7846i			0.795884i
$683$			3.46410i			0.132550i	0.997801	+	0.0662751i	$0.0211115\pi$
$683$			3.46410i			0.132550i	−0.997801	+	0.0662751i	$0.978889\pi$
$684$			3.46410i			0.132453i
$685$	48.0000			1.83399
$686$	12.0000			0.458162
$687$		0			0
$688$	−40.0000			−1.52499
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$	−72.0000			−2.74099
$691$			3.46410i			0.131781i	0.997827	+	0.0658903i	$0.0209887\pi$
$691$			3.46410i			0.131781i	−0.997827	+	0.0658903i	$0.979011\pi$
$692$	6.00000			0.228086
$693$	−12.0000			−0.455842
$694$		−	10.3923i		−	0.394486i
$695$		−	6.92820i		−	0.262802i
$696$			20.7846i			0.787839i
$697$			3.46410i			0.131212i
$698$		0			0
$699$	36.0000			1.36165
$700$			24.2487i			0.916515i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−24.0000	−	6.92820i	−0.905822	−	0.261488i
$703$	−12.0000			−0.452589
$704$		−	3.46410i		−	0.130558i
$705$	−72.0000			−2.71168
$706$		0			0
$707$		−	20.7846i		−	0.781686i
$708$		−	20.7846i		−	0.781133i
$709$		−	3.46410i		−	0.130097i	−0.997882	−	0.0650485i	$-0.979280\pi$
$709$		−	3.46410i		−	0.130097i	0.997882	−	0.0650485i	$-0.0207202\pi$
$710$			62.3538i			2.34010i
$711$	−2.00000			−0.0750059
$712$	−24.0000			−0.899438
$713$			20.7846i			0.778390i
$714$	12.0000			0.449089
$715$	−12.0000	+	41.5692i	−0.448775	+	1.55460i
$716$	−24.0000			−0.896922
$717$		−	6.92820i		−	0.258738i
$718$	−42.0000			−1.56743
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$			17.3205i			0.645497i
$721$		−	55.4256i		−	2.06416i
$722$		−	12.1244i		−	0.451222i
$723$			20.7846i			0.772988i
$724$	−2.00000			−0.0743294
$725$	42.0000			1.55984
$726$			3.46410i			0.128565i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−6.00000	+	20.7846i	−0.222375	+	0.770329i
$729$	13.0000			0.481481
$730$		−	62.3538i		−	2.30782i
$731$	8.00000			0.295891
$732$	−20.0000			−0.739221
$733$		−	13.8564i		−	0.511798i	−0.966704	−	0.255899i	$-0.917629\pi$
$733$		−	13.8564i		−	0.511798i	0.966704	−	0.255899i	$-0.0823715\pi$
$734$		−	24.2487i		−	0.895036i
$735$			34.6410i			1.27775i
$736$			31.1769i			1.14920i
$737$	−12.0000			−0.442026
$738$	6.00000			0.220863
$739$		−	24.2487i		−	0.892003i	−0.895032	−	0.446002i	$-0.852848\pi$
$739$		−	24.2487i		−	0.892003i	0.895032	−	0.446002i	$-0.147152\pi$
$740$	12.0000			0.441129
$741$	24.0000	+	6.92820i	0.881662	+	0.254514i
$742$	−36.0000			−1.32160
$743$		−	24.2487i		−	0.889599i	−0.895630	−	0.444799i	$-0.853275\pi$
$743$		−	24.2487i		−	0.889599i	0.895630	−	0.444799i	$-0.146725\pi$
$744$	12.0000			0.439941
$745$	24.0000			0.879292
$746$		−	17.3205i		−	0.634149i
$747$			3.46410i			0.126745i
$748$		−	3.46410i		−	0.126660i
$749$		−	20.7846i		−	0.759453i
$750$	24.0000			0.876356
$751$	50.0000			1.82453			0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000			1.82453			0.912263	+	0.409605i	$0.134333\pi$
$752$			51.9615i			1.89484i
$753$	24.0000			0.874609
$754$	−36.0000	−	10.3923i	−1.31104	−	0.378465i
$755$	−12.0000			−0.436725
$756$			13.8564i			0.503953i
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	30.0000			1.08965
$759$			41.5692i			1.50887i
$760$			20.7846i			0.753937i
$761$		−	27.7128i		−	1.00459i	−0.864697	−	0.502294i	$-0.832489\pi$
$761$		−	27.7128i		−	1.00459i	0.864697	−	0.502294i	$-0.167511\pi$
$762$			69.2820i			2.50982i
$763$	36.0000			1.30329
$764$		0			0
$765$		−	3.46410i		−	0.125245i
$766$	30.0000			1.08394
$767$	−36.0000	−	10.3923i	−1.29988	−	0.375244i
$768$	38.0000			1.37121
$769$		−	41.5692i		−	1.49902i	−0.661991	−	0.749512i	$-0.730288\pi$
$769$		−	41.5692i		−	1.49902i	0.661991	−	0.749512i	$-0.269712\pi$
$770$	72.0000			2.59470
$771$	−60.0000			−2.16085
$772$		−	3.46410i		−	0.124676i
$773$			13.8564i			0.498380i	0.968455	+	0.249190i	$0.0801644\pi$
$773$			13.8564i			0.498380i	−0.968455	+	0.249190i	$0.919836\pi$
$774$		−	13.8564i		−	0.498058i
$775$		−	24.2487i		−	0.871039i
$776$	−6.00000			−0.215387
$777$	24.0000			0.860995
$778$		−	51.9615i		−	1.86291i
$779$	12.0000			0.429945
$780$	−24.0000	−	6.92820i	−0.859338	−	0.248069i
$781$	36.0000			1.28818
$782$		−	10.3923i		−	0.371628i
$783$	24.0000			0.857690
$784$	25.0000			0.892857
$785$		−	6.92820i		−	0.247278i
$786$		−	62.3538i		−	2.22409i
$787$			3.46410i			0.123482i	0.998092	+	0.0617409i	$0.0196653\pi$
$787$			3.46410i			0.123482i	−0.998092	+	0.0617409i	$0.980335\pi$
$788$			24.2487i			0.863825i
$789$	−24.0000			−0.854423
$790$	12.0000			0.426941
$791$		−	20.7846i		−	0.739016i
$792$	6.00000			0.213201
$793$	−10.0000	+	34.6410i	−0.355110	+	1.23014i
$794$	54.0000			1.91639
$795$			41.5692i			1.47431i
$796$	14.0000			0.496217
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		−	41.5692i		−	1.47153i
$799$		−	10.3923i		−	0.367653i
$800$		−	36.3731i		−	1.28598i
$801$		−	13.8564i		−	0.489592i
$802$	−18.0000			−0.635602
$803$	−36.0000			−1.27041
$804$		−	6.92820i		−	0.244339i
$805$	72.0000			2.53767
$806$	−6.00000	+	20.7846i	−0.211341	+	0.732107i
$807$	36.0000			1.26726
$808$			10.3923i			0.365600i
$809$	−54.0000			−1.89854			−0.949269	−	0.314464i	$-0.898175\pi$
$809$	−54.0000			−1.89854			−0.949269	+	0.314464i	$0.898175\pi$
$810$	66.0000			2.31900
$811$			17.3205i			0.608205i	0.952639	+	0.304103i	$0.0983566\pi$
$811$			17.3205i			0.608205i	−0.952639	+	0.304103i	$0.901643\pi$
$812$			20.7846i			0.729397i
$813$		−	6.92820i		−	0.242983i
$814$		−	20.7846i		−	0.728500i
$815$	−36.0000			−1.26102
$816$	−10.0000			−0.350070
$817$		−	27.7128i		−	0.969549i
$818$	48.0000			1.67828
$819$	−12.0000	−	3.46410i	−0.419314	−	0.121046i
$820$	−12.0000			−0.419058
$821$			24.2487i			0.846286i	0.906063	+	0.423143i	$0.139073\pi$
$821$			24.2487i			0.846286i	−0.906063	+	0.423143i	$0.860927\pi$
$822$	48.0000			1.67419
$823$	14.0000			0.488009			0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000			0.488009			0.244005	+	0.969774i	$0.421539\pi$
$824$			27.7128i			0.965422i
$825$		−	48.4974i		−	1.68846i
$826$			62.3538i			2.16957i
$827$			31.1769i			1.08413i	0.840337	+	0.542064i	$0.182357\pi$
$827$			31.1769i			1.08413i	−0.840337	+	0.542064i	$0.817643\pi$
$828$	−6.00000			−0.208514
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$		−	20.7846i		−	0.721444i
$831$	52.0000			1.80386
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$	−5.00000			−0.173240
$834$		−	6.92820i		−	0.239904i
$835$	−36.0000			−1.24583
$836$	−12.0000			−0.415029
$837$		−	13.8564i		−	0.478947i
$838$			31.1769i			1.07699i
$839$			45.0333i			1.55472i	0.629054	+	0.777361i	$0.283442\pi$
$839$			45.0333i			1.55472i	−0.629054	+	0.777361i	$0.716558\pi$
$840$		−	41.5692i		−	1.43427i
$841$	7.00000			0.241379
$842$	12.0000			0.413547
$843$			41.5692i			1.43172i
$844$	−22.0000			−0.757271
$845$	−24.0000	+	38.1051i	−0.825625	+	1.31086i
$846$	−18.0000			−0.618853
$847$		−	3.46410i		−	0.119028i
$848$	30.0000			1.03020
$849$	−4.00000			−0.137280
$850$			12.1244i			0.415862i
$851$		−	20.7846i		−	0.712487i
$852$			20.7846i			0.712069i
$853$			38.1051i			1.30469i	0.757920	+	0.652347i	$0.226216\pi$
$853$			38.1051i			1.30469i	−0.757920	+	0.652347i	$0.773784\pi$
$854$	60.0000			2.05316
$855$	−12.0000			−0.410391
$856$			10.3923i			0.355202i
$857$	−30.0000			−1.02478			−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000			−1.02478			−0.512390	+	0.858753i	$0.671240\pi$
$858$	−12.0000	+	41.5692i	−0.409673	+	1.41915i
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$			27.7128i			0.944999i
$861$	−24.0000			−0.817918
$862$	6.00000			0.204361
$863$		−	3.46410i		−	0.117919i	−0.998260	−	0.0589597i	$-0.981222\pi$
$863$		−	3.46410i		−	0.117919i	0.998260	−	0.0589597i	$-0.0187783\pi$
$864$		−	20.7846i		−	0.707107i
$865$			20.7846i			0.706698i
$866$			45.0333i			1.53029i
$867$	2.00000			0.0679236
$868$	12.0000			0.407307
$869$		−	6.92820i		−	0.235023i
$870$	72.0000			2.44103
$871$	−12.0000	−	3.46410i	−0.406604	−	0.117377i
$872$	−18.0000			−0.609557
$873$		−	3.46410i		−	0.117242i
$874$	−36.0000			−1.21772
$875$	−24.0000			−0.811348
$876$		−	20.7846i		−	0.702247i
$877$			31.1769i			1.05277i	0.850246	+	0.526385i	$0.176453\pi$
$877$			31.1769i			1.05277i	−0.850246	+	0.526385i	$0.823547\pi$
$878$		−	45.0333i		−	1.51980i
$879$			41.5692i			1.40209i
$880$	−60.0000			−2.02260
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$			8.66025i			0.291606i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	1.00000	−	3.46410i	0.0336336	−	0.116510i
$885$	72.0000			2.42025
$886$			20.7846i			0.698273i
$887$	42.0000			1.41022			0.705111	−	0.709097i	$-0.250897\pi$
$887$	42.0000			1.41022			0.705111	+	0.709097i	$0.250897\pi$
$888$	−12.0000			−0.402694
$889$		−	69.2820i		−	2.32364i
$890$			83.1384i			2.78681i
$891$		−	38.1051i		−	1.27657i
$892$		−	10.3923i		−	0.347960i
$893$	−36.0000			−1.20469
$894$	24.0000			0.802680
$895$		−	83.1384i		−	2.77901i
$896$	−42.0000			−1.40312
$897$	−12.0000	+	41.5692i	−0.400668	+	1.38796i
$898$	−18.0000			−0.600668
$899$		−	20.7846i		−	0.693206i
$900$	7.00000			0.233333
$901$	−6.00000			−0.199889
$902$			20.7846i			0.692052i
$903$			55.4256i			1.84445i
$904$			10.3923i			0.345643i
$905$		−	6.92820i		−	0.230301i
$906$	−12.0000			−0.398673
$907$	−26.0000			−0.863316			−0.431658	−	0.902037i	$-0.642071\pi$
$907$	−26.0000			−0.863316			−0.431658	+	0.902037i	$0.642071\pi$
$908$			10.3923i			0.344881i
$909$	−6.00000			−0.199007
$910$	72.0000	+	20.7846i	2.38678	+	0.689003i
$911$	−42.0000			−1.39152			−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000			−1.39152			−0.695761	+	0.718273i	$0.744933\pi$
$912$			34.6410i			1.14708i
$913$	−12.0000			−0.397142
$914$	−36.0000			−1.19077
$915$		−	69.2820i		−	2.29039i
$916$		0			0
$917$			62.3538i			2.05910i
$918$			6.92820i			0.228665i
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	−36.0000			−1.18688
$921$			20.7846i			0.684876i
$922$		0			0
$923$	36.0000	+	10.3923i	1.18495	+	0.342067i
$924$	24.0000			0.789542
$925$			24.2487i			0.797293i
$926$	−66.0000			−2.16889
$927$	−16.0000			−0.525509
$928$		−	31.1769i		−	1.02343i
$929$			17.3205i			0.568267i	0.958785	+	0.284134i	$0.0917060\pi$
$929$			17.3205i			0.568267i	−0.958785	+	0.284134i	$0.908294\pi$
$930$		−	41.5692i		−	1.36311i
$931$			17.3205i			0.567657i
$932$	−18.0000			−0.589610
$933$	−12.0000			−0.392862
$934$		−	41.5692i		−	1.36019i
$935$	12.0000			0.392442
$936$	6.00000	+	1.73205i	0.196116	+	0.0566139i
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$			20.7846i			0.678642i
$939$	20.0000			0.652675
$940$	36.0000			1.17419
$941$			17.3205i			0.564632i	0.959321	+	0.282316i	$0.0911027\pi$
$941$			17.3205i			0.564632i	−0.959321	+	0.282316i	$0.908897\pi$
$942$		−	6.92820i		−	0.225733i
$943$			20.7846i			0.676840i
$944$		−	51.9615i		−	1.69120i
$945$	−48.0000			−1.56144
$946$	48.0000			1.56061
$947$			3.46410i			0.112568i	0.998415	+	0.0562841i	$0.0179253\pi$
$947$			3.46410i			0.112568i	−0.998415	+	0.0562841i	$0.982075\pi$
$948$	4.00000			0.129914
$949$	−36.0000	−	10.3923i	−1.16861	−	0.337348i
$950$	42.0000			1.36266
$951$		−	20.7846i		−	0.673987i
$952$	6.00000			0.194461
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$			10.3923i			0.336463i
$955$		0			0
$956$			3.46410i			0.112037i
$957$		−	41.5692i		−	1.34374i
$958$	30.0000			0.969256
$959$	−48.0000			−1.55000
$960$			6.92820i			0.223607i
$961$	19.0000			0.612903
$962$	6.00000	−	20.7846i	0.193448	−	0.670123i
$963$	−6.00000			−0.193347
$964$		−	10.3923i		−	0.334714i
$965$	12.0000			0.386294
$966$	72.0000			2.31656
$967$			31.1769i			1.00258i	0.865279	+	0.501291i	$0.167141\pi$
$967$			31.1769i			1.00258i	−0.865279	+	0.501291i	$0.832859\pi$
$968$			1.73205i			0.0556702i
$969$		−	6.92820i		−	0.222566i
$970$			20.7846i			0.667354i
$971$	48.0000			1.54039			0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000			1.54039			0.770197	+	0.637806i	$0.220158\pi$
$972$	10.0000			0.320750
$973$			6.92820i			0.222108i
$974$	−42.0000			−1.34577
$975$	14.0000	−	48.4974i	0.448359	−	1.55316i
$976$	−50.0000			−1.60046
$977$			48.4974i			1.55157i	0.630997	+	0.775785i	$0.282646\pi$
$977$			48.4974i			1.55157i	−0.630997	+	0.775785i	$0.717354\pi$
$978$	−36.0000			−1.15115
$979$	48.0000			1.53409
$980$		−	17.3205i		−	0.553283i
$981$		−	10.3923i		−	0.331801i
$982$		−	41.5692i		−	1.32653i
$983$		−	24.2487i		−	0.773414i	−0.922203	−	0.386707i	$-0.873613\pi$
$983$		−	24.2487i		−	0.773414i	0.922203	−	0.386707i	$-0.126387\pi$
$984$	12.0000			0.382546
$985$	−84.0000			−2.67646
$986$			10.3923i			0.330958i
$987$	72.0000			2.29179
$988$	−12.0000	−	3.46410i	−0.381771	−	0.110208i
$989$	48.0000			1.52631
$990$		−	20.7846i		−	0.660578i
$991$	50.0000			1.58830			0.794151	−	0.607720i	$-0.207916\pi$
$991$	50.0000			1.58830			0.794151	+	0.607720i	$0.207916\pi$
$992$	−18.0000			−0.571501
$993$			34.6410i			1.09930i
$994$		−	62.3538i		−	1.97774i
$995$			48.4974i			1.53747i
$996$		−	6.92820i		−	0.219529i
$997$	26.0000			0.823428			0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000			0.823428			0.411714	+	0.911313i	$0.364930\pi$
$998$	−42.0000			−1.32949
$999$			13.8564i			0.438397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.c.a.103.1	✓	2
3.2	odd	2		1989.2.b.a.766.2		2
13.5	odd	4		2873.2.a.g.1.1		2
13.8	odd	4		2873.2.a.g.1.2		2
13.12	even	2	inner	221.2.c.a.103.2	yes	2
39.38	odd	2		1989.2.b.a.766.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.c.a.103.1	✓	2	1.1	even	1	trivial
221.2.c.a.103.2	yes	2	13.12	even	2	inner
1989.2.b.a.766.1		2	39.38	odd	2
1989.2.b.a.766.2		2	3.2	odd	2
2873.2.a.g.1.1		2	13.5	odd	4
2873.2.a.g.1.2		2	13.8	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} +2.00000 q^{3} -1.00000 q^{4} -3.46410i q^{5} -3.46410i q^{6} +3.46410i q^{7} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.73205i q^{2} +2.00000 q^{3} -1.00000 q^{4} -3.46410i q^{5} -3.46410i q^{6} +3.46410i q^{7} -1.73205i q^{8} +1.00000 q^{9} -6.00000 q^{10} +3.46410i q^{11} -2.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +6.00000 q^{14} -6.92820i q^{15} -5.00000 q^{16} +1.00000 q^{17} -1.73205i q^{18} -3.46410i q^{19} +3.46410i q^{20} +6.92820i q^{21} +6.00000 q^{22} +6.00000 q^{23} -3.46410i q^{24} -7.00000 q^{25} +(6.00000 + 1.73205i) q^{26} -4.00000 q^{27} -3.46410i q^{28} -6.00000 q^{29} -12.0000 q^{30} +3.46410i q^{31} +5.19615i q^{32} +6.92820i q^{33} -1.73205i q^{34} +12.0000 q^{35} -1.00000 q^{36} -3.46410i q^{37} -6.00000 q^{38} +(-2.00000 + 6.92820i) q^{39} -6.00000 q^{40} +3.46410i q^{41} +12.0000 q^{42} +8.00000 q^{43} -3.46410i q^{44} -3.46410i q^{45} -10.3923i q^{46} -10.3923i q^{47} -10.0000 q^{48} -5.00000 q^{49} +12.1244i q^{50} +2.00000 q^{51} +(1.00000 - 3.46410i) q^{52} -6.00000 q^{53} +6.92820i q^{54} +12.0000 q^{55} +6.00000 q^{56} -6.92820i q^{57} +10.3923i q^{58} +10.3923i q^{59} +6.92820i q^{60} +10.0000 q^{61} +6.00000 q^{62} +3.46410i q^{63} -1.00000 q^{64} +(12.0000 + 3.46410i) q^{65} +12.0000 q^{66} +3.46410i q^{67} -1.00000 q^{68} +12.0000 q^{69} -20.7846i q^{70} -10.3923i q^{71} -1.73205i q^{72} +10.3923i q^{73} -6.00000 q^{74} -14.0000 q^{75} +3.46410i q^{76} -12.0000 q^{77} +(12.0000 + 3.46410i) q^{78} -2.00000 q^{79} +17.3205i q^{80} -11.0000 q^{81} +6.00000 q^{82} +3.46410i q^{83} -6.92820i q^{84} -3.46410i q^{85} -13.8564i q^{86} -12.0000 q^{87} +6.00000 q^{88} -13.8564i q^{89} -6.00000 q^{90} +(-12.0000 - 3.46410i) q^{91} -6.00000 q^{92} +6.92820i q^{93} -18.0000 q^{94} -12.0000 q^{95} +10.3923i q^{96} -3.46410i q^{97} +8.66025i q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9	\( 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9} - 12 q^{10} - 4 q^{12} - 2 q^{13} + 12 q^{14} - 10 q^{16} + 2 q^{17} + 12 q^{22} + 12 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{27} - 12 q^{29} - 24 q^{30} + 24 q^{35} - 2 q^{36} - 12 q^{38} - 4 q^{39} - 12 q^{40} + 24 q^{42} + 16 q^{43} - 20 q^{48} - 10 q^{49} + 4 q^{51} + 2 q^{52} - 12 q^{53} + 24 q^{55} + 12 q^{56} + 20 q^{61} + 12 q^{62} - 2 q^{64} + 24 q^{65} + 24 q^{66} - 2 q^{68} + 24 q^{69} - 12 q^{74} - 28 q^{75} - 24 q^{77} + 24 q^{78} - 4 q^{79} - 22 q^{81} + 12 q^{82} - 24 q^{87} + 12 q^{88} - 12 q^{90} - 24 q^{91} - 12 q^{92} - 36 q^{94} - 24 q^{95}+O(q^{100}) \) 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9 - 12 * q^10 - 4 * q^12 - 2 * q^13 + 12 * q^14 - 10 * q^16 + 2 * q^17 + 12 * q^22 + 12 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^27 - 12 * q^29 - 24 * q^30 + 24 * q^35 - 2 * q^36 - 12 * q^38 - 4 * q^39 - 12 * q^40 + 24 * q^42 + 16 * q^43 - 20 * q^48 - 10 * q^49 + 4 * q^51 + 2 * q^52 - 12 * q^53 + 24 * q^55 + 12 * q^56 + 20 * q^61 + 12 * q^62 - 2 * q^64 + 24 * q^65 + 24 * q^66 - 2 * q^68 + 24 * q^69 - 12 * q^74 - 28 * q^75 - 24 * q^77 + 24 * q^78 - 4 * q^79 - 22 * q^81 + 12 * q^82 - 24 * q^87 + 12 * q^88 - 12 * q^90 - 24 * q^91 - 12 * q^92 - 36 * q^94 - 24 * q^95

Introduction

L-functions

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