LMFDB - Embedded newform 930.2.d.c.559.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(559,930)] 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("930.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-2,2,2,0,0,-2,4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
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			559.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.c.559.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000 q^{6} +5.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} -1.00000 q^{11} -1.00000i q^{12} +5.00000 q^{14} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -4.00000i q^{17} +1.00000i q^{18} -3.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -5.00000 q^{21} +1.00000i q^{22} +1.00000i q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -1.00000i q^{27} -5.00000i q^{28} -6.00000 q^{29} +(1.00000 + 2.00000i) q^{30} -1.00000 q^{31} -1.00000i q^{32} -1.00000i q^{33} -4.00000 q^{34} +(-10.0000 + 5.00000i) q^{35} +1.00000 q^{36} -4.00000i q^{37} +3.00000i q^{38} +(-2.00000 + 1.00000i) q^{40} +2.00000 q^{41} +5.00000i q^{42} +1.00000i q^{43} +1.00000 q^{44} +(-1.00000 - 2.00000i) q^{45} +1.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} -18.0000 q^{49} +(4.00000 + 3.00000i) q^{50} +4.00000 q^{51} -3.00000i q^{53} -1.00000 q^{54} +(-1.00000 - 2.00000i) q^{55} -5.00000 q^{56} -3.00000i q^{57} +6.00000i q^{58} +14.0000 q^{59} +(2.00000 - 1.00000i) q^{60} +14.0000 q^{61} +1.00000i q^{62} -5.00000i q^{63} -1.00000 q^{64} -1.00000 q^{66} +10.0000i q^{67} +4.00000i q^{68} -1.00000 q^{69} +(5.00000 + 10.0000i) q^{70} +9.00000 q^{71} -1.00000i q^{72} +7.00000i q^{73} -4.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} +3.00000 q^{76} -5.00000i q^{77} -15.0000 q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} -2.00000i q^{82} +10.0000i q^{83} +5.00000 q^{84} +(8.00000 - 4.00000i) q^{85} +1.00000 q^{86} -6.00000i q^{87} -1.00000i q^{88} +1.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} -1.00000i q^{92} -1.00000i q^{93} +4.00000 q^{94} +(-3.00000 - 6.00000i) q^{95} +1.00000 q^{96} +10.0000i q^{97} +18.0000i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 10 q^{14} - 4 q^{15} + 2 q^{16} - 6 q^{19} - 2 q^{20} - 10 q^{21} - 2 q^{24} - 6 q^{25} - 12 q^{29} + 2 q^{30} - 2 q^{31} - 8 q^{34} - 20 q^{35}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9 + 4 * q^10 - 2 * q^11 + 10 * q^14 - 4 * q^15 + 2 * q^16 - 6 * q^19 - 2 * q^20 - 10 * q^21 - 2 * q^24 - 6 * q^25 - 12 * q^29 + 2 * q^30 - 2 * q^31 - 8 * q^34 - 20 * q^35 + 2 * q^36 - 4 * q^40 + 4 * q^41 + 2 * q^44 - 2 * q^45 + 2 * q^46 - 36 * q^49 + 8 * q^50 + 8 * q^51 - 2 * q^54 - 2 * q^55 - 10 * q^56 + 28 * q^59 + 4 * q^60 + 28 * q^61 - 2 * q^64 - 2 * q^66 - 2 * q^69 + 10 * q^70 + 18 * q^71 - 8 * q^74 - 8 * q^75 + 6 * q^76 - 30 * q^79 + 2 * q^80 + 2 * q^81 + 10 * q^84 + 16 * q^85 + 2 * q^86 + 2 * q^89 - 4 * q^90 + 8 * q^94 - 6 * q^95 + 2 * q^96 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	1.00000			0.408248
$7$			5.00000i			1.88982i	0.327327	+	0.944911i	$0.393852\pi$
$7$			5.00000i			1.88982i	−0.327327	+	0.944911i	$0.606148\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		−	1.00000i		−	0.288675i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	5.00000			1.33631
$15$	−2.00000	+	1.00000i	−0.516398	+	0.258199i
$16$	1.00000			0.250000
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$			1.00000i			0.235702i
$19$	−3.00000			−0.688247			−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000			−0.688247			−0.344124	+	0.938924i	$0.611824\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$	−5.00000			−1.09109
$22$			1.00000i			0.213201i
$23$			1.00000i			0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$			1.00000i			0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$	−1.00000			−0.204124
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		−	5.00000i		−	0.944911i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	1.00000	+	2.00000i	0.182574	+	0.365148i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$		−	1.00000i		−	0.176777i
$33$		−	1.00000i		−	0.174078i
$34$	−4.00000			−0.685994
$35$	−10.0000	+	5.00000i	−1.69031	+	0.845154i
$36$	1.00000			0.166667
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$			3.00000i			0.486664i
$39$		0			0
$40$	−2.00000	+	1.00000i	−0.316228	+	0.158114i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$			5.00000i			0.771517i
$43$			1.00000i			0.152499i	0.997089	+	0.0762493i	$0.0242945\pi$
$43$			1.00000i			0.152499i	−0.997089	+	0.0762493i	$0.975706\pi$
$44$	1.00000			0.150756
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$	1.00000			0.147442
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$			1.00000i			0.144338i
$49$	−18.0000			−2.57143
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	4.00000			0.560112
$52$		0			0
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	−1.00000			−0.136083
$55$	−1.00000	−	2.00000i	−0.134840	−	0.269680i
$56$	−5.00000			−0.668153
$57$		−	3.00000i		−	0.397360i
$58$			6.00000i			0.787839i
$59$	14.0000			1.82264			0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000			1.82264			0.911322	+	0.411693i	$0.135063\pi$
$60$	2.00000	−	1.00000i	0.258199	−	0.129099i
$61$	14.0000			1.79252			0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000			1.79252			0.896258	+	0.443533i	$0.146275\pi$
$62$			1.00000i			0.127000i
$63$		−	5.00000i		−	0.629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.00000			−0.123091
$67$			10.0000i			1.22169i	0.791748	+	0.610847i	$0.209171\pi$
$67$			10.0000i			1.22169i	−0.791748	+	0.610847i	$0.790829\pi$
$68$			4.00000i			0.485071i
$69$	−1.00000			−0.120386
$70$	5.00000	+	10.0000i	0.597614	+	1.19523i
$71$	9.00000			1.06810			0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000			1.06810			0.534052	+	0.845452i	$0.320669\pi$
$72$		−	1.00000i		−	0.117851i
$73$			7.00000i			0.819288i	0.912245	+	0.409644i	$0.134347\pi$
$73$			7.00000i			0.819288i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	−4.00000			−0.464991
$75$	−4.00000	−	3.00000i	−0.461880	−	0.346410i
$76$	3.00000			0.344124
$77$		−	5.00000i		−	0.569803i
$78$		0			0
$79$	−15.0000			−1.68763			−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000			−1.68763			−0.843816	+	0.536633i	$0.819696\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	1.00000			0.111111
$82$		−	2.00000i		−	0.220863i
$83$			10.0000i			1.09764i	0.835940	+	0.548821i	$0.184923\pi$
$83$			10.0000i			1.09764i	−0.835940	+	0.548821i	$0.815077\pi$
$84$	5.00000			0.545545
$85$	8.00000	−	4.00000i	0.867722	−	0.433861i
$86$	1.00000			0.107833
$87$		−	6.00000i		−	0.643268i
$88$		−	1.00000i		−	0.106600i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$	−2.00000	+	1.00000i	−0.210819	+	0.105409i
$91$		0			0
$92$		−	1.00000i		−	0.104257i
$93$		−	1.00000i		−	0.103695i
$94$	4.00000			0.412568
$95$	−3.00000	−	6.00000i	−0.307794	−	0.615587i
$96$	1.00000			0.102062
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$			18.0000i			1.81827i
$99$	1.00000			0.100504
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	7.00000			0.696526			0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000			0.696526			0.348263	+	0.937397i	$0.386772\pi$
$102$		−	4.00000i		−	0.396059i
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$		0			0
$105$	−5.00000	−	10.0000i	−0.487950	−	0.975900i
$106$	−3.00000			−0.291386
$107$			9.00000i			0.870063i	0.900415	+	0.435031i	$0.143263\pi$
$107$			9.00000i			0.870063i	−0.900415	+	0.435031i	$0.856737\pi$
$108$			1.00000i			0.0962250i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−2.00000	+	1.00000i	−0.190693	+	0.0953463i
$111$	4.00000			0.379663
$112$			5.00000i			0.472456i
$113$			9.00000i			0.846649i	0.905978	+	0.423324i	$0.139137\pi$
$113$			9.00000i			0.846649i	−0.905978	+	0.423324i	$0.860863\pi$
$114$	−3.00000			−0.280976
$115$	−2.00000	+	1.00000i	−0.186501	+	0.0932505i
$116$	6.00000			0.557086
$117$		0			0
$118$		−	14.0000i		−	1.28880i
$119$	20.0000			1.83340
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	−10.0000			−0.909091
$122$		−	14.0000i		−	1.26750i
$123$			2.00000i			0.180334i
$124$	1.00000			0.0898027
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−5.00000			−0.445435
$127$		−	16.0000i		−	1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$		−	16.0000i		−	1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$			1.00000i			0.0883883i
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$			1.00000i			0.0870388i
$133$		−	15.0000i		−	1.30066i
$134$	10.0000			0.863868
$135$	2.00000	−	1.00000i	0.172133	−	0.0860663i
$136$	4.00000			0.342997
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$			1.00000i			0.0851257i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	10.0000	−	5.00000i	0.845154	−	0.422577i
$141$	−4.00000			−0.336861
$142$		−	9.00000i		−	0.755263i
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−6.00000	−	12.0000i	−0.498273	−	0.996546i
$146$	7.00000			0.579324
$147$		−	18.0000i		−	1.48461i
$148$			4.00000i			0.328798i
$149$	−1.00000			−0.0819232			−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000			−0.0819232			−0.0409616	+	0.999161i	$0.513042\pi$
$150$	−3.00000	+	4.00000i	−0.244949	+	0.326599i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	3.00000i		−	0.243332i
$153$			4.00000i			0.323381i
$154$	−5.00000			−0.402911
$155$	−1.00000	−	2.00000i	−0.0803219	−	0.160644i
$156$		0			0
$157$			1.00000i			0.0798087i	0.999204	+	0.0399043i	$0.0127053\pi$
$157$			1.00000i			0.0798087i	−0.999204	+	0.0399043i	$0.987295\pi$
$158$			15.0000i			1.19334i
$159$	3.00000			0.237915
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$	−5.00000			−0.394055
$162$		−	1.00000i		−	0.0785674i
$163$			8.00000i			0.626608i	0.949653	+	0.313304i	$0.101436\pi$
$163$			8.00000i			0.626608i	−0.949653	+	0.313304i	$0.898564\pi$
$164$	−2.00000			−0.156174
$165$	2.00000	−	1.00000i	0.155700	−	0.0778499i
$166$	10.0000			0.776151
$167$		−	9.00000i		−	0.696441i	−0.937413	−	0.348220i	$-0.886786\pi$
$167$		−	9.00000i		−	0.696441i	0.937413	−	0.348220i	$-0.113214\pi$
$168$		−	5.00000i		−	0.385758i
$169$	13.0000			1.00000
$170$	−4.00000	−	8.00000i	−0.306786	−	0.613572i
$171$	3.00000			0.229416
$172$		−	1.00000i		−	0.0762493i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	−6.00000			−0.454859
$175$	−20.0000	−	15.0000i	−1.51186	−	1.13389i
$176$	−1.00000			−0.0753778
$177$			14.0000i			1.05230i
$178$		−	1.00000i		−	0.0749532i
$179$	8.00000			0.597948			0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000			0.597948			0.298974	+	0.954261i	$0.403356\pi$
$180$	1.00000	+	2.00000i	0.0745356	+	0.149071i
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$		0			0
$183$			14.0000i			1.03491i
$184$	−1.00000			−0.0737210
$185$	8.00000	−	4.00000i	0.588172	−	0.294086i
$186$	−1.00000			−0.0733236
$187$			4.00000i			0.292509i
$188$		−	4.00000i		−	0.291730i
$189$	5.00000			0.363696
$190$	−6.00000	+	3.00000i	−0.435286	+	0.217643i
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			10.0000i			0.719816i	0.932988	+	0.359908i	$0.117192\pi$
$193$			10.0000i			0.719816i	−0.932988	+	0.359908i	$0.882808\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	18.0000			1.28571
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		−	1.00000i		−	0.0710669i
$199$	9.00000			0.637993			0.318997	−	0.947756i	$-0.396654\pi$
$199$	9.00000			0.637993			0.318997	+	0.947756i	$0.396654\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$	−10.0000			−0.705346
$202$		−	7.00000i		−	0.492518i
$203$		−	30.0000i		−	2.10559i
$204$	−4.00000			−0.280056
$205$	2.00000	+	4.00000i	0.139686	+	0.279372i
$206$	8.00000			0.557386
$207$		−	1.00000i		−	0.0695048i
$208$		0			0
$209$	3.00000			0.207514
$210$	−10.0000	+	5.00000i	−0.690066	+	0.345033i
$211$	−21.0000			−1.44570			−0.722850	−	0.691005i	$-0.757168\pi$
$211$	−21.0000			−1.44570			−0.722850	+	0.691005i	$0.757168\pi$
$212$			3.00000i			0.206041i
$213$			9.00000i			0.616670i
$214$	9.00000			0.615227
$215$	−2.00000	+	1.00000i	−0.136399	+	0.0681994i
$216$	1.00000			0.0680414
$217$		−	5.00000i		−	0.339422i
$218$			10.0000i			0.677285i
$219$	−7.00000			−0.473016
$220$	1.00000	+	2.00000i	0.0674200	+	0.134840i
$221$		0			0
$222$		−	4.00000i		−	0.268462i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$	5.00000			0.334077
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	9.00000			0.598671
$227$			29.0000i			1.92480i	0.271640	+	0.962399i	$0.412434\pi$
$227$			29.0000i			1.92480i	−0.271640	+	0.962399i	$0.587566\pi$
$228$			3.00000i			0.198680i
$229$	−23.0000			−1.51988			−0.759941	−	0.649992i	$-0.774772\pi$
$229$	−23.0000			−1.51988			−0.759941	+	0.649992i	$0.774772\pi$
$230$	1.00000	+	2.00000i	0.0659380	+	0.131876i
$231$	5.00000			0.328976
$232$		−	6.00000i		−	0.393919i
$233$		−	13.0000i		−	0.851658i	−0.904804	−	0.425829i	$-0.859982\pi$
$233$		−	13.0000i		−	0.851658i	0.904804	−	0.425829i	$-0.140018\pi$
$234$		0			0
$235$	−8.00000	+	4.00000i	−0.521862	+	0.260931i
$236$	−14.0000			−0.911322
$237$		−	15.0000i		−	0.974355i
$238$		−	20.0000i		−	1.29641i
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$	−2.00000	+	1.00000i	−0.129099	+	0.0645497i
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$			10.0000i			0.642824i
$243$			1.00000i			0.0641500i
$244$	−14.0000			−0.896258
$245$	−18.0000	−	36.0000i	−1.14998	−	2.29996i
$246$	2.00000			0.127515
$247$		0			0
$248$		−	1.00000i		−	0.0635001i
$249$	−10.0000			−0.633724
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$			5.00000i			0.314970i
$253$		−	1.00000i		−	0.0628695i
$254$	−16.0000			−1.00393
$255$	4.00000	+	8.00000i	0.250490	+	0.500979i
$256$	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	$0.970173\pi$
$258$			1.00000i			0.0622573i
$259$	20.0000			1.24274
$260$		0			0
$261$	6.00000			0.371391
$262$		−	18.0000i		−	1.11204i
$263$		−	8.00000i		−	0.493301i	−0.969104	−	0.246651i	$-0.920670\pi$
$263$		−	8.00000i		−	0.493301i	0.969104	−	0.246651i	$-0.0793300\pi$
$264$	1.00000			0.0615457
$265$	6.00000	−	3.00000i	0.368577	−	0.184289i
$266$	−15.0000			−0.919709
$267$			1.00000i			0.0611990i
$268$		−	10.0000i		−	0.610847i
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$	13.0000			0.789694			0.394847	−	0.918747i	$-0.370798\pi$
$271$	13.0000			0.789694			0.394847	+	0.918747i	$0.370798\pi$
$272$		−	4.00000i		−	0.242536i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	3.00000	−	4.00000i	0.180907	−	0.241209i
$276$	1.00000			0.0601929
$277$			26.0000i			1.56219i	0.624413	+	0.781094i	$0.285338\pi$
$277$			26.0000i			1.56219i	−0.624413	+	0.781094i	$0.714662\pi$
$278$			4.00000i			0.239904i
$279$	1.00000			0.0598684
$280$	−5.00000	−	10.0000i	−0.298807	−	0.597614i
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$			4.00000i			0.238197i
$283$		−	22.0000i		−	1.30776i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$		−	22.0000i		−	1.30776i	0.756596	−	0.653882i	$-0.226861\pi$
$284$	−9.00000			−0.534052
$285$	6.00000	−	3.00000i	0.355409	−	0.177705i
$286$		0			0
$287$			10.0000i			0.590281i
$288$			1.00000i			0.0589256i
$289$	1.00000			0.0588235
$290$	−12.0000	+	6.00000i	−0.704664	+	0.352332i
$291$	−10.0000			−0.586210
$292$		−	7.00000i		−	0.409644i
$293$		−	30.0000i		−	1.75262i	−0.481749	−	0.876309i	$-0.659998\pi$
$293$		−	30.0000i		−	1.75262i	0.481749	−	0.876309i	$-0.340002\pi$
$294$	−18.0000			−1.04978
$295$	14.0000	+	28.0000i	0.815112	+	1.63022i
$296$	4.00000			0.232495
$297$			1.00000i			0.0580259i
$298$			1.00000i			0.0579284i
$299$		0			0
$300$	4.00000	+	3.00000i	0.230940	+	0.173205i
$301$	−5.00000			−0.288195
$302$			8.00000i			0.460348i
$303$			7.00000i			0.402139i
$304$	−3.00000			−0.172062
$305$	14.0000	+	28.0000i	0.801638	+	1.60328i
$306$	4.00000			0.228665
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$			5.00000i			0.284901i
$309$	−8.00000			−0.455104
$310$	−2.00000	+	1.00000i	−0.113592	+	0.0567962i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		−	26.0000i		−	1.46961i	−0.678280	−	0.734803i	$-0.737274\pi$
$313$		−	26.0000i		−	1.46961i	0.678280	−	0.734803i	$-0.262726\pi$
$314$	1.00000			0.0564333
$315$	10.0000	−	5.00000i	0.563436	−	0.281718i
$316$	15.0000			0.843816
$317$		−	22.0000i		−	1.23564i	−0.786318	−	0.617822i	$-0.788015\pi$
$317$		−	22.0000i		−	1.23564i	0.786318	−	0.617822i	$-0.211985\pi$
$318$		−	3.00000i		−	0.168232i
$319$	6.00000			0.335936
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$	−9.00000			−0.502331
$322$			5.00000i			0.278639i
$323$			12.0000i			0.667698i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	8.00000			0.443079
$327$		−	10.0000i		−	0.553001i
$328$			2.00000i			0.110432i
$329$	−20.0000			−1.10264
$330$	−1.00000	−	2.00000i	−0.0550482	−	0.110096i
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$		−	10.0000i		−	0.548821i
$333$			4.00000i			0.219199i
$334$	−9.00000			−0.492458
$335$	−20.0000	+	10.0000i	−1.09272	+	0.546358i
$336$	−5.00000			−0.272772
$337$		−	10.0000i		−	0.544735i	−0.962193	−	0.272367i	$-0.912193\pi$
$337$		−	10.0000i		−	0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$		−	13.0000i		−	0.707107i
$339$	−9.00000			−0.488813
$340$	−8.00000	+	4.00000i	−0.433861	+	0.216930i
$341$	1.00000			0.0541530
$342$		−	3.00000i		−	0.162221i
$343$		−	55.0000i		−	2.96972i
$344$	−1.00000			−0.0539164
$345$	−1.00000	−	2.00000i	−0.0538382	−	0.107676i
$346$	2.00000			0.107521
$347$			30.0000i			1.61048i	0.592946	+	0.805242i	$0.297965\pi$
$347$			30.0000i			1.61048i	−0.592946	+	0.805242i	$0.702035\pi$
$348$			6.00000i			0.321634i
$349$	32.0000			1.71292			0.856460	−	0.516213i	$-0.172659\pi$
$349$	32.0000			1.71292			0.856460	+	0.516213i	$0.172659\pi$
$350$	−15.0000	+	20.0000i	−0.801784	+	1.06904i
$351$		0			0
$352$			1.00000i			0.0533002i
$353$			8.00000i			0.425797i	0.977074	+	0.212899i	$0.0682904\pi$
$353$			8.00000i			0.425797i	−0.977074	+	0.212899i	$0.931710\pi$
$354$	14.0000			0.744092
$355$	9.00000	+	18.0000i	0.477670	+	0.955341i
$356$	−1.00000			−0.0529999
$357$			20.0000i			1.05851i
$358$		−	8.00000i		−	0.422813i
$359$	15.0000			0.791670			0.395835	−	0.918322i	$-0.370455\pi$
$359$	15.0000			0.791670			0.395835	+	0.918322i	$0.370455\pi$
$360$	2.00000	−	1.00000i	0.105409	−	0.0527046i
$361$	−10.0000			−0.526316
$362$		−	11.0000i		−	0.578147i
$363$		−	10.0000i		−	0.524864i
$364$		0			0
$365$	−14.0000	+	7.00000i	−0.732793	+	0.366397i
$366$	14.0000			0.731792
$367$			26.0000i			1.35719i	0.734513	+	0.678594i	$0.237411\pi$
$367$			26.0000i			1.35719i	−0.734513	+	0.678594i	$0.762589\pi$
$368$			1.00000i			0.0521286i
$369$	−2.00000			−0.104116
$370$	−4.00000	−	8.00000i	−0.207950	−	0.415900i
$371$	15.0000			0.778761
$372$			1.00000i			0.0518476i
$373$			3.00000i			0.155334i	0.996979	+	0.0776671i	$0.0247471\pi$
$373$			3.00000i			0.155334i	−0.996979	+	0.0776671i	$0.975253\pi$
$374$	4.00000			0.206835
$375$	2.00000	−	11.0000i	0.103280	−	0.568038i
$376$	−4.00000			−0.206284
$377$		0			0
$378$		−	5.00000i		−	0.257172i
$379$	19.0000			0.975964			0.487982	−	0.872854i	$-0.337733\pi$
$379$	19.0000			0.975964			0.487982	+	0.872854i	$0.337733\pi$
$380$	3.00000	+	6.00000i	0.153897	+	0.307794i
$381$	16.0000			0.819705
$382$		−	24.0000i		−	1.22795i
$383$			20.0000i			1.02195i	0.859595	+	0.510976i	$0.170716\pi$
$383$			20.0000i			1.02195i	−0.859595	+	0.510976i	$0.829284\pi$
$384$	−1.00000			−0.0510310
$385$	10.0000	−	5.00000i	0.509647	−	0.254824i
$386$	10.0000			0.508987
$387$		−	1.00000i		−	0.0508329i
$388$		−	10.0000i		−	0.507673i
$389$	16.0000			0.811232			0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000			0.811232			0.405616	+	0.914044i	$0.367057\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		−	18.0000i		−	0.909137i
$393$			18.0000i			0.907980i
$394$	−2.00000			−0.100759
$395$	−15.0000	−	30.0000i	−0.754732	−	1.50946i
$396$	−1.00000			−0.0502519
$397$			17.0000i			0.853206i	0.904439	+	0.426603i	$0.140290\pi$
$397$			17.0000i			0.853206i	−0.904439	+	0.426603i	$0.859710\pi$
$398$		−	9.00000i		−	0.451129i
$399$	15.0000			0.750939
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	−29.0000			−1.44819			−0.724095	−	0.689700i	$-0.757743\pi$
$401$	−29.0000			−1.44819			−0.724095	+	0.689700i	$0.757743\pi$
$402$			10.0000i			0.498755i
$403$		0			0
$404$	−7.00000			−0.348263
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$	−30.0000			−1.48888
$407$			4.00000i			0.198273i
$408$			4.00000i			0.198030i
$409$	16.0000			0.791149			0.395575	−	0.918434i	$-0.370545\pi$
$409$	16.0000			0.791149			0.395575	+	0.918434i	$0.370545\pi$
$410$	4.00000	−	2.00000i	0.197546	−	0.0987730i
$411$	6.00000			0.295958
$412$		−	8.00000i		−	0.394132i
$413$			70.0000i			3.44447i
$414$	−1.00000			−0.0491473
$415$	−20.0000	+	10.0000i	−0.981761	+	0.490881i
$416$		0			0
$417$		−	4.00000i		−	0.195881i
$418$		−	3.00000i		−	0.146735i
$419$	−26.0000			−1.27018			−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000			−1.27018			−0.635092	+	0.772437i	$0.719038\pi$
$420$	5.00000	+	10.0000i	0.243975	+	0.487950i
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$			21.0000i			1.02226i
$423$		−	4.00000i		−	0.194487i
$424$	3.00000			0.145693
$425$	16.0000	+	12.0000i	0.776114	+	0.582086i
$426$	9.00000			0.436051
$427$			70.0000i			3.38754i
$428$		−	9.00000i		−	0.435031i
$429$		0			0
$430$	1.00000	+	2.00000i	0.0482243	+	0.0964486i
$431$	8.00000			0.385346			0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000			0.385346			0.192673	+	0.981263i	$0.438284\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	11.0000i		−	0.528626i	−0.964437	−	0.264313i	$-0.914855\pi$
$433$		−	11.0000i		−	0.528626i	0.964437	−	0.264313i	$-0.0851452\pi$
$434$	−5.00000			−0.240008
$435$	12.0000	−	6.00000i	0.575356	−	0.287678i
$436$	10.0000			0.478913
$437$		−	3.00000i		−	0.143509i
$438$			7.00000i			0.334473i
$439$	−36.0000			−1.71819			−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000			−1.71819			−0.859093	+	0.511819i	$0.828972\pi$
$440$	2.00000	−	1.00000i	0.0953463	−	0.0476731i
$441$	18.0000			0.857143
$442$		0			0
$443$		−	15.0000i		−	0.712672i	−0.934358	−	0.356336i	$-0.884026\pi$
$443$		−	15.0000i		−	0.712672i	0.934358	−	0.356336i	$-0.115974\pi$
$444$	−4.00000			−0.189832
$445$	1.00000	+	2.00000i	0.0474045	+	0.0948091i
$446$	−8.00000			−0.378811
$447$		−	1.00000i		−	0.0472984i
$448$		−	5.00000i		−	0.236228i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$	−2.00000			−0.0941763
$452$		−	9.00000i		−	0.423324i
$453$		−	8.00000i		−	0.375873i
$454$	29.0000			1.36104
$455$		0			0
$456$	3.00000			0.140488
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$			23.0000i			1.07472i
$459$	−4.00000			−0.186704
$460$	2.00000	−	1.00000i	0.0932505	−	0.0466252i
$461$	24.0000			1.11779			0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000			1.11779			0.558896	+	0.829238i	$0.311225\pi$
$462$		−	5.00000i		−	0.232621i
$463$			6.00000i			0.278844i	0.990233	+	0.139422i	$0.0445244\pi$
$463$			6.00000i			0.278844i	−0.990233	+	0.139422i	$0.955476\pi$
$464$	−6.00000			−0.278543
$465$	2.00000	−	1.00000i	0.0927478	−	0.0463739i
$466$	−13.0000			−0.602213
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$		0			0
$469$	−50.0000			−2.30879
$470$	4.00000	+	8.00000i	0.184506	+	0.369012i
$471$	−1.00000			−0.0460776
$472$			14.0000i			0.644402i
$473$		−	1.00000i		−	0.0459800i
$474$	−15.0000			−0.688973
$475$	9.00000	−	12.0000i	0.412948	−	0.550598i
$476$	−20.0000			−0.916698
$477$			3.00000i			0.137361i
$478$		−	22.0000i		−	1.00626i
$479$	−29.0000			−1.32504			−0.662522	−	0.749043i	$-0.730514\pi$
$479$	−29.0000			−1.32504			−0.662522	+	0.749043i	$0.730514\pi$
$480$	1.00000	+	2.00000i	0.0456435	+	0.0912871i
$481$		0			0
$482$		−	4.00000i		−	0.182195i
$483$		−	5.00000i		−	0.227508i
$484$	10.0000			0.454545
$485$	−20.0000	+	10.0000i	−0.908153	+	0.454077i
$486$	1.00000			0.0453609
$487$			36.0000i			1.63132i	0.578535	+	0.815658i	$0.303625\pi$
$487$			36.0000i			1.63132i	−0.578535	+	0.815658i	$0.696375\pi$
$488$			14.0000i			0.633750i
$489$	−8.00000			−0.361773
$490$	−36.0000	+	18.0000i	−1.62631	+	0.813157i
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$		−	2.00000i		−	0.0901670i
$493$			24.0000i			1.08091i
$494$		0			0
$495$	1.00000	+	2.00000i	0.0449467	+	0.0898933i
$496$	−1.00000			−0.0449013
$497$			45.0000i			2.01853i
$498$			10.0000i			0.448111i
$499$	42.0000			1.88018			0.940089	−	0.340929i	$-0.110742\pi$
$499$	42.0000			1.88018			0.940089	+	0.340929i	$0.110742\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$	9.00000			0.402090
$502$			12.0000i			0.535586i
$503$		−	42.0000i		−	1.87269i	−0.351085	−	0.936344i	$-0.614187\pi$
$503$		−	42.0000i		−	1.87269i	0.351085	−	0.936344i	$-0.385813\pi$
$504$	5.00000			0.222718
$505$	7.00000	+	14.0000i	0.311496	+	0.622992i
$506$	−1.00000			−0.0444554
$507$			13.0000i			0.577350i
$508$			16.0000i			0.709885i
$509$	36.0000			1.59567			0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000			1.59567			0.797836	+	0.602875i	$0.205978\pi$
$510$	8.00000	−	4.00000i	0.354246	−	0.177123i
$511$	−35.0000			−1.54831
$512$		−	1.00000i		−	0.0441942i
$513$			3.00000i			0.132453i
$514$	3.00000			0.132324
$515$	−16.0000	+	8.00000i	−0.705044	+	0.352522i
$516$	1.00000			0.0440225
$517$		−	4.00000i		−	0.175920i
$518$		−	20.0000i		−	0.878750i
$519$	−2.00000			−0.0877903
$520$		0			0
$521$	−20.0000			−0.876216			−0.438108	−	0.898922i	$-0.644351\pi$
$521$	−20.0000			−0.876216			−0.438108	+	0.898922i	$0.644351\pi$
$522$		−	6.00000i		−	0.262613i
$523$			41.0000i			1.79280i	0.443241	+	0.896402i	$0.353829\pi$
$523$			41.0000i			1.79280i	−0.443241	+	0.896402i	$0.646171\pi$
$524$	−18.0000			−0.786334
$525$	15.0000	−	20.0000i	0.654654	−	0.872872i
$526$	−8.00000			−0.348817
$527$			4.00000i			0.174243i
$528$		−	1.00000i		−	0.0435194i
$529$	22.0000			0.956522
$530$	−3.00000	−	6.00000i	−0.130312	−	0.260623i
$531$	−14.0000			−0.607548
$532$			15.0000i			0.650332i
$533$		0			0
$534$	1.00000			0.0432742
$535$	−18.0000	+	9.00000i	−0.778208	+	0.389104i
$536$	−10.0000			−0.431934
$537$			8.00000i			0.345225i
$538$			30.0000i			1.29339i
$539$	18.0000			0.775315
$540$	−2.00000	+	1.00000i	−0.0860663	+	0.0430331i
$541$	4.00000			0.171973			0.0859867	−	0.996296i	$-0.472596\pi$
$541$	4.00000			0.171973			0.0859867	+	0.996296i	$0.472596\pi$
$542$		−	13.0000i		−	0.558398i
$543$			11.0000i			0.472055i
$544$	−4.00000			−0.171499
$545$	−10.0000	−	20.0000i	−0.428353	−	0.856706i
$546$		0			0
$547$			20.0000i			0.855138i	0.903983	+	0.427569i	$0.140630\pi$
$547$			20.0000i			0.855138i	−0.903983	+	0.427569i	$0.859370\pi$
$548$			6.00000i			0.256307i
$549$	−14.0000			−0.597505
$550$	−4.00000	−	3.00000i	−0.170561	−	0.127920i
$551$	18.0000			0.766826
$552$		−	1.00000i		−	0.0425628i
$553$		−	75.0000i		−	3.18932i
$554$	26.0000			1.10463
$555$	4.00000	+	8.00000i	0.169791	+	0.339581i
$556$	4.00000			0.169638
$557$		−	33.0000i		−	1.39825i	−0.714997	−	0.699127i	$-0.753572\pi$
$557$		−	33.0000i		−	1.39825i	0.714997	−	0.699127i	$-0.246428\pi$
$558$		−	1.00000i		−	0.0423334i
$559$		0			0
$560$	−10.0000	+	5.00000i	−0.422577	+	0.211289i
$561$	−4.00000			−0.168880
$562$		0			0
$563$		−	4.00000i		−	0.168580i	−0.996441	−	0.0842900i	$-0.973138\pi$
$563$		−	4.00000i		−	0.168580i	0.996441	−	0.0842900i	$-0.0268622\pi$
$564$	4.00000			0.168430
$565$	−18.0000	+	9.00000i	−0.757266	+	0.378633i
$566$	−22.0000			−0.924729
$567$			5.00000i			0.209980i
$568$			9.00000i			0.377632i
$569$	1.00000			0.0419222			0.0209611	−	0.999780i	$-0.493327\pi$
$569$	1.00000			0.0419222			0.0209611	+	0.999780i	$0.493327\pi$
$570$	−3.00000	−	6.00000i	−0.125656	−	0.251312i
$571$	34.0000			1.42286			0.711428	−	0.702759i	$-0.248049\pi$
$571$	34.0000			1.42286			0.711428	+	0.702759i	$0.248049\pi$
$572$		0			0
$573$			24.0000i			1.00261i
$574$	10.0000			0.417392
$575$	−4.00000	−	3.00000i	−0.166812	−	0.125109i
$576$	1.00000			0.0416667
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$		−	1.00000i		−	0.0415945i
$579$	−10.0000			−0.415586
$580$	6.00000	+	12.0000i	0.249136	+	0.498273i
$581$	−50.0000			−2.07435
$582$			10.0000i			0.414513i
$583$			3.00000i			0.124247i
$584$	−7.00000			−0.289662
$585$		0			0
$586$	−30.0000			−1.23929
$587$		−	30.0000i		−	1.23823i	−0.785299	−	0.619116i	$-0.787491\pi$
$587$		−	30.0000i		−	1.23823i	0.785299	−	0.619116i	$-0.212509\pi$
$588$			18.0000i			0.742307i
$589$	3.00000			0.123613
$590$	28.0000	−	14.0000i	1.15274	−	0.576371i
$591$	2.00000			0.0822690
$592$		−	4.00000i		−	0.164399i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	1.00000			0.0410305
$595$	20.0000	+	40.0000i	0.819920	+	1.63984i
$596$	1.00000			0.0409616
$597$			9.00000i			0.368345i
$598$		0			0
$599$	−15.0000			−0.612883			−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000			−0.612883			−0.306442	+	0.951889i	$0.599138\pi$
$600$	3.00000	−	4.00000i	0.122474	−	0.163299i
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$			5.00000i			0.203785i
$603$		−	10.0000i		−	0.407231i
$604$	8.00000			0.325515
$605$	−10.0000	−	20.0000i	−0.406558	−	0.813116i
$606$	7.00000			0.284356
$607$		−	23.0000i		−	0.933541i	−0.884378	−	0.466771i	$-0.845417\pi$
$607$		−	23.0000i		−	0.933541i	0.884378	−	0.466771i	$-0.154583\pi$
$608$			3.00000i			0.121666i
$609$	30.0000			1.21566
$610$	28.0000	−	14.0000i	1.13369	−	0.566843i
$611$		0			0
$612$		−	4.00000i		−	0.161690i
$613$			16.0000i			0.646234i	0.946359	+	0.323117i	$0.104731\pi$
$613$			16.0000i			0.646234i	−0.946359	+	0.323117i	$0.895269\pi$
$614$	12.0000			0.484281
$615$	−4.00000	+	2.00000i	−0.161296	+	0.0806478i
$616$	5.00000			0.201456
$617$		−	13.0000i		−	0.523360i	−0.965155	−	0.261680i	$-0.915723\pi$
$617$		−	13.0000i		−	0.523360i	0.965155	−	0.261680i	$-0.0842766\pi$
$618$			8.00000i			0.321807i
$619$	28.0000			1.12542			0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000			1.12542			0.562708	+	0.826656i	$0.309760\pi$
$620$	1.00000	+	2.00000i	0.0401610	+	0.0803219i
$621$	1.00000			0.0401286
$622$		0			0
$623$			5.00000i			0.200321i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−26.0000			−1.03917
$627$			3.00000i			0.119808i
$628$		−	1.00000i		−	0.0399043i
$629$	−16.0000			−0.637962
$630$	−5.00000	−	10.0000i	−0.199205	−	0.398410i
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$		−	15.0000i		−	0.596668i
$633$		−	21.0000i		−	0.834675i
$634$	−22.0000			−0.873732
$635$	32.0000	−	16.0000i	1.26988	−	0.634941i
$636$	−3.00000			−0.118958
$637$		0			0
$638$		−	6.00000i		−	0.237542i
$639$	−9.00000			−0.356034
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	38.0000			1.50091			0.750455	−	0.660922i	$-0.229834\pi$
$641$	38.0000			1.50091			0.750455	+	0.660922i	$0.229834\pi$
$642$			9.00000i			0.355202i
$643$			3.00000i			0.118308i	0.998249	+	0.0591542i	$0.0188404\pi$
$643$			3.00000i			0.118308i	−0.998249	+	0.0591542i	$0.981160\pi$
$644$	5.00000			0.197028
$645$	−1.00000	−	2.00000i	−0.0393750	−	0.0787499i
$646$	12.0000			0.472134
$647$		−	27.0000i		−	1.06148i	−0.847535	−	0.530740i	$-0.821914\pi$
$647$		−	27.0000i		−	1.06148i	0.847535	−	0.530740i	$-0.178086\pi$
$648$			1.00000i			0.0392837i
$649$	−14.0000			−0.549548
$650$		0			0
$651$	5.00000			0.195965
$652$		−	8.00000i		−	0.313304i
$653$		−	2.00000i		−	0.0782660i	−0.999234	−	0.0391330i	$-0.987540\pi$
$653$		−	2.00000i		−	0.0782660i	0.999234	−	0.0391330i	$-0.0124596\pi$
$654$	−10.0000			−0.391031
$655$	18.0000	+	36.0000i	0.703318	+	1.40664i
$656$	2.00000			0.0780869
$657$		−	7.00000i		−	0.273096i
$658$			20.0000i			0.779681i
$659$	−10.0000			−0.389545			−0.194772	−	0.980848i	$-0.562397\pi$
$659$	−10.0000			−0.389545			−0.194772	+	0.980848i	$0.562397\pi$
$660$	−2.00000	+	1.00000i	−0.0778499	+	0.0389249i
$661$	−40.0000			−1.55582			−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000			−1.55582			−0.777910	+	0.628376i	$0.783720\pi$
$662$		−	28.0000i		−	1.08825i
$663$		0			0
$664$	−10.0000			−0.388075
$665$	30.0000	−	15.0000i	1.16335	−	0.581675i
$666$	4.00000			0.154997
$667$		−	6.00000i		−	0.232321i
$668$			9.00000i			0.348220i
$669$	8.00000			0.309298
$670$	10.0000	+	20.0000i	0.386334	+	0.772667i
$671$	−14.0000			−0.540464
$672$			5.00000i			0.192879i
$673$			6.00000i			0.231283i	0.993291	+	0.115642i	$0.0368924\pi$
$673$			6.00000i			0.231283i	−0.993291	+	0.115642i	$0.963108\pi$
$674$	−10.0000			−0.385186
$675$	4.00000	+	3.00000i	0.153960	+	0.115470i
$676$	−13.0000			−0.500000
$677$			11.0000i			0.422764i	0.977403	+	0.211382i	$0.0677965\pi$
$677$			11.0000i			0.422764i	−0.977403	+	0.211382i	$0.932204\pi$
$678$			9.00000i			0.345643i
$679$	−50.0000			−1.91882
$680$	4.00000	+	8.00000i	0.153393	+	0.306786i
$681$	−29.0000			−1.11128
$682$		−	1.00000i		−	0.0382920i
$683$			31.0000i			1.18618i	0.805135	+	0.593091i	$0.202093\pi$
$683$			31.0000i			1.18618i	−0.805135	+	0.593091i	$0.797907\pi$
$684$	−3.00000			−0.114708
$685$	12.0000	−	6.00000i	0.458496	−	0.229248i
$686$	−55.0000			−2.09991
$687$		−	23.0000i		−	0.877505i
$688$			1.00000i			0.0381246i
$689$		0			0
$690$	−2.00000	+	1.00000i	−0.0761387	+	0.0380693i
$691$	−5.00000			−0.190209			−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000			−0.190209			−0.0951045	+	0.995467i	$0.530319\pi$
$692$		−	2.00000i		−	0.0760286i
$693$			5.00000i			0.189934i
$694$	30.0000			1.13878
$695$	−4.00000	−	8.00000i	−0.151729	−	0.303457i
$696$	6.00000			0.227429
$697$		−	8.00000i		−	0.303022i
$698$		−	32.0000i		−	1.21122i
$699$	13.0000			0.491705
$700$	20.0000	+	15.0000i	0.755929	+	0.566947i
$701$	35.0000			1.32193			0.660966	−	0.750416i	$-0.270147\pi$
$701$	35.0000			1.32193			0.660966	+	0.750416i	$0.270147\pi$
$702$		0			0
$703$			12.0000i			0.452589i
$704$	1.00000			0.0376889
$705$	−4.00000	−	8.00000i	−0.150649	−	0.301297i
$706$	8.00000			0.301084
$707$			35.0000i			1.31631i
$708$		−	14.0000i		−	0.526152i
$709$	−21.0000			−0.788672			−0.394336	−	0.918966i	$-0.629025\pi$
$709$	−21.0000			−0.788672			−0.394336	+	0.918966i	$0.629025\pi$
$710$	18.0000	−	9.00000i	0.675528	−	0.337764i
$711$	15.0000			0.562544
$712$			1.00000i			0.0374766i
$713$		−	1.00000i		−	0.0374503i
$714$	20.0000			0.748481
$715$		0			0
$716$	−8.00000			−0.298974
$717$			22.0000i			0.821605i
$718$		−	15.0000i		−	0.559795i
$719$	−50.0000			−1.86469			−0.932343	−	0.361576i	$-0.882239\pi$
$719$	−50.0000			−1.86469			−0.932343	+	0.361576i	$0.882239\pi$
$720$	−1.00000	−	2.00000i	−0.0372678	−	0.0745356i
$721$	−40.0000			−1.48968
$722$			10.0000i			0.372161i
$723$			4.00000i			0.148762i
$724$	−11.0000			−0.408812
$725$	18.0000	−	24.0000i	0.668503	−	0.891338i
$726$	−10.0000			−0.371135
$727$		−	27.0000i		−	1.00137i	−0.865628	−	0.500687i	$-0.833081\pi$
$727$		−	27.0000i		−	1.00137i	0.865628	−	0.500687i	$-0.166919\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	7.00000	+	14.0000i	0.259082	+	0.518163i
$731$	4.00000			0.147945
$732$		−	14.0000i		−	0.517455i
$733$		−	34.0000i		−	1.25582i	−0.778287	−	0.627909i	$-0.783911\pi$
$733$		−	34.0000i		−	1.25582i	0.778287	−	0.627909i	$-0.216089\pi$
$734$	26.0000			0.959678
$735$	36.0000	−	18.0000i	1.32788	−	0.663940i
$736$	1.00000			0.0368605
$737$		−	10.0000i		−	0.368355i
$738$			2.00000i			0.0736210i
$739$	−46.0000			−1.69214			−0.846069	−	0.533074i	$-0.821037\pi$
$739$	−46.0000			−1.69214			−0.846069	+	0.533074i	$0.821037\pi$
$740$	−8.00000	+	4.00000i	−0.294086	+	0.147043i
$741$		0			0
$742$		−	15.0000i		−	0.550667i
$743$		−	21.0000i		−	0.770415i	−0.922830	−	0.385208i	$-0.874130\pi$
$743$		−	21.0000i		−	0.770415i	0.922830	−	0.385208i	$-0.125870\pi$
$744$	1.00000			0.0366618
$745$	−1.00000	−	2.00000i	−0.0366372	−	0.0732743i
$746$	3.00000			0.109838
$747$		−	10.0000i		−	0.365881i
$748$		−	4.00000i		−	0.146254i
$749$	−45.0000			−1.64426
$750$	−11.0000	−	2.00000i	−0.401663	−	0.0730297i
$751$	2.00000			0.0729810			0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000			0.0729810			0.0364905	+	0.999334i	$0.488382\pi$
$752$			4.00000i			0.145865i
$753$		−	12.0000i		−	0.437304i
$754$		0			0
$755$	−8.00000	−	16.0000i	−0.291150	−	0.582300i
$756$	−5.00000			−0.181848
$757$		−	4.00000i		−	0.145382i	−0.997354	−	0.0726912i	$-0.976841\pi$
$757$		−	4.00000i		−	0.145382i	0.997354	−	0.0726912i	$-0.0231588\pi$
$758$		−	19.0000i		−	0.690111i
$759$	1.00000			0.0362977
$760$	6.00000	−	3.00000i	0.217643	−	0.108821i
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$		−	16.0000i		−	0.579619i
$763$		−	50.0000i		−	1.81012i
$764$	−24.0000			−0.868290
$765$	−8.00000	+	4.00000i	−0.289241	+	0.144620i
$766$	20.0000			0.722629
$767$		0			0
$768$			1.00000i			0.0360844i
$769$	27.0000			0.973645			0.486822	−	0.873501i	$-0.338156\pi$
$769$	27.0000			0.973645			0.486822	+	0.873501i	$0.338156\pi$
$770$	−5.00000	−	10.0000i	−0.180187	−	0.360375i
$771$	−3.00000			−0.108042
$772$		−	10.0000i		−	0.359908i
$773$			51.0000i			1.83434i	0.398493	+	0.917171i	$0.369533\pi$
$773$			51.0000i			1.83434i	−0.398493	+	0.917171i	$0.630467\pi$
$774$	−1.00000			−0.0359443
$775$	3.00000	−	4.00000i	0.107763	−	0.143684i
$776$	−10.0000			−0.358979
$777$			20.0000i			0.717496i
$778$		−	16.0000i		−	0.573628i
$779$	−6.00000			−0.214972
$780$		0			0
$781$	−9.00000			−0.322045
$782$		−	4.00000i		−	0.143040i
$783$			6.00000i			0.214423i
$784$	−18.0000			−0.642857
$785$	−2.00000	+	1.00000i	−0.0713831	+	0.0356915i
$786$	18.0000			0.642039
$787$		−	25.0000i		−	0.891154i	−0.895244	−	0.445577i	$-0.852999\pi$
$787$		−	25.0000i		−	0.891154i	0.895244	−	0.445577i	$-0.147001\pi$
$788$			2.00000i			0.0712470i
$789$	8.00000			0.284808
$790$	−30.0000	+	15.0000i	−1.06735	+	0.533676i
$791$	−45.0000			−1.60002
$792$			1.00000i			0.0355335i
$793$		0			0
$794$	17.0000			0.603307
$795$	3.00000	+	6.00000i	0.106399	+	0.212798i
$796$	−9.00000			−0.318997
$797$		−	34.0000i		−	1.20434i	−0.798367	−	0.602171i	$-0.794303\pi$
$797$		−	34.0000i		−	1.20434i	0.798367	−	0.602171i	$-0.205697\pi$
$798$		−	15.0000i		−	0.530994i
$799$	16.0000			0.566039
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$	−1.00000			−0.0353333
$802$			29.0000i			1.02403i
$803$		−	7.00000i		−	0.247025i
$804$	10.0000			0.352673
$805$	−5.00000	−	10.0000i	−0.176227	−	0.352454i
$806$		0			0
$807$		−	30.0000i		−	1.05605i
$808$			7.00000i			0.246259i
$809$	−15.0000			−0.527372			−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000			−0.527372			−0.263686	+	0.964609i	$0.584938\pi$
$810$	2.00000	−	1.00000i	0.0702728	−	0.0351364i
$811$	−17.0000			−0.596951			−0.298475	−	0.954417i	$-0.596478\pi$
$811$	−17.0000			−0.596951			−0.298475	+	0.954417i	$0.596478\pi$
$812$			30.0000i			1.05279i
$813$			13.0000i			0.455930i
$814$	4.00000			0.140200
$815$	−16.0000	+	8.00000i	−0.560456	+	0.280228i
$816$	4.00000			0.140028
$817$		−	3.00000i		−	0.104957i
$818$		−	16.0000i		−	0.559427i
$819$		0			0
$820$	−2.00000	−	4.00000i	−0.0698430	−	0.139686i
$821$	10.0000			0.349002			0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000			0.349002			0.174501	+	0.984657i	$0.444169\pi$
$822$		−	6.00000i		−	0.209274i
$823$		−	18.0000i		−	0.627441i	−0.949515	−	0.313720i	$-0.898425\pi$
$823$		−	18.0000i		−	0.627441i	0.949515	−	0.313720i	$-0.101575\pi$
$824$	−8.00000			−0.278693
$825$	4.00000	+	3.00000i	0.139262	+	0.104447i
$826$	70.0000			2.43561
$827$		−	34.0000i		−	1.18230i	−0.806563	−	0.591148i	$-0.798675\pi$
$827$		−	34.0000i		−	1.18230i	0.806563	−	0.591148i	$-0.201325\pi$
$828$			1.00000i			0.0347524i
$829$	−39.0000			−1.35453			−0.677263	−	0.735741i	$-0.736834\pi$
$829$	−39.0000			−1.35453			−0.677263	+	0.735741i	$0.736834\pi$
$830$	10.0000	+	20.0000i	0.347105	+	0.694210i
$831$	−26.0000			−0.901930
$832$		0			0
$833$			72.0000i			2.49465i
$834$	−4.00000			−0.138509
$835$	18.0000	−	9.00000i	0.622916	−	0.311458i
$836$	−3.00000			−0.103757
$837$			1.00000i			0.0345651i
$838$			26.0000i			0.898155i
$839$	35.0000			1.20833			0.604167	−	0.796858i	$-0.293506\pi$
$839$	35.0000			1.20833			0.604167	+	0.796858i	$0.293506\pi$
$840$	10.0000	−	5.00000i	0.345033	−	0.172516i
$841$	7.00000			0.241379
$842$		−	22.0000i		−	0.758170i
$843$		0			0
$844$	21.0000			0.722850
$845$	13.0000	+	26.0000i	0.447214	+	0.894427i
$846$	−4.00000			−0.137523
$847$		−	50.0000i		−	1.71802i
$848$		−	3.00000i		−	0.103020i
$849$	22.0000			0.755038
$850$	12.0000	−	16.0000i	0.411597	−	0.548795i
$851$	4.00000			0.137118
$852$		−	9.00000i		−	0.308335i
$853$		−	49.0000i		−	1.67773i	−0.544341	−	0.838864i	$-0.683220\pi$
$853$		−	49.0000i		−	1.67773i	0.544341	−	0.838864i	$-0.316780\pi$
$854$	70.0000			2.39535
$855$	3.00000	+	6.00000i	0.102598	+	0.205196i
$856$	−9.00000			−0.307614
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	2.00000	−	1.00000i	0.0681994	−	0.0340997i
$861$	−10.0000			−0.340799
$862$		−	8.00000i		−	0.272481i
$863$		−	57.0000i		−	1.94030i	−0.242500	−	0.970151i	$-0.577968\pi$
$863$		−	57.0000i		−	1.94030i	0.242500	−	0.970151i	$-0.422032\pi$
$864$	−1.00000			−0.0340207
$865$	−4.00000	+	2.00000i	−0.136004	+	0.0680020i
$866$	−11.0000			−0.373795
$867$			1.00000i			0.0339618i
$868$			5.00000i			0.169711i
$869$	15.0000			0.508840
$870$	−6.00000	−	12.0000i	−0.203419	−	0.406838i
$871$		0			0
$872$		−	10.0000i		−	0.338643i
$873$		−	10.0000i		−	0.338449i
$874$	−3.00000			−0.101477
$875$	10.0000	−	55.0000i	0.338062	−	1.85934i
$876$	7.00000			0.236508
$877$			34.0000i			1.14810i	0.818821	+	0.574049i	$0.194628\pi$
$877$			34.0000i			1.14810i	−0.818821	+	0.574049i	$0.805372\pi$
$878$			36.0000i			1.21494i
$879$	30.0000			1.01187
$880$	−1.00000	−	2.00000i	−0.0337100	−	0.0674200i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		−	18.0000i		−	0.606092i
$883$			39.0000i			1.31245i	0.754563	+	0.656227i	$0.227849\pi$
$883$			39.0000i			1.31245i	−0.754563	+	0.656227i	$0.772151\pi$
$884$		0			0
$885$	−28.0000	+	14.0000i	−0.941210	+	0.470605i
$886$	−15.0000			−0.503935
$887$			48.0000i			1.61168i	0.592132	+	0.805841i	$0.298286\pi$
$887$			48.0000i			1.61168i	−0.592132	+	0.805841i	$0.701714\pi$
$888$			4.00000i			0.134231i
$889$	80.0000			2.68311
$890$	2.00000	−	1.00000i	0.0670402	−	0.0335201i
$891$	−1.00000			−0.0335013
$892$			8.00000i			0.267860i
$893$		−	12.0000i		−	0.401565i
$894$	−1.00000			−0.0334450
$895$	8.00000	+	16.0000i	0.267411	+	0.534821i
$896$	−5.00000			−0.167038
$897$		0			0
$898$			6.00000i			0.200223i
$899$	6.00000			0.200111
$900$	−3.00000	+	4.00000i	−0.100000	+	0.133333i
$901$	−12.0000			−0.399778
$902$			2.00000i			0.0665927i
$903$		−	5.00000i		−	0.166390i
$904$	−9.00000			−0.299336
$905$	11.0000	+	22.0000i	0.365652	+	0.731305i
$906$	−8.00000			−0.265782
$907$			24.0000i			0.796907i	0.917189	+	0.398453i	$0.130453\pi$
$907$			24.0000i			0.796907i	−0.917189	+	0.398453i	$0.869547\pi$
$908$		−	29.0000i		−	0.962399i
$909$	−7.00000			−0.232175
$910$		0			0
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$		−	3.00000i		−	0.0993399i
$913$		−	10.0000i		−	0.330952i
$914$	−10.0000			−0.330771
$915$	−28.0000	+	14.0000i	−0.925651	+	0.462826i
$916$	23.0000			0.759941
$917$			90.0000i			2.97206i
$918$			4.00000i			0.132020i
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$	−1.00000	−	2.00000i	−0.0329690	−	0.0659380i
$921$	−12.0000			−0.395413
$922$		−	24.0000i		−	0.790398i
$923$		0			0
$924$	−5.00000			−0.164488
$925$	16.0000	+	12.0000i	0.526077	+	0.394558i
$926$	6.00000			0.197172
$927$		−	8.00000i		−	0.262754i
$928$			6.00000i			0.196960i
$929$	−33.0000			−1.08269			−0.541347	−	0.840799i	$-0.682086\pi$
$929$	−33.0000			−1.08269			−0.541347	+	0.840799i	$0.682086\pi$
$930$	−1.00000	−	2.00000i	−0.0327913	−	0.0655826i
$931$	54.0000			1.76978
$932$			13.0000i			0.425829i
$933$		0			0
$934$	−12.0000			−0.392652
$935$	−8.00000	+	4.00000i	−0.261628	+	0.130814i
$936$		0			0
$937$		−	38.0000i		−	1.24141i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$		−	38.0000i		−	1.24141i	0.784046	−	0.620703i	$-0.213153\pi$
$938$			50.0000i			1.63256i
$939$	26.0000			0.848478
$940$	8.00000	−	4.00000i	0.260931	−	0.130466i
$941$	−52.0000			−1.69515			−0.847576	−	0.530674i	$-0.821939\pi$
$941$	−52.0000			−1.69515			−0.847576	+	0.530674i	$0.821939\pi$
$942$			1.00000i			0.0325818i
$943$			2.00000i			0.0651290i
$944$	14.0000			0.455661
$945$	5.00000	+	10.0000i	0.162650	+	0.325300i
$946$	−1.00000			−0.0325128
$947$			18.0000i			0.584921i	0.956278	+	0.292461i	$0.0944741\pi$
$947$			18.0000i			0.584921i	−0.956278	+	0.292461i	$0.905526\pi$
$948$			15.0000i			0.487177i
$949$		0			0
$950$	−12.0000	−	9.00000i	−0.389331	−	0.291999i
$951$	22.0000			0.713399
$952$			20.0000i			0.648204i
$953$		−	4.00000i		−	0.129573i	−0.997899	−	0.0647864i	$-0.979363\pi$
$953$		−	4.00000i		−	0.129573i	0.997899	−	0.0647864i	$-0.0206366\pi$
$954$	3.00000			0.0971286
$955$	24.0000	+	48.0000i	0.776622	+	1.55324i
$956$	−22.0000			−0.711531
$957$			6.00000i			0.193952i
$958$			29.0000i			0.936947i
$959$	30.0000			0.968751
$960$	2.00000	−	1.00000i	0.0645497	−	0.0322749i
$961$	1.00000			0.0322581
$962$		0			0
$963$		−	9.00000i		−	0.290021i
$964$	−4.00000			−0.128831
$965$	−20.0000	+	10.0000i	−0.643823	+	0.321911i
$966$	−5.00000			−0.160872
$967$			28.0000i			0.900419i	0.892923	+	0.450210i	$0.148651\pi$
$967$			28.0000i			0.900419i	−0.892923	+	0.450210i	$0.851349\pi$
$968$		−	10.0000i		−	0.321412i
$969$	−12.0000			−0.385496
$970$	10.0000	+	20.0000i	0.321081	+	0.642161i
$971$	−6.00000			−0.192549			−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000			−0.192549			−0.0962746	+	0.995355i	$0.530693\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	20.0000i		−	0.641171i
$974$	36.0000			1.15351
$975$		0			0
$976$	14.0000			0.448129
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$			8.00000i			0.255812i
$979$	−1.00000			−0.0319601
$980$	18.0000	+	36.0000i	0.574989	+	1.14998i
$981$	10.0000			0.319275
$982$		−	27.0000i		−	0.861605i
$983$		−	28.0000i		−	0.893061i	−0.894768	−	0.446531i	$-0.852659\pi$
$983$		−	28.0000i		−	0.893061i	0.894768	−	0.446531i	$-0.147341\pi$
$984$	−2.00000			−0.0637577
$985$	4.00000	−	2.00000i	0.127451	−	0.0637253i
$986$	24.0000			0.764316
$987$		−	20.0000i		−	0.636607i
$988$		0			0
$989$	−1.00000			−0.0317982
$990$	2.00000	−	1.00000i	0.0635642	−	0.0317821i
$991$	−17.0000			−0.540023			−0.270011	−	0.962857i	$-0.587027\pi$
$991$	−17.0000			−0.540023			−0.270011	+	0.962857i	$0.587027\pi$
$992$			1.00000i			0.0317500i
$993$			28.0000i			0.888553i
$994$	45.0000			1.42731
$995$	9.00000	+	18.0000i	0.285319	+	0.570638i
$996$	10.0000			0.316862
$997$			6.00000i			0.190022i	0.995476	+	0.0950110i	$0.0302886\pi$
$997$			6.00000i			0.190022i	−0.995476	+	0.0950110i	$0.969711\pi$
$998$		−	42.0000i		−	1.32949i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.c.559.1	✓	2
3.2	odd	2		2790.2.d.e.559.2		2
5.2	odd	4		4650.2.a.bi.1.1		1
5.3	odd	4		4650.2.a.m.1.1		1
5.4	even	2	inner	930.2.d.c.559.2	yes	2
15.14	odd	2		2790.2.d.e.559.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.c.559.1	✓	2	1.1	even	1	trivial
930.2.d.c.559.2	yes	2	5.4	even	2	inner
2790.2.d.e.559.1		2	15.14	odd	2
2790.2.d.e.559.2		2	3.2	odd	2
4650.2.a.m.1.1		1	5.3	odd	4
4650.2.a.bi.1.1		1	5.2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +1.00000 q^{6} +5.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} -1.00000 q^{11} -1.00000i q^{12} +5.00000 q^{14} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -4.00000i q^{17} +1.00000i q^{18} -3.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -5.00000 q^{21} +1.00000i q^{22} +1.00000i q^{23} -1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -1.00000i q^{27} -5.00000i q^{28} -6.00000 q^{29} +(1.00000 + 2.00000i) q^{30} -1.00000 q^{31} -1.00000i q^{32} -1.00000i q^{33} -4.00000 q^{34} +(-10.0000 + 5.00000i) q^{35} +1.00000 q^{36} -4.00000i q^{37} +3.00000i q^{38} +(-2.00000 + 1.00000i) q^{40} +2.00000 q^{41} +5.00000i q^{42} +1.00000i q^{43} +1.00000 q^{44} +(-1.00000 - 2.00000i) q^{45} +1.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} -18.0000 q^{49} +(4.00000 + 3.00000i) q^{50} +4.00000 q^{51} -3.00000i q^{53} -1.00000 q^{54} +(-1.00000 - 2.00000i) q^{55} -5.00000 q^{56} -3.00000i q^{57} +6.00000i q^{58} +14.0000 q^{59} +(2.00000 - 1.00000i) q^{60} +14.0000 q^{61} +1.00000i q^{62} -5.00000i q^{63} -1.00000 q^{64} -1.00000 q^{66} +10.0000i q^{67} +4.00000i q^{68} -1.00000 q^{69} +(5.00000 + 10.0000i) q^{70} +9.00000 q^{71} -1.00000i q^{72} +7.00000i q^{73} -4.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} +3.00000 q^{76} -5.00000i q^{77} -15.0000 q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} -2.00000i q^{82} +10.0000i q^{83} +5.00000 q^{84} +(8.00000 - 4.00000i) q^{85} +1.00000 q^{86} -6.00000i q^{87} -1.00000i q^{88} +1.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} -1.00000i q^{92} -1.00000i q^{93} +4.00000 q^{94} +(-3.00000 - 6.00000i) q^{95} +1.00000 q^{96} +10.0000i q^{97} +18.0000i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 10 q^{14} - 4 q^{15} + 2 q^{16} - 6 q^{19} - 2 q^{20} - 10 q^{21} - 2 q^{24} - 6 q^{25} - 12 q^{29} + 2 q^{30} - 2 q^{31} - 8 q^{34} - 20 q^{35}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^9 + 4 * q^10 - 2 * q^11 + 10 * q^14 - 4 * q^15 + 2 * q^16 - 6 * q^19 - 2 * q^20 - 10 * q^21 - 2 * q^24 - 6 * q^25 - 12 * q^29 + 2 * q^30 - 2 * q^31 - 8 * q^34 - 20 * q^35 + 2 * q^36 - 4 * q^40 + 4 * q^41 + 2 * q^44 - 2 * q^45 + 2 * q^46 - 36 * q^49 + 8 * q^50 + 8 * q^51 - 2 * q^54 - 2 * q^55 - 10 * q^56 + 28 * q^59 + 4 * q^60 + 28 * q^61 - 2 * q^64 - 2 * q^66 - 2 * q^69 + 10 * q^70 + 18 * q^71 - 8 * q^74 - 8 * q^75 + 6 * q^76 - 30 * q^79 + 2 * q^80 + 2 * q^81 + 10 * q^84 + 16 * q^85 + 2 * q^86 + 2 * q^89 - 4 * q^90 + 8 * q^94 - 6 * q^95 + 2 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more