LMFDB - Embedded newform 1071.2.n.b.820.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(64,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1071.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.n (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:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 32 x^{18} + 426 x^{16} + 3072 x^{14} + 13121 x^{12} + 34148 x^{10} + 53608 x^{8} + 48276 x^{6} + \cdots + 4 $ x^20 + 32x^18 + 426x^16 + 3072x^14 + 13121x^12 + 34148x^10 + 53608x^8 + 48276x^6 + 22224x^4 + 3920*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			820.4
Root			$-1.51109i$ of defining polynomial
Character	$\chi$	$=$	1071.820
Dual form			1071.2.n.b.64.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.51109i q^{2} -0.283389 q^{4} +(1.65084 - 1.65084i) q^{5} +(-0.707107 - 0.707107i) q^{7} -2.59395i q^{8} +O(q^{10})$	\(q-1.51109i q^{2} -0.283389 q^{4} +(1.65084 - 1.65084i) q^{5} +(-0.707107 - 0.707107i) q^{7} -2.59395i q^{8} +(-2.49457 - 2.49457i) q^{10} +(-2.73442 - 2.73442i) q^{11} -7.04427 q^{13} +(-1.06850 + 1.06850i) q^{14} -4.48647 q^{16} +(-0.965114 + 4.00856i) q^{17} +0.992753i q^{19} +(-0.467830 + 0.467830i) q^{20} +(-4.13195 + 4.13195i) q^{22} +(0.461170 + 0.461170i) q^{23} -0.450549i q^{25} +10.6445i q^{26} +(0.200386 + 0.200386i) q^{28} +(3.56926 - 3.56926i) q^{29} +(1.46992 - 1.46992i) q^{31} +1.59155i q^{32} +(6.05729 + 1.45837i) q^{34} -2.33464 q^{35} +(4.07799 - 4.07799i) q^{37} +1.50014 q^{38} +(-4.28220 - 4.28220i) q^{40} +(-8.45995 - 8.45995i) q^{41} +2.40741i q^{43} +(0.774904 + 0.774904i) q^{44} +(0.696868 - 0.696868i) q^{46} +6.81302 q^{47} +1.00000i q^{49} -0.680819 q^{50} +1.99627 q^{52} -5.04239i q^{53} -9.02818 q^{55} +(-1.83420 + 1.83420i) q^{56} +(-5.39348 - 5.39348i) q^{58} -1.56548i q^{59} +(8.83396 + 8.83396i) q^{61} +(-2.22118 - 2.22118i) q^{62} -6.56797 q^{64} +(-11.6290 + 11.6290i) q^{65} +4.95686 q^{67} +(0.273503 - 1.13598i) q^{68} +3.52785i q^{70} +(5.53082 - 5.53082i) q^{71} +(3.24064 - 3.24064i) q^{73} +(-6.16220 - 6.16220i) q^{74} -0.281335i q^{76} +3.86705i q^{77} +(0.679318 + 0.679318i) q^{79} +(-7.40644 + 7.40644i) q^{80} +(-12.7837 + 12.7837i) q^{82} -12.8881i q^{83} +(5.02425 + 8.21074i) q^{85} +3.63780 q^{86} +(-7.09295 + 7.09295i) q^{88} -3.82872 q^{89} +(4.98105 + 4.98105i) q^{91} +(-0.130690 - 0.130690i) q^{92} -10.2951i q^{94} +(1.63888 + 1.63888i) q^{95} +(2.10281 - 2.10281i) q^{97} +1.51109 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{4} - 8 q^{5}+O(q^{10}) $ 20 * q - 24 * q^4 - 8 * q^5	$ 20 q - 24 q^{4} - 8 q^{5} + 16 q^{10} - 4 q^{11} - 12 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{17} + 52 q^{20} - 24 q^{22} + 4 q^{23} + 8 q^{29} + 8 q^{31} - 44 q^{34} - 12 q^{35} + 24 q^{37} + 64 q^{38} - 52 q^{40} + 20 q^{41} - 72 q^{44} + 28 q^{46} + 32 q^{47} - 104 q^{50} + 48 q^{52} - 36 q^{55} + 4 q^{56} - 60 q^{58} + 28 q^{61} - 36 q^{62} - 112 q^{64} + 4 q^{65} + 40 q^{67} + 52 q^{68} - 16 q^{71} - 72 q^{73} + 24 q^{74} - 8 q^{79} - 120 q^{80} + 108 q^{82} + 40 q^{85} - 28 q^{88} + 64 q^{89} - 12 q^{91} + 56 q^{92} - 60 q^{95} + 60 q^{97} + 8 q^{98}+O(q^{100}) $ 20 * q - 24 * q^4 - 8 * q^5 + 16 * q^10 - 4 * q^11 - 12 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^17 + 52 * q^20 - 24 * q^22 + 4 * q^23 + 8 * q^29 + 8 * q^31 - 44 * q^34 - 12 * q^35 + 24 * q^37 + 64 * q^38 - 52 * q^40 + 20 * q^41 - 72 * q^44 + 28 * q^46 + 32 * q^47 - 104 * q^50 + 48 * q^52 - 36 * q^55 + 4 * q^56 - 60 * q^58 + 28 * q^61 - 36 * q^62 - 112 * q^64 + 4 * q^65 + 40 * q^67 + 52 * q^68 - 16 * q^71 - 72 * q^73 + 24 * q^74 - 8 * q^79 - 120 * q^80 + 108 * q^82 + 40 * q^85 - 28 * q^88 + 64 * q^89 - 12 * q^91 + 56 * q^92 - 60 * q^95 + 60 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$		−	1.51109i		−	1.06850i	−0.845326	−	0.534251i	$-0.820594\pi$
$2$		−	1.51109i		−	1.06850i	0.845326	−	0.534251i	$-0.179406\pi$
$3$		0			0
$3$		0			0
$4$	−0.283389			−0.141694
$5$	1.65084	−	1.65084i	0.738278	−	0.738278i	−0.233966	−	0.972245i	$-0.575171\pi$
$5$	1.65084	−	1.65084i	0.738278	−	0.738278i	0.972245	+	0.233966i	$0.0751706\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		−	2.59395i		−	0.917100i
$9$		0			0
$10$	−2.49457	−	2.49457i	−0.788851	−	0.788851i
$11$	−2.73442	−	2.73442i	−0.824459	−	0.824459i	0.162285	−	0.986744i	$-0.448114\pi$
$11$	−2.73442	−	2.73442i	−0.824459	−	0.824459i	−0.986744	+	0.162285i	$0.948114\pi$
$12$		0			0
$13$	−7.04427			−1.95373			−0.976864	−	0.213859i	$-0.931397\pi$
$13$	−7.04427			−1.95373			−0.976864	+	0.213859i	$0.931397\pi$
$14$	−1.06850	+	1.06850i	−0.285569	+	0.285569i
$15$		0			0
$16$	−4.48647			−1.12162
$17$	−0.965114	+	4.00856i	−0.234074	+	0.972219i
$17$	−0.965114	+	4.00856i	−0.234074	+	0.972219i
$18$		0			0
$19$			0.992753i			0.227753i	0.993495	+	0.113877i	$0.0363269\pi$
$19$			0.992753i			0.227753i	−0.993495	+	0.113877i	$0.963673\pi$
$20$	−0.467830	+	0.467830i	−0.104610	+	0.104610i
$21$		0			0
$22$	−4.13195	+	4.13195i	−0.880935	+	0.880935i
$23$	0.461170	+	0.461170i	0.0961605	+	0.0961605i	0.753551	−	0.657390i	$-0.228340\pi$
$23$	0.461170	+	0.461170i	0.0961605	+	0.0961605i	−0.657390	+	0.753551i	$0.728340\pi$
$24$		0			0
$25$		−	0.450549i		−	0.0901097i
$26$			10.6445i			2.08756i
$27$		0			0
$28$	0.200386	+	0.200386i	0.0378694	+	0.0378694i
$29$	3.56926	−	3.56926i	0.662796	−	0.662796i	−0.293242	−	0.956038i	$-0.594734\pi$
$29$	3.56926	−	3.56926i	0.662796	−	0.662796i	0.956038	+	0.293242i	$0.0947343\pi$
$30$		0			0
$31$	1.46992	−	1.46992i	0.264006	−	0.264006i	−0.562673	−	0.826679i	$-0.690227\pi$
$31$	1.46992	−	1.46992i	0.264006	−	0.264006i	0.826679	+	0.562673i	$0.190227\pi$
$32$			1.59155i			0.281349i
$33$		0			0
$34$	6.05729	+	1.45837i	1.03882	+	0.250109i
$35$	−2.33464			−0.394626
$36$		0			0
$37$	4.07799	−	4.07799i	0.670417	−	0.670417i	−0.287395	−	0.957812i	$-0.592789\pi$
$37$	4.07799	−	4.07799i	0.670417	−	0.670417i	0.957812	+	0.287395i	$0.0927892\pi$
$38$	1.50014			0.243355
$39$		0			0
$40$	−4.28220	−	4.28220i	−0.677075	−	0.677075i
$41$	−8.45995	−	8.45995i	−1.32122	−	1.32122i	−0.912788	−	0.408433i	$-0.866075\pi$
$41$	−8.45995	−	8.45995i	−1.32122	−	1.32122i	−0.408433	−	0.912788i	$-0.633925\pi$
$42$		0			0
$43$			2.40741i			0.367126i	0.983008	+	0.183563i	$0.0587631\pi$
$43$			2.40741i			0.367126i	−0.983008	+	0.183563i	$0.941237\pi$
$44$	0.774904	+	0.774904i	0.116821	+	0.116821i
$45$		0			0
$46$	0.696868	−	0.696868i	0.102748	−	0.102748i
$47$	6.81302			0.993781			0.496890	−	0.867813i	$-0.334475\pi$
$47$	6.81302			0.993781			0.496890	+	0.867813i	$0.334475\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−0.680819			−0.0962823
$51$		0			0
$52$	1.99627			0.276833
$53$		−	5.04239i		−	0.692626i	−0.938119	−	0.346313i	$-0.887434\pi$
$53$		−	5.04239i		−	0.692626i	0.938119	−	0.346313i	$-0.112566\pi$
$54$		0			0
$55$	−9.02818			−1.21736
$56$	−1.83420	+	1.83420i	−0.245105	+	0.245105i
$57$		0			0
$58$	−5.39348	−	5.39348i	−0.708198	−	0.708198i
$59$		−	1.56548i		−	0.203808i	−0.994794	−	0.101904i	$-0.967507\pi$
$59$		−	1.56548i		−	0.203808i	0.994794	−	0.101904i	$-0.0324934\pi$
$60$		0			0
$61$	8.83396	+	8.83396i	1.13107	+	1.13107i	0.989999	+	0.141074i	$0.0450555\pi$
$61$	8.83396	+	8.83396i	1.13107	+	1.13107i	0.141074	+	0.989999i	$0.454944\pi$
$62$	−2.22118	−	2.22118i	−0.282090	−	0.282090i
$63$		0			0
$64$	−6.56797			−0.820996
$65$	−11.6290	+	11.6290i	−1.44240	+	1.44240i
$66$		0			0
$67$	4.95686			0.605577			0.302788	−	0.953058i	$-0.402082\pi$
$67$	4.95686			0.605577			0.302788	+	0.953058i	$0.402082\pi$
$68$	0.273503	−	1.13598i	0.0331671	−	0.137758i
$69$		0			0
$70$			3.52785i			0.421659i
$71$	5.53082	−	5.53082i	0.656387	−	0.656387i	−0.298136	−	0.954523i	$-0.596365\pi$
$71$	5.53082	−	5.53082i	0.656387	−	0.656387i	0.954523	+	0.298136i	$0.0963649\pi$
$72$		0			0
$73$	3.24064	−	3.24064i	0.379289	−	0.379289i	−0.491557	−	0.870846i	$-0.663572\pi$
$73$	3.24064	−	3.24064i	0.379289	−	0.379289i	0.870846	+	0.491557i	$0.163572\pi$
$74$	−6.16220	−	6.16220i	−0.716341	−	0.716341i
$75$		0			0
$76$		−	0.281335i		−	0.0322714i
$77$			3.86705i			0.440692i
$78$		0			0
$79$	0.679318	+	0.679318i	0.0764293	+	0.0764293i	0.744288	−	0.667859i	$-0.232789\pi$
$79$	0.679318	+	0.679318i	0.0764293	+	0.0764293i	−0.667859	+	0.744288i	$0.732789\pi$
$80$	−7.40644	+	7.40644i	−0.828066	+	0.828066i
$81$		0			0
$82$	−12.7837	+	12.7837i	−1.41173	+	1.41173i
$83$		−	12.8881i		−	1.41465i	−0.706889	−	0.707324i	$-0.749902\pi$
$83$		−	12.8881i		−	1.41465i	0.706889	−	0.707324i	$-0.250098\pi$
$84$		0			0
$85$	5.02425	+	8.21074i	0.544956	+	0.890580i
$86$	3.63780			0.392275
$87$		0			0
$88$	−7.09295	+	7.09295i	−0.756111	+	0.756111i
$89$	−3.82872			−0.405843			−0.202922	−	0.979195i	$-0.565044\pi$
$89$	−3.82872			−0.405843			−0.202922	+	0.979195i	$0.565044\pi$
$90$		0			0
$91$	4.98105	+	4.98105i	0.522156	+	0.522156i
$92$	−0.130690	−	0.130690i	−0.0136254	−	0.0136254i
$93$		0			0
$94$		−	10.2951i		−	1.06186i
$95$	1.63888	+	1.63888i	0.168145	+	0.168145i
$96$		0			0
$97$	2.10281	−	2.10281i	0.213508	−	0.213508i	−0.592248	−	0.805756i	$-0.701759\pi$
$97$	2.10281	−	2.10281i	0.213508	−	0.213508i	0.805756	+	0.592248i	$0.201759\pi$
$98$	1.51109			0.152643
$99$		0			0
$100$			0.127680i			0.0127680i
$101$	1.00557			0.100058			0.0500290	−	0.998748i	$-0.484069\pi$
$101$	1.00557			0.100058			0.0500290	+	0.998748i	$0.484069\pi$
$102$		0			0
$103$	−1.58496			−0.156170			−0.0780852	−	0.996947i	$-0.524881\pi$
$103$	−1.58496			−0.156170			−0.0780852	+	0.996947i	$0.524881\pi$
$104$			18.2725i			1.79177i
$105$		0			0
$106$	−7.61950			−0.740071
$107$	−4.33329	+	4.33329i	−0.418915	+	0.418915i	−0.884829	−	0.465915i	$-0.845725\pi$
$107$	−4.33329	+	4.33329i	−0.418915	+	0.418915i	0.465915	+	0.884829i	$0.345725\pi$
$108$		0			0
$109$	9.35507	+	9.35507i	0.896053	+	0.896053i	0.995084	−	0.0990316i	$-0.0315745\pi$
$109$	9.35507	+	9.35507i	0.896053	+	0.896053i	−0.0990316	+	0.995084i	$0.531574\pi$
$110$			13.6424i			1.30075i
$111$		0			0
$112$	3.17241	+	3.17241i	0.299765	+	0.299765i
$113$	−13.3488	−	13.3488i	−1.25575	−	1.25575i	−0.953104	−	0.302642i	$-0.902131\pi$
$113$	−13.3488	−	13.3488i	−1.25575	−	1.25575i	−0.302642	−	0.953104i	$-0.597869\pi$
$114$		0			0
$115$	1.52264			0.141986
$116$	−1.01149	+	1.01149i	−0.0939145	+	0.0939145i
$117$		0			0
$118$	−2.36558			−0.217769
$119$	3.51692	−	2.15204i	0.322395	−	0.197277i
$120$		0			0
$121$			3.95411i			0.359464i
$122$	13.3489	−	13.3489i	1.20855	−	1.20855i
$123$		0			0
$124$	−0.416560	+	0.416560i	−0.0374082	+	0.0374082i
$125$	7.51042	+	7.51042i	0.671752	+	0.671752i
$126$		0			0
$127$		−	22.2222i		−	1.97190i	−0.167035	−	0.985951i	$-0.553419\pi$
$127$		−	22.2222i		−	1.97190i	0.167035	−	0.985951i	$-0.446581\pi$
$128$			13.1079i			1.15858i
$129$		0			0
$130$	17.5724	+	17.5724i	1.54120	+	1.54120i
$131$	5.73121	−	5.73121i	0.500738	−	0.500738i	−0.410929	−	0.911667i	$-0.634796\pi$
$131$	5.73121	−	5.73121i	0.500738	−	0.500738i	0.911667	+	0.410929i	$0.134796\pi$
$132$		0			0
$133$	0.701983	−	0.701983i	0.0608696	−	0.0608696i
$134$		−	7.49025i		−	0.647059i
$135$		0			0
$136$	10.3980	+	2.50346i	0.891622	+	0.214670i
$137$	7.66715			0.655049			0.327524	−	0.944843i	$-0.393786\pi$
$137$	7.66715			0.655049			0.327524	+	0.944843i	$0.393786\pi$
$138$		0			0
$139$	−3.45909	+	3.45909i	−0.293396	+	0.293396i	−0.838420	−	0.545024i	$-0.816520\pi$
$139$	−3.45909	+	3.45909i	−0.293396	+	0.293396i	0.545024	+	0.838420i	$0.316520\pi$
$140$	0.661611			0.0559164
$141$		0			0
$142$	−8.35755	−	8.35755i	−0.701350	−	0.701350i
$143$	19.2620	+	19.2620i	1.61077	+	1.61077i
$144$		0			0
$145$		−	11.7846i		−	0.978655i
$146$	−4.89690	−	4.89690i	−0.405270	−	0.405270i
$147$		0			0
$148$	−1.15566	+	1.15566i	−0.0949944	+	0.0949944i
$149$	−13.7753			−1.12852			−0.564258	−	0.825599i	$-0.690838\pi$
$149$	−13.7753			−1.12852			−0.564258	+	0.825599i	$0.690838\pi$
$150$		0			0
$151$		−	20.5923i		−	1.67578i	−0.545841	−	0.837889i	$-0.683790\pi$
$151$		−	20.5923i		−	1.67578i	0.545841	−	0.837889i	$-0.316210\pi$
$152$	2.57515			0.208873
$153$		0			0
$154$	5.84346			0.470880
$155$		−	4.85321i		−	0.389819i
$156$		0			0
$157$	−23.0384			−1.83866			−0.919331	−	0.393484i	$-0.871270\pi$
$157$	−23.0384			−1.83866			−0.919331	+	0.393484i	$0.871270\pi$
$158$	1.02651	−	1.02651i	0.0816648	−	0.0816648i
$159$		0			0
$160$	2.62739	+	2.62739i	0.207714	+	0.207714i
$161$		−	0.652192i		−	0.0514000i
$162$		0			0
$163$	−3.40803	−	3.40803i	−0.266937	−	0.266937i	0.560927	−	0.827865i	$-0.310445\pi$
$163$	−3.40803	−	3.40803i	−0.266937	−	0.266937i	−0.827865	+	0.560927i	$0.810445\pi$
$164$	2.39745	+	2.39745i	0.187210	+	0.187210i
$165$		0			0
$166$	−19.4750			−1.51155
$167$	−10.0111	+	10.0111i	−0.774680	+	0.774680i	−0.978921	−	0.204241i	$-0.934527\pi$
$167$	−10.0111	+	10.0111i	−0.774680	+	0.774680i	0.204241	+	0.978921i	$0.434527\pi$
$168$		0			0
$169$	36.6217			2.81706
$170$	12.4072	−	7.59208i	0.951586	−	0.582286i
$171$		0			0
$172$		−	0.682232i		−	0.0520197i
$173$	−14.3926	+	14.3926i	−1.09425	+	1.09425i	−0.0991809	+	0.995069i	$0.531622\pi$
$173$	−14.3926	+	14.3926i	−1.09425	+	1.09425i	−0.995069	+	0.0991809i	$0.968378\pi$
$174$		0			0
$175$	−0.318586	+	0.318586i	−0.0240828	+	0.0240828i
$176$	12.2679	+	12.2679i	0.924727	+	0.924727i
$177$		0			0
$178$			5.78553i			0.433644i
$179$			15.0614i			1.12574i	0.826544	+	0.562872i	$0.190304\pi$
$179$			15.0614i			1.12574i	−0.826544	+	0.562872i	$0.809696\pi$
$180$		0			0
$181$	−3.31493	−	3.31493i	−0.246397	−	0.246397i	0.573093	−	0.819490i	$-0.305743\pi$
$181$	−3.31493	−	3.31493i	−0.246397	−	0.246397i	−0.819490	+	0.573093i	$0.805743\pi$
$182$	7.52681	−	7.52681i	0.557924	−	0.557924i
$183$		0			0
$184$	1.19625	−	1.19625i	0.0881889	−	0.0881889i
$185$		−	13.4642i		−	0.989909i
$186$		0			0
$187$	13.6001	−	8.32206i	0.994539	−	0.608569i
$188$	−1.93073			−0.140813
$189$		0			0
$190$	2.47649	−	2.47649i	0.179663	−	0.179663i
$191$	17.6598			1.27782			0.638908	−	0.769283i	$-0.279386\pi$
$191$	17.6598			1.27782			0.638908	+	0.769283i	$0.279386\pi$
$192$		0			0
$193$	−10.4528	−	10.4528i	−0.752408	−	0.752408i	0.222520	−	0.974928i	$-0.428572\pi$
$193$	−10.4528	−	10.4528i	−0.752408	−	0.752408i	−0.974928	+	0.222520i	$0.928572\pi$
$194$	−3.17753	−	3.17753i	−0.228133	−	0.228133i
$195$		0			0
$196$		−	0.283389i		−	0.0202421i
$197$	−3.21831	−	3.21831i	−0.229295	−	0.229295i	0.583103	−	0.812398i	$-0.301838\pi$
$197$	−3.21831	−	3.21831i	−0.229295	−	0.229295i	−0.812398	+	0.583103i	$0.801838\pi$
$198$		0			0
$199$	14.3092	−	14.3092i	1.01435	−	1.01435i	0.0144592	−	0.999895i	$-0.495397\pi$
$199$	14.3092	−	14.3092i	1.01435	−	1.01435i	0.999895	−	0.0144592i	$-0.00460267\pi$
$200$	−1.16870			−0.0826396
$201$		0			0
$202$		−	1.51951i		−	0.106912i
$203$	−5.04770			−0.354279
$204$		0			0
$205$	−27.9320			−1.95086
$206$			2.39501i			0.166868i
$207$		0			0
$208$	31.6039			2.19134
$209$	2.71461	−	2.71461i	0.187773	−	0.187773i
$210$		0			0
$211$	1.06695	+	1.06695i	0.0734519	+	0.0734519i	0.742878	−	0.669426i	$-0.233460\pi$
$211$	1.06695	+	1.06695i	0.0734519	+	0.0734519i	−0.669426	+	0.742878i	$0.733460\pi$
$212$			1.42896i			0.0981412i
$213$		0			0
$214$	6.54798	+	6.54798i	0.447611	+	0.447611i
$215$	3.97424	+	3.97424i	0.271041	+	0.271041i
$216$		0			0
$217$	−2.07878			−0.141117
$218$	14.1363	−	14.1363i	0.957433	−	0.957433i
$219$		0			0
$220$	2.55849			0.172493
$221$	6.79852	−	28.2374i	0.457318	−	1.89945i
$222$		0			0
$223$			29.2730i			1.96027i	0.198337	+	0.980134i	$0.436446\pi$
$223$			29.2730i			1.96027i	−0.198337	+	0.980134i	$0.563554\pi$
$224$	1.12539	−	1.12539i	0.0751936	−	0.0751936i
$225$		0			0
$226$	−20.1712	+	20.1712i	−1.34177	+	1.34177i
$227$	16.0152	+	16.0152i	1.06296	+	1.06296i	0.997880	+	0.0650831i	$0.0207312\pi$
$227$	16.0152	+	16.0152i	1.06296	+	1.06296i	0.0650831	+	0.997880i	$0.479269\pi$
$228$		0			0
$229$			20.5349i			1.35699i	0.734607	+	0.678493i	$0.237367\pi$
$229$			20.5349i			1.35699i	−0.734607	+	0.678493i	$0.762633\pi$
$230$		−	2.30084i		−	0.151713i
$231$		0			0
$232$	−9.25850	−	9.25850i	−0.607850	−	0.607850i
$233$	−2.75026	+	2.75026i	−0.180176	+	0.180176i	−0.791432	−	0.611257i	$-0.790664\pi$
$233$	−2.75026	+	2.75026i	−0.180176	+	0.180176i	0.611257	+	0.791432i	$0.290664\pi$
$234$		0			0
$235$	11.2472	−	11.2472i	0.733687	−	0.733687i
$236$			0.443639i			0.0288785i
$237$		0			0
$238$	−3.25193	−	5.31438i	−0.210791	−	0.344480i
$239$	7.00766			0.453288			0.226644	−	0.973978i	$-0.427225\pi$
$239$	7.00766			0.453288			0.226644	+	0.973978i	$0.427225\pi$
$240$		0			0
$241$	11.6350	−	11.6350i	0.749476	−	0.749476i	−0.224905	−	0.974381i	$-0.572207\pi$
$241$	11.6350	−	11.6350i	0.749476	−	0.749476i	0.974381	+	0.224905i	$0.0722070\pi$
$242$	5.97501			0.384088
$243$		0			0
$244$	−2.50345	−	2.50345i	−0.160267	−	0.160267i
$245$	1.65084	+	1.65084i	0.105468	+	0.105468i
$246$		0			0
$247$		−	6.99322i		−	0.444968i
$248$	−3.81291	−	3.81291i	−0.242120	−	0.242120i
$249$		0			0
$250$	11.3489	−	11.3489i	0.717768	−	0.717768i
$251$	12.6735			0.799941			0.399971	−	0.916528i	$-0.369020\pi$
$251$	12.6735			0.799941			0.399971	+	0.916528i	$0.369020\pi$
$252$		0			0
$253$		−	2.52206i		−	0.158561i
$254$	−33.5797			−2.10698
$255$		0			0
$256$	6.67123			0.416952
$257$		−	14.4557i		−	0.901719i	−0.892595	−	0.450859i	$-0.851118\pi$
$257$		−	14.4557i		−	0.901719i	0.892595	−	0.450859i	$-0.148882\pi$
$258$		0			0
$259$	−5.76715			−0.358353
$260$	3.29552	−	3.29552i	0.204379	−	0.204379i
$261$		0			0
$262$	−8.66036	−	8.66036i	−0.535039	−	0.535039i
$263$		−	17.9342i		−	1.10587i	−0.833225	−	0.552935i	$-0.813508\pi$
$263$		−	17.9342i		−	1.10587i	0.833225	−	0.552935i	$-0.186492\pi$
$264$		0			0
$265$	−8.32418	−	8.32418i	−0.511351	−	0.511351i
$266$	−1.06076	−	1.06076i	−0.0650393	−	0.0650393i
$267$		0			0
$268$	−1.40472			−0.0858069
$269$	−3.04172	+	3.04172i	−0.185457	+	0.185457i	−0.793729	−	0.608272i	$-0.791863\pi$
$269$	−3.04172	+	3.04172i	−0.185457	+	0.185457i	0.608272	+	0.793729i	$0.291863\pi$
$270$		0			0
$271$	26.7775			1.62662			0.813310	−	0.581831i	$-0.197664\pi$
$271$	26.7775			1.62662			0.813310	+	0.581831i	$0.197664\pi$
$272$	4.32995	−	17.9843i	0.262542	−	1.09046i
$273$		0			0
$274$		−	11.5857i		−	0.699920i
$275$	−1.23199	+	1.23199i	−0.0742917	+	0.0742917i
$276$		0			0
$277$	−6.21835	+	6.21835i	−0.373625	+	0.373625i	−0.868796	−	0.495171i	$-0.835105\pi$
$277$	−6.21835	+	6.21835i	−0.373625	+	0.373625i	0.495171	+	0.868796i	$0.335105\pi$
$278$	5.22699	+	5.22699i	0.313494	+	0.313494i
$279$		0			0
$280$			6.05595i			0.361912i
$281$		−	13.5121i		−	0.806065i	−0.915186	−	0.403033i	$-0.867956\pi$
$281$		−	13.5121i		−	0.806065i	0.915186	−	0.403033i	$-0.132044\pi$
$282$		0			0
$283$	18.1685	+	18.1685i	1.08000	+	1.08000i	0.996508	+	0.0834957i	$0.0266085\pi$
$283$	18.1685	+	18.1685i	1.08000	+	1.08000i	0.0834957	+	0.996508i	$0.473392\pi$
$284$	−1.56737	+	1.56737i	−0.0930064	+	0.0930064i
$285$		0			0
$286$	29.1066	−	29.1066i	1.72111	−	1.72111i
$287$			11.9642i			0.706223i
$288$		0			0
$289$	−15.1371	−	7.73743i	−0.890418	−	0.455143i
$290$	−17.8075			−1.04569
$291$		0			0
$292$	−0.918363	+	0.918363i	−0.0537431	+	0.0537431i
$293$	−19.3056			−1.12784			−0.563922	−	0.825828i	$-0.690708\pi$
$293$	−19.3056			−1.12784			−0.563922	+	0.825828i	$0.690708\pi$
$294$		0			0
$295$	−2.58436	−	2.58436i	−0.150467	−	0.150467i
$296$	−10.5781	−	10.5781i	−0.614840	−	0.614840i
$297$		0			0
$298$			20.8157i			1.20582i
$299$	−3.24860	−	3.24860i	−0.187872	−	0.187872i
$300$		0			0
$301$	1.70229	−	1.70229i	0.0981186	−	0.0981186i
$302$	−31.1168			−1.79057
$303$		0			0
$304$		−	4.45396i		−	0.255452i
$305$	29.1669			1.67009
$306$		0			0
$307$	−0.224246			−0.0127984			−0.00639920	−	0.999980i	$-0.502037\pi$
$307$	−0.224246			−0.0127984			−0.00639920	+	0.999980i	$0.502037\pi$
$308$		−	1.09588i		−	0.0624436i
$309$		0			0
$310$	−7.33364			−0.416523
$311$	22.8463	−	22.8463i	1.29549	−	1.29549i	0.364153	−	0.931339i	$-0.381358\pi$
$311$	22.8463	−	22.8463i	1.29549	−	1.29549i	0.931339	−	0.364153i	$-0.118642\pi$
$312$		0			0
$313$	6.97873	+	6.97873i	0.394461	+	0.394461i	0.876274	−	0.481813i	$-0.160022\pi$
$313$	6.97873	+	6.97873i	0.394461	+	0.394461i	−0.481813	+	0.876274i	$0.660022\pi$
$314$			34.8130i			1.96461i
$315$		0			0
$316$	−0.192511	−	0.192511i	−0.0108296	−	0.0108296i
$317$	−2.70321	−	2.70321i	−0.151827	−	0.151827i	0.627106	−	0.778934i	$-0.284239\pi$
$317$	−2.70321	−	2.70321i	−0.151827	−	0.151827i	−0.778934	+	0.627106i	$0.784239\pi$
$318$		0			0
$319$	−19.5197			−1.09290
$320$	−10.8427	+	10.8427i	−0.606123	+	0.606123i
$321$		0			0
$322$	−0.985521			−0.0549209
$323$	−3.97951	−	0.958120i	−0.221426	−	0.0533112i
$324$		0			0
$325$			3.17379i			0.176050i
$326$	−5.14983	+	5.14983i	−0.285223	+	0.285223i
$327$		0			0
$328$	−21.9447	+	21.9447i	−1.21169	+	1.21169i
$329$	−4.81753	−	4.81753i	−0.265599	−	0.265599i
$330$		0			0
$331$		−	20.4933i		−	1.12641i	−0.826317	−	0.563206i	$-0.809568\pi$
$331$		−	20.4933i		−	1.12641i	0.826317	−	0.563206i	$-0.190432\pi$
$332$			3.65233i			0.200448i
$333$		0			0
$334$	15.1276	+	15.1276i	0.827746	+	0.827746i
$335$	8.18298	−	8.18298i	0.447084	−	0.447084i
$336$		0			0
$337$	−16.3891	+	16.3891i	−0.892772	+	0.892772i	−0.994783	−	0.102011i	$-0.967472\pi$
$337$	−16.3891	+	16.3891i	−0.892772	+	0.892772i	0.102011	+	0.994783i	$0.467472\pi$
$338$		−	55.3387i		−	3.01003i
$339$		0			0
$340$	−1.42382	−	2.32683i	−0.0772172	−	0.126190i
$341$	−8.03877			−0.435324
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	6.24470			0.336691
$345$		0			0
$346$	21.7485	+	21.7485i	1.16921	+	1.16921i
$347$	−0.767240	−	0.767240i	−0.0411876	−	0.0411876i	0.686213	−	0.727401i	$-0.259272\pi$
$347$	−0.767240	−	0.767240i	−0.0411876	−	0.0411876i	−0.727401	+	0.686213i	$0.759272\pi$
$348$		0			0
$349$		−	12.8669i		−	0.688749i	−0.938832	−	0.344374i	$-0.888091\pi$
$349$		−	12.8669i		−	0.688749i	0.938832	−	0.344374i	$-0.111909\pi$
$350$	0.481412	+	0.481412i	0.0257325	+	0.0257325i
$351$		0			0
$352$	4.35196	−	4.35196i	0.231960	−	0.231960i
$353$	−6.81692			−0.362828			−0.181414	−	0.983407i	$-0.558067\pi$
$353$	−6.81692			−0.362828			−0.181414	+	0.983407i	$0.558067\pi$
$354$		0			0
$355$		−	18.2610i		−	0.969193i
$356$	1.08502			0.0575058
$357$		0			0
$358$	22.7592			1.20286
$359$		−	6.71484i		−	0.354396i	−0.984175	−	0.177198i	$-0.943297\pi$
$359$		−	6.71484i		−	0.354396i	0.984175	−	0.177198i	$-0.0567033\pi$
$360$		0			0
$361$	18.0144			0.948128
$362$	−5.00916	+	5.00916i	−0.263275	+	0.263275i
$363$		0			0
$364$	−1.41157	−	1.41157i	−0.0739866	−	0.0739866i
$365$		−	10.6996i		−	0.560041i
$366$		0			0
$367$	13.7945	+	13.7945i	0.720070	+	0.720070i	0.968619	−	0.248550i	$-0.0799539\pi$
$367$	13.7945	+	13.7945i	0.720070	+	0.720070i	−0.248550	+	0.968619i	$0.579954\pi$
$368$	−2.06902	−	2.06902i	−0.107855	−	0.107855i
$369$		0			0
$370$	−20.3456			−1.05772
$371$	−3.56551	+	3.56551i	−0.185112	+	0.185112i
$372$		0			0
$373$	11.5715			0.599152			0.299576	−	0.954072i	$-0.403155\pi$
$373$	11.5715			0.599152			0.299576	+	0.954072i	$0.403155\pi$
$374$	−12.5754	−	20.5510i	−0.650257	−	1.06267i
$375$		0			0
$376$		−	17.6726i		−	0.911397i
$377$	−25.1429	+	25.1429i	−1.29492	+	1.29492i
$378$		0			0
$379$	10.0319	−	10.0319i	0.515306	−	0.515306i	−0.400842	−	0.916147i	$-0.631282\pi$
$379$	10.0319	−	10.0319i	0.515306	−	0.515306i	0.916147	+	0.400842i	$0.131282\pi$
$380$	−0.464440	−	0.464440i	−0.0238253	−	0.0238253i
$381$		0			0
$382$		−	26.6855i		−	1.36535i
$383$			10.0566i			0.513871i	0.966429	+	0.256935i	$0.0827128\pi$
$383$			10.0566i			0.513871i	−0.966429	+	0.256935i	$0.917287\pi$
$384$		0			0
$385$	6.38389	+	6.38389i	0.325353	+	0.325353i
$386$	−15.7951	+	15.7951i	−0.803949	+	0.803949i
$387$		0			0
$388$	−0.595912	+	0.595912i	−0.0302528	+	0.0302528i
$389$			15.1409i			0.767672i	0.923401	+	0.383836i	$0.125397\pi$
$389$			15.1409i			0.767672i	−0.923401	+	0.383836i	$0.874603\pi$
$390$		0			0
$391$	−2.29371	+	1.40355i	−0.115998	+	0.0709803i
$392$	2.59395			0.131014
$393$		0			0
$394$	−4.86315	+	4.86315i	−0.245002	+	0.245002i
$395$	2.24289			0.112852
$396$		0			0
$397$	20.2301	+	20.2301i	1.01532	+	1.01532i	0.999881	+	0.0154374i	$0.00491407\pi$
$397$	20.2301	+	20.2301i	1.01532	+	1.01532i	0.0154374	+	0.999881i	$0.495086\pi$
$398$	−21.6225	−	21.6225i	−1.08384	−	1.08384i
$399$		0			0
$400$			2.02137i			0.101069i
$401$	4.45942	+	4.45942i	0.222693	+	0.222693i	0.809631	−	0.586939i	$-0.199667\pi$
$401$	4.45942	+	4.45942i	0.222693	+	0.222693i	−0.586939	+	0.809631i	$0.699667\pi$
$402$		0			0
$403$	−10.3545	+	10.3545i	−0.515796	+	0.515796i
$404$	−0.284968			−0.0141777
$405$		0			0
$406$			7.62753i			0.378548i
$407$	−22.3019			−1.10546
$408$		0			0
$409$	−0.539984			−0.0267005			−0.0133503	−	0.999911i	$-0.504250\pi$
$409$	−0.539984			−0.0267005			−0.0133503	+	0.999911i	$0.504250\pi$
$410$			42.2078i			2.08449i
$411$		0			0
$412$	0.449159			0.0221285
$413$	−1.10696	+	1.10696i	−0.0544700	+	0.0544700i
$414$		0			0
$415$	−21.2761	−	21.2761i	−1.04440	−	1.04440i
$416$		−	11.2113i		−	0.549679i
$417$		0			0
$418$	−4.10201	−	4.10201i	−0.200636	−	0.200636i
$419$	22.3051	+	22.3051i	1.08967	+	1.08967i	0.995562	+	0.0941132i	$0.0300016\pi$
$419$	22.3051	+	22.3051i	1.08967	+	1.08967i	0.0941132	+	0.995562i	$0.469998\pi$
$420$		0			0
$421$	1.65742			0.0807778			0.0403889	−	0.999184i	$-0.487140\pi$
$421$	1.65742			0.0807778			0.0403889	+	0.999184i	$0.487140\pi$
$422$	1.61226	−	1.61226i	0.0784834	−	0.0784834i
$423$		0			0
$424$	−13.0797			−0.635207
$425$	1.80605	+	0.434830i	0.0876063	+	0.0210924i
$426$		0			0
$427$		−	12.4931i		−	0.604584i
$428$	1.22801	−	1.22801i	0.0593579	−	0.0593579i
$429$		0			0
$430$	6.00543	−	6.00543i	0.289608	−	0.289608i
$431$	19.6916	+	19.6916i	0.948510	+	0.948510i	0.998738	−	0.0502281i	$-0.0159948\pi$
$431$	19.6916	+	19.6916i	0.948510	+	0.948510i	−0.0502281	+	0.998738i	$0.515995\pi$
$432$		0			0
$433$			27.9567i			1.34352i	0.740771	+	0.671758i	$0.234460\pi$
$433$			27.9567i			1.34352i	−0.740771	+	0.671758i	$0.765540\pi$
$434$			3.14123i			0.150784i
$435$		0			0
$436$	−2.65112	−	2.65112i	−0.126966	−	0.126966i
$437$	−0.457828	+	0.457828i	−0.0219009	+	0.0219009i
$438$		0			0
$439$	−1.51580	+	1.51580i	−0.0723453	+	0.0723453i	−0.742354	−	0.670008i	$-0.766291\pi$
$439$	−1.51580	+	1.51580i	−0.0723453	+	0.0723453i	0.670008	+	0.742354i	$0.266291\pi$
$440$			23.4187i			1.11644i
$441$		0			0
$442$	−42.6692	−	10.2732i	−2.02957	−	0.488645i
$443$	26.1035			1.24022			0.620108	−	0.784516i	$-0.287089\pi$
$443$	26.1035			1.24022			0.620108	+	0.784516i	$0.287089\pi$
$444$		0			0
$445$	−6.32060	+	6.32060i	−0.299625	+	0.299625i
$446$	44.2342			2.09455
$447$		0			0
$448$	4.64425	+	4.64425i	0.219420	+	0.219420i
$449$	16.3399	+	16.3399i	0.771126	+	0.771126i	0.978303	−	0.207177i	$-0.0664277\pi$
$449$	16.3399	+	16.3399i	0.771126	+	0.771126i	−0.207177	+	0.978303i	$0.566428\pi$
$450$		0			0
$451$			46.2661i			2.17859i
$452$	3.78289	+	3.78289i	0.177932	+	0.177932i
$453$		0			0
$454$	24.2003	−	24.2003i	1.13578	−	1.13578i
$455$	16.4458			0.770993
$456$		0			0
$457$		−	28.4649i		−	1.33153i	−0.746160	−	0.665766i	$-0.768105\pi$
$457$		−	28.4649i		−	1.33153i	0.746160	−	0.665766i	$-0.231895\pi$
$458$	31.0301			1.44994
$459$		0			0
$460$	−0.431498			−0.0201187
$461$			23.9790i			1.11681i	0.829567	+	0.558407i	$0.188587\pi$
$461$			23.9790i			1.11681i	−0.829567	+	0.558407i	$0.811413\pi$
$462$		0			0
$463$	−20.5076			−0.953068			−0.476534	−	0.879156i	$-0.658107\pi$
$463$	−20.5076			−0.953068			−0.476534	+	0.879156i	$0.658107\pi$
$464$	−16.0134	+	16.0134i	−0.743403	+	0.743403i
$465$		0			0
$466$	4.15589	+	4.15589i	0.192518	+	0.192518i
$467$		−	17.9740i		−	0.831739i	−0.909424	−	0.415869i	$-0.863477\pi$
$467$		−	17.9740i		−	0.831739i	0.909424	−	0.415869i	$-0.136523\pi$
$468$		0			0
$469$	−3.50503	−	3.50503i	−0.161847	−	0.161847i
$470$	−16.9955	−	16.9955i	−0.783945	−	0.783945i
$471$		0			0
$472$	−4.06078			−0.186912
$473$	6.58286	−	6.58286i	0.302680	−	0.302680i
$474$		0			0
$475$	0.447284			0.0205228
$476$	−0.996656	+	0.609865i	−0.0456816	+	0.0279531i
$477$		0			0
$478$		−	10.5892i		−	0.484339i
$479$	−16.6378	+	16.6378i	−0.760202	+	0.760202i	−0.976359	−	0.216157i	$-0.930648\pi$
$479$	−16.6378	+	16.6378i	−0.760202	+	0.760202i	0.216157	+	0.976359i	$0.430648\pi$
$480$		0			0
$481$	−28.7265	+	28.7265i	−1.30981	+	1.30981i
$482$	−17.5815	−	17.5815i	−0.800816	−	0.800816i
$483$		0			0
$484$		−	1.12055i		−	0.0509341i
$485$		−	6.94279i		−	0.315256i
$486$		0			0
$487$	0.249268	+	0.249268i	0.0112954	+	0.0112954i	0.712732	−	0.701437i	$-0.247458\pi$
$487$	0.249268	+	0.249268i	0.0112954	+	0.0112954i	−0.701437	+	0.712732i	$0.747458\pi$
$488$	22.9149	−	22.9149i	1.03731	−	1.03731i
$489$		0			0
$490$	2.49457	−	2.49457i	0.112693	−	0.112693i
$491$		−	9.73907i		−	0.439518i	−0.975554	−	0.219759i	$-0.929473\pi$
$491$		−	9.73907i		−	0.439518i	0.975554	−	0.219759i	$-0.0705271\pi$
$492$		0			0
$493$	10.8629	+	17.7524i	0.489239	+	0.799526i
$494$	−10.5674			−0.475449
$495$		0			0
$496$	−6.59476	+	6.59476i	−0.296113	+	0.296113i
$497$	−7.82176			−0.350854
$498$		0			0
$499$	18.5957	+	18.5957i	0.832459	+	0.832459i	0.987853	−	0.155393i	$-0.0496645\pi$
$499$	18.5957	+	18.5957i	0.832459	+	0.832459i	−0.155393	+	0.987853i	$0.549664\pi$
$500$	−2.12837	−	2.12837i	−0.0951836	−	0.0951836i
$501$		0			0
$502$		−	19.1507i		−	0.854738i
$503$	−2.35428	−	2.35428i	−0.104972	−	0.104972i	0.652670	−	0.757642i	$-0.273649\pi$
$503$	−2.35428	−	2.35428i	−0.104972	−	0.104972i	−0.757642	+	0.652670i	$0.773649\pi$
$504$		0			0
$505$	1.66004	−	1.66004i	0.0738706	−	0.0738706i
$506$	−3.81106			−0.169422
$507$		0			0
$508$			6.29753i			0.279408i
$509$	−13.6249			−0.603914			−0.301957	−	0.953321i	$-0.597640\pi$
$509$	−13.6249			−0.603914			−0.301957	+	0.953321i	$0.597640\pi$
$510$		0			0
$511$	−4.58296			−0.202738
$512$			16.1349i			0.713070i
$513$		0			0
$514$	−21.8438			−0.963488
$515$	−2.61651	+	2.61651i	−0.115297	+	0.115297i
$516$		0			0
$517$	−18.6297	−	18.6297i	−0.819331	−	0.819331i
$518$			8.71467i			0.382901i
$519$		0			0
$520$	30.1650	+	30.1650i	1.32282	+	1.32282i
$521$	1.76032	+	1.76032i	0.0771212	+	0.0771212i	0.744615	−	0.667494i	$-0.232633\pi$
$521$	1.76032	+	1.76032i	0.0771212	+	0.0771212i	−0.667494	+	0.744615i	$0.732633\pi$
$522$		0			0
$523$	−5.84412			−0.255546			−0.127773	−	0.991803i	$-0.540783\pi$
$523$	−5.84412			−0.255546			−0.127773	+	0.991803i	$0.540783\pi$
$524$	−1.62416	+	1.62416i	−0.0709518	+	0.0709518i
$525$		0			0
$526$	−27.1001			−1.18162
$527$	4.47363	+	7.31091i	0.194874	+	0.318468i
$528$		0			0
$529$		−	22.5746i		−	0.981506i
$530$	−12.5786	+	12.5786i	−0.546379	+	0.546379i
$531$		0			0
$532$	−0.198934	+	0.198934i	−0.00862489	+	0.00862489i
$533$	59.5941	+	59.5941i	2.58131	+	2.58131i
$534$		0			0
$535$			14.3071i			0.618551i
$536$		−	12.8578i		−	0.555374i
$537$		0			0
$538$	4.59631	+	4.59631i	0.198161	+	0.198161i
$539$	2.73442	−	2.73442i	0.117780	−	0.117780i
$540$		0			0
$541$	−17.7427	+	17.7427i	−0.762819	+	0.762819i	−0.976831	−	0.214012i	$-0.931347\pi$
$541$	−17.7427	+	17.7427i	−0.762819	+	0.762819i	0.214012	+	0.976831i	$0.431347\pi$
$542$		−	40.4632i		−	1.73804i
$543$		0			0
$544$	−6.37982	−	1.53603i	−0.273532	−	0.0658565i
$545$	30.8874			1.32307
$546$		0			0
$547$	−31.4484	+	31.4484i	−1.34463	+	1.34463i	−0.453253	+	0.891382i	$0.649736\pi$
$547$	−31.4484	+	31.4484i	−1.34463	+	1.34463i	−0.891382	+	0.453253i	$0.850264\pi$
$548$	−2.17278			−0.0928168
$549$		0			0
$550$	1.86164	+	1.86164i	0.0793808	+	0.0793808i
$551$	3.54340	+	3.54340i	0.150954	+	0.150954i
$552$		0			0
$553$		−	0.960701i		−	0.0408532i
$554$	9.39649	+	9.39649i	0.399218	+	0.399218i
$555$		0			0
$556$	0.980268	−	0.980268i	0.0415726	−	0.0415726i
$557$	−23.7598			−1.00674			−0.503368	−	0.864072i	$-0.667906\pi$
$557$	−23.7598			−1.00674			−0.503368	+	0.864072i	$0.667906\pi$
$558$		0			0
$559$		−	16.9584i		−	0.717265i
$560$	10.4743			0.442620
$561$		0			0
$562$	−20.4180			−0.861282
$563$			41.4704i			1.74777i	0.486134	+	0.873884i	$0.338407\pi$
$563$			41.4704i			1.74777i	−0.486134	+	0.873884i	$0.661593\pi$
$564$		0			0
$565$	−44.0734			−1.85418
$566$	27.4542	−	27.4542i	1.15399	−	1.15399i
$567$		0			0
$568$	−14.3467	−	14.3467i	−0.601973	−	0.601973i
$569$			2.56184i			0.107398i	0.998557	+	0.0536990i	$0.0171011\pi$
$569$			2.56184i			0.107398i	−0.998557	+	0.0536990i	$0.982899\pi$
$570$		0			0
$571$	16.2523	+	16.2523i	0.680137	+	0.680137i	0.960031	−	0.279894i	$-0.0902992\pi$
$571$	16.2523	+	16.2523i	0.680137	+	0.680137i	−0.279894	+	0.960031i	$0.590299\pi$
$572$	−5.45864	−	5.45864i	−0.228237	−	0.228237i
$573$		0			0
$574$	18.0789			0.754600
$575$	0.207779	−	0.207779i	0.00866500	−	0.00866500i
$576$		0			0
$577$	−6.98932			−0.290969			−0.145485	−	0.989361i	$-0.546474\pi$
$577$	−6.98932			−0.290969			−0.145485	+	0.989361i	$0.546474\pi$
$578$	−11.6919	+	22.8735i	−0.486321	+	0.951413i
$579$		0			0
$580$			3.33962i			0.138670i
$581$	−9.11323	+	9.11323i	−0.378081	+	0.378081i
$582$		0			0
$583$	−13.7880	+	13.7880i	−0.571041	+	0.571041i
$584$	−8.40607	−	8.40607i	−0.347846	−	0.347846i
$585$		0			0
$586$			29.1724i			1.20510i
$587$		−	22.3808i		−	0.923753i	−0.886944	−	0.461877i	$-0.847176\pi$
$587$		−	22.3808i		−	0.923753i	0.886944	−	0.461877i	$-0.152824\pi$
$588$		0			0
$589$	1.45927	+	1.45927i	0.0601282	+	0.0601282i
$590$	−3.90519	+	3.90519i	−0.160774	+	0.160774i
$591$		0			0
$592$	−18.2958	+	18.2958i	−0.751951	+	0.751951i
$593$		−	14.3719i		−	0.590183i	−0.955469	−	0.295092i	$-0.904650\pi$
$593$		−	14.3719i		−	0.590183i	0.955469	−	0.295092i	$-0.0953502\pi$
$594$		0			0
$595$	2.25319	−	9.35855i	0.0923719	−	0.383663i
$596$	3.90376			0.159904
$597$		0			0
$598$	−4.90893	+	4.90893i	−0.200741	+	0.200741i
$599$	−13.0016			−0.531231			−0.265616	−	0.964079i	$-0.585575\pi$
$599$	−13.0016			−0.531231			−0.265616	+	0.964079i	$0.585575\pi$
$600$		0			0
$601$	−9.67071	−	9.67071i	−0.394477	−	0.394477i	0.481803	−	0.876280i	$-0.339982\pi$
$601$	−9.67071	−	9.67071i	−0.394477	−	0.394477i	−0.876280	+	0.481803i	$0.839982\pi$
$602$	−2.57232	−	2.57232i	−0.104840	−	0.104840i
$603$		0			0
$604$			5.83563i			0.237448i
$605$	6.52760	+	6.52760i	0.265385	+	0.265385i
$606$		0			0
$607$	−9.95811	+	9.95811i	−0.404187	+	0.404187i	−0.879706	−	0.475519i	$-0.842260\pi$
$607$	−9.95811	+	9.95811i	−0.404187	+	0.404187i	0.475519	+	0.879706i	$0.342260\pi$
$608$	−1.58002			−0.0640781
$609$		0			0
$610$		−	44.0738i		−	1.78450i
$611$	−47.9927			−1.94158
$612$		0			0
$613$	31.7030			1.28047			0.640236	−	0.768178i	$-0.278836\pi$
$613$	31.7030			1.28047			0.640236	+	0.768178i	$0.278836\pi$
$614$			0.338856i			0.0136751i
$615$		0			0
$616$	10.0310			0.404159
$617$	−10.5201	+	10.5201i	−0.423524	+	0.423524i	−0.886415	−	0.462891i	$-0.846812\pi$
$617$	−10.5201	+	10.5201i	−0.423524	+	0.423524i	0.462891	+	0.886415i	$0.346812\pi$
$618$		0			0
$619$	15.2920	+	15.2920i	0.614638	+	0.614638i	0.944151	−	0.329513i	$-0.106885\pi$
$619$	15.2920	+	15.2920i	0.614638	+	0.614638i	−0.329513	+	0.944151i	$0.606885\pi$
$620$			1.37535i			0.0552353i
$621$		0			0
$622$	−34.5227	−	34.5227i	−1.38423	−	1.38423i
$623$	2.70731	+	2.70731i	0.108466	+	0.108466i
$624$		0			0
$625$	27.0497			1.08199
$626$	10.5455	−	10.5455i	0.421482	−	0.421482i
$627$		0			0
$628$	6.52882			0.260528
$629$	12.4111	+	20.2826i	0.494865	+	0.808720i
$630$		0			0
$631$			17.3657i			0.691319i	0.938360	+	0.345659i	$0.112345\pi$
$631$			17.3657i			0.691319i	−0.938360	+	0.345659i	$0.887655\pi$
$632$	1.76212	−	1.76212i	0.0700933	−	0.0700933i
$633$		0			0
$634$	−4.08478	+	4.08478i	−0.162227	+	0.162227i
$635$	−36.6853	−	36.6853i	−1.45581	−	1.45581i
$636$		0			0
$637$		−	7.04427i		−	0.279104i
$638$			29.4961i			1.16776i
$639$		0			0
$640$	21.6390	+	21.6390i	0.855357	+	0.855357i
$641$	3.19471	−	3.19471i	0.126183	−	0.126183i	−0.641195	−	0.767378i	$-0.721561\pi$
$641$	3.19471	−	3.19471i	0.126183	−	0.126183i	0.767378	+	0.641195i	$0.221561\pi$
$642$		0			0
$643$	4.29555	−	4.29555i	0.169400	−	0.169400i	−0.617316	−	0.786716i	$-0.711780\pi$
$643$	4.29555	−	4.29555i	0.169400	−	0.169400i	0.786716	+	0.617316i	$0.211780\pi$
$644$			0.184824i			0.00728309i
$645$		0			0
$646$	−1.44780	+	6.01340i	−0.0569631	+	0.236594i
$647$	−44.3110			−1.74204			−0.871022	−	0.491245i	$-0.836542\pi$
$647$	−44.3110			−1.74204			−0.871022	+	0.491245i	$0.836542\pi$
$648$		0			0
$649$	−4.28068	+	4.28068i	−0.168031	+	0.168031i
$650$	4.79587			0.188110
$651$		0			0
$652$	0.965798	+	0.965798i	0.0378236	+	0.0378236i
$653$	−35.1940	−	35.1940i	−1.37725	−	1.37725i	−0.849237	−	0.528012i	$-0.822937\pi$
$653$	−35.1940	−	35.1940i	−1.37725	−	1.37725i	−0.528012	−	0.849237i	$-0.677063\pi$
$654$		0			0
$655$		−	18.9226i		−	0.739368i
$656$	37.9553	+	37.9553i	1.48190	+	1.48190i
$657$		0			0
$658$	−7.27972	+	7.27972i	−0.283793	+	0.283793i
$659$	−32.2608			−1.25670			−0.628351	−	0.777930i	$-0.716270\pi$
$659$	−32.2608			−1.25670			−0.628351	+	0.777930i	$0.716270\pi$
$660$		0			0
$661$		−	43.8186i		−	1.70435i	−0.523260	−	0.852173i	$-0.675284\pi$
$661$		−	43.8186i		−	1.70435i	0.523260	−	0.852173i	$-0.324716\pi$
$662$	−30.9671			−1.20357
$663$		0			0
$664$	−33.4310			−1.29737
$665$		−	2.31772i		−	0.0898774i
$666$		0			0
$667$	3.29207			0.127470
$668$	2.83703	−	2.83703i	0.109768	−	0.109768i
$669$		0			0
$670$	−12.3652	−	12.3652i	−0.477710	−	0.477710i
$671$		−	48.3115i		−	1.86505i
$672$		0			0
$673$	−1.49798	−	1.49798i	−0.0577430	−	0.0577430i	0.677646	−	0.735389i	$-0.263000\pi$
$673$	−1.49798	−	1.49798i	−0.0577430	−	0.0577430i	−0.735389	+	0.677646i	$0.763000\pi$
$674$	24.7654	+	24.7654i	0.953928	+	0.953928i
$675$		0			0
$676$	−10.3782			−0.399161
$677$	−7.71518	+	7.71518i	−0.296519	+	0.296519i	−0.839649	−	0.543130i	$-0.817239\pi$
$677$	−7.71518	+	7.71518i	−0.296519	+	0.296519i	0.543130	+	0.839649i	$0.317239\pi$
$678$		0			0
$679$	−2.97382			−0.114125
$680$	21.2983	−	13.0326i	0.816751	−	0.499779i
$681$		0			0
$682$			12.1473i			0.465144i
$683$	3.26234	−	3.26234i	0.124830	−	0.124830i	−0.641932	−	0.766762i	$-0.721867\pi$
$683$	3.26234	−	3.26234i	0.124830	−	0.124830i	0.766762	+	0.641932i	$0.221867\pi$
$684$		0			0
$685$	12.6572	−	12.6572i	0.483608	−	0.483608i
$686$	−1.06850	−	1.06850i	−0.0407956	−	0.0407956i
$687$		0			0
$688$		−	10.8008i		−	0.411775i
$689$			35.5200i			1.35320i
$690$		0			0
$691$	−25.3809	−	25.3809i	−0.965534	−	0.965534i	0.0338916	−	0.999426i	$-0.489210\pi$
$691$	−25.3809	−	25.3809i	−0.965534	−	0.965534i	−0.999426	+	0.0338916i	$0.989210\pi$
$692$	4.07871	−	4.07871i	0.155049	−	0.155049i
$693$		0			0
$694$	−1.15937	+	1.15937i	−0.0440090	+	0.0440090i
$695$			11.4208i			0.433216i
$696$		0			0
$697$	42.0770	−	25.7474i	1.59378	−	0.975252i
$698$	−19.4430			−0.735929
$699$		0			0
$700$	0.0902837	−	0.0902837i	0.00341240	−	0.00341240i
$701$	−10.4646			−0.395244			−0.197622	−	0.980278i	$-0.563322\pi$
$701$	−10.4646			−0.395244			−0.197622	+	0.980278i	$0.563322\pi$
$702$		0			0
$703$	4.04844	+	4.04844i	0.152690	+	0.152690i
$704$	17.9596	+	17.9596i	0.676877	+	0.676877i
$705$		0			0
$706$			10.3010i			0.387682i
$707$	−0.711046	−	0.711046i	−0.0267416	−	0.0267416i
$708$		0			0
$709$	−15.6687	+	15.6687i	−0.588451	+	0.588451i	−0.937212	−	0.348760i	$-0.886603\pi$
$709$	−15.6687	+	15.6687i	−0.588451	+	0.588451i	0.348760	+	0.937212i	$0.386603\pi$
$710$	−27.5940			−1.03558
$711$		0			0
$712$			9.93151i			0.372199i
$713$	1.35577			0.0507739
$714$		0			0
$715$	63.5970			2.37839
$716$		−	4.26825i		−	0.159512i
$717$		0			0
$718$	−10.1467			−0.378672
$719$	22.3270	−	22.3270i	0.832657	−	0.832657i	−0.155223	−	0.987880i	$-0.549609\pi$
$719$	22.3270	−	22.3270i	0.832657	−	0.832657i	0.987880	+	0.155223i	$0.0496095\pi$
$720$		0			0
$721$	1.12073	+	1.12073i	0.0417383	+	0.0417383i
$722$		−	27.2214i		−	1.01308i
$723$		0			0
$724$	0.939415	+	0.939415i	0.0349131	+	0.0349131i
$725$	−1.60813	−	1.60813i	−0.0597243	−	0.0597243i
$726$		0			0
$727$	−8.26117			−0.306390			−0.153195	−	0.988196i	$-0.548956\pi$
$727$	−8.26117			−0.306390			−0.153195	+	0.988196i	$0.548956\pi$
$728$	12.9206	−	12.9206i	0.478869	−	0.478869i
$729$		0			0
$730$	−16.1680			−0.598405
$731$	−9.65023	−	2.32342i	−0.356927	−	0.0859348i
$732$		0			0
$733$		−	2.49710i		−	0.0922326i	−0.998936	−	0.0461163i	$-0.985316\pi$
$733$		−	2.49710i		−	0.0922326i	0.998936	−	0.0461163i	$-0.0146845\pi$
$734$	20.8448	−	20.8448i	0.769395	−	0.769395i
$735$		0			0
$736$	−0.733974	+	0.733974i	−0.0270546	+	0.0270546i
$737$	−13.5541	−	13.5541i	−0.499273	−	0.499273i
$738$		0			0
$739$		−	42.6527i		−	1.56900i	−0.620127	−	0.784502i	$-0.712919\pi$
$739$		−	42.6527i		−	1.56900i	0.620127	−	0.784502i	$-0.287081\pi$
$740$			3.81561i			0.140265i
$741$		0			0
$742$	5.38780	+	5.38780i	0.197792	+	0.197792i
$743$	−1.94900	+	1.94900i	−0.0715017	+	0.0715017i	−0.741953	−	0.670452i	$-0.766100\pi$
$743$	−1.94900	+	1.94900i	−0.0715017	+	0.0715017i	0.670452	+	0.741953i	$0.266100\pi$
$744$		0			0
$745$	−22.7408	+	22.7408i	−0.833158	+	0.833158i
$746$		−	17.4856i		−	0.640195i
$747$		0			0
$748$	−3.85412	+	2.35838i	−0.140921	+	0.0862309i
$749$	6.12819			0.223919
$750$		0			0
$751$	37.4310	−	37.4310i	1.36588	−	1.36588i	0.499645	−	0.866230i	$-0.333464\pi$
$751$	37.4310	−	37.4310i	1.36588	−	1.36588i	0.866230	−	0.499645i	$-0.166536\pi$
$752$	−30.5664			−1.11464
$753$		0			0
$754$	37.9931	+	37.9931i	1.38363	+	1.38363i
$755$	−33.9946	−	33.9946i	−1.23719	−	1.23719i
$756$		0			0
$757$			40.7526i			1.48118i	0.671957	+	0.740590i	$0.265454\pi$
$757$			40.7526i			1.48118i	−0.671957	+	0.740590i	$0.734546\pi$
$758$	−15.1591	−	15.1591i	−0.550604	−	0.550604i
$759$		0			0
$760$	4.25117	−	4.25117i	0.154206	−	0.154206i
$761$	15.2173			0.551628			0.275814	−	0.961211i	$-0.411053\pi$
$761$	15.2173			0.551628			0.275814	+	0.961211i	$0.411053\pi$
$762$		0			0
$763$		−	13.2301i		−	0.478960i
$764$	−5.00459			−0.181060
$765$		0			0
$766$	15.1965			0.549071
$767$			11.0277i			0.398185i
$768$		0			0
$769$	5.04641			0.181978			0.0909891	−	0.995852i	$-0.470997\pi$
$769$	5.04641			0.181978			0.0909891	+	0.995852i	$0.470997\pi$
$770$	9.64662	−	9.64662i	0.347640	−	0.347640i
$771$		0			0
$772$	2.96221	+	2.96221i	0.106612	+	0.106612i
$773$			23.6553i			0.850823i	0.905000	+	0.425411i	$0.139871\pi$
$773$			23.6553i			0.850823i	−0.905000	+	0.425411i	$0.860129\pi$
$774$		0			0
$775$	−0.662271	−	0.662271i	−0.0237895	−	0.0237895i
$776$	−5.45458	−	5.45458i	−0.195808	−	0.195808i
$777$		0			0
$778$	22.8792			0.820258
$779$	8.39864	−	8.39864i	0.300913	−	0.300913i
$780$		0			0
$781$	−30.2472			−1.08233
$782$	2.12088	+	3.46600i	0.0758426	+	0.123944i
$783$		0			0
$784$		−	4.48647i		−	0.160231i
$785$	−38.0327	+	38.0327i	−1.35744	+	1.35744i
$786$		0			0
$787$	26.5970	−	26.5970i	0.948081	−	0.948081i	−0.0506365	−	0.998717i	$-0.516125\pi$
$787$	26.5970	−	26.5970i	0.948081	−	0.948081i	0.998717	+	0.0506365i	$0.0161250\pi$
$788$	0.912034	+	0.912034i	0.0324899	+	0.0324899i
$789$		0			0
$790$		−	3.38921i		−	0.120583i
$791$			18.8780i			0.671225i
$792$		0			0
$793$	−62.2288	−	62.2288i	−2.20981	−	2.20981i
$794$	30.5694	−	30.5694i	1.08487	−	1.08487i
$795$		0			0
$796$	−4.05508	+	4.05508i	−0.143728	+	0.143728i
$797$		−	39.1927i		−	1.38828i	−0.719841	−	0.694139i	$-0.755785\pi$
$797$		−	39.1927i		−	1.38828i	0.719841	−	0.694139i	$-0.244215\pi$
$798$		0			0
$799$	−6.57533	+	27.3104i	−0.232619	+	0.966172i
$800$	0.717070			0.0253523
$801$		0			0
$802$	6.73857	−	6.73857i	0.237947	−	0.237947i
$803$	−17.7226			−0.625416
$804$		0			0
$805$	−1.07667	−	1.07667i	−0.0379475	−	0.0379475i
$806$	15.6466	+	15.6466i	0.551128	+	0.551128i
$807$		0			0
$808$		−	2.60840i		−	0.0917632i
$809$	−1.40949	−	1.40949i	−0.0495551	−	0.0495551i	0.681895	−	0.731450i	$-0.261156\pi$
$809$	−1.40949	−	1.40949i	−0.0495551	−	0.0495551i	−0.731450	+	0.681895i	$0.761156\pi$
$810$		0			0
$811$	9.31564	−	9.31564i	0.327116	−	0.327116i	−0.524373	−	0.851489i	$-0.675700\pi$
$811$	9.31564	−	9.31564i	0.327116	−	0.327116i	0.851489	+	0.524373i	$0.175700\pi$
$812$	1.43046			0.0501994
$813$		0			0
$814$			33.7001i			1.18119i
$815$	−11.2522			−0.394148
$816$		0			0
$817$	−2.38996			−0.0836142
$818$			0.815964i			0.0285295i
$819$		0			0
$820$	7.91563			0.276426
$821$	30.5863	−	30.5863i	1.06747	−	1.06747i	0.0699175	−	0.997553i	$-0.477726\pi$
$821$	30.5863	−	30.5863i	1.06747	−	1.06747i	0.997553	−	0.0699175i	$-0.0222736\pi$
$822$		0			0
$823$	3.51823	+	3.51823i	0.122638	+	0.122638i	0.765762	−	0.643124i	$-0.222362\pi$
$823$	3.51823	+	3.51823i	0.122638	+	0.122638i	−0.643124	+	0.765762i	$0.722362\pi$
$824$			4.11130i			0.143224i
$825$		0			0
$826$	1.67272	+	1.67272i	0.0582012	+	0.0582012i
$827$	18.1677	+	18.1677i	0.631753	+	0.631753i	0.948507	−	0.316755i	$-0.102593\pi$
$827$	18.1677	+	18.1677i	0.631753	+	0.631753i	−0.316755	+	0.948507i	$0.602593\pi$
$828$		0			0
$829$	19.6638			0.682952			0.341476	−	0.939891i	$-0.389073\pi$
$829$	19.6638			0.682952			0.341476	+	0.939891i	$0.389073\pi$
$830$	−32.1501	+	32.1501i	−1.11595	+	1.11595i
$831$		0			0
$832$	46.2665			1.60400
$833$	−4.00856	−	0.965114i	−0.138888	−	0.0334392i
$834$		0			0
$835$			33.0534i			1.14386i
$836$	−0.769289	+	0.769289i	−0.0266064	+	0.0266064i
$837$		0			0
$838$	33.7050	−	33.7050i	1.16432	−	1.16432i
$839$	−20.2884	−	20.2884i	−0.700435	−	0.700435i	0.264069	−	0.964504i	$-0.414935\pi$
$839$	−20.2884	−	20.2884i	−0.700435	−	0.700435i	−0.964504	+	0.264069i	$0.914935\pi$
$840$		0			0
$841$			3.52070i			0.121404i
$842$		−	2.50451i		−	0.0863111i
$843$		0			0
$844$	−0.302362	−	0.302362i	−0.0104077	−	0.0104077i
$845$	60.4567	−	60.4567i	2.07977	−	2.07977i
$846$		0			0
$847$	2.79598	−	2.79598i	0.0960709	−	0.0960709i
$848$			22.6225i			0.776861i
$849$		0			0
$850$	0.657067	−	2.72910i	0.0225372	−	0.0936075i
$851$	3.76129			0.128935
$852$		0			0
$853$	−8.46564	+	8.46564i	−0.289858	+	0.289858i	−0.837024	−	0.547166i	$-0.815707\pi$
$853$	−8.46564	+	8.46564i	−0.289858	+	0.289858i	0.547166	+	0.837024i	$0.315707\pi$
$854$	−18.8782			−0.645999
$855$		0			0
$856$	11.2403	+	11.2403i	0.384187	+	0.384187i
$857$	−14.8086	−	14.8086i	−0.505852	−	0.505852i	0.407399	−	0.913250i	$-0.366436\pi$
$857$	−14.8086	−	14.8086i	−0.505852	−	0.505852i	−0.913250	+	0.407399i	$0.866436\pi$
$858$		0			0
$859$		−	17.7440i		−	0.605416i	−0.953083	−	0.302708i	$-0.902109\pi$
$859$		−	17.7440i		−	0.605416i	0.953083	−	0.302708i	$-0.0978908\pi$
$860$	−1.12626	−	1.12626i	−0.0384050	−	0.0384050i
$861$		0			0
$862$	29.7557	−	29.7557i	1.01348	−	1.01348i
$863$	51.0360			1.73729			0.868643	−	0.495438i	$-0.164992\pi$
$863$	51.0360			1.73729			0.868643	+	0.495438i	$0.164992\pi$
$864$		0			0
$865$			47.5198i			1.61572i
$866$	42.2451			1.43555
$867$		0			0
$868$	0.589104			0.0199955
$869$		−	3.71508i		−	0.126026i
$870$		0			0
$871$	−34.9174			−1.18313
$872$	24.2666	−	24.2666i	0.821770	−	0.821770i
$873$		0			0
$874$	0.691818	+	0.691818i	0.0234011	+	0.0234011i
$875$		−	10.6213i		−	0.359067i
$876$		0			0
$877$	35.0271	+	35.0271i	1.18278	+	1.18278i	0.979020	+	0.203762i	$0.0653168\pi$
$877$	35.0271	+	35.0271i	1.18278	+	1.18278i	0.203762	+	0.979020i	$0.434683\pi$
$878$	2.29051	+	2.29051i	0.0773010	+	0.0773010i
$879$		0			0
$880$	40.5047			1.36541
$881$	−30.7682	+	30.7682i	−1.03661	+	1.03661i	−0.0373037	+	0.999304i	$0.511877\pi$
$881$	−30.7682	+	30.7682i	−1.03661	+	1.03661i	−0.999304	+	0.0373037i	$0.988123\pi$
$882$		0			0
$883$	4.04610			0.136162			0.0680810	−	0.997680i	$-0.478312\pi$
$883$	4.04610			0.136162			0.0680810	+	0.997680i	$0.478312\pi$
$884$	−1.92663	+	8.00216i	−0.0647994	+	0.269142i
$885$		0			0
$886$		−	39.4447i		−	1.32517i
$887$	5.63293	−	5.63293i	0.189135	−	0.189135i	−0.606187	−	0.795322i	$-0.707302\pi$
$887$	5.63293	−	5.63293i	0.189135	−	0.189135i	0.795322	+	0.606187i	$0.207302\pi$
$888$		0			0
$889$	−15.7135	+	15.7135i	−0.527013	+	0.527013i
$890$	9.55099	+	9.55099i	0.320150	+	0.320150i
$891$		0			0
$892$		−	8.29566i		−	0.277759i
$893$			6.76365i			0.226337i
$894$		0			0
$895$	24.8640	+	24.8640i	0.831113	+	0.831113i
$896$	9.26867	−	9.26867i	0.309644	−	0.309644i
$897$		0			0
$898$	24.6910	−	24.6910i	0.823949	−	0.823949i
$899$		−	10.4931i		−	0.349964i
$900$		0			0
$901$	20.2127	+	4.86648i	0.673384	+	0.162126i
$902$	69.9122			2.32782
$903$		0			0
$904$	−34.6261	+	34.6261i	−1.15165	+	1.15165i
$905$	−10.9448			−0.363819
$906$		0			0
$907$	9.69792	+	9.69792i	0.322014	+	0.322014i	0.849539	−	0.527525i	$-0.176880\pi$
$907$	9.69792	+	9.69792i	0.322014	+	0.322014i	−0.527525	+	0.849539i	$0.676880\pi$
$908$	−4.53852	−	4.53852i	−0.150616	−	0.150616i
$909$		0			0
$910$		−	24.8511i		−	0.823807i
$911$	23.3268	+	23.3268i	0.772851	+	0.772851i	0.978604	−	0.205753i	$-0.0659644\pi$
$911$	23.3268	+	23.3268i	0.772851	+	0.772851i	−0.205753	+	0.978604i	$0.565964\pi$
$912$		0			0
$913$	−35.2414	+	35.2414i	−1.16632	+	1.16632i
$914$	−43.0130			−1.42274
$915$		0			0
$916$		−	5.81937i		−	0.192277i
$917$	−8.10515			−0.267656
$918$		0			0
$919$	−42.3458			−1.39686			−0.698430	−	0.715678i	$-0.746118\pi$
$919$	−42.3458			−1.39686			−0.698430	+	0.715678i	$0.746118\pi$
$920$		−	3.94964i		−	0.130216i
$921$		0			0
$922$	36.2344			1.19332
$923$	−38.9606	+	38.9606i	−1.28240	+	1.28240i
$924$		0			0
$925$	−1.83733	−	1.83733i	−0.0604111	−	0.0604111i
$926$			30.9888i			1.01835i
$927$		0			0
$928$	5.68066	+	5.68066i	0.186477	+	0.186477i
$929$	−5.25405	−	5.25405i	−0.172380	−	0.172380i	0.615644	−	0.788024i	$-0.288896\pi$
$929$	−5.25405	−	5.25405i	−0.172380	−	0.172380i	−0.788024	+	0.615644i	$0.788896\pi$
$930$		0			0
$931$	−0.992753			−0.0325362
$932$	0.779393	−	0.779393i	0.0255299	−	0.0255299i
$933$		0			0
$934$	−27.1604			−0.888714
$935$	8.71322	−	36.1900i	0.284953	−	1.18354i
$936$		0			0
$937$			2.79023i			0.0911529i	0.998961	+	0.0455765i	$0.0145125\pi$
$937$			2.79023i			0.0911529i	−0.998961	+	0.0455765i	$0.985488\pi$
$938$	−5.29641	+	5.29641i	−0.172934	+	0.172934i
$939$		0			0
$940$	−3.18733	+	3.18733i	−0.103959	+	0.103959i
$941$	−18.1581	−	18.1581i	−0.591937	−	0.591937i	0.346217	−	0.938154i	$-0.387466\pi$
$941$	−18.1581	−	18.1581i	−0.591937	−	0.591937i	−0.938154	+	0.346217i	$0.887466\pi$
$942$		0			0
$943$		−	7.80294i		−	0.254099i
$944$			7.02347i			0.228594i
$945$		0			0
$946$	−9.94729	−	9.94729i	−0.323414	−	0.323414i
$947$	−16.9612	+	16.9612i	−0.551165	+	0.551165i	−0.926777	−	0.375612i	$-0.877433\pi$
$947$	−16.9612	+	16.9612i	−0.551165	+	0.551165i	0.375612	+	0.926777i	$0.377433\pi$
$948$		0			0
$949$	−22.8280	+	22.8280i	−0.741027	+	0.741027i
$950$		−	0.675885i		−	0.0219286i
$951$		0			0
$952$	−5.58229	−	9.12272i	−0.180923	−	0.295669i
$953$	5.89788			0.191051			0.0955255	−	0.995427i	$-0.469547\pi$
$953$	5.89788			0.191051			0.0955255	+	0.995427i	$0.469547\pi$
$954$		0			0
$955$	29.1535	−	29.1535i	0.943385	−	0.943385i
$956$	−1.98589			−0.0642284
$957$		0			0
$958$	25.1412	+	25.1412i	0.812276	+	0.812276i
$959$	−5.42149	−	5.42149i	−0.175069	−	0.175069i
$960$		0			0
$961$			26.6787i			0.860602i
$962$	43.4082	+	43.4082i	1.39954	+	1.39954i
$963$		0			0
$964$	−3.29723	+	3.29723i	−0.106197	+	0.106197i
$965$	−34.5118			−1.11097
$966$		0			0
$967$		−	41.8868i		−	1.34699i	−0.739192	−	0.673495i	$-0.764792\pi$
$967$		−	41.8868i		−	1.34699i	0.739192	−	0.673495i	$-0.235208\pi$
$968$	10.2568			0.329665
$969$		0			0
$970$	−10.4912			−0.336851
$971$		−	43.4097i		−	1.39308i	−0.717517	−	0.696541i	$-0.754721\pi$
$971$		−	43.4097i		−	1.39308i	0.717517	−	0.696541i	$-0.245279\pi$
$972$		0			0
$973$	4.89189			0.156827
$974$	0.376666	−	0.376666i	0.0120691	−	0.0120691i
$975$		0			0
$976$	−39.6333	−	39.6333i	−1.26863	−	1.26863i
$977$		−	33.0140i		−	1.05621i	−0.849179	−	0.528105i	$-0.822903\pi$
$977$		−	33.0140i		−	1.05621i	0.849179	−	0.528105i	$-0.177097\pi$
$978$		0			0
$979$	10.4693	+	10.4693i	0.334601	+	0.334601i
$980$	−0.467830	−	0.467830i	−0.0149443	−	0.0149443i
$981$		0			0
$982$	−14.7166			−0.469625
$983$	31.2458	−	31.2458i	0.996586	−	0.996586i	−0.00340834	−	0.999994i	$-0.501085\pi$
$983$	31.2458	−	31.2458i	0.996586	−	0.996586i	0.999994	+	0.00340834i	$0.00108491\pi$
$984$		0			0
$985$	−10.6258			−0.338567
$986$	26.8254	−	16.4148i	0.854294	−	0.522752i
$987$		0			0
$988$			1.98180i			0.0630495i
$989$	−1.11022	+	1.11022i	−0.0353030	+	0.0353030i
$990$		0			0
$991$	−6.79452	+	6.79452i	−0.215835	+	0.215835i	−0.806741	−	0.590906i	$-0.798771\pi$
$991$	−6.79452	+	6.79452i	−0.215835	+	0.215835i	0.590906	+	0.806741i	$0.298771\pi$
$992$	2.33945	+	2.33945i	0.0742777	+	0.0742777i
$993$		0			0
$994$			11.8194i			0.374888i
$995$		−	47.2445i		−	1.49775i
$996$		0			0
$997$	−34.4116	−	34.4116i	−1.08983	−	1.08983i	−0.995546	−	0.0942822i	$-0.969944\pi$
$997$	−34.4116	−	34.4116i	−1.08983	−	1.08983i	−0.0942822	−	0.995546i	$-0.530056\pi$
$998$	28.0998	−	28.0998i	0.889484	−	0.889484i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.n.b.820.4		20
3.2	odd	2		357.2.k.b.106.7	yes	20
17.13	even	4	inner	1071.2.n.b.64.7		20
51.8	odd	8		6069.2.a.be.1.7		10
51.26	odd	8		6069.2.a.bd.1.7		10
51.47	odd	4		357.2.k.b.64.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.4	✓	20	51.47	odd	4
357.2.k.b.106.7	yes	20	3.2	odd	2
1071.2.n.b.64.7		20	17.13	even	4	inner
1071.2.n.b.820.4		20	1.1	even	1	trivial
6069.2.a.bd.1.7		10	51.26	odd	8
6069.2.a.be.1.7		10	51.8	odd	8

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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.51109i q^{2} -0.283389 q^{4} +(1.65084 - 1.65084i) q^{5} +(-0.707107 - 0.707107i) q^{7} -2.59395i q^{8} +O(q^{10})\)	\(q-1.51109i q^{2} -0.283389 q^{4} +(1.65084 - 1.65084i) q^{5} +(-0.707107 - 0.707107i) q^{7} -2.59395i q^{8} +(-2.49457 - 2.49457i) q^{10} +(-2.73442 - 2.73442i) q^{11} -7.04427 q^{13} +(-1.06850 + 1.06850i) q^{14} -4.48647 q^{16} +(-0.965114 + 4.00856i) q^{17} +0.992753i q^{19} +(-0.467830 + 0.467830i) q^{20} +(-4.13195 + 4.13195i) q^{22} +(0.461170 + 0.461170i) q^{23} -0.450549i q^{25} +10.6445i q^{26} +(0.200386 + 0.200386i) q^{28} +(3.56926 - 3.56926i) q^{29} +(1.46992 - 1.46992i) q^{31} +1.59155i q^{32} +(6.05729 + 1.45837i) q^{34} -2.33464 q^{35} +(4.07799 - 4.07799i) q^{37} +1.50014 q^{38} +(-4.28220 - 4.28220i) q^{40} +(-8.45995 - 8.45995i) q^{41} +2.40741i q^{43} +(0.774904 + 0.774904i) q^{44} +(0.696868 - 0.696868i) q^{46} +6.81302 q^{47} +1.00000i q^{49} -0.680819 q^{50} +1.99627 q^{52} -5.04239i q^{53} -9.02818 q^{55} +(-1.83420 + 1.83420i) q^{56} +(-5.39348 - 5.39348i) q^{58} -1.56548i q^{59} +(8.83396 + 8.83396i) q^{61} +(-2.22118 - 2.22118i) q^{62} -6.56797 q^{64} +(-11.6290 + 11.6290i) q^{65} +4.95686 q^{67} +(0.273503 - 1.13598i) q^{68} +3.52785i q^{70} +(5.53082 - 5.53082i) q^{71} +(3.24064 - 3.24064i) q^{73} +(-6.16220 - 6.16220i) q^{74} -0.281335i q^{76} +3.86705i q^{77} +(0.679318 + 0.679318i) q^{79} +(-7.40644 + 7.40644i) q^{80} +(-12.7837 + 12.7837i) q^{82} -12.8881i q^{83} +(5.02425 + 8.21074i) q^{85} +3.63780 q^{86} +(-7.09295 + 7.09295i) q^{88} -3.82872 q^{89} +(4.98105 + 4.98105i) q^{91} +(-0.130690 - 0.130690i) q^{92} -10.2951i q^{94} +(1.63888 + 1.63888i) q^{95} +(2.10281 - 2.10281i) q^{97} +1.51109 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{4} - 8 q^{5}+O(q^{10}) \) 20 * q - 24 * q^4 - 8 * q^5	\( 20 q - 24 q^{4} - 8 q^{5} + 16 q^{10} - 4 q^{11} - 12 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{17} + 52 q^{20} - 24 q^{22} + 4 q^{23} + 8 q^{29} + 8 q^{31} - 44 q^{34} - 12 q^{35} + 24 q^{37} + 64 q^{38} - 52 q^{40} + 20 q^{41} - 72 q^{44} + 28 q^{46} + 32 q^{47} - 104 q^{50} + 48 q^{52} - 36 q^{55} + 4 q^{56} - 60 q^{58} + 28 q^{61} - 36 q^{62} - 112 q^{64} + 4 q^{65} + 40 q^{67} + 52 q^{68} - 16 q^{71} - 72 q^{73} + 24 q^{74} - 8 q^{79} - 120 q^{80} + 108 q^{82} + 40 q^{85} - 28 q^{88} + 64 q^{89} - 12 q^{91} + 56 q^{92} - 60 q^{95} + 60 q^{97} + 8 q^{98}+O(q^{100}) \) 20 * q - 24 * q^4 - 8 * q^5 + 16 * q^10 - 4 * q^11 - 12 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^17 + 52 * q^20 - 24 * q^22 + 4 * q^23 + 8 * q^29 + 8 * q^31 - 44 * q^34 - 12 * q^35 + 24 * q^37 + 64 * q^38 - 52 * q^40 + 20 * q^41 - 72 * q^44 + 28 * q^46 + 32 * q^47 - 104 * q^50 + 48 * q^52 - 36 * q^55 + 4 * q^56 - 60 * q^58 + 28 * q^61 - 36 * q^62 - 112 * q^64 + 4 * q^65 + 40 * q^67 + 52 * q^68 - 16 * q^71 - 72 * q^73 + 24 * q^74 - 8 * q^79 - 120 * q^80 + 108 * q^82 + 40 * q^85 - 28 * q^88 + 64 * q^89 - 12 * q^91 + 56 * q^92 - 60 * q^95 + 60 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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