LMFDB - Embedded newform 731.2.f.b.302.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, degree $2$, 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:	$5.83706438776$
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:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			302.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	731.302
Dual form			731.2.f.b.259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(2.00000 + 2.00000i) q^{3} +1.00000 q^{4} +(-2.00000 + 2.00000i) q^{6} +3.00000i q^{8} +5.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(2.00000 + 2.00000i) q^{3} +1.00000 q^{4} +(-2.00000 + 2.00000i) q^{6} +3.00000i q^{8} +5.00000i q^{9} +(-1.00000 + 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{12} +2.00000 q^{13} -1.00000 q^{16} +(-4.00000 - 1.00000i) q^{17} -5.00000 q^{18} -8.00000i q^{19} +(-1.00000 - 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-6.00000 + 6.00000i) q^{24} -5.00000i q^{25} +2.00000i q^{26} +(-4.00000 + 4.00000i) q^{27} +(6.00000 + 6.00000i) q^{29} +(1.00000 + 1.00000i) q^{31} +5.00000i q^{32} -4.00000 q^{33} +(1.00000 - 4.00000i) q^{34} +5.00000i q^{36} +(-2.00000 - 2.00000i) q^{37} +8.00000 q^{38} +(4.00000 + 4.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} -1.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} +2.00000 q^{47} +(-2.00000 - 2.00000i) q^{48} +7.00000i q^{49} +5.00000 q^{50} +(-6.00000 - 10.0000i) q^{51} +2.00000 q^{52} -12.0000i q^{53} +(-4.00000 - 4.00000i) q^{54} +(16.0000 - 16.0000i) q^{57} +(-6.00000 + 6.00000i) q^{58} -6.00000i q^{59} +(-6.00000 + 6.00000i) q^{61} +(-1.00000 + 1.00000i) q^{62} -7.00000 q^{64} -4.00000i q^{66} -2.00000 q^{67} +(-4.00000 - 1.00000i) q^{68} -4.00000 q^{69} +(-4.00000 - 4.00000i) q^{71} -15.0000 q^{72} +(6.00000 + 6.00000i) q^{73} +(2.00000 - 2.00000i) q^{74} +(10.0000 - 10.0000i) q^{75} -8.00000i q^{76} +(-4.00000 + 4.00000i) q^{78} +(7.00000 - 7.00000i) q^{79} -1.00000 q^{81} +(1.00000 + 1.00000i) q^{82} +12.0000i q^{83} +1.00000 q^{86} +24.0000i q^{87} +(-3.00000 - 3.00000i) q^{88} +6.00000 q^{89} +(-1.00000 + 1.00000i) q^{92} +4.00000i q^{93} +2.00000i q^{94} +(-10.0000 + 10.0000i) q^{96} +(-13.0000 - 13.0000i) q^{97} -7.00000 q^{98} +(-5.00000 - 5.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} + 2 q^{4} - 4 q^{6}+O(q^{10}) $ 2 * q + 4 * q^3 + 2 * q^4 - 4 * q^6	$ 2 q + 4 q^{3} + 2 q^{4} - 4 q^{6} - 2 q^{11} + 4 q^{12} + 4 q^{13} - 2 q^{16} - 8 q^{17} - 10 q^{18} - 2 q^{22} - 2 q^{23} - 12 q^{24} - 8 q^{27} + 12 q^{29} + 2 q^{31} - 8 q^{33} + 2 q^{34} - 4 q^{37} + 16 q^{38} + 8 q^{39} + 2 q^{41} - 2 q^{44} - 2 q^{46} + 4 q^{47} - 4 q^{48} + 10 q^{50} - 12 q^{51} + 4 q^{52} - 8 q^{54} + 32 q^{57} - 12 q^{58} - 12 q^{61} - 2 q^{62} - 14 q^{64} - 4 q^{67} - 8 q^{68} - 8 q^{69} - 8 q^{71} - 30 q^{72} + 12 q^{73} + 4 q^{74} + 20 q^{75} - 8 q^{78} + 14 q^{79} - 2 q^{81} + 2 q^{82} + 2 q^{86} - 6 q^{88} + 12 q^{89} - 2 q^{92} - 20 q^{96} - 26 q^{97} - 14 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 + 2 * q^4 - 4 * q^6 - 2 * q^11 + 4 * q^12 + 4 * q^13 - 2 * q^16 - 8 * q^17 - 10 * q^18 - 2 * q^22 - 2 * q^23 - 12 * q^24 - 8 * q^27 + 12 * q^29 + 2 * q^31 - 8 * q^33 + 2 * q^34 - 4 * q^37 + 16 * q^38 + 8 * q^39 + 2 * q^41 - 2 * q^44 - 2 * q^46 + 4 * q^47 - 4 * q^48 + 10 * q^50 - 12 * q^51 + 4 * q^52 - 8 * q^54 + 32 * q^57 - 12 * q^58 - 12 * q^61 - 2 * q^62 - 14 * q^64 - 4 * q^67 - 8 * q^68 - 8 * q^69 - 8 * q^71 - 30 * q^72 + 12 * q^73 + 4 * q^74 + 20 * q^75 - 8 * q^78 + 14 * q^79 - 2 * q^81 + 2 * q^82 + 2 * q^86 - 6 * q^88 + 12 * q^89 - 2 * q^92 - 20 * q^96 - 26 * q^97 - 14 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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	$0.884973\pi$
$3$	2.00000	+	2.00000i	1.15470	+	1.15470i	0.985599	+	0.169102i	$0.0540867\pi$
$3$	2.00000	+	2.00000i	1.15470	+	1.15470i	0.169102	+	0.985599i	$0.445913\pi$
$4$	1.00000			0.500000
$5$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$5$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$6$	−2.00000	+	2.00000i	−0.816497	+	0.816497i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$			3.00000i			1.06066i
$9$			5.00000i			1.66667i
$10$		0			0
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	−0.841605	−	0.540094i	$-0.818389\pi$
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	0.540094	+	0.841605i	$0.318389\pi$
$12$	2.00000	+	2.00000i	0.577350	+	0.577350i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.00000	−	1.00000i	−0.970143	−	0.242536i
$17$	−4.00000	−	1.00000i	−0.970143	−	0.242536i
$18$	−5.00000			−1.17851
$19$		−	8.00000i		−	1.83533i	−0.397360	−	0.917663i	$-0.630073\pi$
$19$		−	8.00000i		−	1.83533i	0.397360	−	0.917663i	$-0.369927\pi$
$20$		0			0
$21$		0			0
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	−6.00000	+	6.00000i	−1.22474	+	1.22474i
$25$		−	5.00000i		−	1.00000i
$26$			2.00000i			0.392232i
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$	6.00000	+	6.00000i	1.11417	+	1.11417i	0.992580	+	0.121592i	$0.0387999\pi$
$29$	6.00000	+	6.00000i	1.11417	+	1.11417i	0.121592	+	0.992580i	$0.461200\pi$
$30$		0			0
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$			5.00000i			0.883883i
$33$	−4.00000			−0.696311
$34$	1.00000	−	4.00000i	0.171499	−	0.685994i
$35$		0			0
$36$			5.00000i			0.833333i
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$	8.00000			1.29777
$39$	4.00000	+	4.00000i	0.640513	+	0.640513i
$40$		0			0
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$		0			0
$46$	−1.00000	−	1.00000i	−0.147442	−	0.147442i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	−2.00000	−	2.00000i	−0.288675	−	0.288675i
$49$			7.00000i			1.00000i
$50$	5.00000			0.707107
$51$	−6.00000	−	10.0000i	−0.840168	−	1.40028i
$52$	2.00000			0.277350
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$	−4.00000	−	4.00000i	−0.544331	−	0.544331i
$55$		0			0
$56$		0			0
$57$	16.0000	−	16.0000i	2.11925	−	2.11925i
$58$	−6.00000	+	6.00000i	−0.787839	+	0.787839i
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		0			0
$61$	−6.00000	+	6.00000i	−0.768221	+	0.768221i	−0.977793	−	0.209572i	$-0.932793\pi$
$61$	−6.00000	+	6.00000i	−0.768221	+	0.768221i	0.209572	+	0.977793i	$0.432793\pi$
$62$	−1.00000	+	1.00000i	−0.127000	+	0.127000i
$63$		0			0
$64$	−7.00000			−0.875000
$65$		0			0
$66$		−	4.00000i		−	0.492366i
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−4.00000	−	1.00000i	−0.485071	−	0.121268i
$69$	−4.00000			−0.481543
$70$		0			0
$71$	−4.00000	−	4.00000i	−0.474713	−	0.474713i	0.428723	−	0.903436i	$-0.358964\pi$
$71$	−4.00000	−	4.00000i	−0.474713	−	0.474713i	−0.903436	+	0.428723i	$0.858964\pi$
$72$	−15.0000			−1.76777
$73$	6.00000	+	6.00000i	0.702247	+	0.702247i	0.964892	−	0.262646i	$-0.0845950\pi$
$73$	6.00000	+	6.00000i	0.702247	+	0.702247i	−0.262646	+	0.964892i	$0.584595\pi$
$74$	2.00000	−	2.00000i	0.232495	−	0.232495i
$75$	10.0000	−	10.0000i	1.15470	−	1.15470i
$76$		−	8.00000i		−	0.917663i
$77$		0			0
$78$	−4.00000	+	4.00000i	−0.452911	+	0.452911i
$79$	7.00000	−	7.00000i	0.787562	−	0.787562i	−0.193532	−	0.981094i	$-0.561994\pi$
$79$	7.00000	−	7.00000i	0.787562	−	0.787562i	0.981094	+	0.193532i	$0.0619944\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	1.00000	+	1.00000i	0.110432	+	0.110432i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$		0			0
$86$	1.00000			0.107833
$87$			24.0000i			2.57307i
$88$	−3.00000	−	3.00000i	−0.319801	−	0.319801i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$		0			0
$92$	−1.00000	+	1.00000i	−0.104257	+	0.104257i
$93$			4.00000i			0.414781i
$94$			2.00000i			0.206284i
$95$		0			0
$96$	−10.0000	+	10.0000i	−1.02062	+	1.02062i
$97$	−13.0000	−	13.0000i	−1.31995	−	1.31995i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−13.0000	−	13.0000i	−1.31995	−	1.31995i	−0.406138	−	0.913812i	$-0.633125\pi$
$98$	−7.00000			−0.707107
$99$	−5.00000	−	5.00000i	−0.502519	−	0.502519i
$100$		−	5.00000i		−	0.500000i
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$	10.0000	−	6.00000i	0.990148	−	0.594089i
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$			6.00000i			0.588348i
$105$		0			0
$106$	12.0000			1.16554
$107$	−1.00000	−	1.00000i	−0.0966736	−	0.0966736i	0.657116	−	0.753790i	$-0.271776\pi$
$107$	−1.00000	−	1.00000i	−0.0966736	−	0.0966736i	−0.753790	+	0.657116i	$0.771776\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$	13.0000	−	13.0000i	1.24517	−	1.24517i	0.287348	−	0.957826i	$-0.407226\pi$
$109$	13.0000	−	13.0000i	1.24517	−	1.24517i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$		0			0
$111$		−	8.00000i		−	0.759326i
$112$		0			0
$113$	−2.00000	+	2.00000i	−0.188144	+	0.188144i	−0.794893	−	0.606749i	$-0.792473\pi$
$113$	−2.00000	+	2.00000i	−0.188144	+	0.188144i	0.606749	+	0.794893i	$0.292473\pi$
$114$	16.0000	+	16.0000i	1.49854	+	1.49854i
$115$		0			0
$116$	6.00000	+	6.00000i	0.557086	+	0.557086i
$117$			10.0000i			0.924500i
$118$	6.00000			0.552345
$119$		0			0
$120$		0			0
$121$			9.00000i			0.818182i
$122$	−6.00000	−	6.00000i	−0.543214	−	0.543214i
$123$	4.00000			0.360668
$124$	1.00000	+	1.00000i	0.0898027	+	0.0898027i
$125$		0			0
$126$		0			0
$127$		−	10.0000i		−	0.887357i	−0.896186	−	0.443678i	$-0.853673\pi$
$127$		−	10.0000i		−	0.887357i	0.896186	−	0.443678i	$-0.146327\pi$
$128$			3.00000i			0.265165i
$129$	2.00000	−	2.00000i	0.176090	−	0.176090i
$130$		0			0
$131$	8.00000	+	8.00000i	0.698963	+	0.698963i	0.964187	−	0.265224i	$-0.0854458\pi$
$131$	8.00000	+	8.00000i	0.698963	+	0.698963i	−0.265224	+	0.964187i	$0.585446\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$	3.00000	−	12.0000i	0.257248	−	1.02899i
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		−	4.00000i		−	0.340503i
$139$	13.0000	+	13.0000i	1.10265	+	1.10265i	0.994090	+	0.108555i	$0.0346224\pi$
$139$	13.0000	+	13.0000i	1.10265	+	1.10265i	0.108555	+	0.994090i	$0.465378\pi$
$140$		0			0
$141$	4.00000	+	4.00000i	0.336861	+	0.336861i
$142$	4.00000	−	4.00000i	0.335673	−	0.335673i
$143$	−2.00000	+	2.00000i	−0.167248	+	0.167248i
$144$		−	5.00000i		−	0.416667i
$145$		0			0
$146$	−6.00000	+	6.00000i	−0.496564	+	0.496564i
$147$	−14.0000	+	14.0000i	−1.15470	+	1.15470i
$148$	−2.00000	−	2.00000i	−0.164399	−	0.164399i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	10.0000	+	10.0000i	0.816497	+	0.816497i
$151$		−	4.00000i		−	0.325515i	−0.986666	−	0.162758i	$-0.947961\pi$
$151$		−	4.00000i		−	0.325515i	0.986666	−	0.162758i	$-0.0520389\pi$
$152$	24.0000			1.94666
$153$	5.00000	−	20.0000i	0.404226	−	1.61690i
$154$		0			0
$155$		0			0
$156$	4.00000	+	4.00000i	0.320256	+	0.320256i
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	7.00000	+	7.00000i	0.556890	+	0.556890i
$159$	24.0000	−	24.0000i	1.90332	−	1.90332i
$160$		0			0
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−8.00000	+	8.00000i	−0.626608	+	0.626608i	−0.947213	−	0.320605i	$-0.896114\pi$
$163$	−8.00000	+	8.00000i	−0.626608	+	0.626608i	0.320605	+	0.947213i	$0.396114\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$		0			0
$166$	−12.0000			−0.931381
$167$	7.00000	+	7.00000i	0.541676	+	0.541676i	0.924020	−	0.382344i	$-0.124883\pi$
$167$	7.00000	+	7.00000i	0.541676	+	0.541676i	−0.382344	+	0.924020i	$0.624883\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	40.0000			3.05888
$172$		−	1.00000i		−	0.0762493i
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	0.152057	−	0.988372i	$-0.451410\pi$
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	−0.988372	+	0.152057i	$0.951410\pi$
$174$	−24.0000			−1.81944
$175$		0			0
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	12.0000	−	12.0000i	0.901975	−	0.901975i
$178$			6.00000i			0.449719i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$	−9.00000	+	9.00000i	−0.668965	+	0.668965i	−0.957476	−	0.288512i	$-0.906840\pi$
$181$	−9.00000	+	9.00000i	−0.668965	+	0.668965i	0.288512	+	0.957476i	$0.406840\pi$
$182$		0			0
$183$	−24.0000			−1.77413
$184$	−3.00000	−	3.00000i	−0.221163	−	0.221163i
$185$		0			0
$186$	−4.00000			−0.293294
$187$	5.00000	−	3.00000i	0.365636	−	0.219382i
$188$	2.00000			0.145865
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−14.0000	−	14.0000i	−1.01036	−	1.01036i
$193$	17.0000	−	17.0000i	1.22369	−	1.22369i	0.257375	−	0.966312i	$-0.417142\pi$
$193$	17.0000	−	17.0000i	1.22369	−	1.22369i	0.966312	−	0.257375i	$-0.0828576\pi$
$194$	13.0000	−	13.0000i	0.933346	−	0.933346i
$195$		0			0
$196$			7.00000i			0.500000i
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	−0.741832	−	0.670585i	$-0.766043\pi$
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	0.670585	+	0.741832i	$0.266043\pi$
$198$	5.00000	−	5.00000i	0.355335	−	0.355335i
$199$	14.0000	+	14.0000i	0.992434	+	0.992434i	0.999972	−	0.00753790i	$-0.00239941\pi$
$199$	14.0000	+	14.0000i	0.992434	+	0.992434i	−0.00753790	+	0.999972i	$0.502399\pi$
$200$	15.0000			1.06066
$201$	−4.00000	−	4.00000i	−0.282138	−	0.282138i
$202$		−	12.0000i		−	0.844317i
$203$		0			0
$204$	−6.00000	−	10.0000i	−0.420084	−	0.700140i
$205$		0			0
$206$		−	6.00000i		−	0.418040i
$207$	−5.00000	−	5.00000i	−0.347524	−	0.347524i
$208$	−2.00000			−0.138675
$209$	8.00000	+	8.00000i	0.553372	+	0.553372i
$210$		0			0
$211$	12.0000	−	12.0000i	0.826114	−	0.826114i	−0.160863	−	0.986977i	$-0.551428\pi$
$211$	12.0000	−	12.0000i	0.826114	−	0.826114i	0.986977	+	0.160863i	$0.0514276\pi$
$212$		−	12.0000i		−	0.824163i
$213$		−	16.0000i		−	1.09630i
$214$	1.00000	−	1.00000i	0.0683586	−	0.0683586i
$215$		0			0
$216$	−12.0000	−	12.0000i	−0.816497	−	0.816497i
$217$		0			0
$218$	13.0000	+	13.0000i	0.880471	+	0.880471i
$219$			24.0000i			1.62177i
$220$		0			0
$221$	−8.00000	−	2.00000i	−0.538138	−	0.134535i
$222$	8.00000			0.536925
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	25.0000			1.66667
$226$	−2.00000	−	2.00000i	−0.133038	−	0.133038i
$227$	−8.00000	+	8.00000i	−0.530979	+	0.530979i	−0.920864	−	0.389885i	$-0.872515\pi$
$227$	−8.00000	+	8.00000i	−0.530979	+	0.530979i	0.389885	+	0.920864i	$0.372515\pi$
$228$	16.0000	−	16.0000i	1.05963	−	1.05963i
$229$		−	20.0000i		−	1.32164i	−0.750546	−	0.660819i	$-0.770209\pi$
$229$		−	20.0000i		−	1.32164i	0.750546	−	0.660819i	$-0.229791\pi$
$230$		0			0
$231$		0			0
$232$	−18.0000	+	18.0000i	−1.18176	+	1.18176i
$233$	−10.0000	−	10.0000i	−0.655122	−	0.655122i	0.299100	−	0.954222i	$-0.403314\pi$
$233$	−10.0000	−	10.0000i	−0.655122	−	0.655122i	−0.954222	+	0.299100i	$0.903314\pi$
$234$	−10.0000			−0.653720
$235$		0			0
$236$		−	6.00000i		−	0.390567i
$237$	28.0000			1.81880
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−8.00000	−	8.00000i	−0.515325	−	0.515325i	0.400828	−	0.916153i	$-0.368722\pi$
$241$	−8.00000	−	8.00000i	−0.515325	−	0.515325i	−0.916153	+	0.400828i	$0.868722\pi$
$242$	−9.00000			−0.578542
$243$	10.0000	+	10.0000i	0.641500	+	0.641500i
$244$	−6.00000	+	6.00000i	−0.384111	+	0.384111i
$245$		0			0
$246$			4.00000i			0.255031i
$247$		−	16.0000i		−	1.01806i
$248$	−3.00000	+	3.00000i	−0.190500	+	0.190500i
$249$	−24.0000	+	24.0000i	−1.52094	+	1.52094i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	2.00000i		−	0.125739i
$254$	10.0000			0.627456
$255$		0			0
$256$	−17.0000			−1.06250
$257$			26.0000i			1.62184i	0.585160	+	0.810918i	$0.301032\pi$
$257$			26.0000i			1.62184i	−0.585160	+	0.810918i	$0.698968\pi$
$258$	2.00000	+	2.00000i	0.124515	+	0.124515i
$259$		0			0
$260$		0			0
$261$	−30.0000	+	30.0000i	−1.85695	+	1.85695i
$262$	−8.00000	+	8.00000i	−0.494242	+	0.494242i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		−	12.0000i		−	0.738549i
$265$		0			0
$266$		0			0
$267$	12.0000	+	12.0000i	0.734388	+	0.734388i
$268$	−2.00000			−0.122169
$269$	−3.00000	−	3.00000i	−0.182913	−	0.182913i	0.609711	−	0.792624i	$-0.291286\pi$
$269$	−3.00000	−	3.00000i	−0.182913	−	0.182913i	−0.792624	+	0.609711i	$0.791286\pi$
$270$		0			0
$271$	10.0000			0.607457			0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000			0.607457			0.303728	+	0.952759i	$0.401768\pi$
$272$	4.00000	+	1.00000i	0.242536	+	0.0606339i
$273$		0			0
$274$			2.00000i			0.120824i
$275$	5.00000	+	5.00000i	0.301511	+	0.301511i
$276$	−4.00000			−0.240772
$277$	−10.0000	−	10.0000i	−0.600842	−	0.600842i	0.339694	−	0.940536i	$-0.389676\pi$
$277$	−10.0000	−	10.0000i	−0.600842	−	0.600842i	−0.940536	+	0.339694i	$0.889676\pi$
$278$	−13.0000	+	13.0000i	−0.779688	+	0.779688i
$279$	−5.00000	+	5.00000i	−0.299342	+	0.299342i
$280$		0			0
$281$			16.0000i			0.954480i	0.878773	+	0.477240i	$0.158363\pi$
$281$			16.0000i			0.954480i	−0.878773	+	0.477240i	$0.841637\pi$
$282$	−4.00000	+	4.00000i	−0.238197	+	0.238197i
$283$	−13.0000	+	13.0000i	−0.772770	+	0.772770i	−0.978590	−	0.205820i	$-0.934014\pi$
$283$	−13.0000	+	13.0000i	−0.772770	+	0.772770i	0.205820	+	0.978590i	$0.434014\pi$
$284$	−4.00000	−	4.00000i	−0.237356	−	0.237356i
$285$		0			0
$286$	−2.00000	−	2.00000i	−0.118262	−	0.118262i
$287$		0			0
$288$	−25.0000			−1.47314
$289$	15.0000	+	8.00000i	0.882353	+	0.470588i
$290$		0			0
$291$		−	52.0000i		−	3.04829i
$292$	6.00000	+	6.00000i	0.351123	+	0.351123i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	−14.0000	−	14.0000i	−0.816497	−	0.816497i
$295$		0			0
$296$	6.00000	−	6.00000i	0.348743	−	0.348743i
$297$		−	8.00000i		−	0.464207i
$298$			6.00000i			0.347571i
$299$	−2.00000	+	2.00000i	−0.115663	+	0.115663i
$300$	10.0000	−	10.0000i	0.577350	−	0.577350i
$301$		0			0
$302$	4.00000			0.230174
$303$	−24.0000	−	24.0000i	−1.37876	−	1.37876i
$304$			8.00000i			0.458831i
$305$		0			0
$306$	20.0000	+	5.00000i	1.14332	+	0.285831i
$307$	−6.00000			−0.342438			−0.171219	−	0.985233i	$-0.554771\pi$
$307$	−6.00000			−0.342438			−0.171219	+	0.985233i	$0.554771\pi$
$308$		0			0
$309$	−12.0000	−	12.0000i	−0.682656	−	0.682656i
$310$		0			0
$311$	−9.00000	−	9.00000i	−0.510343	−	0.510343i	0.404288	−	0.914632i	$-0.367519\pi$
$311$	−9.00000	−	9.00000i	−0.510343	−	0.510343i	−0.914632	+	0.404288i	$0.867519\pi$
$312$	−12.0000	+	12.0000i	−0.679366	+	0.679366i
$313$	−16.0000	+	16.0000i	−0.904373	+	0.904373i	−0.995811	−	0.0914374i	$-0.970854\pi$
$313$	−16.0000	+	16.0000i	−0.904373	+	0.904373i	0.0914374	+	0.995811i	$0.470854\pi$
$314$		−	18.0000i		−	1.01580i
$315$		0			0
$316$	7.00000	−	7.00000i	0.393781	−	0.393781i
$317$	−15.0000	+	15.0000i	−0.842484	+	0.842484i	−0.989181	−	0.146697i	$-0.953136\pi$
$317$	−15.0000	+	15.0000i	−0.842484	+	0.842484i	0.146697	+	0.989181i	$0.453136\pi$
$318$	24.0000	+	24.0000i	1.34585	+	1.34585i
$319$	−12.0000			−0.671871
$320$		0			0
$321$		−	4.00000i		−	0.223258i
$322$		0			0
$323$	−8.00000	+	32.0000i	−0.445132	+	1.78053i
$324$	−1.00000			−0.0555556
$325$		−	10.0000i		−	0.554700i
$326$	−8.00000	−	8.00000i	−0.443079	−	0.443079i
$327$	52.0000			2.87561
$328$	3.00000	+	3.00000i	0.165647	+	0.165647i
$329$		0			0
$330$		0			0
$331$		−	4.00000i		−	0.219860i	−0.993939	−	0.109930i	$-0.964937\pi$
$331$		−	4.00000i		−	0.219860i	0.993939	−	0.109930i	$-0.0350627\pi$
$332$			12.0000i			0.658586i
$333$	10.0000	−	10.0000i	0.547997	−	0.547997i
$334$	−7.00000	+	7.00000i	−0.383023	+	0.383023i
$335$		0			0
$336$		0			0
$337$	17.0000	+	17.0000i	0.926049	+	0.926049i	0.997448	−	0.0713988i	$-0.0227463\pi$
$337$	17.0000	+	17.0000i	0.926049	+	0.926049i	−0.0713988	+	0.997448i	$0.522746\pi$
$338$		−	9.00000i		−	0.489535i
$339$	−8.00000			−0.434500
$340$		0			0
$341$	−2.00000			−0.108306
$342$			40.0000i			2.16295i
$343$		0			0
$344$	3.00000			0.161749
$345$		0			0
$346$	11.0000	−	11.0000i	0.591364	−	0.591364i
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$			24.0000i			1.28654i
$349$		−	14.0000i		−	0.749403i	−0.927146	−	0.374701i	$-0.877745\pi$
$349$		−	14.0000i		−	0.749403i	0.927146	−	0.374701i	$-0.122255\pi$
$350$		0			0
$351$	−8.00000	+	8.00000i	−0.427008	+	0.427008i
$352$	−5.00000	−	5.00000i	−0.266501	−	0.266501i
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$	12.0000	+	12.0000i	0.637793	+	0.637793i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$		0			0
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$		0			0
$361$	−45.0000			−2.36842
$362$	−9.00000	−	9.00000i	−0.473029	−	0.473029i
$363$	−18.0000	+	18.0000i	−0.944755	+	0.944755i
$364$		0			0
$365$		0			0
$366$		−	24.0000i		−	1.25450i
$367$	−7.00000	+	7.00000i	−0.365397	+	0.365397i	−0.865795	−	0.500398i	$-0.833187\pi$
$367$	−7.00000	+	7.00000i	−0.365397	+	0.365397i	0.500398	+	0.865795i	$0.333187\pi$
$368$	1.00000	−	1.00000i	0.0521286	−	0.0521286i
$369$	5.00000	+	5.00000i	0.260290	+	0.260290i
$370$		0			0
$371$		0			0
$372$			4.00000i			0.207390i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$	3.00000	+	5.00000i	0.155126	+	0.258544i
$375$		0			0
$376$			6.00000i			0.309426i
$377$	12.0000	+	12.0000i	0.618031	+	0.618031i
$378$		0			0
$379$	21.0000	+	21.0000i	1.07870	+	1.07870i	0.996626	+	0.0820711i	$0.0261534\pi$
$379$	21.0000	+	21.0000i	1.07870	+	1.07870i	0.0820711	+	0.996626i	$0.473847\pi$
$380$		0			0
$381$	20.0000	−	20.0000i	1.02463	−	1.02463i
$382$		0			0
$383$		−	36.0000i		−	1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$383$		−	36.0000i		−	1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$384$	−6.00000	+	6.00000i	−0.306186	+	0.306186i
$385$		0			0
$386$	17.0000	+	17.0000i	0.865277	+	0.865277i
$387$	5.00000			0.254164
$388$	−13.0000	−	13.0000i	−0.659975	−	0.659975i
$389$		−	30.0000i		−	1.52106i	−0.649303	−	0.760530i	$-0.724939\pi$
$389$		−	30.0000i		−	1.52106i	0.649303	−	0.760530i	$-0.275061\pi$
$390$		0			0
$391$	5.00000	−	3.00000i	0.252861	−	0.151717i
$392$	−21.0000			−1.06066
$393$			32.0000i			1.61419i
$394$	−1.00000	−	1.00000i	−0.0503793	−	0.0503793i
$395$		0			0
$396$	−5.00000	−	5.00000i	−0.251259	−	0.251259i
$397$	3.00000	−	3.00000i	0.150566	−	0.150566i	−0.627805	−	0.778371i	$-0.716046\pi$
$397$	3.00000	−	3.00000i	0.150566	−	0.150566i	0.778371	+	0.627805i	$0.216046\pi$
$398$	−14.0000	+	14.0000i	−0.701757	+	0.701757i
$399$		0			0
$400$			5.00000i			0.250000i
$401$	−1.00000	+	1.00000i	−0.0499376	+	0.0499376i	−0.731635	−	0.681697i	$-0.761242\pi$
$401$	−1.00000	+	1.00000i	−0.0499376	+	0.0499376i	0.681697	+	0.731635i	$0.261242\pi$
$402$	4.00000	−	4.00000i	0.199502	−	0.199502i
$403$	2.00000	+	2.00000i	0.0996271	+	0.0996271i
$404$	−12.0000			−0.597022
$405$		0			0
$406$		0			0
$407$	4.00000			0.198273
$408$	30.0000	−	18.0000i	1.48522	−	0.891133i
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$		0			0
$411$	4.00000	+	4.00000i	0.197305	+	0.197305i
$412$	−6.00000			−0.295599
$413$		0			0
$414$	5.00000	−	5.00000i	0.245737	−	0.245737i
$415$		0			0
$416$			10.0000i			0.490290i
$417$			52.0000i			2.54645i
$418$	−8.00000	+	8.00000i	−0.391293	+	0.391293i
$419$	−6.00000	+	6.00000i	−0.293119	+	0.293119i	−0.838311	−	0.545192i	$-0.816457\pi$
$419$	−6.00000	+	6.00000i	−0.293119	+	0.293119i	0.545192	+	0.838311i	$0.316457\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$	12.0000	+	12.0000i	0.584151	+	0.584151i
$423$			10.0000i			0.486217i
$424$	36.0000			1.74831
$425$	−5.00000	+	20.0000i	−0.242536	+	0.970143i
$426$	16.0000			0.775203
$427$		0			0
$428$	−1.00000	−	1.00000i	−0.0483368	−	0.0483368i
$429$	−8.00000			−0.386244
$430$		0			0
$431$	−7.00000	+	7.00000i	−0.337178	+	0.337178i	−0.855304	−	0.518126i	$-0.826630\pi$
$431$	−7.00000	+	7.00000i	−0.337178	+	0.337178i	0.518126	+	0.855304i	$0.326630\pi$
$432$	4.00000	−	4.00000i	0.192450	−	0.192450i
$433$		−	10.0000i		−	0.480569i	−0.970702	−	0.240285i	$-0.922759\pi$
$433$		−	10.0000i		−	0.480569i	0.970702	−	0.240285i	$-0.0772408\pi$
$434$		0			0
$435$		0			0
$436$	13.0000	−	13.0000i	0.622587	−	0.622587i
$437$	8.00000	+	8.00000i	0.382692	+	0.382692i
$438$	−24.0000			−1.14676
$439$	−21.0000	−	21.0000i	−1.00228	−	1.00228i	−0.999997	−	0.00227791i	$-0.999275\pi$
$439$	−21.0000	−	21.0000i	−1.00228	−	1.00228i	−0.00227791	−	0.999997i	$-0.500725\pi$
$440$		0			0
$441$	−35.0000			−1.66667
$442$	2.00000	−	8.00000i	0.0951303	−	0.380521i
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$		−	8.00000i		−	0.379663i
$445$		0			0
$446$	8.00000			0.378811
$447$	12.0000	+	12.0000i	0.567581	+	0.567581i
$448$		0			0
$449$	8.00000	−	8.00000i	0.377543	−	0.377543i	−0.492672	−	0.870215i	$-0.663980\pi$
$449$	8.00000	−	8.00000i	0.377543	−	0.377543i	0.870215	+	0.492672i	$0.163980\pi$
$450$			25.0000i			1.17851i
$451$			2.00000i			0.0941763i
$452$	−2.00000	+	2.00000i	−0.0940721	+	0.0940721i
$453$	8.00000	−	8.00000i	0.375873	−	0.375873i
$454$	−8.00000	−	8.00000i	−0.375459	−	0.375459i
$455$		0			0
$456$	48.0000	+	48.0000i	2.24781	+	2.24781i
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	20.0000			0.934539
$459$	20.0000	−	12.0000i	0.933520	−	0.560112i
$460$		0			0
$461$		−	10.0000i		−	0.465746i	−0.972507	−	0.232873i	$-0.925187\pi$
$461$		−	10.0000i		−	0.465746i	0.972507	−	0.232873i	$-0.0748127\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−6.00000	−	6.00000i	−0.278543	−	0.278543i
$465$		0			0
$466$	10.0000	−	10.0000i	0.463241	−	0.463241i
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$			10.0000i			0.462250i
$469$		0			0
$470$		0			0
$471$	−36.0000	−	36.0000i	−1.65879	−	1.65879i
$472$	18.0000			0.828517
$473$	1.00000	+	1.00000i	0.0459800	+	0.0459800i
$474$			28.0000i			1.28608i
$475$	−40.0000			−1.83533
$476$		0			0
$477$	60.0000			2.74721
$478$			24.0000i			1.09773i
$479$	−29.0000	−	29.0000i	−1.32504	−	1.32504i	−0.909635	−	0.415409i	$-0.863638\pi$
$479$	−29.0000	−	29.0000i	−1.32504	−	1.32504i	−0.415409	−	0.909635i	$-0.636362\pi$
$480$		0			0
$481$	−4.00000	−	4.00000i	−0.182384	−	0.182384i
$482$	8.00000	−	8.00000i	0.364390	−	0.364390i
$483$		0			0
$484$			9.00000i			0.409091i
$485$		0			0
$486$	−10.0000	+	10.0000i	−0.453609	+	0.453609i
$487$	−3.00000	+	3.00000i	−0.135943	+	0.135943i	−0.771804	−	0.635861i	$-0.780645\pi$
$487$	−3.00000	+	3.00000i	−0.135943	+	0.135943i	0.635861	+	0.771804i	$0.280645\pi$
$488$	−18.0000	−	18.0000i	−0.814822	−	0.814822i
$489$	−32.0000			−1.44709
$490$		0			0
$491$			36.0000i			1.62466i	0.583200	+	0.812329i	$0.301800\pi$
$491$			36.0000i			1.62466i	−0.583200	+	0.812329i	$0.698200\pi$
$492$	4.00000			0.180334
$493$	−18.0000	−	30.0000i	−0.810679	−	1.35113i
$494$	16.0000			0.719874
$495$		0			0
$496$	−1.00000	−	1.00000i	−0.0449013	−	0.0449013i
$497$		0			0
$498$	−24.0000	−	24.0000i	−1.07547	−	1.07547i
$499$	14.0000	−	14.0000i	0.626726	−	0.626726i	−0.320517	−	0.947243i	$-0.603857\pi$
$499$	14.0000	−	14.0000i	0.626726	−	0.626726i	0.947243	+	0.320517i	$0.103857\pi$
$500$		0			0
$501$			28.0000i			1.25095i
$502$		−	12.0000i		−	0.535586i
$503$	−6.00000	+	6.00000i	−0.267527	+	0.267527i	−0.828103	−	0.560576i	$-0.810580\pi$
$503$	−6.00000	+	6.00000i	−0.267527	+	0.267527i	0.560576	+	0.828103i	$0.310580\pi$
$504$		0			0
$505$		0			0
$506$	2.00000			0.0889108
$507$	−18.0000	−	18.0000i	−0.799408	−	0.799408i
$508$		−	10.0000i		−	0.443678i
$509$	−36.0000			−1.59567			−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000			−1.59567			−0.797836	+	0.602875i	$0.794022\pi$
$510$		0			0
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$	32.0000	+	32.0000i	1.41283	+	1.41283i
$514$	−26.0000			−1.14681
$515$		0			0
$516$	2.00000	−	2.00000i	0.0880451	−	0.0880451i
$517$	−2.00000	+	2.00000i	−0.0879599	+	0.0879599i
$518$		0			0
$519$		−	44.0000i		−	1.93139i
$520$		0			0
$521$	20.0000	−	20.0000i	0.876216	−	0.876216i	−0.116925	−	0.993141i	$-0.537304\pi$
$521$	20.0000	−	20.0000i	0.876216	−	0.876216i	0.993141	+	0.116925i	$0.0373037\pi$
$522$	−30.0000	−	30.0000i	−1.31306	−	1.31306i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	8.00000	+	8.00000i	0.349482	+	0.349482i
$525$		0			0
$526$		0			0
$527$	−3.00000	−	5.00000i	−0.130682	−	0.217803i
$528$	4.00000			0.174078
$529$			21.0000i			0.913043i
$530$		0			0
$531$	30.0000			1.30189
$532$		0			0
$533$	2.00000	−	2.00000i	0.0866296	−	0.0866296i
$534$	−12.0000	+	12.0000i	−0.519291	+	0.519291i
$535$		0			0
$536$		−	6.00000i		−	0.259161i
$537$		0			0
$538$	3.00000	−	3.00000i	0.129339	−	0.129339i
$539$	−7.00000	−	7.00000i	−0.301511	−	0.301511i
$540$		0			0
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	0.951756	−	0.306856i	$-0.0992769\pi$
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	−0.306856	+	0.951756i	$0.599277\pi$
$542$			10.0000i			0.429537i
$543$	−36.0000			−1.54491
$544$	5.00000	−	20.0000i	0.214373	−	0.857493i
$545$		0			0
$546$		0			0
$547$	17.0000	+	17.0000i	0.726868	+	0.726868i	0.969994	−	0.243127i	$-0.0781732\pi$
$547$	17.0000	+	17.0000i	0.726868	+	0.726868i	−0.243127	+	0.969994i	$0.578173\pi$
$548$	2.00000			0.0854358
$549$	−30.0000	−	30.0000i	−1.28037	−	1.28037i
$550$	−5.00000	+	5.00000i	−0.213201	+	0.213201i
$551$	48.0000	−	48.0000i	2.04487	−	2.04487i
$552$		−	12.0000i		−	0.510754i
$553$		0			0
$554$	10.0000	−	10.0000i	0.424859	−	0.424859i
$555$		0			0
$556$	13.0000	+	13.0000i	0.551323	+	0.551323i
$557$	−24.0000			−1.01691			−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$	−5.00000	−	5.00000i	−0.211667	−	0.211667i
$559$		−	2.00000i		−	0.0845910i
$560$		0			0
$561$	16.0000	+	4.00000i	0.675521	+	0.168880i
$562$	−16.0000			−0.674919
$563$		−	22.0000i		−	0.927189i	−0.886047	−	0.463595i	$-0.846559\pi$
$563$		−	22.0000i		−	0.927189i	0.886047	−	0.463595i	$-0.153441\pi$
$564$	4.00000	+	4.00000i	0.168430	+	0.168430i
$565$		0			0
$566$	−13.0000	−	13.0000i	−0.546431	−	0.546431i
$567$		0			0
$568$	12.0000	−	12.0000i	0.503509	−	0.503509i
$569$			26.0000i			1.08998i	0.838444	+	0.544988i	$0.183466\pi$
$569$			26.0000i			1.08998i	−0.838444	+	0.544988i	$0.816534\pi$
$570$		0			0
$571$	4.00000	−	4.00000i	0.167395	−	0.167395i	−0.618438	−	0.785833i	$-0.712234\pi$
$571$	4.00000	−	4.00000i	0.167395	−	0.167395i	0.785833	+	0.618438i	$0.212234\pi$
$572$	−2.00000	+	2.00000i	−0.0836242	+	0.0836242i
$573$		0			0
$574$		0			0
$575$	5.00000	+	5.00000i	0.208514	+	0.208514i
$576$		−	35.0000i		−	1.45833i
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$	68.0000			2.82598
$580$		0			0
$581$		0			0
$582$	52.0000			2.15547
$583$	12.0000	+	12.0000i	0.496989	+	0.496989i
$584$	−18.0000	+	18.0000i	−0.744845	+	0.744845i
$585$		0			0
$586$			6.00000i			0.247858i
$587$		−	24.0000i		−	0.990586i	−0.868726	−	0.495293i	$-0.835061\pi$
$587$		−	24.0000i		−	0.990586i	0.868726	−	0.495293i	$-0.164939\pi$
$588$	−14.0000	+	14.0000i	−0.577350	+	0.577350i
$589$	8.00000	−	8.00000i	0.329634	−	0.329634i
$590$		0			0
$591$	−4.00000			−0.164538
$592$	2.00000	+	2.00000i	0.0821995	+	0.0821995i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$	8.00000			0.328244
$595$		0			0
$596$	6.00000			0.245770
$597$			56.0000i			2.29193i
$598$	−2.00000	−	2.00000i	−0.0817861	−	0.0817861i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	30.0000	+	30.0000i	1.22474	+	1.22474i
$601$	−6.00000	+	6.00000i	−0.244745	+	0.244745i	−0.818810	−	0.574065i	$-0.805366\pi$
$601$	−6.00000	+	6.00000i	−0.244745	+	0.244745i	0.574065	+	0.818810i	$0.305366\pi$
$602$		0			0
$603$		−	10.0000i		−	0.407231i
$604$		−	4.00000i		−	0.162758i
$605$		0			0
$606$	24.0000	−	24.0000i	0.974933	−	0.974933i
$607$	30.0000	+	30.0000i	1.21766	+	1.21766i	0.968448	+	0.249214i	$0.0801723\pi$
$607$	30.0000	+	30.0000i	1.21766	+	1.21766i	0.249214	+	0.968448i	$0.419828\pi$
$608$	40.0000			1.62221
$609$		0			0
$610$		0			0
$611$	4.00000			0.161823
$612$	5.00000	−	20.0000i	0.202113	−	0.808452i
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$		−	6.00000i		−	0.242140i
$615$		0			0
$616$		0			0
$617$	7.00000	+	7.00000i	0.281809	+	0.281809i	0.833830	−	0.552021i	$-0.186143\pi$
$617$	7.00000	+	7.00000i	0.281809	+	0.281809i	−0.552021	+	0.833830i	$0.686143\pi$
$618$	12.0000	−	12.0000i	0.482711	−	0.482711i
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	−0.644242	−	0.764822i	$-0.722827\pi$
$619$	3.00000	−	3.00000i	0.120580	−	0.120580i	0.764822	+	0.644242i	$0.222827\pi$
$620$		0			0
$621$		−	8.00000i		−	0.321029i
$622$	9.00000	−	9.00000i	0.360867	−	0.360867i
$623$		0			0
$624$	−4.00000	−	4.00000i	−0.160128	−	0.160128i
$625$	−25.0000			−1.00000
$626$	−16.0000	−	16.0000i	−0.639489	−	0.639489i
$627$			32.0000i			1.27796i
$628$	−18.0000			−0.718278
$629$	6.00000	+	10.0000i	0.239236	+	0.398726i
$630$		0			0
$631$		−	36.0000i		−	1.43314i	−0.697517	−	0.716569i	$-0.745712\pi$
$631$		−	36.0000i		−	1.43314i	0.697517	−	0.716569i	$-0.254288\pi$
$632$	21.0000	+	21.0000i	0.835335	+	0.835335i
$633$	48.0000			1.90783
$634$	−15.0000	−	15.0000i	−0.595726	−	0.595726i
$635$		0			0
$636$	24.0000	−	24.0000i	0.951662	−	0.951662i
$637$			14.0000i			0.554700i
$638$		−	12.0000i		−	0.475085i
$639$	20.0000	−	20.0000i	0.791188	−	0.791188i
$640$		0			0
$641$	24.0000	+	24.0000i	0.947943	+	0.947943i	0.998710	−	0.0507675i	$-0.0161667\pi$
$641$	24.0000	+	24.0000i	0.947943	+	0.947943i	−0.0507675	+	0.998710i	$0.516167\pi$
$642$	4.00000			0.157867
$643$	9.00000	+	9.00000i	0.354925	+	0.354925i	0.861938	−	0.507013i	$-0.169250\pi$
$643$	9.00000	+	9.00000i	0.354925	+	0.354925i	−0.507013	+	0.861938i	$0.669250\pi$
$644$		0			0
$645$		0			0
$646$	−32.0000	−	8.00000i	−1.25902	−	0.314756i
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$		−	3.00000i		−	0.117851i
$649$	6.00000	+	6.00000i	0.235521	+	0.235521i
$650$	10.0000			0.392232
$651$		0			0
$652$	−8.00000	+	8.00000i	−0.313304	+	0.313304i
$653$	−10.0000	+	10.0000i	−0.391330	+	0.391330i	−0.875161	−	0.483831i	$-0.839245\pi$
$653$	−10.0000	+	10.0000i	−0.391330	+	0.391330i	0.483831	+	0.875161i	$0.339245\pi$
$654$			52.0000i			2.03336i
$655$		0			0
$656$	−1.00000	+	1.00000i	−0.0390434	+	0.0390434i
$657$	−30.0000	+	30.0000i	−1.17041	+	1.17041i
$658$		0			0
$659$	−10.0000			−0.389545			−0.194772	−	0.980848i	$-0.562397\pi$
$659$	−10.0000			−0.389545			−0.194772	+	0.980848i	$0.562397\pi$
$660$		0			0
$661$			22.0000i			0.855701i	0.903850	+	0.427850i	$0.140729\pi$
$661$			22.0000i			0.855701i	−0.903850	+	0.427850i	$0.859271\pi$
$662$	4.00000			0.155464
$663$	−12.0000	−	20.0000i	−0.466041	−	0.776736i
$664$	−36.0000			−1.39707
$665$		0			0
$666$	10.0000	+	10.0000i	0.387492	+	0.387492i
$667$	−12.0000			−0.464642
$668$	7.00000	+	7.00000i	0.270838	+	0.270838i
$669$	16.0000	−	16.0000i	0.618596	−	0.618596i
$670$		0			0
$671$		−	12.0000i		−	0.463255i
$672$		0			0
$673$	18.0000	−	18.0000i	0.693849	−	0.693849i	−0.269228	−	0.963077i	$-0.586768\pi$
$673$	18.0000	−	18.0000i	0.693849	−	0.693849i	0.963077	+	0.269228i	$0.0867684\pi$
$674$	−17.0000	+	17.0000i	−0.654816	+	0.654816i
$675$	20.0000	+	20.0000i	0.769800	+	0.769800i
$676$	−9.00000			−0.346154
$677$	10.0000	+	10.0000i	0.384331	+	0.384331i	0.872660	−	0.488329i	$-0.162393\pi$
$677$	10.0000	+	10.0000i	0.384331	+	0.384331i	−0.488329	+	0.872660i	$0.662393\pi$
$678$		−	8.00000i		−	0.307238i
$679$		0			0
$680$		0			0
$681$	−32.0000			−1.22624
$682$		−	2.00000i		−	0.0765840i
$683$	15.0000	+	15.0000i	0.573959	+	0.573959i	0.933232	−	0.359273i	$-0.116975\pi$
$683$	15.0000	+	15.0000i	0.573959	+	0.573959i	−0.359273	+	0.933232i	$0.616975\pi$
$684$	40.0000			1.52944
$685$		0			0
$686$		0			0
$687$	40.0000	−	40.0000i	1.52610	−	1.52610i
$688$			1.00000i			0.0381246i
$689$		−	24.0000i		−	0.914327i
$690$		0			0
$691$	26.0000	−	26.0000i	0.989087	−	0.989087i	−0.0108545	−	0.999941i	$-0.503455\pi$
$691$	26.0000	−	26.0000i	0.989087	−	0.989087i	0.999941	+	0.0108545i	$0.00345515\pi$
$692$	−11.0000	−	11.0000i	−0.418157	−	0.418157i
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−72.0000			−2.72915
$697$	−5.00000	+	3.00000i	−0.189389	+	0.113633i
$698$	14.0000			0.529908
$699$		−	40.0000i		−	1.51294i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−8.00000	−	8.00000i	−0.301941	−	0.301941i
$703$	−16.0000	+	16.0000i	−0.603451	+	0.603451i
$704$	7.00000	−	7.00000i	0.263822	−	0.263822i
$705$		0			0
$706$		−	30.0000i		−	1.12906i
$707$		0			0
$708$	12.0000	−	12.0000i	0.450988	−	0.450988i
$709$	21.0000	+	21.0000i	0.788672	+	0.788672i	0.981276	−	0.192605i	$-0.0616936\pi$
$709$	21.0000	+	21.0000i	0.788672	+	0.788672i	−0.192605	+	0.981276i	$0.561694\pi$
$710$		0			0
$711$	35.0000	+	35.0000i	1.31260	+	1.31260i
$712$			18.0000i			0.674579i
$713$	−2.00000			−0.0749006
$714$		0			0
$715$		0			0
$716$		0			0
$717$	48.0000	+	48.0000i	1.79259	+	1.79259i
$718$	−24.0000			−0.895672
$719$	−33.0000	−	33.0000i	−1.23069	−	1.23069i	−0.963698	−	0.266994i	$-0.913970\pi$
$719$	−33.0000	−	33.0000i	−1.23069	−	1.23069i	−0.266994	−	0.963698i	$-0.586030\pi$
$720$		0			0
$721$		0			0
$722$		−	45.0000i		−	1.67473i
$723$		−	32.0000i		−	1.19009i
$724$	−9.00000	+	9.00000i	−0.334482	+	0.334482i
$725$	30.0000	−	30.0000i	1.11417	−	1.11417i
$726$	−18.0000	−	18.0000i	−0.668043	−	0.668043i
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$			43.0000i			1.59259i
$730$		0			0
$731$	−1.00000	+	4.00000i	−0.0369863	+	0.147945i
$732$	−24.0000			−0.887066
$733$			34.0000i			1.25582i	0.778287	+	0.627909i	$0.216089\pi$
$733$			34.0000i			1.25582i	−0.778287	+	0.627909i	$0.783911\pi$
$734$	−7.00000	−	7.00000i	−0.258375	−	0.258375i
$735$		0			0
$736$	−5.00000	−	5.00000i	−0.184302	−	0.184302i
$737$	2.00000	−	2.00000i	0.0736709	−	0.0736709i
$738$	−5.00000	+	5.00000i	−0.184053	+	0.184053i
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$		0			0
$741$	32.0000	−	32.0000i	1.17555	−	1.17555i
$742$		0			0
$743$	10.0000	+	10.0000i	0.366864	+	0.366864i	0.866332	−	0.499468i	$-0.166471\pi$
$743$	10.0000	+	10.0000i	0.366864	+	0.366864i	−0.499468	+	0.866332i	$0.666471\pi$
$744$	−12.0000			−0.439941
$745$		0			0
$746$		−	6.00000i		−	0.219676i
$747$	−60.0000			−2.19529
$748$	5.00000	−	3.00000i	0.182818	−	0.109691i
$749$		0			0
$750$		0			0
$751$	−14.0000	−	14.0000i	−0.510867	−	0.510867i	0.403925	−	0.914792i	$-0.367646\pi$
$751$	−14.0000	−	14.0000i	−0.510867	−	0.510867i	−0.914792	+	0.403925i	$0.867646\pi$
$752$	−2.00000			−0.0729325
$753$	−24.0000	−	24.0000i	−0.874609	−	0.874609i
$754$	−12.0000	+	12.0000i	−0.437014	+	0.437014i
$755$		0			0
$756$		0			0
$757$			34.0000i			1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$			34.0000i			1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$	−21.0000	+	21.0000i	−0.762754	+	0.762754i
$759$	4.00000	−	4.00000i	0.145191	−	0.145191i
$760$		0			0
$761$	14.0000			0.507500			0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000			0.507500			0.253750	+	0.967270i	$0.418336\pi$
$762$	20.0000	+	20.0000i	0.724524	+	0.724524i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	36.0000			1.30073
$767$		−	12.0000i		−	0.433295i
$768$	−34.0000	−	34.0000i	−1.22687	−	1.22687i
$769$	−16.0000			−0.576975			−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000			−0.576975			−0.288487	+	0.957484i	$0.593152\pi$
$770$		0			0
$771$	−52.0000	+	52.0000i	−1.87273	+	1.87273i
$772$	17.0000	−	17.0000i	0.611843	−	0.611843i
$773$		−	26.0000i		−	0.935155i	−0.883952	−	0.467578i	$-0.845127\pi$
$773$		−	26.0000i		−	0.935155i	0.883952	−	0.467578i	$-0.154873\pi$
$774$			5.00000i			0.179721i
$775$	5.00000	−	5.00000i	0.179605	−	0.179605i
$776$	39.0000	−	39.0000i	1.40002	−	1.40002i
$777$		0			0
$778$	30.0000			1.07555
$779$	−8.00000	−	8.00000i	−0.286630	−	0.286630i
$780$		0			0
$781$	8.00000			0.286263
$782$	3.00000	+	5.00000i	0.107280	+	0.178800i
$783$	−48.0000			−1.71538
$784$		−	7.00000i		−	0.250000i
$785$		0			0
$786$	−32.0000			−1.14140
$787$	29.0000	+	29.0000i	1.03374	+	1.03374i	0.999411	+	0.0343277i	$0.0109290\pi$
$787$	29.0000	+	29.0000i	1.03374	+	1.03374i	0.0343277	+	0.999411i	$0.489071\pi$
$788$	−1.00000	+	1.00000i	−0.0356235	+	0.0356235i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	15.0000	−	15.0000i	0.533002	−	0.533002i
$793$	−12.0000	+	12.0000i	−0.426132	+	0.426132i
$794$	3.00000	+	3.00000i	0.106466	+	0.106466i
$795$		0			0
$796$	14.0000	+	14.0000i	0.496217	+	0.496217i
$797$			56.0000i			1.98362i	0.127715	+	0.991811i	$0.459236\pi$
$797$			56.0000i			1.98362i	−0.127715	+	0.991811i	$0.540764\pi$
$798$		0			0
$799$	−8.00000	−	2.00000i	−0.283020	−	0.0707549i
$800$	25.0000			0.883883
$801$			30.0000i			1.06000i
$802$	−1.00000	−	1.00000i	−0.0353112	−	0.0353112i
$803$	−12.0000			−0.423471
$804$	−4.00000	−	4.00000i	−0.141069	−	0.141069i
$805$		0			0
$806$	−2.00000	+	2.00000i	−0.0704470	+	0.0704470i
$807$		−	12.0000i		−	0.422420i
$808$		−	36.0000i		−	1.26648i
$809$	−7.00000	+	7.00000i	−0.246107	+	0.246107i	−0.819371	−	0.573264i	$-0.805677\pi$
$809$	−7.00000	+	7.00000i	−0.246107	+	0.246107i	0.573264	+	0.819371i	$0.305677\pi$
$810$		0			0
$811$	−30.0000	−	30.0000i	−1.05344	−	1.05344i	−0.998489	−	0.0549536i	$-0.982499\pi$
$811$	−30.0000	−	30.0000i	−1.05344	−	1.05344i	−0.0549536	−	0.998489i	$-0.517501\pi$
$812$		0			0
$813$	20.0000	+	20.0000i	0.701431	+	0.701431i
$814$			4.00000i			0.140200i
$815$		0			0
$816$	6.00000	+	10.0000i	0.210042	+	0.350070i
$817$	−8.00000			−0.279885
$818$		−	14.0000i		−	0.489499i
$819$		0			0
$820$		0			0
$821$	5.00000	+	5.00000i	0.174501	+	0.174501i	0.788954	−	0.614453i	$-0.210623\pi$
$821$	5.00000	+	5.00000i	0.174501	+	0.174501i	−0.614453	+	0.788954i	$0.710623\pi$
$822$	−4.00000	+	4.00000i	−0.139516	+	0.139516i
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	−0.971018	−	0.239004i	$-0.923179\pi$
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	0.239004	+	0.971018i	$0.423179\pi$
$824$		−	18.0000i		−	0.627060i
$825$			20.0000i			0.696311i
$826$		0			0
$827$	17.0000	−	17.0000i	0.591148	−	0.591148i	−0.346794	−	0.937941i	$-0.612730\pi$
$827$	17.0000	−	17.0000i	0.591148	−	0.591148i	0.937941	+	0.346794i	$0.112730\pi$
$828$	−5.00000	−	5.00000i	−0.173762	−	0.173762i
$829$	50.0000			1.73657			0.868286	−	0.496064i	$-0.165222\pi$
$829$	50.0000			1.73657			0.868286	+	0.496064i	$0.165222\pi$
$830$		0			0
$831$		−	40.0000i		−	1.38758i
$832$	−14.0000			−0.485363
$833$	7.00000	−	28.0000i	0.242536	−	0.970143i
$834$	−52.0000			−1.80061
$835$		0			0
$836$	8.00000	+	8.00000i	0.276686	+	0.276686i
$837$	−8.00000			−0.276520
$838$	−6.00000	−	6.00000i	−0.207267	−	0.207267i
$839$	−4.00000	+	4.00000i	−0.138095	+	0.138095i	−0.772775	−	0.634680i	$-0.781132\pi$
$839$	−4.00000	+	4.00000i	−0.138095	+	0.138095i	0.634680	+	0.772775i	$0.281132\pi$
$840$		0			0
$841$			43.0000i			1.48276i
$842$		−	14.0000i		−	0.482472i
$843$	−32.0000	+	32.0000i	−1.10214	+	1.10214i
$844$	12.0000	−	12.0000i	0.413057	−	0.413057i
$845$		0			0
$846$	−10.0000			−0.343807
$847$		0			0
$848$			12.0000i			0.412082i
$849$	−52.0000			−1.78464
$850$	−20.0000	−	5.00000i	−0.685994	−	0.171499i
$851$	4.00000			0.137118
$852$		−	16.0000i		−	0.548151i
$853$	21.0000	+	21.0000i	0.719026	+	0.719026i	0.968406	−	0.249380i	$-0.0802267\pi$
$853$	21.0000	+	21.0000i	0.719026	+	0.719026i	−0.249380	+	0.968406i	$0.580227\pi$
$854$		0			0
$855$		0			0
$856$	3.00000	−	3.00000i	0.102538	−	0.102538i
$857$	−27.0000	+	27.0000i	−0.922302	+	0.922302i	−0.997192	−	0.0748894i	$-0.976140\pi$
$857$	−27.0000	+	27.0000i	−0.922302	+	0.922302i	0.0748894	+	0.997192i	$0.476140\pi$
$858$		−	8.00000i		−	0.273115i
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$		0			0
$861$		0			0
$862$	−7.00000	−	7.00000i	−0.238421	−	0.238421i
$863$	44.0000			1.49778			0.748889	−	0.662696i	$-0.230588\pi$
$863$	44.0000			1.49778			0.748889	+	0.662696i	$0.230588\pi$
$864$	−20.0000	−	20.0000i	−0.680414	−	0.680414i
$865$		0			0
$866$	10.0000			0.339814
$867$	14.0000	+	46.0000i	0.475465	+	1.56224i
$868$		0			0
$869$			14.0000i			0.474917i
$870$		0			0
$871$	−4.00000			−0.135535
$872$	39.0000	+	39.0000i	1.32071	+	1.32071i
$873$	65.0000	−	65.0000i	2.19992	−	2.19992i
$874$	−8.00000	+	8.00000i	−0.270604	+	0.270604i
$875$		0			0
$876$			24.0000i			0.810885i
$877$	13.0000	−	13.0000i	0.438979	−	0.438979i	−0.452689	−	0.891668i	$-0.649535\pi$
$877$	13.0000	−	13.0000i	0.438979	−	0.438979i	0.891668	+	0.452689i	$0.149535\pi$
$878$	21.0000	−	21.0000i	0.708716	−	0.708716i
$879$	12.0000	+	12.0000i	0.404750	+	0.404750i
$880$		0			0
$881$	17.0000	+	17.0000i	0.572745	+	0.572745i	0.932894	−	0.360150i	$-0.117274\pi$
$881$	17.0000	+	17.0000i	0.572745	+	0.572745i	−0.360150	+	0.932894i	$0.617274\pi$
$882$		−	35.0000i		−	1.17851i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	−8.00000	−	2.00000i	−0.269069	−	0.0672673i
$885$		0			0
$886$		−	20.0000i		−	0.671913i
$887$	−32.0000	−	32.0000i	−1.07445	−	1.07445i	−0.996996	−	0.0774593i	$-0.975319\pi$
$887$	−32.0000	−	32.0000i	−1.07445	−	1.07445i	−0.0774593	−	0.996996i	$-0.524681\pi$
$888$	24.0000			0.805387
$889$		0			0
$890$		0			0
$891$	1.00000	−	1.00000i	0.0335013	−	0.0335013i
$892$		−	8.00000i		−	0.267860i
$893$		−	16.0000i		−	0.535420i
$894$	−12.0000	+	12.0000i	−0.401340	+	0.401340i
$895$		0			0
$896$		0			0
$897$	−8.00000			−0.267112
$898$	8.00000	+	8.00000i	0.266963	+	0.266963i
$899$			12.0000i			0.400222i
$900$	25.0000			0.833333
$901$	−12.0000	+	48.0000i	−0.399778	+	1.59911i
$902$	−2.00000			−0.0665927
$903$		0			0
$904$	−6.00000	−	6.00000i	−0.199557	−	0.199557i
$905$		0			0
$906$	8.00000	+	8.00000i	0.265782	+	0.265782i
$907$	3.00000	−	3.00000i	0.0996134	−	0.0996134i	−0.655544	−	0.755157i	$-0.727561\pi$
$907$	3.00000	−	3.00000i	0.0996134	−	0.0996134i	0.755157	+	0.655544i	$0.227561\pi$
$908$	−8.00000	+	8.00000i	−0.265489	+	0.265489i
$909$		−	60.0000i		−	1.99007i
$910$		0			0
$911$	−10.0000	+	10.0000i	−0.331315	+	0.331315i	−0.853086	−	0.521771i	$-0.825272\pi$
$911$	−10.0000	+	10.0000i	−0.331315	+	0.331315i	0.521771	+	0.853086i	$0.325272\pi$
$912$	−16.0000	+	16.0000i	−0.529813	+	0.529813i
$913$	−12.0000	−	12.0000i	−0.397142	−	0.397142i
$914$	10.0000			0.330771
$915$		0			0
$916$		−	20.0000i		−	0.660819i
$917$		0			0
$918$	12.0000	+	20.0000i	0.396059	+	0.660098i
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$	−12.0000	−	12.0000i	−0.395413	−	0.395413i
$922$	10.0000			0.329332
$923$	−8.00000	−	8.00000i	−0.263323	−	0.263323i
$924$		0			0
$925$	−10.0000	+	10.0000i	−0.328798	+	0.328798i
$926$		−	8.00000i		−	0.262896i
$927$		−	30.0000i		−	0.985329i
$928$	−30.0000	+	30.0000i	−0.984798	+	0.984798i
$929$	28.0000	−	28.0000i	0.918650	−	0.918650i	−0.0782811	−	0.996931i	$-0.524943\pi$
$929$	28.0000	−	28.0000i	0.918650	−	0.918650i	0.996931	+	0.0782811i	$0.0249432\pi$
$930$		0			0
$931$	56.0000			1.83533
$932$	−10.0000	−	10.0000i	−0.327561	−	0.327561i
$933$		−	36.0000i		−	1.17859i
$934$	8.00000			0.261768
$935$		0			0
$936$	−30.0000			−0.980581
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$		0			0
$939$	−64.0000			−2.08856
$940$		0			0
$941$	−1.00000	+	1.00000i	−0.0325991	+	0.0325991i	−0.723218	−	0.690619i	$-0.757338\pi$
$941$	−1.00000	+	1.00000i	−0.0325991	+	0.0325991i	0.690619	+	0.723218i	$0.257338\pi$
$942$	36.0000	−	36.0000i	1.17294	−	1.17294i
$943$			2.00000i			0.0651290i
$944$			6.00000i			0.195283i
$945$		0			0
$946$	−1.00000	+	1.00000i	−0.0325128	+	0.0325128i
$947$	19.0000	+	19.0000i	0.617417	+	0.617417i	0.944868	−	0.327451i	$-0.106190\pi$
$947$	19.0000	+	19.0000i	0.617417	+	0.617417i	−0.327451	+	0.944868i	$0.606190\pi$
$948$	28.0000			0.909398
$949$	12.0000	+	12.0000i	0.389536	+	0.389536i
$950$		−	40.0000i		−	1.29777i
$951$	−60.0000			−1.94563
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$			60.0000i			1.94257i
$955$		0			0
$956$	24.0000			0.776215
$957$	−24.0000	−	24.0000i	−0.775810	−	0.775810i
$958$	29.0000	−	29.0000i	0.936947	−	0.936947i
$959$		0			0
$960$		0			0
$961$		−	29.0000i		−	0.935484i
$962$	4.00000	−	4.00000i	0.128965	−	0.128965i
$963$	5.00000	−	5.00000i	0.161123	−	0.161123i
$964$	−8.00000	−	8.00000i	−0.257663	−	0.257663i
$965$		0			0
$966$		0			0
$967$			40.0000i			1.28631i	0.765735	+	0.643157i	$0.222376\pi$
$967$			40.0000i			1.28631i	−0.765735	+	0.643157i	$0.777624\pi$
$968$	−27.0000			−0.867813
$969$	−80.0000	+	48.0000i	−2.56997	+	1.54198i
$970$		0			0
$971$			36.0000i			1.15529i	0.816286	+	0.577647i	$0.196029\pi$
$971$			36.0000i			1.15529i	−0.816286	+	0.577647i	$0.803971\pi$
$972$	10.0000	+	10.0000i	0.320750	+	0.320750i
$973$		0			0
$974$	−3.00000	−	3.00000i	−0.0961262	−	0.0961262i
$975$	20.0000	−	20.0000i	0.640513	−	0.640513i
$976$	6.00000	−	6.00000i	0.192055	−	0.192055i
$977$		−	2.00000i		−	0.0639857i	−0.999488	−	0.0319928i	$-0.989815\pi$
$977$		−	2.00000i		−	0.0639857i	0.999488	−	0.0319928i	$-0.0101854\pi$
$978$		−	32.0000i		−	1.02325i
$979$	−6.00000	+	6.00000i	−0.191761	+	0.191761i
$980$		0			0
$981$	65.0000	+	65.0000i	2.07529	+	2.07529i
$982$	−36.0000			−1.14881
$983$	−26.0000	−	26.0000i	−0.829271	−	0.829271i	0.158145	−	0.987416i	$-0.449449\pi$
$983$	−26.0000	−	26.0000i	−0.829271	−	0.829271i	−0.987416	+	0.158145i	$0.949449\pi$
$984$			12.0000i			0.382546i
$985$		0			0
$986$	30.0000	−	18.0000i	0.955395	−	0.573237i
$987$		0			0
$988$		−	16.0000i		−	0.509028i
$989$	1.00000	+	1.00000i	0.0317982	+	0.0317982i
$990$		0			0
$991$	−4.00000	−	4.00000i	−0.127064	−	0.127064i	0.640715	−	0.767779i	$-0.278638\pi$
$991$	−4.00000	−	4.00000i	−0.127064	−	0.127064i	−0.767779	+	0.640715i	$0.778638\pi$
$992$	−5.00000	+	5.00000i	−0.158750	+	0.158750i
$993$	8.00000	−	8.00000i	0.253872	−	0.253872i
$994$		0			0
$995$		0			0
$996$	−24.0000	+	24.0000i	−0.760469	+	0.760469i
$997$	4.00000	−	4.00000i	0.126681	−	0.126681i	−0.640923	−	0.767605i	$-0.721448\pi$
$997$	4.00000	−	4.00000i	0.126681	−	0.126681i	0.767605	+	0.640923i	$0.221448\pi$
$998$	14.0000	+	14.0000i	0.443162	+	0.443162i
$999$	16.0000			0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.b.302.1	yes	2
17.4	even	4	inner	731.2.f.b.259.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.b.259.1	✓	2	17.4	even	4	inner
731.2.f.b.302.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(2.00000 + 2.00000i) q^{3} +1.00000 q^{4} +(-2.00000 + 2.00000i) q^{6} +3.00000i q^{8} +5.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(2.00000 + 2.00000i) q^{3} +1.00000 q^{4} +(-2.00000 + 2.00000i) q^{6} +3.00000i q^{8} +5.00000i q^{9} +(-1.00000 + 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{12} +2.00000 q^{13} -1.00000 q^{16} +(-4.00000 - 1.00000i) q^{17} -5.00000 q^{18} -8.00000i q^{19} +(-1.00000 - 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-6.00000 + 6.00000i) q^{24} -5.00000i q^{25} +2.00000i q^{26} +(-4.00000 + 4.00000i) q^{27} +(6.00000 + 6.00000i) q^{29} +(1.00000 + 1.00000i) q^{31} +5.00000i q^{32} -4.00000 q^{33} +(1.00000 - 4.00000i) q^{34} +5.00000i q^{36} +(-2.00000 - 2.00000i) q^{37} +8.00000 q^{38} +(4.00000 + 4.00000i) q^{39} +(1.00000 - 1.00000i) q^{41} -1.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} +2.00000 q^{47} +(-2.00000 - 2.00000i) q^{48} +7.00000i q^{49} +5.00000 q^{50} +(-6.00000 - 10.0000i) q^{51} +2.00000 q^{52} -12.0000i q^{53} +(-4.00000 - 4.00000i) q^{54} +(16.0000 - 16.0000i) q^{57} +(-6.00000 + 6.00000i) q^{58} -6.00000i q^{59} +(-6.00000 + 6.00000i) q^{61} +(-1.00000 + 1.00000i) q^{62} -7.00000 q^{64} -4.00000i q^{66} -2.00000 q^{67} +(-4.00000 - 1.00000i) q^{68} -4.00000 q^{69} +(-4.00000 - 4.00000i) q^{71} -15.0000 q^{72} +(6.00000 + 6.00000i) q^{73} +(2.00000 - 2.00000i) q^{74} +(10.0000 - 10.0000i) q^{75} -8.00000i q^{76} +(-4.00000 + 4.00000i) q^{78} +(7.00000 - 7.00000i) q^{79} -1.00000 q^{81} +(1.00000 + 1.00000i) q^{82} +12.0000i q^{83} +1.00000 q^{86} +24.0000i q^{87} +(-3.00000 - 3.00000i) q^{88} +6.00000 q^{89} +(-1.00000 + 1.00000i) q^{92} +4.00000i q^{93} +2.00000i q^{94} +(-10.0000 + 10.0000i) q^{96} +(-13.0000 - 13.0000i) q^{97} -7.00000 q^{98} +(-5.00000 - 5.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} + 2 q^{4} - 4 q^{6}+O(q^{10}) \) 2 * q + 4 * q^3 + 2 * q^4 - 4 * q^6	\( 2 q + 4 q^{3} + 2 q^{4} - 4 q^{6} - 2 q^{11} + 4 q^{12} + 4 q^{13} - 2 q^{16} - 8 q^{17} - 10 q^{18} - 2 q^{22} - 2 q^{23} - 12 q^{24} - 8 q^{27} + 12 q^{29} + 2 q^{31} - 8 q^{33} + 2 q^{34} - 4 q^{37} + 16 q^{38} + 8 q^{39} + 2 q^{41} - 2 q^{44} - 2 q^{46} + 4 q^{47} - 4 q^{48} + 10 q^{50} - 12 q^{51} + 4 q^{52} - 8 q^{54} + 32 q^{57} - 12 q^{58} - 12 q^{61} - 2 q^{62} - 14 q^{64} - 4 q^{67} - 8 q^{68} - 8 q^{69} - 8 q^{71} - 30 q^{72} + 12 q^{73} + 4 q^{74} + 20 q^{75} - 8 q^{78} + 14 q^{79} - 2 q^{81} + 2 q^{82} + 2 q^{86} - 6 q^{88} + 12 q^{89} - 2 q^{92} - 20 q^{96} - 26 q^{97} - 14 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 + 2 * q^4 - 4 * q^6 - 2 * q^11 + 4 * q^12 + 4 * q^13 - 2 * q^16 - 8 * q^17 - 10 * q^18 - 2 * q^22 - 2 * q^23 - 12 * q^24 - 8 * q^27 + 12 * q^29 + 2 * q^31 - 8 * q^33 + 2 * q^34 - 4 * q^37 + 16 * q^38 + 8 * q^39 + 2 * q^41 - 2 * q^44 - 2 * q^46 + 4 * q^47 - 4 * q^48 + 10 * q^50 - 12 * q^51 + 4 * q^52 - 8 * q^54 + 32 * q^57 - 12 * q^58 - 12 * q^61 - 2 * q^62 - 14 * q^64 - 4 * q^67 - 8 * q^68 - 8 * q^69 - 8 * q^71 - 30 * q^72 + 12 * q^73 + 4 * q^74 + 20 * q^75 - 8 * q^78 + 14 * q^79 - 2 * q^81 + 2 * q^82 + 2 * q^86 - 6 * q^88 + 12 * q^89 - 2 * q^92 - 20 * q^96 - 26 * q^97 - 14 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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