LMFDB - Embedded newform 375.2.i.c.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, 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 $\Q(\zeta_{10})$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.4
Root			$2.35083i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.c.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23577 - 0.726446i) q^{2} +(0.587785 + 0.809017i) q^{3} +(2.85292 - 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} -3.48189i q^{7} +(2.10915 - 2.90300i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(2.23577 - 0.726446i) q^{2} +(0.587785 + 0.809017i) q^{3} +(2.85292 - 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} -3.48189i q^{7} +(2.10915 - 2.90300i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(0.905762 + 2.78765i) q^{11} +(3.35381 + 1.08972i) q^{12} +(-1.78394 - 0.579638i) q^{13} +(-2.52940 - 7.78470i) q^{14} +(0.427277 - 1.31502i) q^{16} +(-3.98851 + 5.48972i) q^{17} +2.35083i q^{18} +(-2.38620 - 1.73367i) q^{19} +(2.81691 - 2.04660i) q^{21} +(4.05015 + 5.57456i) q^{22} +(5.22149 - 1.69656i) q^{23} +3.58831 q^{24} -4.40956 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-7.21714 - 9.93354i) q^{28} +(2.06779 - 1.50234i) q^{29} +(-0.338237 - 0.245744i) q^{31} +3.92613i q^{32} +(-1.72286 + 2.37132i) q^{33} +(-4.92942 + 15.1712i) q^{34} +(1.08972 + 3.35381i) q^{36} +(-4.98314 - 1.61912i) q^{37} +(-6.59441 - 2.14265i) q^{38} +(-0.579638 - 1.78394i) q^{39} +(0.518744 - 1.59653i) q^{41} +(4.81121 - 6.62206i) q^{42} +10.9233i q^{43} +(8.36221 + 6.07550i) q^{44} +(10.4416 - 7.58626i) q^{46} +(-4.40356 - 6.06098i) q^{47} +(1.31502 - 0.427277i) q^{48} -5.12353 q^{49} -6.78566 q^{51} +(-6.29089 + 2.04403i) q^{52} +(-2.18041 - 3.00107i) q^{53} +(-1.90186 + 1.38178i) q^{54} +(-10.1079 - 7.34383i) q^{56} -2.94950i q^{57} +(3.53175 - 4.86103i) q^{58} +(2.19666 - 6.76062i) q^{59} +(-1.98917 - 6.12204i) q^{61} +(-0.934741 - 0.303716i) q^{62} +(3.31147 + 1.07596i) q^{63} +(3.70667 + 11.4080i) q^{64} +(-2.12929 + 6.55329i) q^{66} +(-5.90225 + 8.12376i) q^{67} +23.9290i q^{68} +(4.44166 + 3.22706i) q^{69} +(-0.589451 + 0.428261i) q^{71} +(2.10915 + 2.90300i) q^{72} +(3.41685 - 1.11020i) q^{73} -12.3174 q^{74} -10.4011 q^{76} +(9.70628 - 3.15376i) q^{77} +(-2.59188 - 3.56741i) q^{78} +(2.48583 - 1.80606i) q^{79} +(-0.809017 - 0.587785i) q^{81} -3.94632i q^{82} +(5.94559 - 8.18340i) q^{83} +(3.79427 - 11.6776i) q^{84} +(7.93517 + 24.4219i) q^{86} +(2.43084 + 0.789827i) q^{87} +(10.0029 + 3.25015i) q^{88} +(-0.0888461 - 0.273440i) q^{89} +(-2.01823 + 6.21148i) q^{91} +(11.3799 - 15.6631i) q^{92} -0.418084i q^{93} +(-14.2483 - 10.3520i) q^{94} +(-3.17630 + 2.30772i) q^{96} +(-6.11828 - 8.42109i) q^{97} +(-11.4551 + 3.72197i) q^{98} -2.93111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	2.23577	−	0.726446i	1.58093	−	0.513675i	0.618634	−	0.785680i	$-0.287687\pi$
$2$	2.23577	−	0.726446i	1.58093	−	0.513675i	0.962296	+	0.272005i	$0.0876866\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	2.85292	−	2.07277i	1.42646	−	1.03638i
$5$		0			0
$5$		0			0
$6$	1.90186	+	1.38178i	0.776432	+	0.564111i
$7$		−	3.48189i		−	1.31603i	−0.753005	−	0.658015i	$-0.771396\pi$
$7$		−	3.48189i		−	1.31603i	0.753005	−	0.658015i	$-0.228604\pi$
$8$	2.10915	−	2.90300i	0.745698	−	1.02637i
$9$	−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	$0.754311\pi$
$12$	3.35381	+	1.08972i	0.968160	+	0.314574i
$13$	−1.78394	−	0.579638i	−0.494776	−	0.160763i	0.0509914	−	0.998699i	$-0.483762\pi$
$13$	−1.78394	−	0.579638i	−0.494776	−	0.160763i	−0.545768	+	0.837937i	$0.683762\pi$
$14$	−2.52940	−	7.78470i	−0.676012	−	2.08055i
$15$		0			0
$16$	0.427277	−	1.31502i	0.106819	−	0.328756i
$17$	−3.98851	+	5.48972i	−0.967356	+	1.33145i	−0.0239850	+	0.999712i	$0.507635\pi$
$17$	−3.98851	+	5.48972i	−0.967356	+	1.33145i	−0.943371	+	0.331739i	$0.892365\pi$
$18$			2.35083i			0.554096i
$19$	−2.38620	−	1.73367i	−0.547431	−	0.397732i	0.279406	−	0.960173i	$-0.409862\pi$
$19$	−2.38620	−	1.73367i	−0.547431	−	0.397732i	−0.826837	+	0.562441i	$0.809862\pi$
$20$		0			0
$21$	2.81691	−	2.04660i	0.614699	−	0.446605i
$22$	4.05015	+	5.57456i	0.863496	+	1.18850i
$23$	5.22149	−	1.69656i	1.08876	−	0.353758i	0.290990	−	0.956726i	$-0.406015\pi$
$23$	5.22149	−	1.69656i	1.08876	−	0.353758i	0.797765	+	0.602968i	$0.206015\pi$
$24$	3.58831			0.732460
$25$		0			0
$26$	−4.40956			−0.864786
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−7.21714	−	9.93354i	−1.36391	−	1.87726i
$29$	2.06779	−	1.50234i	0.383980	−	0.278978i	−0.379004	−	0.925395i	$-0.623733\pi$
$29$	2.06779	−	1.50234i	0.383980	−	0.278978i	0.762984	+	0.646417i	$0.223733\pi$
$30$		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	$0.711954\pi$
$32$			3.92613i			0.694048i
$33$	−1.72286	+	2.37132i	−0.299912	+	0.412793i
$34$	−4.92942	+	15.1712i	−0.845388	+	2.60184i
$35$		0			0
$36$	1.08972	+	3.35381i	0.181620	+	0.558968i
$37$	−4.98314	−	1.61912i	−0.819224	−	0.266182i	−0.130724	−	0.991419i	$-0.541730\pi$
$37$	−4.98314	−	1.61912i	−0.819224	−	0.266182i	−0.688500	+	0.725237i	$0.741730\pi$
$38$	−6.59441	−	2.14265i	−1.06975	−	0.347584i
$39$	−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	$0.0581543\pi$
$42$	4.81121	−	6.62206i	0.742386	−	1.02181i
$43$			10.9233i			1.66578i	0.553436	+	0.832892i	$0.313316\pi$
$43$			10.9233i			1.66578i	−0.553436	+	0.832892i	$0.686684\pi$
$44$	8.36221	+	6.07550i	1.26065	+	0.915916i
$45$		0			0
$46$	10.4416	−	7.58626i	1.53953	−	1.11853i
$47$	−4.40356	−	6.06098i	−0.642325	−	0.884084i	0.356412	−	0.934329i	$-0.384000\pi$
$47$	−4.40356	−	6.06098i	−0.642325	−	0.884084i	−0.998737	+	0.0502446i	$0.984000\pi$
$48$	1.31502	−	0.427277i	0.189807	−	0.0616721i
$49$	−5.12353			−0.731933
$50$		0			0
$51$	−6.78566			−0.950183
$52$	−6.29089	+	2.04403i	−0.872390	+	0.283457i
$53$	−2.18041	−	3.00107i	−0.299502	−	0.412229i	0.632570	−	0.774504i	$-0.282000\pi$
$53$	−2.18041	−	3.00107i	−0.299502	−	0.412229i	−0.932071	+	0.362275i	$0.882000\pi$
$54$	−1.90186	+	1.38178i	−0.258811	+	0.188037i
$55$		0			0
$56$	−10.1079	−	7.34383i	−1.35073	−	0.981361i
$57$		−	2.94950i		−	0.390671i
$58$	3.53175	−	4.86103i	0.463741	−	0.638285i
$59$	2.19666	−	6.76062i	0.285981	−	0.880158i	−0.700122	−	0.714023i	$-0.746871\pi$
$59$	2.19666	−	6.76062i	0.285981	−	0.880158i	0.986103	−	0.166135i	$-0.0531288\pi$
$60$		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	$-0.235202\pi$
$62$	−0.934741	−	0.303716i	−0.118712	−	0.0385719i
$63$	3.31147	+	1.07596i	0.417206	+	0.135558i
$64$	3.70667	+	11.4080i	0.463334	+	1.42600i
$65$		0			0
$66$	−2.12929	+	6.55329i	−0.262098	+	0.806654i
$67$	−5.90225	+	8.12376i	−0.721075	+	0.992475i	0.278412	+	0.960462i	$0.410192\pi$
$67$	−5.90225	+	8.12376i	−0.721075	+	0.992475i	−0.999487	+	0.0320131i	$0.989808\pi$
$68$			23.9290i			2.90181i
$69$	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	$0.313766\pi$
$72$	2.10915	+	2.90300i	0.248566	+	0.342122i
$73$	3.41685	−	1.11020i	0.399912	−	0.129939i	−0.102154	−	0.994769i	$-0.532573\pi$
$73$	3.41685	−	1.11020i	0.399912	−	0.129939i	0.502066	+	0.864829i	$0.332573\pi$
$74$	−12.3174			−1.43187
$75$		0			0
$76$	−10.4011			−1.19309
$77$	9.70628	−	3.15376i	1.10613	−	0.359404i
$78$	−2.59188	−	3.56741i	−0.293472	−	0.403930i
$79$	2.48583	−	1.80606i	0.279677	−	0.203197i	−0.439099	−	0.898439i	$-0.644702\pi$
$79$	2.48583	−	1.80606i	0.279677	−	0.203197i	0.718777	+	0.695241i	$0.244702\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		−	3.94632i		−	0.435798i
$83$	5.94559	−	8.18340i	0.652613	−	0.898245i	−0.346595	−	0.938015i	$-0.612662\pi$
$83$	5.94559	−	8.18340i	0.652613	−	0.898245i	0.999209	+	0.0397694i	$0.0126623\pi$
$84$	3.79427	−	11.6776i	0.413989	−	1.27413i
$85$		0			0
$86$	7.93517	+	24.4219i	0.855672	+	2.63349i
$87$	2.43084	+	0.789827i	0.260613	+	0.0846784i
$88$	10.0029	+	3.25015i	1.06632	+	0.346467i
$89$	−0.0888461	−	0.273440i	−0.00941767	−	0.0289846i	0.946237	−	0.323473i	$-0.104851\pi$
$89$	−0.0888461	−	0.273440i	−0.00941767	−	0.0289846i	−0.955655	+	0.294489i	$0.904851\pi$
$90$		0			0
$91$	−2.01823	+	6.21148i	−0.211568	+	0.651140i
$92$	11.3799	−	15.6631i	1.18644	−	1.63299i
$93$		−	0.418084i		−	0.0433533i
$94$	−14.2483	−	10.3520i	−1.46960	−	1.06773i
$95$		0			0
$96$	−3.17630	+	2.30772i	−0.324180	+	0.235531i
$97$	−6.11828	−	8.42109i	−0.621217	−	0.855032i	0.376224	−	0.926529i	$-0.377222\pi$
$97$	−6.11828	−	8.42109i	−0.621217	−	0.855032i	−0.997441	+	0.0714966i	$0.977222\pi$
$98$	−11.4551	+	3.72197i	−1.15714	+	0.375976i
$99$	−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	$0.375590\pi$
$102$	−15.1712	+	4.92942i	−1.50217	+	0.488085i
$103$	1.75514	+	2.41574i	0.172939	+	0.238030i	0.886684	−	0.462375i	$-0.153003\pi$
$103$	1.75514	+	2.41574i	0.172939	+	0.238030i	−0.713745	+	0.700405i	$0.753003\pi$
$104$	−5.44530	+	3.95624i	−0.533955	+	0.387941i
$105$		0			0
$106$	−7.05501	−	5.12576i	−0.685243	−	0.497858i
$107$			7.07213i			0.683689i	0.939757	+	0.341844i	$0.111052\pi$
$107$			7.07213i			0.683689i	−0.939757	+	0.341844i	$0.888948\pi$
$108$	−2.07277	+	2.85292i	−0.199452	+	0.274522i
$109$	4.11060	−	12.6511i	0.393724	−	1.21176i	−0.536227	−	0.844074i	$-0.680151\pi$
$109$	4.11060	−	12.6511i	0.393724	−	1.21176i	0.929951	−	0.367683i	$-0.119849\pi$
$110$		0			0
$111$	−1.61912	−	4.98314i	−0.153680	−	0.472979i
$112$	−4.57876	−	1.48773i	−0.432653	−	0.140577i
$113$	9.53271	+	3.09737i	0.896762	+	0.291376i	0.720900	−	0.693039i	$-0.243729\pi$
$113$	9.53271	+	3.09737i	0.896762	+	0.291376i	0.175862	+	0.984415i	$0.443729\pi$
$114$	−2.14265	−	6.59441i	−0.200678	−	0.617623i
$115$		0			0
$116$	2.78525	−	8.57211i	0.258604	−	0.795900i
$117$	1.10254	−	1.51751i	0.101930	−	0.140294i
$118$		−	16.7110i		−	1.53837i
$119$	19.1146	+	13.8875i	1.75223	+	1.27307i
$120$		0			0
$121$	1.94861	−	1.41575i	0.177146	−	0.128704i
$122$	−8.89467	−	12.2425i	−0.805286	−	1.10838i
$123$	1.59653	−	0.518744i	0.143954	−	0.0467736i
$124$	−1.47433			−0.132399
$125$		0			0
$126$	8.18532			0.729206
$127$	10.0556	−	3.26725i	0.892286	−	0.289921i	0.173237	−	0.984880i	$-0.444577\pi$
$127$	10.0556	−	3.26725i	0.892286	−	0.289921i	0.719049	+	0.694959i	$0.244577\pi$
$128$	11.9591	+	16.4603i	1.05705	+	1.45490i
$129$	−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	$0.570985\pi$
$132$			10.3363i			0.899656i
$133$	−6.03645	+	8.30847i	−0.523427	+	0.720435i
$134$	−7.29462	+	22.4505i	−0.630159	+	1.93943i
$135$		0			0
$136$	7.52427	+	23.1573i	0.645200	+	1.98572i
$137$	18.7021	+	6.07669i	1.59783	+	0.519167i	0.966570	−	0.256404i	$-0.0825377\pi$
$137$	18.7021	+	6.07669i	1.59783	+	0.519167i	0.631261	+	0.775571i	$0.282538\pi$
$138$	12.2748	+	3.98833i	1.04490	+	0.339509i
$139$	3.60067	+	11.0817i	0.305404	+	0.939938i	0.979526	+	0.201318i	$0.0645224\pi$
$139$	3.60067	+	11.0817i	0.305404	+	0.939938i	−0.674122	+	0.738620i	$0.735478\pi$
$140$		0			0
$141$	2.31509	−	7.12511i	0.194965	−	0.600042i
$142$	−1.00677	+	1.38570i	−0.0844862	+	0.116285i
$143$		−	5.49801i		−	0.459767i
$144$	1.11863	+	0.812729i	0.0932188	+	0.0677275i
$145$		0			0
$146$	6.83280	−	4.96432i	0.565486	−	0.410850i
$147$	−3.01154	−	4.14503i	−0.248387	−	0.341876i
$148$	−17.5726	+	5.70967i	−1.44446	+	0.469332i
$149$	7.33020			0.600513			0.300257	−	0.953858i	$-0.402928\pi$
$149$	7.33020			0.600513			0.300257	+	0.953858i	$0.402928\pi$
$150$		0			0
$151$	−16.7358			−1.36194			−0.680968	−	0.732313i	$-0.738441\pi$
$151$	−16.7358			−1.36194			−0.680968	+	0.732313i	$0.738441\pi$
$152$	−10.0657	+	3.27055i	−0.816437	+	0.265276i
$153$	−3.98851	−	5.48972i	−0.322452	−	0.443817i
$154$	19.4100	−	14.1022i	1.56410	−	1.13639i
$155$		0			0
$156$	−5.35135	−	3.88798i	−0.428451	−	0.311288i
$157$		−	7.88635i		−	0.629399i	−0.949191	−	0.314700i	$-0.898096\pi$
$157$		−	7.88635i		−	0.629399i	0.949191	−	0.314700i	$-0.101904\pi$
$158$	4.24574	−	5.84375i	0.337773	−	0.464904i
$159$	1.14631	−	3.52797i	0.0909081	−	0.279786i
$160$		0			0
$161$	−5.90724	−	18.1806i	−0.465556	−	1.43283i
$162$	−2.23577	−	0.726446i	−0.175659	−	0.0570750i
$163$	−9.45343	−	3.07160i	−0.740450	−	0.240587i	−0.0855829	−	0.996331i	$-0.527275\pi$
$163$	−9.45343	−	3.07160i	−0.740450	−	0.240587i	−0.654867	+	0.755744i	$0.727275\pi$
$164$	−1.82930	−	5.63000i	−0.142844	−	0.439629i
$165$		0			0
$166$	7.34818	−	22.6154i	0.570330	−	1.75529i
$167$	−3.27847	+	4.51243i	−0.253696	+	0.349182i	−0.916801	−	0.399344i	$-0.869238\pi$
$167$	−3.27847	+	4.51243i	−0.253696	+	0.349182i	0.663106	+	0.748526i	$0.269238\pi$
$168$		−	12.4941i		−	0.963939i
$169$	−7.67075	−	5.57313i	−0.590058	−	0.428702i
$170$		0			0
$171$	2.38620	−	1.73367i	0.182477	−	0.132577i
$172$	22.6414	+	31.1632i	1.72639	+	2.37617i
$173$	−15.7573	+	5.11985i	−1.19800	+	0.389255i	−0.839026	−	0.544091i	$-0.816875\pi$
$173$	−15.7573	+	5.11985i	−1.19800	+	0.389255i	−0.358978	+	0.933346i	$0.616875\pi$
$174$	6.00857			0.455508
$175$		0			0
$176$	4.05284			0.305494
$177$	6.76062	−	2.19666i	0.508160	−	0.165111i
$178$	−0.397279	−	0.546808i	−0.0297773	−	0.0409850i
$179$	−4.33650	+	3.15065i	−0.324125	+	0.235491i	−0.737934	−	0.674873i	$-0.764198\pi$
$179$	−4.33650	+	3.15065i	−0.324125	+	0.235491i	0.413808	+	0.910364i	$0.364198\pi$
$180$		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	$0.696123\pi$
$182$			15.3536i			1.13808i
$183$	3.78363	−	5.20772i	0.279694	−	0.384966i
$184$	6.08779	−	18.7363i	0.448798	−	1.38126i
$185$		0			0
$186$	−0.303716	−	0.934741i	−0.0222695	−	0.0685385i
$187$	−18.9160	−	6.14619i	−1.38328	−	0.449454i
$188$	−25.1260	−	8.16392i	−1.83250	−	0.595415i
$189$	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	$0.140065\pi$
$192$	−7.05051	+	9.70420i	−0.508827	+	0.700340i
$193$		−	24.3134i		−	1.75012i	−0.484018	−	0.875058i	$-0.660823\pi$
$193$		−	24.3134i		−	1.75012i	0.484018	−	0.875058i	$-0.339177\pi$
$194$	−19.7966	−	14.3830i	−1.42131	−	1.03264i
$195$		0			0
$196$	−14.6170	+	10.6199i	−1.04407	+	0.758563i
$197$	8.79098	+	12.0997i	0.626331	+	0.862071i	0.997795	−	0.0663764i	$-0.0211438\pi$
$197$	8.79098	+	12.0997i	0.626331	+	0.862071i	−0.371463	+	0.928448i	$0.621144\pi$
$198$	−6.55329	+	2.12929i	−0.465722	+	0.151322i
$199$	11.3251			0.802817			0.401408	−	0.915899i	$-0.368521\pi$
$199$	11.3251			0.802817			0.401408	+	0.915899i	$0.368521\pi$
$200$		0			0
$201$	−10.0415			−0.708274
$202$	17.1203	−	5.56272i	1.20458	−	0.391391i
$203$	−5.23098	−	7.19983i	−0.367143	−	0.505329i
$204$	−19.3589	+	14.0651i	−1.35540	+	0.984753i
$205$		0			0
$206$	5.67900	+	4.12603i	0.395674	+	0.287474i
$207$			5.49019i			0.381595i
$208$	−1.52447	+	2.09826i	−0.105703	+	0.145488i
$209$	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	$0.816398\pi$
$212$	−12.4410	−	4.04234i	−0.854454	−	0.277629i
$213$	−0.692941	−	0.225150i	−0.0474796	−	0.0154270i
$214$	5.13752	+	15.8117i	0.351194	+	1.08086i
$215$		0			0
$216$	−1.10885	+	3.41268i	−0.0754475	+	0.232204i
$217$	−0.855651	+	1.17770i	−0.0580854	+	0.0799477i
$218$		−	31.2711i		−	2.11795i
$219$	2.90655	+	2.11173i	0.196406	+	0.142697i
$220$		0			0
$221$	10.2973	−	7.48144i	0.692672	−	0.503256i
$222$	−7.23997	−	9.96497i	−0.485915	−	0.668805i
$223$	7.41386	−	2.40891i	0.496469	−	0.161313i	−0.0500709	−	0.998746i	$-0.515945\pi$
$223$	7.41386	−	2.40891i	0.496469	−	0.161313i	0.546540	+	0.837433i	$0.315945\pi$
$224$	13.6703			0.913387
$225$		0			0
$226$	23.5630			1.56739
$227$	−12.2039	+	3.96529i	−0.810001	+	0.263185i	−0.684598	−	0.728921i	$-0.740022\pi$
$227$	−12.2039	+	3.96529i	−0.810001	+	0.263185i	−0.125403	+	0.992106i	$0.540022\pi$
$228$	−6.11363	−	8.41468i	−0.404885	−	0.557276i
$229$	−11.7334	+	8.52483i	−0.775366	+	0.563337i	−0.903585	−	0.428409i	$-0.859074\pi$
$229$	−11.7334	+	8.52483i	−0.775366	+	0.563337i	0.128218	+	0.991746i	$0.459074\pi$
$230$		0			0
$231$	8.25665	+	5.99881i	0.543248	+	0.394693i
$232$		−	9.17148i		−	0.602137i
$233$	6.69902	−	9.22041i	0.438867	−	0.604049i	−0.531093	−	0.847314i	$-0.678218\pi$
$233$	6.69902	−	9.22041i	0.438867	−	0.604049i	0.969960	+	0.243265i	$0.0782184\pi$
$234$	1.36263	−	4.19374i	0.0890779	−	0.274153i
$235$		0			0
$236$	−7.74630	−	23.8407i	−0.504241	−	1.55190i
$237$	2.92226	+	0.949501i	0.189821	+	0.0616767i
$238$	52.8244	+	17.1637i	3.42410	+	1.11256i
$239$	−2.13244	−	6.56298i	−0.137936	−	0.424524i	0.858099	−	0.513484i	$-0.171646\pi$
$239$	−2.13244	−	6.56298i	−0.137936	−	0.424524i	−0.996035	+	0.0889605i	$0.971646\pi$
$240$		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	$0.731234\pi$
$242$	3.32818	−	4.58085i	0.213943	−	0.294468i
$243$		−	1.00000i		−	0.0641500i
$244$	−18.3645	−	13.3426i	−1.17567	−	0.854172i
$245$		0			0
$246$	3.19264	−	2.31959i	0.203555	−	0.147891i
$247$	3.25193	+	4.47590i	0.206915	+	0.284795i
$248$	−1.42679	+	0.463592i	−0.0906011	+	0.0294381i
$249$	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	$0.627179\pi$
$252$	11.6776	−	3.79427i	0.735618	−	0.239017i
$253$	9.45885	+	13.0190i	0.594673	+	0.818496i
$254$	20.1084	−	14.6096i	1.26172	−	0.916690i
$255$		0			0
$256$	19.2870	+	14.0128i	1.20544	+	0.875801i
$257$		−	20.8274i		−	1.29918i	−0.760285	−	0.649590i	$-0.774941\pi$
$257$		−	20.8274i		−	1.29918i	0.760285	−	0.649590i	$-0.225059\pi$
$258$	−15.0936	+	20.7745i	−0.939686	+	1.29337i
$259$	−5.63760	+	17.3507i	−0.350303	+	1.07812i
$260$		0			0
$261$	0.789827	+	2.43084i	0.0488891	+	0.150465i
$262$	20.1802	+	6.55696i	1.24674	+	0.405090i
$263$	2.12577	+	0.690704i	0.131080	+	0.0425906i	0.373823	−	0.927500i	$-0.378047\pi$
$263$	2.12577	+	0.690704i	0.131080	+	0.0425906i	−0.242742	+	0.970091i	$0.578047\pi$
$264$	3.25015	+	10.0029i	0.200033	+	0.615638i
$265$		0			0
$266$	−7.46048	+	22.9610i	−0.457431	+	1.40783i
$267$	0.168995	−	0.232602i	0.0103423	−	0.0142350i
$268$			35.4104i			2.16303i
$269$	−15.6170	−	11.3464i	−0.952183	−	0.691802i	−0.000861106	−	1.00000i	$-0.500274\pi$
$269$	−15.6170	−	11.3464i	−0.952183	−	0.691802i	−0.951322	+	0.308198i	$0.900274\pi$
$270$		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	$0.181860\pi$
$272$	5.51491	+	7.59062i	0.334390	+	0.460249i
$273$	−6.21148	+	2.01823i	−0.375936	+	0.122149i
$274$	46.2281			2.79274
$275$		0			0
$276$	19.3606			1.16537
$277$	24.8669	−	8.07975i	1.49411	−	0.485465i	0.555815	−	0.831306i	$-0.312406\pi$
$277$	24.8669	−	8.07975i	1.49411	−	0.485465i	0.938293	+	0.345841i	$0.112406\pi$
$278$	16.1005	+	22.1605i	0.965646	+	1.32910i
$279$	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	$0.797624\pi$
$282$		−	17.6119i		−	1.04877i
$283$	−18.7290	+	25.7783i	−1.11333	+	1.53236i	−0.296903	+	0.954907i	$0.595954\pi$
$283$	−18.7290	+	25.7783i	−1.11333	+	1.53236i	−0.816423	+	0.577455i	$0.804046\pi$
$284$	−0.793970	+	2.44359i	−0.0471135	+	0.145000i
$285$		0			0
$286$	−3.99401	−	12.2923i	−0.236171	−	0.726859i
$287$	−5.55893	−	1.80621i	−0.328134	−	0.106617i
$288$	−3.73397	−	1.21324i	−0.220026	−	0.0714908i
$289$	−8.97546	−	27.6236i	−0.527968	−	1.62492i
$290$		0			0
$291$	3.21657	−	9.89959i	0.188559	−	0.580324i
$292$	7.44680	−	10.2496i	0.435791	−	0.599815i
$293$			16.6235i			0.971153i	0.874194	+	0.485576i	$0.161390\pi$
$293$			16.6235i			0.971153i	−0.874194	+	0.485576i	$0.838610\pi$
$294$	−9.74425	−	7.07961i	−0.568296	−	0.412891i
$295$		0			0
$296$	−15.2105	+	11.0511i	−0.884094	+	0.642332i
$297$	−1.72286	−	2.37132i	−0.0999706	−	0.137598i
$298$	16.3886	−	5.32499i	0.949369	−	0.308469i
$299$	−10.2982			−0.595561
$300$		0			0
$301$	38.0336			2.19222
$302$	−37.4173	+	12.1576i	−2.15312	+	0.699593i
$303$	4.50093	+	6.19500i	0.258572	+	0.355893i
$304$	−3.29939	+	2.39715i	−0.189233	+	0.137486i
$305$		0			0
$306$	−12.9054	−	9.37631i	−0.737752	−	0.536008i
$307$			14.1643i			0.808402i	0.914670	+	0.404201i	$0.132450\pi$
$307$			14.1643i			0.808402i	−0.914670	+	0.404201i	$0.867550\pi$
$308$	21.1542	−	29.1163i	1.20537	−	1.65905i
$309$	−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	$0.759675\pi$
$312$	−6.40133	−	2.07992i	−0.362404	−	0.117752i
$313$	−3.39980	−	1.10466i	−0.192168	−	0.0624392i	0.211352	−	0.977410i	$-0.432213\pi$
$313$	−3.39980	−	1.10466i	−0.192168	−	0.0624392i	−0.403520	+	0.914971i	$0.632213\pi$
$314$	−5.72901	−	17.6321i	−0.323307	−	0.995036i
$315$		0			0
$316$	3.34832	−	10.3051i	0.188358	−	0.579706i
$317$	−7.51306	+	10.3408i	−0.421975	+	0.580799i	−0.966088	−	0.258213i	$-0.916866\pi$
$317$	−7.51306	+	10.3408i	−0.421975	+	0.580799i	0.544113	+	0.839012i	$0.316866\pi$
$318$		−	8.72047i		−	0.489020i
$319$	6.06093	+	4.40352i	0.339347	+	0.246550i
$320$		0			0
$321$	−5.72147	+	4.15689i	−0.319342	+	0.232015i
$322$	−26.4145	−	36.3564i	−1.47202	−	2.02606i
$323$	19.0347	−	6.18476i	1.05912	−	0.344129i
$324$	−3.52640			−0.195911
$325$		0			0
$326$	−23.3671			−1.29418
$327$	12.6511	−	4.11060i	0.699608	−	0.227317i
$328$	−3.54062	−	4.87324i	−0.195498	−	0.269080i
$329$	−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	$0.741275\pi$
$332$		−	35.6704i		−	1.95767i
$333$	3.07975	−	4.23892i	0.168769	−	0.232291i
$334$	−4.05187	+	12.4704i	−0.221709	+	0.682349i
$335$		0			0
$336$	−1.48773	−	4.57876i	−0.0811624	−	0.249792i
$337$	16.5529	+	5.37837i	0.901694	+	0.292978i	0.722936	−	0.690915i	$-0.242792\pi$
$337$	16.5529	+	5.37837i	0.901694	+	0.292978i	0.178758	+	0.983893i	$0.442792\pi$
$338$	−21.1986	−	6.88785i	−1.15305	−	0.374650i
$339$	3.09737	+	9.53271i	0.168226	+	0.517746i
$340$		0			0
$341$	0.378685	−	1.16547i	0.0205069	−	0.0631138i
$342$	4.07557	−	5.60954i	0.220382	−	0.303329i
$343$		−	6.53364i		−	0.352783i
$344$	31.7103	+	23.0389i	1.70970	+	1.24217i
$345$		0			0
$346$	−31.5104	+	22.8936i	−1.69401	+	1.23077i
$347$	8.23525	+	11.3348i	0.442091	+	0.608486i	0.970675	−	0.240395i	$-0.0772769\pi$
$347$	8.23525	+	11.3348i	0.442091	+	0.608486i	−0.528584	+	0.848881i	$0.677277\pi$
$348$	8.57211	−	2.78525i	0.459513	−	0.149305i
$349$	−35.9459			−1.92414			−0.962069	−	0.272806i	$-0.912048\pi$
$349$	−35.9459			−1.92414			−0.962069	+	0.272806i	$0.912048\pi$
$350$		0			0
$351$	1.87575			0.100120
$352$	−10.9447	+	3.55614i	−0.583352	+	0.189543i
$353$	−5.17367	−	7.12095i	−0.275367	−	0.379010i	0.648826	−	0.760937i	$-0.275260\pi$
$353$	−5.17367	−	7.12095i	−0.275367	−	0.379010i	−0.924192	+	0.381927i	$0.875260\pi$
$354$	13.5195	−	9.82246i	0.718551	−	0.522058i
$355$		0			0
$356$	−0.820248	−	0.595945i	−0.0434731	−	0.0315850i
$357$			23.6269i			1.25047i
$358$	−7.40665	+	10.1944i	−0.391454	+	0.538790i
$359$	−1.86326	+	5.73451i	−0.0983389	+	0.302656i	−0.988109	−	0.153752i	$-0.950864\pi$
$359$	−1.86326	+	5.73451i	−0.0983389	+	0.302656i	0.889771	+	0.456408i	$0.150864\pi$
$360$		0			0
$361$	−3.18301	−	9.79630i	−0.167527	−	0.515595i
$362$	0.732762	+	0.238089i	0.0385131	+	0.0125137i
$363$	2.29073	+	0.744302i	0.120232	+	0.0390657i
$364$	7.11710	+	21.9042i	0.373037	+	1.14809i
$365$		0			0
$366$	4.67621	−	14.3919i	0.244429	−	0.752276i
$367$	−16.9084	+	23.2724i	−0.882609	+	1.21481i	0.0930825	+	0.995658i	$0.470328\pi$
$367$	−16.9084	+	23.2724i	−0.882609	+	1.21481i	−0.975691	+	0.219149i	$0.929672\pi$
$368$		−	7.59128i		−	0.395723i
$369$	1.35809	+	0.986709i	0.0706993	+	0.0513660i
$370$		0			0
$371$	−10.4494	+	7.59193i	−0.542505	+	0.394153i
$372$	−0.866590	−	1.19276i	−0.0449306	−	0.0618417i
$373$	−31.9555	+	10.3830i	−1.65459	+	0.537610i	−0.979729	−	0.200330i	$-0.935799\pi$
$373$	−31.9555	+	10.3830i	−1.65459	+	0.537610i	−0.674866	+	0.737940i	$0.735799\pi$
$374$	−46.7568			−2.41774
$375$		0			0
$376$	−26.8828			−1.38637
$377$	−4.55964	+	1.48152i	−0.234833	+	0.0763020i
$378$	4.81121	+	6.62206i	0.247462	+	0.340602i
$379$	3.74901	−	2.72381i	0.192574	−	0.139913i	−0.487321	−	0.873223i	$-0.662026\pi$
$379$	3.74901	−	2.72381i	0.192574	−	0.139913i	0.679894	+	0.733310i	$0.262026\pi$
$380$		0			0
$381$	8.55377	+	6.21467i	0.438223	+	0.318387i
$382$			8.15718i			0.417358i
$383$	−7.58581	+	10.4410i	−0.387617	+	0.533509i	−0.957582	−	0.288160i	$-0.906957\pi$
$383$	−7.58581	+	10.4410i	−0.387617	+	0.533509i	0.569965	+	0.821669i	$0.306957\pi$
$384$	−6.28728	+	19.3503i	−0.320846	+	0.987464i
$385$		0			0
$386$	−17.6624	−	54.3592i	−0.898991	−	2.76681i
$387$	−10.3886	−	3.37548i	−0.528085	−	0.171585i
$388$	−34.9099	−	11.3429i	−1.77228	−	0.575849i
$389$	5.41540	+	16.6669i	0.274571	+	0.845044i	0.989332	+	0.145675i	$0.0465355\pi$
$389$	5.41540	+	16.6669i	0.274571	+	0.845044i	−0.714761	+	0.699369i	$0.753465\pi$
$390$		0			0
$391$	−11.5123	+	35.4312i	−0.582202	+	1.79183i
$392$	−10.8063	+	14.8736i	−0.545802	+	0.751232i
$393$			9.02608i			0.455305i
$394$	28.4444	+	20.6661i	1.43301	+	1.04114i
$395$		0			0
$396$	−8.36221	+	6.07550i	−0.420217	+	0.305305i
$397$	−15.8805	−	21.8577i	−0.797021	−	1.09701i	−0.993198	−	0.116437i	$-0.962853\pi$
$397$	−15.8805	−	21.8577i	−0.797021	−	1.09701i	0.196177	−	0.980569i	$-0.437147\pi$
$398$	25.3204	−	8.22709i	1.26920	−	0.412387i
$399$	−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	$0.630637\pi$
$402$	−22.4505	+	7.29462i	−1.11973	+	0.363823i
$403$	0.460953	+	0.634447i	0.0229617	+	0.0316041i
$404$	21.8460	−	15.8721i	1.08688	−	0.789665i
$405$		0			0
$406$	−16.9256	−	12.2971i	−0.840002	−	0.610297i
$407$		−	15.3578i		−	0.761258i
$408$	−14.3120	+	19.6988i	−0.708550	+	0.975235i
$409$	9.57834	−	29.4791i	0.473618	−	1.45765i	−0.374193	−	0.927351i	$-0.622080\pi$
$409$	9.57834	−	29.4791i	0.473618	−	1.45765i	0.847812	−	0.530297i	$-0.177920\pi$
$410$		0			0
$411$	6.07669	+	18.7021i	0.299741	+	0.922508i
$412$	10.0145	+	3.25392i	0.493381	+	0.160309i
$413$	−23.5397	−	7.64852i	−1.15831	−	0.376359i
$414$	3.98833	+	12.2748i	0.196016	+	0.603275i
$415$		0			0
$416$	2.27573	−	7.00398i	0.111577	−	0.343398i
$417$	−6.84887	+	9.42666i	−0.335391	+	0.461626i
$418$		−	20.3236i		−	0.994061i
$419$	20.9660	+	15.2327i	1.02425	+	0.744164i	0.967151	−	0.254204i	$-0.0818135\pi$
$419$	20.9660	+	15.2327i	1.02425	+	0.744164i	0.0571034	+	0.998368i	$0.481814\pi$
$420$		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	$0.330503\pi$
$422$	10.4226	+	14.3454i	0.507362	+	0.698324i
$423$	7.12511	−	2.31509i	0.346434	−	0.112563i
$424$	−13.3109			−0.646436
$425$		0			0
$426$	−1.71282			−0.0829863
$427$	−21.3163	+	6.92607i	−1.03157	+	0.335176i
$428$	14.6589	+	20.1762i	0.708563	+	0.975254i
$429$	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	$0.374108\pi$
$432$			1.38270i			0.0665251i
$433$	5.93423	−	8.16776i	0.285181	−	0.392518i	−0.642261	−	0.766486i	$-0.722003\pi$
$433$	5.93423	−	8.16776i	0.285181	−	0.392518i	0.927441	+	0.373969i	$0.122003\pi$
$434$	−1.05750	+	3.25466i	−0.0507618	+	0.156229i
$435$		0			0
$436$	−14.4956	−	44.6129i	−0.694214	−	2.13657i
$437$	−15.4008	−	5.00402i	−0.736719	−	0.239375i
$438$	8.03243	+	2.60990i	0.383804	+	0.124706i
$439$	−2.19575	−	6.75783i	−0.104798	−	0.322534i	0.884885	−	0.465809i	$-0.154237\pi$
$439$	−2.19575	−	6.75783i	−0.104798	−	0.322534i	−0.989683	+	0.143275i	$0.954237\pi$
$440$		0			0
$441$	1.58326	−	4.87277i	0.0753933	−	0.232037i
$442$	17.5876	−	24.2072i	0.836556	−	1.15142i
$443$			20.6841i			0.982733i	0.870953	+	0.491366i	$0.163502\pi$
$443$			20.6841i			0.982733i	−0.870953	+	0.491366i	$0.836498\pi$
$444$	−14.9481	−	10.8604i	−0.709406	−	0.515414i
$445$		0			0
$446$	14.8258	−	10.7715i	0.702020	−	0.510047i
$447$	4.30858	+	5.93025i	0.203789	+	0.280491i
$448$	39.7213	−	12.9062i	1.87665	−	0.609762i
$449$	−19.4940			−0.919980			−0.459990	−	0.887924i	$-0.652147\pi$
$449$	−19.4940			−0.919980			−0.459990	+	0.887924i	$0.652147\pi$
$450$		0			0
$451$	4.92042			0.231694
$452$	33.6162	−	10.9225i	1.58117	−	0.513754i
$453$	−9.83703	−	13.5395i	−0.462184	−	0.636142i
$454$	−24.4046	+	17.7310i	−1.14536	+	0.832155i
$455$		0			0
$456$	−8.56240	−	6.22095i	−0.400971	−	0.291323i
$457$			4.34194i			0.203107i	0.994830	+	0.101554i	$0.0323813\pi$
$457$			4.34194i			0.203107i	−0.994830	+	0.101554i	$0.967619\pi$
$458$	−20.0404	+	27.5833i	−0.936427	+	1.28888i
$459$	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	$0.811471\pi$
$462$	22.8178	+	7.41395i	1.06158	+	0.344928i
$463$	−8.63436	−	2.80547i	−0.401273	−	0.130381i	0.101426	−	0.994843i	$-0.467659\pi$
$463$	−8.63436	−	2.80547i	−0.401273	−	0.130381i	−0.502699	+	0.864462i	$0.667659\pi$
$464$	−1.09209	−	3.36112i	−0.0506991	−	0.156036i
$465$		0			0
$466$	8.27934	−	25.4812i	0.383533	−	1.18039i
$467$	20.5244	−	28.2494i	0.949755	−	1.30723i	−0.00188168	−	0.999998i	$-0.500599\pi$
$467$	20.5244	−	28.2494i	0.949755	−	1.30723i	0.951636	−	0.307227i	$-0.0994010\pi$
$468$		−	6.61463i		−	0.305762i
$469$	28.2860	+	20.5510i	1.30613	+	0.948956i
$470$		0			0
$471$	6.38019	−	4.63548i	0.293984	−	0.213592i
$472$	−14.9930	−	20.6361i	−0.690109	−	0.949854i
$473$	−30.4502	+	9.89388i	−1.40010	+	0.454921i
$474$	7.22328			0.331776
$475$		0			0
$476$	83.3179			3.81887
$477$	3.52797	−	1.14631i	0.161535	−	0.0524858i
$478$	−9.53530	−	13.1242i	−0.436135	−	0.600288i
$479$	−6.99515	+	5.08228i	−0.319617	+	0.232215i	−0.736012	−	0.676969i	$-0.763293\pi$
$479$	−6.99515	+	5.08228i	−0.319617	+	0.232215i	0.416395	+	0.909184i	$0.363293\pi$
$480$		0			0
$481$	7.95113	+	5.77684i	0.362540	+	0.263401i
$482$			66.8734i			3.04600i
$483$	11.2362	−	15.4654i	0.511267	−	0.703698i
$484$	2.62471	−	8.07802i	0.119305	−	0.367183i
$485$		0			0
$486$	−0.726446	−	2.23577i	−0.0329523	−	0.101417i
$487$	−2.70539	−	0.879035i	−0.122593	−	0.0398329i	0.247078	−	0.968996i	$-0.420530\pi$
$487$	−2.70539	−	0.879035i	−0.122593	−	0.0398329i	−0.369671	+	0.929163i	$0.620530\pi$
$488$	−21.9678	−	7.13776i	−0.994434	−	0.323111i
$489$	−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	$-0.211930\pi$
$492$	3.47953	−	4.78917i	0.156869	−	0.215912i
$493$			17.3437i			0.781121i
$494$	10.5221	+	7.64474i	0.473411	+	0.343953i
$495$		0			0
$496$	−0.467680	+	0.339789i	−0.0209994	+	0.0152570i
$497$	1.49116	+	2.05240i	0.0668876	+	0.0920628i
$498$	22.6154	−	7.34818i	1.01342	−	0.329280i
$499$	−5.85775			−0.262229			−0.131114	−	0.991367i	$-0.541856\pi$
$499$	−5.85775			−0.262229			−0.131114	+	0.991367i	$0.541856\pi$
$500$		0			0
$501$	−5.57767			−0.249192
$502$	−27.5577	+	8.95405i	−1.22996	+	0.399639i
$503$	17.8025	+	24.5030i	0.793773	+	1.09253i	0.993628	+	0.112709i	$0.0359528\pi$
$503$	17.8025	+	24.5030i	0.793773	+	1.09253i	−0.199855	+	0.979825i	$0.564047\pi$
$504$	10.1079	−	7.34383i	0.450243	−	0.327120i
$505$		0			0
$506$	30.6054	+	22.2361i	1.36058	+	0.988517i
$507$		−	9.48157i		−	0.421091i
$508$	21.9154	−	30.1640i	0.972340	−	1.33831i
$509$	−4.67944	+	14.4018i	−0.207413	+	0.638350i	0.792193	+	0.610270i	$0.208939\pi$
$509$	−4.67944	+	14.4018i	−0.207413	+	0.638350i	−0.999606	+	0.0280797i	$0.991061\pi$
$510$		0			0
$511$	−3.86560	−	11.8971i	−0.171004	−	0.526296i
$512$	14.6004	+	4.74395i	0.645251	+	0.209655i
$513$	2.80514	+	0.911446i	0.123850	+	0.0402413i
$514$	−15.1300	−	46.5654i	−0.667356	−	2.05391i
$515$		0			0
$516$	−11.9033	+	36.6345i	−0.524013	+	1.61275i
$517$	12.9073	−	17.7654i	0.567662	−	0.781320i
$518$			42.8877i			1.88438i
$519$	−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	$0.972860\pi$
$522$	3.53175	+	4.86103i	0.154580	+	0.212762i
$523$	36.8987	−	11.9891i	1.61347	−	0.524248i	0.643081	−	0.765798i	$-0.277656\pi$
$523$	36.8987	−	11.9891i	1.61347	−	0.524248i	0.970388	+	0.241550i	$0.0776558\pi$
$524$	31.8296			1.39048
$525$		0			0
$526$	5.25449			0.229107
$527$	2.69813	−	0.876674i	0.117532	−	0.0381885i
$528$	2.38220	+	3.27881i	0.103672	+	0.142692i
$529$	5.77819	−	4.19810i	0.251226	−	0.182526i
$530$		0			0
$531$	5.75093	+	4.17830i	0.249569	+	0.181323i
$532$			36.2155i			1.57014i
$533$	−1.85082	+	2.54743i	−0.0801678	+	0.110341i
$534$	0.208862	−	0.642811i	0.00903835	−	0.0278172i
$535$		0			0
$536$	11.1345	+	34.2685i	0.480938	+	1.48017i
$537$	−5.09787	−	1.65640i	−0.219989	−	0.0714788i
$538$	−43.1585	−	14.0231i	−1.86070	−	0.604577i
$539$	−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	$0.00105778\pi$
$542$	16.5001	−	22.7104i	0.708738	−	0.975494i
$543$			0.327745i			0.0140649i
$544$	−21.5533	−	15.6594i	−0.924091	−	0.671391i
$545$		0			0
$546$	−12.4213	+	9.02462i	−0.531583	+	0.386218i
$547$	23.1134	+	31.8129i	0.988259	+	1.36022i	0.932259	+	0.361790i	$0.117834\pi$
$547$	23.1134	+	31.8129i	0.988259	+	1.36022i	0.0559991	+	0.998431i	$0.482166\pi$
$548$	65.9512	−	21.4288i	2.81730	−	0.915395i
$549$	6.43710			0.274729
$550$		0			0
$551$	−7.53873			−0.321161
$552$	18.7363	−	6.08779i	0.797470	−	0.259114i
$553$	−6.28849	−	8.65537i	−0.267414	−	0.368064i
$554$	49.7272	−	36.1290i	2.11271	−	1.53497i
$555$		0			0
$556$	33.2422	+	24.1519i	1.40978	+	1.02427i
$557$		−	35.3849i		−	1.49931i	−0.661830	−	0.749654i	$-0.730220\pi$
$557$		−	35.3849i		−	1.49931i	0.661830	−	0.749654i	$-0.269780\pi$
$558$	0.577701	−	0.795138i	0.0244561	−	0.0336609i
$559$	6.33154	−	19.4865i	0.267796	−	0.824190i
$560$		0			0
$561$	−6.14619	−	18.9160i	−0.259492	−	0.798636i
$562$	−22.6302	−	7.35299i	−0.954597	−	0.310167i
$563$	14.3025	+	4.64717i	0.602780	+	0.195855i	0.594480	−	0.804111i	$-0.297358\pi$
$563$	14.3025	+	4.64717i	0.602780	+	0.195855i	0.00830000	+	0.999966i	$0.497358\pi$
$564$	−8.16392	−	25.1260i	−0.343763	−	1.05799i
$565$		0			0
$566$	−23.1473	+	71.2401i	−0.972954	+	2.99444i
$567$	−2.04660	+	2.81691i	−0.0859492	+	0.118299i
$568$			2.61445i			0.109700i
$569$	−2.20383	−	1.60118i	−0.0923895	−	0.0671249i	0.540632	−	0.841260i	$-0.318185\pi$
$569$	−2.20383	−	1.60118i	−0.0923895	−	0.0671249i	−0.633021	+	0.774135i	$0.718185\pi$
$570$		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	$0.385088\pi$
$572$	−11.3961	−	15.6854i	−0.476495	−	0.655839i
$573$	−3.30009	+	1.07226i	−0.137863	+	0.0447944i
$574$	−13.7406			−0.573522
$575$		0			0
$576$	−11.9951			−0.499794
$577$	−22.4301	+	7.28797i	−0.933776	+	0.303402i	−0.736106	−	0.676866i	$-0.763338\pi$
$577$	−22.4301	+	7.28797i	−0.933776	+	0.303402i	−0.197670	+	0.980269i	$0.563338\pi$
$578$	−40.1342	−	55.2399i	−1.66936	−	2.29768i
$579$	19.6700	−	14.2911i	0.817455	−	0.593916i
$580$		0			0
$581$	−28.4937	−	20.7019i	−1.18212	−	0.858858i
$582$		−	24.4699i		−	1.01431i
$583$	6.39100	−	8.79646i	0.264688	−	0.364312i
$584$	3.98374	−	12.2607i	0.164849	−	0.507352i
$585$		0			0
$586$	12.0761	+	37.1663i	0.498857	+	1.53532i
$587$	21.5673	+	7.00764i	0.890177	+	0.289236i	0.718177	−	0.695861i	$-0.244977\pi$
$587$	21.5673	+	7.00764i	0.890177	+	0.289236i	0.172000	+	0.985097i	$0.444977\pi$
$588$	−17.1833	−	5.58321i	−0.708629	−	0.230248i
$589$	0.381061	+	1.17279i	0.0157013	+	0.0483238i
$590$		0			0
$591$	−4.62169	+	14.2241i	−0.190111	+	0.585102i
$592$	−4.25837	+	5.86114i	−0.175018	+	0.240891i
$593$		−	8.74287i		−	0.359027i	−0.983756	−	0.179513i	$-0.942548\pi$
$593$		−	8.74287i		−	0.359027i	0.983756	−	0.179513i	$-0.0574523\pi$
$594$	−5.57456	−	4.05015i	−0.228727	−	0.166180i
$595$		0			0
$596$	20.9124	−	15.1938i	0.856607	−	0.622362i
$597$	6.65674	+	9.16222i	0.272442	+	0.374985i
$598$	−23.0245	+	7.48110i	−0.941540	+	0.305925i
$599$	−16.3209			−0.666854			−0.333427	−	0.942776i	$-0.608205\pi$
$599$	−16.3209			−0.666854			−0.333427	+	0.942776i	$0.608205\pi$
$600$		0			0
$601$	36.2713			1.47954			0.739768	−	0.672862i	$-0.234935\pi$
$601$	36.2713			1.47954			0.739768	+	0.672862i	$0.234935\pi$
$602$	85.0344	−	27.6294i	3.46575	−	1.12609i
$603$	−5.90225	−	8.12376i	−0.240358	−	0.330825i
$604$	−47.7457	+	34.6893i	−1.94275	+	1.41149i
$605$		0			0
$606$	14.5634	+	10.5809i	0.591597	+	0.429820i
$607$			16.6820i			0.677102i	0.940948	+	0.338551i	$0.109937\pi$
$607$			16.6820i			0.677102i	−0.940948	+	0.338551i	$0.890063\pi$
$608$	6.80662	−	9.36851i	0.276045	−	0.379943i
$609$	2.75009	−	8.46390i	0.111439	−	0.342975i
$610$		0			0
$611$	4.34252	+	13.3649i	0.175679	+	0.540686i
$612$	−22.7578	−	7.39445i	−0.919929	−	0.298903i
$613$	23.5831	+	7.66260i	0.952511	+	0.309490i	0.743736	−	0.668474i	$-0.233052\pi$
$613$	23.5831	+	7.66260i	0.952511	+	0.309490i	0.208776	+	0.977964i	$0.433052\pi$
$614$	10.2896	+	31.6682i	0.415256	+	1.27803i
$615$		0			0
$616$	11.3167	−	34.8291i	0.455961	−	1.40330i
$617$	−16.4386	+	22.6257i	−0.661791	+	0.910877i	−0.999539	−	0.0303592i	$-0.990335\pi$
$617$	−16.4386	+	22.6257i	−0.661791	+	0.910877i	0.337748	+	0.941237i	$0.390335\pi$
$618$			7.01963i			0.282371i
$619$	22.0608	+	16.0281i	0.886697	+	0.644223i	0.935015	−	0.354609i	$-0.115386\pi$
$619$	22.0608	+	16.0281i	0.886697	+	0.644223i	−0.0483179	+	0.998832i	$0.515386\pi$
$620$		0			0
$621$	−4.44166	+	3.22706i	−0.178238	+	0.129497i
$622$	20.7958	+	28.6230i	0.833836	+	1.14768i
$623$	−0.952088	+	0.309352i	−0.0381446	+	0.0123939i
$624$	−2.59359			−0.103827
$625$		0			0
$626$	−8.40365			−0.335878
$627$	8.22217	−	2.67155i	0.328362	−	0.106691i
$628$	−16.3466	−	22.4991i	−0.652299	−	0.897812i
$629$	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	$-0.618137\pi$
$632$		−	11.0256i		−	0.438575i
$633$	−4.43356	+	6.10228i	−0.176218	+	0.242544i
$634$	−9.28542	+	28.5776i	−0.368771	+	1.13496i
$635$		0			0
$636$	−4.04234	−	12.4410i	−0.160289	−	0.493319i
$637$	9.14008	+	2.96979i	0.362143	+	0.117667i
$638$	16.7498	+	5.44233i	0.663130	+	0.215464i
$639$	−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	$-0.260426\pi$
$642$	−9.77215	+	13.4502i	−0.385676	+	0.530837i
$643$		−	46.6710i		−	1.84052i	−0.391304	−	0.920261i	$-0.627976\pi$
$643$		−	46.6710i		−	1.84052i	0.391304	−	0.920261i	$-0.372024\pi$
$644$	−54.5370	−	39.6235i	−2.14906	−	1.56138i
$645$		0			0
$646$	38.0644	−	27.6554i	1.49763	−	1.08809i
$647$	−7.12775	−	9.81050i	−0.280221	−	0.385691i	0.645586	−	0.763687i	$-0.276613\pi$
$647$	−7.12775	−	9.81050i	−0.280221	−	0.385691i	−0.925807	+	0.377997i	$0.876613\pi$
$648$	−3.41268	+	1.10885i	−0.134063	+	0.0435597i
$649$	20.8359			0.817880
$650$		0			0
$651$	−1.45572			−0.0570542
$652$	−33.3366	+	10.8317i	−1.30556	+	0.424202i
$653$	1.01109	+	1.39164i	0.0395670	+	0.0544593i	0.828342	−	0.560223i	$-0.189284\pi$
$653$	1.01109	+	1.39164i	0.0395670	+	0.0544593i	−0.788775	+	0.614682i	$0.789284\pi$
$654$	25.2989	−	18.3807i	0.989264	−	0.718743i
$655$		0			0
$656$	−1.87783	−	1.36432i	−0.0733168	−	0.0532678i
$657$			3.59269i			0.140164i
$658$	−36.0445	+	49.6110i	−1.40516	+	1.93404i
$659$	−1.69325	+	5.21129i	−0.0659596	+	0.203003i	−0.978604	−	0.205751i	$-0.934036\pi$
$659$	−1.69325	+	5.21129i	−0.0659596	+	0.203003i	0.912645	+	0.408754i	$0.134036\pi$
$660$		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	$0.895063\pi$
$662$	−10.5194	−	3.41796i	−0.408848	−	0.132843i
$663$	12.1052	+	3.93322i	0.470128	+	0.152754i
$664$	−11.2163	−	34.5201i	−0.435276	−	1.33964i
$665$		0			0
$666$	3.80628	−	11.7145i	0.147490	−	0.453929i
$667$	8.24814	−	11.3526i	0.319369	−	0.439574i
$668$			19.6691i			0.761020i
$669$	6.30661	+	4.58202i	0.243827	+	0.177151i
$670$		0			0
$671$	15.2644	−	11.0902i	0.589275	−	0.428133i
$672$	8.03522	+	11.0595i	0.309965	+	0.426631i
$673$	48.8158	−	15.8612i	1.88171	−	0.611405i	0.895716	−	0.444627i	$-0.146664\pi$
$673$	48.8158	−	15.8612i	1.88171	−	0.611405i	0.985995	−	0.166777i	$-0.0533361\pi$
$674$	40.9156			1.57601
$675$		0			0
$676$	−33.4358			−1.28599
$677$	14.3542	−	4.66397i	0.551678	−	0.179251i	−0.0198952	−	0.999802i	$-0.506333\pi$
$677$	14.3542	−	4.66397i	0.551678	−	0.179251i	0.571573	+	0.820551i	$0.306333\pi$
$678$	13.8500	+	19.0629i	0.531906	+	0.732106i
$679$	−29.3213	+	21.3032i	−1.12525	+	0.817540i
$680$		0			0
$681$	−10.3813	−	7.54242i	−0.397811	−	0.289026i
$682$		−	2.88082i		−	0.110312i
$683$	−6.38347	+	8.78610i	−0.244257	+	0.336191i	−0.913490	−	0.406862i	$-0.866623\pi$
$683$	−6.38347	+	8.78610i	−0.244257	+	0.336191i	0.669233	+	0.743053i	$0.266623\pi$
$684$	3.21412	−	9.89205i	0.122895	−	0.378232i
$685$		0			0
$686$	−4.74634	−	14.6077i	−0.181216	−	0.557726i
$687$	−13.7935	−	4.48177i	−0.526253	−	0.170990i
$688$	14.3644	+	4.66726i	0.547636	+	0.177938i
$689$	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	$0.0486438\pi$
$692$	−34.3420	+	47.2677i	−1.30549	+	1.79685i
$693$			10.2058i			0.387686i
$694$	26.6463	+	19.3597i	1.01148	+	0.734883i
$695$		0			0
$696$	7.41988	−	5.39086i	0.281250	−	0.204340i
$697$	6.69548	+	9.21553i	0.253609	+	0.349063i
$698$	−80.3668	+	26.1127i	−3.04193	+	0.988382i
$699$	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	$0.124719\pi$
$702$	4.19374	−	1.36263i	0.158283	−	0.0514291i
$703$	9.08373	+	12.5027i	0.342599	+	0.471548i
$704$	−28.4440	+	20.6658i	−1.07203	+	0.778872i
$705$		0			0
$706$	−16.7401	−	12.1624i	−0.630023	−	0.457739i
$707$		−	26.6623i		−	1.00274i
$708$	14.7343	−	20.2801i	0.553750	−	0.762172i
$709$	−7.65850	+	23.5705i	−0.287621	+	0.885207i	0.697980	+	0.716118i	$0.254083\pi$
$709$	−7.65850	+	23.5705i	−0.287621	+	0.885207i	−0.985601	+	0.169089i	$0.945917\pi$
$710$		0			0
$711$	0.949501	+	2.92226i	0.0356091	+	0.109593i
$712$	−0.981187	−	0.318807i	−0.0367716	−	0.0119478i
$713$	−2.18302	−	0.709306i	−0.0817547	−	0.0265637i
$714$	17.1637	+	52.8244i	0.642334	+	1.97690i
$715$		0			0
$716$	−5.84112	+	17.9771i	−0.218293	+	0.671836i
$717$	4.05614	−	5.58280i	0.151479	−	0.208494i
$718$			14.1746i			0.528992i
$719$	−14.7379	−	10.7077i	−0.549631	−	0.399331i	0.278018	−	0.960576i	$-0.410322\pi$
$719$	−14.7379	−	10.7077i	−0.549631	−	0.399331i	−0.827650	+	0.561245i	$0.810322\pi$
$720$		0			0
$721$	8.41134	−	6.11119i	0.313255	−	0.227593i
$722$	−14.2330	−	19.5900i	−0.529697	−	0.729065i
$723$	−27.0545	+	8.79052i	−1.00617	+	0.326923i
$724$	1.15576			0.0429534
$725$		0			0
$726$	5.66224			0.210145
$727$	15.8540	−	5.15129i	0.587994	−	0.191051i	0.000115145	−	1.00000i	$-0.499963\pi$
$727$	15.8540	−	5.15129i	0.587994	−	0.191051i	0.587878	+	0.808949i	$0.299963\pi$
$728$	13.7752	+	18.9599i	0.510542	+	0.702701i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−59.9657	−	43.5676i	−2.21791	−	1.61141i
$732$		−	22.6998i		−	0.839008i
$733$	11.7935	−	16.2324i	0.435604	−	0.599558i	−0.533624	−	0.845722i	$-0.679170\pi$
$733$	11.7935	−	16.2324i	0.435604	−	0.599558i	0.969228	+	0.246164i	$0.0791702\pi$
$734$	−20.8971	+	64.3147i	−0.771326	+	2.37390i
$735$		0			0
$736$	6.66092	+	20.5002i	0.245525	+	0.755648i
$737$	−27.9922	−	9.09522i	−1.03111	−	0.335027i
$738$	3.75317	+	1.21948i	0.138156	+	0.0448896i
$739$	10.5242	+	32.3903i	0.387140	+	1.19149i	0.934916	+	0.354870i	$0.115475\pi$
$739$	10.5242	+	32.3903i	0.387140	+	1.19149i	−0.547776	+	0.836625i	$0.684525\pi$
$740$		0			0
$741$	−1.70964	+	5.26174i	−0.0628053	+	0.193295i
$742$	−17.8473	+	24.5647i	−0.655196	+	0.901800i
$743$		−	38.5355i		−	1.41373i	−0.707348	−	0.706865i	$-0.750109\pi$
$743$		−	38.5355i		−	1.41373i	0.707348	−	0.706865i	$-0.249891\pi$
$744$	−1.21370	−	0.881804i	−0.0444963	−	0.0323285i
$745$		0			0
$746$	−63.9026	+	46.4280i	−2.33964	+	1.69985i
$747$	5.94559	+	8.18340i	0.217538	+	0.299415i
$748$	−66.7055	+	21.6739i	−2.43900	+	0.792478i
$749$	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	$0.728373\pi$
$752$	−9.85187	+	3.20107i	−0.359261	+	0.116731i
$753$	−7.24494	−	9.97181i	−0.264020	−	0.363393i
$754$	−9.11807	+	6.62466i	−0.332060	+	0.241256i
$755$		0			0
$756$	9.93354	+	7.21714i	0.361279	+	0.262485i
$757$		−	35.0131i		−	1.27257i	−0.771453	−	0.636287i	$-0.780470\pi$
$757$		−	35.0131i		−	1.27257i	0.771453	−	0.636287i	$-0.219530\pi$
$758$	6.40322	−	8.81328i	0.232576	−	0.320113i
$759$	−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	$0.707579\pi$
$762$	23.6389	+	7.68074i	0.856347	+	0.278244i
$763$	−44.0497	−	14.3126i	−1.59471	−	0.518152i
$764$	3.78123	+	11.6374i	0.136800	+	0.421027i
$765$		0			0
$766$	−9.37534	+	28.8543i	−0.338745	+	1.04255i
$767$	−7.83742	+	10.7873i	−0.282993	+	0.389506i
$768$			23.8400i			0.860253i
$769$	1.94014	+	1.40959i	0.0699633	+	0.0508313i	0.622217	−	0.782845i	$-0.286232\pi$
$769$	1.94014	+	1.40959i	0.0699633	+	0.0508313i	−0.552254	+	0.833676i	$0.686232\pi$
$770$		0			0
$771$	16.8497	−	12.2421i	0.606829	−	0.440887i
$772$	−50.3960	−	69.3641i	−1.81379	−	2.49647i
$773$	10.3880	−	3.37526i	0.373630	−	0.121400i	−0.116182	−	0.993228i	$-0.537065\pi$
$773$	10.3880	−	3.37526i	0.373630	−	0.121400i	0.489812	+	0.871828i	$0.337065\pi$
$774$	−25.6788			−0.923004
$775$		0			0
$776$	−37.3508			−1.34082
$777$	−17.3507	+	5.63760i	−0.622454	+	0.202248i
$778$	24.2152	+	33.3293i	0.868156	+	1.19491i
$779$	−4.00568	+	2.91030i	−0.143519	+	0.104272i
$780$		0			0
$781$	−1.72774	−	1.25528i	−0.0618236	−	0.0449174i
$782$			87.5792i			3.13183i
$783$	−1.50234	+	2.06779i	−0.0536893	+	0.0738970i
$784$	−2.18917	+	6.73757i	−0.0781846	+	0.240627i
$785$		0			0
$786$	6.55696	+	20.1802i	0.233879	+	0.719806i
$787$	−11.0060	−	3.57607i	−0.392321	−	0.127473i	0.106212	−	0.994344i	$-0.466128\pi$
$787$	−11.0060	−	3.57607i	−0.392321	−	0.127473i	−0.498533	+	0.866871i	$0.666128\pi$
$788$	50.1599	+	16.2979i	1.78687	+	0.580590i
$789$	0.690704	+	2.12577i	0.0245897	+	0.0756794i
$790$		0			0
$791$	10.7847	−	33.1918i	0.383459	−	1.18017i
$792$	−6.18216	+	8.50901i	−0.219673	+	0.302354i
$793$			12.0744i			0.428773i
$794$	−51.3837	−	37.3324i	−1.82354	−	1.32488i
$795$		0			0
$796$	32.3096	−	23.4743i	1.14518	−	0.832026i
$797$	12.8680	+	17.7113i	0.455808	+	0.627366i	0.973633	−	0.228121i	$-0.0732581\pi$
$797$	12.8680	+	17.7113i	0.455808	+	0.627366i	−0.517825	+	0.855487i	$0.673258\pi$
$798$	−22.9610	+	7.46048i	−0.812810	+	0.264098i
$799$	50.8367			1.79847
$800$		0			0
$801$	0.287512			0.0101587
$802$	−35.7259	+	11.6081i	−1.26153	+	0.409895i
$803$	6.18970	+	8.51940i	0.218430	+	0.300643i
$804$	−28.6476	+	20.8137i	−1.01032	+	0.734043i
$805$		0			0
$806$	1.49148	+	1.08362i	0.0525350	+	0.0381689i
$807$		−	19.3036i		−	0.679520i
$808$	16.1507	−	22.2295i	0.568180	−	0.782033i
$809$	6.65926	−	20.4951i	0.234127	−	0.720570i	−0.763109	−	0.646270i	$-0.776328\pi$
$809$	6.65926	−	20.4951i	0.234127	−	0.720570i	0.997236	−	0.0742994i	$-0.0236721\pi$
$810$		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	$-0.380667\pi$
$812$	−29.8471	−	9.69791i	−1.04743	−	0.340330i
$813$	11.3567	+	3.69001i	0.398297	+	0.129414i
$814$	−11.1566	−	34.3365i	−0.391039	−	1.20349i
$815$		0			0
$816$	−2.89936	+	8.92331i	−0.101498	+	0.312378i
$817$	18.9374	−	26.0651i	0.662535	−	0.911901i
$818$		−	72.8667i		−	2.54772i
$819$	−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	$0.498782\pi$
$822$	27.1722	+	37.3993i	0.947739	+	1.30445i
$823$	−53.2458	+	17.3006i	−1.85603	+	0.603061i	−0.860409	+	0.509604i	$0.829792\pi$
$823$	−53.2458	+	17.3006i	−1.85603	+	0.603061i	−0.995623	+	0.0934576i	$0.970208\pi$
$824$	10.7148			0.373266
$825$		0			0
$826$	−58.1857			−2.02454
$827$	−38.8126	+	12.6110i	−1.34965	+	0.438527i	−0.892574	−	0.450901i	$-0.851103\pi$
$827$	−38.8126	+	12.6110i	−1.34965	+	0.438527i	−0.457074	+	0.889429i	$0.651103\pi$
$828$	11.3799	+	15.6631i	0.395478	+	0.544329i
$829$	0.0994391	−	0.0722468i	0.00345366	−	0.00250923i	−0.586057	−	0.810270i	$-0.699321\pi$
$829$	0.0994391	−	0.0722468i	0.00345366	−	0.00250923i	0.589511	+	0.807761i	$0.299321\pi$
$830$		0			0
$831$	21.1531	+	15.3686i	0.733791	+	0.533131i
$832$		−	22.4997i		−	0.780036i
$833$	20.4353	−	28.1267i	0.708040	−	0.974534i
$834$	−8.46455	+	26.0512i	−0.293103	+	0.902080i
$835$		0			0
$836$	−9.42094	−	28.9947i	−0.325830	−	1.00280i
$837$	0.397622	+	0.129195i	0.0137438	+	0.00446564i
$838$	57.9408	+	18.8261i	2.00153	+	0.650337i
$839$	−4.57603	−	14.0836i	−0.157982	−	0.486219i	0.840469	−	0.541860i	$-0.182280\pi$
$839$	−4.57603	−	14.0836i	−0.157982	−	0.486219i	−0.998451	+	0.0556411i	$0.982280\pi$
$840$		0			0
$841$	−6.94275	+	21.3676i	−0.239405	+	0.736813i
$842$	−5.42552	+	7.46759i	−0.186976	+	0.257350i
$843$		−	10.1219i		−	0.348616i
$844$	21.5191	+	15.6345i	0.740717	+	0.538162i
$845$		0			0
$846$	14.2483	−	10.3520i	0.489867	−	0.355910i
$847$	−4.92947	−	6.78483i	−0.169379	−	0.233130i
$848$	−4.87812	+	1.58500i	−0.167515	+	0.0544290i
$849$	−31.8638			−1.09356
$850$		0			0
$851$	−28.7664			−0.986098
$852$	−2.44359	+	0.793970i	−0.0837160	+	0.0272010i
$853$	−4.27011	−	5.87730i	−0.146206	−	0.201235i	0.729633	−	0.683839i	$-0.239691\pi$
$853$	−4.27011	−	5.87730i	−0.146206	−	0.201235i	−0.875839	+	0.482604i	$0.839691\pi$
$854$	−42.6269	+	30.9702i	−1.45866	+	1.05978i
$855$		0			0
$856$	20.5304	+	14.9162i	0.701715	+	0.509826i
$857$			26.8175i			0.916068i	0.888935	+	0.458034i	$0.151446\pi$
$857$			26.8175i			0.916068i	−0.888935	+	0.458034i	$0.848554\pi$
$858$	7.59706	−	10.4565i	0.259359	−	0.356978i
$859$	6.36691	−	19.5953i	0.217236	−	0.668584i	−0.781751	−	0.623591i	$-0.785673\pi$
$859$	6.36691	−	19.5953i	0.217236	−	0.668584i	0.998987	−	0.0449937i	$-0.0143268\pi$
$860$		0			0
$861$	−1.80621	−	5.55893i	−0.0615554	−	0.189448i
$862$	79.2876	+	25.7621i	2.70055	+	0.877461i
$863$	13.0759	+	4.24862i	0.445109	+	0.144625i	0.522991	−	0.852338i	$-0.324816\pi$
$863$	13.0759	+	4.24862i	0.445109	+	0.144625i	−0.0778827	+	0.996963i	$0.524816\pi$
$864$	−1.21324	−	3.73397i	−0.0412753	−	0.127032i
$865$		0			0
$866$	7.33413	−	22.5721i	0.249224	−	0.767033i
$867$	17.0723	−	23.4981i	0.579807	−	0.798036i
$868$			5.13346i			0.174241i
$869$	7.28622	+	5.29375i	0.247168	+	0.179578i
$870$		0			0
$871$	15.2381	−	11.0711i	0.516324	−	0.375131i
$872$	−28.0563	−	38.6162i	−0.950107	−	1.30771i
$873$	9.89959	−	3.21657i	0.335050	−	0.108864i
$874$	−38.0678			−1.28766
$875$		0			0
$876$	12.6693			0.428055
$877$	20.9641	−	6.81166i	0.707909	−	0.230014i	0.0671357	−	0.997744i	$-0.478614\pi$
$877$	20.9641	−	6.81166i	0.707909	−	0.230014i	0.640773	+	0.767730i	$0.278614\pi$
$878$	−9.81840	−	13.5139i	−0.331355	−	0.456071i
$879$	−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	$0.651341\pi$
$882$		−	12.0446i		−	0.405561i
$883$	−0.941165	+	1.29540i	−0.0316727	+	0.0435937i	−0.824560	−	0.565775i	$-0.808577\pi$
$883$	−0.941165	+	1.29540i	−0.0316727	+	0.0435937i	0.792887	+	0.609369i	$0.208577\pi$
$884$	13.8701	−	42.6879i	0.466503	−	1.43575i
$885$		0			0
$886$	15.0259	+	46.2450i	0.504805	+	1.55363i
$887$	−16.5724	−	5.38470i	−0.556447	−	0.180801i	0.0172750	−	0.999851i	$-0.494501\pi$
$887$	−16.5724	−	5.38470i	−0.556447	−	0.180801i	−0.573722	+	0.819050i	$0.694501\pi$
$888$	−17.8811	−	5.80991i	−0.600049	−	0.194968i
$889$	−11.3762	−	35.0123i	−0.381545	−	1.17427i
$890$		0			0
$891$	0.905762	−	2.78765i	0.0303442	−	0.0933897i
$892$	16.1580	−	22.2396i	0.541011	−	0.744638i
$893$			22.0970i			0.739448i
$894$	13.9410	+	10.1287i	0.466257	+	0.338756i
$895$		0			0
$896$	57.3129	−	41.6403i	1.91469	−	1.39110i
$897$	−6.05314	−	8.33143i	−0.202108	−	0.278178i
$898$	−43.5842	+	14.1614i	−1.45442	+	0.472571i
$899$	−1.06860			−0.0356397
$900$		0			0
$901$	25.1716			0.838588
$902$	11.0009	−	3.57442i	0.366291	−	0.119015i
$903$	22.3556	+	30.7698i	0.743947	+	1.02396i
$904$	29.0976	−	21.1406i	0.967772	−	0.703128i
$905$		0			0
$906$	−31.8291	−	23.1252i	−1.05745	−	0.768283i
$907$			20.8690i			0.692942i	0.938061	+	0.346471i	$0.112620\pi$
$907$			20.8690i			0.692942i	−0.938061	+	0.346471i	$0.887380\pi$
$908$	−26.5976	+	36.6085i	−0.882673	+	1.21489i
$909$	−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	$0.596947\pi$
$912$	−3.87866	−	1.26025i	−0.128435	−	0.0417312i
$913$	28.1977	+	9.16200i	0.933209	+	0.303218i
$914$	3.15418	+	9.70758i	0.104331	+	0.321098i
$915$		0			0
$916$	−15.8045	+	48.6413i	−0.522196	+	1.60715i
$917$	18.4728	−	25.4256i	0.610025	−	0.839627i
$918$		−	15.9519i		−	0.526492i
$919$	−9.05765	−	6.58077i	−0.298784	−	0.217079i	0.428285	−	0.903644i	$-0.359118\pi$
$919$	−9.05765	−	6.58077i	−0.298784	−	0.217079i	−0.727069	+	0.686564i	$0.759118\pi$
$920$		0			0
$921$	−11.4592	+	8.32559i	−0.377593	+	0.274338i
$922$	16.2908	+	22.4224i	0.536510	+	0.738443i
$923$	1.29978	−	0.422325i	0.0427829	−	0.0139010i
$924$	35.9897			1.18397
$925$		0			0
$926$	−21.3425			−0.701357
$927$	−2.83987	+	0.922731i	−0.0932737	+	0.0303065i
$928$	5.89838	+	8.11842i	0.193624	+	0.266500i
$929$	39.0181	−	28.3483i	1.28014	−	0.930077i	0.280584	−	0.959830i	$-0.409472\pi$
$929$	39.0181	−	28.3483i	1.28014	−	0.930077i	0.999557	+	0.0297529i	$0.00947204\pi$
$930$		0			0
$931$	12.2258	+	8.88253i	0.400683	+	0.291113i
$932$		−	40.1906i		−	1.31649i
$933$	−8.84615	+	12.1757i	−0.289610	+	0.398614i
$934$	25.3662	−	78.0690i	0.830006	−	2.55450i
$935$		0			0
$936$	−2.07992	−	6.40133i	−0.0679842	−	0.209234i
$937$	−48.0661	−	15.6176i	−1.57025	−	0.510205i	−0.610728	−	0.791840i	$-0.709123\pi$
$937$	−48.0661	−	15.6176i	−1.57025	−	0.510205i	−0.959522	+	0.281635i	$0.909123\pi$
$938$	78.1702	+	25.3990i	2.55235	+	0.829308i
$939$	−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	$0.886295\pi$
$942$	10.8972	−	14.9987i	0.355051	−	0.488686i
$943$		−	9.21634i		−	0.300125i
$944$	−7.95180	−	5.77732i	−0.258809	−	0.188036i
$945$		0			0
$946$	−60.8924	+	44.2409i	−1.97978	+	1.43840i
$947$	14.4119	+	19.8363i	0.468323	+	0.644592i	0.976209	−	0.216833i	$-0.0695726\pi$
$947$	14.4119	+	19.8363i	0.468323	+	0.644592i	−0.507885	+	0.861425i	$0.669573\pi$
$948$	10.3051	−	3.34832i	0.334693	−	0.108748i
$949$	−6.73897			−0.218756
$950$		0			0
$951$	−12.7820			−0.414484
$952$	80.6311	−	26.1986i	2.61327	−	0.849103i
$953$	−7.64232	−	10.5187i	−0.247559	−	0.340736i	0.667096	−	0.744972i	$-0.267537\pi$
$953$	−7.64232	−	10.5187i	−0.247559	−	0.340736i	−0.914655	+	0.404236i	$0.867537\pi$
$954$	7.05501	−	5.12576i	0.228414	−	0.165953i
$955$		0			0
$956$	−19.6872	−	14.3036i	−0.636729	−	0.462611i
$957$			7.49172i			0.242173i
$958$	−11.9476	+	16.4444i	−0.386008	+	0.531295i
$959$	21.1583	−	65.1187i	0.683239	−	2.10279i
$960$		0			0
$961$	−9.52551	−	29.3165i	−0.307275	−	0.945694i
$962$	21.9735	+	7.13962i	0.708453	+	0.230190i
$963$	−6.72600	−	2.18541i	−0.216742	−	0.0704238i
$964$	30.9989	+	95.4048i	0.998408	+	3.07278i
$965$		0			0
$966$	13.8869	−	42.7395i	0.446804	−	1.37512i
$967$	25.4636	−	35.0476i	0.818854	−	1.12706i	−0.171043	−	0.985264i	$-0.554714\pi$
$967$	25.4636	−	35.0476i	0.818854	−	1.12706i	0.989896	−	0.141792i	$-0.0452864\pi$
$968$		−	8.64284i		−	0.277791i
$969$	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	$0.142857\pi$
$972$	−2.07277	−	2.85292i	−0.0664840	−	0.0915074i
$973$	38.5853	−	12.5371i	1.23699	−	0.401921i
$974$	−6.68721			−0.214272
$975$		0			0
$976$	−8.90056			−0.284900
$977$	−57.6486	+	18.7312i	−1.84434	+	0.599263i	−0.846591	+	0.532244i	$0.821349\pi$
$977$	−57.6486	+	18.7312i	−1.84434	+	0.599263i	−0.997752	+	0.0670189i	$0.978651\pi$
$978$	−13.7348	−	18.9044i	−0.439191	−	0.604495i
$979$	0.681782	−	0.495343i	0.0217898	−	0.0158312i
$980$		0			0
$981$	10.7617	+	7.81882i	0.343594	+	0.249636i
$982$		−	86.5202i		−	2.76097i
$983$	−23.6757	+	32.5868i	−0.755138	+	1.03936i	0.242465	+	0.970160i	$0.422044\pi$
$983$	−23.6757	+	32.5868i	−0.755138	+	1.03936i	−0.997603	+	0.0691986i	$0.977956\pi$
$984$	1.86141	−	5.72884i	0.0593397	−	0.182629i
$985$		0			0
$986$	12.5993	+	38.7766i	0.401243	+	1.23490i
$987$	−24.8088	−	8.06087i	−0.789673	−	0.256580i
$988$	18.5550	+	6.02888i	0.590313	+	0.191804i
$989$	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	$-0.107199\pi$
$992$	0.964821	−	1.32796i	0.0306331	−	0.0421628i
$993$		−	4.70504i		−	0.149310i
$994$	4.82485	+	3.50546i	0.153035	+	0.111186i
$995$		0			0
$996$	28.8580	−	20.9665i	0.914399	−	0.664350i
$997$	15.6220	+	21.5018i	0.494753	+	0.680969i	0.981256	−	0.192710i	$-0.0617277\pi$
$997$	15.6220	+	21.5018i	0.494753	+	0.680969i	−0.486503	+	0.873679i	$0.661728\pi$
$998$	−13.0966	+	4.25534i	−0.414565	+	0.134700i
$999$	5.23959			0.165773

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.1	✓	16	25.21	even	5
75.2.i.a.19.1	yes	16	5.4	even	2
225.2.m.b.19.4		16	15.14	odd	2
225.2.m.b.154.4		16	75.71	odd	10
375.2.g.d.151.4		16	5.2	odd	4
375.2.g.d.226.4		16	25.22	odd	20
375.2.g.e.151.1		16	5.3	odd	4
375.2.g.e.226.1		16	25.3	odd	20
375.2.i.c.274.4		16	25.4	even	10	inner
375.2.i.c.349.4		16	1.1	even	1	trivial
1875.2.a.m.1.2		8	25.23	odd	20
1875.2.a.p.1.7		8	25.2	odd	20
1875.2.b.h.1249.2		16	25.11	even	5
1875.2.b.h.1249.15		16	25.14	even	10
5625.2.a.t.1.2		8	75.2	even	20
5625.2.a.bd.1.7		8	75.23	even	20

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.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.23577 - 0.726446i) q^{2} +(0.587785 + 0.809017i) q^{3} +(2.85292 - 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} -3.48189i q^{7} +(2.10915 - 2.90300i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(2.23577 - 0.726446i) q^{2} +(0.587785 + 0.809017i) q^{3} +(2.85292 - 2.07277i) q^{4} +(1.90186 + 1.38178i) q^{6} -3.48189i q^{7} +(2.10915 - 2.90300i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(0.905762 + 2.78765i) q^{11} +(3.35381 + 1.08972i) q^{12} +(-1.78394 - 0.579638i) q^{13} +(-2.52940 - 7.78470i) q^{14} +(0.427277 - 1.31502i) q^{16} +(-3.98851 + 5.48972i) q^{17} +2.35083i q^{18} +(-2.38620 - 1.73367i) q^{19} +(2.81691 - 2.04660i) q^{21} +(4.05015 + 5.57456i) q^{22} +(5.22149 - 1.69656i) q^{23} +3.58831 q^{24} -4.40956 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-7.21714 - 9.93354i) q^{28} +(2.06779 - 1.50234i) q^{29} +(-0.338237 - 0.245744i) q^{31} +3.92613i q^{32} +(-1.72286 + 2.37132i) q^{33} +(-4.92942 + 15.1712i) q^{34} +(1.08972 + 3.35381i) q^{36} +(-4.98314 - 1.61912i) q^{37} +(-6.59441 - 2.14265i) q^{38} +(-0.579638 - 1.78394i) q^{39} +(0.518744 - 1.59653i) q^{41} +(4.81121 - 6.62206i) q^{42} +10.9233i q^{43} +(8.36221 + 6.07550i) q^{44} +(10.4416 - 7.58626i) q^{46} +(-4.40356 - 6.06098i) q^{47} +(1.31502 - 0.427277i) q^{48} -5.12353 q^{49} -6.78566 q^{51} +(-6.29089 + 2.04403i) q^{52} +(-2.18041 - 3.00107i) q^{53} +(-1.90186 + 1.38178i) q^{54} +(-10.1079 - 7.34383i) q^{56} -2.94950i q^{57} +(3.53175 - 4.86103i) q^{58} +(2.19666 - 6.76062i) q^{59} +(-1.98917 - 6.12204i) q^{61} +(-0.934741 - 0.303716i) q^{62} +(3.31147 + 1.07596i) q^{63} +(3.70667 + 11.4080i) q^{64} +(-2.12929 + 6.55329i) q^{66} +(-5.90225 + 8.12376i) q^{67} +23.9290i q^{68} +(4.44166 + 3.22706i) q^{69} +(-0.589451 + 0.428261i) q^{71} +(2.10915 + 2.90300i) q^{72} +(3.41685 - 1.11020i) q^{73} -12.3174 q^{74} -10.4011 q^{76} +(9.70628 - 3.15376i) q^{77} +(-2.59188 - 3.56741i) q^{78} +(2.48583 - 1.80606i) q^{79} +(-0.809017 - 0.587785i) q^{81} -3.94632i q^{82} +(5.94559 - 8.18340i) q^{83} +(3.79427 - 11.6776i) q^{84} +(7.93517 + 24.4219i) q^{86} +(2.43084 + 0.789827i) q^{87} +(10.0029 + 3.25015i) q^{88} +(-0.0888461 - 0.273440i) q^{89} +(-2.01823 + 6.21148i) q^{91} +(11.3799 - 15.6631i) q^{92} -0.418084i q^{93} +(-14.2483 - 10.3520i) q^{94} +(-3.17630 + 2.30772i) q^{96} +(-6.11828 - 8.42109i) q^{97} +(-11.4551 + 3.72197i) q^{98} -2.93111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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