LMFDB - Embedded newform 315.2.i.f.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.i (of order $3$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} - 2 x^{15} + 8 x^{14} - 10 x^{13} + 40 x^{12} - 45 x^{11} + 159 x^{10} - 180 x^{9} + 576 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 8x^14 - 10x^13 + 40x^12 - 45x^11 + 159x^10 - 180x^9 + 576x^8 - 540x^7 + 1431x^6 - 1215x^5 + 3240x^4 - 2430x^3 + 5832x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.3
Root			$-1.26474 - 1.18340i$ of defining polynomial
Character	$\chi$	$=$	315.211
Dual form			315.2.i.f.106.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.522039 - 0.904198i) q^{2} +(0.392487 - 1.68700i) q^{3} +(0.454951 - 0.787999i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.73027 + 0.525791i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.03816 q^{8} +(-2.69191 - 1.32425i) q^{9} +O(q^{10})$	\(q+(-0.522039 - 0.904198i) q^{2} +(0.392487 - 1.68700i) q^{3} +(0.454951 - 0.787999i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.73027 + 0.525791i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.03816 q^{8} +(-2.69191 - 1.32425i) q^{9} +1.04408 q^{10} +(-2.85318 - 4.94185i) q^{11} +(-1.15079 - 1.07678i) q^{12} +(1.04644 - 1.81250i) q^{13} +(0.522039 - 0.904198i) q^{14} +(1.26474 + 1.18340i) q^{15} +(0.676136 + 1.17110i) q^{16} +3.21203 q^{17} +(0.207899 + 3.12532i) q^{18} -1.22268 q^{19} +(0.454951 + 0.787999i) q^{20} +(1.65722 - 0.503594i) q^{21} +(-2.97894 + 5.15967i) q^{22} +(-1.83579 + 3.17969i) q^{23} +(-1.19244 + 5.12537i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.18514 q^{26} +(-3.29054 + 4.02149i) q^{27} +0.909902 q^{28} +(0.588958 + 1.02010i) q^{29} +(0.409787 - 1.76135i) q^{30} +(3.29269 - 5.70311i) q^{31} +(-2.33222 + 4.03953i) q^{32} +(-9.45671 + 2.87369i) q^{33} +(-1.67681 - 2.90431i) q^{34} -1.00000 q^{35} +(-2.26819 + 1.51875i) q^{36} +9.74729 q^{37} +(0.638288 + 1.10555i) q^{38} +(-2.64696 - 2.47673i) q^{39} +(1.51908 - 2.63113i) q^{40} +(5.12553 - 8.87767i) q^{41} +(-1.32048 - 1.23556i) q^{42} +(4.76655 + 8.25590i) q^{43} -5.19223 q^{44} +(2.49279 - 1.66914i) q^{45} +3.83342 q^{46} +(-3.46156 - 5.99560i) q^{47} +(2.24102 - 0.680997i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.522039 + 0.904198i) q^{50} +(1.26068 - 5.41869i) q^{51} +(-0.952163 - 1.64919i) q^{52} +4.52461 q^{53} +(5.35401 + 0.875924i) q^{54} +5.70635 q^{55} +(-1.51908 - 2.63113i) q^{56} +(-0.479887 + 2.06266i) q^{57} +(0.614917 - 1.06507i) q^{58} +(-5.91477 + 10.2447i) q^{59} +(1.50791 - 0.458222i) q^{60} +(-4.46980 - 7.74192i) q^{61} -6.87565 q^{62} +(-0.199123 - 2.99338i) q^{63} +7.57459 q^{64} +(1.04644 + 1.81250i) q^{65} +(7.53515 + 7.05056i) q^{66} +(-2.96701 + 5.13901i) q^{67} +(1.46132 - 2.53108i) q^{68} +(4.64359 + 4.34496i) q^{69} +(0.522039 + 0.904198i) q^{70} +14.0375 q^{71} +(8.17846 + 4.02328i) q^{72} +5.49723 q^{73} +(-5.08846 - 8.81348i) q^{74} +(-1.65722 + 0.503594i) q^{75} +(-0.556261 + 0.963472i) q^{76} +(2.85318 - 4.94185i) q^{77} +(-0.857638 + 3.68632i) q^{78} +(-6.68275 - 11.5749i) q^{79} -1.35227 q^{80} +(5.49274 + 7.12950i) q^{81} -10.7029 q^{82} +(-1.74535 - 3.02303i) q^{83} +(0.357125 - 1.53500i) q^{84} +(-1.60602 + 2.78170i) q^{85} +(4.97664 - 8.61980i) q^{86} +(1.95207 - 0.593191i) q^{87} +(8.66842 + 15.0141i) q^{88} +16.2386 q^{89} +(-2.81056 - 1.38262i) q^{90} +2.09289 q^{91} +(1.67039 + 2.89320i) q^{92} +(-8.32878 - 7.79315i) q^{93} +(-3.61414 + 6.25987i) q^{94} +(0.611341 - 1.05887i) q^{95} +(5.89930 + 5.51992i) q^{96} +(-1.04577 - 1.81132i) q^{97} +1.04408 q^{98} +(1.13626 + 17.0813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.522039	−	0.904198i	−0.369137	−	0.639364i	0.620294	−	0.784370i	$-0.287013\pi$
$2$	−0.522039	−	0.904198i	−0.369137	−	0.639364i	−0.989431	+	0.145005i	$0.953680\pi$
$3$	0.392487	−	1.68700i	0.226602	−	0.973987i
$3$	0.392487	−	1.68700i	0.226602	−	0.973987i
$4$	0.454951	−	0.787999i	0.227476	−	0.393999i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.73027	+	0.525791i	−0.706380	+	0.214653i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−3.03816			−1.07415
$9$	−2.69191	−	1.32425i	−0.897303	−	0.441416i
$10$	1.04408			0.330166
$11$	−2.85318	−	4.94185i	−0.860265	−	1.49002i	−0.871673	−	0.490088i	$-0.836965\pi$
$11$	−2.85318	−	4.94185i	−0.860265	−	1.49002i	0.0114077	−	0.999935i	$-0.496369\pi$
$12$	−1.15079	−	1.07678i	−0.332204	−	0.310840i
$13$	1.04644	−	1.81250i	0.290232	−	0.502696i	−0.683633	−	0.729826i	$-0.739601\pi$
$13$	1.04644	−	1.81250i	0.290232	−	0.502696i	0.973864	+	0.227130i	$0.0729343\pi$
$14$	0.522039	−	0.904198i	0.139521	−	0.241657i
$15$	1.26474	+	1.18340i	0.326554	+	0.305553i
$16$	0.676136	+	1.17110i	0.169034	+	0.292776i
$17$	3.21203			0.779033			0.389516	−	0.921020i	$-0.372642\pi$
$17$	3.21203			0.779033			0.389516	+	0.921020i	$0.372642\pi$
$18$	0.207899	+	3.12532i	0.0490023	+	0.736646i
$19$	−1.22268			−0.280503			−0.140251	−	0.990116i	$-0.544791\pi$
$19$	−1.22268			−0.280503			−0.140251	+	0.990116i	$0.544791\pi$
$20$	0.454951	+	0.787999i	0.101730	+	0.176202i
$21$	1.65722	−	0.503594i	0.361636	−	0.109893i
$22$	−2.97894	+	5.15967i	−0.635112	+	1.10005i
$23$	−1.83579	+	3.17969i	−0.382789	+	0.663011i	−0.991460	−	0.130413i	$-0.958370\pi$
$23$	−1.83579	+	3.17969i	−0.382789	+	0.663011i	0.608671	+	0.793423i	$0.291703\pi$
$24$	−1.19244	+	5.12537i	−0.243406	+	1.04621i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.18514			−0.428541
$27$	−3.29054	+	4.02149i	−0.633264	+	0.773936i
$28$	0.909902			0.171955
$29$	0.588958	+	1.02010i	0.109367	+	0.189429i	0.915514	−	0.402286i	$-0.131784\pi$
$29$	0.588958	+	1.02010i	0.109367	+	0.189429i	−0.806147	+	0.591715i	$0.798451\pi$
$30$	0.409787	−	1.76135i	0.0748165	−	0.321578i
$31$	3.29269	−	5.70311i	0.591385	−	1.02431i	−0.402661	−	0.915349i	$-0.631915\pi$
$31$	3.29269	−	5.70311i	0.591385	−	1.02431i	0.994046	−	0.108960i	$-0.0347519\pi$
$32$	−2.33222	+	4.03953i	−0.412283	+	0.714095i
$33$	−9.45671	+	2.87369i	−1.64620	+	0.500245i
$34$	−1.67681	−	2.90431i	−0.287570	−	0.498086i
$35$	−1.00000			−0.169031
$36$	−2.26819	+	1.51875i	−0.378032	+	0.253125i
$37$	9.74729			1.60245			0.801223	−	0.598366i	$-0.204183\pi$
$37$	9.74729			1.60245			0.801223	+	0.598366i	$0.204183\pi$
$38$	0.638288	+	1.10555i	0.103544	+	0.179343i
$39$	−2.64696	−	2.47673i	−0.423852	−	0.396594i
$40$	1.51908	−	2.63113i	0.240188	−	0.416018i
$41$	5.12553	−	8.87767i	0.800473	−	1.38646i	−0.118832	−	0.992914i	$-0.537915\pi$
$41$	5.12553	−	8.87767i	0.800473	−	1.38646i	0.919305	−	0.393545i	$-0.128752\pi$
$42$	−1.32048	−	1.23556i	−0.203755	−	0.190651i
$43$	4.76655	+	8.25590i	0.726892	+	1.25901i	0.958191	+	0.286131i	$0.0923692\pi$
$43$	4.76655	+	8.25590i	0.726892	+	1.25901i	−0.231299	+	0.972883i	$0.574298\pi$
$44$	−5.19223			−0.782757
$45$	2.49279	−	1.66914i	0.371603	−	0.248820i
$46$	3.83342			0.565207
$47$	−3.46156	−	5.99560i	−0.504921	−	0.874548i	−0.999984	−	0.00569117i	$-0.998188\pi$
$47$	−3.46156	−	5.99560i	−0.504921	−	0.874548i	0.495063	−	0.868857i	$-0.335145\pi$
$48$	2.24102	−	0.680997i	0.323463	−	0.0982934i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.522039	+	0.904198i	−0.0738274	+	0.127873i
$51$	1.26068	−	5.41869i	0.176531	−	0.758768i
$52$	−0.952163	−	1.64919i	−0.132041	−	0.228702i
$53$	4.52461			0.621503			0.310752	−	0.950491i	$-0.399419\pi$
$53$	4.52461			0.621503			0.310752	+	0.950491i	$0.399419\pi$
$54$	5.35401	+	0.875924i	0.728588	+	0.119198i
$55$	5.70635			0.769445
$56$	−1.51908	−	2.63113i	−0.202996	−	0.351599i
$57$	−0.479887	+	2.06266i	−0.0635626	+	0.273206i
$58$	0.614917	−	1.06507i	0.0807426	−	0.139850i
$59$	−5.91477	+	10.2447i	−0.770037	+	1.33374i	0.167505	+	0.985871i	$0.446429\pi$
$59$	−5.91477	+	10.2447i	−0.770037	+	1.33374i	−0.937542	+	0.347872i	$0.886904\pi$
$60$	1.50791	−	0.458222i	0.194671	−	0.0591562i
$61$	−4.46980	−	7.74192i	−0.572299	−	0.991251i	−0.996329	−	0.0856032i	$-0.972718\pi$
$61$	−4.46980	−	7.74192i	−0.572299	−	0.991251i	0.424030	−	0.905648i	$-0.360615\pi$
$62$	−6.87565			−0.873208
$63$	−0.199123	−	2.99338i	−0.0250871	−	0.377131i
$64$	7.57459			0.946824
$65$	1.04644	+	1.81250i	0.129795	+	0.224812i
$66$	7.53515	+	7.05056i	0.927513	+	0.867864i
$67$	−2.96701	+	5.13901i	−0.362478	+	0.627830i	−0.988368	−	0.152081i	$-0.951403\pi$
$67$	−2.96701	+	5.13901i	−0.362478	+	0.627830i	0.625890	+	0.779911i	$0.284736\pi$
$68$	1.46132	−	2.53108i	0.177211	−	0.306938i
$69$	4.64359	+	4.34496i	0.559023	+	0.523072i
$70$	0.522039	+	0.904198i	0.0623956	+	0.108072i
$71$	14.0375			1.66594			0.832971	−	0.553316i	$-0.186638\pi$
$71$	14.0375			1.66594			0.832971	+	0.553316i	$0.186638\pi$
$72$	8.17846	+	4.02328i	0.963840	+	0.474148i
$73$	5.49723			0.643402			0.321701	−	0.946841i	$-0.395745\pi$
$73$	5.49723			0.643402			0.321701	+	0.946841i	$0.395745\pi$
$74$	−5.08846	−	8.81348i	−0.591522	−	1.02455i
$75$	−1.65722	+	0.503594i	−0.191360	+	0.0581501i
$76$	−0.556261	+	0.963472i	−0.0638075	+	0.110518i
$77$	2.85318	−	4.94185i	0.325150	−	0.563176i
$78$	−0.857638	+	3.68632i	−0.0971084	+	0.417393i
$79$	−6.68275	−	11.5749i	−0.751868	−	1.30227i	−0.946917	−	0.321480i	$-0.895820\pi$
$79$	−6.68275	−	11.5749i	−0.751868	−	1.30227i	0.195049	−	0.980794i	$-0.437513\pi$
$80$	−1.35227			−0.151189
$81$	5.49274	+	7.12950i	0.610304	+	0.792167i
$82$	−10.7029			−1.18194
$83$	−1.74535	−	3.02303i	−0.191577	−	0.331821i	0.754196	−	0.656649i	$-0.228027\pi$
$83$	−1.74535	−	3.02303i	−0.191577	−	0.331821i	−0.945773	+	0.324828i	$0.894693\pi$
$84$	0.357125	−	1.53500i	0.0389655	−	0.167482i
$85$	−1.60602	+	2.78170i	−0.174197	+	0.301718i
$86$	4.97664	−	8.61980i	0.536645	−	0.929497i
$87$	1.95207	−	0.593191i	0.209284	−	0.0635968i
$88$	8.66842	+	15.0141i	0.924056	+	1.60051i
$89$	16.2386			1.72129			0.860645	−	0.509206i	$-0.170061\pi$
$89$	16.2386			1.72129			0.860645	+	0.509206i	$0.170061\pi$
$90$	−2.81056	−	1.38262i	−0.296259	−	0.145741i
$91$	2.09289			0.219394
$92$	1.67039	+	2.89320i	0.174150	+	0.301637i
$93$	−8.32878	−	7.79315i	−0.863654	−	0.808112i
$94$	−3.61414	+	6.25987i	−0.372770	+	0.645656i
$95$	0.611341	−	1.05887i	0.0627223	−	0.108638i
$96$	5.89930	+	5.51992i	0.602095	+	0.563374i
$97$	−1.04577	−	1.81132i	−0.106182	−	0.183912i	0.808039	−	0.589129i	$-0.200529\pi$
$97$	−1.04577	−	1.81132i	−0.106182	−	0.183912i	−0.914220	+	0.405217i	$0.867196\pi$
$98$	1.04408			0.105468
$99$	1.13626	+	17.0813i	0.114199	+	1.71674i
$100$	−0.909902			−0.0909902
$101$	1.98287	+	3.43443i	0.197303	+	0.341738i	0.947653	−	0.319302i	$-0.103448\pi$
$101$	1.98287	+	3.43443i	0.197303	+	0.341738i	−0.750350	+	0.661041i	$0.770115\pi$
$102$	−5.55769	+	1.68886i	−0.550293	+	0.167222i
$103$	3.33236	−	5.77181i	0.328347	−	0.568714i	−0.653837	−	0.756635i	$-0.726842\pi$
$103$	3.33236	−	5.77181i	0.328347	−	0.568714i	0.982184	+	0.187922i	$0.0601751\pi$
$104$	−3.17927	+	5.50666i	−0.311753	+	0.539972i
$105$	−0.392487	+	1.68700i	−0.0383028	+	0.164634i
$106$	−2.36202	−	4.09114i	−0.229420	−	0.397367i
$107$	−7.34307			−0.709881			−0.354941	−	0.934889i	$-0.615499\pi$
$107$	−7.34307			−0.709881			−0.354941	+	0.934889i	$0.615499\pi$
$108$	1.67189	+	4.42252i	0.160878	+	0.425557i
$109$	−5.33766			−0.511255			−0.255628	−	0.966775i	$-0.582282\pi$
$109$	−5.33766			−0.511255			−0.255628	+	0.966775i	$0.582282\pi$
$110$	−2.97894	−	5.15967i	−0.284031	−	0.491955i
$111$	3.82568	−	16.4436i	0.363118	−	1.56076i
$112$	−0.676136	+	1.17110i	−0.0638889	+	0.110659i
$113$	3.58016	−	6.20103i	0.336794	−	0.583344i	−0.647034	−	0.762461i	$-0.723991\pi$
$113$	3.58016	−	6.20103i	0.336794	−	0.583344i	0.983828	+	0.179117i	$0.0573242\pi$
$114$	2.11557	−	0.642876i	0.198141	−	0.0602109i
$115$	−1.83579	−	3.17969i	−0.171189	−	0.296507i
$116$	1.07179			0.0995130
$117$	−5.21712	+	3.49332i	−0.482323	+	0.322958i
$118$	12.3509			1.13700
$119$	1.60602	+	2.78170i	0.147223	+	0.254998i
$120$	−3.84248	−	3.59537i	−0.350769	−	0.328211i
$121$	−10.7812	+	18.6737i	−0.980112	+	1.69760i
$122$	−4.66682	+	8.08316i	−0.422514	+	0.731815i
$123$	−12.9649	−	12.1311i	−1.16901	−	1.09383i
$124$	−2.99603	−	5.18927i	−0.269051	−	0.466010i
$125$	1.00000			0.0894427
$126$	−2.60266	+	1.74271i	−0.231863	+	0.155253i
$127$	−2.73775			−0.242936			−0.121468	−	0.992595i	$-0.538760\pi$
$127$	−2.73775			−0.242936			−0.121468	+	0.992595i	$0.538760\pi$
$128$	0.710220	+	1.23014i	0.0627752	+	0.108730i
$129$	15.7985	−	4.80081i	1.39098	−	0.422688i
$130$	1.09257	−	1.89239i	0.0958247	−	0.165973i
$131$	2.69327	−	4.66488i	0.235312	−	0.407573i	−0.724051	−	0.689746i	$-0.757722\pi$
$131$	2.69327	−	4.66488i	0.235312	−	0.407573i	0.959363	+	0.282173i	$0.0910554\pi$
$132$	−2.03788	+	8.75926i	−0.177375	+	0.762396i
$133$	−0.611341	−	1.05887i	−0.0530100	−	0.0918160i
$134$	6.19558			0.535216
$135$	−1.83744	−	4.86043i	−0.158142	−	0.418319i
$136$	−9.75868			−0.836800
$137$	−0.980572	−	1.69840i	−0.0837759	−	0.145104i	0.821093	−	0.570794i	$-0.193365\pi$
$137$	−0.980572	−	1.69840i	−0.0837759	−	0.145104i	−0.904869	+	0.425690i	$0.860031\pi$
$138$	1.50457	−	6.46696i	0.128077	−	0.550504i
$139$	−4.13585	+	7.16351i	−0.350798	+	0.607601i	−0.986390	−	0.164425i	$-0.947423\pi$
$139$	−4.13585	+	7.16351i	−0.350798	+	0.607601i	0.635591	+	0.772026i	$0.280756\pi$
$140$	−0.454951	+	0.787999i	−0.0384504	+	0.0665980i
$141$	−11.4732	+	3.48644i	−0.966215	+	0.293612i
$142$	−7.32811	−	12.6927i	−0.614961	−	1.06514i
$143$	−11.9428			−0.998704
$144$	−0.269268	−	4.04787i	−0.0224390	−	0.337323i
$145$	−1.17792			−0.0978206
$146$	−2.86977	−	4.97058i	−0.237504	−	0.411368i
$147$	1.26474	+	1.18340i	0.104314	+	0.0976053i
$148$	4.43454	−	7.68085i	0.364517	−	0.631362i
$149$	−5.14104	+	8.90454i	−0.421170	+	0.729488i	−0.996054	−	0.0887467i	$-0.971714\pi$
$149$	−5.14104	+	8.90454i	−0.421170	+	0.729488i	0.574884	+	0.818235i	$0.305047\pi$
$150$	1.32048	+	1.23556i	0.107817	+	0.100883i
$151$	−0.955153	−	1.65437i	−0.0777293	−	0.134631i	0.824541	−	0.565803i	$-0.191434\pi$
$151$	−0.955153	−	1.65437i	−0.0777293	−	0.134631i	−0.902270	+	0.431172i	$0.858100\pi$
$152$	3.71471			0.301303
$153$	−8.64650	−	4.25353i	−0.699028	−	0.343877i
$154$	−5.95787			−0.480099
$155$	3.29269	+	5.70311i	0.264475	+	0.458085i
$156$	−3.15589	+	0.959007i	−0.252674	+	0.0767820i
$157$	−9.80281	+	16.9790i	−0.782349	+	1.35507i	0.148221	+	0.988954i	$0.452645\pi$
$157$	−9.80281	+	16.9790i	−0.782349	+	1.35507i	−0.930570	+	0.366114i	$0.880688\pi$
$158$	−6.97730	+	12.0850i	−0.555085	+	0.961435i
$159$	1.77585	−	7.63300i	0.140834	−	0.605336i
$160$	−2.33222	−	4.03953i	−0.184379	−	0.319353i
$161$	−3.67159			−0.289362
$162$	3.57906	−	8.68840i	0.281197	−	0.682625i
$163$	−2.64581			−0.207236			−0.103618	−	0.994617i	$-0.533042\pi$
$163$	−2.64581			−0.207236			−0.103618	+	0.994617i	$0.533042\pi$
$164$	−4.66373	−	8.07782i	−0.364176	−	0.630772i
$165$	2.23967	−	9.62659i	0.174358	−	0.749429i
$166$	−1.82228	+	3.15628i	−0.141436	+	0.244975i
$167$	6.54217	−	11.3314i	0.506248	−	0.876847i	−0.493726	−	0.869618i	$-0.664365\pi$
$167$	6.54217	−	11.3314i	0.506248	−	0.876847i	0.999974	−	0.00722973i	$-0.00230131\pi$
$168$	−5.03492	+	1.53000i	−0.388452	+	0.118042i
$169$	4.30991	+	7.46498i	0.331531	+	0.574229i
$170$	3.35361			0.257210
$171$	3.29135	+	1.61913i	0.251696	+	0.123818i
$172$	8.67419			0.661401
$173$	11.5075	+	19.9316i	0.874901	+	1.51537i	0.856868	+	0.515535i	$0.172407\pi$
$173$	11.5075	+	19.9316i	0.874901	+	1.51537i	0.0180323	+	0.999837i	$0.494260\pi$
$174$	−1.55542	−	1.45539i	−0.117916	−	0.110333i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	3.85827	−	6.68272i	0.290828	−	0.503729i
$177$	14.9613	+	13.9991i	1.12456	+	1.05224i
$178$	−8.47718	−	14.6829i	−0.635392	−	1.10053i
$179$	−8.12890			−0.607583			−0.303791	−	0.952739i	$-0.598253\pi$
$179$	−8.12890			−0.607583			−0.303791	+	0.952739i	$0.598253\pi$
$180$	−0.181182	−	2.72369i	−0.0135045	−	0.203012i
$181$	−2.59150			−0.192625			−0.0963123	−	0.995351i	$-0.530705\pi$
$181$	−2.59150			−0.192625			−0.0963123	+	0.995351i	$0.530705\pi$
$182$	−1.09257	−	1.89239i	−0.0809866	−	0.140273i
$183$	−14.8149	+	4.50193i	−1.09515	+	0.332792i
$184$	5.57744	−	9.66041i	0.411174	−	0.712175i
$185$	−4.87365	+	8.44140i	−0.358318	+	0.620624i
$186$	−2.69860	+	11.5992i	−0.197871	+	0.850494i
$187$	−9.16450	−	15.8734i	−0.670175	−	1.16078i
$188$	−6.29937			−0.459429
$189$	−5.12798	−	0.838945i	−0.373006	−	0.0610243i
$190$	−1.27658			−0.0926125
$191$	7.51242	+	13.0119i	0.543579	+	0.941507i	0.998695	+	0.0510746i	$0.0162646\pi$
$191$	7.51242	+	13.0119i	0.543579	+	0.941507i	−0.455116	+	0.890432i	$0.650402\pi$
$192$	2.97293	−	12.7783i	0.214553	−	0.922195i
$193$	−8.71819	+	15.1003i	−0.627549	+	1.08695i	0.360493	+	0.932762i	$0.382608\pi$
$193$	−8.71819	+	15.1003i	−0.627549	+	1.08695i	−0.988042	+	0.154185i	$0.950725\pi$
$194$	−1.09186	+	1.89116i	−0.0783911	+	0.135777i
$195$	3.46839	−	1.05397i	0.248376	−	0.0754761i
$196$	0.454951	+	0.787999i	0.0324965	+	0.0562856i
$197$	4.31991			0.307781			0.153890	−	0.988088i	$-0.450820\pi$
$197$	4.31991			0.307781			0.153890	+	0.988088i	$0.450820\pi$
$198$	14.8517	−	9.94451i	1.05546	−	0.706726i
$199$	−8.01186			−0.567946			−0.283973	−	0.958832i	$-0.591653\pi$
$199$	−8.01186			−0.567946			−0.283973	+	0.958832i	$0.591653\pi$
$200$	1.51908	+	2.63113i	0.107415	+	0.186049i
$201$	7.50498	+	7.02233i	0.529361	+	0.495317i
$202$	2.07027	−	3.58581i	0.145664	−	0.252297i
$203$	−0.588958	+	1.02010i	−0.0413367	+	0.0715973i
$204$	−3.69637	−	3.45865i	−0.258798	−	0.242154i
$205$	5.12553	+	8.87767i	0.357982	+	0.620044i
$206$	−6.95848			−0.484820
$207$	9.15248	−	6.12838i	0.636141	−	0.425952i
$208$	2.83016			0.196236
$209$	3.48853	+	6.04231i	0.241307	+	0.417955i
$210$	1.73027	−	0.525791i	0.119400	−	0.0362830i
$211$	−12.8909	+	22.3277i	−0.887447	+	1.53710i	−0.0445645	+	0.999007i	$0.514190\pi$
$211$	−12.8909	+	22.3277i	−0.887447	+	1.53710i	−0.842883	+	0.538097i	$0.819143\pi$
$212$	2.05848	−	3.56539i	0.141377	−	0.244872i
$213$	5.50953	−	23.6812i	0.377507	−	1.62261i
$214$	3.83337	+	6.63959i	0.262044	+	0.453873i
$215$	−9.53310			−0.650152
$216$	9.99719	−	12.2179i	0.680223	−	0.831325i
$217$	6.58538			0.447045
$218$	2.78647	+	4.82630i	0.188723	+	0.326878i
$219$	2.15759	−	9.27380i	0.145796	−	0.626665i
$220$	2.59611	−	4.49660i	0.175030	−	0.303161i
$221$	3.36122	−	5.82180i	0.226100	−	0.391616i
$222$	−16.8655	+	5.12504i	−1.13194	+	0.343970i
$223$	−8.58024	−	14.8614i	−0.574575	−	0.995194i	−0.996088	−	0.0883709i	$-0.971834\pi$
$223$	−8.58024	−	14.8614i	−0.574575	−	0.995194i	0.421512	−	0.906823i	$-0.361499\pi$
$224$	−4.66445			−0.311657
$225$	0.199123	+	2.99338i	0.0132748	+	0.199559i
$226$	−7.47594			−0.497292
$227$	8.96908	+	15.5349i	0.595299	+	1.03109i	0.993505	+	0.113792i	$0.0362997\pi$
$227$	8.96908	+	15.5349i	0.595299	+	1.03109i	−0.398206	+	0.917296i	$0.630367\pi$
$228$	1.40705	+	1.31656i	0.0931841	+	0.0871913i
$229$	7.89652	−	13.6772i	0.521817	−	0.903813i	−0.477861	−	0.878435i	$-0.658588\pi$
$229$	7.89652	−	13.6772i	0.521817	−	0.903813i	0.999678	−	0.0253778i	$-0.00807887\pi$
$230$	−1.91671	+	3.31984i	−0.126384	+	0.218904i
$231$	−7.21704	−	6.75291i	−0.474846	−	0.444309i
$232$	−1.78935	−	3.09924i	−0.117477	−	0.203475i
$233$	−17.9023			−1.17282			−0.586411	−	0.810014i	$-0.699459\pi$
$233$	−17.9023			−1.17282			−0.586411	+	0.810014i	$0.699459\pi$
$234$	5.88219	+	2.89366i	0.384531	+	0.189165i
$235$	6.92312			0.451615
$236$	5.38186	+	9.32166i	0.350329	+	0.606788i
$237$	−22.1496	+	6.73079i	−1.43877	+	0.437211i
$238$	1.67681	−	2.90431i	0.108691	−	0.188259i
$239$	−1.61297	+	2.79375i	−0.104335	+	0.180713i	−0.913466	−	0.406915i	$-0.866605\pi$
$239$	−1.61297	+	2.79375i	−0.104335	+	0.180713i	0.809132	+	0.587627i	$0.199938\pi$
$240$	−0.530749	+	2.28128i	−0.0342597	+	0.147256i
$241$	−2.45300	−	4.24873i	−0.158012	−	0.273685i	0.776140	−	0.630561i	$-0.217175\pi$
$241$	−2.45300	−	4.24873i	−0.158012	−	0.273685i	−0.934152	+	0.356876i	$0.883842\pi$
$242$	22.5129			1.44718
$243$	14.1833	−	6.46799i	0.909857	−	0.414922i
$244$	−8.13416			−0.520736
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	−4.20075	+	18.0557i	−0.267830	+	1.15119i
$247$	−1.27947	+	2.21611i	−0.0814107	+	0.141007i
$248$	−10.0037	+	17.3270i	−0.635238	+	1.10026i
$249$	−5.78487	+	1.75789i	−0.366601	+	0.111402i
$250$	−0.522039	−	0.904198i	−0.0330166	−	0.0571865i
$251$	22.1097			1.39555			0.697775	−	0.716317i	$-0.254174\pi$
$251$	22.1097			1.39555			0.697775	+	0.716317i	$0.254174\pi$
$252$	−2.44937	−	1.20494i	−0.154296	−	0.0759038i
$253$	20.9514			1.31720
$254$	1.42921	+	2.47546i	0.0896766	+	0.155324i
$255$	4.06238	+	3.80113i	0.254396	+	0.238036i
$256$	8.31612	−	14.4039i	0.519757	−	0.900246i
$257$	5.13926	−	8.90146i	0.320578	−	0.555258i	−0.660029	−	0.751240i	$-0.729456\pi$
$257$	5.13926	−	8.90146i	0.320578	−	0.555258i	0.980607	+	0.195982i	$0.0627895\pi$
$258$	−12.5883	−	11.7787i	−0.783713	−	0.733312i
$259$	4.87365	+	8.44140i	0.302834	+	0.524523i
$260$	1.90433			0.118101
$261$	−0.234549	−	3.52595i	−0.0145182	−	0.218251i
$262$	−5.62397			−0.347450
$263$	5.43600	+	9.41543i	0.335198	+	0.580580i	0.983523	−	0.180784i	$-0.0578634\pi$
$263$	5.43600	+	9.41543i	0.335198	+	0.580580i	−0.648325	+	0.761364i	$0.724530\pi$
$264$	28.7310	−	8.73073i	1.76827	−	0.537339i
$265$	−2.26231	+	3.91843i	−0.138972	+	0.240707i
$266$	−0.638288	+	1.10555i	−0.0391359	+	0.0677854i
$267$	6.37344	−	27.3945i	0.390048	−	1.67651i
$268$	2.69969	+	4.67600i	0.164910	+	0.285632i
$269$	0.401545			0.0244826			0.0122413	−	0.999925i	$-0.496103\pi$
$269$	0.401545			0.0244826			0.0122413	+	0.999925i	$0.496103\pi$
$270$	−3.43558	+	4.19874i	−0.209082	+	0.255527i
$271$	0.436199			0.0264972			0.0132486	−	0.999912i	$-0.495783\pi$
$271$	0.436199			0.0264972			0.0132486	+	0.999912i	$0.495783\pi$
$272$	2.17177	+	3.76162i	0.131683	+	0.228082i
$273$	0.821431	−	3.53070i	0.0497153	−	0.213687i
$274$	−1.02379	+	1.77326i	−0.0618496	+	0.107127i
$275$	−2.85318	+	4.94185i	−0.172053	+	0.298005i
$276$	5.53643	−	1.68240i	0.333254	−	0.101269i
$277$	12.7476	+	22.0795i	0.765930	+	1.32663i	0.939753	+	0.341853i	$0.111055\pi$
$277$	12.7476	+	22.0795i	0.765930	+	1.32663i	−0.173823	+	0.984777i	$0.555612\pi$
$278$	8.63630			0.517971
$279$	−16.4159	+	10.9919i	−0.982797	+	0.658068i
$280$	3.03816			0.181565
$281$	−6.14918	−	10.6507i	−0.366829	−	0.635367i	0.622239	−	0.782828i	$-0.286223\pi$
$281$	−6.14918	−	10.6507i	−0.366829	−	0.635367i	−0.989068	+	0.147461i	$0.952890\pi$
$282$	9.14187	+	8.55395i	0.544391	+	0.509380i
$283$	12.6274	−	21.8712i	0.750619	−	1.30011i	−0.196904	−	0.980423i	$-0.563089\pi$
$283$	12.6274	−	21.8712i	0.750619	−	1.30011i	0.947523	−	0.319687i	$-0.103578\pi$
$284$	6.38637	−	11.0615i	0.378961	−	0.656380i
$285$	−1.54637	−	1.44692i	−0.0915992	−	0.0857084i
$286$	6.23459	+	10.7986i	0.368659	+	0.638536i
$287$	10.2511			0.605101
$288$	11.6275	−	7.78561i	0.685155	−	0.458771i
$289$	−6.68284			−0.393108
$290$	0.614917	+	1.06507i	0.0361092	+	0.0625430i
$291$	−3.46614	+	1.05328i	−0.203189	+	0.0617446i
$292$	2.50097	−	4.33181i	0.146358	−	0.253500i
$293$	0.436664	−	0.756325i	0.0255102	−	0.0441850i	−0.852988	−	0.521930i	$-0.825212\pi$
$293$	0.436664	−	0.756325i	0.0255102	−	0.0441850i	0.878499	+	0.477745i	$0.158546\pi$
$294$	0.409787	−	1.76135i	0.0238992	−	0.102724i
$295$	−5.91477	−	10.2447i	−0.344371	−	0.596468i
$296$	−29.6139			−1.72127
$297$	29.2621	+	4.78732i	1.69796	+	0.277788i
$298$	10.7353			0.621878
$299$	3.84211	+	6.65473i	0.222195	+	0.384853i
$300$	−0.357125	+	1.53500i	−0.0206186	+	0.0886233i
$301$	−4.76655	+	8.25590i	−0.274739	+	0.475862i
$302$	−0.997254	+	1.72729i	−0.0573855	+	0.0993946i
$303$	6.57212	−	1.99712i	0.377558	−	0.114732i
$304$	−0.826700	−	1.43189i	−0.0474145	−	0.0821243i
$305$	8.93960			0.511880
$306$	0.667780	+	10.0386i	0.0381744	+	0.573871i
$307$	−13.0527			−0.744959			−0.372480	−	0.928040i	$-0.621492\pi$
$307$	−13.0527			−0.744959			−0.372480	+	0.928040i	$0.621492\pi$
$308$	−2.59611	−	4.49660i	−0.147927	−	0.256218i
$309$	−8.42912	−	7.88703i	−0.479516	−	0.448678i
$310$	3.43782	−	5.95449i	0.195255	−	0.338192i
$311$	1.37894	−	2.38839i	0.0781924	−	0.135433i	−0.824278	−	0.566186i	$-0.808418\pi$
$311$	1.37894	−	2.38839i	0.0781924	−	0.135433i	0.902470	+	0.430753i	$0.141752\pi$
$312$	8.04188	+	7.52470i	0.455282	+	0.426003i
$313$	9.87688	+	17.1073i	0.558274	+	0.966959i	0.997641	+	0.0686514i	$0.0218696\pi$
$313$	9.87688	+	17.1073i	0.558274	+	0.966959i	−0.439366	+	0.898308i	$0.644797\pi$
$314$	20.4698			1.15518
$315$	2.69191	+	1.32425i	0.151672	+	0.0746129i
$316$	−12.1613			−0.684126
$317$	0.865776	+	1.49957i	0.0486268	+	0.0842241i	0.889314	−	0.457296i	$-0.151182\pi$
$317$	0.865776	+	1.49957i	0.0486268	+	0.0842241i	−0.840688	+	0.541521i	$0.817849\pi$
$318$	−7.82880	+	2.37900i	−0.439017	+	0.133408i
$319$	3.36080	−	5.82108i	0.188169	−	0.325918i
$320$	−3.78730	+	6.55979i	−0.211716	+	0.366703i
$321$	−2.88206	+	12.3877i	−0.160861	+	0.691416i
$322$	1.91671	+	3.31984i	0.106814	+	0.185007i
$323$	−3.92730			−0.218521
$324$	8.11697	−	1.08470i	0.450943	−	0.0602608i
$325$	−2.09289			−0.116093
$326$	1.38121	+	2.39233i	0.0764984	+	0.132499i
$327$	−2.09496	+	9.00461i	−0.115852	+	0.497956i
$328$	−15.5722	+	26.9718i	−0.859830	+	1.48927i
$329$	3.46156	−	5.99560i	0.190842	−	0.330548i
$330$	−9.87354	+	3.00035i	−0.543520	+	0.165164i
$331$	−9.00619	−	15.5992i	−0.495025	−	0.857408i	0.504959	−	0.863143i	$-0.331508\pi$
$331$	−9.00619	−	15.5992i	−0.495025	−	0.857408i	−0.999984	+	0.00573548i	$0.998174\pi$
$332$	−3.17619			−0.174316
$333$	−26.2388	−	12.9078i	−1.43788	−	0.707344i
$334$	−13.6611			−0.747500
$335$	−2.96701	−	5.13901i	−0.162105	−	0.280774i
$336$	1.71027	+	1.60028i	0.0933029	+	0.0873025i
$337$	−5.29638	+	9.17360i	−0.288512	+	0.499718i	−0.973455	−	0.228879i	$-0.926494\pi$
$337$	−5.29638	+	9.17360i	−0.288512	+	0.499718i	0.684943	+	0.728597i	$0.259827\pi$
$338$	4.49988	−	7.79401i	0.244761	−	0.423938i
$339$	−9.05594	−	8.47354i	−0.491851	−	0.460220i
$340$	1.46132	+	2.53108i	0.0792511	+	0.137267i
$341$	−37.5785			−2.03499
$342$	−0.254195	−	3.82128i	−0.0137453	−	0.206631i
$343$	−1.00000			−0.0539949
$344$	−14.4816	−	25.0828i	−0.780793	−	1.35237i
$345$	−6.08464	+	1.84899i	−0.327586	+	0.0995463i
$346$	12.0147	−	20.8101i	0.645917	−	1.11876i
$347$	6.02254	−	10.4313i	0.323307	−	0.559984i	−0.657862	−	0.753139i	$-0.728539\pi$
$347$	6.02254	−	10.4313i	0.323307	−	0.559984i	0.981168	+	0.193155i	$0.0618721\pi$
$348$	0.420663	−	1.80810i	0.0225499	−	0.0969244i
$349$	8.56495	+	14.8349i	0.458471	+	0.794096i	0.998880	−	0.0473068i	$-0.0150638\pi$
$349$	8.56495	+	14.8349i	0.458471	+	0.794096i	−0.540409	+	0.841402i	$0.681731\pi$
$350$	−1.04408			−0.0558083
$351$	3.84556	+	10.1723i	0.205261	+	0.542960i
$352$	26.6170			1.41869
$353$	2.48636	+	4.30649i	0.132335	+	0.229212i	0.924576	−	0.380997i	$-0.124419\pi$
$353$	2.48636	+	4.30649i	0.132335	+	0.229212i	−0.792241	+	0.610208i	$0.791086\pi$
$354$	4.84758	−	20.8360i	0.257646	−	1.10742i
$355$	−7.01874	+	12.1568i	−0.372516	+	0.645217i
$356$	7.38777	−	12.7960i	0.391551	−	0.678187i
$357$	5.32306	−	1.61756i	0.281726	−	0.0856104i
$358$	4.24360	+	7.35013i	0.224281	+	0.388467i
$359$	15.4741			0.816691			0.408346	−	0.912827i	$-0.366106\pi$
$359$	15.4741			0.816691			0.408346	+	0.912827i	$0.366106\pi$
$360$	−7.57349	+	5.07111i	−0.399158	+	0.267271i
$361$	−17.5050			−0.921318
$362$	1.35286	+	2.34323i	0.0711049	+	0.123157i
$363$	27.2709	+	25.5171i	1.43135	+	1.33930i
$364$	0.952163	−	1.64919i	0.0499069	−	0.0864413i
$365$	−2.74861	+	4.76074i	−0.143869	+	0.249189i
$366$	11.8046	+	11.0454i	0.617036	+	0.577354i
$367$	−7.59702	−	13.1584i	−0.396561	−	0.686864i	0.596738	−	0.802436i	$-0.296463\pi$
$367$	−7.59702	−	13.1584i	−0.396561	−	0.686864i	−0.993299	+	0.115572i	$0.963130\pi$
$368$	−4.96499			−0.258818
$369$	−25.5537	+	17.1104i	−1.33027	+	0.890733i
$370$	10.1769			0.529073
$371$	2.26231	+	3.91843i	0.117453	+	0.203435i
$372$	−9.93018	+	3.01757i	−0.514856	+	0.156453i
$373$	−6.52399	+	11.2999i	−0.337800	+	0.585086i	−0.984019	−	0.178066i	$-0.943016\pi$
$373$	−6.52399	+	11.2999i	−0.337800	+	0.585086i	0.646219	+	0.763152i	$0.276349\pi$
$374$	−9.56845	+	16.5730i	−0.494773	+	0.856971i
$375$	0.392487	−	1.68700i	0.0202679	−	0.0871161i
$376$	10.5168	+	18.2156i	0.542362	+	0.939398i
$377$	2.46525			0.126967
$378$	1.91843	+	5.07467i	0.0986735	+	0.261013i
$379$	30.8515			1.58473			0.792367	−	0.610045i	$-0.208849\pi$
$379$	30.8515			1.58473			0.792367	+	0.610045i	$0.208849\pi$
$380$	−0.556261	−	0.963472i	−0.0285356	−	0.0494251i
$381$	−1.07453	+	4.61857i	−0.0550498	+	0.236616i
$382$	7.84354	−	13.5854i	0.401311	−	0.695090i
$383$	−0.160953	+	0.278778i	−0.00822430	+	0.0142449i	−0.870108	−	0.492861i	$-0.835951\pi$
$383$	−0.160953	+	0.278778i	−0.00822430	+	0.0142449i	0.861884	+	0.507106i	$0.169285\pi$
$384$	2.35399	−	0.715325i	0.120126	−	0.0365038i
$385$	2.85318	+	4.94185i	0.145411	+	0.251860i
$386$	18.2049			0.926606
$387$	−1.89825	−	28.5362i	−0.0964937	−	1.45058i
$388$	−1.90309			−0.0966149
$389$	−8.39039	−	14.5326i	−0.425410	−	0.736831i	0.571049	−	0.820916i	$-0.306537\pi$
$389$	−8.39039	−	14.5326i	−0.425410	−	0.736831i	−0.996459	+	0.0840850i	$0.973203\pi$
$390$	−2.76363	−	2.58590i	−0.139942	−	0.130942i
$391$	−5.89663	+	10.2133i	−0.298205	+	0.516507i
$392$	1.51908	−	2.63113i	0.0767252	−	0.132892i
$393$	−6.81257	−	6.37444i	−0.343649	−	0.321548i
$394$	−2.25516	−	3.90605i	−0.113613	−	0.196784i
$395$	13.3655			0.672491
$396$	13.9770	+	6.87579i	0.702370	+	0.345521i
$397$	1.53433			0.0770058			0.0385029	−	0.999258i	$-0.487741\pi$
$397$	1.53433			0.0770058			0.0385029	+	0.999258i	$0.487741\pi$
$398$	4.18250	+	7.24430i	0.209650	+	0.363124i
$399$	−2.02626	+	0.615736i	−0.101440	+	0.0308254i
$400$	0.676136	−	1.17110i	0.0338068	−	0.0585551i
$401$	−11.1388	+	19.2930i	−0.556245	+	0.963445i	0.441561	+	0.897231i	$0.354425\pi$
$401$	−11.1388	+	19.2930i	−0.556245	+	0.963445i	−0.997806	+	0.0662131i	$0.978908\pi$
$402$	2.43168	−	10.4519i	0.121281	−	0.521294i
$403$	−6.89124	−	11.9360i	−0.343277	−	0.594573i
$404$	3.60843			0.179526
$405$	−8.92070	+	1.19210i	−0.443273	+	0.0592360i
$406$	1.22983			0.0610357
$407$	−27.8108	−	48.1696i	−1.37853	−	2.38768i
$408$	−3.83015	+	16.4629i	−0.189621	+	0.815033i
$409$	5.79352	−	10.0347i	0.286471	−	0.496183i	−0.686494	−	0.727136i	$-0.740851\pi$
$409$	5.79352	−	10.0347i	0.286471	−	0.496183i	0.972965	+	0.230953i	$0.0741844\pi$
$410$	5.35145	−	9.26898i	0.264289	−	0.457762i
$411$	−3.25006	+	0.987621i	−0.160313	+	0.0487157i
$412$	−3.03212	−	5.25179i	−0.149382	−	0.258737i
$413$	−11.8295			−0.582093
$414$	−10.3192	−	5.07639i	−0.507162	−	0.249491i
$415$	3.49070			0.171352
$416$	4.88109	+	8.45429i	0.239315	+	0.414506i
$417$	10.4615	+	9.78874i	0.512304	+	0.479357i
$418$	3.64230	−	6.30864i	0.178150	−	0.308566i
$419$	3.11016	−	5.38695i	0.151941	−	0.263170i	−0.780000	−	0.625780i	$-0.784781\pi$
$419$	3.11016	−	5.38695i	0.151941	−	0.263170i	0.931941	+	0.362610i	$0.118114\pi$
$420$	1.15079	+	1.07678i	0.0561527	+	0.0525415i
$421$	−17.4018	−	30.1409i	−0.848114	−	1.46898i	−0.882889	−	0.469581i	$-0.844405\pi$
$421$	−17.4018	−	30.1409i	−0.848114	−	1.46898i	0.0347758	−	0.999395i	$-0.488928\pi$
$422$	26.9182			1.31036
$423$	1.37855	+	20.7236i	0.0670274	+	1.00761i
$424$	−13.7465			−0.667589
$425$	−1.60602	−	2.78170i	−0.0779033	−	0.134932i
$426$	−24.2886	+	7.38079i	−1.17679	+	0.357600i
$427$	4.46980	−	7.74192i	0.216309	−	0.374658i
$428$	−3.34074	+	5.78633i	−0.161481	+	0.279693i
$429$	−4.68738	+	20.1474i	−0.226309	+	0.972725i
$430$	4.97664	+	8.61980i	0.239995	+	0.415684i
$431$	−22.7514			−1.09589			−0.547947	−	0.836513i	$-0.684591\pi$
$431$	−22.7514			−1.09589			−0.547947	+	0.836513i	$0.684591\pi$
$432$	−6.93443	−	1.13448i	−0.333633	−	0.0545828i
$433$	32.2442			1.54956			0.774779	−	0.632232i	$-0.217861\pi$
$433$	32.2442			1.54956			0.774779	+	0.632232i	$0.217861\pi$
$434$	−3.43782	−	5.95449i	−0.165021	−	0.285825i
$435$	−0.462316	+	1.98714i	−0.0221664	+	0.0952760i
$436$	−2.42838	+	4.20607i	−0.116298	+	0.201434i
$437$	2.24459	−	3.88775i	0.107373	−	0.185976i
$438$	−9.51169	+	2.89040i	−0.454486	+	0.138108i
$439$	13.5843	+	23.5287i	0.648343	+	1.12296i	0.983519	+	0.180807i	$0.0578709\pi$
$439$	13.5843	+	23.5287i	0.648343	+	1.12296i	−0.335176	+	0.942156i	$0.608796\pi$
$440$	−17.3368			−0.826501
$441$	2.49279	−	1.66914i	0.118704	−	0.0794827i
$442$	−7.01874			−0.333847
$443$	8.23508	+	14.2636i	0.391261	+	0.677683i	0.992616	−	0.121298i	$-0.0387057\pi$
$443$	8.23508	+	14.2636i	0.391261	+	0.677683i	−0.601355	+	0.798982i	$0.705372\pi$
$444$	−11.2171	−	10.4957i	−0.532338	−	0.498103i
$445$	−8.11930	+	14.0630i	−0.384892	+	0.666652i
$446$	−8.95843	+	15.5165i	−0.424194	+	0.734726i
$447$	13.0041	+	12.1678i	0.615074	+	0.575518i
$448$	3.78730	+	6.55979i	0.178933	+	0.309921i
$449$	6.10283			0.288011			0.144005	−	0.989577i	$-0.454002\pi$
$449$	6.10283			0.288011			0.144005	+	0.989577i	$0.454002\pi$
$450$	2.60266	−	1.74271i	0.122691	−	0.0821521i
$451$	−58.4961			−2.75448
$452$	−3.25760	−	5.64233i	−0.153225	−	0.265393i
$453$	−3.16581	+	0.962019i	−0.148743	+	0.0451996i
$454$	9.36442	−	16.2196i	0.439494	−	0.761226i
$455$	−1.04644	+	1.81250i	−0.0490581	+	0.0849711i
$456$	1.45797	−	6.26670i	0.0682759	−	0.293465i
$457$	−14.0077	−	24.2620i	−0.655252	−	1.13493i	−0.981831	−	0.189760i	$-0.939229\pi$
$457$	−14.0077	−	24.2620i	−0.655252	−	1.13493i	0.326579	−	0.945170i	$-0.394104\pi$
$458$	−16.4892			−0.770488
$459$	−10.5693	+	12.9172i	−0.493334	+	0.602921i
$460$	−3.34079			−0.155765
$461$	−4.02453	−	6.97069i	−0.187441	−	0.324657i	0.756955	−	0.653467i	$-0.226686\pi$
$461$	−4.02453	−	6.97069i	−0.187441	−	0.324657i	−0.944396	+	0.328809i	$0.893353\pi$
$462$	−2.33839	+	10.0509i	−0.108792	+	0.467611i
$463$	15.2062	−	26.3379i	0.706692	−	1.22403i	−0.259385	−	0.965774i	$-0.583520\pi$
$463$	15.2062	−	26.3379i	0.706692	−	1.22403i	0.966077	−	0.258253i	$-0.0831467\pi$
$464$	−0.796431	+	1.37946i	−0.0369734	+	0.0640398i
$465$	10.9135	−	3.31636i	0.506100	−	0.153793i
$466$	9.34571	+	16.1872i	0.432932	+	0.749860i
$467$	−39.4761			−1.82674			−0.913368	−	0.407135i	$-0.866528\pi$
$467$	−39.4761			−1.82674			−0.913368	+	0.407135i	$0.866528\pi$
$468$	0.379194	+	5.70038i	0.0175283	+	0.263500i
$469$	−5.93402			−0.274008
$470$	−3.61414	−	6.25987i	−0.166708	−	0.288746i
$471$	24.7960	+	23.2013i	1.14254	+	1.06906i
$472$	17.9700	−	31.1250i	0.827138	−	1.43264i
$473$	27.1996	−	47.1111i	1.25064	−	2.16617i
$474$	17.6489	+	16.5139i	0.810642	+	0.758509i
$475$	0.611341	+	1.05887i	0.0280503	+	0.0485845i
$476$	2.92264			0.133959
$477$	−12.1798	−	5.99170i	−0.557676	−	0.274341i
$478$	3.36814			0.154055
$479$	−9.64479	−	16.7053i	−0.440682	−	0.763283i	0.557058	−	0.830473i	$-0.311930\pi$
$479$	−9.64479	−	16.7053i	−0.440682	−	0.763283i	−0.997740	+	0.0671900i	$0.978597\pi$
$480$	−7.73004	+	2.34899i	−0.352826	+	0.107216i
$481$	10.2000	−	17.6669i	0.465080	−	0.805542i
$482$	−2.56113	+	4.43600i	−0.116656	+	0.202054i
$483$	−1.44105	+	6.19395i	−0.0655700	+	0.281834i
$484$	9.80987	+	16.9912i	0.445903	+	0.772327i
$485$	2.09153			0.0949717
$486$	−13.2526	−	9.44793i	−0.601148	−	0.428567i
$487$	−11.6399			−0.527454			−0.263727	−	0.964597i	$-0.584952\pi$
$487$	−11.6399			−0.527454			−0.263727	+	0.964597i	$0.584952\pi$
$488$	13.5800	+	23.5212i	0.614737	+	1.06476i
$489$	−1.03845	+	4.46347i	−0.0469601	+	0.201845i
$490$	−0.522039	+	0.904198i	−0.0235833	+	0.0408475i
$491$	8.77092	−	15.1917i	0.395826	−	0.685591i	−0.597380	−	0.801958i	$-0.703792\pi$
$491$	8.77092	−	15.1917i	0.395826	−	0.685591i	0.993206	+	0.116367i	$0.0371250\pi$
$492$	−15.4577	+	4.69726i	−0.696887	+	0.211769i
$493$	1.89175	+	3.27661i	0.0852002	+	0.147571i
$494$	2.67173			0.120207
$495$	−15.3610	−	7.55662i	−0.690425	−	0.339645i
$496$	8.90523			0.399857
$497$	7.01874	+	12.1568i	0.314834	+	0.545308i
$498$	4.60941	+	4.31297i	0.206552	+	0.193269i
$499$	1.05281	−	1.82353i	0.0471304	−	0.0816323i	−0.841498	−	0.540260i	$-0.818326\pi$
$499$	1.05281	−	1.82353i	0.0471304	−	0.0816323i	0.888628	+	0.458628i	$0.151659\pi$
$500$	0.454951	−	0.787999i	0.0203460	−	0.0352404i
$501$	−16.5482	−	15.4840i	−0.739321	−	0.691775i
$502$	−11.5421	−	19.9915i	−0.515149	−	0.892264i
$503$	−19.8625			−0.885624			−0.442812	−	0.896614i	$-0.646019\pi$
$503$	−19.8625			−0.885624			−0.442812	+	0.896614i	$0.646019\pi$
$504$	0.604967	+	9.09439i	0.0269474	+	0.405096i
$505$	−3.96574			−0.176473
$506$	−10.9374	−	18.9442i	−0.486228	−	0.842171i
$507$	14.2850	−	4.34089i	0.634418	−	0.192786i
$508$	−1.24554	+	2.15734i	−0.0552620	+	0.0957166i
$509$	13.0865	−	22.6665i	0.580049	−	1.00467i	−0.415424	−	0.909628i	$-0.636367\pi$
$509$	13.0865	−	22.6665i	0.580049	−	1.00467i	0.995473	−	0.0950460i	$-0.0302998\pi$
$510$	1.31625	−	5.65753i	0.0582845	−	0.250520i
$511$	2.74861	+	4.76074i	0.121592	+	0.210603i
$512$	−14.5245			−0.641896
$513$	4.02328	−	4.91700i	0.177632	−	0.217091i
$514$	−10.7316			−0.473349
$515$	3.33236	+	5.77181i	0.146841	+	0.254336i
$516$	3.40450	−	14.6333i	0.149875	−	0.644196i
$517$	−19.7529	+	34.2130i	−0.868731	+	1.50469i
$518$	5.08846	−	8.81348i	0.223574	−	0.387242i
$519$	38.1411	−	11.5902i	1.67421	−	0.508755i
$520$	−3.17927	−	5.50666i	−0.139420	−	0.241483i
$521$	39.3258			1.72290			0.861448	−	0.507846i	$-0.169558\pi$
$521$	39.3258			1.72290			0.861448	+	0.507846i	$0.169558\pi$
$522$	−3.06571	+	2.05276i	−0.134183	+	0.0898470i
$523$	−32.4989			−1.42108			−0.710538	−	0.703659i	$-0.751548\pi$
$523$	−32.4989			−1.42108			−0.710538	+	0.703659i	$0.751548\pi$
$524$	−2.45062	−	4.24459i	−0.107056	−	0.185426i
$525$	−1.26474	−	1.18340i	−0.0551977	−	0.0516479i
$526$	5.67561	−	9.83044i	0.247468	−	0.428628i
$527$	10.5762	−	18.3186i	0.460708	−	0.797970i
$528$	−9.75941	−	9.13177i	−0.424724	−	0.397409i
$529$	4.75973	+	8.24409i	0.206945	+	0.358439i
$530$	4.72404			0.205199
$531$	29.4885	−	19.7451i	1.27969	−	0.856865i
$532$	−1.11252			−0.0482339
$533$	−10.7272	−	18.5800i	−0.464645	−	0.804789i
$534$	−28.0972	+	8.53812i	−1.21588	+	0.369481i
$535$	3.67154	−	6.35929i	0.158734	−	0.274936i
$536$	9.01426	−	15.6132i	0.389357	−	0.674386i
$537$	−3.19049	+	13.7134i	−0.137680	+	0.591778i
$538$	−0.209622	−	0.363076i	−0.00903744	−	0.0156533i
$539$	5.70635			0.245790
$540$	−4.66596	−	0.763358i	−0.200791	−	0.0328497i
$541$	28.0397			1.20552			0.602760	−	0.797922i	$-0.294067\pi$
$541$	28.0397			1.20552			0.602760	+	0.797922i	$0.294067\pi$
$542$	−0.227712	−	0.394410i	−0.00978109	−	0.0169413i
$543$	−1.01713	+	4.37185i	−0.0436492	+	0.187614i
$544$	−7.49118	+	12.9751i	−0.321182	+	0.556303i
$545$	2.66883	−	4.62255i	0.114320	−	0.198008i
$546$	−3.62126	+	1.10042i	−0.154976	+	0.0470938i
$547$	17.4680	+	30.2555i	0.746879	+	1.29363i	0.949312	+	0.314336i	$0.101782\pi$
$547$	17.4680	+	30.2555i	0.746879	+	1.29363i	−0.202433	+	0.979296i	$0.564885\pi$
$548$	−1.78445			−0.0762279
$549$	1.78008	+	26.7597i	0.0759718	+	1.14207i
$550$	5.95787			0.254045
$551$	−0.720108	−	1.24726i	−0.0306776	−	0.0531352i
$552$	−14.1080	−	13.2007i	−0.600476	−	0.561859i
$553$	6.68275	−	11.5749i	0.284179	−	0.492213i
$554$	13.3095	−	23.0527i	0.565466	−	0.979417i
$555$	12.3278	+	11.5350i	0.523285	+	0.489632i
$556$	3.76322	+	6.51809i	0.159596	+	0.276429i
$557$	−39.8206			−1.68725			−0.843627	−	0.536929i	$-0.819584\pi$
$557$	−39.8206			−1.68725			−0.843627	+	0.536929i	$0.819584\pi$
$558$	18.5086	+	9.10506i	0.783532	+	0.385448i
$559$	19.9517			0.843868
$560$	−0.676136	−	1.17110i	−0.0285720	−	0.0494881i
$561$	−30.3753	+	9.23038i	−1.28244	+	0.389707i
$562$	−6.42022	+	11.1201i	−0.270820	+	0.469075i
$563$	−13.7835	+	23.8738i	−0.580907	+	1.00616i	0.414465	+	0.910065i	$0.363969\pi$
$563$	−13.7835	+	23.8738i	−0.580907	+	1.00616i	−0.995372	+	0.0960952i	$0.969365\pi$
$564$	−2.47242	+	10.6270i	−0.104108	+	0.447478i
$565$	3.58016	+	6.20103i	0.150619	+	0.260879i
$566$	−26.3679			−1.10833
$567$	−3.42796	+	8.32160i	−0.143961	+	0.349474i
$568$	−42.6482			−1.78948
$569$	−3.47353	−	6.01633i	−0.145618	−	0.252218i	0.783985	−	0.620779i	$-0.213184\pi$
$569$	−3.47353	−	6.01633i	−0.145618	−	0.252218i	−0.929603	+	0.368562i	$0.879850\pi$
$570$	−0.501039	+	2.15358i	−0.0209862	+	0.0902034i
$571$	8.51812	−	14.7538i	0.356472	−	0.617428i	−0.630896	−	0.775867i	$-0.717313\pi$
$571$	8.51812	−	14.7538i	0.356472	−	0.617428i	0.987369	+	0.158439i	$0.0506460\pi$
$572$	−5.43338	+	9.41088i	−0.227181	+	0.393489i
$573$	24.8995	−	7.56642i	1.04019	−	0.316092i
$574$	−5.35145	−	9.26898i	−0.223365	−	0.386880i
$575$	3.67159			0.153116
$576$	−20.3901	−	10.0306i	−0.849588	−	0.417943i
$577$	36.5826			1.52295			0.761476	−	0.648193i	$-0.224475\pi$
$577$	36.5826			1.52295			0.761476	+	0.648193i	$0.224475\pi$
$578$	3.48870	+	6.04261i	0.145111	+	0.251339i
$579$	22.0524	+	20.6342i	0.916468	+	0.857530i
$580$	−0.535894	+	0.928196i	−0.0222518	+	0.0385412i
$581$	1.74535	−	3.02303i	0.0724092	−	0.125416i
$582$	2.76184	+	2.58422i	0.114482	+	0.107119i
$583$	−12.9095	−	22.3599i	−0.534657	−	0.926054i
$584$	−16.7015			−0.691112
$585$	−0.416741	−	6.26482i	−0.0172301	−	0.259019i
$586$	−0.911823			−0.0376671
$587$	−2.80654	−	4.86107i	−0.115838	−	0.200638i	0.802276	−	0.596953i	$-0.203622\pi$
$587$	−2.80654	−	4.86107i	−0.115838	−	0.200638i	−0.918115	+	0.396315i	$0.870289\pi$
$588$	1.50791	−	0.458222i	0.0621853	−	0.0188967i
$589$	−4.02592	+	6.97309i	−0.165885	+	0.287321i
$590$	−6.17547	+	10.6962i	−0.254240	+	0.440357i
$591$	1.69551	−	7.28767i	0.0697439	−	0.299775i
$592$	6.59050	+	11.4151i	0.270868	+	0.469157i
$593$	−8.90733			−0.365780			−0.182890	−	0.983133i	$-0.558545\pi$
$593$	−8.90733			−0.365780			−0.182890	+	0.983133i	$0.558545\pi$
$594$	−10.9472	−	28.9579i	−0.449171	−	1.18816i
$595$	−3.21203			−0.131681
$596$	4.67784	+	8.10226i	0.191612	+	0.331882i
$597$	−3.14455	+	13.5160i	−0.128698	+	0.553172i
$598$	4.01146	−	6.94806i	0.164041	−	0.284127i
$599$	−24.1083	+	41.7569i	−0.985040	+	1.70614i	−0.343281	+	0.939233i	$0.611538\pi$
$599$	−24.1083	+	41.7569i	−0.985040	+	1.70614i	−0.641759	+	0.766906i	$0.721795\pi$
$600$	5.03492	−	1.53000i	0.205550	−	0.0624621i
$601$	18.5642	+	32.1541i	0.757248	+	1.31159i	0.944249	+	0.329232i	$0.106790\pi$
$601$	18.5642	+	32.1541i	0.757248	+	1.31159i	−0.187001	+	0.982360i	$0.559877\pi$
$602$	9.95329			0.405666
$603$	14.7922	−	9.90470i	0.602387	−	0.403350i
$604$	−1.73819			−0.0707261
$605$	−10.7812	−	18.6737i	−0.438320	−	0.759192i
$606$	−5.23669	−	4.89992i	−0.212726	−	0.199045i
$607$	5.07701	−	8.79365i	0.206070	−	0.356923i	−0.744403	−	0.667730i	$-0.767266\pi$
$607$	5.07701	−	8.79365i	0.206070	−	0.356923i	0.950473	+	0.310807i	$0.100599\pi$
$608$	2.85157	−	4.93907i	0.115646	−	0.200306i
$609$	1.48975	+	1.39395i	0.0603679	+	0.0564856i
$610$	−4.66682	−	8.08316i	−0.188954	−	0.327278i
$611$	−14.4893			−0.586176
$612$	−7.28551	+	4.87828i	−0.294499	+	0.197193i
$613$	−23.3434			−0.942832			−0.471416	−	0.881911i	$-0.656257\pi$
$613$	−23.3434			−0.942832			−0.471416	+	0.881911i	$0.656257\pi$
$614$	6.81403	+	11.8023i	0.274992	+	0.476300i
$615$	16.9883	−	5.16237i	0.685034	−	0.208167i
$616$	−8.66842	+	15.0141i	−0.349260	+	0.604937i
$617$	−15.1330	+	26.2111i	−0.609230	+	1.05522i	0.382137	+	0.924106i	$0.375188\pi$
$617$	−15.1330	+	26.2111i	−0.609230	+	1.05522i	−0.991368	+	0.131112i	$0.958145\pi$
$618$	−2.73111	+	11.7389i	−0.109861	+	0.472209i
$619$	−7.18396	−	12.4430i	−0.288748	−	0.500126i	0.684763	−	0.728765i	$-0.259906\pi$
$619$	−7.18396	−	12.4430i	−0.288748	−	0.500126i	−0.973511	+	0.228640i	$0.926572\pi$
$620$	5.99206			0.240647
$621$	−6.74633	−	17.8455i	−0.270721	−	0.716115i
$622$	−2.87944			−0.115455
$623$	8.11930	+	14.0630i	0.325293	+	0.563424i
$624$	1.11080	−	4.77446i	0.0444676	−	0.191131i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.3122	−	17.8613i	0.412159	−	0.713881i
$627$	11.5626	−	3.51361i	0.461764	−	0.140320i
$628$	8.91960	+	15.4492i	0.355931	+	0.616490i
$629$	31.3086			1.24836
$630$	−0.207899	−	3.12532i	−0.00828291	−	0.124516i
$631$	35.2840			1.40463			0.702317	−	0.711865i	$-0.252149\pi$
$631$	35.2840			1.40463			0.702317	+	0.711865i	$0.252149\pi$
$632$	20.3033	+	35.1663i	0.807621	+	1.39884i
$633$	32.6073	+	30.5103i	1.29602	+	1.21267i
$634$	0.903937	−	1.56566i	0.0358999	−	0.0621805i
$635$	1.36887	−	2.37096i	0.0543221	−	0.0940886i
$636$	−5.20687	−	4.87201i	−0.206466	−	0.193188i
$637$	1.04644	+	1.81250i	0.0414616	+	0.0718137i
$638$	−7.01787			−0.277840
$639$	−37.7876	−	18.5891i	−1.49485	−	0.735373i
$640$	−1.42044			−0.0561478
$641$	2.53211	+	4.38574i	0.100012	+	0.173226i	0.911689	−	0.410880i	$-0.134778\pi$
$641$	2.53211	+	4.38574i	0.100012	+	0.173226i	−0.811677	+	0.584106i	$0.801445\pi$
$642$	12.7055	−	3.86092i	0.501446	−	0.152378i
$643$	20.6382	−	35.7465i	0.813892	−	1.40970i	−0.0962280	−	0.995359i	$-0.530678\pi$
$643$	20.6382	−	35.7465i	0.813892	−	1.40970i	0.910120	−	0.414344i	$-0.135989\pi$
$644$	−1.67039	+	2.89320i	−0.0658227	+	0.114008i
$645$	−3.74161	+	16.0823i	−0.147326	+	0.633240i
$646$	2.05020	+	3.55105i	0.0806641	+	0.139714i
$647$	−28.1009			−1.10476			−0.552380	−	0.833592i	$-0.686280\pi$
$647$	−28.1009			−1.10476			−0.552380	+	0.833592i	$0.686280\pi$
$648$	−16.6878	−	21.6606i	−0.655560	−	0.850908i
$649$	67.5035			2.64974
$650$	1.09257	+	1.89239i	0.0428541	+	0.0742255i
$651$	2.58468	−	11.1095i	0.101301	−	0.435416i
$652$	−1.20371	+	2.08489i	−0.0471411	+	0.0816508i
$653$	−9.96464	+	17.2593i	−0.389946	+	0.675407i	−0.992442	−	0.122715i	$-0.960840\pi$
$653$	−9.96464	+	17.2593i	−0.389946	+	0.675407i	0.602496	+	0.798122i	$0.294173\pi$
$654$	9.23560	−	2.80650i	0.361141	−	0.109743i
$655$	2.69327	+	4.66488i	0.105235	+	0.182272i
$656$	13.8622			0.541229
$657$	−14.7980	−	7.27969i	−0.577326	−	0.284008i
$658$	−7.22828			−0.281788
$659$	7.42359	+	12.8580i	0.289182	+	0.500878i	0.973615	−	0.228198i	$-0.0732833\pi$
$659$	7.42359	+	12.8580i	0.289182	+	0.500878i	−0.684433	+	0.729076i	$0.739950\pi$
$660$	−6.56680	−	6.14449i	−0.255612	−	0.239174i
$661$	−1.32787	+	2.29994i	−0.0516483	+	0.0894575i	−0.890694	−	0.454604i	$-0.849781\pi$
$661$	−1.32787	+	2.29994i	−0.0516483	+	0.0894575i	0.839045	+	0.544061i	$0.183114\pi$
$662$	−9.40315	+	16.2867i	−0.365464	+	0.633002i
$663$	−8.50211	−	7.95533i	−0.330195	−	0.308960i
$664$	5.30265	+	9.18446i	0.205783	+	0.356426i
$665$	1.22268			0.0474136
$666$	2.02646	+	30.4635i	0.0785236	+	1.18044i
$667$	−4.32482			−0.167458
$668$	−5.95273	−	10.3104i	−0.230318	−	0.398923i
$669$	−28.4388	+	8.64192i	−1.09951	+	0.334116i
$670$	−3.09779	+	5.36553i	−0.119678	+	0.207288i
$671$	−25.5063	+	44.1781i	−0.984658	+	1.70548i
$672$	−1.83073	+	7.86891i	−0.0706221	+	0.303550i
$673$	10.2634	+	17.7767i	0.395624	+	0.685242i	0.993181	−	0.116585i	$-0.0371949\pi$
$673$	10.2634	+	17.7767i	0.395624	+	0.685242i	−0.597556	+	0.801827i	$0.703862\pi$
$674$	11.0597			0.426002
$675$	5.12798	+	0.838945i	0.197376	+	0.0322910i
$676$	7.84319			0.301661
$677$	−11.7938	−	20.4275i	−0.453274	−	0.785093i	0.545313	−	0.838232i	$-0.316411\pi$
$677$	−11.7938	−	20.4275i	−0.453274	−	0.785093i	−0.998587	+	0.0531391i	$0.983077\pi$
$678$	−2.93421	+	12.6119i	−0.112688	+	0.484356i
$679$	1.04577	−	1.81132i	0.0401329	−	0.0695122i
$680$	4.87934	−	8.45127i	0.187114	−	0.324091i
$681$	29.7276	−	9.03356i	1.13916	−	0.346167i
$682$	19.6174	+	33.9784i	0.751191	+	1.30110i
$683$	19.5124			0.746623			0.373311	−	0.927706i	$-0.378222\pi$
$683$	19.5124			0.746623			0.373311	+	0.927706i	$0.378222\pi$
$684$	2.77328	−	1.85695i	0.106039	−	0.0710023i
$685$	1.96114			0.0749315
$686$	0.522039	+	0.904198i	0.0199315	+	0.0345224i
$687$	−19.9741	−	18.6895i	−0.762058	−	0.713049i
$688$	−6.44567	+	11.1642i	−0.245739	+	0.425632i
$689$	4.73475	−	8.20084i	0.180380	−	0.312427i
$690$	4.84827	+	4.53647i	0.184570	+	0.172701i
$691$	24.6195	+	42.6422i	0.936568	+	1.62218i	0.771813	+	0.635850i	$0.219350\pi$
$691$	24.6195	+	42.6422i	0.936568	+	1.62218i	0.164755	+	0.986334i	$0.447317\pi$
$692$	20.9414			0.796074
$693$	−14.2247	+	9.52469i	−0.540352	+	0.361813i
$694$	−12.5760			−0.477378
$695$	−4.13585	−	7.16351i	−0.156882	−	0.271727i
$696$	−5.93071	+	1.80221i	−0.224803	+	0.0683127i
$697$	16.4634	−	28.5154i	0.623595	−	1.08010i
$698$	8.94247	−	15.4888i	0.338478	−	0.586260i
$699$	−7.02643	+	30.2012i	−0.265764	+	1.14231i
$700$	−0.454951	−	0.787999i	−0.0171955	−	0.0297835i
$701$	48.0473			1.81472			0.907360	−	0.420354i	$-0.138094\pi$
$701$	48.0473			1.81472			0.907360	+	0.420354i	$0.138094\pi$
$702$	7.19028	−	8.78751i	0.271380	−	0.331663i
$703$	−11.9178			−0.449490
$704$	−21.6116	−	37.4325i	−0.814520	−	1.41079i
$705$	2.71723	−	11.6793i	0.102337	−	0.439867i
$706$	2.59595	−	4.49631i	0.0976998	−	0.169221i
$707$	−1.98287	+	3.43443i	−0.0745734	+	0.129165i
$708$	17.8379	−	5.42055i	0.670389	−	0.203717i
$709$	−6.93037	−	12.0038i	−0.260276	−	0.450811i	0.706039	−	0.708172i	$-0.250480\pi$
$709$	−6.93037	−	12.0038i	−0.260276	−	0.450811i	−0.966315	+	0.257362i	$0.917147\pi$
$710$	14.6562			0.550038
$711$	2.66137	+	40.0081i	0.0998092	+	1.50042i
$712$	−49.3355			−1.84893
$713$	12.0894	+	20.9395i	0.452752	+	0.784189i
$714$	−4.24144	−	3.96867i	−0.158732	−	0.148524i
$715$	5.97138	−	10.3427i	0.223317	−	0.386797i
$716$	−3.69825	+	6.40557i	−0.138210	+	0.239387i
$717$	4.07997	+	3.81759i	0.152369	+	0.142570i
$718$	−8.07808	−	13.9916i	−0.301471	−	0.522163i
$719$	−6.26796			−0.233755			−0.116878	−	0.993146i	$-0.537289\pi$
$719$	−6.26796			−0.233755			−0.116878	+	0.993146i	$0.537289\pi$
$720$	3.64019	+	1.79074i	0.135662	+	0.0667371i
$721$	6.66472			0.248207
$722$	9.13831	+	15.8280i	0.340093	+	0.589058i
$723$	−8.13036	+	2.47064i	−0.302371	+	0.0918840i
$724$	−1.17901	+	2.04210i	−0.0438174	+	0.0758939i
$725$	0.588958	−	1.02010i	0.0218733	−	0.0378857i
$726$	8.83601	−	37.9791i	0.327935	−	1.40954i
$727$	7.72159	+	13.3742i	0.286378	+	0.496021i	0.972942	−	0.231048i	$-0.0742154\pi$
$727$	7.72159	+	13.3742i	0.286378	+	0.496021i	−0.686564	+	0.727069i	$0.740882\pi$
$728$	−6.35854			−0.235663
$729$	−5.34473	−	26.4657i	−0.197953	−	0.980212i
$730$	5.73953			0.212430
$731$	15.3103	+	26.5182i	0.566272	+	0.980813i
$732$	−3.19255	+	13.7223i	−0.118000	+	0.507191i
$733$	15.1965	−	26.3212i	0.561297	−	0.972195i	−0.436087	−	0.899905i	$-0.643636\pi$
$733$	15.1965	−	26.3212i	0.561297	−	0.972195i	0.997384	−	0.0722901i	$-0.0230307\pi$
$734$	−7.93187	+	13.7384i	−0.292771	+	0.507094i
$735$	−1.65722	+	0.503594i	−0.0611276	+	0.0185754i
$736$	−8.56296	−	14.8315i	−0.315635	−	0.546696i
$737$	33.8616			1.24731
$738$	28.8112	+	14.1733i	1.06056	+	0.521726i
$739$	−30.2487			−1.11272			−0.556358	−	0.830943i	$-0.687802\pi$
$739$	−30.2487			−1.11272			−0.556358	+	0.830943i	$0.687802\pi$
$740$	4.43454	+	7.68085i	0.163017	+	0.282354i
$741$	3.23639	+	3.02825i	0.118892	+	0.111246i
$742$	2.36202	−	4.09114i	0.0867125	−	0.150191i
$743$	3.92485	−	6.79804i	0.143989	−	0.249396i	−0.785006	−	0.619488i	$-0.787340\pi$
$743$	3.92485	−	6.79804i	0.143989	−	0.249396i	0.928995	+	0.370092i	$0.120674\pi$
$744$	25.3042	+	23.6769i	0.927697	+	0.868036i
$745$	−5.14104	−	8.90454i	−0.188353	−	0.326237i
$746$	13.6231			0.498777
$747$	0.695076	+	10.4490i	0.0254315	+	0.382309i
$748$	−16.6776			−0.609794
$749$	−3.67154	−	6.35929i	−0.134155	−	0.232363i
$750$	−1.73027	+	0.525791i	−0.0631805	+	0.0191992i
$751$	21.7439	−	37.6615i	0.793444	−	1.37429i	−0.130378	−	0.991464i	$-0.541619\pi$
$751$	21.7439	−	37.6615i	0.793444	−	1.37429i	0.923822	−	0.382822i	$-0.125048\pi$
$752$	4.68097	−	8.10769i	0.170698	−	0.295657i
$753$	8.67775	−	37.2989i	0.316235	−	1.35925i
$754$	−1.28695	−	2.22907i	−0.0468681	−	0.0811779i
$755$	1.91031			0.0695232
$756$	−2.99407	+	3.65916i	−0.108893	+	0.133082i
$757$	51.0833			1.85665			0.928327	−	0.371764i	$-0.121247\pi$
$757$	51.0833			1.85665			0.928327	+	0.371764i	$0.121247\pi$
$758$	−16.1057	−	27.8958i	−0.584984	−	1.01322i
$759$	8.22314	−	35.3449i	0.298481	−	1.28294i
$760$	−1.85735	+	3.21703i	−0.0673733	+	0.116694i
$761$	−1.31066	+	2.27013i	−0.0475115	+	0.0822923i	−0.888803	−	0.458289i	$-0.848462\pi$
$761$	−1.31066	+	2.27013i	−0.0475115	+	0.0822923i	0.841292	+	0.540582i	$0.181796\pi$
$762$	4.73704	−	1.43948i	0.171605	−	0.0521470i
$763$	−2.66883	−	4.62255i	−0.0966182	−	0.167348i
$764$	13.6711			0.494604
$765$	8.00691	−	5.36133i	0.289491	−	0.193839i
$766$	0.336094			0.0121436
$767$	12.3790	+	21.4410i	0.446978	+	0.774189i
$768$	−21.0354	−	19.6826i	−0.759050	−	0.710235i
$769$	0.944844	−	1.63652i	0.0340720	−	0.0590144i	−0.848487	−	0.529217i	$-0.822486\pi$
$769$	0.944844	−	1.63652i	0.0340720	−	0.0590144i	0.882559	+	0.470203i	$0.155819\pi$
$770$	2.97894	−	5.15967i	0.107353	−	0.185942i
$771$	−12.9996	−	12.1636i	−0.468170	−	0.438062i
$772$	7.93270	+	13.7398i	0.285504	+	0.494508i
$773$	23.1346			0.832094			0.416047	−	0.909343i	$-0.363415\pi$
$773$	23.1346			0.832094			0.416047	+	0.909343i	$0.363415\pi$
$774$	−24.8114	+	16.6134i	−0.891828	+	0.597157i
$775$	−6.58538			−0.236554
$776$	3.17721	+	5.50309i	0.114055	+	0.197549i
$777$	16.1535	−	4.90868i	0.579502	−	0.176098i
$778$	−8.76021	+	15.1731i	−0.314069	+	0.543983i
$779$	−6.26689	+	10.8546i	−0.224535	+	0.388906i
$780$	0.747423	−	3.21259i	0.0267620	−	0.115029i
$781$	−40.0514	−	69.3711i	−1.43315	−	2.48229i
$782$	12.3131			0.440315
$783$	−6.04033	−	0.988206i	−0.215864	−	0.0353156i
$784$	−1.35227			−0.0482954
$785$	−9.80281	−	16.9790i	−0.349877	−	0.606005i
$786$	−2.20733	+	9.48761i	−0.0787330	+	0.338412i
$787$	−16.0217	+	27.7505i	−0.571113	+	0.989198i	0.425338	+	0.905034i	$0.360155\pi$
$787$	−16.0217	+	27.7505i	−0.571113	+	0.989198i	−0.996452	+	0.0841632i	$0.973178\pi$
$788$	1.96535	−	3.40408i	0.0700126	−	0.121265i
$789$	18.0174	−	5.47508i	0.641435	−	0.194918i
$790$	−6.97730	−	12.0850i	−0.248241	−	0.429967i
$791$	7.16033			0.254592
$792$	−3.45215	−	51.8958i	−0.122667	−	1.84404i
$793$	−18.7096			−0.664397
$794$	−0.800980	−	1.38734i	−0.0284257	−	0.0492348i
$795$	5.72245	+	5.35443i	0.202954	+	0.189902i
$796$	−3.64501	+	6.31333i	−0.129194	+	0.223770i
$797$	15.2728	−	26.4532i	0.540989	−	0.937020i	−0.457859	−	0.889025i	$-0.651384\pi$
$797$	15.2728	−	26.4532i	0.540989	−	0.937020i	0.998848	−	0.0479950i	$-0.0152831\pi$
$798$	1.61453	+	1.51070i	0.0571538	+	0.0534782i
$799$	−11.1187	−	19.2581i	−0.393350	−	0.681302i
$800$	4.66445			0.164913
$801$	−43.7128	−	21.5039i	−1.54452	−	0.759804i
$802$	23.2595			0.821323
$803$	−15.6846	−	27.1665i	−0.553496	−	0.958684i
$804$	8.94799	−	2.71910i	0.315571	−	0.0958952i
$805$	1.83579	−	3.17969i	0.0647032	−	0.112069i
$806$	−7.19499	+	12.4621i	−0.253433	+	0.438958i
$807$	0.157601	−	0.677404i	0.00554782	−	0.0238457i
$808$	−6.02428	−	10.4344i	−0.211933	−	0.367079i
$809$	34.7688			1.22241			0.611204	−	0.791473i	$-0.290686\pi$
$809$	34.7688			1.22241			0.611204	+	0.791473i	$0.290686\pi$
$810$	5.73485	+	7.44375i	0.201502	+	0.261547i
$811$	6.69661			0.235150			0.117575	−	0.993064i	$-0.462488\pi$
$811$	6.69661			0.235150			0.117575	+	0.993064i	$0.462488\pi$
$812$	0.535894	+	0.928196i	0.0188062	+	0.0325733i
$813$	0.171202	−	0.735865i	0.00600432	−	0.0258079i
$814$	−29.0366	+	50.2928i	−1.01773	+	1.76276i
$815$	1.32290	−	2.29134i	0.0463393	−	0.0802621i
$816$	7.19823	−	2.18738i	0.251988	−	0.0765738i
$817$	−5.82798	−	10.0944i	−0.203895	−	0.353157i
$818$	−12.0978			−0.422989
$819$	−5.63387	−	2.77150i	−0.196863	−	0.0968441i
$820$	9.32746			0.325729
$821$	−5.50199	−	9.52972i	−0.192021	−	0.332589i	0.753899	−	0.656990i	$-0.228171\pi$
$821$	−5.50199	−	9.52972i	−0.192021	−	0.332589i	−0.945920	+	0.324401i	$0.894837\pi$
$822$	2.58966	+	2.42312i	0.0903247	+	0.0845159i
$823$	−15.4882	+	26.8264i	−0.539886	+	0.935111i	0.459023	+	0.888424i	$0.348199\pi$
$823$	−15.4882	+	26.8264i	−0.539886	+	0.935111i	−0.998910	+	0.0466864i	$0.985134\pi$
$824$	−10.1242	+	17.5357i	−0.352695	+	0.610885i
$825$	7.21704	+	6.75291i	0.251265	+	0.235106i
$826$	6.17547	+	10.6962i	0.214872	+	0.372170i
$827$	−47.3376			−1.64609			−0.823044	−	0.567978i	$-0.807726\pi$
$827$	−47.3376			−1.64609			−0.823044	+	0.567978i	$0.807726\pi$
$828$	−0.665226	−	10.0003i	−0.0231182	−	0.347533i
$829$	−34.4343			−1.19595			−0.597976	−	0.801514i	$-0.704028\pi$
$829$	−34.4343			−1.19595			−0.597976	+	0.801514i	$0.704028\pi$
$830$	−1.82228	−	3.15628i	−0.0632522	−	0.109556i
$831$	42.2513	−	12.8393i	1.46568	−	0.445389i
$832$	7.92639	−	13.7289i	0.274798	−	0.475964i
$833$	−1.60602	+	2.78170i	−0.0556452	+	0.0963803i
$834$	3.38963	−	14.5694i	0.117373	−	0.504497i
$835$	6.54217	+	11.3314i	0.226401	+	0.392138i
$836$	6.34844			0.219566
$837$	12.1003	+	32.0078i	0.418246	+	1.10635i
$838$	−6.49449			−0.224348
$839$	−5.09048	−	8.81697i	−0.175743	−	0.304396i	0.764675	−	0.644416i	$-0.222899\pi$
$839$	−5.09048	−	8.81697i	−0.175743	−	0.304396i	−0.940418	+	0.340020i	$0.889566\pi$
$840$	1.19244	−	5.12537i	0.0411431	−	0.176842i
$841$	13.8063	−	23.9131i	0.476078	−	0.824591i
$842$	−18.1689	+	31.4694i	−0.626140	+	1.08451i
$843$	−20.3811	+	6.19338i	−0.701963	+	0.213311i
$844$	11.7295	+	20.3160i	0.403745	+	0.699307i
$845$	−8.61981			−0.296531
$846$	18.0185	−	12.0650i	0.619490	−	0.414803i
$847$	−21.5625			−0.740895
$848$	3.05925	+	5.29878i	0.105055	+	0.181961i
$849$	−31.9406	−	29.8865i	−1.09620	−	1.02570i
$850$	−1.67681	+	2.90431i	−0.0575140	+	0.0996171i
$851$	−17.8940	+	30.9933i	−0.613399	+	1.06244i
$852$	−16.1542	−	15.1153i	−0.553433	−	0.517841i
$853$	−12.3848	−	21.4511i	−0.424048	−	0.734472i	0.572283	−	0.820056i	$-0.306058\pi$
$853$	−12.3848	−	21.4511i	−0.424048	−	0.734472i	−0.996331	+	0.0855839i	$0.972724\pi$
$854$	−9.33363			−0.319390
$855$	−3.04789	+	2.04083i	−0.104236	+	0.0697948i
$856$	22.3094			0.762521
$857$	−5.58270	−	9.66951i	−0.190701	−	0.330304i	0.754782	−	0.655976i	$-0.227743\pi$
$857$	−5.58270	−	9.66951i	−0.190701	−	0.330304i	−0.945483	+	0.325672i	$0.894410\pi$
$858$	20.6642	−	6.27940i	0.705465	−	0.214375i
$859$	−3.64004	+	6.30474i	−0.124197	+	0.215115i	−0.921419	−	0.388571i	$-0.872969\pi$
$859$	−3.64004	+	6.30474i	−0.124197	+	0.215115i	0.797222	+	0.603686i	$0.206302\pi$
$860$	−4.33709	+	7.51207i	−0.147894	+	0.256159i
$861$	4.02340	−	17.2935i	0.137117	−	0.589360i
$862$	11.8771	+	20.5717i	0.404535	+	0.700676i
$863$	41.7986			1.42284			0.711420	−	0.702767i	$-0.248052\pi$
$863$	41.7986			1.42284			0.711420	+	0.702767i	$0.248052\pi$
$864$	−8.57065	−	22.6712i	−0.291580	−	0.771291i
$865$	−23.0150			−0.782535
$866$	−16.8327	−	29.1551i	−0.571999	−	0.990732i
$867$	−2.62293	+	11.2739i	−0.0890792	+	0.382882i
$868$	2.99603	−	5.18927i	0.101692	−	0.176135i
$869$	−38.1341	+	66.0502i	−1.29361	+	2.24060i
$870$	2.03811	−	0.619338i	0.0690985	−	0.0209975i
$871$	6.20963	+	10.7554i	0.210405	+	0.364432i
$872$	16.2167			0.549166
$873$	0.416472	+	6.26077i	0.0140954	+	0.211895i
$874$	−4.68706			−0.158542
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	−6.32614	−	5.91930i	−0.213741	−	0.199995i
$877$	−18.5228	+	32.0825i	−0.625471	+	1.08335i	0.362979	+	0.931797i	$0.381760\pi$
$877$	−18.5228	+	32.0825i	−0.625471	+	1.08335i	−0.988450	+	0.151550i	$0.951574\pi$
$878$	14.1830	−	24.5658i	0.478655	−	0.829054i
$879$	−1.10453	−	1.03350i	−0.0372549	−	0.0348590i
$880$	3.85827	+	6.68272i	0.130062	+	0.225275i
$881$	−41.7454			−1.40644			−0.703218	−	0.710974i	$-0.748254\pi$
$881$	−41.7454			−1.40644			−0.703218	+	0.710974i	$0.748254\pi$
$882$	−2.81056	−	1.38262i	−0.0946365	−	0.0465551i
$883$	−19.4379			−0.654137			−0.327069	−	0.945001i	$-0.606061\pi$
$883$	−19.4379			−0.654137			−0.327069	+	0.945001i	$0.606061\pi$
$884$	−3.05838	−	5.29727i	−0.102864	−	0.178166i
$885$	−19.6042	+	5.95729i	−0.658988	+	0.200252i
$886$	8.59807	−	14.8923i	0.288858	−	0.500316i
$887$	−21.0611	+	36.4789i	−0.707164	+	1.22484i	0.258742	+	0.965947i	$0.416692\pi$
$887$	−21.0611	+	36.4789i	−0.707164	+	1.22484i	−0.965905	+	0.258897i	$0.916641\pi$
$888$	−11.6231	+	49.9585i	−0.390044	+	1.67650i
$889$	−1.36887	−	2.37096i	−0.0459106	−	0.0795194i
$890$	16.9544			0.568312
$891$	19.5612	−	47.4860i	0.655323	−	1.59084i
$892$	−15.6144			−0.522807
$893$	4.23239	+	7.33072i	0.141632	+	0.245313i
$894$	4.21346	−	18.1104i	0.140919	−	0.605702i
$895$	4.06445	−	7.03984i	0.135860	−	0.235316i
$896$	−0.710220	+	1.23014i	−0.0237268	+	0.0410960i
$897$	12.7345	−	3.86973i	0.425192	−	0.129207i
$898$	−3.18592	−	5.51817i	−0.106315	−	0.184144i
$899$	7.75702			0.258711
$900$	2.44937	+	1.20494i	0.0816458	+	0.0401645i
$901$	14.5332			0.484171
$902$	30.5373	+	52.8921i	1.01678	+	1.76111i
$903$	12.0569	+	11.2815i	0.401227	+	0.375424i
$904$	−10.8771	+	18.8397i	−0.361768	+	0.626600i
$905$	1.29575	−	2.24430i	0.0430722	−	0.0746032i
$906$	2.52253	+	2.36030i	0.0838054	+	0.0784158i
$907$	−7.81890	−	13.5427i	−0.259622	−	0.449679i	0.706518	−	0.707695i	$-0.250265\pi$
$907$	−7.81890	−	13.5427i	−0.259622	−	0.449679i	−0.966141	+	0.258016i	$0.916931\pi$
$908$	16.3220			0.541664
$909$	−0.789668	−	11.8710i	−0.0261916	−	0.393735i
$910$	2.18514			0.0724366
$911$	23.7469	+	41.1308i	0.786770	+	1.36273i	0.927936	+	0.372739i	$0.121581\pi$
$911$	23.7469	+	41.1308i	0.786770	+	1.36273i	−0.141166	+	0.989986i	$0.545085\pi$
$912$	−2.74006	+	0.832643i	−0.0907323	+	0.0275716i
$913$	−9.95957	+	17.2505i	−0.329614	+	0.570908i
$914$	−14.6251	+	25.3314i	−0.483756	+	0.837889i
$915$	3.50867	−	15.0811i	0.115993	−	0.498565i
$916$	−7.18506	−	12.4449i	−0.237401	−	0.411191i
$917$	5.38654			0.177879
$918$	17.1973	+	2.81350i	0.567594	+	0.0928592i
$919$	5.78909			0.190964			0.0954822	−	0.995431i	$-0.469561\pi$
$919$	5.78909			0.190964			0.0954822	+	0.995431i	$0.469561\pi$
$920$	5.57744	+	9.66041i	0.183883	+	0.318494i
$921$	−5.12303	+	22.0199i	−0.168809	+	0.725581i
$922$	−4.20192	+	7.27794i	−0.138383	+	0.239686i
$923$	14.6894	−	25.4429i	0.483509	−	0.837462i
$924$	−8.60468	+	2.61477i	−0.283073	+	0.0860198i
$925$	−4.87365	−	8.44140i	−0.160245	−	0.277552i
$926$	−31.7529			−1.04347
$927$	−16.6137	+	11.1243i	−0.545666	+	0.365371i
$928$	−5.49433			−0.180360
$929$	−4.20145	−	7.27713i	−0.137845	−	0.238755i	0.788836	−	0.614604i	$-0.210684\pi$
$929$	−4.20145	−	7.27713i	−0.137845	−	0.238755i	−0.926681	+	0.375850i	$0.877351\pi$
$930$	−8.69589	−	8.13665i	−0.285150	−	0.266811i
$931$	0.611341	−	1.05887i	0.0200359	−	0.0347032i
$932$	−8.14469	+	14.1070i	−0.266788	+	0.462091i
$933$	−3.48799	−	3.26367i	−0.114192	−	0.106848i
$934$	20.6080	+	35.6942i	0.674316	+	1.16795i
$935$	18.3290			0.599422
$936$	15.8505	−	10.6133i	0.518089	−	0.346906i
$937$	−44.2946			−1.44704			−0.723521	−	0.690303i	$-0.757477\pi$
$937$	−44.2946			−1.44704			−0.723521	+	0.690303i	$0.757477\pi$
$938$	3.09779	+	5.36553i	0.101146	+	0.175191i
$939$	32.7364	−	9.94788i	1.06831	−	0.324637i
$940$	3.14968	−	5.45541i	0.102731	−	0.177936i
$941$	6.76590	−	11.7189i	0.220562	−	0.382025i	−0.734417	−	0.678699i	$-0.762544\pi$
$941$	6.76590	−	11.7189i	0.220562	−	0.382025i	0.954979	+	0.296674i	$0.0958775\pi$
$942$	8.03412	−	34.5324i	0.261766	−	1.12513i
$943$	18.8188	+	32.5951i	0.612825	+	1.06144i
$944$	−15.9968			−0.520650
$945$	3.29054	−	4.02149i	0.107041	−	0.130819i
$946$	−56.7970			−1.84663
$947$	0.00536174	+	0.00928680i	0.000174233	+	0.000301781i	0.866113	−	0.499849i	$-0.166611\pi$
$947$	0.00536174	+	0.00928680i	0.000174233	+	0.000301781i	−0.865938	+	0.500151i	$0.833278\pi$
$948$	−4.77315	+	20.5161i	−0.155025	+	0.666330i
$949$	5.75255	−	9.96370i	0.186736	−	0.323435i
$950$	0.638288	−	1.10555i	0.0207088	−	0.0358687i
$951$	2.86957	−	0.871999i	0.0930522	−	0.0282765i
$952$	−4.87934	−	8.45127i	−0.158140	−	0.273907i
$953$	−37.3545			−1.21003			−0.605016	−	0.796213i	$-0.706833\pi$
$953$	−37.3545			−1.21003			−0.605016	+	0.796213i	$0.706833\pi$
$954$	0.940663	+	14.1409i	0.0304551	+	0.457828i
$955$	−15.0248			−0.486192
$956$	1.46765	+	2.54204i	0.0474671	+	0.0822155i
$957$	−8.50106	−	7.95435i	−0.274800	−	0.257128i
$958$	−10.0699	+	17.4416i	−0.325344	+	0.563512i
$959$	0.980572	−	1.69840i	0.0316643	−	0.0548442i
$960$	9.57987	+	8.96378i	0.309189	+	0.289305i
$961$	−6.18364	−	10.7104i	−0.199472	−	0.345496i
$962$	−21.2992			−0.686713
$963$	19.7669	+	9.72404i	0.636979	+	0.313353i
$964$	−4.46399			−0.143775
$965$	−8.71819	−	15.1003i	−0.280648	−	0.486097i
$966$	6.35284	−	1.93049i	0.204399	−	0.0621124i
$967$	−14.2723	+	24.7203i	−0.458965	+	0.794951i	−0.998907	−	0.0467516i	$-0.985113\pi$
$967$	−14.2723	+	24.7203i	−0.458965	+	0.794951i	0.539941	+	0.841703i	$0.318446\pi$
$968$	32.7552	−	56.7336i	1.05279	−	1.82349i
$969$	−1.54141	+	6.62534i	−0.0495173	+	0.212836i
$970$	−1.09186	−	1.89116i	−0.0350576	−	0.0607215i
$971$	−41.8142			−1.34188			−0.670941	−	0.741511i	$-0.734109\pi$
$971$	−41.8142			−1.34188			−0.670941	+	0.741511i	$0.734109\pi$
$972$	1.35593	−	14.1190i	0.0434914	−	0.452868i
$973$	−8.27170			−0.265179
$974$	6.07648	+	10.5248i	0.194703	+	0.337235i
$975$	−0.821431	+	3.53070i	−0.0263069	+	0.113073i
$976$	6.04439	−	10.4692i	0.193476	−	0.335110i
$977$	3.85489	−	6.67687i	0.123329	−	0.213612i	−0.797750	−	0.602989i	$-0.793976\pi$
$977$	3.85489	−	6.67687i	0.123329	−	0.213612i	0.921078	+	0.389377i	$0.127310\pi$
$978$	4.57797	−	1.39114i	0.146387	−	0.0444839i
$979$	−46.3316	−	80.2487i	−1.48077	−	2.56476i
$980$	−0.909902			−0.0290658
$981$	14.3685	+	7.06838i	0.458751	+	0.225676i
$982$	−18.3150			−0.584456
$983$	−5.43820	−	9.41924i	−0.173452	−	0.300427i	0.766173	−	0.642635i	$-0.222159\pi$
$983$	−5.43820	−	9.41924i	−0.173452	−	0.300427i	−0.939624	+	0.342208i	$0.888825\pi$
$984$	39.3895	+	36.8563i	1.25569	+	1.17494i
$985$	−2.15996	+	3.74115i	−0.0688219	+	0.119203i
$986$	1.97514	−	3.42104i	0.0629011	−	0.108948i
$987$	−8.75593	−	8.19283i	−0.278704	−	0.260781i
$988$	1.16419	+	2.01644i	0.0370379	+	0.0641515i
$989$	−35.0016			−1.11299
$990$	1.18635	+	17.8342i	0.0377046	+	0.566808i
$991$	41.6132			1.32189			0.660944	−	0.750435i	$-0.270156\pi$
$991$	41.6132			1.32189			0.660944	+	0.750435i	$0.270156\pi$
$992$	15.3586	+	26.6019i	0.487636	+	0.844610i
$993$	−29.8505	+	9.07093i	−0.947278	+	0.287857i
$994$	7.32811	−	12.6927i	0.232434	−	0.402587i
$995$	4.00593	−	6.93847i	0.126997	−	0.219964i
$996$	−1.24661	+	5.35822i	−0.0395005	+	0.169782i
$997$	2.14023	+	3.70698i	0.0677816	+	0.117401i	0.897925	−	0.440149i	$-0.145075\pi$
$997$	2.14023	+	3.70698i	0.0677816	+	0.117401i	−0.830143	+	0.557551i	$0.811741\pi$
$998$	−2.19844			−0.0695903
$999$	−32.0738	+	39.1986i	−1.01477	+	1.24019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.f.211.3	yes	16
3.2	odd	2		945.2.i.f.631.6		16
9.2	odd	6		945.2.i.f.316.6		16
9.4	even	3		2835.2.a.x.1.6		8
9.5	odd	6		2835.2.a.y.1.3		8
9.7	even	3	inner	315.2.i.f.106.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.f.106.3	✓	16	9.7	even	3	inner
315.2.i.f.211.3	yes	16	1.1	even	1	trivial
945.2.i.f.316.6		16	9.2	odd	6
945.2.i.f.631.6		16	3.2	odd	2
2835.2.a.x.1.6		8	9.4	even	3
2835.2.a.y.1.3		8	9.5	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.522039 - 0.904198i) q^{2} +(0.392487 - 1.68700i) q^{3} +(0.454951 - 0.787999i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.73027 + 0.525791i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.03816 q^{8} +(-2.69191 - 1.32425i) q^{9} +O(q^{10})\)	\(q+(-0.522039 - 0.904198i) q^{2} +(0.392487 - 1.68700i) q^{3} +(0.454951 - 0.787999i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.73027 + 0.525791i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.03816 q^{8} +(-2.69191 - 1.32425i) q^{9} +1.04408 q^{10} +(-2.85318 - 4.94185i) q^{11} +(-1.15079 - 1.07678i) q^{12} +(1.04644 - 1.81250i) q^{13} +(0.522039 - 0.904198i) q^{14} +(1.26474 + 1.18340i) q^{15} +(0.676136 + 1.17110i) q^{16} +3.21203 q^{17} +(0.207899 + 3.12532i) q^{18} -1.22268 q^{19} +(0.454951 + 0.787999i) q^{20} +(1.65722 - 0.503594i) q^{21} +(-2.97894 + 5.15967i) q^{22} +(-1.83579 + 3.17969i) q^{23} +(-1.19244 + 5.12537i) q^{24} +(-0.500000 - 0.866025i) q^{25} -2.18514 q^{26} +(-3.29054 + 4.02149i) q^{27} +0.909902 q^{28} +(0.588958 + 1.02010i) q^{29} +(0.409787 - 1.76135i) q^{30} +(3.29269 - 5.70311i) q^{31} +(-2.33222 + 4.03953i) q^{32} +(-9.45671 + 2.87369i) q^{33} +(-1.67681 - 2.90431i) q^{34} -1.00000 q^{35} +(-2.26819 + 1.51875i) q^{36} +9.74729 q^{37} +(0.638288 + 1.10555i) q^{38} +(-2.64696 - 2.47673i) q^{39} +(1.51908 - 2.63113i) q^{40} +(5.12553 - 8.87767i) q^{41} +(-1.32048 - 1.23556i) q^{42} +(4.76655 + 8.25590i) q^{43} -5.19223 q^{44} +(2.49279 - 1.66914i) q^{45} +3.83342 q^{46} +(-3.46156 - 5.99560i) q^{47} +(2.24102 - 0.680997i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.522039 + 0.904198i) q^{50} +(1.26068 - 5.41869i) q^{51} +(-0.952163 - 1.64919i) q^{52} +4.52461 q^{53} +(5.35401 + 0.875924i) q^{54} +5.70635 q^{55} +(-1.51908 - 2.63113i) q^{56} +(-0.479887 + 2.06266i) q^{57} +(0.614917 - 1.06507i) q^{58} +(-5.91477 + 10.2447i) q^{59} +(1.50791 - 0.458222i) q^{60} +(-4.46980 - 7.74192i) q^{61} -6.87565 q^{62} +(-0.199123 - 2.99338i) q^{63} +7.57459 q^{64} +(1.04644 + 1.81250i) q^{65} +(7.53515 + 7.05056i) q^{66} +(-2.96701 + 5.13901i) q^{67} +(1.46132 - 2.53108i) q^{68} +(4.64359 + 4.34496i) q^{69} +(0.522039 + 0.904198i) q^{70} +14.0375 q^{71} +(8.17846 + 4.02328i) q^{72} +5.49723 q^{73} +(-5.08846 - 8.81348i) q^{74} +(-1.65722 + 0.503594i) q^{75} +(-0.556261 + 0.963472i) q^{76} +(2.85318 - 4.94185i) q^{77} +(-0.857638 + 3.68632i) q^{78} +(-6.68275 - 11.5749i) q^{79} -1.35227 q^{80} +(5.49274 + 7.12950i) q^{81} -10.7029 q^{82} +(-1.74535 - 3.02303i) q^{83} +(0.357125 - 1.53500i) q^{84} +(-1.60602 + 2.78170i) q^{85} +(4.97664 - 8.61980i) q^{86} +(1.95207 - 0.593191i) q^{87} +(8.66842 + 15.0141i) q^{88} +16.2386 q^{89} +(-2.81056 - 1.38262i) q^{90} +2.09289 q^{91} +(1.67039 + 2.89320i) q^{92} +(-8.32878 - 7.79315i) q^{93} +(-3.61414 + 6.25987i) q^{94} +(0.611341 - 1.05887i) q^{95} +(5.89930 + 5.51992i) q^{96} +(-1.04577 - 1.81132i) q^{97} +1.04408 q^{98} +(1.13626 + 17.0813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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