LMFDB - Embedded newform 1155.2.c.b.694.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
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			694.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.b.694.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} +1.00000 q^{11} +1.00000i q^{12} +1.00000 q^{14} +(1.00000 - 2.00000i) q^{15} -1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} +1.00000 q^{21} +1.00000i q^{22} +6.00000i q^{23} -3.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} -1.00000i q^{28} +(2.00000 + 1.00000i) q^{30} -6.00000 q^{31} +5.00000i q^{32} +1.00000i q^{33} -6.00000 q^{34} +(-1.00000 + 2.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +(3.00000 - 6.00000i) q^{40} -6.00000 q^{41} +1.00000i q^{42} -4.00000i q^{43} +1.00000 q^{44} +(2.00000 + 1.00000i) q^{45} -6.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -6.00000 q^{51} +2.00000i q^{53} +1.00000 q^{54} +(-2.00000 - 1.00000i) q^{55} +3.00000 q^{56} +(1.00000 - 2.00000i) q^{60} +2.00000 q^{61} -6.00000i q^{62} +1.00000i q^{63} -7.00000 q^{64} -1.00000 q^{66} +4.00000i q^{67} +6.00000i q^{68} -6.00000 q^{69} +(-2.00000 - 1.00000i) q^{70} +8.00000 q^{71} -3.00000i q^{72} +4.00000i q^{73} -4.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -1.00000i q^{77} -2.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} -6.00000i q^{83} +1.00000 q^{84} +(6.00000 - 12.0000i) q^{85} +4.00000 q^{86} +3.00000i q^{88} +12.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} +6.00000i q^{92} -6.00000i q^{93} -8.00000 q^{94} -5.00000 q^{96} -6.00000i q^{97} -1.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9	$ 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} - 2 q^{16} - 4 q^{20} + 2 q^{21} - 6 q^{24} + 6 q^{25} + 4 q^{30} - 12 q^{31} - 12 q^{34} - 2 q^{35} - 2 q^{36} + 6 q^{40} - 12 q^{41} + 2 q^{44} + 4 q^{45} - 12 q^{46} - 2 q^{49} - 8 q^{50} - 12 q^{51} + 2 q^{54} - 4 q^{55} + 6 q^{56} + 2 q^{60} + 4 q^{61} - 14 q^{64} - 2 q^{66} - 12 q^{69} - 4 q^{70} + 16 q^{71} - 8 q^{74} - 8 q^{75} - 4 q^{79} + 4 q^{80} + 2 q^{81} + 2 q^{84} + 12 q^{85} + 8 q^{86} + 24 q^{89} - 2 q^{90} - 16 q^{94} - 10 q^{96} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 + 2 * q^15 - 2 * q^16 - 4 * q^20 + 2 * q^21 - 6 * q^24 + 6 * q^25 + 4 * q^30 - 12 * q^31 - 12 * q^34 - 2 * q^35 - 2 * q^36 + 6 * q^40 - 12 * q^41 + 2 * q^44 + 4 * q^45 - 12 * q^46 - 2 * q^49 - 8 * q^50 - 12 * q^51 + 2 * q^54 - 4 * q^55 + 6 * q^56 + 2 * q^60 + 4 * q^61 - 14 * q^64 - 2 * q^66 - 12 * q^69 - 4 * q^70 + 16 * q^71 - 8 * q^74 - 8 * q^75 - 4 * q^79 + 4 * q^80 + 2 * q^81 + 2 * q^84 + 12 * q^85 + 8 * q^86 + 24 * q^89 - 2 * q^90 - 16 * q^94 - 10 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	−1.00000			−0.408248
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			3.00000i			1.06066i
$9$	−1.00000			−0.333333
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			1.00000i			0.288675i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	1.00000			0.267261
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	−1.00000			−0.250000
$17$			6.00000i			1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$			6.00000i			1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	1.00000			0.218218
$22$			1.00000i			0.213201i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−3.00000			−0.612372
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		−	1.00000i		−	0.188982i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	2.00000	+	1.00000i	0.365148	+	0.182574i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$			5.00000i			0.883883i
$33$			1.00000i			0.174078i
$34$	−6.00000			−1.02899
$35$	−1.00000	+	2.00000i	−0.169031	+	0.338062i
$36$	−1.00000			−0.166667
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$		0			0
$39$		0			0
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$			1.00000i			0.154303i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	1.00000			0.150756
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$	−6.00000			−0.884652
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000			−0.142857
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	−6.00000			−0.840168
$52$		0			0
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	1.00000			0.136083
$55$	−2.00000	−	1.00000i	−0.269680	−	0.134840i
$56$	3.00000			0.400892
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	1.00000	−	2.00000i	0.129099	−	0.258199i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		−	6.00000i		−	0.762001i
$63$			1.00000i			0.125988i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	−1.00000			−0.123091
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			6.00000i			0.727607i
$69$	−6.00000			−0.722315
$70$	−2.00000	−	1.00000i	−0.239046	−	0.119523i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		−	3.00000i		−	0.353553i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−4.00000			−0.464991
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$		0			0
$77$		−	1.00000i		−	0.113961i
$78$		0			0
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	1.00000			0.111111
$82$		−	6.00000i		−	0.662589i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	1.00000			0.109109
$85$	6.00000	−	12.0000i	0.650791	−	1.30158i
$86$	4.00000			0.431331
$87$		0			0
$88$			3.00000i			0.319801i
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$	−1.00000	+	2.00000i	−0.105409	+	0.210819i
$91$		0			0
$92$			6.00000i			0.625543i
$93$		−	6.00000i		−	0.622171i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	−5.00000			−0.510310
$97$		−	6.00000i		−	0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$97$		−	6.00000i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$		−	1.00000i		−	0.101015i
$99$	−1.00000			−0.100504
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	−14.0000			−1.39305			−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000			−1.39305			−0.696526	+	0.717532i	$0.745272\pi$
$102$		−	6.00000i		−	0.594089i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$		0			0
$105$	−2.00000	−	1.00000i	−0.195180	−	0.0975900i
$106$	−2.00000			−0.194257
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$	1.00000	−	2.00000i	0.0953463	−	0.190693i
$111$	−4.00000			−0.379663
$112$			1.00000i			0.0944911i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	6.00000	−	12.0000i	0.559503	−	1.11901i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.00000			0.550019
$120$	6.00000	+	3.00000i	0.547723	+	0.273861i
$121$	1.00000			0.0909091
$122$			2.00000i			0.181071i
$123$		−	6.00000i		−	0.541002i
$124$	−6.00000			−0.538816
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	−1.00000			−0.0890871
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$			3.00000i			0.265165i
$129$	4.00000			0.352180
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$			1.00000i			0.0870388i
$133$		0			0
$134$	−4.00000			−0.345547
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$	−18.0000			−1.54349
$137$		−	14.0000i		−	1.19610i	−0.801459	−	0.598050i	$-0.795942\pi$
$137$		−	14.0000i		−	1.19610i	0.801459	−	0.598050i	$-0.204058\pi$
$138$		−	6.00000i		−	0.510754i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−1.00000	+	2.00000i	−0.0845154	+	0.169031i
$141$	−8.00000			−0.673722
$142$			8.00000i			0.671345i
$143$		0			0
$144$	1.00000			0.0833333
$145$		0			0
$146$	−4.00000			−0.331042
$147$		−	1.00000i		−	0.0824786i
$148$			4.00000i			0.328798i
$149$	−8.00000			−0.655386			−0.327693	−	0.944784i	$-0.606271\pi$
$149$	−8.00000			−0.655386			−0.327693	+	0.944784i	$0.606271\pi$
$150$	−3.00000	−	4.00000i	−0.244949	−	0.326599i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$		−	6.00000i		−	0.485071i
$154$	1.00000			0.0805823
$155$	12.0000	+	6.00000i	0.963863	+	0.481932i
$156$		0			0
$157$		−	14.0000i		−	1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$		−	14.0000i		−	1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$		−	2.00000i		−	0.159111i
$159$	−2.00000			−0.158610
$160$	5.00000	−	10.0000i	0.395285	−	0.790569i
$161$	6.00000			0.472866
$162$			1.00000i			0.0785674i
$163$			24.0000i			1.87983i	0.341415	+	0.939913i	$0.389094\pi$
$163$			24.0000i			1.87983i	−0.341415	+	0.939913i	$0.610906\pi$
$164$	−6.00000			−0.468521
$165$	1.00000	−	2.00000i	0.0778499	−	0.155700i
$166$	6.00000			0.465690
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$			3.00000i			0.231455i
$169$	13.0000			1.00000
$170$	12.0000	+	6.00000i	0.920358	+	0.460179i
$171$		0			0
$172$		−	4.00000i		−	0.304997i
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$		0			0
$175$	4.00000	−	3.00000i	0.302372	−	0.226779i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$			12.0000i			0.899438i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$	−18.0000			−1.32698
$185$	4.00000	−	8.00000i	0.294086	−	0.588172i
$186$	6.00000			0.439941
$187$			6.00000i			0.438763i
$188$			8.00000i			0.583460i
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$		−	7.00000i		−	0.505181i
$193$			2.00000i			0.143963i	0.997406	+	0.0719816i	$0.0229323\pi$
$193$			2.00000i			0.143963i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	−1.00000			−0.0714286
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		−	1.00000i		−	0.0710669i
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	−12.0000	+	9.00000i	−0.848528	+	0.636396i
$201$	−4.00000			−0.282138
$202$		−	14.0000i		−	0.985037i
$203$		0			0
$204$	−6.00000			−0.420084
$205$	12.0000	+	6.00000i	0.838116	+	0.419058i
$206$	8.00000			0.557386
$207$		−	6.00000i		−	0.417029i
$208$		0			0
$209$		0			0
$210$	1.00000	−	2.00000i	0.0690066	−	0.138013i
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$			2.00000i			0.137361i
$213$			8.00000i			0.548151i
$214$		0			0
$215$	−4.00000	+	8.00000i	−0.272798	+	0.545595i
$216$	3.00000			0.204124
$217$			6.00000i			0.407307i
$218$			18.0000i			1.21911i
$219$	−4.00000			−0.270295
$220$	−2.00000	−	1.00000i	−0.134840	−	0.0674200i
$221$		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
$226$	−6.00000			−0.399114
$227$			22.0000i			1.46019i	0.683345	+	0.730096i	$0.260525\pi$
$227$			22.0000i			1.46019i	−0.683345	+	0.730096i	$0.739475\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	12.0000	+	6.00000i	0.791257	+	0.395628i
$231$	1.00000			0.0657952
$232$		0			0
$233$			26.0000i			1.70332i	0.524097	+	0.851658i	$0.324403\pi$
$233$			26.0000i			1.70332i	−0.524097	+	0.851658i	$0.675597\pi$
$234$		0			0
$235$	8.00000	−	16.0000i	0.521862	−	1.04372i
$236$		0			0
$237$		−	2.00000i		−	0.129914i
$238$			6.00000i			0.388922i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	−1.00000	+	2.00000i	−0.0645497	+	0.129099i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$			1.00000i			0.0642824i
$243$			1.00000i			0.0641500i
$244$	2.00000			0.128037
$245$	2.00000	+	1.00000i	0.127775	+	0.0638877i
$246$	6.00000			0.382546
$247$		0			0
$248$		−	18.0000i		−	1.14300i
$249$	6.00000			0.380235
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$			1.00000i			0.0629941i
$253$			6.00000i			0.377217i
$254$		0			0
$255$	12.0000	+	6.00000i	0.751469	+	0.375735i
$256$	−17.0000			−1.06250
$257$			14.0000i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$257$			14.0000i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$258$			4.00000i			0.249029i
$259$	4.00000			0.248548
$260$		0			0
$261$		0			0
$262$		−	12.0000i		−	0.741362i
$263$		−	28.0000i		−	1.72655i	−0.504730	−	0.863277i	$-0.668408\pi$
$263$		−	28.0000i		−	1.72655i	0.504730	−	0.863277i	$-0.331592\pi$
$264$	−3.00000			−0.184637
$265$	2.00000	−	4.00000i	0.122859	−	0.245718i
$266$		0			0
$267$			12.0000i			0.734388i
$268$			4.00000i			0.244339i
$269$	24.0000			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$270$	−2.00000	−	1.00000i	−0.121716	−	0.0608581i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$		−	6.00000i		−	0.363803i
$273$		0			0
$274$	14.0000			0.845771
$275$	3.00000	+	4.00000i	0.180907	+	0.241209i
$276$	−6.00000			−0.361158
$277$		−	10.0000i		−	0.600842i	−0.953807	−	0.300421i	$-0.902873\pi$
$277$		−	10.0000i		−	0.600842i	0.953807	−	0.300421i	$-0.0971271\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$	−6.00000	−	3.00000i	−0.358569	−	0.179284i
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		−	8.00000i		−	0.476393i
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	8.00000			0.474713
$285$		0			0
$286$		0			0
$287$			6.00000i			0.354169i
$288$		−	5.00000i		−	0.294628i
$289$	−19.0000			−1.11765
$290$		0			0
$291$	6.00000			0.351726
$292$			4.00000i			0.234082i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	1.00000			0.0583212
$295$		0			0
$296$	−12.0000			−0.697486
$297$		−	1.00000i		−	0.0580259i
$298$		−	8.00000i		−	0.463428i
$299$		0			0
$300$	−4.00000	+	3.00000i	−0.230940	+	0.173205i
$301$	−4.00000			−0.230556
$302$			10.0000i			0.575435i
$303$		−	14.0000i		−	0.804279i
$304$		0			0
$305$	−4.00000	−	2.00000i	−0.229039	−	0.114520i
$306$	6.00000			0.342997
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$		−	1.00000i		−	0.0569803i
$309$	8.00000			0.455104
$310$	−6.00000	+	12.0000i	−0.340777	+	0.681554i
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$		0			0
$313$		−	2.00000i		−	0.113047i	−0.998401	−	0.0565233i	$-0.981998\pi$
$313$		−	2.00000i		−	0.113047i	0.998401	−	0.0565233i	$-0.0180015\pi$
$314$	14.0000			0.790066
$315$	1.00000	−	2.00000i	0.0563436	−	0.112687i
$316$	−2.00000			−0.112509
$317$		−	34.0000i		−	1.90963i	−0.297200	−	0.954815i	$-0.596053\pi$
$317$		−	34.0000i		−	1.90963i	0.297200	−	0.954815i	$-0.403947\pi$
$318$		−	2.00000i		−	0.112154i
$319$		0			0
$320$	14.0000	+	7.00000i	0.782624	+	0.391312i
$321$		0			0
$322$			6.00000i			0.334367i
$323$		0			0
$324$	1.00000			0.0555556
$325$		0			0
$326$	−24.0000			−1.32924
$327$			18.0000i			0.995402i
$328$		−	18.0000i		−	0.993884i
$329$	8.00000			0.441054
$330$	2.00000	+	1.00000i	0.110096	+	0.0550482i
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$		−	6.00000i		−	0.329293i
$333$		−	4.00000i		−	0.219199i
$334$	−2.00000			−0.109435
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$	−1.00000			−0.0545545
$337$			18.0000i			0.980522i	0.871576	+	0.490261i	$0.163099\pi$
$337$			18.0000i			0.980522i	−0.871576	+	0.490261i	$0.836901\pi$
$338$			13.0000i			0.707107i
$339$	−6.00000			−0.325875
$340$	6.00000	−	12.0000i	0.325396	−	0.650791i
$341$	−6.00000			−0.324918
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	12.0000			0.646997
$345$	12.0000	+	6.00000i	0.646058	+	0.323029i
$346$	−6.00000			−0.322562
$347$			16.0000i			0.858925i	0.903085	+	0.429463i	$0.141297\pi$
$347$			16.0000i			0.858925i	−0.903085	+	0.429463i	$0.858703\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	3.00000	+	4.00000i	0.160357	+	0.213809i
$351$		0			0
$352$			5.00000i			0.266501i
$353$		−	10.0000i		−	0.532246i	−0.963939	−	0.266123i	$-0.914257\pi$
$353$		−	10.0000i		−	0.532246i	0.963939	−	0.266123i	$-0.0857428\pi$
$354$		0			0
$355$	−16.0000	−	8.00000i	−0.849192	−	0.424596i
$356$	12.0000			0.635999
$357$			6.00000i			0.317554i
$358$			12.0000i			0.634220i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$	−3.00000	+	6.00000i	−0.158114	+	0.316228i
$361$	−19.0000			−1.00000
$362$		−	2.00000i		−	0.105118i
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	4.00000	−	8.00000i	0.209370	−	0.418739i
$366$	−2.00000			−0.104542
$367$			16.0000i			0.835193i	0.908633	+	0.417597i	$0.137127\pi$
$367$			16.0000i			0.835193i	−0.908633	+	0.417597i	$0.862873\pi$
$368$		−	6.00000i		−	0.312772i
$369$	6.00000			0.312348
$370$	8.00000	+	4.00000i	0.415900	+	0.207950i
$371$	2.00000			0.103835
$372$		−	6.00000i		−	0.311086i
$373$		−	2.00000i		−	0.103556i	−0.998659	−	0.0517780i	$-0.983511\pi$
$373$		−	2.00000i		−	0.103556i	0.998659	−	0.0517780i	$-0.0164888\pi$
$374$	−6.00000			−0.310253
$375$	11.0000	−	2.00000i	0.568038	−	0.103280i
$376$	−24.0000			−1.23771
$377$		0			0
$378$		−	1.00000i		−	0.0514344i
$379$	24.0000			1.23280			0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000			1.23280			0.616399	+	0.787434i	$0.288591\pi$
$380$		0			0
$381$		0			0
$382$		−	16.0000i		−	0.818631i
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$	−3.00000			−0.153093
$385$	−1.00000	+	2.00000i	−0.0509647	+	0.101929i
$386$	−2.00000			−0.101797
$387$			4.00000i			0.203331i
$388$		−	6.00000i		−	0.304604i
$389$	−14.0000			−0.709828			−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000			−0.709828			−0.354914	+	0.934899i	$0.615490\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$		−	3.00000i		−	0.151523i
$393$		−	12.0000i		−	0.605320i
$394$	18.0000			0.906827
$395$	4.00000	+	2.00000i	0.201262	+	0.100631i
$396$	−1.00000			−0.0502519
$397$			14.0000i			0.702640i	0.936255	+	0.351320i	$0.114267\pi$
$397$			14.0000i			0.702640i	−0.936255	+	0.351320i	$0.885733\pi$
$398$			14.0000i			0.701757i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	34.0000			1.69788			0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000			1.69788			0.848939	+	0.528490i	$0.177242\pi$
$402$		−	4.00000i		−	0.199502i
$403$		0			0
$404$	−14.0000			−0.696526
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$		0			0
$407$			4.00000i			0.198273i
$408$		−	18.0000i		−	0.891133i
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$	−6.00000	+	12.0000i	−0.296319	+	0.592638i
$411$	14.0000			0.690569
$412$		−	8.00000i		−	0.394132i
$413$		0			0
$414$	6.00000			0.294884
$415$	−6.00000	+	12.0000i	−0.294528	+	0.589057i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	36.0000			1.75872			0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000			1.75872			0.879358	+	0.476162i	$0.157972\pi$
$420$	−2.00000	−	1.00000i	−0.0975900	−	0.0487950i
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$			2.00000i			0.0973585i
$423$		−	8.00000i		−	0.388973i
$424$	−6.00000			−0.291386
$425$	−24.0000	+	18.0000i	−1.16417	+	0.873128i
$426$	−8.00000			−0.387601
$427$		−	2.00000i		−	0.0967868i
$428$		0			0
$429$		0			0
$430$	−8.00000	−	4.00000i	−0.385794	−	0.192897i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$			1.00000i			0.0481125i
$433$			34.0000i			1.63394i	0.576683	+	0.816968i	$0.304347\pi$
$433$			34.0000i			1.63394i	−0.576683	+	0.816968i	$0.695653\pi$
$434$	−6.00000			−0.288009
$435$		0			0
$436$	18.0000			0.862044
$437$		0			0
$438$		−	4.00000i		−	0.191127i
$439$	−28.0000			−1.33637			−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000			−1.33637			−0.668184	+	0.743996i	$0.732928\pi$
$440$	3.00000	−	6.00000i	0.143019	−	0.286039i
$441$	1.00000			0.0476190
$442$		0			0
$443$		−	22.0000i		−	1.04525i	−0.852562	−	0.522626i	$-0.824953\pi$
$443$		−	22.0000i		−	1.04525i	0.852562	−	0.522626i	$-0.175047\pi$
$444$	−4.00000			−0.189832
$445$	−24.0000	−	12.0000i	−1.13771	−	0.568855i
$446$	8.00000			0.378811
$447$		−	8.00000i		−	0.378387i
$448$			7.00000i			0.330719i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	−6.00000			−0.282529
$452$			6.00000i			0.282216i
$453$			10.0000i			0.469841i
$454$	−22.0000			−1.03251
$455$		0			0
$456$		0			0
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$			22.0000i			1.02799i
$459$	6.00000			0.280056
$460$	6.00000	−	12.0000i	0.279751	−	0.559503i
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$			1.00000i			0.0465242i
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$		0			0
$465$	−6.00000	+	12.0000i	−0.278243	+	0.556487i
$466$	−26.0000			−1.20443
$467$			36.0000i			1.66588i	0.553362	+	0.832941i	$0.313345\pi$
$467$			36.0000i			1.66588i	−0.553362	+	0.832941i	$0.686655\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$	16.0000	+	8.00000i	0.738025	+	0.369012i
$471$	14.0000			0.645086
$472$		0			0
$473$		−	4.00000i		−	0.183920i
$474$	2.00000			0.0918630
$475$		0			0
$476$	6.00000			0.275010
$477$		−	2.00000i		−	0.0915737i
$478$			24.0000i			1.09773i
$479$	16.0000			0.731059			0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000			0.731059			0.365529	+	0.930800i	$0.380888\pi$
$480$	10.0000	+	5.00000i	0.456435	+	0.228218i
$481$		0			0
$482$		−	14.0000i		−	0.637683i
$483$			6.00000i			0.273009i
$484$	1.00000			0.0454545
$485$	−6.00000	+	12.0000i	−0.272446	+	0.544892i
$486$	−1.00000			−0.0453609
$487$		−	4.00000i		−	0.181257i	−0.995885	−	0.0906287i	$-0.971112\pi$
$487$		−	4.00000i		−	0.181257i	0.995885	−	0.0906287i	$-0.0288876\pi$
$488$			6.00000i			0.271607i
$489$	−24.0000			−1.08532
$490$	−1.00000	+	2.00000i	−0.0451754	+	0.0903508i
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		−	6.00000i		−	0.270501i
$493$		0			0
$494$		0			0
$495$	2.00000	+	1.00000i	0.0898933	+	0.0449467i
$496$	6.00000			0.269408
$497$		−	8.00000i		−	0.358849i
$498$			6.00000i			0.268866i
$499$	12.0000			0.537194			0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000			0.537194			0.268597	+	0.963253i	$0.413440\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	−2.00000			−0.0893534
$502$			12.0000i			0.535586i
$503$		−	30.0000i		−	1.33763i	−0.743427	−	0.668817i	$-0.766801\pi$
$503$		−	30.0000i		−	1.33763i	0.743427	−	0.668817i	$-0.233199\pi$
$504$	−3.00000			−0.133631
$505$	28.0000	+	14.0000i	1.24598	+	0.622992i
$506$	−6.00000			−0.266733
$507$			13.0000i			0.577350i
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$	−6.00000	+	12.0000i	−0.265684	+	0.531369i
$511$	4.00000			0.176950
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$	−14.0000			−0.617514
$515$	−8.00000	+	16.0000i	−0.352522	+	0.705044i
$516$	4.00000			0.176090
$517$			8.00000i			0.351840i
$518$			4.00000i			0.175750i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−36.0000			−1.57719			−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000			−1.57719			−0.788594	+	0.614914i	$0.789191\pi$
$522$		0			0
$523$			8.00000i			0.349816i	0.984585	+	0.174908i	$0.0559627\pi$
$523$			8.00000i			0.349816i	−0.984585	+	0.174908i	$0.944037\pi$
$524$	−12.0000			−0.524222
$525$	3.00000	+	4.00000i	0.130931	+	0.174574i
$526$	28.0000			1.22086
$527$		−	36.0000i		−	1.56818i
$528$		−	1.00000i		−	0.0435194i
$529$	−13.0000			−0.565217
$530$	4.00000	+	2.00000i	0.173749	+	0.0868744i
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−12.0000			−0.519291
$535$		0			0
$536$	−12.0000			−0.518321
$537$			12.0000i			0.517838i
$538$			24.0000i			1.03471i
$539$	−1.00000			−0.0430730
$540$	−1.00000	+	2.00000i	−0.0430331	+	0.0860663i
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$			16.0000i			0.687259i
$543$		−	2.00000i		−	0.0858282i
$544$	−30.0000			−1.28624
$545$	−36.0000	−	18.0000i	−1.54207	−	0.771035i
$546$		0			0
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$		−	14.0000i		−	0.598050i
$549$	−2.00000			−0.0853579
$550$	−4.00000	+	3.00000i	−0.170561	+	0.127920i
$551$		0			0
$552$		−	18.0000i		−	0.766131i
$553$			2.00000i			0.0850487i
$554$	10.0000			0.424859
$555$	8.00000	+	4.00000i	0.339581	+	0.169791i
$556$		0			0
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$			6.00000i			0.254000i
$559$		0			0
$560$	1.00000	−	2.00000i	0.0422577	−	0.0845154i
$561$	−6.00000			−0.253320
$562$		−	24.0000i		−	1.01238i
$563$		−	6.00000i		−	0.252870i	−0.991975	−	0.126435i	$-0.959647\pi$
$563$		−	6.00000i		−	0.252870i	0.991975	−	0.126435i	$-0.0403535\pi$
$564$	−8.00000			−0.336861
$565$	6.00000	−	12.0000i	0.252422	−	0.504844i
$566$	−4.00000			−0.168133
$567$		−	1.00000i		−	0.0419961i
$568$			24.0000i			1.00702i
$569$	−28.0000			−1.17382			−0.586911	−	0.809652i	$-0.699656\pi$
$569$	−28.0000			−1.17382			−0.586911	+	0.809652i	$0.699656\pi$
$570$		0			0
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$		0			0
$573$		−	16.0000i		−	0.668410i
$574$	−6.00000			−0.250435
$575$	−24.0000	+	18.0000i	−1.00087	+	0.750652i
$576$	7.00000			0.291667
$577$		−	2.00000i		−	0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$		−	2.00000i		−	0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$		−	19.0000i		−	0.790296i
$579$	−2.00000			−0.0831172
$580$		0			0
$581$	−6.00000			−0.248922
$582$			6.00000i			0.248708i
$583$			2.00000i			0.0828315i
$584$	−12.0000			−0.496564
$585$		0			0
$586$	26.0000			1.07405
$587$		−	24.0000i		−	0.990586i	−0.868726	−	0.495293i	$-0.835061\pi$
$587$		−	24.0000i		−	0.990586i	0.868726	−	0.495293i	$-0.164939\pi$
$588$		−	1.00000i		−	0.0412393i
$589$		0			0
$590$		0			0
$591$	18.0000			0.740421
$592$		−	4.00000i		−	0.164399i
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$	1.00000			0.0410305
$595$	−12.0000	−	6.00000i	−0.491952	−	0.245976i
$596$	−8.00000			−0.327693
$597$			14.0000i			0.572982i
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	−9.00000	−	12.0000i	−0.367423	−	0.489898i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		−	4.00000i		−	0.163028i
$603$		−	4.00000i		−	0.162893i
$604$	10.0000			0.406894
$605$	−2.00000	−	1.00000i	−0.0813116	−	0.0406558i
$606$	14.0000			0.568711
$607$		−	40.0000i		−	1.62355i	−0.583970	−	0.811775i	$-0.698502\pi$
$607$		−	40.0000i		−	1.62355i	0.583970	−	0.811775i	$-0.301498\pi$
$608$		0			0
$609$		0			0
$610$	2.00000	−	4.00000i	0.0809776	−	0.161955i
$611$		0			0
$612$		−	6.00000i		−	0.242536i
$613$		−	38.0000i		−	1.53481i	−0.641165	−	0.767403i	$-0.721549\pi$
$613$		−	38.0000i		−	1.53481i	0.641165	−	0.767403i	$-0.278451\pi$
$614$	20.0000			0.807134
$615$	−6.00000	+	12.0000i	−0.241943	+	0.483887i
$616$	3.00000			0.120873
$617$		−	18.0000i		−	0.724653i	−0.932051	−	0.362326i	$-0.881983\pi$
$617$		−	18.0000i		−	0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$			8.00000i			0.321807i
$619$	−18.0000			−0.723481			−0.361741	−	0.932279i	$-0.617817\pi$
$619$	−18.0000			−0.723481			−0.361741	+	0.932279i	$0.617817\pi$
$620$	12.0000	+	6.00000i	0.481932	+	0.240966i
$621$	6.00000			0.240772
$622$			16.0000i			0.641542i
$623$		−	12.0000i		−	0.480770i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	2.00000			0.0799361
$627$		0			0
$628$		−	14.0000i		−	0.558661i
$629$	−24.0000			−0.956943
$630$	2.00000	+	1.00000i	0.0796819	+	0.0398410i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	6.00000i		−	0.238667i
$633$			2.00000i			0.0794929i
$634$	34.0000			1.35031
$635$		0			0
$636$	−2.00000			−0.0793052
$637$		0			0
$638$		0			0
$639$	−8.00000			−0.316475
$640$	3.00000	−	6.00000i	0.118585	−	0.237171i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		0			0
$643$			12.0000i			0.473234i	0.971603	+	0.236617i	$0.0760386\pi$
$643$			12.0000i			0.473234i	−0.971603	+	0.236617i	$0.923961\pi$
$644$	6.00000			0.236433
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$		0			0
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$			3.00000i			0.117851i
$649$		0			0
$650$		0			0
$651$	−6.00000			−0.235159
$652$			24.0000i			0.939913i
$653$		−	6.00000i		−	0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$		−	6.00000i		−	0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	−18.0000			−0.703856
$655$	24.0000	+	12.0000i	0.937758	+	0.468879i
$656$	6.00000			0.234261
$657$		−	4.00000i		−	0.156055i
$658$			8.00000i			0.311872i
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$	1.00000	−	2.00000i	0.0389249	−	0.0778499i
$661$	46.0000			1.78919			0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000			1.78919			0.894596	+	0.446875i	$0.147463\pi$
$662$			32.0000i			1.24372i
$663$		0			0
$664$	18.0000			0.698535
$665$		0			0
$666$	4.00000			0.154997
$667$		0			0
$668$			2.00000i			0.0773823i
$669$	8.00000			0.309298
$670$	8.00000	+	4.00000i	0.309067	+	0.154533i
$671$	2.00000			0.0772091
$672$			5.00000i			0.192879i
$673$			46.0000i			1.77317i	0.462566	+	0.886585i	$0.346929\pi$
$673$			46.0000i			1.77317i	−0.462566	+	0.886585i	$0.653071\pi$
$674$	−18.0000			−0.693334
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	13.0000			0.500000
$677$			30.0000i			1.15299i	0.817099	+	0.576497i	$0.195581\pi$
$677$			30.0000i			1.15299i	−0.817099	+	0.576497i	$0.804419\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−6.00000			−0.230259
$680$	36.0000	+	18.0000i	1.38054	+	0.690268i
$681$	−22.0000			−0.843042
$682$		−	6.00000i		−	0.229752i
$683$			10.0000i			0.382639i	0.981528	+	0.191320i	$0.0612767\pi$
$683$			10.0000i			0.382639i	−0.981528	+	0.191320i	$0.938723\pi$
$684$		0			0
$685$	−14.0000	+	28.0000i	−0.534913	+	1.06983i
$686$	−1.00000			−0.0381802
$687$			22.0000i			0.839352i
$688$			4.00000i			0.152499i
$689$		0			0
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	34.0000			1.29342			0.646710	−	0.762736i	$-0.276144\pi$
$691$	34.0000			1.29342			0.646710	+	0.762736i	$0.276144\pi$
$692$			6.00000i			0.228086i
$693$			1.00000i			0.0379869i
$694$	−16.0000			−0.607352
$695$		0			0
$696$		0			0
$697$		−	36.0000i		−	1.36360i
$698$		−	14.0000i		−	0.529908i
$699$	−26.0000			−0.983410
$700$	4.00000	−	3.00000i	0.151186	−	0.113389i
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$		0			0
$703$		0			0
$704$	−7.00000			−0.263822
$705$	16.0000	+	8.00000i	0.602595	+	0.301297i
$706$	10.0000			0.376355
$707$			14.0000i			0.526524i
$708$		0			0
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	8.00000	−	16.0000i	0.300235	−	0.600469i
$711$	2.00000			0.0750059
$712$			36.0000i			1.34916i
$713$		−	36.0000i		−	1.34821i
$714$	−6.00000			−0.224544
$715$		0			0
$716$	12.0000			0.448461
$717$			24.0000i			0.896296i
$718$			12.0000i			0.447836i
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	−8.00000			−0.297936
$722$		−	19.0000i		−	0.707107i
$723$		−	14.0000i		−	0.520666i
$724$	−2.00000			−0.0743294
$725$		0			0
$726$	−1.00000			−0.0371135
$727$		−	16.0000i		−	0.593407i	−0.954970	−	0.296704i	$-0.904113\pi$
$727$		−	16.0000i		−	0.593407i	0.954970	−	0.296704i	$-0.0958873\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	8.00000	+	4.00000i	0.296093	+	0.148047i
$731$	24.0000			0.887672
$732$			2.00000i			0.0739221i
$733$			20.0000i			0.738717i	0.929287	+	0.369358i	$0.120423\pi$
$733$			20.0000i			0.738717i	−0.929287	+	0.369358i	$0.879577\pi$
$734$	−16.0000			−0.590571
$735$	−1.00000	+	2.00000i	−0.0368856	+	0.0737711i
$736$	−30.0000			−1.10581
$737$			4.00000i			0.147342i
$738$			6.00000i			0.220863i
$739$	14.0000			0.514998			0.257499	−	0.966279i	$-0.417102\pi$
$739$	14.0000			0.514998			0.257499	+	0.966279i	$0.417102\pi$
$740$	4.00000	−	8.00000i	0.147043	−	0.294086i
$741$		0			0
$742$			2.00000i			0.0734223i
$743$		−	36.0000i		−	1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$		−	36.0000i		−	1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$	18.0000			0.659912
$745$	16.0000	+	8.00000i	0.586195	+	0.293097i
$746$	2.00000			0.0732252
$747$			6.00000i			0.219529i
$748$			6.00000i			0.219382i
$749$		0			0
$750$	2.00000	+	11.0000i	0.0730297	+	0.401663i
$751$	−20.0000			−0.729810			−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000			−0.729810			−0.364905	+	0.931045i	$0.618899\pi$
$752$		−	8.00000i		−	0.291730i
$753$			12.0000i			0.437304i
$754$		0			0
$755$	−20.0000	−	10.0000i	−0.727875	−	0.363937i
$756$	−1.00000			−0.0363696
$757$			12.0000i			0.436147i	0.975932	+	0.218074i	$0.0699773\pi$
$757$			12.0000i			0.436147i	−0.975932	+	0.218074i	$0.930023\pi$
$758$			24.0000i			0.871719i
$759$	−6.00000			−0.217786
$760$		0			0
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$		0			0
$763$		−	18.0000i		−	0.651644i
$764$	−16.0000			−0.578860
$765$	−6.00000	+	12.0000i	−0.216930	+	0.433861i
$766$	24.0000			0.867155
$767$		0			0
$768$		−	17.0000i		−	0.613435i
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$	−2.00000	−	1.00000i	−0.0720750	−	0.0360375i
$771$	−14.0000			−0.504198
$772$			2.00000i			0.0719816i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$	−4.00000			−0.143777
$775$	−18.0000	−	24.0000i	−0.646579	−	0.862105i
$776$	18.0000			0.646162
$777$			4.00000i			0.143499i
$778$		−	14.0000i		−	0.501924i
$779$		0			0
$780$		0			0
$781$	8.00000			0.286263
$782$		−	36.0000i		−	1.28736i
$783$		0			0
$784$	1.00000			0.0357143
$785$	−14.0000	+	28.0000i	−0.499681	+	0.999363i
$786$	12.0000			0.428026
$787$			20.0000i			0.712923i	0.934310	+	0.356462i	$0.116017\pi$
$787$			20.0000i			0.712923i	−0.934310	+	0.356462i	$0.883983\pi$
$788$		−	18.0000i		−	0.641223i
$789$	28.0000			0.996826
$790$	−2.00000	+	4.00000i	−0.0711568	+	0.142314i
$791$	6.00000			0.213335
$792$		−	3.00000i		−	0.106600i
$793$		0			0
$794$	−14.0000			−0.496841
$795$	4.00000	+	2.00000i	0.141865	+	0.0709327i
$796$	14.0000			0.496217
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$	−48.0000			−1.69812
$800$	−20.0000	+	15.0000i	−0.707107	+	0.530330i
$801$	−12.0000			−0.423999
$802$			34.0000i			1.20058i
$803$			4.00000i			0.141157i
$804$	−4.00000			−0.141069
$805$	−12.0000	−	6.00000i	−0.422944	−	0.211472i
$806$		0			0
$807$			24.0000i			0.844840i
$808$		−	42.0000i		−	1.47755i
$809$	−40.0000			−1.40633			−0.703163	−	0.711029i	$-0.748229\pi$
$809$	−40.0000			−1.40633			−0.703163	+	0.711029i	$0.748229\pi$
$810$	1.00000	−	2.00000i	0.0351364	−	0.0702728i
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$			16.0000i			0.561144i
$814$	−4.00000			−0.140200
$815$	24.0000	−	48.0000i	0.840683	−	1.68137i
$816$	6.00000			0.210042
$817$		0			0
$818$		−	26.0000i		−	0.909069i
$819$		0			0
$820$	12.0000	+	6.00000i	0.419058	+	0.209529i
$821$	−28.0000			−0.977207			−0.488603	−	0.872506i	$-0.662493\pi$
$821$	−28.0000			−0.977207			−0.488603	+	0.872506i	$0.662493\pi$
$822$			14.0000i			0.488306i
$823$			16.0000i			0.557725i	0.960331	+	0.278862i	$0.0899574\pi$
$823$			16.0000i			0.557725i	−0.960331	+	0.278862i	$0.910043\pi$
$824$	24.0000			0.836080
$825$	−4.00000	+	3.00000i	−0.139262	+	0.104447i
$826$		0			0
$827$		−	24.0000i		−	0.834562i	−0.908778	−	0.417281i	$-0.862983\pi$
$827$		−	24.0000i		−	0.834562i	0.908778	−	0.417281i	$-0.137017\pi$
$828$		−	6.00000i		−	0.208514i
$829$	18.0000			0.625166			0.312583	−	0.949890i	$-0.398806\pi$
$829$	18.0000			0.625166			0.312583	+	0.949890i	$0.398806\pi$
$830$	−12.0000	−	6.00000i	−0.416526	−	0.208263i
$831$	10.0000			0.346896
$832$		0			0
$833$		−	6.00000i		−	0.207888i
$834$		0			0
$835$	2.00000	−	4.00000i	0.0692129	−	0.138426i
$836$		0			0
$837$			6.00000i			0.207390i
$838$			36.0000i			1.24360i
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$	3.00000	−	6.00000i	0.103510	−	0.207020i
$841$	−29.0000			−1.00000
$842$		−	22.0000i		−	0.758170i
$843$		−	24.0000i		−	0.826604i
$844$	2.00000			0.0688428
$845$	−26.0000	−	13.0000i	−0.894427	−	0.447214i
$846$	8.00000			0.275046
$847$		−	1.00000i		−	0.0343604i
$848$		−	2.00000i		−	0.0686803i
$849$	−4.00000			−0.137280
$850$	−18.0000	−	24.0000i	−0.617395	−	0.823193i
$851$	−24.0000			−0.822709
$852$			8.00000i			0.274075i
$853$			44.0000i			1.50653i	0.657716	+	0.753266i	$0.271523\pi$
$853$			44.0000i			1.50653i	−0.657716	+	0.753266i	$0.728477\pi$
$854$	2.00000			0.0684386
$855$		0			0
$856$		0			0
$857$		−	10.0000i		−	0.341593i	−0.985306	−	0.170797i	$-0.945366\pi$
$857$		−	10.0000i		−	0.341593i	0.985306	−	0.170797i	$-0.0546341\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$	−6.00000			−0.204479
$862$		−	24.0000i		−	0.817443i
$863$			42.0000i			1.42970i	0.699280	+	0.714848i	$0.253504\pi$
$863$			42.0000i			1.42970i	−0.699280	+	0.714848i	$0.746496\pi$
$864$	5.00000			0.170103
$865$	6.00000	−	12.0000i	0.204006	−	0.408012i
$866$	−34.0000			−1.15537
$867$		−	19.0000i		−	0.645274i
$868$			6.00000i			0.203653i
$869$	−2.00000			−0.0678454
$870$		0			0
$871$		0			0
$872$			54.0000i			1.82867i
$873$			6.00000i			0.203069i
$874$		0			0
$875$	−11.0000	+	2.00000i	−0.371868	+	0.0676123i
$876$	−4.00000			−0.135147
$877$		−	26.0000i		−	0.877958i	−0.898497	−	0.438979i	$-0.855340\pi$
$877$		−	26.0000i		−	0.877958i	0.898497	−	0.438979i	$-0.144660\pi$
$878$		−	28.0000i		−	0.944954i
$879$	26.0000			0.876958
$880$	2.00000	+	1.00000i	0.0674200	+	0.0337100i
$881$	52.0000			1.75192			0.875962	−	0.482380i	$-0.160227\pi$
$881$	52.0000			1.75192			0.875962	+	0.482380i	$0.160227\pi$
$882$			1.00000i			0.0336718i
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$		0			0
$885$		0			0
$886$	22.0000			0.739104
$887$			26.0000i			0.872995i	0.899706	+	0.436497i	$0.143781\pi$
$887$			26.0000i			0.872995i	−0.899706	+	0.436497i	$0.856219\pi$
$888$		−	12.0000i		−	0.402694i
$889$		0			0
$890$	12.0000	−	24.0000i	0.402241	−	0.804482i
$891$	1.00000			0.0335013
$892$		−	8.00000i		−	0.267860i
$893$		0			0
$894$	8.00000			0.267560
$895$	−24.0000	−	12.0000i	−0.802232	−	0.401116i
$896$	3.00000			0.100223
$897$		0			0
$898$			6.00000i			0.200223i
$899$		0			0
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$	−12.0000			−0.399778
$902$		−	6.00000i		−	0.199778i
$903$		−	4.00000i		−	0.133112i
$904$	−18.0000			−0.598671
$905$	4.00000	+	2.00000i	0.132964	+	0.0664822i
$906$	−10.0000			−0.332228
$907$		−	20.0000i		−	0.664089i	−0.943264	−	0.332045i	$-0.892262\pi$
$907$		−	20.0000i		−	0.664089i	0.943264	−	0.332045i	$-0.107738\pi$
$908$			22.0000i			0.730096i
$909$	14.0000			0.464351
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$		−	6.00000i		−	0.198571i
$914$	−10.0000			−0.330771
$915$	2.00000	−	4.00000i	0.0661180	−	0.132236i
$916$	22.0000			0.726900
$917$			12.0000i			0.396275i
$918$			6.00000i			0.198030i
$919$	34.0000			1.12156			0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000			1.12156			0.560778	+	0.827966i	$0.310502\pi$
$920$	36.0000	+	18.0000i	1.18688	+	0.593442i
$921$	20.0000			0.659022
$922$		−	2.00000i		−	0.0658665i
$923$		0			0
$924$	1.00000			0.0328976
$925$	−16.0000	+	12.0000i	−0.526077	+	0.394558i
$926$	4.00000			0.131448
$927$			8.00000i			0.262754i
$928$		0			0
$929$	−56.0000			−1.83730			−0.918650	−	0.395072i	$-0.870720\pi$
$929$	−56.0000			−1.83730			−0.918650	+	0.395072i	$0.870720\pi$
$930$	−12.0000	−	6.00000i	−0.393496	−	0.196748i
$931$		0			0
$932$			26.0000i			0.851658i
$933$			16.0000i			0.523816i
$934$	−36.0000			−1.17796
$935$	6.00000	−	12.0000i	0.196221	−	0.392442i
$936$		0			0
$937$		−	8.00000i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$937$		−	8.00000i		−	0.261349i	0.991425	−	0.130674i	$-0.0417142\pi$
$938$			4.00000i			0.130605i
$939$	2.00000			0.0652675
$940$	8.00000	−	16.0000i	0.260931	−	0.521862i
$941$	38.0000			1.23876			0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000			1.23876			0.619382	+	0.785090i	$0.287383\pi$
$942$			14.0000i			0.456145i
$943$		−	36.0000i		−	1.17232i
$944$		0			0
$945$	2.00000	+	1.00000i	0.0650600	+	0.0325300i
$946$	4.00000			0.130051
$947$		−	14.0000i		−	0.454939i	−0.973785	−	0.227469i	$-0.926955\pi$
$947$		−	14.0000i		−	0.454939i	0.973785	−	0.227469i	$-0.0730452\pi$
$948$		−	2.00000i		−	0.0649570i
$949$		0			0
$950$		0			0
$951$	34.0000			1.10253
$952$			18.0000i			0.583383i
$953$		−	58.0000i		−	1.87880i	−0.342817	−	0.939402i	$-0.611381\pi$
$953$		−	58.0000i		−	1.87880i	0.342817	−	0.939402i	$-0.388619\pi$
$954$	2.00000			0.0647524
$955$	32.0000	+	16.0000i	1.03550	+	0.517748i
$956$	24.0000			0.776215
$957$		0			0
$958$			16.0000i			0.516937i
$959$	−14.0000			−0.452084
$960$	−7.00000	+	14.0000i	−0.225924	+	0.451848i
$961$	5.00000			0.161290
$962$		0			0
$963$		0			0
$964$	−14.0000			−0.450910
$965$	2.00000	−	4.00000i	0.0643823	−	0.128765i
$966$	−6.00000			−0.193047
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$			3.00000i			0.0964237i
$969$		0			0
$970$	−12.0000	−	6.00000i	−0.385297	−	0.192648i
$971$	48.0000			1.54039			0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000			1.54039			0.770197	+	0.637806i	$0.220158\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	4.00000			0.128168
$975$		0			0
$976$	−2.00000			−0.0640184
$977$			22.0000i			0.703842i	0.936030	+	0.351921i	$0.114471\pi$
$977$			22.0000i			0.703842i	−0.936030	+	0.351921i	$0.885529\pi$
$978$		−	24.0000i		−	0.767435i
$979$	12.0000			0.383522
$980$	2.00000	+	1.00000i	0.0638877	+	0.0319438i
$981$	−18.0000			−0.574696
$982$		−	36.0000i		−	1.14881i
$983$			60.0000i			1.91370i	0.290578	+	0.956851i	$0.406153\pi$
$983$			60.0000i			1.91370i	−0.290578	+	0.956851i	$0.593847\pi$
$984$	18.0000			0.573819
$985$	−18.0000	+	36.0000i	−0.573528	+	1.14706i
$986$		0			0
$987$			8.00000i			0.254643i
$988$		0			0
$989$	24.0000			0.763156
$990$	−1.00000	+	2.00000i	−0.0317821	+	0.0635642i
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		−	30.0000i		−	0.952501i
$993$			32.0000i			1.01549i
$994$	8.00000			0.253745
$995$	−28.0000	−	14.0000i	−0.887660	−	0.443830i
$996$	6.00000			0.190117
$997$			44.0000i			1.39349i	0.717317	+	0.696747i	$0.245370\pi$
$997$			44.0000i			1.39349i	−0.717317	+	0.696747i	$0.754630\pi$
$998$			12.0000i			0.379853i
$999$	4.00000			0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.b.694.2	yes	2
5.2	odd	4		5775.2.a.i.1.1		1
5.3	odd	4		5775.2.a.r.1.1		1
5.4	even	2	inner	1155.2.c.b.694.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.b.694.1	✓	2	5.4	even	2	inner
1155.2.c.b.694.2	yes	2	1.1	even	1	trivial
5775.2.a.i.1.1		1	5.2	odd	4
5775.2.a.r.1.1		1	5.3	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} +1.00000 q^{11} +1.00000i q^{12} +1.00000 q^{14} +(1.00000 - 2.00000i) q^{15} -1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} +1.00000 q^{21} +1.00000i q^{22} +6.00000i q^{23} -3.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} -1.00000i q^{28} +(2.00000 + 1.00000i) q^{30} -6.00000 q^{31} +5.00000i q^{32} +1.00000i q^{33} -6.00000 q^{34} +(-1.00000 + 2.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +(3.00000 - 6.00000i) q^{40} -6.00000 q^{41} +1.00000i q^{42} -4.00000i q^{43} +1.00000 q^{44} +(2.00000 + 1.00000i) q^{45} -6.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -6.00000 q^{51} +2.00000i q^{53} +1.00000 q^{54} +(-2.00000 - 1.00000i) q^{55} +3.00000 q^{56} +(1.00000 - 2.00000i) q^{60} +2.00000 q^{61} -6.00000i q^{62} +1.00000i q^{63} -7.00000 q^{64} -1.00000 q^{66} +4.00000i q^{67} +6.00000i q^{68} -6.00000 q^{69} +(-2.00000 - 1.00000i) q^{70} +8.00000 q^{71} -3.00000i q^{72} +4.00000i q^{73} -4.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -1.00000i q^{77} -2.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} -6.00000i q^{83} +1.00000 q^{84} +(6.00000 - 12.0000i) q^{85} +4.00000 q^{86} +3.00000i q^{88} +12.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} +6.00000i q^{92} -6.00000i q^{93} -8.00000 q^{94} -5.00000 q^{96} -6.00000i q^{97} -1.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9	\( 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} - 2 q^{16} - 4 q^{20} + 2 q^{21} - 6 q^{24} + 6 q^{25} + 4 q^{30} - 12 q^{31} - 12 q^{34} - 2 q^{35} - 2 q^{36} + 6 q^{40} - 12 q^{41} + 2 q^{44} + 4 q^{45} - 12 q^{46} - 2 q^{49} - 8 q^{50} - 12 q^{51} + 2 q^{54} - 4 q^{55} + 6 q^{56} + 2 q^{60} + 4 q^{61} - 14 q^{64} - 2 q^{66} - 12 q^{69} - 4 q^{70} + 16 q^{71} - 8 q^{74} - 8 q^{75} - 4 q^{79} + 4 q^{80} + 2 q^{81} + 2 q^{84} + 12 q^{85} + 8 q^{86} + 24 q^{89} - 2 q^{90} - 16 q^{94} - 10 q^{96} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 + 2 * q^15 - 2 * q^16 - 4 * q^20 + 2 * q^21 - 6 * q^24 + 6 * q^25 + 4 * q^30 - 12 * q^31 - 12 * q^34 - 2 * q^35 - 2 * q^36 + 6 * q^40 - 12 * q^41 + 2 * q^44 + 4 * q^45 - 12 * q^46 - 2 * q^49 - 8 * q^50 - 12 * q^51 + 2 * q^54 - 4 * q^55 + 6 * q^56 + 2 * q^60 + 4 * q^61 - 14 * q^64 - 2 * q^66 - 12 * q^69 - 4 * q^70 + 16 * q^71 - 8 * q^74 - 8 * q^75 - 4 * q^79 + 4 * q^80 + 2 * q^81 + 2 * q^84 + 12 * q^85 + 8 * q^86 + 24 * q^89 - 2 * q^90 - 16 * q^94 - 10 * q^96 - 2 * q^99

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