LMFDB - Embedded newform 930.2.n.f.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 10 x^{10} - 15 x^{9} + 61 x^{8} - 25 x^{7} + 316 x^{6} + 50 x^{5} + 1336 x^{4} + \cdots + 121 $ x^12 - 3x^11 + 10x^10 - 15x^9 + 61x^8 - 25x^7 + 316x^6 + 50x^5 + 1336x^4 - 1720x^3 + 1235x^2 - 462*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Root			$0.472164 - 0.343047i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.f.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.31116 - 4.03534i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.31116 - 4.03534i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.399170 + 1.22852i) q^{11} +(0.809017 + 0.587785i) q^{12} +(0.763978 - 0.555062i) q^{13} +(1.31116 - 4.03534i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.37094 - 4.21932i) q^{17} +(0.809017 - 0.587785i) q^{18} +(5.50566 + 4.00010i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-3.43266 - 2.49398i) q^{21} +(-0.399170 + 1.22852i) q^{22} +(1.49726 - 4.60810i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +0.944328 q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.43266 - 2.49398i) q^{28} +(-6.88755 - 5.00410i) q^{29} +1.00000 q^{30} +(2.91834 + 4.74166i) q^{31} -1.00000 q^{32} +(1.04504 + 0.759266i) q^{33} +(3.58917 - 2.60768i) q^{34} +(-1.31116 - 4.03534i) q^{35} +1.00000 q^{36} +11.2154 q^{37} +(2.10297 + 6.47229i) q^{38} +(0.291813 - 0.898110i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(3.23164 + 2.34792i) q^{41} +(-1.31116 - 4.03534i) q^{42} +(-10.3176 - 7.49614i) q^{43} +(-1.04504 + 0.759266i) q^{44} +(0.309017 - 0.951057i) q^{45} +(3.91989 - 2.84797i) q^{46} +(2.42609 - 1.76266i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-8.90170 + 6.46746i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.37094 - 4.21932i) q^{51} +(0.763978 + 0.555062i) q^{52} +(-4.17533 + 12.8503i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.399170 + 1.22852i) q^{55} +4.24301 q^{56} +6.80537 q^{57} +(-2.63081 - 8.09680i) q^{58} +(-8.27968 + 6.01554i) q^{59} +(0.809017 + 0.587785i) q^{60} +1.47470 q^{61} +(-0.426093 + 5.55144i) q^{62} -4.24301 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.763978 - 0.555062i) q^{65} +(0.399170 + 1.22852i) q^{66} -3.14457 q^{67} +4.43645 q^{68} +(-1.49726 - 4.60810i) q^{69} +(1.31116 - 4.03534i) q^{70} +(0.155251 - 0.477813i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.63084 + 5.01921i) q^{73} +(9.07344 + 6.59224i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-2.10297 + 6.47229i) q^{76} +(4.43411 - 3.22157i) q^{77} +(0.763978 - 0.555062i) q^{78} +(-0.331101 + 1.01902i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.23438 + 3.79902i) q^{82} +(-3.66105 - 2.65991i) q^{83} +(1.31116 - 4.03534i) q^{84} +(1.37094 - 4.21932i) q^{85} +(-3.94095 - 12.1290i) q^{86} -8.51348 q^{87} -1.29174 q^{88} +(5.55143 + 17.0855i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-3.24156 - 2.35513i) q^{91} +4.84525 q^{92} +(5.14806 + 2.12073i) q^{93} +2.99882 q^{94} +(5.50566 + 4.00010i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(4.11658 + 12.6695i) q^{97} -11.0031 q^{98} +1.29174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	−1.31116	−	4.03534i	−0.495572	−	1.52521i	−0.816063	−	0.577963i	$-0.803848\pi$
$7$	−1.31116	−	4.03534i	−0.495572	−	1.52521i	0.320491	−	0.947252i	$-0.396152\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	0.399170	+	1.22852i	0.120354	+	0.370412i	0.993026	−	0.117895i	$-0.0376146\pi$
$11$	0.399170	+	1.22852i	0.120354	+	0.370412i	−0.872672	+	0.488307i	$0.837615\pi$
$12$	0.809017	+	0.587785i	0.233543	+	0.169679i
$13$	0.763978	−	0.555062i	0.211889	−	0.153947i	−0.476779	−	0.879023i	$-0.658196\pi$
$13$	0.763978	−	0.555062i	0.211889	−	0.153947i	0.688668	+	0.725077i	$0.258196\pi$
$14$	1.31116	−	4.03534i	0.350423	−	1.07849i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.37094	−	4.21932i	0.332502	−	1.02334i	−0.635438	−	0.772152i	$-0.719180\pi$
$17$	1.37094	−	4.21932i	0.332502	−	1.02334i	0.967940	−	0.251183i	$-0.0808196\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	5.50566	+	4.00010i	1.26308	+	0.917685i	0.998905	−	0.0467886i	$-0.0148987\pi$
$19$	5.50566	+	4.00010i	1.26308	+	0.917685i	0.264180	+	0.964473i	$0.414899\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	−3.43266	−	2.49398i	−0.749069	−	0.544230i
$22$	−0.399170	+	1.22852i	−0.0851032	+	0.261921i
$23$	1.49726	−	4.60810i	0.312201	−	0.960856i	−0.664690	−	0.747119i	$-0.731436\pi$
$23$	1.49726	−	4.60810i	0.312201	−	0.960856i	0.976891	−	0.213737i	$-0.0685636\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	0.944328			0.185198
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	3.43266	−	2.49398i	0.648713	−	0.471317i
$29$	−6.88755	−	5.00410i	−1.27899	−	0.929238i	−0.279464	−	0.960156i	$-0.590157\pi$
$29$	−6.88755	−	5.00410i	−1.27899	−	0.929238i	−0.999522	+	0.0309183i	$0.990157\pi$
$30$	1.00000			0.182574
$31$	2.91834	+	4.74166i	0.524149	+	0.851627i
$31$	2.91834	+	4.74166i	0.524149	+	0.851627i
$32$	−1.00000			−0.176777
$33$	1.04504	+	0.759266i	0.181918	+	0.132171i
$34$	3.58917	−	2.60768i	0.615537	−	0.447214i
$35$	−1.31116	−	4.03534i	−0.221627	−	0.682097i
$36$	1.00000			0.166667
$37$	11.2154			1.84380			0.921899	−	0.387429i	$-0.126637\pi$
$37$	11.2154			1.84380			0.921899	+	0.387429i	$0.126637\pi$
$38$	2.10297	+	6.47229i	0.341148	+	1.04994i
$39$	0.291813	−	0.898110i	0.0467276	−	0.143813i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	3.23164	+	2.34792i	0.504698	+	0.366684i	0.810808	−	0.585312i	$-0.199028\pi$
$41$	3.23164	+	2.34792i	0.504698	+	0.366684i	−0.306111	+	0.951996i	$0.599028\pi$
$42$	−1.31116	−	4.03534i	−0.202317	−	0.622666i
$43$	−10.3176	−	7.49614i	−1.57341	−	1.14315i	−0.923794	−	0.382890i	$-0.874929\pi$
$43$	−10.3176	−	7.49614i	−1.57341	−	1.14315i	−0.649618	−	0.760260i	$-0.725071\pi$
$44$	−1.04504	+	0.759266i	−0.157546	+	0.114464i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	3.91989	−	2.84797i	0.577956	−	0.419910i
$47$	2.42609	−	1.76266i	0.353882	−	0.257110i	−0.396614	−	0.917986i	$-0.629815\pi$
$47$	2.42609	−	1.76266i	0.353882	−	0.257110i	0.750496	+	0.660875i	$0.229815\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−8.90170	+	6.46746i	−1.27167	+	0.923923i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	−1.37094	−	4.21932i	−0.191970	−	0.590823i
$52$	0.763978	+	0.555062i	0.105945	+	0.0769733i
$53$	−4.17533	+	12.8503i	−0.573526	+	1.76513i	0.0676187	+	0.997711i	$0.478460\pi$
$53$	−4.17533	+	12.8503i	−0.573526	+	1.76513i	−0.641145	+	0.767420i	$0.721540\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	0.399170	+	1.22852i	0.0538240	+	0.165653i
$56$	4.24301			0.566996
$57$	6.80537			0.901393
$58$	−2.63081	−	8.09680i	−0.345442	−	1.06316i
$59$	−8.27968	+	6.01554i	−1.07792	+	0.783156i	−0.977319	−	0.211770i	$-0.932077\pi$
$59$	−8.27968	+	6.01554i	−1.07792	+	0.783156i	−0.100603	+	0.994927i	$0.532077\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	1.47470			0.188815			0.0944077	−	0.995534i	$-0.469904\pi$
$61$	1.47470			0.188815			0.0944077	+	0.995534i	$0.469904\pi$
$62$	−0.426093	+	5.55144i	−0.0541139	+	0.705033i
$63$	−4.24301			−0.534569
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.763978	−	0.555062i	0.0947598	−	0.0688470i
$66$	0.399170	+	1.22852i	0.0491344	+	0.151220i
$67$	−3.14457			−0.384170			−0.192085	−	0.981378i	$-0.561525\pi$
$67$	−3.14457			−0.384170			−0.192085	+	0.981378i	$0.561525\pi$
$68$	4.43645			0.537999
$69$	−1.49726	−	4.60810i	−0.180249	−	0.554751i
$70$	1.31116	−	4.03534i	0.156714	−	0.482315i
$71$	0.155251	−	0.477813i	0.0184249	−	0.0567060i	−0.941421	−	0.337233i	$-0.890509\pi$
$71$	0.155251	−	0.477813i	0.0184249	−	0.0567060i	0.959846	+	0.280527i	$0.0905091\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.63084	+	5.01921i	0.190875	+	0.587454i	1.00000		0.000183359i	$-5.83649e-5\pi$
$73$	1.63084	+	5.01921i	0.190875	+	0.587454i	−0.809125	+	0.587637i	$0.800058\pi$
$74$	9.07344	+	6.59224i	1.05477	+	0.766332i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	−2.10297	+	6.47229i	−0.241228	+	0.742423i
$77$	4.43411	−	3.22157i	0.505314	−	0.367132i
$78$	0.763978	−	0.555062i	0.0865034	−	0.0628484i
$79$	−0.331101	+	1.01902i	−0.0372517	+	0.114649i	−0.967953	−	0.251131i	$-0.919198\pi$
$79$	−0.331101	+	1.01902i	−0.0372517	+	0.114649i	0.930701	+	0.365780i	$0.119198\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.23438	+	3.79902i	0.136314	+	0.419532i
$83$	−3.66105	−	2.65991i	−0.401852	−	0.291963i	0.368443	−	0.929650i	$-0.379891\pi$
$83$	−3.66105	−	2.65991i	−0.401852	−	0.291963i	−0.770295	+	0.637688i	$0.779891\pi$
$84$	1.31116	−	4.03534i	0.143059	−	0.440292i
$85$	1.37094	−	4.21932i	0.148699	−	0.457649i
$86$	−3.94095	−	12.1290i	−0.424964	−	1.30790i
$87$	−8.51348			−0.912741
$88$	−1.29174			−0.137700
$89$	5.55143	+	17.0855i	0.588451	+	1.81106i	0.584948	+	0.811071i	$0.301115\pi$
$89$	5.55143	+	17.0855i	0.588451	+	1.81106i	0.00350254	+	0.999994i	$0.498885\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	−3.24156	−	2.35513i	−0.339808	−	0.246885i
$92$	4.84525			0.505152
$93$	5.14806	+	2.12073i	0.533829	+	0.219909i
$94$	2.99882			0.309304
$95$	5.50566	+	4.00010i	0.564869	+	0.410401i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	4.11658	+	12.6695i	0.417975	+	1.28640i	0.909563	+	0.415567i	$0.136417\pi$
$97$	4.11658	+	12.6695i	0.417975	+	1.28640i	−0.491587	+	0.870828i	$0.663583\pi$
$98$	−11.0031			−1.11148
$99$	1.29174			0.129825
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−2.06555	+	6.35711i	−0.205530	+	0.632556i	0.794161	+	0.607707i	$0.207911\pi$
$101$	−2.06555	+	6.35711i	−0.205530	+	0.632556i	−0.999691	+	0.0248492i	$0.992089\pi$
$102$	1.37094	−	4.21932i	0.135743	−	0.417775i
$103$	−15.0867	−	10.9611i	−1.48653	−	1.08003i	−0.975377	−	0.220543i	$-0.929217\pi$
$103$	−15.0867	−	10.9611i	−1.48653	−	1.08003i	−0.511157	−	0.859487i	$-0.670783\pi$
$104$	0.291813	+	0.898110i	0.0286147	+	0.0880669i
$105$	−3.43266	−	2.49398i	−0.334994	−	0.243387i
$106$	−10.9312	+	7.94195i	−1.06173	+	0.771391i
$107$	−2.51418	+	7.73784i	−0.243055	+	0.748045i	0.752896	+	0.658140i	$0.228656\pi$
$107$	−2.51418	+	7.73784i	−0.243055	+	0.748045i	−0.995950	+	0.0899052i	$0.971344\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	10.2609	−	7.45494i	0.982811	−	0.714054i	0.0244761	−	0.999700i	$-0.492208\pi$
$109$	10.2609	−	7.45494i	0.982811	−	0.714054i	0.958335	+	0.285646i	$0.0922082\pi$
$110$	−0.399170	+	1.22852i	−0.0380593	+	0.117135i
$111$	9.07344	−	6.59224i	0.861213	−	0.625708i
$112$	3.43266	+	2.49398i	0.324356	+	0.235659i
$113$	1.78699	+	5.49980i	0.168106	+	0.517377i	0.999252	−	0.0386774i	$-0.0123145\pi$
$113$	1.78699	+	5.49980i	0.168106	+	0.517377i	−0.831146	+	0.556055i	$0.812314\pi$
$114$	5.50566	+	4.00010i	0.515652	+	0.374643i
$115$	1.49726	−	4.60810i	0.139621	−	0.429708i
$116$	2.63081	−	8.09680i	0.244265	−	0.751769i
$117$	−0.291813	−	0.898110i	−0.0269782	−	0.0830303i
$118$	−10.2342			−0.942138
$119$	−18.8239			−1.72558
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	7.54927	−	5.48486i	0.686297	−	0.498624i
$122$	1.19305	+	0.866804i	0.108014	+	0.0784767i
$123$	3.99453			0.360174
$124$	−3.60777	+	4.24075i	−0.323987	+	0.380831i
$125$	1.00000			0.0894427
$126$	−3.43266	−	2.49398i	−0.305806	−	0.222181i
$127$	10.9227	−	7.93580i	0.969232	−	0.704188i	0.0139557	−	0.999903i	$-0.495558\pi$
$127$	10.9227	−	7.93580i	0.969232	−	0.704188i	0.955276	+	0.295714i	$0.0955576\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−12.7532			−1.12286
$130$	0.944328			0.0828231
$131$	−5.28516	−	16.2660i	−0.461766	−	1.42117i	−0.863004	−	0.505197i	$-0.831420\pi$
$131$	−5.28516	−	16.2660i	−0.461766	−	1.42117i	0.401238	−	0.915974i	$-0.368580\pi$
$132$	−0.399170	+	1.22852i	−0.0347432	+	0.106929i
$133$	8.92293	−	27.4620i	0.773717	−	2.38125i
$134$	−2.54401	−	1.84833i	−0.219769	−	0.159671i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	3.58917	+	2.60768i	0.307768	+	0.223607i
$137$	−14.4427	+	10.4932i	−1.23392	+	0.896496i	−0.997178	−	0.0750760i	$-0.976080\pi$
$137$	−14.4427	+	10.4932i	−1.23392	+	0.896496i	−0.236743	+	0.971572i	$0.576080\pi$
$138$	1.49726	−	4.60810i	0.127456	−	0.392268i
$139$	1.78724	−	1.29851i	0.151592	−	0.110138i	−0.509404	−	0.860527i	$-0.670134\pi$
$139$	1.78724	−	1.29851i	0.151592	−	0.110138i	0.660996	+	0.750390i	$0.270134\pi$
$140$	3.43266	−	2.49398i	0.290113	−	0.210779i
$141$	0.926685	−	2.85204i	0.0780410	−	0.240185i
$142$	0.406452	−	0.295305i	0.0341087	−	0.0247814i
$143$	0.986860	+	0.716996i	0.0825254	+	0.0599582i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−6.88755	−	5.00410i	−0.571980	−	0.415568i
$146$	−1.63084	+	5.01921i	−0.134969	+	0.415392i
$147$	−3.40015	+	10.4646i	−0.280439	+	0.863104i
$148$	3.46575	+	10.6665i	0.284883	+	0.876778i
$149$	−16.6896			−1.36726			−0.683632	−	0.729827i	$-0.739601\pi$
$149$	−16.6896			−1.36726			−0.683632	+	0.729827i	$0.739601\pi$
$150$	1.00000			0.0816497
$151$	4.00793	+	12.3351i	0.326160	+	1.00382i	0.970914	+	0.239428i	$0.0769600\pi$
$151$	4.00793	+	12.3351i	0.326160	+	1.00382i	−0.644754	+	0.764391i	$0.723040\pi$
$152$	−5.50566	+	4.00010i	−0.446568	+	0.324451i
$153$	−3.58917	−	2.60768i	−0.290167	−	0.210819i
$154$	5.48086			0.441660
$155$	2.91834	+	4.74166i	0.234406	+	0.380859i
$156$	0.944328			0.0756068
$157$	−9.15205	−	6.64935i	−0.730413	−	0.530676i	0.159281	−	0.987233i	$-0.449082\pi$
$157$	−9.15205	−	6.64935i	−0.730413	−	0.530676i	−0.889694	+	0.456557i	$0.849082\pi$
$158$	−0.866833	+	0.629791i	−0.0689615	+	0.0501035i
$159$	4.17533	+	12.8503i	0.331125	+	1.01910i
$160$	−1.00000			−0.0790569
$161$	−20.5584			−1.62023
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−3.23835	+	9.96662i	−0.253647	+	0.780646i	0.740446	+	0.672116i	$0.234614\pi$
$163$	−3.23835	+	9.96662i	−0.253647	+	0.780646i	−0.994093	+	0.108530i	$0.965386\pi$
$164$	−1.23438	+	3.79902i	−0.0963887	+	0.296654i
$165$	1.04504	+	0.759266i	0.0813562	+	0.0591087i
$166$	−1.39840	−	4.30382i	−0.108537	−	0.334041i
$167$	15.1098	+	10.9779i	1.16923	+	0.849497i	0.990917	−	0.134476i	$-0.0429352\pi$
$167$	15.1098	+	10.9779i	1.16923	+	0.849497i	0.178316	+	0.983973i	$0.442935\pi$
$168$	3.43266	−	2.49398i	0.264836	−	0.192414i
$169$	−3.74165	+	11.5156i	−0.287819	+	0.885817i
$170$	3.58917	−	2.60768i	0.275277	−	0.200000i
$171$	5.50566	−	4.00010i	0.421028	−	0.305895i
$172$	3.94095	−	12.1290i	0.300495	−	0.924828i
$173$	−2.14742	+	1.56019i	−0.163265	+	0.118619i	−0.666418	−	0.745578i	$-0.732173\pi$
$173$	−2.14742	+	1.56019i	−0.163265	+	0.118619i	0.503153	+	0.864198i	$0.332173\pi$
$174$	−6.88755	−	5.00410i	−0.522144	−	0.379360i
$175$	−1.31116	−	4.03534i	−0.0991145	−	0.305043i
$176$	−1.04504	−	0.759266i	−0.0787728	−	0.0572318i
$177$	−3.16256	+	9.73334i	−0.237712	+	0.731603i
$178$	−5.55143	+	17.0855i	−0.416097	+	1.28062i
$179$	−5.99171	−	18.4406i	−0.447841	−	1.37831i	−0.879337	−	0.476199i	$-0.842014\pi$
$179$	−5.99171	−	18.4406i	−0.447841	−	1.37831i	0.431496	−	0.902115i	$-0.357986\pi$
$180$	1.00000			0.0745356
$181$	8.29722			0.616727			0.308364	−	0.951269i	$-0.400219\pi$
$181$	8.29722			0.616727			0.308364	+	0.951269i	$0.400219\pi$
$182$	−1.23817	−	3.81068i	−0.0917790	−	0.282467i
$183$	1.19305	−	0.866804i	0.0881930	−	0.0640760i
$184$	3.91989	+	2.84797i	0.288978	+	0.209955i
$185$	11.2154			0.824572
$186$	2.91834	+	4.74166i	0.213983	+	0.347675i
$187$	5.73074			0.419073
$188$	2.42609	+	1.76266i	0.176941	+	0.128555i
$189$	−3.43266	+	2.49398i	−0.249690	+	0.181410i
$190$	2.10297	+	6.47229i	0.152566	+	0.469549i
$191$	5.24124			0.379242			0.189621	−	0.981857i	$-0.439274\pi$
$191$	5.24124			0.379242			0.189621	+	0.981857i	$0.439274\pi$
$192$	−1.00000			−0.0721688
$193$	7.96515	+	24.5142i	0.573344	+	1.76457i	0.641749	+	0.766915i	$0.278209\pi$
$193$	7.96515	+	24.5142i	0.573344	+	1.76457i	−0.0684046	+	0.997658i	$0.521791\pi$
$194$	−4.11658	+	12.6695i	−0.295553	+	0.909619i
$195$	0.291813	−	0.898110i	0.0208972	−	0.0643150i
$196$	−8.90170	−	6.46746i	−0.635836	−	0.461962i
$197$	−2.93308	−	9.02708i	−0.208973	−	0.643153i	−0.999527	−	0.0307602i	$-0.990207\pi$
$197$	−2.93308	−	9.02708i	−0.208973	−	0.643153i	0.790554	−	0.612393i	$-0.209793\pi$
$198$	1.04504	+	0.759266i	0.0742677	+	0.0539587i
$199$	−12.2061	+	8.86822i	−0.865265	+	0.628652i	−0.929312	−	0.369295i	$-0.879599\pi$
$199$	−12.2061	+	8.86822i	−0.865265	+	0.628652i	0.0640473	+	0.997947i	$0.479599\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	−2.54401	+	1.84833i	−0.179440	+	0.130371i
$202$	−5.40768	+	3.92891i	−0.380483	+	0.276437i
$203$	−11.1625	+	34.3548i	−0.783457	+	2.41123i
$204$	3.58917	−	2.60768i	0.251292	−	0.182574i
$205$	3.23164	+	2.34792i	0.225708	+	0.163986i
$206$	−5.76260	−	17.7355i	−0.401499	−	1.23569i
$207$	−3.91989	−	2.84797i	−0.272451	−	0.197947i
$208$	−0.291813	+	0.898110i	−0.0202336	+	0.0622727i
$209$	−2.71650	+	8.36051i	−0.187904	+	0.578309i
$210$	−1.31116	−	4.03534i	−0.0904787	−	0.278465i
$211$	0.341792			0.0235299			0.0117650	−	0.999931i	$-0.496255\pi$
$211$	0.341792			0.0235299			0.0117650	+	0.999931i	$0.496255\pi$
$212$	−13.5117			−0.927984
$213$	−0.155251	−	0.477813i	−0.0106376	−	0.0327392i
$214$	−6.58220	+	4.78225i	−0.449950	+	0.326908i
$215$	−10.3176	−	7.49614i	−0.703651	−	0.511233i
$216$	1.00000			0.0680414
$217$	15.3078	−	17.9936i	1.03916	−	1.22148i
$218$	12.6831			0.859008
$219$	4.26959	+	3.10204i	0.288512	+	0.209616i
$220$	−1.04504	+	0.759266i	−0.0704565	+	0.0511897i
$221$	−1.29462	−	3.98442i	−0.0870854	−	0.268021i
$222$	11.2154			0.752728
$223$	7.68709			0.514765			0.257383	−	0.966310i	$-0.417140\pi$
$223$	7.68709			0.514765			0.257383	+	0.966310i	$0.417140\pi$
$224$	1.31116	+	4.03534i	0.0876056	+	0.269622i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−1.78699	+	5.49980i	−0.118869	+	0.365841i
$227$	−1.24953	−	0.907838i	−0.0829344	−	0.0602553i	0.545545	−	0.838081i	$-0.316323\pi$
$227$	−1.24953	−	0.907838i	−0.0829344	−	0.0602553i	−0.628480	+	0.777826i	$0.716323\pi$
$228$	2.10297	+	6.47229i	0.139273	+	0.428638i
$229$	−6.00598	−	4.36360i	−0.396887	−	0.288355i	0.371385	−	0.928479i	$-0.378883\pi$
$229$	−6.00598	−	4.36360i	−0.396887	−	0.288355i	−0.768272	+	0.640124i	$0.778883\pi$
$230$	3.91989	−	2.84797i	0.258470	−	0.187789i
$231$	1.69368	−	5.21261i	0.111436	−	0.342964i
$232$	6.88755	−	5.00410i	0.452190	−	0.328535i
$233$	−17.4684	+	12.6915i	−1.14439	+	0.831451i	−0.987725	−	0.156200i	$-0.950075\pi$
$233$	−17.4684	+	12.6915i	−1.14439	+	0.831451i	−0.156668	+	0.987651i	$0.550075\pi$
$234$	0.291813	−	0.898110i	0.0190764	−	0.0587113i
$235$	2.42609	−	1.76266i	0.158261	−	0.114983i
$236$	−8.27968	−	6.01554i	−0.538961	−	0.391578i
$237$	0.331101	+	1.01902i	0.0215073	+	0.0661927i
$238$	−15.2289	−	11.0644i	−0.987140	−	0.717199i
$239$	−1.36603	+	4.20422i	−0.0883614	+	0.271949i	−0.985467	−	0.169868i	$-0.945666\pi$
$239$	−1.36603	+	4.20422i	−0.0883614	+	0.271949i	0.897105	+	0.441817i	$0.145666\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	−5.15747	−	15.8731i	−0.332222	−	1.02247i	−0.968074	−	0.250664i	$-0.919351\pi$
$241$	−5.15747	−	15.8731i	−0.332222	−	1.02247i	0.635852	−	0.771811i	$-0.280649\pi$
$242$	9.33141			0.599846
$243$	−1.00000			−0.0641500
$244$	0.455706	+	1.40252i	0.0291736	+	0.0897870i
$245$	−8.90170	+	6.46746i	−0.568709	+	0.413191i
$246$	3.23164	+	2.34792i	0.206042	+	0.149698i
$247$	6.42650			0.408909
$248$	−5.41140	+	1.31025i	−0.343624	+	0.0832009i
$249$	−4.52530			−0.286780
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−1.75153	+	1.27256i	−0.110555	+	0.0803231i	−0.641689	−	0.766965i	$-0.721766\pi$
$251$	−1.75153	+	1.27256i	−0.110555	+	0.0803231i	0.531134	+	0.847288i	$0.321766\pi$
$252$	−1.31116	−	4.03534i	−0.0825954	−	0.254202i
$253$	6.25880			0.393487
$254$	13.5012			0.847140
$255$	−1.37094	−	4.21932i	−0.0858516	−	0.264224i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.74579	−	14.6060i	0.296034	−	0.911099i	−0.686838	−	0.726811i	$-0.741002\pi$
$257$	4.74579	−	14.6060i	0.296034	−	0.911099i	0.982872	−	0.184289i	$-0.0589982\pi$
$258$	−10.3176	−	7.49614i	−0.642343	−	0.466689i
$259$	−14.7052	−	45.2579i	−0.913736	−	2.81219i
$260$	0.763978	+	0.555062i	0.0473799	+	0.0344235i
$261$	−6.88755	+	5.00410i	−0.426329	+	0.309746i
$262$	5.28516	−	16.2660i	0.326518	−	1.00492i
$263$	0.255339	−	0.185514i	0.0157449	−	0.0114393i	−0.579885	−	0.814698i	$-0.696903\pi$
$263$	0.255339	−	0.185514i	0.0157449	−	0.0114393i	0.595630	+	0.803259i	$0.296903\pi$
$264$	−1.04504	+	0.759266i	−0.0643177	+	0.0467296i
$265$	−4.17533	+	12.8503i	−0.256489	+	0.789391i
$266$	23.3605	−	16.9724i	1.43233	−	1.04065i
$267$	14.5338	+	10.5595i	0.889456	+	0.646228i
$268$	−0.971725	−	2.99066i	−0.0593575	−	0.182684i
$269$	7.45208	+	5.41425i	0.454361	+	0.330113i	0.791315	−	0.611408i	$-0.209397\pi$
$269$	7.45208	+	5.41425i	0.454361	+	0.330113i	−0.336954	+	0.941521i	$0.609397\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	−0.585301	+	1.80137i	−0.0355545	+	0.109425i	−0.967259	−	0.253793i	$-0.918322\pi$
$271$	−0.585301	+	1.80137i	−0.0355545	+	0.109425i	0.931704	+	0.363218i	$0.118322\pi$
$272$	1.37094	+	4.21932i	0.0831254	+	0.255834i
$273$	−4.00679			−0.242502
$274$	−17.8521			−1.07849
$275$	0.399170	+	1.22852i	0.0240708	+	0.0740824i
$276$	3.91989	−	2.84797i	0.235950	−	0.171427i
$277$	9.54764	+	6.93677i	0.573662	+	0.416790i	0.836434	−	0.548068i	$-0.184637\pi$
$277$	9.54764	+	6.93677i	0.573662	+	0.416790i	−0.262772	+	0.964858i	$0.584637\pi$
$278$	2.20915			0.132496
$279$	5.41140	−	1.31025i	0.323972	−	0.0784426i
$280$	4.24301			0.253568
$281$	3.65705	+	2.65700i	0.218161	+	0.158504i	0.691499	−	0.722378i	$-0.256951\pi$
$281$	3.65705	+	2.65700i	0.218161	+	0.158504i	−0.473337	+	0.880881i	$0.656951\pi$
$282$	2.42609	−	1.76266i	0.144472	−	0.104965i
$283$	−8.52089	−	26.2246i	−0.506514	−	1.55889i	−0.798210	−	0.602379i	$-0.794219\pi$
$283$	−8.52089	−	26.2246i	−0.506514	−	1.55889i	0.291696	−	0.956511i	$-0.405781\pi$
$284$	0.502402			0.0298121
$285$	6.80537			0.403115
$286$	0.376947	+	1.16012i	0.0222893	+	0.0685996i
$287$	5.23747	−	16.1193i	0.309158	−	0.951491i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−2.16988	−	1.57651i	−0.127640	−	0.0927360i
$290$	−2.63081	−	8.09680i	−0.154487	−	0.475461i
$291$	10.7773	+	7.83020i	0.631779	+	0.459014i
$292$	−4.26959	+	3.10204i	−0.249859	+	0.181533i
$293$	−1.27656	+	3.92883i	−0.0745772	+	0.229525i	−0.981396	−	0.191997i	$-0.938504\pi$
$293$	−1.27656	+	3.92883i	−0.0745772	+	0.229525i	0.906818	+	0.421521i	$0.138504\pi$
$294$	−8.90170	+	6.46746i	−0.519158	+	0.377190i
$295$	−8.27968	+	6.01554i	−0.482061	+	0.350238i
$296$	−3.46575	+	10.6665i	−0.201442	+	0.619976i
$297$	1.04504	−	0.759266i	0.0606393	−	0.0440571i
$298$	−13.5022	−	9.80989i	−0.782159	−	0.568272i
$299$	−1.41391	−	4.35156i	−0.0817684	−	0.251657i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	−16.7215	+	51.4635i	−0.963811	+	2.96631i
$302$	−4.00793	+	12.3351i	−0.230630	+	0.709807i
$303$	2.06555	+	6.35711i	0.118663	+	0.365207i
$304$	−6.80537			−0.390315
$305$	1.47470			0.0844408
$306$	−1.37094	−	4.21932i	−0.0783714	−	0.241202i
$307$	3.78146	−	2.74739i	0.215819	−	0.156802i	−0.474624	−	0.880189i	$-0.657416\pi$
$307$	3.78146	−	2.74739i	0.215819	−	0.156802i	0.690443	+	0.723387i	$0.257416\pi$
$308$	4.43411	+	3.22157i	0.252657	+	0.183566i
$309$	−18.6482			−1.06086
$310$	−0.426093	+	5.55144i	−0.0242005	+	0.315300i
$311$	−3.36080			−0.190573			−0.0952866	−	0.995450i	$-0.530377\pi$
$311$	−3.36080			−0.190573			−0.0952866	+	0.995450i	$0.530377\pi$
$312$	0.763978	+	0.555062i	0.0432517	+	0.0314242i
$313$	20.3115	−	14.7572i	1.14807	−	0.834125i	0.159851	−	0.987141i	$-0.448899\pi$
$313$	20.3115	−	14.7572i	1.14807	−	0.834125i	0.988224	+	0.153016i	$0.0488986\pi$
$314$	−3.49577	−	10.7589i	−0.197278	−	0.607159i
$315$	−4.24301			−0.239066
$316$	−1.07146			−0.0602746
$317$	−1.54899	−	4.76730i	−0.0869999	−	0.267758i	0.898086	−	0.439819i	$-0.144957\pi$
$317$	−1.54899	−	4.76730i	−0.0869999	−	0.267758i	−0.985086	+	0.172061i	$0.944957\pi$
$318$	−4.17533	+	12.8503i	−0.234141	+	0.720612i
$319$	3.39832	−	10.4590i	0.190270	−	0.585589i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	2.51418	+	7.73784i	0.140328	+	0.431884i
$322$	−16.6321	−	12.0839i	−0.926871	−	0.673411i
$323$	24.4256	−	17.7462i	1.35908	−	0.987427i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	0.763978	−	0.555062i	0.0423779	−	0.0307893i
$326$	−8.47812	+	6.15971i	−0.469559	+	0.341155i
$327$	3.91930	−	12.0624i	0.216738	−	0.667050i
$328$	−3.23164	+	2.34792i	−0.178438	+	0.129642i
$329$	−10.2939	−	7.47898i	−0.567523	−	0.412329i
$330$	0.399170	+	1.22852i	0.0219736	+	0.0676277i
$331$	−19.1667	−	13.9254i	−1.05350	−	0.765412i	−0.0806243	−	0.996745i	$-0.525691\pi$
$331$	−19.1667	−	13.9254i	−1.05350	−	0.765412i	−0.972875	+	0.231333i	$0.925691\pi$
$332$	1.39840	−	4.30382i	0.0767470	−	0.236203i
$333$	3.46575	−	10.6665i	0.189922	−	0.584519i
$334$	5.77144	+	17.7627i	0.315799	+	0.971929i
$335$	−3.14457			−0.171806
$336$	4.24301			0.231475
$337$	−6.24132	−	19.2088i	−0.339986	−	1.04637i	−0.964214	−	0.265127i	$-0.914586\pi$
$337$	−6.24132	−	19.2088i	−0.339986	−	1.04637i	0.624227	−	0.781243i	$-0.285414\pi$
$338$	−9.79578	+	7.11705i	−0.532820	+	0.387116i
$339$	4.67841	+	3.39906i	0.254096	+	0.184612i
$340$	4.43645			0.240600
$341$	−4.66030	+	5.47795i	−0.252369	+	0.296648i
$342$	6.80537			0.367992
$343$	13.7413	+	9.98365i	0.741961	+	0.539066i
$344$	10.3176	−	7.49614i	0.556285	−	0.404165i
$345$	−1.49726	−	4.60810i	−0.0806100	−	0.248092i
$346$	−2.65436			−0.142699
$347$	15.4353			0.828608			0.414304	−	0.910138i	$-0.364025\pi$
$347$	15.4353			0.828608			0.414304	+	0.910138i	$0.364025\pi$
$348$	−2.63081	−	8.09680i	−0.141026	−	0.434034i
$349$	−5.52006	+	16.9890i	−0.295482	+	0.909401i	0.687577	+	0.726112i	$0.258674\pi$
$349$	−5.52006	+	16.9890i	−0.295482	+	0.909401i	−0.983059	+	0.183289i	$0.941326\pi$
$350$	1.31116	−	4.03534i	0.0700845	−	0.215698i
$351$	−0.763978	−	0.555062i	−0.0407781	−	0.0296270i
$352$	−0.399170	−	1.22852i	−0.0212758	−	0.0654802i
$353$	0.195464	+	0.142013i	0.0104035	+	0.00755860i	0.592975	−	0.805221i	$-0.297953\pi$
$353$	0.195464	+	0.142013i	0.0104035	+	0.00755860i	−0.582571	+	0.812780i	$0.697953\pi$
$354$	−8.27968	+	6.01554i	−0.440060	+	0.319722i
$355$	0.155251	−	0.477813i	0.00823986	−	0.0253597i
$356$	−14.5338	+	10.5595i	−0.770292	+	0.559650i
$357$	−15.2289	+	11.0644i	−0.805997	+	0.585591i
$358$	5.99171	−	18.4406i	0.316672	−	0.974615i
$359$	−14.3716	+	10.4415i	−0.758502	+	0.551084i	−0.898450	−	0.439075i	$-0.855306\pi$
$359$	−14.3716	+	10.4415i	−0.758502	+	0.551084i	0.139949	+	0.990159i	$0.455306\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	8.44019	+	25.9762i	0.444221	+	1.36717i
$362$	6.71259	+	4.87698i	0.352806	+	0.256328i
$363$	2.88356	−	8.87470i	0.151348	−	0.465801i
$364$	1.23817	−	3.81068i	0.0648976	−	0.199734i
$365$	1.63084	+	5.01921i	0.0853620	+	0.262717i
$366$	1.47470			0.0770835
$367$	11.9833			0.625522			0.312761	−	0.949832i	$-0.398746\pi$
$367$	11.9833			0.625522			0.312761	+	0.949832i	$0.398746\pi$
$368$	1.49726	+	4.60810i	0.0780503	+	0.240214i
$369$	3.23164	−	2.34792i	0.168233	−	0.122228i
$370$	9.07344	+	6.59224i	0.471706	+	0.342714i
$371$	57.3300			2.97643
$372$	−0.426093	+	5.55144i	−0.0220919	+	0.287829i
$373$	21.2595			1.10078			0.550388	−	0.834909i	$-0.314480\pi$
$373$	21.2595			1.10078			0.550388	+	0.834909i	$0.314480\pi$
$374$	4.63627	+	3.36845i	0.239736	+	0.174178i
$375$	0.809017	−	0.587785i	0.0417775	−	0.0303531i
$376$	0.926685	+	2.85204i	0.0477901	+	0.147083i
$377$	−8.03952			−0.414056
$378$	−4.24301			−0.218237
$379$	−2.80451	−	8.63139i	−0.144058	−	0.443365i	0.852831	−	0.522188i	$-0.174884\pi$
$379$	−2.80451	−	8.63139i	−0.144058	−	0.443365i	−0.996889	+	0.0788228i	$0.974884\pi$
$380$	−2.10297	+	6.47229i	−0.107880	+	0.332021i
$381$	4.17210	−	12.8404i	0.213743	−	0.657833i
$382$	4.24025	+	3.08072i	0.216950	+	0.157623i
$383$	−1.82277	−	5.60990i	−0.0931390	−	0.286652i	0.893625	−	0.448814i	$-0.148153\pi$
$383$	−1.82277	−	5.60990i	−0.0931390	−	0.286652i	−0.986764	+	0.162162i	$0.948153\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	4.43411	−	3.22157i	0.225983	−	0.164186i
$386$	−7.96515	+	24.5142i	−0.405416	+	1.24774i
$387$	−10.3176	+	7.49614i	−0.524471	+	0.381050i
$388$	−10.7773	+	7.83020i	−0.547137	+	0.397518i
$389$	8.12724	−	25.0131i	0.412067	−	1.26821i	−0.502780	−	0.864414i	$-0.667690\pi$
$389$	8.12724	−	25.0131i	0.412067	−	1.26821i	0.914848	−	0.403799i	$-0.132310\pi$
$390$	0.763978	−	0.555062i	0.0386855	−	0.0281067i
$391$	−17.3904	−	12.6349i	−0.879470	−	0.638973i
$392$	−3.40015	−	10.4646i	−0.171733	−	0.528541i
$393$	−13.8367	−	10.0530i	−0.697970	−	0.507105i
$394$	2.93308	−	9.02708i	0.147766	−	0.454778i
$395$	−0.331101	+	1.01902i	−0.0166595	+	0.0512726i
$396$	0.399170	+	1.22852i	0.0200590	+	0.0617353i
$397$	10.3759			0.520750			0.260375	−	0.965508i	$-0.416154\pi$
$397$	10.3759			0.520750			0.260375	+	0.965508i	$0.416154\pi$
$398$	−15.0875			−0.756269
$399$	−8.92293	−	27.4620i	−0.446705	−	1.37482i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	26.9651	+	19.5913i	1.34658	+	0.978344i	0.999174	+	0.0406274i	$0.0129357\pi$
$401$	26.9651	+	19.5913i	1.34658	+	0.978344i	0.347401	+	0.937717i	$0.387064\pi$
$402$	−3.14457			−0.156837
$403$	4.86146	+	2.00266i	0.242166	+	0.0997597i
$404$	−6.68426			−0.332555
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	−29.2239	+	21.2324i	−1.45036	+	1.05375i
$407$	4.47684	+	13.7783i	0.221909	+	0.682965i
$408$	4.43645			0.219637
$409$	−7.28358			−0.360150			−0.180075	−	0.983653i	$-0.557634\pi$
$409$	−7.28358			−0.360150			−0.180075	+	0.983653i	$0.557634\pi$
$410$	1.23438	+	3.79902i	0.0609615	+	0.187620i
$411$	−5.51661	+	16.9784i	−0.272114	+	0.837482i
$412$	5.76260	−	17.7355i	0.283903	−	0.873763i
$413$	35.1307	+	25.5240i	1.72867	+	1.25595i
$414$	−1.49726	−	4.60810i	−0.0735865	−	0.226476i
$415$	−3.66105	−	2.65991i	−0.179714	−	0.130570i
$416$	−0.763978	+	0.555062i	−0.0374571	+	0.0272142i
$417$	0.682665	−	2.10103i	0.0334302	−	0.102888i
$418$	−7.11188	+	5.16708i	−0.347853	+	0.252730i
$419$	−30.8733	+	22.4308i	−1.50826	+	1.09582i	−0.541319	+	0.840817i	$0.682075\pi$
$419$	−30.8733	+	22.4308i	−1.50826	+	1.09582i	−0.966942	+	0.254998i	$0.917925\pi$
$420$	1.31116	−	4.03534i	0.0639781	−	0.196904i
$421$	−4.94986	+	3.59629i	−0.241242	+	0.175272i	−0.701836	−	0.712338i	$-0.747636\pi$
$421$	−4.94986	+	3.59629i	−0.241242	+	0.175272i	0.460595	+	0.887611i	$0.347636\pi$
$422$	0.276515	+	0.200900i	0.0134606	+	0.00977967i
$423$	−0.926685	−	2.85204i	−0.0450570	−	0.138671i
$424$	−10.9312	−	7.94195i	−0.530864	−	0.385695i
$425$	1.37094	−	4.21932i	0.0665003	−	0.204667i
$426$	0.155251	−	0.477813i	0.00752193	−	0.0231501i
$427$	−1.93356	−	5.95089i	−0.0935717	−	0.287984i
$428$	−8.13604			−0.393270
$429$	1.21983			0.0588938
$430$	−3.94095	−	12.1290i	−0.190050	−	0.584913i
$431$	22.8066	−	16.5700i	1.09856	−	0.798149i	0.117734	−	0.993045i	$-0.462437\pi$
$431$	22.8066	−	16.5700i	1.09856	−	0.798149i	0.980824	+	0.194896i	$0.0624371\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	17.1380			0.823600			0.411800	−	0.911274i	$-0.364900\pi$
$433$	17.1380			0.823600			0.411800	+	0.911274i	$0.364900\pi$
$434$	22.9606	−	5.55940i	1.10214	−	0.266860i
$435$	−8.51348			−0.408190
$436$	10.2609	+	7.45494i	0.491406	+	0.357027i
$437$	26.6763	−	19.3815i	1.27610	−	0.927141i
$438$	1.63084	+	5.01921i	0.0779245	+	0.239827i
$439$	28.2634			1.34894			0.674470	−	0.738302i	$-0.264372\pi$
$439$	28.2634			1.34894			0.674470	+	0.738302i	$0.264372\pi$
$440$	−1.29174			−0.0615813
$441$	3.40015	+	10.4646i	0.161912	+	0.498313i
$442$	1.29462	−	3.98442i	0.0615787	−	0.189520i
$443$	−8.12699	+	25.0123i	−0.386125	+	1.18837i	0.549536	+	0.835470i	$0.314805\pi$
$443$	−8.12699	+	25.0123i	−0.386125	+	1.18837i	−0.935661	+	0.352901i	$0.885195\pi$
$444$	9.07344	+	6.59224i	0.430606	+	0.312854i
$445$	5.55143	+	17.0855i	0.263163	+	0.809933i
$446$	6.21898	+	4.51836i	0.294477	+	0.213950i
$447$	−13.5022	+	9.80989i	−0.638630	+	0.463992i
$448$	−1.31116	+	4.03534i	−0.0619465	+	0.190652i
$449$	−4.82567	+	3.50605i	−0.227737	+	0.165461i	−0.695803	−	0.718233i	$-0.744951\pi$
$449$	−4.82567	+	3.50605i	−0.227737	+	0.165461i	0.468065	+	0.883694i	$0.344951\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	−1.59449	+	4.90735i	−0.0750818	+	0.231078i
$452$	−4.67841	+	3.39906i	−0.220054	+	0.159878i
$453$	10.4929	+	7.62353i	0.492999	+	0.358185i
$454$	−0.477279	−	1.46891i	−0.0223998	−	0.0689395i
$455$	−3.24156	−	2.35513i	−0.151967	−	0.110410i
$456$	−2.10297	+	6.47229i	−0.0984808	+	0.303093i
$457$	5.78202	−	17.7952i	0.270471	−	0.832426i	−0.719911	−	0.694067i	$-0.755817\pi$
$457$	5.78202	−	17.7952i	0.270471	−	0.832426i	0.990382	−	0.138359i	$-0.0441827\pi$
$458$	−2.29408	−	7.06046i	−0.107195	−	0.329914i
$459$	−4.43645			−0.207076
$460$	4.84525			0.225911
$461$	−3.96850	−	12.2138i	−0.184832	−	0.568853i	0.815114	−	0.579301i	$-0.196674\pi$
$461$	−3.96850	−	12.2138i	−0.184832	−	0.568853i	−0.999945	+	0.0104478i	$0.996674\pi$
$462$	4.43411	−	3.22157i	0.206293	−	0.149881i
$463$	30.1357	+	21.8949i	1.40053	+	1.01754i	0.994616	+	0.103630i	$0.0330457\pi$
$463$	30.1357	+	21.8949i	1.40053	+	1.01754i	0.405911	+	0.913913i	$0.366954\pi$
$464$	8.51348			0.395228
$465$	5.14806	+	2.12073i	0.238736	+	0.0983464i
$466$	−21.5921			−1.00024
$467$	8.97851	+	6.52327i	0.415476	+	0.301861i	0.775815	−	0.630960i	$-0.217339\pi$
$467$	8.97851	+	6.52327i	0.415476	+	0.301861i	−0.360339	+	0.932821i	$0.617339\pi$
$468$	0.763978	−	0.555062i	0.0353149	−	0.0256578i
$469$	4.12303	+	12.6894i	0.190384	+	0.585942i
$470$	2.99882			0.138325
$471$	−11.3126			−0.521255
$472$	−3.16256	−	9.73334i	−0.145568	−	0.448013i
$473$	5.09069	−	15.6675i	0.234070	−	0.720394i
$474$	−0.331101	+	1.01902i	−0.0152080	+	0.0468053i
$475$	5.50566	+	4.00010i	0.252617	+	0.183537i
$476$	−5.81691	−	17.9026i	−0.266617	−	0.820564i
$477$	10.9312	+	7.94195i	0.500503	+	0.363637i
$478$	−3.57633	+	2.59835i	−0.163577	+	0.118846i
$479$	−5.08012	+	15.6350i	−0.232117	+	0.714382i	0.765374	+	0.643586i	$0.222554\pi$
$479$	−5.08012	+	15.6350i	−0.232117	+	0.714382i	−0.997491	+	0.0707962i	$0.977446\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	8.56831	−	6.22524i	0.390681	−	0.283846i
$482$	5.15747	−	15.8731i	0.234917	−	0.722999i
$483$	−16.6321	+	12.0839i	−0.756787	+	0.549838i
$484$	7.54927	+	5.48486i	0.343149	+	0.249312i
$485$	4.11658	+	12.6695i	0.186924	+	0.575293i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	8.89343	−	27.3712i	0.403000	−	1.24031i	−0.519554	−	0.854438i	$-0.673902\pi$
$487$	8.89343	−	27.3712i	0.403000	−	1.24031i	0.922554	−	0.385868i	$-0.126098\pi$
$488$	−0.455706	+	1.40252i	−0.0206288	+	0.0634890i
$489$	3.23835	+	9.96662i	0.146443	+	0.450706i
$490$	−11.0031			−0.497070
$491$	12.6411			0.570485			0.285242	−	0.958455i	$-0.407926\pi$
$491$	12.6411			0.570485			0.285242	+	0.958455i	$0.407926\pi$
$492$	1.23438	+	3.79902i	0.0556500	+	0.171273i
$493$	−30.5563	+	22.2005i	−1.37619	+	0.999858i
$494$	5.19915	+	3.77740i	0.233921	+	0.169953i
$495$	1.29174			0.0580594
$496$	−5.14806	−	2.12073i	−0.231155	−	0.0952234i
$497$	−2.13170			−0.0956196
$498$	−3.66105	−	2.65991i	−0.164056	−	0.119193i
$499$	26.0963	−	18.9601i	1.16823	−	0.848769i	0.177434	−	0.984133i	$-0.443220\pi$
$499$	26.0963	−	18.9601i	1.16823	−	0.848769i	0.990796	+	0.135364i	$0.0432204\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	18.6768			0.834416
$502$	−2.16500			−0.0966289
$503$	−11.4666	−	35.2906i	−0.511271	−	1.57353i	−0.789965	−	0.613151i	$-0.789902\pi$
$503$	−11.4666	−	35.2906i	−0.511271	−	1.57353i	0.278694	−	0.960380i	$-0.410098\pi$
$504$	1.31116	−	4.03534i	0.0584038	−	0.179748i
$505$	−2.06555	+	6.35711i	−0.0919158	+	0.282888i
$506$	5.06347	+	3.67883i	0.225099	+	0.163544i
$507$	3.74165	+	11.5156i	0.166173	+	0.511427i
$508$	10.9227	+	7.93580i	0.484616	+	0.352094i
$509$	5.81886	−	4.22765i	0.257916	−	0.187387i	−0.451312	−	0.892366i	$-0.649044\pi$
$509$	5.81886	−	4.22765i	0.257916	−	0.187387i	0.709228	+	0.704979i	$0.249044\pi$
$510$	1.37094	−	4.21932i	0.0607062	−	0.186835i
$511$	18.1159	−	13.1620i	0.801400	−	0.582251i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	2.10297	−	6.47229i	0.0928486	−	0.285759i
$514$	12.4246	−	9.02703i	0.548027	−	0.398165i
$515$	−15.0867	−	10.9611i	−0.664798	−	0.483004i
$516$	−3.94095	−	12.1290i	−0.173491	−	0.533950i
$517$	3.13388	+	2.27690i	0.137828	+	0.100138i
$518$	14.7052	−	45.2579i	0.646109	−	1.98852i
$519$	−0.820241	+	2.52444i	−0.0360046	+	0.110811i
$520$	0.291813	+	0.898110i	0.0127969	+	0.0393847i
$521$	3.74655			0.164140			0.0820698	−	0.996627i	$-0.473847\pi$
$521$	3.74655			0.164140			0.0820698	+	0.996627i	$0.473847\pi$
$522$	−8.51348			−0.372625
$523$	−1.50795	−	4.64098i	−0.0659379	−	0.202936i	0.912659	−	0.408721i	$-0.134025\pi$
$523$	−1.50795	−	4.64098i	−0.0659379	−	0.202936i	−0.978597	+	0.205785i	$0.934025\pi$
$524$	13.8367	−	10.0530i	0.604460	−	0.439166i
$525$	−3.43266	−	2.49398i	−0.149814	−	0.108846i
$526$	0.315616			0.0137615
$527$	24.0074	−	5.81286i	1.04578	−	0.253212i
$528$	−1.29174			−0.0562158
$529$	−0.385438	−	0.280037i	−0.0167582	−	0.0121755i
$530$	−10.9312	+	7.94195i	−0.474819	+	0.344976i
$531$	3.16256	+	9.73334i	0.137243	+	0.422391i
$532$	28.8752			1.25190
$533$	3.77215			0.163390
$534$	5.55143	+	17.0855i	0.240234	+	0.739364i
$535$	−2.51418	+	7.73784i	−0.108697	+	0.334536i
$536$	0.971725	−	2.99066i	0.0419721	−	0.129177i
$537$	−15.6865	−	11.3969i	−0.676922	−	0.491813i
$538$	2.84644	+	8.76045i	0.122719	+	0.377690i
$539$	−11.4987	−	8.35428i	−0.495283	−	0.359844i
$540$	0.809017	−	0.587785i	0.0348145	−	0.0252942i
$541$	−5.56171	+	17.1172i	−0.239116	+	0.735925i	0.757432	+	0.652914i	$0.226454\pi$
$541$	−5.56171	+	17.1172i	−0.239116	+	0.735925i	−0.996549	+	0.0830108i	$0.973546\pi$
$542$	−1.53234	+	1.11331i	−0.0658195	+	0.0478207i
$543$	6.71259	−	4.87698i	0.288065	−	0.209291i
$544$	−1.37094	+	4.21932i	−0.0587786	+	0.180902i
$545$	10.2609	−	7.45494i	0.439527	−	0.319335i
$546$	−3.24156	−	2.35513i	−0.138726	−	0.100790i
$547$	4.72713	+	14.5486i	0.202117	+	0.622053i	0.999819	+	0.0190016i	$0.00604877\pi$
$547$	4.72713	+	14.5486i	0.202117	+	0.622053i	−0.797702	+	0.603052i	$0.793951\pi$
$548$	−14.4427	−	10.4932i	−0.616961	−	0.448248i
$549$	0.455706	−	1.40252i	0.0194491	−	0.0598580i
$550$	−0.399170	+	1.22852i	−0.0170206	+	0.0523842i
$551$	−17.9036	−	55.1017i	−0.762721	−	2.34741i
$552$	4.84525			0.206227
$553$	4.54623			0.193325
$554$	3.64687	+	11.2239i	0.154941	+	0.476859i
$555$	9.07344	−	6.59224i	0.385146	−	0.279825i
$556$	1.78724	+	1.29851i	0.0757958	+	0.0550689i
$557$	35.0608			1.48557			0.742787	−	0.669528i	$-0.233504\pi$
$557$	35.0608			1.48557			0.742787	+	0.669528i	$0.233504\pi$
$558$	5.14806	+	2.12073i	0.217935	+	0.0897775i
$559$	−12.0432			−0.509373
$560$	3.43266	+	2.49398i	0.145057	+	0.105390i
$561$	4.63627	−	3.36845i	0.195743	−	0.142216i
$562$	1.39687	+	4.29912i	0.0589234	+	0.181347i
$563$	−9.28442			−0.391292			−0.195646	−	0.980675i	$-0.562680\pi$
$563$	−9.28442			−0.391292			−0.195646	+	0.980675i	$0.562680\pi$
$564$	2.99882			0.126273
$565$	1.78699	+	5.49980i	0.0751793	+	0.231378i
$566$	8.52089	−	26.2246i	0.358160	−	1.10230i
$567$	−1.31116	+	4.03534i	−0.0550636	+	0.169468i
$568$	0.406452	+	0.295305i	0.0170543	+	0.0123907i
$569$	−2.01986	−	6.21647i	−0.0846767	−	0.260608i	0.899749	−	0.436407i	$-0.143749\pi$
$569$	−2.01986	−	6.21647i	−0.0846767	−	0.260608i	−0.984426	+	0.175799i	$0.943749\pi$
$570$	5.50566	+	4.00010i	0.230607	+	0.167546i
$571$	−11.6761	+	8.48321i	−0.488631	+	0.355011i	−0.804658	−	0.593739i	$-0.797651\pi$
$571$	−11.6761	+	8.48321i	−0.488631	+	0.355011i	0.316027	+	0.948750i	$0.397651\pi$
$572$	−0.376947	+	1.16012i	−0.0157609	+	0.0485072i
$573$	4.24025	−	3.08072i	0.177139	−	0.128699i
$574$	13.7119	−	9.96226i	0.572323	−	0.415817i
$575$	1.49726	−	4.60810i	0.0624402	−	0.192171i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	10.0211	+	7.28073i	0.417182	+	0.303101i	0.776503	−	0.630113i	$-0.216992\pi$
$577$	10.0211	+	7.28073i	0.417182	+	0.303101i	−0.359321	+	0.933214i	$0.616992\pi$
$578$	−0.828822	−	2.55085i	−0.0344744	−	0.106101i
$579$	20.8530	+	15.1506i	0.866623	+	0.629638i
$580$	2.63081	−	8.09680i	0.109238	−	0.336201i
$581$	−5.93340	+	18.2611i	−0.246159	+	0.757600i
$582$	4.11658	+	12.6695i	0.170638	+	0.525169i
$583$	−17.4535			−0.722852
$584$	−5.27750			−0.218385
$585$	−0.291813	−	0.898110i	−0.0120650	−	0.0371323i
$586$	−3.34206	+	2.42815i	−0.138059	+	0.100306i
$587$	−30.4316	−	22.1098i	−1.25604	−	0.912570i	−0.257488	−	0.966281i	$-0.582895\pi$
$587$	−30.4316	−	22.1098i	−1.25604	−	0.912570i	−0.998556	+	0.0537117i	$0.982895\pi$
$588$	−11.0031			−0.453760
$589$	−2.89972	+	37.7796i	−0.119481	+	1.55668i
$590$	−10.2342			−0.421337
$591$	−7.67889	−	5.57904i	−0.315867	−	0.229491i
$592$	−9.07344	+	6.59224i	−0.372916	+	0.270939i
$593$	10.8035	+	33.2496i	0.443645	+	1.36540i	0.883963	+	0.467556i	$0.154866\pi$
$593$	10.8035	+	33.2496i	0.443645	+	1.36540i	−0.440319	+	0.897842i	$0.645134\pi$
$594$	1.29174			0.0530007
$595$	−18.8239			−0.771705
$596$	−5.15737	−	15.8727i	−0.211254	−	0.650173i
$597$	−4.66230	+	14.3491i	−0.190815	+	0.587269i
$598$	1.41391	−	4.35156i	0.0578190	−	0.177949i
$599$	7.53991	+	5.47806i	0.308072	+	0.223828i	0.731069	−	0.682304i	$-0.239022\pi$
$599$	7.53991	+	5.47806i	0.308072	+	0.223828i	−0.422997	+	0.906131i	$0.639022\pi$
$600$	0.309017	+	0.951057i	0.0126156	+	0.0388267i
$601$	−27.4705	−	19.9585i	−1.12054	−	0.814123i	−0.136253	−	0.990674i	$-0.543506\pi$
$601$	−27.4705	−	19.9585i	−1.12054	−	0.814123i	−0.984292	+	0.176551i	$0.943506\pi$
$602$	−43.7774	+	31.8062i	−1.78424	+	1.29632i
$603$	−0.971725	+	2.99066i	−0.0395717	+	0.121789i
$604$	−10.4929	+	7.62353i	−0.426950	+	0.310197i
$605$	7.54927	−	5.48486i	0.306921	−	0.222991i
$606$	−2.06555	+	6.35711i	−0.0839073	+	0.258240i
$607$	−9.68860	+	7.03918i	−0.393248	+	0.285712i	−0.766785	−	0.641904i	$-0.778145\pi$
$607$	−9.68860	+	7.03918i	−0.393248	+	0.285712i	0.373537	+	0.927615i	$0.378145\pi$
$608$	−5.50566	−	4.00010i	−0.223284	−	0.162225i
$609$	11.1625	+	34.3548i	0.452329	+	1.39213i
$610$	1.19305	+	0.866804i	0.0483053	+	0.0350959i
$611$	0.875095	−	2.69327i	0.0354026	−	0.108958i
$612$	1.37094	−	4.21932i	0.0554170	−	0.170556i
$613$	3.22699	+	9.93164i	0.130337	+	0.401135i	0.994836	−	0.101500i	$-0.0323640\pi$
$613$	3.22699	+	9.93164i	0.130337	+	0.401135i	−0.864499	+	0.502635i	$0.832364\pi$
$614$	4.67414			0.188633
$615$	3.99453			0.161075
$616$	1.69368	+	5.21261i	0.0682403	+	0.210022i
$617$	−34.7069	+	25.2161i	−1.39725	+	1.01516i	−0.402222	+	0.915542i	$0.631762\pi$
$617$	−34.7069	+	25.2161i	−1.39725	+	1.01516i	−0.995026	+	0.0996180i	$0.968238\pi$
$618$	−15.0867	−	10.9611i	−0.606875	−	0.440921i
$619$	−15.9291			−0.640243			−0.320122	−	0.947376i	$-0.603724\pi$
$619$	−15.9291			−0.640243			−0.320122	+	0.947376i	$0.603724\pi$
$620$	−3.60777	+	4.24075i	−0.144891	+	0.170313i
$621$	−4.84525			−0.194433
$622$	−2.71894	−	1.97543i	−0.109020	−	0.0792074i
$623$	61.6672	−	44.8038i	2.47064	−	1.79503i
$624$	0.291813	+	0.898110i	0.0116819	+	0.0359532i
$625$	1.00000			0.0400000
$626$	25.1064			1.00345
$627$	2.71650	+	8.36051i	0.108486	+	0.333887i
$628$	3.49577	−	10.7589i	0.139496	−	0.429326i
$629$	15.3756	−	47.3213i	0.613066	−	1.88682i
$630$	−3.43266	−	2.49398i	−0.136761	−	0.0993624i
$631$	3.85773	+	11.8729i	0.153574	+	0.472652i	0.998014	−	0.0629988i	$-0.0200664\pi$
$631$	3.85773	+	11.8729i	0.153574	+	0.472652i	−0.844440	+	0.535651i	$0.820066\pi$
$632$	−0.866833	−	0.629791i	−0.0344808	−	0.0250517i
$633$	0.276515	−	0.200900i	0.0109905	−	0.00798507i
$634$	1.54899	−	4.76730i	0.0615183	−	0.189334i
$635$	10.9227	−	7.93580i	0.433454	−	0.314923i
$636$	−10.9312	+	7.94195i	−0.433449	+	0.314919i
$637$	−3.21085	+	9.88199i	−0.127219	+	0.391539i
$638$	8.89692	−	6.46399i	0.352233	−	0.255912i
$639$	−0.406452	−	0.295305i	−0.0160790	−	0.0116821i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−32.4368	−	23.5667i	−1.28118	−	0.930829i	−0.281588	−	0.959535i	$-0.590861\pi$
$641$	−32.4368	−	23.5667i	−1.28118	−	0.930829i	−0.999588	+	0.0287065i	$0.990861\pi$
$642$	−2.51418	+	7.73784i	−0.0992266	+	0.305388i
$643$	8.10447	−	24.9430i	0.319609	−	0.983656i	−0.654206	−	0.756316i	$-0.726997\pi$
$643$	8.10447	−	24.9430i	0.319609	−	0.983656i	0.973816	−	0.227340i	$-0.0730027\pi$
$644$	−6.35290	−	19.5522i	−0.250339	−	0.770465i
$645$	−12.7532			−0.502157
$646$	30.1917			1.18788
$647$	1.78951	+	5.50755i	0.0703529	+	0.216524i	0.980051	−	0.198746i	$-0.0636870\pi$
$647$	1.78951	+	5.50755i	0.0703529	+	0.216524i	−0.909698	+	0.415270i	$0.863687\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	−10.6952	−	7.77051i	−0.419823	−	0.305019i
$650$	0.944328			0.0370396
$651$	1.80792	−	23.5548i	0.0708578	−	0.923185i
$652$	−10.4795			−0.410410
$653$	−25.8810	−	18.8037i	−1.01280	−	0.735844i	−0.0480074	−	0.998847i	$-0.515287\pi$
$653$	−25.8810	−	18.8037i	−1.01280	−	0.735844i	−0.964795	+	0.263003i	$0.915287\pi$
$654$	10.2609	−	7.45494i	0.401231	−	0.291511i
$655$	−5.28516	−	16.2660i	−0.206508	−	0.635567i
$656$	−3.99453			−0.155960
$657$	5.27750			0.205895
$658$	−3.93193	−	12.1012i	−0.153283	−	0.471755i
$659$	0.297208	−	0.914713i	0.0115776	−	0.0356322i	−0.945101	−	0.326779i	$-0.894037\pi$
$659$	0.297208	−	0.914713i	0.0115776	−	0.0356322i	0.956678	+	0.291147i	$0.0940368\pi$
$660$	−0.399170	+	1.22852i	−0.0155377	+	0.0478200i
$661$	32.7971	+	23.8285i	1.27566	+	0.926820i	0.999413	−	0.0342668i	$-0.0109096\pi$
$661$	32.7971	+	23.8285i	1.27566	+	0.926820i	0.276246	+	0.961087i	$0.410910\pi$
$662$	−7.32104	−	22.5318i	−0.284540	−	0.875725i
$663$	−3.38935	−	2.46251i	−0.131632	−	0.0956359i
$664$	3.66105	−	2.65991i	0.142076	−	0.103224i
$665$	8.92293	−	27.4620i	0.346017	−	1.06493i
$666$	9.07344	−	6.59224i	0.351589	−	0.255444i
$667$	−33.3719	+	24.2461i	−1.29216	+	0.938813i
$668$	−5.77144	+	17.7627i	−0.223304	+	0.687258i
$669$	6.21898	−	4.51836i	0.240440	−	0.174690i
$670$	−2.54401	−	1.84833i	−0.0982836	−	0.0714072i
$671$	0.588653	+	1.81169i	0.0227247	+	0.0699395i
$672$	3.43266	+	2.49398i	0.132418	+	0.0962072i
$673$	−4.71354	+	14.5068i	−0.181694	+	0.559195i	−0.999876	−	0.0157639i	$-0.994982\pi$
$673$	−4.71354	+	14.5068i	−0.181694	+	0.559195i	0.818182	+	0.574959i	$0.194982\pi$
$674$	6.24132	−	19.2088i	0.240406	−	0.739895i
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$	−12.1082			−0.465702
$677$	3.64072			0.139924			0.0699622	−	0.997550i	$-0.477712\pi$
$677$	3.64072			0.139924			0.0699622	+	0.997550i	$0.477712\pi$
$678$	1.78699	+	5.49980i	0.0686290	+	0.211218i
$679$	45.7283	−	33.2236i	1.75489	−	1.27500i
$680$	3.58917	+	2.60768i	0.137638	+	0.100000i
$681$	−1.54451			−0.0591856
$682$	−6.99012	+	1.69250i	−0.267666	+	0.0648092i
$683$	−27.1103			−1.03735			−0.518674	−	0.854972i	$-0.673574\pi$
$683$	−27.1103			−1.03735			−0.518674	+	0.854972i	$0.673574\pi$
$684$	5.50566	+	4.00010i	0.210514	+	0.152947i
$685$	−14.4427	+	10.4932i	−0.551826	+	0.400925i
$686$	5.24871	+	16.1539i	0.200397	+	0.616758i
$687$	−7.42380			−0.283236
$688$	12.7532			0.486211
$689$	3.94288	+	12.1349i	0.150212	+	0.462305i
$690$	1.49726	−	4.60810i	0.0569999	−	0.175428i
$691$	−3.75966	+	11.5710i	−0.143024	+	0.440183i	−0.996752	−	0.0805372i	$-0.974336\pi$
$691$	−3.75966	+	11.5710i	−0.143024	+	0.440183i	0.853728	+	0.520720i	$0.174336\pi$
$692$	−2.14742	−	1.56019i	−0.0816326	−	0.0593096i
$693$	−1.69368	−	5.21261i	−0.0643375	−	0.198011i
$694$	12.4874	+	9.07262i	0.474015	+	0.344392i
$695$	1.78724	−	1.29851i	0.0677938	−	0.0492551i
$696$	2.63081	−	8.09680i	0.0997206	−	0.306908i
$697$	14.3370	−	10.4165i	0.543054	−	0.394552i
$698$	−14.4517	+	10.4998i	−0.547005	+	0.397423i
$699$	−6.67234	+	20.5354i	−0.252371	+	0.776718i
$700$	3.43266	−	2.49398i	0.129743	−	0.0942635i
$701$	−31.6523	−	22.9967i	−1.19549	−	0.868574i	−0.201656	−	0.979456i	$-0.564632\pi$
$701$	−31.6523	−	22.9967i	−1.19549	−	0.868574i	−0.993834	+	0.110882i	$0.964632\pi$
$702$	−0.291813	−	0.898110i	−0.0110138	−	0.0338970i
$703$	61.7481	+	44.8626i	2.32887	+	1.69203i
$704$	0.399170	−	1.22852i	0.0150443	−	0.0463015i
$705$	0.926685	−	2.85204i	0.0349010	−	0.107414i
$706$	0.0746608	+	0.229782i	0.00280989	+	0.00864797i
$707$	28.3614			1.06664
$708$	−10.2342			−0.384626
$709$	−10.2047	−	31.4067i	−0.383244	−	1.17950i	−0.937746	−	0.347321i	$-0.887091\pi$
$709$	−10.2047	−	31.4067i	−0.383244	−	1.17950i	0.554503	−	0.832182i	$-0.312909\pi$
$710$	0.406452	−	0.295305i	0.0152539	−	0.0110826i
$711$	0.866833	+	0.629791i	0.0325088	+	0.0236190i
$712$	−17.9648			−0.673260
$713$	26.2196	−	6.34848i	0.981931	−	0.237753i
$714$	−18.8239			−0.704467
$715$	0.986860	+	0.716996i	0.0369065	+	0.0268141i
$716$	15.6865	−	11.3969i	0.586232	−	0.425922i
$717$	1.36603	+	4.20422i	0.0510155	+	0.157010i
$718$	−17.7642			−0.662955
$719$	−16.9972			−0.633889			−0.316944	−	0.948444i	$-0.602657\pi$
$719$	−16.9972			−0.633889			−0.316944	+	0.948444i	$0.602657\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	−24.4507	+	75.2516i	−0.910593	+	2.80252i
$722$	−8.44019	+	25.9762i	−0.314112	+	0.966736i
$723$	−13.5024	−	9.81010i	−0.502161	−	0.364842i
$724$	2.56398	+	7.89112i	0.0952896	+	0.293271i
$725$	−6.88755	−	5.00410i	−0.255797	−	0.185848i
$726$	7.54927	−	5.48486i	0.280180	−	0.203562i
$727$	−7.24989	+	22.3129i	−0.268883	+	0.827538i	0.721890	+	0.692008i	$0.243274\pi$
$727$	−7.24989	+	22.3129i	−0.268883	+	0.827538i	−0.990773	+	0.135530i	$0.956726\pi$
$728$	3.24156	−	2.35513i	0.120140	−	0.0872870i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.63084	+	5.01921i	−0.0603600	+	0.185769i
$731$	−45.7733	+	33.2563i	−1.69299	+	1.23003i
$732$	1.19305	+	0.866804i	0.0440965	+	0.0320380i
$733$	−6.81258	−	20.9670i	−0.251629	−	0.774433i	−0.994475	−	0.104971i	$-0.966525\pi$
$733$	−6.81258	−	20.9670i	−0.251629	−	0.774433i	0.742847	−	0.669462i	$-0.233475\pi$
$734$	9.69467	+	7.04359i	0.357837	+	0.259984i
$735$	−3.40015	+	10.4646i	−0.125416	+	0.385992i
$736$	−1.49726	+	4.60810i	−0.0551899	+	0.169857i
$737$	−1.25522	−	3.86316i	−0.0462364	−	0.142301i
$738$	3.99453			0.147041
$739$	12.4433			0.457733			0.228867	−	0.973458i	$-0.426498\pi$
$739$	12.4433			0.457733			0.228867	+	0.973458i	$0.426498\pi$
$740$	3.46575	+	10.6665i	0.127403	+	0.392107i
$741$	5.19915	−	3.77740i	0.190996	−	0.138766i
$742$	46.3810	+	33.6978i	1.70270	+	1.23708i
$743$	−4.40377			−0.161559			−0.0807793	−	0.996732i	$-0.525741\pi$
$743$	−4.40377			−0.161559			−0.0807793	+	0.996732i	$0.525741\pi$
$744$	−3.60777	+	4.24075i	−0.132267	+	0.155474i
$745$	−16.6896			−0.611459
$746$	17.1993	+	12.4960i	0.629711	+	0.457512i
$747$	−3.66105	+	2.65991i	−0.133951	+	0.0973209i
$748$	1.77090	+	5.45026i	0.0647504	+	0.199281i
$749$	34.5213			1.26138
$750$	1.00000			0.0365148
$751$	−6.12241	−	18.8429i	−0.223410	−	0.687585i	−0.998449	−	0.0556721i	$-0.982270\pi$
$751$	−6.12241	−	18.8429i	−0.223410	−	0.687585i	0.775039	−	0.631913i	$-0.217730\pi$
$752$	−0.926685	+	2.85204i	−0.0337927	+	0.104003i
$753$	−0.669023	+	2.05904i	−0.0243806	+	0.0750357i
$754$	−6.50411	−	4.72551i	−0.236866	−	0.172093i
$755$	4.00793	+	12.3351i	0.145863	+	0.448921i
$756$	−3.43266	−	2.49398i	−0.124845	−	0.0907051i
$757$	8.43346	−	6.12727i	0.306519	−	0.222699i	−0.423882	−	0.905717i	$-0.639333\pi$
$757$	8.43346	−	6.12727i	0.306519	−	0.222699i	0.730402	+	0.683018i	$0.239333\pi$
$758$	2.80451	−	8.63139i	0.101864	−	0.313506i
$759$	5.06347	−	3.67883i	0.183792	−	0.133533i
$760$	−5.50566	+	4.00010i	−0.199711	+	0.145099i
$761$	0.899635	−	2.76879i	0.0326117	−	0.100369i	−0.933426	−	0.358771i	$-0.883196\pi$
$761$	0.899635	−	2.76879i	0.0326117	−	0.100369i	0.966037	+	0.258402i	$0.0831960\pi$
$762$	10.9227	−	7.93580i	0.395687	−	0.287484i
$763$	−43.5369	−	31.6314i	−1.57614	−	1.14513i
$764$	1.61963	+	4.98471i	0.0585962	+	0.180341i
$765$	−3.58917	−	2.60768i	−0.129767	−	0.0942809i
$766$	1.82277	−	5.60990i	0.0658592	−	0.202694i
$767$	−2.98649	+	9.19147i	−0.107836	+	0.331885i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	36.0845			1.30124			0.650621	−	0.759403i	$-0.274509\pi$
$769$	36.0845			1.30124			0.650621	+	0.759403i	$0.274509\pi$
$770$	5.48086			0.197516
$771$	−4.74579	−	14.6060i	−0.170915	−	0.526023i
$772$	−20.8530	+	15.1506i	−0.750518	+	0.545283i
$773$	−15.5432	−	11.2928i	−0.559050	−	0.406174i	0.272061	−	0.962280i	$-0.412295\pi$
$773$	−15.5432	−	11.2928i	−0.559050	−	0.406174i	−0.831111	+	0.556106i	$0.812295\pi$
$774$	−12.7532			−0.458404
$775$	2.91834	+	4.74166i	0.104830	+	0.170325i
$776$	−13.3215			−0.478215
$777$	−38.4987	−	27.9709i	−1.38113	−	1.00345i
$778$	21.2774	−	15.4589i	0.762831	−	0.554229i
$779$	8.40039	+	25.8537i	0.300975	+	0.926307i
$780$	0.944328			0.0338124
$781$	0.648973			0.0232221
$782$	−6.64254	−	20.4436i	−0.237537	−	0.731063i
$783$	−2.63081	+	8.09680i	−0.0940175	+	0.289356i
$784$	3.40015	−	10.4646i	0.121434	−	0.373735i
$785$	−9.15205	−	6.64935i	−0.326651	−	0.237326i
$786$	−5.28516	−	16.2660i	−0.188515	−	0.580190i
$787$	−40.3521	−	29.3175i	−1.43840	−	1.04506i	−0.988375	−	0.152038i	$-0.951416\pi$
$787$	−40.3521	−	29.3175i	−1.43840	−	1.04506i	−0.450021	−	0.893018i	$-0.648584\pi$
$788$	7.67889	−	5.57904i	0.273549	−	0.198745i
$789$	0.0975307	−	0.300169i	0.00347218	−	0.0106863i
$790$	−0.866833	+	0.629791i	−0.0308405	+	0.0224070i
$791$	19.8505	−	14.4222i	0.705803	−	0.512796i
$792$	−0.399170	+	1.22852i	−0.0141839	+	0.0436535i
$793$	1.12663	−	0.818548i	0.0400079	−	0.0290675i
$794$	8.39425	+	6.09878i	0.297901	+	0.216438i
$795$	4.17533	+	12.8503i	0.148084	+	0.455755i
$796$	−12.2061	−	8.86822i	−0.432632	−	0.314326i
$797$	12.5681	−	38.6805i	0.445183	−	1.37013i	−0.437099	−	0.899413i	$-0.643994\pi$
$797$	12.5681	−	38.6805i	0.445183	−	1.37013i	0.882283	−	0.470720i	$-0.156006\pi$
$798$	8.92293	−	27.4620i	0.315868	−	0.972143i
$799$	−4.11120	−	12.6530i	−0.145444	−	0.447630i
$800$	−1.00000			−0.0353553
$801$	17.9648			0.634755
$802$	10.2998	+	31.6994i	0.363698	+	1.11935i
$803$	−5.51520	+	4.00703i	−0.194627	+	0.141405i
$804$	−2.54401	−	1.84833i	−0.0897202	−	0.0651856i
$805$	−20.5584			−0.724589
$806$	2.75587	+	4.47768i	0.0970713	+	0.157720i
$807$	9.21128			0.324252
$808$	−5.40768	−	3.92891i	−0.190242	−	0.138219i
$809$	−38.9051	+	28.2662i	−1.36783	+	0.993786i	−0.369926	+	0.929061i	$0.620617\pi$
$809$	−38.9051	+	28.2662i	−1.36783	+	0.993786i	−0.997903	+	0.0647253i	$0.979383\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−26.2511			−0.921800			−0.460900	−	0.887452i	$-0.652473\pi$
$811$	−26.2511			−0.921800			−0.460900	+	0.887452i	$0.652473\pi$
$812$	−36.1228			−1.26766
$813$	0.585301	+	1.80137i	0.0205274	+	0.0631768i
$814$	−4.47684	+	13.7783i	−0.156913	+	0.482929i
$815$	−3.23835	+	9.96662i	−0.113435	+	0.349116i
$816$	3.58917	+	2.60768i	0.125646	+	0.0912871i
$817$	−26.8197	−	82.5424i	−0.938301	−	2.88779i
$818$	−5.89254	−	4.28118i	−0.206028	−	0.149688i
$819$	−3.24156	+	2.35513i	−0.113269	+	0.0822950i
$820$	−1.23438	+	3.79902i	−0.0431063	+	0.132668i
$821$	16.8227	−	12.2224i	0.587116	−	0.426565i	−0.254166	−	0.967160i	$-0.581801\pi$
$821$	16.8227	−	12.2224i	0.587116	−	0.426565i	0.841283	+	0.540596i	$0.181801\pi$
$822$	−14.4427	+	10.4932i	−0.503746	+	0.365993i
$823$	2.94900	−	9.07610i	0.102796	−	0.316373i	−0.886411	−	0.462899i	$-0.846809\pi$
$823$	2.94900	−	9.07610i	0.102796	−	0.316373i	0.989207	+	0.146526i	$0.0468092\pi$
$824$	15.0867	−	10.9611i	0.525569	−	0.381848i
$825$	1.04504	+	0.759266i	0.0363836	+	0.0264342i
$826$	13.4187	+	41.2986i	0.466898	+	1.43696i
$827$	−13.8030	−	10.0284i	−0.479976	−	0.348723i	0.321341	−	0.946964i	$-0.395867\pi$
$827$	−13.8030	−	10.0284i	−0.479976	−	0.348723i	−0.801316	+	0.598241i	$0.795867\pi$
$828$	1.49726	−	4.60810i	0.0520335	−	0.160143i
$829$	−2.31124	+	7.11326i	−0.0802726	+	0.247054i	−0.983137	−	0.182873i	$-0.941460\pi$
$829$	−2.31124	+	7.11326i	−0.0802726	+	0.247054i	0.902864	+	0.429926i	$0.141460\pi$
$830$	−1.39840	−	4.30382i	−0.0485390	−	0.149388i
$831$	11.8015			0.409391
$832$	−0.944328			−0.0327387
$833$	15.0846	+	46.4256i	0.522650	+	1.60855i
$834$	1.78724	−	1.29851i	0.0618870	−	0.0449636i
$835$	15.1098	+	10.9779i	0.522897	+	0.379907i
$836$	−8.79077			−0.304035
$837$	3.60777	−	4.24075i	0.124703	−	0.146582i
$838$	−38.1615			−1.31827
$839$	4.44777	+	3.23149i	0.153554	+	0.111563i	0.661909	−	0.749584i	$-0.269746\pi$
$839$	4.44777	+	3.23149i	0.153554	+	0.111563i	−0.508355	+	0.861147i	$0.669746\pi$
$840$	3.43266	−	2.49398i	0.118438	−	0.0860504i
$841$	13.4359	+	41.3513i	0.463306	+	1.42591i
$842$	−6.11837			−0.210853
$843$	4.52036			0.155690
$844$	0.105619	+	0.325063i	0.00363557	+	0.0111891i
$845$	−3.74165	+	11.5156i	−0.128717	+	0.396150i
$846$	0.926685	−	2.85204i	0.0318601	−	0.0980553i
$847$	−32.0316	−	23.2723i	−1.10062	−	0.799646i
$848$	−4.17533	−	12.8503i	−0.143381	−	0.441283i
$849$	−22.3080	−	16.2077i	−0.765608	−	0.556247i
$850$	3.58917	−	2.60768i	0.123107	−	0.0894428i
$851$	16.7924	−	51.6817i	0.575636	−	1.77163i
$852$	0.406452	−	0.295305i	0.0139248	−	0.0101170i
$853$	−38.0785	+	27.6656i	−1.30378	+	0.947253i	−0.999985	−	0.00548328i	$-0.998255\pi$
$853$	−38.0785	+	27.6656i	−1.30378	+	0.947253i	−0.303797	+	0.952737i	$0.598255\pi$
$854$	1.93356	−	5.95089i	0.0661652	−	0.203635i
$855$	5.50566	−	4.00010i	0.188290	−	0.136800i
$856$	−6.58220	−	4.78225i	−0.224975	−	0.163454i
$857$	−6.35706	−	19.5650i	−0.217153	−	0.668328i	−0.998994	−	0.0448498i	$-0.985719\pi$
$857$	−6.35706	−	19.5650i	−0.217153	−	0.668328i	0.781841	−	0.623478i	$-0.214281\pi$
$858$	0.986860	+	0.716996i	0.0336909	+	0.0244778i
$859$	0.849216	−	2.61362i	0.0289749	−	0.0891755i	−0.935523	−	0.353265i	$-0.885071\pi$
$859$	0.849216	−	2.61362i	0.0289749	−	0.0891755i	0.964498	+	0.264089i	$0.0850714\pi$
$860$	3.94095	−	12.1290i	0.134385	−	0.413596i
$861$	−5.23747	−	16.1193i	−0.178492	−	0.549343i
$862$	28.1906			0.960175
$863$	−7.91434			−0.269407			−0.134704	−	0.990886i	$-0.543008\pi$
$863$	−7.91434			−0.269407			−0.134704	+	0.990886i	$0.543008\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−2.14742	+	1.56019i	−0.0730145	+	0.0530481i
$866$	13.8649	+	10.0735i	0.471150	+	0.342310i
$867$	−2.68212			−0.0910897
$868$	21.8433	+	8.99826i	0.741408	+	0.305421i
$869$	−1.38405			−0.0469508
$870$	−6.88755	−	5.00410i	−0.233510	−	0.169655i
$871$	−2.40238	+	1.74543i	−0.0814015	+	0.0591416i
$872$	3.91930	+	12.0624i	0.132724	+	0.408483i
$873$	13.3215			0.450865
$874$	32.9737			1.11535
$875$	−1.31116	−	4.03534i	−0.0443253	−	0.136419i
$876$	−1.63084	+	5.01921i	−0.0551009	+	0.169583i
$877$	−10.8196	+	33.2993i	−0.365352	+	1.12444i	0.584409	+	0.811459i	$0.301326\pi$
$877$	−10.8196	+	33.2993i	−0.365352	+	1.12444i	−0.949761	+	0.312977i	$0.898674\pi$
$878$	22.8656	+	16.6128i	0.771676	+	0.560656i
$879$	1.27656	+	3.92883i	0.0430571	+	0.132516i
$880$	−1.04504	−	0.759266i	−0.0352283	−	0.0255948i
$881$	12.6171	−	9.16682i	0.425079	−	0.308838i	−0.354599	−	0.935018i	$-0.615383\pi$
$881$	12.6171	−	9.16682i	0.425079	−	0.308838i	0.779678	+	0.626180i	$0.215383\pi$
$882$	−3.40015	+	10.4646i	−0.114489	+	0.352361i
$883$	−20.1616	+	14.6483i	−0.678492	+	0.492953i	−0.872857	−	0.487976i	$-0.837735\pi$
$883$	−20.1616	+	14.6483i	−0.678492	+	0.492953i	0.194365	+	0.980929i	$0.437735\pi$
$884$	3.38935	−	2.46251i	0.113996	−	0.0828231i
$885$	−3.16256	+	9.73334i	−0.106308	+	0.327183i
$886$	−21.2767	+	15.4585i	−0.714806	+	0.519337i
$887$	20.9910	+	15.2509i	0.704809	+	0.512074i	0.881495	−	0.472193i	$-0.156538\pi$
$887$	20.9910	+	15.2509i	0.704809	+	0.512074i	−0.176686	+	0.984267i	$0.556538\pi$
$888$	3.46575	+	10.6665i	0.116303	+	0.357943i
$889$	−46.3451	−	33.6717i	−1.55436	−	1.12931i
$890$	−5.55143	+	17.0855i	−0.186084	+	0.572709i
$891$	0.399170	−	1.22852i	0.0133727	−	0.0411569i
$892$	2.37544	+	7.31085i	0.0795356	+	0.244785i
$893$	20.4080			0.682929
$894$	−16.6896			−0.558183
$895$	−5.99171	−	18.4406i	−0.200281	−	0.616401i
$896$	−3.43266	+	2.49398i	−0.114677	+	0.0833179i
$897$	−3.70166	−	2.68941i	−0.123595	−	0.0897969i
$898$	−5.96485			−0.199050
$899$	3.62754	−	47.2621i	0.120985	−	1.57628i
$900$	1.00000			0.0333333
$901$	48.4956	+	35.2341i	1.61562	+	1.17382i
$902$	−4.17444	+	3.03291i	−0.138994	+	0.100985i
$903$	16.7215	+	51.4635i	0.556457	+	1.71260i
$904$	−5.78283			−0.192334
$905$	8.29722			0.275809
$906$	4.00793	+	12.3351i	0.133154	+	0.409807i
$907$	−2.06741	+	6.36284i	−0.0686473	+	0.211275i	−0.979495	−	0.201468i	$-0.935429\pi$
$907$	−2.06741	+	6.36284i	−0.0686473	+	0.211275i	0.910848	+	0.412742i	$0.135429\pi$
$908$	0.477279	−	1.46891i	0.0158391	−	0.0487476i
$909$	5.40768	+	3.92891i	0.179362	+	0.130314i
$910$	−1.23817	−	3.81068i	−0.0410448	−	0.126323i
$911$	−9.21531	−	6.69532i	−0.305317	−	0.221826i	0.424567	−	0.905396i	$-0.360426\pi$
$911$	−9.21531	−	6.69532i	−0.305317	−	0.221826i	−0.729884	+	0.683571i	$0.760426\pi$
$912$	−5.50566	+	4.00010i	−0.182311	+	0.132456i
$913$	1.80636	−	5.55942i	0.0597819	−	0.183990i
$914$	15.1375	−	10.9981i	0.500705	−	0.363783i
$915$	1.19305	−	0.866804i	0.0394411	−	0.0286557i
$916$	2.29408	−	7.06046i	0.0757986	−	0.233284i
$917$	−58.7093	+	42.6548i	−1.93875	+	1.40859i
$918$	−3.58917	−	2.60768i	−0.118460	−	0.0860663i
$919$	−9.08105	−	27.9486i	−0.299556	−	0.921939i	−0.981653	−	0.190677i	$-0.938932\pi$
$919$	−9.08105	−	27.9486i	−0.299556	−	0.921939i	0.682097	−	0.731262i	$-0.261068\pi$
$920$	3.91989	+	2.84797i	0.129235	+	0.0938946i
$921$	1.44439	−	4.44537i	0.0475942	−	0.146480i
$922$	3.96850	−	12.2138i	0.130696	−	0.402240i
$923$	−0.146608	−	0.451212i	−0.00482565	−	0.0148518i
$924$	5.48086			0.180307
$925$	11.2154			0.368760
$926$	11.5108	+	35.4267i	0.378269	+	1.16419i
$927$	−15.0867	+	10.9611i	−0.495511	+	0.360010i
$928$	6.88755	+	5.00410i	0.226095	+	0.164268i
$929$	28.9130			0.948606			0.474303	−	0.880362i	$-0.342700\pi$
$929$	28.9130			0.948606			0.474303	+	0.880362i	$0.342700\pi$
$930$	2.91834	+	4.74166i	0.0956960	+	0.155485i
$931$	−74.8802			−2.45410
$932$	−17.4684	−	12.6915i	−0.572197	−	0.415725i
$933$	−2.71894	+	1.97543i	−0.0890141	+	0.0646725i
$934$	3.42949	+	10.5549i	0.112216	+	0.345366i
$935$	5.73074			0.187415
$936$	0.944328			0.0308663
$937$	18.3035	+	56.3323i	0.597948	+	1.84029i	0.539468	+	0.842006i	$0.318625\pi$
$937$	18.3035	+	56.3323i	0.597948	+	1.84029i	0.0584801	+	0.998289i	$0.481375\pi$
$938$	−4.12303	+	12.6894i	−0.134622	+	0.414323i
$939$	7.75831	−	23.8776i	0.253183	−	0.779217i
$940$	2.42609	+	1.76266i	0.0791304	+	0.0574916i
$941$	6.27172	+	19.3024i	0.204452	+	0.629239i	0.999735	+	0.0230012i	$0.00732216\pi$
$941$	6.27172	+	19.3024i	0.204452	+	0.629239i	−0.795283	+	0.606238i	$0.792678\pi$
$942$	−9.15205	−	6.64935i	−0.298190	−	0.216648i
$943$	15.6581	−	11.3763i	0.509898	−	0.370463i
$944$	3.16256	−	9.73334i	0.102932	−	0.316793i
$945$	−3.43266	+	2.49398i	−0.111665	+	0.0811291i
$946$	13.3276	−	9.68306i	0.433317	−	0.314824i
$947$	−12.2601	+	37.7326i	−0.398398	+	1.22614i	0.527885	+	0.849316i	$0.322985\pi$
$947$	−12.2601	+	37.7326i	−0.398398	+	1.22614i	−0.926283	+	0.376828i	$0.877015\pi$
$948$	−0.866833	+	0.629791i	−0.0281534	+	0.0204547i
$949$	4.03190	+	2.92934i	0.130881	+	0.0950905i
$950$	2.10297	+	6.47229i	0.0682295	+	0.209989i
$951$	−4.05531	−	2.94635i	−0.131502	−	0.0955421i
$952$	5.81691	−	17.9026i	0.188527	−	0.580226i
$953$	−8.78836	+	27.0478i	−0.284683	+	0.876164i	0.701810	+	0.712364i	$0.252375\pi$
$953$	−8.78836	+	27.0478i	−0.284683	+	0.876164i	−0.986493	+	0.163801i	$0.947625\pi$
$954$	4.17533	+	12.8503i	0.135181	+	0.416045i
$955$	5.24124			0.169602
$956$	−4.42058			−0.142972
$957$	−3.39832	−	10.4590i	−0.109852	−	0.338090i
$958$	−13.2999	+	9.66297i	−0.429701	+	0.312196i
$959$	61.2804	+	44.5228i	1.97885	+	1.43772i
$960$	−1.00000			−0.0322749
$961$	−13.9666	+	27.6755i	−0.450537	+	0.892758i
$962$	10.5910			0.341468
$963$	6.58220	+	4.78225i	0.212108	+	0.154106i
$964$	13.5024	−	9.81010i	0.434884	−	0.315962i
$965$	7.96515	+	24.5142i	0.256407	+	0.789141i
$966$	−20.5584			−0.661456
$967$	−19.6437			−0.631700			−0.315850	−	0.948809i	$-0.602290\pi$
$967$	−19.6437			−0.631700			−0.315850	+	0.948809i	$0.602290\pi$
$968$	2.88356	+	8.87470i	0.0926813	+	0.285244i
$969$	9.32975	−	28.7140i	0.299715	−	0.922427i
$970$	−4.11658	+	12.6695i	−0.132175	+	0.406794i
$971$	19.3661	+	14.0703i	0.621488	+	0.451538i	0.853441	−	0.521189i	$-0.174511\pi$
$971$	19.3661	+	14.0703i	0.621488	+	0.451538i	−0.231953	+	0.972727i	$0.574511\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−7.58327	−	5.50957i	−0.243108	−	0.176629i
$974$	23.2833	−	16.9163i	0.746045	−	0.542034i
$975$	0.291813	−	0.898110i	0.00934551	−	0.0287625i
$976$	−1.19305	+	0.866804i	−0.0381887	+	0.0277457i
$977$	8.50836	−	6.18168i	0.272206	−	0.197770i	−0.443304	−	0.896371i	$-0.646194\pi$
$977$	8.50836	−	6.18168i	0.272206	−	0.197770i	0.715511	+	0.698602i	$0.246194\pi$
$978$	−3.23835	+	9.96662i	−0.103551	+	0.318697i
$979$	−18.7739	+	13.6401i	−0.600018	+	0.435938i
$980$	−8.90170	−	6.46746i	−0.284354	−	0.206596i
$981$	−3.91930	−	12.0624i	−0.125133	−	0.385121i
$982$	10.2269	+	7.43025i	0.326352	+	0.237109i
$983$	4.66371	−	14.3534i	0.148749	−	0.457803i	−0.848725	−	0.528835i	$-0.822629\pi$
$983$	4.66371	−	14.3534i	0.148749	−	0.457803i	0.997474	+	0.0710317i	$0.0226291\pi$
$984$	−1.23438	+	3.79902i	−0.0393505	+	0.121108i
$985$	−2.93308	−	9.02708i	−0.0934556	−	0.287627i
$986$	−37.7697			−1.20283
$987$	−12.7240			−0.405009
$988$	1.98590	+	6.11197i	0.0631798	+	0.194448i
$989$	−49.9911	+	36.3207i	−1.58962	+	1.15493i
$990$	1.04504	+	0.759266i	0.0332135	+	0.0241310i
$991$	7.75806			0.246443			0.123221	−	0.992379i	$-0.460677\pi$
$991$	7.75806			0.246443			0.123221	+	0.992379i	$0.460677\pi$
$992$	−2.91834	−	4.74166i	−0.0926573	−	0.150548i
$993$	−23.6914			−0.751823
$994$	−1.72458	−	1.25298i	−0.0547003	−	0.0397421i
$995$	−12.2061	+	8.86822i	−0.386958	+	0.281142i
$996$	−1.39840	−	4.30382i	−0.0443099	−	0.136372i
$997$	−25.5242			−0.808359			−0.404180	−	0.914680i	$-0.632443\pi$
$997$	−25.5242			−0.808359			−0.404180	+	0.914680i	$0.632443\pi$
$998$	32.2568			1.02107
$999$	−3.46575	−	10.6665i	−0.109651	−	0.337472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.f.901.1	yes	12
31.16	even	5	inner	930.2.n.f.481.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.f.481.1	✓	12	31.16	even	5	inner
930.2.n.f.901.1	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.31116 - 4.03534i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-1.31116 - 4.03534i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.399170 + 1.22852i) q^{11} +(0.809017 + 0.587785i) q^{12} +(0.763978 - 0.555062i) q^{13} +(1.31116 - 4.03534i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.37094 - 4.21932i) q^{17} +(0.809017 - 0.587785i) q^{18} +(5.50566 + 4.00010i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-3.43266 - 2.49398i) q^{21} +(-0.399170 + 1.22852i) q^{22} +(1.49726 - 4.60810i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +0.944328 q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.43266 - 2.49398i) q^{28} +(-6.88755 - 5.00410i) q^{29} +1.00000 q^{30} +(2.91834 + 4.74166i) q^{31} -1.00000 q^{32} +(1.04504 + 0.759266i) q^{33} +(3.58917 - 2.60768i) q^{34} +(-1.31116 - 4.03534i) q^{35} +1.00000 q^{36} +11.2154 q^{37} +(2.10297 + 6.47229i) q^{38} +(0.291813 - 0.898110i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(3.23164 + 2.34792i) q^{41} +(-1.31116 - 4.03534i) q^{42} +(-10.3176 - 7.49614i) q^{43} +(-1.04504 + 0.759266i) q^{44} +(0.309017 - 0.951057i) q^{45} +(3.91989 - 2.84797i) q^{46} +(2.42609 - 1.76266i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-8.90170 + 6.46746i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.37094 - 4.21932i) q^{51} +(0.763978 + 0.555062i) q^{52} +(-4.17533 + 12.8503i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.399170 + 1.22852i) q^{55} +4.24301 q^{56} +6.80537 q^{57} +(-2.63081 - 8.09680i) q^{58} +(-8.27968 + 6.01554i) q^{59} +(0.809017 + 0.587785i) q^{60} +1.47470 q^{61} +(-0.426093 + 5.55144i) q^{62} -4.24301 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.763978 - 0.555062i) q^{65} +(0.399170 + 1.22852i) q^{66} -3.14457 q^{67} +4.43645 q^{68} +(-1.49726 - 4.60810i) q^{69} +(1.31116 - 4.03534i) q^{70} +(0.155251 - 0.477813i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.63084 + 5.01921i) q^{73} +(9.07344 + 6.59224i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-2.10297 + 6.47229i) q^{76} +(4.43411 - 3.22157i) q^{77} +(0.763978 - 0.555062i) q^{78} +(-0.331101 + 1.01902i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.23438 + 3.79902i) q^{82} +(-3.66105 - 2.65991i) q^{83} +(1.31116 - 4.03534i) q^{84} +(1.37094 - 4.21932i) q^{85} +(-3.94095 - 12.1290i) q^{86} -8.51348 q^{87} -1.29174 q^{88} +(5.55143 + 17.0855i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-3.24156 - 2.35513i) q^{91} +4.84525 q^{92} +(5.14806 + 2.12073i) q^{93} +2.99882 q^{94} +(5.50566 + 4.00010i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(4.11658 + 12.6695i) q^{97} -11.0031 q^{98} +1.29174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

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