LMFDB - Embedded newform 375.2.g.e.226.1

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			226.1
Root			$-2.35083i$ of defining polynomial
Character	$\chi$	$=$	375.226
Dual form			375.2.g.e.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.726446 + 2.23577i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-2.85292 - 2.07277i) q^{4} +(1.90186 - 1.38178i) q^{6} -3.48189 q^{7} +(2.90300 - 2.10915i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	0.272005	+	0.962296i	$0.412313\pi$
$2$	−0.726446	+	2.23577i	−0.513675	+	1.58093i	−0.785680	+	0.618634i	$0.787687\pi$
$3$	−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	$-0.728604\pi$
$7$	−3.48189			−1.31603			−0.658015	+	0.753005i	$0.728604\pi$
$8$	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	−0.716619	−	0.697465i	$-0.754311\pi$
$11$	0.905762	−	2.78765i	0.273097	−	0.840508i	0.989717	−	0.143043i	$-0.0456887\pi$
$12$	1.08972	+	3.35381i	0.314574	+	0.968160i
$13$	0.579638	+	1.78394i	0.160763	+	0.494776i	0.998699	−	0.0509914i	$-0.0162381\pi$
$13$	0.579638	+	1.78394i	0.160763	+	0.494776i	−0.837937	+	0.545768i	$0.816238\pi$
$14$	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	0.331739	−	0.943371i	$-0.392365\pi$
$17$	5.48972	−	3.98851i	1.33145	−	0.967356i	0.999712	−	0.0239850i	$-0.00763540\pi$
$18$	−2.35083			−0.554096
$19$	2.38620	−	1.73367i	0.547431	−	0.397732i	−0.279406	−	0.960173i	$-0.590138\pi$
$19$	2.38620	−	1.73367i	0.547431	−	0.397732i	0.826837	+	0.562441i	$0.190138\pi$
$20$		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	−0.602968	−	0.797765i	$-0.706015\pi$
$23$	1.69656	−	5.22149i	0.353758	−	1.08876i	0.956726	−	0.290990i	$-0.0939846\pi$
$24$	−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	0.379004	−	0.925395i	$-0.376267\pi$
$29$	−2.06779	−	1.50234i	−0.383980	−	0.278978i	−0.762984	+	0.646417i	$0.776267\pi$
$30$		0			0
$31$	−0.338237	+	0.245744i	−0.0607492	+	0.0441369i	−0.617745	−	0.786378i	$-0.711954\pi$
$31$	−0.338237	+	0.245744i	−0.0607492	+	0.0441369i	0.556996	+	0.830515i	$0.311954\pi$
$32$	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	−0.991419	−	0.130724i	$-0.958270\pi$
$37$	−1.61912	−	4.98314i	−0.266182	−	0.819224i	0.725237	−	0.688500i	$-0.241730\pi$
$38$	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	0.983357	−	0.181683i	$-0.0581543\pi$
$41$	0.518744	+	1.59653i	0.0810142	+	0.249336i	−0.902343	+	0.431019i	$0.858154\pi$
$42$	−6.62206	+	4.81121i	−1.02181	+	0.742386i
$43$	−10.9233			−1.66578			−0.832892	−	0.553436i	$-0.813316\pi$
$43$	−10.9233			−1.66578			−0.832892	+	0.553436i	$0.813316\pi$
$44$	−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	$-0.484000\pi$
$47$	−6.06098	−	4.40356i	−0.884084	−	0.642325i	−0.934329	+	0.356412i	$0.884000\pi$
$48$	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	$-0.218000\pi$
$53$	3.00107	+	2.18041i	0.412229	+	0.299502i	−0.362275	+	0.932071i	$0.618000\pi$
$54$	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	−0.986103	−	0.166135i	$-0.946871\pi$
$59$	−2.19666	−	6.76062i	−0.285981	−	0.880158i	0.700122	−	0.714023i	$-0.253129\pi$
$60$		0			0
$61$	−1.98917	+	6.12204i	−0.254687	+	0.783847i	0.739204	+	0.673482i	$0.235202\pi$
$61$	−1.98917	+	6.12204i	−0.254687	+	0.783847i	−0.993891	+	0.110365i	$0.964798\pi$
$62$	−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	$-0.489808\pi$
$67$	8.12376	−	5.90225i	0.992475	−	0.721075i	0.960462	+	0.278412i	$0.0898082\pi$
$68$	−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	0.552258	−	0.833673i	$-0.313766\pi$
$71$	−0.589451	−	0.428261i	−0.0699550	−	0.0508253i	−0.622213	+	0.782848i	$0.713766\pi$
$72$	2.90300	+	2.10915i	0.342122	+	0.248566i
$73$	1.11020	−	3.41685i	0.129939	−	0.399912i	−0.864829	−	0.502066i	$-0.832573\pi$
$73$	1.11020	−	3.41685i	0.129939	−	0.399912i	0.994769	+	0.102154i	$0.0325734\pi$
$74$	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	0.439099	−	0.898439i	$-0.355298\pi$
$79$	−2.48583	−	1.80606i	−0.279677	−	0.203197i	−0.718777	+	0.695241i	$0.755298\pi$
$80$		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	$-0.512662\pi$
$83$	8.18340	−	5.94559i	0.898245	−	0.652613i	0.938015	+	0.346595i	$0.112662\pi$
$84$	−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	−0.946237	−	0.323473i	$-0.895149\pi$
$89$	0.0888461	−	0.273440i	0.00941767	−	0.0289846i	0.955655	+	0.294489i	$0.0951494\pi$
$90$		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	$-0.477222\pi$
$97$	−8.42109	−	6.11828i	−0.855032	−	0.621217i	−0.926529	+	0.376224i	$0.877222\pi$
$98$	−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	$-0.346997\pi$
$103$	−2.41574	−	1.75514i	−0.238030	−	0.172939i	−0.700405	+	0.713745i	$0.746997\pi$
$104$	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	$-0.388948\pi$
$107$	7.07213			0.683689			0.341844	+	0.939757i	$0.388948\pi$
$108$	−2.85292	+	2.07277i	−0.274522	+	0.199452i
$109$	−4.11060	−	12.6511i	−0.393724	−	1.21176i	−0.929951	−	0.367683i	$-0.880151\pi$
$109$	−4.11060	−	12.6511i	−0.393724	−	1.21176i	0.536227	−	0.844074i	$-0.319849\pi$
$110$		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	−0.984415	−	0.175862i	$-0.943729\pi$
$113$	−3.09737	−	9.53271i	−0.291376	−	0.896762i	0.693039	−	0.720900i	$-0.256271\pi$
$114$	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	0.694959	+	0.719049i	$0.255423\pi$
$127$	−3.26725	+	10.0556i	−0.289921	+	0.892286i	−0.984880	+	0.173237i	$0.944577\pi$
$128$	−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	−0.221162	−	0.975237i	$-0.570985\pi$
$131$	7.30225	−	5.30540i	0.638001	−	0.463535i	0.859163	+	0.511703i	$0.170985\pi$
$132$	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	0.775571	+	0.631261i	$0.217462\pi$
$137$	6.07669	+	18.7021i	0.519167	+	1.59783i	−0.256404	+	0.966570i	$0.582538\pi$
$138$	−3.98833	−	12.2748i	−0.339509	−	1.04490i
$139$	−3.60067	+	11.0817i	−0.305404	+	0.939938i	0.674122	+	0.738620i	$0.264522\pi$
$139$	−3.60067	+	11.0817i	−0.305404	+	0.939938i	−0.979526	+	0.201318i	$0.935478\pi$
$140$		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	$-0.601904\pi$
$157$	−7.88635			−0.629399			−0.314700	+	0.949191i	$0.601904\pi$
$158$	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	0.996331	+	0.0855829i	$0.0272752\pi$
$163$	3.07160	+	9.45343i	0.240587	+	0.740450i	−0.755744	+	0.654867i	$0.772725\pi$
$164$	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	$-0.630762\pi$
$167$	4.51243	−	3.27847i	0.349182	−	0.253696i	0.748526	+	0.663106i	$0.230762\pi$
$168$	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	0.544091	+	0.839026i	$0.316875\pi$
$173$	−5.11985	+	15.7573i	−0.389255	+	1.19800i	−0.933346	+	0.358978i	$0.883125\pi$
$174$	−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	0.737934	−	0.674873i	$-0.235802\pi$
$179$	4.33650	+	3.15065i	0.324125	+	0.235491i	−0.413808	+	0.910364i	$0.635802\pi$
$180$		0			0
$181$	0.265151	−	0.192643i	0.0197085	−	0.0143191i	−0.577887	−	0.816117i	$-0.696123\pi$
$181$	0.265151	−	0.192643i	0.0197085	−	0.0143191i	0.597596	+	0.801797i	$0.296123\pi$
$182$	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	0.904740	−	0.425965i	$-0.140065\pi$
$191$	−1.07226	−	3.30009i	−0.0775862	−	0.238786i	−0.982326	+	0.187179i	$0.940065\pi$
$192$	9.70420	−	7.05051i	0.700340	−	0.508827i
$193$	24.3134			1.75012			0.875058	−	0.484018i	$-0.160823\pi$
$193$	24.3134			1.75012			0.875058	+	0.484018i	$0.160823\pi$
$194$	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	$-0.121144\pi$
$197$	12.0997	+	8.79098i	0.862071	+	0.626331i	−0.0663764	+	0.997795i	$0.521144\pi$
$198$	−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	−0.838210	−	0.545347i	$-0.816398\pi$
$211$	2.33086	−	7.17366i	0.160463	−	0.493855i	0.998673	+	0.0514924i	$0.0163978\pi$
$212$	−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	$-0.815945\pi$
$223$	2.40891	−	7.41386i	0.161313	−	0.496469i	0.998746	+	0.0500709i	$0.0159447\pi$
$224$	−13.6703			−0.913387
$225$		0			0
$226$	23.5630			1.56739
$227$	3.96529	−	12.2039i	0.263185	−	0.810001i	−0.728921	−	0.684598i	$-0.759978\pi$
$227$	3.96529	−	12.2039i	0.263185	−	0.810001i	0.992106	−	0.125403i	$-0.0400224\pi$
$228$	8.41468	+	6.11363i	0.557276	+	0.404885i
$229$	11.7334	+	8.52483i	0.775366	+	0.563337i	0.903585	−	0.428409i	$-0.140926\pi$
$229$	11.7334	+	8.52483i	0.775366	+	0.563337i	−0.128218	+	0.991746i	$0.540926\pi$
$230$		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	$-0.578218\pi$
$233$	9.22041	−	6.69902i	0.604049	−	0.438867i	0.847314	+	0.531093i	$0.178218\pi$
$234$	−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	−0.858099	−	0.513484i	$-0.828354\pi$
$239$	2.13244	−	6.56298i	0.137936	−	0.424524i	0.996035	+	0.0889605i	$0.0283545\pi$
$240$		0			0
$241$	−8.79052	−	27.0545i	−0.566247	−	1.74273i	−0.664216	−	0.747541i	$-0.731234\pi$
$241$	−8.79052	−	27.0545i	−0.566247	−	1.74273i	0.0979683	−	0.995190i	$-0.468766\pi$
$242$	−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	$-0.725059\pi$
$257$	−20.8274			−1.29918			−0.649590	+	0.760285i	$0.725059\pi$
$258$	−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	$-0.121953\pi$
$263$	−0.690704	−	2.12577i	−0.0425906	−	0.131080i	−0.970091	+	0.242742i	$0.921953\pi$
$264$	−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	0.000861106	−	1.00000i	$-0.499726\pi$
$269$	15.6170	−	11.3464i	0.952183	−	0.691802i	0.951322	+	0.308198i	$0.0997259\pi$
$270$		0			0
$271$	9.66058	+	7.01882i	0.586838	+	0.426363i	0.841183	−	0.540751i	$-0.181860\pi$
$271$	9.66058	+	7.01882i	0.586838	+	0.426363i	−0.254345	+	0.967114i	$0.581860\pi$
$272$	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	0.345841	+	0.938293i	$0.387594\pi$
$277$	−8.07975	+	24.8669i	−0.485465	+	1.49411i	−0.831306	+	0.555815i	$0.812406\pi$
$278$	−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	−0.804607	−	0.593807i	$-0.797624\pi$
$281$	−8.18876	+	5.94948i	−0.488500	+	0.354916i	0.316107	+	0.948724i	$0.397624\pi$
$282$	−17.6119			−1.04877
$283$	−25.7783	+	18.7290i	−1.53236	+	1.11333i	−0.577455	+	0.816423i	$0.695954\pi$
$283$	−25.7783	+	18.7290i	−1.53236	+	1.11333i	−0.954907	+	0.296903i	$0.904046\pi$
$284$	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	$-0.661390\pi$
$293$	−16.6235			−0.971153			−0.485576	+	0.874194i	$0.661390\pi$
$294$	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	$-0.367550\pi$
$307$	14.1643			0.808402			0.404201	+	0.914670i	$0.367550\pi$
$308$	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	−0.728269	−	0.685291i	$-0.759675\pi$
$311$	4.65070	−	14.3134i	0.263717	−	0.811637i	0.991986	−	0.126346i	$-0.0403250\pi$
$312$	−2.07992	−	6.40133i	−0.117752	−	0.362404i
$313$	1.10466	+	3.39980i	0.0624392	+	0.192168i	0.977410	−	0.211352i	$-0.0677866\pi$
$313$	1.10466	+	3.39980i	0.0624392	+	0.192168i	−0.914971	+	0.403520i	$0.867787\pi$
$314$	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	$-0.583134\pi$
$317$	10.3408	−	7.51306i	0.580799	−	0.421975i	0.839012	+	0.544113i	$0.183134\pi$
$318$	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	−0.687462	−	0.726221i	$-0.741275\pi$
$331$	−3.80646	+	2.76555i	−0.209222	+	0.152009i	0.478240	+	0.878229i	$0.341275\pi$
$332$	−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	0.983893	+	0.178758i	$0.0572080\pi$
$337$	5.37837	+	16.5529i	0.292978	+	0.901694i	−0.690915	+	0.722936i	$0.742792\pi$
$338$	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	$-0.177277\pi$
$347$	11.3348	+	8.23525i	0.608486	+	0.442091i	−0.240395	+	0.970675i	$0.577277\pi$
$348$	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	$-0.224740\pi$
$353$	7.12095	+	5.17367i	0.379010	+	0.275367i	−0.381927	+	0.924192i	$0.624740\pi$
$354$	−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	0.988109	−	0.153752i	$-0.0491357\pi$
$359$	1.86326	+	5.73451i	0.0983389	+	0.302656i	−0.889771	+	0.456408i	$0.849136\pi$
$360$		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	$-0.429672\pi$
$367$	23.2724	−	16.9084i	1.21481	−	0.882609i	0.995658	+	0.0930825i	$0.0296720\pi$
$368$	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	0.200330	+	0.979729i	$0.435799\pi$
$373$	−10.3830	+	31.9555i	−0.537610	+	1.65459i	−0.737940	+	0.674866i	$0.764201\pi$
$374$	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	0.487321	−	0.873223i	$-0.337974\pi$
$379$	−3.74901	−	2.72381i	−0.192574	−	0.139913i	−0.679894	+	0.733310i	$0.737974\pi$
$380$		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	$-0.806957\pi$
$383$	−10.4410	+	7.58581i	−0.533509	+	0.387617i	0.288160	+	0.957582i	$0.406957\pi$
$384$	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	0.714761	+	0.699369i	$0.246535\pi$
$389$	−5.41540	+	16.6669i	−0.274571	+	0.845044i	−0.989332	+	0.145675i	$0.953465\pi$
$390$		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	$-0.537147\pi$
$397$	−21.8577	−	15.8805i	−1.09701	−	0.797021i	−0.980569	+	0.196177i	$0.937147\pi$
$398$	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	−0.847812	−	0.530297i	$-0.822080\pi$
$409$	−9.57834	−	29.4791i	−0.473618	−	1.45765i	0.374193	−	0.927351i	$-0.377920\pi$
$410$		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	−0.967151	−	0.254204i	$-0.918186\pi$
$419$	−20.9660	+	15.2327i	−1.02425	+	0.744164i	−0.0571034	+	0.998368i	$0.518186\pi$
$420$		0			0
$421$	−3.17658	−	2.30792i	−0.154817	−	0.112481i	0.507680	−	0.861546i	$-0.330503\pi$
$421$	−3.17658	−	2.30792i	−0.154817	−	0.112481i	−0.662497	+	0.749065i	$0.730503\pi$
$422$	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	0.385270	−	0.922804i	$-0.374108\pi$
$431$	28.6903	−	20.8447i	1.38196	−	1.00406i	0.996694	−	0.0812518i	$-0.0258918\pi$
$432$	1.38270			0.0665251
$433$	8.16776	−	5.93423i	0.392518	−	0.285181i	−0.373969	−	0.927441i	$-0.622003\pi$
$433$	8.16776	−	5.93423i	0.392518	−	0.285181i	0.766486	+	0.642261i	$0.222003\pi$
$434$	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	−0.884885	−	0.465809i	$-0.845763\pi$
$439$	2.19575	−	6.75783i	0.104798	−	0.322534i	0.989683	+	0.143275i	$0.0457634\pi$
$440$		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	$-0.663502\pi$
$443$	−20.6841			−0.982733			−0.491366	+	0.870953i	$0.663502\pi$
$444$	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	$-0.467619\pi$
$457$	4.34194			0.203107			0.101554	+	0.994830i	$0.467619\pi$
$458$	−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	−0.829669	−	0.558256i	$-0.811471\pi$
$461$	3.64322	−	11.2127i	0.169682	−	0.522227i	0.999351	+	0.0360287i	$0.0114708\pi$
$462$	7.41395	+	22.8178i	0.344928	+	1.06158i
$463$	2.80547	+	8.63436i	0.130381	+	0.401273i	0.994843	−	0.101426i	$-0.0323405\pi$
$463$	2.80547	+	8.63436i	0.130381	+	0.401273i	−0.864462	+	0.502699i	$0.832341\pi$
$464$	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	$-0.999401\pi$
$467$	−28.2494	+	20.5244i	−1.30723	+	0.949755i	−0.307227	+	0.951636i	$0.599401\pi$
$468$	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	0.736012	−	0.676969i	$-0.236707\pi$
$479$	6.99515	+	5.08228i	0.319617	+	0.232215i	−0.416395	+	0.909184i	$0.636707\pi$
$480$		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	$-0.120530\pi$
$487$	−0.879035	−	2.70539i	−0.0398329	−	0.122593i	−0.968996	+	0.247078i	$0.920530\pi$
$488$	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	0.786425	+	0.617686i	$0.211930\pi$
$491$	11.3731	+	35.0028i	0.513260	+	1.57965i	−0.273165	+	0.961967i	$0.588070\pi$
$492$	−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	$-0.535953\pi$
$503$	−24.5030	−	17.8025i	−1.09253	−	0.793773i	−0.979825	+	0.199855i	$0.935953\pi$
$504$	−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	0.999606	+	0.0280797i	$0.00893923\pi$
$509$	4.67944	+	14.4018i	0.207413	+	0.638350i	−0.792193	+	0.610270i	$0.791061\pi$
$510$		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	−0.996367	−	0.0851601i	$-0.972860\pi$
$521$	−31.6190	−	22.9726i	−1.38525	−	1.00645i	−0.388887	−	0.921286i	$-0.627140\pi$
$522$	4.86103	+	3.53175i	0.212762	+	0.154580i
$523$	11.9891	−	36.8987i	0.524248	−	1.61347i	−0.241550	−	0.970388i	$-0.577656\pi$
$523$	11.9891	−	36.8987i	0.524248	−	1.61347i	0.765798	−	0.643081i	$-0.222344\pi$
$524$	−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	0.999994	−	0.00332312i	$-0.00105778\pi$
$541$	4.39669	+	13.5316i	0.189029	+	0.581770i	−0.810966	+	0.585094i	$0.801058\pi$
$542$	−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	0.998431	+	0.0559991i	$0.0178344\pi$
$547$	31.8129	+	23.1134i	1.36022	+	0.988259i	0.361790	+	0.932259i	$0.382166\pi$
$548$	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	$-0.769780\pi$
$557$	−35.3849			−1.49931			−0.749654	+	0.661830i	$0.769780\pi$
$558$	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	−0.999966	−	0.00830000i	$-0.997358\pi$
$563$	−4.64717	−	14.3025i	−0.195855	−	0.602780i	0.804111	−	0.594480i	$-0.202642\pi$
$564$	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	−0.540632	−	0.841260i	$-0.681815\pi$
$569$	2.20383	−	1.60118i	0.0923895	−	0.0671249i	0.633021	+	0.774135i	$0.281815\pi$
$570$		0			0
$571$	−10.2127	−	7.41997i	−0.427389	−	0.310516i	0.353215	−	0.935542i	$-0.385088\pi$
$571$	−10.2127	−	7.41997i	−0.427389	−	0.310516i	−0.780604	+	0.625026i	$0.785088\pi$
$572$	−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	−0.676866	−	0.736106i	$-0.736662\pi$
$577$	7.28797	−	22.4301i	0.303402	−	0.933776i	0.980269	−	0.197670i	$-0.0633376\pi$
$578$	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	0.985097	+	0.172000i	$0.0550231\pi$
$587$	7.00764	+	21.5673i	0.289236	+	0.890177i	−0.695861	+	0.718177i	$0.744977\pi$
$588$	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	$-0.442548\pi$
$593$	8.74287			0.359027			0.179513	+	0.983756i	$0.442548\pi$
$594$	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	$-0.390063\pi$
$607$	16.6820			0.677102			0.338551	+	0.940948i	$0.390063\pi$
$608$	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	−0.977964	−	0.208776i	$-0.933052\pi$
$613$	−7.66260	−	23.5831i	−0.309490	−	0.952511i	0.668474	−	0.743736i	$-0.266948\pi$
$614$	−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	$-0.509665\pi$
$617$	22.6257	−	16.4386i	0.910877	−	0.661791i	0.941237	+	0.337748i	$0.109665\pi$
$618$	−7.01963			−0.282371
$619$	−22.0608	+	16.0281i	−0.886697	+	0.644223i	−0.935015	−	0.354609i	$-0.884614\pi$
$619$	−22.0608	+	16.0281i	−0.886697	+	0.644223i	0.0483179	+	0.998832i	$0.484614\pi$
$620$		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	−0.362676	+	0.931915i	$0.618137\pi$
$631$	−34.1893	+	24.8400i	−1.36105	+	0.988863i	−0.998377	+	0.0569481i	$0.981863\pi$
$632$	−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	0.683571	+	0.729884i	$0.260426\pi$
$641$	14.1671	+	43.6017i	0.559565	+	1.72217i	−0.124006	+	0.992281i	$0.539574\pi$
$642$	13.4502	−	9.77215i	0.530837	−	0.385676i
$643$	46.6710			1.84052			0.920261	−	0.391304i	$-0.127976\pi$
$643$	46.6710			1.84052			0.920261	+	0.391304i	$0.127976\pi$
$644$	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	$-0.376613\pi$
$647$	−9.81050	−	7.12775i	−0.385691	−	0.280221i	−0.763687	+	0.645586i	$0.776613\pi$
$648$	−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	$-0.310716\pi$
$653$	−1.39164	−	1.01109i	−0.0544593	−	0.0395670i	−0.614682	+	0.788775i	$0.710716\pi$
$654$	−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	0.978604	−	0.205751i	$-0.0659636\pi$
$659$	1.69325	+	5.21129i	0.0659596	+	0.203003i	−0.912645	+	0.408754i	$0.865964\pi$
$660$		0			0
$661$	0.246425	−	0.758418i	0.00958482	−	0.0294990i	−0.946150	−	0.323729i	$-0.895063\pi$
$661$	0.246425	−	0.758418i	0.00958482	−	0.0294990i	0.955735	+	0.294230i	$0.0950633\pi$
$662$	−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	0.166777	−	0.985995i	$-0.446664\pi$
$673$	15.8612	−	48.8158i	0.611405	−	1.88171i	0.444627	−	0.895716i	$-0.353336\pi$
$674$	−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	$-0.993667\pi$
$677$	−4.66397	+	14.3542i	−0.179251	+	0.551678i	0.820551	+	0.571573i	$0.193667\pi$
$678$	−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	$-0.766623\pi$
$683$	−8.78610	+	6.38347i	−0.336191	+	0.244257i	0.406862	+	0.913490i	$0.366623\pi$
$684$	−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	0.988346	−	0.152225i	$-0.0486438\pi$
$691$	2.60981	+	8.03217i	0.0992818	+	0.305558i	−0.889064	+	0.457783i	$0.848644\pi$
$692$	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	0.985601	+	0.169089i	$0.0540826\pi$
$709$	7.65850	+	23.5705i	0.287621	+	0.885207i	−0.697980	+	0.716118i	$0.745917\pi$
$710$		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	−0.278018	−	0.960576i	$-0.589678\pi$
$719$	14.7379	−	10.7077i	0.549631	−	0.399331i	0.827650	+	0.561245i	$0.189678\pi$
$720$		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	0.808949	+	0.587878i	$0.200037\pi$
$727$	−5.15129	+	15.8540i	−0.191051	+	0.587994i	−1.00000		0.000115145i	$0.999963\pi$
$728$	−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	$-0.579170\pi$
$733$	16.2324	−	11.7935i	0.599558	−	0.435604i	0.845722	+	0.533624i	$0.179170\pi$
$734$	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	0.547776	+	0.836625i	$0.315475\pi$
$739$	−10.5242	+	32.3903i	−0.387140	+	1.19149i	−0.934916	+	0.354870i	$0.884525\pi$
$740$		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	$-0.250109\pi$
$743$	38.5355			1.41373			0.706865	+	0.707348i	$0.250109\pi$
$744$	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	$-0.719530\pi$
$757$	−35.0131			−1.27257			−0.636287	+	0.771453i	$0.719530\pi$
$758$	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	−0.606879	−	0.794794i	$-0.707579\pi$
$761$	9.69007	−	29.8230i	0.351265	−	1.08108i	0.958144	−	0.286288i	$-0.0924213\pi$
$762$	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	−0.622217	−	0.782845i	$-0.713768\pi$
$769$	−1.94014	+	1.40959i	−0.0699633	+	0.0508313i	0.552254	+	0.833676i	$0.313768\pi$
$770$		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	$-0.837065\pi$
$773$	3.37526	−	10.3880i	0.121400	−	0.373630i	0.993228	+	0.116182i	$0.0370655\pi$
$774$	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	$-0.166128\pi$
$787$	−3.57607	−	11.0060i	−0.127473	−	0.392321i	−0.994344	+	0.106212i	$0.966128\pi$
$788$	−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	$-0.173258\pi$
$797$	17.7113	+	12.8680i	0.627366	+	0.455808i	−0.228121	+	0.973633i	$0.573258\pi$
$798$	−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	−0.997236	−	0.0742994i	$-0.976328\pi$
$809$	−6.65926	−	20.4951i	−0.234127	−	0.720570i	0.763109	−	0.646270i	$-0.223672\pi$
$810$		0			0
$811$	−13.5848	+	41.8098i	−0.477028	+	1.46814i	0.366175	+	0.930546i	$0.380667\pi$
$811$	−13.5848	+	41.8098i	−0.477028	+	1.46814i	−0.843203	+	0.537596i	$0.819333\pi$
$812$	−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	0.00382568	−	0.999993i	$-0.498782\pi$
$821$	−27.1070	−	19.6944i	−0.946042	−	0.687340i	−0.949867	+	0.312653i	$0.898782\pi$
$822$	37.3993	+	27.1722i	1.30445	+	0.947739i
$823$	−17.3006	+	53.2458i	−0.603061	+	1.85603i	−0.0934576	+	0.995623i	$0.529792\pi$
$823$	−17.3006	+	53.2458i	−0.603061	+	1.85603i	−0.509604	+	0.860409i	$0.670208\pi$
$824$	−10.7148			−0.373266
$825$		0			0
$826$	−58.1857			−2.02454
$827$	12.6110	−	38.8126i	0.438527	−	1.34965i	−0.450901	−	0.892574i	$-0.648897\pi$
$827$	12.6110	−	38.8126i	0.438527	−	1.34965i	0.889429	−	0.457074i	$-0.151103\pi$
$828$	−15.6631	−	11.3799i	−0.544329	−	0.395478i
$829$	−0.0994391	−	0.0722468i	−0.00345366	−	0.00250923i	0.586057	−	0.810270i	$-0.300679\pi$
$829$	−0.0994391	−	0.0722468i	−0.00345366	−	0.00250923i	−0.589511	+	0.807761i	$0.700679\pi$
$830$		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	−0.840469	−	0.541860i	$-0.817720\pi$
$839$	4.57603	−	14.0836i	0.157982	−	0.486219i	0.998451	+	0.0556411i	$0.0177203\pi$
$840$		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	$-0.260309\pi$
$853$	5.87730	+	4.27011i	0.201235	+	0.146206i	−0.482604	+	0.875839i	$0.660309\pi$
$854$	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	$-0.348554\pi$
$857$	26.8175			0.916068			0.458034	+	0.888935i	$0.348554\pi$
$858$	10.4565	−	7.59706i	0.356978	−	0.259359i
$859$	−6.36691	−	19.5953i	−0.217236	−	0.668584i	−0.998987	−	0.0449937i	$-0.985673\pi$
$859$	−6.36691	−	19.5953i	−0.217236	−	0.668584i	0.781751	−	0.623591i	$-0.214327\pi$
$860$		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	$-0.175184\pi$
$863$	−4.24862	−	13.0759i	−0.144625	−	0.445109i	−0.996963	+	0.0778827i	$0.975184\pi$
$864$	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	0.767730	+	0.640773i	$0.221386\pi$
$877$	−6.81166	+	20.9641i	−0.230014	+	0.707909i	−0.997744	+	0.0671357i	$0.978614\pi$
$878$	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	−0.457741	−	0.889085i	$-0.651341\pi$
$881$	7.31294	−	5.31316i	0.246379	−	0.179005i	0.704121	+	0.710080i	$0.251341\pi$
$882$	−12.0446			−0.405561
$883$	−1.29540	+	0.941165i	−0.0435937	+	0.0316727i	−0.609369	−	0.792887i	$-0.708577\pi$
$883$	−1.29540	+	0.941165i	−0.0435937	+	0.0316727i	0.565775	+	0.824560i	$0.308577\pi$
$884$	−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	$-0.194501\pi$
$887$	−5.38470	−	16.5724i	−0.180801	−	0.556447i	−0.999851	+	0.0172750i	$0.994501\pi$
$888$	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	$-0.387380\pi$
$907$	20.8690			0.692942			0.346471	+	0.938061i	$0.387380\pi$
$908$	−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	−0.299882	−	0.953976i	$-0.596947\pi$
$911$	15.1958	−	46.7680i	0.503461	−	1.54949i	0.803343	−	0.595517i	$-0.203053\pi$
$912$	−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	−0.428285	−	0.903644i	$-0.640882\pi$
$919$	9.05765	−	6.58077i	0.298784	−	0.217079i	0.727069	+	0.686564i	$0.240882\pi$
$920$		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	−0.280584	−	0.959830i	$-0.590528\pi$
$929$	−39.0181	−	28.3483i	−1.28014	−	0.930077i	−0.999557	+	0.0297529i	$0.990528\pi$
$930$		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	−0.791840	−	0.610728i	$-0.790877\pi$
$937$	−15.6176	−	48.0661i	−0.510205	−	1.57025i	0.281635	−	0.959522i	$-0.409123\pi$
$938$	−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	−0.936875	−	0.349665i	$-0.886295\pi$
$941$	−11.7934	−	36.2965i	−0.384455	−	1.18323i	0.552420	−	0.833566i	$-0.313705\pi$
$942$	−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	$-0.169573\pi$
$947$	19.8363	+	14.4119i	0.644592	+	0.468323i	−0.216833	+	0.976209i	$0.569573\pi$
$948$	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	$-0.232463\pi$
$953$	10.5187	+	7.64232i	0.340736	+	0.247559i	−0.404236	+	0.914655i	$0.632463\pi$
$954$	−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	$-0.945286\pi$
$967$	−35.0476	+	25.4636i	−1.12706	+	0.818854i	−0.141792	+	0.989896i	$0.545286\pi$
$968$	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	0.900970	−	0.433882i	$-0.142857\pi$
$971$	23.8922	+	17.3587i	0.766738	+	0.557068i	−0.134231	+	0.990950i	$0.542857\pi$
$972$	−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	0.0670189	−	0.997752i	$-0.478651\pi$
$977$	18.7312	−	57.6486i	0.599263	−	1.84434i	0.532244	−	0.846591i	$-0.321349\pi$
$978$	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	$-0.922044\pi$
$983$	−32.5868	+	23.6757i	−1.03936	+	0.755138i	−0.0691986	+	0.997603i	$0.522044\pi$
$984$	−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	0.943825	+	0.330445i	$0.107199\pi$
$991$	11.7889	+	36.2824i	0.374485	+	1.15255i	−0.569340	+	0.822102i	$0.692801\pi$
$992$	−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	$-0.161728\pi$
$997$	21.5018	+	15.6220i	0.680969	+	0.494753i	−0.192710	+	0.981256i	$0.561728\pi$
$998$	−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.e.226.1		16
5.2	odd	4		75.2.i.a.4.1	✓	16
5.3	odd	4		375.2.i.c.274.4		16
5.4	even	2		375.2.g.d.226.4		16
15.2	even	4		225.2.m.b.154.4		16
25.6	even	5	inner	375.2.g.e.151.1		16
25.8	odd	20		75.2.i.a.19.1	yes	16
25.9	even	10		1875.2.a.p.1.7		8
25.12	odd	20		1875.2.b.h.1249.2		16
25.13	odd	20		1875.2.b.h.1249.15		16
25.16	even	5		1875.2.a.m.1.2		8
25.17	odd	20		375.2.i.c.349.4		16
25.19	even	10		375.2.g.d.151.4		16
75.8	even	20		225.2.m.b.19.4		16
75.41	odd	10		5625.2.a.bd.1.7		8
75.59	odd	10		5625.2.a.t.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.1	✓	16	5.2	odd	4
75.2.i.a.19.1	yes	16	25.8	odd	20
225.2.m.b.19.4		16	75.8	even	20
225.2.m.b.154.4		16	15.2	even	4
375.2.g.d.151.4		16	25.19	even	10
375.2.g.d.226.4		16	5.4	even	2
375.2.g.e.151.1		16	25.6	even	5	inner
375.2.g.e.226.1		16	1.1	even	1	trivial
375.2.i.c.274.4		16	5.3	odd	4
375.2.i.c.349.4		16	25.17	odd	20
1875.2.a.m.1.2		8	25.16	even	5
1875.2.a.p.1.7		8	25.9	even	10
1875.2.b.h.1249.2		16	25.12	odd	20
1875.2.b.h.1249.15		16	25.13	odd	20
5625.2.a.t.1.2		8	75.59	odd	10
5625.2.a.bd.1.7		8	75.41	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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