LMFDB - Embedded newform 539.2.q.b.214.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + \cdots + 625 $ x^16 - x^15 - 5x^14 + 16x^13 + 4x^12 - 29x^11 + 10x^10 - 156x^9 + 251x^8 + 240x^7 + 390x^6 - 1375x^5 - 300x^4 + 500x^3 + 375x^2 + 625x + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			214.2
Root			$-0.710267 - 0.316231i$ of defining polynomial
Character	$\chi$	$=$	539.214
Dual form			539.2.q.b.471.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18937 - 1.32093i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(-0.121196 - 1.15310i) q^{4} +(-2.71679 + 0.577471i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(-1.75181 + 1.94558i) q^{9} +O(q^{10})$	\(q+(1.18937 - 1.32093i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(-0.121196 - 1.15310i) q^{4} +(-2.71679 + 0.577471i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(-1.75181 + 1.94558i) q^{9} +(-2.46847 + 4.27551i) q^{10} +(2.12033 + 2.55033i) q^{11} +(0.358290 + 0.620576i) q^{12} +(1.32676 + 4.08334i) q^{13} +(1.38874 - 1.00898i) q^{15} +(4.86587 - 1.03427i) q^{16} +(1.84383 + 2.04778i) q^{17} +(0.486425 + 4.62802i) q^{18} +(0.202691 - 1.92847i) q^{19} +(0.995144 + 3.06274i) q^{20} +(5.89066 + 0.232480i) q^{22} +(-2.18505 - 3.78461i) q^{23} +(-0.903204 - 0.191982i) q^{24} +(2.47974 - 1.10405i) q^{25} +(6.97180 + 3.10405i) q^{26} +(1.07295 - 3.30220i) q^{27} +(-6.98027 + 5.07146i) q^{29} +(0.318937 - 3.03448i) q^{30} +(-0.196204 - 0.0417045i) q^{31} +(2.92705 - 5.06980i) q^{32} +(-1.83824 - 0.906920i) q^{33} +4.89796 q^{34} +(2.45576 + 1.78421i) q^{36} +(0.945958 + 0.421168i) q^{37} +(-2.30630 - 2.56141i) q^{38} +(-1.77555 - 1.97195i) q^{39} +(-3.79098 - 1.68785i) q^{40} +(7.77155 + 5.64636i) q^{41} -4.70820 q^{43} +(2.68381 - 2.75404i) q^{44} +(3.63577 - 6.29735i) q^{45} +(-7.59803 - 1.61501i) q^{46} +(-1.36363 + 12.9741i) q^{47} +(-2.48729 + 1.80712i) q^{48} +(1.49096 - 4.58869i) q^{50} +(-1.55579 - 0.692684i) q^{51} +(4.54770 - 2.02476i) q^{52} +(3.81489 + 0.810880i) q^{53} +(-3.08583 - 5.34482i) q^{54} +(-7.23324 - 5.70428i) q^{55} +(0.370334 + 1.13977i) q^{57} +(-1.60308 + 15.2523i) q^{58} +(-0.894464 - 8.51025i) q^{59} +(-1.33176 - 1.47907i) q^{60} +(-0.967005 + 0.205543i) q^{61} +(-0.288448 + 0.209570i) q^{62} +(-0.141042 - 0.434084i) q^{64} +(-5.96253 - 10.3274i) q^{65} +(-3.38432 + 1.34952i) q^{66} +(2.70872 - 4.69165i) q^{67} +(2.13783 - 2.37430i) q^{68} +(2.18505 + 1.58753i) q^{69} +(-0.623302 + 1.91833i) q^{71} +(-3.82603 + 0.813249i) q^{72} +(-1.04226 - 9.91646i) q^{73} +(1.68143 - 0.748619i) q^{74} +(-1.12254 + 1.24670i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(4.21116 - 4.67696i) q^{79} +(-12.6223 + 5.61980i) q^{80} +(-0.596670 - 5.67693i) q^{81} +(16.7017 - 3.55005i) q^{82} +(0.531960 - 1.63720i) q^{83} +(-6.19182 - 4.49862i) q^{85} +(-5.59979 + 6.21920i) q^{86} +(2.66623 - 4.61804i) q^{87} +(0.323221 + 4.94470i) q^{88} +(-7.65177 - 13.2532i) q^{89} +(-3.99406 - 12.2925i) q^{90} +(-4.09921 + 2.97825i) q^{92} +(0.121261 - 0.0257748i) q^{93} +(15.5160 + 17.2322i) q^{94} +(0.562970 + 5.35630i) q^{95} +(-0.378188 + 3.59821i) q^{96} +(-3.58961 - 11.0477i) q^{97} +(-8.67628 - 0.342417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.18937	−	1.32093i	0.841011	−	0.934037i	−0.157558	−	0.987510i	$-0.550362\pi$
$2$	1.18937	−	1.32093i	0.841011	−	0.934037i	0.998569	+	0.0534724i	$0.0170289\pi$
$3$	−0.564602	+	0.251377i	−0.325973	+	0.145133i	−0.563198	−	0.826322i	$-0.690429\pi$
$3$	−0.564602	+	0.251377i	−0.325973	+	0.145133i	0.237224	+	0.971455i	$0.423762\pi$
$4$	−0.121196	−	1.15310i	−0.0605978	−	0.576549i
$5$	−2.71679	+	0.577471i	−1.21499	+	0.258253i	−0.770445	−	0.637506i	$-0.779966\pi$
$5$	−2.71679	+	0.577471i	−1.21499	+	0.258253i	−0.444540	+	0.895759i	$0.646633\pi$
$6$	−0.339469	+	1.04478i	−0.138588	+	0.426529i
$7$		0			0
$7$		0			0
$8$	1.20872	+	0.878189i	0.427348	+	0.310487i
$9$	−1.75181	+	1.94558i	−0.583936	+	0.648526i
$10$	−2.46847	+	4.27551i	−0.780598	+	1.35204i
$11$	2.12033	+	2.55033i	0.639304	+	0.768954i
$11$	2.12033	+	2.55033i	0.639304	+	0.768954i
$12$	0.358290	+	0.620576i	0.103429	+	0.179145i
$13$	1.32676	+	4.08334i	0.367976	+	1.13251i	0.948096	+	0.317983i	$0.103006\pi$
$13$	1.32676	+	4.08334i	0.367976	+	1.13251i	−0.580120	+	0.814531i	$0.696994\pi$
$14$		0			0
$15$	1.38874	−	1.00898i	0.358572	−	0.260518i
$16$	4.86587	−	1.03427i	1.21647	−	0.258568i
$17$	1.84383	+	2.04778i	0.447194	+	0.496659i	0.924023	−	0.382337i	$-0.124881\pi$
$17$	1.84383	+	2.04778i	0.447194	+	0.496659i	−0.476829	+	0.878996i	$0.658214\pi$
$18$	0.486425	+	4.62802i	0.114651	+	1.09084i
$19$	0.202691	−	1.92847i	0.0465004	−	0.442422i	−0.946358	−	0.323121i	$-0.895268\pi$
$19$	0.202691	−	1.92847i	0.0465004	−	0.442422i	0.992858	−	0.119301i	$-0.0380654\pi$
$20$	0.995144	+	3.06274i	0.222521	+	0.684849i
$21$		0			0
$22$	5.89066	+	0.232480i	1.25589	+	0.0495649i
$23$	−2.18505	−	3.78461i	−0.455614	−	0.789146i	0.543109	−	0.839662i	$-0.317247\pi$
$23$	−2.18505	−	3.78461i	−0.455614	−	0.789146i	−0.998723	+	0.0505157i	$0.983914\pi$
$24$	−0.903204	−	0.191982i	−0.184366	−	0.0391882i
$25$	2.47974	−	1.10405i	0.495949	−	0.220811i
$26$	6.97180	+	3.10405i	1.36728	+	0.608753i
$27$	1.07295	−	3.30220i	0.206489	−	0.635508i
$28$		0			0
$29$	−6.98027	+	5.07146i	−1.29620	+	0.941747i	−0.999911	−	0.0133499i	$-0.995750\pi$
$29$	−6.98027	+	5.07146i	−1.29620	+	0.941747i	−0.296293	+	0.955097i	$0.595750\pi$
$30$	0.318937	−	3.03448i	0.0582296	−	0.554017i
$31$	−0.196204	−	0.0417045i	−0.0352394	−	0.00749036i	0.190258	−	0.981734i	$-0.439067\pi$
$31$	−0.196204	−	0.0417045i	−0.0352394	−	0.00749036i	−0.225498	+	0.974244i	$0.572401\pi$
$32$	2.92705	−	5.06980i	0.517434	−	0.896223i
$33$	−1.83824	−	0.906920i	−0.319996	−	0.157875i
$34$	4.89796			0.839993
$35$		0			0
$36$	2.45576	+	1.78421i	0.409293	+	0.297368i
$37$	0.945958	+	0.421168i	0.155515	+	0.0692395i	0.483018	−	0.875610i	$-0.339541\pi$
$37$	0.945958	+	0.421168i	0.155515	+	0.0692395i	−0.327503	+	0.944850i	$0.606207\pi$
$38$	−2.30630	−	2.56141i	−0.374131	−	0.415515i
$39$	−1.77555	−	1.97195i	−0.284315	−	0.315764i
$40$	−3.79098	−	1.68785i	−0.599406	−	0.266873i
$41$	7.77155	+	5.64636i	1.21371	+	0.881813i	0.995563	−	0.0941021i	$-0.0299980\pi$
$41$	7.77155	+	5.64636i	1.21371	+	0.881813i	0.218149	+	0.975915i	$0.429998\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	2.68381	−	2.75404i	0.404600	−	0.415187i
$45$	3.63577	−	6.29735i	0.541989	−	0.938753i
$46$	−7.59803	−	1.61501i	−1.12027	−	0.238120i
$47$	−1.36363	+	12.9741i	−0.198906	+	1.89246i	0.206684	+	0.978408i	$0.433733\pi$
$47$	−1.36363	+	12.9741i	−0.198906	+	1.89246i	−0.405590	+	0.914055i	$0.632934\pi$
$48$	−2.48729	+	1.80712i	−0.359009	+	0.260835i
$49$		0			0
$50$	1.49096	−	4.58869i	0.210853	−	0.648939i
$51$	−1.55579	−	0.692684i	−0.217855	−	0.0969951i
$52$	4.54770	−	2.02476i	0.630652	−	0.280784i
$53$	3.81489	+	0.810880i	0.524016	+	0.111383i	0.462322	−	0.886712i	$-0.347016\pi$
$53$	3.81489	+	0.810880i	0.524016	+	0.111383i	0.0616938	+	0.998095i	$0.480350\pi$
$54$	−3.08583	−	5.34482i	−0.419929	−	0.727338i
$55$	−7.23324	−	5.70428i	−0.975330	−	0.769165i
$56$		0			0
$57$	0.370334	+	1.13977i	0.0490520	+	0.150966i
$58$	−1.60308	+	15.2523i	−0.210495	+	2.00272i
$59$	−0.894464	−	8.51025i	−0.116449	−	1.10794i	−0.884173	−	0.467160i	$-0.845277\pi$
$59$	−0.894464	−	8.51025i	−0.116449	−	1.10794i	0.767724	−	0.640781i	$-0.221389\pi$
$60$	−1.33176	−	1.47907i	−0.171930	−	0.190947i
$61$	−0.967005	+	0.205543i	−0.123812	+	0.0263171i	−0.269401	−	0.963028i	$-0.586826\pi$
$61$	−0.967005	+	0.205543i	−0.123812	+	0.0263171i	0.145589	+	0.989345i	$0.453492\pi$
$62$	−0.288448	+	0.209570i	−0.0366330	+	0.0266154i
$63$		0			0
$64$	−0.141042	−	0.434084i	−0.0176303	−	0.0542605i
$65$	−5.96253	−	10.3274i	−0.739561	−	1.28096i
$66$	−3.38432	+	1.34952i	−0.416581	+	0.166114i
$67$	2.70872	−	4.69165i	0.330923	−	0.573176i	−0.651770	−	0.758417i	$-0.725973\pi$
$67$	2.70872	−	4.69165i	0.330923	−	0.573176i	0.982693	+	0.185241i	$0.0593066\pi$
$68$	2.13783	−	2.37430i	0.259249	−	0.287926i
$69$	2.18505	+	1.58753i	0.263049	+	0.191116i
$70$		0			0
$71$	−0.623302	+	1.91833i	−0.0739724	+	0.227664i	−0.981206	−	0.192964i	$-0.938190\pi$
$71$	−0.623302	+	1.91833i	−0.0739724	+	0.227664i	0.907234	+	0.420627i	$0.138190\pi$
$72$	−3.82603	+	0.813249i	−0.450902	+	0.0958423i
$73$	−1.04226	−	9.91646i	−0.121987	−	1.16063i	−0.868649	−	0.495429i	$-0.835011\pi$
$73$	−1.04226	−	9.91646i	−0.121987	−	1.16063i	0.746661	−	0.665205i	$-0.231656\pi$
$74$	1.68143	−	0.748619i	0.195462	−	0.0870252i
$75$	−1.12254	+	1.24670i	−0.129619	+	0.143957i
$76$	−2.24828			−0.257896
$77$		0			0
$78$	−4.71658			−0.534047
$79$	4.21116	−	4.67696i	0.473792	−	0.526200i	−0.458117	−	0.888892i	$-0.651476\pi$
$79$	4.21116	−	4.67696i	0.473792	−	0.526200i	0.931909	+	0.362693i	$0.118142\pi$
$80$	−12.6223	+	5.61980i	−1.41121	+	0.628313i
$81$	−0.596670	−	5.67693i	−0.0662966	−	0.630770i
$82$	16.7017	−	3.55005i	1.84439	−	0.392038i
$83$	0.531960	−	1.63720i	0.0583902	−	0.179707i	−0.917607	−	0.397488i	$-0.869882\pi$
$83$	0.531960	−	1.63720i	0.0583902	−	0.179707i	0.975998	+	0.217781i	$0.0698820\pi$
$84$		0			0
$85$	−6.19182	−	4.49862i	−0.671598	−	0.487944i
$86$	−5.59979	+	6.21920i	−0.603841	+	0.670634i
$87$	2.66623	−	4.61804i	0.285849	−	0.495106i
$88$	0.323221	+	4.94470i	0.0344555	+	0.527106i
$89$	−7.65177	−	13.2532i	−0.811086	−	1.40484i	−0.912105	−	0.409957i	$-0.865544\pi$
$89$	−7.65177	−	13.2532i	−0.811086	−	1.40484i	0.101019	−	0.994884i	$-0.467790\pi$
$90$	−3.99406	−	12.2925i	−0.421011	−	1.29574i
$91$		0			0
$92$	−4.09921	+	2.97825i	−0.427373	+	0.310504i
$93$	0.121261	−	0.0257748i	0.0125742	−	0.00267272i
$94$	15.5160	+	17.2322i	1.60035	+	1.77737i
$95$	0.562970	+	5.35630i	0.0577595	+	0.549545i
$96$	−0.378188	+	3.59821i	−0.0385986	+	0.367241i
$97$	−3.58961	−	11.0477i	−0.364470	−	1.12172i	−0.950313	−	0.311297i	$-0.899236\pi$
$97$	−3.58961	−	11.0477i	−0.364470	−	1.12172i	0.585843	−	0.810425i	$-0.300764\pi$
$98$		0			0
$99$	−8.67628	−	0.342417i	−0.871999	−	0.0344142i
$100$	−1.57362	−	2.72558i	−0.157362	−	0.272558i
$101$	3.33723	+	0.709351i	0.332067	+	0.0705830i	0.370928	−	0.928662i	$-0.379040\pi$
$101$	3.33723	+	0.709351i	0.332067	+	0.0705830i	−0.0388610	+	0.999245i	$0.512373\pi$
$102$	−2.76540	+	1.23123i	−0.273815	+	0.121910i
$103$	16.6106	+	7.39552i	1.63669	+	0.728702i	0.999130	−	0.0416969i	$-0.0132764\pi$
$103$	16.6106	+	7.39552i	1.63669	+	0.728702i	0.637562	+	0.770399i	$0.279943\pi$
$104$	−1.98226	+	6.10077i	−0.194377	+	0.598230i
$105$		0			0
$106$	5.60843	−	4.07476i	0.544739	−	0.395776i
$107$	−0.339452	+	3.22967i	−0.0328161	+	0.312224i	0.965785	+	0.259345i	$0.0835065\pi$
$107$	−0.339452	+	3.22967i	−0.0328161	+	0.312224i	−0.998601	+	0.0528793i	$0.983160\pi$
$108$	−3.93780	−	0.837004i	−0.378915	−	0.0805408i
$109$	−6.34558	+	10.9909i	−0.607796	+	1.05273i	0.383807	+	0.923413i	$0.374613\pi$
$109$	−6.34558	+	10.9909i	−0.607796	+	1.05273i	−0.991603	+	0.129320i	$0.958720\pi$
$110$	−16.1379	+	2.77009i	−1.53869	+	0.264118i
$111$	−0.639962			−0.0607425
$112$		0			0
$113$	14.9248	+	10.8435i	1.40401	+	1.02007i	0.994160	+	0.107915i	$0.0344173\pi$
$113$	14.9248	+	10.8435i	1.40401	+	1.02007i	0.409845	+	0.912155i	$0.365583\pi$
$114$	1.94602	+	0.866424i	0.182262	+	0.0811481i
$115$	8.12182	+	9.02019i	0.757363	+	0.841137i
$116$	6.69388	+	7.43430i	0.621511	+	0.690258i
$117$	−10.2687	−	4.57191i	−0.949340	−	0.422673i
$118$	−12.3053	−	8.94031i	−1.13279	−	0.823022i
$119$		0			0
$120$	2.56468			0.234122
$121$	−2.00839	+	10.8151i	−0.182581	+	0.983191i
$122$	−0.878618	+	1.52181i	−0.0795464	+	0.137778i
$123$	−5.80720	−	1.23436i	−0.523617	−	0.111298i
$124$	−0.0243103	+	0.231298i	−0.00218313	+	0.0207711i
$125$	5.13577	−	3.73136i	0.459358	−	0.333743i
$126$		0			0
$127$	6.02870	−	18.5544i	0.534961	−	1.64644i	−0.208772	−	0.977964i	$-0.566947\pi$
$127$	6.02870	−	18.5544i	0.534961	−	1.64644i	0.743733	−	0.668476i	$-0.233053\pi$
$128$	9.95483	+	4.43218i	0.879891	+	0.391753i
$129$	2.65826	−	1.18353i	0.234047	−	0.104204i
$130$	−20.7334	−	4.40702i	−1.81844	−	0.386521i
$131$	−3.44898	−	5.97381i	−0.301339	−	0.521934i	0.675101	−	0.737726i	$-0.264100\pi$
$131$	−3.44898	−	5.97381i	−0.301339	−	0.521934i	−0.976439	+	0.215792i	$0.930767\pi$
$132$	−0.822982	+	2.22959i	−0.0716314	+	0.194061i
$133$		0			0
$134$	−2.97566	−	9.15813i	−0.257058	−	0.791142i
$135$	−1.00805	+	9.59097i	−0.0867593	+	0.825460i
$136$	0.430341	+	4.09442i	0.0369015	+	0.351094i
$137$	−1.74690	−	1.94013i	−0.149247	−	0.165756i	0.663885	−	0.747834i	$-0.268906\pi$
$137$	−1.74690	−	1.94013i	−0.149247	−	0.165756i	−0.813133	+	0.582078i	$0.802240\pi$
$138$	4.69584	−	0.998132i	0.399736	−	0.0849666i
$139$	−0.810097	+	0.588570i	−0.0687116	+	0.0499219i	−0.621611	−	0.783326i	$-0.713521\pi$
$139$	−0.810097	+	0.588570i	−0.0687116	+	0.0499219i	0.552899	+	0.833248i	$0.313521\pi$
$140$		0			0
$141$	−2.49148	−	7.66797i	−0.209820	−	0.645760i
$142$	1.79264	+	3.10494i	0.150435	+	0.260561i
$143$	−7.60070	+	12.0417i	−0.635603	+	1.00698i
$144$	−6.51180	+	11.2788i	−0.542650	+	0.939898i
$145$	16.0353	−	17.8090i	1.33166	−	1.47896i
$146$	−14.3386	−	10.4176i	−1.18667	−	0.862165i
$147$		0			0
$148$	0.371002	−	1.14183i	0.0304962	−	0.0938576i
$149$	14.5693	−	3.09679i	1.19356	−	0.253699i	0.432049	−	0.901850i	$-0.357791\pi$
$149$	14.5693	−	3.09679i	1.19356	−	0.253699i	0.761512	+	0.648151i	$0.224457\pi$
$150$	0.311695	+	2.96558i	0.0254498	+	0.242138i
$151$	14.4382	−	6.42831i	1.17496	−	0.523128i	0.276004	−	0.961157i	$-0.410990\pi$
$151$	14.4382	−	6.42831i	1.17496	−	0.523128i	0.898961	+	0.438028i	$0.144323\pi$
$152$	1.93856	−	2.15299i	0.157238	−	0.174630i
$153$	−7.21414			−0.583229
$154$		0			0
$155$	0.557129			0.0447497
$156$	−2.05866	+	2.28637i	−0.164825	+	0.183056i
$157$	−4.19429	+	1.86742i	−0.334741	+	0.149036i	−0.567223	−	0.823564i	$-0.691982\pi$
$157$	−4.19429	+	1.86742i	−0.334741	+	0.149036i	0.232482	+	0.972601i	$0.425315\pi$
$158$	−1.16931	−	11.1253i	−0.0930256	−	0.885079i
$159$	−2.35773	+	0.501152i	−0.186980	+	0.0397439i
$160$	−5.02452	+	15.4639i	−0.397223	+	1.22253i
$161$		0			0
$162$	−8.20848	−	5.96381i	−0.644919	−	0.468561i
$163$	5.37823	−	5.97313i	0.421256	−	0.467852i	−0.494739	−	0.869041i	$-0.664736\pi$
$163$	5.37823	−	5.97313i	0.421256	−	0.467852i	0.915995	+	0.401190i	$0.131403\pi$
$164$	5.56893	−	9.64568i	0.434861	−	0.753201i
$165$	5.51783	+	1.40238i	0.429562	+	0.109175i
$166$	−1.52993	−	2.64992i	−0.118746	−	0.205674i
$167$	4.14296	+	12.7507i	0.320592	+	0.986681i	0.973391	+	0.229150i	$0.0735946\pi$
$167$	4.14296	+	12.7507i	0.320592	+	0.986681i	−0.652799	+	0.757531i	$0.726405\pi$
$168$		0			0
$169$	−4.39615	+	3.19399i	−0.338165	+	0.245691i
$170$	−13.3067	+	2.82843i	−1.02058	+	0.216931i
$171$	3.39692	+	3.77266i	0.259769	+	0.288503i
$172$	0.570613	+	5.42902i	0.0435089	+	0.413959i
$173$	−2.15141	+	20.4693i	−0.163569	+	1.55625i	0.537564	+	0.843223i	$0.319345\pi$
$173$	−2.15141	+	20.4693i	−0.163569	+	1.55625i	−0.701133	+	0.713031i	$0.747322\pi$
$174$	−2.92897	−	9.01445i	−0.222045	−	0.683383i
$175$		0			0
$176$	12.9550	+	10.2166i	0.976520	+	0.770104i
$177$	2.64430	+	4.58006i	0.198758	+	0.344258i
$178$	−26.6074	−	5.65557i	−1.99431	−	0.423903i
$179$	−3.39400	+	1.51111i	−0.253680	+	0.112945i	−0.529637	−	0.848224i	$-0.677672\pi$
$179$	−3.39400	+	1.51111i	−0.253680	+	0.112945i	0.275957	+	0.961170i	$0.411005\pi$
$180$	−7.70210	−	3.42920i	−0.574081	−	0.255597i
$181$	−1.47458	+	4.53828i	−0.109604	+	0.337327i	−0.990783	−	0.135455i	$-0.956750\pi$
$181$	−1.47458	+	4.53828i	−0.109604	+	0.337327i	0.881179	+	0.472783i	$0.156750\pi$
$182$		0			0
$183$	0.494304	−	0.359133i	0.0365400	−	0.0265479i
$184$	0.682487	−	6.49343i	0.0503136	−	0.478702i
$185$	−2.81318	−	0.597960i	−0.206829	−	0.0439629i
$186$	0.110177	−	0.190833i	0.00807860	−	0.0139925i
$187$	−1.31299	+	9.04434i	−0.0960151	+	0.661388i
$188$	15.1257			1.10315
$189$		0			0
$190$	7.74487	+	5.62698i	0.561872	+	0.408224i
$191$	−0.757474	−	0.337249i	−0.0548089	−	0.0244025i	0.379149	−	0.925336i	$-0.376217\pi$
$191$	−0.757474	−	0.337249i	−0.0548089	−	0.0244025i	−0.433958	+	0.900933i	$0.642883\pi$
$192$	0.188752	+	0.209630i	0.0136220	+	0.0151287i
$193$	−4.50862	−	5.00733i	−0.324538	−	0.360435i	0.558693	−	0.829375i	$-0.311303\pi$
$193$	−4.50862	−	5.00733i	−0.324538	−	0.360435i	−0.883231	+	0.468939i	$0.844636\pi$
$194$	−18.8626	−	8.39815i	−1.35425	−	0.602952i
$195$	5.96253	+	4.33203i	0.426986	+	0.310223i
$196$		0			0
$197$	−10.9216			−0.778129			−0.389065	−	0.921210i	$-0.627202\pi$
$197$	−10.9216			−0.778129			−0.389065	+	0.921210i	$0.627202\pi$
$198$	−10.7716	+	11.0535i	−0.765505	+	0.785537i
$199$	10.4873	−	18.1645i	0.743424	−	1.28765i	−0.207503	−	0.978234i	$-0.566534\pi$
$199$	10.4873	−	18.1645i	0.743424	−	1.28765i	0.950927	−	0.309414i	$-0.100133\pi$
$200$	3.96689	+	0.843189i	0.280502	+	0.0596225i
$201$	−0.349979	+	3.32982i	−0.0246856	+	0.234868i
$202$	4.90620	−	3.56457i	0.345199	−	0.250802i
$203$		0			0
$204$	−0.610177	+	1.87793i	−0.0427210	+	0.131482i
$205$	−24.3743	−	10.8521i	−1.70237	−	0.757945i
$206$	29.5251	−	13.1454i	2.05711	−	0.915885i
$207$	11.1910	+	2.37873i	0.777831	+	0.165333i
$208$	10.6791	+	18.4968i	0.740463	+	1.28252i
$209$	5.34802	−	3.57207i	0.369930	−	0.247086i
$210$		0			0
$211$	−1.86140	−	5.72879i	−0.128144	−	0.394386i	0.866317	−	0.499495i	$-0.166481\pi$
$211$	−1.86140	−	5.72879i	−0.128144	−	0.394386i	−0.994461	+	0.105109i	$0.966481\pi$
$212$	0.472677	−	4.49722i	0.0324636	−	0.308870i
$213$	−0.130306	−	1.23978i	−0.00892840	−	0.0849480i
$214$	3.86243	+	4.28966i	0.264030	+	0.293235i
$215$	12.7912	−	2.71885i	0.872353	−	0.185424i
$216$	4.19685	−	3.04919i	0.285560	−	0.207471i
$217$		0			0
$218$	6.97091	+	21.4542i	0.472129	+	1.45306i
$219$	3.08123	+	5.33685i	0.208210	+	0.360631i
$220$	−5.70097	+	9.03197i	−0.384359	+	0.608935i
$221$	−5.91546	+	10.2459i	−0.397917	+	0.689212i
$222$	−0.761151	+	0.845344i	−0.0510851	+	0.0567358i
$223$	−3.74176	−	2.71855i	−0.250567	−	0.182048i	0.455411	−	0.890281i	$-0.349492\pi$
$223$	−3.74176	−	2.71855i	−0.250567	−	0.182048i	−0.705978	+	0.708234i	$0.749492\pi$
$224$		0			0
$225$	−2.19601	+	6.75863i	−0.146401	+	0.450575i
$226$	32.0745	−	6.81766i	2.13357	−	0.453504i
$227$	1.80838	+	17.2056i	0.120026	+	1.14197i	0.874291	+	0.485403i	$0.161327\pi$
$227$	1.80838	+	17.2056i	0.120026	+	1.14197i	−0.754265	+	0.656571i	$0.772006\pi$
$228$	1.26939	−	0.565167i	0.0840672	−	0.0374291i
$229$	2.96165	−	3.28925i	0.195711	−	0.217360i	−0.637299	−	0.770616i	$-0.719948\pi$
$229$	2.96165	−	3.28925i	0.195711	−	0.217360i	0.833011	+	0.553257i	$0.186615\pi$
$230$	21.5749			1.42260
$231$		0			0
$232$	−12.8909			−0.846330
$233$	−7.04798	+	7.82757i	−0.461729	+	0.512801i	−0.928376	−	0.371642i	$-0.878795\pi$
$233$	−7.04798	+	7.82757i	−0.461729	+	0.512801i	0.466648	+	0.884443i	$0.345462\pi$
$234$	−18.2524	+	8.12650i	−1.19320	+	0.531246i
$235$	−3.78746	−	36.0353i	−0.247067	−	2.35068i
$236$	−9.70476	+	2.06281i	−0.631726	+	0.134277i
$237$	−1.20195	+	3.69921i	−0.0780748	+	0.240290i
$238$		0			0
$239$	7.89314	+	5.73470i	0.510565	+	0.370947i	0.813038	−	0.582211i	$-0.197812\pi$
$239$	7.89314	+	5.73470i	0.510565	+	0.370947i	−0.302473	+	0.953158i	$0.597812\pi$
$240$	5.71388	−	6.34590i	0.368829	−	0.409626i
$241$	6.27504	−	10.8687i	0.404211	−	0.700114i	−0.590018	−	0.807390i	$-0.700879\pi$
$241$	6.27504	−	10.8687i	0.404211	−	0.700114i	0.994229	+	0.107276i	$0.0342128\pi$
$242$	11.8973	+	15.5161i	0.764785	+	0.997411i
$243$	6.97214	+	12.0761i	0.447263	+	0.774682i
$244$	0.354208	+	1.09014i	0.0226759	+	0.0697892i
$245$		0			0
$246$	−8.53740	+	6.20278i	−0.544325	+	0.395475i
$247$	8.14353	−	1.73096i	0.518160	−	0.110138i
$248$	−0.200532	−	0.222714i	−0.0127338	−	0.0141423i
$249$	0.111210	+	1.05809i	0.00704764	+	0.0670538i
$250$	1.17947	−	11.2220i	0.0745965	−	0.709739i
$251$	3.39646	+	10.4532i	0.214383	+	0.659803i	0.999197	+	0.0400713i	$0.0127585\pi$
$251$	3.39646	+	10.4532i	0.214383	+	0.659803i	−0.784814	+	0.619732i	$0.787241\pi$
$252$		0			0
$253$	5.01899	−	13.5972i	0.315541	−	0.854850i
$254$	−17.3387	−	30.0316i	−1.08793	−	1.88435i
$255$	4.62677	+	0.983450i	0.289739	+	0.0615860i
$256$	18.5285	−	8.24941i	1.15803	−	0.515588i
$257$	−4.87175	−	2.16904i	−0.303892	−	0.135301i	0.249125	−	0.968471i	$-0.419857\pi$
$257$	−4.87175	−	2.16904i	−0.303892	−	0.135301i	−0.553017	+	0.833170i	$0.686524\pi$
$258$	1.59829	−	4.91903i	0.0995052	−	0.306246i
$259$		0			0
$260$	−11.1859	+	8.12702i	−0.693719	+	0.504017i
$261$	2.36116	−	22.4649i	0.146152	−	1.39054i
$262$	−11.9931	−	2.54921i	−0.740935	−	0.157491i
$263$	4.09017	−	7.08438i	0.252211	−	0.436842i	−0.711923	−	0.702257i	$-0.752176\pi$
$263$	4.09017	−	7.08438i	0.252211	−	0.436842i	0.964134	+	0.265415i	$0.0855091\pi$
$264$	−1.42547	−	2.71054i	−0.0877319	−	0.166822i
$265$	−10.8325			−0.665436
$266$		0			0
$267$	7.65177	+	5.55933i	0.468280	+	0.340226i
$268$	−5.73822	−	2.55482i	−0.350517	−	0.156060i
$269$	−8.59425	−	9.54489i	−0.524001	−	0.581962i	0.421808	−	0.906685i	$-0.361396\pi$
$269$	−8.59425	−	9.54489i	−0.524001	−	0.581962i	−0.945809	+	0.324723i	$0.894729\pi$
$270$	11.4700	+	12.7388i	0.698044	+	0.775257i
$271$	20.1411	+	8.96741i	1.22349	+	0.544731i	0.913822	−	0.406114i	$-0.133117\pi$
$271$	20.1411	+	8.96741i	1.22349	+	0.544731i	0.309665	+	0.950846i	$0.399783\pi$
$272$	11.0898	+	8.05720i	0.672417	+	0.488539i
$273$		0			0
$274$	−4.64047			−0.280341
$275$	8.07359	+	3.98321i	0.486856	+	0.240197i
$276$	1.56576	−	2.71198i	0.0942477	−	0.163242i
$277$	−23.5508	−	5.00588i	−1.41503	−	0.300774i	−0.563951	−	0.825808i	$-0.690719\pi$
$277$	−23.5508	−	5.00588i	−1.41503	−	0.300774i	−0.851081	+	0.525034i	$0.824053\pi$
$278$	−0.186046	+	1.77011i	−0.0111583	+	0.106164i
$279$	0.424852	−	0.308673i	0.0254352	−	0.0184798i
$280$		0			0
$281$	4.77179	−	14.6861i	0.284661	−	0.876097i	−0.701839	−	0.712336i	$-0.747637\pi$
$281$	4.77179	−	14.6861i	0.284661	−	0.876097i	0.986500	−	0.163761i	$-0.0523626\pi$
$282$	−13.0921	−	5.82899i	−0.779625	−	0.347111i
$283$	3.06706	−	1.36554i	0.182318	−	0.0811732i	−0.313548	−	0.949572i	$-0.601518\pi$
$283$	3.06706	−	1.36554i	0.182318	−	0.0811732i	0.495866	+	0.868399i	$0.334851\pi$
$284$	2.28756	+	0.486236i	0.135742	+	0.0288528i
$285$	−1.66431	−	2.88266i	−0.0985850	−	0.170754i
$286$	6.86618	+	24.3620i	0.406006	+	1.44056i
$287$		0			0
$288$	4.73607	+	14.5761i	0.279075	+	0.858906i
$289$	0.983290	−	9.35538i	0.0578406	−	0.550316i
$290$	−4.45253	−	42.3630i	−0.261461	−	2.48764i
$291$	4.80383	+	5.33520i	0.281606	+	0.312755i
$292$	−11.3083	+	2.40366i	−0.661770	+	0.140664i
$293$	5.53129	−	4.01872i	0.323142	−	0.234776i	−0.414373	−	0.910107i	$-0.635999\pi$
$293$	5.53129	−	4.01872i	0.323142	−	0.234776i	0.737515	+	0.675331i	$0.235999\pi$
$294$		0			0
$295$	7.34450	+	22.6040i	0.427613	+	1.31606i
$296$	0.773537	+	1.33981i	0.0449609	+	0.0778746i
$297$	10.6967	−	4.26538i	0.620686	−	0.247502i
$298$	13.2376	−	22.9282i	0.766834	−	1.32819i
$299$	12.5548	−	13.9435i	0.726064	−	0.806376i
$300$	1.57362	+	1.14330i	0.0908528	+	0.0660084i
$301$		0			0
$302$	8.68103	−	26.7175i	0.499537	−	1.53742i
$303$	−2.06252	+	0.438403i	−0.118489	+	0.0251856i
$304$	−1.00830	−	9.59333i	−0.0578300	−	0.550215i
$305$	2.50845	−	1.11684i	0.143634	−	0.0639498i
$306$	−8.58028	+	9.52936i	−0.490502	+	0.544757i
$307$	11.7970			0.673293			0.336646	−	0.941631i	$-0.390707\pi$
$307$	11.7970			0.673293			0.336646	+	0.941631i	$0.390707\pi$
$308$		0			0
$309$	−11.2375			−0.639276
$310$	0.662633	−	0.735928i	0.0376350	−	0.0417979i
$311$	−23.1254	+	10.2961i	−1.31132	+	0.583837i	−0.938888	−	0.344222i	$-0.888143\pi$
$311$	−23.1254	+	10.2961i	−1.31132	+	0.583837i	−0.372432	+	0.928059i	$0.621476\pi$
$312$	−0.414405	−	3.94280i	−0.0234611	−	0.223217i
$313$	−19.2248	+	4.08637i	−1.08665	+	0.230975i	−0.716213	−	0.697882i	$-0.754126\pi$
$313$	−19.2248	+	4.08637i	−1.08665	+	0.230975i	−0.370439	+	0.928857i	$0.620793\pi$
$314$	−2.52184	+	7.76141i	−0.142315	+	0.438002i
$315$		0			0
$316$	−5.90337	−	4.28905i	−0.332091	−	0.241278i
$317$	2.41594	−	2.68317i	0.135693	−	0.150702i	−0.671469	−	0.741033i	$-0.734336\pi$
$317$	2.41594	−	2.68317i	0.135693	−	0.150702i	0.807161	+	0.590331i	$0.201003\pi$
$318$	−2.14223	+	3.71045i	−0.120130	+	0.208072i
$319$	−27.7344	−	7.04882i	−1.55283	−	0.394658i
$320$	0.633854	+	1.09787i	0.0354335	+	0.0613726i
$321$	−0.620210	−	1.90881i	−0.0346167	−	0.106539i
$322$		0			0
$323$	4.32281	−	3.14071i	0.240528	−	0.174754i
$324$	−6.47375	+	1.37604i	−0.359653	+	0.0764466i
$325$	7.79824	+	8.66083i	0.432569	+	0.480416i
$326$	−1.49338	−	14.2085i	−0.0827104	−	0.786937i
$327$	0.819876	−	7.80060i	0.0453392	−	0.431374i
$328$	4.43508	+	13.6498i	0.244886	+	0.753683i
$329$		0			0
$330$	8.41518	−	5.62071i	0.463240	−	0.309410i
$331$	13.2667	+	22.9787i	0.729205	+	1.26302i	0.957219	+	0.289363i	$0.0934435\pi$
$331$	13.2667	+	22.9787i	0.729205	+	1.26302i	−0.228014	+	0.973658i	$0.573223\pi$
$332$	−1.95233	−	0.414981i	−0.107148	−	0.0227750i
$333$	−2.47655	+	1.10263i	−0.135714	+	0.0604238i
$334$	21.7703	+	9.69277i	1.19122	+	0.530365i
$335$	−4.64974	+	14.3104i	−0.254042	+	0.781862i
$336$		0			0
$337$	0.554969	−	0.403208i	0.0302311	−	0.0219642i	−0.572567	−	0.819858i	$-0.694052\pi$
$337$	0.554969	−	0.403208i	0.0302311	−	0.0219642i	0.602798	+	0.797894i	$0.294052\pi$
$338$	−1.00961	+	9.60583i	−0.0549157	+	0.522488i
$339$	−11.1524	−	2.37051i	−0.605714	−	0.128748i
$340$	−4.43693	+	7.68500i	−0.240627	+	0.416777i
$341$	−0.309658	−	0.588814i	−0.0167689	−	0.0318861i
$342$	9.02361			0.487941
$343$		0			0
$344$	−5.69091	−	4.13469i	−0.306834	−	0.222928i
$345$	−6.85307	−	3.05118i	−0.368957	−	0.164270i
$346$	24.4797	+	27.1874i	1.31604	+	1.46161i
$347$	14.3900	+	15.9817i	0.772493	+	0.857941i	0.993082	−	0.117426i	$-0.0374643\pi$
$347$	14.3900	+	15.9817i	0.772493	+	0.857941i	−0.220588	+	0.975367i	$0.570798\pi$
$348$	−5.64819	−	2.51474i	−0.302775	−	0.134804i
$349$	15.7296	+	11.4282i	0.841987	+	0.611739i	0.922925	−	0.384980i	$-0.125792\pi$
$349$	15.7296	+	11.4282i	0.841987	+	0.611739i	−0.0809381	+	0.996719i	$0.525792\pi$
$350$		0			0
$351$	14.9075			0.795705
$352$	19.1360	−	3.28471i	1.01995	−	0.175076i
$353$	−10.4654	+	18.1265i	−0.557015	+	0.964778i	0.440729	+	0.897640i	$0.354720\pi$
$353$	−10.4654	+	18.1265i	−0.557015	+	0.964778i	−0.997744	+	0.0671378i	$0.978613\pi$
$354$	9.19498	+	1.95445i	0.488707	+	0.103878i
$355$	0.585602	−	5.57163i	0.0310805	−	0.295711i
$356$	−14.3549	+	10.4295i	−0.760810	+	0.552761i
$357$		0			0
$358$	−2.04066	+	6.28050i	−0.107852	+	0.331935i
$359$	8.92650	+	3.97433i	0.471123	+	0.209757i	0.628544	−	0.777774i	$-0.283651\pi$
$359$	8.92650	+	3.97433i	0.471123	+	0.209757i	−0.157421	+	0.987532i	$0.550318\pi$
$360$	9.92490	−	4.41885i	0.523088	−	0.232894i
$361$	14.9069	+	3.16856i	0.784573	+	0.166766i
$362$	4.24092	+	7.34550i	0.222898	+	0.386071i
$363$	−1.58473	−	6.61109i	−0.0831767	−	0.346992i
$364$		0			0
$365$	8.55808	+	26.3390i	0.447950	+	1.37865i
$366$	0.113521	−	1.08008i	0.00593385	−	0.0564568i
$367$	1.03480	+	9.84545i	0.0540161	+	0.513929i	0.987759	+	0.155985i	$0.0498552\pi$
$367$	1.03480	+	9.84545i	0.0540161	+	0.513929i	−0.933743	+	0.357943i	$0.883478\pi$
$368$	−14.5465	−	16.1555i	−0.758287	−	0.842163i
$369$	−24.5997	+	5.22882i	−1.28061	+	0.272202i
$370$	−4.13577	+	3.00482i	−0.215009	+	0.156213i
$371$		0			0
$372$	−0.0444172	−	0.136702i	−0.00230293	−	0.00708768i
$373$	2.13737	+	3.70204i	0.110669	+	0.191684i	0.916040	−	0.401086i	$-0.131367\pi$
$373$	2.13737	+	3.70204i	0.110669	+	0.191684i	−0.805371	+	0.592771i	$0.798034\pi$
$374$	10.3853	+	12.4914i	0.537011	+	0.645916i
$375$	−1.96169	+	3.39775i	−0.101301	+	0.175459i
$376$	−13.0419	+	14.4845i	−0.672586	+	0.746983i
$377$	−29.9696	−	21.7742i	−1.54351	−	1.12143i
$378$		0			0
$379$	1.33679	−	4.11421i	0.0686662	−	0.211333i	−0.910835	−	0.412770i	$-0.864561\pi$
$379$	1.33679	−	4.11421i	0.0686662	−	0.211333i	0.979501	+	0.201437i	$0.0645612\pi$
$380$	6.10812	−	1.29832i	0.313340	−	0.0666024i
$381$	1.26034	+	11.9914i	0.0645693	+	0.614336i
$382$	−1.34640	+	0.599455i	−0.0688877	+	0.0306708i
$383$	0.884657	−	0.982512i	0.0452039	−	0.0502040i	−0.720119	−	0.693851i	$-0.755913\pi$
$383$	0.884657	−	0.982512i	0.0452039	−	0.0502040i	0.765323	+	0.643647i	$0.222579\pi$
$384$	−6.73467			−0.343677
$385$		0			0
$386$	−11.9767			−0.609600
$387$	8.24786	−	9.16018i	0.419262	−	0.465638i
$388$	−12.3040	+	5.47810i	−0.624642	+	0.278109i
$389$	4.02530	+	38.2982i	0.204091	+	1.94180i	0.317524	+	0.948250i	$0.397149\pi$
$389$	4.02530	+	38.2982i	0.204091	+	1.94180i	−0.113433	+	0.993546i	$0.536185\pi$
$390$	12.8140	−	2.72369i	0.648860	−	0.137919i
$391$	3.72119	−	11.4527i	0.188189	−	0.579186i
$392$		0			0
$393$	3.44898	+	2.50583i	0.173978	+	0.126402i
$394$	−12.9898	+	14.4266i	−0.654415	+	0.726802i
$395$	−8.74002	+	15.1382i	−0.439758	+	0.761683i
$396$	0.656687	+	10.0461i	0.0329998	+	0.504836i
$397$	−0.205054	−	0.355165i	−0.0102914	−	0.0178252i	0.860834	−	0.508886i	$-0.169943\pi$
$397$	−0.205054	−	0.355165i	−0.0102914	−	0.0178252i	−0.871125	+	0.491061i	$0.836609\pi$
$398$	−11.5208	−	35.4573i	−0.577484	−	1.77731i
$399$		0			0
$400$	10.9242	−	7.93691i	0.546211	−	0.396846i
$401$	1.53260	−	0.325764i	0.0765345	−	0.0162679i	−0.169485	−	0.985533i	$-0.554211\pi$
$401$	1.53260	−	0.325764i	0.0765345	−	0.0162679i	0.246020	+	0.969265i	$0.420877\pi$
$402$	3.98221	+	4.42269i	0.198614	+	0.220584i
$403$	−0.0900219	−	0.856501i	−0.00448431	−	0.0426654i
$404$	0.413494	−	3.93413i	0.0205721	−	0.195730i
$405$	4.89929	+	15.0785i	0.243448	+	0.749255i
$406$		0			0
$407$	0.931628	+	3.30552i	0.0461791	+	0.163849i
$408$	−1.27222	−	2.20354i	−0.0629841	−	0.109092i
$409$	−6.63040	−	1.40933i	−0.327852	−	0.0696871i	0.0410452	−	0.999157i	$-0.486931\pi$
$409$	−6.63040	−	1.40933i	−0.327852	−	0.0696871i	−0.368897	+	0.929470i	$0.620265\pi$
$410$	−43.3249	+	19.2895i	−2.13966	+	0.952640i
$411$	1.47400	+	0.656269i	0.0727073	+	0.0323714i
$412$	6.51463	−	20.0500i	0.320953	−	0.987792i
$413$		0			0
$414$	16.4524	−	11.9534i	0.808592	−	0.587476i
$415$	−0.499785	+	4.75513i	−0.0245335	+	0.233420i
$416$	24.5852	+	5.22575i	1.20539	+	0.256213i
$417$	0.309430	−	0.535948i	0.0151528	−	0.0262455i
$418$	1.64231	−	11.3129i	0.0803282	−	0.553330i
$419$	−28.7218			−1.40315			−0.701577	−	0.712594i	$-0.747520\pi$
$419$	−28.7218			−1.40315			−0.701577	+	0.712594i	$0.747520\pi$
$420$		0			0
$421$	−9.89070	−	7.18601i	−0.482043	−	0.350225i	0.320073	−	0.947393i	$-0.396293\pi$
$421$	−9.89070	−	7.18601i	−0.482043	−	0.350225i	−0.802116	+	0.597168i	$0.796293\pi$
$422$	−9.78121	−	4.35488i	−0.476142	−	0.211992i
$423$	−22.8533	−	25.3811i	−1.11116	−	1.23407i
$424$	3.89904	+	4.33032i	0.189354	+	0.210299i
$425$	6.83308	+	3.04228i	0.331453	+	0.147572i
$426$	−1.79264	−	1.30243i	−0.0868535	−	0.0631028i
$427$		0			0
$428$	3.76527			0.182001
$429$	1.26437	−	8.70941i	0.0610441	−	0.420494i
$430$	11.6220	−	20.1300i	0.560465	−	0.970754i
$431$	−3.61063	−	0.767463i	−0.173918	−	0.0369674i	0.120130	−	0.992758i	$-0.461669\pi$
$431$	−3.61063	−	0.767463i	−0.173918	−	0.0369674i	−0.294047	+	0.955791i	$0.595002\pi$
$432$	1.80546	−	17.1778i	0.0868651	−	0.826466i
$433$	23.5221	−	17.0898i	1.13040	−	0.821283i	0.144646	−	0.989483i	$-0.453796\pi$
$433$	23.5221	−	17.0898i	1.13040	−	0.821283i	0.985753	+	0.168201i	$0.0537957\pi$
$434$		0			0
$435$	−4.57679	+	14.0859i	−0.219440	+	0.675368i
$436$	13.4426	+	5.98503i	0.643784	+	0.286631i
$437$	−7.74141	+	3.44670i	−0.370322	+	0.164878i
$438$	10.7143	+	2.27740i	0.511950	+	0.108818i
$439$	−7.10086	−	12.2990i	−0.338905	−	0.587001i	0.645322	−	0.763911i	$-0.276723\pi$
$439$	−7.10086	−	12.2990i	−0.338905	−	0.587001i	−0.984227	+	0.176910i	$0.943390\pi$
$440$	−3.73355	−	13.2470i	−0.177990	−	0.631528i
$441$		0			0
$442$	6.49840	+	20.0000i	0.309097	+	0.951304i
$443$	−2.84689	+	27.0864i	−0.135260	+	1.28691i	0.690682	+	0.723158i	$0.257310\pi$
$443$	−2.84689	+	27.0864i	−0.135260	+	1.28691i	−0.825942	+	0.563755i	$0.809356\pi$
$444$	0.0775605	+	0.737939i	0.00368086	+	0.0350210i
$445$	28.4416	+	31.5876i	1.34826	+	1.49740i
$446$	−8.04135	+	1.70924i	−0.380769	+	0.0809349i
$447$	−7.44738	+	5.41084i	−0.352249	+	0.255924i
$448$		0			0
$449$	−12.9527	−	39.8644i	−0.611277	−	1.88132i	−0.445888	−	0.895089i	$-0.647112\pi$
$449$	−12.9527	−	39.8644i	−0.611277	−	1.88132i	−0.165389	−	0.986228i	$-0.552888\pi$
$450$	6.31579	+	10.9393i	0.297729	+	0.515682i
$451$	2.07817	+	31.7922i	0.0978571	+	1.49704i
$452$	10.6948	−	18.5239i	0.503041	−	0.871292i
$453$	−6.53592	+	7.25887i	−0.307084	+	0.341051i
$454$	24.8781	+	18.0750i	1.16759	+	0.848303i
$455$		0			0
$456$	−0.553303	+	1.70289i	−0.0259108	+	0.0797452i
$457$	−19.0716	+	4.05380i	−0.892132	+	0.189629i	−0.631100	−	0.775701i	$-0.717396\pi$
$457$	−19.0716	+	4.05380i	−0.892132	+	0.189629i	−0.261032	+	0.965330i	$0.584063\pi$
$458$	−0.822363	−	7.82426i	−0.0384265	−	0.365604i
$459$	8.74050	−	3.89152i	0.407972	−	0.181641i
$460$	9.41684	−	10.4585i	0.439063	−	0.487628i
$461$	−12.2251			−0.569380			−0.284690	−	0.958620i	$-0.591891\pi$
$461$	−12.2251			−0.569380			−0.284690	+	0.958620i	$0.591891\pi$
$462$		0			0
$463$	13.8550			0.643894			0.321947	−	0.946758i	$-0.395663\pi$
$463$	13.8550			0.643894			0.321947	+	0.946758i	$0.395663\pi$
$464$	−28.7198	+	31.8966i	−1.33328	+	1.48076i
$465$	−0.314556	+	0.140050i	−0.0145872	+	0.00649464i
$466$	1.95701	+	18.6198i	0.0906570	+	0.862543i
$467$	−16.0619	+	3.41406i	−0.743256	+	0.157984i	−0.563949	−	0.825809i	$-0.690719\pi$
$467$	−16.0619	+	3.41406i	−0.743256	+	0.157984i	−0.179307	+	0.983793i	$0.557385\pi$
$468$	−4.02734	+	12.3949i	−0.186164	+	0.572954i
$469$		0			0
$470$	−52.1047	−	37.8563i	−2.40341	−	1.74618i
$471$	1.89868	−	2.10870i	0.0874866	−	0.0971637i
$472$	6.39245	−	11.0720i	0.294236	−	0.509632i
$473$	−9.98295	−	12.0075i	−0.459017	−	0.552105i
$474$	3.45684	+	5.98741i	0.158778	+	0.275011i
$475$	−1.62652	−	5.00590i	−0.0746297	−	0.229687i
$476$		0			0
$477$	−8.26058	+	6.00167i	−0.378226	+	0.274797i
$478$	16.9630	−	3.60559i	0.775869	−	0.164916i
$479$	16.5887	+	18.4236i	0.757956	+	0.841795i	0.991440	−	0.130566i	$-0.0416793\pi$
$479$	16.5887	+	18.4236i	0.757956	+	0.841795i	−0.233484	+	0.972361i	$0.575013\pi$
$480$	−1.05041	−	9.99398i	−0.0479444	−	0.456161i
$481$	−0.464714	+	4.42145i	−0.0211891	+	0.201601i
$482$	−6.89342	−	21.2158i	−0.313987	−	0.966352i
$483$		0			0
$484$	12.7143	+	1.00512i	0.577922	+	0.0456875i
$485$	16.1319	+	27.9413i	0.732513	+	1.26875i
$486$	24.2441	+	5.15324i	1.09973	+	0.233756i
$487$	−13.0949	+	5.83024i	−0.593388	+	0.264193i	−0.681382	−	0.731928i	$-0.738621\pi$
$487$	−13.0949	+	5.83024i	−0.593388	+	0.264193i	0.0879946	+	0.996121i	$0.471954\pi$
$488$	−1.34935	−	0.600768i	−0.0610821	−	0.0271955i
$489$	−1.53505	+	4.72441i	−0.0694175	+	0.213645i
$490$		0			0
$491$	17.8140	−	12.9426i	0.803935	−	0.584093i	−0.108131	−	0.994137i	$-0.534486\pi$
$491$	17.8140	−	12.9426i	0.803935	−	0.584093i	0.912066	+	0.410044i	$0.134486\pi$
$492$	−0.719530	+	6.84587i	−0.0324389	+	0.308636i
$493$	−23.2556	−	4.94314i	−1.04738	−	0.222628i
$494$	7.39919	−	12.8158i	0.332905	−	0.576609i
$495$	23.7694	−	4.08003i	1.06835	−	0.183384i
$496$	−0.997839			−0.0448043
$497$		0			0
$498$	1.52993	+	1.11156i	0.0685579	+	0.0498103i
$499$	−23.1234	−	10.2952i	−1.03515	−	0.460877i	−0.182412	−	0.983222i	$-0.558390\pi$
$499$	−23.1234	−	10.2952i	−1.03515	−	0.460877i	−0.852734	+	0.522345i	$0.825057\pi$
$500$	−4.92506	−	5.46983i	−0.220255	−	0.244618i
$501$	−5.54437	−	6.15764i	−0.247704	−	0.275103i
$502$	17.8476	+	7.94628i	0.796579	+	0.354660i
$503$	−21.0518	−	15.2950i	−0.938653	−	0.681971i	0.00944301	−	0.999955i	$-0.496994\pi$
$503$	−21.0518	−	15.2950i	−0.938653	−	0.681971i	−0.948096	+	0.317984i	$0.896994\pi$
$504$		0			0
$505$	−9.47619			−0.421685
$506$	−11.9915	−	22.8019i	−0.533088	−	1.01367i
$507$	1.67918	−	2.90842i	0.0745750	−	0.129168i
$508$	−22.1258	−	4.70297i	−0.981672	−	0.208661i
$509$	3.98535	−	37.9180i	0.176647	−	1.68069i	−0.443556	−	0.896246i	$-0.646283\pi$
$509$	3.98535	−	37.9180i	0.176647	−	1.68069i	0.620204	−	0.784441i	$-0.287050\pi$
$510$	6.80200	−	4.94194i	0.301198	−	0.218833i
$511$		0			0
$512$	4.40566	−	13.5592i	0.194704	−	0.599238i
$513$	−6.15072	−	2.73848i	−0.271561	−	0.120907i
$514$	−8.65946	+	3.85544i	−0.381953	+	0.170056i
$515$	−49.3982	−	10.4999i	−2.17675	−	0.462682i
$516$	−1.68690	−	2.92180i	−0.0742617	−	0.128625i
$517$	−35.9795	+	24.0316i	−1.58238	+	1.05691i
$518$		0			0
$519$	−3.93083	−	12.0978i	−0.172544	−	0.531036i
$520$	1.86236	−	17.7192i	0.0816700	−	0.777038i
$521$	−2.72213	−	25.8993i	−0.119259	−	1.13467i	−0.876455	−	0.481483i	$-0.840098\pi$
$521$	−2.72213	−	25.8993i	−0.119259	−	1.13467i	0.757197	−	0.653187i	$-0.226568\pi$
$522$	−26.8662	−	29.8380i	−1.17590	−	1.30597i
$523$	18.7051	−	3.97589i	0.817917	−	0.173854i	0.220091	−	0.975479i	$-0.429365\pi$
$523$	18.7051	−	3.97589i	0.817917	−	0.173854i	0.597826	+	0.801626i	$0.296031\pi$
$524$	−6.47039	+	4.70101i	−0.282660	+	0.205365i
$525$		0			0
$526$	−4.49324	−	13.8288i	−0.195915	−	0.602963i
$527$	−0.276365	−	0.478679i	−0.0120387	−	0.0208516i
$528$	−9.88263	−	2.51171i	−0.430086	−	0.109308i
$529$	1.95114	−	3.37947i	0.0848322	−	0.146934i
$530$	−12.8839	+	14.3090i	−0.559639	+	0.621542i
$531$	18.1243	+	13.1681i	0.786527	+	0.571445i
$532$		0			0
$533$	−12.7450	+	39.2252i	−0.552049	+	1.69903i
$534$	16.4443	−	3.49533i	0.711612	−	0.151258i
$535$	−0.942822	−	8.97036i	−0.0407618	−	0.387822i
$536$	7.39425	−	3.29213i	0.319383	−	0.142198i
$537$	1.53640	−	1.70635i	0.0663007	−	0.0736344i
$538$	−22.8298			−0.984265
$539$		0			0
$540$	11.1815			0.481176
$541$	7.28418	−	8.08990i	0.313171	−	0.347812i	−0.565924	−	0.824457i	$-0.691481\pi$
$541$	7.28418	−	8.08990i	0.313171	−	0.347812i	0.879096	+	0.476645i	$0.158147\pi$
$542$	35.8005	−	15.9394i	1.53777	−	0.684657i
$543$	−0.308270	−	2.93300i	−0.0132291	−	0.125867i
$544$	15.7788	−	3.35389i	0.676510	−	0.143797i
$545$	10.8927	−	33.5243i	0.466592	−	1.43602i
$546$		0			0
$547$	10.4436	+	7.58775i	0.446538	+	0.324429i	0.788227	−	0.615384i	$-0.210999\pi$
$547$	10.4436	+	7.58775i	0.446538	+	0.324429i	−0.341689	+	0.939813i	$0.610999\pi$
$548$	−2.02544	+	2.24948i	−0.0865225	+	0.0960930i
$549$	1.29411	−	2.24146i	0.0552311	−	0.0956630i
$550$	14.8640	−	5.92712i	0.633804	−	0.252733i
$551$	8.36534	+	14.4892i	0.356376	+	0.617261i
$552$	1.24697	+	3.83777i	0.0530744	+	0.163346i
$553$		0			0
$554$	−34.6230	+	25.1551i	−1.47099	+	1.06874i
$555$	1.73864	−	0.369560i	0.0738012	−	0.0156869i
$556$	0.776860	+	0.862790i	0.0329462	+	0.0365905i
$557$	0.0797161	+	0.758448i	0.00337768	+	0.0321365i	0.996081	−	0.0884466i	$-0.0281903\pi$
$557$	0.0797161	+	0.758448i	0.00337768	+	0.0321365i	−0.992703	+	0.120583i	$0.961524\pi$
$558$	0.0975708	−	0.928325i	0.00413050	−	0.0392991i
$559$	−6.24664	−	19.2252i	−0.264205	−	0.813139i
$560$		0			0
$561$	−1.53222	−	5.43651i	−0.0646906	−	0.229530i
$562$	−13.7238	−	23.7703i	−0.578904	−	1.00269i
$563$	−21.7424	−	4.62148i	−0.916332	−	0.194772i	−0.274473	−	0.961595i	$-0.588503\pi$
$563$	−21.7424	−	4.62148i	−0.916332	−	0.194772i	−0.641859	+	0.766823i	$0.721837\pi$
$564$	−8.53997	+	3.80224i	−0.359598	+	0.160103i
$565$	−46.8093	−	20.8408i	−1.96928	−	0.876781i
$566$	1.84408	−	5.67551i	0.0775127	−	0.238559i
$567$		0			0
$568$	−2.43805	+	1.77135i	−0.102298	+	0.0743242i
$569$	2.14421	−	20.4008i	0.0898898	−	0.855245i	−0.852949	−	0.521995i	$-0.825188\pi$
$569$	2.14421	−	20.4008i	0.0898898	−	0.855245i	0.942839	−	0.333250i	$-0.108145\pi$
$570$	−5.78726	−	1.23012i	−0.242402	−	0.0515241i
$571$	9.78268	−	16.9441i	0.409393	−	0.709089i	−0.585429	−	0.810724i	$-0.699074\pi$
$571$	9.78268	−	16.9441i	0.409393	−	0.709089i	0.994822	+	0.101635i	$0.0324073\pi$
$572$	14.8064	+	7.30496i	0.619089	+	0.305436i
$573$	0.512448			0.0214078
$574$		0			0
$575$	−9.59677	−	6.97246i	−0.400213	−	0.290772i
$576$	1.09162	+	0.486022i	0.0454843	+	0.0202509i
$577$	13.0959	+	14.5445i	0.545191	+	0.605496i	0.951277	−	0.308339i	$-0.0997731\pi$
$577$	13.0959	+	14.5445i	0.545191	+	0.605496i	−0.406085	+	0.913835i	$0.633106\pi$
$578$	−11.1883	−	12.4259i	−0.465371	−	0.516847i
$579$	3.80430	+	1.69379i	0.158101	+	0.0703913i
$580$	−22.4790	−	16.3319i	−0.933388	−	0.678146i
$581$		0			0
$582$	12.7609			0.528958
$583$	6.02082	+	11.4486i	0.249357	+	0.474152i
$584$	7.44871	−	12.9016i	0.308230	−	0.533870i
$585$	30.5380	+	6.49105i	1.26259	+	0.268372i
$586$	1.27031	−	12.0862i	0.0524760	−	0.499276i
$587$	1.27071	−	0.923224i	0.0524477	−	0.0381055i	−0.561253	−	0.827645i	$-0.689680\pi$
$587$	1.27071	−	0.923224i	0.0524477	−	0.0381055i	0.613700	+	0.789539i	$0.289680\pi$
$588$		0			0
$589$	−0.120195	+	0.369922i	−0.00495254	+	0.0152424i
$590$	38.5936	+	17.1830i	1.58887	+	0.707413i
$591$	6.16634	−	2.74543i	0.253649	−	0.112932i
$592$	5.03851	+	1.07097i	0.207082	+	0.0440165i
$593$	−15.0615	−	26.0873i	−0.618502	−	1.07128i	−0.989759	−	0.142747i	$-0.954407\pi$
$593$	−15.0615	−	26.0873i	−0.618502	−	1.07128i	0.371257	−	0.928530i	$-0.378927\pi$
$594$	7.08807	−	19.2027i	0.290827	−	0.787896i
$595$		0			0
$596$	−5.33664	−	16.4245i	−0.218597	−	0.672773i
$597$	−1.35500	+	12.8920i	−0.0554566	+	0.527634i
$598$	−3.48610	−	33.1680i	−0.142557	−	1.35634i
$599$	3.86618	+	4.29383i	0.157968	+	0.175441i	0.816933	−	0.576732i	$-0.195672\pi$
$599$	3.86618	+	4.29383i	0.157968	+	0.175441i	−0.658965	+	0.752173i	$0.729006\pi$
$600$	−2.45167	+	0.521119i	−0.100089	+	0.0212746i
$601$	36.8625	−	26.7822i	1.50365	−	1.09247i	0.534754	−	0.845008i	$-0.320404\pi$
$601$	36.8625	−	26.7822i	1.50365	−	1.09247i	0.968898	−	0.247460i	$-0.0795958\pi$
$602$		0			0
$603$	4.38281	+	13.4889i	0.178482	+	0.549310i
$604$	−9.16232	−	15.8696i	−0.372809	−	0.645725i
$605$	−0.789050	−	30.5421i	−0.0320795	−	1.24171i
$606$	−1.87400	+	3.24587i	−0.0761262	+	0.131854i
$607$	−23.2329	+	25.8028i	−0.942995	+	1.04730i	0.0558104	+	0.998441i	$0.482226\pi$
$607$	−23.2329	+	25.8028i	−0.942995	+	1.04730i	−0.998806	+	0.0488608i	$0.984441\pi$
$608$	−9.18369	−	6.67234i	−0.372448	−	0.270599i
$609$		0			0
$610$	1.50822	−	4.64182i	0.0610660	−	0.187942i
$611$	−54.7867	+	11.6453i	−2.21643	+	0.471118i
$612$	0.874322	+	8.31862i	0.0353424	+	0.336260i
$613$	−22.0551	+	9.81954i	−0.890795	+	0.396608i	−0.800518	−	0.599309i	$-0.795442\pi$
$613$	−22.0551	+	9.81954i	−0.890795	+	0.396608i	−0.0902776	+	0.995917i	$0.528775\pi$
$614$	14.0310	−	15.5830i	0.566246	−	0.628880i
$615$	16.4897			0.664931
$616$		0			0
$617$	−13.4967			−0.543358			−0.271679	−	0.962388i	$-0.587579\pi$
$617$	−13.4967			−0.543358			−0.271679	+	0.962388i	$0.587579\pi$
$618$	−13.3655	+	14.8439i	−0.537638	+	0.597108i
$619$	39.7261	−	17.6872i	1.59673	−	0.710909i	0.600659	−	0.799505i	$-0.294905\pi$
$619$	39.7261	−	17.6872i	1.59673	−	0.710909i	0.996068	+	0.0885967i	$0.0282382\pi$
$620$	−0.0675216	−	0.642425i	−0.00271173	−	0.0258004i
$621$	−14.8420	+	3.15476i	−0.595588	+	0.126596i
$622$	−13.9042	+	42.7928i	−0.557509	+	1.71584i
$623$		0			0
$624$	−10.6791	−	7.75883i	−0.427507	−	0.310602i
$625$	−20.8796	+	23.1891i	−0.835183	+	0.927564i
$626$	−17.4676	+	30.2548i	−0.698147	+	1.20923i
$627$	−2.12156	+	3.36117i	−0.0847271	+	0.134232i
$628$	2.66165	+	4.61011i	0.106211	+	0.183964i
$629$	0.881726	+	2.71367i	0.0351567	+	0.108201i
$630$		0			0
$631$	−5.19398	+	3.77365i	−0.206769	+	0.150227i	−0.686351	−	0.727271i	$-0.740788\pi$
$631$	−5.19398	+	3.77365i	−0.206769	+	0.150227i	0.479581	+	0.877497i	$0.340788\pi$
$632$	9.19738	−	1.95496i	0.365852	−	0.0777643i
$633$	2.49104	+	2.76658i	0.0990098	+	0.109962i
$634$	−0.670834	−	6.38256i	−0.0266422	−	0.253484i
$635$	−5.66406	+	53.8899i	−0.224771	+	2.13856i
$636$	0.863624	+	2.65796i	0.0342449	+	0.105395i
$637$		0			0
$638$	−42.2974	+	28.2515i	−1.67457	+	1.11849i
$639$	−2.64035	−	4.57322i	−0.104451	−	0.180914i
$640$	−29.6046	−	6.29266i	−1.17023	−	0.248739i
$641$	−5.84304	+	2.60149i	−0.230786	+	0.102753i	−0.518872	−	0.854852i	$-0.673648\pi$
$641$	−5.84304	+	2.60149i	−0.230786	+	0.102753i	0.288086	+	0.957605i	$0.406981\pi$
$642$	−3.25906	−	1.45103i	−0.128625	−	0.0572674i
$643$	−0.201683	+	0.620716i	−0.00795360	+	0.0244787i	−0.954955	−	0.296752i	$-0.904097\pi$
$643$	−0.201683	+	0.620716i	−0.00795360	+	0.0244787i	0.947001	+	0.321231i	$0.104097\pi$
$644$		0			0
$645$	−6.53848	+	4.75048i	−0.257452	+	0.187050i
$646$	0.992770	−	9.44558i	0.0390600	−	0.371631i
$647$	17.5696	+	3.73454i	0.690733	+	0.146820i	0.539887	−	0.841737i	$-0.318467\pi$
$647$	17.5696	+	3.73454i	0.690733	+	0.146820i	0.150846	+	0.988557i	$0.451800\pi$
$648$	4.26421	−	7.38583i	0.167514	−	0.290143i
$649$	19.8074	−	20.3257i	0.777509	−	0.797855i
$650$	20.7153			0.812522
$651$		0			0
$652$	−7.53943	−	5.47771i	−0.295267	−	0.214524i
$653$	−15.4554	−	6.88120i	−0.604818	−	0.269282i	0.0813965	−	0.996682i	$-0.474062\pi$
$653$	−15.4554	−	6.88120i	−0.604818	−	0.269282i	−0.686214	+	0.727400i	$0.740729\pi$
$654$	−9.32889	−	10.3608i	−0.364789	−	0.405139i
$655$	12.8199	+	14.2379i	0.500913	+	0.556320i
$656$	43.6552	+	19.4366i	1.70445	+	0.758870i
$657$	21.1191	+	15.3439i	0.823934	+	0.598623i
$658$		0			0
$659$	23.6249			0.920297			0.460148	−	0.887842i	$-0.347796\pi$
$659$	23.6249			0.920297			0.460148	+	0.887842i	$0.347796\pi$
$660$	0.948347	−	6.53256i	0.0369143	−	0.254280i
$661$	−10.4910	+	18.1709i	−0.408051	+	0.706766i	−0.994671	−	0.103097i	$-0.967125\pi$
$661$	−10.4910	+	18.1709i	−0.408051	+	0.706766i	0.586620	+	0.809862i	$0.300458\pi$
$662$	46.1322	+	9.80570i	1.79298	+	0.381109i
$663$	0.764302	−	7.27185i	0.0296830	−	0.282415i
$664$	2.08077	−	1.51177i	0.0807494	−	0.0586679i
$665$		0			0
$666$	−1.48904	+	4.58278i	−0.0576990	+	0.177579i
$667$	34.4457	+	15.3362i	1.33374	+	0.593821i
$668$	14.2007	−	6.32258i	0.549443	−	0.244628i
$669$	2.79599	+	0.594306i	0.108099	+	0.0229772i
$670$	13.3728	+	23.1623i	0.516636	+	0.894840i
$671$	−2.57458	−	2.03036i	−0.0993904	−	0.0783813i
$672$		0			0
$673$	3.73868	+	11.5065i	0.144116	+	0.443542i	0.996896	−	0.0787272i	$-0.0250856\pi$
$673$	3.73868	+	11.5065i	0.144116	+	0.443542i	−0.852781	+	0.522269i	$0.825086\pi$
$674$	0.127453	−	1.21264i	0.00490932	−	0.0467090i
$675$	−0.985163	−	9.37320i	−0.0379189	−	0.360775i
$676$	4.21578	+	4.68209i	0.162145	+	0.180081i
$677$	−9.22381	+	1.96058i	−0.354500	+	0.0753513i	−0.381720	−	0.924278i	$-0.624668\pi$
$677$	−9.22381	+	1.96058i	−0.354500	+	0.0753513i	0.0272197	+	0.999629i	$0.491335\pi$
$678$	−16.3956	+	11.9121i	−0.629668	+	0.457480i
$679$		0			0
$680$	−3.53356	−	10.8752i	−0.135506	−	0.417044i
$681$	−5.34610	−	9.25971i	−0.204863	−	0.354833i
$682$	−1.14608	−	0.291281i	−0.0438856	−	0.0111537i
$683$	7.64930	−	13.2490i	0.292692	−	0.506958i	−0.681753	−	0.731582i	$-0.738782\pi$
$683$	7.64930	−	13.2490i	0.292692	−	0.506958i	0.974445	+	0.224624i	$0.0721155\pi$
$684$	3.93856	−	4.37421i	0.150595	−	0.167252i
$685$	5.86632	+	4.26213i	0.224141	+	0.162848i
$686$		0			0
$687$	−0.845314	+	2.60161i	−0.0322507	+	0.0992575i
$688$	−22.9095	+	4.86957i	−0.873417	+	0.185650i
$689$	1.75034	+	16.6533i	0.0666825	+	0.634442i
$690$	−12.1812	+	5.42343i	−0.463731	+	0.206466i
$691$	−15.2691	+	16.9580i	−0.580863	+	0.645113i	−0.959925	−	0.280258i	$-0.909580\pi$
$691$	−15.2691	+	16.9580i	−0.580863	+	0.645113i	0.379062	+	0.925371i	$0.376247\pi$
$692$	23.8639			0.907169
$693$		0			0
$694$	38.2256			1.45102
$695$	1.86098	−	2.06683i	0.0705911	−	0.0783993i
$696$	7.27824	−	3.24048i	0.275881	−	0.122830i
$697$	2.76690	+	26.3253i	0.104804	+	0.997142i
$698$	33.8042	−	7.18530i	1.27951	−	0.271968i
$699$	2.01163	−	6.19117i	0.0760869	−	0.234171i
$700$		0			0
$701$	26.1508	+	18.9997i	0.987702	+	0.717607i	0.959417	−	0.281992i	$-0.0909953\pi$
$701$	26.1508	+	18.9997i	0.987702	+	0.717607i	0.0282853	+	0.999600i	$0.490995\pi$
$702$	17.7306	−	19.6918i	0.669197	−	0.743218i
$703$	1.00395	−	1.73889i	0.0378646	−	0.0655834i
$704$	0.808001	−	1.28011i	0.0304527	−	0.0482458i
$705$	11.1969	+	19.3935i	0.421698	+	0.730402i
$706$	11.4967	+	35.3831i	0.432683	+	1.33166i
$707$		0			0
$708$	4.96078	−	3.60422i	0.186438	−	0.135455i
$709$	−14.2416	+	3.02715i	−0.534855	+	0.113687i	−0.467418	−	0.884037i	$-0.654816\pi$
$709$	−14.2416	+	3.02715i	−0.534855	+	0.113687i	−0.0674371	+	0.997724i	$0.521482\pi$
$710$	−6.66323	−	7.40026i	−0.250066	−	0.277727i
$711$	1.72227	+	16.3863i	0.0645901	+	0.614533i
$712$	2.38999	−	22.7392i	0.0895685	−	0.852188i
$713$	0.270880	+	0.833684i	0.0101446	+	0.0312217i
$714$		0			0
$715$	13.6958	−	37.1040i	0.512193	−	1.38761i
$716$	2.15379	+	3.73048i	0.0804910	+	0.139415i
$717$	−5.89806	−	1.25367i	−0.220267	−	0.0468192i
$718$	15.8667	−	7.06431i	0.592140	−	0.263638i
$719$	−40.9818	−	18.2463i	−1.52836	−	0.680471i	−0.541304	−	0.840827i	$-0.682069\pi$
$719$	−40.9818	−	18.2463i	−1.52836	−	0.680471i	−0.987059	+	0.160355i	$0.948736\pi$
$720$	11.1780	−	34.4024i	0.416581	−	1.28210i
$721$		0			0
$722$	21.9152	−	15.9223i	0.815600	−	0.592568i
$723$	−0.810763	+	7.71389i	−0.0301526	+	0.286883i
$724$	5.41179	+	1.15031i	0.201128	+	0.0427510i
$725$	−11.7101	+	20.2825i	−0.434903	+	0.753274i
$726$	−10.6176	−	5.76971i	−0.394056	−	0.214134i
$727$	−28.3582			−1.05175			−0.525874	−	0.850562i	$-0.676262\pi$
$727$	−28.3582			−1.05175			−0.525874	+	0.850562i	$0.676262\pi$
$728$		0			0
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	44.9707	+	20.0222i	1.66444	+	0.741057i
$731$	−8.68111	−	9.64135i	−0.321083	−	0.356598i
$732$	−0.474023	−	0.526456i	−0.0175204	−	0.0194584i
$733$	−5.71602	−	2.54493i	−0.211126	−	0.0939993i	0.298449	−	0.954426i	$-0.403531\pi$
$733$	−5.71602	−	2.54493i	−0.211126	−	0.0939993i	−0.509575	+	0.860426i	$0.670197\pi$
$734$	14.2359	+	10.3430i	0.525456	+	0.381766i
$735$		0			0
$736$	−25.5830			−0.943001
$737$	17.7086	−	3.03970i	0.652306	−	0.111969i
$738$	−22.3512	+	38.7134i	−0.822759	+	1.42506i
$739$	−9.14764	−	1.94439i	−0.336501	−	0.0715256i	0.0365621	−	0.999331i	$-0.488359\pi$
$739$	−9.14764	−	1.94439i	−0.336501	−	0.0715256i	−0.373064	+	0.927806i	$0.621693\pi$
$740$	−0.348562	+	3.31635i	−0.0128134	+	0.121911i
$741$	−4.16273	+	3.02440i	−0.152922	+	0.111104i
$742$		0			0
$743$	7.78926	−	23.9729i	0.285760	−	0.879480i	−0.700409	−	0.713741i	$-0.746999\pi$
$743$	7.78926	−	23.9729i	0.285760	−	0.879480i	0.986170	−	0.165739i	$-0.0530008\pi$
$744$	0.169206	+	0.0753354i	0.00620340	+	0.00276193i
$745$	−37.7933	+	16.8267i	−1.38464	+	0.616482i
$746$	7.43226	+	1.57977i	0.272114	+	0.0578397i
$747$	2.25342	+	3.90304i	0.0824483	+	0.142805i
$748$	10.5881	+	0.417870i	0.387141	+	0.0152788i
$749$		0			0
$750$	2.15501	+	6.63243i	0.0786897	+	0.242182i
$751$	3.63229	−	34.5589i	0.132544	−	1.26107i	−0.702817	−	0.711371i	$-0.748075\pi$
$751$	3.63229	−	34.5589i	0.132544	−	1.26107i	0.835361	−	0.549702i	$-0.185259\pi$
$752$	6.78348	+	64.5405i	0.247368	+	2.35355i
$753$	−4.54536	−	5.04813i	−0.165642	−	0.183964i
$754$	−64.4071	+	13.6902i	−2.34557	+	0.498566i
$755$	−35.5134	+	25.8020i	−1.29247	+	0.939031i
$756$		0			0
$757$	10.7526	+	33.0930i	0.390808	+	1.20278i	0.932178	+	0.362000i	$0.117906\pi$
$757$	10.7526	+	33.0930i	0.390808	+	1.20278i	−0.541370	+	0.840784i	$0.682094\pi$
$758$	−3.84465	−	6.65912i	−0.139644	−	0.241870i
$759$	0.584297	+	8.93868i	0.0212087	+	0.324454i
$760$	−4.02337	+	6.96868i	−0.145943	+	0.252781i
$761$	8.18043	−	9.08528i	0.296540	−	0.329341i	−0.576401	−	0.817167i	$-0.695543\pi$
$761$	8.18043	−	9.08528i	0.296540	−	0.329341i	0.872941	+	0.487826i	$0.162210\pi$
$762$	17.3387	+	12.5973i	0.628116	+	0.456353i
$763$		0			0
$764$	−0.297079	+	0.914315i	−0.0107479	+	0.0330788i
$765$	19.5993	−	4.16596i	0.708614	−	0.150621i
$766$	−0.245643	−	2.33714i	−0.00887545	−	0.0844442i
$767$	33.5635	−	14.9434i	1.21191	−	0.539576i
$768$	−8.38751	+	9.31527i	−0.302658	+	0.336136i
$769$	2.61946			0.0944603			0.0472301	−	0.998884i	$-0.484961\pi$
$769$	2.61946			0.0944603			0.0472301	+	0.998884i	$0.484961\pi$
$770$		0			0
$771$	3.29585			0.118697
$772$	−5.22752	+	5.80575i	−0.188143	+	0.208954i
$773$	0.194407	−	0.0865554i	0.00699232	−	0.00311318i	−0.403238	−	0.915095i	$-0.632115\pi$
$773$	0.194407	−	0.0865554i	0.00699232	−	0.00311318i	0.410230	+	0.911982i	$0.365448\pi$
$774$	−2.29019	−	21.7897i	−0.0823191	−	0.783214i
$775$	−0.532581	+	0.113204i	−0.0191309	+	0.00406639i
$776$	5.36310	−	16.5059i	0.192524	−	0.592529i
$777$		0			0
$778$	55.3767	+	40.2336i	1.98535	+	1.44244i
$779$	12.4641	−	13.8428i	0.446572	−	0.495968i
$780$	4.27263	−	7.40041i	0.152985	−	0.264977i
$781$	−6.21398	+	2.47786i	−0.222354	+	0.0886649i
$782$	−10.7023	−	18.5369i	−0.382712	−	0.662877i
$783$	9.25750	+	28.4917i	0.330836	+	1.01821i
$784$		0			0
$785$	10.3166	−	7.49547i	0.368216	−	0.267525i
$786$	7.41213	−	1.57550i	0.264382	−	0.0561961i
$787$	−19.4968	−	21.6534i	−0.694986	−	0.771860i	0.287583	−	0.957756i	$-0.407148\pi$
$787$	−19.4968	−	21.6534i	−0.694986	−	0.771860i	−0.982570	+	0.185895i	$0.940481\pi$
$788$	1.32365	+	12.5936i	0.0471529	+	0.448630i
$789$	−0.528467	+	5.02803i	−0.0188139	+	0.179003i
$790$	9.60131	+	29.5498i	0.341599	+	1.05133i
$791$		0			0
$792$	−10.1865	−	8.03330i	−0.361962	−	0.285451i
$793$	−2.12228	−	3.67590i	−0.0753645	−	0.130535i
$794$	−0.713032	−	0.151560i	−0.0253046	−	0.00537865i
$795$	6.11606	−	2.72305i	0.216914	−	0.0965765i
$796$	−22.2165	−	9.89142i	−0.787443	−	0.350592i
$797$	−9.95913	+	30.6510i	−0.352770	+	1.08572i	0.604521	+	0.796589i	$0.293365\pi$
$797$	−9.95913	+	30.6510i	−0.352770	+	1.08572i	−0.957291	+	0.289126i	$0.906635\pi$
$798$		0			0
$799$	−29.0823	+	21.1295i	−1.02886	+	0.747509i
$800$	1.66101	−	15.8034i	0.0587255	−	0.558736i
$801$	39.1896	+	8.33002i	1.38470	+	0.294327i
$802$	1.39252	−	2.41191i	0.0491715	−	0.0851675i
$803$	23.0803	−	23.6843i	0.814487	−	0.835801i
$804$	3.88203			0.136909
$805$		0			0
$806$	−1.23845	−	0.899783i	−0.0436224	−	0.0316935i
$807$	7.25170	+	3.22866i	0.255272	+	0.113654i
$808$	3.41085	+	3.78813i	0.119993	+	0.133266i
$809$	−19.6364	−	21.8084i	−0.690378	−	0.766742i	0.291436	−	0.956590i	$-0.405867\pi$
$809$	−19.6364	−	21.8084i	−0.690378	−	0.766742i	−0.981813	+	0.189848i	$0.939200\pi$
$810$	25.7447	+	11.4623i	0.904575	+	0.402743i
$811$	0.840891	+	0.610943i	0.0295277	+	0.0214531i	0.602451	−	0.798156i	$-0.294191\pi$
$811$	0.840891	+	0.610943i	0.0295277	+	0.0214531i	−0.572924	+	0.819609i	$0.694191\pi$
$812$		0			0
$813$	−13.6259			−0.477882
$814$	5.47441	+	2.70087i	0.191878	+	0.0946656i
$815$	−11.1622	+	19.3335i	−0.390995	+	0.677224i
$816$	−8.28671	−	1.76139i	−0.290093	−	0.0616611i
$817$	−0.954309	+	9.07964i	−0.0333870	+	0.317657i
$818$	−9.74762	+	7.08206i	−0.340817	+	0.247618i
$819$		0			0
$820$	−9.55952	+	29.4212i	−0.333833	+	1.02743i
$821$	26.0656	+	11.6051i	0.909695	+	0.405022i	0.807585	−	0.589751i	$-0.200774\pi$
$821$	26.0656	+	11.6051i	0.909695	+	0.405022i	0.102110	+	0.994773i	$0.467441\pi$
$822$	2.62002	−	1.16651i	0.0913837	−	0.0406866i
$823$	−26.0751	−	5.54244i	−0.908921	−	0.193197i	−0.270352	−	0.962762i	$-0.587140\pi$
$823$	−26.0751	−	5.54244i	−0.908921	−	0.193197i	−0.638569	+	0.769564i	$0.720473\pi$
$824$	13.5830	+	23.5264i	0.473185	+	0.819581i
$825$	−5.55965	−	0.219416i	−0.193562	−	0.00763909i
$826$		0			0
$827$	0.531399	+	1.63548i	0.0184785	+	0.0568711i	0.959871	−	0.280443i	$-0.0904815\pi$
$827$	0.531399	+	1.63548i	0.0184785	+	0.0568711i	−0.941392	+	0.337314i	$0.890481\pi$
$828$	1.38660	−	13.1927i	0.0481879	−	0.458477i
$829$	2.92266	+	27.8073i	0.101508	+	0.965787i	0.920172	+	0.391514i	$0.128049\pi$
$829$	2.92266	+	27.8073i	0.101508	+	0.965787i	−0.818664	+	0.574273i	$0.805285\pi$
$830$	5.68676	+	6.31579i	0.197390	+	0.219224i
$831$	14.5552	−	3.09381i	0.504915	−	0.107323i
$832$	1.58538	−	1.15185i	0.0549632	−	0.0399331i
$833$		0			0
$834$	−0.339923	−	1.04617i	−0.0117706	−	0.0362261i
$835$	−18.6187	−	32.2486i	−0.644328	−	1.11601i
$836$	−4.76711	−	5.73387i	−0.164874	−	0.198310i
$837$	−0.348234	+	0.603159i	−0.0120367	+	0.0208482i
$838$	−34.1609	+	37.9395i	−1.18007	+	1.31060i
$839$	29.0133	+	21.0794i	1.00165	+	0.727742i	0.962441	−	0.271489i	$-0.0875162\pi$
$839$	29.0133	+	21.0794i	1.00165	+	0.727742i	0.0392091	+	0.999231i	$0.487516\pi$
$840$		0			0
$841$	14.0429	−	43.2197i	0.484240	−	1.49034i
$842$	−21.2559	+	4.51808i	−0.732527	+	0.155703i
$843$	0.997575	+	9.49130i	0.0343583	+	0.326898i
$844$	−6.38027	+	2.84068i	−0.219618	+	0.0977802i
$845$	10.0990	−	11.2160i	0.347415	−	0.385844i
$846$	−60.7076			−2.08717
$847$		0			0
$848$	19.4014			0.666248
$849$	−1.38840	+	1.54198i	−0.0476499	+	0.0529206i
$850$	12.1457	−	5.40761i	0.416594	−	0.185479i
$851$	−0.473007	−	4.50036i	−0.0162145	−	0.154270i
$852$	−1.41379	+	0.300511i	−0.0484357	+	0.0102953i
$853$	4.67937	−	14.4016i	0.160218	−	0.493102i	−0.838434	−	0.545004i	$-0.816528\pi$
$853$	4.67937	−	14.4016i	0.160218	−	0.493102i	0.998652	+	0.0519019i	$0.0165283\pi$
$854$		0			0
$855$	−11.4073	−	8.28790i	−0.390122	−	0.283440i
$856$	−3.24656	+	3.60567i	−0.110965	+	0.123239i
$857$	12.6633	−	21.9335i	0.432571	−	0.749235i	−0.564523	−	0.825417i	$-0.690940\pi$
$857$	12.6633	−	21.9335i	0.432571	−	0.749235i	0.997094	+	0.0761824i	$0.0242731\pi$
$858$	−10.0007	−	12.0288i	−0.341419	−	0.410658i
$859$	20.7646	+	35.9653i	0.708478	+	1.22712i	0.965422	+	0.260694i	$0.0839513\pi$
$859$	20.7646	+	35.9653i	0.708478	+	1.22712i	−0.256943	+	0.966426i	$0.582715\pi$
$860$	−4.68534	−	14.4200i	−0.159769	−	0.491718i
$861$		0			0
$862$	−5.30813	+	3.85658i	−0.180796	+	0.131356i
$863$	23.5248	−	5.00035i	0.800794	−	0.170214i	0.210702	−	0.977550i	$-0.432425\pi$
$863$	23.5248	−	5.00035i	0.800794	−	0.170214i	0.590092	+	0.807336i	$0.299092\pi$
$864$	−13.6009	−	15.1053i	−0.462712	−	0.513894i
$865$	−5.97551	−	56.8532i	−0.203174	−	1.93307i
$866$	5.40205	−	51.3970i	0.183569	−	1.74654i
$867$	1.79656	+	5.52924i	0.0610144	+	0.187783i
$868$		0			0
$869$	20.8569	+	0.823133i	0.707521	+	0.0279229i
$870$	13.1630	+	22.7990i	0.446267	+	0.772957i
$871$	22.7514	+	4.83596i	0.770902	+	0.163860i
$872$	−17.3221	+	7.71230i	−0.586600	+	0.261171i
$873$	27.7824	+	12.3695i	0.940293	+	0.418645i
$874$	−4.65455	+	14.3252i	−0.157443	+	0.484559i
$875$		0			0
$876$	5.78049	−	4.19977i	0.195304	−	0.141897i
$877$	−3.53360	+	33.6200i	−0.119321	+	1.13527i	0.756958	+	0.653464i	$0.226685\pi$
$877$	−3.53360	+	33.6200i	−0.119321	+	1.13527i	−0.876279	+	0.481803i	$0.839982\pi$
$878$	−24.6917	−	5.24838i	−0.833304	−	0.177124i
$879$	−2.11277	+	3.65942i	−0.0712618	+	0.123429i
$880$	−41.0958	−	20.2752i	−1.38534	−	0.683475i
$881$	36.8296			1.24082			0.620410	−	0.784278i	$-0.286966\pi$
$881$	36.8296			1.24082			0.620410	+	0.784278i	$0.286966\pi$
$882$		0			0
$883$	−43.2099	−	31.3938i	−1.45413	−	1.05649i	−0.984845	−	0.173438i	$-0.944512\pi$
$883$	−43.2099	−	31.3938i	−1.45413	−	1.05649i	−0.469283	−	0.883048i	$-0.655488\pi$
$884$	12.5314	+	5.57935i	0.421478	+	0.187654i
$885$	−9.82886	−	10.9161i	−0.330393	−	0.366939i
$886$	32.3932	+	35.9763i	1.08827	+	1.20865i
$887$	−10.4707	−	4.66185i	−0.351571	−	0.156530i	0.223350	−	0.974738i	$-0.428301\pi$
$887$	−10.4707	−	4.66185i	−0.351571	−	0.156530i	−0.574921	+	0.818209i	$0.694967\pi$
$888$	−0.773537	−	0.562007i	−0.0259582	−	0.0188597i
$889$		0			0
$890$	75.5525			2.53253
$891$	13.2129	−	13.5587i	0.442650	−	0.454233i
$892$	−2.68127	+	4.64410i	−0.0897756	+	0.155496i
$893$	24.7437	+	5.25945i	0.828018	+	0.176001i
$894$	−1.71035	+	16.2729i	−0.0572028	+	0.544248i
$895$	8.34817	−	6.06530i	0.279048	−	0.202741i
$896$		0			0
$897$	−3.58339	+	11.0286i	−0.119646	+	0.368233i
$898$	−68.0636	−	30.3039i	−2.27131	−	1.01125i
$899$	1.58106	−	0.703935i	0.0527314	−	0.0234775i
$900$	8.05951	+	1.71310i	0.268650	+	0.0571034i
$901$	5.37350	+	9.30717i	0.179017	+	0.310067i
$902$	44.4669	+	35.0675i	1.48059	+	1.16762i
$903$		0			0
$904$	8.51730	+	26.2136i	0.283281	+	0.871850i
$905$	1.38539	−	13.1811i	0.0460518	−	0.438154i
$906$	1.81483	+	17.2670i	0.0602937	+	0.573656i
$907$	38.1794	+	42.4025i	1.26773	+	1.40795i	0.871943	+	0.489607i	$0.162860\pi$
$907$	38.1794	+	42.4025i	1.26773	+	1.40795i	0.395782	+	0.918345i	$0.370474\pi$
$908$	19.6205	−	4.17047i	0.651131	−	0.138402i
$909$	−7.22628	+	5.25020i	−0.239681	+	0.174138i
$910$		0			0
$911$	2.06289	+	6.34893i	0.0683467	+	0.210350i	0.979396	−	0.201947i	$-0.0647268\pi$
$911$	2.06289	+	6.34893i	0.0683467	+	0.210350i	−0.911050	+	0.412296i	$0.864727\pi$
$912$	2.98083	+	5.16295i	0.0987052	+	0.170962i
$913$	5.30335	−	2.11474i	0.175515	−	0.0699878i
$914$	−17.3284	+	30.0137i	−0.573173	+	0.992765i
$915$	−1.13553	+	1.26114i	−0.0375395	+	0.0416919i
$916$	−4.15177	−	3.01643i	−0.137178	−	0.0996658i
$917$		0			0
$918$	5.25526	−	16.1740i	0.173449	−	0.533822i
$919$	28.4972	−	6.05728i	0.940037	−	0.199811i	0.287683	−	0.957726i	$-0.407115\pi$
$919$	28.4972	−	6.05728i	0.940037	−	0.199811i	0.652354	+	0.757914i	$0.273782\pi$
$920$	1.89560	+	18.0354i	0.0624960	+	0.594610i
$921$	−6.66063	+	2.96550i	−0.219475	+	0.0977167i
$922$	−14.5402	+	16.1485i	−0.478854	+	0.531822i
$923$	−8.66015			−0.285052
$924$		0			0
$925$	2.81073			0.0924161
$926$	16.4787	−	18.3014i	0.541522	−	0.601421i
$927$	−43.4871	+	19.3617i	−1.42831	+	0.635922i
$928$	5.27970	+	50.2330i	0.173315	+	1.64898i
$929$	2.29348	−	0.487494i	0.0752466	−	0.0159942i	−0.170135	−	0.985421i	$-0.554420\pi$
$929$	2.29348	−	0.487494i	0.0752466	−	0.0159942i	0.245381	+	0.969427i	$0.421087\pi$
$930$	−0.189128	+	0.582077i	−0.00620176	+	0.0190871i
$931$		0			0
$932$	9.88015	+	7.17835i	0.323635	+	0.235135i
$933$	10.4684	−	11.6264i	0.342721	−	0.380631i
$934$	−14.5938	+	25.2772i	−0.477524	+	0.827095i
$935$	−1.65574	−	25.3298i	−0.0541484	−	0.828372i
$936$	−8.39699	−	14.5440i	−0.274464	−	0.475386i
$937$	−2.71558	−	8.35769i	−0.0887141	−	0.273034i	0.896850	−	0.442334i	$-0.145849\pi$
$937$	−2.71558	−	8.35769i	−0.0887141	−	0.273034i	−0.985565	+	0.169300i	$0.945849\pi$
$938$		0			0
$939$	9.82717	−	7.13986i	0.320698	−	0.233000i
$940$	−41.0932	+	8.73463i	−1.34031	+	0.284892i
$941$	−5.94771	−	6.60560i	−0.193890	−	0.215336i	0.638359	−	0.769739i	$-0.279614\pi$
$941$	−5.94771	−	6.60560i	−0.193890	−	0.215336i	−0.832249	+	0.554402i	$0.812947\pi$
$942$	−0.527207	−	5.01604i	−0.0171773	−	0.163431i
$943$	4.38809	−	41.7499i	0.142896	−	1.35956i
$944$	−13.1543	−	40.4847i	−0.428135	−	1.31766i
$945$		0			0
$946$	−27.7344	−	1.09456i	−0.901724	−	0.0355873i
$947$	3.93137	+	6.80934i	0.127752	+	0.221274i	0.922805	−	0.385266i	$-0.125890\pi$
$947$	3.93137	+	6.80934i	0.127752	+	0.221274i	−0.795053	+	0.606540i	$0.792557\pi$
$948$	4.41123	+	0.937635i	0.143270	+	0.0304530i
$949$	39.1094	−	17.4126i	1.26955	−	0.565238i
$950$	−8.54697	−	3.80535i	−0.277300	−	0.123462i
$951$	−0.689556	+	2.12223i	−0.0223604	+	0.0688182i
$952$		0			0
$953$	14.1290	−	10.2653i	0.457683	−	0.332526i	−0.334939	−	0.942240i	$-0.608716\pi$
$953$	14.1290	−	10.2653i	0.457683	−	0.332526i	0.792622	+	0.609714i	$0.208716\pi$
$954$	−1.89711	+	18.0498i	−0.0614213	+	0.584385i
$955$	2.25265	+	0.478815i	0.0728940	+	0.0154941i
$956$	5.65606	−	9.79659i	0.182930	−	0.316844i
$957$	17.4308	−	2.99201i	0.563458	−	0.0967181i
$958$	44.0663			1.42372
$959$		0			0
$960$	−0.633854	−	0.460522i	−0.0204575	−	0.0148633i
$961$	−28.2832	−	12.5925i	−0.912360	−	0.406209i
$962$	5.28771	+	5.87260i	0.170483	+	0.189340i
$963$	−5.68892	−	6.31819i	−0.183323	−	0.203601i
$964$	−13.2932	−	5.91851i	−0.428145	−	0.190622i
$965$	15.1406	+	11.0003i	0.487392	+	0.354111i
$966$		0			0
$967$	−45.6122			−1.46679			−0.733395	−	0.679802i	$-0.762066\pi$
$967$	−45.6122			−1.46679			−0.733395	+	0.679802i	$0.762066\pi$
$968$	−11.9253	+	11.3087i	−0.383293	+	0.363476i
$969$	−1.65117	+	2.85990i	−0.0530431	+	0.0918734i
$970$	56.0953	+	11.9234i	1.80111	+	0.382838i
$971$	0.249173	−	2.37072i	0.00799635	−	0.0760801i	−0.989796	−	0.142492i	$-0.954488\pi$
$971$	0.249173	−	2.37072i	0.00799635	−	0.0760801i	0.997792	+	0.0664119i	$0.0211551\pi$
$972$	13.0799	−	9.50313i	0.419539	−	0.304813i
$973$		0			0
$974$	−7.87338	+	24.2318i	−0.252279	+	0.776436i
$975$	−6.58004	−	2.92962i	−0.210730	−	0.0938230i
$976$	−4.49273	+	2.00029i	−0.143809	+	0.0640278i
$977$	18.8452	+	4.00567i	0.602911	+	0.128153i	0.499247	−	0.866460i	$-0.333610\pi$
$977$	18.8452	+	4.00567i	0.602911	+	0.128153i	0.103664	+	0.994612i	$0.466943\pi$
$978$	4.41486	+	7.64676i	0.141172	+	0.244516i
$979$	17.5759	−	47.6158i	0.561728	−	1.52181i
$980$		0			0
$981$	−10.2674	−	31.5997i	−0.327812	−	1.00890i
$982$	4.09114	−	38.9246i	0.130554	−	1.24213i
$983$	−1.69604	−	16.1367i	−0.0540953	−	0.514682i	−0.987698	−	0.156373i	$-0.950020\pi$
$983$	−1.69604	−	16.1367i	−0.0540953	−	0.514682i	0.933603	−	0.358309i	$-0.116647\pi$
$984$	−5.93530	−	6.59181i	−0.189210	−	0.210139i
$985$	29.6716	−	6.30689i	0.945416	−	0.200954i
$986$	−34.1891	+	24.8398i	−1.08880	+	0.791061i
$987$		0			0
$988$	−2.98293	−	9.18051i	−0.0948996	−	0.292071i
$989$	10.2876	+	17.8187i	0.327128	+	0.566603i
$990$	22.8811	−	36.2503i	0.727210	−	1.15211i
$991$	25.2607	−	43.7528i	0.802433	−	1.38985i	−0.115578	−	0.993298i	$-0.536872\pi$
$991$	25.2607	−	43.7528i	0.802433	−	1.38985i	0.918011	−	0.396556i	$-0.129795\pi$
$992$	−0.785734	+	0.872646i	−0.0249471	+	0.0277065i
$993$	−13.2667	−	9.63884i	−0.421007	−	0.305879i
$994$		0			0
$995$	−18.0023	+	55.4053i	−0.570710	+	1.75647i
$996$	1.20661	−	0.256472i	0.0382328	−	0.00812663i
$997$	−4.70594	−	44.7740i	−0.149038	−	1.41801i	−0.771935	−	0.635702i	$-0.780711\pi$
$997$	−4.70594	−	44.7740i	−0.149038	−	1.41801i	0.622896	−	0.782305i	$-0.285956\pi$
$998$	−41.1015	+	18.2996i	−1.30105	+	0.579263i
$999$	2.40574	−	2.67185i	0.0761144	−	0.0845336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.b.214.2		16
7.2	even	3	inner	539.2.q.b.324.1		16
7.3	odd	6		77.2.f.a.71.2	yes	8
7.4	even	3		539.2.f.d.148.2		8
7.5	odd	6		539.2.q.c.324.1		16
7.6	odd	2		539.2.q.c.214.2		16
11.9	even	5	inner	539.2.q.b.361.1		16
21.17	even	6		693.2.m.g.379.1		8
77.3	odd	30		847.2.a.l.1.3		4
77.9	even	15	inner	539.2.q.b.471.2		16
77.10	even	6		847.2.f.q.148.1		8
77.17	even	30		847.2.f.s.323.2		8
77.20	odd	10		539.2.q.c.361.1		16
77.24	even	30		847.2.f.q.372.1		8
77.25	even	15		5929.2.a.bi.1.3		4
77.31	odd	30		77.2.f.a.64.2	✓	8
77.38	odd	30		847.2.f.p.323.1		8
77.52	even	30		847.2.a.k.1.2		4
77.53	even	15		539.2.f.d.295.2		8
77.59	odd	30		847.2.f.p.729.1		8
77.73	even	30		847.2.f.s.729.2		8
77.74	odd	30		5929.2.a.bb.1.2		4
77.75	odd	30		539.2.q.c.471.2		16
231.80	even	30		7623.2.a.ch.1.2		4
231.185	even	30		693.2.m.g.64.1		8
231.206	odd	30		7623.2.a.co.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	77.31	odd	30
77.2.f.a.71.2	yes	8	7.3	odd	6
539.2.f.d.148.2		8	7.4	even	3
539.2.f.d.295.2		8	77.53	even	15
539.2.q.b.214.2		16	1.1	even	1	trivial
539.2.q.b.324.1		16	7.2	even	3	inner
539.2.q.b.361.1		16	11.9	even	5	inner
539.2.q.b.471.2		16	77.9	even	15	inner
539.2.q.c.214.2		16	7.6	odd	2
539.2.q.c.324.1		16	7.5	odd	6
539.2.q.c.361.1		16	77.20	odd	10
539.2.q.c.471.2		16	77.75	odd	30
693.2.m.g.64.1		8	231.185	even	30
693.2.m.g.379.1		8	21.17	even	6
847.2.a.k.1.2		4	77.52	even	30
847.2.a.l.1.3		4	77.3	odd	30
847.2.f.p.323.1		8	77.38	odd	30
847.2.f.p.729.1		8	77.59	odd	30
847.2.f.q.148.1		8	77.10	even	6
847.2.f.q.372.1		8	77.24	even	30
847.2.f.s.323.2		8	77.17	even	30
847.2.f.s.729.2		8	77.73	even	30
5929.2.a.bb.1.2		4	77.74	odd	30
5929.2.a.bi.1.3		4	77.25	even	15
7623.2.a.ch.1.2		4	231.80	even	30
7623.2.a.co.1.3		4	231.206	odd	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18937 - 1.32093i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(-0.121196 - 1.15310i) q^{4} +(-2.71679 + 0.577471i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(-1.75181 + 1.94558i) q^{9} +O(q^{10})\)	\(q+(1.18937 - 1.32093i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(-0.121196 - 1.15310i) q^{4} +(-2.71679 + 0.577471i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(-1.75181 + 1.94558i) q^{9} +(-2.46847 + 4.27551i) q^{10} +(2.12033 + 2.55033i) q^{11} +(0.358290 + 0.620576i) q^{12} +(1.32676 + 4.08334i) q^{13} +(1.38874 - 1.00898i) q^{15} +(4.86587 - 1.03427i) q^{16} +(1.84383 + 2.04778i) q^{17} +(0.486425 + 4.62802i) q^{18} +(0.202691 - 1.92847i) q^{19} +(0.995144 + 3.06274i) q^{20} +(5.89066 + 0.232480i) q^{22} +(-2.18505 - 3.78461i) q^{23} +(-0.903204 - 0.191982i) q^{24} +(2.47974 - 1.10405i) q^{25} +(6.97180 + 3.10405i) q^{26} +(1.07295 - 3.30220i) q^{27} +(-6.98027 + 5.07146i) q^{29} +(0.318937 - 3.03448i) q^{30} +(-0.196204 - 0.0417045i) q^{31} +(2.92705 - 5.06980i) q^{32} +(-1.83824 - 0.906920i) q^{33} +4.89796 q^{34} +(2.45576 + 1.78421i) q^{36} +(0.945958 + 0.421168i) q^{37} +(-2.30630 - 2.56141i) q^{38} +(-1.77555 - 1.97195i) q^{39} +(-3.79098 - 1.68785i) q^{40} +(7.77155 + 5.64636i) q^{41} -4.70820 q^{43} +(2.68381 - 2.75404i) q^{44} +(3.63577 - 6.29735i) q^{45} +(-7.59803 - 1.61501i) q^{46} +(-1.36363 + 12.9741i) q^{47} +(-2.48729 + 1.80712i) q^{48} +(1.49096 - 4.58869i) q^{50} +(-1.55579 - 0.692684i) q^{51} +(4.54770 - 2.02476i) q^{52} +(3.81489 + 0.810880i) q^{53} +(-3.08583 - 5.34482i) q^{54} +(-7.23324 - 5.70428i) q^{55} +(0.370334 + 1.13977i) q^{57} +(-1.60308 + 15.2523i) q^{58} +(-0.894464 - 8.51025i) q^{59} +(-1.33176 - 1.47907i) q^{60} +(-0.967005 + 0.205543i) q^{61} +(-0.288448 + 0.209570i) q^{62} +(-0.141042 - 0.434084i) q^{64} +(-5.96253 - 10.3274i) q^{65} +(-3.38432 + 1.34952i) q^{66} +(2.70872 - 4.69165i) q^{67} +(2.13783 - 2.37430i) q^{68} +(2.18505 + 1.58753i) q^{69} +(-0.623302 + 1.91833i) q^{71} +(-3.82603 + 0.813249i) q^{72} +(-1.04226 - 9.91646i) q^{73} +(1.68143 - 0.748619i) q^{74} +(-1.12254 + 1.24670i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(4.21116 - 4.67696i) q^{79} +(-12.6223 + 5.61980i) q^{80} +(-0.596670 - 5.67693i) q^{81} +(16.7017 - 3.55005i) q^{82} +(0.531960 - 1.63720i) q^{83} +(-6.19182 - 4.49862i) q^{85} +(-5.59979 + 6.21920i) q^{86} +(2.66623 - 4.61804i) q^{87} +(0.323221 + 4.94470i) q^{88} +(-7.65177 - 13.2532i) q^{89} +(-3.99406 - 12.2925i) q^{90} +(-4.09921 + 2.97825i) q^{92} +(0.121261 - 0.0257748i) q^{93} +(15.5160 + 17.2322i) q^{94} +(0.562970 + 5.35630i) q^{95} +(-0.378188 + 3.59821i) q^{96} +(-3.58961 - 11.0477i) q^{97} +(-8.67628 - 0.342417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

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