LMFDB - Embedded newform 930.2.n.h.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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 60 x^{13} + 480 x^{12} - 1202 x^{11} - 147 x^{10} - 2185 x^{9} + \cdots + 12851 $ x^16 - 4x^15 + 5x^14 - 60x^13 + 480x^12 - 1202x^11 - 147x^10 - 2185x^9 + 62400x^8 - 289745x^7 + 699483x^6 - 1042897x^5 + 1014415x^4 - 652345x^3 + 274580x^2 - 73519*x + 12851
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Root			$2.41373 - 0.0663824i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.h.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-1.42081 - 4.37281i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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} +(-1.42081 - 4.37281i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.56890 + 4.82859i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(3.90550 - 2.83751i) q^{13} +(1.42081 - 4.37281i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.68809 + 5.19539i) q^{17} +(0.809017 - 0.587785i) q^{18} +(6.31622 + 4.58900i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(3.71974 + 2.70255i) q^{21} +(-1.56890 + 4.82859i) q^{22} +(-0.296369 + 0.912131i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +4.82746 q^{26} +(0.309017 + 0.951057i) q^{27} +(3.71974 - 2.70255i) q^{28} +(5.43153 + 3.94623i) q^{29} +1.00000 q^{30} +(4.79002 - 2.83826i) q^{31} -1.00000 q^{32} +(-4.10744 - 2.98423i) q^{33} +(-4.41947 + 3.21093i) q^{34} +(1.42081 + 4.37281i) q^{35} +1.00000 q^{36} -1.84573 q^{37} +(2.41258 + 7.42516i) q^{38} +(-1.49177 + 4.59119i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-6.03198 - 4.38249i) q^{41} +(1.42081 + 4.37281i) q^{42} +(5.96022 + 4.33035i) q^{43} +(-4.10744 + 2.98423i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-0.775905 + 0.563728i) q^{46} +(3.15006 - 2.28865i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-11.4397 + 8.31141i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.68809 - 5.19539i) q^{51} +(3.90550 + 2.83751i) q^{52} +(-1.77764 + 5.47103i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.56890 - 4.82859i) q^{55} +4.59785 q^{56} -7.80728 q^{57} +(2.07466 + 6.38514i) q^{58} +(6.48159 - 4.70915i) q^{59} +(0.809017 + 0.587785i) q^{60} +3.50817 q^{61} +(5.54349 + 0.519301i) q^{62} -4.59785 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-3.90550 + 2.83751i) q^{65} +(-1.56890 - 4.82859i) q^{66} -5.54173 q^{67} -5.46276 q^{68} +(-0.296369 - 0.912131i) q^{69} +(-1.42081 + 4.37281i) q^{70} +(4.19446 - 12.9092i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-4.31211 - 13.2713i) q^{73} +(-1.49323 - 1.08489i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(-2.41258 + 7.42516i) q^{76} +(18.8854 - 13.7210i) q^{77} +(-3.90550 + 2.83751i) q^{78} +(-5.42202 + 16.6873i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.30401 - 7.09102i) q^{82} +(0.0635902 + 0.0462010i) q^{83} +(-1.42081 + 4.37281i) q^{84} +(1.68809 - 5.19539i) q^{85} +(2.27660 + 7.00666i) q^{86} -6.71373 q^{87} -5.07708 q^{88} +(4.99808 + 15.3825i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-17.9569 - 13.0464i) q^{91} -0.959072 q^{92} +(-2.20692 + 5.11170i) q^{93} +3.89368 q^{94} +(-6.31622 - 4.58900i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-0.164841 - 0.507330i) q^{97} -14.1402 q^{98} +5.07708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * 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
$7$	−1.42081	−	4.37281i	−0.537017	−	1.65277i	−0.739250	−	0.673431i	$-0.764820\pi$
$7$	−1.42081	−	4.37281i	−0.537017	−	1.65277i	0.202233	−	0.979337i	$-0.435180\pi$
$8$	−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
$11$	1.56890	+	4.82859i	0.473042	+	1.45587i	0.848580	+	0.529067i	$0.177458\pi$
$11$	1.56890	+	4.82859i	0.473042	+	1.45587i	−0.375538	+	0.926807i	$0.622542\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	3.90550	−	2.83751i	1.08319	−	0.786984i	0.104954	−	0.994477i	$-0.466531\pi$
$13$	3.90550	−	2.83751i	1.08319	−	0.786984i	0.978236	+	0.207493i	$0.0665306\pi$
$14$	1.42081	−	4.37281i	0.379728	−	1.16868i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.68809	+	5.19539i	−0.409421	+	1.26007i	0.507726	+	0.861519i	$0.330486\pi$
$17$	−1.68809	+	5.19539i	−0.409421	+	1.26007i	−0.917147	+	0.398549i	$0.869514\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	6.31622	+	4.58900i	1.44904	+	1.05279i	0.986054	+	0.166423i	$0.0532218\pi$
$19$	6.31622	+	4.58900i	1.44904	+	1.05279i	0.462986	+	0.886366i	$0.346778\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	3.71974	+	2.70255i	0.811713	+	0.589744i
$22$	−1.56890	+	4.82859i	−0.334491	+	1.02946i
$23$	−0.296369	+	0.912131i	−0.0617973	+	0.190193i	−0.977189	−	0.212372i	$-0.931881\pi$
$23$	−0.296369	+	0.912131i	−0.0617973	+	0.190193i	0.915392	+	0.402565i	$0.131881\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	4.82746			0.946743
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	3.71974	−	2.70255i	0.702964	−	0.510734i
$29$	5.43153	+	3.94623i	1.00861	+	0.732797i	0.963917	−	0.266204i	$-0.0857693\pi$
$29$	5.43153	+	3.94623i	1.00861	+	0.732797i	0.0446921	+	0.999001i	$0.485769\pi$
$30$	1.00000			0.182574
$31$	4.79002	−	2.83826i	0.860313	−	0.509767i
$31$	4.79002	−	2.83826i	0.860313	−	0.509767i
$32$	−1.00000			−0.176777
$33$	−4.10744	−	2.98423i	−0.715014	−	0.519488i
$34$	−4.41947	+	3.21093i	−0.757932	+	0.550670i
$35$	1.42081	+	4.37281i	0.240161	+	0.739141i
$36$	1.00000			0.166667
$37$	−1.84573			−0.303436			−0.151718	−	0.988424i	$-0.548481\pi$
$37$	−1.84573			−0.303436			−0.151718	+	0.988424i	$0.548481\pi$
$38$	2.41258	+	7.42516i	0.391372	+	1.20452i
$39$	−1.49177	+	4.59119i	−0.238874	+	0.735178i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−6.03198	−	4.38249i	−0.942038	−	0.684430i	0.00687264	−	0.999976i	$-0.497812\pi$
$41$	−6.03198	−	4.38249i	−0.942038	−	0.684430i	−0.948910	+	0.315546i	$0.897812\pi$
$42$	1.42081	+	4.37281i	0.219236	+	0.674740i
$43$	5.96022	+	4.33035i	0.908925	+	0.660373i	0.940743	−	0.339121i	$-0.110130\pi$
$43$	5.96022	+	4.33035i	0.908925	+	0.660373i	−0.0318178	+	0.999494i	$0.510130\pi$
$44$	−4.10744	+	2.98423i	−0.619220	+	0.449890i
$45$	−0.309017	+	0.951057i	−0.0460655	+	0.141775i
$46$	−0.775905	+	0.563728i	−0.114401	+	0.0831172i
$47$	3.15006	−	2.28865i	0.459483	−	0.333834i	−0.333845	−	0.942628i	$-0.608346\pi$
$47$	3.15006	−	2.28865i	0.459483	−	0.333834i	0.793328	+	0.608794i	$0.208346\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−11.4397	+	8.31141i	−1.63424	+	1.18734i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	−1.68809	−	5.19539i	−0.236379	−	0.727501i
$52$	3.90550	+	2.83751i	0.541595	+	0.393492i
$53$	−1.77764	+	5.47103i	−0.244178	+	0.751503i	0.751592	+	0.659628i	$0.229286\pi$
$53$	−1.77764	+	5.47103i	−0.244178	+	0.751503i	−0.995771	+	0.0918753i	$0.970714\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−1.56890	−	4.82859i	−0.211551	−	0.651086i
$56$	4.59785			0.614413
$57$	−7.80728			−1.03410
$58$	2.07466	+	6.38514i	0.272416	+	0.838410i
$59$	6.48159	−	4.70915i	0.843831	−	0.613079i	−0.0796070	−	0.996826i	$-0.525367\pi$
$59$	6.48159	−	4.70915i	0.843831	−	0.613079i	0.923438	+	0.383747i	$0.125367\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	3.50817			0.449175			0.224587	−	0.974454i	$-0.427897\pi$
$61$	3.50817			0.449175			0.224587	+	0.974454i	$0.427897\pi$
$62$	5.54349	+	0.519301i	0.704024	+	0.0659514i
$63$	−4.59785			−0.579275
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−3.90550	+	2.83751i	−0.484417	+	0.351950i
$66$	−1.56890	−	4.82859i	−0.193119	−	0.594358i
$67$	−5.54173			−0.677030			−0.338515	−	0.940961i	$-0.609925\pi$
$67$	−5.54173			−0.677030			−0.338515	+	0.940961i	$0.609925\pi$
$68$	−5.46276			−0.662457
$69$	−0.296369	−	0.912131i	−0.0356787	−	0.109808i
$70$	−1.42081	+	4.37281i	−0.169820	+	0.522651i
$71$	4.19446	−	12.9092i	0.497791	−	1.53204i	−0.314771	−	0.949168i	$-0.601928\pi$
$71$	4.19446	−	12.9092i	0.497791	−	1.53204i	0.812562	−	0.582875i	$-0.198072\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	−4.31211	−	13.2713i	−0.504695	−	1.55329i	−0.801283	−	0.598285i	$-0.795849\pi$
$73$	−4.31211	−	13.2713i	−0.504695	−	1.55329i	0.296588	−	0.955005i	$-0.404151\pi$
$74$	−1.49323	−	1.08489i	−0.173584	−	0.126116i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	−2.41258	+	7.42516i	−0.276742	+	0.851724i
$77$	18.8854	−	13.7210i	2.15219	−	1.56366i
$78$	−3.90550	+	2.83751i	−0.442210	+	0.321285i
$79$	−5.42202	+	16.6873i	−0.610025	+	1.87746i	−0.152400	+	0.988319i	$0.548700\pi$
$79$	−5.42202	+	16.6873i	−0.610025	+	1.87746i	−0.457625	+	0.889145i	$0.651300\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−2.30401	−	7.09102i	−0.254436	−	0.783072i
$83$	0.0635902	+	0.0462010i	0.00697994	+	0.00507122i	0.591270	−	0.806474i	$-0.298627\pi$
$83$	0.0635902	+	0.0462010i	0.00697994	+	0.00507122i	−0.584290	+	0.811545i	$0.698627\pi$
$84$	−1.42081	+	4.37281i	−0.155023	+	0.477113i
$85$	1.68809	−	5.19539i	0.183099	−	0.563520i
$86$	2.27660	+	7.00666i	0.245492	+	0.755547i
$87$	−6.71373			−0.719788
$88$	−5.07708			−0.541218
$89$	4.99808	+	15.3825i	0.529795	+	1.63054i	0.754633	+	0.656147i	$0.227815\pi$
$89$	4.99808	+	15.3825i	0.529795	+	1.63054i	−0.224838	+	0.974396i	$0.572185\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	−17.9569	−	13.0464i	−1.88239	−	1.36764i
$92$	−0.959072			−0.0999901
$93$	−2.20692	+	5.11170i	−0.228847	+	0.530059i
$94$	3.89368			0.401603
$95$	−6.31622	−	4.58900i	−0.648030	−	0.470822i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−0.164841	−	0.507330i	−0.0167371	−	0.0515115i	0.942339	−	0.334659i	$-0.108621\pi$
$97$	−0.164841	−	0.507330i	−0.0167371	−	0.0515115i	−0.959076	+	0.283148i	$0.908621\pi$
$98$	−14.1402			−1.42838
$99$	5.07708			0.510265
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−3.42507	+	10.5413i	−0.340808	+	1.04890i	0.622983	+	0.782236i	$0.285921\pi$
$101$	−3.42507	+	10.5413i	−0.340808	+	1.04890i	−0.963790	+	0.266662i	$0.914079\pi$
$102$	1.68809	−	5.19539i	0.167145	−	0.514421i
$103$	8.01126	+	5.82052i	0.789373	+	0.573513i	0.907777	−	0.419453i	$-0.137778\pi$
$103$	8.01126	+	5.82052i	0.789373	+	0.573513i	−0.118404	+	0.992965i	$0.537778\pi$
$104$	1.49177	+	4.59119i	0.146280	+	0.450203i
$105$	−3.71974	−	2.70255i	−0.363009	−	0.263742i
$106$	−4.65393	+	3.38128i	−0.452030	+	0.328419i
$107$	1.88347	−	5.79671i	0.182081	−	0.560389i	−0.817804	−	0.575496i	$-0.804809\pi$
$107$	1.88347	−	5.79671i	0.182081	−	0.560389i	0.999886	+	0.0151071i	$0.00480894\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	7.81321	−	5.67663i	0.748370	−	0.543722i	−0.146951	−	0.989144i	$-0.546946\pi$
$109$	7.81321	−	5.67663i	0.748370	−	0.543722i	0.895321	+	0.445421i	$0.146946\pi$
$110$	1.56890	−	4.82859i	0.149589	−	0.460388i
$111$	1.49323	−	1.08489i	0.141731	−	0.102973i
$112$	3.71974	+	2.70255i	0.351482	+	0.255367i
$113$	−2.70654	−	8.32988i	−0.254610	−	0.783609i	−0.993906	−	0.110229i	$-0.964842\pi$
$113$	−2.70654	−	8.32988i	−0.254610	−	0.783609i	0.739296	−	0.673380i	$-0.235158\pi$
$114$	−6.31622	−	4.58900i	−0.591568	−	0.429799i
$115$	0.296369	−	0.912131i	0.0276366	−	0.0850567i
$116$	−2.07466	+	6.38514i	−0.192627	+	0.592845i
$117$	−1.49177	−	4.59119i	−0.137914	−	0.424455i
$118$	8.01169			0.737536
$119$	25.1170			2.30247
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	−11.9546	+	8.68552i	−1.08678	+	0.789593i
$122$	2.83817	+	2.06205i	0.256955	+	0.186689i
$123$	7.45594			0.672280
$124$	4.17954	+	3.67851i	0.375334	+	0.330340i
$125$	−1.00000			−0.0894427
$126$	−3.71974	−	2.70255i	−0.331381	−	0.240762i
$127$	17.3482	−	12.6042i	1.53940	−	1.11844i	0.588694	−	0.808356i	$-0.299642\pi$
$127$	17.3482	−	12.6042i	1.53940	−	1.11844i	0.950709	−	0.310085i	$-0.100358\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−7.36724			−0.648649
$130$	−4.82746			−0.423396
$131$	1.22252	+	3.76253i	0.106812	+	0.328733i	0.990151	−	0.140000i	$-0.0447104\pi$
$131$	1.22252	+	3.76253i	0.106812	+	0.328733i	−0.883339	+	0.468734i	$0.844710\pi$
$132$	1.56890	−	4.82859i	0.136555	−	0.420274i
$133$	11.0927	−	34.1398i	0.961858	−	2.96029i
$134$	−4.48335	−	3.25735i	−0.387303	−	0.281392i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	−4.41947	−	3.21093i	−0.378966	−	0.275335i
$137$	−5.85610	+	4.25471i	−0.500321	+	0.363504i	−0.809139	−	0.587617i	$-0.800066\pi$
$137$	−5.85610	+	4.25471i	−0.500321	+	0.363504i	0.308819	+	0.951121i	$0.400066\pi$
$138$	0.296369	−	0.912131i	0.0252286	−	0.0776458i
$139$	2.02431	−	1.47075i	0.171700	−	0.124747i	−0.498616	−	0.866823i	$-0.666158\pi$
$139$	2.02431	−	1.47075i	0.171700	−	0.124747i	0.670316	+	0.742075i	$0.266158\pi$
$140$	−3.71974	+	2.70255i	−0.314375	+	0.228407i
$141$	−1.20321	+	3.70311i	−0.101329	+	0.311858i
$142$	10.9812	−	7.97834i	0.921525	−	0.669527i
$143$	19.8285	+	14.4063i	1.65814	+	1.20471i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−5.43153	−	3.94623i	−0.451064	−	0.327717i
$146$	4.31211	−	13.2713i	0.356873	−	1.09834i
$147$	4.36957	−	13.4481i	0.360396	−	1.10918i
$148$	−0.570362	−	1.75539i	−0.0468834	−	0.144292i
$149$	−15.3127			−1.25447			−0.627233	−	0.778832i	$-0.715812\pi$
$149$	−15.3127			−1.25447			−0.627233	+	0.778832i	$0.715812\pi$
$150$	−1.00000			−0.0816497
$151$	−2.42057	−	7.44976i	−0.196983	−	0.606253i	−0.999948	−	0.0102255i	$-0.996745\pi$
$151$	−2.42057	−	7.44976i	−0.196983	−	0.606253i	0.802964	−	0.596027i	$-0.203255\pi$
$152$	−6.31622	+	4.58900i	−0.512313	+	0.372217i
$153$	4.41947	+	3.21093i	0.357293	+	0.259588i
$154$	23.3436			1.88108
$155$	−4.79002	+	2.83826i	−0.384744	+	0.227975i
$156$	−4.82746			−0.386506
$157$	10.5240	+	7.64616i	0.839909	+	0.610230i	0.922345	−	0.386367i	$-0.126270\pi$
$157$	10.5240	+	7.64616i	0.839909	+	0.610230i	−0.0824362	+	0.996596i	$0.526270\pi$
$158$	−14.1950	+	10.3133i	−1.12930	+	0.820482i
$159$	−1.77764	−	5.47103i	−0.140976	−	0.433881i
$160$	1.00000			0.0790569
$161$	4.40967			0.347530
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−4.09673	+	12.6084i	−0.320881	+	0.987569i	0.652385	+	0.757888i	$0.273768\pi$
$163$	−4.09673	+	12.6084i	−0.320881	+	0.987569i	−0.973266	+	0.229682i	$0.926232\pi$
$164$	2.30401	−	7.09102i	0.179913	−	0.553716i
$165$	4.10744	+	2.98423i	0.319764	+	0.232322i
$166$	0.0242893	+	0.0747548i	0.00188522	+	0.00580210i
$167$	−1.22442	−	0.889590i	−0.0947481	−	0.0688386i	0.539403	−	0.842048i	$-0.318650\pi$
$167$	−1.22442	−	0.889590i	−0.0947481	−	0.0688386i	−0.634151	+	0.773209i	$0.718650\pi$
$168$	−3.71974	+	2.70255i	−0.286984	+	0.208506i
$169$	3.18423	−	9.80004i	0.244940	−	0.753849i
$170$	4.41947	−	3.21093i	0.338958	−	0.246267i
$171$	6.31622	−	4.58900i	0.483013	−	0.350930i
$172$	−2.27660	+	7.00666i	−0.173589	+	0.534253i
$173$	−0.241360	+	0.175358i	−0.0183503	+	0.0133322i	−0.596923	−	0.802299i	$-0.703610\pi$
$173$	−0.241360	+	0.175358i	−0.0183503	+	0.0133322i	0.578572	+	0.815631i	$0.303610\pi$
$174$	−5.43153	−	3.94623i	−0.411763	−	0.299163i
$175$	−1.42081	−	4.37281i	−0.107403	−	0.330554i
$176$	−4.10744	−	2.98423i	−0.309610	−	0.224945i
$177$	−2.47575	+	7.61957i	−0.186089	+	0.572722i
$178$	−4.99808	+	15.3825i	−0.374622	+	1.15297i
$179$	−0.893987	−	2.75141i	−0.0668198	−	0.205650i	0.912072	−	0.410031i	$-0.134482\pi$
$179$	−0.893987	−	2.75141i	−0.0668198	−	0.205650i	−0.978892	+	0.204381i	$0.934482\pi$
$180$	−1.00000			−0.0745356
$181$	−23.1895			−1.72366			−0.861830	−	0.507198i	$-0.830681\pi$
$181$	−23.1895			−1.72366			−0.861830	+	0.507198i	$0.830681\pi$
$182$	−6.85892	−	21.1096i	−0.508417	−	1.56475i
$183$	−2.83817	+	2.06205i	−0.209803	+	0.152431i
$184$	−0.775905	−	0.563728i	−0.0572005	−	0.0415586i
$185$	1.84573			0.135701
$186$	−4.79002	+	2.83826i	−0.351221	+	0.208111i
$187$	−27.7348			−2.02817
$188$	3.15006	+	2.28865i	0.229741	+	0.166917i
$189$	3.71974	−	2.70255i	0.270571	−	0.196581i
$190$	−2.41258	−	7.42516i	−0.175027	−	0.538678i
$191$	−8.16422			−0.590742			−0.295371	−	0.955383i	$-0.595443\pi$
$191$	−8.16422			−0.590742			−0.295371	+	0.955383i	$0.595443\pi$
$192$	1.00000			0.0721688
$193$	−5.33612	−	16.4229i	−0.384103	−	1.18215i	−0.937129	−	0.348983i	$-0.886527\pi$
$193$	−5.33612	−	16.4229i	−0.384103	−	1.18215i	0.553027	−	0.833164i	$-0.313473\pi$
$194$	0.164841	−	0.507330i	0.0118349	−	0.0364241i
$195$	1.49177	−	4.59119i	0.106828	−	0.328782i
$196$	−11.4397	−	8.31141i	−0.817120	−	0.593672i
$197$	−1.34657	−	4.14431i	−0.0959390	−	0.295270i	0.891558	−	0.452906i	$-0.149613\pi$
$197$	−1.34657	−	4.14431i	−0.0959390	−	0.295270i	−0.987497	+	0.157636i	$0.949613\pi$
$198$	4.10744	+	2.98423i	0.291903	+	0.212080i
$199$	−2.04641	+	1.48681i	−0.145066	+	0.105397i	−0.657951	−	0.753060i	$-0.728577\pi$
$199$	−2.04641	+	1.48681i	−0.145066	+	0.105397i	0.512885	+	0.858457i	$0.328577\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	4.48335	−	3.25735i	0.316231	−	0.229756i
$202$	−8.96696	+	6.51488i	−0.630913	+	0.458385i
$203$	9.53897	−	29.3579i	0.669504	−	2.06052i
$204$	4.41947	−	3.21093i	0.309425	−	0.224810i
$205$	6.03198	+	4.38249i	0.421292	+	0.306087i
$206$	3.06003	+	9.41780i	0.213202	+	0.656169i
$207$	0.775905	+	0.563728i	0.0539291	+	0.0391818i
$208$	−1.49177	+	4.59119i	−0.103435	+	0.318342i
$209$	−12.2489	+	37.6981i	−0.847271	+	2.60763i
$210$	−1.42081	−	4.37281i	−0.0980455	−	0.301753i
$211$	−13.3542			−0.919341			−0.459670	−	0.888090i	$-0.652032\pi$
$211$	−13.3542			−0.919341			−0.459670	+	0.888090i	$0.652032\pi$
$212$	−5.75258			−0.395089
$213$	4.19446	+	12.9092i	0.287400	+	0.884526i
$214$	4.93098	−	3.58256i	0.337075	−	0.244899i
$215$	−5.96022	−	4.33035i	−0.406484	−	0.295328i
$216$	−1.00000			−0.0680414
$217$	−19.2169	−	16.9132i	−1.30453	−	1.14814i
$218$	9.65766			0.654099
$219$	11.2893	+	8.20213i	0.762858	+	0.554248i
$220$	4.10744	−	2.98423i	0.276924	−	0.201197i
$221$	8.14917	+	25.0806i	0.548172	+	1.68710i
$222$	1.84573			0.123877
$223$	2.29691			0.153812			0.0769062	−	0.997038i	$-0.475496\pi$
$223$	2.29691			0.153812			0.0769062	+	0.997038i	$0.475496\pi$
$224$	1.42081	+	4.37281i	0.0949321	+	0.292171i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	2.70654	−	8.32988i	0.180037	−	0.554095i
$227$	−8.88697	−	6.45676i	−0.589849	−	0.428550i	0.252413	−	0.967620i	$-0.418776\pi$
$227$	−8.88697	−	6.45676i	−0.589849	−	0.428550i	−0.842261	+	0.539070i	$0.818776\pi$
$228$	−2.41258	−	7.42516i	−0.159777	−	0.491743i
$229$	−7.47849	−	5.43344i	−0.494193	−	0.359052i	0.312602	−	0.949884i	$-0.398799\pi$
$229$	−7.47849	−	5.43344i	−0.494193	−	0.359052i	−0.806794	+	0.590832i	$0.798799\pi$
$230$	0.775905	−	0.563728i	0.0511617	−	0.0371711i
$231$	−7.21358	+	22.2011i	−0.474619	+	1.46073i
$232$	−5.43153	+	3.94623i	−0.356597	+	0.259083i
$233$	0.307514	−	0.223422i	0.0201459	−	0.0146368i	−0.577667	−	0.816273i	$-0.696037\pi$
$233$	0.307514	−	0.223422i	0.0201459	−	0.0146368i	0.597813	+	0.801636i	$0.296037\pi$
$234$	1.49177	−	4.59119i	0.0975199	−	0.300135i
$235$	−3.15006	+	2.28865i	−0.205487	+	0.149295i
$236$	6.48159	+	4.70915i	0.421916	+	0.306540i
$237$	−5.42202	−	16.6873i	−0.352198	−	1.08395i
$238$	20.3200	+	14.7634i	1.31715	+	0.956967i
$239$	−0.137337	+	0.422679i	−0.00888358	+	0.0273409i	−0.955400	−	0.295315i	$-0.904576\pi$
$239$	−0.137337	+	0.422679i	−0.00888358	+	0.0273409i	0.946516	+	0.322656i	$0.104576\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	−2.81026	−	8.64908i	−0.181025	−	0.557136i	0.818833	−	0.574032i	$-0.194622\pi$
$241$	−2.81026	−	8.64908i	−0.181025	−	0.557136i	−0.999857	+	0.0168960i	$0.994622\pi$
$242$	−14.7767			−0.949882
$243$	1.00000			0.0641500
$244$	1.08408	+	3.33646i	0.0694013	+	0.213595i
$245$	11.4397	−	8.31141i	0.730854	−	0.530997i
$246$	6.03198	+	4.38249i	0.384585	+	0.279418i
$247$	37.6893			2.39811
$248$	1.21915	+	5.43265i	0.0774160	+	0.344974i
$249$	−0.0786019			−0.00498119
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	21.9017	−	15.9125i	1.38242	−	1.00439i	0.385773	−	0.922594i	$-0.373935\pi$
$251$	21.9017	−	15.9125i	1.38242	−	1.00439i	0.996649	−	0.0817947i	$-0.0260652\pi$
$252$	−1.42081	−	4.37281i	−0.0895028	−	0.275461i
$253$	−4.86928			−0.306129
$254$	21.4435			1.34549
$255$	1.68809	+	5.19539i	0.105712	+	0.325348i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	0.408653	−	1.25770i	0.0254911	−	0.0784535i	−0.937502	−	0.347981i	$-0.886867\pi$
$257$	0.408653	−	1.25770i	0.0254911	−	0.0784535i	0.962993	+	0.269527i	$0.0868674\pi$
$258$	−5.96022	−	4.33035i	−0.371067	−	0.269596i
$259$	2.62244	+	8.07103i	0.162950	+	0.501510i
$260$	−3.90550	−	2.83751i	−0.242209	−	0.175975i
$261$	5.43153	−	3.94623i	0.336203	−	0.244266i
$262$	−1.22252	+	3.76253i	−0.0755275	+	0.232450i
$263$	−8.79230	+	6.38798i	−0.542157	+	0.393900i	−0.824885	−	0.565300i	$-0.808760\pi$
$263$	−8.79230	+	6.38798i	−0.542157	+	0.393900i	0.282729	+	0.959200i	$0.408760\pi$
$264$	4.10744	−	2.98423i	0.252795	−	0.183667i
$265$	1.77764	−	5.47103i	0.109200	−	0.336082i
$266$	29.0410	−	21.0995i	1.78062	−	1.29370i
$267$	−13.0851	−	9.50691i	−0.800798	−	0.581814i
$268$	−1.71249	−	5.27050i	−0.104607	−	0.321947i
$269$	−3.54940	−	2.57879i	−0.216411	−	0.157231i	0.474299	−	0.880364i	$-0.342702\pi$
$269$	−3.54940	−	2.57879i	−0.216411	−	0.157231i	−0.690709	+	0.723132i	$0.742702\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	0.575506	−	1.77122i	0.0349595	−	0.107594i	−0.932054	−	0.362319i	$-0.881985\pi$
$271$	0.575506	−	1.77122i	0.0349595	−	0.107594i	0.967014	+	0.254725i	$0.0819850\pi$
$272$	−1.68809	−	5.19539i	−0.102355	−	0.315017i
$273$	22.1959			1.34336
$274$	−7.23854			−0.437296
$275$	1.56890	+	4.82859i	0.0946084	+	0.291175i
$276$	0.775905	−	0.563728i	0.0467040	−	0.0339324i
$277$	−21.5390	−	15.6490i	−1.29415	−	0.940258i	−0.294273	−	0.955721i	$-0.595077\pi$
$277$	−21.5390	−	15.6490i	−1.29415	−	0.940258i	−0.999880	+	0.0154639i	$0.995077\pi$
$278$	2.50219			0.150071
$279$	−1.21915	−	5.43265i	−0.0729885	−	0.325244i
$280$	−4.59785			−0.274774
$281$	−23.9712	−	17.4161i	−1.43000	−	1.03896i	−0.990016	−	0.140955i	$-0.954983\pi$
$281$	−23.9712	−	17.4161i	−1.43000	−	1.03896i	−0.439988	−	0.898004i	$-0.645017\pi$
$282$	−3.15006	+	2.28865i	−0.187583	+	0.136287i
$283$	8.86469	+	27.2827i	0.526951	+	1.62179i	0.760425	+	0.649426i	$0.224991\pi$
$283$	8.86469	+	27.2827i	0.526951	+	1.62179i	−0.233474	+	0.972363i	$0.575009\pi$
$284$	13.5736			0.805443
$285$	7.80728			0.462463
$286$	7.57381	+	23.3098i	0.447849	+	1.37834i
$287$	−10.5935	+	32.6035i	−0.625315	+	1.92452i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−10.3892	−	7.54819i	−0.611129	−	0.444011i
$290$	−2.07466	−	6.38514i	−0.121828	−	0.374948i
$291$	0.431560	+	0.313547i	0.0252985	+	0.0183804i
$292$	11.2893	−	8.20213i	0.660654	−	0.479993i
$293$	4.76773	−	14.6736i	0.278534	−	0.857239i	−0.709729	−	0.704475i	$-0.751183\pi$
$293$	4.76773	−	14.6736i	0.278534	−	0.857239i	0.988263	−	0.152764i	$-0.0488174\pi$
$294$	11.4397	−	8.31141i	0.667176	−	0.484731i
$295$	−6.48159	+	4.70915i	−0.377373	+	0.274177i
$296$	0.570362	−	1.75539i	0.0331516	−	0.102030i
$297$	−4.10744	+	2.98423i	−0.238338	+	0.173163i
$298$	−12.3882	−	9.00058i	−0.717631	−	0.521390i
$299$	1.43071	+	4.40328i	0.0827402	+	0.254648i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	10.4675	−	32.2156i	0.603335	−	1.85687i
$302$	2.42057	−	7.44976i	0.139288	−	0.428685i
$303$	−3.42507	−	10.5413i	−0.196765	−	0.605581i
$304$	−7.80728			−0.447778
$305$	−3.50817			−0.200877
$306$	1.68809	+	5.19539i	0.0965014	+	0.297001i
$307$	5.14525	−	3.73824i	0.293655	−	0.213353i	−0.431197	−	0.902258i	$-0.641908\pi$
$307$	5.14525	−	3.73824i	0.293655	−	0.213353i	0.724851	+	0.688905i	$0.241908\pi$
$308$	18.8854	+	13.7210i	1.07610	+	0.781829i
$309$	−9.90246			−0.563331
$310$	−5.54349	−	0.519301i	−0.314849	−	0.0294943i
$311$	32.5495			1.84571			0.922857	−	0.385142i	$-0.125848\pi$
$311$	32.5495			1.84571			0.922857	+	0.385142i	$0.125848\pi$
$312$	−3.90550	−	2.83751i	−0.221105	−	0.160642i
$313$	−16.9027	+	12.2805i	−0.955396	+	0.694136i	−0.952077	−	0.305858i	$-0.901057\pi$
$313$	−16.9027	+	12.2805i	−0.955396	+	0.694136i	−0.00331934	+	0.999994i	$0.501057\pi$
$314$	4.01982	+	12.3717i	0.226852	+	0.698178i
$315$	4.59785			0.259059
$316$	−17.5460			−0.987041
$317$	−4.42872	−	13.6302i	−0.248742	−	0.765549i	−0.994998	−	0.0998904i	$-0.968151\pi$
$317$	−4.42872	−	13.6302i	−0.248742	−	0.765549i	0.746257	−	0.665658i	$-0.231849\pi$
$318$	1.77764	−	5.47103i	0.0996853	−	0.306800i
$319$	−10.5332	+	32.4178i	−0.589746	+	1.81505i
$320$	0.809017	+	0.587785i	0.0452254	+	0.0328582i
$321$	1.88347	+	5.79671i	0.105125	+	0.323541i
$322$	3.56750	+	2.59194i	0.198809	+	0.144443i
$323$	−34.5040	+	25.0686i	−1.91985	+	1.39486i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	3.90550	−	2.83751i	0.216638	−	0.157397i
$326$	−10.7254	+	7.79244i	−0.594024	+	0.431584i
$327$	−2.98438	+	9.18498i	−0.165037	+	0.507931i
$328$	6.03198	−	4.38249i	0.333061	−	0.241983i
$329$	−14.4835	−	10.5229i	−0.798500	−	0.580144i
$330$	1.56890	+	4.82859i	0.0863652	+	0.265805i
$331$	−4.63590	−	3.36818i	−0.254812	−	0.185132i	0.453045	−	0.891488i	$-0.350338\pi$
$331$	−4.63590	−	3.36818i	−0.254812	−	0.185132i	−0.707857	+	0.706356i	$0.750338\pi$
$332$	−0.0242893	+	0.0747548i	−0.00133305	+	0.00410270i
$333$	−0.570362	+	1.75539i	−0.0312556	+	0.0961949i
$334$	−0.467685	−	1.43939i	−0.0255906	−	0.0787598i
$335$	5.54173			0.302777
$336$	−4.59785			−0.250833
$337$	8.00314	+	24.6311i	0.435959	+	1.34174i	0.892101	+	0.451837i	$0.149231\pi$
$337$	8.00314	+	24.6311i	0.435959	+	1.34174i	−0.456142	+	0.889907i	$0.650769\pi$
$338$	8.33641	−	6.05676i	0.453441	−	0.329444i
$339$	7.08582	+	5.14815i	0.384849	+	0.279609i
$340$	5.46276			0.296260
$341$	21.2199	+	18.6761i	1.14912	+	1.01137i
$342$	7.80728			0.422169
$343$	26.5598	+	19.2968i	1.43409	+	1.04193i
$344$	−5.96022	+	4.33035i	−0.321353	+	0.233477i
$345$	0.296369	+	0.912131i	0.0159560	+	0.0491075i
$346$	−0.298337			−0.0160387
$347$	19.2206			1.03182			0.515908	−	0.856644i	$-0.327454\pi$
$347$	19.2206			1.03182			0.515908	+	0.856644i	$0.327454\pi$
$348$	−2.07466	−	6.38514i	−0.111213	−	0.342279i
$349$	−5.21964	+	16.0644i	−0.279401	+	0.859908i	0.708620	+	0.705590i	$0.249318\pi$
$349$	−5.21964	+	16.0644i	−0.279401	+	0.859908i	−0.988021	+	0.154318i	$0.950682\pi$
$350$	1.42081	−	4.37281i	0.0759457	−	0.233737i
$351$	3.90550	+	2.83751i	0.208460	+	0.151455i
$352$	−1.56890	−	4.82859i	−0.0836228	−	0.257364i
$353$	−2.31102	−	1.67905i	−0.123003	−	0.0893669i	0.524583	−	0.851359i	$-0.324221\pi$
$353$	−2.31102	−	1.67905i	−0.123003	−	0.0893669i	−0.647586	+	0.761992i	$0.724221\pi$
$354$	−6.48159	+	4.70915i	−0.344493	+	0.250289i
$355$	−4.19446	+	12.9092i	−0.222619	+	0.685151i
$356$	−13.0851	+	9.50691i	−0.693511	+	0.503865i
$357$	−20.3200	+	14.7634i	−1.07545	+	0.781361i
$358$	0.893987	−	2.75141i	0.0472487	−	0.145417i
$359$	−5.06232	+	3.67799i	−0.267179	+	0.194117i	−0.713306	−	0.700853i	$-0.752803\pi$
$359$	−5.06232	+	3.67799i	−0.267179	+	0.194117i	0.446127	+	0.894970i	$0.352803\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	12.9644	+	39.9002i	0.682335	+	2.10001i
$362$	−18.7607	−	13.6304i	−0.986039	−	0.716399i
$363$	4.56625	−	14.0535i	0.239666	−	0.737616i
$364$	6.85892	−	21.1096i	0.359505	−	1.10644i
$365$	4.31211	+	13.2713i	0.225706	+	0.694653i
$366$	−3.50817			−0.183375
$367$	−4.83545			−0.252409			−0.126204	−	0.992004i	$-0.540279\pi$
$367$	−4.83545			−0.252409			−0.126204	+	0.992004i	$0.540279\pi$
$368$	−0.296369	−	0.912131i	−0.0154493	−	0.0475481i
$369$	−6.03198	+	4.38249i	−0.314013	+	0.228143i
$370$	1.49323	+	1.08489i	0.0776291	+	0.0564009i
$371$	26.4495			1.37319
$372$	−5.54349	−	0.519301i	−0.287417	−	0.0269245i
$373$	−33.8287			−1.75158			−0.875792	−	0.482688i	$-0.839660\pi$
$373$	−33.8287			−1.75158			−0.875792	+	0.482688i	$0.839660\pi$
$374$	−22.4380	−	16.3021i	−1.16024	−	0.842963i
$375$	0.809017	−	0.587785i	0.0417775	−	0.0303531i
$376$	1.20321	+	3.70311i	0.0620510	+	0.190973i
$377$	32.4103			1.66921
$378$	4.59785			0.236488
$379$	−3.32718	−	10.2400i	−0.170906	−	0.525994i	0.828517	−	0.559964i	$-0.189185\pi$
$379$	−3.32718	−	10.2400i	−0.170906	−	0.525994i	−0.999423	+	0.0339700i	$0.989185\pi$
$380$	2.41258	−	7.42516i	0.123763	−	0.380903i
$381$	−6.62642	+	20.3940i	−0.339482	+	1.04482i
$382$	−6.60499	−	4.79881i	−0.337941	−	0.245528i
$383$	−4.63268	−	14.2579i	−0.236719	−	0.728545i	−0.996889	−	0.0788212i	$-0.974884\pi$
$383$	−4.63268	−	14.2579i	−0.236719	−	0.728545i	0.760170	−	0.649724i	$-0.225116\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−18.8854	+	13.7210i	−0.962489	+	0.699289i
$386$	5.33612	−	16.4229i	0.271602	−	0.835903i
$387$	5.96022	−	4.33035i	0.302975	−	0.220124i
$388$	0.431560	−	0.313547i	0.0219092	−	0.0159179i
$389$	−2.61114	+	8.03625i	−0.132390	+	0.407454i	−0.995175	−	0.0981169i	$-0.968718\pi$
$389$	−2.61114	+	8.03625i	−0.132390	+	0.407454i	0.862785	+	0.505571i	$0.168718\pi$
$390$	3.90550	−	2.83751i	0.197763	−	0.143683i
$391$	−4.23858	−	3.07951i	−0.214354	−	0.155738i
$392$	−4.36957	−	13.4481i	−0.220697	−	0.679234i
$393$	−3.20060	−	2.32537i	−0.161449	−	0.117299i
$394$	1.34657	−	4.14431i	0.0678391	−	0.208787i
$395$	5.42202	−	16.6873i	0.272812	−	0.839627i
$396$	1.56890	+	4.82859i	0.0788403	+	0.242646i
$397$	17.3601			0.871277			0.435639	−	0.900122i	$-0.356523\pi$
$397$	17.3601			0.871277			0.435639	+	0.900122i	$0.356523\pi$
$398$	−2.52951			−0.126793
$399$	11.0927	+	34.1398i	0.555329	+	1.70913i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	2.84837	+	2.06946i	0.142241	+	0.103344i	0.656630	−	0.754213i	$-0.271981\pi$
$401$	2.84837	+	2.06946i	0.142241	+	0.103344i	−0.514389	+	0.857557i	$0.671981\pi$
$402$	5.54173			0.276396
$403$	10.6538	−	24.6765i	0.530704	−	1.22923i
$404$	−11.0838			−0.551438
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	24.9733	−	18.1442i	1.23941	−	0.900481i
$407$	−2.89577	−	8.91226i	−0.143538	−	0.441764i
$408$	5.46276			0.270447
$409$	4.83747			0.239198			0.119599	−	0.992822i	$-0.461839\pi$
$409$	4.83747			0.239198			0.119599	+	0.992822i	$0.461839\pi$
$410$	2.30401	+	7.09102i	0.113787	+	0.350201i
$411$	2.23683	−	6.88426i	0.110335	−	0.339576i
$412$	−3.06003	+	9.41780i	−0.150757	+	0.463982i
$413$	−29.8014	−	21.6520i	−1.46643	−	1.06542i
$414$	0.296369	+	0.912131i	0.0145658	+	0.0448288i
$415$	−0.0635902	−	0.0462010i	−0.00312152	−	0.00226792i
$416$	−3.90550	+	2.83751i	−0.191483	+	0.139120i
$417$	−0.773219	+	2.37972i	−0.0378647	+	0.116536i
$418$	−32.0679	+	23.2987i	−1.56849	+	1.13958i
$419$	20.4433	−	14.8529i	0.998720	−	0.725613i	0.0369069	−	0.999319i	$-0.488250\pi$
$419$	20.4433	−	14.8529i	0.998720	−	0.725613i	0.961813	+	0.273706i	$0.0882495\pi$
$420$	1.42081	−	4.37281i	0.0693286	−	0.213372i
$421$	16.2624	−	11.8153i	0.792582	−	0.575844i	−0.116147	−	0.993232i	$-0.537054\pi$
$421$	16.2624	−	11.8153i	0.792582	−	0.575844i	0.908728	+	0.417388i	$0.137054\pi$
$422$	−10.8038	−	7.84940i	−0.525919	−	0.382103i
$423$	−1.20321	−	3.70311i	−0.0585023	−	0.180052i
$424$	−4.65393	−	3.38128i	−0.226015	−	0.164209i
$425$	−1.68809	+	5.19539i	−0.0818842	+	0.252014i
$426$	−4.19446	+	12.9092i	−0.203222	+	0.625454i
$427$	−4.98445	−	15.3406i	−0.241214	−	0.742382i
$428$	6.09502			0.294614
$429$	−24.5094			−1.18332
$430$	−2.27660	−	7.00666i	−0.109787	−	0.337891i
$431$	−16.4067	+	11.9202i	−0.790283	+	0.574174i	−0.908047	−	0.418867i	$-0.862427\pi$
$431$	−16.4067	+	11.9202i	−0.790283	+	0.574174i	0.117764	+	0.993042i	$0.462427\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	21.5222			1.03429			0.517144	−	0.855898i	$-0.326995\pi$
$433$	21.5222			1.03429			0.517144	+	0.855898i	$0.326995\pi$
$434$	−5.60546	−	24.9785i	−0.269071	−	1.19901i
$435$	6.71373			0.321899
$436$	7.81321	+	5.67663i	0.374185	+	0.271861i
$437$	−6.05771	+	4.40118i	−0.289779	+	0.210537i
$438$	4.31211	+	13.2713i	0.206041	+	0.634128i
$439$	7.28526			0.347706			0.173853	−	0.984772i	$-0.444378\pi$
$439$	7.28526			0.347706			0.173853	+	0.984772i	$0.444378\pi$
$440$	5.07708			0.242040
$441$	4.36957	+	13.4481i	0.208075	+	0.640388i
$442$	−8.14917	+	25.0806i	−0.387616	+	1.19296i
$443$	−8.69339	+	26.7555i	−0.413035	+	1.27119i	0.500961	+	0.865470i	$0.332980\pi$
$443$	−8.69339	+	26.7555i	−0.413035	+	1.27119i	−0.913997	+	0.405722i	$0.867020\pi$
$444$	1.49323	+	1.08489i	0.0708654	+	0.0514867i
$445$	−4.99808	−	15.3825i	−0.236932	−	0.729201i
$446$	1.85824	+	1.35009i	0.0879901	+	0.0639286i
$447$	12.3882	−	9.00058i	0.585943	−	0.425713i
$448$	−1.42081	+	4.37281i	−0.0671271	+	0.206596i
$449$	24.4060	−	17.7320i	1.15179	−	0.836826i	0.163074	−	0.986614i	$-0.447859\pi$
$449$	24.4060	−	17.7320i	1.15179	−	0.836826i	0.988718	+	0.149788i	$0.0478591\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	11.6976	−	36.0017i	0.550821	−	1.69525i
$452$	7.08582	−	5.14815i	0.333289	−	0.242149i
$453$	6.33714	+	4.60420i	0.297745	+	0.216324i
$454$	−3.39452	−	10.4473i	−0.159313	−	0.490314i
$455$	17.9569	+	13.0464i	0.841832	+	0.611627i
$456$	2.41258	−	7.42516i	0.112979	−	0.347715i
$457$	0.234835	−	0.722747i	0.0109851	−	0.0338087i	−0.945414	−	0.325873i	$-0.894342\pi$
$457$	0.234835	−	0.722747i	0.0109851	−	0.0338087i	0.956399	+	0.292064i	$0.0943420\pi$
$458$	−2.85653	−	8.79149i	−0.133477	−	0.410800i
$459$	−5.46276			−0.254980
$460$	0.959072			0.0447169
$461$	−6.82083	−	20.9923i	−0.317678	−	0.977711i	−0.974638	−	0.223786i	$-0.928158\pi$
$461$	−6.82083	−	20.9923i	−0.317678	−	0.977711i	0.656961	−	0.753925i	$-0.271842\pi$
$462$	−18.8854	+	13.7210i	−0.878628	+	0.638361i
$463$	1.37350	+	0.997905i	0.0638319	+	0.0463766i	0.619244	−	0.785199i	$-0.287439\pi$
$463$	1.37350	+	0.997905i	0.0638319	+	0.0463766i	−0.555412	+	0.831575i	$0.687439\pi$
$464$	−6.71373			−0.311677
$465$	2.20692	−	5.11170i	0.102343	−	0.237050i
$466$	0.380108			0.0176082
$467$	6.36434	+	4.62396i	0.294506	+	0.213971i	0.725220	−	0.688517i	$-0.241738\pi$
$467$	6.36434	+	4.62396i	0.294506	+	0.213971i	−0.430714	+	0.902489i	$0.641738\pi$
$468$	3.90550	−	2.83751i	0.180532	−	0.131164i
$469$	7.87377	+	24.2330i	0.363577	+	1.11897i
$470$	−3.89368			−0.179602
$471$	−13.0084			−0.599396
$472$	2.47575	+	7.61957i	0.113956	+	0.350719i
$473$	−11.5585	+	35.5733i	−0.531459	+	1.63566i
$474$	5.42202	−	16.6873i	0.249042	−	0.766472i
$475$	6.31622	+	4.58900i	0.289808	+	0.210558i
$476$	7.76156	+	23.8876i	0.355751	+	1.09489i
$477$	4.65393	+	3.38128i	0.213089	+	0.154818i
$478$	−0.359553	+	0.261230i	−0.0164456	+	0.0119484i
$479$	−5.40002	+	16.6196i	−0.246733	+	0.759367i	0.748613	+	0.663007i	$0.230720\pi$
$479$	−5.40002	+	16.6196i	−0.246733	+	0.759367i	−0.995347	+	0.0963599i	$0.969280\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−7.20849	+	5.23727i	−0.328679	+	0.238799i
$482$	2.81026	−	8.64908i	0.128004	−	0.393955i
$483$	−3.56750	+	2.59194i	−0.162327	+	0.117937i
$484$	−11.9546	−	8.68552i	−0.543391	−	0.394797i
$485$	0.164841	+	0.507330i	0.00748506	+	0.0230367i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	3.06053	−	9.41936i	0.138686	−	0.426832i	−0.857459	−	0.514552i	$-0.827958\pi$
$487$	3.06053	−	9.41936i	0.138686	−	0.426832i	0.996145	+	0.0877203i	$0.0279582\pi$
$488$	−1.08408	+	3.33646i	−0.0490741	+	0.151035i
$489$	−4.09673	−	12.6084i	−0.185261	−	0.570173i
$490$	14.1402			0.638790
$491$	−6.18842			−0.279279			−0.139640	−	0.990202i	$-0.544594\pi$
$491$	−6.18842			−0.279279			−0.139640	+	0.990202i	$0.544594\pi$
$492$	2.30401	+	7.09102i	0.103873	+	0.319688i
$493$	−29.6711	+	21.5573i	−1.33632	+	0.970893i
$494$	30.4913	+	22.1532i	1.37187	+	0.996721i
$495$	−5.07708			−0.228198
$496$	−2.20692	+	5.11170i	−0.0990936	+	0.229522i
$497$	−62.4092			−2.79944
$498$	−0.0635902	−	0.0462010i	−0.00284955	−	0.00207032i
$499$	−11.9108	+	8.65367i	−0.533199	+	0.387392i	−0.821553	−	0.570132i	$-0.806892\pi$
$499$	−11.9108	+	8.65367i	−0.533199	+	0.387392i	0.288354	+	0.957524i	$0.406892\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	1.51346			0.0676165
$502$	27.0720			1.20828
$503$	−4.14240	−	12.7490i	−0.184701	−	0.568450i	0.815243	−	0.579120i	$-0.196604\pi$
$503$	−4.14240	−	12.7490i	−0.184701	−	0.568450i	−0.999943	+	0.0106699i	$0.996604\pi$
$504$	1.42081	−	4.37281i	0.0632881	−	0.194781i
$505$	3.42507	−	10.5413i	0.152414	−	0.469081i
$506$	−3.93933	−	2.86209i	−0.175125	−	0.127235i
$507$	3.18423	+	9.80004i	0.141416	+	0.435235i
$508$	17.3482	+	12.6042i	0.769701	+	0.559221i
$509$	7.75041	−	5.63100i	0.343531	−	0.249590i	−0.402619	−	0.915368i	$-0.631900\pi$
$509$	7.75041	−	5.63100i	0.343531	−	0.249590i	0.746150	+	0.665778i	$0.231900\pi$
$510$	−1.68809	+	5.19539i	−0.0747497	+	0.230056i
$511$	−51.9063	+	37.7122i	−2.29620	+	1.66829i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.41258	+	7.42516i	−0.106518	+	0.327829i
$514$	1.06987	−	0.777304i	0.0471898	−	0.0342854i
$515$	−8.01126	−	5.82052i	−0.353018	−	0.256483i
$516$	−2.27660	−	7.00666i	−0.100222	−	0.308451i
$517$	15.9931	+	11.6196i	0.703375	+	0.511032i
$518$	−2.62244	+	8.07103i	−0.115223	+	0.354621i
$519$	0.0921913	−	0.283736i	0.00404675	−	0.0124546i
$520$	−1.49177	−	4.59119i	−0.0654183	−	0.201337i
$521$	1.05196			0.0460871			0.0230436	−	0.999734i	$-0.492664\pi$
$521$	1.05196			0.0460871			0.0230436	+	0.999734i	$0.492664\pi$
$522$	6.71373			0.293852
$523$	−6.60835	−	20.3384i	−0.288963	−	0.889337i	−0.985183	−	0.171508i	$-0.945136\pi$
$523$	−6.60835	−	20.3384i	−0.288963	−	0.889337i	0.696220	−	0.717829i	$-0.254864\pi$
$524$	−3.20060	+	2.32537i	−0.139819	+	0.101584i
$525$	3.71974	+	2.70255i	0.162343	+	0.117949i
$526$	−10.8679			−0.473862
$527$	6.65992	+	29.6773i	0.290111	+	1.29276i
$528$	5.07708			0.220951
$529$	17.8632	+	12.9784i	0.776663	+	0.564278i
$530$	4.65393	−	3.38128i	0.202154	−	0.146873i
$531$	−2.47575	−	7.61957i	−0.107438	−	0.330661i
$532$	35.8967			1.55632
$533$	−35.9933			−1.55904
$534$	−4.99808	−	15.3825i	−0.216288	−	0.665666i
$535$	−1.88347	+	5.79671i	−0.0814293	+	0.250614i
$536$	1.71249	−	5.27050i	0.0739683	−	0.227651i
$537$	2.34049	+	1.70047i	0.101000	+	0.0733805i
$538$	−1.35575	−	4.17257i	−0.0584505	−	0.179892i
$539$	−58.0801	−	42.1977i	−2.50169	−	1.81758i
$540$	0.809017	−	0.587785i	0.0348145	−	0.0252942i
$541$	−5.45596	+	16.7917i	−0.234570	+	0.721933i	0.762608	+	0.646861i	$0.223919\pi$
$541$	−5.45596	+	16.7917i	−0.234570	+	0.721933i	−0.997178	+	0.0750717i	$0.976081\pi$
$542$	1.50669	−	1.09468i	0.0647180	−	0.0470204i
$543$	18.7607	−	13.6304i	0.805097	−	0.584938i
$544$	1.68809	−	5.19539i	0.0723761	−	0.222751i
$545$	−7.81321	+	5.67663i	−0.334681	+	0.243160i
$546$	17.9569	+	13.0464i	0.768484	+	0.558336i
$547$	−1.23883	−	3.81272i	−0.0529685	−	0.163020i	0.921073	−	0.389390i	$-0.127314\pi$
$547$	−1.23883	−	3.81272i	−0.0529685	−	0.163020i	−0.974041	+	0.226370i	$0.927314\pi$
$548$	−5.85610	−	4.25471i	−0.250160	−	0.181752i
$549$	1.08408	−	3.33646i	0.0462675	−	0.142397i
$550$	−1.56890	+	4.82859i	−0.0668982	+	0.205892i
$551$	16.1974	+	49.8506i	0.690034	+	2.12371i
$552$	0.959072			0.0408208
$553$	80.6740			3.43061
$554$	−8.22717	−	25.3206i	−0.349539	−	1.07577i
$555$	−1.49323	+	1.08489i	−0.0633839	+	0.0460511i
$556$	2.02431	+	1.47075i	0.0858500	+	0.0623737i
$557$	−30.8232			−1.30602			−0.653011	−	0.757348i	$-0.726495\pi$
$557$	−30.8232			−1.30602			−0.653011	+	0.757348i	$0.726495\pi$
$558$	2.20692	−	5.11170i	0.0934263	−	0.216396i
$559$	35.5650			1.50424
$560$	−3.71974	−	2.70255i	−0.157188	−	0.114204i
$561$	22.4380	−	16.3021i	0.947332	−	0.688277i
$562$	−9.15620	−	28.1799i	−0.386231	−	1.18870i
$563$	26.7682			1.12814			0.564072	−	0.825726i	$-0.309234\pi$
$563$	26.7682			1.12814			0.564072	+	0.825726i	$0.309234\pi$
$564$	−3.89368			−0.163954
$565$	2.70654	+	8.32988i	0.113865	+	0.350441i
$566$	−8.86469	+	27.2827i	−0.372611	+	1.14678i
$567$	−1.42081	+	4.37281i	−0.0596686	+	0.183641i
$568$	10.9812	+	7.97834i	0.460763	+	0.334764i
$569$	−1.06833	−	3.28799i	−0.0447868	−	0.137840i	0.926163	−	0.377124i	$-0.123087\pi$
$569$	−1.06833	−	3.28799i	−0.0447868	−	0.137840i	−0.970949	+	0.239285i	$0.923087\pi$
$570$	6.31622	+	4.58900i	0.264557	+	0.192212i
$571$	33.5450	−	24.3719i	1.40382	−	1.01993i	0.409631	−	0.912251i	$-0.365658\pi$
$571$	33.5450	−	24.3719i	1.40382	−	1.01993i	0.994186	−	0.107681i	$-0.0343425\pi$
$572$	−7.57381	+	23.3098i	−0.316677	+	0.974632i
$573$	6.60499	−	4.79881i	0.275927	−	0.200473i
$574$	−27.7342	+	20.1500i	−1.15760	+	0.841047i
$575$	−0.296369	+	0.912131i	−0.0123595	+	0.0380385i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−11.5527	−	8.39351i	−0.480944	−	0.349426i	0.320747	−	0.947165i	$-0.396066\pi$
$577$	−11.5527	−	8.39351i	−0.480944	−	0.349426i	−0.801691	+	0.597739i	$0.796066\pi$
$578$	−3.96832	−	12.2132i	−0.165060	−	0.508003i
$579$	13.9702	+	10.1499i	0.580580	+	0.421816i
$580$	2.07466	−	6.38514i	0.0861455	−	0.265129i
$581$	0.111679	−	0.343711i	0.00463321	−	0.0142595i
$582$	0.164841	+	0.507330i	0.00683290	+	0.0210295i
$583$	−29.2063			−1.20960
$584$	13.9543			0.577433
$585$	1.49177	+	4.59119i	0.0616770	+	0.189822i
$586$	12.4821	−	9.06876i	0.515630	−	0.374627i
$587$	−9.41355	−	6.83934i	−0.388539	−	0.282290i	0.376318	−	0.926491i	$-0.377190\pi$
$587$	−9.41355	−	6.83934i	−0.388539	−	0.282290i	−0.764856	+	0.644201i	$0.777190\pi$
$588$	14.1402			0.583133
$589$	43.2796	+	4.05433i	1.78330	+	0.167056i
$590$	−8.01169			−0.329836
$591$	3.52536	+	2.56132i	0.145014	+	0.105359i
$592$	1.49323	−	1.08489i	0.0613712	−	0.0445888i
$593$	9.29484	+	28.6066i	0.381693	+	1.17473i	0.938851	+	0.344324i	$0.111892\pi$
$593$	9.29484	+	28.6066i	0.381693	+	1.17473i	−0.557157	+	0.830407i	$0.688108\pi$
$594$	−5.07708			−0.208315
$595$	−25.1170			−1.02969
$596$	−4.73188	−	14.5632i	−0.193826	−	0.596534i
$597$	0.781661	−	2.40570i	0.0319912	−	0.0984589i
$598$	−1.43071	+	4.40328i	−0.0585062	+	0.180063i
$599$	−32.1046	−	23.3254i	−1.31176	−	0.953049i	−0.999996	−	0.00288868i	$-0.999081\pi$
$599$	−32.1046	−	23.3254i	−1.31176	−	0.953049i	−0.311763	−	0.950160i	$-0.600919\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	−11.1746	−	8.11881i	−0.455821	−	0.331173i	0.336069	−	0.941837i	$-0.390903\pi$
$601$	−11.1746	−	8.11881i	−0.455821	−	0.331173i	−0.791890	+	0.610664i	$0.790903\pi$
$602$	27.4042	−	19.9103i	1.11691	−	0.811484i
$603$	−1.71249	+	5.27050i	−0.0697379	+	0.214631i
$604$	6.33714	−	4.60420i	0.257855	−	0.187342i
$605$	11.9546	−	8.68552i	0.486024	−	0.353117i
$606$	3.42507	−	10.5413i	0.139134	−	0.428211i
$607$	7.27605	−	5.28636i	0.295326	−	0.214567i	−0.430249	−	0.902710i	$-0.641574\pi$
$607$	7.27605	−	5.28636i	0.295326	−	0.214567i	0.725575	+	0.688144i	$0.241574\pi$
$608$	−6.31622	−	4.58900i	−0.256156	−	0.186109i
$609$	9.53897	+	29.3579i	0.386538	+	1.18964i
$610$	−2.83817	−	2.06205i	−0.114914	−	0.0834899i
$611$	5.80847	−	17.8766i	0.234986	−	0.723211i
$612$	−1.68809	+	5.19539i	−0.0682368	+	0.210011i
$613$	4.11881	+	12.6764i	0.166357	+	0.511995i	0.999134	−	0.0416143i	$-0.0132501\pi$
$613$	4.11881	+	12.6764i	0.166357	+	0.511995i	−0.832776	+	0.553609i	$0.813250\pi$
$614$	6.35987			0.256664
$615$	−7.45594			−0.300653
$616$	7.21358	+	22.2011i	0.290643	+	0.894508i
$617$	−9.99339	+	7.26063i	−0.402319	+	0.292302i	−0.770485	−	0.637458i	$-0.779986\pi$
$617$	−9.99339	+	7.26063i	−0.402319	+	0.292302i	0.368166	+	0.929760i	$0.379986\pi$
$618$	−8.01126	−	5.82052i	−0.322260	−	0.234136i
$619$	38.0732			1.53029			0.765145	−	0.643858i	$-0.222667\pi$
$619$	38.0732			1.53029			0.765145	+	0.643858i	$0.222667\pi$
$620$	−4.17954	−	3.67851i	−0.167854	−	0.147732i
$621$	−0.959072			−0.0384862
$622$	26.3331	+	19.1321i	1.05586	+	0.767129i
$623$	60.1635	−	43.7114i	2.41040	−	1.75126i
$624$	−1.49177	−	4.59119i	−0.0597185	−	0.183795i
$625$	1.00000			0.0400000
$626$	−20.8929			−0.835047
$627$	−12.2489	−	37.6981i	−0.489172	−	1.50552i
$628$	−4.01982	+	12.3717i	−0.160408	+	0.493686i
$629$	3.11575	−	9.58929i	0.124233	−	0.382350i
$630$	3.71974	+	2.70255i	0.148198	+	0.107672i
$631$	−7.76738	−	23.9055i	−0.309214	−	0.951664i	−0.978071	−	0.208273i	$-0.933216\pi$
$631$	−7.76738	−	23.9055i	−0.309214	−	0.951664i	0.668856	−	0.743392i	$-0.266784\pi$
$632$	−14.1950	−	10.3133i	−0.564648	−	0.410241i
$633$	10.8038	−	7.84940i	0.429411	−	0.311986i
$634$	4.42872	−	13.6302i	0.175887	−	0.541325i
$635$	−17.3482	+	12.6042i	−0.688442	+	0.500182i
$636$	4.65393	−	3.38128i	0.184540	−	0.134076i
$637$	−21.0939	+	64.9204i	−0.835771	+	2.57224i
$638$	−27.5763	+	20.0353i	−1.09175	+	0.793206i
$639$	−10.9812	−	7.97834i	−0.434411	−	0.315618i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−5.09309	−	3.70034i	−0.201165	−	0.146155i	0.482642	−	0.875817i	$-0.339677\pi$
$641$	−5.09309	−	3.70034i	−0.201165	−	0.146155i	−0.683807	+	0.729663i	$0.739677\pi$
$642$	−1.88347	+	5.79671i	−0.0743344	+	0.228778i
$643$	−4.00485	+	12.3257i	−0.157936	+	0.486077i	−0.998447	−	0.0557183i	$-0.982255\pi$
$643$	−4.00485	+	12.3257i	−0.157936	+	0.486077i	0.840511	+	0.541795i	$0.182255\pi$
$644$	1.36266	+	4.19384i	0.0536964	+	0.165261i
$645$	7.36724			0.290085
$646$	−42.6493			−1.67801
$647$	−2.84398	−	8.75288i	−0.111809	−	0.344111i	0.879460	−	0.475974i	$-0.157904\pi$
$647$	−2.84398	−	8.75288i	−0.111809	−	0.344111i	−0.991268	+	0.131863i	$0.957904\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	32.9075	+	23.9087i	1.29173	+	0.938499i
$650$	4.82746			0.189349
$651$	25.4882	+	2.38767i	0.998959	+	0.0935802i
$652$	−13.2573			−0.519196
$653$	−6.30236	−	4.57893i	−0.246630	−	0.179187i	0.457602	−	0.889157i	$-0.348709\pi$
$653$	−6.30236	−	4.57893i	−0.246630	−	0.179187i	−0.704232	+	0.709970i	$0.748709\pi$
$654$	−7.81321	+	5.67663i	−0.305521	+	0.221974i
$655$	−1.22252	−	3.76253i	−0.0477678	−	0.147014i
$656$	7.45594			0.291106
$657$	−13.9543			−0.544409
$658$	−5.53220	−	17.0264i	−0.215668	−	0.663756i
$659$	−11.8083	+	36.3422i	−0.459986	+	1.41569i	0.405194	+	0.914231i	$0.367204\pi$
$659$	−11.8083	+	36.3422i	−0.459986	+	1.41569i	−0.865180	+	0.501462i	$0.832796\pi$
$660$	−1.56890	+	4.82859i	−0.0610695	+	0.187952i
$661$	−13.6083	−	9.88703i	−0.529303	−	0.384561i	0.290794	−	0.956786i	$-0.406081\pi$
$661$	−13.6083	−	9.88703i	−0.529303	−	0.384561i	−0.820097	+	0.572225i	$0.806081\pi$
$662$	−1.77076	−	5.44982i	−0.0688224	−	0.211813i
$663$	−21.3348	−	15.5006i	−0.828575	−	0.601995i
$664$	−0.0635902	+	0.0462010i	−0.00246778	+	0.00179295i
$665$	−11.0927	+	34.1398i	−0.430156	+	1.32388i
$666$	−1.49323	+	1.08489i	−0.0578613	+	0.0420387i
$667$	−5.20922	+	3.78472i	−0.201702	+	0.146545i
$668$	0.467685	−	1.43939i	0.0180953	−	0.0556916i
$669$	−1.85824	+	1.35009i	−0.0718436	+	0.0521975i
$670$	4.48335	+	3.25735i	0.173207	+	0.125842i
$671$	5.50397	+	16.9395i	0.212478	+	0.653941i
$672$	−3.71974	−	2.70255i	−0.143492	−	0.104253i
$673$	−6.99508	+	21.5286i	−0.269641	+	0.829868i	0.720947	+	0.692990i	$0.243707\pi$
$673$	−6.99508	+	21.5286i	−0.269641	+	0.829868i	−0.990588	+	0.136878i	$0.956293\pi$
$674$	−8.00314	+	24.6311i	−0.308270	+	0.948756i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	10.3044			0.396322
$677$	32.0416			1.23146			0.615730	−	0.787957i	$-0.288861\pi$
$677$	32.0416			1.23146			0.615730	+	0.787957i	$0.288861\pi$
$678$	2.70654	+	8.32988i	0.103944	+	0.319907i
$679$	−1.98425	+	1.44164i	−0.0761485	+	0.0553251i
$680$	4.41947	+	3.21093i	0.169479	+	0.123134i
$681$	10.9849			0.420942
$682$	6.18971	+	27.5820i	0.237016	+	1.05617i
$683$	−41.1535			−1.57469			−0.787347	−	0.616510i	$-0.788546\pi$
$683$	−41.1535			−1.57469			−0.787347	+	0.616510i	$0.788546\pi$
$684$	6.31622	+	4.58900i	0.241507	+	0.175465i
$685$	5.85610	−	4.25471i	0.223750	−	0.162564i
$686$	10.1449	+	31.2229i	0.387335	+	1.19209i
$687$	9.24392			0.352678
$688$	−7.36724			−0.280873
$689$	8.58151	+	26.4112i	0.326929	+	1.00619i
$690$	−0.296369	+	0.912131i	−0.0112826	+	0.0347242i
$691$	−5.28396	+	16.2624i	−0.201011	+	0.618649i	0.798842	+	0.601541i	$0.205446\pi$
$691$	−5.28396	+	16.2624i	−0.201011	+	0.618649i	−0.999854	+	0.0171088i	$0.994554\pi$
$692$	−0.241360	−	0.175358i	−0.00917513	−	0.00666612i
$693$	−7.21358	−	22.2011i	−0.274021	−	0.843350i
$694$	15.5498	+	11.2976i	0.590263	+	0.428851i
$695$	−2.02431	+	1.47075i	−0.0767866	+	0.0557887i
$696$	2.07466	−	6.38514i	0.0786397	−	0.242028i
$697$	32.9513	−	23.9405i	1.24812	−	0.906811i
$698$	−13.6652	+	9.92835i	−0.517235	+	0.375793i
$699$	−0.117460	+	0.361504i	−0.00444274	+	0.0136733i
$700$	3.71974	−	2.70255i	0.140593	−	0.102147i
$701$	−1.82168	−	1.32353i	−0.0688039	−	0.0499890i	0.552852	−	0.833280i	$-0.313540\pi$
$701$	−1.82168	−	1.32353i	−0.0688039	−	0.0499890i	−0.621656	+	0.783291i	$0.713540\pi$
$702$	1.49177	+	4.59119i	0.0563031	+	0.173283i
$703$	−11.6580	−	8.47005i	−0.439691	−	0.319454i
$704$	1.56890	−	4.82859i	0.0591302	−	0.181984i
$705$	1.20321	−	3.70311i	0.0453157	−	0.139467i
$706$	−0.882730	−	2.71676i	−0.0332220	−	0.102247i
$707$	50.9615			1.91660
$708$	−8.01169			−0.301098
$709$	−3.80018	−	11.6958i	−0.142719	−	0.439243i	0.853992	−	0.520286i	$-0.174175\pi$
$709$	−3.80018	−	11.6958i	−0.142719	−	0.439243i	−0.996711	+	0.0810433i	$0.974175\pi$
$710$	−10.9812	+	7.97834i	−0.412119	+	0.299422i
$711$	14.1950	+	10.3133i	0.532355	+	0.386779i
$712$	−16.1741			−0.606151
$713$	1.16925	+	5.21030i	0.0437888	+	0.195127i
$714$	−25.1170			−0.939978
$715$	−19.8285	−	14.4063i	−0.741544	−	0.538763i
$716$	2.34049	−	1.70047i	0.0874682	−	0.0635494i
$717$	−0.137337	−	0.422679i	−0.00512894	−	0.0157853i
$718$	−6.25737			−0.233523
$719$	10.1686			0.379225			0.189612	−	0.981859i	$-0.439277\pi$
$719$	10.1686			0.379225			0.189612	+	0.981859i	$0.439277\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	14.0696	−	43.3016i	0.523977	−	1.61264i
$722$	−12.9644	+	39.9002i	−0.482484	+	1.48493i
$723$	7.35735	+	5.34543i	0.273623	+	0.198799i
$724$	−7.16594	−	22.0545i	−0.266320	−	0.819649i
$725$	5.43153	+	3.94623i	0.201722	+	0.146559i
$726$	11.9546	−	8.68552i	0.443677	−	0.322350i
$727$	10.8060	−	33.2574i	0.400772	−	1.23345i	−0.523602	−	0.851963i	$-0.675412\pi$
$727$	10.8060	−	33.2574i	0.400772	−	1.23345i	0.924374	−	0.381487i	$-0.124588\pi$
$728$	17.9569	−	13.0464i	0.665527	−	0.483533i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−4.31211	+	13.2713i	−0.159598	+	0.491194i
$731$	−32.5592	+	23.6557i	−1.20425	+	0.874937i
$732$	−2.83817	−	2.06205i	−0.104902	−	0.0762155i
$733$	−1.20436	−	3.70664i	−0.0444841	−	0.136908i	0.926348	−	0.376669i	$-0.122931\pi$
$733$	−1.20436	−	3.70664i	−0.0444841	−	0.136908i	−0.970832	+	0.239762i	$0.922931\pi$
$734$	−3.91196	−	2.84221i	−0.144393	−	0.104908i
$735$	−4.36957	+	13.4481i	−0.161174	+	0.496042i
$736$	0.296369	−	0.912131i	0.0109243	−	0.0336216i
$737$	−8.69444	−	26.7587i	−0.320264	−	0.985670i
$738$	−7.45594			−0.274457
$739$	16.6585			0.612792			0.306396	−	0.951904i	$-0.400877\pi$
$739$	16.6585			0.612792			0.306396	+	0.951904i	$0.400877\pi$
$740$	0.570362	+	1.75539i	0.0209669	+	0.0645295i
$741$	−30.4913	+	22.1532i	−1.12013	+	0.813819i
$742$	21.3981	+	15.5466i	0.785548	+	0.570734i
$743$	9.66019			0.354398			0.177199	−	0.984175i	$-0.443296\pi$
$743$	9.66019			0.354398			0.177199	+	0.984175i	$0.443296\pi$
$744$	−4.17954	−	3.67851i	−0.153229	−	0.134861i
$745$	15.3127			0.561014
$746$	−27.3680	−	19.8840i	−1.00201	−	0.728006i
$747$	0.0635902	−	0.0462010i	0.00232665	−	0.00169041i
$748$	−8.57054	−	26.3774i	−0.313370	−	0.964454i
$749$	−28.0240			−1.02397
$750$	1.00000			0.0365148
$751$	−1.41556	−	4.35663i	−0.0516544	−	0.158976i	0.921902	−	0.387424i	$-0.126635\pi$
$751$	−1.41556	−	4.35663i	−0.0516544	−	0.158976i	−0.973556	+	0.228448i	$0.926635\pi$
$752$	−1.20321	+	3.70311i	−0.0438767	+	0.135039i
$753$	−8.36570	+	25.7470i	−0.304863	+	0.938272i
$754$	26.2205	+	19.0503i	0.954893	+	0.693771i
$755$	2.42057	+	7.44976i	0.0880937	+	0.271124i
$756$	3.71974	+	2.70255i	0.135286	+	0.0982907i
$757$	1.22952	−	0.893298i	0.0446876	−	0.0324675i	−0.565217	−	0.824942i	$-0.691208\pi$
$757$	1.22952	−	0.893298i	0.0446876	−	0.0324675i	0.609905	+	0.792475i	$0.291208\pi$
$758$	3.32718	−	10.2400i	0.120849	−	0.371934i
$759$	3.93933	−	2.86209i	0.142989	−	0.103887i
$760$	6.31622	−	4.58900i	0.229113	−	0.166461i
$761$	5.51041	−	16.9593i	0.199752	−	0.614774i	−0.800136	−	0.599819i	$-0.795239\pi$
$761$	5.51041	−	16.9593i	0.199752	−	0.614774i	0.999888	−	0.0149555i	$-0.00476068\pi$
$762$	−17.3482	+	12.6042i	−0.628458	+	0.456602i
$763$	−35.9240	−	26.1003i	−1.30053	−	0.944894i
$764$	−2.52288	−	7.76463i	−0.0912747	−	0.280914i
$765$	−4.41947	−	3.21093i	−0.159786	−	0.116091i
$766$	4.63268	−	14.2579i	0.167385	−	0.515159i
$767$	11.9516	−	36.7832i	0.431546	−	1.32816i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−4.08938			−0.147467			−0.0737334	−	0.997278i	$-0.523491\pi$
$769$	−4.08938			−0.147467			−0.0737334	+	0.997278i	$0.523491\pi$
$770$	−23.3436			−0.841246
$771$	0.408653	+	1.25770i	0.0147173	+	0.0452951i
$772$	13.9702	−	10.1499i	0.502797	−	0.365303i
$773$	−15.7839	−	11.4677i	−0.567708	−	0.412464i	0.266564	−	0.963817i	$-0.414112\pi$
$773$	−15.7839	−	11.4677i	−0.567708	−	0.412464i	−0.834272	+	0.551353i	$0.814112\pi$
$774$	7.36724			0.264810
$775$	4.79002	−	2.83826i	0.172063	−	0.101953i
$776$	0.533438			0.0191493
$777$	−6.86563	−	4.98817i	−0.246303	−	0.178950i
$778$	−6.83604	+	4.96667i	−0.245084	+	0.178064i
$779$	−17.9881	−	55.3616i	−0.644489	−	1.98353i
$780$	4.82746			0.172851
$781$	68.9140			2.46594
$782$	−1.61900	−	4.98276i	−0.0578952	−	0.178183i
$783$	−2.07466	+	6.38514i	−0.0741422	+	0.228186i
$784$	4.36957	−	13.4481i	0.156056	−	0.480291i
$785$	−10.5240	−	7.64616i	−0.375619	−	0.272903i
$786$	−1.22252	−	3.76253i	−0.0436058	−	0.134205i
$787$	−12.7132	−	9.23665i	−0.453175	−	0.329251i	0.337673	−	0.941264i	$-0.390360\pi$
$787$	−12.7132	−	9.23665i	−0.453175	−	0.329251i	−0.790848	+	0.612012i	$0.790360\pi$
$788$	3.52536	−	2.56132i	0.125586	−	0.0912434i
$789$	3.35836	−	10.3360i	0.119561	−	0.367970i
$790$	14.1950	−	10.3133i	0.505037	−	0.366931i
$791$	−32.5795	+	23.6704i	−1.15839	+	0.841623i
$792$	−1.56890	+	4.82859i	−0.0557485	+	0.171576i
$793$	13.7011	−	9.95446i	0.486542	−	0.353493i
$794$	14.0446	+	10.2040i	0.498424	+	0.362126i
$795$	1.77764	+	5.47103i	0.0630465	+	0.194037i
$796$	−2.04641	−	1.48681i	−0.0725332	−	0.0526985i
$797$	−16.0218	+	49.3100i	−0.567521	+	1.74665i	0.0928190	+	0.995683i	$0.470412\pi$
$797$	−16.0218	+	49.3100i	−0.567521	+	1.74665i	−0.660340	+	0.750967i	$0.729588\pi$
$798$	−11.0927	+	34.1398i	−0.392677	+	1.20853i
$799$	6.57287	+	20.2292i	0.232531	+	0.715658i
$800$	−1.00000			−0.0353553
$801$	16.1741			0.571485
$802$	1.08798	+	3.34846i	0.0384179	+	0.118238i
$803$	57.3164	−	41.6428i	2.02265	−	1.46954i
$804$	4.48335	+	3.25735i	0.158116	+	0.114878i
$805$	−4.40967			−0.155420
$806$	23.1236	−	13.7016i	0.814495	−	0.482618i
$807$	4.38730			0.154440
$808$	−8.96696	−	6.51488i	−0.315456	−	0.229193i
$809$	7.03529	−	5.11144i	0.247348	−	0.179709i	−0.457203	−	0.889362i	$-0.651149\pi$
$809$	7.03529	−	5.11144i	0.247348	−	0.179709i	0.704551	+	0.709654i	$0.251149\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	−15.6600			−0.549898			−0.274949	−	0.961459i	$-0.588661\pi$
$811$	−15.6600			−0.549898			−0.274949	+	0.961459i	$0.588661\pi$
$812$	30.8687			1.08328
$813$	0.575506	+	1.77122i	0.0201839	+	0.0621196i
$814$	2.89577	−	8.91226i	0.101497	−	0.312375i
$815$	4.09673	−	12.6084i	0.143502	−	0.441654i
$816$	4.41947	+	3.21093i	0.154712	+	0.112405i
$817$	17.7741	+	54.7029i	0.621835	+	1.91381i
$818$	3.91360	+	2.84339i	0.136836	+	0.0994170i
$819$	−17.9569	+	13.0464i	−0.627464	+	0.455880i
$820$	−2.30401	+	7.09102i	−0.0804596	+	0.247629i
$821$	35.6620	−	25.9100i	1.24461	−	0.904264i	0.246716	−	0.969088i	$-0.420649\pi$
$821$	35.6620	−	25.9100i	1.24461	−	0.904264i	0.997897	+	0.0648239i	$0.0206486\pi$
$822$	5.85610	−	4.25471i	0.204255	−	0.148400i
$823$	9.38306	−	28.8781i	0.327073	−	1.00663i	−0.643423	−	0.765511i	$-0.722486\pi$
$823$	9.38306	−	28.8781i	0.327073	−	1.00663i	0.970496	−	0.241117i	$-0.0775136\pi$
$824$	−8.01126	+	5.82052i	−0.279085	+	0.202767i
$825$	−4.10744	−	2.98423i	−0.143003	−	0.103898i
$826$	−11.3831	−	35.0336i	−0.396069	−	1.21898i
$827$	−9.94129	−	7.22277i	−0.345693	−	0.251160i	0.401367	−	0.915917i	$-0.368535\pi$
$827$	−9.94129	−	7.22277i	−0.345693	−	0.251160i	−0.747060	+	0.664757i	$0.768535\pi$
$828$	−0.296369	+	0.912131i	−0.0102996	+	0.0316988i
$829$	−11.0022	+	33.8614i	−0.382124	+	1.17606i	0.556421	+	0.830900i	$0.312174\pi$
$829$	−11.0022	+	33.8614i	−0.382124	+	1.17606i	−0.938545	+	0.345156i	$0.887826\pi$
$830$	−0.0242893	−	0.0747548i	−0.000843094	−	0.00259478i
$831$	26.6237			0.923565
$832$	−4.82746			−0.167362
$833$	−23.8699	−	73.4640i	−0.827043	−	2.54538i
$834$	−2.02431	+	1.47075i	−0.0700963	+	0.0509279i
$835$	1.22442	+	0.889590i	0.0423727	+	0.0307855i
$836$	−39.6381			−1.37091
$837$	4.17954	+	3.67851i	0.144466	+	0.127148i
$838$	25.2693			0.872914
$839$	−19.2729	−	14.0026i	−0.665374	−	0.483423i	0.203099	−	0.979158i	$-0.434899\pi$
$839$	−19.2729	−	14.0026i	−0.665374	−	0.483423i	−0.868474	+	0.495735i	$0.834899\pi$
$840$	3.71974	−	2.70255i	0.128343	−	0.0932468i
$841$	4.96721	+	15.2875i	0.171283	+	0.527155i
$842$	20.1015			0.692742
$843$	29.6301			1.02051
$844$	−4.12667	−	12.7006i	−0.142046	−	0.437173i
$845$	−3.18423	+	9.80004i	−0.109541	+	0.337132i
$846$	1.20321	−	3.70311i	0.0413674	−	0.127316i
$847$	54.9654	+	39.9347i	1.88863	+	1.37217i
$848$	−1.77764	−	5.47103i	−0.0610445	−	0.187876i
$849$	−23.2081	−	16.8616i	−0.796499	−	0.578690i
$850$	−4.41947	+	3.21093i	−0.151586	+	0.110134i
$851$	0.547018	−	1.68355i	0.0187515	−	0.0577113i
$852$	−10.9812	+	7.97834i	−0.376211	+	0.273333i
$853$	13.3822	−	9.72276i	0.458199	−	0.332901i	−0.334626	−	0.942351i	$-0.608610\pi$
$853$	13.3822	−	9.72276i	0.458199	−	0.332901i	0.792824	+	0.609450i	$0.208610\pi$
$854$	4.98445	−	15.3406i	0.170564	−	0.524943i
$855$	−6.31622	+	4.58900i	−0.216010	+	0.156941i
$856$	4.93098	+	3.58256i	0.168537	+	0.122450i
$857$	−2.62479	−	8.07828i	−0.0896612	−	0.275949i	0.896164	−	0.443722i	$-0.146342\pi$
$857$	−2.62479	−	8.07828i	−0.0896612	−	0.275949i	−0.985826	+	0.167773i	$0.946342\pi$
$858$	−19.8285	−	14.4063i	−0.676934	−	0.491821i
$859$	11.8704	−	36.5332i	0.405012	−	1.24650i	−0.515874	−	0.856665i	$-0.672533\pi$
$859$	11.8704	−	36.5332i	0.405012	−	1.24650i	0.920886	−	0.389833i	$-0.127467\pi$
$860$	2.27660	−	7.00666i	0.0776315	−	0.238925i
$861$	−10.5935	−	32.6035i	−0.361026	−	1.11112i
$862$	−20.2798			−0.690733
$863$	−23.7772			−0.809384			−0.404692	−	0.914453i	$-0.632621\pi$
$863$	−23.7772			−0.809384			−0.404692	+	0.914453i	$0.632621\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	0.241360	−	0.175358i	0.00820649	−	0.00596236i
$866$	17.4118	+	12.6504i	0.591677	+	0.429878i
$867$	12.8418			0.436129
$868$	10.1471	−	23.5028i	0.344414	−	0.797738i
$869$	−89.0825			−3.02192
$870$	5.43153	+	3.94623i	0.184146	+	0.133790i
$871$	−21.6432	+	15.7247i	−0.733352	+	0.532812i
$872$	2.98438	+	9.18498i	0.101064	+	0.311043i
$873$	−0.533438			−0.0180541
$874$	−7.48774			−0.253276
$875$	1.42081	+	4.37281i	0.0480323	+	0.147828i
$876$	−4.31211	+	13.2713i	−0.145693	+	0.448396i
$877$	15.4833	−	47.6526i	0.522832	−	1.60911i	−0.245730	−	0.969338i	$-0.579028\pi$
$877$	15.4833	−	47.6526i	0.522832	−	1.60911i	0.768563	−	0.639774i	$-0.220972\pi$
$878$	5.89390	+	4.28217i	0.198909	+	0.144516i
$879$	4.76773	+	14.6736i	0.160812	+	0.494927i
$880$	4.10744	+	2.98423i	0.138462	+	0.100598i
$881$	35.6202	−	25.8796i	1.20008	−	0.871906i	0.205784	−	0.978598i	$-0.434026\pi$
$881$	35.6202	−	25.8796i	1.20008	−	0.871906i	0.994292	+	0.106692i	$0.0340257\pi$
$882$	−4.36957	+	13.4481i	−0.147131	+	0.452823i
$883$	−15.2565	+	11.0845i	−0.513423	+	0.373024i	−0.814121	−	0.580696i	$-0.802781\pi$
$883$	−15.2565	+	11.0845i	−0.513423	+	0.373024i	0.300698	+	0.953720i	$0.402781\pi$
$884$	−21.3348	+	15.5006i	−0.717567	+	0.521343i
$885$	2.47575	−	7.61957i	0.0832213	−	0.256129i
$886$	−22.7596	+	16.5358i	−0.764623	+	0.555531i
$887$	−20.3566	−	14.7900i	−0.683509	−	0.496598i	0.191011	−	0.981588i	$-0.438823\pi$
$887$	−20.3566	−	14.7900i	−0.683509	−	0.496598i	−0.874520	+	0.484990i	$0.838823\pi$
$888$	0.570362	+	1.75539i	0.0191401	+	0.0589071i
$889$	−79.7643	−	57.9522i	−2.67521	−	1.94365i
$890$	4.99808	−	15.3825i	0.167536	−	0.515623i
$891$	1.56890	−	4.82859i	0.0525602	−	0.161764i
$892$	0.709784	+	2.18449i	0.0237653	+	0.0731421i
$893$	30.3991			1.01727
$894$	15.3127			0.512133
$895$	0.893987	+	2.75141i	0.0298827	+	0.0919695i
$896$	−3.71974	+	2.70255i	−0.124268	+	0.0902858i
$897$	−3.74565	−	2.72138i	−0.125064	−	0.0908641i
$898$	30.1675			1.00670
$899$	37.2175	+	3.48645i	1.24127	+	0.116280i
$900$	1.00000			0.0333333
$901$	−25.4233	−	18.4711i	−0.846974	−	0.615362i
$902$	30.6248	−	22.2502i	1.01970	−	0.740852i
$903$	10.4675	+	32.2156i	0.348336	+	1.07207i
$904$	8.75856			0.291305
$905$	23.1895			0.770844
$906$	2.42057	+	7.44976i	0.0804181	+	0.247502i
$907$	−12.6780	+	39.0190i	−0.420967	+	1.29560i	0.485836	+	0.874050i	$0.338515\pi$
$907$	−12.6780	+	39.0190i	−0.420967	+	1.29560i	−0.906803	+	0.421554i	$0.861485\pi$
$908$	3.39452	−	10.4473i	0.112651	−	0.346704i
$909$	8.96696	+	6.51488i	0.297415	+	0.216085i
$910$	6.85892	+	21.1096i	0.227371	+	0.699776i
$911$	−10.2409	−	7.44043i	−0.339295	−	0.246513i	0.405069	−	0.914286i	$-0.367247\pi$
$911$	−10.2409	−	7.44043i	−0.339295	−	0.246513i	−0.744365	+	0.667773i	$0.767247\pi$
$912$	6.31622	−	4.58900i	0.209151	−	0.151957i
$913$	−0.123319	+	0.379536i	−0.00408125	+	0.0125608i
$914$	0.614806	−	0.446682i	0.0203360	−	0.0147749i
$915$	2.83817	−	2.06205i	0.0938269	−	0.0681692i
$916$	2.85653	−	8.79149i	0.0943824	−	0.290479i
$917$	14.7159	−	10.6917i	0.485960	−	0.353071i
$918$	−4.41947	−	3.21093i	−0.145864	−	0.105976i
$919$	2.44980	+	7.53972i	0.0808116	+	0.248713i	0.983297	−	0.182008i	$-0.0582596\pi$
$919$	2.44980	+	7.53972i	0.0808116	+	0.248713i	−0.902486	+	0.430720i	$0.858260\pi$
$920$	0.775905	+	0.563728i	0.0255808	+	0.0185856i
$921$	−1.96531	+	6.04860i	−0.0647591	+	0.199308i
$922$	6.82083	−	20.9923i	0.224632	−	0.691346i
$923$	−20.2486	−	62.3188i	−0.666491	−	2.05125i
$924$	−23.3436			−0.767949
$925$	−1.84573			−0.0606872
$926$	0.524630	+	1.61464i	0.0172404	+	0.0530605i
$927$	8.01126	−	5.82052i	0.263124	−	0.191171i
$928$	−5.43153	−	3.94623i	−0.178299	−	0.129541i
$929$	−6.12230			−0.200866			−0.100433	−	0.994944i	$-0.532023\pi$
$929$	−6.12230			−0.200866			−0.100433	+	0.994944i	$0.532023\pi$
$930$	4.79002	−	2.83826i	0.157071	−	0.0930702i
$931$	−110.397			−3.61810
$932$	0.307514	+	0.223422i	0.0100729	+	0.00731842i
$933$	−26.3331	+	19.1321i	−0.862108	+	0.626358i
$934$	2.43096	+	7.48173i	0.0795435	+	0.244810i
$935$	27.7348			0.907026
$936$	4.82746			0.157790
$937$	−7.95730	−	24.4900i	−0.259954	−	0.800055i	−0.992813	−	0.119675i	$-0.961815\pi$
$937$	−7.95730	−	24.4900i	−0.259954	−	0.800055i	0.732859	−	0.680380i	$-0.238185\pi$
$938$	−7.87377	+	24.2330i	−0.257088	+	0.791234i
$939$	6.45625	−	19.8703i	0.210692	−	0.648443i
$940$	−3.15006	−	2.28865i	−0.102744	−	0.0746475i
$941$	−12.1556	−	37.4111i	−0.396261	−	1.21957i	−0.927975	−	0.372642i	$-0.878452\pi$
$941$	−12.1556	−	37.4111i	−0.396261	−	1.21957i	0.531714	−	0.846924i	$-0.321548\pi$
$942$	−10.5240	−	7.64616i	−0.342891	−	0.249125i
$943$	5.78511	−	4.20312i	0.188389	−	0.136873i
$944$	−2.47575	+	7.61957i	−0.0805787	+	0.247996i
$945$	−3.71974	+	2.70255i	−0.121003	+	0.0879139i
$946$	−30.2605	+	21.9855i	−0.983853	+	0.714811i
$947$	−12.0229	+	37.0027i	−0.390692	+	1.20243i	0.541573	+	0.840653i	$0.317829\pi$
$947$	−12.0229	+	37.0027i	−0.390692	+	1.20243i	−0.932266	+	0.361774i	$0.882171\pi$
$948$	14.1950	−	10.3133i	0.461033	−	0.334960i
$949$	−54.4985	−	39.5954i	−1.76909	−	1.28532i
$950$	2.41258	+	7.42516i	0.0782745	+	0.240904i
$951$	11.5945	+	8.42393i	0.375979	+	0.273165i
$952$	−7.76156	+	23.8876i	−0.251554	+	0.774203i
$953$	11.9739	−	36.8519i	0.387873	−	1.19375i	−0.546501	−	0.837458i	$-0.684041\pi$
$953$	11.9739	−	36.8519i	0.387873	−	1.19375i	0.934375	−	0.356292i	$-0.115959\pi$
$954$	1.77764	+	5.47103i	0.0575534	+	0.177131i
$955$	8.16422			0.264188
$956$	−0.444432			−0.0143739
$957$	−10.5332	−	32.4178i	−0.340490	−	1.04792i
$958$	−14.1374	+	10.2714i	−0.456760	+	0.331855i
$959$	26.9255	+	19.5625i	0.869469	+	0.631706i
$960$	−1.00000			−0.0322749
$961$	14.8886	−	27.1906i	0.480276	−	0.877117i
$962$	−8.91018			−0.287276
$963$	−4.93098	−	3.58256i	−0.158898	−	0.115447i
$964$	7.35735	−	5.34543i	0.236964	−	0.172165i
$965$	5.33612	+	16.4229i	0.171776	+	0.528672i
$966$	−4.40967			−0.141879
$967$	−26.6251			−0.856206			−0.428103	−	0.903730i	$-0.640818\pi$
$967$	−26.6251			−0.856206			−0.428103	+	0.903730i	$0.640818\pi$
$968$	−4.56625	−	14.0535i	−0.146765	−	0.451696i
$969$	13.1794	−	40.5619i	0.423382	−	1.30304i
$970$	−0.164841	+	0.507330i	−0.00529274	+	0.0162894i
$971$	8.31212	+	6.03911i	0.266749	+	0.193804i	0.713117	−	0.701045i	$-0.247283\pi$
$971$	8.31212	+	6.03911i	0.266749	+	0.193804i	−0.446368	+	0.894849i	$0.647283\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−9.30749	−	6.76229i	−0.298384	−	0.216789i
$974$	8.01258	−	5.82148i	0.256740	−	0.186532i
$975$	−1.49177	+	4.59119i	−0.0477748	+	0.147036i
$976$	−2.83817	+	2.06205i	−0.0908475	+	0.0660046i
$977$	−24.1014	+	17.5107i	−0.771072	+	0.560217i	−0.902286	−	0.431137i	$-0.858112\pi$
$977$	−24.1014	+	17.5107i	−0.771072	+	0.560217i	0.131214	+	0.991354i	$0.458112\pi$
$978$	4.09673	−	12.6084i	0.130999	−	0.403173i
$979$	−66.4343	+	48.2673i	−2.12325	+	1.54263i
$980$	11.4397	+	8.31141i	0.365427	+	0.265498i
$981$	−2.98438	−	9.18498i	−0.0952839	−	0.293254i
$982$	−5.00654	−	3.63746i	−0.159765	−	0.116076i
$983$	−6.40093	+	19.7000i	−0.204158	+	0.628334i	0.795589	+	0.605837i	$0.207162\pi$
$983$	−6.40093	+	19.7000i	−0.204158	+	0.628334i	−0.999747	+	0.0224970i	$0.992838\pi$
$984$	−2.30401	+	7.09102i	−0.0734492	+	0.226054i
$985$	1.34657	+	4.14431i	0.0429052	+	0.132049i
$986$	−36.6755			−1.16799
$987$	17.9026			0.569845
$988$	11.6466	+	35.8447i	0.370529	+	1.14037i
$989$	−5.71628	+	4.15312i	−0.181767	+	0.132061i
$990$	−4.10744	−	2.98423i	−0.130543	−	0.0948451i
$991$	40.1082			1.27408			0.637040	−	0.770831i	$-0.280159\pi$
$991$	40.1082			1.27408			0.637040	+	0.770831i	$0.280159\pi$
$992$	−4.79002	+	2.83826i	−0.152083	+	0.0901149i
$993$	5.73028			0.181845
$994$	−50.4901	−	36.6832i	−1.60145	−	1.16352i
$995$	2.04641	−	1.48681i	0.0648757	−	0.0471350i
$996$	−0.0242893	−	0.0747548i	−0.000769636	−	0.00236870i
$997$	3.04049			0.0962932			0.0481466	−	0.998840i	$-0.484669\pi$
$997$	3.04049			0.0962932			0.0481466	+	0.998840i	$0.484669\pi$
$998$	−14.7225			−0.466033
$999$	−0.570362	−	1.75539i	−0.0180454	−	0.0555382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.h.901.1	yes	16
31.16	even	5	inner	930.2.n.h.481.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.h.481.1	✓	16	31.16	even	5	inner
930.2.n.h.901.1	yes	16	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-1.42081 - 4.37281i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(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} +(-1.42081 - 4.37281i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.56890 + 4.82859i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(3.90550 - 2.83751i) q^{13} +(1.42081 - 4.37281i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.68809 + 5.19539i) q^{17} +(0.809017 - 0.587785i) q^{18} +(6.31622 + 4.58900i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(3.71974 + 2.70255i) q^{21} +(-1.56890 + 4.82859i) q^{22} +(-0.296369 + 0.912131i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +4.82746 q^{26} +(0.309017 + 0.951057i) q^{27} +(3.71974 - 2.70255i) q^{28} +(5.43153 + 3.94623i) q^{29} +1.00000 q^{30} +(4.79002 - 2.83826i) q^{31} -1.00000 q^{32} +(-4.10744 - 2.98423i) q^{33} +(-4.41947 + 3.21093i) q^{34} +(1.42081 + 4.37281i) q^{35} +1.00000 q^{36} -1.84573 q^{37} +(2.41258 + 7.42516i) q^{38} +(-1.49177 + 4.59119i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-6.03198 - 4.38249i) q^{41} +(1.42081 + 4.37281i) q^{42} +(5.96022 + 4.33035i) q^{43} +(-4.10744 + 2.98423i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-0.775905 + 0.563728i) q^{46} +(3.15006 - 2.28865i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-11.4397 + 8.31141i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.68809 - 5.19539i) q^{51} +(3.90550 + 2.83751i) q^{52} +(-1.77764 + 5.47103i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.56890 - 4.82859i) q^{55} +4.59785 q^{56} -7.80728 q^{57} +(2.07466 + 6.38514i) q^{58} +(6.48159 - 4.70915i) q^{59} +(0.809017 + 0.587785i) q^{60} +3.50817 q^{61} +(5.54349 + 0.519301i) q^{62} -4.59785 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-3.90550 + 2.83751i) q^{65} +(-1.56890 - 4.82859i) q^{66} -5.54173 q^{67} -5.46276 q^{68} +(-0.296369 - 0.912131i) q^{69} +(-1.42081 + 4.37281i) q^{70} +(4.19446 - 12.9092i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-4.31211 - 13.2713i) q^{73} +(-1.49323 - 1.08489i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(-2.41258 + 7.42516i) q^{76} +(18.8854 - 13.7210i) q^{77} +(-3.90550 + 2.83751i) q^{78} +(-5.42202 + 16.6873i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.30401 - 7.09102i) q^{82} +(0.0635902 + 0.0462010i) q^{83} +(-1.42081 + 4.37281i) q^{84} +(1.68809 - 5.19539i) q^{85} +(2.27660 + 7.00666i) q^{86} -6.71373 q^{87} -5.07708 q^{88} +(4.99808 + 15.3825i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-17.9569 - 13.0464i) q^{91} -0.959072 q^{92} +(-2.20692 + 5.11170i) q^{93} +3.89368 q^{94} +(-6.31622 - 4.58900i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-0.164841 - 0.507330i) q^{97} -14.1402 q^{98} +5.07708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

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