LMFDB - Embedded newform 930.2.n.d.841.3

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} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 13x^10 - 9x^9 + 60x^8 + x^7 + 263x^6 + 823x^5 + 1931x^4 + 1170x^3 + 1340x^2 + 1000x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			841.3
Root			$-1.32494 + 0.962628i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.d.721.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(2.14380 - 1.55756i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(2.14380 - 1.55756i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(3.05265 - 2.21788i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(0.0808923 - 0.248961i) q^{13} +(2.14380 + 1.55756i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.72143 + 1.97723i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.47735 + 4.54681i) q^{19} +(0.809017 - 0.587785i) q^{20} +(0.818860 + 2.52019i) q^{21} +(3.05265 + 2.21788i) q^{22} +(6.19805 + 4.50315i) q^{23} +(0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +0.261773 q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.818860 + 2.52019i) q^{28} +(1.38432 + 4.26049i) q^{29} +1.00000 q^{30} +(-1.08039 - 5.46194i) q^{31} +1.00000 q^{32} +(1.16601 + 3.58860i) q^{33} +(-1.03949 + 3.19923i) q^{34} +(-2.14380 + 1.55756i) q^{35} +1.00000 q^{36} -6.85410 q^{37} +(-3.86775 + 2.81008i) q^{38} +(0.211779 + 0.153866i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-0.633657 - 1.95020i) q^{41} +(-2.14380 + 1.55756i) q^{42} +(-2.18250 - 6.71705i) q^{43} +(-1.16601 + 3.58860i) q^{44} +(0.809017 + 0.587785i) q^{45} +(-2.36745 + 7.28625i) q^{46} +(-0.326352 + 1.00441i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.00676897 - 0.0208327i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-2.72143 + 1.97723i) q^{51} +(0.0808923 + 0.248961i) q^{52} +(8.26172 + 6.00249i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-3.05265 + 2.21788i) q^{55} -2.64989 q^{56} -4.78080 q^{57} +(-3.62419 + 2.63313i) q^{58} +(-1.46567 + 4.51088i) q^{59} +(0.309017 + 0.951057i) q^{60} +1.91964 q^{61} +(4.86075 - 2.71535i) q^{62} -2.64989 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.0808923 + 0.248961i) q^{65} +(-3.05265 + 2.21788i) q^{66} +4.02523 q^{67} -3.36387 q^{68} +(-6.19805 + 4.50315i) q^{69} +(-2.14380 - 1.55756i) q^{70} +(-0.666814 - 0.484468i) q^{71} +(0.309017 + 0.951057i) q^{72} +(6.91929 - 5.02716i) q^{73} +(-2.11803 - 6.51864i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-3.86775 - 2.81008i) q^{76} +(3.08979 - 9.50940i) q^{77} +(-0.0808923 + 0.248961i) q^{78} +(4.06969 + 2.95680i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.65894 - 1.20529i) q^{82} +(3.49795 + 10.7656i) q^{83} +(-2.14380 - 1.55756i) q^{84} +(-2.72143 - 1.97723i) q^{85} +(5.71386 - 4.15137i) q^{86} -4.47975 q^{87} -3.77328 q^{88} +(-4.84923 + 3.52317i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(-0.214355 - 0.659718i) q^{91} -7.66122 q^{92} +(5.52847 + 0.660315i) q^{93} -1.05610 q^{94} +(-1.47735 - 4.54681i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(5.68828 - 4.13278i) q^{97} +0.0219048 q^{98} -3.77328 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	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	2.14380	−	1.55756i	0.810282	−	0.588704i	−0.103630	−	0.994616i	$-0.533046\pi$
$7$	2.14380	−	1.55756i	0.810282	−	0.588704i	0.913912	+	0.405912i	$0.133046\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.309017	−	0.951057i	−0.0977198	−	0.300750i
$11$	3.05265	−	2.21788i	0.920408	−	0.668716i	−0.0232172	−	0.999730i	$-0.507391\pi$
$11$	3.05265	−	2.21788i	0.920408	−	0.668716i	0.943626	+	0.331015i	$0.107391\pi$
$12$	−0.309017	−	0.951057i	−0.0892055	−	0.274546i
$13$	0.0808923	−	0.248961i	0.0224355	−	0.0690493i	−0.939212	−	0.343338i	$-0.888442\pi$
$13$	0.0808923	−	0.248961i	0.0224355	−	0.0690493i	0.961647	+	0.274289i	$0.0884424\pi$
$14$	2.14380	+	1.55756i	0.572956	+	0.416277i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.72143	+	1.97723i	0.660043	+	0.479550i	0.866678	−	0.498869i	$-0.166251\pi$
$17$	2.72143	+	1.97723i	0.660043	+	0.479550i	−0.206634	+	0.978418i	$0.566251\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	1.47735	+	4.54681i	0.338927	+	1.04311i	0.964755	+	0.263149i	$0.0847612\pi$
$19$	1.47735	+	4.54681i	0.338927	+	1.04311i	−0.625828	+	0.779961i	$0.715239\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	0.818860	+	2.52019i	0.178690	+	0.549951i
$22$	3.05265	+	2.21788i	0.650827	+	0.472854i
$23$	6.19805	+	4.50315i	1.29238	+	0.938972i	0.999851	−	0.0172837i	$-0.00550185\pi$
$23$	6.19805	+	4.50315i	1.29238	+	0.938972i	0.292533	+	0.956255i	$0.405502\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	1.00000			0.200000
$26$	0.261773			0.0513379
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.818860	+	2.52019i	−0.154750	+	0.476272i
$29$	1.38432	+	4.26049i	0.257061	+	0.791153i	0.993417	+	0.114558i	$0.0365452\pi$
$29$	1.38432	+	4.26049i	0.257061	+	0.791153i	−0.736355	+	0.676595i	$0.763455\pi$
$30$	1.00000			0.182574
$31$	−1.08039	−	5.46194i	−0.194045	−	0.980993i
$31$	−1.08039	−	5.46194i	−0.194045	−	0.980993i
$32$	1.00000			0.176777
$33$	1.16601	+	3.58860i	0.202976	+	0.624696i
$34$	−1.03949	+	3.19923i	−0.178272	+	0.548664i
$35$	−2.14380	+	1.55756i	−0.362369	+	0.263277i
$36$	1.00000			0.166667
$37$	−6.85410			−1.12681			−0.563404	−	0.826182i	$-0.690508\pi$
$37$	−6.85410			−1.12681			−0.563404	+	0.826182i	$0.690508\pi$
$38$	−3.86775	+	2.81008i	−0.627432	+	0.455856i
$39$	0.211779	+	0.153866i	0.0339117	+	0.0246383i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−0.633657	−	1.95020i	−0.0989606	−	0.304569i	0.889305	−	0.457315i	$-0.151189\pi$
$41$	−0.633657	−	1.95020i	−0.0989606	−	0.304569i	−0.988266	+	0.152745i	$0.951189\pi$
$42$	−2.14380	+	1.55756i	−0.330796	+	0.240337i
$43$	−2.18250	−	6.71705i	−0.332828	−	1.02434i	−0.967782	−	0.251790i	$-0.918981\pi$
$43$	−2.18250	−	6.71705i	−0.332828	−	1.02434i	0.634953	−	0.772550i	$-0.281019\pi$
$44$	−1.16601	+	3.58860i	−0.175782	+	0.541003i
$45$	0.809017	+	0.587785i	0.120601	+	0.0876219i
$46$	−2.36745	+	7.28625i	−0.349061	+	1.07430i
$47$	−0.326352	+	1.00441i	−0.0476034	+	0.146508i	−0.972033	−	0.234845i	$-0.924542\pi$
$47$	−0.326352	+	1.00441i	−0.0476034	+	0.146508i	0.924429	+	0.381353i	$0.124542\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	0.00676897	−	0.0208327i	0.000966996	−	0.00297611i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−2.72143	+	1.97723i	−0.381076	+	0.276868i
$52$	0.0808923	+	0.248961i	0.0112177	+	0.0345247i
$53$	8.26172	+	6.00249i	1.13483	+	0.824505i	0.986391	−	0.164416i	$-0.0525739\pi$
$53$	8.26172	+	6.00249i	1.13483	+	0.824505i	0.148443	+	0.988921i	$0.452574\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	−3.05265	+	2.21788i	−0.411619	+	0.299059i
$56$	−2.64989			−0.354106
$57$	−4.78080			−0.633233
$58$	−3.62419	+	2.63313i	−0.475879	+	0.345747i
$59$	−1.46567	+	4.51088i	−0.190814	+	0.587267i	−1.00000		0.000286736i	$-0.999909\pi$
$59$	−1.46567	+	4.51088i	−0.190814	+	0.587267i	0.809186	+	0.587553i	$0.199909\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	1.91964			0.245785			0.122893	−	0.992420i	$-0.460783\pi$
$61$	1.91964			0.245785			0.122893	+	0.992420i	$0.460783\pi$
$62$	4.86075	−	2.71535i	0.617316	−	0.344849i
$63$	−2.64989			−0.333854
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.0808923	+	0.248961i	−0.0100335	+	0.0308798i
$66$	−3.05265	+	2.21788i	−0.375755	+	0.273002i
$67$	4.02523			0.491760			0.245880	−	0.969300i	$-0.420923\pi$
$67$	4.02523			0.491760			0.245880	+	0.969300i	$0.420923\pi$
$68$	−3.36387			−0.407929
$69$	−6.19805	+	4.50315i	−0.746158	+	0.542116i
$70$	−2.14380	−	1.55756i	−0.256234	−	0.186165i
$71$	−0.666814	−	0.484468i	−0.0791362	−	0.0574958i	0.547514	−	0.836797i	$-0.315574\pi$
$71$	−0.666814	−	0.484468i	−0.0791362	−	0.0574958i	−0.626650	+	0.779301i	$0.715574\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	6.91929	−	5.02716i	0.809842	−	0.588384i	−0.103943	−	0.994583i	$-0.533146\pi$
$73$	6.91929	−	5.02716i	0.809842	−	0.588384i	0.913785	+	0.406199i	$0.133146\pi$
$74$	−2.11803	−	6.51864i	−0.246216	−	0.757776i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	−3.86775	−	2.81008i	−0.443661	−	0.322339i
$77$	3.08979	−	9.50940i	0.352114	−	1.08370i
$78$	−0.0808923	+	0.248961i	−0.00915925	+	0.0281893i
$79$	4.06969	+	2.95680i	0.457875	+	0.332666i	0.792697	−	0.609616i	$-0.208676\pi$
$79$	4.06969	+	2.95680i	0.457875	+	0.332666i	−0.334822	+	0.942281i	$0.608676\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.65894	−	1.20529i	0.183199	−	0.133102i
$83$	3.49795	+	10.7656i	0.383950	+	1.18168i	0.937239	+	0.348687i	$0.113372\pi$
$83$	3.49795	+	10.7656i	0.383950	+	1.18168i	−0.553289	+	0.832989i	$0.686628\pi$
$84$	−2.14380	−	1.55756i	−0.233908	−	0.169944i
$85$	−2.72143	−	1.97723i	−0.295180	−	0.214461i
$86$	5.71386	−	4.15137i	0.616142	−	0.447653i
$87$	−4.47975			−0.480279
$88$	−3.77328			−0.402233
$89$	−4.84923	+	3.52317i	−0.514018	+	0.373456i	−0.814346	−	0.580380i	$-0.802904\pi$
$89$	−4.84923	+	3.52317i	−0.514018	+	0.373456i	0.300328	+	0.953836i	$0.402904\pi$
$90$	−0.309017	+	0.951057i	−0.0325733	+	0.100250i
$91$	−0.214355	−	0.659718i	−0.0224706	−	0.0691573i
$92$	−7.66122			−0.798737
$93$	5.52847	+	0.660315i	0.573276	+	0.0684715i
$94$	−1.05610			−0.108928
$95$	−1.47735	−	4.54681i	−0.151573	−	0.466493i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	5.68828	−	4.13278i	0.577558	−	0.419620i	−0.260285	−	0.965532i	$-0.583817\pi$
$97$	5.68828	−	4.13278i	0.577558	−	0.419620i	0.837843	+	0.545912i	$0.183817\pi$
$98$	0.0219048			0.00221272
$99$	−3.77328			−0.379229
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	−4.98499	−	3.62181i	−0.496025	−	0.360383i	0.311472	−	0.950255i	$-0.399178\pi$
$101$	−4.98499	−	3.62181i	−0.496025	−	0.360383i	−0.807497	+	0.589872i	$0.799178\pi$
$102$	−2.72143	−	1.97723i	−0.269462	−	0.195775i
$103$	−1.96309	−	6.04177i	−0.193429	−	0.595314i	−0.999991	−	0.00416436i	$-0.998674\pi$
$103$	−1.96309	−	6.04177i	−0.193429	−	0.595314i	0.806562	−	0.591149i	$-0.201326\pi$
$104$	−0.211779	+	0.153866i	−0.0207666	+	0.0150878i
$105$	−0.818860	−	2.52019i	−0.0799126	−	0.245946i
$106$	−3.15570	+	9.71223i	−0.306508	+	0.943335i
$107$	12.3401	+	8.96558i	1.19296	+	0.866735i	0.993574	−	0.113186i	$-0.0361055\pi$
$107$	12.3401	+	8.96558i	1.19296	+	0.866735i	0.199385	+	0.979921i	$0.436106\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	0.686074	−	2.11152i	0.0657140	−	0.202247i	−0.912808	−	0.408389i	$-0.866091\pi$
$109$	0.686074	−	2.11152i	0.0657140	−	0.202247i	0.978522	+	0.206142i	$0.0660908\pi$
$110$	−3.05265	−	2.21788i	−0.291059	−	0.211467i
$111$	2.11803	−	6.51864i	0.201035	−	0.618722i
$112$	−0.818860	−	2.52019i	−0.0773750	−	0.238136i
$113$	3.27728	−	2.38108i	0.308301	−	0.223994i	−0.422866	−	0.906192i	$-0.638976\pi$
$113$	3.27728	−	2.38108i	0.308301	−	0.223994i	0.731167	+	0.682199i	$0.238976\pi$
$114$	−1.47735	−	4.54681i	−0.138366	−	0.425848i
$115$	−6.19805	−	4.50315i	−0.577972	−	0.419921i
$116$	−3.62419	−	2.63313i	−0.336498	−	0.244480i
$117$	−0.211779	+	0.153866i	−0.0195790	+	0.0142249i
$118$	−4.74302			−0.436630
$119$	8.91388			0.817134
$120$	−0.809017	+	0.587785i	−0.0738528	+	0.0536572i
$121$	1.00049	−	3.07920i	0.0909538	−	0.279927i
$122$	0.593202	+	1.82569i	0.0537060	+	0.165290i
$123$	2.05056			0.184893
$124$	4.08450	+	3.78376i	0.366799	+	0.339792i
$125$	−1.00000			−0.0894427
$126$	−0.818860	−	2.52019i	−0.0729499	−	0.224517i
$127$	1.92169	−	5.91436i	0.170523	−	0.524815i	−0.828878	−	0.559429i	$-0.811020\pi$
$127$	1.92169	−	5.91436i	0.170523	−	0.524815i	0.999401	+	0.0346147i	$0.0110204\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	7.06272			0.621838
$130$	−0.261773			−0.0229590
$131$	−9.24191	+	6.71464i	−0.807470	+	0.586661i	−0.913096	−	0.407745i	$-0.866315\pi$
$131$	−9.24191	+	6.71464i	−0.807470	+	0.586661i	0.105626	+	0.994406i	$0.466315\pi$
$132$	−3.05265	−	2.21788i	−0.265699	−	0.193042i
$133$	10.2491	+	7.44641i	0.888710	+	0.645686i
$134$	1.24386	+	3.82822i	0.107453	+	0.330708i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	−1.03949	−	3.19923i	−0.0891358	−	0.274332i
$137$	5.22942	−	16.0945i	0.446779	−	1.37504i	−0.433742	−	0.901037i	$-0.642807\pi$
$137$	5.22942	−	16.0945i	0.446779	−	1.37504i	0.880521	−	0.474008i	$-0.157193\pi$
$138$	−6.19805	−	4.50315i	−0.527613	−	0.383334i
$139$	2.74009	−	8.43312i	0.232411	−	0.715288i	−0.765043	−	0.643979i	$-0.777282\pi$
$139$	2.74009	−	8.43312i	0.232411	−	0.715288i	0.997454	−	0.0713089i	$-0.0227176\pi$
$140$	0.818860	−	2.52019i	0.0692063	−	0.212995i
$141$	−0.854401	−	0.620759i	−0.0719536	−	0.0522773i
$142$	0.254700	−	0.783886i	0.0213740	−	0.0657823i
$143$	−0.305229	−	0.939400i	−0.0255246	−	0.0785565i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	−1.38432	−	4.26049i	−0.114961	−	0.353815i
$146$	6.91929	+	5.02716i	0.572645	+	0.416051i
$147$	0.0177214	+	0.0128753i	0.00146164	+	0.00106194i
$148$	5.54508	−	4.02874i	0.455803	−	0.331160i
$149$	3.51099			0.287632			0.143816	−	0.989604i	$-0.454063\pi$
$149$	3.51099			0.287632			0.143816	+	0.989604i	$0.454063\pi$
$150$	−1.00000			−0.0816497
$151$	−15.1219	+	10.9867i	−1.23060	+	0.894086i	−0.996935	−	0.0782302i	$-0.975073\pi$
$151$	−15.1219	+	10.9867i	−1.23060	+	0.894086i	−0.233669	+	0.972316i	$0.575073\pi$
$152$	1.47735	−	4.54681i	0.119829	−	0.368795i
$153$	−1.03949	−	3.19923i	−0.0840380	−	0.258642i
$154$	9.99877			0.805724
$155$	1.08039	+	5.46194i	0.0867794	+	0.438713i
$156$	−0.261773			−0.0209586
$157$	−5.97761	−	18.3972i	−0.477065	−	1.46825i	−0.843153	−	0.537674i	$-0.819303\pi$
$157$	−5.97761	−	18.3972i	−0.477065	−	1.46825i	0.366088	−	0.930580i	$-0.380697\pi$
$158$	−1.55448	+	4.78420i	−0.123668	+	0.380611i
$159$	−8.26172	+	6.00249i	−0.655197	+	0.476028i
$160$	−1.00000			−0.0790569
$161$	20.3014			1.59997
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−10.6779	−	7.75798i	−0.836361	−	0.607652i	0.0849904	−	0.996382i	$-0.472914\pi$
$163$	−10.6779	−	7.75798i	−0.836361	−	0.607652i	−0.921352	+	0.388730i	$0.872914\pi$
$164$	1.65894	+	1.20529i	0.129541	+	0.0941171i
$165$	−1.16601	−	3.58860i	−0.0907736	−	0.279372i
$166$	−9.15775	+	6.65350i	−0.710780	+	0.516412i
$167$	−5.93750	−	18.2738i	−0.459458	−	1.41407i	−0.865821	−	0.500354i	$-0.833203\pi$
$167$	−5.93750	−	18.2738i	−0.459458	−	1.41407i	0.406363	−	0.913712i	$-0.366797\pi$
$168$	0.818860	−	2.52019i	0.0631764	−	0.194437i
$169$	10.4618	+	7.60093i	0.804753	+	0.584687i
$170$	1.03949	−	3.19923i	0.0797255	−	0.245370i
$171$	1.47735	−	4.54681i	0.112976	−	0.347703i
$172$	5.71386	+	4.15137i	0.435678	+	0.316539i
$173$	−1.28750	+	3.96251i	−0.0978867	+	0.301264i	−0.987995	−	0.154484i	$-0.950628\pi$
$173$	−1.28750	+	3.96251i	−0.0978867	+	0.301264i	0.890109	+	0.455749i	$0.150628\pi$
$174$	−1.38432	−	4.26049i	−0.104945	−	0.322987i
$175$	2.14380	−	1.55756i	0.162056	−	0.117741i
$176$	−1.16601	−	3.58860i	−0.0878912	−	0.270501i
$177$	−3.83718	−	2.78788i	−0.288420	−	0.209550i
$178$	−4.84923	−	3.52317i	−0.363465	−	0.264073i
$179$	−9.96407	+	7.23932i	−0.744750	+	0.541092i	−0.894195	−	0.447678i	$-0.852251\pi$
$179$	−9.96407	+	7.23932i	−0.744750	+	0.541092i	0.149445	+	0.988770i	$0.452251\pi$
$180$	−1.00000			−0.0745356
$181$	−15.5982			−1.15940			−0.579702	−	0.814828i	$-0.696831\pi$
$181$	−15.5982			−1.15940			−0.579702	+	0.814828i	$0.696831\pi$
$182$	0.561190	−	0.407728i	0.0415982	−	0.0302228i
$183$	−0.593202	+	1.82569i	−0.0438508	+	0.134959i
$184$	−2.36745	−	7.28625i	−0.174530	−	0.537149i
$185$	6.85410			0.503924
$186$	1.08039	+	5.46194i	0.0792184	+	0.400489i
$187$	12.6928			0.928192
$188$	−0.326352	−	1.00441i	−0.0238017	−	0.0732541i
$189$	0.818860	−	2.52019i	0.0595633	−	0.183317i
$190$	3.86775	−	2.81008i	0.280596	−	0.203865i
$191$	12.9529			0.937240			0.468620	−	0.883400i	$-0.344751\pi$
$191$	12.9529			0.937240			0.468620	+	0.883400i	$0.344751\pi$
$192$	−1.00000			−0.0721688
$193$	2.91667	−	2.11909i	0.209947	−	0.152535i	−0.477843	−	0.878445i	$-0.658581\pi$
$193$	2.91667	−	2.11909i	0.209947	−	0.152535i	0.687790	+	0.725910i	$0.258581\pi$
$194$	5.68828	+	4.13278i	0.408395	+	0.296716i
$195$	−0.211779	−	0.153866i	−0.0151658	−	0.0110186i
$196$	0.00676897	+	0.0208327i	0.000483498	+	0.00148805i
$197$	20.3846	−	14.8103i	1.45234	−	1.05519i	0.467066	−	0.884222i	$-0.345311\pi$
$197$	20.3846	−	14.8103i	1.45234	−	1.05519i	0.985277	−	0.170967i	$-0.0546891\pi$
$198$	−1.16601	−	3.58860i	−0.0828646	−	0.255031i
$199$	−8.29708	+	25.5358i	−0.588165	+	1.81018i	−0.00199268	+	0.999998i	$0.500634\pi$
$199$	−8.29708	+	25.5358i	−0.588165	+	1.81018i	−0.586172	+	0.810187i	$0.699366\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	−1.24386	+	3.82822i	−0.0877354	+	0.270022i
$202$	1.90410	−	5.86021i	0.133972	−	0.412323i
$203$	9.60370	+	6.97749i	0.674047	+	0.489724i
$204$	1.03949	−	3.19923i	0.0727791	−	0.223991i
$205$	0.633657	+	1.95020i	0.0442565	+	0.136208i
$206$	5.13944	−	3.73402i	0.358082	−	0.260162i
$207$	−2.36745	−	7.28625i	−0.164549	−	0.506429i
$208$	−0.211779	−	0.153866i	−0.0146842	−	0.0106687i
$209$	14.5941	+	10.6032i	1.00950	+	0.733442i
$210$	2.14380	−	1.55756i	0.147937	−	0.107482i
$211$	−17.3117			−1.19179			−0.595893	−	0.803064i	$-0.703202\pi$
$211$	−17.3117			−1.19179			−0.595893	+	0.803064i	$0.703202\pi$
$212$	−10.2120			−0.701366
$213$	0.666814	−	0.484468i	0.0456893	−	0.0331952i
$214$	−4.71349	+	14.5066i	−0.322207	+	0.991652i
$215$	2.18250	+	6.71705i	0.148845	+	0.458099i
$216$	−1.00000			−0.0680414
$217$	−10.8235	−	10.0265i	−0.734745	−	0.680646i
$218$	2.22018			0.150370
$219$	2.64293	+	8.13411i	0.178593	+	0.549652i
$220$	1.16601	−	3.58860i	0.0786123	−	0.241944i
$221$	0.712396	−	0.517586i	0.0479210	−	0.0348166i
$222$	6.85410			0.460017
$223$	−22.9482			−1.53673			−0.768363	−	0.640014i	$-0.778928\pi$
$223$	−22.9482			−1.53673			−0.768363	+	0.640014i	$0.778928\pi$
$224$	2.14380	−	1.55756i	0.143239	−	0.104069i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	3.27728	+	2.38108i	0.218001	+	0.158387i
$227$	0.396024	+	1.21884i	0.0262851	+	0.0808971i	0.963339	−	0.268289i	$-0.0864582\pi$
$227$	0.396024	+	1.21884i	0.0262851	+	0.0808971i	−0.937053	+	0.349186i	$0.886458\pi$
$228$	3.86775	−	2.81008i	0.256148	−	0.186102i
$229$	−3.99411	−	12.2926i	−0.263938	−	0.812317i	−0.991936	−	0.126738i	$-0.959549\pi$
$229$	−3.99411	−	12.2926i	−0.263938	−	0.812317i	0.727998	−	0.685579i	$-0.240451\pi$
$230$	2.36745	−	7.28625i	0.156105	−	0.480441i
$231$	8.08918	+	5.87713i	0.532229	+	0.386687i
$232$	1.38432	−	4.26049i	0.0908849	−	0.279715i
$233$	1.48993	−	4.58552i	0.0976083	−	0.300407i	−0.890316	−	0.455342i	$-0.849517\pi$
$233$	1.48993	−	4.58552i	0.0976083	−	0.300407i	0.987925	+	0.154935i	$0.0495168\pi$
$234$	−0.211779	−	0.153866i	−0.0138444	−	0.0100586i
$235$	0.326352	−	1.00441i	0.0212889	−	0.0655204i
$236$	−1.46567	−	4.51088i	−0.0954072	−	0.293633i
$237$	−4.06969	+	2.95680i	−0.264354	+	0.192065i
$238$	2.75454	+	8.47760i	0.178550	+	0.549521i
$239$	−13.4153	−	9.74679i	−0.867764	−	0.630467i	0.0622220	−	0.998062i	$-0.480181\pi$
$239$	−13.4153	−	9.74679i	−0.867764	−	0.630467i	−0.929986	+	0.367595i	$0.880181\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	17.4932	−	12.7095i	1.12683	−	0.818693i	0.141603	−	0.989924i	$-0.454774\pi$
$241$	17.4932	−	12.7095i	1.12683	−	0.818693i	0.985231	+	0.171231i	$0.0547745\pi$
$242$	3.23766			0.208125
$243$	−1.00000			−0.0641500
$244$	−1.55302	+	1.12834i	−0.0994222	+	0.0722344i
$245$	−0.00676897	+	0.0208327i	−0.000432454	+	0.00133096i
$246$	0.633657	+	1.95020i	0.0404005	+	0.124340i
$247$	1.25148			0.0796301
$248$	−2.33639	+	5.05384i	−0.148361	+	0.320919i
$249$	−11.3196			−0.717351
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−2.38223	+	7.33173i	−0.150365	+	0.462775i	−0.997662	−	0.0683442i	$-0.978228\pi$
$251$	−2.38223	+	7.33173i	−0.150365	+	0.462775i	0.847297	+	0.531119i	$0.178228\pi$
$252$	2.14380	−	1.55756i	0.135047	−	0.0981174i
$253$	28.9079			1.81743
$254$	6.21873			0.390198
$255$	2.72143	−	1.97723i	0.170422	−	0.123819i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−14.9973	−	10.8962i	−0.935508	−	0.679686i	0.0118272	−	0.999930i	$-0.496235\pi$
$257$	−14.9973	−	10.8962i	−0.935508	−	0.679686i	−0.947335	+	0.320244i	$0.896235\pi$
$258$	2.18250	+	6.71705i	0.135877	+	0.418185i
$259$	−14.6939	+	10.6757i	−0.913032	+	0.663356i
$260$	−0.0808923	−	0.248961i	−0.00501673	−	0.0154399i
$261$	1.38432	−	4.26049i	0.0856871	−	0.263718i
$262$	−9.24191	−	6.71464i	−0.570967	−	0.414832i
$263$	0.333705	−	1.02704i	0.0205771	−	0.0633299i	−0.940241	−	0.340511i	$-0.889400\pi$
$263$	0.333705	−	1.02704i	0.0205771	−	0.0633299i	0.960818	+	0.277181i	$0.0894001\pi$
$264$	1.16601	−	3.58860i	0.0717629	−	0.220863i
$265$	−8.26172	−	6.00249i	−0.507513	−	0.368730i
$266$	−3.91481	+	12.0485i	−0.240032	+	0.738744i
$267$	−1.85224	−	5.70062i	−0.113355	−	0.348872i
$268$	−3.25648	+	2.36597i	−0.198921	+	0.144525i
$269$	−3.46620	−	10.6679i	−0.211338	−	0.650431i	−0.999393	−	0.0348269i	$-0.988912\pi$
$269$	−3.46620	−	10.6679i	−0.211338	−	0.650431i	0.788055	−	0.615604i	$-0.211088\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−17.0825	−	12.4112i	−1.03769	−	0.753925i	−0.0678559	−	0.997695i	$-0.521616\pi$
$271$	−17.0825	−	12.4112i	−1.03769	−	0.753925i	−0.969833	+	0.243770i	$0.921616\pi$
$272$	2.72143	−	1.97723i	0.165011	−	0.119887i
$273$	0.693669			0.0419828
$274$	16.9227			1.02234
$275$	3.05265	−	2.21788i	0.184082	−	0.133743i
$276$	2.36745	−	7.28625i	0.142504	−	0.438581i
$277$	3.53829	+	10.8897i	0.212595	+	0.654301i	0.999316	+	0.0369914i	$0.0117774\pi$
$277$	3.53829	+	10.8897i	0.212595	+	0.654301i	−0.786720	+	0.617310i	$0.788223\pi$
$278$	8.86711			0.531814
$279$	−2.33639	+	5.05384i	−0.139876	+	0.302565i
$280$	2.64989			0.158361
$281$	2.62489	+	8.07857i	0.156588	+	0.481927i	0.998318	−	0.0579707i	$-0.0184630\pi$
$281$	2.62489	+	8.07857i	0.156588	+	0.481927i	−0.841731	+	0.539898i	$0.818463\pi$
$282$	0.326352	−	1.00441i	0.0194340	−	0.0598117i
$283$	1.82756	−	1.32780i	0.108637	−	0.0789295i	−0.532140	−	0.846656i	$-0.678612\pi$
$283$	1.82756	−	1.32780i	0.108637	−	0.0789295i	0.640777	+	0.767727i	$0.278612\pi$
$284$	0.824227			0.0489089
$285$	4.78080			0.283190
$286$	0.799101	−	0.580581i	0.0472518	−	0.0343305i
$287$	−4.39599	−	3.19388i	−0.259487	−	0.188529i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−1.75657	−	5.40616i	−0.103328	−	0.318010i
$290$	3.62419	−	2.63313i	0.212820	−	0.154623i
$291$	2.17273	+	6.68698i	0.127368	+	0.391998i
$292$	−2.64293	+	8.13411i	−0.154666	+	0.476013i
$293$	−13.1386	−	9.54577i	−0.767567	−	0.557670i	0.133655	−	0.991028i	$-0.457329\pi$
$293$	−13.1386	−	9.54577i	−0.767567	−	0.557670i	−0.901222	+	0.433358i	$0.857329\pi$
$294$	−0.00676897	+	0.0208327i	−0.000394774	+	0.00121499i
$295$	1.46567	−	4.51088i	0.0853348	−	0.262634i
$296$	5.54508	+	4.02874i	0.322302	+	0.234166i
$297$	1.16601	−	3.58860i	0.0676587	−	0.208232i
$298$	1.08496	+	3.33915i	0.0628498	+	0.193432i
$299$	1.62248	−	1.17880i	0.0938306	−	0.0681719i
$300$	−0.309017	−	0.951057i	−0.0178411	−	0.0549093i
$301$	−15.1411	−	11.0007i	−0.872718	−	0.634067i
$302$	−15.1219	−	10.9867i	−0.870168	−	0.632214i
$303$	4.98499	−	3.62181i	0.286380	−	0.208067i
$304$	4.78080			0.274198
$305$	−1.91964			−0.109918
$306$	2.72143	−	1.97723i	0.155574	−	0.113031i
$307$	−3.58854	+	11.0444i	−0.204809	+	0.630337i	0.794912	+	0.606724i	$0.207517\pi$
$307$	−3.58854	+	11.0444i	−0.204809	+	0.630337i	−0.999721	+	0.0236123i	$0.992483\pi$
$308$	3.08979	+	9.50940i	0.176057	+	0.541848i
$309$	6.35270			0.361392
$310$	−4.86075	+	2.71535i	−0.276072	+	0.154221i
$311$	20.9071			1.18553			0.592766	−	0.805375i	$-0.298036\pi$
$311$	20.9071			1.18553			0.592766	+	0.805375i	$0.298036\pi$
$312$	−0.0808923	−	0.248961i	−0.00457962	−	0.0140946i
$313$	1.77810	−	5.47242i	0.100504	−	0.309320i	−0.888145	−	0.459563i	$-0.848006\pi$
$313$	1.77810	−	5.47242i	0.100504	−	0.309320i	0.988649	+	0.150244i	$0.0480059\pi$
$314$	15.6496	−	11.3701i	0.883157	−	0.641651i
$315$	2.64989			0.149304
$316$	−5.03041			−0.282983
$317$	−20.4047	+	14.8249i	−1.14604	+	0.832650i	−0.987950	−	0.154774i	$-0.950535\pi$
$317$	−20.4047	+	14.8249i	−1.14604	+	0.832650i	−0.158094	+	0.987424i	$0.550535\pi$
$318$	−8.26172	−	6.00249i	−0.463294	−	0.336603i
$319$	13.6751	+	9.93554i	0.765658	+	0.556283i
$320$	−0.309017	−	0.951057i	−0.0172746	−	0.0531657i
$321$	−12.3401	+	8.96558i	−0.688755	+	0.500410i
$322$	6.27347	+	19.3077i	0.349607	+	1.07598i
$323$	−4.96961	+	15.2949i	−0.276517	+	0.851030i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	0.0808923	−	0.248961i	0.00448710	−	0.0138099i
$326$	4.07861	−	12.5527i	0.225894	−	0.695229i
$327$	1.79616	+	1.30499i	0.0993281	+	0.0721661i
$328$	−0.633657	+	1.95020i	−0.0349879	+	0.107682i
$329$	0.864797	+	2.66157i	0.0476778	+	0.146737i
$330$	3.05265	−	2.21788i	0.168043	−	0.122090i
$331$	−5.37658	−	16.5474i	−0.295524	−	0.909528i	−0.983045	−	0.183364i	$-0.941301\pi$
$331$	−5.37658	−	16.5474i	−0.295524	−	0.909528i	0.687521	−	0.726164i	$-0.258699\pi$
$332$	−9.15775	−	6.65350i	−0.502597	−	0.365158i
$333$	5.54508	+	4.02874i	0.303869	+	0.220774i
$334$	15.5446	−	11.2938i	0.850562	−	0.617969i
$335$	−4.02523			−0.219922
$336$	2.64989			0.144563
$337$	9.62843	−	6.99546i	0.524494	−	0.381067i	−0.293800	−	0.955867i	$-0.594920\pi$
$337$	9.62843	−	6.99546i	0.524494	−	0.381067i	0.818294	+	0.574800i	$0.194920\pi$
$338$	−3.99605	+	12.2986i	−0.217356	+	0.668954i
$339$	1.25181	+	3.85267i	0.0679890	+	0.209249i
$340$	3.36387			0.182431
$341$	−15.4120	−	14.2772i	−0.834606	−	0.773153i
$342$	4.78080			0.258516
$343$	5.71409	+	17.5861i	0.308532	+	0.949563i
$344$	−2.18250	+	6.71705i	−0.117673	+	0.362159i
$345$	6.19805	−	4.50315i	0.333692	−	0.242441i
$346$	−4.16643			−0.223989
$347$	−20.1620			−1.08236			−0.541178	−	0.840908i	$-0.682021\pi$
$347$	−20.1620			−1.08236			−0.541178	+	0.840908i	$0.682021\pi$
$348$	3.62419	−	2.63313i	0.194277	−	0.141150i
$349$	14.2698	+	10.3676i	0.763843	+	0.554964i	0.900087	−	0.435711i	$-0.143503\pi$
$349$	14.2698	+	10.3676i	0.763843	+	0.554964i	−0.136244	+	0.990675i	$0.543503\pi$
$350$	2.14380	+	1.55756i	0.114591	+	0.0832553i
$351$	−0.0808923	−	0.248961i	−0.00431771	−	0.0132885i
$352$	3.05265	−	2.21788i	0.162707	−	0.118213i
$353$	−9.87459	−	30.3909i	−0.525571	−	1.61754i	−0.763183	−	0.646182i	$-0.776365\pi$
$353$	−9.87459	−	30.3909i	−0.525571	−	1.61754i	0.237612	−	0.971360i	$-0.423635\pi$
$354$	1.46567	−	4.51088i	0.0778997	−	0.239751i
$355$	0.666814	+	0.484468i	0.0353908	+	0.0257129i
$356$	1.85224	−	5.70062i	0.0981686	−	0.302132i
$357$	−2.75454	+	8.47760i	−0.145786	+	0.448682i
$358$	−9.96407	−	7.23932i	−0.526618	−	0.382610i
$359$	4.34721	−	13.3793i	0.229437	−	0.706135i	−0.768374	−	0.640002i	$-0.778934\pi$
$359$	4.34721	−	13.3793i	0.229437	−	0.706135i	0.997811	−	0.0661334i	$-0.0210663\pi$
$360$	−0.309017	−	0.951057i	−0.0162866	−	0.0501251i
$361$	−3.11962	+	2.26654i	−0.164191	+	0.119292i
$362$	−4.82011	−	14.8348i	−0.253339	−	0.779698i
$363$	2.61932	+	1.90305i	0.137479	+	0.0998841i
$364$	0.561190	+	0.407728i	0.0294143	+	0.0213708i
$365$	−6.91929	+	5.02716i	−0.362172	+	0.263134i
$366$	−1.91964			−0.100341
$367$	13.4970			0.704537			0.352268	−	0.935899i	$-0.385410\pi$
$367$	13.4970			0.704537			0.352268	+	0.935899i	$0.385410\pi$
$368$	6.19805	−	4.50315i	0.323096	−	0.234743i
$369$	−0.633657	+	1.95020i	−0.0329869	+	0.101523i
$370$	2.11803	+	6.51864i	0.110111	+	0.338888i
$371$	27.0608			1.40493
$372$	−4.86075	+	2.71535i	−0.252018	+	0.140784i
$373$	−2.43206			−0.125927			−0.0629637	−	0.998016i	$-0.520055\pi$
$373$	−2.43206			−0.125927			−0.0629637	+	0.998016i	$0.520055\pi$
$374$	3.92230	+	12.0716i	0.202817	+	0.624208i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	0.854401	−	0.620759i	0.0440624	−	0.0320132i
$377$	1.17268			0.0603959
$378$	2.64989			0.136296
$379$	−24.9016	+	18.0921i	−1.27911	+	0.929329i	−0.999526	−	0.0307924i	$-0.990197\pi$
$379$	−24.9016	+	18.0921i	−1.27911	+	0.929329i	−0.279585	+	0.960121i	$0.590197\pi$
$380$	3.86775	+	2.81008i	0.198411	+	0.144154i
$381$	5.03105	+	3.65528i	0.257749	+	0.187265i
$382$	4.00267	+	12.3190i	0.204795	+	0.630293i
$383$	−18.1952	+	13.2196i	−0.929730	+	0.675488i	−0.945927	−	0.324380i	$-0.894844\pi$
$383$	−18.1952	+	13.2196i	−0.929730	+	0.675488i	0.0161967	+	0.999869i	$0.494844\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$	−3.08979	+	9.50940i	−0.157470	+	0.484644i
$386$	2.91667	+	2.11909i	0.148455	+	0.107859i
$387$	−2.18250	+	6.71705i	−0.110943	+	0.341447i
$388$	−2.17273	+	6.68698i	−0.110304	+	0.339480i
$389$	−20.3543	−	14.7883i	−1.03201	−	0.749796i	−0.0632968	−	0.997995i	$-0.520161\pi$
$389$	−20.3543	−	14.7883i	−1.03201	−	0.749796i	−0.968709	+	0.248198i	$0.920161\pi$
$390$	0.0808923	−	0.248961i	0.00409614	−	0.0126066i
$391$	7.96378	+	24.5100i	0.402746	+	1.23952i
$392$	−0.0177214	+	0.0128753i	−0.000895065	+	0.000650303i
$393$	−3.53010	−	10.8645i	−0.178070	−	0.548043i
$394$	20.3846	+	14.8103i	1.02696	+	0.746131i
$395$	−4.06969	−	2.95680i	−0.204768	−	0.148773i
$396$	3.05265	−	2.21788i	0.153401	−	0.111453i
$397$	10.2715			0.515511			0.257755	−	0.966210i	$-0.417017\pi$
$397$	10.2715			0.515511			0.257755	+	0.966210i	$0.417017\pi$
$398$	−26.8499			−1.34587
$399$	−10.2491	+	7.44641i	−0.513097	+	0.372787i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	4.50166	+	13.8547i	0.224802	+	0.691870i	0.998312	+	0.0580853i	$0.0184995\pi$
$401$	4.50166	+	13.8547i	0.224802	+	0.691870i	−0.773509	+	0.633785i	$0.781500\pi$
$402$	−4.02523			−0.200760
$403$	−1.44720	−	0.172853i	−0.0720904	−	0.00861040i
$404$	6.16178			0.306560
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−3.66829	+	11.2898i	−0.182054	+	0.560304i
$407$	−20.9232	+	15.2016i	−1.03712	+	0.753514i
$408$	3.36387			0.166536
$409$	−37.1194			−1.83543			−0.917717	−	0.397235i	$-0.869970\pi$
$409$	−37.1194			−1.83543			−0.917717	+	0.397235i	$0.869970\pi$
$410$	−1.65894	+	1.20529i	−0.0819290	+	0.0595249i
$411$	13.6908	+	9.94694i	0.675317	+	0.490646i
$412$	5.13944	+	3.73402i	0.253202	+	0.183962i
$413$	3.88387	+	11.9533i	0.191113	+	0.588185i
$414$	6.19805	−	4.50315i	0.304618	−	0.221318i
$415$	−3.49795	−	10.7656i	−0.171708	−	0.528462i
$416$	0.0808923	−	0.248961i	0.00396607	−	0.0122063i
$417$	7.17364	+	5.21195i	0.351295	+	0.255231i
$418$	−5.57445	+	17.1564i	−0.272656	+	0.839147i
$419$	−11.1114	+	34.1975i	−0.542830	+	1.67066i	0.183265	+	0.983064i	$0.441333\pi$
$419$	−11.1114	+	34.1975i	−0.542830	+	1.67066i	−0.726095	+	0.687595i	$0.758667\pi$
$420$	2.14380	+	1.55756i	0.104607	+	0.0760014i
$421$	−8.88769	+	27.3535i	−0.433160	+	1.33313i	0.461801	+	0.886984i	$0.347203\pi$
$421$	−8.88769	+	27.3535i	−0.433160	+	1.33313i	−0.894961	+	0.446145i	$0.852797\pi$
$422$	−5.34961	−	16.4644i	−0.260415	−	0.801475i
$423$	0.854401	−	0.620759i	0.0415424	−	0.0301823i
$424$	−3.15570	−	9.71223i	−0.153254	−	0.471668i
$425$	2.72143	+	1.97723i	0.132009	+	0.0959099i
$426$	0.666814	+	0.484468i	0.0323072	+	0.0234726i
$427$	4.11534	−	2.98997i	0.199155	−	0.144695i
$428$	−15.2532			−0.737289
$429$	0.987743			0.0476887
$430$	−5.71386	+	4.15137i	−0.275547	+	0.200197i
$431$	11.2475	−	34.6163i	0.541774	−	1.66741i	−0.186764	−	0.982405i	$-0.559800\pi$
$431$	11.2475	−	34.6163i	0.541774	−	1.66741i	0.728538	−	0.685005i	$-0.240200\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	20.9297			1.00582			0.502910	−	0.864339i	$-0.332263\pi$
$433$	20.9297			1.00582			0.502910	+	0.864339i	$0.332263\pi$
$434$	6.19117	−	13.3921i	0.297185	−	0.642842i
$435$	4.47975			0.214787
$436$	0.686074	+	2.11152i	0.0328570	+	0.101123i
$437$	−11.3183	+	34.8341i	−0.541427	+	1.66634i
$438$	−6.91929	+	5.02716i	−0.330616	+	0.240207i
$439$	9.59652			0.458017			0.229008	−	0.973424i	$-0.426452\pi$
$439$	9.59652			0.458017			0.229008	+	0.973424i	$0.426452\pi$
$440$	3.77328			0.179884
$441$	−0.0177214	+	0.0128753i	−0.000843876	+	0.000613112i
$442$	0.712396	+	0.517586i	0.0338852	+	0.0246191i
$443$	17.1453	+	12.4568i	0.814599	+	0.591841i	0.915160	−	0.403090i	$-0.132064\pi$
$443$	17.1453	+	12.4568i	0.814599	+	0.591841i	−0.100561	+	0.994931i	$0.532064\pi$
$444$	2.11803	+	6.51864i	0.100517	+	0.309361i
$445$	4.84923	−	3.52317i	0.229876	−	0.167014i
$446$	−7.09139	−	21.8250i	−0.335787	−	1.03345i
$447$	−1.08496	+	3.33915i	−0.0513167	+	0.157936i
$448$	2.14380	+	1.55756i	0.101285	+	0.0735880i
$449$	5.01151	−	15.4238i	0.236508	−	0.727896i	−0.760410	−	0.649443i	$-0.775002\pi$
$449$	5.01151	−	15.4238i	0.236508	−	0.727896i	0.996918	−	0.0784525i	$-0.0249979\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	−6.25963	−	4.54789i	−0.294755	−	0.214152i
$452$	−1.25181	+	3.85267i	−0.0588802	+	0.181215i
$453$	−5.77606	−	17.7769i	−0.271383	−	0.835231i
$454$	−1.03680	+	0.753283i	−0.0486597	+	0.0353533i
$455$	0.214355	+	0.659718i	0.0100491	+	0.0309281i
$456$	3.86775	+	2.81008i	0.181124	+	0.131594i
$457$	18.9566	+	13.7728i	0.886754	+	0.644264i	0.935030	−	0.354570i	$-0.115373\pi$
$457$	18.9566	+	13.7728i	0.886754	+	0.644264i	−0.0482759	+	0.998834i	$0.515373\pi$
$458$	10.4567	−	7.59724i	0.488610	−	0.354996i
$459$	3.36387			0.157012
$460$	7.66122			0.357206
$461$	−12.7913	+	9.29341i	−0.595750	+	0.432837i	−0.844368	−	0.535764i	$-0.820024\pi$
$461$	−12.7913	+	9.29341i	−0.595750	+	0.432837i	0.248618	+	0.968602i	$0.420024\pi$
$462$	−3.08979	+	9.50940i	−0.143750	+	0.442417i
$463$	0.750024	+	2.30834i	0.0348566	+	0.107278i	0.966971	−	0.254886i	$-0.0820381\pi$
$463$	0.750024	+	2.30834i	0.0348566	+	0.107278i	−0.932114	+	0.362164i	$0.882038\pi$
$464$	4.47975			0.207967
$465$	−5.52847	−	0.660315i	−0.256377	−	0.0306214i
$466$	4.82150			0.223352
$467$	5.08197	+	15.6407i	0.235165	+	0.723765i	0.997099	+	0.0761101i	$0.0242500\pi$
$467$	5.08197	+	15.6407i	0.235165	+	0.723765i	−0.761934	+	0.647655i	$0.775750\pi$
$468$	0.0808923	−	0.248961i	0.00373925	−	0.0115082i
$469$	8.62930	−	6.26955i	0.398464	−	0.289501i
$470$	1.05610			0.0487142
$471$	19.3439			0.891322
$472$	3.83718	−	2.78788i	0.176621	−	0.128322i
$473$	−21.5600	−	15.6643i	−0.991331	−	0.720244i
$474$	−4.06969	−	2.95680i	−0.186927	−	0.135810i
$475$	1.47735	+	4.54681i	0.0677854	+	0.208622i
$476$	−7.21148	+	5.23945i	−0.330538	+	0.240150i
$477$	−3.15570	−	9.71223i	−0.144489	−	0.444692i
$478$	5.12419	−	15.7706i	0.234375	−	0.721332i
$479$	−26.7154	−	19.4099i	−1.22066	−	0.886861i	−0.224505	−	0.974473i	$-0.572077\pi$
$479$	−26.7154	−	19.4099i	−1.22066	−	0.886861i	−0.996155	+	0.0876115i	$0.972077\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−0.554444	+	1.70640i	−0.0252805	+	0.0778053i
$482$	17.4932	+	12.7095i	0.796792	+	0.578903i
$483$	−6.27347	+	19.3077i	−0.285453	+	0.878533i
$484$	1.00049	+	3.07920i	0.0454769	+	0.139963i
$485$	−5.68828	+	4.13278i	−0.258292	+	0.187660i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−30.8094	−	22.3843i	−1.39611	−	1.01433i	−0.995164	−	0.0982290i	$-0.968682\pi$
$487$	−30.8094	−	22.3843i	−1.39611	−	1.01433i	−0.400944	−	0.916103i	$-0.631318\pi$
$488$	−1.55302	−	1.12834i	−0.0703021	−	0.0510775i
$489$	10.6779	−	7.75798i	0.482874	−	0.350828i
$490$	−0.0219048			−0.000989560
$491$	14.0274			0.633046			0.316523	−	0.948585i	$-0.397485\pi$
$491$	14.0274			0.633046			0.316523	+	0.948585i	$0.397485\pi$
$492$	−1.65894	+	1.20529i	−0.0747906	+	0.0543385i
$493$	−4.65666	+	14.3317i	−0.209726	+	0.645469i
$494$	0.386730	+	1.19023i	0.0173998	+	0.0535511i
$495$	3.77328			0.169596
$496$	−5.52847	−	0.660315i	−0.248236	−	0.0296490i
$497$	−2.18411			−0.0979707
$498$	−3.49795	−	10.7656i	−0.156747	−	0.482417i
$499$	3.59328	−	11.0590i	0.160857	−	0.495067i	−0.837850	−	0.545900i	$-0.816188\pi$
$499$	3.59328	−	11.0590i	0.160857	−	0.495067i	0.998707	+	0.0508332i	$0.0161877\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	19.2142			0.858425
$502$	−7.70904			−0.344071
$503$	−23.9399	+	17.3934i	−1.06743	+	0.775533i	−0.975448	−	0.220228i	$-0.929320\pi$
$503$	−23.9399	+	17.3934i	−1.06743	+	0.775533i	−0.0919811	+	0.995761i	$0.529320\pi$
$504$	2.14380	+	1.55756i	0.0954926	+	0.0693795i
$505$	4.98499	+	3.62181i	0.221829	+	0.161168i
$506$	8.93304	+	27.4931i	0.397122	+	1.22222i
$507$	−10.4618	+	7.60093i	−0.464624	+	0.337569i
$508$	1.92169	+	5.91436i	0.0852613	+	0.262407i
$509$	−7.02104	+	21.6085i	−0.311202	+	0.957782i	0.666088	+	0.745874i	$0.267968\pi$
$509$	−7.02104	+	21.6085i	−0.311202	+	0.957782i	−0.977290	+	0.211908i	$0.932032\pi$
$510$	2.72143	+	1.97723i	0.120507	+	0.0875534i
$511$	7.00348	−	21.5545i	0.309816	−	0.953514i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	3.86775	+	2.81008i	0.170765	+	0.124068i
$514$	5.72847	−	17.6304i	0.252672	−	0.777645i
$515$	1.96309	+	6.04177i	0.0865041	+	0.266232i
$516$	−5.71386	+	4.15137i	−0.251539	+	0.182754i
$517$	1.23142	+	3.78992i	0.0541578	+	0.166680i
$518$	−14.6939	−	10.6757i	−0.645611	−	0.469064i
$519$	−3.37071	−	2.44897i	−0.147958	−	0.107498i
$520$	0.211779	−	0.153866i	0.00928711	−	0.00674748i
$521$	22.7771			0.997885			0.498943	−	0.866635i	$-0.333722\pi$
$521$	22.7771			0.997885			0.498943	+	0.866635i	$0.333722\pi$
$522$	4.47975			0.196073
$523$	8.37938	−	6.08798i	0.366405	−	0.266209i	−0.389314	−	0.921105i	$-0.627288\pi$
$523$	8.37938	−	6.08798i	0.366405	−	0.266209i	0.755719	+	0.654897i	$0.227288\pi$
$524$	3.53010	−	10.8645i	0.154213	−	0.474619i
$525$	0.818860	+	2.52019i	0.0357380	+	0.109990i
$526$	1.07989			0.0470855
$527$	7.85931	−	17.0005i	0.342357	−	0.740552i
$528$	3.77328			0.164211
$529$	11.0301	+	33.9472i	0.479571	+	1.47597i
$530$	3.15570	−	9.71223i	0.137075	−	0.421872i
$531$	3.83718	−	2.78788i	0.166520	−	0.120984i
$532$	−12.6686			−0.549253
$533$	−0.536780			−0.0232505
$534$	4.84923	−	3.52317i	0.209847	−	0.152463i
$535$	−12.3401	−	8.96558i	−0.533507	−	0.387616i
$536$	−3.25648	−	2.36597i	−0.140658	−	0.102194i
$537$	−3.80594	−	11.7135i	−0.164238	−	0.505473i
$538$	9.07463	−	6.59310i	0.391235	−	0.284249i
$539$	−0.0255412	−	0.0786078i	−0.00110014	−	0.00338588i
$540$	0.309017	−	0.951057i	0.0132980	−	0.0409270i
$541$	−23.1012	−	16.7840i	−0.993196	−	0.721599i	−0.0325776	−	0.999469i	$-0.510372\pi$
$541$	−23.1012	−	16.7840i	−0.993196	−	0.721599i	−0.960619	+	0.277870i	$0.910372\pi$
$542$	6.52494	−	20.0817i	0.280270	−	0.862583i
$543$	4.82011	−	14.8348i	0.206851	−	0.636621i
$544$	2.72143	+	1.97723i	0.116680	+	0.0847732i
$545$	−0.686074	+	2.11152i	−0.0293882	+	0.0904475i
$546$	0.214355	+	0.659718i	0.00917357	+	0.0282333i
$547$	21.5125	−	15.6298i	0.919808	−	0.668280i	−0.0236680	−	0.999720i	$-0.507534\pi$
$547$	21.5125	−	15.6298i	0.919808	−	0.668280i	0.943476	+	0.331440i	$0.107534\pi$
$548$	5.22942	+	16.0945i	0.223390	+	0.687522i
$549$	−1.55302	−	1.12834i	−0.0662814	−	0.0481563i
$550$	3.05265	+	2.21788i	0.130165	+	0.0945707i
$551$	−17.3265	+	12.5885i	−0.738135	+	0.536287i
$552$	7.66122			0.326083
$553$	13.3300			0.566850
$554$	−9.26337	+	6.73023i	−0.393563	+	0.285940i
$555$	−2.11803	+	6.51864i	−0.0899055	+	0.276701i
$556$	2.74009	+	8.43312i	0.116206	+	0.357644i
$557$	−10.3004			−0.436444			−0.218222	−	0.975899i	$-0.570026\pi$
$557$	−10.3004			−0.436444			−0.218222	+	0.975899i	$0.570026\pi$
$558$	−5.52847	−	0.660315i	−0.234039	−	0.0279534i
$559$	−1.84883			−0.0781972
$560$	0.818860	+	2.52019i	0.0346032	+	0.106498i
$561$	−3.92230	+	12.0716i	−0.165600	+	0.509663i
$562$	−6.87204	+	4.99283i	−0.289879	+	0.210610i
$563$	−3.92067			−0.165237			−0.0826184	−	0.996581i	$-0.526328\pi$
$563$	−3.92067			−0.165237			−0.0826184	+	0.996581i	$0.526328\pi$
$564$	1.05610			0.0444698
$565$	−3.27728	+	2.38108i	−0.137876	+	0.100173i
$566$	1.82756	+	1.32780i	0.0768181	+	0.0558116i
$567$	2.14380	+	1.55756i	0.0900313	+	0.0654116i
$568$	0.254700	+	0.783886i	0.0106870	+	0.0328911i
$569$	−34.6204	+	25.1532i	−1.45136	+	1.05448i	−0.465853	+	0.884862i	$0.654253\pi$
$569$	−34.6204	+	25.1532i	−1.45136	+	1.05448i	−0.985510	+	0.169615i	$0.945747\pi$
$570$	1.47735	+	4.54681i	0.0618793	+	0.190445i
$571$	−3.49711	+	10.7630i	−0.146350	+	0.450418i	−0.997182	−	0.0750192i	$-0.976098\pi$
$571$	−3.49711	+	10.7630i	−0.146350	+	0.450418i	0.850832	+	0.525437i	$0.176098\pi$
$572$	0.799101	+	0.580581i	0.0334121	+	0.0242753i
$573$	−4.00267	+	12.3190i	−0.167214	+	0.514632i
$574$	1.67912	−	5.16780i	0.0700851	−	0.215700i
$575$	6.19805	+	4.50315i	0.258477	+	0.187794i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−7.67148	−	23.6104i	−0.319368	−	0.982914i	−0.973919	−	0.226896i	$-0.927142\pi$
$577$	−7.67148	−	23.6104i	−0.319368	−	0.982914i	0.654551	−	0.756018i	$-0.272858\pi$
$578$	4.59876	−	3.34119i	0.191283	−	0.138975i
$579$	1.11407	+	3.42876i	0.0462992	+	0.142494i
$580$	3.62419	+	2.63313i	0.150486	+	0.109335i
$581$	24.2670	+	17.6310i	1.00677	+	0.731458i
$582$	−5.68828	+	4.13278i	−0.235787	+	0.171309i
$583$	38.5329			1.59587
$584$	−8.55271			−0.353914
$585$	0.211779	−	0.153866i	0.00875597	−	0.00636159i
$586$	5.01851	−	15.4454i	0.207313	−	0.638043i
$587$	14.7100	+	45.2726i	0.607145	+	1.86860i	0.481313	+	0.876549i	$0.340160\pi$
$587$	14.7100	+	45.2726i	0.607145	+	1.86860i	0.125832	+	0.992052i	$0.459840\pi$
$588$	−0.0219048			−0.000903341
$589$	23.2383	−	12.9815i	0.957517	−	0.534895i
$590$	4.74302			0.195267
$591$	7.78623	+	23.9635i	0.320283	+	0.985729i
$592$	−2.11803	+	6.51864i	−0.0870507	+	0.267914i
$593$	1.02412	−	0.744067i	0.0420556	−	0.0305552i	−0.566559	−	0.824021i	$-0.691726\pi$
$593$	1.02412	−	0.744067i	0.0420556	−	0.0305552i	0.608614	+	0.793466i	$0.291726\pi$
$594$	3.77328			0.154820
$595$	−8.91388			−0.365433
$596$	−2.84045	+	2.06371i	−0.116349	+	0.0845328i
$597$	−21.7220	−	15.7820i	−0.889024	−	0.645914i
$598$	1.62248	+	1.17880i	0.0663483	+	0.0482048i
$599$	−1.04605	−	3.21943i	−0.0427406	−	0.131542i	0.927409	−	0.374048i	$-0.122031\pi$
$599$	−1.04605	−	3.21943i	−0.0427406	−	0.131542i	−0.970150	+	0.242506i	$0.922031\pi$
$600$	0.809017	−	0.587785i	0.0330280	−	0.0239962i
$601$	4.48156	+	13.7928i	0.182807	+	0.562621i	0.999904	−	0.0138794i	$-0.00441808\pi$
$601$	4.48156	+	13.7928i	0.182807	+	0.562621i	−0.817097	+	0.576500i	$0.804418\pi$
$602$	5.78338	−	17.7994i	0.235713	−	0.725451i
$603$	−3.25648	−	2.36597i	−0.132614	−	0.0963497i
$604$	5.77606	−	17.7769i	0.235024	−	0.723331i
$605$	−1.00049	+	3.07920i	−0.0406758	+	0.125187i
$606$	4.98499	+	3.62181i	0.202501	+	0.147126i
$607$	3.68466	−	11.3402i	0.149556	−	0.460285i	−0.848013	−	0.529976i	$-0.822201\pi$
$607$	3.68466	−	11.3402i	0.149556	−	0.460285i	0.997569	+	0.0696902i	$0.0222011\pi$
$608$	1.47735	+	4.54681i	0.0599144	+	0.184398i
$609$	−9.60370	+	6.97749i	−0.389161	+	0.282742i
$610$	−0.593202	−	1.82569i	−0.0240181	−	0.0739200i
$611$	0.223659	+	0.162498i	0.00904828	+	0.00657396i
$612$	2.72143	+	1.97723i	0.110007	+	0.0799249i
$613$	−9.21920	+	6.69814i	−0.372360	+	0.270535i	−0.758189	−	0.652035i	$-0.773916\pi$
$613$	−9.21920	+	6.69814i	−0.372360	+	0.270535i	0.385829	+	0.922570i	$0.373916\pi$
$614$	−11.6128			−0.468653
$615$	−2.05056			−0.0826864
$616$	−8.08918	+	5.87713i	−0.325922	+	0.236796i
$617$	8.64693	−	26.6125i	0.348112	−	1.07138i	−0.611784	−	0.791025i	$-0.709548\pi$
$617$	8.64693	−	26.6125i	0.348112	−	1.07138i	0.959896	−	0.280355i	$-0.0904521\pi$
$618$	1.96309	+	6.04177i	0.0789671	+	0.243036i
$619$	−34.2713			−1.37748			−0.688740	−	0.725008i	$-0.741836\pi$
$619$	−34.2713			−1.37748			−0.688740	+	0.725008i	$0.741836\pi$
$620$	−4.08450	−	3.78376i	−0.164038	−	0.151959i
$621$	7.66122			0.307434
$622$	6.46064	+	19.8838i	0.259048	+	0.797269i
$623$	−4.90823	+	15.1060i	−0.196644	+	0.605209i
$624$	0.211779	−	0.153866i	0.00847794	−	0.00615958i
$625$	1.00000			0.0400000
$626$	5.75405			0.229978
$627$	−14.5941	+	10.6032i	−0.582833	+	0.423453i
$628$	15.6496	+	11.3701i	0.624486	+	0.453716i
$629$	−18.6529	−	13.5522i	−0.743742	−	0.540360i
$630$	0.818860	+	2.52019i	0.0326242	+	0.100407i
$631$	2.47155	−	1.79569i	0.0983910	−	0.0714852i	−0.537502	−	0.843262i	$-0.680632\pi$
$631$	2.47155	−	1.79569i	0.0983910	−	0.0714852i	0.635893	+	0.771777i	$0.280632\pi$
$632$	−1.55448	−	4.78420i	−0.0618340	−	0.190305i
$633$	5.34961	−	16.4644i	0.212628	−	0.654401i
$634$	−20.4047	−	14.8249i	−0.810375	−	0.588772i
$635$	−1.92169	+	5.91436i	−0.0762600	+	0.234704i
$636$	3.15570	−	9.71223i	0.125131	−	0.385115i
$637$	−0.00463898	−	0.00337042i	−0.000183803	−	0.000133541i
$638$	−5.22342	+	16.0760i	−0.206797	+	0.636456i
$639$	0.254700	+	0.783886i	0.0100758	+	0.0310101i
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	−0.883530	−	2.71923i	−0.0348973	−	0.107403i	0.932091	−	0.362225i	$-0.117983\pi$
$641$	−0.883530	−	2.71923i	−0.0348973	−	0.107403i	−0.966988	+	0.254823i	$0.917983\pi$
$642$	−12.3401	−	8.96558i	−0.487023	−	0.353843i
$643$	3.82110	+	2.77619i	0.150689	+	0.109482i	0.660575	−	0.750760i	$-0.270312\pi$
$643$	3.82110	+	2.77619i	0.150689	+	0.109482i	−0.509886	+	0.860242i	$0.670312\pi$
$644$	−16.4241	+	11.9328i	−0.647202	+	0.470220i
$645$	−7.06272			−0.278094
$646$	−16.0820			−0.632738
$647$	−19.8790	+	14.4430i	−0.781525	+	0.567811i	−0.905436	−	0.424482i	$-0.860456\pi$
$647$	−19.8790	+	14.4430i	−0.781525	+	0.567811i	0.123911	+	0.992293i	$0.460456\pi$
$648$	0.309017	−	0.951057i	0.0121393	−	0.0373610i
$649$	5.53040	+	17.0208i	0.217087	+	0.668126i
$650$	0.261773			0.0102676
$651$	12.8804	−	7.19537i	0.504824	−	0.282009i
$652$	13.1987			0.516900
$653$	−0.190651	−	0.586762i	−0.00746073	−	0.0229618i	0.947257	−	0.320475i	$-0.103843\pi$
$653$	−0.190651	−	0.586762i	−0.00746073	−	0.0229618i	−0.954718	+	0.297514i	$0.903843\pi$
$654$	−0.686074	+	2.11152i	−0.0268276	+	0.0825669i
$655$	9.24191	−	6.71464i	0.361111	−	0.262363i
$656$	−2.05056			−0.0800608
$657$	−8.55271			−0.333673
$658$	−2.26407	+	1.64494i	−0.0882625	+	0.0641265i
$659$	14.7501	+	10.7166i	0.574583	+	0.417459i	0.836767	−	0.547559i	$-0.184443\pi$
$659$	14.7501	+	10.7166i	0.574583	+	0.417459i	−0.262184	+	0.965018i	$0.584443\pi$
$660$	3.05265	+	2.21788i	0.118824	+	0.0863308i
$661$	10.2128	+	31.4318i	0.397233	+	1.22256i	0.927209	+	0.374544i	$0.122201\pi$
$661$	10.2128	+	31.4318i	0.397233	+	1.22256i	−0.529976	+	0.848012i	$0.677799\pi$
$662$	14.0761	−	10.2269i	0.547082	−	0.397478i
$663$	0.272111	+	0.837472i	0.0105679	+	0.0325247i
$664$	3.49795	−	10.7656i	0.135747	−	0.417786i
$665$	−10.2491	−	7.44641i	−0.397443	−	0.288759i
$666$	−2.11803	+	6.51864i	−0.0820721	+	0.252592i
$667$	−10.6056	+	32.6405i	−0.410649	+	1.26385i
$668$	15.5446	+	11.2938i	0.601438	+	0.436970i
$669$	7.09139	−	21.8250i	0.274169	−	0.843805i
$670$	−1.24386	−	3.82822i	−0.0480546	−	0.147897i
$671$	5.86000	−	4.25754i	0.226223	−	0.164360i
$672$	0.818860	+	2.52019i	0.0315882	+	0.0972186i
$673$	17.8325	+	12.9561i	0.687394	+	0.499421i	0.875802	−	0.482670i	$-0.160333\pi$
$673$	17.8325	+	12.9561i	0.687394	+	0.499421i	−0.188408	+	0.982091i	$0.560333\pi$
$674$	9.62843	+	6.99546i	0.370873	+	0.269455i
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	−12.9315			−0.497364
$677$	7.61209			0.292556			0.146278	−	0.989243i	$-0.453271\pi$
$677$	7.61209			0.292556			0.146278	+	0.989243i	$0.453271\pi$
$678$	−3.27728	+	2.38108i	−0.125863	+	0.0914450i
$679$	5.75749	−	17.7197i	0.220952	−	0.680021i
$680$	1.03949	+	3.19923i	0.0398627	+	0.122685i
$681$	−1.28156			−0.0491095
$682$	8.81585	−	19.0696i	0.337576	−	0.730211i
$683$	−7.79093			−0.298112			−0.149056	−	0.988829i	$-0.547623\pi$
$683$	−7.79093			−0.298112			−0.149056	+	0.988829i	$0.547623\pi$
$684$	1.47735	+	4.54681i	0.0564879	+	0.173852i
$685$	−5.22942	+	16.0945i	−0.199806	+	0.614939i
$686$	−14.9597	+	10.8688i	−0.571163	+	0.414974i
$687$	12.9252			0.493127
$688$	−7.06272			−0.269264
$689$	2.16269	−	1.57129i	0.0823921	−	0.0598614i
$690$	6.19805	+	4.50315i	0.235956	+	0.171432i
$691$	−8.56404	−	6.22214i	−0.325791	−	0.236701i	0.412851	−	0.910798i	$-0.364533\pi$
$691$	−8.56404	−	6.22214i	−0.325791	−	0.236701i	−0.738643	+	0.674097i	$0.764533\pi$
$692$	−1.28750	−	3.96251i	−0.0489433	−	0.150632i
$693$	−8.08918	+	5.87713i	−0.307282	+	0.223254i
$694$	−6.23042	−	19.1752i	−0.236503	−	0.727882i
$695$	−2.74009	+	8.43312i	−0.103937	+	0.319886i
$696$	3.62419	+	2.63313i	0.137375	+	0.0998085i
$697$	2.13154	−	6.56021i	0.0807378	−	0.248485i
$698$	−5.45056	+	16.7751i	−0.206307	+	0.634947i
$699$	3.90068	+	2.83401i	0.147537	+	0.107192i
$700$	−0.818860	+	2.52019i	−0.0309500	+	0.0952543i
$701$	0.507677	+	1.56247i	0.0191747	+	0.0590136i	0.960186	−	0.279361i	$-0.0901228\pi$
$701$	0.507677	+	1.56247i	0.0191747	+	0.0590136i	−0.941011	+	0.338375i	$0.890123\pi$
$702$	0.211779	−	0.153866i	0.00799307	−	0.00580731i
$703$	−10.1259	−	31.1643i	−0.381906	−	1.17538i
$704$	3.05265	+	2.21788i	0.115051	+	0.0835895i
$705$	0.854401	+	0.620759i	0.0321786	+	0.0233791i
$706$	25.8520	−	18.7826i	0.972953	−	0.706892i
$707$	−16.3280			−0.614079
$708$	4.74302			0.178254
$709$	17.6756	−	12.8420i	0.663819	−	0.482293i	−0.204131	−	0.978944i	$-0.565437\pi$
$709$	17.6756	−	12.8420i	0.663819	−	0.482293i	0.867951	+	0.496651i	$0.165437\pi$
$710$	−0.254700	+	0.783886i	−0.00955873	+	0.0294187i
$711$	−1.55448	−	4.78420i	−0.0582976	−	0.179422i
$712$	5.99398			0.224634
$713$	17.8996	−	38.7186i	0.670344	−	1.45002i
$714$	−8.91388			−0.333594
$715$	0.305229	+	0.939400i	0.0114149	+	0.0351316i
$716$	3.80594	−	11.7135i	0.142235	−	0.437753i
$717$	13.4153	−	9.74679i	0.501004	−	0.364001i
$718$	14.0679			0.525009
$719$	−36.8919			−1.37584			−0.687918	−	0.725789i	$-0.741475\pi$
$719$	−36.8919			−1.37584			−0.687918	+	0.725789i	$0.741475\pi$
$720$	0.809017	−	0.587785i	0.0301503	−	0.0219055i
$721$	−13.6189	−	9.89474i	−0.507196	−	0.368499i
$722$	−3.11962	−	2.26654i	−0.116100	−	0.0843519i
$723$	6.68179	+	20.5644i	0.248499	+	0.764800i
$724$	12.6192	−	9.16839i	0.468989	−	0.340740i
$725$	1.38432	+	4.26049i	0.0514123	+	0.158231i
$726$	−1.00049	+	3.07920i	−0.0371317	+	0.114280i
$727$	37.5069	+	27.2503i	1.39105	+	1.01066i	0.995749	+	0.0921088i	$0.0293607\pi$
$727$	37.5069	+	27.2503i	1.39105	+	1.01066i	0.395304	+	0.918550i	$0.370639\pi$
$728$	−0.214355	+	0.659718i	−0.00794454	+	0.0244508i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−6.91929	−	5.02716i	−0.256094	−	0.186063i
$731$	7.34165	−	22.5953i	0.271541	−	0.835717i
$732$	−0.593202	−	1.82569i	−0.0219254	−	0.0674794i
$733$	−29.9370	+	21.7505i	−1.10575	+	0.803373i	−0.981989	−	0.188939i	$-0.939495\pi$
$733$	−29.9370	+	21.7505i	−1.10575	+	0.803373i	−0.123760	+	0.992312i	$0.539495\pi$
$734$	4.17080	+	12.8364i	0.153947	+	0.473800i
$735$	−0.0177214	−	0.0128753i	−0.000653663	−	0.000474914i
$736$	6.19805	+	4.50315i	0.228463	+	0.165988i
$737$	12.2876	−	8.92747i	0.452620	−	0.328848i
$738$	−2.05056			−0.0754820
$739$	5.34102			0.196473			0.0982363	−	0.995163i	$-0.468680\pi$
$739$	5.34102			0.196473			0.0982363	+	0.995163i	$0.468680\pi$
$740$	−5.54508	+	4.02874i	−0.203841	+	0.148099i
$741$	−0.386730	+	1.19023i	−0.0142069	+	0.0437243i
$742$	8.36224	+	25.7363i	0.306987	+	0.944810i
$743$	38.5485			1.41421			0.707103	−	0.707111i	$-0.250002\pi$
$743$	38.5485			1.41421			0.707103	+	0.707111i	$0.250002\pi$
$744$	−4.08450	−	3.78376i	−0.149745	−	0.138719i
$745$	−3.51099			−0.128633
$746$	−0.751548	−	2.31303i	−0.0275161	−	0.0846859i
$747$	3.49795	−	10.7656i	0.127983	−	0.393892i
$748$	−10.2687	+	7.46066i	−0.375461	+	0.272789i
$749$	40.4192			1.47688
$750$	1.00000			0.0365148
$751$	32.4189	−	23.5537i	1.18298	−	0.859486i	0.190476	−	0.981692i	$-0.438997\pi$
$751$	32.4189	−	23.5537i	1.18298	−	0.859486i	0.992505	+	0.122206i	$0.0389969\pi$
$752$	0.854401	+	0.620759i	0.0311568	+	0.0226367i
$753$	−6.23675	−	4.53126i	−0.227280	−	0.165128i
$754$	0.362377	+	1.11528i	0.0131970	+	0.0406161i
$755$	15.1219	−	10.9867i	0.550343	−	0.399847i
$756$	0.818860	+	2.52019i	0.0297817	+	0.0916585i
$757$	12.0696	−	37.1465i	0.438679	−	1.35011i	−0.450591	−	0.892731i	$-0.648787\pi$
$757$	12.0696	−	37.1465i	0.438679	−	1.35011i	0.889270	−	0.457384i	$-0.151213\pi$
$758$	−24.9016	−	18.0921i	−0.904468	−	0.657134i
$759$	−8.93304	+	27.4931i	−0.324249	+	0.997935i
$760$	−1.47735	+	4.54681i	−0.0535891	+	0.164930i
$761$	−31.5110	−	22.8941i	−1.14227	−	0.829910i	−0.154839	−	0.987940i	$-0.549486\pi$
$761$	−31.5110	−	22.8941i	−1.14227	−	0.829910i	−0.987434	+	0.158030i	$0.949486\pi$
$762$	−1.92169	+	5.91436i	−0.0696155	+	0.214255i
$763$	−1.81802	−	5.59529i	−0.0658167	−	0.202563i
$764$	−10.4791	+	7.61354i	−0.379122	+	0.275448i
$765$	1.03949	+	3.19923i	0.0375830	+	0.115668i
$766$	−18.1952	−	13.2196i	−0.657418	−	0.477642i
$767$	1.00447	+	0.729791i	0.0362693	+	0.0263512i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	33.5236			1.20889			0.604446	−	0.796646i	$-0.293395\pi$
$769$	33.5236			1.20889			0.604446	+	0.796646i	$0.293395\pi$
$770$	−9.99877			−0.360331
$771$	14.9973	−	10.8962i	0.540116	−	0.392417i
$772$	−1.11407	+	3.42876i	−0.0400963	+	0.123404i
$773$	−15.5320	−	47.8026i	−0.558647	−	1.71934i	−0.686112	−	0.727496i	$-0.740684\pi$
$773$	−15.5320	−	47.8026i	−0.558647	−	1.71934i	0.127465	−	0.991843i	$-0.459316\pi$
$774$	−7.06272			−0.253864
$775$	−1.08039	−	5.46194i	−0.0388089	−	0.196199i
$776$	−7.03111			−0.252402
$777$	−5.61255	−	17.2737i	−0.201349	−	0.619689i
$778$	7.77467	−	23.9280i	0.278735	−	0.857859i
$779$	7.93104	−	5.76224i	0.284159	−	0.206454i
$780$	0.261773			0.00937298
$781$	−3.11004			−0.111286
$782$	−20.8495	+	15.1480i	−0.745575	+	0.541692i
$783$	3.62419	+	2.63313i	0.129518	+	0.0941003i
$784$	−0.0177214	−	0.0128753i	−0.000632907	−	0.000459834i
$785$	5.97761	+	18.3972i	0.213350	+	0.656623i
$786$	9.24191	−	6.71464i	0.329648	−	0.239503i
$787$	14.2543	+	43.8702i	0.508111	+	1.56380i	0.795478	+	0.605983i	$0.207220\pi$
$787$	14.2543	+	43.8702i	0.508111	+	1.56380i	−0.287367	+	0.957821i	$0.592780\pi$
$788$	−7.78623	+	23.9635i	−0.277373	+	0.853666i
$789$	0.873651	+	0.634744i	0.0311028	+	0.0225975i
$790$	1.55448	−	4.78420i	0.0553060	−	0.170214i
$791$	3.31716	−	10.2092i	0.117944	−	0.362996i
$792$	3.05265	+	2.21788i	0.108471	+	0.0788089i
$793$	0.155284	−	0.477916i	0.00551431	−	0.0169713i
$794$	3.17406	+	9.76876i	0.112643	+	0.346680i
$795$	8.26172	−	6.00249i	0.293013	−	0.212886i
$796$	−8.29708	−	25.5358i	−0.294082	−	0.905092i
$797$	−22.7524	−	16.5306i	−0.805932	−	0.585544i	0.106716	−	0.994290i	$-0.465966\pi$
$797$	−22.7524	−	16.5306i	−0.805932	−	0.585544i	−0.912648	+	0.408745i	$0.865966\pi$
$798$	−10.2491	−	7.44641i	−0.362814	−	0.263600i
$799$	−2.87410	+	2.08815i	−0.101678	+	0.0738735i
$800$	1.00000			0.0353553
$801$	5.99398			0.211787
$802$	−11.7855	+	8.56267i	−0.416161	+	0.302358i
$803$	9.97254	−	30.6923i	0.351923	−	1.08311i
$804$	−1.24386	−	3.82822i	−0.0438677	−	0.135011i
$805$	−20.3014			−0.715529
$806$	−0.282818	−	1.42979i	−0.00996184	−	0.0503621i
$807$	11.2169			0.394852
$808$	1.90410	+	5.86021i	0.0669859	+	0.206161i
$809$	5.90149	−	18.1629i	0.207485	−	0.638574i	−0.792117	−	0.610369i	$-0.791021\pi$
$809$	5.90149	−	18.1629i	0.207485	−	0.638574i	0.999602	−	0.0282047i	$-0.00897902\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	21.4788			0.754221			0.377111	−	0.926168i	$-0.376918\pi$
$811$	21.4788			0.754221			0.377111	+	0.926168i	$0.376918\pi$
$812$	−11.8708			−0.416584
$813$	17.0825	−	12.4112i	0.599110	−	0.435279i
$814$	−20.9232	−	15.2016i	−0.733357	−	0.532815i
$815$	10.6779	+	7.75798i	0.374032	+	0.271750i
$816$	1.03949	+	3.19923i	0.0363895	+	0.111995i
$817$	27.3169	−	19.8469i	0.955696	−	0.694354i
$818$	−11.4705	−	35.3026i	−0.401057	−	1.23433i
$819$	−0.214355	+	0.659718i	−0.00749019	+	0.0230524i
$820$	−1.65894	−	1.20529i	−0.0579325	−	0.0420905i
$821$	6.04716	−	18.6113i	0.211048	−	0.649537i	−0.788363	−	0.615210i	$-0.789071\pi$
$821$	6.04716	−	18.6113i	0.211048	−	0.649537i	0.999411	−	0.0343273i	$-0.0109289\pi$
$822$	−5.22942	+	16.0945i	−0.182397	+	0.561360i
$823$	−41.0952	−	29.8574i	−1.43249	−	1.04076i	−0.989547	−	0.144213i	$-0.953935\pi$
$823$	−41.0952	−	29.8574i	−1.43249	−	1.04076i	−0.442941	−	0.896551i	$-0.646065\pi$
$824$	−1.96309	+	6.04177i	−0.0683875	+	0.210475i
$825$	1.16601	+	3.58860i	0.0405952	+	0.124939i
$826$	−10.1681	+	7.38756i	−0.353794	+	0.257046i
$827$	4.29940	+	13.2322i	0.149505	+	0.460129i	0.997563	−	0.0697748i	$-0.0222281\pi$
$827$	4.29940	+	13.2322i	0.149505	+	0.460129i	−0.848058	+	0.529904i	$0.822228\pi$
$828$	6.19805	+	4.50315i	0.215397	+	0.156495i
$829$	−21.9568	−	15.9525i	−0.762590	−	0.554054i	0.137114	−	0.990555i	$-0.456217\pi$
$829$	−21.9568	−	15.9525i	−0.762590	−	0.554054i	−0.899704	+	0.436501i	$0.856217\pi$
$830$	9.15775	−	6.65350i	0.317870	−	0.230946i
$831$	−11.4502			−0.397201
$832$	0.261773			0.00907534
$833$	0.0596125	−	0.0433110i	0.00206545	−	0.00150064i
$834$	−2.74009	+	8.43312i	−0.0948814	+	0.292015i
$835$	5.93750	+	18.2738i	0.205476	+	0.632389i
$836$	−18.0393			−0.623903
$837$	−4.08450	−	3.78376i	−0.141181	−	0.130786i
$838$	−35.9574			−1.24213
$839$	−17.1629	−	52.8221i	−0.592530	−	1.82362i	−0.566653	−	0.823956i	$-0.691762\pi$
$839$	−17.1629	−	52.8221i	−0.592530	−	1.82362i	−0.0258770	−	0.999665i	$-0.508238\pi$
$840$	−0.818860	+	2.52019i	−0.0282534	+	0.0869549i
$841$	7.22604	−	5.25003i	0.249174	−	0.181035i
$842$	−28.7612			−0.991176
$843$	−8.49431			−0.292559
$844$	14.0055	−	10.1756i	0.482088	−	0.350257i
$845$	−10.4618	−	7.60093i	−0.359896	−	0.261480i
$846$	0.854401	+	0.620759i	0.0293749	+	0.0213421i
$847$	−2.65119	−	8.15953i	−0.0910960	−	0.280365i
$848$	8.26172	−	6.00249i	0.283709	−	0.206126i
$849$	0.698066	+	2.14843i	0.0239575	+	0.0737338i
$850$	−1.03949	+	3.19923i	−0.0356543	+	0.109733i
$851$	−42.4821	−	30.8651i	−1.45627	−	1.05804i
$852$	−0.254700	+	0.783886i	−0.00872588	+	0.0268555i
$853$	0.369131	−	1.13607i	0.0126388	−	0.0388983i	−0.944538	−	0.328402i	$-0.893490\pi$
$853$	0.369131	−	1.13607i	0.0126388	−	0.0388983i	0.957177	+	0.289503i	$0.0934901\pi$
$854$	4.11534	+	2.98997i	0.140824	+	0.102315i
$855$	−1.47735	+	4.54681i	−0.0505243	+	0.155498i
$856$	−4.71349	−	14.5066i	−0.161104	−	0.495826i
$857$	−27.1012	+	19.6902i	−0.925760	+	0.672604i	−0.944951	−	0.327212i	$-0.893891\pi$
$857$	−27.1012	+	19.6902i	−0.925760	+	0.672604i	0.0191914	+	0.999816i	$0.493891\pi$
$858$	0.305229	+	0.939400i	0.0104204	+	0.0320706i
$859$	−6.38510	−	4.63905i	−0.217857	−	0.158282i	0.473505	−	0.880791i	$-0.342989\pi$
$859$	−6.38510	−	4.63905i	−0.217857	−	0.158282i	−0.691361	+	0.722509i	$0.742989\pi$
$860$	−5.71386	−	4.15137i	−0.194841	−	0.141560i
$861$	4.39599	−	3.19388i	0.149815	−	0.108847i
$862$	36.3978			1.23971
$863$	24.6428			0.838852			0.419426	−	0.907790i	$-0.362231\pi$
$863$	24.6428			0.838852			0.419426	+	0.907790i	$0.362231\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	1.28750	−	3.96251i	0.0437763	−	0.134729i
$866$	6.46765	+	19.9054i	0.219780	+	0.676412i
$867$	5.68438			0.193052
$868$	14.6498	+	1.74976i	0.497247	+	0.0593907i
$869$	18.9811			0.643891
$870$	1.38432	+	4.26049i	0.0469328	+	0.144444i
$871$	0.325610	−	1.00212i	0.0110329	−	0.0339557i
$872$	−1.79616	+	1.30499i	−0.0608258	+	0.0441925i
$873$	−7.03111			−0.237967
$874$	−36.6268			−1.23892
$875$	−2.14380	+	1.55756i	−0.0724738	+	0.0526553i
$876$	−6.91929	−	5.02716i	−0.233781	−	0.169852i
$877$	31.4159	+	22.8250i	1.06084	+	0.770744i	0.974243	−	0.225499i	$-0.0724014\pi$
$877$	31.4159	+	22.8250i	1.06084	+	0.770744i	0.0865950	+	0.996244i	$0.472401\pi$
$878$	2.96549	+	9.12683i	0.100080	+	0.308016i
$879$	13.1386	−	9.54577i	0.443155	−	0.321971i
$880$	1.16601	+	3.58860i	0.0393061	+	0.120972i
$881$	−12.1033	+	37.2502i	−0.407771	+	1.25499i	0.510788	+	0.859707i	$0.329354\pi$
$881$	−12.1033	+	37.2502i	−0.407771	+	1.25499i	−0.918559	+	0.395283i	$0.870646\pi$
$882$	−0.0177214	−	0.0128753i	−0.000596710	−	0.000433535i
$883$	16.4249	−	50.5505i	0.552741	−	1.70116i	−0.149095	−	0.988823i	$-0.547636\pi$
$883$	16.4249	−	50.5505i	0.552741	−	1.70116i	0.701836	−	0.712338i	$-0.252364\pi$
$884$	−0.272111	+	0.837472i	−0.00915209	+	0.0281672i
$885$	3.83718	+	2.78788i	0.128986	+	0.0937135i
$886$	−6.54893	+	20.1555i	−0.220016	+	0.677139i
$887$	13.6182	+	41.9125i	0.457254	+	1.40728i	0.868468	+	0.495745i	$0.165105\pi$
$887$	13.6182	+	41.9125i	0.457254	+	1.40728i	−0.411214	+	0.911539i	$0.634895\pi$
$888$	−5.54508	+	4.02874i	−0.186081	+	0.135196i
$889$	−5.09227	−	15.6724i	−0.170789	−	0.525635i
$890$	4.84923	+	3.52317i	0.162547	+	0.118097i
$891$	3.05265	+	2.21788i	0.102268	+	0.0743018i
$892$	18.5655	−	13.4886i	0.621619	−	0.451632i
$893$	−5.04900			−0.168958
$894$	−3.51099			−0.117425
$895$	9.96407	−	7.23932i	0.333062	−	0.241984i
$896$	−0.818860	+	2.52019i	−0.0273562	+	0.0841937i
$897$	0.619733	+	1.90734i	0.0206923	+	0.0636843i
$898$	16.2176			0.541188
$899$	21.7749	−	12.1641i	0.726234	−	0.405694i
$900$	1.00000			0.0333333
$901$	10.6153	+	32.6707i	0.353649	+	1.08842i
$902$	2.39097	−	7.35864i	0.0796105	−	0.245016i
$903$	15.1411	−	11.0007i	0.503864	−	0.366079i
$904$	−4.05094			−0.134732
$905$	15.5982			0.518502
$906$	15.1219	−	10.9867i	0.502392	−	0.365009i
$907$	−21.6906	−	15.7591i	−0.720224	−	0.523274i	0.166232	−	0.986087i	$-0.446840\pi$
$907$	−21.6906	−	15.7591i	−0.720224	−	0.523274i	−0.886456	+	0.462813i	$0.846840\pi$
$908$	−1.03680	−	0.753283i	−0.0344076	−	0.0249986i
$909$	1.90410	+	5.86021i	0.0631549	+	0.194371i
$910$	−0.561190	+	0.407728i	−0.0186033	+	0.0135161i
$911$	−8.79514	−	27.0686i	−0.291396	−	0.896824i	−0.984408	−	0.175899i	$-0.943717\pi$
$911$	−8.79514	−	27.0686i	−0.291396	−	0.896824i	0.693012	−	0.720926i	$-0.256283\pi$
$912$	−1.47735	+	4.54681i	−0.0489199	+	0.150560i
$913$	34.5548	+	25.1055i	1.14360	+	0.830872i
$914$	−7.24079	+	22.2849i	−0.239504	+	0.737117i
$915$	0.593202	−	1.82569i	0.0196107	−	0.0603554i
$916$	10.4567	+	7.59724i	0.345499	+	0.251020i
$917$	−9.35436	+	28.7898i	−0.308908	+	0.950722i
$918$	1.03949	+	3.19923i	0.0343084	+	0.105590i
$919$	25.7256	−	18.6907i	0.848609	−	0.616550i	−0.0761533	−	0.997096i	$-0.524264\pi$
$919$	25.7256	−	18.6907i	0.848609	−	0.616550i	0.924762	+	0.380546i	$0.124264\pi$
$920$	2.36745	+	7.28625i	0.0780524	+	0.240221i
$921$	−9.39492	−	6.82581i	−0.309573	−	0.224918i
$922$	−12.7913	−	9.29341i	−0.421259	−	0.306062i
$923$	−0.174554	+	0.126821i	−0.00574551	+	0.00417436i
$924$	−9.99877			−0.328936
$925$	−6.85410			−0.225361
$926$	−1.96359	+	1.42663i	−0.0645275	+	0.0468820i
$927$	−1.96309	+	6.04177i	−0.0644764	+	0.198438i
$928$	1.38432	+	4.26049i	0.0454424	+	0.139857i
$929$	−39.0023			−1.27962			−0.639811	−	0.768532i	$-0.720988\pi$
$929$	−39.0023			−1.27962			−0.639811	+	0.768532i	$0.720988\pi$
$930$	−1.08039	−	5.46194i	−0.0354275	−	0.179104i
$931$	0.104723			0.00343215
$932$	1.48993	+	4.58552i	0.0488041	+	0.150204i
$933$	−6.46064	+	19.8838i	−0.211512	+	0.650967i
$934$	−13.3048	+	9.66648i	−0.435345	+	0.316297i
$935$	−12.6928			−0.415100
$936$	0.261773			0.00855632
$937$	9.43171	−	6.85254i	0.308121	−	0.223863i	−0.422969	−	0.906144i	$-0.639012\pi$
$937$	9.43171	−	6.85254i	0.308121	−	0.223863i	0.731090	+	0.682281i	$0.239012\pi$
$938$	8.62930	+	6.26955i	0.281757	+	0.204708i
$939$	4.65512	+	3.38214i	0.151914	+	0.110372i
$940$	0.326352	+	1.00441i	0.0106444	+	0.0327602i
$941$	11.1193	−	8.07867i	0.362480	−	0.263357i	−0.391606	−	0.920133i	$-0.628080\pi$
$941$	11.1193	−	8.07867i	0.362480	−	0.263357i	0.754086	+	0.656776i	$0.228080\pi$
$942$	5.97761	+	18.3972i	0.194761	+	0.599412i
$943$	4.85458	−	14.9409i	0.158087	−	0.486542i
$944$	3.83718	+	2.78788i	0.124890	+	0.0907377i
$945$	−0.818860	+	2.52019i	−0.0266375	+	0.0819819i
$946$	8.23520	−	25.3453i	0.267749	−	0.824048i
$947$	10.0672	+	7.31428i	0.327142	+	0.237682i	0.739217	−	0.673468i	$-0.235196\pi$
$947$	10.0672	+	7.31428i	0.327142	+	0.237682i	−0.412075	+	0.911150i	$0.635196\pi$
$948$	1.55448	−	4.78420i	0.0504872	−	0.155384i
$949$	−0.691849	−	2.12929i	−0.0224584	−	0.0691197i
$950$	−3.86775	+	2.81008i	−0.125486	+	0.0911712i
$951$	−7.79391	−	23.9872i	−0.252735	−	0.777838i
$952$	−7.21148	−	5.23945i	−0.233725	−	0.169811i
$953$	45.6481	+	33.1653i	1.47869	+	1.07433i	0.977976	+	0.208716i	$0.0669284\pi$
$953$	45.6481	+	33.1653i	1.47869	+	1.07433i	0.500712	+	0.865614i	$0.333072\pi$
$954$	8.26172	−	6.00249i	0.267483	−	0.194338i
$955$	−12.9529			−0.419147
$956$	16.5822			0.536308
$957$	−13.6751	+	9.93554i	−0.442053	+	0.321170i
$958$	10.2044	−	31.4059i	0.329689	−	1.01468i
$959$	−13.8574	−	42.6486i	−0.447478	−	1.37719i
$960$	1.00000			0.0322749
$961$	−28.6655	+	11.8021i	−0.924693	+	0.380713i
$962$	−1.79422			−0.0578479
$963$	−4.71349	−	14.5066i	−0.151890	−	0.467469i
$964$	−6.68179	+	20.5644i	−0.215206	+	0.662336i
$965$	−2.91667	+	2.11909i	−0.0938911	+	0.0682159i
$966$	−20.3014			−0.653186
$967$	−54.4575			−1.75124			−0.875618	−	0.483004i	$-0.839546\pi$
$967$	−54.4575			−1.75124			−0.875618	+	0.483004i	$0.839546\pi$
$968$	−2.61932	+	1.90305i	−0.0841882	+	0.0611663i
$969$	−13.0106	−	9.45276i	−0.417961	−	0.303666i
$970$	−5.68828	−	4.13278i	−0.182640	−	0.132696i
$971$	3.13366	+	9.64442i	0.100564	+	0.309504i	0.988664	−	0.150147i	$-0.0479746\pi$
$971$	3.13366	+	9.64442i	0.100564	+	0.309504i	−0.888100	+	0.459651i	$0.847975\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−7.26092	−	22.3468i	−0.232774	−	0.716406i
$974$	11.7681	−	36.2186i	0.377076	−	1.16052i
$975$	0.211779	+	0.153866i	0.00678235	+	0.00492766i
$976$	0.593202	−	1.82569i	0.0189879	−	0.0584389i
$977$	−7.99559	+	24.6079i	−0.255802	+	0.787276i	0.737869	+	0.674944i	$0.235832\pi$
$977$	−7.99559	+	24.6079i	−0.255802	+	0.787276i	−0.993671	+	0.112332i	$0.964168\pi$
$978$	10.6779	+	7.75798i	0.341443	+	0.248073i
$979$	−6.98903	+	21.5100i	−0.223370	+	0.687464i
$980$	−0.00676897	−	0.0208327i	−0.000216227	−	0.000665478i
$981$	−1.79616	+	1.30499i	−0.0573471	+	0.0416651i
$982$	4.33469	+	13.3408i	0.138326	+	0.425722i
$983$	−44.9272	−	32.6415i	−1.43296	−	1.04110i	−0.989457	−	0.144829i	$-0.953737\pi$
$983$	−44.9272	−	32.6415i	−1.43296	−	1.04110i	−0.443500	−	0.896275i	$-0.646263\pi$
$984$	−1.65894	−	1.20529i	−0.0528849	−	0.0384232i
$985$	−20.3846	+	14.8103i	−0.649508	+	0.471895i
$986$	−15.0693			−0.479904
$987$	−2.79854			−0.0890786
$988$	−1.01247	+	0.735604i	−0.0322110	+	0.0234027i
$989$	16.7206	−	51.4608i	0.531685	−	1.63636i
$990$	1.16601	+	3.58860i	0.0370582	+	0.114053i
$991$	−20.9801			−0.666455			−0.333227	−	0.942846i	$-0.608138\pi$
$991$	−20.9801			−0.666455			−0.333227	+	0.942846i	$0.608138\pi$
$992$	−1.08039	−	5.46194i	−0.0343026	−	0.173417i
$993$	17.3990			0.552140
$994$	−0.674927	−	2.07721i	−0.0214074	−	0.0658851i
$995$	8.29708	−	25.5358i	0.263035	−	0.809539i
$996$	9.15775	−	6.65350i	0.290175	−	0.210824i
$997$	30.7098			0.972590			0.486295	−	0.873795i	$-0.338348\pi$
$997$	30.7098			0.972590			0.486295	+	0.873795i	$0.338348\pi$
$998$	11.6281			0.368081
$999$	−5.54508	+	4.02874i	−0.175439	+	0.127464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.d.841.3	yes	12
31.8	even	5	inner	930.2.n.d.721.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.d.721.3	✓	12	31.8	even	5	inner
930.2.n.d.841.3	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(2.14380 - 1.55756i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(2.14380 - 1.55756i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(3.05265 - 2.21788i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(0.0808923 - 0.248961i) q^{13} +(2.14380 + 1.55756i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.72143 + 1.97723i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.47735 + 4.54681i) q^{19} +(0.809017 - 0.587785i) q^{20} +(0.818860 + 2.52019i) q^{21} +(3.05265 + 2.21788i) q^{22} +(6.19805 + 4.50315i) q^{23} +(0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +0.261773 q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.818860 + 2.52019i) q^{28} +(1.38432 + 4.26049i) q^{29} +1.00000 q^{30} +(-1.08039 - 5.46194i) q^{31} +1.00000 q^{32} +(1.16601 + 3.58860i) q^{33} +(-1.03949 + 3.19923i) q^{34} +(-2.14380 + 1.55756i) q^{35} +1.00000 q^{36} -6.85410 q^{37} +(-3.86775 + 2.81008i) q^{38} +(0.211779 + 0.153866i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-0.633657 - 1.95020i) q^{41} +(-2.14380 + 1.55756i) q^{42} +(-2.18250 - 6.71705i) q^{43} +(-1.16601 + 3.58860i) q^{44} +(0.809017 + 0.587785i) q^{45} +(-2.36745 + 7.28625i) q^{46} +(-0.326352 + 1.00441i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.00676897 - 0.0208327i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-2.72143 + 1.97723i) q^{51} +(0.0808923 + 0.248961i) q^{52} +(8.26172 + 6.00249i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-3.05265 + 2.21788i) q^{55} -2.64989 q^{56} -4.78080 q^{57} +(-3.62419 + 2.63313i) q^{58} +(-1.46567 + 4.51088i) q^{59} +(0.309017 + 0.951057i) q^{60} +1.91964 q^{61} +(4.86075 - 2.71535i) q^{62} -2.64989 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.0808923 + 0.248961i) q^{65} +(-3.05265 + 2.21788i) q^{66} +4.02523 q^{67} -3.36387 q^{68} +(-6.19805 + 4.50315i) q^{69} +(-2.14380 - 1.55756i) q^{70} +(-0.666814 - 0.484468i) q^{71} +(0.309017 + 0.951057i) q^{72} +(6.91929 - 5.02716i) q^{73} +(-2.11803 - 6.51864i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-3.86775 - 2.81008i) q^{76} +(3.08979 - 9.50940i) q^{77} +(-0.0808923 + 0.248961i) q^{78} +(4.06969 + 2.95680i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.65894 - 1.20529i) q^{82} +(3.49795 + 10.7656i) q^{83} +(-2.14380 - 1.55756i) q^{84} +(-2.72143 - 1.97723i) q^{85} +(5.71386 - 4.15137i) q^{86} -4.47975 q^{87} -3.77328 q^{88} +(-4.84923 + 3.52317i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(-0.214355 - 0.659718i) q^{91} -7.66122 q^{92} +(5.52847 + 0.660315i) q^{93} -1.05610 q^{94} +(-1.47735 - 4.54681i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(5.68828 - 4.13278i) q^{97} +0.0219048 q^{98} -3.77328 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	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

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