LMFDB - Embedded newform 375.2.g.d.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			151.4
Root			$2.35083i$ of defining polynomial
Character	$\chi$	$=$	375.151
Dual form			375.2.g.d.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.726446 + 2.23577i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-2.85292 + 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} +3.48189 q^{7} +(-2.90300 - 2.10915i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.726446 + 2.23577i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-2.85292 + 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} +3.48189 q^{7} +(-2.90300 - 2.10915i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.905762 + 2.78765i) q^{11} +(-1.08972 + 3.35381i) q^{12} +(-0.579638 + 1.78394i) q^{13} +(2.52940 + 7.78470i) q^{14} +(0.427277 - 1.31502i) q^{16} +(-5.48972 - 3.98851i) q^{17} +2.35083 q^{18} +(2.38620 + 1.73367i) q^{19} +(2.81691 - 2.04660i) q^{21} +(-5.57456 + 4.05015i) q^{22} +(-1.69656 - 5.22149i) q^{23} -3.58831 q^{24} -4.40956 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-9.93354 + 7.21714i) q^{28} +(-2.06779 + 1.50234i) q^{29} +(-0.338237 - 0.245744i) q^{31} -3.92613 q^{32} +(2.37132 + 1.72286i) q^{33} +(4.92942 - 15.1712i) q^{34} +(1.08972 + 3.35381i) q^{36} +(1.61912 - 4.98314i) q^{37} +(-2.14265 + 6.59441i) q^{38} +(0.579638 + 1.78394i) q^{39} +(0.518744 - 1.59653i) q^{41} +(6.62206 + 4.81121i) q^{42} +10.9233 q^{43} +(-8.36221 - 6.07550i) q^{44} +(10.4416 - 7.58626i) q^{46} +(6.06098 - 4.40356i) q^{47} +(-0.427277 - 1.31502i) q^{48} +5.12353 q^{49} -6.78566 q^{51} +(-2.04403 - 6.29089i) q^{52} +(-3.00107 + 2.18041i) q^{53} +(1.90186 - 1.38178i) q^{54} +(-10.1079 - 7.34383i) q^{56} +2.94950 q^{57} +(-4.86103 - 3.53175i) q^{58} +(-2.19666 + 6.76062i) q^{59} +(-1.98917 - 6.12204i) q^{61} +(0.303716 - 0.934741i) q^{62} +(1.07596 - 3.31147i) q^{63} +(-3.70667 - 11.4080i) q^{64} +(-2.12929 + 6.55329i) q^{66} +(-8.12376 - 5.90225i) q^{67} +23.9290 q^{68} +(-4.44166 - 3.22706i) q^{69} +(-0.589451 + 0.428261i) q^{71} +(-2.90300 + 2.10915i) q^{72} +(-1.11020 - 3.41685i) q^{73} +12.3174 q^{74} -10.4011 q^{76} +(3.15376 + 9.70628i) q^{77} +(-3.56741 + 2.59188i) q^{78} +(-2.48583 + 1.80606i) q^{79} +(-0.809017 - 0.587785i) q^{81} +3.94632 q^{82} +(-8.18340 - 5.94559i) q^{83} +(-3.79427 + 11.6776i) q^{84} +(7.93517 + 24.4219i) q^{86} +(-0.789827 + 2.43084i) q^{87} +(3.25015 - 10.0029i) q^{88} +(0.0888461 + 0.273440i) q^{89} +(-2.01823 + 6.21148i) q^{91} +(15.6631 + 11.3799i) q^{92} -0.418084 q^{93} +(14.2483 + 10.3520i) q^{94} +(-3.17630 + 2.30772i) q^{96} +(8.42109 - 6.11828i) q^{97} +(3.72197 + 11.4551i) q^{98} +2.93111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9	$ 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 8 q^{13} + 12 q^{14} - 10 q^{16} - 8 q^{17} + 8 q^{18} + 2 q^{19} + 4 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 12 q^{26} + 4 q^{27} - 28 q^{28} - 16 q^{29} + 6 q^{31} - 4 q^{32} - 4 q^{33} + 36 q^{34} - 2 q^{36} - 24 q^{37} + 38 q^{38} + 8 q^{39} - 14 q^{41} + 18 q^{42} + 40 q^{43} - 26 q^{44} + 16 q^{46} + 10 q^{47} + 10 q^{48} - 32 q^{51} - 48 q^{52} - 12 q^{53} + 2 q^{54} + 28 q^{57} - 44 q^{58} - 12 q^{59} - 28 q^{62} - 4 q^{63} - 8 q^{64} + 16 q^{66} + 12 q^{67} - 4 q^{68} + 12 q^{69} - 8 q^{71} - 6 q^{72} + 8 q^{73} + 52 q^{74} - 32 q^{76} - 18 q^{77} - 32 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{82} - 6 q^{83} - 12 q^{84} - 36 q^{86} - 14 q^{87} - 16 q^{88} - 18 q^{89} + 26 q^{91} + 36 q^{92} + 44 q^{93} + 38 q^{94} - 26 q^{96} - 8 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 - 8 * q^13 + 12 * q^14 - 10 * q^16 - 8 * q^17 + 8 * q^18 + 2 * q^19 + 4 * q^21 + 4 * q^22 - 2 * q^23 - 24 * q^24 + 12 * q^26 + 4 * q^27 - 28 * q^28 - 16 * q^29 + 6 * q^31 - 4 * q^32 - 4 * q^33 + 36 * q^34 - 2 * q^36 - 24 * q^37 + 38 * q^38 + 8 * q^39 - 14 * q^41 + 18 * q^42 + 40 * q^43 - 26 * q^44 + 16 * q^46 + 10 * q^47 + 10 * q^48 - 32 * q^51 - 48 * q^52 - 12 * q^53 + 2 * q^54 + 28 * q^57 - 44 * q^58 - 12 * q^59 - 28 * q^62 - 4 * q^63 - 8 * q^64 + 16 * q^66 + 12 * q^67 - 4 * q^68 + 12 * q^69 - 8 * q^71 - 6 * q^72 + 8 * q^73 + 52 * q^74 - 32 * q^76 - 18 * q^77 - 32 * q^78 + 20 * q^79 - 4 * q^81 + 32 * q^82 - 6 * q^83 - 12 * q^84 - 36 * q^86 - 14 * q^87 - 16 * q^88 - 18 * q^89 + 26 * q^91 + 36 * q^92 + 44 * q^93 + 38 * q^94 - 26 * q^96 - 8 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.726446	+	2.23577i	0.513675	+	1.58093i	0.785680	+	0.618634i	$0.212313\pi$
$2$	0.726446	+	2.23577i	0.513675	+	1.58093i	−0.272005	+	0.962296i	$0.587687\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−2.85292	+	2.07277i	−1.42646	+	1.03638i
$5$		0			0
$5$		0			0
$6$	1.90186	+	1.38178i	0.776432	+	0.564111i
$7$	3.48189			1.31603			0.658015	−	0.753005i	$-0.271396\pi$
$7$	3.48189			1.31603			0.658015	+	0.753005i	$0.271396\pi$
$8$	−2.90300	−	2.10915i	−1.02637	−	0.745698i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	0.905762	+	2.78765i	0.273097	+	0.840508i	0.989717	+	0.143043i	$0.0456887\pi$
$11$	0.905762	+	2.78765i	0.273097	+	0.840508i	−0.716619	+	0.697465i	$0.754311\pi$
$12$	−1.08972	+	3.35381i	−0.314574	+	0.968160i
$13$	−0.579638	+	1.78394i	−0.160763	+	0.494776i	−0.998699	−	0.0509914i	$-0.983762\pi$
$13$	−0.579638	+	1.78394i	−0.160763	+	0.494776i	0.837937	+	0.545768i	$0.183762\pi$
$14$	2.52940	+	7.78470i	0.676012	+	2.08055i
$15$		0			0
$16$	0.427277	−	1.31502i	0.106819	−	0.328756i
$17$	−5.48972	−	3.98851i	−1.33145	−	0.967356i	−0.999712	−	0.0239850i	$-0.992365\pi$
$17$	−5.48972	−	3.98851i	−1.33145	−	0.967356i	−0.331739	−	0.943371i	$-0.607635\pi$
$18$	2.35083			0.554096
$19$	2.38620	+	1.73367i	0.547431	+	0.397732i	0.826837	−	0.562441i	$-0.190138\pi$
$19$	2.38620	+	1.73367i	0.547431	+	0.397732i	−0.279406	+	0.960173i	$0.590138\pi$
$20$		0			0
$21$	2.81691	−	2.04660i	0.614699	−	0.446605i
$22$	−5.57456	+	4.05015i	−1.18850	+	0.863496i
$23$	−1.69656	−	5.22149i	−0.353758	−	1.08876i	−0.956726	−	0.290990i	$-0.906015\pi$
$23$	−1.69656	−	5.22149i	−0.353758	−	1.08876i	0.602968	−	0.797765i	$-0.293985\pi$
$24$	−3.58831			−0.732460
$25$		0			0
$26$	−4.40956			−0.864786
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−9.93354	+	7.21714i	−1.87726	+	1.36391i
$29$	−2.06779	+	1.50234i	−0.383980	+	0.278978i	−0.762984	−	0.646417i	$-0.776267\pi$
$29$	−2.06779	+	1.50234i	−0.383980	+	0.278978i	0.379004	+	0.925395i	$0.376267\pi$
$30$		0			0
$31$	−0.338237	−	0.245744i	−0.0607492	−	0.0441369i	0.556996	−	0.830515i	$-0.311954\pi$
$31$	−0.338237	−	0.245744i	−0.0607492	−	0.0441369i	−0.617745	+	0.786378i	$0.711954\pi$
$32$	−3.92613			−0.694048
$33$	2.37132	+	1.72286i	0.412793	+	0.299912i
$34$	4.92942	−	15.1712i	0.845388	−	2.60184i
$35$		0			0
$36$	1.08972	+	3.35381i	0.181620	+	0.558968i
$37$	1.61912	−	4.98314i	0.266182	−	0.819224i	−0.725237	−	0.688500i	$-0.758270\pi$
$37$	1.61912	−	4.98314i	0.266182	−	0.819224i	0.991419	−	0.130724i	$-0.0417303\pi$
$38$	−2.14265	+	6.59441i	−0.347584	+	1.06975i
$39$	0.579638	+	1.78394i	0.0928163	+	0.285659i
$40$		0			0
$41$	0.518744	−	1.59653i	0.0810142	−	0.249336i	−0.902343	−	0.431019i	$-0.858154\pi$
$41$	0.518744	−	1.59653i	0.0810142	−	0.249336i	0.983357	+	0.181683i	$0.0581543\pi$
$42$	6.62206	+	4.81121i	1.02181	+	0.742386i
$43$	10.9233			1.66578			0.832892	−	0.553436i	$-0.186684\pi$
$43$	10.9233			1.66578			0.832892	+	0.553436i	$0.186684\pi$
$44$	−8.36221	−	6.07550i	−1.26065	−	0.915916i
$45$		0			0
$46$	10.4416	−	7.58626i	1.53953	−	1.11853i
$47$	6.06098	−	4.40356i	0.884084	−	0.642325i	−0.0502446	−	0.998737i	$-0.516000\pi$
$47$	6.06098	−	4.40356i	0.884084	−	0.642325i	0.934329	+	0.356412i	$0.116000\pi$
$48$	−0.427277	−	1.31502i	−0.0616721	−	0.189807i
$49$	5.12353			0.731933
$50$		0			0
$51$	−6.78566			−0.950183
$52$	−2.04403	−	6.29089i	−0.283457	−	0.872390i
$53$	−3.00107	+	2.18041i	−0.412229	+	0.299502i	−0.774504	−	0.632570i	$-0.782000\pi$
$53$	−3.00107	+	2.18041i	−0.412229	+	0.299502i	0.362275	+	0.932071i	$0.382000\pi$
$54$	1.90186	−	1.38178i	0.258811	−	0.188037i
$55$		0			0
$56$	−10.1079	−	7.34383i	−1.35073	−	0.981361i
$57$	2.94950			0.390671
$58$	−4.86103	−	3.53175i	−0.638285	−	0.463741i
$59$	−2.19666	+	6.76062i	−0.285981	+	0.880158i	0.700122	+	0.714023i	$0.253129\pi$
$59$	−2.19666	+	6.76062i	−0.285981	+	0.880158i	−0.986103	+	0.166135i	$0.946871\pi$
$60$		0			0
$61$	−1.98917	−	6.12204i	−0.254687	−	0.783847i	−0.993891	−	0.110365i	$-0.964798\pi$
$61$	−1.98917	−	6.12204i	−0.254687	−	0.783847i	0.739204	−	0.673482i	$-0.235202\pi$
$62$	0.303716	−	0.934741i	0.0385719	−	0.118712i
$63$	1.07596	−	3.31147i	0.135558	−	0.417206i
$64$	−3.70667	−	11.4080i	−0.463334	−	1.42600i
$65$		0			0
$66$	−2.12929	+	6.55329i	−0.262098	+	0.806654i
$67$	−8.12376	−	5.90225i	−0.992475	−	0.721075i	−0.0320131	−	0.999487i	$-0.510192\pi$
$67$	−8.12376	−	5.90225i	−0.992475	−	0.721075i	−0.960462	+	0.278412i	$0.910192\pi$
$68$	23.9290			2.90181
$69$	−4.44166	−	3.22706i	−0.534713	−	0.388492i
$70$		0			0
$71$	−0.589451	+	0.428261i	−0.0699550	+	0.0508253i	−0.622213	−	0.782848i	$-0.713766\pi$
$71$	−0.589451	+	0.428261i	−0.0699550	+	0.0508253i	0.552258	+	0.833673i	$0.313766\pi$
$72$	−2.90300	+	2.10915i	−0.342122	+	0.248566i
$73$	−1.11020	−	3.41685i	−0.129939	−	0.399912i	0.864829	−	0.502066i	$-0.167427\pi$
$73$	−1.11020	−	3.41685i	−0.129939	−	0.399912i	−0.994769	+	0.102154i	$0.967427\pi$
$74$	12.3174			1.43187
$75$		0			0
$76$	−10.4011			−1.19309
$77$	3.15376	+	9.70628i	0.359404	+	1.10613i
$78$	−3.56741	+	2.59188i	−0.403930	+	0.293472i
$79$	−2.48583	+	1.80606i	−0.279677	+	0.203197i	−0.718777	−	0.695241i	$-0.755298\pi$
$79$	−2.48583	+	1.80606i	−0.279677	+	0.203197i	0.439099	+	0.898439i	$0.355298\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.94632			0.435798
$83$	−8.18340	−	5.94559i	−0.898245	−	0.652613i	0.0397694	−	0.999209i	$-0.487338\pi$
$83$	−8.18340	−	5.94559i	−0.898245	−	0.652613i	−0.938015	+	0.346595i	$0.887338\pi$
$84$	−3.79427	+	11.6776i	−0.413989	+	1.27413i
$85$		0			0
$86$	7.93517	+	24.4219i	0.855672	+	2.63349i
$87$	−0.789827	+	2.43084i	−0.0846784	+	0.260613i
$88$	3.25015	−	10.0029i	0.346467	−	1.06632i
$89$	0.0888461	+	0.273440i	0.00941767	+	0.0289846i	0.955655	−	0.294489i	$-0.0951494\pi$
$89$	0.0888461	+	0.273440i	0.00941767	+	0.0289846i	−0.946237	+	0.323473i	$0.895149\pi$
$90$		0			0
$91$	−2.01823	+	6.21148i	−0.211568	+	0.651140i
$92$	15.6631	+	11.3799i	1.63299	+	1.18644i
$93$	−0.418084			−0.0433533
$94$	14.2483	+	10.3520i	1.46960	+	1.06773i
$95$		0			0
$96$	−3.17630	+	2.30772i	−0.324180	+	0.235531i
$97$	8.42109	−	6.11828i	0.855032	−	0.621217i	−0.0714966	−	0.997441i	$-0.522778\pi$
$97$	8.42109	−	6.11828i	0.855032	−	0.621217i	0.926529	+	0.376224i	$0.122778\pi$
$98$	3.72197	+	11.4551i	0.375976	+	1.15714i
$99$	2.93111			0.294587
$100$		0			0
$101$	7.65744			0.761943			0.380972	−	0.924587i	$-0.375590\pi$
$101$	7.65744			0.761943			0.380972	+	0.924587i	$0.375590\pi$
$102$	−4.92942	−	15.1712i	−0.488085	−	1.50217i
$103$	2.41574	−	1.75514i	0.238030	−	0.172939i	−0.462375	−	0.886684i	$-0.653003\pi$
$103$	2.41574	−	1.75514i	0.238030	−	0.172939i	0.700405	+	0.713745i	$0.253003\pi$
$104$	5.44530	−	3.95624i	0.533955	−	0.387941i
$105$		0			0
$106$	−7.05501	−	5.12576i	−0.685243	−	0.497858i
$107$	−7.07213			−0.683689			−0.341844	−	0.939757i	$-0.611052\pi$
$107$	−7.07213			−0.683689			−0.341844	+	0.939757i	$0.611052\pi$
$108$	2.85292	+	2.07277i	0.274522	+	0.199452i
$109$	−4.11060	+	12.6511i	−0.393724	+	1.21176i	0.536227	+	0.844074i	$0.319849\pi$
$109$	−4.11060	+	12.6511i	−0.393724	+	1.21176i	−0.929951	+	0.367683i	$0.880151\pi$
$110$		0			0
$111$	−1.61912	−	4.98314i	−0.153680	−	0.472979i
$112$	1.48773	−	4.57876i	0.140577	−	0.432653i
$113$	3.09737	−	9.53271i	0.291376	−	0.896762i	−0.693039	−	0.720900i	$-0.743729\pi$
$113$	3.09737	−	9.53271i	0.291376	−	0.896762i	0.984415	−	0.175862i	$-0.0562713\pi$
$114$	2.14265	+	6.59441i	0.200678	+	0.617623i
$115$		0			0
$116$	2.78525	−	8.57211i	0.258604	−	0.795900i
$117$	1.51751	+	1.10254i	0.140294	+	0.101930i
$118$	−16.7110			−1.53837
$119$	−19.1146	−	13.8875i	−1.75223	−	1.27307i
$120$		0			0
$121$	1.94861	−	1.41575i	0.177146	−	0.128704i
$122$	12.2425	−	8.89467i	1.10838	−	0.805286i
$123$	−0.518744	−	1.59653i	−0.0467736	−	0.143954i
$124$	1.47433			0.132399
$125$		0			0
$126$	8.18532			0.729206
$127$	3.26725	+	10.0556i	0.289921	+	0.892286i	0.984880	+	0.173237i	$0.0554225\pi$
$127$	3.26725	+	10.0556i	0.289921	+	0.892286i	−0.694959	+	0.719049i	$0.744577\pi$
$128$	16.4603	−	11.9591i	1.45490	−	1.05705i
$129$	8.83711	−	6.42054i	0.778064	−	0.565297i
$130$		0			0
$131$	7.30225	+	5.30540i	0.638001	+	0.463535i	0.859163	−	0.511703i	$-0.170985\pi$
$131$	7.30225	+	5.30540i	0.638001	+	0.463535i	−0.221162	+	0.975237i	$0.570985\pi$
$132$	−10.3363			−0.899656
$133$	8.30847	+	6.03645i	0.720435	+	0.523427i
$134$	7.29462	−	22.4505i	0.630159	−	1.93943i
$135$		0			0
$136$	7.52427	+	23.1573i	0.645200	+	1.98572i
$137$	−6.07669	+	18.7021i	−0.519167	+	1.59783i	0.256404	+	0.966570i	$0.417462\pi$
$137$	−6.07669	+	18.7021i	−0.519167	+	1.59783i	−0.775571	+	0.631261i	$0.782538\pi$
$138$	3.98833	−	12.2748i	0.339509	−	1.04490i
$139$	−3.60067	−	11.0817i	−0.305404	−	0.939938i	−0.979526	−	0.201318i	$-0.935478\pi$
$139$	−3.60067	−	11.0817i	−0.305404	−	0.939938i	0.674122	−	0.738620i	$-0.264522\pi$
$140$		0			0
$141$	2.31509	−	7.12511i	0.194965	−	0.600042i
$142$	−1.38570	−	1.00677i	−0.116285	−	0.0844862i
$143$	−5.49801			−0.459767
$144$	−1.11863	−	0.812729i	−0.0932188	−	0.0677275i
$145$		0			0
$146$	6.83280	−	4.96432i	0.565486	−	0.410850i
$147$	4.14503	−	3.01154i	0.341876	−	0.248387i
$148$	5.70967	+	17.5726i	0.469332	+	1.44446i
$149$	−7.33020			−0.600513			−0.300257	−	0.953858i	$-0.597072\pi$
$149$	−7.33020			−0.600513			−0.300257	+	0.953858i	$0.597072\pi$
$150$		0			0
$151$	−16.7358			−1.36194			−0.680968	−	0.732313i	$-0.738441\pi$
$151$	−16.7358			−1.36194			−0.680968	+	0.732313i	$0.738441\pi$
$152$	−3.27055	−	10.0657i	−0.265276	−	0.816437i
$153$	−5.48972	+	3.98851i	−0.443817	+	0.322452i
$154$	−19.4100	+	14.1022i	−1.56410	+	1.13639i
$155$		0			0
$156$	−5.35135	−	3.88798i	−0.428451	−	0.311288i
$157$	7.88635			0.629399			0.314700	−	0.949191i	$-0.398096\pi$
$157$	7.88635			0.629399			0.314700	+	0.949191i	$0.398096\pi$
$158$	−5.84375	−	4.24574i	−0.464904	−	0.337773i
$159$	−1.14631	+	3.52797i	−0.0909081	+	0.279786i
$160$		0			0
$161$	−5.90724	−	18.1806i	−0.465556	−	1.43283i
$162$	0.726446	−	2.23577i	0.0570750	−	0.175659i
$163$	−3.07160	+	9.45343i	−0.240587	+	0.740450i	0.755744	+	0.654867i	$0.227275\pi$
$163$	−3.07160	+	9.45343i	−0.240587	+	0.740450i	−0.996331	+	0.0855829i	$0.972725\pi$
$164$	1.82930	+	5.63000i	0.142844	+	0.439629i
$165$		0			0
$166$	7.34818	−	22.6154i	0.570330	−	1.75529i
$167$	−4.51243	−	3.27847i	−0.349182	−	0.253696i	0.399344	−	0.916801i	$-0.369238\pi$
$167$	−4.51243	−	3.27847i	−0.349182	−	0.253696i	−0.748526	+	0.663106i	$0.769238\pi$
$168$	−12.4941			−0.963939
$169$	7.67075	+	5.57313i	0.590058	+	0.428702i
$170$		0			0
$171$	2.38620	−	1.73367i	0.182477	−	0.132577i
$172$	−31.1632	+	22.6414i	−2.37617	+	1.72639i
$173$	5.11985	+	15.7573i	0.389255	+	1.19800i	0.933346	+	0.358978i	$0.116875\pi$
$173$	5.11985	+	15.7573i	0.389255	+	1.19800i	−0.544091	+	0.839026i	$0.683125\pi$
$174$	−6.00857			−0.455508
$175$		0			0
$176$	4.05284			0.305494
$177$	2.19666	+	6.76062i	0.165111	+	0.508160i
$178$	−0.546808	+	0.397279i	−0.0409850	+	0.0297773i
$179$	4.33650	−	3.15065i	0.324125	−	0.235491i	−0.413808	−	0.910364i	$-0.635802\pi$
$179$	4.33650	−	3.15065i	0.324125	−	0.235491i	0.737934	+	0.674873i	$0.235802\pi$
$180$		0			0
$181$	0.265151	+	0.192643i	0.0197085	+	0.0143191i	0.597596	−	0.801797i	$-0.296123\pi$
$181$	0.265151	+	0.192643i	0.0197085	+	0.0143191i	−0.577887	+	0.816117i	$0.696123\pi$
$182$	−15.3536			−1.13808
$183$	−5.20772	−	3.78363i	−0.384966	−	0.279694i
$184$	−6.08779	+	18.7363i	−0.448798	+	1.38126i
$185$		0			0
$186$	−0.303716	−	0.934741i	−0.0222695	−	0.0685385i
$187$	6.14619	−	18.9160i	0.449454	−	1.38328i
$188$	−8.16392	+	25.1260i	−0.595415	+	1.83250i
$189$	−1.07596	−	3.31147i	−0.0782647	−	0.240874i
$190$		0			0
$191$	−1.07226	+	3.30009i	−0.0775862	+	0.238786i	−0.982326	−	0.187179i	$-0.940065\pi$
$191$	−1.07226	+	3.30009i	−0.0775862	+	0.238786i	0.904740	+	0.425965i	$0.140065\pi$
$192$	−9.70420	−	7.05051i	−0.700340	−	0.508827i
$193$	−24.3134			−1.75012			−0.875058	−	0.484018i	$-0.839177\pi$
$193$	−24.3134			−1.75012			−0.875058	+	0.484018i	$0.839177\pi$
$194$	19.7966	+	14.3830i	1.42131	+	1.03264i
$195$		0			0
$196$	−14.6170	+	10.6199i	−1.04407	+	0.758563i
$197$	−12.0997	+	8.79098i	−0.862071	+	0.626331i	−0.928448	−	0.371463i	$-0.878856\pi$
$197$	−12.0997	+	8.79098i	−0.862071	+	0.626331i	0.0663764	+	0.997795i	$0.478856\pi$
$198$	2.12929	+	6.55329i	0.151322	+	0.465722i
$199$	−11.3251			−0.802817			−0.401408	−	0.915899i	$-0.631479\pi$
$199$	−11.3251			−0.802817			−0.401408	+	0.915899i	$0.631479\pi$
$200$		0			0
$201$	−10.0415			−0.708274
$202$	5.56272	+	17.1203i	0.391391	+	1.20458i
$203$	−7.19983	+	5.23098i	−0.505329	+	0.367143i
$204$	19.3589	−	14.0651i	1.35540	−	0.984753i
$205$		0			0
$206$	5.67900	+	4.12603i	0.395674	+	0.287474i
$207$	−5.49019			−0.381595
$208$	2.09826	+	1.52447i	0.145488	+	0.105703i
$209$	−2.67155	+	8.22217i	−0.184795	+	0.568739i
$210$		0			0
$211$	2.33086	+	7.17366i	0.160463	+	0.493855i	0.998673	−	0.0514924i	$-0.0163978\pi$
$211$	2.33086	+	7.17366i	0.160463	+	0.493855i	−0.838210	+	0.545347i	$0.816398\pi$
$212$	4.04234	−	12.4410i	0.277629	−	0.854454i
$213$	−0.225150	+	0.692941i	−0.0154270	+	0.0474796i
$214$	−5.13752	−	15.8117i	−0.351194	−	1.08086i
$215$		0			0
$216$	−1.10885	+	3.41268i	−0.0754475	+	0.232204i
$217$	−1.17770	−	0.855651i	−0.0799477	−	0.0580854i
$218$	−31.2711			−2.11795
$219$	−2.90655	−	2.11173i	−0.196406	−	0.142697i
$220$		0			0
$221$	10.2973	−	7.48144i	0.692672	−	0.503256i
$222$	9.96497	−	7.23997i	0.668805	−	0.485915i
$223$	−2.40891	−	7.41386i	−0.161313	−	0.496469i	0.837433	−	0.546540i	$-0.184055\pi$
$223$	−2.40891	−	7.41386i	−0.161313	−	0.496469i	−0.998746	+	0.0500709i	$0.984055\pi$
$224$	−13.6703			−0.913387
$225$		0			0
$226$	23.5630			1.56739
$227$	−3.96529	−	12.2039i	−0.263185	−	0.810001i	−0.992106	−	0.125403i	$-0.959978\pi$
$227$	−3.96529	−	12.2039i	−0.263185	−	0.810001i	0.728921	−	0.684598i	$-0.240022\pi$
$228$	−8.41468	+	6.11363i	−0.557276	+	0.404885i
$229$	11.7334	−	8.52483i	0.775366	−	0.563337i	−0.128218	−	0.991746i	$-0.540926\pi$
$229$	11.7334	−	8.52483i	0.775366	−	0.563337i	0.903585	+	0.428409i	$0.140926\pi$
$230$		0			0
$231$	8.25665	+	5.99881i	0.543248	+	0.394693i
$232$	9.17148			0.602137
$233$	−9.22041	−	6.69902i	−0.604049	−	0.438867i	0.243265	−	0.969960i	$-0.421782\pi$
$233$	−9.22041	−	6.69902i	−0.604049	−	0.438867i	−0.847314	+	0.531093i	$0.821782\pi$
$234$	−1.36263	+	4.19374i	−0.0890779	+	0.274153i
$235$		0			0
$236$	−7.74630	−	23.8407i	−0.504241	−	1.55190i
$237$	−0.949501	+	2.92226i	−0.0616767	+	0.189821i
$238$	17.1637	−	52.8244i	1.11256	−	3.42410i
$239$	2.13244	+	6.56298i	0.137936	+	0.424524i	0.996035	−	0.0889605i	$-0.0283545\pi$
$239$	2.13244	+	6.56298i	0.137936	+	0.424524i	−0.858099	+	0.513484i	$0.828354\pi$
$240$		0			0
$241$	−8.79052	+	27.0545i	−0.566247	+	1.74273i	0.0979683	+	0.995190i	$0.468766\pi$
$241$	−8.79052	+	27.0545i	−0.566247	+	1.74273i	−0.664216	+	0.747541i	$0.731234\pi$
$242$	4.58085	+	3.32818i	0.294468	+	0.213943i
$243$	−1.00000			−0.0641500
$244$	18.3645	+	13.3426i	1.17567	+	0.854172i
$245$		0			0
$246$	3.19264	−	2.31959i	0.203555	−	0.147891i
$247$	−4.47590	+	3.25193i	−0.284795	+	0.206915i
$248$	0.463592	+	1.42679i	0.0294381	+	0.0906011i
$249$	−10.1152			−0.641028
$250$		0			0
$251$	−12.3258			−0.777999			−0.389000	−	0.921238i	$-0.627179\pi$
$251$	−12.3258			−0.777999			−0.389000	+	0.921238i	$0.627179\pi$
$252$	3.79427	+	11.6776i	0.239017	+	0.735618i
$253$	13.0190	−	9.45885i	0.818496	−	0.594673i
$254$	−20.1084	+	14.6096i	−1.26172	+	0.916690i
$255$		0			0
$256$	19.2870	+	14.0128i	1.20544	+	0.875801i
$257$	20.8274			1.29918			0.649590	−	0.760285i	$-0.274941\pi$
$257$	20.8274			1.29918			0.649590	+	0.760285i	$0.274941\pi$
$258$	20.7745	+	15.0936i	1.29337	+	0.939686i
$259$	5.63760	−	17.3507i	0.350303	−	1.07812i
$260$		0			0
$261$	0.789827	+	2.43084i	0.0488891	+	0.150465i
$262$	−6.55696	+	20.1802i	−0.405090	+	1.24674i
$263$	0.690704	−	2.12577i	0.0425906	−	0.131080i	−0.927500	−	0.373823i	$-0.878047\pi$
$263$	0.690704	−	2.12577i	0.0425906	−	0.131080i	0.970091	+	0.242742i	$0.0780469\pi$
$264$	−3.25015	−	10.0029i	−0.200033	−	0.615638i
$265$		0			0
$266$	−7.46048	+	22.9610i	−0.457431	+	1.40783i
$267$	0.232602	+	0.168995i	0.0142350	+	0.0103423i
$268$	35.4104			2.16303
$269$	15.6170	+	11.3464i	0.952183	+	0.691802i	0.951322	−	0.308198i	$-0.0997259\pi$
$269$	15.6170	+	11.3464i	0.952183	+	0.691802i	0.000861106		1.00000i	$0.499726\pi$
$270$		0			0
$271$	9.66058	−	7.01882i	0.586838	−	0.426363i	−0.254345	−	0.967114i	$-0.581860\pi$
$271$	9.66058	−	7.01882i	0.586838	−	0.426363i	0.841183	+	0.540751i	$0.181860\pi$
$272$	−7.59062	+	5.51491i	−0.460249	+	0.334390i
$273$	2.01823	+	6.21148i	0.122149	+	0.375936i
$274$	−46.2281			−2.79274
$275$		0			0
$276$	19.3606			1.16537
$277$	8.07975	+	24.8669i	0.485465	+	1.49411i	0.831306	+	0.555815i	$0.187594\pi$
$277$	8.07975	+	24.8669i	0.485465	+	1.49411i	−0.345841	+	0.938293i	$0.612406\pi$
$278$	22.1605	−	16.1005i	1.32910	−	0.965646i
$279$	−0.338237	+	0.245744i	−0.0202497	+	0.0147123i
$280$		0			0
$281$	−8.18876	−	5.94948i	−0.488500	−	0.354916i	0.316107	−	0.948724i	$-0.397624\pi$
$281$	−8.18876	−	5.94948i	−0.488500	−	0.354916i	−0.804607	+	0.593807i	$0.797624\pi$
$282$	17.6119			1.04877
$283$	25.7783	+	18.7290i	1.53236	+	1.11333i	0.954907	+	0.296903i	$0.0959540\pi$
$283$	25.7783	+	18.7290i	1.53236	+	1.11333i	0.577455	+	0.816423i	$0.304046\pi$
$284$	0.793970	−	2.44359i	0.0471135	−	0.145000i
$285$		0			0
$286$	−3.99401	−	12.2923i	−0.236171	−	0.726859i
$287$	1.80621	−	5.55893i	0.106617	−	0.328134i
$288$	−1.21324	+	3.73397i	−0.0714908	+	0.220026i
$289$	8.97546	+	27.6236i	0.527968	+	1.62492i
$290$		0			0
$291$	3.21657	−	9.89959i	0.188559	−	0.580324i
$292$	10.2496	+	7.44680i	0.599815	+	0.435791i
$293$	16.6235			0.971153			0.485576	−	0.874194i	$-0.338610\pi$
$293$	16.6235			0.971153			0.485576	+	0.874194i	$0.338610\pi$
$294$	9.74425	+	7.07961i	0.568296	+	0.412891i
$295$		0			0
$296$	−15.2105	+	11.0511i	−0.884094	+	0.642332i
$297$	2.37132	−	1.72286i	0.137598	−	0.0999706i
$298$	−5.32499	−	16.3886i	−0.308469	−	0.949369i
$299$	10.2982			0.595561
$300$		0			0
$301$	38.0336			2.19222
$302$	−12.1576	−	37.4173i	−0.699593	−	2.15312i
$303$	6.19500	−	4.50093i	0.355893	−	0.258572i
$304$	3.29939	−	2.39715i	0.189233	−	0.137486i
$305$		0			0
$306$	−12.9054	−	9.37631i	−0.737752	−	0.536008i
$307$	−14.1643			−0.808402			−0.404201	−	0.914670i	$-0.632450\pi$
$307$	−14.1643			−0.808402			−0.404201	+	0.914670i	$0.632450\pi$
$308$	−29.1163	−	21.1542i	−1.65905	−	1.20537i
$309$	0.922731	−	2.83987i	0.0524923	−	0.161555i
$310$		0			0
$311$	4.65070	+	14.3134i	0.263717	+	0.811637i	0.991986	+	0.126346i	$0.0403250\pi$
$311$	4.65070	+	14.3134i	0.263717	+	0.811637i	−0.728269	+	0.685291i	$0.759675\pi$
$312$	2.07992	−	6.40133i	0.117752	−	0.362404i
$313$	−1.10466	+	3.39980i	−0.0624392	+	0.192168i	−0.977410	−	0.211352i	$-0.932213\pi$
$313$	−1.10466	+	3.39980i	−0.0624392	+	0.192168i	0.914971	+	0.403520i	$0.132213\pi$
$314$	5.72901	+	17.6321i	0.323307	+	0.995036i
$315$		0			0
$316$	3.34832	−	10.3051i	0.188358	−	0.579706i
$317$	−10.3408	−	7.51306i	−0.580799	−	0.421975i	0.258213	−	0.966088i	$-0.416866\pi$
$317$	−10.3408	−	7.51306i	−0.580799	−	0.421975i	−0.839012	+	0.544113i	$0.816866\pi$
$318$	−8.72047			−0.489020
$319$	−6.06093	−	4.40352i	−0.339347	−	0.246550i
$320$		0			0
$321$	−5.72147	+	4.15689i	−0.319342	+	0.232015i
$322$	36.3564	−	26.4145i	2.02606	−	1.47202i
$323$	−6.18476	−	19.0347i	−0.344129	−	1.05912i
$324$	3.52640			0.195911
$325$		0			0
$326$	−23.3671			−1.29418
$327$	4.11060	+	12.6511i	0.227317	+	0.699608i
$328$	−4.87324	+	3.54062i	−0.269080	+	0.195498i
$329$	21.1036	−	15.3327i	1.16348	−	0.845318i
$330$		0			0
$331$	−3.80646	−	2.76555i	−0.209222	−	0.152009i	0.478240	−	0.878229i	$-0.341275\pi$
$331$	−3.80646	−	2.76555i	−0.209222	−	0.152009i	−0.687462	+	0.726221i	$0.741275\pi$
$332$	35.6704			1.95767
$333$	−4.23892	−	3.07975i	−0.232291	−	0.168769i
$334$	4.05187	−	12.4704i	0.221709	−	0.682349i
$335$		0			0
$336$	−1.48773	−	4.57876i	−0.0811624	−	0.249792i
$337$	−5.37837	+	16.5529i	−0.292978	+	0.901694i	0.690915	+	0.722936i	$0.257208\pi$
$337$	−5.37837	+	16.5529i	−0.292978	+	0.901694i	−0.983893	+	0.178758i	$0.942792\pi$
$338$	−6.88785	+	21.1986i	−0.374650	+	1.15305i
$339$	−3.09737	−	9.53271i	−0.168226	−	0.517746i
$340$		0			0
$341$	0.378685	−	1.16547i	0.0205069	−	0.0631138i
$342$	5.60954	+	4.07557i	0.303329	+	0.220382i
$343$	−6.53364			−0.352783
$344$	−31.7103	−	23.0389i	−1.70970	−	1.24217i
$345$		0			0
$346$	−31.5104	+	22.8936i	−1.69401	+	1.23077i
$347$	−11.3348	+	8.23525i	−0.608486	+	0.442091i	−0.848881	−	0.528584i	$-0.822723\pi$
$347$	−11.3348	+	8.23525i	−0.608486	+	0.442091i	0.240395	+	0.970675i	$0.422723\pi$
$348$	−2.78525	−	8.57211i	−0.149305	−	0.459513i
$349$	35.9459			1.92414			0.962069	−	0.272806i	$-0.0879518\pi$
$349$	35.9459			1.92414			0.962069	+	0.272806i	$0.0879518\pi$
$350$		0			0
$351$	1.87575			0.100120
$352$	−3.55614	−	10.9447i	−0.189543	−	0.583352i
$353$	−7.12095	+	5.17367i	−0.379010	+	0.275367i	−0.760937	−	0.648826i	$-0.775260\pi$
$353$	−7.12095	+	5.17367i	−0.379010	+	0.275367i	0.381927	+	0.924192i	$0.375260\pi$
$354$	−13.5195	+	9.82246i	−0.718551	+	0.522058i
$355$		0			0
$356$	−0.820248	−	0.595945i	−0.0434731	−	0.0315850i
$357$	−23.6269			−1.25047
$358$	10.1944	+	7.40665i	0.538790	+	0.391454i
$359$	1.86326	−	5.73451i	0.0983389	−	0.302656i	−0.889771	−	0.456408i	$-0.849136\pi$
$359$	1.86326	−	5.73451i	0.0983389	−	0.302656i	0.988109	+	0.153752i	$0.0491357\pi$
$360$		0			0
$361$	−3.18301	−	9.79630i	−0.167527	−	0.515595i
$362$	−0.238089	+	0.732762i	−0.0125137	+	0.0385131i
$363$	0.744302	−	2.29073i	0.0390657	−	0.120232i
$364$	−7.11710	−	21.9042i	−0.373037	−	1.14809i
$365$		0			0
$366$	4.67621	−	14.3919i	0.244429	−	0.752276i
$367$	−23.2724	−	16.9084i	−1.21481	−	0.882609i	−0.219149	−	0.975691i	$-0.570328\pi$
$367$	−23.2724	−	16.9084i	−1.21481	−	0.882609i	−0.995658	+	0.0930825i	$0.970328\pi$
$368$	−7.59128			−0.395723
$369$	−1.35809	−	0.986709i	−0.0706993	−	0.0513660i
$370$		0			0
$371$	−10.4494	+	7.59193i	−0.542505	+	0.394153i
$372$	1.19276	−	0.866590i	0.0618417	−	0.0449306i
$373$	10.3830	+	31.9555i	0.537610	+	1.65459i	0.737940	+	0.674866i	$0.235799\pi$
$373$	10.3830	+	31.9555i	0.537610	+	1.65459i	−0.200330	+	0.979729i	$0.564201\pi$
$374$	46.7568			2.41774
$375$		0			0
$376$	−26.8828			−1.38637
$377$	−1.48152	−	4.55964i	−0.0763020	−	0.234833i
$378$	6.62206	−	4.81121i	0.340602	−	0.247462i
$379$	−3.74901	+	2.72381i	−0.192574	+	0.139913i	−0.679894	−	0.733310i	$-0.737974\pi$
$379$	−3.74901	+	2.72381i	−0.192574	+	0.139913i	0.487321	+	0.873223i	$0.337974\pi$
$380$		0			0
$381$	8.55377	+	6.21467i	0.438223	+	0.318387i
$382$	−8.15718			−0.417358
$383$	10.4410	+	7.58581i	0.533509	+	0.387617i	0.821669	−	0.569965i	$-0.193043\pi$
$383$	10.4410	+	7.58581i	0.533509	+	0.387617i	−0.288160	+	0.957582i	$0.593043\pi$
$384$	6.28728	−	19.3503i	0.320846	−	0.987464i
$385$		0			0
$386$	−17.6624	−	54.3592i	−0.898991	−	2.76681i
$387$	3.37548	−	10.3886i	0.171585	−	0.528085i
$388$	−11.3429	+	34.9099i	−0.575849	+	1.77228i
$389$	−5.41540	−	16.6669i	−0.274571	−	0.845044i	−0.989332	−	0.145675i	$-0.953465\pi$
$389$	−5.41540	−	16.6669i	−0.274571	−	0.845044i	0.714761	−	0.699369i	$-0.246535\pi$
$390$		0			0
$391$	−11.5123	+	35.4312i	−0.582202	+	1.79183i
$392$	−14.8736	−	10.8063i	−0.751232	−	0.545802i
$393$	9.02608			0.455305
$394$	−28.4444	−	20.6661i	−1.43301	−	1.04114i
$395$		0			0
$396$	−8.36221	+	6.07550i	−0.420217	+	0.305305i
$397$	21.8577	−	15.8805i	1.09701	−	0.797021i	0.116437	−	0.993198i	$-0.462853\pi$
$397$	21.8577	−	15.8805i	1.09701	−	0.797021i	0.980569	+	0.196177i	$0.0628527\pi$
$398$	−8.22709	−	25.3204i	−0.412387	−	1.26920i
$399$	10.2698			0.514134
$400$		0			0
$401$	−15.9792			−0.797965			−0.398983	−	0.916958i	$-0.630637\pi$
$401$	−15.9792			−0.797965			−0.398983	+	0.916958i	$0.630637\pi$
$402$	−7.29462	−	22.4505i	−0.363823	−	1.11973i
$403$	0.634447	−	0.460953i	0.0316041	−	0.0229617i
$404$	−21.8460	+	15.8721i	−1.08688	+	0.789665i
$405$		0			0
$406$	−16.9256	−	12.2971i	−0.840002	−	0.610297i
$407$	15.3578			0.761258
$408$	19.6988	+	14.3120i	0.975235	+	0.708550i
$409$	−9.57834	+	29.4791i	−0.473618	+	1.45765i	0.374193	+	0.927351i	$0.377920\pi$
$409$	−9.57834	+	29.4791i	−0.473618	+	1.45765i	−0.847812	+	0.530297i	$0.822080\pi$
$410$		0			0
$411$	6.07669	+	18.7021i	0.299741	+	0.922508i
$412$	−3.25392	+	10.0145i	−0.160309	+	0.493381i
$413$	−7.64852	+	23.5397i	−0.376359	+	1.15831i
$414$	−3.98833	−	12.2748i	−0.196016	−	0.603275i
$415$		0			0
$416$	2.27573	−	7.00398i	0.111577	−	0.343398i
$417$	−9.42666	−	6.84887i	−0.461626	−	0.335391i
$418$	−20.3236			−0.994061
$419$	−20.9660	−	15.2327i	−1.02425	−	0.744164i	−0.0571034	−	0.998368i	$-0.518186\pi$
$419$	−20.9660	−	15.2327i	−1.02425	−	0.744164i	−0.967151	+	0.254204i	$0.918186\pi$
$420$		0			0
$421$	−3.17658	+	2.30792i	−0.154817	+	0.112481i	−0.662497	−	0.749065i	$-0.730503\pi$
$421$	−3.17658	+	2.30792i	−0.154817	+	0.112481i	0.507680	+	0.861546i	$0.330503\pi$
$422$	−14.3454	+	10.4226i	−0.698324	+	0.507362i
$423$	−2.31509	−	7.12511i	−0.112563	−	0.346434i
$424$	13.3109			0.646436
$425$		0			0
$426$	−1.71282			−0.0829863
$427$	−6.92607	−	21.3163i	−0.335176	−	1.03157i
$428$	20.1762	−	14.6589i	0.975254	−	0.708563i
$429$	−4.44799	+	3.23165i	−0.214751	+	0.156026i
$430$		0			0
$431$	28.6903	+	20.8447i	1.38196	+	1.00406i	0.996694	+	0.0812518i	$0.0258918\pi$
$431$	28.6903	+	20.8447i	1.38196	+	1.00406i	0.385270	+	0.922804i	$0.374108\pi$
$432$	−1.38270			−0.0665251
$433$	−8.16776	−	5.93423i	−0.392518	−	0.285181i	0.373969	−	0.927441i	$-0.377997\pi$
$433$	−8.16776	−	5.93423i	−0.392518	−	0.285181i	−0.766486	+	0.642261i	$0.777997\pi$
$434$	1.05750	−	3.25466i	0.0507618	−	0.156229i
$435$		0			0
$436$	−14.4956	−	44.6129i	−0.694214	−	2.13657i
$437$	5.00402	−	15.4008i	0.239375	−	0.736719i
$438$	2.60990	−	8.03243i	0.124706	−	0.383804i
$439$	2.19575	+	6.75783i	0.104798	+	0.322534i	0.989683	−	0.143275i	$-0.0457634\pi$
$439$	2.19575	+	6.75783i	0.104798	+	0.322534i	−0.884885	+	0.465809i	$0.845763\pi$
$440$		0			0
$441$	1.58326	−	4.87277i	0.0753933	−	0.232037i
$442$	24.2072	+	17.5876i	1.15142	+	0.836556i
$443$	20.6841			0.982733			0.491366	−	0.870953i	$-0.336498\pi$
$443$	20.6841			0.982733			0.491366	+	0.870953i	$0.336498\pi$
$444$	14.9481	+	10.8604i	0.709406	+	0.515414i
$445$		0			0
$446$	14.8258	−	10.7715i	0.702020	−	0.510047i
$447$	−5.93025	+	4.30858i	−0.280491	+	0.203789i
$448$	−12.9062	−	39.7213i	−0.609762	−	1.87665i
$449$	19.4940			0.919980			0.459990	−	0.887924i	$-0.347853\pi$
$449$	19.4940			0.919980			0.459990	+	0.887924i	$0.347853\pi$
$450$		0			0
$451$	4.92042			0.231694
$452$	10.9225	+	33.6162i	0.513754	+	1.58117i
$453$	−13.5395	+	9.83703i	−0.636142	+	0.462184i
$454$	24.4046	−	17.7310i	1.14536	−	0.832155i
$455$		0			0
$456$	−8.56240	−	6.22095i	−0.400971	−	0.291323i
$457$	−4.34194			−0.203107			−0.101554	−	0.994830i	$-0.532381\pi$
$457$	−4.34194			−0.203107			−0.101554	+	0.994830i	$0.532381\pi$
$458$	27.5833	+	20.0404i	1.28888	+	0.936427i
$459$	−2.09688	+	6.45355i	−0.0978742	+	0.301226i
$460$		0			0
$461$	3.64322	+	11.2127i	0.169682	+	0.522227i	0.999351	−	0.0360287i	$-0.0114708\pi$
$461$	3.64322	+	11.2127i	0.169682	+	0.522227i	−0.829669	+	0.558256i	$0.811471\pi$
$462$	−7.41395	+	22.8178i	−0.344928	+	1.06158i
$463$	−2.80547	+	8.63436i	−0.130381	+	0.401273i	−0.994843	−	0.101426i	$-0.967659\pi$
$463$	−2.80547	+	8.63436i	−0.130381	+	0.401273i	0.864462	+	0.502699i	$0.167659\pi$
$464$	1.09209	+	3.36112i	0.0506991	+	0.156036i
$465$		0			0
$466$	8.27934	−	25.4812i	0.383533	−	1.18039i
$467$	28.2494	+	20.5244i	1.30723	+	0.949755i	0.999998	−	0.00188168i	$-0.000598959\pi$
$467$	28.2494	+	20.5244i	1.30723	+	0.949755i	0.307227	+	0.951636i	$0.400599\pi$
$468$	−6.61463			−0.305762
$469$	−28.2860	−	20.5510i	−1.30613	−	0.948956i
$470$		0			0
$471$	6.38019	−	4.63548i	0.293984	−	0.213592i
$472$	20.6361	−	14.9930i	0.949854	−	0.690109i
$473$	9.89388	+	30.4502i	0.454921	+	1.40010i
$474$	−7.22328			−0.331776
$475$		0			0
$476$	83.3179			3.81887
$477$	1.14631	+	3.52797i	0.0524858	+	0.161535i
$478$	−13.1242	+	9.53530i	−0.600288	+	0.436135i
$479$	6.99515	−	5.08228i	0.319617	−	0.232215i	−0.416395	−	0.909184i	$-0.636707\pi$
$479$	6.99515	−	5.08228i	0.319617	−	0.232215i	0.736012	+	0.676969i	$0.236707\pi$
$480$		0			0
$481$	7.95113	+	5.77684i	0.362540	+	0.263401i
$482$	−66.8734			−3.04600
$483$	−15.4654	−	11.2362i	−0.703698	−	0.511267i
$484$	−2.62471	+	8.07802i	−0.119305	+	0.367183i
$485$		0			0
$486$	−0.726446	−	2.23577i	−0.0329523	−	0.101417i
$487$	0.879035	−	2.70539i	0.0398329	−	0.122593i	−0.929163	−	0.369671i	$-0.879470\pi$
$487$	0.879035	−	2.70539i	0.0398329	−	0.122593i	0.968996	+	0.247078i	$0.0794704\pi$
$488$	−7.13776	+	21.9678i	−0.323111	+	0.994434i
$489$	3.07160	+	9.45343i	0.138903	+	0.427499i
$490$		0			0
$491$	11.3731	−	35.0028i	0.513260	−	1.57965i	−0.273165	−	0.961967i	$-0.588070\pi$
$491$	11.3731	−	35.0028i	0.513260	−	1.57965i	0.786425	−	0.617686i	$-0.211930\pi$
$492$	4.78917	+	3.47953i	0.215912	+	0.156869i
$493$	17.3437			0.781121
$494$	−10.5221	−	7.64474i	−0.473411	−	0.343953i
$495$		0			0
$496$	−0.467680	+	0.339789i	−0.0209994	+	0.0152570i
$497$	−2.05240	+	1.49116i	−0.0920628	+	0.0668876i
$498$	−7.34818	−	22.6154i	−0.329280	−	1.01342i
$499$	5.85775			0.262229			0.131114	−	0.991367i	$-0.458144\pi$
$499$	5.85775			0.262229			0.131114	+	0.991367i	$0.458144\pi$
$500$		0			0
$501$	−5.57767			−0.249192
$502$	−8.95405	−	27.5577i	−0.399639	−	1.22996i
$503$	24.5030	−	17.8025i	1.09253	−	0.793773i	0.112709	−	0.993628i	$-0.464047\pi$
$503$	24.5030	−	17.8025i	1.09253	−	0.793773i	0.979825	+	0.199855i	$0.0640472\pi$
$504$	−10.1079	+	7.34383i	−0.450243	+	0.327120i
$505$		0			0
$506$	30.6054	+	22.2361i	1.36058	+	0.988517i
$507$	9.48157			0.421091
$508$	−30.1640	−	21.9154i	−1.33831	−	0.972340i
$509$	4.67944	−	14.4018i	0.207413	−	0.638350i	−0.792193	−	0.610270i	$-0.791061\pi$
$509$	4.67944	−	14.4018i	0.207413	−	0.638350i	0.999606	−	0.0280797i	$-0.00893923\pi$
$510$		0			0
$511$	−3.86560	−	11.8971i	−0.171004	−	0.526296i
$512$	−4.74395	+	14.6004i	−0.209655	+	0.645251i
$513$	0.911446	−	2.80514i	0.0402413	−	0.123850i
$514$	15.1300	+	46.5654i	0.667356	+	2.05391i
$515$		0			0
$516$	−11.9033	+	36.6345i	−0.524013	+	1.61275i
$517$	17.7654	+	12.9073i	0.781320	+	0.567662i
$518$	42.8877			1.88438
$519$	13.4039	+	9.73854i	0.588368	+	0.427474i
$520$		0			0
$521$	−31.6190	+	22.9726i	−1.38525	+	1.00645i	−0.388887	+	0.921286i	$0.627140\pi$
$521$	−31.6190	+	22.9726i	−1.38525	+	1.00645i	−0.996367	+	0.0851601i	$0.972860\pi$
$522$	−4.86103	+	3.53175i	−0.212762	+	0.154580i
$523$	−11.9891	−	36.8987i	−0.524248	−	1.61347i	−0.765798	−	0.643081i	$-0.777656\pi$
$523$	−11.9891	−	36.8987i	−0.524248	−	1.61347i	0.241550	−	0.970388i	$-0.422344\pi$
$524$	−31.8296			−1.39048
$525$		0			0
$526$	5.25449			0.229107
$527$	0.876674	+	2.69813i	0.0381885	+	0.117532i
$528$	3.27881	−	2.38220i	0.142692	−	0.103672i
$529$	−5.77819	+	4.19810i	−0.251226	+	0.182526i
$530$		0			0
$531$	5.75093	+	4.17830i	0.249569	+	0.181323i
$532$	−36.2155			−1.57014
$533$	2.54743	+	1.85082i	0.110341	+	0.0801678i
$534$	−0.208862	+	0.642811i	−0.00903835	+	0.0278172i
$535$		0			0
$536$	11.1345	+	34.2685i	0.480938	+	1.48017i
$537$	1.65640	−	5.09787i	0.0714788	−	0.219989i
$538$	−14.0231	+	43.1585i	−0.604577	+	1.86070i
$539$	4.64070	+	14.2826i	0.199889	+	0.615196i
$540$		0			0
$541$	4.39669	−	13.5316i	0.189029	−	0.581770i	−0.810966	−	0.585094i	$-0.801058\pi$
$541$	4.39669	−	13.5316i	0.189029	−	0.581770i	0.999994	+	0.00332312i	$0.00105778\pi$
$542$	22.7104	+	16.5001i	0.975494	+	0.708738i
$543$	0.327745			0.0140649
$544$	21.5533	+	15.6594i	0.924091	+	0.671391i
$545$		0			0
$546$	−12.4213	+	9.02462i	−0.531583	+	0.386218i
$547$	−31.8129	+	23.1134i	−1.36022	+	0.988259i	−0.361790	+	0.932259i	$0.617834\pi$
$547$	−31.8129	+	23.1134i	−1.36022	+	0.988259i	−0.998431	+	0.0559991i	$0.982166\pi$
$548$	−21.4288	−	65.9512i	−0.915395	−	2.81730i
$549$	−6.43710			−0.274729
$550$		0			0
$551$	−7.53873			−0.321161
$552$	6.08779	+	18.7363i	0.259114	+	0.797470i
$553$	−8.65537	+	6.28849i	−0.368064	+	0.267414i
$554$	−49.7272	+	36.1290i	−2.11271	+	1.53497i
$555$		0			0
$556$	33.2422	+	24.1519i	1.40978	+	1.02427i
$557$	35.3849			1.49931			0.749654	−	0.661830i	$-0.230220\pi$
$557$	35.3849			1.49931			0.749654	+	0.661830i	$0.230220\pi$
$558$	−0.795138	−	0.577701i	−0.0336609	−	0.0244561i
$559$	−6.33154	+	19.4865i	−0.267796	+	0.824190i
$560$		0			0
$561$	−6.14619	−	18.9160i	−0.259492	−	0.798636i
$562$	7.35299	−	22.6302i	0.310167	−	0.954597i
$563$	4.64717	−	14.3025i	0.195855	−	0.602780i	−0.804111	−	0.594480i	$-0.797358\pi$
$563$	4.64717	−	14.3025i	0.195855	−	0.602780i	0.999966	−	0.00830000i	$-0.00264200\pi$
$564$	8.16392	+	25.1260i	0.343763	+	1.05799i
$565$		0			0
$566$	−23.1473	+	71.2401i	−0.972954	+	2.99444i
$567$	−2.81691	−	2.04660i	−0.118299	−	0.0859492i
$568$	2.61445			0.109700
$569$	2.20383	+	1.60118i	0.0923895	+	0.0671249i	0.633021	−	0.774135i	$-0.281815\pi$
$569$	2.20383	+	1.60118i	0.0923895	+	0.0671249i	−0.540632	+	0.841260i	$0.681815\pi$
$570$		0			0
$571$	−10.2127	+	7.41997i	−0.427389	+	0.310516i	−0.780604	−	0.625026i	$-0.785088\pi$
$571$	−10.2127	+	7.41997i	−0.427389	+	0.310516i	0.353215	+	0.935542i	$0.385088\pi$
$572$	15.6854	−	11.3961i	0.655839	−	0.476495i
$573$	1.07226	+	3.30009i	0.0447944	+	0.137863i
$574$	13.7406			0.573522
$575$		0			0
$576$	−11.9951			−0.499794
$577$	−7.28797	−	22.4301i	−0.303402	−	0.933776i	−0.980269	−	0.197670i	$-0.936662\pi$
$577$	−7.28797	−	22.4301i	−0.303402	−	0.933776i	0.676866	−	0.736106i	$-0.263338\pi$
$578$	−55.2399	+	40.1342i	−2.29768	+	1.66936i
$579$	−19.6700	+	14.2911i	−0.817455	+	0.593916i
$580$		0			0
$581$	−28.4937	−	20.7019i	−1.18212	−	0.858858i
$582$	24.4699			1.01431
$583$	−8.79646	−	6.39100i	−0.364312	−	0.264688i
$584$	−3.98374	+	12.2607i	−0.164849	+	0.507352i
$585$		0			0
$586$	12.0761	+	37.1663i	0.498857	+	1.53532i
$587$	−7.00764	+	21.5673i	−0.289236	+	0.890177i	0.695861	+	0.718177i	$0.255023\pi$
$587$	−7.00764	+	21.5673i	−0.289236	+	0.890177i	−0.985097	+	0.172000i	$0.944977\pi$
$588$	−5.58321	+	17.1833i	−0.230248	+	0.708629i
$589$	−0.381061	−	1.17279i	−0.0157013	−	0.0483238i
$590$		0			0
$591$	−4.62169	+	14.2241i	−0.190111	+	0.585102i
$592$	−5.86114	−	4.25837i	−0.240891	−	0.175018i
$593$	−8.74287			−0.359027			−0.179513	−	0.983756i	$-0.557452\pi$
$593$	−8.74287			−0.359027			−0.179513	+	0.983756i	$0.557452\pi$
$594$	5.57456	+	4.05015i	0.228727	+	0.166180i
$595$		0			0
$596$	20.9124	−	15.1938i	0.856607	−	0.622362i
$597$	−9.16222	+	6.65674i	−0.374985	+	0.272442i
$598$	7.48110	+	23.0245i	0.305925	+	0.941540i
$599$	16.3209			0.666854			0.333427	−	0.942776i	$-0.391795\pi$
$599$	16.3209			0.666854			0.333427	+	0.942776i	$0.391795\pi$
$600$		0			0
$601$	36.2713			1.47954			0.739768	−	0.672862i	$-0.234935\pi$
$601$	36.2713			1.47954			0.739768	+	0.672862i	$0.234935\pi$
$602$	27.6294	+	85.0344i	1.12609	+	3.46575i
$603$	−8.12376	+	5.90225i	−0.330825	+	0.240358i
$604$	47.7457	−	34.6893i	1.94275	−	1.41149i
$605$		0			0
$606$	14.5634	+	10.5809i	0.591597	+	0.429820i
$607$	−16.6820			−0.677102			−0.338551	−	0.940948i	$-0.609937\pi$
$607$	−16.6820			−0.677102			−0.338551	+	0.940948i	$0.609937\pi$
$608$	−9.36851	−	6.80662i	−0.379943	−	0.276045i
$609$	−2.75009	+	8.46390i	−0.111439	+	0.342975i
$610$		0			0
$611$	4.34252	+	13.3649i	0.175679	+	0.540686i
$612$	7.39445	−	22.7578i	0.298903	−	0.919929i
$613$	7.66260	−	23.5831i	0.309490	−	0.952511i	−0.668474	−	0.743736i	$-0.733052\pi$
$613$	7.66260	−	23.5831i	0.309490	−	0.952511i	0.977964	−	0.208776i	$-0.0669479\pi$
$614$	−10.2896	−	31.6682i	−0.415256	−	1.27803i
$615$		0			0
$616$	11.3167	−	34.8291i	0.455961	−	1.40330i
$617$	−22.6257	−	16.4386i	−0.910877	−	0.661791i	0.0303592	−	0.999539i	$-0.490335\pi$
$617$	−22.6257	−	16.4386i	−0.910877	−	0.661791i	−0.941237	+	0.337748i	$0.890335\pi$
$618$	7.01963			0.282371
$619$	−22.0608	−	16.0281i	−0.886697	−	0.644223i	0.0483179	−	0.998832i	$-0.484614\pi$
$619$	−22.0608	−	16.0281i	−0.886697	−	0.644223i	−0.935015	+	0.354609i	$0.884614\pi$
$620$		0			0
$621$	−4.44166	+	3.22706i	−0.178238	+	0.129497i
$622$	−28.6230	+	20.7958i	−1.14768	+	0.833836i
$623$	0.309352	+	0.952088i	0.0123939	+	0.0381446i
$624$	2.59359			0.103827
$625$		0			0
$626$	−8.40365			−0.335878
$627$	2.67155	+	8.22217i	0.106691	+	0.328362i
$628$	−22.4991	+	16.3466i	−0.897812	+	0.652299i
$629$	−28.7638	+	20.8982i	−1.14689	+	0.833264i
$630$		0			0
$631$	−34.1893	−	24.8400i	−1.36105	−	0.988863i	−0.998377	−	0.0569481i	$-0.981863\pi$
$631$	−34.1893	−	24.8400i	−1.36105	−	0.988863i	−0.362676	−	0.931915i	$-0.618137\pi$
$632$	11.0256			0.438575
$633$	6.10228	+	4.43356i	0.242544	+	0.176218i
$634$	9.28542	−	28.5776i	0.368771	−	1.13496i
$635$		0			0
$636$	−4.04234	−	12.4410i	−0.160289	−	0.493319i
$637$	−2.96979	+	9.14008i	−0.117667	+	0.362143i
$638$	5.44233	−	16.7498i	0.215464	−	0.663130i
$639$	0.225150	+	0.692941i	0.00890681	+	0.0274123i
$640$		0			0
$641$	14.1671	−	43.6017i	0.559565	−	1.72217i	−0.124006	−	0.992281i	$-0.539574\pi$
$641$	14.1671	−	43.6017i	0.559565	−	1.72217i	0.683571	−	0.729884i	$-0.260426\pi$
$642$	−13.4502	−	9.77215i	−0.530837	−	0.385676i
$643$	−46.6710			−1.84052			−0.920261	−	0.391304i	$-0.872024\pi$
$643$	−46.6710			−1.84052			−0.920261	+	0.391304i	$0.872024\pi$
$644$	54.5370	+	39.6235i	2.14906	+	1.56138i
$645$		0			0
$646$	38.0644	−	27.6554i	1.49763	−	1.08809i
$647$	9.81050	−	7.12775i	0.385691	−	0.280221i	−0.377997	−	0.925807i	$-0.623387\pi$
$647$	9.81050	−	7.12775i	0.385691	−	0.280221i	0.763687	+	0.645586i	$0.223387\pi$
$648$	1.10885	+	3.41268i	0.0435597	+	0.134063i
$649$	−20.8359			−0.817880
$650$		0			0
$651$	−1.45572			−0.0570542
$652$	−10.8317	−	33.3366i	−0.424202	−	1.30556i
$653$	1.39164	−	1.01109i	0.0544593	−	0.0395670i	−0.560223	−	0.828342i	$-0.689284\pi$
$653$	1.39164	−	1.01109i	0.0544593	−	0.0395670i	0.614682	+	0.788775i	$0.289284\pi$
$654$	−25.2989	+	18.3807i	−0.989264	+	0.718743i
$655$		0			0
$656$	−1.87783	−	1.36432i	−0.0733168	−	0.0532678i
$657$	−3.59269			−0.140164
$658$	49.6110	+	36.0445i	1.93404	+	1.40516i
$659$	1.69325	−	5.21129i	0.0659596	−	0.203003i	−0.912645	−	0.408754i	$-0.865964\pi$
$659$	1.69325	−	5.21129i	0.0659596	−	0.203003i	0.978604	+	0.205751i	$0.0659636\pi$
$660$		0			0
$661$	0.246425	+	0.758418i	0.00958482	+	0.0294990i	0.955735	−	0.294230i	$-0.0950633\pi$
$661$	0.246425	+	0.758418i	0.00958482	+	0.0294990i	−0.946150	+	0.323729i	$0.895063\pi$
$662$	3.41796	−	10.5194i	0.132843	−	0.408848i
$663$	3.93322	−	12.1052i	0.152754	−	0.470128i
$664$	11.2163	+	34.5201i	0.435276	+	1.33964i
$665$		0			0
$666$	3.80628	−	11.7145i	0.147490	−	0.453929i
$667$	11.3526	+	8.24814i	0.439574	+	0.319369i
$668$	19.6691			0.761020
$669$	−6.30661	−	4.58202i	−0.243827	−	0.177151i
$670$		0			0
$671$	15.2644	−	11.0902i	0.589275	−	0.428133i
$672$	−11.0595	+	8.03522i	−0.426631	+	0.309965i
$673$	−15.8612	−	48.8158i	−0.611405	−	1.88171i	−0.444627	−	0.895716i	$-0.646664\pi$
$673$	−15.8612	−	48.8158i	−0.611405	−	1.88171i	−0.166777	−	0.985995i	$-0.553336\pi$
$674$	−40.9156			−1.57601
$675$		0			0
$676$	−33.4358			−1.28599
$677$	4.66397	+	14.3542i	0.179251	+	0.551678i	0.999802	−	0.0198952i	$-0.00633326\pi$
$677$	4.66397	+	14.3542i	0.179251	+	0.551678i	−0.820551	+	0.571573i	$0.806333\pi$
$678$	19.0629	−	13.8500i	0.732106	−	0.531906i
$679$	29.3213	−	21.3032i	1.12525	−	0.817540i
$680$		0			0
$681$	−10.3813	−	7.54242i	−0.397811	−	0.289026i
$682$	2.88082			0.110312
$683$	8.78610	+	6.38347i	0.336191	+	0.244257i	0.743053	−	0.669233i	$-0.233377\pi$
$683$	8.78610	+	6.38347i	0.336191	+	0.244257i	−0.406862	+	0.913490i	$0.633377\pi$
$684$	−3.21412	+	9.89205i	−0.122895	+	0.378232i
$685$		0			0
$686$	−4.74634	−	14.6077i	−0.181216	−	0.557726i
$687$	4.48177	−	13.7935i	0.170990	−	0.526253i
$688$	4.66726	−	14.3644i	0.177938	−	0.547636i
$689$	−2.15018	−	6.61758i	−0.0819154	−	0.252110i
$690$		0			0
$691$	2.60981	−	8.03217i	0.0992818	−	0.305558i	−0.889064	−	0.457783i	$-0.848644\pi$
$691$	2.60981	−	8.03217i	0.0992818	−	0.305558i	0.988346	+	0.152225i	$0.0486438\pi$
$692$	−47.2677	−	34.3420i	−1.79685	−	1.30549i
$693$	10.2058			0.387686
$694$	−26.6463	−	19.3597i	−1.01148	−	0.734883i
$695$		0			0
$696$	7.41988	−	5.39086i	0.281250	−	0.204340i
$697$	−9.21553	+	6.69548i	−0.349063	+	0.253609i
$698$	26.1127	+	80.3668i	0.988382	+	3.04193i
$699$	−11.3970			−0.431076
$700$		0			0
$701$	48.9399			1.84843			0.924216	−	0.381869i	$-0.124719\pi$
$701$	48.9399			1.84843			0.924216	+	0.381869i	$0.124719\pi$
$702$	1.36263	+	4.19374i	0.0514291	+	0.158283i
$703$	12.5027	−	9.08373i	0.471548	−	0.342599i
$704$	28.4440	−	20.6658i	1.07203	−	0.778872i
$705$		0			0
$706$	−16.7401	−	12.1624i	−0.630023	−	0.457739i
$707$	26.6623			1.00274
$708$	−20.2801	−	14.7343i	−0.762172	−	0.553750i
$709$	7.65850	−	23.5705i	0.287621	−	0.885207i	−0.697980	−	0.716118i	$-0.745917\pi$
$709$	7.65850	−	23.5705i	0.287621	−	0.885207i	0.985601	−	0.169089i	$-0.0540826\pi$
$710$		0			0
$711$	0.949501	+	2.92226i	0.0356091	+	0.109593i
$712$	0.318807	−	0.981187i	0.0119478	−	0.0367716i
$713$	−0.709306	+	2.18302i	−0.0265637	+	0.0817547i
$714$	−17.1637	−	52.8244i	−0.642334	−	1.97690i
$715$		0			0
$716$	−5.84112	+	17.9771i	−0.218293	+	0.671836i
$717$	5.58280	+	4.05614i	0.208494	+	0.151479i
$718$	14.1746			0.528992
$719$	14.7379	+	10.7077i	0.549631	+	0.399331i	0.827650	−	0.561245i	$-0.189678\pi$
$719$	14.7379	+	10.7077i	0.549631	+	0.399331i	−0.278018	+	0.960576i	$0.589678\pi$
$720$		0			0
$721$	8.41134	−	6.11119i	0.313255	−	0.227593i
$722$	19.5900	−	14.2330i	0.729065	−	0.529697i
$723$	8.79052	+	27.0545i	0.326923	+	1.00617i
$724$	−1.15576			−0.0429534
$725$		0			0
$726$	5.66224			0.210145
$727$	5.15129	+	15.8540i	0.191051	+	0.587994i	1.00000		0.000115145i	$3.66518e-5\pi$
$727$	5.15129	+	15.8540i	0.191051	+	0.587994i	−0.808949	+	0.587878i	$0.799963\pi$
$728$	18.9599	−	13.7752i	0.702701	−	0.510542i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−59.9657	−	43.5676i	−2.21791	−	1.61141i
$732$	22.6998			0.839008
$733$	−16.2324	−	11.7935i	−0.599558	−	0.435604i	0.246164	−	0.969228i	$-0.420830\pi$
$733$	−16.2324	−	11.7935i	−0.599558	−	0.435604i	−0.845722	+	0.533624i	$0.820830\pi$
$734$	20.8971	−	64.3147i	0.771326	−	2.37390i
$735$		0			0
$736$	6.66092	+	20.5002i	0.245525	+	0.755648i
$737$	9.09522	−	27.9922i	0.335027	−	1.03111i
$738$	1.21948	−	3.75317i	0.0448896	−	0.138156i
$739$	−10.5242	−	32.3903i	−0.387140	−	1.19149i	−0.934916	−	0.354870i	$-0.884525\pi$
$739$	−10.5242	−	32.3903i	−0.387140	−	1.19149i	0.547776	−	0.836625i	$-0.315475\pi$
$740$		0			0
$741$	−1.70964	+	5.26174i	−0.0628053	+	0.193295i
$742$	−24.5647	−	17.8473i	−0.901800	−	0.655196i
$743$	−38.5355			−1.41373			−0.706865	−	0.707348i	$-0.749891\pi$
$743$	−38.5355			−1.41373			−0.706865	+	0.707348i	$0.749891\pi$
$744$	1.21370	+	0.881804i	0.0444963	+	0.0323285i
$745$		0			0
$746$	−63.9026	+	46.4280i	−2.33964	+	1.69985i
$747$	−8.18340	+	5.94559i	−0.299415	+	0.217538i
$748$	21.6739	+	66.7055i	0.792478	+	2.43900i
$749$	−24.6244			−0.899754
$750$		0			0
$751$	−36.0351			−1.31494			−0.657470	−	0.753481i	$-0.728373\pi$
$751$	−36.0351			−1.31494			−0.657470	+	0.753481i	$0.728373\pi$
$752$	−3.20107	−	9.85187i	−0.116731	−	0.359261i
$753$	−9.97181	+	7.24494i	−0.363393	+	0.264020i
$754$	9.11807	−	6.62466i	0.332060	−	0.241256i
$755$		0			0
$756$	9.93354	+	7.21714i	0.361279	+	0.262485i
$757$	35.0131			1.27257			0.636287	−	0.771453i	$-0.280470\pi$
$757$	35.0131			1.27257			0.636287	+	0.771453i	$0.280470\pi$
$758$	−8.81328	−	6.40322i	−0.320113	−	0.232576i
$759$	4.97281	−	15.3047i	0.180502	−	0.555527i
$760$		0			0
$761$	9.69007	+	29.8230i	0.351265	+	1.08108i	0.958144	+	0.286288i	$0.0924213\pi$
$761$	9.69007	+	29.8230i	0.351265	+	1.08108i	−0.606879	+	0.794794i	$0.707579\pi$
$762$	−7.68074	+	23.6389i	−0.278244	+	0.856347i
$763$	−14.3126	+	44.0497i	−0.518152	+	1.59471i
$764$	−3.78123	−	11.6374i	−0.136800	−	0.421027i
$765$		0			0
$766$	−9.37534	+	28.8543i	−0.338745	+	1.04255i
$767$	−10.7873	−	7.83742i	−0.389506	−	0.282993i
$768$	23.8400			0.860253
$769$	−1.94014	−	1.40959i	−0.0699633	−	0.0508313i	0.552254	−	0.833676i	$-0.313768\pi$
$769$	−1.94014	−	1.40959i	−0.0699633	−	0.0508313i	−0.622217	+	0.782845i	$0.713768\pi$
$770$		0			0
$771$	16.8497	−	12.2421i	0.606829	−	0.440887i
$772$	69.3641	−	50.3960i	2.49647	−	1.81379i
$773$	−3.37526	−	10.3880i	−0.121400	−	0.373630i	0.871828	−	0.489812i	$-0.162935\pi$
$773$	−3.37526	−	10.3880i	−0.121400	−	0.373630i	−0.993228	+	0.116182i	$0.962935\pi$
$774$	25.6788			0.923004
$775$		0			0
$776$	−37.3508			−1.34082
$777$	−5.63760	−	17.3507i	−0.202248	−	0.622454i
$778$	33.3293	−	24.2152i	1.19491	−	0.868156i
$779$	4.00568	−	2.91030i	0.143519	−	0.104272i
$780$		0			0
$781$	−1.72774	−	1.25528i	−0.0618236	−	0.0449174i
$782$	−87.5792			−3.13183
$783$	2.06779	+	1.50234i	0.0738970	+	0.0536893i
$784$	2.18917	−	6.73757i	0.0781846	−	0.240627i
$785$		0			0
$786$	6.55696	+	20.1802i	0.233879	+	0.719806i
$787$	3.57607	−	11.0060i	0.127473	−	0.392321i	−0.866871	−	0.498533i	$-0.833872\pi$
$787$	3.57607	−	11.0060i	0.127473	−	0.392321i	0.994344	+	0.106212i	$0.0338722\pi$
$788$	16.2979	−	50.1599i	0.580590	−	1.78687i
$789$	−0.690704	−	2.12577i	−0.0245897	−	0.0756794i
$790$		0			0
$791$	10.7847	−	33.1918i	0.383459	−	1.18017i
$792$	−8.50901	−	6.18216i	−0.302354	−	0.219673i
$793$	12.0744			0.428773
$794$	51.3837	+	37.3324i	1.82354	+	1.32488i
$795$		0			0
$796$	32.3096	−	23.4743i	1.14518	−	0.832026i
$797$	−17.7113	+	12.8680i	−0.627366	+	0.455808i	−0.855487	−	0.517825i	$-0.826742\pi$
$797$	−17.7113	+	12.8680i	−0.627366	+	0.455808i	0.228121	+	0.973633i	$0.426742\pi$
$798$	7.46048	+	22.9610i	0.264098	+	0.812810i
$799$	−50.8367			−1.79847
$800$		0			0
$801$	0.287512			0.0101587
$802$	−11.6081	−	35.7259i	−0.409895	−	1.26153i
$803$	8.51940	−	6.18970i	0.300643	−	0.218430i
$804$	28.6476	−	20.8137i	1.01032	−	0.734043i
$805$		0			0
$806$	1.49148	+	1.08362i	0.0525350	+	0.0381689i
$807$	19.3036			0.679520
$808$	−22.2295	−	16.1507i	−0.782033	−	0.568180i
$809$	−6.65926	+	20.4951i	−0.234127	+	0.720570i	0.763109	+	0.646270i	$0.223672\pi$
$809$	−6.65926	+	20.4951i	−0.234127	+	0.720570i	−0.997236	+	0.0742994i	$0.976328\pi$
$810$		0			0
$811$	−13.5848	−	41.8098i	−0.477028	−	1.46814i	−0.843203	−	0.537596i	$-0.819333\pi$
$811$	−13.5848	−	41.8098i	−0.477028	−	1.46814i	0.366175	−	0.930546i	$-0.380667\pi$
$812$	9.69791	−	29.8471i	0.340330	−	1.04743i
$813$	3.69001	−	11.3567i	0.129414	−	0.398297i
$814$	11.1566	+	34.3365i	0.391039	+	1.20349i
$815$		0			0
$816$	−2.89936	+	8.92331i	−0.101498	+	0.312378i
$817$	26.0651	+	18.9374i	0.911901	+	0.662535i
$818$	−72.8667			−2.54772
$819$	5.28380	+	3.83891i	0.184631	+	0.134142i
$820$		0			0
$821$	−27.1070	+	19.6944i	−0.946042	+	0.687340i	−0.949867	−	0.312653i	$-0.898782\pi$
$821$	−27.1070	+	19.6944i	−0.946042	+	0.687340i	0.00382568	+	0.999993i	$0.498782\pi$
$822$	−37.3993	+	27.1722i	−1.30445	+	0.947739i
$823$	17.3006	+	53.2458i	0.603061	+	1.85603i	0.509604	+	0.860409i	$0.329792\pi$
$823$	17.3006	+	53.2458i	0.603061	+	1.85603i	0.0934576	+	0.995623i	$0.470208\pi$
$824$	−10.7148			−0.373266
$825$		0			0
$826$	−58.1857			−2.02454
$827$	−12.6110	−	38.8126i	−0.438527	−	1.34965i	−0.889429	−	0.457074i	$-0.848897\pi$
$827$	−12.6110	−	38.8126i	−0.438527	−	1.34965i	0.450901	−	0.892574i	$-0.351103\pi$
$828$	15.6631	−	11.3799i	0.544329	−	0.395478i
$829$	−0.0994391	+	0.0722468i	−0.00345366	+	0.00250923i	−0.589511	−	0.807761i	$-0.700679\pi$
$829$	−0.0994391	+	0.0722468i	−0.00345366	+	0.00250923i	0.586057	+	0.810270i	$0.300679\pi$
$830$		0			0
$831$	21.1531	+	15.3686i	0.733791	+	0.533131i
$832$	22.4997			0.780036
$833$	−28.1267	−	20.4353i	−0.974534	−	0.708040i
$834$	8.46455	−	26.0512i	0.293103	−	0.902080i
$835$		0			0
$836$	−9.42094	−	28.9947i	−0.325830	−	1.00280i
$837$	−0.129195	+	0.397622i	−0.00446564	+	0.0137438i
$838$	18.8261	−	57.9408i	0.650337	−	2.00153i
$839$	4.57603	+	14.0836i	0.157982	+	0.486219i	0.998451	−	0.0556411i	$-0.0177203\pi$
$839$	4.57603	+	14.0836i	0.157982	+	0.486219i	−0.840469	+	0.541860i	$0.817720\pi$
$840$		0			0
$841$	−6.94275	+	21.3676i	−0.239405	+	0.736813i
$842$	−7.46759	−	5.42552i	−0.257350	−	0.186976i
$843$	−10.1219			−0.348616
$844$	−21.5191	−	15.6345i	−0.740717	−	0.538162i
$845$		0			0
$846$	14.2483	−	10.3520i	0.489867	−	0.355910i
$847$	6.78483	−	4.92947i	0.233130	−	0.169379i
$848$	1.58500	+	4.87812i	0.0544290	+	0.167515i
$849$	31.8638			1.09356
$850$		0			0
$851$	−28.7664			−0.986098
$852$	−0.793970	−	2.44359i	−0.0272010	−	0.0837160i
$853$	−5.87730	+	4.27011i	−0.201235	+	0.146206i	−0.683839	−	0.729633i	$-0.739691\pi$
$853$	−5.87730	+	4.27011i	−0.201235	+	0.146206i	0.482604	+	0.875839i	$0.339691\pi$
$854$	42.6269	−	30.9702i	1.45866	−	1.05978i
$855$		0			0
$856$	20.5304	+	14.9162i	0.701715	+	0.509826i
$857$	−26.8175			−0.916068			−0.458034	−	0.888935i	$-0.651446\pi$
$857$	−26.8175			−0.916068			−0.458034	+	0.888935i	$0.651446\pi$
$858$	−10.4565	−	7.59706i	−0.356978	−	0.259359i
$859$	−6.36691	+	19.5953i	−0.217236	+	0.668584i	0.781751	+	0.623591i	$0.214327\pi$
$859$	−6.36691	+	19.5953i	−0.217236	+	0.668584i	−0.998987	+	0.0449937i	$0.985673\pi$
$860$		0			0
$861$	−1.80621	−	5.55893i	−0.0615554	−	0.189448i
$862$	−25.7621	+	79.2876i	−0.877461	+	2.70055i
$863$	4.24862	−	13.0759i	0.144625	−	0.445109i	−0.852338	−	0.522991i	$-0.824816\pi$
$863$	4.24862	−	13.0759i	0.144625	−	0.445109i	0.996963	+	0.0778827i	$0.0248160\pi$
$864$	1.21324	+	3.73397i	0.0412753	+	0.127032i
$865$		0			0
$866$	7.33413	−	22.5721i	0.249224	−	0.767033i
$867$	23.4981	+	17.0723i	0.798036	+	0.579807i
$868$	5.13346			0.174241
$869$	−7.28622	−	5.29375i	−0.247168	−	0.179578i
$870$		0			0
$871$	15.2381	−	11.0711i	0.516324	−	0.375131i
$872$	38.6162	−	28.0563i	1.30771	−	0.950107i
$873$	−3.21657	−	9.89959i	−0.108864	−	0.335050i
$874$	38.0678			1.28766
$875$		0			0
$876$	12.6693			0.428055
$877$	6.81166	+	20.9641i	0.230014	+	0.707909i	0.997744	+	0.0671357i	$0.0213861\pi$
$877$	6.81166	+	20.9641i	0.230014	+	0.707909i	−0.767730	+	0.640773i	$0.778614\pi$
$878$	−13.5139	+	9.81840i	−0.456071	+	0.331355i
$879$	13.4487	−	9.77103i	0.453612	−	0.329569i
$880$		0			0
$881$	7.31294	+	5.31316i	0.246379	+	0.179005i	0.704121	−	0.710080i	$-0.251341\pi$
$881$	7.31294	+	5.31316i	0.246379	+	0.179005i	−0.457741	+	0.889085i	$0.651341\pi$
$882$	12.0446			0.405561
$883$	1.29540	+	0.941165i	0.0435937	+	0.0316727i	0.609369	−	0.792887i	$-0.291423\pi$
$883$	1.29540	+	0.941165i	0.0435937	+	0.0316727i	−0.565775	+	0.824560i	$0.691423\pi$
$884$	−13.8701	+	42.6879i	−0.466503	+	1.43575i
$885$		0			0
$886$	15.0259	+	46.2450i	0.504805	+	1.55363i
$887$	5.38470	−	16.5724i	0.180801	−	0.556447i	−0.819050	−	0.573722i	$-0.805499\pi$
$887$	5.38470	−	16.5724i	0.180801	−	0.556447i	0.999851	+	0.0172750i	$0.00549908\pi$
$888$	−5.80991	+	17.8811i	−0.194968	+	0.600049i
$889$	11.3762	+	35.0123i	0.381545	+	1.17427i
$890$		0			0
$891$	0.905762	−	2.78765i	0.0303442	−	0.0933897i
$892$	22.2396	+	16.1580i	0.744638	+	0.541011i
$893$	22.0970			0.739448
$894$	−13.9410	−	10.1287i	−0.466257	−	0.338756i
$895$		0			0
$896$	57.3129	−	41.6403i	1.91469	−	1.39110i
$897$	8.33143	−	6.05314i	0.278178	−	0.202108i
$898$	14.1614	+	43.5842i	0.472571	+	1.45442i
$899$	1.06860			0.0356397
$900$		0			0
$901$	25.1716			0.838588
$902$	3.57442	+	11.0009i	0.119015	+	0.366291i
$903$	30.7698	−	22.3556i	1.02396	−	0.743947i
$904$	−29.0976	+	21.1406i	−0.967772	+	0.703128i
$905$		0			0
$906$	−31.8291	−	23.1252i	−1.05745	−	0.768283i
$907$	−20.8690			−0.692942			−0.346471	−	0.938061i	$-0.612620\pi$
$907$	−20.8690			−0.692942			−0.346471	+	0.938061i	$0.612620\pi$
$908$	36.6085	+	26.5976i	1.21489	+	0.882673i
$909$	2.36628	−	7.28266i	0.0784845	−	0.241550i
$910$		0			0
$911$	15.1958	+	46.7680i	0.503461	+	1.54949i	0.803343	+	0.595517i	$0.203053\pi$
$911$	15.1958	+	46.7680i	0.503461	+	1.54949i	−0.299882	+	0.953976i	$0.596947\pi$
$912$	1.26025	−	3.87866i	0.0417312	−	0.128435i
$913$	9.16200	−	28.1977i	0.303218	−	0.933209i
$914$	−3.15418	−	9.70758i	−0.104331	−	0.321098i
$915$		0			0
$916$	−15.8045	+	48.6413i	−0.522196	+	1.60715i
$917$	25.4256	+	18.4728i	0.839627	+	0.610025i
$918$	−15.9519			−0.526492
$919$	9.05765	+	6.58077i	0.298784	+	0.217079i	0.727069	−	0.686564i	$-0.240882\pi$
$919$	9.05765	+	6.58077i	0.298784	+	0.217079i	−0.428285	+	0.903644i	$0.640882\pi$
$920$		0			0
$921$	−11.4592	+	8.32559i	−0.377593	+	0.274338i
$922$	−22.4224	+	16.2908i	−0.738443	+	0.536510i
$923$	−0.422325	−	1.29978i	−0.0139010	−	0.0427829i
$924$	−35.9897			−1.18397
$925$		0			0
$926$	−21.3425			−0.701357
$927$	−0.922731	−	2.83987i	−0.0303065	−	0.0932737i
$928$	8.11842	−	5.89838i	0.266500	−	0.193624i
$929$	−39.0181	+	28.3483i	−1.28014	+	0.930077i	−0.999557	−	0.0297529i	$-0.990528\pi$
$929$	−39.0181	+	28.3483i	−1.28014	+	0.930077i	−0.280584	+	0.959830i	$0.590528\pi$
$930$		0			0
$931$	12.2258	+	8.88253i	0.400683	+	0.291113i
$932$	40.1906			1.31649
$933$	12.1757	+	8.84615i	0.398614	+	0.289610i
$934$	−25.3662	+	78.0690i	−0.830006	+	2.55450i
$935$		0			0
$936$	−2.07992	−	6.40133i	−0.0679842	−	0.209234i
$937$	15.6176	−	48.0661i	0.510205	−	1.57025i	−0.281635	−	0.959522i	$-0.590877\pi$
$937$	15.6176	−	48.0661i	0.510205	−	1.57025i	0.791840	−	0.610728i	$-0.209123\pi$
$938$	25.3990	−	78.1702i	0.829308	−	2.55235i
$939$	1.10466	+	3.39980i	0.0360493	+	0.110948i
$940$		0			0
$941$	−11.7934	+	36.2965i	−0.384455	+	1.18323i	0.552420	+	0.833566i	$0.313705\pi$
$941$	−11.7934	+	36.2965i	−0.384455	+	1.18323i	−0.936875	+	0.349665i	$0.886295\pi$
$942$	14.9987	+	10.8972i	0.488686	+	0.355051i
$943$	−9.21634			−0.300125
$944$	7.95180	+	5.77732i	0.258809	+	0.188036i
$945$		0			0
$946$	−60.8924	+	44.2409i	−1.97978	+	1.43840i
$947$	−19.8363	+	14.4119i	−0.644592	+	0.468323i	−0.861425	−	0.507885i	$-0.830427\pi$
$947$	−19.8363	+	14.4119i	−0.644592	+	0.468323i	0.216833	+	0.976209i	$0.430427\pi$
$948$	−3.34832	−	10.3051i	−0.108748	−	0.334693i
$949$	6.73897			0.218756
$950$		0			0
$951$	−12.7820			−0.414484
$952$	26.1986	+	80.6311i	0.849103	+	2.61327i
$953$	−10.5187	+	7.64232i	−0.340736	+	0.247559i	−0.744972	−	0.667096i	$-0.767537\pi$
$953$	−10.5187	+	7.64232i	−0.340736	+	0.247559i	0.404236	+	0.914655i	$0.367537\pi$
$954$	−7.05501	+	5.12576i	−0.228414	+	0.165953i
$955$		0			0
$956$	−19.6872	−	14.3036i	−0.636729	−	0.462611i
$957$	−7.49172			−0.242173
$958$	16.4444	+	11.9476i	0.531295	+	0.386008i
$959$	−21.1583	+	65.1187i	−0.683239	+	2.10279i
$960$		0			0
$961$	−9.52551	−	29.3165i	−0.307275	−	0.945694i
$962$	−7.13962	+	21.9735i	−0.230190	+	0.708453i
$963$	−2.18541	+	6.72600i	−0.0704238	+	0.216742i
$964$	−30.9989	−	95.4048i	−0.998408	−	3.07278i
$965$		0			0
$966$	13.8869	−	42.7395i	0.446804	−	1.37512i
$967$	35.0476	+	25.4636i	1.12706	+	0.818854i	0.985264	−	0.171043i	$-0.0547136\pi$
$967$	35.0476	+	25.4636i	1.12706	+	0.818854i	0.141792	+	0.989896i	$0.454714\pi$
$968$	−8.64284			−0.277791
$969$	−16.1919	−	11.7641i	−0.520159	−	0.377918i
$970$		0			0
$971$	23.8922	−	17.3587i	0.766738	−	0.557068i	−0.134231	−	0.990950i	$-0.542857\pi$
$971$	23.8922	−	17.3587i	0.766738	−	0.557068i	0.900970	+	0.433882i	$0.142857\pi$
$972$	2.85292	−	2.07277i	0.0915074	−	0.0664840i
$973$	−12.5371	−	38.5853i	−0.401921	−	1.23699i
$974$	6.68721			0.214272
$975$		0			0
$976$	−8.90056			−0.284900
$977$	−18.7312	−	57.6486i	−0.599263	−	1.84434i	−0.532244	−	0.846591i	$-0.678651\pi$
$977$	−18.7312	−	57.6486i	−0.599263	−	1.84434i	−0.0670189	−	0.997752i	$-0.521349\pi$
$978$	−18.9044	+	13.7348i	−0.604495	+	0.439191i
$979$	−0.681782	+	0.495343i	−0.0217898	+	0.0158312i
$980$		0			0
$981$	10.7617	+	7.81882i	0.343594	+	0.249636i
$982$	86.5202			2.76097
$983$	32.5868	+	23.6757i	1.03936	+	0.755138i	0.970160	−	0.242465i	$-0.0779558\pi$
$983$	32.5868	+	23.6757i	1.03936	+	0.755138i	0.0691986	+	0.997603i	$0.477956\pi$
$984$	−1.86141	+	5.72884i	−0.0593397	+	0.182629i
$985$		0			0
$986$	12.5993	+	38.7766i	0.401243	+	1.23490i
$987$	8.06087	−	24.8088i	0.256580	−	0.789673i
$988$	6.02888	−	18.5550i	0.191804	−	0.590313i
$989$	−18.5320	−	57.0357i	−0.589284	−	1.81363i
$990$		0			0
$991$	11.7889	−	36.2824i	0.374485	−	1.15255i	−0.569340	−	0.822102i	$-0.692801\pi$
$991$	11.7889	−	36.2824i	0.374485	−	1.15255i	0.943825	−	0.330445i	$-0.107199\pi$
$992$	1.32796	+	0.964821i	0.0421628	+	0.0306331i
$993$	−4.70504			−0.149310
$994$	−4.82485	−	3.50546i	−0.153035	−	0.111186i
$995$		0			0
$996$	28.8580	−	20.9665i	0.914399	−	0.664350i
$997$	−21.5018	+	15.6220i	−0.680969	+	0.494753i	−0.873679	−	0.486503i	$-0.838272\pi$
$997$	−21.5018	+	15.6220i	−0.680969	+	0.494753i	0.192710	+	0.981256i	$0.438272\pi$
$998$	4.25534	+	13.0966i	0.134700	+	0.414565i
$999$	−5.23959			−0.165773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.d.151.4		16
5.2	odd	4		75.2.i.a.19.1	yes	16
5.3	odd	4		375.2.i.c.349.4		16
5.4	even	2		375.2.g.e.151.1		16
15.2	even	4		225.2.m.b.19.4		16
25.2	odd	20		1875.2.b.h.1249.15		16
25.3	odd	20		75.2.i.a.4.1	✓	16
25.4	even	10		375.2.g.e.226.1		16
25.11	even	5		1875.2.a.p.1.7		8
25.14	even	10		1875.2.a.m.1.2		8
25.21	even	5	inner	375.2.g.d.226.4		16
25.22	odd	20		375.2.i.c.274.4		16
25.23	odd	20		1875.2.b.h.1249.2		16
75.11	odd	10		5625.2.a.t.1.2		8
75.14	odd	10		5625.2.a.bd.1.7		8
75.53	even	20		225.2.m.b.154.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.1	✓	16	25.3	odd	20
75.2.i.a.19.1	yes	16	5.2	odd	4
225.2.m.b.19.4		16	15.2	even	4
225.2.m.b.154.4		16	75.53	even	20
375.2.g.d.151.4		16	1.1	even	1	trivial
375.2.g.d.226.4		16	25.21	even	5	inner
375.2.g.e.151.1		16	5.4	even	2
375.2.g.e.226.1		16	25.4	even	10
375.2.i.c.274.4		16	25.22	odd	20
375.2.i.c.349.4		16	5.3	odd	4
1875.2.a.m.1.2		8	25.14	even	10
1875.2.a.p.1.7		8	25.11	even	5
1875.2.b.h.1249.2		16	25.23	odd	20
1875.2.b.h.1249.15		16	25.2	odd	20
5625.2.a.t.1.2		8	75.11	odd	10
5625.2.a.bd.1.7		8	75.14	odd	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.726446 + 2.23577i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-2.85292 + 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} +3.48189 q^{7} +(-2.90300 - 2.10915i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.726446 + 2.23577i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-2.85292 + 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} +3.48189 q^{7} +(-2.90300 - 2.10915i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.905762 + 2.78765i) q^{11} +(-1.08972 + 3.35381i) q^{12} +(-0.579638 + 1.78394i) q^{13} +(2.52940 + 7.78470i) q^{14} +(0.427277 - 1.31502i) q^{16} +(-5.48972 - 3.98851i) q^{17} +2.35083 q^{18} +(2.38620 + 1.73367i) q^{19} +(2.81691 - 2.04660i) q^{21} +(-5.57456 + 4.05015i) q^{22} +(-1.69656 - 5.22149i) q^{23} -3.58831 q^{24} -4.40956 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-9.93354 + 7.21714i) q^{28} +(-2.06779 + 1.50234i) q^{29} +(-0.338237 - 0.245744i) q^{31} -3.92613 q^{32} +(2.37132 + 1.72286i) q^{33} +(4.92942 - 15.1712i) q^{34} +(1.08972 + 3.35381i) q^{36} +(1.61912 - 4.98314i) q^{37} +(-2.14265 + 6.59441i) q^{38} +(0.579638 + 1.78394i) q^{39} +(0.518744 - 1.59653i) q^{41} +(6.62206 + 4.81121i) q^{42} +10.9233 q^{43} +(-8.36221 - 6.07550i) q^{44} +(10.4416 - 7.58626i) q^{46} +(6.06098 - 4.40356i) q^{47} +(-0.427277 - 1.31502i) q^{48} +5.12353 q^{49} -6.78566 q^{51} +(-2.04403 - 6.29089i) q^{52} +(-3.00107 + 2.18041i) q^{53} +(1.90186 - 1.38178i) q^{54} +(-10.1079 - 7.34383i) q^{56} +2.94950 q^{57} +(-4.86103 - 3.53175i) q^{58} +(-2.19666 + 6.76062i) q^{59} +(-1.98917 - 6.12204i) q^{61} +(0.303716 - 0.934741i) q^{62} +(1.07596 - 3.31147i) q^{63} +(-3.70667 - 11.4080i) q^{64} +(-2.12929 + 6.55329i) q^{66} +(-8.12376 - 5.90225i) q^{67} +23.9290 q^{68} +(-4.44166 - 3.22706i) q^{69} +(-0.589451 + 0.428261i) q^{71} +(-2.90300 + 2.10915i) q^{72} +(-1.11020 - 3.41685i) q^{73} +12.3174 q^{74} -10.4011 q^{76} +(3.15376 + 9.70628i) q^{77} +(-3.56741 + 2.59188i) q^{78} +(-2.48583 + 1.80606i) q^{79} +(-0.809017 - 0.587785i) q^{81} +3.94632 q^{82} +(-8.18340 - 5.94559i) q^{83} +(-3.79427 + 11.6776i) q^{84} +(7.93517 + 24.4219i) q^{86} +(-0.789827 + 2.43084i) q^{87} +(3.25015 - 10.0029i) q^{88} +(0.0888461 + 0.273440i) q^{89} +(-2.01823 + 6.21148i) q^{91} +(15.6631 + 11.3799i) q^{92} -0.418084 q^{93} +(14.2483 + 10.3520i) q^{94} +(-3.17630 + 2.30772i) q^{96} +(8.42109 - 6.11828i) q^{97} +(3.72197 + 11.4551i) q^{98} +2.93111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9	\( 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 8 q^{13} + 12 q^{14} - 10 q^{16} - 8 q^{17} + 8 q^{18} + 2 q^{19} + 4 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 12 q^{26} + 4 q^{27} - 28 q^{28} - 16 q^{29} + 6 q^{31} - 4 q^{32} - 4 q^{33} + 36 q^{34} - 2 q^{36} - 24 q^{37} + 38 q^{38} + 8 q^{39} - 14 q^{41} + 18 q^{42} + 40 q^{43} - 26 q^{44} + 16 q^{46} + 10 q^{47} + 10 q^{48} - 32 q^{51} - 48 q^{52} - 12 q^{53} + 2 q^{54} + 28 q^{57} - 44 q^{58} - 12 q^{59} - 28 q^{62} - 4 q^{63} - 8 q^{64} + 16 q^{66} + 12 q^{67} - 4 q^{68} + 12 q^{69} - 8 q^{71} - 6 q^{72} + 8 q^{73} + 52 q^{74} - 32 q^{76} - 18 q^{77} - 32 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{82} - 6 q^{83} - 12 q^{84} - 36 q^{86} - 14 q^{87} - 16 q^{88} - 18 q^{89} + 26 q^{91} + 36 q^{92} + 44 q^{93} + 38 q^{94} - 26 q^{96} - 8 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 - 8 * q^13 + 12 * q^14 - 10 * q^16 - 8 * q^17 + 8 * q^18 + 2 * q^19 + 4 * q^21 + 4 * q^22 - 2 * q^23 - 24 * q^24 + 12 * q^26 + 4 * q^27 - 28 * q^28 - 16 * q^29 + 6 * q^31 - 4 * q^32 - 4 * q^33 + 36 * q^34 - 2 * q^36 - 24 * q^37 + 38 * q^38 + 8 * q^39 - 14 * q^41 + 18 * q^42 + 40 * q^43 - 26 * q^44 + 16 * q^46 + 10 * q^47 + 10 * q^48 - 32 * q^51 - 48 * q^52 - 12 * q^53 + 2 * q^54 + 28 * q^57 - 44 * q^58 - 12 * q^59 - 28 * q^62 - 4 * q^63 - 8 * q^64 + 16 * q^66 + 12 * q^67 - 4 * q^68 + 12 * q^69 - 8 * q^71 - 6 * q^72 + 8 * q^73 + 52 * q^74 - 32 * q^76 - 18 * q^77 - 32 * q^78 + 20 * q^79 - 4 * q^81 + 32 * q^82 - 6 * q^83 - 12 * q^84 - 36 * q^86 - 14 * q^87 - 16 * q^88 - 18 * q^89 + 26 * q^91 + 36 * q^92 + 44 * q^93 + 38 * q^94 - 26 * q^96 - 8 * q^97 + 18 * q^98 + 4 * q^99

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