LMFDB - Embedded newform 507.2.j.i.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$1.56052 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.i.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.33136 + 1.34601i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.62349 - 4.54402i) q^{4} +1.04892i q^{5} +(-2.33136 - 1.34601i) q^{6} +(-0.480608 - 0.277479i) q^{7} +8.74094i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.33136 + 1.34601i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.62349 - 4.54402i) q^{4} +1.04892i q^{5} +(-2.33136 - 1.34601i) q^{6} +(-0.480608 - 0.277479i) q^{7} +8.74094i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.41185 - 2.44540i) q^{10} +(2.52174 - 1.45593i) q^{11} +5.24698 q^{12} +1.49396 q^{14} +(-0.908389 + 0.524459i) q^{15} +(-6.51842 - 11.2902i) q^{16} +(-2.42543 + 4.20096i) q^{17} -2.69202i q^{18} +(-0.652135 - 0.376510i) q^{19} +(4.76630 + 2.75182i) q^{20} -0.554958i q^{21} +(-3.91939 + 6.78858i) q^{22} +(2.88135 + 4.99065i) q^{23} +(-7.56988 + 4.37047i) q^{24} +3.89977 q^{25} -1.00000 q^{27} +(-2.52174 + 1.45593i) q^{28} +(0.955927 + 1.65571i) q^{29} +(1.41185 - 2.44540i) q^{30} +9.51573i q^{31} +(15.2538 + 8.80678i) q^{32} +(2.52174 + 1.45593i) q^{33} -13.0586i q^{34} +(0.291053 - 0.504118i) q^{35} +(2.62349 + 4.54402i) q^{36} +(4.98226 - 2.87651i) q^{37} +2.02715 q^{38} -9.16852 q^{40} +(-4.25379 + 2.45593i) q^{41} +(0.746980 + 1.29381i) q^{42} +(-5.54892 + 9.61101i) q^{43} -15.2784i q^{44} +(-0.908389 - 0.524459i) q^{45} +(-13.4349 - 7.75667i) q^{46} +0.753020i q^{47} +(6.51842 - 11.2902i) q^{48} +(-3.34601 - 5.79546i) q^{49} +(-9.09177 + 5.24914i) q^{50} -4.85086 q^{51} -7.58211 q^{53} +(2.33136 - 1.34601i) q^{54} +(1.52715 + 2.64510i) q^{55} +(2.42543 - 4.20096i) q^{56} -0.753020i q^{57} +(-4.45722 - 2.57338i) q^{58} +(-3.54883 - 2.04892i) q^{59} +5.50365i q^{60} +(1.71164 - 2.96464i) q^{61} +(-12.8083 - 22.1846i) q^{62} +(0.480608 - 0.277479i) q^{63} -21.3424 q^{64} -7.83877 q^{66} +(1.62174 - 0.936313i) q^{67} +(12.7262 + 22.0424i) q^{68} +(-2.88135 + 4.99065i) q^{69} +1.56704i q^{70} +(-9.09643 - 5.25182i) q^{71} +(-7.56988 - 4.37047i) q^{72} +10.4765i q^{73} +(-7.74363 + 13.4124i) q^{74} +(1.94989 + 3.37730i) q^{75} +(-3.42174 + 1.97554i) q^{76} -1.61596 q^{77} +1.33513 q^{79} +(11.8425 - 6.83728i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.61141 - 11.4513i) q^{82} -2.64310i q^{83} +(-2.52174 - 1.45593i) q^{84} +(-4.40646 - 2.54407i) q^{85} -29.8756i q^{86} +(-0.955927 + 1.65571i) q^{87} +(12.7262 + 22.0424i) q^{88} +(8.59696 - 4.96346i) q^{89} +2.82371 q^{90} +30.2368 q^{92} +(-8.24086 + 4.75786i) q^{93} +(-1.01357 - 1.75556i) q^{94} +(0.394928 - 0.684035i) q^{95} +17.6136i q^{96} +(14.7862 + 8.53684i) q^{97} +(15.6015 + 9.00753i) q^{98} +2.91185i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9	$ 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43} + 22 q^{48} - 30 q^{49} - 4 q^{51} - 68 q^{53} - 6 q^{55} + 2 q^{56} + 26 q^{61} - 4 q^{62} + 36 q^{66} + 26 q^{68} - 30 q^{74} - 22 q^{75} - 60 q^{77} + 12 q^{79} - 6 q^{81} - 6 q^{82} - 4 q^{87} + 26 q^{88} + 4 q^{90} + 28 q^{92} - 42 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9 - 2 * q^10 + 44 * q^12 - 20 * q^14 - 22 * q^16 - 2 * q^17 + 18 * q^22 - 44 * q^25 - 12 * q^27 + 4 * q^29 + 2 * q^30 - 8 * q^35 + 22 * q^36 + 12 * q^40 - 10 * q^42 - 30 * q^43 + 22 * q^48 - 30 * q^49 - 4 * q^51 - 68 * q^53 - 6 * q^55 + 2 * q^56 + 26 * q^61 - 4 * q^62 + 36 * q^66 + 26 * q^68 - 30 * q^74 - 22 * q^75 - 60 * q^77 + 12 * q^79 - 6 * q^81 - 6 * q^82 - 4 * q^87 + 26 * q^88 + 4 * q^90 + 28 * q^92 - 42 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.33136	+	1.34601i	−1.64852	+	0.951773i	−0.670859	+	0.741585i	$0.734074\pi$
$2$	−2.33136	+	1.34601i	−1.64852	+	0.951773i	−0.977661	+	0.210188i	$0.932592\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.62349	−	4.54402i	1.31174	−	2.27201i
$5$			1.04892i			0.469090i	0.972105	+	0.234545i	$0.0753600\pi$
$5$			1.04892i			0.469090i	−0.972105	+	0.234545i	$0.924640\pi$
$6$	−2.33136	−	1.34601i	−0.951773	−	0.549507i
$7$	−0.480608	−	0.277479i	−0.181653	−	0.104877i	0.406416	−	0.913688i	$-0.366778\pi$
$7$	−0.480608	−	0.277479i	−0.181653	−	0.104877i	−0.588069	+	0.808811i	$0.700112\pi$
$8$			8.74094i			3.09039i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.41185	−	2.44540i	−0.446467	−	0.773304i
$11$	2.52174	−	1.45593i	0.760333	−	0.438979i	−0.0690822	−	0.997611i	$-0.522007\pi$
$11$	2.52174	−	1.45593i	0.760333	−	0.438979i	0.829415	+	0.558632i	$0.188674\pi$
$12$	5.24698			1.51467
$13$		0			0
$13$		0			0
$14$	1.49396			0.399277
$15$	−0.908389	+	0.524459i	−0.234545	+	0.135415i
$16$	−6.51842	−	11.2902i	−1.62960	−	2.82256i
$17$	−2.42543	+	4.20096i	−0.588253	+	1.01888i	0.406209	+	0.913780i	$0.366851\pi$
$17$	−2.42543	+	4.20096i	−0.588253	+	1.01888i	−0.994461	+	0.105103i	$0.966483\pi$
$18$		−	2.69202i		−	0.634516i
$19$	−0.652135	−	0.376510i	−0.149610	−	0.0863774i	0.423326	−	0.905977i	$-0.360862\pi$
$19$	−0.652135	−	0.376510i	−0.149610	−	0.0863774i	−0.572936	+	0.819600i	$0.694196\pi$
$20$	4.76630	+	2.75182i	1.06578	+	0.615327i
$21$		−	0.554958i		−	0.121102i
$22$	−3.91939	+	6.78858i	−0.835616	+	1.44733i
$23$	2.88135	+	4.99065i	0.600804	+	1.04062i	0.992700	+	0.120613i	$0.0384861\pi$
$23$	2.88135	+	4.99065i	0.600804	+	1.04062i	−0.391896	+	0.920010i	$0.628181\pi$
$24$	−7.56988	+	4.37047i	−1.54519	+	0.892118i
$25$	3.89977			0.779954
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−2.52174	+	1.45593i	−0.476564	+	0.275144i
$29$	0.955927	+	1.65571i	0.177511	+	0.307458i	0.941027	−	0.338330i	$-0.109862\pi$
$29$	0.955927	+	1.65571i	0.177511	+	0.307458i	−0.763516	+	0.645789i	$0.776529\pi$
$30$	1.41185	−	2.44540i	0.257768	−	0.446467i
$31$			9.51573i			1.70908i	0.519389	+	0.854538i	$0.326159\pi$
$31$			9.51573i			1.70908i	−0.519389	+	0.854538i	$0.673841\pi$
$32$	15.2538	+	8.80678i	2.69652	+	1.55683i
$33$	2.52174	+	1.45593i	0.438979	+	0.253444i
$34$		−	13.0586i		−	2.23953i
$35$	0.291053	−	0.504118i	0.0491969	−	0.0852115i
$36$	2.62349	+	4.54402i	0.437248	+	0.757336i
$37$	4.98226	−	2.87651i	0.819079	−	0.472895i	−0.0310199	−	0.999519i	$-0.509876\pi$
$37$	4.98226	−	2.87651i	0.819079	−	0.472895i	0.850099	+	0.526623i	$0.176542\pi$
$38$	2.02715			0.328847
$39$		0			0
$40$	−9.16852			−1.44967
$41$	−4.25379	+	2.45593i	−0.664330	+	0.383551i	−0.793925	−	0.608016i	$-0.791966\pi$
$41$	−4.25379	+	2.45593i	−0.664330	+	0.383551i	0.129595	+	0.991567i	$0.458632\pi$
$42$	0.746980	+	1.29381i	0.115261	+	0.199639i
$43$	−5.54892	+	9.61101i	−0.846202	+	1.46566i	0.0383713	+	0.999264i	$0.487783\pi$
$43$	−5.54892	+	9.61101i	−0.846202	+	1.46566i	−0.884573	+	0.466401i	$0.845550\pi$
$44$		−	15.2784i		−	2.30331i
$45$	−0.908389	−	0.524459i	−0.135415	−	0.0781817i
$46$	−13.4349	−	7.75667i	−1.98087	−	1.14366i
$47$			0.753020i			0.109839i	0.998491	+	0.0549197i	$0.0174903\pi$
$47$			0.753020i			0.109839i	−0.998491	+	0.0549197i	$0.982510\pi$
$48$	6.51842	−	11.2902i	0.940853	−	1.62960i
$49$	−3.34601	−	5.79546i	−0.478002	−	0.827923i
$50$	−9.09177	+	5.24914i	−1.28577	+	0.742340i
$51$	−4.85086			−0.679256
$52$		0			0
$53$	−7.58211			−1.04148			−0.520741	−	0.853715i	$-0.674344\pi$
$53$	−7.58211			−1.04148			−0.520741	+	0.853715i	$0.674344\pi$
$54$	2.33136	−	1.34601i	0.317258	−	0.183169i
$55$	1.52715	+	2.64510i	0.205920	+	0.356665i
$56$	2.42543	−	4.20096i	0.324111	−	0.561377i
$57$		−	0.753020i		−	0.0997400i
$58$	−4.45722	−	2.57338i	−0.585261	−	0.337901i
$59$	−3.54883	−	2.04892i	−0.462018	−	0.266746i	0.250874	−	0.968020i	$-0.419282\pi$
$59$	−3.54883	−	2.04892i	−0.462018	−	0.266746i	−0.712892	+	0.701273i	$0.752615\pi$
$60$			5.50365i			0.710518i
$61$	1.71164	−	2.96464i	0.219153	−	0.379583i	−0.735397	−	0.677637i	$-0.763004\pi$
$61$	1.71164	−	2.96464i	0.219153	−	0.379583i	0.954549	+	0.298054i	$0.0963374\pi$
$62$	−12.8083	−	22.1846i	−1.62665	−	2.81744i
$63$	0.480608	−	0.277479i	0.0605509	−	0.0349591i
$64$	−21.3424			−2.66780
$65$		0			0
$66$	−7.83877			−0.964886
$67$	1.62174	−	0.936313i	0.198127	−	0.114389i	−0.397654	−	0.917535i	$-0.630176\pi$
$67$	1.62174	−	0.936313i	0.198127	−	0.114389i	0.595782	+	0.803146i	$0.296842\pi$
$68$	12.7262	+	22.0424i	1.54327	+	2.67303i
$69$	−2.88135	+	4.99065i	−0.346874	+	0.600804i
$70$			1.56704i			0.187297i
$71$	−9.09643	−	5.25182i	−1.07955	−	0.623277i	−0.148773	−	0.988871i	$-0.547532\pi$
$71$	−9.09643	−	5.25182i	−1.07955	−	0.623277i	−0.930774	+	0.365595i	$0.880866\pi$
$72$	−7.56988	−	4.37047i	−0.892118	−	0.515065i
$73$			10.4765i			1.22618i	0.790012	+	0.613091i	$0.210074\pi$
$73$			10.4765i			1.22618i	−0.790012	+	0.613091i	$0.789926\pi$
$74$	−7.74363	+	13.4124i	−0.900178	+	1.55915i
$75$	1.94989	+	3.37730i	0.225153	+	0.389977i
$76$	−3.42174	+	1.97554i	−0.392500	+	0.226610i
$77$	−1.61596			−0.184155
$78$		0			0
$79$	1.33513			0.150213			0.0751067	−	0.997176i	$-0.476070\pi$
$79$	1.33513			0.150213			0.0751067	+	0.997176i	$0.476070\pi$
$80$	11.8425	−	6.83728i	1.32403	−	0.764431i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.61141	−	11.4513i	0.730108	−	1.26458i
$83$		−	2.64310i		−	0.290118i	−0.989423	−	0.145059i	$-0.953663\pi$
$83$		−	2.64310i		−	0.290118i	0.989423	−	0.145059i	$-0.0463373\pi$
$84$	−2.52174	−	1.45593i	−0.275144	−	0.158855i
$85$	−4.40646	−	2.54407i	−0.477948	−	0.275943i
$86$		−	29.8756i		−	3.22157i
$87$	−0.955927	+	1.65571i	−0.102486	+	0.177511i
$88$	12.7262	+	22.0424i	1.35661	+	2.34972i
$89$	8.59696	−	4.96346i	0.911276	−	0.526126i	0.0304348	−	0.999537i	$-0.490311\pi$
$89$	8.59696	−	4.96346i	0.911276	−	0.526126i	0.880842	+	0.473411i	$0.156977\pi$
$90$	2.82371			0.297645
$91$		0			0
$92$	30.2368			3.15241
$93$	−8.24086	+	4.75786i	−0.854538	+	0.493368i
$94$	−1.01357	−	1.75556i	−0.104542	−	0.181072i
$95$	0.394928	−	0.684035i	0.0405188	−	0.0701806i
$96$			17.6136i			1.79768i
$97$	14.7862	+	8.53684i	1.50131	+	0.866784i	0.999999	+	0.00151988i	$0.000483794\pi$
$97$	14.7862	+	8.53684i	1.50131	+	0.866784i	0.501316	+	0.865264i	$0.332850\pi$
$98$	15.6015	+	9.00753i	1.57599	+	0.909898i
$99$			2.91185i			0.292652i
$100$	10.2310	−	17.7206i	1.02310	−	1.77206i
$101$	3.66152	+	6.34194i	0.364335	+	0.631047i	0.988669	−	0.150111i	$-0.0479630\pi$
$101$	3.66152	+	6.34194i	0.364335	+	0.631047i	−0.624334	+	0.781157i	$0.714630\pi$
$102$	11.3091	−	6.52930i	1.11977	−	0.646497i
$103$	4.21983			0.415792			0.207896	−	0.978151i	$-0.433338\pi$
$103$	4.21983			0.415792			0.207896	+	0.978151i	$0.433338\pi$
$104$		0			0
$105$	0.582105			0.0568077
$106$	17.6766	−	10.2056i	1.71690	−	0.991255i
$107$	−3.19687	−	5.53713i	−0.309053	−	0.535295i	0.669103	−	0.743170i	$-0.266679\pi$
$107$	−3.19687	−	5.53713i	−0.309053	−	0.535295i	−0.978155	+	0.207875i	$0.933345\pi$
$108$	−2.62349	+	4.54402i	−0.252445	+	0.437248i
$109$			3.46011i			0.331418i	0.986175	+	0.165709i	$0.0529913\pi$
$109$			3.46011i			0.331418i	−0.986175	+	0.165709i	$0.947009\pi$
$110$	−7.12066	−	4.11111i	−0.678928	−	0.391979i
$111$	4.98226	+	2.87651i	0.472895	+	0.273026i
$112$			7.23490i			0.683634i
$113$	−4.67845	+	8.10331i	−0.440111	+	0.762295i	−0.997697	−	0.0678240i	$-0.978394\pi$
$113$	−4.67845	+	8.10331i	−0.440111	+	0.762295i	0.557586	+	0.830119i	$0.311728\pi$
$114$	1.01357	+	1.75556i	0.0949299	+	0.164423i
$115$	−5.23478	+	3.02230i	−0.488146	+	0.281831i
$116$	10.0315			0.931398
$117$		0			0
$118$	11.0315			1.01553
$119$	2.33136	−	1.34601i	0.213715	−	0.123389i
$120$	−4.58426	−	7.94017i	−0.418484	−	0.724835i
$121$	−1.26055	+	2.18334i	−0.114596	+	0.198486i
$122$			9.21552i			0.834334i
$123$	−4.25379	−	2.45593i	−0.383551	−	0.221443i
$124$	43.2396	+	24.9644i	3.88303	+	2.24187i
$125$			9.33513i			0.834959i
$126$	−0.746980	+	1.29381i	−0.0665462	+	0.115261i
$127$	−2.24094	−	3.88142i	−0.198851	−	0.344420i	0.749305	−	0.662225i	$-0.230388\pi$
$127$	−2.24094	−	3.88142i	−0.198851	−	0.344420i	−0.948156	+	0.317805i	$0.897054\pi$
$128$	19.2493	−	11.1136i	1.70141	−	0.982310i
$129$	−11.0978			−0.977110
$130$		0			0
$131$	−9.21744			−0.805331			−0.402666	−	0.915347i	$-0.631916\pi$
$131$	−9.21744			−0.805331			−0.402666	+	0.915347i	$0.631916\pi$
$132$	13.2315	−	7.63922i	1.15166	−	0.664909i
$133$	0.208947	+	0.361908i	0.0181180	+	0.0313814i
$134$	−2.52057	+	4.36576i	−0.217744	+	0.377144i
$135$		−	1.04892i		−	0.0902764i
$136$	−36.7204	−	21.2005i	−3.14875	−	1.81793i
$137$	6.46903	+	3.73490i	0.552687	+	0.319094i	0.750205	−	0.661205i	$-0.229955\pi$
$137$	6.46903	+	3.73490i	0.552687	+	0.319094i	−0.197518	+	0.980299i	$0.563288\pi$
$138$		−	15.5133i		−	1.32058i
$139$	8.99880	−	15.5864i	0.763269	−	1.32202i	−0.177889	−	0.984051i	$-0.556927\pi$
$139$	8.99880	−	15.5864i	0.763269	−	1.32202i	0.941157	−	0.337969i	$-0.109740\pi$
$140$	−1.52715	−	2.64510i	−0.129067	−	0.223551i
$141$	−0.652135	+	0.376510i	−0.0549197	+	0.0317079i
$142$	28.2760			2.37287
$143$		0			0
$144$	13.0368			1.08640
$145$	−1.73671	+	1.00269i	−0.144226	+	0.0832687i
$146$	−14.1015	−	24.4245i	−1.16705	−	2.02138i
$147$	3.34601	−	5.79546i	0.275974	−	0.478002i
$148$		−	30.1860i		−	2.48127i
$149$	13.2806	+	7.66756i	1.08799	+	0.628151i	0.933041	−	0.359771i	$-0.117145\pi$
$149$	13.2806	+	7.66756i	1.08799	+	0.628151i	0.154949	+	0.987922i	$0.450479\pi$
$150$	−9.09177	−	5.24914i	−0.742340	−	0.428590i
$151$			2.53079i			0.205953i	0.994684	+	0.102977i	$0.0328367\pi$
$151$			2.53079i			0.205953i	−0.994684	+	0.102977i	$0.967163\pi$
$152$	3.29105	−	5.70027i	0.266940	−	0.462353i
$153$	−2.42543	−	4.20096i	−0.196084	−	0.339628i
$154$	3.76738	−	2.17510i	0.303584	−	0.175274i
$155$	−9.98121			−0.801710
$156$		0			0
$157$	17.2392			1.37584			0.687919	−	0.725787i	$-0.258524\pi$
$157$	17.2392			1.37584			0.687919	+	0.725787i	$0.258524\pi$
$158$	−3.11266	+	1.79709i	−0.247630	+	0.142969i
$159$	−3.79105	−	6.56630i	−0.300650	−	0.520741i
$160$	−9.23759	+	16.0000i	−0.730295	+	1.26491i
$161$		−	3.19806i		−	0.252043i
$162$	2.33136	+	1.34601i	0.183169	+	0.105753i
$163$	−13.6027	−	7.85354i	−1.06545	−	0.615137i	−0.138514	−	0.990360i	$-0.544233\pi$
$163$	−13.6027	−	7.85354i	−1.06545	−	0.615137i	−0.926934	+	0.375223i	$0.877566\pi$
$164$			25.7724i			2.01249i
$165$	−1.52715	+	2.64510i	−0.118888	+	0.205920i
$166$	3.55765	+	6.16202i	0.276127	+	0.478266i
$167$	4.67318	−	2.69806i	0.361622	−	0.208782i	−0.308170	−	0.951331i	$-0.599717\pi$
$167$	4.67318	−	2.69806i	0.361622	−	0.208782i	0.669792	+	0.742549i	$0.266383\pi$
$168$	4.85086			0.374252
$169$		0			0
$170$	13.6974			1.05054
$171$	0.652135	−	0.376510i	0.0498700	−	0.0287925i
$172$	29.1151	+	50.4288i	2.22000	+	3.84516i
$173$	11.9710	−	20.7344i	0.910138	−	1.57640i	0.0962694	−	0.995355i	$-0.469309\pi$
$173$	11.9710	−	20.7344i	0.910138	−	1.57640i	0.813868	−	0.581049i	$-0.197358\pi$
$174$		−	5.14675i		−	0.390174i
$175$	−1.87426	−	1.08211i	−0.141681	−	0.0817995i
$176$	−32.8755	−	18.9807i	−2.47808	−	1.43072i
$177$		−	4.09783i		−	0.308012i
$178$	−13.3617	+	23.1432i	−1.00150	+	1.73466i
$179$	9.20440	+	15.9425i	0.687969	+	1.19160i	0.972494	+	0.232929i	$0.0748309\pi$
$179$	9.20440	+	15.9425i	0.687969	+	1.19160i	−0.284525	+	0.958669i	$0.591836\pi$
$180$	−4.76630	+	2.75182i	−0.355259	+	0.205109i
$181$	3.63342			0.270070			0.135035	−	0.990841i	$-0.456885\pi$
$181$	3.63342			0.270070			0.135035	+	0.990841i	$0.456885\pi$
$182$		0			0
$183$	3.42327			0.253056
$184$	−43.6230	+	25.1857i	−3.21593	+	1.85672i
$185$	3.01722	+	5.22598i	0.221831	+	0.384222i
$186$	12.8083	−	22.1846i	0.939148	−	1.62665i
$187$			14.1250i			1.03292i
$188$	3.42174	+	1.97554i	0.249556	+	0.144081i
$189$	0.480608	+	0.277479i	0.0349591	+	0.0201836i
$190$			2.12631i			0.154259i
$191$	10.5891	−	18.3409i	0.766201	−	1.32710i	−0.173409	−	0.984850i	$-0.555478\pi$
$191$	10.5891	−	18.3409i	0.766201	−	1.32710i	0.939609	−	0.342249i	$-0.111189\pi$
$192$	−10.6712	−	18.4831i	−0.770128	−	1.33390i
$193$	−15.2517	+	8.80559i	−1.09784	+	0.633840i	−0.935654	−	0.352920i	$-0.885189\pi$
$193$	−15.2517	+	8.80559i	−1.09784	+	0.633840i	−0.162189	+	0.986760i	$0.551856\pi$
$194$	−45.9627			−3.29993
$195$		0			0
$196$	−35.1129			−2.50806
$197$	4.03783	−	2.33124i	0.287683	−	0.166094i	−0.349213	−	0.937043i	$-0.613551\pi$
$197$	4.03783	−	2.33124i	0.287683	−	0.166094i	0.636897	+	0.770949i	$0.280218\pi$
$198$	−3.91939	−	6.78858i	−0.278539	−	0.482443i
$199$	7.51842	−	13.0223i	0.532967	−	0.923125i	−0.466292	−	0.884631i	$-0.654410\pi$
$199$	7.51842	−	13.0223i	0.532967	−	0.923125i	0.999259	−	0.0384944i	$-0.0122562\pi$
$200$			34.0877i			2.41036i
$201$	1.62174	+	0.936313i	0.114389	+	0.0660424i
$202$	−17.0726	−	9.85690i	−1.20123	−	0.693529i
$203$		−	1.06100i		−	0.0744675i
$204$	−12.7262	+	22.0424i	−0.891010	+	1.54327i
$205$	−2.57606	−	4.46187i	−0.179920	−	0.311631i
$206$	−9.83794	+	5.67994i	−0.685442	+	0.395740i
$207$	−5.76271			−0.400536
$208$		0			0
$209$	−2.19269			−0.151671
$210$	−1.35710	+	0.783520i	−0.0936485	+	0.0540680i
$211$	0.230054	+	0.398465i	0.0158375	+	0.0274314i	0.873836	−	0.486222i	$-0.161625\pi$
$211$	0.230054	+	0.398465i	0.0158375	+	0.0274314i	−0.857998	+	0.513653i	$0.828292\pi$
$212$	−19.8916	+	34.4532i	−1.36616	+	2.36626i
$213$		−	10.5036i		−	0.719698i
$214$	14.9061	+	8.60603i	1.01896	+	0.588296i
$215$	−10.0812	−	5.82036i	−0.687529	−	0.396945i
$216$		−	8.74094i		−	0.594746i
$217$	2.64042	−	4.57333i	0.179243	−	0.310458i
$218$	−4.65734	−	8.06675i	−0.315435	−	0.546349i
$219$	−9.07292	+	5.23825i	−0.613091	+	0.353968i
$220$	16.0258			1.08046
$221$		0			0
$222$	−15.4873			−1.03944
$223$	14.1597	−	8.17510i	0.948202	−	0.547445i	0.0556803	−	0.998449i	$-0.482267\pi$
$223$	14.1597	−	8.17510i	0.948202	−	0.547445i	0.892522	+	0.451004i	$0.148934\pi$
$224$	−4.88740	−	8.46522i	−0.326553	−	0.565606i
$225$	−1.94989	+	3.37730i	−0.129992	+	0.225153i
$226$		−	25.1890i		−	1.67555i
$227$	5.68142	+	3.28017i	0.377089	+	0.217712i	0.676551	−	0.736396i	$-0.263474\pi$
$227$	5.68142	+	3.28017i	0.377089	+	0.217712i	−0.299462	+	0.954108i	$0.596807\pi$
$228$	−3.42174	−	1.97554i	−0.226610	−	0.130833i
$229$		−	3.95539i		−	0.261380i	−0.991423	−	0.130690i	$-0.958281\pi$
$229$		−	3.95539i		−	0.261380i	0.991423	−	0.130690i	$-0.0417192\pi$
$230$	8.13610	−	14.0921i	0.536479	−	0.929209i
$231$	−0.807979	−	1.39946i	−0.0531611	−	0.0920777i
$232$	−14.4725	+	8.35570i	−0.950166	+	0.548579i
$233$	−8.35690			−0.547478			−0.273739	−	0.961804i	$-0.588261\pi$
$233$	−8.35690			−0.547478			−0.273739	+	0.961804i	$0.588261\pi$
$234$		0			0
$235$	−0.789856			−0.0515245
$236$	−18.6206	+	10.7506i	−1.21210	+	0.699806i
$237$	0.667563	+	1.15625i	0.0433629	+	0.0751067i
$238$	−3.62349	+	6.27607i	−0.234876	+	0.406817i
$239$		−	20.1008i		−	1.30021i	−0.759843	−	0.650107i	$-0.774724\pi$
$239$		−	20.1008i		−	1.30021i	0.759843	−	0.650107i	$-0.225276\pi$
$240$	11.8425	+	6.83728i	0.764431	+	0.441345i
$241$	16.4655	+	9.50634i	1.06063	+	0.612357i	0.925607	−	0.378485i	$-0.123555\pi$
$241$	16.4655	+	9.50634i	1.06063	+	0.612357i	0.135026	+	0.990842i	$0.456888\pi$
$242$		−	6.78687i		−	0.436277i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−8.98092	−	15.5554i	−0.574944	−	0.995833i
$245$	6.07896	−	3.50969i	0.388370	−	0.224226i
$246$	13.2228			0.843056
$247$		0			0
$248$	−83.1764			−5.28171
$249$	2.28900	−	1.32155i	0.145059	−	0.0837500i
$250$	−12.5652	−	21.7635i	−0.794692	−	1.37645i
$251$	−0.381887	+	0.661448i	−0.0241045	+	0.0417502i	−0.877826	−	0.478980i	$-0.841007\pi$
$251$	−0.381887	+	0.661448i	−0.0241045	+	0.0417502i	0.853722	+	0.520730i	$0.174340\pi$
$252$		−	2.91185i		−	0.183430i
$253$	14.5321	+	8.39008i	0.913622	+	0.527480i
$254$	10.4489	+	6.03266i	0.655620	+	0.378522i
$255$		−	5.08815i		−	0.318632i
$256$	−8.57553	+	14.8533i	−0.535971	+	0.928329i
$257$	−6.54556	−	11.3373i	−0.408301	−	0.707198i	0.586398	−	0.810023i	$-0.300545\pi$
$257$	−6.54556	−	11.3373i	−0.408301	−	0.707198i	−0.994700	+	0.102825i	$0.967212\pi$
$258$	25.8730	−	14.9378i	1.61078	−	0.929987i
$259$	−3.19269			−0.198384
$260$		0			0
$261$	−1.91185			−0.118341
$262$	21.4892	−	12.4068i	1.32760	−	0.766493i
$263$	−9.18867	−	15.9152i	−0.566598	−	0.981376i	−0.996899	−	0.0786906i	$-0.974926\pi$
$263$	−9.18867	−	15.9152i	−0.566598	−	0.981376i	0.430301	−	0.902685i	$-0.358407\pi$
$264$	−12.7262	+	22.0424i	−0.783242	+	1.35661i
$265$		−	7.95300i		−	0.488549i
$266$	−0.974263	−	0.562491i	−0.0597359	−	0.0344885i
$267$	8.59696	+	4.96346i	0.526126	+	0.303759i
$268$		−	9.82563i		−	0.600196i
$269$	−11.8312	+	20.4923i	−0.721363	+	1.24944i	0.239090	+	0.970997i	$0.423151\pi$
$269$	−11.8312	+	20.4923i	−0.721363	+	1.24944i	−0.960453	+	0.278441i	$0.910182\pi$
$270$	1.41185	+	2.44540i	0.0859227	+	0.148822i
$271$	−17.1066	+	9.87651i	−1.03915	+	0.599955i	−0.919593	−	0.392872i	$-0.871482\pi$
$271$	−17.1066	+	9.87651i	−1.03915	+	0.599955i	−0.119560	+	0.992827i	$0.538148\pi$
$272$	63.2398			3.83448
$273$		0			0
$274$	−20.1089			−1.21482
$275$	9.83421	−	5.67778i	0.593025	−	0.342383i
$276$	15.1184	+	26.1859i	0.910021	+	1.57620i
$277$	0.888887	−	1.53960i	0.0534081	−	0.0925055i	−0.838085	−	0.545539i	$-0.816325\pi$
$277$	0.888887	−	1.53960i	0.0534081	−	0.0925055i	0.891493	+	0.453034i	$0.149658\pi$
$278$			48.4499i			2.90583i
$279$	−8.24086	−	4.75786i	−0.493368	−	0.284846i
$280$	4.40646	+	2.54407i	0.263337	+	0.152037i
$281$			1.62133i			0.0967207i	0.998830	+	0.0483603i	$0.0153996\pi$
$281$			1.62133i			0.0967207i	−0.998830	+	0.0483603i	$0.984600\pi$
$282$	1.01357	−	1.75556i	0.0603574	−	0.104542i
$283$	2.49180	+	4.31593i	0.148122	+	0.256555i	0.930533	−	0.366207i	$-0.119344\pi$
$283$	2.49180	+	4.31593i	0.148122	+	0.256555i	−0.782411	+	0.622762i	$0.786010\pi$
$284$	−47.7288	+	27.5562i	−2.83218	+	1.63516i
$285$	0.789856			0.0467870
$286$		0			0
$287$	2.72587			0.160903
$288$	−15.2538	+	8.80678i	−0.898838	+	0.518945i
$289$	−3.26540	−	5.65583i	−0.192082	−	0.332696i
$290$	2.69926	−	4.67525i	0.158506	−	0.274540i
$291$			17.0737i			1.00088i
$292$	47.6054	+	27.4850i	2.78590	+	1.60844i
$293$	0.0621395	+	0.0358763i	0.00363023	+	0.00209591i	0.501814	−	0.864976i	$-0.332666\pi$
$293$	0.0621395	+	0.0358763i	0.00363023	+	0.00209591i	−0.498184	+	0.867071i	$0.666000\pi$
$294$			18.0151i			1.05066i
$295$	2.14914	−	3.72243i	0.125128	−	0.216728i
$296$	25.1434	+	43.5496i	1.46143	+	2.53127i
$297$	−2.52174	+	1.45593i	−0.146326	+	0.0844815i
$298$	−41.2825			−2.39143
$299$		0			0
$300$	20.4620			1.18138
$301$	5.33371	−	3.07942i	0.307430	−	0.177495i
$302$	−3.40648	−	5.90019i	−0.196021	−	0.339518i
$303$	−3.66152	+	6.34194i	−0.210349	+	0.364335i
$304$			9.81700i			0.563044i
$305$	3.10966	+	1.79536i	0.178059	+	0.102802i
$306$	11.3091	+	6.52930i	0.646497	+	0.373255i
$307$		−	5.19806i		−	0.296669i	−0.988937	−	0.148335i	$-0.952609\pi$
$307$		−	5.19806i		−	0.296669i	0.988937	−	0.148335i	$-0.0473912\pi$
$308$	−4.23945	+	7.34294i	−0.241565	+	0.418403i
$309$	2.10992	+	3.65448i	0.120029	+	0.207896i
$310$	23.2698	−	13.4348i	1.32164	−	0.763047i
$311$	22.5429			1.27829			0.639145	−	0.769087i	$-0.279289\pi$
$311$	22.5429			1.27829			0.639145	+	0.769087i	$0.279289\pi$
$312$		0			0
$313$	22.6612			1.28088			0.640442	−	0.768006i	$-0.278751\pi$
$313$	22.6612			1.28088			0.640442	+	0.768006i	$0.278751\pi$
$314$	−40.1908	+	23.2042i	−2.26810	+	1.30949i
$315$	0.291053	+	0.504118i	0.0163990	+	0.0284038i
$316$	3.50269	−	6.06683i	0.197042	−	0.341286i
$317$		−	26.3424i		−	1.47954i	−0.672861	−	0.739769i	$-0.734935\pi$
$317$		−	26.3424i		−	1.47954i	0.672861	−	0.739769i	$-0.265065\pi$
$318$	17.6766	+	10.2056i	0.991255	+	0.572301i
$319$	4.82120	+	2.78352i	0.269935	+	0.155847i
$320$		−	22.3864i		−	1.25144i
$321$	3.19687	−	5.53713i	0.178432	−	0.309053i
$322$	4.30463	+	7.45583i	0.239887	+	0.415497i
$323$	3.16341	−	1.82640i	0.176017	−	0.101623i
$324$	−5.24698			−0.291499
$325$		0			0
$326$	42.2838			2.34188
$327$	−2.99654	+	1.73005i	−0.165709	+	0.0956722i
$328$	−21.4671	−	37.1821i	−1.18532	−	2.05304i
$329$	0.208947	−	0.361908i	0.0115196	−	0.0199526i
$330$		−	8.22223i		−	0.452619i
$331$	−9.72505	−	5.61476i	−0.534537	−	0.308615i	0.208325	−	0.978060i	$-0.433199\pi$
$331$	−9.72505	−	5.61476i	−0.534537	−	0.308615i	−0.742862	+	0.669445i	$0.766532\pi$
$332$	−12.0103	−	6.93416i	−0.659151	−	0.380561i
$333$			5.75302i			0.315264i
$334$	−7.26324	+	12.5803i	−0.397427	+	0.688364i
$335$	0.982115	+	1.70107i	0.0536587	+	0.0929395i
$336$	−6.26561	+	3.61745i	−0.341817	+	0.197348i
$337$	−2.30798			−0.125724			−0.0628618	−	0.998022i	$-0.520023\pi$
$337$	−2.30798			−0.125724			−0.0628618	+	0.998022i	$0.520023\pi$
$338$		0			0
$339$	−9.35690			−0.508197
$340$	−23.1206	+	13.3487i	−1.25389	+	0.723935i
$341$	13.8542	+	23.9962i	0.750247	+	1.29947i
$342$	−1.01357	+	1.75556i	−0.0548078	+	0.0949299i
$343$			7.59850i			0.410280i
$344$	−84.0092	−	48.5027i	−4.52947	−	2.61509i
$345$	−5.23478	−	3.02230i	−0.281831	−	0.162715i
$346$			64.4523i			3.46498i
$347$	4.56853	−	7.91293i	0.245252	−	0.424788i	−0.716951	−	0.697124i	$-0.754463\pi$
$347$	4.56853	−	7.91293i	0.245252	−	0.424788i	0.962202	+	0.272336i	$0.0877961\pi$
$348$	5.01573	+	8.68750i	0.268871	+	0.465699i
$349$	20.7637	−	11.9879i	1.11145	−	0.641699i	0.172249	−	0.985053i	$-0.444897\pi$
$349$	20.7637	−	11.9879i	1.11145	−	0.641699i	0.939206	+	0.343355i	$0.111563\pi$
$350$	5.82610			0.311418
$351$		0			0
$352$	51.2881			2.73367
$353$	23.4900	−	13.5620i	1.25025	−	0.721830i	0.279088	−	0.960265i	$-0.409968\pi$
$353$	23.4900	−	13.5620i	1.25025	−	0.721830i	0.971158	+	0.238435i	$0.0766345\pi$
$354$	5.51573	+	9.55352i	0.293158	+	0.507764i
$355$	5.50873	−	9.54140i	0.292373	−	0.506405i
$356$		−	52.0863i		−	2.76057i
$357$	2.33136	+	1.34601i	0.123389	+	0.0712384i
$358$	−42.9175	−	24.7784i	−2.26826	−	1.30958i
$359$		−	26.0790i		−	1.37640i	−0.725521	−	0.688200i	$-0.758401\pi$
$359$		−	26.0790i		−	1.37640i	0.725521	−	0.688200i	$-0.241599\pi$
$360$	4.58426	−	7.94017i	0.241612	−	0.418484i
$361$	−9.21648	−	15.9634i	−0.485078	−	0.840180i
$362$	−8.47080	+	4.89062i	−0.445215	+	0.257045i
$363$	−2.52111			−0.132324
$364$		0			0
$365$	−10.9890			−0.575190
$366$	−7.98088	+	4.60776i	−0.417167	+	0.240851i
$367$	−4.78717	−	8.29162i	−0.249888	−	0.432819i	0.713606	−	0.700547i	$-0.247061\pi$
$367$	−4.78717	−	8.29162i	−0.249888	−	0.432819i	−0.963495	+	0.267728i	$0.913727\pi$
$368$	37.5637	−	65.0623i	1.95815	−	3.39161i
$369$		−	4.91185i		−	0.255701i
$370$	−14.0685	−	8.12242i	−0.731384	−	0.422265i
$371$	3.64402	+	2.10388i	0.189188	+	0.109228i
$372$			49.9288i			2.58869i
$373$	−14.0749	+	24.3784i	−0.728769	+	1.26227i	0.228635	+	0.973512i	$0.426574\pi$
$373$	−14.0749	+	24.3784i	−0.728769	+	1.26227i	−0.957404	+	0.288753i	$0.906759\pi$
$374$	−19.0124	−	32.9304i	−0.983107	−	1.70279i
$375$	−8.08446	+	4.66756i	−0.417480	+	0.241032i
$376$	−6.58211			−0.339446
$377$		0			0
$378$	−1.49396			−0.0768410
$379$	−13.8967	+	8.02326i	−0.713825	+	0.412127i	−0.812476	−	0.582995i	$-0.801881\pi$
$379$	−13.8967	+	8.02326i	−0.713825	+	0.412127i	0.0986504	+	0.995122i	$0.468547\pi$
$380$	−2.07218	−	3.58912i	−0.106301	−	0.184118i
$381$	2.24094	−	3.88142i	0.114807	−	0.198851i
$382$			57.0122i			2.91700i
$383$	−21.3186	−	12.3083i	−1.08933	−	0.628923i	−0.155930	−	0.987768i	$-0.549837\pi$
$383$	−21.3186	−	12.3083i	−1.08933	−	0.628923i	−0.933397	+	0.358845i	$0.883171\pi$
$384$	19.2493	+	11.1136i	0.982310	+	0.567137i
$385$		−	1.69501i		−	0.0863855i
$386$	23.7048	−	41.0580i	1.20654	−	2.08980i
$387$	−5.54892	−	9.61101i	−0.282067	−	0.488555i
$388$	77.5831	−	44.7926i	3.93868	−	2.27400i
$389$	17.2198			0.873080			0.436540	−	0.899685i	$-0.356204\pi$
$389$	17.2198			0.873080			0.436540	+	0.899685i	$0.356204\pi$
$390$		0			0
$391$	−27.9541			−1.41370
$392$	50.6578	−	29.2473i	2.55860	−	1.47721i
$393$	−4.60872	−	7.98254i	−0.232479	−	0.402666i
$394$	−6.27575	+	10.8699i	−0.316168	+	0.547619i
$395$			1.40044i			0.0704636i
$396$	13.2315	+	7.63922i	0.664909	+	0.383885i
$397$	1.76602	+	1.01961i	0.0886342	+	0.0511730i	0.543662	−	0.839304i	$-0.317037\pi$
$397$	1.76602	+	1.01961i	0.0886342	+	0.0511730i	−0.455028	+	0.890477i	$0.650371\pi$
$398$			40.4795i			2.02905i
$399$	−0.208947	+	0.361908i	−0.0104605	+	0.0181180i
$400$	−25.4203	−	44.0293i	−1.27102	−	2.20147i
$401$	−1.26564	+	0.730718i	−0.0632031	+	0.0364903i	−0.531269	−	0.847203i	$-0.678284\pi$
$401$	−1.26564	+	0.730718i	−0.0632031	+	0.0364903i	0.468065	+	0.883694i	$0.344951\pi$
$402$	−5.04115			−0.251430
$403$		0			0
$404$	38.4239			1.91166
$405$	0.908389	−	0.524459i	0.0451382	−	0.0260606i
$406$	1.42812	+	2.47357i	0.0708762	+	0.122761i
$407$	8.37598	−	14.5076i	0.415182	−	0.719116i
$408$		−	42.4010i		−	2.09916i
$409$	−25.9279	−	14.9695i	−1.28205	−	0.740194i	−0.304830	−	0.952407i	$-0.598600\pi$
$409$	−25.9279	−	14.9695i	−1.28205	−	0.740194i	−0.977224	+	0.212213i	$0.931933\pi$
$410$	12.0115	+	6.93482i	0.593204	+	0.342486i
$411$			7.46980i			0.368458i
$412$	11.0707	−	19.1750i	0.545414	−	0.944684i
$413$	1.13706	+	1.96945i	0.0559512	+	0.0969104i
$414$	13.4349	−	7.75667i	0.660291	−	0.381219i
$415$	2.77240			0.136092
$416$		0			0
$417$	17.9976			0.881347
$418$	5.11194	−	2.95138i	0.250033	−	0.144357i
$419$	−3.32371	−	5.75683i	−0.162374	−	0.281240i	0.773346	−	0.633984i	$-0.218582\pi$
$419$	−3.32371	−	5.75683i	−0.162374	−	0.281240i	−0.935720	+	0.352745i	$0.885248\pi$
$420$	1.52715	−	2.64510i	0.0745171	−	0.129067i
$421$		−	13.5646i		−	0.661100i	−0.943788	−	0.330550i	$-0.892766\pi$
$421$		−	13.5646i		−	0.661100i	0.943788	−	0.330550i	$-0.107234\pi$
$422$	−1.07268	−	0.619309i	−0.0522170	−	0.0301475i
$423$	−0.652135	−	0.376510i	−0.0317079	−	0.0183066i
$424$		−	66.2747i		−	3.21858i
$425$	−9.45862	+	16.3828i	−0.458810	+	0.794683i
$426$	14.1380	+	24.4878i	0.684989	+	1.18644i
$427$	−1.64525	+	0.949886i	−0.0796193	+	0.0459682i
$428$	−33.5478			−1.62159
$429$		0			0
$430$	31.3370			1.51121
$431$	−31.1304	+	17.9731i	−1.49950	+	0.865736i	−1.00000		0.000578325i	$-0.999816\pi$
$431$	−31.1304	+	17.9731i	−1.49950	+	0.865736i	−0.499499	+	0.866314i	$0.666483\pi$
$432$	6.51842	+	11.2902i	0.313618	+	0.543201i
$433$	−16.2371	+	28.1234i	−0.780303	+	1.35152i	0.151462	+	0.988463i	$0.451602\pi$
$433$	−16.2371	+	28.1234i	−0.780303	+	1.35152i	−0.931765	+	0.363061i	$0.881732\pi$
$434$			14.2161i			0.682395i
$435$	−1.73671	−	1.00269i	−0.0832687	−	0.0480752i
$436$	15.7228	+	9.07756i	0.752985	+	0.434736i
$437$		−	4.33944i		−	0.207583i
$438$	14.1015	−	24.4245i	0.673795	−	1.16705i
$439$	6.41603	+	11.1129i	0.306221	+	0.530390i	0.977532	−	0.210785i	$-0.0676021\pi$
$439$	6.41603	+	11.1129i	0.306221	+	0.530390i	−0.671312	+	0.741175i	$0.734269\pi$
$440$	−23.1206	+	13.3487i	−1.10223	+	0.636374i
$441$	6.69202			0.318668
$442$		0			0
$443$	11.9608			0.568273			0.284137	−	0.958784i	$-0.408293\pi$
$443$	11.9608			0.568273			0.284137	+	0.958784i	$0.408293\pi$
$444$	26.1418	−	15.0930i	1.24064	−	0.716282i
$445$	5.20626	+	9.01751i	0.246800	+	0.427471i
$446$	−22.0075	+	38.1182i	−1.04209	+	1.80495i
$447$			15.3351i			0.725327i
$448$	10.2573	+	5.92208i	0.484614	+	0.279792i
$449$	10.8070	+	6.23945i	0.510016	+	0.294458i	0.732840	−	0.680401i	$-0.238194\pi$
$449$	10.8070	+	6.23945i	0.510016	+	0.294458i	−0.222824	+	0.974859i	$0.571528\pi$
$450$		−	10.4983i		−	0.494893i
$451$	−7.15130	+	12.3864i	−0.336742	+	0.583254i
$452$	24.5477	+	42.5179i	1.15463	+	1.99987i
$453$	−2.19173	+	1.26540i	−0.102977	+	0.0594536i
$454$	−17.6606			−0.828851
$455$		0			0
$456$	6.58211			0.308235
$457$	−28.1045	+	16.2262i	−1.31468	+	0.759028i	−0.982867	−	0.184319i	$-0.940992\pi$
$457$	−28.1045	+	16.2262i	−1.31468	+	0.759028i	−0.331809	+	0.943347i	$0.607659\pi$
$458$	5.32400	+	9.22144i	0.248774	+	0.430890i
$459$	2.42543	−	4.20096i	0.113209	−	0.196084i
$460$			31.7159i			1.47876i
$461$	21.1340	+	12.2017i	0.984308	+	0.568290i	0.903568	−	0.428445i	$-0.140938\pi$
$461$	21.1340	+	12.2017i	0.984308	+	0.568290i	0.0807398	+	0.996735i	$0.474272\pi$
$462$	3.76738	+	2.17510i	0.175274	+	0.101195i
$463$		−	33.1836i		−	1.54217i	−0.636731	−	0.771086i	$-0.719714\pi$
$463$		−	33.1836i		−	1.54217i	0.636731	−	0.771086i	$-0.280286\pi$
$464$	12.4623	−	21.5853i	0.578546	−	1.00207i
$465$	−4.99061	−	8.64398i	−0.231434	−	0.400855i
$466$	19.4829	−	11.2485i	0.902529	−	0.521075i
$467$	38.5206			1.78252			0.891261	−	0.453490i	$-0.149821\pi$
$467$	38.5206			1.78252			0.891261	+	0.453490i	$0.149821\pi$
$468$		0			0
$469$	−1.03923			−0.0479871
$470$	1.84144	−	1.06315i	0.0849392	−	0.0490397i
$471$	8.61960	+	14.9296i	0.397170	+	0.687919i
$472$	17.9095	−	31.0201i	0.824350	−	1.42782i
$473$			32.3153i			1.48586i
$474$	−3.11266	−	1.79709i	−0.142969	−	0.0825432i
$475$	−2.54318	−	1.46830i	−0.116689	−	0.0673704i
$476$		−	14.1250i		−	0.647417i
$477$	3.79105	−	6.56630i	0.173580	−	0.300650i
$478$	27.0559	+	46.8622i	1.23751	+	2.14343i
$479$	−7.22682	+	4.17241i	−0.330202	+	0.190642i	−0.655931	−	0.754821i	$-0.727724\pi$
$479$	−7.22682	+	4.17241i	−0.330202	+	0.190642i	0.325729	+	0.945463i	$0.394390\pi$
$480$	−18.4752			−0.843272
$481$		0			0
$482$	−51.1825			−2.33130
$483$	2.76960	−	1.59903i	0.126021	−	0.0727584i
$484$	6.61410	+	11.4560i	0.300641	+	0.520725i
$485$	−8.95444	+	15.5095i	−0.406600	+	0.704252i
$486$			2.69202i			0.122113i
$487$	−12.8679	−	7.42931i	−0.583102	−	0.336654i	0.179263	−	0.983801i	$-0.442629\pi$
$487$	−12.8679	−	7.42931i	−0.583102	−	0.336654i	−0.762365	+	0.647147i	$0.775962\pi$
$488$	25.9137	+	14.9613i	1.17306	+	0.677266i
$489$		−	15.7071i		−	0.710299i
$490$	−9.44816	+	16.3647i	−0.426824	+	0.739281i
$491$	2.49947	+	4.32920i	0.112799	+	0.195374i	0.916898	−	0.399122i	$-0.130685\pi$
$491$	2.49947	+	4.32920i	0.112799	+	0.195374i	−0.804099	+	0.594496i	$0.797352\pi$
$492$	−22.3196	+	12.8862i	−1.00624	+	0.580955i
$493$	−9.27413			−0.417686
$494$		0			0
$495$	−3.05429			−0.137280
$496$	107.435	−	62.0275i	4.82396	−	2.78512i
$497$	2.91454	+	5.04814i	0.130735	+	0.226440i
$498$	−3.55765	+	6.16202i	−0.159422	+	0.276127i
$499$			0.385371i			0.0172516i	0.999963	+	0.00862579i	$0.00274571\pi$
$499$			0.385371i			0.0172516i	−0.999963	+	0.00862579i	$0.997254\pi$
$500$	42.4190	+	24.4906i	1.89703	+	1.09525i
$501$	4.67318	+	2.69806i	0.208782	+	0.120541i
$502$		−	2.05610i		−	0.0917681i
$503$	−11.3089	+	19.5877i	−0.504241	+	0.873370i	0.495747	+	0.868467i	$0.334894\pi$
$503$	−11.3089	+	19.5877i	−0.504241	+	0.873370i	−0.999988	+	0.00490359i	$0.998439\pi$
$504$	2.42543	+	4.20096i	0.108037	+	0.187126i
$505$	−6.65217	+	3.84063i	−0.296018	+	0.170906i
$506$	−45.1726			−2.00817
$507$		0			0
$508$	−23.5163			−1.04337
$509$	10.0493	−	5.80194i	0.445425	−	0.257166i	−0.260471	−	0.965482i	$-0.583878\pi$
$509$	10.0493	−	5.80194i	0.445425	−	0.257166i	0.705896	+	0.708315i	$0.250544\pi$
$510$	6.84870	+	11.8623i	0.303265	+	0.525271i
$511$	2.90701	−	5.03509i	0.128599	−	0.222739i
$512$		−	1.71678i		−	0.0758715i
$513$	0.652135	+	0.376510i	0.0287925	+	0.0166233i
$514$	30.5201	+	17.6208i	1.34618	+	0.777220i
$515$			4.42626i			0.195044i
$516$	−29.1151	+	50.4288i	−1.28172	+	2.22000i
$517$	1.09634	+	1.89892i	0.0482171	+	0.0835145i
$518$	7.44330	−	4.29739i	0.327040	−	0.188816i
$519$	23.9420			1.05094
$520$		0			0
$521$	−1.62671			−0.0712675			−0.0356337	−	0.999365i	$-0.511345\pi$
$521$	−1.62671			−0.0712675			−0.0356337	+	0.999365i	$0.511345\pi$
$522$	4.45722	−	2.57338i	0.195087	−	0.112634i
$523$	−5.03588	−	8.72239i	−0.220203	−	0.381404i	0.734666	−	0.678429i	$-0.237339\pi$
$523$	−5.03588	−	8.72239i	−0.220203	−	0.381404i	−0.954870	+	0.297025i	$0.904005\pi$
$524$	−24.1819	+	41.8842i	−1.05639	+	1.82972i
$525$		−	2.16421i		−	0.0944539i
$526$	42.8442	+	24.7361i	1.86809	+	1.07854i
$527$	−39.9752	−	23.0797i	−1.74135	−	1.00537i
$528$		−	37.9614i		−	1.65206i
$529$	−5.10441	+	8.84109i	−0.221931	+	0.384395i
$530$	10.7048	+	18.5413i	0.464988	+	0.805383i
$531$	3.54883	−	2.04892i	0.154006	−	0.0889154i
$532$	2.19269			0.0950650
$533$		0			0
$534$	−26.7235			−1.15644
$535$	5.80800	−	3.35325i	0.251102	−	0.144974i
$536$	8.18425	+	14.1755i	0.353506	+	0.612290i
$537$	−9.20440	+	15.9425i	−0.397199	+	0.687969i
$538$		−	63.6999i		−	2.74630i
$539$	−16.8755	−	9.74309i	−0.726881	−	0.419665i
$540$	−4.76630	−	2.75182i	−0.205109	−	0.118420i
$541$		−	20.4674i		−	0.879962i	−0.898007	−	0.439981i	$-0.854985\pi$
$541$		−	20.4674i		−	0.879962i	0.898007	−	0.439981i	$-0.145015\pi$
$542$	26.5878	−	46.0514i	1.14204	−	1.97808i
$543$	1.81671	+	3.14663i	0.0779624	+	0.135035i
$544$	−73.9939	+	42.7204i	−3.17246	+	1.83162i
$545$	−3.62937			−0.155465
$546$		0			0
$547$	−27.5478			−1.17786			−0.588929	−	0.808185i	$-0.700450\pi$
$547$	−27.5478			−1.17786			−0.588929	+	0.808185i	$0.700450\pi$
$548$	33.9429	−	19.5969i	1.44997	−	0.837140i
$549$	1.71164	+	2.96464i	0.0730508	+	0.126528i
$550$	−15.2847	+	26.4739i	−0.651742	+	1.12885i
$551$		−	1.43967i		−	0.0613318i
$552$	−43.6230	−	25.1857i	−1.85672	−	1.07198i
$553$	−0.641672	−	0.370469i	−0.0272867	−	0.0157540i
$554$			4.78581i			0.203329i
$555$	−3.01722	+	5.22598i	−0.128074	+	0.221831i
$556$	−47.2165	−	81.7814i	−2.00243	−	3.46831i
$557$	32.8964	−	18.9928i	1.39387	−	0.804749i	0.400126	−	0.916460i	$-0.368966\pi$
$557$	32.8964	−	18.9928i	1.39387	−	0.804749i	0.993741	+	0.111711i	$0.0356331\pi$
$558$	25.6165			1.08443
$559$		0			0
$560$	−7.58881			−0.320686
$561$	−12.2326	+	7.06249i	−0.516460	+	0.298179i
$562$	−2.18233	−	3.77991i	−0.0920562	−	0.159446i
$563$	−14.8862	+	25.7837i	−0.627378	+	1.08665i	0.360697	+	0.932683i	$0.382539\pi$
$563$	−14.8862	+	25.7837i	−0.627378	+	1.08665i	−0.988076	+	0.153968i	$0.950795\pi$
$564$			3.95108i			0.166371i
$565$	−8.49970	−	4.90731i	−0.357585	−	0.206452i
$566$	−11.6186	−	6.70799i	−0.488365	−	0.281958i
$567$			0.554958i			0.0233061i
$568$	45.9059	−	79.5113i	1.92617	−	3.33622i
$569$	−10.9770	−	19.0128i	−0.460181	−	0.797057i	0.538788	−	0.842441i	$-0.318882\pi$
$569$	−10.9770	−	19.0128i	−0.460181	−	0.797057i	−0.998970	+	0.0453839i	$0.985549\pi$
$570$	−1.84144	+	1.06315i	−0.0771294	+	0.0445307i
$571$	−2.46575			−0.103188			−0.0515942	−	0.998668i	$-0.516430\pi$
$571$	−2.46575			−0.103188			−0.0515942	+	0.998668i	$0.516430\pi$
$572$		0			0
$573$	21.1782			0.884732
$574$	−6.35499	+	3.66905i	−0.265252	+	0.153143i
$575$	11.2366	+	19.4624i	0.468600	+	0.811639i
$576$	10.6712	−	18.4831i	0.444634	−	0.770128i
$577$		−	17.4547i		−	0.726650i	−0.931662	−	0.363325i	$-0.881641\pi$
$577$		−	17.4547i		−	0.726650i	0.931662	−	0.363325i	$-0.118359\pi$
$578$	15.2256	+	8.79052i	0.633303	+	0.365637i
$579$	−15.2517	−	8.80559i	−0.633840	−	0.365948i
$580$			10.5222i			0.436909i
$581$	−0.733406	+	1.27030i	−0.0304268	+	0.0527008i
$582$	−22.9813	−	39.8049i	−0.952607	−	1.64996i
$583$	−19.1201	+	11.0390i	−0.791873	+	0.457188i
$584$	−91.5745			−3.78938
$585$		0			0
$586$	−0.193159			−0.00797934
$587$	−5.42424	+	3.13169i	−0.223882	+	0.129259i	−0.607747	−	0.794131i	$-0.707926\pi$
$587$	−5.42424	+	3.13169i	−0.223882	+	0.129259i	0.383864	+	0.923390i	$0.374593\pi$
$588$	−17.5565	−	30.4087i	−0.724016	−	1.25403i
$589$	3.58277	−	6.20554i	0.147625	−	0.255695i
$590$			11.5711i			0.476374i
$591$	4.03783	+	2.33124i	0.166094	+	0.0958944i
$592$	−64.9529	−	37.5006i	−2.66955	−	1.54126i
$593$			22.8745i			0.939345i	0.882841	+	0.469672i	$0.155628\pi$
$593$			22.8745i			0.939345i	−0.882841	+	0.469672i	$0.844372\pi$
$594$	3.91939	−	6.78858i	0.160814	−	0.278539i
$595$	1.41185	+	2.44540i	0.0578804	+	0.100252i
$596$	69.6831	−	40.2315i	2.85433	−	1.64795i
$597$	15.0368			0.615417
$598$		0			0
$599$	−1.05621			−0.0431557			−0.0215778	−	0.999767i	$-0.506869\pi$
$599$	−1.05621			−0.0431557			−0.0215778	+	0.999767i	$0.506869\pi$
$600$	−29.5208	+	17.0438i	−1.20518	+	0.695812i
$601$	16.6618	+	28.8591i	0.679650	+	1.17719i	0.975086	+	0.221826i	$0.0712015\pi$
$601$	16.6618	+	28.8591i	0.679650	+	1.17719i	−0.295437	+	0.955362i	$0.595465\pi$
$602$	−8.28986	+	14.3585i	−0.337869	+	0.585207i
$603$			1.87263i			0.0762592i
$604$	11.5000	+	6.63951i	0.467927	+	0.270158i
$605$	−2.29015	−	1.32222i	−0.0931076	−	0.0537557i
$606$		−	19.7138i		−	0.800818i
$607$	−8.12014	+	14.0645i	−0.329586	+	0.570860i	−0.982430	−	0.186633i	$-0.940243\pi$
$607$	−8.12014	+	14.0645i	−0.329586	+	0.570860i	0.652844	+	0.757493i	$0.273576\pi$
$608$	−6.63169	−	11.4864i	−0.268950	−	0.465836i
$609$	0.918852	−	0.530499i	0.0372338	−	0.0214969i
$610$	−9.66632			−0.391378
$611$		0			0
$612$	−25.4523			−1.02885
$613$	−9.56772	+	5.52393i	−0.386437	+	0.223109i	−0.680615	−	0.732641i	$-0.738287\pi$
$613$	−9.56772	+	5.52393i	−0.386437	+	0.223109i	0.294178	+	0.955751i	$0.404954\pi$
$614$	6.99665	+	12.1185i	0.282362	+	0.489065i
$615$	2.57606	−	4.46187i	0.103877	−	0.179920i
$616$		−	14.1250i		−	0.569112i
$617$	−4.03524	−	2.32975i	−0.162453	−	0.0937922i	0.416570	−	0.909104i	$-0.363232\pi$
$617$	−4.03524	−	2.32975i	−0.162453	−	0.0937922i	−0.579022	+	0.815312i	$0.696566\pi$
$618$	−9.83794	−	5.67994i	−0.395740	−	0.228481i
$619$			31.9259i			1.28321i	0.767036	+	0.641604i	$0.221731\pi$
$619$			31.9259i			1.28321i	−0.767036	+	0.641604i	$0.778269\pi$
$620$	−26.1856	+	45.3548i	−1.05164	+	1.82149i
$621$	−2.88135	−	4.99065i	−0.115625	−	0.200268i
$622$	−52.5555	+	30.3430i	−2.10729	+	1.21664i
$623$	−5.50902			−0.220714
$624$		0			0
$625$	9.70709			0.388283
$626$	−52.8313	+	30.5022i	−2.11156	+	1.21911i
$627$	−1.09634	−	1.89892i	−0.0437837	−	0.0758356i
$628$	45.2269	−	78.3353i	1.80475	−	3.12592i
$629$			27.9071i			1.11273i
$630$	−1.35710	−	0.783520i	−0.0540680	−	0.0312162i
$631$	34.1572	+	19.7207i	1.35978	+	0.785067i	0.989593	−	0.143892i	$-0.0459618\pi$
$631$	34.1572	+	19.7207i	1.35978	+	0.785067i	0.370183	+	0.928959i	$0.379295\pi$
$632$			11.6703i			0.464218i
$633$	−0.230054	+	0.398465i	−0.00914381	+	0.0158375i
$634$	35.4572	+	61.4136i	1.40818	+	2.43905i
$635$	4.07129	−	2.35056i	0.161564	−	0.0932791i
$636$	−39.7832			−1.57750
$637$		0			0
$638$	−14.9866			−0.593325
$639$	9.09643	−	5.25182i	0.359849	−	0.207759i
$640$	11.6572	+	20.1909i	0.460792	+	0.798115i
$641$	22.7255	−	39.3617i	0.897603	−	1.55469i	0.0670544	−	0.997749i	$-0.478640\pi$
$641$	22.7255	−	39.3617i	0.897603	−	1.55469i	0.830549	−	0.556946i	$-0.188027\pi$
$642$			17.2121i			0.679306i
$643$	−25.7616	−	14.8735i	−1.01594	−	0.586552i	−0.103013	−	0.994680i	$-0.532848\pi$
$643$	−25.7616	−	14.8735i	−1.01594	−	0.586552i	−0.912925	+	0.408128i	$0.866182\pi$
$644$	−14.5321	−	8.39008i	−0.572643	−	0.330616i
$645$		−	11.6407i		−	0.458353i
$646$	−4.91670	+	8.51597i	−0.193445	+	0.335056i
$647$	−8.46562	−	14.6629i	−0.332818	−	0.576457i	0.650245	−	0.759724i	$-0.274666\pi$
$647$	−8.46562	−	14.6629i	−0.332818	−	0.576457i	−0.983063	+	0.183267i	$0.941333\pi$
$648$	7.56988	−	4.37047i	0.297373	−	0.171688i
$649$	−11.9323			−0.468384
$650$		0			0
$651$	5.28083			0.206972
$652$	−71.3733	+	41.2074i	−2.79519	+	1.61381i
$653$	16.5988	+	28.7500i	0.649561	+	1.12507i	0.983228	+	0.182382i	$0.0583806\pi$
$653$	16.5988	+	28.7500i	0.649561	+	1.12507i	−0.333667	+	0.942691i	$0.608286\pi$
$654$	4.65734	−	8.06675i	0.182116	−	0.315435i
$655$		−	9.66833i		−	0.377773i
$656$	55.4560	+	32.0175i	2.16519	+	1.25007i
$657$	−9.07292	−	5.23825i	−0.353968	−	0.204364i
$658$			1.12498i			0.0438564i
$659$	21.3286	−	36.9421i	0.830842	−	1.43906i	−0.0665286	−	0.997785i	$-0.521192\pi$
$659$	21.3286	−	36.9421i	0.830842	−	1.43906i	0.897371	−	0.441277i	$-0.145474\pi$
$660$	8.01291	+	13.8788i	0.311902	+	0.540230i
$661$	33.5067	−	19.3451i	1.30326	−	0.752438i	0.322298	−	0.946638i	$-0.395545\pi$
$661$	33.5067	−	19.3451i	1.30326	−	0.752438i	0.980962	+	0.194201i	$0.0622113\pi$
$662$	30.2301			1.17493
$663$		0			0
$664$	23.1032			0.896578
$665$	−0.379611	+	0.219169i	−0.0147207	+	0.00849899i
$666$	−7.74363	−	13.4124i	−0.300059	−	0.519718i
$667$	−5.50873	+	9.54140i	−0.213299	+	0.369444i
$668$		−	28.3134i		−	1.09548i
$669$	14.1597	+	8.17510i	0.547445	+	0.316067i
$670$	−4.57932	−	2.64387i	−0.176915	−	0.102142i
$671$		−	9.96807i		−	0.384813i
$672$	4.88740	−	8.46522i	0.188535	−	0.326553i
$673$	−1.29709	−	2.24663i	−0.0499993	−	0.0866013i	0.839943	−	0.542675i	$-0.182589\pi$
$673$	−1.29709	−	2.24663i	−0.0499993	−	0.0866013i	−0.889942	+	0.456074i	$0.849255\pi$
$674$	5.38073	−	3.10656i	0.207258	−	0.119660i
$675$	−3.89977			−0.150102
$676$		0			0
$677$	1.75302			0.0673740			0.0336870	−	0.999432i	$-0.489275\pi$
$677$	1.75302			0.0673740			0.0336870	+	0.999432i	$0.489275\pi$
$678$	21.8143	−	12.5945i	0.837773	−	0.483688i
$679$	−4.73759	−	8.20574i	−0.181812	−	0.314907i
$680$	22.2376	−	38.5166i	0.852773	−	1.47705i
$681$			6.56033i			0.251393i
$682$	−64.5983	−	37.2958i	−2.47360	−	1.42813i
$683$	−14.1466	−	8.16756i	−0.541306	−	0.312523i	0.204302	−	0.978908i	$-0.434508\pi$
$683$	−14.1466	−	8.16756i	−0.541306	−	0.312523i	−0.745608	+	0.666385i	$0.767841\pi$
$684$		−	3.95108i		−	0.151073i
$685$	−3.91760	+	6.78548i	−0.149684	+	0.259260i
$686$	−10.2277	−	17.7148i	−0.390494	−	0.676355i
$687$	3.42547	−	1.97770i	0.130690	−	0.0754539i
$688$	144.681			5.51590
$689$		0			0
$690$	16.2722			0.619472
$691$	−13.7789	+	7.95526i	−0.524175	+	0.302632i	−0.738641	−	0.674099i	$-0.764532\pi$
$691$	−13.7789	+	7.95526i	−0.524175	+	0.302632i	0.214466	+	0.976731i	$0.431199\pi$
$692$	−62.8116	−	108.793i	−2.38774	−	4.13568i
$693$	0.807979	−	1.39946i	0.0306926	−	0.0531611i
$694$			24.5972i			0.933696i
$695$	16.3488	+	9.43900i	0.620146	+	0.358042i
$696$	−14.4725	−	8.35570i	−0.548579	−	0.316722i
$697$		−	23.8267i		−	0.902500i
$698$	−32.2717	+	55.8963i	−1.22150	+	2.11571i
$699$	−4.17845	−	7.23728i	−0.158043	−	0.273739i
$700$	−9.83421	+	5.67778i	−0.371698	+	0.214600i
$701$	20.8635			0.788005			0.394002	−	0.919109i	$-0.371090\pi$
$701$	20.8635			0.788005			0.394002	+	0.919109i	$0.371090\pi$
$702$		0			0
$703$	−4.33214			−0.163390
$704$	−53.8200	+	31.0730i	−2.02842	+	1.17111i
$705$	−0.394928	−	0.684035i	−0.0148739	−	0.0257623i
$706$	−36.5091	+	63.2356i	−1.37404	+	2.37990i
$707$		−	4.06398i		−	0.152842i
$708$	−18.6206	−	10.7506i	−0.699806	−	0.404033i
$709$	−13.5520	−	7.82424i	−0.508955	−	0.293846i	0.223449	−	0.974716i	$-0.428268\pi$
$709$	−13.5520	−	7.82424i	−0.508955	−	0.293846i	−0.732404	+	0.680870i	$0.761602\pi$
$710$			29.6592i			1.11309i
$711$	−0.667563	+	1.15625i	−0.0250356	+	0.0433629i
$712$	43.3853	+	75.1455i	1.62593	+	2.81620i
$713$	−47.4897	+	27.4182i	−1.77850	+	1.02682i
$714$	−7.24698			−0.271211
$715$		0			0
$716$	96.5906			3.60976
$717$	17.4078	−	10.0504i	0.650107	−	0.375339i
$718$	35.1027	+	60.7996i	1.31002	+	2.26902i
$719$	−13.5797	+	23.5208i	−0.506438	+	0.877176i	0.493534	+	0.869726i	$0.335705\pi$
$719$	−13.5797	+	23.5208i	−0.506438	+	0.877176i	−0.999972	+	0.00744977i	$0.997629\pi$
$720$			13.6746i			0.509621i
$721$	−2.02808	−	1.17092i	−0.0755298	−	0.0436072i
$722$	42.9738	+	24.8110i	1.59932	+	0.923368i
$723$			19.0127i			0.707089i
$724$	9.53223	−	16.5103i	0.354262	−	0.613601i
$725$	3.72790	+	6.45691i	0.138451	+	0.239804i
$726$	5.87760	−	3.39344i	0.218138	−	0.125942i
$727$	−31.7784			−1.17859			−0.589297	−	0.807916i	$-0.700595\pi$
$727$	−31.7784			−1.17859			−0.589297	+	0.807916i	$0.700595\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	25.6193	−	14.7913i	0.948212	−	0.547450i
$731$	−26.9170	−	46.6216i	−0.995561	−	1.72436i
$732$	8.98092	−	15.5554i	0.331944	−	0.574944i
$733$		−	46.8907i		−	1.73195i	−0.500090	−	0.865973i	$-0.666700\pi$
$733$		−	46.8907i		−	1.73195i	0.500090	−	0.865973i	$-0.333300\pi$
$734$	22.3212	+	12.8872i	0.823891	+	0.475674i
$735$	6.07896	+	3.50969i	0.224226	+	0.129457i
$736$			101.502i			3.74141i
$737$	2.72641	−	4.72227i	0.100428	−	0.173947i
$738$	6.61141	+	11.4513i	0.243369	+	0.421528i
$739$	14.7639	−	8.52393i	0.543098	−	0.313558i	−0.203236	−	0.979130i	$-0.565146\pi$
$739$	14.7639	−	8.52393i	0.543098	−	0.313558i	0.746334	+	0.665572i	$0.231812\pi$
$740$	31.6626			1.16394
$741$		0			0
$742$	−11.3274			−0.415840
$743$	10.0739	−	5.81618i	0.369576	−	0.213375i	−0.303697	−	0.952769i	$-0.598221\pi$
$743$	10.0739	−	5.81618i	0.369576	−	0.213375i	0.673273	+	0.739394i	$0.264888\pi$
$744$	−41.5882	−	72.0329i	−1.52470	−	2.64085i
$745$	−8.04264	+	13.9303i	−0.294660	+	0.510365i
$746$		−	75.7797i		−	2.77449i
$747$	2.28900	+	1.32155i	0.0837500	+	0.0483531i
$748$	64.1842	+	37.0567i	2.34681	+	1.35493i
$749$			3.54825i			0.129650i
$750$	12.5652	−	21.7635i	0.458815	−	0.794692i
$751$	−6.51477	−	11.2839i	−0.237727	−	0.411756i	0.722334	−	0.691544i	$-0.243069\pi$
$751$	−6.51477	−	11.2839i	−0.237727	−	0.411756i	−0.960062	+	0.279788i	$0.909736\pi$
$752$	8.50177	−	4.90850i	0.310028	−	0.178995i
$753$	−0.763774			−0.0278335
$754$		0			0
$755$	−2.65459			−0.0966106
$756$	2.52174	−	1.45593i	0.0917148	−	0.0529516i
$757$	−11.3949	−	19.7366i	−0.414156	−	0.717339i	0.581184	−	0.813772i	$-0.302590\pi$
$757$	−11.3949	−	19.7366i	−0.414156	−	0.717339i	−0.995339	+	0.0964337i	$0.969256\pi$
$758$	21.5988	−	37.4102i	0.784504	−	1.35880i
$759$			16.7802i			0.609081i
$760$	5.97911	+	3.45204i	0.216885	+	0.125219i
$761$	33.2055	+	19.1712i	1.20370	+	0.694956i	0.961376	−	0.275240i	$-0.0887572\pi$
$761$	33.2055	+	19.1712i	1.20370	+	0.694956i	0.242323	+	0.970196i	$0.422091\pi$
$762$			12.0653i			0.437080i
$763$	0.960107	−	1.66295i	0.0347582	−	0.0602030i
$764$	−55.5608	−	96.2342i	−2.01012	−	3.48163i
$765$	4.40646	−	2.54407i	0.159316	−	0.0919812i
$766$	66.2683			2.39437
$767$		0			0
$768$	−17.1511			−0.618886
$769$	3.15129	−	1.81940i	0.113638	−	0.0656091i	−0.442104	−	0.896964i	$-0.645768\pi$
$769$	3.15129	−	1.81940i	0.113638	−	0.0656091i	0.555742	+	0.831355i	$0.312434\pi$
$770$	2.28150	+	3.95167i	0.0822194	+	0.142408i
$771$	6.54556	−	11.3373i	0.235733	−	0.408301i
$772$			92.4055i			3.32575i
$773$	−34.0715	−	19.6712i	−1.22547	−	0.707524i	−0.259389	−	0.965773i	$-0.583521\pi$
$773$	−34.0715	−	19.6712i	−1.22547	−	0.707524i	−0.966079	+	0.258249i	$0.916855\pi$
$774$	25.8730	+	14.9378i	0.929987	+	0.536928i
$775$			37.1092i			1.33300i
$776$	−74.6200	+	129.246i	−2.67870	+	4.63965i
$777$	−1.59634	−	2.76495i	−0.0572685	−	0.0991919i
$778$	−40.1456	+	23.1781i	−1.43929	+	0.830974i
$779$	3.69873			0.132521
$780$		0			0
$781$	−30.5851			−1.09442
$782$	65.1710	−	37.6265i	2.33051	−	1.34552i
$783$	−0.955927	−	1.65571i	−0.0341620	−	0.0591704i
$784$	−43.6214	+	75.5545i	−1.55791	+	2.69837i
$785$			18.0825i			0.645392i
$786$	21.4892	+	12.4068i	0.766493	+	0.442535i
$787$	22.0189	+	12.7126i	0.784888	+	0.453155i	0.838160	−	0.545425i	$-0.183632\pi$
$787$	22.0189	+	12.7126i	0.784888	+	0.453155i	−0.0532720	+	0.998580i	$0.516965\pi$
$788$		−	24.4639i		−	0.871492i
$789$	9.18867	−	15.9152i	0.327125	−	0.566598i
$790$	−1.88500	−	3.26492i	−0.0670654	−	0.116161i
$791$	4.49700	−	2.59634i	0.159895	−	0.0923153i
$792$	−25.4523			−0.904409
$793$		0			0
$794$	−5.48965			−0.194820
$795$	6.88750	−	3.97650i	0.244275	−	0.141032i
$796$	−39.4490	−	68.3276i	−1.39823	−	2.42181i
$797$	10.3569	−	17.9387i	0.366860	−	0.635420i	−0.622213	−	0.782848i	$-0.713766\pi$
$797$	10.3569	−	17.9387i	0.366860	−	0.635420i	0.989073	+	0.147428i	$0.0470994\pi$
$798$		−	1.12498i		−	0.0398239i
$799$	−3.16341	−	1.82640i	−0.111913	−	0.0646133i
$800$	59.4863	+	34.3444i	2.10316	+	1.21426i
$801$			9.92692i			0.350750i
$802$	1.96711	−	3.40713i	0.0694610	−	0.120310i
$803$	15.2530	+	26.4190i	0.538267	+	0.932306i
$804$	8.50924	−	4.91281i	0.300098	−	0.173262i
$805$	3.35450			0.118231
$806$		0			0
$807$	−23.6625			−0.832959
$808$	−55.4345	+	32.0051i	−1.95018	+	1.12594i
$809$	−5.54892	−	9.61101i	−0.195090	−	0.337905i	0.751840	−	0.659345i	$-0.229166\pi$
$809$	−5.54892	−	9.61101i	−0.195090	−	0.337905i	−0.946930	+	0.321440i	$0.895833\pi$
$810$	−1.41185	+	2.44540i	−0.0496075	+	0.0859227i
$811$			4.84223i			0.170034i	0.996380	+	0.0850169i	$0.0270944\pi$
$811$			4.84223i			0.170034i	−0.996380	+	0.0850169i	$0.972906\pi$
$812$	−4.82120	−	2.78352i	−0.169191	−	0.0976824i
$813$	−17.1066	−	9.87651i	−0.599955	−	0.346384i
$814$			45.0966i			1.58064i
$815$	8.23772	−	14.2681i	0.288555	−	0.499791i
$816$	31.6199	+	54.7673i	1.10692	+	1.91724i
$817$	7.23728	−	4.17845i	0.253201	−	0.146185i
$818$	80.5964			2.81799
$819$		0			0
$820$	−27.0331			−0.944037
$821$	37.8783	−	21.8690i	1.32196	−	0.763235i	0.337920	−	0.941175i	$-0.390277\pi$
$821$	37.8783	−	21.8690i	1.32196	−	0.763235i	0.984041	+	0.177940i	$0.0569434\pi$
$822$	−10.0544	−	17.4148i	−0.350688	−	0.607410i
$823$	6.04988	−	10.4787i	0.210885	−	0.365264i	−0.741106	−	0.671388i	$-0.765699\pi$
$823$	6.04988	−	10.4787i	0.210885	−	0.365264i	0.951992	+	0.306123i	$0.0990320\pi$
$824$			36.8853i			1.28496i
$825$	9.83421	+	5.67778i	0.342383	+	0.197675i
$826$	−5.30181	−	3.06100i	−0.184473	−	0.106506i
$827$		−	35.3212i		−	1.22824i	−0.789213	−	0.614120i	$-0.789511\pi$
$827$		−	35.3212i		−	1.22824i	0.789213	−	0.614120i	$-0.210489\pi$
$828$	−15.1184	+	26.1859i	−0.525401	+	0.910021i
$829$	26.7473	+	46.3276i	0.928971	+	1.60903i	0.785047	+	0.619437i	$0.212639\pi$
$829$	26.7473	+	46.3276i	0.928971	+	1.60903i	0.143925	+	0.989589i	$0.454028\pi$
$830$	−6.46345	+	3.73168i	−0.224350	+	0.129528i
$831$	1.77777			0.0616703
$832$		0			0
$833$	32.4620			1.12474
$834$	−41.9589	+	24.2250i	−1.45292	+	0.838842i
$835$	2.83004	+	4.90178i	0.0979377	+	0.169633i
$836$	−5.75249	+	9.96360i	−0.198954	+	0.344598i
$837$		−	9.51573i		−	0.328912i
$838$	15.4975	+	8.94749i	0.535353	+	0.309086i
$839$	−20.0503	−	11.5761i	−0.692214	−	0.399650i	0.112227	−	0.993683i	$-0.464202\pi$
$839$	−20.0503	−	11.5761i	−0.692214	−	0.399650i	−0.804441	+	0.594033i	$0.797535\pi$
$840$			5.08815i			0.175558i
$841$	12.6724	−	21.9493i	0.436980	−	0.756871i
$842$	18.2582	+	31.6241i	0.629218	+	1.08984i
$843$	−1.40412	+	0.810667i	−0.0483603	+	0.0279209i
$844$	2.41417			0.0830993
$845$		0			0
$846$	2.02715			0.0696948
$847$	1.21166	−	0.699554i	0.0416332	−	0.0240370i
$848$	49.4233	+	85.6037i	1.69720	+	2.93964i
$849$	−2.49180	+	4.31593i	−0.0855185	+	0.148122i
$850$		−	50.9256i		−	1.74673i
$851$	28.7113	+	16.5765i	0.984212	+	0.568235i
$852$	−47.7288	−	27.5562i	−1.63516	−	0.944060i
$853$			26.7265i			0.915097i	0.889185	+	0.457548i	$0.151272\pi$
$853$			26.7265i			0.915097i	−0.889185	+	0.457548i	$0.848728\pi$
$854$	2.55711	−	4.42905i	0.0875026	−	0.151559i
$855$	0.394928	+	0.684035i	0.0135063	+	0.0233935i
$856$	48.3997	−	27.9436i	1.65427	−	0.955093i
$857$	−42.6064			−1.45541			−0.727703	−	0.685892i	$-0.759412\pi$
$857$	−42.6064			−1.45541			−0.727703	+	0.685892i	$0.759412\pi$
$858$		0			0
$859$	33.6079			1.14669			0.573344	−	0.819315i	$-0.305646\pi$
$859$	33.6079			1.14669			0.573344	+	0.819315i	$0.305646\pi$
$860$	−52.8956	+	30.5393i	−1.80372	+	1.04138i
$861$	1.36294	+	2.36068i	0.0464488	+	0.0804516i
$862$	48.3841	−	83.8037i	1.64797	−	2.85437i
$863$		−	18.7047i		−	0.636715i	−0.947971	−	0.318358i	$-0.896869\pi$
$863$		−	18.7047i		−	0.636715i	0.947971	−	0.318358i	$-0.103131\pi$
$864$	−15.2538	−	8.80678i	−0.518945	−	0.299613i
$865$	21.7486	+	12.5566i	0.739476	+	0.426937i
$866$		−	87.4210i		−	2.97069i
$867$	3.26540	−	5.65583i	0.110899	−	0.192082i
$868$	−13.8542	−	23.9962i	−0.470242	−	0.814484i
$869$	3.36684	−	1.94385i	0.114212	−	0.0659404i
$870$	5.39852			0.183027
$871$		0			0
$872$	−30.2446			−1.02421
$873$	−14.7862	+	8.53684i	−0.500438	+	0.288928i
$874$	5.84093	+	10.1168i	0.197572	+	0.342205i
$875$	2.59030	−	4.48653i	0.0875682	−	0.151673i
$876$			54.9700i			1.85726i
$877$	31.8903	+	18.4119i	1.07686	+	0.621724i	0.930047	−	0.367440i	$-0.119766\pi$
$877$	31.8903	+	18.4119i	1.07686	+	0.621724i	0.146811	+	0.989165i	$0.453099\pi$
$878$	−29.9162	−	17.2721i	−1.00962	−	0.582905i
$879$			0.0717525i			0.00242015i
$880$	19.9092	−	34.4837i	0.671138	−	1.16244i
$881$	−20.5625	−	35.6153i	−0.692768	−	1.19991i	−0.970927	−	0.239374i	$-0.923058\pi$
$881$	−20.5625	−	35.6153i	−0.692768	−	1.19991i	0.278159	−	0.960535i	$-0.410276\pi$
$882$	−15.6015	+	9.00753i	−0.525330	+	0.303299i
$883$	−30.7482			−1.03476			−0.517380	−	0.855756i	$-0.673093\pi$
$883$	−30.7482			−1.03476			−0.517380	+	0.855756i	$0.673093\pi$
$884$		0			0
$885$	4.29829			0.144485
$886$	−27.8849	+	16.0993i	−0.936810	+	0.540867i
$887$	−3.79470	−	6.57261i	−0.127414	−	0.220687i	0.795260	−	0.606268i	$-0.207334\pi$
$887$	−3.79470	−	6.57261i	−0.127414	−	0.220687i	−0.922674	+	0.385581i	$0.874001\pi$
$888$	−25.1434	+	43.5496i	−0.843757	+	1.46143i
$889$			2.48725i			0.0834198i
$890$	−24.2753	−	14.0154i	−0.813710	−	0.469796i
$891$	−2.52174	−	1.45593i	−0.0844815	−	0.0487754i
$892$		−	85.7891i		−	2.87243i
$893$	0.283520	−	0.491071i	0.00948763	−	0.0164331i
$894$	−20.6412	−	35.7517i	−0.690346	−	1.19572i
$895$	−16.7223	+	9.65465i	−0.558967	+	0.322719i
$896$	−12.3351			−0.412088
$897$		0			0
$898$	−33.5934			−1.12103
$899$	−15.7553	+	9.09634i	−0.525470	+	0.303380i
$900$	10.2310	+	17.7206i	0.341034	+	0.590688i
$901$	18.3898	−	31.8521i	0.612655	−	1.06115i
$902$		−	38.5029i		−	1.28201i
$903$	5.33371	+	3.07942i	0.177495	+	0.102477i
$904$	−70.8305	−	40.8940i	−2.35579	−	1.36012i
$905$			3.81115i			0.126687i
$906$	3.40648	−	5.90019i	0.113173	−	0.196021i
$907$	9.66666	+	16.7431i	0.320976	+	0.555947i	0.980690	−	0.195570i	$-0.0626557\pi$
$907$	9.66666	+	16.7431i	0.320976	+	0.555947i	−0.659713	+	0.751517i	$0.729322\pi$
$908$	29.8103	−	17.2110i	0.989289	−	0.571166i
$909$	−7.32304			−0.242890
$910$		0			0
$911$	22.7149			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$911$	22.7149			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$912$	−8.50177	+	4.90850i	−0.281522	+	0.162537i
$913$	−3.84817	−	6.66522i	−0.127356	−	0.220587i
$914$	43.6812	−	75.6580i	1.44485	−	2.50255i
$915$			3.59073i			0.118706i
$916$	−17.9734	−	10.3769i	−0.593857	−	0.342864i
$917$	4.42997	+	2.55765i	0.146291	+	0.0844609i
$918$			13.0586i			0.430998i
$919$	−7.14556	+	12.3765i	−0.235710	+	0.408262i	−0.959479	−	0.281781i	$-0.909075\pi$
$919$	−7.14556	+	12.3765i	−0.235710	+	0.408262i	0.723769	+	0.690043i	$0.242408\pi$
$920$	−26.4178	−	45.7569i	−0.870968	−	1.50856i
$921$	4.50165	−	2.59903i	0.148335	−	0.0856410i
$922$	−65.6945			−2.16353
$923$		0			0
$924$	−8.47889			−0.278935
$925$	19.4297	−	11.2177i	0.638844	−	0.368837i
$926$	44.6655	+	77.3629i	1.46780	+	2.54230i
$927$	−2.10992	+	3.65448i	−0.0692987	+	0.120029i
$928$			33.6746i			1.10542i
$929$	28.3373	+	16.3605i	0.929716	+	0.536772i	0.886722	−	0.462303i	$-0.152977\pi$
$929$	28.3373	+	16.3605i	0.929716	+	0.536772i	0.0429946	+	0.999075i	$0.486310\pi$
$930$	23.2698	+	13.4348i	0.763047	+	0.440545i
$931$			5.03923i			0.165154i
$932$	−21.9242	+	37.9739i	−0.718152	+	1.24388i
$933$	11.2714	+	19.5227i	0.369010	+	0.639145i
$934$	−89.8054	+	51.8492i	−2.93852	+	1.69656i
$935$	−14.8159			−0.484533
$936$		0			0
$937$	−4.01400			−0.131132			−0.0655658	−	0.997848i	$-0.520885\pi$
$937$	−4.01400			−0.131132			−0.0655658	+	0.997848i	$0.520885\pi$
$938$	2.42282	−	1.39881i	0.0791077	−	0.0456729i
$939$	11.3306	+	19.6251i	0.369759	+	0.640442i
$940$	−2.07218	+	3.58912i	−0.0675870	+	0.117064i
$941$			28.2669i			0.921476i	0.887536	+	0.460738i	$0.152415\pi$
$941$			28.2669i			0.921476i	−0.887536	+	0.460738i	$0.847585\pi$
$942$	−40.1908	−	23.2042i	−1.30949	−	0.756032i
$943$	−24.5134	−	14.1528i	−0.798265	−	0.460878i
$944$			53.4228i			1.73876i
$945$	−0.291053	+	0.504118i	−0.00946794	+	0.0163990i
$946$	−43.4967	−	75.3385i	−1.41420	−	2.44947i
$947$	−32.7751	+	18.9227i	−1.06505	+	0.614906i	−0.926825	−	0.375495i	$-0.877473\pi$
$947$	−32.7751	+	18.9227i	−1.06505	+	0.614906i	−0.138225	+	0.990401i	$0.544140\pi$
$948$	7.00538			0.227524
$949$		0			0
$950$	7.90541			0.256485
$951$	22.8132	−	13.1712i	0.739769	−	0.427106i
$952$	11.7654	+	20.3783i	0.381319	+	0.660463i
$953$	−20.4128	+	35.3560i	−0.661236	+	1.14529i	0.319055	+	0.947736i	$0.396634\pi$
$953$	−20.4128	+	35.3560i	−0.661236	+	1.14529i	−0.980291	+	0.197558i	$0.936699\pi$
$954$			20.4112i			0.660837i
$955$	19.2381	+	11.1071i	0.622529	+	0.359417i
$956$	−91.3385	−	52.7343i	−2.95410	−	1.70555i
$957$			5.56704i			0.179957i
$958$	11.2322	−	19.4548i	0.362896	−	0.628555i
$959$	−2.07271	−	3.59004i	−0.0669314	−	0.115929i
$960$	19.3872	−	11.1932i	0.625720	−	0.361260i
$961$	−59.5491			−1.92094
$962$		0			0
$963$	6.39373			0.206035
$964$	86.3939	−	49.8796i	2.78256	−	1.60651i
$965$	−9.23633	−	15.9978i	−0.297328	−	0.514987i
$966$	−4.30463	+	7.45583i	−0.138499	+	0.239887i
$967$		−	10.2798i		−	0.330575i	−0.986245	−	0.165288i	$-0.947145\pi$
$967$		−	10.2798i		−	0.330575i	0.986245	−	0.165288i	$-0.0528552\pi$
$968$	−19.0845	−	11.0184i	−0.613398	−	0.354145i
$969$	3.16341	+	1.82640i	0.101623	+	0.0586723i
$970$		−	48.2111i		−	1.54796i
$971$	9.74027	−	16.8707i	0.312580	−	0.541405i	−0.666340	−	0.745648i	$-0.732140\pi$
$971$	9.74027	−	16.8707i	0.312580	−	0.541405i	0.978920	+	0.204243i	$0.0654733\pi$
$972$	−2.62349	−	4.54402i	−0.0841485	−	0.145749i
$973$	−8.64979	+	4.99396i	−0.277300	+	0.160099i
$974$	39.9997			1.28167
$975$		0			0
$976$	−44.6286			−1.42853
$977$	−40.7498	+	23.5269i	−1.30370	+	0.752693i	−0.981037	−	0.193821i	$-0.937912\pi$
$977$	−40.7498	+	23.5269i	−1.30370	+	0.752693i	−0.322665	+	0.946513i	$0.604579\pi$
$978$	21.1419	+	36.6189i	0.676044	+	1.17094i
$979$	14.4529	−	25.0331i	0.461916	−	0.800062i
$980$		−	36.8305i		−	1.17651i
$981$	−2.99654	−	1.73005i	−0.0956722	−	0.0552364i
$982$	−11.6543	−	6.72862i	−0.371904	−	0.214719i
$983$			34.4295i			1.09813i	0.835779	+	0.549065i	$0.185016\pi$
$983$			34.4295i			1.09813i	−0.835779	+	0.549065i	$0.814984\pi$
$984$	21.4671	−	37.1821i	0.684346	−	1.18532i
$985$	2.44528	+	4.23535i	0.0779131	+	0.134949i
$986$	21.6213	−	12.4831i	0.688563	−	0.397542i
$987$	0.417895			0.0133017
$988$		0			0
$989$	−63.9536			−2.03361
$990$	7.12066	−	4.11111i	0.226309	−	0.130660i
$991$	−3.65399	−	6.32890i	−0.116073	−	0.201044i	0.802135	−	0.597142i	$-0.203697\pi$
$991$	−3.65399	−	6.32890i	−0.116073	−	0.201044i	−0.918208	+	0.396098i	$0.870364\pi$
$992$	−83.8030	+	145.151i	−2.66075	+	4.60855i
$993$		−	11.2295i		−	0.356358i
$994$	−13.5897	−	7.84601i	−0.431039	−	0.248860i
$995$	13.6593	+	7.88620i	0.433029	+	0.250009i
$996$		−	13.8683i		−	0.439434i
$997$	17.8458	−	30.9098i	0.565181	−	0.978923i	−0.431851	−	0.901945i	$-0.642140\pi$
$997$	17.8458	−	30.9098i	0.565181	−	0.978923i	0.997033	−	0.0769780i	$-0.0245271\pi$
$998$	−0.518713	−	0.898438i	−0.0164196	−	0.0284396i
$999$	−4.98226	+	2.87651i	−0.157632	+	0.0910088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.i.361.1		12
13.2	odd	12		507.2.a.i.1.1	✓	3
13.3	even	3		507.2.b.f.337.1		6
13.4	even	6	inner	507.2.j.i.316.1		12
13.5	odd	4		507.2.e.l.484.3		6
13.6	odd	12		507.2.e.l.22.3		6
13.7	odd	12		507.2.e.i.22.1		6
13.8	odd	4		507.2.e.i.484.1		6
13.9	even	3	inner	507.2.j.i.316.6		12
13.10	even	6		507.2.b.f.337.6		6
13.11	odd	12		507.2.a.l.1.3	yes	3
13.12	even	2	inner	507.2.j.i.361.6		12
39.2	even	12		1521.2.a.s.1.3		3
39.11	even	12		1521.2.a.n.1.1		3
39.23	odd	6		1521.2.b.k.1351.1		6
39.29	odd	6		1521.2.b.k.1351.6		6
52.11	even	12		8112.2.a.cp.1.1		3
52.15	even	12		8112.2.a.cg.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.1	✓	3	13.2	odd	12
507.2.a.l.1.3	yes	3	13.11	odd	12
507.2.b.f.337.1		6	13.3	even	3
507.2.b.f.337.6		6	13.10	even	6
507.2.e.i.22.1		6	13.7	odd	12
507.2.e.i.484.1		6	13.8	odd	4
507.2.e.l.22.3		6	13.6	odd	12
507.2.e.l.484.3		6	13.5	odd	4
507.2.j.i.316.1		12	13.4	even	6	inner
507.2.j.i.316.6		12	13.9	even	3	inner
507.2.j.i.361.1		12	1.1	even	1	trivial
507.2.j.i.361.6		12	13.12	even	2	inner
1521.2.a.n.1.1		3	39.11	even	12
1521.2.a.s.1.3		3	39.2	even	12
1521.2.b.k.1351.1		6	39.23	odd	6
1521.2.b.k.1351.6		6	39.29	odd	6
8112.2.a.cg.1.3		3	52.15	even	12
8112.2.a.cp.1.1		3	52.11	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.33136 + 1.34601i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.62349 - 4.54402i) q^{4} +1.04892i q^{5} +(-2.33136 - 1.34601i) q^{6} +(-0.480608 - 0.277479i) q^{7} +8.74094i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.33136 + 1.34601i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.62349 - 4.54402i) q^{4} +1.04892i q^{5} +(-2.33136 - 1.34601i) q^{6} +(-0.480608 - 0.277479i) q^{7} +8.74094i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.41185 - 2.44540i) q^{10} +(2.52174 - 1.45593i) q^{11} +5.24698 q^{12} +1.49396 q^{14} +(-0.908389 + 0.524459i) q^{15} +(-6.51842 - 11.2902i) q^{16} +(-2.42543 + 4.20096i) q^{17} -2.69202i q^{18} +(-0.652135 - 0.376510i) q^{19} +(4.76630 + 2.75182i) q^{20} -0.554958i q^{21} +(-3.91939 + 6.78858i) q^{22} +(2.88135 + 4.99065i) q^{23} +(-7.56988 + 4.37047i) q^{24} +3.89977 q^{25} -1.00000 q^{27} +(-2.52174 + 1.45593i) q^{28} +(0.955927 + 1.65571i) q^{29} +(1.41185 - 2.44540i) q^{30} +9.51573i q^{31} +(15.2538 + 8.80678i) q^{32} +(2.52174 + 1.45593i) q^{33} -13.0586i q^{34} +(0.291053 - 0.504118i) q^{35} +(2.62349 + 4.54402i) q^{36} +(4.98226 - 2.87651i) q^{37} +2.02715 q^{38} -9.16852 q^{40} +(-4.25379 + 2.45593i) q^{41} +(0.746980 + 1.29381i) q^{42} +(-5.54892 + 9.61101i) q^{43} -15.2784i q^{44} +(-0.908389 - 0.524459i) q^{45} +(-13.4349 - 7.75667i) q^{46} +0.753020i q^{47} +(6.51842 - 11.2902i) q^{48} +(-3.34601 - 5.79546i) q^{49} +(-9.09177 + 5.24914i) q^{50} -4.85086 q^{51} -7.58211 q^{53} +(2.33136 - 1.34601i) q^{54} +(1.52715 + 2.64510i) q^{55} +(2.42543 - 4.20096i) q^{56} -0.753020i q^{57} +(-4.45722 - 2.57338i) q^{58} +(-3.54883 - 2.04892i) q^{59} +5.50365i q^{60} +(1.71164 - 2.96464i) q^{61} +(-12.8083 - 22.1846i) q^{62} +(0.480608 - 0.277479i) q^{63} -21.3424 q^{64} -7.83877 q^{66} +(1.62174 - 0.936313i) q^{67} +(12.7262 + 22.0424i) q^{68} +(-2.88135 + 4.99065i) q^{69} +1.56704i q^{70} +(-9.09643 - 5.25182i) q^{71} +(-7.56988 - 4.37047i) q^{72} +10.4765i q^{73} +(-7.74363 + 13.4124i) q^{74} +(1.94989 + 3.37730i) q^{75} +(-3.42174 + 1.97554i) q^{76} -1.61596 q^{77} +1.33513 q^{79} +(11.8425 - 6.83728i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.61141 - 11.4513i) q^{82} -2.64310i q^{83} +(-2.52174 - 1.45593i) q^{84} +(-4.40646 - 2.54407i) q^{85} -29.8756i q^{86} +(-0.955927 + 1.65571i) q^{87} +(12.7262 + 22.0424i) q^{88} +(8.59696 - 4.96346i) q^{89} +2.82371 q^{90} +30.2368 q^{92} +(-8.24086 + 4.75786i) q^{93} +(-1.01357 - 1.75556i) q^{94} +(0.394928 - 0.684035i) q^{95} +17.6136i q^{96} +(14.7862 + 8.53684i) q^{97} +(15.6015 + 9.00753i) q^{98} +2.91185i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9	\( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43} + 22 q^{48} - 30 q^{49} - 4 q^{51} - 68 q^{53} - 6 q^{55} + 2 q^{56} + 26 q^{61} - 4 q^{62} + 36 q^{66} + 26 q^{68} - 30 q^{74} - 22 q^{75} - 60 q^{77} + 12 q^{79} - 6 q^{81} - 6 q^{82} - 4 q^{87} + 26 q^{88} + 4 q^{90} + 28 q^{92} - 42 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9 - 2 * q^10 + 44 * q^12 - 20 * q^14 - 22 * q^16 - 2 * q^17 + 18 * q^22 - 44 * q^25 - 12 * q^27 + 4 * q^29 + 2 * q^30 - 8 * q^35 + 22 * q^36 + 12 * q^40 - 10 * q^42 - 30 * q^43 + 22 * q^48 - 30 * q^49 - 4 * q^51 - 68 * q^53 - 6 * q^55 + 2 * q^56 + 26 * q^61 - 4 * q^62 + 36 * q^66 + 26 * q^68 - 30 * q^74 - 22 * q^75 - 60 * q^77 + 12 * q^79 - 6 * q^81 - 6 * q^82 - 4 * q^87 + 26 * q^88 + 4 * q^90 + 28 * q^92 - 42 * q^95

Introduction

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