LMFDB - Embedded newform 475.2.l.c.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.3
Root			$-0.791558 + 1.37102i$ of defining polynomial
Character	$\chi$	$=$	475.251
Dual form			475.2.l.c.176.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.42733 + 0.883478i) q^{2} +(0.0430161 + 0.243956i) q^{3} +(3.57933 + 3.00342i) q^{4} +(-0.111115 + 0.630167i) q^{6} +(-0.200820 + 0.347830i) q^{7} +(3.45167 + 5.97847i) q^{8} +(2.76141 - 1.00507i) q^{9} +O(q^{10})$	\(q+(2.42733 + 0.883478i) q^{2} +(0.0430161 + 0.243956i) q^{3} +(3.57933 + 3.00342i) q^{4} +(-0.111115 + 0.630167i) q^{6} +(-0.200820 + 0.347830i) q^{7} +(3.45167 + 5.97847i) q^{8} +(2.76141 - 1.00507i) q^{9} +(-2.59530 - 4.49520i) q^{11} +(-0.578733 + 1.00240i) q^{12} +(-0.501737 + 2.84549i) q^{13} +(-0.794758 + 0.666881i) q^{14} +(1.47378 + 8.35823i) q^{16} +(-3.89339 - 1.41708i) q^{17} +7.59083 q^{18} +(0.386682 + 4.34171i) q^{19} +(-0.0934938 - 0.0340290i) q^{21} +(-2.32827 - 13.2043i) q^{22} +(-2.57278 - 2.15882i) q^{23} +(-1.31001 + 1.09923i) q^{24} +(-3.73181 + 6.46368i) q^{26} +(0.735558 + 1.27402i) q^{27} +(-1.76348 + 0.641855i) q^{28} +(-6.18683 + 2.25182i) q^{29} +(3.13119 - 5.42339i) q^{31} +(-1.40944 + 7.99334i) q^{32} +(0.984992 - 0.826506i) q^{33} +(-8.19861 - 6.87945i) q^{34} +(12.9027 + 4.69619i) q^{36} -1.14106 q^{37} +(-2.89720 + 10.8804i) q^{38} -0.715757 q^{39} +(0.496543 + 2.81603i) q^{41} +(-0.196877 - 0.165199i) q^{42} +(9.52394 - 7.99153i) q^{43} +(4.21150 - 23.8846i) q^{44} +(-4.33773 - 7.51317i) q^{46} +(6.35381 - 2.31260i) q^{47} +(-1.97565 + 0.719076i) q^{48} +(3.41934 + 5.92248i) q^{49} +(0.178227 - 1.01077i) q^{51} +(-10.3421 + 8.67803i) q^{52} +(-9.42382 - 7.90752i) q^{53} +(0.659874 + 3.74233i) q^{54} -2.77266 q^{56} +(-1.04255 + 0.281097i) q^{57} -17.0069 q^{58} +(1.42380 + 0.518220i) q^{59} +(-5.35269 - 4.49144i) q^{61} +(12.3919 - 10.3980i) q^{62} +(-0.204952 + 1.16234i) q^{63} +(-1.99595 + 3.45709i) q^{64} +(3.12111 - 1.13599i) q^{66} +(-0.711451 + 0.258947i) q^{67} +(-9.67967 - 16.7657i) q^{68} +(0.415986 - 0.720510i) q^{69} +(-6.38582 + 5.35834i) q^{71} +(15.5403 + 13.0399i) q^{72} +(1.72232 + 9.76776i) q^{73} +(-2.76974 - 1.00810i) q^{74} +(-11.6559 + 16.7018i) q^{76} +2.08476 q^{77} +(-1.73738 - 0.632356i) q^{78} +(0.553655 + 3.13994i) q^{79} +(6.47421 - 5.43251i) q^{81} +(-1.28263 + 7.27414i) q^{82} +(2.75971 - 4.77995i) q^{83} +(-0.232442 - 0.402602i) q^{84} +(30.1781 - 10.9839i) q^{86} +(-0.815478 - 1.41245i) q^{87} +(17.9163 - 31.0319i) q^{88} +(-2.17478 + 12.3338i) q^{89} +(-0.888989 - 0.745950i) q^{91} +(-2.72500 - 15.4543i) q^{92} +(1.45776 + 0.530581i) q^{93} +17.4660 q^{94} -2.01065 q^{96} +(-8.35815 - 3.04212i) q^{97} +(3.06752 + 17.3967i) q^{98} +(-11.6847 - 9.80464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	2.42733	+	0.883478i	1.71639	+	0.624713i	0.997517	−	0.0704330i	$-0.0224381\pi$
$2$	2.42733	+	0.883478i	1.71639	+	0.624713i	0.718869	+	0.695146i	$0.244660\pi$
$3$	0.0430161	+	0.243956i	0.0248353	+	0.140848i	0.994704	−	0.102780i	$-0.0327736\pi$
$3$	0.0430161	+	0.243956i	0.0248353	+	0.140848i	−0.969869	+	0.243628i	$0.921663\pi$
$4$	3.57933	+	3.00342i	1.78967	+	1.50171i
$5$		0			0
$5$		0			0
$6$	−0.111115	+	0.630167i	−0.0453627	+	0.257265i
$7$	−0.200820	+	0.347830i	−0.0759028	+	0.131468i	−0.901479	−	0.432824i	$-0.857517\pi$
$7$	−0.200820	+	0.347830i	−0.0759028	+	0.131468i	0.825576	+	0.564291i	$0.190851\pi$
$8$	3.45167	+	5.97847i	1.22035	+	2.11371i
$9$	2.76141	−	1.00507i	0.920471	−	0.335024i
$10$		0			0
$11$	−2.59530	−	4.49520i	−0.782514	−	1.35535i	−0.930473	−	0.366360i	$-0.880604\pi$
$11$	−2.59530	−	4.49520i	−0.782514	−	1.35535i	0.147959	−	0.988993i	$-0.452730\pi$
$12$	−0.578733	+	1.00240i	−0.167066	+	0.289367i
$13$	−0.501737	+	2.84549i	−0.139157	+	0.789197i	0.832718	+	0.553698i	$0.186784\pi$
$13$	−0.501737	+	2.84549i	−0.139157	+	0.789197i	−0.971875	+	0.235499i	$0.924327\pi$
$14$	−0.794758	+	0.666881i	−0.212408	+	0.178231i
$15$		0			0
$16$	1.47378	+	8.35823i	0.368445	+	2.08956i
$17$	−3.89339	−	1.41708i	−0.944286	−	0.343692i	−0.176429	−	0.984313i	$-0.556455\pi$
$17$	−3.89339	−	1.41708i	−0.944286	−	0.343692i	−0.767857	+	0.640621i	$0.778677\pi$
$18$	7.59083			1.78918
$19$	0.386682	+	4.34171i	0.0887110	+	0.996057i
$19$	0.386682	+	4.34171i	0.0887110	+	0.996057i
$20$		0			0
$21$	−0.0934938	−	0.0340290i	−0.0204020	−	0.00742573i
$22$	−2.32827	−	13.2043i	−0.496388	−	2.81516i
$23$	−2.57278	−	2.15882i	−0.536462	−	0.450145i	0.333864	−	0.942621i	$-0.391647\pi$
$23$	−2.57278	−	2.15882i	−0.536462	−	0.450145i	−0.870326	+	0.492476i	$0.836092\pi$
$24$	−1.31001	+	1.09923i	−0.267404	+	0.224379i
$25$		0			0
$26$	−3.73181	+	6.46368i	−0.731868	+	1.26763i
$27$	0.735558	+	1.27402i	0.141558	+	0.245186i
$28$	−1.76348	+	0.641855i	−0.333267	+	0.121299i
$29$	−6.18683	+	2.25182i	−1.14887	+	0.418153i	−0.845107	−	0.534597i	$-0.820464\pi$
$29$	−6.18683	+	2.25182i	−1.14887	+	0.418153i	−0.303758	+	0.952749i	$0.598241\pi$
$30$		0			0
$31$	3.13119	−	5.42339i	0.562379	−	0.974069i	−0.434909	−	0.900474i	$-0.643220\pi$
$31$	3.13119	−	5.42339i	0.562379	−	0.974069i	0.997288	−	0.0735948i	$-0.0234472\pi$
$32$	−1.40944	+	7.99334i	−0.249156	+	1.41304i
$33$	0.984992	−	0.826506i	0.171465	−	0.143876i
$34$	−8.19861	−	6.87945i	−1.40605	−	1.17982i
$35$		0			0
$36$	12.9027	+	4.69619i	2.15045	+	0.782698i
$37$	−1.14106			−0.187590			−0.0937949	−	0.995592i	$-0.529900\pi$
$37$	−1.14106			−0.187590			−0.0937949	+	0.995592i	$0.529900\pi$
$38$	−2.89720	+	10.8804i	−0.469988	+	1.76504i
$39$	−0.715757			−0.114613
$40$		0			0
$41$	0.496543	+	2.81603i	0.0775469	+	0.439790i	0.998717	+	0.0506312i	$0.0161233\pi$
$41$	0.496543	+	2.81603i	0.0775469	+	0.439790i	−0.921171	+	0.389159i	$0.872766\pi$
$42$	−0.196877	−	0.165199i	−0.0303788	−	0.0254908i
$43$	9.52394	−	7.99153i	1.45239	−	1.21870i	0.521572	−	0.853207i	$-0.325346\pi$
$43$	9.52394	−	7.99153i	1.45239	−	1.21870i	0.930815	−	0.365491i	$-0.119099\pi$
$44$	4.21150	−	23.8846i	0.634908	−	3.60074i
$45$		0			0
$46$	−4.33773	−	7.51317i	−0.639564	−	1.10776i
$47$	6.35381	−	2.31260i	0.926798	−	0.337327i	0.165859	−	0.986150i	$-0.446960\pi$
$47$	6.35381	−	2.31260i	0.926798	−	0.337327i	0.760940	+	0.648822i	$0.224738\pi$
$48$	−1.97565	+	0.719076i	−0.285160	+	0.103790i
$49$	3.41934	+	5.92248i	0.488478	+	0.846068i
$50$		0			0
$51$	0.178227	−	1.01077i	0.0249567	−	0.141537i
$52$	−10.3421	+	8.67803i	−1.43419	+	1.20343i
$53$	−9.42382	−	7.90752i	−1.29446	−	1.08618i	−0.991074	−	0.133314i	$-0.957438\pi$
$53$	−9.42382	−	7.90752i	−1.29446	−	1.08618i	−0.303387	−	0.952867i	$-0.598117\pi$
$54$	0.659874	+	3.74233i	0.0897975	+	0.509267i
$55$		0			0
$56$	−2.77266			−0.370512
$57$	−1.04255	+	0.281097i	−0.138090	+	0.0372322i
$58$	−17.0069			−2.23312
$59$	1.42380	+	0.518220i	0.185363	+	0.0674665i	0.433034	−	0.901378i	$-0.357443\pi$
$59$	1.42380	+	0.518220i	0.185363	+	0.0674665i	−0.247671	+	0.968844i	$0.579665\pi$
$60$		0			0
$61$	−5.35269	−	4.49144i	−0.685342	−	0.575070i	0.232220	−	0.972663i	$-0.425401\pi$
$61$	−5.35269	−	4.49144i	−0.685342	−	0.575070i	−0.917562	+	0.397593i	$0.869845\pi$
$62$	12.3919	−	10.3980i	1.57377	−	1.32055i
$63$	−0.204952	+	1.16234i	−0.0258216	+	0.146441i
$64$	−1.99595	+	3.45709i	−0.249494	+	0.432136i
$65$		0			0
$66$	3.12111	−	1.13599i	0.384182	−	0.139831i
$67$	−0.711451	+	0.258947i	−0.0869175	+	0.0316354i	−0.385113	−	0.922869i	$-0.625838\pi$
$67$	−0.711451	+	0.258947i	−0.0869175	+	0.0316354i	0.298195	+	0.954505i	$0.403615\pi$
$68$	−9.67967	−	16.7657i	−1.17383	−	2.03314i
$69$	0.415986	−	0.720510i	0.0500789	−	0.0867392i
$70$		0			0
$71$	−6.38582	+	5.35834i	−0.757857	+	0.635918i	−0.937568	−	0.347802i	$-0.886928\pi$
$71$	−6.38582	+	5.35834i	−0.757857	+	0.635918i	0.179711	+	0.983719i	$0.442484\pi$
$72$	15.5403	+	13.0399i	1.83144	+	1.53676i
$73$	1.72232	+	9.76776i	0.201582	+	1.14323i	0.902728	+	0.430212i	$0.141561\pi$
$73$	1.72232	+	9.76776i	0.201582	+	1.14323i	−0.701146	+	0.713018i	$0.747328\pi$
$74$	−2.76974	−	1.00810i	−0.321976	−	0.117190i
$75$		0			0
$76$	−11.6559	+	16.7018i	−1.33702	+	1.91583i
$77$	2.08476			0.237580
$78$	−1.73738	−	0.632356i	−0.196720	−	0.0716002i
$79$	0.553655	+	3.13994i	0.0622911	+	0.353270i	0.999983	+	0.00580301i	$0.00184717\pi$
$79$	0.553655	+	3.13994i	0.0622911	+	0.353270i	−0.937692	+	0.347467i	$0.887042\pi$
$80$		0			0
$81$	6.47421	−	5.43251i	0.719357	−	0.603612i
$82$	−1.28263	+	7.27414i	−0.141642	+	0.803294i
$83$	2.75971	−	4.77995i	0.302917	−	0.524668i	−0.673878	−	0.738842i	$-0.735373\pi$
$83$	2.75971	−	4.77995i	0.302917	−	0.524668i	0.976795	+	0.214174i	$0.0687061\pi$
$84$	−0.232442	−	0.402602i	−0.0253615	−	0.0439275i
$85$		0			0
$86$	30.1781	−	10.9839i	3.25419	−	1.18443i
$87$	−0.815478	−	1.41245i	−0.0874285	−	0.151431i
$88$	17.9163	−	31.0319i	1.90988	−	3.30801i
$89$	−2.17478	+	12.3338i	−0.230527	+	1.30738i	0.621306	+	0.783568i	$0.286602\pi$
$89$	−2.17478	+	12.3338i	−0.230527	+	1.30738i	−0.851833	+	0.523814i	$0.824509\pi$
$90$		0			0
$91$	−0.888989	−	0.745950i	−0.0931914	−	0.0781968i
$92$	−2.72500	−	15.4543i	−0.284101	−	1.61122i
$93$	1.45776	+	0.530581i	0.151163	+	0.0550187i
$94$	17.4660			1.80148
$95$		0			0
$96$	−2.01065			−0.205211
$97$	−8.35815	−	3.04212i	−0.848642	−	0.308880i	−0.119155	−	0.992876i	$-0.538019\pi$
$97$	−8.35815	−	3.04212i	−0.848642	−	0.308880i	−0.729487	+	0.683995i	$0.760241\pi$
$98$	3.06752	+	17.3967i	0.309866	+	1.75734i
$99$	−11.6847	−	9.80464i	−1.17436	−	0.985403i
$100$		0			0
$101$	0.233727	−	1.32553i	0.0232567	−	0.131895i	−0.970969	−	0.239206i	$-0.923113\pi$
$101$	0.233727	−	1.32553i	0.0232567	−	0.131895i	0.994226	+	0.107311i	$0.0342240\pi$
$102$	1.32561	−	2.29603i	0.131255	−	0.227341i
$103$	6.21391	+	10.7628i	0.612275	+	1.06049i	0.990856	+	0.134923i	$0.0430787\pi$
$103$	6.21391	+	10.7628i	0.612275	+	1.06049i	−0.378581	+	0.925568i	$0.623588\pi$
$104$	−18.7435	+	6.82208i	−1.83795	+	0.668960i
$105$		0			0
$106$	−15.8886	−	27.5199i	−1.54324	−	2.67297i
$107$	−7.28110	+	12.6112i	−0.703890	+	1.21917i	0.263200	+	0.964741i	$0.415222\pi$
$107$	−7.28110	+	12.6112i	−0.703890	+	1.21917i	−0.967091	+	0.254432i	$0.918111\pi$
$108$	−1.19362	+	6.76934i	−0.114856	+	0.651380i
$109$	3.38582	−	2.84104i	0.324303	−	0.272122i	−0.466071	−	0.884747i	$-0.654331\pi$
$109$	3.38582	−	2.84104i	0.324303	−	0.272122i	0.790374	+	0.612625i	$0.209886\pi$
$110$		0			0
$111$	−0.0490841	−	0.278370i	−0.00465885	−	0.0264217i
$112$	−3.20321	−	1.16587i	−0.302675	−	0.110165i
$113$	−8.08453			−0.760528			−0.380264	−	0.924878i	$-0.624167\pi$
$113$	−8.08453			−0.760528			−0.380264	+	0.924878i	$0.624167\pi$
$114$	−2.77897	−	0.238757i	−0.260274	−	0.0223616i
$115$		0			0
$116$	−28.9079	−	10.5216i	−2.68403	−	0.976907i
$117$	1.47442	+	8.36186i	0.136310	+	0.773054i
$118$	2.99820	+	2.51579i	0.276006	+	0.231597i
$119$	1.27477	−	1.06966i	0.116858	−	0.0980557i
$120$		0			0
$121$	−7.97122	+	13.8065i	−0.724656	+	1.25514i
$122$	−9.02468	−	15.6312i	−0.817056	−	1.41518i
$123$	−0.665629	+	0.242269i	−0.0600178	+	0.0218447i
$124$	27.4963	−	10.0078i	2.46924	−	0.898730i
$125$		0			0
$126$	−1.52439	+	2.64032i	−0.135804	+	0.235219i
$127$	0.0974458	−	0.552642i	0.00864691	−	0.0490391i	−0.980179	−	0.198114i	$-0.936518\pi$
$127$	0.0974458	−	0.552642i	0.00864691	−	0.0490391i	0.988826	+	0.149075i	$0.0476295\pi$
$128$	4.53632	−	3.80642i	0.400958	−	0.336444i
$129$	2.35927	+	1.97966i	0.207722	+	0.174299i
$130$		0			0
$131$	9.28037	+	3.37778i	0.810830	+	0.295118i	0.713967	−	0.700180i	$-0.246897\pi$
$131$	9.28037	+	3.37778i	0.810830	+	0.295118i	0.0968634	+	0.995298i	$0.469119\pi$
$132$	6.00796			0.522926
$133$	−1.58783	−	0.737403i	−0.137683	−	0.0639409i
$134$	−1.95570			−0.168947
$135$		0			0
$136$	−4.96675	−	28.1678i	−0.425895	−	2.41537i
$137$	6.86600	+	5.76126i	0.586602	+	0.492217i	0.887108	−	0.461563i	$-0.152711\pi$
$137$	6.86600	+	5.76126i	0.586602	+	0.492217i	−0.300506	+	0.953780i	$0.597155\pi$
$138$	1.64629	−	1.38140i	0.140142	−	0.117593i
$139$	−2.28639	+	12.9668i	−0.193929	+	1.09983i	0.720006	+	0.693968i	$0.244139\pi$
$139$	−2.28639	+	12.9668i	−0.193929	+	1.09983i	−0.913935	+	0.405860i	$0.866972\pi$
$140$		0			0
$141$	0.837488	+	1.45057i	0.0705292	+	0.122160i
$142$	−20.2345	+	7.36475i	−1.69804	+	0.618036i
$143$	14.0932	−	5.12951i	1.17853	−	0.428951i
$144$	12.4703	+	21.5993i	1.03920	+	1.79994i
$145$		0			0
$146$	−4.44895	+	25.2313i	−0.368198	+	2.08815i
$147$	−1.29774	+	1.08893i	−0.107036	+	0.0898135i
$148$	−4.08425	−	3.42709i	−0.335723	−	0.281705i
$149$	−1.42107	−	8.05930i	−0.116419	−	0.660243i	−0.986038	−	0.166520i	$-0.946747\pi$
$149$	−1.42107	−	8.05930i	−0.116419	−	0.660243i	0.869619	−	0.493723i	$-0.164364\pi$
$150$		0			0
$151$	7.60636			0.618997			0.309498	−	0.950900i	$-0.399839\pi$
$151$	7.60636			0.618997			0.309498	+	0.950900i	$0.399839\pi$
$152$	−24.6221	+	17.2979i	−1.99712	+	1.40305i
$153$	−12.1755			−0.984333
$154$	5.06040	+	1.84184i	0.407779	+	0.148419i
$155$		0			0
$156$	−2.56193	−	2.14972i	−0.205119	−	0.172115i
$157$	9.62566	−	8.07689i	0.768212	−	0.644606i	−0.172039	−	0.985090i	$-0.555035\pi$
$157$	9.62566	−	8.07689i	0.768212	−	0.644606i	0.940250	+	0.340484i	$0.110591\pi$
$158$	−1.43016	+	8.11082i	−0.113777	+	0.645262i
$159$	1.52371	−	2.63915i	0.120838	−	0.209298i
$160$		0			0
$161$	1.26757	−	0.461357i	0.0998984	−	0.0363600i
$162$	20.5146	−	7.46669i	1.61178	−	0.586639i
$163$	−1.64175	−	2.84359i	−0.128591	−	0.222727i	0.794540	−	0.607212i	$-0.207712\pi$
$163$	−1.64175	−	2.84359i	−0.128591	−	0.222727i	−0.923131	+	0.384485i	$0.874379\pi$
$164$	−6.68043	+	11.5708i	−0.521654	+	0.903531i
$165$		0			0
$166$	10.9217	−	9.16441i	0.847689	−	0.711296i
$167$	4.00460	+	3.36026i	0.309885	+	0.260025i	0.784445	−	0.620199i	$-0.212948\pi$
$167$	4.00460	+	3.36026i	0.309885	+	0.260025i	−0.474559	+	0.880224i	$0.657393\pi$
$168$	−0.119269	−	0.676407i	−0.00920179	−	0.0521860i
$169$	4.37093	+	1.59089i	0.336226	+	0.122376i
$170$		0			0
$171$	5.43153	+	11.6006i	0.415359	+	0.887122i
$172$	58.0913			4.42942
$173$	4.23385	+	1.54100i	0.321894	+	0.117160i	0.497913	−	0.867227i	$-0.334100\pi$
$173$	4.23385	+	1.54100i	0.321894	+	0.117160i	−0.176019	+	0.984387i	$0.556322\pi$
$174$	−0.731571	−	4.14895i	−0.0554603	−	0.314531i
$175$		0			0
$176$	33.7470	−	28.3171i	2.54378	−	2.13448i
$177$	−0.0651768	+	0.369636i	−0.00489899	+	0.0277835i
$178$	−16.1756	+	28.0169i	−1.21241	+	2.09996i
$179$	1.88583	+	3.26636i	0.140954	+	0.244139i	0.927856	−	0.372939i	$-0.121650\pi$
$179$	1.88583	+	3.26636i	0.140954	+	0.244139i	−0.786902	+	0.617078i	$0.788316\pi$
$180$		0			0
$181$	−17.9437	+	6.53096i	−1.33374	+	0.485442i	−0.907836	−	0.419325i	$-0.862267\pi$
$181$	−17.9437	+	6.53096i	−1.33374	+	0.485442i	−0.425906	+	0.904767i	$0.640045\pi$
$182$	−1.49884	−	2.59607i	−0.111102	−	0.192434i
$183$	0.865463	−	1.49903i	0.0639768	−	0.110811i
$184$	4.02605	−	22.8328i	0.296804	−	1.68326i
$185$		0			0
$186$	3.06972	+	2.57580i	0.225082	+	0.188867i
$187$	3.73449	+	21.1793i	0.273093	+	1.54879i
$188$	29.6881	+	10.8056i	2.16523	+	0.788078i
$189$	−0.590859			−0.0429787
$190$		0			0
$191$	2.89599			0.209547			0.104773	−	0.994496i	$-0.466588\pi$
$191$	2.89599			0.209547			0.104773	+	0.994496i	$0.466588\pi$
$192$	−0.929236	−	0.338214i	−0.0670619	−	0.0244085i
$193$	−1.97618	−	11.2075i	−0.142249	−	0.806733i	−0.969535	−	0.244952i	$-0.921228\pi$
$193$	−1.97618	−	11.2075i	−0.142249	−	0.806733i	0.827286	−	0.561781i	$-0.189883\pi$
$194$	−17.6004	−	14.7685i	−1.26363	−	1.06032i
$195$		0			0
$196$	−5.54870	+	31.4682i	−0.396336	+	2.24773i
$197$	−5.07545	+	8.79093i	−0.361610	+	0.626328i	−0.988226	−	0.153001i	$-0.951106\pi$
$197$	−5.07545	+	8.79093i	−0.361610	+	0.626328i	0.626616	+	0.779329i	$0.284440\pi$
$198$	−19.7005	−	34.1223i	−1.40006	−	2.42497i
$199$	2.75352	−	1.00220i	0.195192	−	0.0710440i	−0.242575	−	0.970133i	$-0.577992\pi$
$199$	2.75352	−	1.00220i	0.195192	−	0.0710440i	0.437766	+	0.899089i	$0.355770\pi$
$200$		0			0
$201$	−0.0937755	−	0.162424i	−0.00661441	−	0.0114565i
$202$	1.73841	−	3.01101i	0.122314	−	0.211854i
$203$	0.459187	−	2.60418i	0.0322286	−	0.182777i
$204$	3.67371	−	3.08261i	0.257211	−	0.215826i
$205$		0			0
$206$	5.57454	+	31.6148i	0.388397	+	2.20271i
$207$	−9.27428	−	3.37556i	−0.644607	−	0.234618i
$208$	−24.5227			−1.70034
$209$	18.5133	−	13.0063i	1.28059	−	0.899664i
$210$		0			0
$211$	5.17374	+	1.88309i	0.356175	+	0.129637i	0.513909	−	0.857845i	$-0.328197\pi$
$211$	5.17374	+	1.88309i	0.356175	+	0.129637i	−0.157734	+	0.987482i	$0.550419\pi$
$212$	−9.98140	−	56.6073i	−0.685525	−	3.88781i
$213$	−1.58189	−	1.32737i	−0.108389	−	0.0909496i
$214$	−28.8154	+	24.1790i	−1.96978	+	1.65284i
$215$		0			0
$216$	−5.07781	+	8.79503i	−0.345501	+	0.598426i
$217$	1.25761	+	2.17825i	0.0853723	+	0.147869i
$218$	10.7285	−	3.90486i	0.726626	−	0.264470i
$219$	−2.30882	+	0.840341i	−0.156015	+	0.0567850i
$220$		0			0
$221$	5.98574	−	10.3676i	0.402644	−	0.697400i
$222$	0.126790	−	0.719061i	0.00850958	−	0.0482602i
$223$	−6.09836	+	5.11713i	−0.408376	+	0.342669i	−0.823721	−	0.566996i	$-0.808106\pi$
$223$	−6.09836	+	5.11713i	−0.408376	+	0.342669i	0.415344	+	0.909664i	$0.363661\pi$
$224$	−2.49728	−	2.09547i	−0.166857	−	0.140009i
$225$		0			0
$226$	−19.6239	−	7.14250i	−1.30536	−	0.475112i
$227$	−8.02439			−0.532597			−0.266299	−	0.963891i	$-0.585801\pi$
$227$	−8.02439			−0.532597			−0.266299	+	0.963891i	$0.585801\pi$
$228$	−4.57590	−	2.12509i	−0.303046	−	0.140737i
$229$	−28.2466			−1.86659			−0.933295	−	0.359111i	$-0.883080\pi$
$229$	−28.2466			−1.86659			−0.933295	+	0.359111i	$0.883080\pi$
$230$		0			0
$231$	0.0896780	+	0.508589i	0.00590038	+	0.0334627i
$232$	−34.8174	−	29.2152i	−2.28587	−	1.91807i
$233$	−7.23338	+	6.06953i	−0.473875	+	0.397628i	−0.848206	−	0.529667i	$-0.822317\pi$
$233$	−7.23338	+	6.06953i	−0.473875	+	0.397628i	0.374331	+	0.927295i	$0.377872\pi$
$234$	−3.80860	+	21.5996i	−0.248976	+	1.41201i
$235$		0			0
$236$	3.53981	+	6.13114i	0.230422	+	0.399103i
$237$	−0.742191	+	0.270135i	−0.0482105	+	0.0175472i
$238$	4.03932	−	1.47019i	0.261831	−	0.0952985i
$239$	−5.89638	−	10.2128i	−0.381405	−	0.660613i	0.609858	−	0.792511i	$-0.291226\pi$
$239$	−5.89638	−	10.2128i	−0.381405	−	0.660613i	−0.991263	+	0.131897i	$0.957893\pi$
$240$		0			0
$241$	−2.22273	+	12.6057i	−0.143179	+	0.812007i	0.825633	+	0.564208i	$0.190818\pi$
$241$	−2.22273	+	12.6057i	−0.143179	+	0.812007i	−0.968811	+	0.247799i	$0.920293\pi$
$242$	−31.5466	+	26.4707i	−2.02789	+	1.70160i
$243$	4.98461	+	4.18258i	0.319763	+	0.268313i
$244$	−5.66939	−	32.1527i	−0.362946	−	2.05837i
$245$		0			0
$246$	−1.82974			−0.116660
$247$	−12.5483	−	1.07810i	−0.798430	−	0.0685976i
$248$	43.2314			2.74520
$249$	1.28481	+	0.467633i	0.0814216	+	0.0296350i
$250$		0			0
$251$	1.83823	+	1.54246i	0.116028	+	0.0973590i	0.698956	−	0.715165i	$-0.253648\pi$
$251$	1.83823	+	1.54246i	0.116028	+	0.0973590i	−0.582928	+	0.812524i	$0.698093\pi$
$252$	−4.22459	+	3.54485i	−0.266124	+	0.223305i
$253$	−3.02717	+	17.1680i	−0.190317	+	1.07934i
$254$	0.724781	−	1.25536i	0.0454768	−	0.0787681i
$255$		0			0
$256$	21.8764	−	7.96235i	1.36727	−	0.497647i
$257$	16.1772	−	5.88802i	1.00911	−	0.367285i	0.216017	−	0.976390i	$-0.430693\pi$
$257$	16.1772	−	5.88802i	1.00911	−	0.367285i	0.793090	+	0.609105i	$0.208471\pi$
$258$	3.97774	+	6.88966i	0.247644	+	0.428931i
$259$	0.229148	−	0.396897i	0.0142386	−	0.0246620i
$260$		0			0
$261$	−14.8211	+	12.4364i	−0.917406	+	0.769795i
$262$	19.5424	+	16.3980i	1.20733	+	1.01307i
$263$	−2.54981	−	14.4607i	−0.157228	−	0.891685i	−0.956720	−	0.291009i	$-0.906009\pi$
$263$	−2.54981	−	14.4607i	−0.157228	−	0.891685i	0.799492	−	0.600677i	$-0.205102\pi$
$264$	8.34112	+	3.03592i	0.513360	+	0.186848i
$265$		0			0
$266$	−3.20272	−	3.19274i	−0.196372	−	0.195759i
$267$	−3.10246			−0.189868
$268$	−3.32424	−	1.20993i	−0.203061	−	0.0739080i
$269$	−3.89891	−	22.1118i	−0.237721	−	1.34818i	−0.836807	−	0.547498i	$-0.815580\pi$
$269$	−3.89891	−	22.1118i	−0.237721	−	1.34818i	0.599086	−	0.800685i	$-0.295531\pi$
$270$		0			0
$271$	10.1742	−	8.53716i	0.618038	−	0.518596i	−0.279148	−	0.960248i	$-0.590052\pi$
$271$	10.1742	−	8.53716i	0.618038	−	0.518596i	0.897186	+	0.441652i	$0.145608\pi$
$272$	6.10626	−	34.6303i	0.370246	−	2.09977i
$273$	0.143738	−	0.248962i	0.00869944	−	0.0150679i
$274$	11.5761	+	20.0505i	0.699340	+	1.21129i
$275$		0			0
$276$	3.65294	−	1.32956i	0.219881	−	0.0800303i
$277$	1.67963	+	2.90921i	0.100919	+	0.174797i	0.912064	−	0.410049i	$-0.134488\pi$
$277$	1.67963	+	2.90921i	0.100919	+	0.174797i	−0.811144	+	0.584846i	$0.801155\pi$
$278$	−17.0057	+	29.4548i	−1.01993	+	1.76658i
$279$	3.19563	−	18.1233i	0.191317	−	1.08501i
$280$		0			0
$281$	15.3380	+	12.8702i	0.914991	+	0.767769i	0.973062	−	0.230544i	$-0.0740504\pi$
$281$	15.3380	+	12.8702i	0.914991	+	0.767769i	−0.0580707	+	0.998312i	$0.518495\pi$
$282$	0.751316	+	4.26093i	0.0447402	+	0.253735i
$283$	0.498021	+	0.181265i	0.0296043	+	0.0107751i	0.356780	−	0.934188i	$-0.383875\pi$
$283$	0.498021	+	0.181265i	0.0296043	+	0.0107751i	−0.327176	+	0.944964i	$0.606097\pi$
$284$	−38.9503			−2.31127
$285$		0			0
$286$	38.7407			2.29079
$287$	−1.07922	−	0.392803i	−0.0637042	−	0.0231864i
$288$	4.14183	+	23.4895i	0.244060	+	1.38413i
$289$	0.127626	+	0.107091i	0.00750741	+	0.00629946i
$290$		0			0
$291$	0.382609	−	2.16988i	0.0224289	−	0.127201i
$292$	−23.1719	+	40.1349i	−1.35603	+	2.34872i
$293$	15.8074	+	27.3793i	0.923480	+	1.59951i	0.793988	+	0.607934i	$0.208001\pi$
$293$	15.8074	+	27.3793i	0.923480	+	1.59951i	0.129492	+	0.991580i	$0.458665\pi$
$294$	−4.11209	+	1.49668i	−0.239822	+	0.0872881i
$295$		0			0
$296$	−3.93858	−	6.82182i	−0.228925	−	0.396510i
$297$	3.81799	−	6.61296i	0.221543	−	0.383723i
$298$	3.67079	−	20.8181i	0.212643	−	1.20596i
$299$	7.43376	−	6.23766i	0.429905	−	0.360733i
$300$		0			0
$301$	0.867101	+	4.91757i	0.0499789	+	0.283444i
$302$	18.4632	+	6.72005i	1.06244	+	0.386695i
$303$	0.333425			0.0191548
$304$	−35.7192	+	9.63072i	−2.04863	+	0.552359i
$305$		0			0
$306$	−29.5541	−	10.7568i	−1.68949	−	0.614926i
$307$	−1.59262	−	9.03222i	−0.0908958	−	0.515496i	−0.995928	−	0.0901527i	$-0.971264\pi$
$307$	−1.59262	−	9.03222i	−0.0908958	−	0.515496i	0.905032	−	0.425343i	$-0.139847\pi$
$308$	7.46204	+	6.26139i	0.425189	+	0.356776i
$309$	−2.35836	+	1.97890i	−0.134162	+	0.112575i
$310$		0			0
$311$	12.0255	−	20.8288i	0.681906	−	1.18110i	−0.292493	−	0.956268i	$-0.594485\pi$
$311$	12.0255	−	20.8288i	0.681906	−	1.18110i	0.974399	−	0.224828i	$-0.0721819\pi$
$312$	−2.47056	−	4.27914i	−0.139868	−	0.242258i
$313$	−2.31124	+	0.841224i	−0.130639	+	0.0475488i	−0.406512	−	0.913645i	$-0.633255\pi$
$313$	−2.31124	+	0.841224i	−0.130639	+	0.0475488i	0.275873	+	0.961194i	$0.411033\pi$
$314$	30.5005	−	11.1013i	1.72124	−	0.626480i
$315$		0			0
$316$	−7.44882	+	12.9017i	−0.419029	+	0.725779i
$317$	−1.21940	+	6.91555i	−0.0684882	+	0.388416i	0.931225	+	0.364446i	$0.118742\pi$
$317$	−1.21940	+	6.91555i	−0.0684882	+	0.388416i	−0.999713	+	0.0239697i	$0.992369\pi$
$318$	6.03019	−	5.05993i	0.338156	−	0.283747i
$319$	26.1791	+	21.9669i	1.46575	+	1.22991i
$320$		0			0
$321$	−3.38979	−	1.23378i	−0.189200	−	0.0688631i
$322$	3.48441			0.194179
$323$	4.64704	−	17.4519i	0.258568	−	0.971052i
$324$	39.4894			2.19386
$325$		0			0
$326$	−1.47282	−	8.35278i	−0.0815720	−	0.462618i
$327$	0.838733	+	0.703781i	0.0463821	+	0.0389192i
$328$	−15.1217	+	12.6886i	−0.834955	+	0.700610i
$329$	−0.471580	+	2.67446i	−0.0259991	+	0.147448i
$330$		0			0
$331$	−8.70524	−	15.0779i	−0.478483	−	0.828758i	0.521212	−	0.853427i	$-0.325480\pi$
$331$	−8.70524	−	15.0779i	−0.478483	−	0.828758i	−0.999696	+	0.0246694i	$0.992147\pi$
$332$	24.2341	−	8.82049i	1.33002	−	0.484087i
$333$	−3.15095	+	1.14685i	−0.172671	+	0.0628471i
$334$	6.75180	+	11.6945i	0.369442	+	0.639892i
$335$		0			0
$336$	0.146632	−	0.831594i	0.00799946	−	0.0453672i
$337$	25.0326	−	21.0048i	1.36361	−	1.14420i	0.388761	−	0.921339i	$-0.372903\pi$
$337$	25.0326	−	21.0048i	1.36361	−	1.14420i	0.974849	−	0.222866i	$-0.0715413\pi$
$338$	9.20420	+	7.72324i	0.500643	+	0.420089i
$339$	−0.347764	−	1.97227i	−0.0188880	−	0.107119i
$340$		0			0
$341$	−32.5056			−1.76028
$342$	2.93524	+	32.9572i	0.158720	+	1.78212i
$343$	−5.55817			−0.300113
$344$	80.6507	+	29.3545i	4.34839	+	1.58269i
$345$		0			0
$346$	8.91554	+	7.48102i	0.479302	+	0.402182i
$347$	−5.46153	+	4.58277i	−0.293191	+	0.246016i	−0.777503	−	0.628879i	$-0.783514\pi$
$347$	−5.46153	+	4.58277i	−0.293191	+	0.246016i	0.484313	+	0.874895i	$0.339070\pi$
$348$	1.32331	−	7.50485i	0.0709368	−	0.402302i
$349$	−11.3504	+	19.6595i	−0.607575	+	1.05235i	0.384064	+	0.923307i	$0.374524\pi$
$349$	−11.3504	+	19.6595i	−0.607575	+	1.05235i	−0.991639	+	0.129044i	$0.958809\pi$
$350$		0			0
$351$	−3.99428	+	1.45380i	−0.213199	+	0.0775980i
$352$	39.5896	−	14.4094i	2.11013	−	0.768025i
$353$	−2.24694	−	3.89182i	−0.119593	−	0.207141i	0.800014	−	0.599982i	$-0.204826\pi$
$353$	−2.24694	−	3.89182i	−0.119593	−	0.207141i	−0.919606	+	0.392841i	$0.871492\pi$
$354$	−0.484771	+	0.839648i	−0.0257653	+	0.0446268i
$355$		0			0
$356$	−44.8279	+	37.6151i	−2.37587	+	1.99359i
$357$	0.315786	+	0.264976i	0.0167132	+	0.0140240i
$358$	1.69179	+	9.59464i	0.0894140	+	0.507092i
$359$	−9.94626	−	3.62014i	−0.524943	−	0.191064i	0.0659357	−	0.997824i	$-0.478997\pi$
$359$	−9.94626	−	3.62014i	−0.524943	−	0.191064i	−0.590879	+	0.806760i	$0.701219\pi$
$360$		0			0
$361$	−18.7010	+	3.35773i	−0.984261	+	0.176723i
$362$	−49.3252			−2.59248
$363$	−3.71108	−	1.35072i	−0.194781	−	0.0708946i
$364$	−0.941588	−	5.34001i	−0.0493526	−	0.279893i
$365$		0			0
$366$	3.42512	−	2.87402i	0.179034	−	0.150227i
$367$	0.313391	−	1.77733i	0.0163589	−	0.0927759i	−0.975535	−	0.219843i	$-0.929445\pi$
$367$	0.313391	−	1.77733i	0.0163589	−	0.0927759i	0.991894	+	0.127067i	$0.0405565\pi$
$368$	14.2522	−	24.6855i	0.742947	−	1.28682i
$369$	4.20148	+	7.27717i	0.218720	+	0.378834i
$370$		0			0
$371$	4.64297	−	1.68990i	0.241051	−	0.0877353i
$372$	3.62425	+	6.27739i	0.187909	+	0.325468i
$373$	−6.48193	+	11.2270i	−0.335622	+	0.581314i	−0.983604	−	0.180342i	$-0.942280\pi$
$373$	−6.48193	+	11.2270i	−0.335622	+	0.581314i	0.647982	+	0.761655i	$0.275613\pi$
$374$	−9.64661	+	54.7086i	−0.498814	+	2.82892i
$375$		0			0
$376$	35.7571	+	30.0038i	1.84403	+	1.54733i
$377$	−3.30338	−	18.7344i	−0.170132	−	0.964869i
$378$	−1.43421	−	0.522011i	−0.0737679	−	0.0268493i
$379$	33.1372			1.70214			0.851071	−	0.525051i	$-0.175954\pi$
$379$	33.1372			1.70214			0.851071	+	0.525051i	$0.175954\pi$
$380$		0			0
$381$	0.139012			0.00712181
$382$	7.02955	+	2.55855i	0.359663	+	0.130907i
$383$	−3.50654	−	19.8866i	−0.179176	−	1.01616i	−0.933213	−	0.359324i	$-0.883007\pi$
$383$	−3.50654	−	19.8866i	−0.179176	−	1.01616i	0.754037	−	0.656832i	$-0.228104\pi$
$384$	1.12374	+	0.942926i	0.0573454	+	0.0481185i
$385$		0			0
$386$	5.10471	−	28.9503i	0.259823	−	1.47353i
$387$	18.2675	−	31.6402i	0.928588	−	1.60836i
$388$	−20.7799	−	35.9918i	−1.05494	−	1.82721i
$389$	1.90648	−	0.693903i	0.0966625	−	0.0351823i	−0.293236	−	0.956040i	$-0.594732\pi$
$389$	1.90648	−	0.693903i	0.0966625	−	0.0351823i	0.389899	+	0.920858i	$0.372510\pi$
$390$		0			0
$391$	6.95762	+	12.0510i	0.351862	+	0.609443i
$392$	−23.6049	+	40.8849i	−1.19223	+	2.06500i
$393$	−0.424825	+	2.40930i	−0.0214296	+	0.121533i
$394$	−20.0864	+	16.8545i	−1.01194	+	0.849117i
$395$		0			0
$396$	−12.3761	−	70.1881i	−0.621920	−	3.52709i
$397$	7.54838	+	2.74738i	0.378842	+	0.137887i	0.524420	−	0.851459i	$-0.324282\pi$
$397$	7.54838	+	2.74738i	0.378842	+	0.137887i	−0.145578	+	0.989347i	$0.546504\pi$
$398$	7.56914			0.379406
$399$	0.111592	−	0.419082i	0.00558657	−	0.0209803i
$400$		0			0
$401$	13.5128	+	4.91825i	0.674796	+	0.245606i	0.656611	−	0.754229i	$-0.271989\pi$
$401$	13.5128	+	4.91825i	0.674796	+	0.245606i	0.0181845	+	0.999835i	$0.494211\pi$
$402$	−0.0841266	−	0.477106i	−0.00419585	−	0.0237959i
$403$	13.8612	+	11.6309i	0.690473	+	0.579376i
$404$	4.81770	−	4.04253i	0.239690	−	0.201124i
$405$		0			0
$406$	3.41533	−	5.91553i	0.169500	−	0.293583i
$407$	2.96141	+	5.12931i	0.146792	+	0.254250i
$408$	6.65806	−	2.42334i	0.329623	−	0.119973i
$409$	−0.227020	+	0.0826284i	−0.0112254	+	0.00408571i	−0.347627	−	0.937633i	$-0.613012\pi$
$409$	−0.227020	+	0.0826284i	−0.0112254	+	0.00408571i	0.336401	+	0.941719i	$0.390790\pi$
$410$		0			0
$411$	−1.11015	+	1.92283i	−0.0547595	+	0.0948462i
$412$	−10.0835	+	57.1867i	−0.496781	+	2.81738i
$413$	−0.466179	+	0.391171i	−0.0229392	+	0.0192483i
$414$	−19.5296	−	16.3872i	−0.959825	−	0.805389i
$415$		0			0
$416$	−22.0378	−	8.02110i	−1.08049	−	0.393267i
$417$	−3.26168			−0.159725
$418$	56.4288	−	15.2145i	2.76002	−	0.744166i
$419$	−22.7086			−1.10939			−0.554693	−	0.832055i	$-0.687164\pi$
$419$	−22.7086			−1.10939			−0.554693	+	0.832055i	$0.687164\pi$
$420$		0			0
$421$	−4.33685	−	24.5955i	−0.211365	−	1.19871i	−0.887103	−	0.461571i	$-0.847286\pi$
$421$	−4.33685	−	24.5955i	−0.211365	−	1.19871i	0.675738	−	0.737142i	$-0.263825\pi$
$422$	10.8947	+	9.14177i	0.530347	+	0.445014i
$423$	15.2212	−	12.7721i	0.740079	−	0.621000i
$424$	14.7470	−	83.6342i	0.716176	−	4.06164i
$425$		0			0
$426$	−2.66708	−	4.61953i	−0.129221	−	0.223817i
$427$	2.63719	−	0.959857i	0.127622	−	0.0464507i
$428$	−63.9383	+	23.2716i	−3.09057	+	1.12488i
$429$	1.85761	+	3.21747i	0.0896862	+	0.155341i
$430$		0			0
$431$	3.10128	−	17.5883i	0.149384	−	0.847196i	−0.814359	−	0.580362i	$-0.802911\pi$
$431$	3.10128	−	17.5883i	0.149384	−	0.847196i	0.963742	−	0.266835i	$-0.0859777\pi$
$432$	−9.56453	+	8.02560i	−0.460174	+	0.386132i
$433$	29.9613	+	25.1405i	1.43985	+	1.20818i	0.939591	+	0.342299i	$0.111206\pi$
$433$	29.9613	+	25.1405i	1.43985	+	1.20818i	0.500257	+	0.865877i	$0.333239\pi$
$434$	1.12821	+	6.39841i	0.0541559	+	0.307134i
$435$		0			0
$436$	20.6518			0.989042
$437$	8.37813	−	12.0051i	0.400780	−	0.574280i
$438$	−6.34670			−0.303257
$439$	−17.6050	−	6.40768i	−0.840239	−	0.305822i	−0.114185	−	0.993460i	$-0.536426\pi$
$439$	−17.6050	−	6.40768i	−0.840239	−	0.305822i	−0.726054	+	0.687638i	$0.758648\pi$
$440$		0			0
$441$	15.3947	+	12.9177i	0.733083	+	0.615129i
$442$	23.6889	−	19.8774i	1.12677	−	0.945471i
$443$	−2.96093	+	16.7923i	−0.140678	+	0.797826i	0.830058	+	0.557677i	$0.188307\pi$
$443$	−2.96093	+	16.7923i	−0.140678	+	0.797826i	−0.970736	+	0.240149i	$0.922804\pi$
$444$	0.660372	−	1.14380i	0.0313399	−	0.0542822i
$445$		0			0
$446$	−19.3236	+	7.03323i	−0.915001	+	0.333033i
$447$	1.90499	−	0.693358i	0.0901028	−	0.0327947i
$448$	−0.801654	−	1.38851i	−0.0378746	−	0.0656007i
$449$	−6.10161	+	10.5683i	−0.287953	+	0.498749i	−0.973321	−	0.229448i	$-0.926308\pi$
$449$	−6.10161	+	10.5683i	−0.287953	+	0.498749i	0.685368	+	0.728197i	$0.259641\pi$
$450$		0			0
$451$	11.3700	−	9.54052i	0.535390	−	0.449246i
$452$	−28.9372	−	24.2812i	−1.36109	−	1.14209i
$453$	0.327195	+	1.85562i	0.0153730	+	0.0871845i
$454$	−19.4779	−	7.08937i	−0.914142	−	0.332721i
$455$		0			0
$456$	−5.27909	−	5.26263i	−0.247216	−	0.246445i
$457$	13.4079			0.627193			0.313596	−	0.949556i	$-0.398466\pi$
$457$	13.4079			0.627193			0.313596	+	0.949556i	$0.398466\pi$
$458$	−68.5640	−	24.9553i	−3.20379	−	1.16608i
$459$	−1.05842	−	6.00262i	−0.0494030	−	0.280178i
$460$		0			0
$461$	−10.7371	+	9.00946i	−0.500075	+	0.419613i	−0.857621	−	0.514283i	$-0.828058\pi$
$461$	−10.7371	+	9.00946i	−0.500075	+	0.419613i	0.357546	+	0.933896i	$0.383614\pi$
$462$	−0.231649	+	1.31374i	−0.0107773	+	0.0611209i
$463$	13.0889	−	22.6706i	0.608292	−	1.05359i	−0.383230	−	0.923653i	$-0.625188\pi$
$463$	13.0889	−	22.6706i	0.608292	−	1.05359i	0.991522	−	0.129940i	$-0.0414785\pi$
$464$	−27.9393	−	48.3922i	−1.29705	−	2.24655i
$465$		0			0
$466$	−22.9201	+	8.34225i	−1.06175	+	0.386447i
$467$	−19.7941	−	34.2843i	−0.915960	−	1.58649i	−0.805490	−	0.592609i	$-0.798098\pi$
$467$	−19.7941	−	34.2843i	−0.915960	−	1.58649i	−0.110470	−	0.993879i	$-0.535236\pi$
$468$	−19.8367	+	34.3582i	−0.916952	+	1.58821i
$469$	0.0528039	−	0.299466i	0.00243826	−	0.0138280i
$470$		0			0
$471$	2.38447	+	2.00080i	0.109870	+	0.0921922i
$472$	1.81632	+	10.3009i	0.0836029	+	0.474135i
$473$	−60.6411	−	22.0715i	−2.78828	−	1.01485i
$474$	−2.04020			−0.0937097
$475$		0			0
$476$	7.77548			0.356389
$477$	−33.9707	−	12.3643i	−1.55541	−	0.566123i
$478$	−5.28968	−	29.9993i	−0.241944	−	1.37214i
$479$	2.89476	+	2.42899i	0.132265	+	0.110983i	0.706520	−	0.707693i	$-0.250264\pi$
$479$	2.89476	+	2.42899i	0.132265	+	0.110983i	−0.574255	+	0.818676i	$0.694708\pi$
$480$		0			0
$481$	0.572514	−	3.24689i	0.0261044	−	0.148045i
$482$	−16.5322	+	28.6346i	−0.753022	+	1.30427i
$483$	0.167077	+	0.289385i	0.00760225	+	0.0131675i
$484$	−69.9985	+	25.4774i	−3.18175	+	1.15806i
$485$		0			0
$486$	8.40410	+	14.5563i	0.381218	+	0.660288i
$487$	3.49493	−	6.05339i	0.158370	−	0.274305i	−0.775911	−	0.630843i	$-0.782709\pi$
$487$	3.49493	−	6.05339i	0.158370	−	0.274305i	0.934281	+	0.356537i	$0.116043\pi$
$488$	8.37622	−	47.5039i	0.379174	−	2.15040i
$489$	0.623089	−	0.522834i	0.0281771	−	0.0236434i
$490$		0			0
$491$	−5.66765	−	32.1428i	−0.255777	−	1.45059i	−0.794069	−	0.607827i	$-0.792041\pi$
$491$	−5.66765	−	32.1428i	−0.255777	−	1.45059i	0.538292	−	0.842758i	$-0.319070\pi$
$492$	−3.11014	−	1.13200i	−0.140216	−	0.0510345i
$493$	27.2787			1.22857
$494$	−29.5065	−	13.7031i	−1.32756	−	0.616530i
$495$		0			0
$496$	49.9446	+	18.1784i	2.24258	+	0.816232i
$497$	−0.581393	−	3.29724i	−0.0260790	−	0.147902i
$498$	2.70552	+	2.27020i	0.121237	+	0.101730i
$499$	21.2906	−	17.8650i	0.953100	−	0.799746i	−0.0267168	−	0.999643i	$-0.508505\pi$
$499$	21.2906	−	17.8650i	0.953100	−	0.799746i	0.979817	+	0.199897i	$0.0640608\pi$
$500$		0			0
$501$	−0.647494	+	1.12149i	−0.0289279	+	0.0501046i
$502$	3.09927	+	5.36809i	0.138327	+	0.239590i
$503$	15.3827	−	5.59886i	0.685883	−	0.249641i	0.0245113	−	0.999700i	$-0.492197\pi$
$503$	15.3827	−	5.59886i	0.685883	−	0.249641i	0.661371	+	0.750059i	$0.269975\pi$
$504$	−7.65646	+	2.78672i	−0.341046	+	0.124131i
$505$		0			0
$506$	−22.5155	+	38.9979i	−1.00093	+	1.73367i
$507$	−0.200087	+	1.13475i	−0.00888618	+	0.0503960i
$508$	2.00861	−	1.68542i	0.0891175	−	0.0747785i
$509$	−27.2953	−	22.9034i	−1.20984	−	1.01518i	−0.999293	−	0.0375938i	$-0.988031\pi$
$509$	−27.2953	−	22.9034i	−1.20984	−	1.01518i	−0.210548	−	0.977584i	$-0.567525\pi$
$510$		0			0
$511$	−3.74340	−	1.36249i	−0.165598	−	0.0602728i
$512$	48.2924			2.13424
$513$	−5.24702	+	3.68622i	−0.231662	+	0.162751i
$514$	44.4694			1.96146
$515$		0			0
$516$	2.49886	+	14.1717i	0.110006	+	0.623875i
$517$	−26.8857	−	22.5598i	−1.18243	−	0.992177i
$518$	0.906869	−	0.760954i	0.0398455	−	0.0334344i
$519$	−0.193812	+	1.09916i	−0.00850739	+	0.0482478i
$520$		0			0
$521$	−17.4659	−	30.2518i	−0.765194	−	1.32536i	−0.940144	−	0.340778i	$-0.889310\pi$
$521$	−17.4659	−	30.2518i	−0.765194	−	1.32536i	0.174950	−	0.984577i	$-0.444024\pi$
$522$	−46.9632	+	17.0932i	−2.05552	+	0.748149i
$523$	−12.7730	+	4.64899i	−0.558524	+	0.203286i	−0.605830	−	0.795594i	$-0.707159\pi$
$523$	−12.7730	+	4.64899i	−0.558524	+	0.203286i	0.0473057	+	0.998880i	$0.484936\pi$
$524$	23.0727	+	39.9630i	1.00793	+	1.74579i
$525$		0			0
$526$	6.58646	−	37.3537i	0.287183	−	1.62870i
$527$	−19.8763	+	16.6782i	−0.865826	+	0.726515i
$528$	8.35979	+	7.01470i	0.363813	+	0.305276i
$529$	−2.03521	−	11.5422i	−0.0884873	−	0.501837i
$530$		0			0
$531$	4.45254			0.193224
$532$	−3.46866	−	7.40834i	−0.150385	−	0.321192i
$533$	−8.26213			−0.357872
$534$	−7.53071	−	2.74096i	−0.325886	−	0.118613i
$535$		0			0
$536$	−4.00380	−	3.35959i	−0.172938	−	0.145112i
$537$	−0.715727	+	0.600566i	−0.0308859	+	0.0259163i
$538$	10.0713	−	57.1174i	0.434206	−	2.46251i
$539$	17.7485	−	30.7413i	0.764481	−	1.32412i
$540$		0			0
$541$	7.38859	−	2.68923i	0.317660	−	0.115619i	−0.178269	−	0.983982i	$-0.557050\pi$
$541$	7.38859	−	2.68923i	0.317660	−	0.115619i	0.495929	+	0.868363i	$0.334828\pi$
$542$	32.2386	−	11.7339i	1.38476	−	0.504013i
$543$	−2.36513	−	4.09653i	−0.101498	−	0.175799i
$544$	16.8147	−	29.1239i	0.720924	−	1.24868i
$545$		0			0
$546$	0.568854	−	0.477325i	0.0243447	−	0.0204276i
$547$	−20.3369	−	17.0647i	−0.869544	−	0.729634i	0.0944579	−	0.995529i	$-0.469888\pi$
$547$	−20.3369	−	17.0647i	−0.869544	−	0.729634i	−0.964002	+	0.265895i	$0.914333\pi$
$548$	7.27224	+	41.2429i	0.310655	+	1.76181i
$549$	−19.2952	−	7.02288i	−0.823500	−	0.299729i
$550$		0			0
$551$	−12.1691	−	25.9907i	−0.518421	−	1.10724i
$552$	5.74340			0.244455
$553$	−1.20335	−	0.437984i	−0.0511717	−	0.0186250i
$554$	1.50681	+	8.54554i	0.0640182	+	0.363065i
$555$		0			0
$556$	−47.1284	+	39.5455i	−1.99869	+	1.67710i
$557$	−0.661630	+	3.75229i	−0.0280342	+	0.158990i	−0.995611	−	0.0935867i	$-0.970167\pi$
$557$	−0.661630	+	3.75229i	−0.0280342	+	0.158990i	0.967577	+	0.252576i	$0.0812779\pi$
$558$	23.7684	−	41.1680i	1.00620	−	1.74278i
$559$	17.9613	+	31.1099i	0.759683	+	1.31581i
$560$		0			0
$561$	−5.00618	+	1.82210i	−0.211361	+	0.0769292i
$562$	25.8601	+	44.7910i	1.09084	+	1.88939i
$563$	−6.08960	+	10.5475i	−0.256646	+	0.444524i	−0.965341	−	0.260991i	$-0.915951\pi$
$563$	−6.08960	+	10.5475i	−0.256646	+	0.444524i	0.708695	+	0.705515i	$0.249284\pi$
$564$	−1.35902	+	7.70741i	−0.0572252	+	0.324540i
$565$		0			0
$566$	1.04872	+	0.879981i	0.0440810	+	0.0369884i
$567$	0.589440	+	3.34288i	0.0247542	+	0.140388i
$568$	−54.0764	−	19.6822i	−2.26900	−	0.825847i
$569$	22.8626			0.958451			0.479226	−	0.877692i	$-0.340918\pi$
$569$	22.8626			0.958451			0.479226	+	0.877692i	$0.340918\pi$
$570$		0			0
$571$	40.3908			1.69030			0.845152	−	0.534527i	$-0.179510\pi$
$571$	40.3908			1.69030			0.845152	+	0.534527i	$0.179510\pi$
$572$	65.8503	+	23.9676i	2.75334	+	1.00213i
$573$	0.124574	+	0.706496i	0.00520416	+	0.0295143i
$574$	−2.27259	−	1.90693i	−0.0948560	−	0.0795937i
$575$		0			0
$576$	−2.03702	+	11.5525i	−0.0848760	+	0.481355i
$577$	−3.93190	+	6.81026i	−0.163687	+	0.283515i	−0.936188	−	0.351499i	$-0.885672\pi$
$577$	−3.93190	+	6.81026i	−0.163687	+	0.283515i	0.772501	+	0.635013i	$0.219005\pi$
$578$	0.215179	+	0.372700i	0.00895025	+	0.0155023i
$579$	2.64913	−	0.964204i	0.110094	−	0.0400710i
$580$		0			0
$581$	1.10841	+	1.91982i	0.0459845	+	0.0796475i
$582$	2.84576	−	4.92901i	0.117961	−	0.204314i
$583$	−11.0882	+	62.8844i	−0.459227	+	2.60440i
$584$	−52.4514	+	44.0120i	−2.17045	+	1.82123i
$585$		0			0
$586$	14.1810	+	80.4242i	0.585810	+	3.32229i
$587$	37.7961	+	13.7566i	1.56001	+	0.567797i	0.970739	−	0.240138i	$-0.0771927\pi$
$587$	37.7961	+	13.7566i	1.56001	+	0.567797i	0.589271	+	0.807935i	$0.299415\pi$
$588$	−7.91555			−0.326432
$589$	24.7576	+	11.4976i	1.02012	+	0.473751i
$590$		0			0
$591$	−2.36293	−	0.860035i	−0.0971978	−	0.0353771i
$592$	−1.68168	−	9.53727i	−0.0691166	−	0.391980i
$593$	−26.1035	−	21.9034i	−1.07194	−	0.899466i	−0.0767145	−	0.997053i	$-0.524443\pi$
$593$	−26.1035	−	21.9034i	−1.07194	−	0.899466i	−0.995227	+	0.0975874i	$0.968887\pi$
$594$	15.1100	−	12.6788i	0.619969	−	0.520216i
$595$		0			0
$596$	19.1189	−	33.1150i	0.783142	−	1.35644i
$597$	0.362938	+	0.628627i	0.0148541	+	0.0257280i
$598$	23.5551	−	8.57334i	0.963238	−	0.350590i
$599$	−16.8047	+	6.11643i	−0.686623	+	0.249910i	−0.661689	−	0.749779i	$-0.730160\pi$
$599$	−16.8047	+	6.11643i	−0.686623	+	0.249910i	−0.0249346	+	0.999689i	$0.507938\pi$
$600$		0			0
$601$	−0.355966	+	0.616551i	−0.0145201	+	0.0251496i	−0.873194	−	0.487372i	$-0.837955\pi$
$601$	−0.355966	+	0.616551i	−0.0145201	+	0.0251496i	0.858674	+	0.512522i	$0.171289\pi$
$602$	−2.23982	+	12.7027i	−0.0912884	+	0.517722i
$603$	−1.70435	+	1.43012i	−0.0694065	+	0.0582389i
$604$	27.2257	+	22.8451i	1.10780	+	0.929553i
$605$		0			0
$606$	0.809335	+	0.294574i	0.0328770	+	0.0119662i
$607$	34.3415			1.39388			0.696940	−	0.717129i	$-0.254544\pi$
$607$	34.3415			1.39388			0.696940	+	0.717129i	$0.254544\pi$
$608$	−35.2498	−	3.02851i	−1.42957	−	0.122822i
$609$	0.655057			0.0265443
$610$		0			0
$611$	3.39253	+	19.2400i	0.137247	+	0.778368i
$612$	−43.5803	−	36.5682i	−1.76163	−	1.47818i
$613$	−22.9647	+	19.2696i	−0.927534	+	0.778293i	−0.975373	−	0.220562i	$-0.929211\pi$
$613$	−22.9647	+	19.2696i	−0.927534	+	0.778293i	0.0478390	+	0.998855i	$0.484767\pi$
$614$	4.11393	−	23.3313i	0.166025	−	0.941573i
$615$		0			0
$616$	7.19590	+	12.4637i	0.289931	+	0.502175i
$617$	20.7677	−	7.55883i	0.836076	−	0.304307i	0.111726	−	0.993739i	$-0.464362\pi$
$617$	20.7677	−	7.55883i	0.836076	−	0.304307i	0.724350	+	0.689432i	$0.242140\pi$
$618$	−7.47283	+	2.71989i	−0.300601	+	0.109410i
$619$	−9.72359	−	16.8417i	−0.390824	−	0.676927i	0.601734	−	0.798696i	$-0.294477\pi$
$619$	−9.72359	−	16.8417i	−0.390824	−	0.676927i	−0.992558	+	0.121769i	$0.961143\pi$
$620$		0			0
$621$	0.857958	−	4.86572i	0.0344287	−	0.195255i
$622$	47.5918	−	39.9343i	1.90826	−	1.60122i
$623$	−3.85334	−	3.23333i	−0.154381	−	0.129541i
$624$	−1.05487	−	5.98246i	−0.0422286	−	0.239490i
$625$		0			0
$626$	−6.35337			−0.253932
$627$	3.96933	+	3.95696i	0.158520	+	0.158026i
$628$	58.7117			2.34285
$629$	4.44261	+	1.61698i	0.177138	+	0.0644731i
$630$		0			0
$631$	3.39379	+	2.84773i	0.135105	+	0.113366i	0.707836	−	0.706377i	$-0.249672\pi$
$631$	3.39379	+	2.84773i	0.135105	+	0.113366i	−0.572731	+	0.819743i	$0.694116\pi$
$632$	−16.8610	+	14.1480i	−0.670694	+	0.562779i
$633$	−0.236837	+	1.34317i	−0.00941342	+	0.0533862i
$634$	−9.06962	+	15.7090i	−0.360201	+	0.623886i
$635$		0			0
$636$	13.3803	−	4.87005i	0.530565	−	0.193110i
$637$	−18.5680	+	6.75818i	−0.735689	+	0.267769i
$638$	44.1382	+	76.4496i	1.74745	+	3.02667i
$639$	−12.2484	+	21.2148i	−0.484538	+	0.839244i
$640$		0			0
$641$	19.6593	−	16.4961i	0.776496	−	0.651558i	−0.165867	−	0.986148i	$-0.553042\pi$
$641$	19.6593	−	16.4961i	0.776496	−	0.651558i	0.942364	+	0.334590i	$0.108598\pi$
$642$	−7.13814	−	5.98961i	−0.281720	−	0.236391i
$643$	−6.45413	−	36.6032i	−0.254526	−	1.44349i	−0.797287	−	0.603601i	$-0.793732\pi$
$643$	−6.45413	−	36.6032i	−0.254526	−	1.44349i	0.542761	−	0.839887i	$-0.317379\pi$
$644$	5.92270	+	2.15569i	0.233387	+	0.0849459i
$645$		0			0
$646$	26.6983	−	38.2562i	1.05043	−	1.50517i
$647$	−20.6750			−0.812819			−0.406409	−	0.913691i	$-0.633219\pi$
$647$	−20.6750			−0.812819			−0.406409	+	0.913691i	$0.633219\pi$
$648$	54.8250	+	19.9547i	2.15373	+	0.783893i
$649$	−1.36569	−	7.74519i	−0.0536079	−	0.304025i
$650$		0			0
$651$	−0.477300	+	0.400502i	−0.0187068	+	0.0156969i
$652$	2.66412	−	15.1090i	0.104335	−	0.591714i
$653$	17.0168	−	29.4740i	0.665919	−	1.15341i	−0.313116	−	0.949715i	$-0.601373\pi$
$653$	17.0168	−	29.4740i	0.665919	−	1.15341i	0.979035	−	0.203691i	$-0.0652939\pi$
$654$	1.41411	+	2.44931i	0.0552962	+	0.0957758i
$655$		0			0
$656$	−22.8053	+	8.30043i	−0.890395	+	0.324077i
$657$	14.5733	+	25.2418i	0.568560	+	0.984775i
$658$	−3.50751	+	6.07519i	−0.136737	+	0.236836i
$659$	−5.38526	+	30.5413i	−0.209780	+	1.18972i	0.679959	+	0.733250i	$0.261998\pi$
$659$	−5.38526	+	30.5413i	−0.209780	+	1.18972i	−0.889739	+	0.456470i	$0.849114\pi$
$660$		0			0
$661$	−13.9912	−	11.7400i	−0.544195	−	0.456634i	0.328775	−	0.944408i	$-0.393364\pi$
$661$	−13.9912	−	11.7400i	−0.544195	−	0.456634i	−0.872970	+	0.487775i	$0.837809\pi$
$662$	−7.80953	−	44.2901i	−0.303526	−	1.72138i
$663$	2.78672	+	1.01428i	0.108227	+	0.0393915i
$664$	38.1024			1.47866
$665$		0			0
$666$	−8.66163			−0.335631
$667$	20.7786	+	7.56280i	0.804552	+	0.292833i
$668$	4.24154	+	24.0550i	0.164110	+	0.930715i
$669$	−1.51068	−	1.26761i	−0.0584064	−	0.0490088i
$670$		0			0
$671$	−6.29806	+	35.7181i	−0.243134	+	1.37888i
$672$	0.403779	−	0.699366i	0.0155761	−	0.0269786i
$673$	13.0160	+	22.5444i	0.501731	+	0.869023i	0.999998	+	0.00199979i	$0.000636552\pi$
$673$	13.0160	+	22.5444i	0.501731	+	0.869023i	−0.498267	+	0.867024i	$0.666030\pi$
$674$	79.3197	−	28.8700i	3.05528	−	1.11203i
$675$		0			0
$676$	10.8669	+	18.8221i	0.417958	+	0.723925i
$677$	−0.0300638	+	0.0520720i	−0.00115545	+	0.00200129i	−0.866603	−	0.498999i	$-0.833701\pi$
$677$	−0.0300638	+	0.0520720i	−0.00115545	+	0.00200129i	0.865447	+	0.501000i	$0.167034\pi$
$678$	0.898316	−	5.09460i	0.0344996	−	0.195657i
$679$	2.73663	−	2.29630i	0.105022	−	0.0881240i
$680$		0			0
$681$	−0.345178	−	1.95760i	−0.0132272	−	0.0750154i
$682$	−78.9020	−	28.7180i	−3.02131	−	1.09967i
$683$	31.5145			1.20587			0.602935	−	0.797790i	$-0.293998\pi$
$683$	31.5145			1.20587			0.602935	+	0.797790i	$0.293998\pi$
$684$	−15.4003	+	57.8356i	−0.588844	+	2.21140i
$685$		0			0
$686$	−13.4915	−	4.91052i	−0.515109	−	0.187484i
$687$	−1.21506	−	6.89094i	−0.0463574	−	0.262906i
$688$	80.8313	+	67.8255i	3.08166	+	2.58582i
$689$	27.2290	−	22.8479i	1.03734	−	0.870435i
$690$		0			0
$691$	−4.69765	+	8.13657i	−0.178707	+	0.309530i	−0.941438	−	0.337186i	$-0.890525\pi$
$691$	−4.69765	+	8.13657i	−0.178707	+	0.309530i	0.762731	+	0.646716i	$0.223858\pi$
$692$	10.5261	+	18.2318i	0.400143	+	0.693067i
$693$	5.75687	−	2.09533i	0.218686	−	0.0795950i
$694$	−17.3057	+	6.29878i	−0.656917	+	0.239098i
$695$		0			0
$696$	5.62953	−	9.75063i	0.213387	−	0.369597i
$697$	2.05730	−	11.6676i	0.0779260	−	0.441940i
$698$	−44.9201	+	37.6924i	−1.70025	+	1.42668i
$699$	−1.79185	−	1.50354i	−0.0677740	−	0.0568691i
$700$		0			0
$701$	6.95262	+	2.53055i	0.262597	+	0.0955775i	0.469964	−	0.882686i	$-0.344267\pi$
$701$	6.95262	+	2.53055i	0.262597	+	0.0955775i	−0.207367	+	0.978263i	$0.566489\pi$
$702$	−10.9798			−0.414408
$703$	−0.441229	−	4.95417i	−0.0166413	−	0.186850i
$704$	20.7204			0.780930
$705$		0			0
$706$	−2.01575	−	11.4319i	−0.0758637	−	0.430245i
$707$	0.414122	+	0.347490i	0.0155747	+	0.0130687i
$708$	−1.34346	+	1.12730i	−0.0504903	+	0.0423664i
$709$	−7.51502	+	42.6198i	−0.282233	+	1.60062i	0.432774	+	0.901502i	$0.357535\pi$
$709$	−7.51502	+	42.6198i	−0.282233	+	1.60062i	−0.715006	+	0.699118i	$0.753576\pi$
$710$		0			0
$711$	4.68474	+	8.11420i	0.175691	+	0.304306i
$712$	−81.2440	+	29.5704i	−3.04475	+	1.10820i
$713$	−19.7640	+	7.19350i	−0.740167	+	0.269399i
$714$	0.532419	+	0.922176i	0.0199253	+	0.0345116i
$715$		0			0
$716$	−3.06021	+	17.3553i	−0.114366	+	0.648599i
$717$	2.23784	−	1.87777i	0.0835738	−	0.0701268i
$718$	−20.9446	−	17.5746i	−0.781645	−	0.655878i
$719$	5.61767	+	31.8594i	0.209504	+	1.18815i	0.890193	+	0.455583i	$0.150569\pi$
$719$	5.61767	+	31.8594i	0.209504	+	1.18815i	−0.680690	+	0.732572i	$0.738320\pi$
$720$		0			0
$721$	−4.99151			−0.185894
$722$	−48.3600	−	8.37154i	−1.79977	−	0.311557i
$723$	−3.17086			−0.117926
$724$	−83.8416	−	30.5158i	−3.11595	−	1.13411i
$725$		0			0
$726$	−7.81471	−	6.55732i	−0.290031	−	0.243365i
$727$	−38.0516	+	31.9291i	−1.41125	+	1.18418i	−0.455421	+	0.890276i	$0.650511\pi$
$727$	−38.0516	+	31.9291i	−1.41125	+	1.18418i	−0.955834	+	0.293907i	$0.905044\pi$
$728$	1.39114	−	7.88957i	0.0515592	−	0.292407i
$729$	11.8713	−	20.5616i	0.439677	−	0.761542i
$730$		0			0
$731$	−48.4051	+	17.6180i	−1.79033	+	0.651625i
$732$	7.59998	−	2.76617i	0.280903	−	0.102240i
$733$	0.684201	+	1.18507i	0.0252715	+	0.0437716i	0.878385	−	0.477955i	$-0.158622\pi$
$733$	0.684201	+	1.18507i	0.0252715	+	0.0437716i	−0.853113	+	0.521726i	$0.825288\pi$
$734$	2.33094	−	4.03730i	0.0860365	−	0.149020i
$735$		0			0
$736$	20.8824	−	17.5224i	0.769734	−	0.645883i
$737$	3.01045	+	2.52607i	0.110891	+	0.0930489i
$738$	3.76917	+	21.3760i	0.138745	+	0.786863i
$739$	−16.6998	−	6.07823i	−0.614312	−	0.223591i	0.0160769	−	0.999871i	$-0.494882\pi$
$739$	−16.6998	−	6.07823i	−0.614312	−	0.223591i	−0.630389	+	0.776279i	$0.717105\pi$
$740$		0			0
$741$	−0.276771	−	3.10761i	−0.0101674	−	0.114161i
$742$	12.7630			0.468545
$743$	36.2978	+	13.2113i	1.33164	+	0.484676i	0.907169	−	0.420766i	$-0.138239\pi$
$743$	36.2978	+	13.2113i	1.33164	+	0.484676i	0.424469	+	0.905443i	$0.360461\pi$
$744$	1.85965	+	10.5466i	0.0681779	+	0.386656i
$745$		0			0
$746$	−25.6526	+	21.5251i	−0.939210	+	0.788091i
$747$	2.81649	−	15.9731i	0.103050	−	0.584426i
$748$	−50.2434	+	87.0241i	−1.83708	+	3.18192i
$749$	−2.92438	−	5.06517i	−0.106854	−	0.185077i
$750$		0			0
$751$	−15.0160	+	5.46539i	−0.547943	+	0.199435i	−0.601132	−	0.799150i	$-0.705284\pi$
$751$	−15.0160	+	5.46539i	−0.547943	+	0.199435i	0.0531894	+	0.998584i	$0.483061\pi$
$752$	28.6933	+	49.6983i	1.04634	+	1.81231i
$753$	−0.297218	+	0.514797i	−0.0108312	+	0.0187603i
$754$	8.53300	−	48.3931i	0.310754	−	1.76237i
$755$		0			0
$756$	−2.11488	−	1.77460i	−0.0769175	−	0.0645414i
$757$	−0.338466	−	1.91954i	−0.0123018	−	0.0697668i	0.978039	−	0.208423i	$-0.0668329\pi$
$757$	−0.338466	−	1.91954i	−0.0123018	−	0.0697668i	−0.990341	+	0.138656i	$0.955722\pi$
$758$	80.4350	+	29.2759i	2.92153	+	1.06335i
$759$	−4.31845			−0.156750
$760$		0			0
$761$	−48.1168			−1.74423			−0.872115	−	0.489300i	$-0.837252\pi$
$761$	−48.1168			−1.74423			−0.872115	+	0.489300i	$0.837252\pi$
$762$	0.337429	+	0.122814i	0.0122238	+	0.00444909i
$763$	0.308260	+	1.74823i	0.0111597	+	0.0632901i
$764$	10.3657	+	8.69788i	0.375019	+	0.314678i
$765$		0			0
$766$	9.05780	−	51.3693i	0.327272	−	1.85605i
$767$	−2.18896	+	3.79139i	−0.0790388	+	0.136899i
$768$	2.88350	+	4.99437i	0.104049	+	0.180219i
$769$	6.00593	−	2.18598i	0.216579	−	0.0788284i	−0.231452	−	0.972846i	$-0.574348\pi$
$769$	6.00593	−	2.18598i	0.216579	−	0.0788284i	0.448031	+	0.894018i	$0.352125\pi$
$770$		0			0
$771$	2.13230	+	3.69325i	0.0767929	+	0.133009i
$772$	26.5874	−	46.0507i	0.956900	−	1.65740i
$773$	6.20576	−	35.1946i	0.223206	−	1.26586i	−0.642880	−	0.765967i	$-0.722261\pi$
$773$	6.20576	−	35.1946i	0.223206	−	1.26586i	0.866086	−	0.499895i	$-0.166628\pi$
$774$	72.2947	−	60.6624i	2.59858	−	2.18047i
$775$		0			0
$776$	−10.6624	−	60.4694i	−0.382757	−	2.17073i
$777$	0.106682	+	0.0388292i	0.00382721	+	0.00139299i
$778$	5.24072			0.187889
$779$	−12.0344	+	3.24476i	−0.431177	+	0.116255i
$780$		0			0
$781$	40.6599	+	14.7990i	1.45493	+	0.529550i
$782$	6.24173	+	35.3986i	0.223204	+	1.26585i
$783$	−7.41964	−	6.22582i	−0.265156	−	0.222493i
$784$	−44.4620	+	37.3081i	−1.58793	+	1.33243i
$785$		0			0
$786$	−3.15976	+	5.47286i	−0.112705	+	0.195211i
$787$	0.970153	+	1.68035i	0.0345822	+	0.0598982i	0.882799	−	0.469752i	$-0.155657\pi$
$787$	0.970153	+	1.68035i	0.0345822	+	0.0598982i	−0.848216	+	0.529650i	$0.822323\pi$
$788$	−44.5695	+	16.2220i	−1.58772	+	0.577884i
$789$	3.41810	−	1.24409i	0.121687	−	0.0442906i
$790$		0			0
$791$	1.62353	−	2.81204i	0.0577262	−	0.0999848i
$792$	18.2850	−	103.699i	0.649728	−	3.68479i
$793$	15.4660	−	12.9775i	0.549213	−	0.460845i
$794$	15.8952	+	13.3376i	0.564099	+	0.473335i
$795$		0			0
$796$	12.8658	+	4.68276i	0.456016	+	0.165976i
$797$	−44.3436			−1.57073			−0.785365	−	0.619033i	$-0.787525\pi$
$797$	−44.3436			−1.57073			−0.785365	+	0.619033i	$0.787525\pi$
$798$	0.641120	−	0.918663i	0.0226954	−	0.0325203i
$799$	−28.0150			−0.991099
$800$		0			0
$801$	6.39090	+	36.2446i	0.225811	+	1.28064i
$802$	28.4549	+	23.8765i	1.00478	+	0.843108i
$803$	39.4381	−	33.0925i	1.39174	−	1.16781i
$804$	0.152173	−	0.863016i	0.00536673	−	0.0304362i
$805$		0			0
$806$	23.3700	+	40.4781i	0.823175	+	1.42578i
$807$	5.22660	−	1.90233i	0.183985	−	0.0669651i
$808$	8.73139	−	3.17797i	0.307169	−	0.111800i
$809$	13.9319	+	24.1307i	0.489819	+	0.848392i	0.999931	−	0.0117160i	$-0.00372940\pi$
$809$	13.9319	+	24.1307i	0.489819	+	0.848392i	−0.510112	+	0.860108i	$0.670396\pi$
$810$		0			0
$811$	5.29449	−	30.0265i	0.185915	−	1.05437i	−0.738860	−	0.673859i	$-0.764636\pi$
$811$	5.29449	−	30.0265i	0.185915	−	1.05437i	0.924775	−	0.380515i	$-0.124253\pi$
$812$	9.46501	−	7.94209i	0.332157	−	0.278713i
$813$	2.52035	+	2.11482i	0.0883924	+	0.0741700i
$814$	2.65670	+	15.0669i	0.0931173	+	0.528094i
$815$		0			0
$816$	8.71095			0.304944
$817$	38.3797	+	38.2600i	1.34274	+	1.33855i
$818$	−0.624053			−0.0218195
$819$	−3.20460	−	1.16638i	−0.111978	−	0.0407566i
$820$		0			0
$821$	38.4716	+	32.2815i	1.34267	+	1.12663i	0.980932	+	0.194354i	$0.0622609\pi$
$821$	38.4716	+	32.2815i	1.34267	+	1.12663i	0.361738	+	0.932280i	$0.382184\pi$
$822$	−4.39347	+	3.68656i	−0.153240	+	0.128584i
$823$	−7.55147	+	42.8265i	−0.263228	+	1.49284i	0.510807	+	0.859695i	$0.329347\pi$
$823$	−7.55147	+	42.8265i	−0.263228	+	1.49284i	−0.774035	+	0.633143i	$0.781765\pi$
$824$	−42.8968	+	74.2994i	−1.49438	+	2.58834i
$825$		0			0
$826$	−1.47716	+	0.537644i	−0.0513971	+	0.0187070i
$827$	−0.559803	+	0.203752i	−0.0194663	+	0.00708514i	−0.351735	−	0.936100i	$-0.614408\pi$
$827$	−0.559803	+	0.203752i	−0.0194663	+	0.00708514i	0.332269	+	0.943185i	$0.392186\pi$
$828$	−23.0575	−	39.9368i	−0.801304	−	1.38790i
$829$	−9.62397	+	16.6692i	−0.334254	+	0.578946i	−0.983341	−	0.181769i	$-0.941818\pi$
$829$	−9.62397	+	16.6692i	−0.334254	+	0.578946i	0.649087	+	0.760714i	$0.275151\pi$
$830$		0			0
$831$	−0.637468	+	0.534900i	−0.0221135	+	0.0185555i
$832$	−8.83567	−	7.41401i	−0.306322	−	0.257035i
$833$	−4.92023	−	27.9040i	−0.170476	−	0.966816i
$834$	−7.91719	−	2.88162i	−0.274150	−	0.0997824i
$835$		0			0
$836$	105.329	+	9.04937i	3.64287	+	0.312979i
$837$	9.21270			0.318438
$838$	−55.1213	−	20.0625i	−1.90413	−	0.693048i
$839$	−8.84381	−	50.1557i	−0.305322	−	1.73157i	−0.621984	−	0.783030i	$-0.713673\pi$
$839$	−8.84381	−	50.1557i	−0.305322	−	1.73157i	0.316662	−	0.948539i	$-0.397438\pi$
$840$		0			0
$841$	10.9908	−	9.22242i	0.378995	−	0.318014i
$842$	11.2026	−	63.5331i	0.386067	−	2.18949i
$843$	−2.47997	+	4.29543i	−0.0854147	+	0.147943i
$844$	12.8628	+	22.2791i	0.442757	+	0.766878i
$845$		0			0
$846$	48.2307	−	17.5545i	1.65821	−	0.603538i
$847$	−3.20156	−	5.54526i	−0.110007	−	0.190537i
$848$	52.2042	−	90.4204i	1.79270	−	3.10505i
$849$	−0.0227978	+	0.129293i	−0.000782418	+	0.00443731i
$850$		0			0
$851$	2.93571	+	2.46335i	0.100635	+	0.0844426i
$852$	−1.67549	−	9.50216i	−0.0574013	−	0.325539i
$853$	−2.44273	−	0.889082i	−0.0836375	−	0.0304416i	0.299863	−	0.953982i	$-0.403059\pi$
$853$	−2.44273	−	0.889082i	−0.0836375	−	0.0304416i	−0.383500	+	0.923541i	$0.625281\pi$
$854$	7.24935			0.248067
$855$		0			0
$856$	−100.528			−3.43597
$857$	37.7972	+	13.7570i	1.29113	+	0.469932i	0.894097	−	0.447874i	$-0.147819\pi$
$857$	37.7972	+	13.7570i	1.29113	+	0.469932i	0.397030	+	0.917806i	$0.370041\pi$
$858$	1.66647	+	9.45104i	0.0568925	+	0.322653i
$859$	−21.5150	−	18.0532i	−0.734083	−	0.615969i	0.197159	−	0.980372i	$-0.436829\pi$
$859$	−21.5150	−	18.0532i	−0.734083	−	0.615969i	−0.931241	+	0.364403i	$0.881273\pi$
$860$		0			0
$861$	0.0494030	−	0.280179i	0.00168365	−	0.00954846i
$862$	23.0667	−	39.9527i	0.785654	−	1.36079i
$863$	−14.9698	−	25.9284i	−0.509577	−	0.882613i	−0.999938	−	0.0110937i	$-0.996469\pi$
$863$	−14.9698	−	25.9284i	−0.509577	−	0.882613i	0.490362	−	0.871519i	$-0.336865\pi$
$864$	−11.2204	+	4.08390i	−0.381727	+	0.138937i
$865$		0			0
$866$	50.5150	+	87.4946i	1.71657	+	2.97319i
$867$	−0.0206355	+	0.0357418i	−0.000700819	+	0.00121385i
$868$	−2.04078	+	11.5738i	−0.0692684	+	0.392841i
$869$	12.6777	−	10.6379i	0.430063	−	0.360866i
$870$		0			0
$871$	−0.379870	−	2.15435i	−0.0128714	−	0.0729973i
$872$	28.6718	+	10.4357i	0.970950	+	0.353397i
$873$	−26.1379			−0.884633
$874$	30.9427	−	21.7384i	1.04665	−	0.735312i
$875$		0			0
$876$	−10.7879	−	3.92648i	−0.364490	−	0.132664i
$877$	1.40747	+	7.98213i	0.0475267	+	0.269537i	0.999306	−	0.0372458i	$-0.0118584\pi$
$877$	1.40747	+	7.98213i	0.0475267	+	0.269537i	−0.951779	+	0.306783i	$0.900747\pi$
$878$	−37.0721	−	31.1072i	−1.25112	−	1.04982i
$879$	−5.99937	+	5.03407i	−0.202354	+	0.169795i
$880$		0			0
$881$	−4.46598	+	7.73530i	−0.150463	+	0.260609i	−0.931398	−	0.364003i	$-0.881410\pi$
$881$	−4.46598	+	7.73530i	−0.150463	+	0.260609i	0.780935	+	0.624612i	$0.214743\pi$
$882$	25.9557	+	44.9565i	0.873973	+	1.51377i
$883$	−1.42061	+	0.517061i	−0.0478074	+	0.0174005i	−0.365813	−	0.930688i	$-0.619209\pi$
$883$	−1.42061	+	0.517061i	−0.0478074	+	0.0174005i	0.318006	+	0.948089i	$0.396987\pi$
$884$	52.5632	−	19.1314i	1.76789	−	0.643460i
$885$		0			0
$886$	−22.0228	+	38.1446i	−0.739870	+	1.28149i
$887$	−4.83393	+	27.4146i	−0.162307	+	0.920491i	0.789490	+	0.613764i	$0.210345\pi$
$887$	−4.83393	+	27.4146i	−0.162307	+	0.920491i	−0.951797	+	0.306728i	$0.900766\pi$
$888$	1.49480	−	1.25429i	0.0501623	−	0.0420912i
$889$	0.172657	+	0.144876i	0.00579072	+	0.00485899i
$890$		0			0
$891$	−41.2228	−	15.0039i	−1.38101	−	0.502648i
$892$	−37.1970			−1.24545
$893$	12.4975	+	26.6922i	0.418214	+	0.893220i
$894$	5.23661			0.175138
$895$		0			0
$896$	0.413006	+	2.34228i	0.0137976	+	0.0782499i
$897$	1.84149	+	1.54519i	0.0614855	+	0.0515924i
$898$	−24.1475	+	20.2622i	−0.805813	+	0.676157i
$899$	−7.15966	+	40.6045i	−0.238788	+	1.35423i
$900$		0			0
$901$	25.4850	+	44.1414i	0.849029	+	1.47056i
$902$	36.0275	−	13.1129i	1.19959	−	0.436613i
$903$	−1.16237	+	0.423069i	−0.0386814	+	0.0140789i
$904$	−27.9051	−	48.3331i	−0.928111	−	1.60754i
$905$		0			0
$906$	−0.845184	+	4.79328i	−0.0280794	+	0.159246i
$907$	−24.2585	+	20.3553i	−0.805492	+	0.675888i	−0.949527	−	0.313685i	$-0.898436\pi$
$907$	−24.2585	+	20.3553i	−0.805492	+	0.675888i	0.144036	+	0.989573i	$0.453992\pi$
$908$	−28.7220	−	24.1006i	−0.953172	−	0.799806i
$909$	−0.686837	−	3.89525i	−0.0227810	−	0.129197i
$910$		0			0
$911$	10.4766			0.347104			0.173552	−	0.984825i	$-0.444476\pi$
$911$	10.4766			0.347104			0.173552	+	0.984825i	$0.444476\pi$
$912$	−3.88597	−	8.29963i	−0.128677	−	0.274828i
$913$	−28.6491			−0.948148
$914$	32.5454	+	11.8455i	1.07650	+	0.391816i
$915$		0			0
$916$	−101.104	−	84.8364i	−3.34057	−	2.80307i
$917$	−3.03858	+	2.54967i	−0.100343	+	0.0841975i
$918$	2.73403	−	15.5055i	0.0902364	−	0.511756i
$919$	5.30464	−	9.18791i	0.174984	−	0.303081i	−0.765172	−	0.643826i	$-0.777346\pi$
$919$	5.30464	−	9.18791i	0.174984	−	0.303081i	0.940156	+	0.340745i	$0.110679\pi$
$920$		0			0
$921$	2.13496	−	0.777061i	0.0703492	−	0.0256050i
$922$	−34.0221	+	12.3830i	−1.12046	+	0.407814i
$923$	−12.0431	−	20.8593i	−0.396403	−	0.686591i
$924$	−1.20652	+	2.08975i	−0.0396915	+	0.0687477i
$925$		0			0
$926$	51.8001	−	43.4655i	1.70226	−	1.42836i
$927$	27.9766	+	23.4751i	0.918871	+	0.771025i
$928$	−9.27960	−	52.6272i	−0.304618	−	1.72757i
$929$	13.3285	+	4.85116i	0.437293	+	0.159162i	0.551279	−	0.834321i	$-0.314140\pi$
$929$	13.3285	+	4.85116i	0.437293	+	0.159162i	−0.113987	+	0.993482i	$0.536362\pi$
$930$		0			0
$931$	−24.3915	+	17.1359i	−0.799399	+	0.561607i
$932$	−44.1200			−1.44520
$933$	5.59862	+	2.03773i	0.183290	+	0.0667123i
$934$	−17.7574	−	100.707i	−0.581039	−	3.29524i
$935$		0			0
$936$	−44.9019	+	37.6772i	−1.46766	+	1.23152i
$937$	−7.73465	+	43.8654i	−0.252680	+	1.43302i	0.549278	+	0.835640i	$0.314903\pi$
$937$	−7.73465	+	43.8654i	−0.252680	+	1.43302i	−0.801958	+	0.597380i	$0.796208\pi$
$938$	0.392744	−	0.680253i	0.0128235	−	0.0222110i
$939$	−0.304642	−	0.527656i	−0.00994163	−	0.0172194i
$940$		0			0
$941$	28.5593	−	10.3947i	0.931006	−	0.338859i	0.168398	−	0.985719i	$-0.446141\pi$
$941$	28.5593	−	10.3947i	0.931006	−	0.338859i	0.762608	+	0.646860i	$0.223918\pi$
$942$	4.02023	+	6.96324i	0.130986	+	0.226875i
$943$	4.80181	−	8.31698i	0.156368	−	0.270838i
$944$	−2.23303	+	12.6642i	−0.0726791	+	0.412183i
$945$		0			0
$946$	−127.696	−	107.150i	−4.15177	−	3.48375i
$947$	5.37877	+	30.5045i	0.174787	+	0.991264i	0.938390	+	0.345578i	$0.112317\pi$
$947$	5.37877	+	30.5045i	0.174787	+	0.991264i	−0.763603	+	0.645686i	$0.776572\pi$
$948$	−3.46788	−	1.26220i	−0.112631	−	0.0409945i
$949$	−28.6582			−0.930285
$950$		0			0
$951$	−1.73954			−0.0564086
$952$	10.7950	+	3.92908i	0.349869	+	0.127342i
$953$	3.86599	+	21.9251i	0.125232	+	0.710224i	0.981170	+	0.193146i	$0.0618691\pi$
$953$	3.86599	+	21.9251i	0.125232	+	0.710224i	−0.855938	+	0.517078i	$0.827020\pi$
$954$	−71.5346	−	60.0247i	−2.31602	−	1.94337i
$955$		0			0
$956$	9.56828	−	54.2644i	0.309460	−	1.75504i
$957$	−4.23283	+	7.33148i	−0.136828	+	0.236993i
$958$	4.88059	+	8.45343i	0.157685	+	0.273118i
$959$	−3.38277	+	1.23123i	−0.109235	+	0.0397584i
$960$		0			0
$961$	−4.10876	−	7.11657i	−0.132540	−	0.229567i
$962$	4.25823	−	7.37548i	0.137291	−	0.237795i
$963$	−7.43092	+	42.1428i	−0.239458	+	1.35803i
$964$	−45.8162	+	38.4444i	−1.47564	+	1.23821i
$965$		0			0
$966$	0.149886	+	0.850044i	0.00482249	+	0.0273497i
$967$	−16.4816	−	5.99883i	−0.530014	−	0.192909i	0.0631307	−	0.998005i	$-0.479892\pi$
$967$	−16.4816	−	5.99883i	−0.530014	−	0.192909i	−0.593145	+	0.805096i	$0.702114\pi$
$968$	−110.056			−3.53734
$969$	4.45741	+	0.382961i	0.143193	+	0.0123025i
$970$		0			0
$971$	15.7599	+	5.73614i	0.505759	+	0.184081i	0.582283	−	0.812986i	$-0.302160\pi$
$971$	15.7599	+	5.73614i	0.505759	+	0.184081i	−0.0765232	+	0.997068i	$0.524382\pi$
$972$	5.27953	+	29.9417i	0.169341	+	0.960381i
$973$	−4.05109	−	3.39927i	−0.129872	−	0.108975i
$974$	13.8314	−	11.6059i	0.443187	−	0.371878i
$975$		0			0
$976$	29.6518	−	51.3584i	0.949131	−	1.64394i
$977$	−14.3920	−	24.9276i	−0.460440	−	0.797506i	0.538543	−	0.842598i	$-0.318975\pi$
$977$	−14.3920	−	24.9276i	−0.460440	−	0.797506i	−0.998983	+	0.0450925i	$0.985642\pi$
$978$	1.97436	−	0.718608i	0.0631330	−	0.0229785i
$979$	61.0872	−	22.2339i	1.95236	−	0.710599i
$980$		0			0
$981$	6.49419	−	11.2483i	0.207344	−	0.359130i
$982$	14.6402	−	83.0287i	0.467187	−	2.64955i
$983$	22.9176	−	19.2302i	0.730959	−	0.613348i	−0.199434	−	0.979911i	$-0.563910\pi$
$983$	22.9176	−	19.2302i	0.730959	−	0.613348i	0.930393	+	0.366564i	$0.119466\pi$
$984$	−3.74593	−	3.14321i	−0.119416	−	0.100202i
$985$		0			0
$986$	66.2147	+	24.1002i	2.10870	+	0.767506i
$987$	−0.672737			−0.0214135
$988$	−41.6766	−	41.5467i	−1.32591	−	1.32178i
$989$	−41.7553			−1.32774
$990$		0			0
$991$	7.97273	+	45.2156i	0.253262	+	1.43632i	0.800495	+	0.599340i	$0.204570\pi$
$991$	7.97273	+	45.2156i	0.253262	+	1.43632i	−0.547232	+	0.836981i	$0.684319\pi$
$992$	38.9377	+	32.6726i	1.23627	+	1.03736i
$993$	3.30389	−	2.77229i	0.104846	−	0.0879760i
$994$	1.50181	−	8.51716i	0.0476344	−	0.270148i
$995$		0			0
$996$	3.19427	+	5.53264i	0.101214	+	0.175308i
$997$	−50.6964	+	18.4520i	−1.60557	+	0.584380i	−0.980557	−	0.196234i	$-0.937129\pi$
$997$	−50.6964	+	18.4520i	−1.60557	+	0.584380i	−0.625014	+	0.780614i	$0.714907\pi$
$998$	67.4628	−	24.5545i	2.13550	−	0.777258i
$999$	−0.839319	−	1.45374i	−0.0265549	−	0.0459944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.251.3		18
5.2	odd	4		475.2.u.b.99.1		36
5.3	odd	4		475.2.u.b.99.6		36
5.4	even	2		95.2.k.a.61.1	✓	18
15.14	odd	2		855.2.bs.c.631.3		18
19.5	even	9	inner	475.2.l.c.176.3		18
19.9	even	9		9025.2.a.cc.1.1		9
19.10	odd	18		9025.2.a.cf.1.9		9
95.9	even	18		1805.2.a.v.1.9		9
95.24	even	18		95.2.k.a.81.1	yes	18
95.29	odd	18		1805.2.a.s.1.1		9
95.43	odd	36		475.2.u.b.24.1		36
95.62	odd	36		475.2.u.b.24.6		36
285.119	odd	18		855.2.bs.c.271.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.1	✓	18	5.4	even	2
95.2.k.a.81.1	yes	18	95.24	even	18
475.2.l.c.176.3		18	19.5	even	9	inner
475.2.l.c.251.3		18	1.1	even	1	trivial
475.2.u.b.24.1		36	95.43	odd	36
475.2.u.b.24.6		36	95.62	odd	36
475.2.u.b.99.1		36	5.2	odd	4
475.2.u.b.99.6		36	5.3	odd	4
855.2.bs.c.271.3		18	285.119	odd	18
855.2.bs.c.631.3		18	15.14	odd	2
1805.2.a.s.1.1		9	95.29	odd	18
1805.2.a.v.1.9		9	95.9	even	18
9025.2.a.cc.1.1		9	19.9	even	9
9025.2.a.cf.1.9		9	19.10	odd	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42733 + 0.883478i) q^{2} +(0.0430161 + 0.243956i) q^{3} +(3.57933 + 3.00342i) q^{4} +(-0.111115 + 0.630167i) q^{6} +(-0.200820 + 0.347830i) q^{7} +(3.45167 + 5.97847i) q^{8} +(2.76141 - 1.00507i) q^{9} +O(q^{10})\)	\(q+(2.42733 + 0.883478i) q^{2} +(0.0430161 + 0.243956i) q^{3} +(3.57933 + 3.00342i) q^{4} +(-0.111115 + 0.630167i) q^{6} +(-0.200820 + 0.347830i) q^{7} +(3.45167 + 5.97847i) q^{8} +(2.76141 - 1.00507i) q^{9} +(-2.59530 - 4.49520i) q^{11} +(-0.578733 + 1.00240i) q^{12} +(-0.501737 + 2.84549i) q^{13} +(-0.794758 + 0.666881i) q^{14} +(1.47378 + 8.35823i) q^{16} +(-3.89339 - 1.41708i) q^{17} +7.59083 q^{18} +(0.386682 + 4.34171i) q^{19} +(-0.0934938 - 0.0340290i) q^{21} +(-2.32827 - 13.2043i) q^{22} +(-2.57278 - 2.15882i) q^{23} +(-1.31001 + 1.09923i) q^{24} +(-3.73181 + 6.46368i) q^{26} +(0.735558 + 1.27402i) q^{27} +(-1.76348 + 0.641855i) q^{28} +(-6.18683 + 2.25182i) q^{29} +(3.13119 - 5.42339i) q^{31} +(-1.40944 + 7.99334i) q^{32} +(0.984992 - 0.826506i) q^{33} +(-8.19861 - 6.87945i) q^{34} +(12.9027 + 4.69619i) q^{36} -1.14106 q^{37} +(-2.89720 + 10.8804i) q^{38} -0.715757 q^{39} +(0.496543 + 2.81603i) q^{41} +(-0.196877 - 0.165199i) q^{42} +(9.52394 - 7.99153i) q^{43} +(4.21150 - 23.8846i) q^{44} +(-4.33773 - 7.51317i) q^{46} +(6.35381 - 2.31260i) q^{47} +(-1.97565 + 0.719076i) q^{48} +(3.41934 + 5.92248i) q^{49} +(0.178227 - 1.01077i) q^{51} +(-10.3421 + 8.67803i) q^{52} +(-9.42382 - 7.90752i) q^{53} +(0.659874 + 3.74233i) q^{54} -2.77266 q^{56} +(-1.04255 + 0.281097i) q^{57} -17.0069 q^{58} +(1.42380 + 0.518220i) q^{59} +(-5.35269 - 4.49144i) q^{61} +(12.3919 - 10.3980i) q^{62} +(-0.204952 + 1.16234i) q^{63} +(-1.99595 + 3.45709i) q^{64} +(3.12111 - 1.13599i) q^{66} +(-0.711451 + 0.258947i) q^{67} +(-9.67967 - 16.7657i) q^{68} +(0.415986 - 0.720510i) q^{69} +(-6.38582 + 5.35834i) q^{71} +(15.5403 + 13.0399i) q^{72} +(1.72232 + 9.76776i) q^{73} +(-2.76974 - 1.00810i) q^{74} +(-11.6559 + 16.7018i) q^{76} +2.08476 q^{77} +(-1.73738 - 0.632356i) q^{78} +(0.553655 + 3.13994i) q^{79} +(6.47421 - 5.43251i) q^{81} +(-1.28263 + 7.27414i) q^{82} +(2.75971 - 4.77995i) q^{83} +(-0.232442 - 0.402602i) q^{84} +(30.1781 - 10.9839i) q^{86} +(-0.815478 - 1.41245i) q^{87} +(17.9163 - 31.0319i) q^{88} +(-2.17478 + 12.3338i) q^{89} +(-0.888989 - 0.745950i) q^{91} +(-2.72500 - 15.4543i) q^{92} +(1.45776 + 0.530581i) q^{93} +17.4660 q^{94} -2.01065 q^{96} +(-8.35815 - 3.04212i) q^{97} +(3.06752 + 17.3967i) q^{98} +(-11.6847 - 9.80464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Introduction

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