LMFDB - Embedded newform 539.2.q.f.361.1

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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.1
Character	$\chi$	$=$	539.361
Dual form			539.2.q.f.324.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49618 + 0.530579i) q^{2} +(-0.0429192 - 0.408349i) q^{3} +(4.12229 - 1.83536i) q^{4} +(-2.29443 + 2.54823i) q^{5} +(0.323795 + 0.996539i) q^{6} +(-5.18703 + 3.76860i) q^{8} +(2.76954 - 0.588683i) q^{9} +O(q^{10})$	\(q+(-2.49618 + 0.530579i) q^{2} +(-0.0429192 - 0.408349i) q^{3} +(4.12229 - 1.83536i) q^{4} +(-2.29443 + 2.54823i) q^{5} +(0.323795 + 0.996539i) q^{6} +(-5.18703 + 3.76860i) q^{8} +(2.76954 - 0.588683i) q^{9} +(4.37528 - 7.57820i) q^{10} +(2.88705 + 1.63246i) q^{11} +(-0.926394 - 1.60456i) q^{12} +(0.672122 - 2.06858i) q^{13} +(1.13904 + 0.827562i) q^{15} +(4.90943 - 5.45247i) q^{16} +(-4.41844 - 0.939168i) q^{17} +(-6.60091 + 2.93891i) q^{18} +(2.21426 + 0.985853i) q^{19} +(-4.78140 + 14.7156i) q^{20} +(-8.07274 - 2.54311i) q^{22} +(-0.324201 - 0.561533i) q^{23} +(1.76153 + 1.95637i) q^{24} +(-0.706391 - 6.72086i) q^{25} +(-0.580191 + 5.52015i) q^{26} +(-0.739900 - 2.27718i) q^{27} +(1.01366 + 0.736466i) q^{29} +(-3.28233 - 1.46139i) q^{30} +(5.37945 + 5.97449i) q^{31} +(-2.95031 + 5.11008i) q^{32} +(0.542705 - 1.24899i) q^{33} +11.5275 q^{34} +(10.3364 - 7.50983i) q^{36} +(-0.524032 + 4.98583i) q^{37} +(-6.05026 - 1.28602i) q^{38} +(-0.873549 - 0.185679i) q^{39} +(2.29806 - 21.8645i) q^{40} +(-2.12100 + 1.54100i) q^{41} -1.46138 q^{43} +(14.8974 + 1.43071i) q^{44} +(-4.85442 + 8.40810i) q^{45} +(1.10720 + 1.22967i) q^{46} +(4.60462 + 2.05011i) q^{47} +(-2.43722 - 1.77074i) q^{48} +(5.32922 + 16.4017i) q^{50} +(-0.193872 + 1.84457i) q^{51} +(-1.02591 - 9.76087i) q^{52} +(8.96503 + 9.95668i) q^{53} +(3.05514 + 5.29166i) q^{54} +(-10.7840 + 3.61128i) q^{55} +(0.307538 - 0.946503i) q^{57} +(-2.92102 - 1.30052i) q^{58} +(-7.00669 + 3.11958i) q^{59} +(6.21433 + 1.32090i) q^{60} +(-9.59187 + 10.6529i) q^{61} +(-16.5980 - 12.0591i) q^{62} +(0.118654 - 0.365178i) q^{64} +(3.72907 + 6.45893i) q^{65} +(-0.692001 + 3.40564i) q^{66} +(-3.11348 + 5.39271i) q^{67} +(-19.9378 + 4.23791i) q^{68} +(-0.215387 + 0.156488i) q^{69} +(1.30713 + 4.02294i) q^{71} +(-12.1472 + 13.4908i) q^{72} +(5.41291 - 2.40998i) q^{73} +(-1.33730 - 12.7235i) q^{74} +(-2.71414 + 0.576908i) q^{75} +10.9372 q^{76} +2.27905 q^{78} +(-9.54983 + 2.02988i) q^{79} +(2.62978 + 25.0207i) q^{80} +(6.86174 - 3.05504i) q^{81} +(4.47678 - 4.97197i) q^{82} +(2.58881 + 7.96754i) q^{83} +(12.5310 - 9.10432i) q^{85} +(3.64786 - 0.775377i) q^{86} +(0.257230 - 0.445535i) q^{87} +(-21.1273 + 2.41250i) q^{88} +(2.38125 + 4.12444i) q^{89} +(7.65633 - 23.5637i) q^{90} +(-2.36707 - 1.71978i) q^{92} +(2.20879 - 2.45311i) q^{93} +(-12.5817 - 2.67432i) q^{94} +(-7.59265 + 3.38047i) q^{95} +(2.21332 + 0.985434i) q^{96} +(2.69021 - 8.27962i) q^{97} +(8.95679 + 2.82161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9	$ 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) $ 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9 + 12 * q^10 + 3 * q^11 + 18 * q^12 + 14 * q^13 - 36 * q^15 - 17 * q^16 - 5 * q^17 - 11 * q^18 + 19 * q^19 - 2 * q^20 - 66 * q^22 - 32 * q^23 - 35 * q^24 - 7 * q^25 - 27 * q^26 - 20 * q^27 + 6 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 26 * q^33 + 48 * q^34 + 104 * q^36 - 4 * q^37 - 5 * q^38 - 11 * q^39 - 10 * q^40 + 20 * q^41 - 16 * q^43 + 38 * q^44 + 70 * q^45 + 42 * q^46 - 23 * q^47 + 72 * q^48 + 104 * q^50 + 29 * q^51 + 33 * q^52 - 4 * q^53 + 60 * q^54 + 24 * q^55 - 22 * q^57 - 20 * q^58 + 17 * q^59 + 30 * q^60 - 7 * q^61 - 158 * q^62 + 14 * q^64 + 8 * q^65 + 8 * q^66 + 38 * q^67 - 2 * q^68 - 20 * q^69 - 28 * q^71 - 35 * q^73 + 29 * q^74 + 9 * q^75 - 104 * q^76 - 116 * q^78 - 15 * q^79 - 87 * q^80 + 14 * q^81 + 19 * q^82 - 10 * q^83 + 12 * q^85 + 52 * q^86 - 72 * q^87 - 55 * q^88 + 74 * q^89 + 28 * q^90 - 110 * q^92 - 32 * q^93 - 24 * q^94 - 32 * q^95 - 42 * q^96 - 40 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.49618	+	0.530579i	−1.76506	+	0.375176i	−0.972187	−	0.234207i	$-0.924751\pi$
$2$	−2.49618	+	0.530579i	−1.76506	+	0.375176i	−0.792876	+	0.609383i	$0.791417\pi$
$3$	−0.0429192	−	0.408349i	−0.0247794	−	0.235760i	−0.999901	−	0.0140886i	$-0.995515\pi$
$3$	−0.0429192	−	0.408349i	−0.0247794	−	0.235760i	0.975121	−	0.221672i	$-0.0711514\pi$
$4$	4.12229	−	1.83536i	2.06115	−	0.917681i
$5$	−2.29443	+	2.54823i	−1.02610	+	1.13960i	−0.0359855	+	0.999352i	$0.511457\pi$
$5$	−2.29443	+	2.54823i	−1.02610	+	1.13960i	−0.990116	+	0.140249i	$0.955210\pi$
$6$	0.323795	+	0.996539i	0.132189	+	0.406835i
$7$		0			0
$7$		0			0
$8$	−5.18703	+	3.76860i	−1.83389	+	1.33240i
$9$	2.76954	−	0.588683i	0.923179	−	0.196228i
$10$	4.37528	−	7.57820i	1.38358	−	2.39644i
$11$	2.88705	+	1.63246i	0.870479	+	0.492206i
$11$	2.88705	+	1.63246i	0.870479	+	0.492206i
$12$	−0.926394	−	1.60456i	−0.267427	−	0.463197i
$13$	0.672122	−	2.06858i	0.186413	−	0.573720i	−0.813557	−	0.581486i	$-0.802472\pi$
$13$	0.672122	−	2.06858i	0.186413	−	0.573720i	0.999970	+	0.00776501i	$0.00247170\pi$
$14$		0			0
$15$	1.13904	+	0.827562i	0.294099	+	0.213675i
$16$	4.90943	−	5.45247i	1.22736	−	1.36312i
$17$	−4.41844	−	0.939168i	−1.07163	−	0.227782i	−0.361871	−	0.932228i	$-0.617862\pi$
$17$	−4.41844	−	0.939168i	−1.07163	−	0.227782i	−0.709757	+	0.704446i	$0.751195\pi$
$18$	−6.60091	+	2.93891i	−1.55585	+	0.692709i
$19$	2.21426	+	0.985853i	0.507986	+	0.226170i	0.644693	−	0.764441i	$-0.276985\pi$
$19$	2.21426	+	0.985853i	0.507986	+	0.226170i	−0.136707	+	0.990612i	$0.543652\pi$
$20$	−4.78140	+	14.7156i	−1.06915	+	3.29052i
$21$		0			0
$22$	−8.07274	−	2.54311i	−1.72111	−	0.542193i
$23$	−0.324201	−	0.561533i	−0.0676006	−	0.117088i	0.830244	−	0.557400i	$-0.188201\pi$
$23$	−0.324201	−	0.561533i	−0.0676006	−	0.117088i	−0.897845	+	0.440312i	$0.854868\pi$
$24$	1.76153	+	1.95637i	0.359570	+	0.399343i
$25$	−0.706391	−	6.72086i	−0.141278	−	1.34417i
$26$	−0.580191	+	5.52015i	−0.113785	+	1.08259i
$27$	−0.739900	−	2.27718i	−0.142394	−	0.438243i
$28$		0			0
$29$	1.01366	+	0.736466i	0.188232	+	0.136758i	0.677910	−	0.735145i	$-0.262886\pi$
$29$	1.01366	+	0.736466i	0.188232	+	0.136758i	−0.489678	+	0.871903i	$0.662886\pi$
$30$	−3.28233	−	1.46139i	−0.599269	−	0.266812i
$31$	5.37945	+	5.97449i	0.966178	+	1.07305i	0.997293	+	0.0735337i	$0.0234276\pi$
$31$	5.37945	+	5.97449i	0.966178	+	1.07305i	−0.0311146	+	0.999516i	$0.509906\pi$
$32$	−2.95031	+	5.11008i	−0.521545	+	0.903343i
$33$	0.542705	−	1.24899i	0.0944728	−	0.217421i
$34$	11.5275			1.97695
$35$		0			0
$36$	10.3364	−	7.50983i	1.72273	−	1.25164i
$37$	−0.524032	+	4.98583i	−0.0861503	+	0.819665i	0.863077	+	0.505073i	$0.168534\pi$
$37$	−0.524032	+	4.98583i	−0.0861503	+	0.819665i	−0.949227	+	0.314592i	$0.898132\pi$
$38$	−6.05026	−	1.28602i	−0.981482	−	0.208620i
$39$	−0.873549	−	0.185679i	−0.139880	−	0.0297324i
$40$	2.29806	−	21.8645i	0.363354	−	3.45709i
$41$	−2.12100	+	1.54100i	−0.331245	+	0.240664i	−0.740959	−	0.671551i	$-0.765629\pi$
$41$	−2.12100	+	1.54100i	−0.331245	+	0.240664i	0.409714	+	0.912214i	$0.365629\pi$
$42$		0			0
$43$	−1.46138			−0.222858			−0.111429	−	0.993772i	$-0.535543\pi$
$43$	−1.46138			−0.222858			−0.111429	+	0.993772i	$0.535543\pi$
$44$	14.8974	+	1.43071i	2.24587	+	0.215687i
$45$	−4.85442	+	8.40810i	−0.723654	+	1.25341i
$46$	1.10720	+	1.22967i	0.163248	+	0.181305i
$47$	4.60462	+	2.05011i	0.671653	+	0.299039i	0.714084	−	0.700060i	$-0.246843\pi$
$47$	4.60462	+	2.05011i	0.671653	+	0.299039i	−0.0424305	+	0.999099i	$0.513510\pi$
$48$	−2.43722	−	1.77074i	−0.351782	−	0.255585i
$49$		0			0
$50$	5.32922	+	16.4017i	0.753666	+	2.31954i
$51$	−0.193872	+	1.84457i	−0.0271476	+	0.258292i
$52$	−1.02591	−	9.76087i	−0.142268	−	1.35359i
$53$	8.96503	+	9.95668i	1.23144	+	1.36765i	0.906658	+	0.421866i	$0.138625\pi$
$53$	8.96503	+	9.95668i	1.23144	+	1.36765i	0.324784	+	0.945788i	$0.394708\pi$
$54$	3.05514	+	5.29166i	0.415752	+	0.720104i
$55$	−10.7840	+	3.61128i	−1.45412	+	0.486945i
$56$		0			0
$57$	0.307538	−	0.946503i	0.0407343	−	0.125367i
$58$	−2.92102	−	1.30052i	−0.383549	−	0.170767i
$59$	−7.00669	+	3.11958i	−0.912194	+	0.406135i	−0.808515	−	0.588476i	$-0.799728\pi$
$59$	−7.00669	+	3.11958i	−0.912194	+	0.406135i	−0.103679	+	0.994611i	$0.533061\pi$
$60$	6.21433	+	1.32090i	0.802267	+	0.170527i
$61$	−9.59187	+	10.6529i	−1.22811	+	1.36396i	−0.318813	+	0.947818i	$0.603284\pi$
$61$	−9.59187	+	10.6529i	−1.22811	+	1.36396i	−0.909300	+	0.416140i	$0.863383\pi$
$62$	−16.5980	−	12.0591i	−2.10795	−	1.53151i
$63$		0			0
$64$	0.118654	−	0.365178i	0.0148317	−	0.0456473i
$65$	3.72907	+	6.45893i	0.462534	+	0.801132i
$66$	−0.692001	+	3.40564i	−0.0851794	+	0.419206i
$67$	−3.11348	+	5.39271i	−0.380372	+	0.658824i	−0.991115	−	0.133005i	$-0.957537\pi$
$67$	−3.11348	+	5.39271i	−0.380372	+	0.658824i	0.610743	+	0.791829i	$0.290871\pi$
$68$	−19.9378	+	4.23791i	−2.41781	+	0.513922i
$69$	−0.215387	+	0.156488i	−0.0259295	+	0.0188389i
$70$		0			0
$71$	1.30713	+	4.02294i	0.155128	+	0.477435i	0.998174	−	0.0604069i	$-0.0192398\pi$
$71$	1.30713	+	4.02294i	0.155128	+	0.477435i	−0.843046	+	0.537842i	$0.819240\pi$
$72$	−12.1472	+	13.4908i	−1.43156	+	1.58991i
$73$	5.41291	−	2.40998i	0.633533	−	0.282067i	−0.0647359	−	0.997902i	$-0.520620\pi$
$73$	5.41291	−	2.40998i	0.633533	−	0.282067i	0.698269	+	0.715835i	$0.253954\pi$
$74$	−1.33730	−	12.7235i	−0.155458	−	1.47908i
$75$	−2.71414	+	0.576908i	−0.313402	+	0.0666156i
$76$	10.9372			1.25459
$77$		0			0
$78$	2.27905			0.258051
$79$	−9.54983	+	2.02988i	−1.07444	+	0.228379i	−0.710967	−	0.703225i	$-0.751743\pi$
$79$	−9.54983	+	2.02988i	−1.07444	+	0.228379i	−0.363473	+	0.931605i	$0.618409\pi$
$80$	2.62978	+	25.0207i	0.294018	+	2.79740i
$81$	6.86174	−	3.05504i	0.762415	−	0.339449i
$82$	4.47678	−	4.97197i	0.494377	−	0.549062i
$83$	2.58881	+	7.96754i	0.284159	+	0.874551i	0.986650	+	0.162858i	$0.0520712\pi$
$83$	2.58881	+	7.96754i	0.284159	+	0.874551i	−0.702491	+	0.711693i	$0.747929\pi$
$84$		0			0
$85$	12.5310	−	9.10432i	1.35918	−	0.987503i
$86$	3.64786	−	0.775377i	0.393359	−	0.0836111i
$87$	0.257230	−	0.445535i	0.0275779	−	0.0477664i
$88$	−21.1273	+	2.41250i	−2.25218	+	0.257173i
$89$	2.38125	+	4.12444i	0.252412	+	0.437190i	0.964189	−	0.265215i	$-0.0854430\pi$
$89$	2.38125	+	4.12444i	0.252412	+	0.437190i	−0.711778	+	0.702405i	$0.752110\pi$
$90$	7.65633	−	23.5637i	0.807048	−	2.48384i
$91$		0			0
$92$	−2.36707	−	1.71978i	−0.246784	−	0.179299i
$93$	2.20879	−	2.45311i	0.229041	−	0.254376i
$94$	−12.5817	−	2.67432i	−1.29770	−	0.275835i
$95$	−7.59265	+	3.38047i	−0.778990	+	0.346828i
$96$	2.21332	+	0.985434i	0.225896	+	0.100575i
$97$	2.69021	−	8.27962i	0.273150	−	0.840668i	−0.716554	−	0.697532i	$-0.754281\pi$
$97$	2.69021	−	8.27962i	0.273150	−	0.840668i	0.989703	−	0.143136i	$-0.0457185\pi$
$98$		0			0
$99$	8.95679	+	2.82161i	0.900192	+	0.283582i
$100$	−15.2472	−	26.4089i	−1.52472	−	2.64089i
$101$	3.86398	+	4.29138i	0.384480	+	0.427008i	0.904055	−	0.427417i	$-0.140576\pi$
$101$	3.86398	+	4.29138i	0.384480	+	0.427008i	−0.519575	+	0.854425i	$0.673910\pi$
$102$	−0.494751	−	4.70724i	−0.0489877	−	0.466087i
$103$	−0.485115	+	4.61556i	−0.0477998	+	0.454784i	0.944277	+	0.329152i	$0.106763\pi$
$103$	−0.485115	+	4.61556i	−0.0477998	+	0.454784i	−0.992077	+	0.125633i	$0.959904\pi$
$104$	4.30933	+	13.2627i	0.422564	+	1.30052i
$105$		0			0
$106$	−27.6611	−	20.0970i	−2.68668	−	1.95199i
$107$	−3.67430	−	1.63590i	−0.355208	−	0.158149i	0.221372	−	0.975189i	$-0.428946\pi$
$107$	−3.67430	−	1.63590i	−0.355208	−	0.158149i	−0.576580	+	0.817041i	$0.695613\pi$
$108$	−7.22953	−	8.02921i	−0.695662	−	0.772611i
$109$	3.07381	−	5.32400i	0.294418	−	0.509946i	−0.680432	−	0.732812i	$-0.738208\pi$
$109$	3.07381	−	5.32400i	0.294418	−	0.509946i	0.974849	+	0.222865i	$0.0715410\pi$
$110$	25.0028	−	14.7362i	2.38392	−	1.40504i
$111$	2.05845			0.195379
$112$		0			0
$113$	2.00504	−	1.45675i	0.188618	−	0.137039i	−0.489469	−	0.872021i	$-0.662809\pi$
$113$	2.00504	−	1.45675i	0.188618	−	0.137039i	0.678087	+	0.734982i	$0.262809\pi$
$114$	−0.265474	+	2.52581i	−0.0248639	+	0.236564i
$115$	2.17477	+	0.462262i	0.202799	+	0.0431062i
$116$	5.53028	+	1.17550i	0.513474	+	0.109142i
$117$	0.643729	−	6.12467i	0.0595127	−	0.566226i
$118$	15.8348	−	11.5046i	1.45771	−	1.05909i
$119$		0			0
$120$	−9.02699			−0.824048
$121$	5.67012	+	9.42601i	0.515466	+	0.856910i
$122$	18.2908	−	31.6806i	1.65597	−	2.86823i
$123$	0.720297	+	0.799971i	0.0649470	+	0.0721310i
$124$	33.1410	+	14.7553i	2.97615	+	1.32507i
$125$	4.87654	+	3.54301i	0.436171	+	0.316897i
$126$		0			0
$127$	−2.14890	−	6.61362i	−0.190684	−	0.586864i	0.809316	−	0.587373i	$-0.199838\pi$
$127$	−2.14890	−	6.61362i	−0.190684	−	0.586864i	−1.00000		0.000509338i	$0.999838\pi$
$128$	1.13114	−	10.7621i	0.0999795	−	0.951241i
$129$	0.0627213	+	0.596753i	0.00552230	+	0.0525412i
$130$	−12.7354	−	14.1441i	−1.11697	−	1.24052i
$131$	−10.4694	−	18.1335i	−0.914715	−	1.58433i	−0.807319	−	0.590116i	$-0.799082\pi$
$131$	−10.4694	−	18.1335i	−0.914715	−	1.58433i	−0.107396	−	0.994216i	$-0.534251\pi$
$132$	−0.0551580	−	6.14475i	−0.00480089	−	0.534832i
$133$		0			0
$134$	4.91054	−	15.1131i	0.424206	−	1.30557i
$135$	7.50041	+	3.33940i	0.645533	+	0.287410i
$136$	26.4579	−	11.7798i	2.26875	−	1.01011i
$137$	−8.93679	−	1.89957i	−0.763521	−	0.162291i	−0.190338	−	0.981719i	$-0.560958\pi$
$137$	−8.93679	−	1.89957i	−0.763521	−	0.162291i	−0.573183	+	0.819427i	$0.694292\pi$
$138$	0.454615	−	0.504901i	0.0386994	−	0.0429800i
$139$	8.69844	+	6.31979i	0.737792	+	0.536037i	0.892019	−	0.451998i	$-0.149289\pi$
$139$	8.69844	+	6.31979i	0.737792	+	0.536037i	−0.154227	+	0.988035i	$0.549289\pi$
$140$		0			0
$141$	0.639534	−	1.96828i	0.0538585	−	0.165759i
$142$	−5.39731	−	9.34842i	−0.452933	−	0.784502i
$143$	5.31733	−	4.87488i	0.444657	−	0.407658i
$144$	10.3871	−	17.9909i	0.865588	−	1.49924i
$145$	−4.20246	+	0.893259i	−0.348995	+	0.0741812i
$146$	−12.2329	+	8.88772i	−1.01240	+	0.735553i
$147$		0			0
$148$	6.99059	+	21.5148i	0.574623	+	1.76851i
$149$	7.19678	−	7.99284i	0.589583	−	0.654799i	−0.372347	−	0.928094i	$-0.621447\pi$
$149$	7.19678	−	7.99284i	0.589583	−	0.654799i	0.961930	+	0.273295i	$0.0881135\pi$
$150$	6.46887	−	2.88013i	0.528181	−	0.235161i
$151$	0.801129	+	7.62224i	0.0651950	+	0.620289i	0.977523	+	0.210829i	$0.0676162\pi$
$151$	0.801129	+	7.62224i	0.0651950	+	0.620289i	−0.912328	+	0.409460i	$0.865717\pi$
$152$	−15.2007	+	3.23102i	−1.23294	+	0.262070i
$153$	−12.7899			−1.03400
$154$		0			0
$155$	−27.5671			−2.21425
$156$	−3.94181	+	0.837858i	−0.315597	+	0.0670823i
$157$	1.91800	+	18.2485i	0.153073	+	1.45639i	0.753889	+	0.657002i	$0.228176\pi$
$157$	1.91800	+	18.2485i	0.153073	+	1.45639i	−0.600816	+	0.799387i	$0.705158\pi$
$158$	22.7611	−	10.1339i	1.81077	−	0.806208i
$159$	3.68103	−	4.08819i	0.291924	−	0.324215i
$160$	−6.25236	−	19.2428i	−0.494292	−	1.52128i
$161$		0			0
$162$	−15.5072	+	11.2666i	−1.21836	+	0.885189i
$163$	−0.369334	+	0.0785043i	−0.0289285	+	0.00614893i	−0.222353	−	0.974966i	$-0.571374\pi$
$163$	−0.369334	+	0.0785043i	−0.0289285	+	0.00614893i	0.193425	+	0.981115i	$0.438040\pi$
$164$	−5.91510	+	10.2453i	−0.461892	+	0.800020i
$165$	1.93750	+	4.24865i	0.150834	+	0.330757i
$166$	−10.6895	−	18.5148i	−0.829668	−	1.43703i
$167$	0.0352708	−	0.108552i	0.00272934	−	0.00840003i	−0.949683	−	0.313214i	$-0.898594\pi$
$167$	0.0352708	−	0.108552i	0.00272934	−	0.00840003i	0.952412	+	0.304814i	$0.0985943\pi$
$168$		0			0
$169$	6.68995	+	4.86053i	0.514612	+	0.373887i
$170$	−26.4491	+	29.3747i	−2.02855	+	2.25294i
$171$	6.71283	+	1.42686i	0.513343	+	0.109114i
$172$	−6.02424	+	2.68216i	−0.459344	+	0.204513i
$173$	12.1511	+	5.41001i	0.923830	+	0.411316i	0.812828	−	0.582504i	$-0.197927\pi$
$173$	12.1511	+	5.41001i	0.923830	+	0.411316i	0.111003	+	0.993820i	$0.464594\pi$
$174$	−0.405700	+	1.24861i	−0.0307560	+	0.0946572i
$175$		0			0
$176$	23.0747	−	7.72710i	1.73932	−	0.582452i
$177$	1.57460	+	2.72729i	0.118354	+	0.204995i
$178$	−8.13235	−	9.03189i	−0.609546	−	0.676969i
$179$	−1.18546	−	11.2789i	−0.0886051	−	0.843021i	−0.945081	−	0.326835i	$-0.894018\pi$
$179$	−1.18546	−	11.2789i	−0.0886051	−	0.843021i	0.856476	−	0.516186i	$-0.172649\pi$
$180$	−4.57942	+	43.5703i	−0.341330	+	3.24753i
$181$	−3.63307	−	11.1814i	−0.270044	−	0.831109i	−0.990488	−	0.137597i	$-0.956062\pi$
$181$	−3.63307	−	11.1814i	−0.270044	−	0.831109i	0.720445	−	0.693512i	$-0.243938\pi$
$182$		0			0
$183$	4.76176	+	3.45962i	0.351999	+	0.255742i
$184$	3.79784	+	1.69091i	0.279980	+	0.124655i
$185$	−11.5027	−	12.7750i	−0.845693	−	0.939237i
$186$	−4.21197	+	7.29534i	−0.308836	+	0.534920i
$187$	−11.2231	−	9.92437i	−0.820714	−	0.725742i
$188$	22.7443			1.65880
$189$		0			0
$190$	17.1590	−	12.4667i	1.24484	−	0.904432i
$191$	2.35548	−	22.4109i	0.170437	−	1.62160i	−0.490697	−	0.871330i	$-0.663258\pi$
$191$	2.35548	−	22.4109i	0.170437	−	1.62160i	0.661134	−	0.750268i	$-0.270076\pi$
$192$	−0.154213	−	0.0327789i	−0.0111293	−	0.00236561i
$193$	−3.36799	−	0.715888i	−0.242433	−	0.0515307i	0.0850925	−	0.996373i	$-0.472881\pi$
$193$	−3.36799	−	0.715888i	−0.242433	−	0.0515307i	−0.327526	+	0.944842i	$0.606215\pi$
$194$	−2.32225	+	22.0948i	−0.166728	+	1.58631i
$195$	2.47745	−	1.79997i	0.177414	−	0.128899i
$196$		0			0
$197$	−2.18213			−0.155470			−0.0777352	−	0.996974i	$-0.524769\pi$
$197$	−2.18213			−0.155470			−0.0777352	+	0.996974i	$0.524769\pi$
$198$	−23.8548	−	2.29095i	−1.69529	−	0.162811i
$199$	1.16717	−	2.02160i	0.0827386	−	0.143307i	−0.821687	−	0.569939i	$-0.806967\pi$
$199$	1.16717	−	2.02160i	0.0827386	−	0.143307i	0.904425	+	0.426632i	$0.140300\pi$
$200$	28.9923	+	32.1992i	2.05007	+	2.27683i
$201$	2.33573	+	1.03994i	0.164750	+	0.0733514i
$202$	−11.9221	−	8.66190i	−0.838835	−	0.609449i
$203$		0			0
$204$	2.58626	+	7.95969i	0.181075	+	0.557290i
$205$	0.939686	−	8.94052i	0.0656305	−	0.624433i
$206$	−1.23798	−	11.7786i	−0.0862545	−	0.820656i
$207$	−1.22845	−	1.36433i	−0.0853833	−	0.0948278i
$208$	−7.97913	−	13.8203i	−0.553253	−	0.958263i
$209$	4.78332	+	6.46091i	0.330869	+	0.446910i
$210$		0			0
$211$	−4.22360	+	12.9989i	−0.290765	+	0.894882i	0.693846	+	0.720123i	$0.255915\pi$
$211$	−4.22360	+	12.9989i	−0.290765	+	0.894882i	−0.984611	+	0.174759i	$0.944085\pi$
$212$	55.2306	+	24.5902i	3.79325	+	1.68886i
$213$	1.58666	−	0.706427i	0.108716	−	0.0484036i
$214$	10.0397	+	2.13400i	0.686298	+	0.145877i
$215$	3.35304	−	3.72393i	0.228675	−	0.253970i
$216$	12.4197	+	9.02341i	0.845051	+	0.613965i
$217$		0			0
$218$	−4.84798	+	14.9205i	−0.328346	+	1.01055i
$219$	−1.21643	−	2.10692i	−0.0821989	−	0.142373i
$220$	−37.8269	+	34.6794i	−2.55029	+	2.33808i
$221$	−4.91247	+	8.50865i	−0.330449	+	0.572354i
$222$	−5.13825	+	1.09217i	−0.344857	+	0.0733016i
$223$	−4.34333	+	3.15561i	−0.290851	+	0.211315i	−0.723636	−	0.690181i	$-0.757531\pi$
$223$	−4.34333	+	3.15561i	−0.290851	+	0.211315i	0.432786	+	0.901497i	$0.357531\pi$
$224$		0			0
$225$	−5.91283	−	18.1978i	−0.394189	−	1.21319i
$226$	−4.23202	+	4.70013i	−0.281510	+	0.312648i
$227$	−9.69544	+	4.31669i	−0.643509	+	0.286509i	−0.702429	−	0.711754i	$-0.747901\pi$
$227$	−9.69544	+	4.31669i	−0.643509	+	0.286509i	0.0589200	+	0.998263i	$0.481234\pi$
$228$	−0.469417	−	4.46621i	−0.0310879	−	0.295782i
$229$	22.1462	−	4.70732i	1.46346	−	0.311069i	0.593759	−	0.804643i	$-0.297643\pi$
$229$	22.1462	−	4.70732i	1.46346	−	0.311069i	0.869704	+	0.493574i	$0.164310\pi$
$230$	−5.67388			−0.374125
$231$		0			0
$232$	−8.03333			−0.527414
$233$	−14.4997	+	3.08201i	−0.949907	+	0.201909i	−0.656710	−	0.754143i	$-0.728052\pi$
$233$	−14.4997	+	3.08201i	−0.949907	+	0.201909i	−0.293197	+	0.956052i	$0.594719\pi$
$234$	1.64276	+	15.6298i	0.107390	+	1.02175i
$235$	−15.7891	+	7.02978i	−1.02997	+	0.458572i
$236$	−23.1581	+	25.7196i	−1.50746	+	1.67421i
$237$	1.23877	+	3.81254i	0.0804668	+	0.247651i
$238$		0			0
$239$	−1.58511	+	1.15165i	−0.102532	+	0.0744938i	−0.637870	−	0.770144i	$-0.720184\pi$
$239$	−1.58511	+	1.15165i	−0.102532	+	0.0744938i	0.535338	+	0.844638i	$0.320184\pi$
$240$	10.1043	−	2.14773i	0.652229	−	0.138636i
$241$	0.395126	−	0.684379i	0.0254523	−	0.0440847i	−0.853019	−	0.521880i	$-0.825231\pi$
$241$	0.395126	−	0.684379i	0.0254523	−	0.0440847i	0.878471	+	0.477796i	$0.158564\pi$
$242$	−19.1549	−	20.5205i	−1.23132	−	1.31911i
$243$	−5.13357	−	8.89161i	−0.329319	−	0.570397i
$244$	−19.9886	+	61.5187i	−1.27964	+	3.93833i
$245$		0			0
$246$	−2.22244	−	1.61469i	−0.141697	−	0.102949i
$247$	3.52757	−	3.91776i	0.224454	−	0.249281i
$248$	−50.4188	−	10.7169i	−3.20160	−	0.680521i
$249$	3.14243	−	1.39910i	0.199143	−	0.0886642i
$250$	−14.0525	−	6.25660i	−0.888761	−	0.395702i
$251$	6.37051	−	19.6064i	0.402103	−	1.23755i	−0.521187	−	0.853442i	$-0.674511\pi$
$251$	6.37051	−	19.6064i	0.402103	−	1.23755i	0.923290	−	0.384103i	$-0.125489\pi$
$252$		0			0
$253$	−0.0193031	−	2.15042i	−0.00121358	−	0.135196i
$254$	8.87307	+	15.3686i	0.556746	+	0.964312i
$255$	−4.25556	−	4.72628i	−0.266494	−	0.295971i
$256$	2.96687	+	28.2279i	0.185430	+	1.76424i
$257$	0.541416	−	5.15123i	0.0337726	−	0.321325i	−0.964572	−	0.263818i	$-0.915018\pi$
$257$	0.541416	−	5.15123i	0.0337726	−	0.321325i	0.998345	−	0.0575071i	$-0.0183152\pi$
$258$	−0.473188	−	1.45632i	−0.0294594	−	0.0906667i
$259$		0			0
$260$	27.2268	+	19.7814i	1.68853	+	1.22679i
$261$	3.24091	+	1.44295i	0.200607	+	0.0893161i
$262$	35.7547	+	39.7096i	2.20893	+	2.45327i
$263$	−11.5960	+	20.0849i	−0.715041	+	1.23849i	0.247903	+	0.968785i	$0.420258\pi$
$263$	−11.5960	+	20.0849i	−0.715041	+	1.23849i	−0.962944	+	0.269702i	$0.913075\pi$
$264$	1.89191	+	8.52378i	0.116439	+	0.524602i
$265$	−45.9415			−2.82217
$266$		0			0
$267$	1.58201	−	1.14940i	0.0968174	−	0.0703420i
$268$	−2.93710	+	27.9447i	−0.179412	+	1.70699i
$269$	18.2522	+	3.87963i	1.11286	+	0.236545i	0.727422	−	0.686190i	$-0.240718\pi$
$269$	18.2522	+	3.87963i	1.11286	+	0.236545i	0.385435	+	0.922735i	$0.374051\pi$
$270$	−20.4942	−	4.35617i	−1.24724	−	0.265108i
$271$	3.15977	−	30.0632i	0.191942	−	1.82621i	−0.298130	−	0.954525i	$-0.596363\pi$
$271$	3.15977	−	30.0632i	0.191942	−	1.82621i	0.490072	−	0.871682i	$-0.336970\pi$
$272$	−26.8128	+	19.4806i	−1.62576	+	1.18119i
$273$		0			0
$274$	23.3157			1.40855
$275$	8.93218	−	20.5566i	0.538630	−	1.23961i
$276$	−0.600676	+	1.04040i	−0.0361565	+	0.0626248i
$277$	9.02796	+	10.0266i	0.542437	+	0.602438i	0.950580	−	0.310481i	$-0.100490\pi$
$277$	9.02796	+	10.0266i	0.542437	+	0.602438i	−0.408142	+	0.912918i	$0.633823\pi$
$278$	−25.0660	−	11.1601i	−1.50336	−	0.669338i
$279$	18.4157	+	13.3798i	1.10252	+	0.801025i
$280$		0			0
$281$	2.50388	+	7.70614i	0.149369	+	0.459710i	0.997547	−	0.0700014i	$-0.0223004\pi$
$281$	2.50388	+	7.70614i	0.149369	+	0.459710i	−0.848178	+	0.529711i	$0.822300\pi$
$282$	−0.552060	+	5.25250i	−0.0328747	+	0.312782i
$283$	1.04436	+	9.93644i	0.0620809	+	0.590660i	0.980700	+	0.195517i	$0.0626384\pi$
$283$	1.04436	+	9.93644i	0.0620809	+	0.590660i	−0.918619	+	0.395143i	$0.870695\pi$
$284$	12.7719	+	14.1847i	0.757874	+	0.841705i
$285$	1.70628	+	2.95536i	0.101071	+	0.175061i
$286$	−10.6865	+	14.9898i	−0.631905	+	0.886366i
$287$		0			0
$288$	−5.16276	+	15.8893i	−0.304219	+	0.936288i
$289$	3.11029	+	1.38479i	0.182958	+	0.0814583i
$290$	10.0161	−	4.45947i	0.588167	−	0.261869i
$291$	−3.49643	−	0.743190i	−0.204965	−	0.0435666i
$292$	17.8904	−	19.8693i	1.04696	−	1.16276i
$293$	24.8608	+	18.0624i	1.45238	+	1.05522i	0.985267	+	0.171022i	$0.0547069\pi$
$293$	24.8608	+	18.0624i	1.45238	+	1.05522i	0.467116	+	0.884196i	$0.345293\pi$
$294$		0			0
$295$	8.12699	−	25.0123i	0.473172	−	1.45627i
$296$	−16.0714	−	27.8365i	−0.934133	−	1.61797i
$297$	1.58128	−	7.78219i	0.0917553	−	0.451568i
$298$	−13.7236	+	23.7700i	−0.794987	+	1.37696i
$299$	−1.37948	+	0.293217i	−0.0797773	+	0.0169572i
$300$	−10.1296	+	7.35961i	−0.584835	+	0.424907i
$301$		0			0
$302$	−6.04396	−	18.6014i	−0.347791	−	1.07039i
$303$	1.58654	−	1.76203i	0.0911444	−	0.101226i
$304$	16.2461	−	7.23322i	0.931777	−	0.414854i
$305$	−5.13797	−	48.8845i	−0.294199	−	2.79912i
$306$	31.9258	−	6.78605i	1.82508	−	0.387932i
$307$	20.0677			1.14532			0.572661	−	0.819792i	$-0.305911\pi$
$307$	20.0677			1.14532			0.572661	+	0.819792i	$0.305911\pi$
$308$		0			0
$309$	1.90558			0.108405
$310$	68.8124	−	14.6265i	3.90828	−	0.830731i
$311$	−2.45289	−	23.3377i	−0.139090	−	1.32336i	−0.812011	−	0.583643i	$-0.801627\pi$
$311$	−2.45289	−	23.3377i	−0.139090	−	1.32336i	0.672920	−	0.739715i	$-0.265040\pi$
$312$	5.23087	−	2.32894i	0.296140	−	0.131850i
$313$	9.81815	−	10.9042i	0.554954	−	0.616339i	−0.398759	−	0.917056i	$-0.630559\pi$
$313$	9.81815	−	10.9042i	0.554954	−	0.616339i	0.953714	+	0.300716i	$0.0972258\pi$
$314$	−14.4699	−	44.5338i	−0.816585	−	2.51319i
$315$		0			0
$316$	−35.6416	+	25.8952i	−2.00500	+	1.45672i
$317$	−17.6565	+	3.75300i	−0.991686	+	0.210789i	−0.675062	−	0.737761i	$-0.735883\pi$
$317$	−17.6565	+	3.75300i	−0.991686	+	0.210789i	−0.316625	+	0.948551i	$0.602550\pi$
$318$	−7.01938	+	12.1579i	−0.393627	+	0.681783i
$319$	1.72423	+	3.78098i	0.0965384	+	0.211694i
$320$	0.658314	+	1.14023i	0.0368009	+	0.0637410i
$321$	−0.510322	+	1.57061i	−0.0284834	+	0.0876628i
$322$		0			0
$323$	−8.85770	−	6.43549i	−0.492855	−	0.358080i
$324$	22.6790	−	25.1875i	1.25994	−	1.39931i
$325$	−14.3774	−	3.05601i	−0.797515	−	0.169517i
$326$	0.880269	−	0.391921i	0.0487536	−	0.0217065i
$327$	−2.30597	−	1.02669i	−0.127521	−	0.0567759i
$328$	5.19431	−	15.9864i	0.286808	−	0.882703i
$329$		0			0
$330$	−7.09060	−	9.57739i	−0.390325	−	0.527218i
$331$	9.91502	+	17.1733i	0.544979	+	0.943931i	0.998608	+	0.0527404i	$0.0167956\pi$
$331$	9.91502	+	17.1733i	0.544979	+	0.943931i	−0.453630	+	0.891190i	$0.649871\pi$
$332$	25.2951	+	28.0931i	1.38825	+	1.54181i
$333$	1.48375	+	14.1169i	0.0813089	+	0.773603i
$334$	−0.0304466	+	0.289680i	−0.00166596	+	0.0158506i
$335$	−6.59816	−	20.3071i	−0.360496	−	1.10949i
$336$		0			0
$337$	15.7826	+	11.4667i	0.859734	+	0.624633i	0.927812	−	0.373047i	$-0.121687\pi$
$337$	15.7826	+	11.4667i	0.859734	+	0.624633i	−0.0680789	+	0.997680i	$0.521687\pi$
$338$	−19.2782	−	8.58320i	−1.04860	−	0.466865i
$339$	−0.680916	−	0.756234i	−0.0369823	−	0.0410730i
$340$	34.9468	−	60.5297i	1.89526	−	3.28268i
$341$	5.77762	+	26.0304i	0.312876	+	1.40963i
$342$	−17.5135			−0.947020
$343$		0			0
$344$	7.58023	−	5.50736i	0.408698	−	0.296937i
$345$	0.0954247	−	0.907906i	0.00513749	−	0.0488800i
$346$	−33.2017	−	7.05724i	−1.78493	−	0.379399i
$347$	27.8235	+	5.91407i	1.49365	+	0.317484i	0.881092	−	0.472945i	$-0.156809\pi$
$347$	27.8235	+	5.91407i	1.49365	+	0.317484i	0.612553	+	0.790429i	$0.290142\pi$
$348$	0.242658	−	2.30874i	0.0130078	−	0.123761i
$349$	16.2506	−	11.8067i	0.869873	−	0.632000i	−0.0606798	−	0.998157i	$-0.519327\pi$
$349$	16.2506	−	11.8067i	0.869873	−	0.632000i	0.930553	+	0.366158i	$0.119327\pi$
$350$		0			0
$351$	−5.20782			−0.277973
$352$	−16.8597	+	9.93679i	−0.898625	+	0.529633i
$353$	4.49850	−	7.79163i	0.239431	−	0.414707i	−0.721120	−	0.692810i	$-0.756372\pi$
$353$	4.49850	−	7.79163i	0.239431	−	0.414707i	0.960551	+	0.278103i	$0.0897058\pi$
$354$	−5.37752	−	5.97234i	−0.285812	−	0.317426i
$355$	−13.2505	−	5.89949i	−0.703262	−	0.313113i
$356$	17.3860	+	12.6317i	0.921458	+	0.669479i
$357$		0			0
$358$	8.94342	+	27.5250i	0.472675	+	1.45474i
$359$	−0.989468	+	9.41415i	−0.0522221	+	0.496860i	0.936882	+	0.349645i	$0.113698\pi$
$359$	−0.989468	+	9.41415i	−0.0522221	+	0.496860i	−0.989104	+	0.147215i	$0.952969\pi$
$360$	−6.50673	−	61.9074i	−0.342935	−	3.26281i
$361$	−8.78243	−	9.75388i	−0.462233	−	0.513362i
$362$	15.0014	+	25.9832i	0.788456	+	1.36565i
$363$	3.60574	−	2.71995i	0.189253	−	0.142760i
$364$		0			0
$365$	−6.27838	+	19.3229i	−0.328625	+	1.01141i
$366$	−13.7218	−	6.10933i	−0.717249	−	0.319340i
$367$	−1.25625	+	0.559317i	−0.0655755	+	0.0291961i	−0.439262	−	0.898359i	$-0.644760\pi$
$367$	−1.25625	+	0.559317i	−0.0655755	+	0.0291961i	0.373687	+	0.927555i	$0.378093\pi$
$368$	−4.65339	−	0.989108i	−0.242575	−	0.0515608i
$369$	−4.96704	+	5.51645i	−0.258574	+	0.287175i
$370$	35.4908	+	25.7856i	1.84508	+	1.34053i
$371$		0			0
$372$	4.60294	−	14.1664i	0.238651	−	0.734493i
$373$	−2.53590	−	4.39230i	−0.131304	−	0.227425i	0.792876	−	0.609384i	$-0.208583\pi$
$373$	−2.53590	−	4.39230i	−0.131304	−	0.227425i	−0.924179	+	0.381959i	$0.875250\pi$
$374$	33.2805	+	18.8182i	1.72089	+	0.973068i
$375$	1.23749	−	2.14339i	0.0639036	−	0.110684i
$376$	−31.6104	+	6.71899i	−1.63018	+	0.346506i
$377$	2.20474	−	1.60184i	0.113550	−	0.0824989i
$378$		0			0
$379$	−8.64698	−	26.6127i	−0.444166	−	1.36700i	−0.883396	−	0.468627i	$-0.844749\pi$
$379$	−8.64698	−	26.6127i	−0.444166	−	1.36700i	0.439231	−	0.898374i	$-0.355251\pi$
$380$	−25.0947	+	27.8705i	−1.28733	+	1.42973i
$381$	−2.60844	+	1.16135i	−0.133634	+	0.0594978i
$382$	6.01106	+	57.1914i	0.307553	+	2.92617i
$383$	−30.5970	+	6.50359i	−1.56343	+	0.332318i	−0.906690	−	0.421797i	$-0.861400\pi$
$383$	−30.5970	+	6.50359i	−1.56343	+	0.332318i	−0.656743	+	0.754115i	$0.728066\pi$
$384$	−4.44323			−0.226742
$385$		0			0
$386$	8.78692			0.447243
$387$	−4.04734	+	0.860290i	−0.205738	+	0.0437310i
$388$	−4.10627	−	39.0685i	−0.208464	−	1.98340i
$389$	9.73253	−	4.33320i	0.493459	−	0.219702i	−0.144892	−	0.989447i	$-0.546284\pi$
$389$	9.73253	−	4.33320i	0.493459	−	0.219702i	0.638351	+	0.769745i	$0.279617\pi$
$390$	−5.22913	+	5.80753i	−0.264787	+	0.294076i
$391$	0.905090	+	2.78558i	0.0457723	+	0.140873i
$392$		0			0
$393$	−6.95546	+	5.05344i	−0.350857	+	0.254912i
$394$	5.44699	−	1.15779i	0.274415	−	0.0583288i
$395$	16.7389	−	28.9926i	0.842224	−	1.45877i
$396$	42.1012	−	4.80747i	2.11566	−	0.241584i
$397$	10.5878	+	18.3385i	0.531385	+	0.920385i	0.999329	+	0.0366273i	$0.0116614\pi$
$397$	10.5878	+	18.3385i	0.531385	+	0.920385i	−0.467944	+	0.883758i	$0.655005\pi$
$398$	−1.84085	+	5.66554i	−0.0922733	+	0.283988i
$399$		0			0
$400$	−40.1133	−	29.1440i	−2.00566	−	1.45720i
$401$	−22.5570	+	25.0521i	−1.12644	+	1.25104i	−0.161990	+	0.986792i	$0.551791\pi$
$401$	−22.5570	+	25.0521i	−1.12644	+	1.25104i	−0.964454	+	0.264251i	$0.914875\pi$
$402$	−6.38217	−	1.35657i	−0.318314	−	0.0676597i
$403$	15.9743	−	7.11224i	0.795739	−	0.354286i
$404$	23.8047	+	10.5985i	1.18433	+	0.527296i
$405$	−7.95886	+	24.4948i	−0.395479	+	1.21716i
$406$		0			0
$407$	−9.65209	+	13.5389i	−0.478436	+	0.671097i
$408$	−5.94584	−	10.2985i	−0.294363	−	0.509851i
$409$	1.76921	+	1.96490i	0.0874816	+	0.0971582i	0.785296	−	0.619120i	$-0.212511\pi$
$409$	1.76921	+	1.96490i	0.0874816	+	0.0971582i	−0.697815	+	0.716279i	$0.745844\pi$
$410$	2.39803	+	22.8157i	0.118430	+	1.12679i
$411$	−0.392129	+	3.73086i	−0.0193423	+	0.184030i
$412$	6.47144	+	19.9170i	0.318825	+	0.981242i
$413$		0			0
$414$	3.79032	+	2.75383i	0.186284	+	0.135343i
$415$	−26.2429	−	11.6841i	−1.28822	−	0.573550i
$416$	8.58763	+	9.53753i	0.421043	+	0.467616i
$417$	2.20735	−	3.82324i	0.108094	−	0.187225i
$418$	−15.3680	−	13.5896i	−0.751674	−	0.664691i
$419$	−33.0757			−1.61585			−0.807926	−	0.589284i	$-0.799410\pi$
$419$	−33.0757			−1.61585			−0.807926	+	0.589284i	$0.799410\pi$
$420$		0			0
$421$	−27.2492	+	19.7977i	−1.32804	+	0.964881i	−0.328251	+	0.944591i	$0.606459\pi$
$421$	−27.2492	+	19.7977i	−1.32804	+	0.964881i	−0.999794	+	0.0202902i	$0.993541\pi$
$422$	3.64591	−	34.6885i	0.177480	−	1.68861i
$423$	13.9595	+	2.96719i	0.678736	+	0.144270i
$424$	−84.0246	−	17.8600i	−4.08060	−	0.867358i
$425$	−3.19087	+	30.3591i	−0.154780	+	1.47263i
$426$	−3.58577	+	2.60521i	−0.173731	+	0.126223i
$427$		0			0
$428$	−18.1490			−0.877266
$429$	−2.21887	−	1.96210i	−0.107128	−	0.0947311i
$430$	−6.39394	+	11.0746i	−0.308343	+	0.534066i
$431$	−19.9084	−	22.1105i	−0.958952	−	1.06502i	−0.997834	−	0.0657804i	$-0.979046\pi$
$431$	−19.9084	−	22.1105i	−0.958952	−	1.06502i	0.0388820	−	0.999244i	$-0.487620\pi$
$432$	−16.0487	−	7.14535i	−0.772145	−	0.343781i
$433$	−18.7295	−	13.6078i	−0.900083	−	0.653949i	0.0384041	−	0.999262i	$-0.487773\pi$
$433$	−18.7295	−	13.6078i	−0.900083	−	0.653949i	−0.938487	+	0.345314i	$0.887773\pi$
$434$		0			0
$435$	0.545128	+	1.67773i	0.0261369	+	0.0804410i
$436$	2.89968	−	27.5886i	0.138870	−	1.32126i
$437$	−0.164277	−	1.56300i	−0.00785846	−	0.0747682i
$438$	4.15432	+	4.61384i	0.198501	+	0.220458i
$439$	7.90829	+	13.6976i	0.377442	+	0.653749i	0.990689	−	0.136142i	$-0.0434704\pi$
$439$	7.90829	+	13.6976i	0.377442	+	0.653749i	−0.613247	+	0.789891i	$0.710137\pi$
$440$	42.3277	−	59.3725i	2.01789	−	2.83047i
$441$		0			0
$442$	7.74789	−	23.8456i	0.368530	−	1.13422i
$443$	−9.15981	−	4.07821i	−0.435196	−	0.193762i	0.177432	−	0.984133i	$-0.443221\pi$
$443$	−9.15981	−	4.07821i	−0.435196	−	0.193762i	−0.612628	+	0.790371i	$0.709888\pi$
$444$	8.48553	−	3.77800i	0.402705	−	0.179296i
$445$	−15.9736	−	3.39530i	−0.757222	−	0.160953i
$446$	9.16741	−	10.1814i	0.434090	−	0.482105i
$447$	−3.57275	−	2.59575i	−0.168985	−	0.122775i
$448$		0			0
$449$	0.496363	−	1.52765i	0.0234248	−	0.0720942i	−0.938661	−	0.344842i	$-0.887932\pi$
$449$	0.496363	−	1.52765i	0.0234248	−	0.0720942i	0.962086	+	0.272748i	$0.0879325\pi$
$450$	24.4148	+	42.2878i	1.15093	+	1.99346i
$451$	−8.63907	+	0.986482i	−0.406798	+	0.0464516i
$452$	5.59171	−	9.68512i	0.263012	−	0.455550i
$453$	3.07815	−	0.654281i	0.144624	−	0.0307408i
$454$	21.9112	−	15.9194i	1.02834	−	0.747134i
$455$		0			0
$456$	1.97178	+	6.06853i	0.0923373	+	0.284185i
$457$	2.51389	−	2.79196i	0.117595	−	0.130602i	−0.681473	−	0.731844i	$-0.738660\pi$
$457$	2.51389	−	2.79196i	0.117595	−	0.130602i	0.799068	+	0.601241i	$0.205327\pi$
$458$	−52.7832	+	23.5006i	−2.46640	+	1.09811i
$459$	1.13055	+	10.7565i	0.0527695	+	0.502069i
$460$	9.81346	−	2.08592i	0.457555	−	0.0972563i
$461$	14.1849			0.660657			0.330329	−	0.943866i	$-0.392840\pi$
$461$	14.1849			0.660657			0.330329	+	0.943866i	$0.392840\pi$
$462$		0			0
$463$	−5.34265			−0.248294			−0.124147	−	0.992264i	$-0.539619\pi$
$463$	−5.34265			−0.248294			−0.124147	+	0.992264i	$0.539619\pi$
$464$	8.99205	−	1.91132i	0.417445	−	0.0887307i
$465$	1.18316	+	11.2570i	0.0548677	+	0.522031i
$466$	34.5585	−	15.3865i	1.60089	−	0.712764i
$467$	15.9719	−	17.7385i	0.739089	−	0.820842i	−0.249987	−	0.968249i	$-0.580426\pi$
$467$	15.9719	−	17.7385i	0.739089	−	0.820842i	0.989076	+	0.147408i	$0.0470929\pi$
$468$	−8.58735	−	26.4292i	−0.396950	−	1.22169i
$469$		0			0
$470$	35.6826	−	25.9250i	1.64592	−	1.19583i
$471$	7.36944	−	1.56642i	0.339566	−	0.0721770i
$472$	24.5875	−	42.5868i	1.13173	−	1.96022i
$473$	−4.21908	−	2.38565i	−0.193993	−	0.109692i
$474$	−5.11504	−	8.85952i	−0.234942	−	0.406931i
$475$	5.06164	−	15.5781i	0.232244	−	0.714774i
$476$		0			0
$477$	30.6903	+	22.2978i	1.40521	+	1.02095i
$478$	3.34566	−	3.71573i	0.153027	−	0.169954i
$479$	−0.426977	−	0.0907569i	−0.0195091	−	0.00414679i	0.198147	−	0.980172i	$-0.436508\pi$
$479$	−0.426977	−	0.0907569i	−0.0195091	−	0.00414679i	−0.217656	+	0.976026i	$0.569841\pi$
$480$	−7.58942	+	3.37903i	−0.346408	+	0.154231i
$481$	9.96137	+	4.43509i	0.454199	+	0.202223i
$482$	−0.623188	+	1.91798i	−0.0283854	+	0.0873614i
$483$		0			0
$484$	40.6741	+	28.4500i	1.84882	+	1.29318i
$485$	14.9258	+	25.8523i	0.677747	+	1.17389i
$486$	17.5320	+	19.4713i	0.795268	+	0.883234i
$487$	−0.0766904	−	0.729661i	−0.00347517	−	0.0330641i	0.992647	−	0.121046i	$-0.0386249\pi$
$487$	−0.0766904	−	0.729661i	−0.00347517	−	0.0330641i	−0.996122	+	0.0879820i	$0.971958\pi$
$488$	9.60701	−	91.4046i	0.434889	−	4.13769i
$489$	0.0479087	+	0.147448i	0.00216650	+	0.00666782i
$490$		0			0
$491$	−2.10952	−	1.53266i	−0.0952013	−	0.0691678i	0.539166	−	0.842199i	$-0.318739\pi$
$491$	−2.10952	−	1.53266i	−0.0952013	−	0.0691678i	−0.634368	+	0.773032i	$0.718739\pi$
$492$	4.43751	+	1.97571i	0.200059	+	0.0890718i
$493$	−3.78712	−	4.20603i	−0.170563	−	0.189430i
$494$	−6.72675	+	11.6511i	−0.302651	+	0.524207i
$495$	−27.7409	+	16.3499i	−1.24686	+	0.734875i
$496$	58.9857			2.64854
$497$		0			0
$498$	−7.10172	+	5.15970i	−0.318236	+	0.231212i
$499$	0.863197	−	8.21277i	0.0386420	−	0.367654i	−0.958064	−	0.286554i	$-0.907490\pi$
$499$	0.863197	−	8.21277i	0.0386420	−	0.367654i	0.996706	−	0.0810997i	$-0.0258432\pi$
$500$	26.6052	+	5.65512i	1.18982	+	0.252904i
$501$	−0.0458410	−	0.00974381i	−0.00204803	−	0.000435321i
$502$	−5.49917	+	52.3211i	−0.245440	+	2.33521i
$503$	27.4351	−	19.9328i	1.22327	−	0.888759i	0.226905	−	0.973917i	$-0.427139\pi$
$503$	27.4351	−	19.9328i	1.22327	−	0.888759i	0.996367	+	0.0851577i	$0.0271394\pi$
$504$		0			0
$505$	−19.8010			−0.881135
$506$	1.18915	+	5.35759i	0.0528642	+	0.238174i
$507$	1.69767	−	2.94044i	0.0753960	−	0.130590i
$508$	−20.9968	−	23.3193i	−0.931581	−	1.03463i
$509$	26.7154	+	11.8945i	1.18414	+	0.527213i	0.901822	−	0.432107i	$-0.142230\pi$
$509$	26.7154	+	11.8945i	1.18414	+	0.527213i	0.282319	+	0.959321i	$0.408896\pi$
$510$	13.1303	+	9.53972i	0.581419	+	0.422426i
$511$		0			0
$512$	−15.6950	−	48.3043i	−0.693628	−	2.13477i
$513$	0.606630	−	5.77170i	0.0267834	−	0.254827i
$514$	1.38166	+	13.1457i	0.0609426	+	0.579830i
$515$	−10.6484	−	11.8263i	−0.469225	−	0.521128i
$516$	1.35381	+	2.34487i	0.0595983	+	0.103227i
$517$	9.94705	+	13.4357i	0.437471	+	0.590899i
$518$		0			0
$519$	1.68766	−	5.19408i	0.0740800	−	0.227995i
$520$	−43.6839	−	19.4493i	−1.91567	−	0.852910i
$521$	8.87555	−	3.95165i	0.388845	−	0.173125i	−0.202996	−	0.979180i	$-0.565068\pi$
$521$	8.87555	−	3.95165i	0.388845	−	0.173125i	0.591841	+	0.806055i	$0.298401\pi$
$522$	−8.85548	−	1.88229i	−0.387594	−	0.0823856i
$523$	8.58210	−	9.53139i	0.375269	−	0.416779i	−0.525694	−	0.850674i	$-0.676194\pi$
$523$	8.58210	−	9.53139i	0.375269	−	0.416779i	0.900963	+	0.433895i	$0.142861\pi$
$524$	−76.4394	−	55.5365i	−3.33927	−	2.42612i
$525$		0			0
$526$	18.2891	−	56.2880i	0.797442	−	2.45427i
$527$	−18.1577	−	31.4501i	−0.790963	−	1.36999i
$528$	−4.14570	−	9.09090i	−0.180418	−	0.395631i
$529$	11.2898	−	19.5545i	0.490860	−	0.850195i
$530$	114.678	−	24.3756i	4.98130	−	1.05881i
$531$	−17.5688	+	12.7645i	−0.762423	+	0.553933i
$532$		0			0
$533$	1.76211	+	5.42320i	0.0763253	+	0.234905i
$534$	−3.33913	+	3.70848i	−0.144498	+	0.160482i
$535$	12.5991	−	5.60948i	0.544706	−	0.242519i
$536$	−4.17323	−	39.7056i	−0.180256	−	1.71502i
$537$	−4.55483	+	0.968159i	−0.196555	+	0.0417791i
$538$	−47.6192			−2.05301
$539$		0			0
$540$	37.0479			1.59429
$541$	6.75045	−	1.43485i	0.290224	−	0.0616891i	−0.0604988	−	0.998168i	$-0.519269\pi$
$541$	6.75045	−	1.43485i	0.290224	−	0.0616891i	0.350723	+	0.936479i	$0.385936\pi$
$542$	8.06354	+	76.7195i	0.346359	+	3.29538i
$543$	−4.41000	+	1.96346i	−0.189251	+	0.0842600i
$544$	17.8350	−	19.8077i	0.764668	−	0.849250i
$545$	6.51410	+	20.0483i	0.279033	+	0.858776i
$546$		0			0
$547$	14.3372	−	10.4166i	0.613016	−	0.445382i	−0.237459	−	0.971398i	$-0.576315\pi$
$547$	14.3372	−	10.4166i	0.613016	−	0.445382i	0.850475	+	0.526015i	$0.176315\pi$
$548$	−40.3265	+	8.57165i	−1.72266	+	0.366163i
$549$	−20.2939	+	35.1500i	−0.866122	+	1.50017i
$550$	−11.3894	+	56.0522i	−0.485645	+	2.39007i
$551$	1.51846	+	2.63005i	0.0646885	+	0.112044i
$552$	0.527479	−	1.62341i	0.0224510	−	0.0690971i
$553$		0			0
$554$	−27.8552	−	20.2380i	−1.18346	−	0.859831i
$555$	−4.72297	+	5.24539i	−0.200479	+	0.222655i
$556$	47.4566	+	10.0872i	2.01261	+	0.427793i
$557$	39.6728	−	17.6635i	1.68099	−	0.748425i	0.681123	−	0.732169i	$-0.261492\pi$
$557$	39.6728	−	17.6635i	1.68099	−	0.748425i	0.999868	−	0.0162560i	$-0.00517468\pi$
$558$	−53.0678	−	23.6273i	−2.24654	−	1.00022i
$559$	−0.982226	+	3.02298i	−0.0415437	+	0.127858i
$560$		0			0
$561$	−3.57092	+	5.00889i	−0.150764	+	0.211475i
$562$	−10.3388	−	17.9074i	−0.436117	−	0.755377i
$563$	−14.9308	−	16.5823i	−0.629258	−	0.698862i	0.341238	−	0.939977i	$-0.389154\pi$
$563$	−14.9308	−	16.5823i	−0.629258	−	0.698862i	−0.970497	+	0.241115i	$0.922487\pi$
$564$	−0.976167	−	9.28761i	−0.0411041	−	0.391079i
$565$	−0.888311	+	8.45171i	−0.0373715	+	0.355566i
$566$	−7.87898	−	24.2490i	−0.331178	−	1.01926i
$567$		0			0
$568$	−21.9410	−	15.9411i	−0.920623	−	0.668872i
$569$	20.7092	+	9.22034i	0.868176	+	0.386537i	0.791974	−	0.610555i	$-0.209054\pi$
$569$	20.7092	+	9.22034i	0.868176	+	0.386537i	0.0762027	+	0.997092i	$0.475720\pi$
$570$	−5.82723	−	6.47179i	−0.244076	−	0.271074i
$571$	−17.5497	+	30.3970i	−0.734432	+	1.27207i	0.220540	+	0.975378i	$0.429218\pi$
$571$	−17.5497	+	30.3970i	−0.734432	+	1.27207i	−0.954972	+	0.296695i	$0.904115\pi$
$572$	12.9724	−	29.8549i	0.542404	−	1.24830i
$573$	−9.25258			−0.386532
$574$		0			0
$575$	−3.54497	+	2.57557i	−0.147836	+	0.107409i
$576$	0.113641	−	1.08122i	0.00473505	−	0.0450510i
$577$	−31.9226	−	6.78536i	−1.32895	−	0.282478i	−0.511904	−	0.859043i	$-0.671059\pi$
$577$	−31.9226	−	6.78536i	−1.32895	−	0.282478i	−0.817051	+	0.576565i	$0.804393\pi$
$578$	−8.49858	−	1.80643i	−0.353494	−	0.0751375i
$579$	−0.147781	+	1.40604i	−0.00614155	+	0.0584330i
$580$	−15.6843	+	11.3953i	−0.651255	+	0.473164i
$581$		0			0
$582$	9.12204			0.378121
$583$	9.62859	+	43.3805i	0.398775	+	1.79664i
$584$	−18.9947	+	32.8998i	−0.786006	+	1.36140i
$585$	14.1301	+	15.6930i	0.584206	+	0.648826i
$586$	−71.6405	−	31.8964i	−2.95944	−	1.31763i
$587$	29.9477	+	21.7583i	1.23607	+	0.898061i	0.997330	−	0.0730216i	$-0.0232642\pi$
$587$	29.9477	+	21.7583i	1.23607	+	0.898061i	0.238744	+	0.971082i	$0.423264\pi$
$588$		0			0
$589$	6.02155	+	18.5324i	0.248114	+	0.763615i
$590$	−7.01541	+	66.7472i	−0.288820	+	2.74794i
$591$	0.0936554	+	0.891071i	0.00385247	+	0.0366538i
$592$	24.6124	+	27.3348i	1.01156	+	1.12345i
$593$	−8.10805	−	14.0436i	−0.332958	−	0.576700i	0.650133	−	0.759821i	$-0.274713\pi$
$593$	−8.10805	−	14.0436i	−0.332958	−	0.576700i	−0.983090	+	0.183121i	$0.941380\pi$
$594$	0.181905	+	20.2647i	0.00746364	+	0.831471i
$595$		0			0
$596$	14.9975	−	46.1575i	0.614321	−	1.89068i
$597$	−0.875612	−	0.389848i	−0.0358364	−	0.0159554i
$598$	3.28785	−	1.46384i	0.134450	−	0.0598610i
$599$	−10.3170	−	2.19295i	−0.421543	−	0.0896017i	−0.00774396	−	0.999970i	$-0.502465\pi$
$599$	−10.3170	−	2.19295i	−0.421543	−	0.0896017i	−0.413799	+	0.910368i	$0.635798\pi$
$600$	11.9042	−	13.2209i	0.485987	−	0.539743i
$601$	−29.5220	−	21.4490i	−1.20423	−	0.874921i	−0.209532	−	0.977802i	$-0.567194\pi$
$601$	−29.5220	−	21.4490i	−1.20423	−	0.874921i	−0.994694	+	0.102880i	$0.967194\pi$
$602$		0			0
$603$	−5.44830	+	16.7681i	−0.221872	+	0.682852i
$604$	17.2921	+	29.9507i	0.703604	+	1.21868i
$605$	−37.0293	−	7.17860i	−1.50546	−	0.291851i
$606$	−3.02539	+	5.24013i	−0.122898	+	0.212866i
$607$	−32.9747	+	7.00900i	−1.33840	+	0.284486i	−0.820840	−	0.571159i	$-0.806494\pi$
$607$	−32.9747	+	7.00900i	−1.33840	+	0.284486i	−0.517563	+	0.855645i	$0.673161\pi$
$608$	−11.5705	+	8.40648i	−0.469247	+	0.340928i
$609$		0			0
$610$	38.7624	+	119.298i	1.56944	+	4.83025i
$611$	7.33568	−	8.14710i	0.296770	−	0.329597i
$612$	−52.7237	+	23.4741i	−2.13123	+	0.948884i
$613$	−2.53028	−	24.0740i	−0.102197	−	0.972341i	−0.918688	−	0.394983i	$-0.870750\pi$
$613$	−2.53028	−	24.0740i	−0.102197	−	0.972341i	0.816491	−	0.577358i	$-0.195916\pi$
$614$	−50.0924	+	10.6475i	−2.02157	+	0.429697i
$615$	−3.69118			−0.148843
$616$		0			0
$617$	17.6040			0.708710			0.354355	−	0.935111i	$-0.384700\pi$
$617$	17.6040			0.708710			0.354355	+	0.935111i	$0.384700\pi$
$618$	−4.75666	+	1.01106i	−0.191341	+	0.0406708i
$619$	−2.54188	−	24.1844i	−0.102167	−	0.972052i	−0.918754	−	0.394830i	$-0.870803\pi$
$619$	−2.54188	−	24.1844i	−0.102167	−	0.972052i	0.816587	−	0.577222i	$-0.195863\pi$
$620$	−113.640	+	50.5957i	−4.56388	+	2.03197i
$621$	−1.03883	+	1.15374i	−0.0416870	+	0.0462981i
$622$	18.5053	+	56.9535i	0.741995	+	2.28363i
$623$		0			0
$624$	−5.30103	+	3.85142i	−0.212211	+	0.154180i
$625$	12.8337	−	2.72789i	0.513349	−	0.109116i
$626$	−18.7223	+	32.4280i	−0.748294	+	1.29608i
$627$	2.43301	−	2.23056i	0.0971650	−	0.0890800i
$628$	41.3992	+	71.7055i	1.65201	+	2.86136i
$629$	6.99793	−	21.5374i	0.279026	−	0.858754i
$630$		0			0
$631$	−3.26881	−	2.37493i	−0.130129	−	0.0945443i	0.520817	−	0.853669i	$-0.325628\pi$
$631$	−3.26881	−	2.37493i	−0.130129	−	0.0945443i	−0.650946	+	0.759124i	$0.725628\pi$
$632$	41.8855	−	46.5186i	1.66612	−	1.85041i
$633$	5.48937	+	1.16680i	0.218183	+	0.0463762i
$634$	42.0824	−	18.7363i	1.67131	−	0.744113i
$635$	21.7835	+	9.69864i	0.864452	+	0.384879i
$636$	7.67095	−	23.6087i	0.304173	−	0.936148i
$637$		0			0
$638$	−6.31009	−	8.52315i	−0.249819	−	0.337435i
$639$	5.98838	+	10.3722i	0.236897	+	0.410317i
$640$	24.8289	+	27.5752i	0.981447	+	1.09001i
$641$	2.23359	+	21.2512i	0.0882214	+	0.839370i	0.945742	+	0.324920i	$0.105337\pi$
$641$	2.23359	+	21.2512i	0.0882214	+	0.839370i	−0.857520	+	0.514450i	$0.827996\pi$
$642$	0.440521	−	4.19128i	0.0173860	−	0.165417i
$643$	−6.97607	−	21.4701i	−0.275109	−	0.846700i	−0.989190	−	0.146637i	$-0.953155\pi$
$643$	−6.97607	−	21.4701i	−0.275109	−	0.846700i	0.714081	−	0.700063i	$-0.246845\pi$
$644$		0			0
$645$	−1.66457	−	1.20938i	−0.0655424	−	0.0476194i
$646$	25.5249	+	11.3644i	1.00426	+	0.447127i
$647$	−11.4536	−	12.7205i	−0.450286	−	0.500094i	0.474672	−	0.880163i	$-0.342567\pi$
$647$	−11.4536	−	12.7205i	−0.450286	−	0.500094i	−0.924958	+	0.380069i	$0.875900\pi$
$648$	−24.0788	+	41.7057i	−0.945905	+	1.63836i
$649$	−25.3213	−	2.43179i	−0.993947	−	0.0954559i
$650$	37.5100			1.47126
$651$		0			0
$652$	−1.37842	+	1.00148i	−0.0539830	+	0.0392209i
$653$	1.38407	−	13.1686i	0.0541630	−	0.515326i	−0.933483	−	0.358622i	$-0.883247\pi$
$653$	1.38407	−	13.1686i	0.0541630	−	0.515326i	0.987646	−	0.156704i	$-0.0500868\pi$
$654$	6.30086	+	1.33929i	0.246383	+	0.0523703i
$655$	70.2296	+	14.9278i	2.74410	+	0.583276i
$656$	−2.01066	+	19.1301i	−0.0785030	+	0.746906i
$657$	13.5725	−	9.86103i	0.529515	−	0.384715i
$658$		0			0
$659$	28.3747			1.10532			0.552660	−	0.833407i	$-0.313613\pi$
$659$	28.3747			1.10532			0.552660	+	0.833407i	$0.313613\pi$
$660$	15.7848	+	13.9582i	0.614422	+	0.543321i
$661$	9.48284	−	16.4248i	0.368840	−	0.638849i	−0.620545	−	0.784171i	$-0.713088\pi$
$661$	9.48284	−	16.4248i	0.368840	−	0.638849i	0.989384	+	0.145322i	$0.0464218\pi$
$662$	−33.8614	−	37.6069i	−1.31606	−	1.46163i
$663$	3.68534	+	1.64082i	0.143127	+	0.0637241i
$664$	−43.4547	−	31.5717i	−1.68637	−	1.22522i
$665$		0			0
$666$	−11.1938	−	34.4511i	−0.433752	−	1.33495i
$667$	0.0849207	−	0.807966i	0.00328814	−	0.0312846i
$668$	−0.0538364	−	0.512219i	−0.00208299	−	0.0198183i
$669$	1.47500	+	1.63816i	0.0570269	+	0.0633348i
$670$	27.2447	+	47.1891i	1.05255	+	1.82308i
$671$	−45.0826	+	15.0969i	−1.74039	+	0.582811i
$672$		0			0
$673$	14.3830	−	44.2662i	0.554423	−	1.70634i	−0.143039	−	0.989717i	$-0.545688\pi$
$673$	14.3830	−	44.2662i	0.554423	−	1.70634i	0.697462	−	0.716621i	$-0.254312\pi$
$674$	−45.4802	−	20.2491i	−1.75183	−	0.779966i
$675$	−14.7819	+	6.58134i	−0.568957	+	0.253316i
$676$	36.4988	+	7.75805i	1.40380	+	0.298387i
$677$	−19.1167	+	21.2312i	−0.734715	+	0.815983i	−0.988491	−	0.151280i	$-0.951661\pi$
$677$	−19.1167	+	21.2312i	−0.734715	+	0.815983i	0.253776	+	0.967263i	$0.418327\pi$
$678$	2.10093	+	1.52641i	0.0806857	+	0.0586216i
$679$		0			0
$680$	−30.6883	+	94.4489i	−1.17684	+	3.62195i
$681$	2.17883	+	3.77385i	0.0834931	+	0.144614i
$682$	−28.2331	−	61.9110i	−1.08110	−	2.37069i
$683$	10.9725	−	19.0050i	0.419852	−	0.727205i	−0.576072	−	0.817399i	$-0.695415\pi$
$683$	10.9725	−	19.0050i	0.419852	−	0.727205i	0.995924	+	0.0901940i	$0.0287487\pi$
$684$	30.2910	−	6.43856i	1.15821	−	0.246185i
$685$	25.3454	−	18.4145i	0.968398	−	0.703582i
$686$		0			0
$687$	−2.87273	−	8.84135i	−0.109601	−	0.337318i
$688$	−7.17454	+	7.96813i	−0.273527	+	0.303782i
$689$	26.6218	−	11.8528i	1.01421	−	0.451555i
$690$	0.243518	+	2.31692i	0.00927059	+	0.0882037i
$691$	10.8864	−	2.31397i	0.414138	−	0.0880277i	0.00386927	−	0.999993i	$-0.498768\pi$
$691$	10.8864	−	2.31397i	0.414138	−	0.0880277i	0.410268	+	0.911965i	$0.365435\pi$
$692$	60.0197			2.28161
$693$		0			0
$694$	−72.5903			−2.75549
$695$	−36.0622	+	7.66526i	−1.36792	+	0.290760i
$696$	0.344784	+	3.28040i	0.0130690	+	0.124343i
$697$	10.8188	−	4.81683i	0.409791	−	0.182451i
$698$	−34.2999	+	38.0939i	−1.29827	+	1.44187i
$699$	1.88085	+	5.78866i	0.0711402	+	0.218947i
$700$		0			0
$701$	31.0633	−	22.5688i	1.17324	−	0.852411i	0.181849	−	0.983326i	$-0.441792\pi$
$701$	31.0633	−	22.5688i	1.17324	−	0.852411i	0.991394	+	0.130915i	$0.0417917\pi$
$702$	12.9996	−	2.76316i	0.490640	−	0.104289i
$703$	−6.07564	+	10.5233i	−0.229147	+	0.396894i
$704$	0.938699	−	0.860590i	0.0353786	−	0.0324347i
$705$	3.54826	+	6.14577i	0.133635	+	0.231463i
$706$	−7.09498	+	21.8361i	−0.267023	+	0.821812i
$707$		0			0
$708$	11.4965	+	8.35271i	0.432066	+	0.313914i
$709$	−0.321519	+	0.357083i	−0.0120749	+	0.0134105i	−0.749152	−	0.662398i	$-0.769539\pi$
$709$	−0.321519	+	0.357083i	−0.0120749	+	0.0134105i	0.737077	+	0.675809i	$0.236205\pi$
$710$	36.2057	+	7.69575i	1.35877	+	0.288817i
$711$	−25.2537	+	11.2437i	−0.947086	+	0.421670i
$712$	−27.8950	−	12.4196i	−1.04541	−	0.465446i
$713$	1.61085	−	4.95768i	0.0603267	−	0.185666i
$714$		0			0
$715$	0.222031	+	24.7348i	0.00830348	+	0.925031i
$716$	−25.5876	−	44.3190i	−0.956253	−	1.65628i
$717$	0.538305	+	0.597848i	0.0201034	+	0.0223271i
$718$	−2.52506	−	24.0244i	−0.0942346	−	0.896582i
$719$	3.81213	−	36.2700i	0.142168	−	1.35264i	−0.658069	−	0.752958i	$-0.728626\pi$
$719$	3.81213	−	36.2700i	0.142168	−	1.35264i	0.800237	−	0.599684i	$-0.204707\pi$
$720$	22.0125	+	67.7475i	0.820358	+	2.52480i
$721$		0			0
$722$	27.0977	+	19.6876i	1.00847	+	0.732698i
$723$	−0.296424	−	0.131976i	−0.0110241	−	0.00490825i
$724$	−35.4985	−	39.4251i	−1.31929	−	1.46522i
$725$	4.23365	−	7.33289i	0.157234	−	0.272337i
$726$	−7.55743	+	8.70260i	−0.280482	+	0.322984i
$727$	33.6867			1.24937			0.624686	−	0.780876i	$-0.285227\pi$
$727$	33.6867			1.24937			0.624686	+	0.780876i	$0.285227\pi$
$728$		0			0
$729$	14.8193	−	10.7668i	0.548862	−	0.398772i
$730$	5.41964	−	51.5645i	0.200590	−	1.90849i
$731$	6.45702	+	1.37248i	0.238821	+	0.0507631i
$732$	25.9790	+	5.52201i	0.960212	+	0.204099i
$733$	−2.82892	+	26.9154i	−0.104489	+	0.994143i	0.809146	+	0.587607i	$0.199930\pi$
$733$	−2.82892	+	26.9154i	−0.104489	+	0.994143i	−0.913635	+	0.406536i	$0.866737\pi$
$734$	2.83905	−	2.06269i	0.104791	−	0.0761353i
$735$		0			0
$736$	3.82597			0.141027
$737$	−17.7922	+	10.4864i	−0.655383	+	0.386270i
$738$	9.47169	−	16.4054i	0.348658	−	0.603893i
$739$	−6.96741	−	7.73809i	−0.256300	−	0.284650i	0.601239	−	0.799070i	$-0.294674\pi$
$739$	−6.96741	−	7.73809i	−0.256300	−	0.284650i	−0.857539	+	0.514419i	$0.828007\pi$
$740$	−70.8641	−	31.5507i	−2.60502	−	1.15983i
$741$	−1.75121	−	1.27233i	−0.0643324	−	0.0467403i
$742$		0			0
$743$	14.6944	+	45.2248i	0.539086	+	1.65914i	0.734651	+	0.678446i	$0.237346\pi$
$743$	14.6944	+	45.2248i	0.539086	+	1.65914i	−0.195565	+	0.980691i	$0.562654\pi$
$744$	−2.21228	+	21.0484i	−0.0811061	+	0.771673i
$745$	3.85502	+	36.6781i	0.141237	+	1.34378i
$746$	8.66051	+	9.61847i	0.317084	+	0.352157i
$747$	11.8602	+	20.5424i	0.433940	+	0.751607i
$748$	−64.4797	−	20.3127i	−2.35761	−	0.742705i
$749$		0			0
$750$	−1.95175	+	6.00687i	−0.0712679	+	0.219340i
$751$	−27.1093	−	12.0698i	−0.989232	−	0.440434i	−0.152652	−	0.988280i	$-0.548781\pi$
$751$	−27.1093	−	12.0698i	−0.989232	−	0.440434i	−0.836579	+	0.547846i	$0.815448\pi$
$752$	33.7842	−	15.0417i	1.23198	−	0.548515i
$753$	−8.27967	−	1.75990i	−0.301728	−	0.0641343i
$754$	−4.65352	+	5.16826i	−0.169471	+	0.188217i
$755$	−21.2613	−	15.4473i	−0.773779	−	0.562183i
$756$		0			0
$757$	−9.57305	+	29.4628i	−0.347938	+	1.07084i	0.612053	+	0.790816i	$0.290344\pi$
$757$	−9.57305	+	29.4628i	−0.347938	+	1.07084i	−0.959992	+	0.280028i	$0.909656\pi$
$758$	35.7045	+	61.8420i	1.29685	+	2.24620i
$759$	−0.877294	+	0.100177i	−0.0318437	+	0.00363619i
$760$	26.6437	−	46.1483i	0.966469	−	1.67397i
$761$	11.5101	−	2.44656i	0.417242	−	0.0886876i	0.00549328	−	0.999985i	$-0.498251\pi$
$761$	11.5101	−	2.44656i	0.417242	−	0.0886876i	0.411749	+	0.911297i	$0.364918\pi$
$762$	5.89493	−	4.28292i	0.213551	−	0.155154i
$763$		0			0
$764$	−31.4222	−	96.7076i	−1.13682	−	3.49876i
$765$	29.3456	−	32.5916i	1.06099	−	1.17835i
$766$	72.9248	−	32.4682i	2.63488	−	1.17312i
$767$	1.74375	+	16.5906i	0.0629630	+	0.599053i
$768$	11.3995	−	2.42304i	0.411344	−	0.0874339i
$769$	−4.17897			−0.150697			−0.0753487	−	0.997157i	$-0.524007\pi$
$769$	−4.17897			−0.150697			−0.0753487	+	0.997157i	$0.524007\pi$
$770$		0			0
$771$	−2.12674			−0.0765926
$772$	−15.1977	+	3.23038i	−0.546978	+	0.116264i
$773$	0.00875885	+	0.0833349i	0.000315034	+	0.00299735i	0.994678	−	0.103030i	$-0.0328537\pi$
$773$	0.00875885	+	0.0833349i	0.000315034	+	0.00299735i	−0.994363	+	0.106027i	$0.966187\pi$
$774$	9.64644	−	4.29487i	0.346734	−	0.154376i
$775$	36.3537	−	40.3749i	1.30586	−	1.45031i
$776$	17.2484	+	53.0850i	0.619180	+	1.90564i
$777$		0			0
$778$	−21.9950	+	15.9803i	−0.788559	+	0.572922i
$779$	−6.21565	+	1.32118i	−0.222699	+	0.0473361i
$780$	6.90917	−	11.9670i	0.247388	−	0.428489i
$781$	−2.79354	+	13.7483i	−0.0999609	+	0.491952i
$782$	−3.73723	−	6.47308i	−0.133643	−	0.231477i
$783$	0.927059	−	2.85319i	0.0331304	−	0.101965i
$784$		0			0
$785$	−50.9020	−	36.9825i	−1.81677	−	1.31996i
$786$	14.6808	−	16.3047i	0.523647	−	0.581569i
$787$	13.1458	+	2.79422i	0.468597	+	0.0996033i	0.436157	−	0.899870i	$-0.356339\pi$
$787$	13.1458	+	2.79422i	0.468597	+	0.0996033i	0.0324393	+	0.999474i	$0.489672\pi$
$788$	−8.99539	+	4.00500i	−0.320447	+	0.142672i
$789$	8.69933	+	3.87319i	0.309704	+	0.137889i
$790$	−26.4003	+	81.2518i	−0.939281	+	2.89081i
$791$		0			0
$792$	−57.0927	+	19.1188i	−2.02870	+	0.679357i
$793$	15.5894	+	27.0016i	0.553594	+	0.958853i
$794$	−36.1590	−	40.1586i	−1.28323	−	1.42518i
$795$	1.97177	+	18.7602i	0.0699316	+	0.665355i
$796$	1.10105	−	10.4758i	0.0390257	−	0.371305i
$797$	4.20197	+	12.9323i	0.148842	+	0.458087i	0.997485	−	0.0708782i	$-0.0225802\pi$
$797$	4.20197	+	12.9323i	0.148842	+	0.458087i	−0.848643	+	0.528965i	$0.822580\pi$
$798$		0			0
$799$	−18.4199	−	13.3828i	−0.651648	−	0.473450i
$800$	36.4282	+	16.2189i	1.28793	+	0.573424i
$801$	9.02294	+	10.0210i	0.318810	+	0.354074i
$802$	43.0142	−	74.5028i	1.51888	−	2.63078i
$803$	19.5616	+	1.87864i	0.690313	+	0.0662957i
$804$	11.5372			0.406887
$805$		0			0
$806$	−36.1012	+	26.2290i	−1.27161	+	0.923879i
$807$	0.800872	−	7.61978i	0.0281920	−	0.268229i
$808$	−36.2151	−	7.69775i	−1.27404	−	0.270806i
$809$	−43.5276	−	9.25208i	−1.53035	−	0.325286i	−0.635658	−	0.771971i	$-0.719271\pi$
$809$	−43.5276	−	9.25208i	−1.53035	−	0.325286i	−0.894691	+	0.446685i	$0.852604\pi$
$810$	6.87027	−	65.3662i	0.241397	−	2.29674i
$811$	−19.5819	+	14.2271i	−0.687612	+	0.499579i	−0.875874	−	0.482539i	$-0.839715\pi$
$811$	−19.5819	+	14.2271i	−0.687612	+	0.499579i	0.188262	+	0.982119i	$0.439715\pi$
$812$		0			0
$813$	−12.4119			−0.435303
$814$	16.9099	−	38.9166i	0.592691	−	1.36403i
$815$	0.647365	−	1.12127i	0.0226762	−	0.0392763i
$816$	9.10568	+	10.1129i	0.318763	+	0.354022i
$817$	−3.23588	−	1.44071i	−0.113209	−	0.0504039i
$818$	−5.45879	−	3.96604i	−0.190862	−	0.138669i
$819$		0			0
$820$	−12.5354	−	38.5801i	−0.437756	−	1.34728i
$821$	0.970062	−	9.22953i	0.0338554	−	0.322113i	−0.964467	−	0.264205i	$-0.914890\pi$
$821$	0.970062	−	9.22953i	0.0338554	−	0.322113i	0.998322	−	0.0579077i	$-0.0184429\pi$
$822$	−1.00069	−	9.52093i	−0.0349031	−	0.332081i
$823$	−15.7134	−	17.4515i	−0.547734	−	0.608321i	0.404182	−	0.914679i	$-0.367556\pi$
$823$	−15.7134	−	17.4515i	−0.547734	−	0.608321i	−0.951916	+	0.306358i	$0.900890\pi$
$824$	−14.8779	−	25.7692i	−0.518296	−	0.897714i
$825$	−8.77764	−	2.76517i	−0.305598	−	0.0962709i
$826$		0			0
$827$	−6.09962	+	18.7727i	−0.212105	+	0.652791i	0.787242	+	0.616644i	$0.211508\pi$
$827$	−6.09962	+	18.7727i	−0.212105	+	0.652791i	−0.999346	+	0.0361466i	$0.988492\pi$
$828$	−7.56809	−	3.36953i	−0.263009	−	0.117099i
$829$	36.5362	−	16.2669i	1.26895	−	0.564974i	0.341841	−	0.939758i	$-0.388950\pi$
$829$	36.5362	−	16.2669i	1.26895	−	0.564974i	0.927112	+	0.374783i	$0.122283\pi$
$830$	71.7063	+	15.2417i	2.48896	+	0.529045i
$831$	3.70686	−	4.11689i	0.128590	−	0.142813i
$832$	−0.675650	−	0.490889i	−0.0234240	−	0.0170185i
$833$		0			0
$834$	−3.48140	+	10.7146i	−0.120551	+	0.371018i
$835$	0.195689	+	0.338944i	0.00677211	+	0.0117296i
$836$	31.5763	+	17.8546i	1.09209	+	0.617515i
$837$	9.62471	−	16.6705i	0.332679	−	0.576216i
$838$	82.5627	−	17.5492i	2.85208	−	0.606228i
$839$	−6.34929	+	4.61303i	−0.219202	+	0.159259i	−0.691967	−	0.721929i	$-0.743256\pi$
$839$	−6.34929	+	4.61303i	−0.219202	+	0.159259i	0.472766	+	0.881188i	$0.343256\pi$
$840$		0			0
$841$	−8.47637	−	26.0876i	−0.292289	−	0.899572i
$842$	57.5146	−	63.8764i	1.98208	−	2.20133i
$843$	3.03933	−	1.35320i	0.104680	−	0.0466066i
$844$	6.44680	+	61.3372i	0.221908	+	2.11131i
$845$	−27.7354	+	5.89534i	−0.954126	+	0.202806i
$846$	−36.4198			−1.25214
$847$		0			0
$848$	98.3017			3.37569
$849$	4.01271	−	0.852928i	0.137716	−	0.0292724i
$850$	−8.14293	−	77.4748i	−0.279300	−	2.65736i
$851$	2.96960	−	1.32215i	0.101797	−	0.0453228i
$852$	5.24413	−	5.82420i	0.179661	−	0.199534i
$853$	12.6694	+	38.9924i	0.433792	+	1.33507i	0.894320	+	0.447428i	$0.147660\pi$
$853$	12.6694	+	38.9924i	0.433792	+	1.33507i	−0.460528	+	0.887645i	$0.652340\pi$
$854$		0			0
$855$	−19.0381	+	13.8320i	−0.651089	+	0.473044i
$856$	25.2238	−	5.36148i	0.862131	−	0.183252i
$857$	15.5946	−	27.0107i	0.532702	−	0.922666i	−0.466569	−	0.884485i	$-0.654510\pi$
$857$	15.5946	−	27.0107i	0.532702	−	0.922666i	0.999271	−	0.0381817i	$-0.0121566\pi$
$858$	6.57973	+	3.72046i	0.224628	+	0.127015i
$859$	3.97913	+	6.89205i	0.135766	+	0.235154i	0.925890	−	0.377794i	$-0.123317\pi$
$859$	3.97913	+	6.89205i	0.135766	+	0.235154i	−0.790124	+	0.612947i	$0.789984\pi$
$860$	6.98745	−	21.5052i	0.238270	−	0.733320i
$861$		0			0
$862$	61.4261	+	44.6287i	2.09218	+	1.52006i
$863$	20.8128	−	23.1150i	0.708476	−	0.786842i	−0.276226	−	0.961093i	$-0.589084\pi$
$863$	20.8128	−	23.1150i	0.708476	−	0.786842i	0.984701	+	0.174251i	$0.0557503\pi$
$864$	13.8195	+	2.93742i	0.470149	+	0.0999332i
$865$	−41.6658	+	18.5508i	−1.41668	+	0.630746i
$866$	53.9722	+	24.0300i	1.83405	+	0.816571i
$867$	0.431987	−	1.32952i	0.0146710	−	0.0451528i
$868$		0			0
$869$	−30.8846	−	9.72939i	−1.04769	−	0.330047i
$870$	−2.25090	−	3.89868i	−0.0763127	−	0.132178i
$871$	9.06260	+	10.0650i	0.307074	+	0.341041i
$872$	4.12006	+	39.1997i	0.139523	+	1.32747i
$873$	2.57657	−	24.5144i	0.0872035	−	0.829686i
$874$	1.23936	+	3.81435i	0.0419219	+	0.129022i
$875$		0			0
$876$	−8.88145	−	6.45275i	−0.300077	−	0.218018i
$877$	−47.4104	−	21.1085i	−1.60094	−	0.712782i	−0.604457	−	0.796637i	$-0.706610\pi$
$877$	−47.4104	−	21.1085i	−1.60094	−	0.712782i	−0.996478	+	0.0838551i	$0.973277\pi$
$878$	−27.0081	−	29.9956i	−0.911480	−	1.01230i
$879$	6.30877	−	10.9271i	0.212789	−	0.368562i
$880$	−33.2530	+	76.5289i	−1.12096	+	2.57979i
$881$	−42.1448			−1.41989			−0.709947	−	0.704256i	$-0.751281\pi$
$881$	−42.1448			−1.41989			−0.709947	+	0.704256i	$0.751281\pi$
$882$		0			0
$883$	14.2855	−	10.3790i	0.480744	−	0.349281i	−0.320870	−	0.947123i	$-0.603975\pi$
$883$	14.2855	−	10.3790i	0.480744	−	0.349281i	0.801614	+	0.597842i	$0.203975\pi$
$884$	−4.63418	+	44.0913i	−0.155864	+	1.48295i
$885$	−10.5626	−	2.24514i	−0.355056	−	0.0754696i
$886$	25.0283	+	5.31993i	0.840843	+	0.178727i
$887$	−1.11354	+	10.5946i	−0.0373890	+	0.355732i	0.959793	+	0.280709i	$0.0905697\pi$
$887$	−1.11354	+	10.5946i	−0.0373890	+	0.355732i	−0.997182	+	0.0750230i	$0.976097\pi$
$888$	−10.6772	+	7.75747i	−0.358305	+	0.260324i
$889$		0			0
$890$	41.6744			1.39693
$891$	24.7974	+	2.38147i	0.830745	+	0.0797824i
$892$	−12.1128	+	20.9799i	−0.405566	+	0.702460i
$893$	8.17473	+	9.07896i	0.273557	+	0.303816i
$894$	10.2955	+	4.58383i	0.344332	+	0.153306i
$895$	31.4610	+	22.8578i	1.05163	+	0.764051i
$896$		0			0
$897$	0.178941	+	0.550724i	0.00597467	+	0.0183881i
$898$	−0.428472	+	4.07664i	−0.0142983	+	0.136039i
$899$	1.05292	+	10.0179i	0.0351169	+	0.334115i
$900$	−57.7740	−	64.1646i	−1.92580	−	2.13882i
$901$	−30.2605	−	52.4126i	−1.00812	−	1.74612i
$902$	21.0412	−	7.04614i	0.700597	−	0.234611i
$903$		0			0
$904$	−4.91032	+	15.1124i	−0.163315	+	0.502631i
$905$	36.8286	+	16.3972i	1.22423	+	0.545060i
$906$	−7.33645	+	3.26640i	−0.243737	+	0.108519i
$907$	−49.2013	−	10.4581i	−1.63370	−	0.347254i	−0.702479	−	0.711704i	$-0.747924\pi$
$907$	−49.2013	−	10.4581i	−1.63370	−	0.347254i	−0.931223	+	0.364450i	$0.881257\pi$
$908$	−32.0447	+	35.5893i	−1.06344	+	1.18107i
$909$	13.2277	+	9.61047i	0.438735	+	0.318759i
$910$		0			0
$911$	−7.11891	+	21.9097i	−0.235860	+	0.725902i	0.761146	+	0.648580i	$0.224637\pi$
$911$	−7.11891	+	21.9097i	−0.235860	+	0.725902i	−0.997006	+	0.0773220i	$0.975363\pi$
$912$	−3.65095	−	6.32363i	−0.120895	−	0.209396i
$913$	−5.53269	+	27.2288i	−0.183105	+	0.901142i
$914$	−4.79377	+	8.30304i	−0.158564	+	0.274640i
$915$	−19.7414	+	4.19617i	−0.652631	+	0.138721i
$916$	82.6535	−	60.0513i	2.73095	−	1.98415i
$917$		0			0
$918$	−8.52920	−	26.2502i	−0.281506	−	0.866385i
$919$	−25.4708	+	28.2882i	−0.840204	+	0.933141i	−0.998528	−	0.0542465i	$-0.982724\pi$
$919$	−25.4708	+	28.2882i	−0.840204	+	0.933141i	0.158324	+	0.987387i	$0.449391\pi$
$920$	−13.0227	+	5.79808i	−0.429345	+	0.191157i
$921$	−0.861288	−	8.19461i	−0.0283804	−	0.270022i
$922$	−35.4080	+	7.52621i	−1.16610	+	0.247863i
$923$	9.20031			0.302832
$924$		0			0
$925$	33.8792			1.11394
$926$	13.3362	−	2.83470i	0.438255	−	0.0931539i
$927$	1.37356	+	13.0685i	0.0451136	+	0.429227i
$928$	−6.75400	+	3.00708i	−0.221711	+	0.0987121i
$929$	11.7353	−	13.0334i	0.385024	−	0.427612i	−0.519212	−	0.854645i	$-0.673775\pi$
$929$	11.7353	−	13.0334i	0.385024	−	0.427612i	0.904236	+	0.427033i	$0.140441\pi$
$930$	−8.92610	−	27.4717i	−0.292699	−	0.900833i
$931$		0			0
$932$	−54.1154	+	39.3171i	−1.77261	+	1.28788i
$933$	−9.42463	+	2.00327i	−0.308549	+	0.0655840i
$934$	−30.4569	+	52.7528i	−0.996579	+	1.72613i
$935$	51.0402	−	5.82820i	1.66919	−	0.190602i
$936$	19.7424	+	34.1948i	0.645300	+	1.11769i
$937$	17.5395	−	53.9810i	0.572990	−	1.76348i	−0.0699341	−	0.997552i	$-0.522279\pi$
$937$	17.5395	−	53.9810i	0.572990	−	1.76348i	0.642924	−	0.765930i	$-0.277721\pi$
$938$		0			0
$939$	−4.87409	−	3.54123i	−0.159060	−	0.115564i
$940$	−52.1853	+	57.9576i	−1.70210	+	1.89037i
$941$	−21.8113	−	4.63613i	−0.711027	−	0.151134i	−0.161821	−	0.986820i	$-0.551737\pi$
$941$	−21.8113	−	4.63613i	−0.711027	−	0.151134i	−0.549207	+	0.835687i	$0.685070\pi$
$942$	−17.5643	+	7.82013i	−0.572276	+	0.254794i
$943$	1.55295	+	0.691420i	0.0505712	+	0.0225157i
$944$	−17.3894	+	53.5192i	−0.565978	+	1.74190i
$945$		0			0
$946$	11.7973	+	3.71645i	0.383565	+	0.120832i
$947$	−22.3891	−	38.7791i	−0.727548	−	1.26015i	−0.957917	−	0.287047i	$-0.907326\pi$
$947$	−22.3891	−	38.7791i	−0.727548	−	1.26015i	0.230368	−	0.973103i	$-0.426007\pi$
$948$	12.1040	+	13.4428i	0.393119	+	0.436603i
$949$	−1.34710	−	12.8168i	−0.0437288	−	0.416052i
$950$	−4.36933	+	41.5714i	−0.141760	+	1.34875i
$951$	2.29034	+	7.04893i	0.0742692	+	0.228577i
$952$		0			0
$953$	−1.49815	−	1.08847i	−0.0485298	−	0.0352590i	0.563256	−	0.826283i	$-0.309549\pi$
$953$	−1.49815	−	1.08847i	−0.0485298	−	0.0352590i	−0.611786	+	0.791024i	$0.709549\pi$
$954$	−88.4392	−	39.3756i	−2.86332	−	1.27483i
$955$	51.7036	+	57.4227i	1.67309	+	1.85816i
$956$	−4.42058	+	7.65666i	−0.142972	+	0.247634i
$957$	1.46996	−	0.866364i	0.0475169	−	0.0280056i
$958$	1.11396			0.0359906
$959$		0			0
$960$	0.437359	−	0.317760i	0.0141157	−	0.0102557i
$961$	−3.51561	+	33.4487i	−0.113407	+	1.07899i
$962$	−27.2185	−	5.78547i	−0.877559	−	0.186531i
$963$	−11.1391	−	2.36770i	−0.358954	−	0.0762980i
$964$	0.372742	−	3.54641i	0.0120052	−	0.114222i
$965$	9.55186	−	6.93984i	0.307485	−	0.223401i
$966$		0			0
$967$	−33.5800			−1.07986			−0.539930	−	0.841710i	$-0.681549\pi$
$967$	−33.5800			−1.07986			−0.539930	+	0.841710i	$0.681549\pi$
$968$	−64.9340	−	27.5246i	−2.08706	−	0.884674i
$969$	−2.24776	+	3.89324i	−0.0722085	+	0.125069i
$970$	−50.9742	−	56.6126i	−1.63668	−	1.81772i
$971$	−38.8022	−	17.2759i	−1.24522	−	0.554409i	−0.324966	−	0.945726i	$-0.605353\pi$
$971$	−38.8022	−	17.2759i	−1.24522	−	0.554409i	−0.920256	+	0.391317i	$0.872020\pi$
$972$	−37.4814	−	27.2318i	−1.20222	−	0.873462i
$973$		0			0
$974$	0.578575	+	1.78067i	0.0185387	+	0.0570564i
$975$	−0.630853	+	6.00216i	−0.0202035	+	0.192223i
$976$	10.9938	+	104.599i	0.351902	+	3.34813i
$977$	31.0026	+	34.4319i	0.991861	+	1.10157i	0.994828	+	0.101578i	$0.0323891\pi$
$977$	31.0026	+	34.4319i	0.991861	+	1.10157i	−0.00296639	+	0.999996i	$0.500944\pi$
$978$	−0.197821	−	0.342636i	−0.00632562	−	0.0109563i
$979$	0.141781	+	15.7948i	0.00453133	+	0.504803i
$980$		0			0
$981$	5.37888	−	16.5545i	0.171735	−	0.528545i
$982$	6.07893	+	2.70651i	0.193986	+	0.0863683i
$983$	−22.9215	+	10.2053i	−0.731081	+	0.325498i	−0.738297	−	0.674476i	$-0.764370\pi$
$983$	−22.9215	+	10.2053i	−0.731081	+	0.325498i	0.00721610	+	0.999974i	$0.497703\pi$
$984$	−6.75098	−	1.43496i	−0.215213	−	0.0457450i
$985$	5.00676	−	5.56057i	0.159529	−	0.177174i
$986$	11.6850	+	8.48962i	0.372125	+	0.270365i
$987$		0			0
$988$	7.35115	−	22.6245i	0.233871	−	0.719782i
$989$	0.473781	+	0.820613i	0.0150654	+	0.0260940i
$990$	60.5712	−	55.5311i	1.92508	−	1.76489i
$991$	−18.7823	+	32.5318i	−0.596638	+	1.03341i	0.396675	+	0.917959i	$0.370164\pi$
$991$	−18.7823	+	32.5318i	−0.596638	+	1.03341i	−0.993313	+	0.115449i	$0.963169\pi$
$992$	−46.4011	+	9.86286i	−1.47324	+	0.313146i
$993$	6.58716	−	4.78585i	0.209037	−	0.151874i
$994$		0			0
$995$	2.47350	+	7.61264i	0.0784151	+	0.241337i
$996$	10.3861	−	11.5350i	0.329097	−	0.365500i
$997$	−32.7406	+	14.5770i	−1.03690	+	0.461660i	−0.853344	−	0.521349i	$-0.825429\pi$
$997$	−32.7406	+	14.5770i	−1.03690	+	0.461660i	−0.183561	+	0.983008i	$0.558762\pi$
$998$	2.20283	+	20.9585i	0.0697293	+	0.663430i
$999$	11.7414	−	2.49570i	0.371480	−	0.0789605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.f.361.1		32
7.2	even	3	inner	539.2.q.f.471.4		32
7.3	odd	6		77.2.f.b.64.4	✓	16
7.4	even	3		539.2.f.e.295.4		16
7.5	odd	6		539.2.q.g.471.4		32
7.6	odd	2		539.2.q.g.361.1		32
11.5	even	5	inner	539.2.q.f.214.4		32
21.17	even	6		693.2.m.i.64.1		16
77.3	odd	30		847.2.f.w.323.1		16
77.4	even	15		5929.2.a.bt.1.8		8
77.5	odd	30		539.2.q.g.324.1		32
77.10	even	6		847.2.f.x.372.1		16
77.16	even	15	inner	539.2.q.f.324.1		32
77.17	even	30		847.2.f.x.148.1		16
77.18	odd	30		5929.2.a.bs.1.1		8
77.24	even	30		847.2.f.v.729.4		16
77.27	odd	10		539.2.q.g.214.4		32
77.31	odd	30		847.2.f.w.729.1		16
77.38	odd	30		77.2.f.b.71.4	yes	16
77.52	even	30		847.2.f.v.323.4		16
77.59	odd	30		847.2.a.p.1.8		8
77.60	even	15		539.2.f.e.148.4		16
77.73	even	30		847.2.a.o.1.1		8
231.38	even	30		693.2.m.i.379.1		16
231.59	even	30		7623.2.a.ct.1.1		8
231.227	odd	30		7623.2.a.cw.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.4	✓	16	7.3	odd	6
77.2.f.b.71.4	yes	16	77.38	odd	30
539.2.f.e.148.4		16	77.60	even	15
539.2.f.e.295.4		16	7.4	even	3
539.2.q.f.214.4		32	11.5	even	5	inner
539.2.q.f.324.1		32	77.16	even	15	inner
539.2.q.f.361.1		32	1.1	even	1	trivial
539.2.q.f.471.4		32	7.2	even	3	inner
539.2.q.g.214.4		32	77.27	odd	10
539.2.q.g.324.1		32	77.5	odd	30
539.2.q.g.361.1		32	7.6	odd	2
539.2.q.g.471.4		32	7.5	odd	6
693.2.m.i.64.1		16	21.17	even	6
693.2.m.i.379.1		16	231.38	even	30
847.2.a.o.1.1		8	77.73	even	30
847.2.a.p.1.8		8	77.59	odd	30
847.2.f.v.323.4		16	77.52	even	30
847.2.f.v.729.4		16	77.24	even	30
847.2.f.w.323.1		16	77.3	odd	30
847.2.f.w.729.1		16	77.31	odd	30
847.2.f.x.148.1		16	77.17	even	30
847.2.f.x.372.1		16	77.10	even	6
5929.2.a.bs.1.1		8	77.18	odd	30
5929.2.a.bt.1.8		8	77.4	even	15
7623.2.a.ct.1.1		8	231.59	even	30
7623.2.a.cw.1.8		8	231.227	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)

\(f(q)\)	\(=\)	\(q+(-2.49618 + 0.530579i) q^{2} +(-0.0429192 - 0.408349i) q^{3} +(4.12229 - 1.83536i) q^{4} +(-2.29443 + 2.54823i) q^{5} +(0.323795 + 0.996539i) q^{6} +(-5.18703 + 3.76860i) q^{8} +(2.76954 - 0.588683i) q^{9} +O(q^{10})\)	\(q+(-2.49618 + 0.530579i) q^{2} +(-0.0429192 - 0.408349i) q^{3} +(4.12229 - 1.83536i) q^{4} +(-2.29443 + 2.54823i) q^{5} +(0.323795 + 0.996539i) q^{6} +(-5.18703 + 3.76860i) q^{8} +(2.76954 - 0.588683i) q^{9} +(4.37528 - 7.57820i) q^{10} +(2.88705 + 1.63246i) q^{11} +(-0.926394 - 1.60456i) q^{12} +(0.672122 - 2.06858i) q^{13} +(1.13904 + 0.827562i) q^{15} +(4.90943 - 5.45247i) q^{16} +(-4.41844 - 0.939168i) q^{17} +(-6.60091 + 2.93891i) q^{18} +(2.21426 + 0.985853i) q^{19} +(-4.78140 + 14.7156i) q^{20} +(-8.07274 - 2.54311i) q^{22} +(-0.324201 - 0.561533i) q^{23} +(1.76153 + 1.95637i) q^{24} +(-0.706391 - 6.72086i) q^{25} +(-0.580191 + 5.52015i) q^{26} +(-0.739900 - 2.27718i) q^{27} +(1.01366 + 0.736466i) q^{29} +(-3.28233 - 1.46139i) q^{30} +(5.37945 + 5.97449i) q^{31} +(-2.95031 + 5.11008i) q^{32} +(0.542705 - 1.24899i) q^{33} +11.5275 q^{34} +(10.3364 - 7.50983i) q^{36} +(-0.524032 + 4.98583i) q^{37} +(-6.05026 - 1.28602i) q^{38} +(-0.873549 - 0.185679i) q^{39} +(2.29806 - 21.8645i) q^{40} +(-2.12100 + 1.54100i) q^{41} -1.46138 q^{43} +(14.8974 + 1.43071i) q^{44} +(-4.85442 + 8.40810i) q^{45} +(1.10720 + 1.22967i) q^{46} +(4.60462 + 2.05011i) q^{47} +(-2.43722 - 1.77074i) q^{48} +(5.32922 + 16.4017i) q^{50} +(-0.193872 + 1.84457i) q^{51} +(-1.02591 - 9.76087i) q^{52} +(8.96503 + 9.95668i) q^{53} +(3.05514 + 5.29166i) q^{54} +(-10.7840 + 3.61128i) q^{55} +(0.307538 - 0.946503i) q^{57} +(-2.92102 - 1.30052i) q^{58} +(-7.00669 + 3.11958i) q^{59} +(6.21433 + 1.32090i) q^{60} +(-9.59187 + 10.6529i) q^{61} +(-16.5980 - 12.0591i) q^{62} +(0.118654 - 0.365178i) q^{64} +(3.72907 + 6.45893i) q^{65} +(-0.692001 + 3.40564i) q^{66} +(-3.11348 + 5.39271i) q^{67} +(-19.9378 + 4.23791i) q^{68} +(-0.215387 + 0.156488i) q^{69} +(1.30713 + 4.02294i) q^{71} +(-12.1472 + 13.4908i) q^{72} +(5.41291 - 2.40998i) q^{73} +(-1.33730 - 12.7235i) q^{74} +(-2.71414 + 0.576908i) q^{75} +10.9372 q^{76} +2.27905 q^{78} +(-9.54983 + 2.02988i) q^{79} +(2.62978 + 25.0207i) q^{80} +(6.86174 - 3.05504i) q^{81} +(4.47678 - 4.97197i) q^{82} +(2.58881 + 7.96754i) q^{83} +(12.5310 - 9.10432i) q^{85} +(3.64786 - 0.775377i) q^{86} +(0.257230 - 0.445535i) q^{87} +(-21.1273 + 2.41250i) q^{88} +(2.38125 + 4.12444i) q^{89} +(7.65633 - 23.5637i) q^{90} +(-2.36707 - 1.71978i) q^{92} +(2.20879 - 2.45311i) q^{93} +(-12.5817 - 2.67432i) q^{94} +(-7.59265 + 3.38047i) q^{95} +(2.21332 + 0.985434i) q^{96} +(2.69021 - 8.27962i) q^{97} +(8.95679 + 2.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9 + 12 * q^10 + 3 * q^11 + 18 * q^12 + 14 * q^13 - 36 * q^15 - 17 * q^16 - 5 * q^17 - 11 * q^18 + 19 * q^19 - 2 * q^20 - 66 * q^22 - 32 * q^23 - 35 * q^24 - 7 * q^25 - 27 * q^26 - 20 * q^27 + 6 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 26 * q^33 + 48 * q^34 + 104 * q^36 - 4 * q^37 - 5 * q^38 - 11 * q^39 - 10 * q^40 + 20 * q^41 - 16 * q^43 + 38 * q^44 + 70 * q^45 + 42 * q^46 - 23 * q^47 + 72 * q^48 + 104 * q^50 + 29 * q^51 + 33 * q^52 - 4 * q^53 + 60 * q^54 + 24 * q^55 - 22 * q^57 - 20 * q^58 + 17 * q^59 + 30 * q^60 - 7 * q^61 - 158 * q^62 + 14 * q^64 + 8 * q^65 + 8 * q^66 + 38 * q^67 - 2 * q^68 - 20 * q^69 - 28 * q^71 - 35 * q^73 + 29 * q^74 + 9 * q^75 - 104 * q^76 - 116 * q^78 - 15 * q^79 - 87 * q^80 + 14 * q^81 + 19 * q^82 - 10 * q^83 + 12 * q^85 + 52 * q^86 - 72 * q^87 - 55 * q^88 + 74 * q^89 + 28 * q^90 - 110 * q^92 - 32 * q^93 - 24 * q^94 - 32 * q^95 - 42 * q^96 - 40 * q^97 + 32 * q^99

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