LMFDB - Embedded newform 539.2.q.b.214.1

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			214.1
Root			$1.62381 + 0.722968i$ of defining polynomial
Character	$\chi$	$=$	539.214
Dual form			539.2.q.b.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.520239 + 0.577783i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(0.145871 + 1.38787i) q^{4} +(-0.217653 + 0.0462636i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-1.75181 + 1.94558i) q^{9} +O(q^{10})$	\(q+(-0.520239 + 0.577783i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(0.145871 + 1.38787i) q^{4} +(-0.217653 + 0.0462636i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-1.75181 + 1.94558i) q^{9} +(0.0865012 - 0.149825i) q^{10} +(-3.14501 - 1.05306i) q^{11} +(-0.431239 - 0.746928i) q^{12} +(-2.01774 - 6.20997i) q^{13} +(0.111258 - 0.0808336i) q^{15} +(-0.722369 + 0.153544i) q^{16} +(2.90042 + 3.22125i) q^{17} +(-0.212766 - 2.02433i) q^{18} +(0.304701 - 2.89904i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} +(1.94898 + 3.37573i) q^{23} +(1.59593 + 0.339226i) q^{24} +(-4.52249 + 2.01354i) q^{25} +(4.63772 + 2.06485i) q^{26} +(1.07295 - 3.30220i) q^{27} +(3.05322 - 2.21829i) q^{29} +(-0.0111763 + 0.106336i) q^{30} +(-6.73903 - 1.43242i) q^{31} +(2.92705 - 5.06980i) q^{32} +(2.04039 - 0.196025i) q^{33} -3.37009 q^{34} +(-2.95576 - 2.14748i) q^{36} +(-5.16474 - 2.29949i) q^{37} +(1.51650 + 1.68424i) q^{38} +(2.70026 + 2.99895i) q^{39} +(0.536647 + 0.238931i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(1.00274 - 4.51848i) q^{44} +(0.291277 - 0.504506i) q^{45} +(-2.96437 - 0.630097i) q^{46} +(0.631931 - 6.01242i) q^{47} +(0.369254 - 0.268279i) q^{48} +(1.18938 - 3.66055i) q^{50} +(-2.44733 - 1.08962i) q^{51} +(8.32432 - 3.70622i) q^{52} +(1.68037 + 0.357175i) q^{53} +(1.34977 + 2.33786i) q^{54} +(0.733239 + 0.0837016i) q^{55} +(0.556717 + 1.71340i) q^{57} +(-0.306709 + 2.91814i) q^{58} +(-0.996474 - 9.48082i) q^{59} +(0.128416 + 0.142621i) q^{60} +(-9.41900 + 2.00207i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} +(0.726463 + 1.25827i) q^{65} +(-0.948230 + 1.28088i) q^{66} +(-0.635774 + 1.10119i) q^{67} +(-4.04759 + 4.49531i) q^{68} +(-1.94898 - 1.41602i) q^{69} +(-2.87670 + 8.85357i) q^{71} +(6.76048 - 1.43698i) q^{72} +(0.584221 + 5.55850i) q^{73} +(4.01551 - 1.78782i) q^{74} +(2.04725 - 2.27370i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-3.03086 + 3.36611i) q^{79} +(0.150123 - 0.0668389i) q^{80} +(-0.596670 - 5.67693i) q^{81} +(-1.01763 + 0.216303i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(2.44939 - 2.72032i) q^{86} +(-1.16623 + 2.01996i) q^{87} +(5.08297 + 7.12929i) q^{88} +(3.96078 + 6.86028i) q^{89} +(0.139962 + 0.430759i) q^{90} +(-4.40079 + 3.19736i) q^{92} +(4.16495 - 0.885287i) q^{93} +(3.14512 + 3.49301i) q^{94} +(0.0678008 + 0.645082i) q^{95} +(-0.378188 + 3.59821i) q^{96} +(2.79781 + 8.61078i) q^{97} +(7.55825 - 4.27411i) 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 $

$2$	−0.520239	+	0.577783i	−0.367864	+	0.408555i	−0.898449	−	0.439077i	$-0.855306\pi$
$2$	−0.520239	+	0.577783i	−0.367864	+	0.408555i	0.530585	+	0.847632i	$0.321972\pi$
$3$	−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	$0.423762\pi$
$4$	0.145871	+	1.38787i	0.0729357	+	0.693937i
$5$	−0.217653	+	0.0462636i	−0.0973375	+	0.0206897i	−0.256323	−	0.966591i	$-0.582511\pi$
$5$	−0.217653	+	0.0462636i	−0.0973375	+	0.0206897i	0.158985	+	0.987281i	$0.449178\pi$
$6$	0.148486	−	0.456994i	0.0606193	−	0.186567i
$7$		0			0
$7$		0			0
$8$	−2.13577	−	1.55173i	−0.755110	−	0.548620i
$9$	−1.75181	+	1.94558i	−0.583936	+	0.648526i
$10$	0.0865012	−	0.149825i	0.0273541	−	0.0473787i
$11$	−3.14501	−	1.05306i	−0.948255	−	0.317508i
$11$	−3.14501	−	1.05306i	−0.948255	−	0.317508i
$12$	−0.431239	−	0.746928i	−0.124488	−	0.215619i
$13$	−2.01774	−	6.20997i	−0.559620	−	1.72233i	−0.683418	−	0.730027i	$-0.739507\pi$
$13$	−2.01774	−	6.20997i	−0.559620	−	1.72233i	0.123798	−	0.992307i	$-0.460493\pi$
$14$		0			0
$15$	0.111258	−	0.0808336i	0.0287267	−	0.0208711i
$16$	−0.722369	+	0.153544i	−0.180592	+	0.0383861i
$17$	2.90042	+	3.22125i	0.703456	+	0.781267i	0.983922	−	0.178597i	$-0.0571558\pi$
$17$	2.90042	+	3.22125i	0.703456	+	0.781267i	−0.280466	+	0.959864i	$0.590489\pi$
$18$	−0.212766	−	2.02433i	−0.0501493	−	0.477139i
$19$	0.304701	−	2.89904i	0.0699032	−	0.665085i	−0.902326	−	0.431054i	$-0.858142\pi$
$19$	0.304701	−	2.89904i	0.0699032	−	0.665085i	0.972229	−	0.234031i	$-0.0751916\pi$
$20$	−0.0959574	−	0.295327i	−0.0214567	−	0.0660370i
$21$		0			0
$22$	2.24459	−	1.26929i	0.478549	−	0.270614i
$23$	1.94898	+	3.37573i	0.406390	+	0.703888i	0.994482	−	0.104906i	$-0.0334540\pi$
$23$	1.94898	+	3.37573i	0.406390	+	0.703888i	−0.588092	+	0.808794i	$0.700121\pi$
$24$	1.59593	+	0.339226i	0.325768	+	0.0692442i
$25$	−4.52249	+	2.01354i	−0.904499	+	0.402709i
$26$	4.63772	+	2.06485i	0.909532	+	0.404950i
$27$	1.07295	−	3.30220i	0.206489	−	0.635508i
$28$		0			0
$29$	3.05322	−	2.21829i	0.566969	−	0.411927i	−0.267034	−	0.963687i	$-0.586044\pi$
$29$	3.05322	−	2.21829i	0.566969	−	0.411927i	0.834003	+	0.551760i	$0.186044\pi$
$30$	−0.0111763	+	0.106336i	−0.00204051	+	0.0194142i
$31$	−6.73903	−	1.43242i	−1.21037	−	0.257271i	−0.441842	−	0.897093i	$-0.645675\pi$
$31$	−6.73903	−	1.43242i	−1.21037	−	0.257271i	−0.768523	+	0.639822i	$0.779008\pi$
$32$	2.92705	−	5.06980i	0.517434	−	0.896223i
$33$	2.04039	−	0.196025i	0.355187	−	0.0341236i
$34$	−3.37009			−0.577966
$35$		0			0
$36$	−2.95576	−	2.14748i	−0.492626	−	0.357914i
$37$	−5.16474	−	2.29949i	−0.849078	−	0.378034i	−0.0643903	−	0.997925i	$-0.520510\pi$
$37$	−5.16474	−	2.29949i	−0.849078	−	0.378034i	−0.784688	+	0.619891i	$0.787177\pi$
$38$	1.51650	+	1.68424i	0.246009	+	0.273220i
$39$	2.70026	+	2.99895i	0.432388	+	0.480216i
$40$	0.536647	+	0.238931i	0.0848513	+	0.0377782i
$41$	1.08255	+	0.786521i	0.169066	+	0.122834i	0.669101	−	0.743171i	$-0.266679\pi$
$41$	1.08255	+	0.786521i	0.169066	+	0.122834i	−0.500035	+	0.866005i	$0.666679\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	1.00274	−	4.51848i	0.151169	−	0.681187i
$45$	0.291277	−	0.504506i	0.0434210	−	0.0752074i
$46$	−2.96437	−	0.630097i	−0.437073	−	0.0929028i
$47$	0.631931	−	6.01242i	0.0921765	−	0.877001i	−0.846543	−	0.532320i	$-0.821320\pi$
$47$	0.631931	−	6.01242i	0.0921765	−	0.877001i	0.938720	−	0.344681i	$-0.112013\pi$
$48$	0.369254	−	0.268279i	0.0532972	−	0.0387227i
$49$		0			0
$50$	1.18938	−	3.66055i	0.168204	−	0.517679i
$51$	−2.44733	−	1.08962i	−0.342695	−	0.152578i
$52$	8.32432	−	3.70622i	1.15437	−	0.513961i
$53$	1.68037	+	0.357175i	0.230817	+	0.0490617i	0.321868	−	0.946785i	$-0.395689\pi$
$53$	1.68037	+	0.357175i	0.230817	+	0.0490617i	−0.0910509	+	0.995846i	$0.529023\pi$
$54$	1.34977	+	2.33786i	0.183680	+	0.318143i
$55$	0.733239	+	0.0837016i	0.0988700	+	0.0112863i
$56$		0			0
$57$	0.556717	+	1.71340i	0.0737389	+	0.226945i
$58$	−0.306709	+	2.91814i	−0.0402729	+	0.383171i
$59$	−0.996474	−	9.48082i	−0.129730	−	1.23430i	−0.844738	−	0.535181i	$-0.820244\pi$
$59$	−0.996474	−	9.48082i	−0.129730	−	1.23430i	0.715008	−	0.699117i	$-0.246423\pi$
$60$	0.128416	+	0.142621i	0.0165784	+	0.0184122i
$61$	−9.41900	+	2.00207i	−1.20598	+	0.256339i	−0.766696	−	0.642010i	$-0.778101\pi$
$61$	−9.41900	+	2.00207i	−1.20598	+	0.256339i	−0.439283	+	0.898349i	$0.644767\pi$
$62$	4.33353	−	3.14850i	0.550359	−	0.399859i
$63$		0			0
$64$	0.950059	+	2.92398i	0.118757	+	0.365498i
$65$	0.726463	+	1.25827i	0.0901067	+	0.156069i
$66$	−0.948230	+	1.28088i	−0.116719	+	0.157666i
$67$	−0.635774	+	1.10119i	−0.0776722	+	0.134532i	−0.902245	−	0.431223i	$-0.858082\pi$
$67$	−0.635774	+	1.10119i	−0.0776722	+	0.134532i	0.824573	+	0.565756i	$0.191415\pi$
$68$	−4.04759	+	4.49531i	−0.490843	+	0.545136i
$69$	−1.94898	−	1.41602i	−0.234629	−	0.170468i
$70$		0			0
$71$	−2.87670	+	8.85357i	−0.341401	+	1.05072i	0.622081	+	0.782953i	$0.286287\pi$
$71$	−2.87670	+	8.85357i	−0.341401	+	1.05072i	−0.963482	+	0.267772i	$0.913713\pi$
$72$	6.76048	−	1.43698i	0.796730	−	0.169350i
$73$	0.584221	+	5.55850i	0.0683779	+	0.650573i	0.974009	+	0.226507i	$0.0727307\pi$
$73$	0.584221	+	5.55850i	0.0683779	+	0.650573i	−0.905632	+	0.424065i	$0.860603\pi$
$74$	4.01551	−	1.78782i	0.466793	−	0.207830i
$75$	2.04725	−	2.27370i	0.236396	−	0.262545i
$76$	4.06794			0.466625
$77$		0			0
$78$	−3.13752			−0.355254
$79$	−3.03086	+	3.36611i	−0.340998	+	0.378717i	−0.889114	−	0.457686i	$-0.848679\pi$
$79$	−3.03086	+	3.36611i	−0.340998	+	0.378717i	0.548116	+	0.836402i	$0.315345\pi$
$80$	0.150123	−	0.0668389i	0.0167842	−	0.00747281i
$81$	−0.596670	−	5.67693i	−0.0662966	−	0.630770i
$82$	−1.01763	+	0.216303i	−0.112378	+	0.0238867i
$83$	−3.48688	+	10.7315i	−0.382734	+	1.17793i	0.555376	+	0.831599i	$0.312574\pi$
$83$	−3.48688	+	10.7315i	−0.382734	+	1.17793i	−0.938111	+	0.346336i	$0.887426\pi$
$84$		0			0
$85$	−0.780313	−	0.566931i	−0.0846368	−	0.0614922i
$86$	2.44939	−	2.72032i	0.264124	−	0.293340i
$87$	−1.16623	+	2.01996i	−0.125033	+	0.216563i
$88$	5.08297	+	7.12929i	0.541846	+	0.759985i
$89$	3.96078	+	6.86028i	0.419842	+	0.727188i	0.995923	−	0.0902046i	$-0.0287521\pi$
$89$	3.96078	+	6.86028i	0.419842	+	0.727188i	−0.576081	+	0.817393i	$0.695419\pi$
$90$	0.139962	+	0.430759i	0.0147533	+	0.0454059i
$91$		0			0
$92$	−4.40079	+	3.19736i	−0.458814	+	0.333348i
$93$	4.16495	−	0.885287i	0.431885	−	0.0918000i
$94$	3.14512	+	3.49301i	0.324394	+	0.360277i
$95$	0.0678008	+	0.645082i	0.00695622	+	0.0661840i
$96$	−0.378188	+	3.59821i	−0.0385986	+	0.367241i
$97$	2.79781	+	8.61078i	0.284075	+	0.874292i	0.986674	+	0.162707i	$0.0520225\pi$
$97$	2.79781	+	8.61078i	0.284075	+	0.874292i	−0.702600	+	0.711585i	$0.747977\pi$
$98$		0			0
$99$	7.55825	−	4.27411i	0.759633	−	0.429564i
$100$	−3.45425	−	5.98293i	−0.345425	−	0.598293i
$101$	−18.7904	−	3.99402i	−1.86971	−	0.397420i	−0.873687	−	0.486489i	$-0.838277\pi$
$101$	−18.7904	−	3.99402i	−1.86971	−	0.397420i	−0.996025	+	0.0890694i	$0.971611\pi$
$102$	1.90276	−	0.847164i	0.188402	−	0.0838818i
$103$	−14.8344	−	6.60471i	−1.46168	−	0.650782i	−0.486800	−	0.873513i	$-0.661836\pi$
$103$	−14.8344	−	6.60471i	−1.46168	−	0.650782i	−0.974880	+	0.222732i	$0.928503\pi$
$104$	−5.32676	+	16.3941i	−0.522332	+	1.60757i
$105$		0			0
$106$	−1.08057	+	0.785077i	−0.104954	+	0.0762534i
$107$	0.563759	−	5.36381i	0.0545007	−	0.518539i	−0.932881	−	0.360184i	$-0.882714\pi$
$107$	0.563759	−	5.36381i	0.0545007	−	0.518539i	0.987382	−	0.158356i	$-0.0506193\pi$
$108$	4.73954	+	1.00742i	0.456063	+	0.0969392i
$109$	−2.69951	+	4.67568i	−0.258566	+	0.447849i	−0.965858	−	0.259072i	$-0.916583\pi$
$109$	−2.69951	+	4.67568i	−0.258566	+	0.447849i	0.707292	+	0.706921i	$0.249917\pi$
$110$	−0.429821	+	0.380109i	−0.0409818	+	0.0362419i
$111$	3.49406			0.331642
$112$		0			0
$113$	13.3457	+	9.69624i	1.25546	+	0.912145i	0.998526	−	0.0542834i	$-0.0172875\pi$
$113$	13.3457	+	9.69624i	1.25546	+	0.912145i	0.256935	+	0.966429i	$0.417287\pi$
$114$	−1.27960	−	0.569714i	−0.119845	−	0.0533586i
$115$	−0.580375	−	0.644572i	−0.0541203	−	0.0601066i
$116$	3.52409	+	3.91390i	0.327203	+	0.363396i
$117$	15.6167	+	6.95299i	1.44376	+	0.642804i
$118$	5.99626	+	4.35654i	0.552001	+	0.401052i
$119$		0			0
$120$	−0.363054			−0.0331421
$121$	8.78215	+	6.62374i	0.798377	+	0.602158i
$122$	3.74336	−	6.48370i	0.338908	−	0.587006i
$123$	−0.808926	−	0.171942i	−0.0729384	−	0.0155035i
$124$	1.00499	−	9.56187i	0.0902510	−	0.858681i
$125$	1.79128	−	1.30144i	0.160217	−	0.116404i
$126$		0			0
$127$	0.617194	−	1.89953i	0.0547671	−	0.168556i	−0.919931	−	0.392079i	$-0.871756\pi$
$127$	0.617194	−	1.89953i	0.0547671	−	0.168556i	0.974699	+	0.223523i	$0.0717559\pi$
$128$	8.51229	+	3.78992i	0.752387	+	0.334984i
$129$	2.65826	−	1.18353i	0.234047	−	0.104204i
$130$	−1.10494	−	0.234863i	−0.0969099	−	0.0205988i
$131$	0.685047	+	1.18654i	0.0598528	+	0.103668i	0.894399	−	0.447270i	$-0.147604\pi$
$131$	0.685047	+	1.18654i	0.0598528	+	0.103668i	−0.834546	+	0.550938i	$0.814270\pi$
$132$	0.569693	+	2.80321i	0.0495854	+	0.243988i
$133$		0			0
$134$	−0.305497	−	0.940223i	−0.0263909	−	0.0812229i
$135$	−0.0807592	+	0.768373i	−0.00695065	+	0.0661310i
$136$	−1.19614	−	11.3805i	−0.102568	−	0.975872i
$137$	1.67232	+	1.85730i	0.142876	+	0.158680i	0.810335	−	0.585966i	$-0.199285\pi$
$137$	1.67232	+	1.85730i	0.142876	+	0.158680i	−0.667460	+	0.744646i	$0.732618\pi$
$138$	1.83208	−	0.389422i	0.155957	−	0.0331498i
$139$	−3.85302	+	2.79938i	−0.326809	+	0.237441i	−0.739075	−	0.673623i	$-0.764737\pi$
$139$	−3.85302	+	2.79938i	−0.326809	+	0.237441i	0.412266	+	0.911063i	$0.364737\pi$
$140$		0			0
$141$	1.15459	+	3.55348i	0.0972344	+	0.299257i
$142$	−3.61887	−	6.26807i	−0.303689	−	0.526005i
$143$	−0.193632	+	21.6552i	−0.0161924	+	1.81090i
$144$	0.966719	−	1.67441i	0.0805599	−	0.139534i
$145$	−0.561917	+	0.624072i	−0.0466647	+	0.0518264i
$146$	−3.51554	−	2.55419i	−0.290948	−	0.211386i
$147$		0			0
$148$	2.43801	−	7.50344i	0.200404	−	0.616779i
$149$	7.07186	−	1.50317i	0.579350	−	0.123145i	0.0910895	−	0.995843i	$-0.470965\pi$
$149$	7.07186	−	1.50317i	0.579350	−	0.123145i	0.488260	+	0.872698i	$0.337632\pi$
$150$	0.248649	+	2.36574i	0.0203021	+	0.193162i
$151$	7.43597	−	3.31071i	0.605131	−	0.269422i	−0.0812154	−	0.996697i	$-0.525880\pi$
$151$	7.43597	−	3.31071i	0.605131	−	0.269422i	0.686346	+	0.727275i	$0.259214\pi$
$152$	−5.14930	+	5.71888i	−0.417663	+	0.463862i
$153$	−11.3482			−0.917445
$154$		0			0
$155$	1.53304			0.123137
$156$	−3.76827	+	4.18508i	−0.301703	+	0.335075i
$157$	−18.4092	+	8.19632i	−1.46922	+	0.654138i	−0.976395	−	0.215993i	$-0.930701\pi$
$157$	−18.4092	+	8.19632i	−1.46922	+	0.654138i	−0.492822	+	0.870130i	$0.664035\pi$
$158$	−0.368113	−	3.50236i	−0.0292855	−	0.278633i
$159$	−1.03853	+	0.220746i	−0.0823607	+	0.0175063i
$160$	−0.402535	+	1.23887i	−0.0318232	+	0.0979416i
$161$		0			0
$162$	3.59045	+	2.60861i	0.282092	+	0.204952i
$163$	4.97465	−	5.52491i	0.389645	−	0.432744i	−0.516126	−	0.856513i	$-0.672626\pi$
$163$	4.97465	−	5.52491i	0.389645	−	0.432744i	0.905770	+	0.423769i	$0.139293\pi$
$164$	−0.933679	+	1.61718i	−0.0729080	+	0.126280i
$165$	−0.435029	+	0.137061i	−0.0338670	+	0.0106702i
$166$	−4.38647	−	7.59760i	−0.340456	−	0.589688i
$167$	0.683275	+	2.10290i	0.0528734	+	0.162728i	0.974006	−	0.226520i	$-0.0727350\pi$
$167$	0.683275	+	2.10290i	0.0528734	+	0.162728i	−0.921133	+	0.389248i	$0.872735\pi$
$168$		0			0
$169$	−23.9752	+	17.4190i	−1.84424	+	1.33992i
$170$	0.733512	−	0.155913i	0.0562578	−	0.0119580i
$171$	5.10653	+	5.67137i	0.390506	+	0.433701i
$172$	−0.686792	−	6.53439i	−0.0523674	−	0.498243i
$173$	−1.08314	+	10.3054i	−0.0823500	+	0.783508i	0.872938	+	0.487831i	$0.162212\pi$
$173$	−1.08314	+	10.3054i	−0.0823500	+	0.783508i	−0.955288	+	0.295677i	$0.904455\pi$
$174$	−0.560385	−	1.72469i	−0.0424827	−	0.130748i
$175$		0			0
$176$	2.43355	+	0.277797i	0.183436	+	0.0209398i
$177$	2.94587	+	5.10240i	0.221425	+	0.383520i
$178$	−6.02431	−	1.28051i	−0.451541	−	0.0959780i
$179$	−21.3856	+	9.52147i	−1.59843	+	0.711668i	−0.996236	−	0.0866804i	$-0.972374\pi$
$179$	−21.3856	+	9.52147i	−1.59843	+	0.711668i	−0.602196	+	0.798348i	$0.705707\pi$
$180$	0.742680	+	0.330662i	0.0553561	+	0.0246461i
$181$	4.23851	−	13.0448i	0.315046	−	0.969611i	−0.660690	−	0.750659i	$-0.729736\pi$
$181$	4.23851	−	13.0448i	0.315046	−	0.969611i	0.975736	−	0.218952i	$-0.0702639\pi$
$182$		0			0
$183$	4.81471	−	3.49809i	0.355914	−	0.258587i
$184$	1.07565	−	10.2341i	0.0792977	−	0.754467i
$185$	1.23051	+	0.261552i	0.0904686	+	0.0192297i
$186$	−1.65526	+	2.86700i	−0.121370	+	0.210219i
$187$	−5.72970	−	13.1851i	−0.418997	−	0.964194i
$188$	8.43666			0.615306
$189$		0			0
$190$	−0.407990	−	0.296422i	−0.0295987	−	0.0215047i
$191$	−10.9853	−	4.89099i	−0.794871	−	0.353899i	−0.0312066	−	0.999513i	$-0.509935\pi$
$191$	−10.9853	−	4.89099i	−0.794871	−	0.353899i	−0.763664	+	0.645614i	$0.776602\pi$
$192$	−1.27143	−	1.41206i	−0.0917574	−	0.101907i
$193$	10.6284	+	11.8041i	0.765050	+	0.849675i	0.992261	−	0.124171i	$-0.0396272\pi$
$193$	10.6284	+	11.8041i	0.765050	+	0.849675i	−0.227210	+	0.973846i	$0.572961\pi$
$194$	−6.43070	−	2.86313i	−0.461697	−	0.205561i
$195$	−0.726463	−	0.527806i	−0.0520231	−	0.0377970i
$196$		0			0
$197$	12.3035			0.876590			0.438295	−	0.898831i	$-0.355582\pi$
$197$	12.3035			0.876590			0.438295	+	0.898831i	$0.355582\pi$
$198$	−1.46258	+	6.59059i	−0.103941	+	0.468373i
$199$	7.63075	−	13.2168i	0.540929	−	0.936917i	−0.457922	−	0.888993i	$-0.651406\pi$
$199$	7.63075	−	13.2168i	0.540929	−	0.936917i	0.998851	−	0.0479244i	$-0.0152607\pi$
$200$	12.7835	+	2.71722i	0.903930	+	0.192136i
$201$	0.0821447	−	0.781555i	0.00579404	−	0.0551266i
$202$	12.0832	−	8.77892i	0.850168	−	0.617683i
$203$		0			0
$204$	1.15526	−	3.55553i	0.0808845	−	0.248937i
$205$	−0.272009	−	0.121106i	−0.0189979	−	0.00845841i
$206$	11.5335	−	5.13506i	0.803580	−	0.357777i
$207$	−9.98198	−	2.12174i	−0.693796	−	0.147471i
$208$	2.41106	+	4.17608i	0.167177	+	0.289559i
$209$	−4.01114	+	8.79663i	−0.277456	+	0.608476i
$210$		0			0
$211$	2.76058	+	8.49620i	0.190046	+	0.584903i	0.999999	−	0.00159295i	$-0.000507051\pi$
$211$	2.76058	+	8.49620i	0.190046	+	0.584903i	−0.809952	+	0.586496i	$0.800507\pi$
$212$	−0.250595	+	2.38425i	−0.0172109	+	0.163751i
$213$	−0.601394	−	5.72188i	−0.0412068	−	0.392057i
$214$	2.80583	+	3.11619i	0.191803	+	0.213019i
$215$	1.02476	−	0.217819i	0.0698878	−	0.0148551i
$216$	−7.41570	+	5.38782i	−0.504574	+	0.366595i
$217$		0			0
$218$	−1.29714	−	3.99220i	−0.0878537	−	0.270386i
$219$	−1.72713	−	2.99148i	−0.116709	−	0.202145i
$220$	−0.00920856	+	1.02985i	−0.000620841	+	0.0694327i
$221$	14.1515	−	24.5112i	0.951935	−	1.64880i
$222$	−1.81775	+	2.01881i	−0.121999	+	0.135494i
$223$	0.578645	+	0.420410i	0.0387489	+	0.0281527i	0.606991	−	0.794709i	$-0.292376\pi$
$223$	0.578645	+	0.420410i	0.0387489	+	0.0281527i	−0.568242	+	0.822861i	$0.692376\pi$
$224$		0			0
$225$	4.00503	−	12.3262i	0.267002	−	0.821747i
$226$	−12.5453	+	2.66658i	−0.834500	+	0.177378i
$227$	−0.556261	−	5.29247i	−0.0369203	−	0.351273i	−0.997350	−	0.0727512i	$-0.976822\pi$
$227$	−0.556261	−	5.29247i	−0.0369203	−	0.351273i	0.960430	−	0.278522i	$-0.0898446\pi$
$228$	−2.29677	+	1.02259i	−0.152107	+	0.0677225i
$229$	4.42183	−	4.91094i	0.292203	−	0.324524i	−0.579113	−	0.815248i	$-0.696601\pi$
$229$	4.42183	−	4.91094i	0.292203	−	0.324524i	0.871315	+	0.490724i	$0.163267\pi$
$230$	0.674356			0.0444657
$231$		0			0
$232$	−9.96318			−0.654115
$233$	−6.39497	+	7.10233i	−0.418948	+	0.465289i	−0.915265	−	0.402852i	$-0.868019\pi$
$233$	−6.39497	+	7.10233i	−0.418948	+	0.465289i	0.496317	+	0.868142i	$0.334685\pi$
$234$	−12.1417	+	5.40584i	−0.793729	+	0.353391i
$235$	0.140615	+	1.33786i	0.00917268	+	0.0872722i
$236$	13.0128	−	2.76596i	0.847062	−	0.180049i
$237$	0.865066	−	2.66240i	0.0561921	−	0.172941i
$238$		0			0
$239$	−21.7194	−	15.7801i	−1.40491	−	1.02073i	−0.994038	−	0.109034i	$-0.965224\pi$
$239$	−21.7194	−	15.7801i	−1.40491	−	1.02073i	−0.410872	−	0.911693i	$-0.634776\pi$
$240$	−0.0679578	+	0.0754747i	−0.00438665	+	0.00487187i
$241$	9.43316	−	16.3387i	0.607643	−	1.05247i	−0.383985	−	0.923340i	$-0.625448\pi$
$241$	9.43316	−	16.3387i	0.607643	−	1.05247i	0.991628	−	0.129129i	$-0.0412183\pi$
$242$	−8.39590	+	1.62826i	−0.539709	+	0.104668i
$243$	6.97214	+	12.0761i	0.447263	+	0.774682i
$244$	−4.15258	−	12.7803i	−0.265842	−	0.818177i
$245$		0			0
$246$	0.520180	−	0.377933i	0.0331654	−	0.0240961i
$247$	−18.6177	+	3.95732i	−1.18462	+	0.251798i
$248$	12.1703	+	13.5165i	0.772815	+	0.858298i
$249$	−0.728955	−	6.93555i	−0.0461957	−	0.439522i
$250$	−0.179941	+	1.71203i	−0.0113805	+	0.108278i
$251$	−9.07680	−	27.9355i	−0.572923	−	1.76328i	−0.643146	−	0.765744i	$-0.722371\pi$
$251$	−9.07680	−	27.9355i	−0.572923	−	1.76328i	0.0702229	−	0.997531i	$-0.477629\pi$
$252$		0			0
$253$	−2.57472	−	12.6691i	−0.161871	−	0.796498i
$254$	0.776427	+	1.34481i	0.0487174	+	0.0843810i
$255$	0.583080	+	0.123937i	0.0365139	+	0.00776126i
$256$	−12.2355	+	5.44759i	−0.764718	+	0.340474i
$257$	15.4539	+	6.88052i	0.963987	+	0.429195i	0.827512	−	0.561449i	$-0.189756\pi$
$257$	15.4539	+	6.88052i	0.963987	+	0.429195i	0.136476	+	0.990643i	$0.456422\pi$
$258$	−0.699104	+	2.15162i	−0.0435243	+	0.133954i
$259$		0			0
$260$	−1.64035	+	1.19178i	−0.101730	+	0.0739114i
$261$	−1.03279	+	9.82630i	−0.0639278	+	0.608233i
$262$	−1.04195	−	0.221473i	−0.0643718	−	0.0136826i
$263$	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	$0.0855091\pi$
$264$	−4.66200	−	2.74747i	−0.286926	−	0.169095i
$265$	−0.382263			−0.0234822
$266$		0			0
$267$	−3.96078	−	2.87768i	−0.242396	−	0.176111i
$268$	−1.62106	−	0.721741i	−0.0990219	−	0.0440874i
$269$	4.18017	+	4.64255i	0.254869	+	0.283061i	0.856978	−	0.515353i	$-0.172339\pi$
$269$	4.18017	+	4.64255i	0.254869	+	0.283061i	−0.602109	+	0.798414i	$0.705673\pi$
$270$	−0.401939	−	0.446398i	−0.0244612	−	0.0271669i
$271$	−7.18675	−	3.19975i	−0.436564	−	0.194371i	0.176673	−	0.984270i	$-0.443466\pi$
$271$	−7.18675	−	3.19975i	−0.436564	−	0.194371i	−0.613237	+	0.789899i	$0.710133\pi$
$272$	−2.58978	−	1.88159i	−0.157029	−	0.114088i
$273$		0			0
$274$	−1.94312			−0.117388
$275$	16.3437	−	1.57017i	0.985559	−	0.0946850i
$276$	1.68095	−	2.91149i	0.101181	−	0.175251i
$277$	−11.7844	−	2.50485i	−0.708055	−	0.150502i	−0.160212	−	0.987083i	$-0.551218\pi$
$277$	−11.7844	−	2.50485i	−0.708055	−	0.150502i	−0.547843	+	0.836581i	$0.684551\pi$
$278$	0.387053	−	3.68256i	0.0232139	−	0.220865i
$279$	14.5924	−	10.6020i	0.873622	−	0.634724i
$280$		0			0
$281$	6.53723	−	20.1195i	0.389978	−	1.20023i	−0.542826	−	0.839846i	$-0.682646\pi$
$281$	6.53723	−	20.1195i	0.389978	−	1.20023i	0.932804	−	0.360384i	$-0.117354\pi$
$282$	−2.65380	−	1.18155i	−0.158032	−	0.0703603i
$283$	22.8417	−	10.1698i	1.35780	−	0.604531i	0.406741	−	0.913544i	$-0.366665\pi$
$283$	22.8417	−	10.1698i	1.35780	−	0.604531i	0.951058	+	0.309013i	$0.0999986\pi$
$284$	−12.7073	−	2.70101i	−0.754037	−	0.160275i
$285$	−0.200439	−	0.347171i	−0.0118730	−	0.0205646i
$286$	−12.4113	−	11.3777i	−0.733894	−	0.672780i
$287$		0			0
$288$	4.73607	+	14.5761i	0.279075	+	0.858906i
$289$	−0.186988	+	1.77908i	−0.0109993	+	0.104652i
$290$	−0.0682476	−	0.649333i	−0.00400764	−	0.0381301i
$291$	−3.74420	−	4.15836i	−0.219489	−	0.243767i
$292$	−7.62927	+	1.62165i	−0.446469	+	0.0948999i
$293$	−0.368173	+	0.267494i	−0.0215089	+	0.0156271i	−0.598488	−	0.801132i	$-0.704231\pi$
$293$	−0.368173	+	0.267494i	−0.0215089	+	0.0156271i	0.576979	+	0.816759i	$0.304231\pi$
$294$		0			0
$295$	0.655503	+	2.01743i	0.0381648	+	0.117459i
$296$	7.46253	+	12.9255i	0.433751	+	0.751278i
$297$	−6.85183	+	9.25556i	−0.397584	+	0.537062i
$298$	−2.81055	+	4.86801i	−0.162811	+	0.281996i
$299$	17.0306	−	18.9144i	0.984907	−	1.09385i
$300$	3.45425	+	2.50966i	0.199431	+	0.144895i
$301$		0			0
$302$	−1.95561	+	6.01874i	−0.112533	+	0.346339i
$303$	11.6131	−	2.46844i	0.667155	−	0.141808i
$304$	0.225024	+	2.14096i	0.0129060	+	0.122793i
$305$	1.95745	−	0.871514i	0.112083	−	0.0499028i
$306$	5.90375	−	6.55678i	0.337495	−	0.374826i
$307$	8.03578			0.458626			0.229313	−	0.973353i	$-0.426352\pi$
$307$	8.03578			0.458626			0.229313	+	0.973353i	$0.426352\pi$
$308$		0			0
$309$	10.0358			0.570918
$310$	−0.797547	+	0.885765i	−0.0452976	+	0.0503081i
$311$	−0.125124	+	0.0557086i	−0.00709511	+	0.00315894i	−0.410281	−	0.911959i	$-0.634569\pi$
$311$	−0.125124	+	0.0557086i	−0.00709511	+	0.00315894i	0.403186	+	0.915118i	$0.367903\pi$
$312$	−1.11360	−	10.5952i	−0.0630449	−	0.599832i
$313$	−14.9558	+	3.17896i	−0.845352	+	0.179685i	−0.610174	−	0.792267i	$-0.708901\pi$
$313$	−14.9558	+	3.17896i	−0.845352	+	0.179685i	−0.235178	+	0.971952i	$0.575567\pi$
$314$	4.84150	−	14.9006i	0.273221	−	0.840889i
$315$		0			0
$316$	−5.11385	−	3.71543i	−0.287676	−	0.209009i
$317$	−22.0763	+	24.5182i	−1.23993	+	1.37708i	−0.340364	+	0.940294i	$0.610550\pi$
$317$	−22.0763	+	24.5182i	−1.23993	+	1.37708i	−0.899565	+	0.436787i	$0.856116\pi$
$318$	0.412739	−	0.714885i	0.0231453	−	0.0400888i
$319$	−11.9384	+	3.76134i	−0.668421	+	0.210595i
$320$	−0.342058	−	0.592461i	−0.0191216	−	0.0331196i
$321$	1.03004	+	3.17014i	0.0574912	+	0.176940i
$322$		0			0
$323$	10.2223	−	7.42692i	0.568783	−	0.413245i
$324$	7.79183	−	1.65620i	0.432879	−	0.0920113i
$325$	21.6293	+	24.0217i	1.19978	+	1.33249i
$326$	0.604196	+	5.74854i	0.0334633	+	0.318382i
$327$	0.348788	−	3.31850i	0.0192880	−	0.183513i
$328$	−1.09162	−	3.35966i	−0.0602747	−	0.185506i
$329$		0			0
$330$	0.147127	−	0.322657i	0.00809908	−	0.0177617i
$331$	−14.7667	−	25.5767i	−0.811653	−	1.40582i	−0.911707	−	0.410842i	$-0.865235\pi$
$331$	−14.7667	−	25.5767i	−0.811653	−	1.40582i	0.100054	−	0.994982i	$-0.468099\pi$
$332$	−15.4026	−	3.27392i	−0.845327	−	0.179680i
$333$	13.5215	−	6.02015i	0.740972	−	0.329902i
$334$	−1.57049	−	0.699227i	−0.0859333	−	0.0382600i
$335$	0.0874331	−	0.269091i	0.00477698	−	0.0147020i
$336$		0			0
$337$	−4.55497	+	3.30938i	−0.248125	+	0.180273i	−0.704895	−	0.709311i	$-0.749006\pi$
$337$	−4.55497	+	3.30938i	−0.248125	+	0.180273i	0.456770	+	0.889585i	$0.349006\pi$
$338$	2.40841	−	22.9145i	0.131000	−	1.24638i
$339$	−9.97244	−	2.11971i	−0.541628	−	0.115127i
$340$	0.673002	−	1.16567i	0.0364987	−	0.0632176i
$341$	19.6859	+	11.6016i	1.06605	+	0.628260i
$342$	−5.93344			−0.320844
$343$		0			0
$344$	10.0557	+	7.30586i	0.542165	+	0.393906i
$345$	0.489712	+	0.218034i	0.0263652	+	0.0117385i
$346$	−5.39081	−	5.98711i	−0.289812	−	0.321869i
$347$	5.84192	+	6.48811i	0.313611	+	0.348300i	0.879257	−	0.476348i	$-0.158040\pi$
$347$	5.84192	+	6.48811i	0.313611	+	0.348300i	−0.565646	+	0.824648i	$0.691373\pi$
$348$	−2.97357	−	1.32392i	−0.159400	−	0.0709695i
$349$	14.9401	+	10.8546i	0.799724	+	0.581034i	0.910833	−	0.412774i	$-0.135440\pi$
$349$	14.9401	+	10.8546i	0.799724	+	0.581034i	−0.111109	+	0.993808i	$0.535440\pi$
$350$		0			0
$351$	−22.6715			−1.21011
$352$	−14.5444	+	12.8622i	−0.775218	+	0.685558i
$353$	−11.7428	+	20.3392i	−0.625009	+	1.08255i	0.363531	+	0.931582i	$0.381571\pi$
$353$	−11.7428	+	20.3392i	−0.625009	+	1.08255i	−0.988539	+	0.150964i	$0.951762\pi$
$354$	−4.48064	−	0.952389i	−0.238143	−	0.0506189i
$355$	0.216525	−	2.06009i	0.0114919	−	0.109338i
$356$	−8.94343	+	6.49778i	−0.474001	+	0.344382i
$357$		0			0
$358$	5.62425	−	17.3097i	0.297251	−	0.914844i
$359$	13.5947	+	6.05273i	0.717499	+	0.319451i	0.732811	−	0.680432i	$-0.238208\pi$
$359$	13.5947	+	6.05273i	0.717499	+	0.319451i	−0.0153128	+	0.999883i	$0.504874\pi$
$360$	−1.40496	+	0.625528i	−0.0740479	+	0.0329682i
$361$	10.2732	+	2.18364i	0.540696	+	0.114929i
$362$	5.33203	+	9.23534i	0.280245	+	0.485399i
$363$	−6.62347	−	1.53215i	−0.347642	−	0.0804168i
$364$		0			0
$365$	−0.384314	−	1.18280i	−0.0201159	−	0.0619104i
$366$	−0.483659	+	4.60170i	−0.0252812	+	0.240535i
$367$	−3.57758	−	34.0384i	−0.186748	−	1.77679i	−0.540394	−	0.841412i	$-0.681725\pi$
$367$	−3.57758	−	34.0384i	−0.186748	−	1.77679i	0.353646	−	0.935379i	$-0.384942\pi$
$368$	−1.92621	−	2.13927i	−0.100410	−	0.111517i
$369$	−3.42666	+	0.728360i	−0.178385	+	0.0379169i
$370$	−0.791277	+	0.574896i	−0.0411365	+	0.0298874i
$371$		0			0
$372$	1.83621	+	5.65128i	0.0952032	+	0.293005i
$373$	−1.50870	−	2.61314i	−0.0781173	−	0.135303i	0.824320	−	0.566124i	$-0.191558\pi$
$373$	−1.50870	−	2.61314i	−0.0781173	−	0.135303i	−0.902438	+	0.430820i	$0.858224\pi$
$374$	10.5990	+	3.54890i	0.548060	+	0.183509i
$375$	−0.684207	+	1.18508i	−0.0353323	+	0.0611973i
$376$	−10.6793	+	11.8606i	−0.550744	+	0.611663i
$377$	−19.9361	−	14.4845i	−1.02676	−	0.745987i
$378$		0			0
$379$	−1.89252	+	5.82457i	−0.0972121	+	0.299188i	−0.987824	−	0.155576i	$-0.950277\pi$
$379$	−1.89252	+	5.82457i	−0.0972121	+	0.299188i	0.890612	+	0.454764i	$0.150277\pi$
$380$	−0.885401	+	0.188198i	−0.0454201	+	0.00965435i
$381$	0.129029	+	1.22763i	0.00661034	+	0.0628932i
$382$	8.54092	−	3.80266i	0.436992	−	0.194561i
$383$	−2.93814	+	3.26314i	−0.150132	+	0.166738i	−0.813520	−	0.581537i	$-0.802451\pi$
$383$	−2.93814	+	3.26314i	−0.150132	+	0.166738i	0.663388	+	0.748276i	$0.269118\pi$
$384$	−5.75876			−0.293875
$385$		0			0
$386$	−12.3495			−0.628573
$387$	8.24786	−	9.16018i	0.419262	−	0.465638i
$388$	−11.5426	+	5.13908i	−0.585984	+	0.260897i
$389$	−1.09713	−	10.4385i	−0.0556268	−	0.529253i	−0.986483	−	0.163866i	$-0.947603\pi$
$389$	−1.09713	−	10.4385i	−0.0556268	−	0.529253i	0.930856	−	0.365387i	$-0.119063\pi$
$390$	0.682892	−	0.145153i	0.0345796	−	0.00735012i
$391$	−5.22119	+	16.0692i	−0.264047	+	0.812654i
$392$		0			0
$393$	−0.685047	−	0.497716i	−0.0345560	−	0.0251064i
$394$	−6.40077	+	7.10878i	−0.322466	+	0.358135i
$395$	0.503947	−	0.872863i	0.0253563	−	0.0439185i
$396$	7.03445	+	9.86642i	0.353495	+	0.495806i
$397$	5.69441	+	9.86301i	0.285794	+	0.495010i	0.972801	−	0.231640i	$-0.0744093\pi$
$397$	5.69441	+	9.86301i	0.285794	+	0.495010i	−0.687007	+	0.726651i	$0.741076\pi$
$398$	3.66666	+	11.2848i	0.183793	+	0.565657i
$399$		0			0
$400$	2.95774	−	2.14893i	0.147887	−	0.107446i
$401$	4.62170	−	0.982373i	0.230797	−	0.0490574i	−0.0910613	−	0.995845i	$-0.529026\pi$
$401$	4.62170	−	0.982373i	0.230797	−	0.0490574i	0.321858	+	0.946788i	$0.395693\pi$
$402$	0.408835	+	0.454057i	0.0203908	+	0.0226463i
$403$	4.70230	+	44.7394i	0.234238	+	2.22863i
$404$	2.80221	−	26.6613i	0.139415	−	1.32645i
$405$	0.392503	+	1.20800i	0.0195036	+	0.0600260i
$406$		0			0
$407$	13.8217	+	12.6707i	0.685114	+	0.628062i
$408$	3.53615	+	6.12479i	0.175065	+	0.303222i
$409$	2.41156	+	0.512594i	0.119244	+	0.0253461i	0.267147	−	0.963656i	$-0.413919\pi$
$409$	2.41156	+	0.512594i	0.119244	+	0.0253461i	−0.147903	+	0.989002i	$0.547252\pi$
$410$	0.211482	−	0.0941581i	0.0104444	−	0.00465014i
$411$	−1.41108	−	0.628252i	−0.0696033	−	0.0309894i
$412$	7.00259	−	21.5518i	0.344993	−	1.06178i
$413$		0			0
$414$	6.41892	−	4.66362i	0.315472	−	0.229204i
$415$	0.262452	−	2.49706i	0.0128832	−	0.122576i
$416$	−37.3893	−	7.94734i	−1.83316	−	0.389651i
$417$	1.47172	−	2.54910i	0.0720706	−	0.124830i
$418$	−2.99580	−	6.89391i	−0.146529	−	0.337192i
$419$	14.3399			0.700548			0.350274	−	0.936647i	$-0.386088\pi$
$419$	14.3399			0.700548			0.350274	+	0.936647i	$0.386088\pi$
$420$		0			0
$421$	14.0087	+	10.1779i	0.682744	+	0.496043i	0.874267	−	0.485446i	$-0.161343\pi$
$421$	14.0087	+	10.1779i	0.682744	+	0.496043i	−0.191523	+	0.981488i	$0.561343\pi$
$422$	−6.34513	−	2.82503i	−0.308876	−	0.137520i
$423$	10.5906	+	11.7621i	0.514933	+	0.571891i
$424$	−3.03466	−	3.37033i	−0.147376	−	0.163678i
$425$	−19.6033	−	8.72794i	−0.950898	−	0.423367i
$426$	3.61887	+	2.62927i	0.175335	+	0.127388i
$427$		0			0
$428$	7.52653			0.363808
$429$	−5.33429	−	12.2752i	−0.257542	−	0.592654i
$430$	−0.407266	+	0.705405i	−0.0196401	+	0.0340176i
$431$	−27.2828	−	5.79914i	−1.31417	−	0.279335i	−0.503069	−	0.864246i	$-0.667796\pi$
$431$	−27.2828	−	5.79914i	−1.31417	−	0.279335i	−0.811097	+	0.584912i	$0.801129\pi$
$432$	−0.268032	+	2.55015i	−0.0128957	+	0.122694i
$433$	−23.9040	+	17.3673i	−1.14875	+	0.834619i	−0.988315	−	0.152426i	$-0.951291\pi$
$433$	−23.9040	+	17.3673i	−1.14875	+	0.834619i	−0.160440	+	0.987046i	$0.551291\pi$
$434$		0			0
$435$	0.160382	−	0.493605i	0.00768973	−	0.0236666i
$436$	−6.88304	−	3.06453i	−0.329638	−	0.146764i
$437$	10.3802	−	4.62157i	0.496554	−	0.221080i
$438$	2.62695	+	0.558375i	0.125520	+	0.0266802i
$439$	−16.8328	−	29.1552i	−0.803384	−	1.39150i	−0.917376	−	0.398021i	$-0.869697\pi$
$439$	−16.8328	−	29.1552i	−0.803384	−	1.39150i	0.113992	−	0.993482i	$-0.463636\pi$
$440$	−1.43615	−	1.31656i	−0.0684658	−	0.0627644i
$441$		0			0
$442$	6.79997	+	20.9282i	0.323442	+	0.995451i
$443$	−1.07944	+	10.2701i	−0.0512856	+	0.487949i	0.938489	+	0.345309i	$0.112226\pi$
$443$	−1.07944	+	10.2701i	−0.0512856	+	0.487949i	−0.989775	+	0.142640i	$0.954441\pi$
$444$	0.509684	+	4.84932i	0.0241885	+	0.230138i
$445$	−1.17946	−	1.30992i	−0.0559117	−	0.0620962i
$446$	−0.543939	+	0.115618i	−0.0257563	+	0.00547466i
$447$	−3.61493	+	2.62640i	−0.170980	+	0.124224i
$448$		0			0
$449$	−0.852224	−	2.62287i	−0.0402189	−	0.123781i	0.928931	−	0.370253i	$-0.120729\pi$
$449$	−0.852224	−	2.62287i	−0.0402189	−	0.123781i	−0.969150	+	0.246471i	$0.920729\pi$
$450$	5.03831	+	8.72661i	0.237508	+	0.411376i
$451$	−2.57639	−	3.61361i	−0.121317	−	0.170158i
$452$	−11.5104	+	19.9366i	−0.541403	+	0.937738i
$453$	−3.36613	+	3.73847i	−0.158155	+	0.175648i
$454$	3.34729	+	2.43195i	0.157096	+	0.114137i
$455$		0			0
$456$	1.46971	−	4.52331i	0.0688255	−	0.211823i
$457$	39.4492	−	8.38518i	1.84535	−	0.392242i	0.853657	−	0.520835i	$-0.174379\pi$
$457$	39.4492	−	8.38518i	1.84535	−	0.392242i	0.991697	+	0.128593i	$0.0410460\pi$
$458$	0.537053	+	5.10972i	0.0250949	+	0.238762i
$459$	13.7492	−	6.12154i	0.641757	−	0.285729i
$460$	0.809924	−	0.899512i	0.0377629	−	0.0419400i
$461$	34.2251			1.59402			0.797011	−	0.603965i	$-0.206413\pi$
$461$	34.2251			1.59402			0.797011	+	0.603965i	$0.206413\pi$
$462$		0			0
$463$	0.707349			0.0328733			0.0164367	−	0.999865i	$-0.494768\pi$
$463$	0.707349			0.0328733			0.0164367	+	0.999865i	$0.494768\pi$
$464$	−1.86495	+	2.07123i	−0.0865780	+	0.0961546i
$465$	−0.865558	+	0.385371i	−0.0401393	+	0.0178712i
$466$	−0.776701	−	7.38981i	−0.0359800	−	0.342326i
$467$	−27.9676	+	5.94470i	−1.29419	+	0.275088i	−0.803007	−	0.595970i	$-0.796768\pi$
$467$	−27.9676	+	5.94470i	−1.29419	+	0.275088i	−0.491180	+	0.871058i	$0.663434\pi$
$468$	−7.37184	+	22.6882i	−0.340764	+	1.04876i
$469$		0			0
$470$	−0.846145	−	0.614760i	−0.0390298	−	0.0283568i
$471$	8.33353	−	9.25532i	0.383989	−	0.426463i
$472$	−12.5834	+	21.7951i	−0.579199	+	1.00320i
$473$	14.8073	+	4.95800i	0.680842	+	0.227969i
$474$	1.08825	+	1.88490i	0.0499850	+	0.0865765i
$475$	4.45933	+	13.7244i	0.204608	+	0.629719i
$476$		0			0
$477$	−3.63860	+	2.64360i	−0.166600	+	0.121042i
$478$	20.4167	−	4.33971i	0.933839	−	0.198494i
$479$	3.41067	+	3.78793i	0.155837	+	0.173075i	0.816008	−	0.578041i	$-0.196183\pi$
$479$	3.41067	+	3.78793i	0.155837	+	0.173075i	−0.660170	+	0.751116i	$0.729516\pi$
$480$	−0.0841527	−	0.800659i	−0.00384103	−	0.0365449i
$481$	−3.85865	+	36.7126i	−0.175940	+	1.67395i
$482$	4.53274	+	13.9503i	0.206461	+	0.635421i
$483$		0			0
$484$	−7.91185	+	13.1547i	−0.359629	+	0.597942i
$485$	−1.00732	−	1.74473i	−0.0457400	−	0.0792240i
$486$	−10.6045	−	2.25406i	−0.481032	−	0.102246i
$487$	26.6648	−	11.8719i	1.20830	−	0.537969i	0.299056	−	0.954236i	$-0.403328\pi$
$487$	26.6648	−	11.8719i	1.20830	−	0.537969i	0.909243	+	0.416266i	$0.136662\pi$
$488$	23.2235	+	10.3398i	1.05128	+	0.468060i
$489$	−1.41986	+	4.36989i	−0.0642084	+	0.197613i
$490$		0			0
$491$	−24.3870	+	17.7182i	−1.10057	+	0.799610i	−0.981153	−	0.193235i	$-0.938102\pi$
$491$	−24.3870	+	17.7182i	−1.10057	+	0.799610i	−0.119416	+	0.992844i	$0.538102\pi$
$492$	0.120635	−	1.14777i	0.00543866	−	0.0517454i
$493$	16.0013	+	3.40118i	0.720662	+	0.153182i
$494$	7.39919	−	12.8158i	0.332905	−	0.576609i
$495$	−1.44734	+	1.27995i	−0.0650532	+	0.0575293i
$496$	5.08801			0.228458
$497$		0			0
$498$	4.38647	+	3.18696i	0.196563	+	0.142811i
$499$	5.43655	+	2.42051i	0.243373	+	0.108357i	0.524799	−	0.851226i	$-0.324141\pi$
$499$	5.43655	+	2.42051i	0.243373	+	0.108357i	−0.281425	+	0.959583i	$0.590807\pi$
$500$	2.06753	+	2.29622i	0.0924627	+	0.102690i
$501$	−0.914400	−	1.01554i	−0.0408524	−	0.0453712i
$502$	20.8628	+	9.28871i	0.931152	+	0.414576i
$503$	−4.02773	−	2.92632i	−0.179588	−	0.130478i	0.494360	−	0.869257i	$-0.335403\pi$
$503$	−4.02773	−	2.92632i	−0.179588	−	0.130478i	−0.673947	+	0.738779i	$0.735403\pi$
$504$		0			0
$505$	4.27456			0.190216
$506$	8.65945	+	5.10331i	0.384960	+	0.226870i
$507$	9.15770	−	15.8616i	0.406708	−	0.704439i
$508$	2.72633	+	0.579500i	0.120962	+	0.0257112i
$509$	−2.22944	+	21.2117i	−0.0988181	+	0.940191i	0.826995	+	0.562209i	$0.190049\pi$
$509$	−2.22944	+	21.2117i	−0.0988181	+	0.940191i	−0.925813	+	0.377982i	$0.876618\pi$
$510$	−0.374949	+	0.272417i	−0.0166030	+	0.0120628i
$511$		0			0
$512$	−2.54091	+	7.82012i	−0.112293	+	0.345604i
$513$	−9.24627	−	4.11670i	−0.408233	−	0.181757i
$514$	−12.0152	+	5.34949i	−0.529966	+	0.235956i
$515$	3.53432	+	0.751243i	0.155741	+	0.0331037i
$516$	2.03036	+	3.51669i	0.0893816	+	0.154814i
$517$	−8.31884	+	18.2436i	−0.365862	+	0.802354i
$518$		0			0
$519$	−1.97900	−	6.09075i	−0.0868686	−	0.267354i
$520$	0.400937	−	3.81466i	0.0175822	−	0.167284i
$521$	−2.31409	−	22.0171i	−0.101382	−	0.964585i	−0.920442	−	0.390878i	$-0.872171\pi$
$521$	−2.31409	−	22.0171i	−0.101382	−	0.964585i	0.819060	−	0.573707i	$-0.194495\pi$
$522$	−5.14018	−	5.70875i	−0.224980	−	0.249865i
$523$	4.80414	−	1.02115i	0.210070	−	0.0446518i	−0.101674	−	0.994818i	$-0.532420\pi$
$523$	4.80414	−	1.02115i	0.210070	−	0.0446518i	0.311745	+	0.950166i	$0.399087\pi$
$524$	−1.54683	+	1.12384i	−0.0675737	+	0.0490952i
$525$		0			0
$526$	1.96537	+	6.04880i	0.0856944	+	0.263740i
$527$	−14.9318	−	25.8627i	−0.650441	−	1.12660i
$528$	−1.44382	+	0.454893i	−0.0628341	+	0.0197967i
$529$	3.90296	−	6.76013i	0.169694	−	0.293919i
$530$	0.198868	−	0.220865i	0.00863828	−	0.00959378i
$531$	20.1913	+	14.6698i	0.876228	+	0.636617i
$532$		0			0
$533$	2.69996	−	8.30962i	0.116948	−	0.359929i
$534$	3.72323	−	0.791396i	0.161120	−	0.0342471i
$535$	0.125445	+	1.19353i	0.00542347	+	0.0516009i
$536$	3.06662	−	1.36535i	0.132458	−	0.0589741i
$537$	9.68086	−	10.7517i	0.417760	−	0.463969i
$538$	−4.85707			−0.209403
$539$		0			0
$540$	−1.07818			−0.0463977
$541$	12.9707	−	14.4055i	0.557656	−	0.619340i	−0.396723	−	0.917938i	$-0.629853\pi$
$541$	12.9707	−	14.4055i	0.557656	−	0.619340i	0.954379	+	0.298599i	$0.0965193\pi$
$542$	5.58758	−	2.48775i	0.240007	−	0.106858i
$543$	0.886089	+	8.43058i	0.0380257	+	0.361791i
$544$	24.8208	−	5.27582i	1.06418	−	0.226199i
$545$	0.371242	−	1.14257i	0.0159023	−	0.0489422i
$546$		0			0
$547$	−11.6904	−	8.49354i	−0.499843	−	0.363158i	0.309114	−	0.951025i	$-0.399968\pi$
$547$	−11.6904	−	8.49354i	−0.499843	−	0.363158i	−0.808957	+	0.587868i	$0.799968\pi$
$548$	−2.33375	+	2.59189i	−0.0996929	+	0.110720i
$549$	12.6051	−	21.8326i	0.537972	−	0.931794i
$550$	−7.59538	+	10.2600i	−0.323868	+	0.437486i
$551$	−5.50060	−	9.52732i	−0.234333	−	0.405877i
$552$	1.96530	+	6.04858i	0.0836489	+	0.257445i
$553$		0			0
$554$	7.57795	−	5.50570i	0.321956	−	0.233915i
$555$	−0.760494	+	0.161648i	−0.0322812	+	0.00686158i
$556$	−4.44724	−	4.93916i	−0.188605	−	0.209467i
$557$	−1.93073	−	18.3696i	−0.0818075	−	0.778347i	−0.956118	−	0.292980i	$-0.905353\pi$
$557$	−1.93073	−	18.3696i	−0.0818075	−	0.778347i	0.874311	−	0.485366i	$-0.161314\pi$
$558$	−1.46587	+	13.9468i	−0.0620551	+	0.590414i
$559$	9.49993	+	29.2378i	0.401804	+	1.23663i
$560$		0			0
$561$	6.54945	+	6.00405i	0.276518	+	0.253491i
$562$	8.22381	+	14.2441i	0.346900	+	0.600849i
$563$	30.6002	+	6.50428i	1.28965	+	0.274123i	0.801160	−	0.598450i	$-0.204216\pi$
$563$	30.6002	+	6.50428i	1.28965	+	0.274123i	0.488485	+	0.872572i	$0.337550\pi$
$564$	−4.76335	+	2.12078i	−0.200573	+	0.0893010i
$565$	−3.35332	−	1.49300i	−0.141075	−	0.0628108i
$566$	−6.00720	+	18.4883i	−0.252502	+	0.777120i
$567$		0			0
$568$	19.8823	−	14.4454i	0.834244	−	0.606114i
$569$	−0.181467	+	1.72654i	−0.00760748	+	0.0723803i	−0.997667	−	0.0682691i	$-0.978252\pi$
$569$	−0.181467	+	1.72654i	−0.00760748	+	0.0723803i	0.990059	+	0.140649i	$0.0449190\pi$
$570$	0.304866	+	0.0648012i	0.0127694	+	0.00271422i
$571$	−6.26546	+	10.8521i	−0.262201	+	0.454146i	−0.966827	−	0.255433i	$-0.917782\pi$
$571$	−6.26546	+	10.8521i	−0.262201	+	0.454146i	0.704625	+	0.709580i	$0.251115\pi$
$572$	−30.0829	+	2.89013i	−1.25783	+	0.120843i
$573$	7.43182			0.310469
$574$		0			0
$575$	−15.6114	−	11.3424i	−0.651042	−	0.473009i
$576$	−7.35316	−	3.27384i	−0.306382	−	0.136410i
$577$	−13.5095	−	15.0038i	−0.562407	−	0.624617i	0.393131	−	0.919482i	$-0.371392\pi$
$577$	−13.5095	−	15.0038i	−0.562407	−	0.624617i	−0.955539	+	0.294866i	$0.904725\pi$
$578$	−0.930642	−	1.03358i	−0.0387096	−	0.0429914i
$579$	−8.96810	−	3.99285i	−0.372701	−	0.165937i
$580$	−0.948101	−	0.688835i	−0.0393677	−	0.0286023i
$581$		0			0
$582$	4.35051			0.180334
$583$	−4.90867	−	2.89285i	−0.203296	−	0.119809i
$584$	7.37752	−	12.7782i	0.305284	−	0.528768i
$585$	−3.72069	−	0.790857i	−0.153832	−	0.0326979i
$586$	0.0369846	−	0.351885i	0.00152782	−	0.0145362i
$587$	−0.00677611	+	0.00492314i	−0.000279680	+	0.000203200i	−0.587925	−	0.808915i	$-0.700055\pi$
$587$	−0.00677611	+	0.00492314i	−0.000279680	+	0.000203200i	0.587645	+	0.809119i	$0.300055\pi$
$588$		0			0
$589$	−6.20604	+	19.1002i	−0.255716	+	0.787012i
$590$	−1.50666	−	0.670806i	−0.0620280	−	0.0276167i
$591$	−6.94660	+	3.09283i	−0.285745	+	0.127222i
$592$	4.08393	+	0.868065i	0.167848	+	0.0356773i
$593$	−0.219649	−	0.380443i	−0.00901989	−	0.0156229i	0.861480	−	0.507791i	$-0.169538\pi$
$593$	−0.219649	−	0.380443i	−0.00901989	−	0.0156229i	−0.870500	+	0.492168i	$0.836204\pi$
$594$	−1.78312	−	8.77397i	−0.0731624	−	0.360001i
$595$		0			0
$596$	3.11779	+	9.59558i	0.127710	+	0.393050i
$597$	−0.985925	+	9.38045i	−0.0403512	+	0.383916i
$598$	2.06846	+	19.6800i	0.0845854	+	0.804777i
$599$	30.2222	+	33.5651i	1.23485	+	1.37143i	0.903877	+	0.427793i	$0.140709\pi$
$599$	30.2222	+	33.5651i	1.23485	+	1.37143i	0.330968	+	0.943642i	$0.392625\pi$
$600$	−7.90064	+	1.67933i	−0.322542	+	0.0685585i
$601$	9.01541	−	6.55008i	0.367746	−	0.267183i	−0.388529	−	0.921436i	$-0.627017\pi$
$601$	9.01541	−	6.55008i	0.367746	−	0.267183i	0.756276	+	0.654253i	$0.227017\pi$
$602$		0			0
$603$	−1.02870	−	3.16603i	−0.0418921	−	0.128931i
$604$	5.67954	+	9.83725i	0.231097	+	0.400272i
$605$	−2.21790	−	1.03538i	−0.0901705	−	0.0420943i
$606$	−4.61535	+	7.99403i	−0.187486	+	0.324735i
$607$	23.8878	−	26.5301i	0.969576	−	1.07682i	−0.0274394	−	0.999623i	$-0.508735\pi$
$607$	23.8878	−	26.5301i	0.969576	−	1.07682i	0.997016	−	0.0772000i	$-0.0245980\pi$
$608$	−13.8057	−	10.0304i	−0.559894	−	0.406787i
$609$		0			0
$610$	−0.514796	+	1.58438i	−0.0208435	+	0.0641496i
$611$	−38.6120	+	8.20723i	−1.56207	+	0.332029i
$612$	−1.65537	−	15.7498i	−0.0669145	−	0.636649i
$613$	15.7111	−	6.99505i	0.634567	−	0.282528i	−0.0641337	−	0.997941i	$-0.520428\pi$
$613$	15.7111	−	6.99505i	0.634567	−	0.282528i	0.698701	+	0.715414i	$0.253762\pi$
$614$	−4.18052	+	4.64294i	−0.168712	+	0.187374i
$615$	0.184020			0.00742040
$616$		0			0
$617$	−16.8852			−0.679774			−0.339887	−	0.940466i	$-0.610389\pi$
$617$	−16.8852			−0.679774			−0.339887	+	0.940466i	$0.610389\pi$
$618$	−5.22102	+	5.79853i	−0.210020	+	0.233251i
$619$	−28.3831	+	12.6370i	−1.14081	+	0.507924i	−0.888115	−	0.459621i	$-0.847985\pi$
$619$	−28.3831	+	12.6370i	−1.14081	+	0.507924i	−0.252700	+	0.967545i	$0.581319\pi$
$620$	0.223627	+	2.12767i	0.00898107	+	0.0854491i
$621$	13.2385	−	2.81393i	0.531242	−	0.112919i
$622$	0.0329066	−	0.101276i	0.00131943	−	0.00406080i
$623$		0			0
$624$	−2.41106	−	1.75174i	−0.0965196	−	0.0701256i
$625$	16.2329	−	18.0285i	0.649318	−	0.721140i
$626$	5.94384	−	10.2950i	0.237564	−	0.411472i
$627$	0.0534253	−	5.97490i	0.00213360	−	0.238615i
$628$	−14.0608	−	24.3541i	−0.561088	−	0.971834i
$629$	−7.57271	−	23.3064i	−0.301944	−	0.929287i
$630$		0			0
$631$	−5.86832	+	4.26359i	−0.233614	+	0.169731i	−0.698434	−	0.715675i	$-0.746119\pi$
$631$	−5.86832	+	4.26359i	−0.233614	+	0.169731i	0.464819	+	0.885406i	$0.346119\pi$
$632$	11.6965	−	2.48617i	0.465262	−	0.0988946i
$633$	−3.69438	−	4.10303i	−0.146839	−	0.163081i
$634$	−2.68128	−	25.5106i	−0.106487	−	1.01316i
$635$	−0.0464552	+	0.441992i	−0.00184352	+	0.0175399i
$636$	−0.457859	−	1.40915i	−0.0181553	−	0.0558763i
$637$		0			0
$638$	4.03757	−	8.85460i	0.159849	−	0.350557i
$639$	−12.1859	−	21.1066i	−0.482066	−	0.834963i
$640$	−2.02806	−	0.431078i	−0.0801662	−	0.0170399i
$641$	−18.9560	+	8.43974i	−0.748716	+	0.333350i	−0.745376	−	0.666645i	$-0.767730\pi$
$641$	−18.9560	+	8.43974i	−0.748716	+	0.333350i	−0.00334027	+	0.999994i	$0.501063\pi$
$642$	−2.36752	−	1.05409i	−0.0934385	−	0.0416015i
$643$	−2.19750	+	6.76322i	−0.0866611	+	0.266715i	−0.984991	−	0.172606i	$-0.944781\pi$
$643$	−2.19750	+	6.76322i	−0.0866611	+	0.266715i	0.898330	+	0.439322i	$0.144781\pi$
$644$		0			0
$645$	−0.523825	+	0.380581i	−0.0206256	+	0.0149854i
$646$	−1.02687	+	9.77003i	−0.0404017	+	0.384397i
$647$	26.9762	+	5.73397i	1.06054	+	0.225426i	0.704981	−	0.709226i	$-0.250956\pi$
$647$	26.9762	+	5.73397i	1.06054	+	0.225426i	0.355564	+	0.934652i	$0.384289\pi$
$648$	−7.53472	+	13.0505i	−0.295992	+	0.512673i
$649$	−6.84991	+	30.8666i	−0.268883	+	1.21162i
$650$	−25.1317			−0.985748
$651$		0			0
$652$	8.39353	+	6.09826i	0.328716	+	0.238826i
$653$	14.7575	+	6.57048i	0.577507	+	0.257123i	0.674638	−	0.738149i	$-0.264300\pi$
$653$	14.7575	+	6.57048i	0.577507	+	0.257123i	−0.0971307	+	0.995272i	$0.530966\pi$
$654$	1.73592	+	1.92793i	0.0678798	+	0.0753881i
$655$	−0.203996	−	0.226561i	−0.00797079	−	0.00885246i
$656$	−0.902770	−	0.401939i	−0.0352472	−	0.0156931i
$657$	−11.8379	−	8.60076i	−0.461842	−	0.335548i
$658$		0			0
$659$	−13.2085			−0.514531			−0.257266	−	0.966341i	$-0.582822\pi$
$659$	−13.2085			−0.514531			−0.257266	+	0.966341i	$0.582822\pi$
$660$	−0.253682	−	0.583772i	−0.00987457	−	0.0227233i
$661$	−2.45330	+	4.24924i	−0.0954223	+	0.165276i	−0.909785	−	0.415080i	$-0.863753\pi$
$661$	−2.45330	+	4.24924i	−0.0954223	+	0.165276i	0.814362	+	0.580357i	$0.197087\pi$
$662$	22.4600	+	4.77403i	0.872934	+	0.185548i
$663$	−1.82844	+	17.3964i	−0.0710106	+	0.675621i
$664$	24.0996	−	17.5094i	0.935245	−	0.679495i
$665$		0			0
$666$	−3.55605	+	10.9444i	−0.137794	+	0.424087i
$667$	13.4390	+	5.98344i	0.520361	+	0.231680i
$668$	−2.81889	+	1.25505i	−0.109066	+	0.0485595i
$669$	−0.432385	−	0.0919064i	−0.0167170	−	0.00355331i
$670$	0.109991	+	0.190509i	0.00424930	+	0.00736001i
$671$	31.7311	+	3.62221i	1.22497	+	0.139834i
$672$		0			0
$673$	−9.26654	−	28.5195i	−0.357199	−	1.09935i	−0.954723	−	0.297495i	$-0.903849\pi$
$673$	−9.26654	−	28.5195i	−0.357199	−	1.09935i	0.597524	−	0.801851i	$-0.296151\pi$
$674$	0.457566	−	4.35345i	0.0176248	−	0.167689i
$675$	1.79671	+	17.0946i	0.0691556	+	0.657972i
$676$	−27.6726	−	30.7336i	−1.06433	−	1.18206i
$677$	12.3138	−	2.61739i	0.473259	−	0.100594i	0.0348934	−	0.999391i	$-0.488891\pi$
$677$	12.3138	−	2.61739i	0.473259	−	0.100594i	0.438366	+	0.898797i	$0.355558\pi$
$678$	6.41278	−	4.65916i	0.246281	−	0.178934i
$679$		0			0
$680$	0.786849	+	2.42167i	0.0301743	+	0.0928668i
$681$	1.64447	+	2.84831i	0.0630163	+	0.109147i
$682$	−16.9445	+	5.33859i	−0.648840	+	0.204425i
$683$	14.2671	−	24.7114i	0.545916	−	0.945554i	−0.452633	−	0.891697i	$-0.649515\pi$
$683$	14.2671	−	24.7114i	0.545916	−	0.945554i	0.998549	−	0.0538567i	$-0.0171514\pi$
$684$	−7.12625	+	7.91451i	−0.272479	+	0.302619i
$685$	−0.449911	−	0.326879i	−0.0171902	−	0.0124894i
$686$		0			0
$687$	−1.26208	+	3.88427i	−0.0481513	+	0.148194i
$688$	3.40106	−	0.722918i	0.129664	−	0.0275610i
$689$	−1.17252	−	11.1558i	−0.0446693	−	0.425000i
$690$	−0.380743	+	0.169518i	−0.0144946	+	0.00645343i
$691$	−16.9787	+	18.8567i	−0.645899	+	0.717344i	−0.973810	−	0.227365i	$-0.926989\pi$
$691$	−16.9787	+	18.8567i	−0.645899	+	0.717344i	0.327910	+	0.944709i	$0.393656\pi$
$692$	−14.4606			−0.549711
$693$		0			0
$694$	−6.78791			−0.257666
$695$	0.709113	−	0.787550i	0.0268982	−	0.0298735i
$696$	5.62524	−	2.50452i	0.213224	−	0.0949334i
$697$	0.606285	+	5.76842i	0.0229647	+	0.218494i
$698$	−14.0440	+	2.98515i	−0.531574	+	0.112990i
$699$	1.82525	−	5.61754i	0.0690373	−	0.212475i
$700$		0			0
$701$	36.9738	+	26.8630i	1.39648	+	1.01460i	0.995119	+	0.0986843i	$0.0314634\pi$
$701$	36.9738	+	26.8630i	1.39648	+	1.01460i	0.401363	+	0.915919i	$0.368537\pi$
$702$	11.7946	−	13.0992i	0.445157	−	0.494397i
$703$	−8.24002	+	14.2721i	−0.310778	+	0.538283i
$704$	0.0911725	−	10.1964i	0.00343619	−	0.384292i
$705$	−0.415698	−	0.720010i	−0.0156561	−	0.0271171i
$706$	−5.64257	−	17.3661i	−0.212361	−	0.653580i
$707$		0			0
$708$	−6.65177	+	4.83279i	−0.249989	+	0.181627i
$709$	−37.6884	+	8.01092i	−1.41542	+	0.300856i	−0.851231	−	0.524791i	$-0.824144\pi$
$709$	−37.6884	+	8.01092i	−1.41542	+	0.300856i	−0.564187	+	0.825647i	$0.690810\pi$
$710$	1.07764	+	1.19684i	0.0404432	+	0.0449168i
$711$	−1.23955	−	11.7935i	−0.0464868	−	0.442292i
$712$	2.18597	−	20.7981i	0.0819225	−	0.779441i
$713$	−8.29874	−	25.5409i	−0.310790	−	0.956515i
$714$		0			0
$715$	−0.959703	−	4.72228i	−0.0358908	−	0.176603i
$716$	−16.3341	−	28.2915i	−0.610435	−	1.05730i
$717$	16.2296	+	3.44970i	0.606104	+	0.128831i
$718$	−10.5696	+	4.70590i	−0.394455	+	0.175623i
$719$	−5.20915	−	2.31926i	−0.194269	−	0.0864939i	0.307297	−	0.951614i	$-0.400576\pi$
$719$	−5.20915	−	2.31926i	−0.194269	−	0.0864939i	−0.501565	+	0.865120i	$0.667242\pi$
$720$	−0.132945	+	0.409164i	−0.00495458	+	0.0152486i
$721$		0			0
$722$	−6.60620	+	4.79969i	−0.245857	+	0.178626i
$723$	−1.21880	+	11.5962i	−0.0453278	+	0.431266i
$724$	18.7228	+	3.97965i	0.695827	+	0.147903i
$725$	−9.34154	+	16.1800i	−0.346936	+	0.600911i
$726$	4.33104	−	3.02985i	0.160740	−	0.112448i
$727$	−11.8221			−0.438458			−0.219229	−	0.975673i	$-0.570354\pi$
$727$	−11.8221			−0.438458			−0.219229	+	0.975673i	$0.570354\pi$
$728$		0			0
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	0.883335	+	0.393286i	0.0326937	+	0.0145562i
$731$	−13.6558	−	15.1663i	−0.505077	−	0.560945i
$732$	5.55724	+	6.17194i	0.205401	+	0.228121i
$733$	−8.05010	−	3.58413i	−0.297337	−	0.132383i	0.252646	−	0.967559i	$-0.418699\pi$
$733$	−8.05010	−	3.58413i	−0.297337	−	0.132383i	−0.549983	+	0.835176i	$0.685366\pi$
$734$	21.5280	+	15.6410i	0.794614	+	0.577321i
$735$		0			0
$736$	22.8190			0.841121
$737$	3.15913	−	2.79375i	0.116368	−	0.102909i
$738$	1.36185	−	2.35879i	0.0501303	−	0.0868283i
$739$	−0.470302	−	0.0999658i	−0.0173003	−	0.00367730i	0.199253	−	0.979948i	$-0.436148\pi$
$739$	−0.470302	−	0.0999658i	−0.0173003	−	0.00367730i	−0.216554	+	0.976271i	$0.569482\pi$
$740$	−0.183506	+	1.74594i	−0.00674580	+	0.0641820i
$741$	9.51683	−	6.91438i	0.349610	−	0.254006i
$742$		0			0
$743$	10.2730	−	31.6172i	0.376881	−	1.15992i	−0.565319	−	0.824872i	$-0.691247\pi$
$743$	10.2730	−	31.6172i	0.376881	−	1.15992i	0.942201	−	0.335049i	$-0.108753\pi$
$744$	−10.2691	−	4.57211i	−0.376484	−	0.167622i
$745$	−1.46967	+	0.654340i	−0.0538446	+	0.0239732i
$746$	2.29471	+	0.487756i	0.0840153	+	0.0178580i
$747$	−14.7706	−	25.5835i	−0.540429	−	0.936051i
$748$	17.4635	−	9.87543i	0.638530	−	0.361082i
$749$		0			0
$750$	−0.328769	−	1.01185i	−0.0120050	−	0.0369475i
$751$	−2.92749	+	27.8532i	−0.106826	+	1.01638i	0.801466	+	0.598040i	$0.204054\pi$
$751$	−2.92749	+	27.8532i	−0.106826	+	1.01638i	−0.908292	+	0.418338i	$0.862613\pi$
$752$	0.466686	+	4.44022i	0.0170183	+	0.161918i
$753$	12.1471	+	13.4908i	0.442666	+	0.491631i
$754$	18.7404	−	3.98340i	0.682486	−	0.145067i
$755$	−1.46530	+	1.06460i	−0.0533276	+	0.0387448i
$756$		0			0
$757$	−6.87465	−	21.1580i	−0.249863	−	0.769001i	−0.994798	−	0.101864i	$-0.967519\pi$
$757$	−6.87465	−	21.1580i	−0.249863	−	0.769001i	0.744935	−	0.667137i	$-0.232481\pi$
$758$	−2.38078	−	4.12363i	−0.0864738	−	0.149777i
$759$	4.63841	+	6.50577i	0.168364	+	0.236144i
$760$	0.856186	−	1.48296i	0.0310571	−	0.0537925i
$761$	32.2691	−	35.8385i	1.16975	−	1.29914i	0.223877	−	0.974618i	$-0.428129\pi$
$761$	32.2691	−	35.8385i	1.16975	−	1.29914i	0.945877	−	0.324525i	$-0.105205\pi$
$762$	−0.776427	−	0.564108i	−0.0281270	−	0.0204355i
$763$		0			0
$764$	5.18562	−	15.9597i	0.187609	−	0.577402i
$765$	2.46997	−	0.525007i	0.0893018	−	0.0189817i
$766$	−0.356852	−	3.39522i	−0.0128936	−	0.122674i
$767$	−56.8649	+	25.3179i	−2.05327	+	0.914176i
$768$	5.53878	−	6.15144i	0.199864	−	0.221971i
$769$	−43.6883			−1.57544			−0.787721	−	0.616032i	$-0.788739\pi$
$769$	−43.6883			−1.57544			−0.787721	+	0.616032i	$0.788739\pi$
$770$		0			0
$771$	−10.4549			−0.376524
$772$	−14.8322	+	16.4728i	−0.533821	+	0.592868i
$773$	0.534944	−	0.238173i	0.0192406	−	0.00856647i	−0.397094	−	0.917778i	$-0.629981\pi$
$773$	0.534944	−	0.238173i	0.0192406	−	0.00856647i	0.416334	+	0.909212i	$0.363315\pi$
$774$	1.00174	+	9.53096i	0.0360069	+	0.342583i
$775$	33.3615	−	7.09120i	1.19838	−	0.254723i
$776$	7.38612	−	22.7321i	0.265146	−	0.816036i
$777$		0			0
$778$	6.60197	+	4.79661i	0.236692	+	0.171967i
$779$	2.61001	−	2.89871i	0.0935133	−	0.103857i
$780$	0.626558	−	1.08523i	0.0224344	−	0.0388575i
$781$	18.3705	−	24.8152i	0.657349	−	0.887958i
$782$	−6.56824	−	11.3765i	−0.234880	−	0.406824i
$783$	−4.04930	−	12.4625i	−0.144710	−	0.445372i
$784$		0			0
$785$	3.62764	−	2.63563i	0.129476	−	0.0940698i
$786$	0.643960	−	0.136878i	0.0229693	−	0.00488227i
$787$	−20.5534	−	22.8269i	−0.732650	−	0.813690i	0.255561	−	0.966793i	$-0.417740\pi$
$787$	−20.5534	−	22.8269i	−0.732650	−	0.813690i	−0.988210	+	0.153103i	$0.951073\pi$
$788$	1.79473	+	17.0757i	0.0639347	+	0.608298i
$789$	−0.528467	+	5.02803i	−0.0188139	+	0.179003i
$790$	0.242153	+	0.745269i	0.00861540	+	0.0265155i
$791$		0			0
$792$	−22.7750	−	2.59984i	−0.809274	−	0.0923811i
$793$	31.4379	+	54.4520i	1.11639	+	1.93365i
$794$	−8.66114	−	1.84098i	−0.307372	−	0.0653340i
$795$	0.215827	−	0.0960922i	0.00765458	−	0.00340804i
$796$	19.4564	+	8.66255i	0.689614	+	0.307036i
$797$	3.34767	−	10.3031i	0.118581	−	0.364953i	−0.874096	−	0.485752i	$-0.838546\pi$
$797$	3.34767	−	10.3031i	0.118581	−	0.364953i	0.992677	+	0.120799i	$0.0385456\pi$
$798$		0			0
$799$	21.2003	−	15.4029i	0.750014	−	0.544917i
$800$	−3.02930	+	28.8219i	−0.107102	+	1.01901i
$801$	−20.2857	−	4.31187i	−0.716761	−	0.152352i
$802$	−1.83679	+	3.18141i	−0.0648593	+	0.112340i
$803$	4.01603	−	18.0967i	0.141722	−	0.638620i
$804$	1.09668			0.0386770
$805$		0			0
$806$	−28.2960	−	20.5582i	−0.996684	−	0.724133i
$807$	−3.52716	−	1.57039i	−0.124162	−	0.0552805i
$808$	33.9344	+	37.6879i	1.19381	+	1.32586i
$809$	−25.8218	−	28.6780i	−0.907846	−	1.00826i	−0.999922	−	0.0125127i	$-0.996017\pi$
$809$	−25.8218	−	28.6780i	−0.907846	−	1.00826i	0.0920761	−	0.995752i	$-0.470650\pi$
$810$	−0.902157	−	0.401666i	−0.0316986	−	0.0141131i
$811$	−41.1737	−	29.9144i	−1.44580	−	1.05044i	−0.986789	−	0.162010i	$-0.948202\pi$
$811$	−41.1737	−	29.9144i	−1.44580	−	1.05044i	−0.459015	−	0.888428i	$-0.651798\pi$
$812$		0			0
$813$	4.86200			0.170518
$814$	−14.5115	+	1.39415i	−0.508627	+	0.0488650i
$815$	−0.827146	+	1.43266i	−0.0289737	+	0.0501839i
$816$	1.93518	+	0.411336i	0.0677450	+	0.0143996i
$817$	−1.43460	+	13.6493i	−0.0501901	+	0.477527i
$818$	−1.55076	+	1.12669i	−0.0542209	+	0.0393938i
$819$		0			0
$820$	0.128402	−	0.395180i	0.00448398	−	0.0138003i
$821$	−36.8245	−	16.3953i	−1.28518	−	0.572201i	−0.353488	−	0.935439i	$-0.615004\pi$
$821$	−36.8245	−	16.3953i	−1.28518	−	0.572201i	−0.931696	+	0.363239i	$0.881671\pi$
$822$	1.09709	−	0.488456i	0.0382654	−	0.0170369i
$823$	−25.1205	−	5.33953i	−0.875647	−	0.186124i	−0.251902	−	0.967753i	$-0.581056\pi$
$823$	−25.1205	−	5.33953i	−0.875647	−	0.186124i	−0.623745	+	0.781628i	$0.714389\pi$
$824$	21.4343	+	37.1252i	0.746698	+	1.29332i
$825$	−8.83296	+	4.99494i	−0.307524	+	0.173902i
$826$		0			0
$827$	−9.87486	−	30.3917i	−0.343382	−	1.05682i	−0.962444	−	0.271480i	$-0.912487\pi$
$827$	−9.87486	−	30.3917i	−0.343382	−	1.05682i	0.619062	−	0.785342i	$-0.287513\pi$
$828$	1.48862	−	14.1632i	0.0517330	−	0.492206i
$829$	5.05920	+	48.1351i	0.175713	+	1.67180i	0.626693	+	0.779266i	$0.284408\pi$
$829$	5.05920	+	48.1351i	0.175713	+	1.67180i	−0.450980	+	0.892534i	$0.648925\pi$
$830$	1.30622	+	1.45071i	0.0453397	+	0.0503548i
$831$	7.28315	−	1.54808i	0.252650	−	0.0537023i
$832$	16.2409	−	11.7997i	0.563050	−	0.409080i
$833$		0			0
$834$	0.707180	+	2.17648i	0.0244876	+	0.0753652i
$835$	−0.246005	−	0.426093i	−0.00851335	−	0.0147456i
$836$	−12.7937	−	4.28377i	−0.442480	−	0.148157i
$837$	−11.9608	+	20.7167i	−0.413425	+	0.716073i
$838$	−7.46015	+	8.28534i	−0.257707	+	0.286212i
$839$	−30.5133	−	22.1692i	−1.05344	−	0.765366i	−0.0805734	−	0.996749i	$-0.525675\pi$
$839$	−30.5133	−	22.1692i	−1.05344	−	0.765366i	−0.972863	+	0.231382i	$0.925675\pi$
$840$		0			0
$841$	−4.56017	+	14.0348i	−0.157247	+	0.483957i
$842$	−13.1685	+	2.79906i	−0.453817	+	0.0964619i
$843$	1.36665	+	13.0028i	0.0470700	+	0.447841i
$844$	−11.3890	+	5.07069i	−0.392024	+	0.174541i
$845$	4.41241	−	4.90048i	0.151791	−	0.168582i
$846$	−12.3056			−0.423074
$847$		0			0
$848$	−1.26869			−0.0435671
$849$	−10.3400	+	11.4838i	−0.354869	+	0.394122i
$850$	15.2412	−	6.78583i	0.522770	−	0.232752i
$851$	−2.30351	−	21.9164i	−0.0789633	−	0.751286i
$852$	7.85352	−	1.66932i	0.269057	−	0.0571898i
$853$	−2.87035	+	8.83403i	−0.0982789	+	0.302471i	−0.988094	−	0.153849i	$-0.950833\pi$
$853$	−2.87035	+	8.83403i	−0.0982789	+	0.302471i	0.889815	+	0.456321i	$0.150833\pi$
$854$		0			0
$855$	−1.37383	−	0.998146i	−0.0469840	−	0.0341359i
$856$	−9.52725	+	10.5811i	−0.325635	+	0.361654i
$857$	−14.8822	+	25.7767i	−0.508365	+	0.880515i	0.491588	+	0.870828i	$0.336417\pi$
$857$	−14.8822	+	25.7767i	−0.508365	+	0.880515i	−0.999953	+	0.00968670i	$0.996917\pi$
$858$	9.86753	+	3.30399i	0.336872	+	0.112796i
$859$	16.6305	+	28.8050i	0.567427	+	0.982812i	0.996819	+	0.0796943i	$0.0253944\pi$
$859$	16.6305	+	28.8050i	0.567427	+	0.982812i	−0.429392	+	0.903118i	$0.641272\pi$
$860$	0.451787	+	1.39046i	0.0154058	+	0.0474142i
$861$		0			0
$862$	17.5442	−	12.7466i	0.597558	−	0.434151i
$863$	18.1619	−	3.86043i	0.618239	−	0.131411i	0.111863	−	0.993724i	$-0.464318\pi$
$863$	18.1619	−	3.86043i	0.618239	−	0.131411i	0.506376	+	0.862313i	$0.330985\pi$
$864$	−13.6009	−	15.1053i	−0.462712	−	0.513894i
$865$	−0.241017	−	2.29312i	−0.00819482	−	0.0779685i
$866$	2.40126	−	22.8465i	0.0815982	−	0.776355i
$867$	−0.341645	−	1.05147i	−0.0116029	−	0.0357100i
$868$		0			0
$869$	13.0768	−	7.39477i	0.443599	−	0.250850i
$870$	0.201760	+	0.349459i	0.00684031	+	0.0118478i
$871$	8.12120	+	1.72621i	0.275176	+	0.0584905i
$872$	13.0209	−	5.79730i	0.440945	−	0.196321i
$873$	−21.6542	−	9.64106i	−0.732883	−	0.326300i
$874$	−2.72992	+	8.40184i	−0.0923411	+	0.284197i
$875$		0			0
$876$	3.89985	−	2.83341i	0.131764	−	0.0957321i
$877$	2.35107	−	22.3689i	0.0793899	−	0.755344i	−0.880326	−	0.474370i	$-0.842676\pi$
$877$	2.35107	−	22.3689i	0.0793899	−	0.755344i	0.959715	−	0.280974i	$-0.0906575\pi$
$878$	25.6025	+	5.44197i	0.864041	+	0.183658i
$879$	0.140630	−	0.243578i	0.00474332	−	0.00821568i
$880$	−0.542522	+	0.0521213i	−0.0182884	+	0.00175701i
$881$	−7.06565			−0.238048			−0.119024	−	0.992891i	$-0.537977\pi$
$881$	−7.06565			−0.238048			−0.119024	+	0.992891i	$0.537977\pi$
$882$		0			0
$883$	16.1304	+	11.7194i	0.542830	+	0.394389i	0.825135	−	0.564936i	$-0.191099\pi$
$883$	16.1304	+	11.7194i	0.542830	+	0.394389i	−0.282305	+	0.959325i	$0.591099\pi$
$884$	36.0827	+	16.0650i	1.21359	+	0.540326i
$885$	−0.877234	−	0.974267i	−0.0294879	−	0.0327496i
$886$	−5.37236	−	5.96661i	−0.180488	−	0.200452i
$887$	−6.35353	−	2.82878i	−0.213331	−	0.0949810i	0.297289	−	0.954787i	$-0.403917\pi$
$887$	−6.35353	−	2.82878i	−0.213331	−	0.0949810i	−0.510620	+	0.859806i	$0.670584\pi$
$888$	−7.46253	−	5.42185i	−0.250426	−	0.181945i
$889$		0			0
$890$	1.37045			0.0459376
$891$	−4.10160	+	18.4823i	−0.137409	+	0.619181i
$892$	−0.499068	+	0.864411i	−0.0167100	+	0.0289426i
$893$	−17.2377	−	3.66398i	−0.576837	−	0.122610i
$894$	0.363135	−	3.45500i	0.0121450	−	0.115552i
$895$	4.21414	−	3.06175i	0.140863	−	0.102343i
$896$		0			0
$897$	−4.86088	+	14.9602i	−0.162300	+	0.499508i
$898$	1.95881	+	0.872120i	0.0653664	+	0.0291030i
$899$	−23.7533	+	10.5756i	−0.792216	+	0.352717i
$900$	17.6914	+	3.76043i	0.589715	+	0.125348i
$901$	3.72325	+	6.44886i	0.124039	+	0.214843i
$902$	3.42822	+	0.391342i	0.114147	+	0.0130303i
$903$		0			0
$904$	−13.4575	−	41.4179i	−0.447590	−	1.37754i
$905$	−0.319026	+	3.03533i	−0.0106048	+	0.100898i
$906$	−0.408833	−	3.88979i	−0.0135826	−	0.129230i
$907$	−15.6845	−	17.4194i	−0.520796	−	0.578402i	0.424165	−	0.905585i	$-0.360568\pi$
$907$	−15.6845	−	17.4194i	−0.520796	−	0.578402i	−0.944961	+	0.327182i	$0.893901\pi$
$908$	7.26413	−	1.54404i	0.241069	−	0.0512407i
$909$	40.6878	−	29.5614i	1.34953	−	0.980490i
$910$		0			0
$911$	14.4650	+	44.5186i	0.479246	+	1.47497i	0.840145	+	0.542362i	$0.182470\pi$
$911$	14.4650	+	44.5186i	0.479246	+	1.47497i	−0.360899	+	0.932605i	$0.617530\pi$
$912$	−0.665238	−	1.15223i	−0.0220282	−	0.0381540i
$913$	22.2671	−	30.0788i	0.736934	−	0.995462i
$914$	−15.6782	+	27.1554i	−0.518588	+	0.898220i
$915$	−0.886103	+	0.984117i	−0.0292937	+	0.0325339i
$916$	7.46078	+	5.42058i	0.246511	+	0.179101i
$917$		0			0
$918$	−3.61594	+	11.1287i	−0.119344	+	0.367302i
$919$	−10.3951	+	2.20954i	−0.342902	+	0.0728861i	−0.376144	−	0.926561i	$-0.622750\pi$
$919$	−10.3951	+	2.20954i	−0.342902	+	0.0728861i	0.0332419	+	0.999447i	$0.489417\pi$
$920$	0.239348	+	2.27725i	0.00789108	+	0.0750786i
$921$	−4.53702	+	2.02001i	−0.149500	+	0.0665616i
$922$	−17.8052	+	19.7747i	−0.586383	+	0.651245i
$923$	60.7848			2.00075
$924$		0			0
$925$	27.9876			0.920228
$926$	−0.367990	+	0.408695i	−0.0120929	+	0.0134305i
$927$	38.8370	−	17.2914i	1.27558	−	0.567923i
$928$	−2.30938	−	21.9723i	−0.0758091	−	0.721275i
$929$	−35.8696	+	7.62432i	−1.17684	+	0.250146i	−0.754506	−	0.656293i	$-0.772124\pi$
$929$	−35.8696	+	7.62432i	−1.17684	+	0.250146i	−0.422337	+	0.906439i	$0.638790\pi$
$930$	0.227635	−	0.700590i	0.00746446	−	0.0229733i
$931$		0			0
$932$	−10.7900	−	7.83938i	−0.353438	−	0.256787i
$933$	0.0566412	−	0.0629064i	0.00185435	−	0.00205946i
$934$	11.1151	−	19.2519i	0.363697	−	0.629941i
$935$	1.85708	+	2.60471i	0.0607330	+	0.0851833i
$936$	−22.5645	−	39.0829i	−0.737544	−	1.27746i
$937$	12.4278	+	38.2490i	0.406000	+	1.24954i	0.920057	+	0.391784i	$0.128142\pi$
$937$	12.4278	+	38.2490i	0.406000	+	1.24954i	−0.514057	+	0.857756i	$0.671858\pi$
$938$		0			0
$939$	7.64497	−	5.55439i	0.249484	−	0.181261i
$940$	−1.83627	+	0.390310i	−0.0598924	+	0.0127305i
$941$	−16.6678	−	18.5115i	−0.543355	−	0.603457i	0.407457	−	0.913224i	$-0.366416\pi$
$941$	−16.6678	−	18.5115i	−0.543355	−	0.603457i	−0.950812	+	0.309767i	$0.899749\pi$
$942$	1.01215	+	9.62995i	0.0329776	+	0.313761i
$943$	−0.545210	+	5.18732i	−0.0177545	+	0.168922i
$944$	2.17555	+	6.69565i	0.0708081	+	0.217925i
$945$		0			0
$946$	−10.5680	+	5.97609i	−0.343595	+	0.194299i
$947$	16.1031	+	27.8913i	0.523279	+	0.906347i	0.999633	+	0.0270927i	$0.00862493\pi$
$947$	16.1031	+	27.8913i	0.523279	+	0.906347i	−0.476353	+	0.879254i	$0.658042\pi$
$948$	3.82126	+	0.812234i	0.124109	+	0.0263801i
$949$	33.3393	−	14.8436i	1.08224	−	0.481843i
$950$	−10.2497	−	4.56344i	−0.332543	−	0.148058i
$951$	6.30101	−	19.3925i	0.204324	−	0.628846i
$952$		0			0
$953$	−36.4552	+	26.4863i	−1.18090	+	0.857975i	−0.992273	−	0.124074i	$-0.960404\pi$
$953$	−36.4552	+	26.4863i	−1.18090	+	0.857975i	−0.188628	+	0.982049i	$0.560404\pi$
$954$	0.365513	−	3.47763i	0.0118339	−	0.112592i
$955$	2.61727	+	0.556317i	0.0846928	+	0.0180020i
$956$	18.7325	−	32.4456i	0.605852	−	1.04937i
$957$	5.79493	−	5.12470i	0.187323	−	0.165658i
$958$	−3.96296			−0.128038
$959$		0			0
$960$	0.342058	+	0.248519i	0.0110399	+	0.00802093i
$961$	15.0428	+	6.69746i	0.485250	+	0.216047i
$962$	−19.2045	−	21.3288i	−0.619179	−	0.687668i
$963$	9.44812	+	10.4932i	0.304461	+	0.338139i
$964$	24.0521	+	10.7087i	0.774666	+	0.344903i
$965$	−2.85941	−	2.07748i	−0.0920476	−	0.0668765i
$966$		0			0
$967$	1.81387			0.0583300			0.0291650	−	0.999575i	$-0.490715\pi$
$967$	1.81387			0.0583300			0.0291650	+	0.999575i	$0.490715\pi$
$968$	−8.47842	−	27.7743i	−0.272507	−	0.892701i
$969$	−3.90456	+	6.76290i	−0.125433	+	0.217256i
$970$	1.53212	+	0.325662i	0.0491934	+	0.0104564i
$971$	2.40979	−	22.9276i	0.0773338	−	0.735782i	−0.885308	−	0.465005i	$-0.846053\pi$
$971$	2.40979	−	22.9276i	0.0773338	−	0.735782i	0.962642	−	0.270777i	$-0.0872808\pi$
$972$	−15.7431	+	11.4380i	−0.504959	+	0.366874i
$973$		0			0
$974$	−7.01266	+	21.5827i	−0.224700	+	0.691555i
$975$	−18.2504	−	8.12562i	−0.584482	−	0.260228i
$976$	6.49659	−	2.89247i	0.207951	−	0.0925857i
$977$	6.93946	+	1.47503i	0.222013	+	0.0471903i	0.317575	−	0.948233i	$-0.397131\pi$
$977$	6.93946	+	1.47503i	0.222013	+	0.0471903i	−0.0955620	+	0.995423i	$0.530465\pi$
$978$	−1.78618	−	3.09376i	−0.0571158	−	0.0989274i
$979$	−5.23244	−	25.7466i	−0.167229	−	0.822863i
$980$		0			0
$981$	−4.36789	−	13.4430i	−0.139456	−	0.429202i
$982$	2.44978	−	23.3081i	0.0781755	−	0.743790i
$983$	4.00869	+	38.1402i	0.127857	+	1.21648i	0.850768	+	0.525541i	$0.176137\pi$
$983$	4.00869	+	38.1402i	0.127857	+	1.21648i	−0.722911	+	0.690941i	$0.757196\pi$
$984$	1.46087	+	1.62246i	0.0465710	+	0.0517223i
$985$	−2.67790	+	0.569206i	−0.0853251	+	0.0181364i
$986$	−10.2896	+	7.47586i	−0.327689	+	0.238080i
$987$		0			0
$988$	−8.20806	−	25.2618i	−0.261133	−	0.803685i
$989$	−9.17619	−	15.8936i	−0.291786	−	0.505388i
$990$	0.0134314	−	1.50213i	0.000426879	−	0.0477407i
$991$	−10.1361	+	17.5562i	−0.321984	+	0.557692i	−0.980897	−	0.194527i	$-0.937683\pi$
$991$	−10.1361	+	17.5562i	−0.321984	+	0.557692i	0.658914	+	0.752219i	$0.271016\pi$
$992$	−26.9876	+	29.9728i	−0.856857	+	0.951636i
$993$	14.7667	+	10.7287i	0.468608	+	0.340464i
$994$		0			0
$995$	−1.04940	+	3.22971i	−0.0332681	+	0.102389i
$996$	9.51933	−	2.02340i	0.301631	−	0.0641137i
$997$	1.61086	+	15.3263i	0.0510164	+	0.485389i	0.989963	+	0.141326i	$0.0451366\pi$
$997$	1.61086	+	15.3263i	0.0510164	+	0.485389i	−0.938947	+	0.344063i	$0.888197\pi$
$998$	−4.22683	+	1.88191i	−0.133798	+	0.0595707i
$999$	−13.1349	+	14.5878i	−0.415569	+	0.461536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.b.214.1		16
7.2	even	3	inner	539.2.q.b.324.2		16
7.3	odd	6		77.2.f.a.71.1	yes	8
7.4	even	3		539.2.f.d.148.1		8
7.5	odd	6		539.2.q.c.324.2		16
7.6	odd	2		539.2.q.c.214.1		16
11.9	even	5	inner	539.2.q.b.361.2		16
21.17	even	6		693.2.m.g.379.2		8
77.3	odd	30		847.2.a.l.1.2		4
77.9	even	15	inner	539.2.q.b.471.1		16
77.10	even	6		847.2.f.q.148.2		8
77.17	even	30		847.2.f.s.323.1		8
77.20	odd	10		539.2.q.c.361.2		16
77.24	even	30		847.2.f.q.372.2		8
77.25	even	15		5929.2.a.bi.1.2		4
77.31	odd	30		77.2.f.a.64.1	✓	8
77.38	odd	30		847.2.f.p.323.2		8
77.52	even	30		847.2.a.k.1.3		4
77.53	even	15		539.2.f.d.295.1		8
77.59	odd	30		847.2.f.p.729.2		8
77.73	even	30		847.2.f.s.729.1		8
77.74	odd	30		5929.2.a.bb.1.3		4
77.75	odd	30		539.2.q.c.471.1		16
231.80	even	30		7623.2.a.ch.1.3		4
231.185	even	30		693.2.m.g.64.2		8
231.206	odd	30		7623.2.a.co.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	77.31	odd	30
77.2.f.a.71.1	yes	8	7.3	odd	6
539.2.f.d.148.1		8	7.4	even	3
539.2.f.d.295.1		8	77.53	even	15
539.2.q.b.214.1		16	1.1	even	1	trivial
539.2.q.b.324.2		16	7.2	even	3	inner
539.2.q.b.361.2		16	11.9	even	5	inner
539.2.q.b.471.1		16	77.9	even	15	inner
539.2.q.c.214.1		16	7.6	odd	2
539.2.q.c.324.2		16	7.5	odd	6
539.2.q.c.361.2		16	77.20	odd	10
539.2.q.c.471.1		16	77.75	odd	30
693.2.m.g.64.2		8	231.185	even	30
693.2.m.g.379.2		8	21.17	even	6
847.2.a.k.1.3		4	77.52	even	30
847.2.a.l.1.2		4	77.3	odd	30
847.2.f.p.323.2		8	77.38	odd	30
847.2.f.p.729.2		8	77.59	odd	30
847.2.f.q.148.2		8	77.10	even	6
847.2.f.q.372.2		8	77.24	even	30
847.2.f.s.323.1		8	77.17	even	30
847.2.f.s.729.1		8	77.73	even	30
5929.2.a.bb.1.3		4	77.74	odd	30
5929.2.a.bi.1.2		4	77.25	even	15
7623.2.a.ch.1.3		4	231.80	even	30
7623.2.a.co.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.520239 + 0.577783i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(0.145871 + 1.38787i) q^{4} +(-0.217653 + 0.0462636i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-1.75181 + 1.94558i) q^{9} +O(q^{10})\)	\(q+(-0.520239 + 0.577783i) q^{2} +(-0.564602 + 0.251377i) q^{3} +(0.145871 + 1.38787i) q^{4} +(-0.217653 + 0.0462636i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-1.75181 + 1.94558i) q^{9} +(0.0865012 - 0.149825i) q^{10} +(-3.14501 - 1.05306i) q^{11} +(-0.431239 - 0.746928i) q^{12} +(-2.01774 - 6.20997i) q^{13} +(0.111258 - 0.0808336i) q^{15} +(-0.722369 + 0.153544i) q^{16} +(2.90042 + 3.22125i) q^{17} +(-0.212766 - 2.02433i) q^{18} +(0.304701 - 2.89904i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} +(1.94898 + 3.37573i) q^{23} +(1.59593 + 0.339226i) q^{24} +(-4.52249 + 2.01354i) q^{25} +(4.63772 + 2.06485i) q^{26} +(1.07295 - 3.30220i) q^{27} +(3.05322 - 2.21829i) q^{29} +(-0.0111763 + 0.106336i) q^{30} +(-6.73903 - 1.43242i) q^{31} +(2.92705 - 5.06980i) q^{32} +(2.04039 - 0.196025i) q^{33} -3.37009 q^{34} +(-2.95576 - 2.14748i) q^{36} +(-5.16474 - 2.29949i) q^{37} +(1.51650 + 1.68424i) q^{38} +(2.70026 + 2.99895i) q^{39} +(0.536647 + 0.238931i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(1.00274 - 4.51848i) q^{44} +(0.291277 - 0.504506i) q^{45} +(-2.96437 - 0.630097i) q^{46} +(0.631931 - 6.01242i) q^{47} +(0.369254 - 0.268279i) q^{48} +(1.18938 - 3.66055i) q^{50} +(-2.44733 - 1.08962i) q^{51} +(8.32432 - 3.70622i) q^{52} +(1.68037 + 0.357175i) q^{53} +(1.34977 + 2.33786i) q^{54} +(0.733239 + 0.0837016i) q^{55} +(0.556717 + 1.71340i) q^{57} +(-0.306709 + 2.91814i) q^{58} +(-0.996474 - 9.48082i) q^{59} +(0.128416 + 0.142621i) q^{60} +(-9.41900 + 2.00207i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} +(0.726463 + 1.25827i) q^{65} +(-0.948230 + 1.28088i) q^{66} +(-0.635774 + 1.10119i) q^{67} +(-4.04759 + 4.49531i) q^{68} +(-1.94898 - 1.41602i) q^{69} +(-2.87670 + 8.85357i) q^{71} +(6.76048 - 1.43698i) q^{72} +(0.584221 + 5.55850i) q^{73} +(4.01551 - 1.78782i) q^{74} +(2.04725 - 2.27370i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-3.03086 + 3.36611i) q^{79} +(0.150123 - 0.0668389i) q^{80} +(-0.596670 - 5.67693i) q^{81} +(-1.01763 + 0.216303i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(2.44939 - 2.72032i) q^{86} +(-1.16623 + 2.01996i) q^{87} +(5.08297 + 7.12929i) q^{88} +(3.96078 + 6.86028i) q^{89} +(0.139962 + 0.430759i) q^{90} +(-4.40079 + 3.19736i) q^{92} +(4.16495 - 0.885287i) q^{93} +(3.14512 + 3.49301i) q^{94} +(0.0678008 + 0.645082i) q^{95} +(-0.378188 + 3.59821i) q^{96} +(2.79781 + 8.61078i) q^{97} +(7.55825 - 4.27411i) 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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