LMFDB - Embedded newform 150.2.g.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.g (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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	150.31
Dual form			150.2.g.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.690983 + 2.12663i) q^{5} +(0.809017 + 0.587785i) q^{6} +0.381966 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.690983 + 2.12663i) q^{5} +(0.809017 + 0.587785i) q^{6} +0.381966 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-1.80902 + 1.31433i) q^{10} +(0.427051 + 1.31433i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(0.763932 - 2.35114i) q^{13} +(0.118034 + 0.363271i) q^{14} +(1.80902 + 1.31433i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.61803 + 1.90211i) q^{17} +1.00000 q^{18} +(-6.23607 - 4.53077i) q^{19} +(-1.80902 - 1.31433i) q^{20} +(0.309017 - 0.224514i) q^{21} +(-1.11803 + 0.812299i) q^{22} +(-1.38197 - 4.25325i) q^{23} -1.00000 q^{24} +(-4.04508 + 2.93893i) q^{25} +2.47214 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.309017 + 0.224514i) q^{28} +(0.381966 - 0.277515i) q^{29} +(-0.690983 + 2.12663i) q^{30} +(-3.54508 - 2.57565i) q^{31} +1.00000 q^{32} +(1.11803 + 0.812299i) q^{33} +(-1.00000 + 3.07768i) q^{34} +(0.263932 + 0.812299i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.47214 - 7.60845i) q^{37} +(2.38197 - 7.33094i) q^{38} +(-0.763932 - 2.35114i) q^{39} +(0.690983 - 2.12663i) q^{40} +(-2.38197 + 7.33094i) q^{41} +(0.309017 + 0.224514i) q^{42} +5.70820 q^{43} +(-1.11803 - 0.812299i) q^{44} +2.23607 q^{45} +(3.61803 - 2.62866i) q^{46} +(9.47214 - 6.88191i) q^{47} +(-0.309017 - 0.951057i) q^{48} -6.85410 q^{49} +(-4.04508 - 2.93893i) q^{50} +3.23607 q^{51} +(0.763932 + 2.35114i) q^{52} +(-7.35410 + 5.34307i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-2.50000 + 1.81636i) q^{55} +(-0.309017 - 0.224514i) q^{56} -7.70820 q^{57} +(0.381966 + 0.277515i) q^{58} +(-0.427051 + 1.31433i) q^{59} -2.23607 q^{60} +(2.23607 + 6.88191i) q^{61} +(1.35410 - 4.16750i) q^{62} +(0.118034 - 0.363271i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.52786 q^{65} +(-0.427051 + 1.31433i) q^{66} +(8.47214 + 6.15537i) q^{67} -3.23607 q^{68} +(-3.61803 - 2.62866i) q^{69} +(-0.690983 + 0.502029i) q^{70} +(-11.7082 + 8.50651i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(3.85410 + 11.8617i) q^{73} +8.00000 q^{74} +(-1.54508 + 4.75528i) q^{75} +7.70820 q^{76} +(0.163119 + 0.502029i) q^{77} +(2.00000 - 1.45309i) q^{78} +(2.73607 - 1.98787i) q^{79} +2.23607 q^{80} +(-0.809017 - 0.587785i) q^{81} -7.70820 q^{82} +(-7.16312 - 5.20431i) q^{83} +(-0.118034 + 0.363271i) q^{84} +(-2.23607 + 6.88191i) q^{85} +(1.76393 + 5.42882i) q^{86} +(0.145898 - 0.449028i) q^{87} +(0.427051 - 1.31433i) q^{88} +(3.85410 + 11.8617i) q^{89} +(0.690983 + 2.12663i) q^{90} +(0.291796 - 0.898056i) q^{91} +(3.61803 + 2.62866i) q^{92} -4.38197 q^{93} +(9.47214 + 6.88191i) q^{94} +(5.32624 - 16.3925i) q^{95} +(0.809017 - 0.587785i) q^{96} +(4.54508 - 3.30220i) q^{97} +(-2.11803 - 6.51864i) q^{98} +1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + 5 q^{5} + q^{6} + 6 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 + 5 * q^5 + q^6 + 6 * q^7 - q^8 - q^9	$ 4 q - q^{2} + q^{3} - q^{4} + 5 q^{5} + q^{6} + 6 q^{7} - q^{8} - q^{9} - 5 q^{10} - 5 q^{11} + q^{12} + 12 q^{13} - 4 q^{14} + 5 q^{15} - q^{16} + 6 q^{17} + 4 q^{18} - 16 q^{19} - 5 q^{20} - q^{21} - 10 q^{23} - 4 q^{24} - 5 q^{25} - 8 q^{26} + q^{27} + q^{28} + 6 q^{29} - 5 q^{30} - 3 q^{31} + 4 q^{32} - 4 q^{34} + 10 q^{35} - q^{36} - 8 q^{37} + 14 q^{38} - 12 q^{39} + 5 q^{40} - 14 q^{41} - q^{42} - 4 q^{43} + 10 q^{46} + 20 q^{47} + q^{48} - 14 q^{49} - 5 q^{50} + 4 q^{51} + 12 q^{52} - 16 q^{53} + q^{54} - 10 q^{55} + q^{56} - 4 q^{57} + 6 q^{58} + 5 q^{59} - 8 q^{62} - 4 q^{63} - q^{64} + 40 q^{65} + 5 q^{66} + 16 q^{67} - 4 q^{68} - 10 q^{69} - 5 q^{70} - 20 q^{71} - q^{72} + 2 q^{73} + 32 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} + 8 q^{78} + 2 q^{79} - q^{81} - 4 q^{82} - 13 q^{83} + 4 q^{84} + 16 q^{86} + 14 q^{87} - 5 q^{88} + 2 q^{89} + 5 q^{90} + 28 q^{91} + 10 q^{92} - 22 q^{93} + 20 q^{94} - 10 q^{95} + q^{96} + 7 q^{97} - 4 q^{98} + 10 q^{99}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + 5 * q^5 + q^6 + 6 * q^7 - q^8 - q^9 - 5 * q^10 - 5 * q^11 + q^12 + 12 * q^13 - 4 * q^14 + 5 * q^15 - q^16 + 6 * q^17 + 4 * q^18 - 16 * q^19 - 5 * q^20 - q^21 - 10 * q^23 - 4 * q^24 - 5 * q^25 - 8 * q^26 + q^27 + q^28 + 6 * q^29 - 5 * q^30 - 3 * q^31 + 4 * q^32 - 4 * q^34 + 10 * q^35 - q^36 - 8 * q^37 + 14 * q^38 - 12 * q^39 + 5 * q^40 - 14 * q^41 - q^42 - 4 * q^43 + 10 * q^46 + 20 * q^47 + q^48 - 14 * q^49 - 5 * q^50 + 4 * q^51 + 12 * q^52 - 16 * q^53 + q^54 - 10 * q^55 + q^56 - 4 * q^57 + 6 * q^58 + 5 * q^59 - 8 * q^62 - 4 * q^63 - q^64 + 40 * q^65 + 5 * q^66 + 16 * q^67 - 4 * q^68 - 10 * q^69 - 5 * q^70 - 20 * q^71 - q^72 + 2 * q^73 + 32 * q^74 + 5 * q^75 + 4 * q^76 - 15 * q^77 + 8 * q^78 + 2 * q^79 - q^81 - 4 * q^82 - 13 * q^83 + 4 * q^84 + 16 * q^86 + 14 * q^87 - 5 * q^88 + 2 * q^89 + 5 * q^90 + 28 * q^91 + 10 * q^92 - 22 * q^93 + 20 * q^94 - 10 * q^95 + q^96 + 7 * q^97 - 4 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	0.381966			0.144370			0.0721848	−	0.997391i	$-0.477003\pi$
$7$	0.381966			0.144370			0.0721848	+	0.997391i	$0.477003\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−1.80902	+	1.31433i	−0.572061	+	0.415627i
$11$	0.427051	+	1.31433i	0.128761	+	0.396285i	0.994567	−	0.104094i	$-0.0331942\pi$
$11$	0.427051	+	1.31433i	0.128761	+	0.396285i	−0.865807	+	0.500378i	$0.833194\pi$
$12$	−0.309017	+	0.951057i	−0.0892055	+	0.274546i
$13$	0.763932	−	2.35114i	0.211877	−	0.652089i	−0.787484	−	0.616335i	$-0.788617\pi$
$13$	0.763932	−	2.35114i	0.211877	−	0.652089i	0.999361	−	0.0357541i	$-0.0113833\pi$
$14$	0.118034	+	0.363271i	0.0315459	+	0.0970883i
$15$	1.80902	+	1.31433i	0.467086	+	0.339358i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.61803	+	1.90211i	0.634967	+	0.461330i	0.858117	−	0.513454i	$-0.171634\pi$
$17$	2.61803	+	1.90211i	0.634967	+	0.461330i	−0.223151	+	0.974784i	$0.571634\pi$
$18$	1.00000			0.235702
$19$	−6.23607	−	4.53077i	−1.43065	−	1.03943i	−0.989895	−	0.141803i	$-0.954710\pi$
$19$	−6.23607	−	4.53077i	−1.43065	−	1.03943i	−0.440757	−	0.897626i	$-0.645290\pi$
$20$	−1.80902	−	1.31433i	−0.404508	−	0.293893i
$21$	0.309017	−	0.224514i	0.0674330	−	0.0489930i
$22$	−1.11803	+	0.812299i	−0.238366	+	0.173183i
$23$	−1.38197	−	4.25325i	−0.288160	−	0.886865i	−0.985434	−	0.170060i	$-0.945604\pi$
$23$	−1.38197	−	4.25325i	−0.288160	−	0.886865i	0.697274	−	0.716805i	$-0.254396\pi$
$24$	−1.00000			−0.204124
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	2.47214			0.484826
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.309017	+	0.224514i	−0.0583987	+	0.0424292i
$29$	0.381966	−	0.277515i	0.0709293	−	0.0515332i	−0.551756	−	0.834006i	$-0.686042\pi$
$29$	0.381966	−	0.277515i	0.0709293	−	0.0515332i	0.622685	+	0.782473i	$0.286042\pi$
$30$	−0.690983	+	2.12663i	−0.126156	+	0.388267i
$31$	−3.54508	−	2.57565i	−0.636716	−	0.462601i	0.222004	−	0.975046i	$-0.428740\pi$
$31$	−3.54508	−	2.57565i	−0.636716	−	0.462601i	−0.858720	+	0.512444i	$0.828740\pi$
$32$	1.00000			0.176777
$33$	1.11803	+	0.812299i	0.194625	+	0.141403i
$34$	−1.00000	+	3.07768i	−0.171499	+	0.527818i
$35$	0.263932	+	0.812299i	0.0446127	+	0.137304i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.47214	−	7.60845i	0.406417	−	1.25082i	−0.513290	−	0.858215i	$-0.671573\pi$
$37$	2.47214	−	7.60845i	0.406417	−	1.25082i	0.919707	−	0.392607i	$-0.128427\pi$
$38$	2.38197	−	7.33094i	0.386406	−	1.18924i
$39$	−0.763932	−	2.35114i	−0.122327	−	0.376484i
$40$	0.690983	−	2.12663i	0.109254	−	0.336249i
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	0.573479	+	0.819220i	$0.305593\pi$
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	−0.945480	+	0.325680i	$0.894407\pi$
$42$	0.309017	+	0.224514i	0.0476824	+	0.0346433i
$43$	5.70820			0.870493			0.435246	−	0.900311i	$-0.356661\pi$
$43$	5.70820			0.870493			0.435246	+	0.900311i	$0.356661\pi$
$44$	−1.11803	−	0.812299i	−0.168550	−	0.122459i
$45$	2.23607			0.333333
$46$	3.61803	−	2.62866i	0.533450	−	0.387574i
$47$	9.47214	−	6.88191i	1.38165	−	1.00383i	0.384929	−	0.922946i	$-0.374226\pi$
$47$	9.47214	−	6.88191i	1.38165	−	1.00383i	0.996724	−	0.0808837i	$-0.0257742\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−6.85410			−0.979157
$50$	−4.04508	−	2.93893i	−0.572061	−	0.415627i
$51$	3.23607			0.453140
$52$	0.763932	+	2.35114i	0.105938	+	0.326045i
$53$	−7.35410	+	5.34307i	−1.01016	+	0.733927i	−0.964243	−	0.265018i	$-0.914622\pi$
$53$	−7.35410	+	5.34307i	−1.01016	+	0.733927i	−0.0459202	+	0.998945i	$0.514622\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−2.50000	+	1.81636i	−0.337100	+	0.244917i
$56$	−0.309017	−	0.224514i	−0.0412941	−	0.0300019i
$57$	−7.70820			−1.02098
$58$	0.381966	+	0.277515i	0.0501546	+	0.0364394i
$59$	−0.427051	+	1.31433i	−0.0555973	+	0.171111i	−0.974999	−	0.222209i	$-0.928673\pi$
$59$	−0.427051	+	1.31433i	−0.0555973	+	0.171111i	0.919402	+	0.393320i	$0.128673\pi$
$60$	−2.23607			−0.288675
$61$	2.23607	+	6.88191i	0.286299	+	0.881138i	0.986006	+	0.166708i	$0.0533138\pi$
$61$	2.23607	+	6.88191i	0.286299	+	0.881138i	−0.699707	+	0.714430i	$0.746686\pi$
$62$	1.35410	−	4.16750i	0.171971	−	0.529273i
$63$	0.118034	−	0.363271i	0.0148709	−	0.0457679i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.52786			0.685647
$66$	−0.427051	+	1.31433i	−0.0525663	+	0.161783i
$67$	8.47214	+	6.15537i	1.03504	+	0.751998i	0.969310	−	0.245840i	$-0.0790638\pi$
$67$	8.47214	+	6.15537i	1.03504	+	0.751998i	0.0657257	+	0.997838i	$0.479064\pi$
$68$	−3.23607			−0.392431
$69$	−3.61803	−	2.62866i	−0.435560	−	0.316453i
$70$	−0.690983	+	0.502029i	−0.0825883	+	0.0600039i
$71$	−11.7082	+	8.50651i	−1.38951	+	1.00954i	−0.393589	+	0.919286i	$0.628767\pi$
$71$	−11.7082	+	8.50651i	−1.38951	+	1.00954i	−0.995919	+	0.0902503i	$0.971233\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	3.85410	+	11.8617i	0.451089	+	1.38831i	0.875667	+	0.482916i	$0.160422\pi$
$73$	3.85410	+	11.8617i	0.451089	+	1.38831i	−0.424578	+	0.905391i	$0.639578\pi$
$74$	8.00000			0.929981
$75$	−1.54508	+	4.75528i	−0.178411	+	0.549093i
$76$	7.70820			0.884192
$77$	0.163119	+	0.502029i	0.0185891	+	0.0572115i
$78$	2.00000	−	1.45309i	0.226455	−	0.164529i
$79$	2.73607	−	1.98787i	0.307832	−	0.223653i	−0.423134	−	0.906067i	$-0.639070\pi$
$79$	2.73607	−	1.98787i	0.307832	−	0.223653i	0.730966	+	0.682414i	$0.239070\pi$
$80$	2.23607			0.250000
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−7.70820			−0.851229
$83$	−7.16312	−	5.20431i	−0.786254	−	0.571247i	0.120595	−	0.992702i	$-0.461520\pi$
$83$	−7.16312	−	5.20431i	−0.786254	−	0.571247i	−0.906850	+	0.421454i	$0.861520\pi$
$84$	−0.118034	+	0.363271i	−0.0128786	+	0.0396361i
$85$	−2.23607	+	6.88191i	−0.242536	+	0.746448i
$86$	1.76393	+	5.42882i	0.190210	+	0.585405i
$87$	0.145898	−	0.449028i	0.0156419	−	0.0481409i
$88$	0.427051	−	1.31433i	0.0455238	−	0.140108i
$89$	3.85410	+	11.8617i	0.408534	+	1.25734i	0.917908	+	0.396793i	$0.129877\pi$
$89$	3.85410	+	11.8617i	0.408534	+	1.25734i	−0.509374	+	0.860545i	$0.670123\pi$
$90$	0.690983	+	2.12663i	0.0728360	+	0.224166i
$91$	0.291796	−	0.898056i	0.0305885	−	0.0941418i
$92$	3.61803	+	2.62866i	0.377206	+	0.274056i
$93$	−4.38197			−0.454389
$94$	9.47214	+	6.88191i	0.976976	+	0.709815i
$95$	5.32624	−	16.3925i	0.546460	−	1.68183i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	4.54508	−	3.30220i	0.461483	−	0.335287i	−0.332629	−	0.943058i	$-0.607936\pi$
$97$	4.54508	−	3.30220i	0.461483	−	0.335287i	0.794113	+	0.607770i	$0.207936\pi$
$98$	−2.11803	−	6.51864i	−0.213954	−	0.658482i
$99$	1.38197			0.138893
$100$	1.54508	−	4.75528i	0.154508	−	0.475528i
$101$	6.61803			0.658519			0.329259	−	0.944239i	$-0.393201\pi$
$101$	6.61803			0.658519			0.329259	+	0.944239i	$0.393201\pi$
$102$	1.00000	+	3.07768i	0.0990148	+	0.304736i
$103$	1.07295	−	0.779543i	0.105721	−	0.0768107i	−0.533669	−	0.845694i	$-0.679187\pi$
$103$	1.07295	−	0.779543i	0.105721	−	0.0768107i	0.639390	+	0.768883i	$0.279187\pi$
$104$	−2.00000	+	1.45309i	−0.196116	+	0.142487i
$105$	0.690983	+	0.502029i	0.0674330	+	0.0489930i
$106$	−7.35410	−	5.34307i	−0.714294	−	0.518965i
$107$	−9.38197			−0.906989			−0.453494	−	0.891259i	$-0.649823\pi$
$107$	−9.38197			−0.906989			−0.453494	+	0.891259i	$0.649823\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	3.94427	−	12.1392i	0.377793	−	1.16273i	−0.563782	−	0.825923i	$-0.690654\pi$
$109$	3.94427	−	12.1392i	0.377793	−	1.16273i	0.941575	−	0.336803i	$-0.109346\pi$
$110$	−2.50000	−	1.81636i	−0.238366	−	0.173183i
$111$	−2.47214	−	7.60845i	−0.234645	−	0.722162i
$112$	0.118034	−	0.363271i	0.0111532	−	0.0343259i
$113$	−4.56231	+	14.0413i	−0.429186	+	1.32090i	0.469743	+	0.882803i	$0.344346\pi$
$113$	−4.56231	+	14.0413i	−0.429186	+	1.32090i	−0.898929	+	0.438095i	$0.855654\pi$
$114$	−2.38197	−	7.33094i	−0.223092	−	0.686605i
$115$	8.09017	−	5.87785i	0.754412	−	0.548113i
$116$	−0.145898	+	0.449028i	−0.0135463	+	0.0416912i
$117$	−2.00000	−	1.45309i	−0.184900	−	0.134338i
$118$	−1.38197			−0.127220
$119$	1.00000	+	0.726543i	0.0916698	+	0.0666020i
$120$	−0.690983	−	2.12663i	−0.0630778	−	0.194134i
$121$	7.35410	−	5.34307i	0.668555	−	0.485733i
$122$	−5.85410	+	4.25325i	−0.530005	+	0.385072i
$123$	2.38197	+	7.33094i	0.214775	+	0.661008i
$124$	4.38197			0.393512
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$	0.381966			0.0340282
$127$	3.51722	+	10.8249i	0.312103	+	0.960554i	0.976931	+	0.213557i	$0.0685050\pi$
$127$	3.51722	+	10.8249i	0.312103	+	0.960554i	−0.664828	+	0.746997i	$0.731495\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	4.61803	−	3.35520i	0.406595	−	0.295409i
$130$	1.70820	+	5.25731i	0.149819	+	0.461097i
$131$	−14.4721	−	10.5146i	−1.26444	−	0.918667i	−0.265470	−	0.964119i	$-0.585527\pi$
$131$	−14.4721	−	10.5146i	−1.26444	−	0.918667i	−0.998967	+	0.0454523i	$0.985527\pi$
$132$	−1.38197			−0.120285
$133$	−2.38197	−	1.73060i	−0.206543	−	0.150062i
$134$	−3.23607	+	9.95959i	−0.279554	+	0.860378i
$135$	1.80902	−	1.31433i	0.155695	−	0.113119i
$136$	−1.00000	−	3.07768i	−0.0857493	−	0.263909i
$137$	3.14590	−	9.68208i	0.268772	−	0.827196i	−0.722028	−	0.691864i	$-0.756790\pi$
$137$	3.14590	−	9.68208i	0.268772	−	0.827196i	0.990800	−	0.135332i	$-0.0432101\pi$
$138$	1.38197	−	4.25325i	0.117641	−	0.362061i
$139$	0.472136	+	1.45309i	0.0400460	+	0.123249i	0.969081	−	0.246743i	$-0.0793604\pi$
$139$	0.472136	+	1.45309i	0.0400460	+	0.123249i	−0.929035	+	0.369992i	$0.879360\pi$
$140$	−0.690983	−	0.502029i	−0.0583987	−	0.0424292i
$141$	3.61803	−	11.1352i	0.304693	−	0.937750i
$142$	−11.7082	−	8.50651i	−0.982531	−	0.713850i
$143$	3.41641			0.285694
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	0.854102	+	0.620541i	0.0709293	+	0.0515332i
$146$	−10.0902	+	7.33094i	−0.835068	+	0.606713i
$147$	−5.54508	+	4.02874i	−0.457351	+	0.332285i
$148$	2.47214	+	7.60845i	0.203208	+	0.625411i
$149$	10.9098			0.893768			0.446884	−	0.894592i	$-0.352534\pi$
$149$	10.9098			0.893768			0.446884	+	0.894592i	$0.352534\pi$
$150$	−5.00000			−0.408248
$151$	2.67376			0.217588			0.108794	−	0.994064i	$-0.465301\pi$
$151$	2.67376			0.217588			0.108794	+	0.994064i	$0.465301\pi$
$152$	2.38197	+	7.33094i	0.193203	+	0.594618i
$153$	2.61803	−	1.90211i	0.211656	−	0.153777i
$154$	−0.427051	+	0.310271i	−0.0344127	+	0.0250023i
$155$	3.02786	−	9.31881i	0.243204	−	0.748505i
$156$	2.00000	+	1.45309i	0.160128	+	0.116340i
$157$	−22.6525			−1.80786			−0.903932	−	0.427676i	$-0.859332\pi$
$157$	−22.6525			−1.80786			−0.903932	+	0.427676i	$0.859332\pi$
$158$	2.73607	+	1.98787i	0.217670	+	0.158146i
$159$	−2.80902	+	8.64527i	−0.222770	+	0.685614i
$160$	0.690983	+	2.12663i	0.0546270	+	0.168125i
$161$	−0.527864	−	1.62460i	−0.0416015	−	0.128036i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	2.61803	−	8.05748i	0.205060	−	0.631111i	−0.794651	−	0.607067i	$-0.792346\pi$
$163$	2.61803	−	8.05748i	0.205060	−	0.631111i	0.999711	−	0.0240436i	$-0.00765404\pi$
$164$	−2.38197	−	7.33094i	−0.186000	−	0.572450i
$165$	−0.954915	+	2.93893i	−0.0743400	+	0.228795i
$166$	2.73607	−	8.42075i	0.212360	−	0.653577i
$167$	1.38197	+	1.00406i	0.106940	+	0.0776963i	0.639970	−	0.768400i	$-0.278947\pi$
$167$	1.38197	+	1.00406i	0.106940	+	0.0776963i	−0.533030	+	0.846096i	$0.678947\pi$
$168$	−0.381966			−0.0294693
$169$	5.57295	+	4.04898i	0.428688	+	0.311460i
$170$	−7.23607			−0.554981
$171$	−6.23607	+	4.53077i	−0.476884	+	0.346477i
$172$	−4.61803	+	3.35520i	−0.352122	+	0.255831i
$173$	−1.88197	−	5.79210i	−0.143083	−	0.440365i	0.853676	−	0.520804i	$-0.174368\pi$
$173$	−1.88197	−	5.79210i	−0.143083	−	0.440365i	−0.996760	+	0.0804391i	$0.974368\pi$
$174$	0.472136			0.0357925
$175$	−1.54508	+	1.12257i	−0.116797	+	0.0848583i
$176$	1.38197			0.104170
$177$	0.427051	+	1.31433i	0.0320991	+	0.0987909i
$178$	−10.0902	+	7.33094i	−0.756290	+	0.549477i
$179$	−2.54508	+	1.84911i	−0.190229	+	0.138209i	−0.678823	−	0.734302i	$-0.737510\pi$
$179$	−2.54508	+	1.84911i	−0.190229	+	0.138209i	0.488595	+	0.872511i	$0.337510\pi$
$180$	−1.80902	+	1.31433i	−0.134836	+	0.0979642i
$181$	−19.9443	−	14.4904i	−1.48245	−	1.07706i	−0.976758	−	0.214344i	$-0.931239\pi$
$181$	−19.9443	−	14.4904i	−1.48245	−	1.07706i	−0.505688	−	0.862717i	$-0.668761\pi$
$182$	0.944272			0.0699941
$183$	5.85410	+	4.25325i	0.432748	+	0.314410i
$184$	−1.38197	+	4.25325i	−0.101880	+	0.313554i
$185$	17.8885			1.31519
$186$	−1.35410	−	4.16750i	−0.0992876	−	0.305576i
$187$	−1.38197	+	4.25325i	−0.101059	+	0.311029i
$188$	−3.61803	+	11.1352i	−0.263872	+	0.812115i
$189$	−0.118034	−	0.363271i	−0.00858571	−	0.0264241i
$190$	17.2361			1.25044
$191$	5.47214	−	16.8415i	0.395950	−	1.21861i	−0.532269	−	0.846575i	$-0.678661\pi$
$191$	5.47214	−	16.8415i	0.395950	−	1.21861i	0.928219	−	0.372033i	$-0.121339\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	11.1459			0.802299			0.401150	−	0.916013i	$-0.368611\pi$
$193$	11.1459			0.802299			0.401150	+	0.916013i	$0.368611\pi$
$194$	4.54508	+	3.30220i	0.326318	+	0.237084i
$195$	4.47214	−	3.24920i	0.320256	−	0.232680i
$196$	5.54508	−	4.02874i	0.396077	−	0.287767i
$197$	4.78115	−	3.47371i	0.340643	−	0.247492i	−0.404290	−	0.914631i	$-0.632481\pi$
$197$	4.78115	−	3.47371i	0.340643	−	0.247492i	0.744933	+	0.667139i	$0.232481\pi$
$198$	0.427051	+	1.31433i	0.0303492	+	0.0934052i
$199$	−18.5066			−1.31190			−0.655948	−	0.754806i	$-0.727731\pi$
$199$	−18.5066			−1.31190			−0.655948	+	0.754806i	$0.727731\pi$
$200$	5.00000			0.353553
$201$	10.4721			0.738648
$202$	2.04508	+	6.29412i	0.143892	+	0.442853i
$203$	0.145898	−	0.106001i	0.0102400	−	0.00743982i
$204$	−2.61803	+	1.90211i	−0.183299	+	0.133175i
$205$	−17.2361			−1.20382
$206$	1.07295	+	0.779543i	0.0747559	+	0.0543133i
$207$	−4.47214			−0.310835
$208$	−2.00000	−	1.45309i	−0.138675	−	0.100753i
$209$	3.29180	−	10.1311i	0.227698	−	0.700783i
$210$	−0.263932	+	0.812299i	−0.0182130	+	0.0560540i
$211$	7.23607	+	22.2703i	0.498151	+	1.53315i	0.811987	+	0.583675i	$0.198386\pi$
$211$	7.23607	+	22.2703i	0.498151	+	1.53315i	−0.313836	+	0.949477i	$0.601614\pi$
$212$	2.80902	−	8.64527i	0.192924	−	0.593759i
$213$	−4.47214	+	13.7638i	−0.306426	+	0.943081i
$214$	−2.89919	−	8.92278i	−0.198184	−	0.609949i
$215$	3.94427	+	12.1392i	0.268997	+	0.827888i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−1.35410	−	0.983813i	−0.0919224	−	0.0667856i
$218$	12.7639			0.864483
$219$	10.0902	+	7.33094i	0.681830	+	0.495379i
$220$	0.954915	−	2.93893i	0.0643804	−	0.198142i
$221$	6.47214	−	4.70228i	0.435363	−	0.316310i
$222$	6.47214	−	4.70228i	0.434381	−	0.315597i
$223$	0.954915	+	2.93893i	0.0639458	+	0.196805i	0.977925	−	0.208956i	$-0.0670065\pi$
$223$	0.954915	+	2.93893i	0.0639458	+	0.196805i	−0.913979	+	0.405761i	$0.867007\pi$
$224$	0.381966			0.0255212
$225$	1.54508	+	4.75528i	0.103006	+	0.317019i
$226$	−14.7639			−0.982082
$227$	3.48278	+	10.7189i	0.231160	+	0.711438i	0.997608	+	0.0691308i	$0.0220226\pi$
$227$	3.48278	+	10.7189i	0.231160	+	0.711438i	−0.766447	+	0.642307i	$0.777977\pi$
$228$	6.23607	−	4.53077i	0.412994	−	0.300057i
$229$	11.7082	−	8.50651i	0.773700	−	0.562126i	−0.129382	−	0.991595i	$-0.541299\pi$
$229$	11.7082	−	8.50651i	0.773700	−	0.562126i	0.903082	+	0.429469i	$0.141299\pi$
$230$	8.09017	+	5.87785i	0.533450	+	0.387574i
$231$	0.427051	+	0.310271i	0.0280979	+	0.0204143i
$232$	−0.472136			−0.0309972
$233$	10.2361	+	7.43694i	0.670587	+	0.487210i	0.870222	−	0.492660i	$-0.163976\pi$
$233$	10.2361	+	7.43694i	0.670587	+	0.487210i	−0.199635	+	0.979870i	$0.563976\pi$
$234$	0.763932	−	2.35114i	0.0499398	−	0.153699i
$235$	21.1803	+	15.3884i	1.38165	+	1.00383i
$236$	−0.427051	−	1.31433i	−0.0277987	−	0.0855555i
$237$	1.04508	−	3.21644i	0.0678856	−	0.208930i
$238$	−0.381966	+	1.17557i	−0.0247592	+	0.0762009i
$239$	7.94427	+	24.4500i	0.513872	+	1.58154i	0.785325	+	0.619084i	$0.212496\pi$
$239$	7.94427	+	24.4500i	0.513872	+	1.58154i	−0.271452	+	0.962452i	$0.587504\pi$
$240$	1.80902	−	1.31433i	0.116772	−	0.0848395i
$241$	−3.26393	+	10.0453i	−0.210248	+	0.647078i	0.789209	+	0.614125i	$0.210491\pi$
$241$	−3.26393	+	10.0453i	−0.210248	+	0.647078i	−0.999457	+	0.0329526i	$0.989509\pi$
$242$	7.35410	+	5.34307i	0.472740	+	0.343465i
$243$	−1.00000			−0.0641500
$244$	−5.85410	−	4.25325i	−0.374770	−	0.272287i
$245$	−4.73607	−	14.5761i	−0.302576	−	0.931234i
$246$	−6.23607	+	4.53077i	−0.397597	+	0.288871i
$247$	−15.4164	+	11.2007i	−0.980923	+	0.712682i
$248$	1.35410	+	4.16750i	0.0859856	+	0.264636i
$249$	−8.85410			−0.561106
$250$	3.45492	−	10.6331i	0.218508	−	0.672499i
$251$	−6.56231			−0.414209			−0.207105	−	0.978319i	$-0.566404\pi$
$251$	−6.56231			−0.414209			−0.207105	+	0.978319i	$0.566404\pi$
$252$	0.118034	+	0.363271i	0.00743544	+	0.0228839i
$253$	5.00000	−	3.63271i	0.314347	−	0.228387i
$254$	−9.20820	+	6.69015i	−0.577774	+	0.419777i
$255$	2.23607	+	6.88191i	0.140028	+	0.430962i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−22.0000			−1.37232			−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000			−1.37232			−0.686161	+	0.727450i	$0.740706\pi$
$258$	4.61803	+	3.35520i	0.287506	+	0.208886i
$259$	0.944272	−	2.90617i	0.0586742	−	0.180581i
$260$	−4.47214	+	3.24920i	−0.277350	+	0.201507i
$261$	−0.145898	−	0.449028i	−0.00903086	−	0.0277941i
$262$	5.52786	−	17.0130i	0.341513	−	1.05107i
$263$	0.527864	−	1.62460i	0.0325495	−	0.100177i	−0.933462	−	0.358677i	$-0.883228\pi$
$263$	0.527864	−	1.62460i	0.0325495	−	0.100177i	0.966011	+	0.258500i	$0.0832281\pi$
$264$	−0.427051	−	1.31433i	−0.0262832	−	0.0808913i
$265$	−16.4443	−	11.9475i	−1.01016	−	0.733927i
$266$	0.909830	−	2.80017i	0.0557853	−	0.171689i
$267$	10.0902	+	7.33094i	0.617508	+	0.448646i
$268$	−10.4721			−0.639688
$269$	−1.69098	−	1.22857i	−0.103101	−	0.0749073i	0.535040	−	0.844827i	$-0.320296\pi$
$269$	−1.69098	−	1.22857i	−0.103101	−	0.0749073i	−0.638141	+	0.769919i	$0.720296\pi$
$270$	1.80902	+	1.31433i	0.110093	+	0.0799874i
$271$	−8.92705	+	6.48588i	−0.542280	+	0.393989i	−0.824931	−	0.565233i	$-0.808786\pi$
$271$	−8.92705	+	6.48588i	−0.542280	+	0.393989i	0.282651	+	0.959223i	$0.408786\pi$
$272$	2.61803	−	1.90211i	0.158742	−	0.115333i
$273$	−0.291796	−	0.898056i	−0.0176603	−	0.0543528i
$274$	10.1803			0.615017
$275$	−5.59017	−	4.06150i	−0.337100	−	0.244917i
$276$	4.47214			0.269191
$277$	−0.291796	−	0.898056i	−0.0175323	−	0.0539590i	0.941908	−	0.335872i	$-0.109031\pi$
$277$	−0.291796	−	0.898056i	−0.0175323	−	0.0539590i	−0.959440	+	0.281913i	$0.909031\pi$
$278$	−1.23607	+	0.898056i	−0.0741344	+	0.0538618i
$279$	−3.54508	+	2.57565i	−0.212239	+	0.154200i
$280$	0.263932	−	0.812299i	0.0157730	−	0.0485442i
$281$	24.1803	+	17.5680i	1.44248	+	1.04802i	0.987517	+	0.157510i	$0.0503467\pi$
$281$	24.1803	+	17.5680i	1.44248	+	1.04802i	0.454961	+	0.890511i	$0.349653\pi$
$282$	11.7082			0.697213
$283$	−25.4164	−	18.4661i	−1.51085	−	1.09770i	−0.965799	−	0.259292i	$-0.916511\pi$
$283$	−25.4164	−	18.4661i	−1.51085	−	1.09770i	−0.545050	−	0.838404i	$-0.683489\pi$
$284$	4.47214	−	13.7638i	0.265372	−	0.816732i
$285$	−5.32624	−	16.3925i	−0.315499	−	0.971006i
$286$	1.05573	+	3.24920i	0.0624265	+	0.192129i
$287$	−0.909830	+	2.80017i	−0.0537056	+	0.165289i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−2.01722	−	6.20837i	−0.118660	−	0.365198i
$290$	−0.326238	+	1.00406i	−0.0191574	+	0.0589603i
$291$	1.73607	−	5.34307i	0.101770	−	0.313216i
$292$	−10.0902	−	7.33094i	−0.590483	−	0.429011i
$293$	−10.9098			−0.637359			−0.318680	−	0.947863i	$-0.603239\pi$
$293$	−10.9098			−0.637359			−0.318680	+	0.947863i	$0.603239\pi$
$294$	−5.54508	−	4.02874i	−0.323396	−	0.234961i
$295$	−3.09017			−0.179917
$296$	−6.47214	+	4.70228i	−0.376185	+	0.273315i
$297$	1.11803	−	0.812299i	0.0648749	−	0.0471344i
$298$	3.37132	+	10.3759i	0.195295	+	0.601058i
$299$	−11.0557			−0.639369
$300$	−1.54508	−	4.75528i	−0.0892055	−	0.274546i
$301$	2.18034			0.125673
$302$	0.826238	+	2.54290i	0.0475446	+	0.146327i
$303$	5.35410	−	3.88998i	0.307585	−	0.223474i
$304$	−6.23607	+	4.53077i	−0.357663	+	0.259857i
$305$	−13.0902	+	9.51057i	−0.749541	+	0.544573i
$306$	2.61803	+	1.90211i	0.149663	+	0.108737i
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$	−0.427051	−	0.310271i	−0.0243335	−	0.0176793i
$309$	0.409830	−	1.26133i	0.0233144	−	0.0717544i
$310$	9.79837			0.556510
$311$	−5.85410	−	18.0171i	−0.331956	−	1.02165i	−0.968202	−	0.250169i	$-0.919514\pi$
$311$	−5.85410	−	18.0171i	−0.331956	−	1.02165i	0.636247	−	0.771486i	$-0.280486\pi$
$312$	−0.763932	+	2.35114i	−0.0432491	+	0.133107i
$313$	5.33688	−	16.4252i	0.301658	−	0.928409i	−0.679245	−	0.733912i	$-0.737693\pi$
$313$	5.33688	−	16.4252i	0.301658	−	0.928409i	0.980903	−	0.194497i	$-0.0623075\pi$
$314$	−7.00000	−	21.5438i	−0.395033	−	1.21579i
$315$	0.854102			0.0481232
$316$	−1.04508	+	3.21644i	−0.0587906	+	0.180939i
$317$	0.354102	+	0.257270i	0.0198883	+	0.0144497i	0.597685	−	0.801731i	$-0.296087\pi$
$317$	0.354102	+	0.257270i	0.0198883	+	0.0144497i	−0.577797	+	0.816181i	$0.696087\pi$
$318$	−9.09017			−0.509751
$319$	0.527864	+	0.383516i	0.0295547	+	0.0214728i
$320$	−1.80902	+	1.31433i	−0.101127	+	0.0734732i
$321$	−7.59017	+	5.51458i	−0.423642	+	0.307794i
$322$	1.38197	−	1.00406i	0.0770140	−	0.0559539i
$323$	−7.70820	−	23.7234i	−0.428896	−	1.32001i
$324$	1.00000			0.0555556
$325$	3.81966	+	11.7557i	0.211877	+	0.652089i
$326$	8.47214			0.469228
$327$	−3.94427	−	12.1392i	−0.218119	−	0.671300i
$328$	6.23607	−	4.53077i	0.344329	−	0.250170i
$329$	3.61803	−	2.62866i	0.199469	−	0.144922i
$330$	−3.09017			−0.170108
$331$	14.5623	+	10.5801i	0.800417	+	0.581537i	0.911036	−	0.412326i	$-0.135284\pi$
$331$	14.5623	+	10.5801i	0.800417	+	0.581537i	−0.110620	+	0.993863i	$0.535284\pi$
$332$	8.85410			0.485932
$333$	−6.47214	−	4.70228i	−0.354671	−	0.257683i
$334$	−0.527864	+	1.62460i	−0.0288834	+	0.0888941i
$335$	−7.23607	+	22.2703i	−0.395349	+	1.21676i
$336$	−0.118034	−	0.363271i	−0.00643928	−	0.0198181i
$337$	3.73607	−	11.4984i	0.203517	−	0.626360i	−0.796254	−	0.604962i	$-0.793188\pi$
$337$	3.73607	−	11.4984i	0.203517	−	0.626360i	0.999771	−	0.0213978i	$-0.00681165\pi$
$338$	−2.12868	+	6.55139i	−0.115785	+	0.356349i
$339$	4.56231	+	14.0413i	0.247790	+	0.762621i
$340$	−2.23607	−	6.88191i	−0.121268	−	0.373224i
$341$	1.87132	−	5.75934i	0.101338	−	0.311886i
$342$	−6.23607	−	4.53077i	−0.337208	−	0.244996i
$343$	−5.29180			−0.285730
$344$	−4.61803	−	3.35520i	−0.248988	−	0.180900i
$345$	3.09017	−	9.51057i	0.166369	−	0.512032i
$346$	4.92705	−	3.57971i	0.264880	−	0.192447i
$347$	−0.354102	+	0.257270i	−0.0190092	+	0.0138110i	−0.597249	−	0.802056i	$-0.703740\pi$
$347$	−0.354102	+	0.257270i	−0.0190092	+	0.0138110i	0.578240	+	0.815867i	$0.303740\pi$
$348$	0.145898	+	0.449028i	0.00782096	+	0.0240704i
$349$	7.88854			0.422264			0.211132	−	0.977458i	$-0.432285\pi$
$349$	7.88854			0.422264			0.211132	+	0.977458i	$0.432285\pi$
$350$	−1.54508	−	1.12257i	−0.0825883	−	0.0600039i
$351$	−2.47214			−0.131953
$352$	0.427051	+	1.31433i	0.0227619	+	0.0700539i
$353$	7.09017	−	5.15131i	0.377372	−	0.274177i	−0.382889	−	0.923794i	$-0.625071\pi$
$353$	7.09017	−	5.15131i	0.377372	−	0.274177i	0.760261	+	0.649618i	$0.225071\pi$
$354$	−1.11803	+	0.812299i	−0.0594228	+	0.0431732i
$355$	−26.1803	−	19.0211i	−1.38951	−	1.00954i
$356$	−10.0902	−	7.33094i	−0.534778	−	0.388539i
$357$	1.23607			0.0654197
$358$	−2.54508	−	1.84911i	−0.134512	−	0.0977286i
$359$	−0.0557281	+	0.171513i	−0.00294122	+	0.00905213i	−0.952516	−	0.304487i	$-0.901515\pi$
$359$	−0.0557281	+	0.171513i	−0.00294122	+	0.00905213i	0.949575	+	0.313540i	$0.101515\pi$
$360$	−1.80902	−	1.31433i	−0.0953436	−	0.0692712i
$361$	12.4894	+	38.4383i	0.657335	+	2.02307i
$362$	7.61803	−	23.4459i	0.400395	−	1.23229i
$363$	2.80902	−	8.64527i	0.147435	−	0.453759i
$364$	0.291796	+	0.898056i	0.0152943	+	0.0470709i
$365$	−22.5623	+	16.3925i	−1.18097	+	0.858021i
$366$	−2.23607	+	6.88191i	−0.116881	+	0.359723i
$367$	22.9615	+	16.6825i	1.19858	+	0.870819i	0.994144	−	0.108060i	$-0.0344640\pi$
$367$	22.9615	+	16.6825i	1.19858	+	0.870819i	0.204436	+	0.978880i	$0.434464\pi$
$368$	−4.47214			−0.233126
$369$	6.23607	+	4.53077i	0.324637	+	0.235862i
$370$	5.52786	+	17.0130i	0.287380	+	0.884465i
$371$	−2.80902	+	2.04087i	−0.145837	+	0.105957i
$372$	3.54508	−	2.57565i	0.183804	−	0.133541i
$373$	−6.32624	−	19.4702i	−0.327560	−	1.00813i	−0.970272	−	0.242018i	$-0.922191\pi$
$373$	−6.32624	−	19.4702i	−0.327560	−	1.00813i	0.642712	−	0.766108i	$-0.277809\pi$
$374$	−4.47214			−0.231249
$375$	−11.1803			−0.577350
$376$	−11.7082			−0.603805
$377$	−0.360680	−	1.11006i	−0.0185760	−	0.0571709i
$378$	0.309017	−	0.224514i	0.0158941	−	0.0115478i
$379$	−1.76393	+	1.28157i	−0.0906071	+	0.0658299i	−0.632166	−	0.774833i	$-0.717834\pi$
$379$	−1.76393	+	1.28157i	−0.0906071	+	0.0658299i	0.541559	+	0.840662i	$0.317834\pi$
$380$	5.32624	+	16.3925i	0.273230	+	0.840916i
$381$	9.20820	+	6.69015i	0.471751	+	0.342747i
$382$	17.7082			0.906031
$383$	16.1803	+	11.7557i	0.826777	+	0.600688i	0.918646	−	0.395083i	$-0.129284\pi$
$383$	16.1803	+	11.7557i	0.826777	+	0.600688i	−0.0918688	+	0.995771i	$0.529284\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−0.954915	+	0.693786i	−0.0486670	+	0.0353586i
$386$	3.44427	+	10.6004i	0.175309	+	0.539545i
$387$	1.76393	−	5.42882i	0.0896657	−	0.275963i
$388$	−1.73607	+	5.34307i	−0.0881355	+	0.271253i
$389$	−4.51722	−	13.9026i	−0.229032	−	0.704889i	−0.997857	−	0.0654294i	$-0.979158\pi$
$389$	−4.51722	−	13.9026i	−0.229032	−	0.704889i	0.768825	−	0.639459i	$-0.220842\pi$
$390$	4.47214	+	3.24920i	0.226455	+	0.164529i
$391$	4.47214	−	13.7638i	0.226166	−	0.696066i
$392$	5.54508	+	4.02874i	0.280069	+	0.203482i
$393$	−17.8885			−0.902358
$394$	4.78115	+	3.47371i	0.240871	+	0.175003i
$395$	6.11803	+	4.44501i	0.307832	+	0.223653i
$396$	−1.11803	+	0.812299i	−0.0561833	+	0.0408196i
$397$	28.5066	−	20.7112i	1.43070	−	1.03947i	0.440819	−	0.897596i	$-0.354688\pi$
$397$	28.5066	−	20.7112i	1.43070	−	1.03947i	0.989885	−	0.141871i	$-0.0453119\pi$
$398$	−5.71885	−	17.6008i	−0.286660	−	0.882248i
$399$	−2.94427			−0.147398
$400$	1.54508	+	4.75528i	0.0772542	+	0.237764i
$401$	12.2918			0.613823			0.306912	−	0.951738i	$-0.400704\pi$
$401$	12.2918			0.613823			0.306912	+	0.951738i	$0.400704\pi$
$402$	3.23607	+	9.95959i	0.161400	+	0.496739i
$403$	−8.76393	+	6.36737i	−0.436563	+	0.317181i
$404$	−5.35410	+	3.88998i	−0.266377	+	0.193534i
$405$	0.690983	−	2.12663i	0.0343352	−	0.105673i
$406$	0.145898	+	0.106001i	0.00724080	+	0.00526075i
$407$	11.0557			0.548012
$408$	−2.61803	−	1.90211i	−0.129612	−	0.0941686i
$409$	−5.80902	+	17.8783i	−0.287237	+	0.884026i	0.698482	+	0.715628i	$0.253859\pi$
$409$	−5.80902	+	17.8783i	−0.287237	+	0.884026i	−0.985719	+	0.168398i	$0.946141\pi$
$410$	−5.32624	−	16.3925i	−0.263044	−	0.809567i
$411$	−3.14590	−	9.68208i	−0.155176	−	0.477582i
$412$	−0.409830	+	1.26133i	−0.0201909	+	0.0621411i
$413$	−0.163119	+	0.502029i	−0.00802656	+	0.0247032i
$414$	−1.38197	−	4.25325i	−0.0679199	−	0.209036i
$415$	6.11803	−	18.8294i	0.300322	−	0.924298i
$416$	0.763932	−	2.35114i	0.0374548	−	0.115274i
$417$	1.23607	+	0.898056i	0.0605305	+	0.0439780i
$418$	10.6525			0.521030
$419$	−6.54508	−	4.75528i	−0.319748	−	0.232311i	0.416320	−	0.909218i	$-0.363320\pi$
$419$	−6.54508	−	4.75528i	−0.319748	−	0.232311i	−0.736068	+	0.676908i	$0.763320\pi$
$420$	−0.854102			−0.0416759
$421$	22.0344	−	16.0090i	1.07389	−	0.780229i	0.0972850	−	0.995257i	$-0.468984\pi$
$421$	22.0344	−	16.0090i	1.07389	−	0.780229i	0.976608	+	0.215028i	$0.0689842\pi$
$422$	−18.9443	+	13.7638i	−0.922193	+	0.670012i
$423$	−3.61803	−	11.1352i	−0.175915	−	0.541410i
$424$	9.09017			0.441458
$425$	−16.1803			−0.784862
$426$	−14.4721			−0.701177
$427$	0.854102	+	2.62866i	0.0413329	+	0.127210i
$428$	7.59017	−	5.51458i	0.366885	−	0.266557i
$429$	2.76393	−	2.00811i	0.133444	−	0.0969527i
$430$	−10.3262	+	7.50245i	−0.497975	+	0.361800i
$431$	29.7984	+	21.6498i	1.43534	+	1.04283i	0.988991	+	0.147973i	$0.0472748\pi$
$431$	29.7984	+	21.6498i	1.43534	+	1.04283i	0.446346	+	0.894861i	$0.352725\pi$
$432$	−1.00000			−0.0481125
$433$	18.2082	+	13.2290i	0.875030	+	0.635747i	0.931932	−	0.362633i	$-0.118122\pi$
$433$	18.2082	+	13.2290i	0.875030	+	0.635747i	−0.0569016	+	0.998380i	$0.518122\pi$
$434$	0.517221	−	1.59184i	0.0248274	−	0.0764109i
$435$	1.05573			0.0506183
$436$	3.94427	+	12.1392i	0.188896	+	0.581363i
$437$	−10.6525	+	32.7849i	−0.509577	+	1.56832i
$438$	−3.85410	+	11.8617i	−0.184156	+	0.566774i
$439$	4.48278	+	13.7966i	0.213951	+	0.658475i	0.999226	+	0.0393275i	$0.0125216\pi$
$439$	4.48278	+	13.7966i	0.213951	+	0.658475i	−0.785275	+	0.619147i	$0.787478\pi$
$440$	3.09017			0.147318
$441$	−2.11803	+	6.51864i	−0.100859	+	0.310411i
$442$	6.47214	+	4.70228i	0.307848	+	0.223665i
$443$	14.3820			0.683308			0.341654	−	0.939826i	$-0.389013\pi$
$443$	14.3820			0.683308			0.341654	+	0.939826i	$0.389013\pi$
$444$	6.47214	+	4.70228i	0.307154	+	0.223160i
$445$	−22.5623	+	16.3925i	−1.06956	+	0.777078i
$446$	−2.50000	+	1.81636i	−0.118378	+	0.0860070i
$447$	8.82624	−	6.41264i	0.417467	−	0.303307i
$448$	0.118034	+	0.363271i	0.00557658	+	0.0171630i
$449$	−14.2918			−0.674472			−0.337236	−	0.941420i	$-0.609492\pi$
$449$	−14.2918			−0.674472			−0.337236	+	0.941420i	$0.609492\pi$
$450$	−4.04508	+	2.93893i	−0.190687	+	0.138542i
$451$	−10.6525			−0.501605
$452$	−4.56231	−	14.0413i	−0.214593	−	0.660449i
$453$	2.16312	−	1.57160i	0.101632	−	0.0738401i
$454$	−9.11803	+	6.62464i	−0.427931	+	0.310910i
$455$	2.11146			0.0989866
$456$	6.23607	+	4.53077i	0.292031	+	0.212173i
$457$	7.09017			0.331664			0.165832	−	0.986154i	$-0.446969\pi$
$457$	7.09017			0.331664			0.165832	+	0.986154i	$0.446969\pi$
$458$	11.7082	+	8.50651i	0.547088	+	0.397483i
$459$	1.00000	−	3.07768i	0.0466760	−	0.143654i
$460$	−3.09017	+	9.51057i	−0.144080	+	0.443432i
$461$	−3.88197	−	11.9475i	−0.180801	−	0.556449i	0.819050	−	0.573723i	$-0.194501\pi$
$461$	−3.88197	−	11.9475i	−0.180801	−	0.556449i	−0.999851	+	0.0172739i	$0.994501\pi$
$462$	−0.163119	+	0.502029i	−0.00758898	+	0.0233565i
$463$	9.52786	−	29.3238i	0.442797	−	1.36279i	−0.442084	−	0.896974i	$-0.645761\pi$
$463$	9.52786	−	29.3238i	0.442797	−	1.36279i	0.884881	−	0.465817i	$-0.154239\pi$
$464$	−0.145898	−	0.449028i	−0.00677315	−	0.0208456i
$465$	−3.02786	−	9.31881i	−0.140414	−	0.432149i
$466$	−3.90983	+	12.0332i	−0.181119	+	0.557428i
$467$	−21.2984	−	15.4742i	−0.985571	−	0.716059i	−0.0266244	−	0.999646i	$-0.508476\pi$
$467$	−21.2984	−	15.4742i	−0.985571	−	0.716059i	−0.958947	+	0.283586i	$0.908476\pi$
$468$	2.47214			0.114275
$469$	3.23607	+	2.35114i	0.149428	+	0.108566i
$470$	−8.09017	+	24.8990i	−0.373172	+	1.14850i
$471$	−18.3262	+	13.3148i	−0.844428	+	0.613513i
$472$	1.11803	−	0.812299i	0.0514617	−	0.0373891i
$473$	2.43769	+	7.50245i	0.112085	+	0.344963i
$474$	3.38197			0.155339
$475$	38.5410			1.76838
$476$	−1.23607			−0.0566551
$477$	2.80902	+	8.64527i	0.128616	+	0.395840i
$478$	−20.7984	+	15.1109i	−0.951295	+	0.691157i
$479$	−9.00000	+	6.53888i	−0.411220	+	0.298769i	−0.774096	−	0.633069i	$-0.781795\pi$
$479$	−9.00000	+	6.53888i	−0.411220	+	0.298769i	0.362875	+	0.931838i	$0.381795\pi$
$480$	1.80902	+	1.31433i	0.0825700	+	0.0599906i
$481$	−16.0000	−	11.6247i	−0.729537	−	0.530040i
$482$	−10.5623			−0.481100
$483$	−1.38197	−	1.00406i	−0.0628816	−	0.0456862i
$484$	−2.80902	+	8.64527i	−0.127683	+	0.392967i
$485$	10.1631	+	7.38394i	0.461483	+	0.335287i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−2.10081	+	6.46564i	−0.0951969	+	0.292986i	−0.987305	−	0.158836i	$-0.949226\pi$
$487$	−2.10081	+	6.46564i	−0.0951969	+	0.292986i	0.892108	+	0.451822i	$0.149226\pi$
$488$	2.23607	−	6.88191i	0.101222	−	0.311529i
$489$	−2.61803	−	8.05748i	−0.118392	−	0.364372i
$490$	12.3992	−	9.00854i	0.560138	−	0.406964i
$491$	2.55573	−	7.86572i	0.115338	−	0.354975i	−0.876679	−	0.481076i	$-0.840246\pi$
$491$	2.55573	−	7.86572i	0.115338	−	0.354975i	0.992017	+	0.126101i	$0.0402462\pi$
$492$	−6.23607	−	4.53077i	−0.281144	−	0.204263i
$493$	1.52786			0.0688115
$494$	−15.4164	−	11.2007i	−0.693617	−	0.503942i
$495$	0.954915	+	2.93893i	0.0429202	+	0.132095i
$496$	−3.54508	+	2.57565i	−0.159179	+	0.115650i
$497$	−4.47214	+	3.24920i	−0.200603	+	0.145746i
$498$	−2.73607	−	8.42075i	−0.122606	−	0.377343i
$499$	−13.5967			−0.608674			−0.304337	−	0.952564i	$-0.598435\pi$
$499$	−13.5967			−0.608674			−0.304337	+	0.952564i	$0.598435\pi$
$500$	11.1803			0.500000
$501$	1.70820			0.0763169
$502$	−2.02786	−	6.24112i	−0.0905080	−	0.278555i
$503$	9.61803	−	6.98791i	0.428847	−	0.311576i	−0.352341	−	0.935872i	$-0.614614\pi$
$503$	9.61803	−	6.98791i	0.428847	−	0.311576i	0.781188	+	0.624296i	$0.214614\pi$
$504$	−0.309017	+	0.224514i	−0.0137647	+	0.0100006i
$505$	4.57295	+	14.0741i	0.203494	+	0.626289i
$506$	5.00000	+	3.63271i	0.222277	+	0.161494i
$507$	6.88854			0.305931
$508$	−9.20820	−	6.69015i	−0.408548	−	0.296827i
$509$	6.33688	−	19.5029i	0.280877	−	0.864451i	−0.706727	−	0.707487i	$-0.749829\pi$
$509$	6.33688	−	19.5029i	0.280877	−	0.864451i	0.987604	−	0.156965i	$-0.0501710\pi$
$510$	−5.85410	+	4.25325i	−0.259224	+	0.188337i
$511$	1.47214	+	4.53077i	0.0651235	+	0.200429i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−2.38197	+	7.33094i	−0.105166	+	0.323669i
$514$	−6.79837	−	20.9232i	−0.299863	−	0.922885i
$515$	2.39919	+	1.74311i	0.105721	+	0.0768107i
$516$	−1.76393	+	5.42882i	−0.0776528	+	0.238991i
$517$	13.0902	+	9.51057i	0.575705	+	0.418274i
$518$	3.05573			0.134261
$519$	−4.92705	−	3.57971i	−0.216274	−	0.157132i
$520$	−4.47214	−	3.24920i	−0.196116	−	0.142487i
$521$	6.61803	−	4.80828i	0.289941	−	0.210655i	−0.433301	−	0.901249i	$-0.642651\pi$
$521$	6.61803	−	4.80828i	0.289941	−	0.210655i	0.723242	+	0.690595i	$0.242651\pi$
$522$	0.381966	−	0.277515i	0.0167182	−	0.0121465i
$523$	8.94427	+	27.5276i	0.391106	+	1.20370i	0.931953	+	0.362579i	$0.118104\pi$
$523$	8.94427	+	27.5276i	0.391106	+	1.20370i	−0.540847	+	0.841121i	$0.681896\pi$
$524$	17.8885			0.781465
$525$	−0.590170	+	1.81636i	−0.0257571	+	0.0792723i
$526$	1.70820			0.0744812
$527$	−4.38197	−	13.4863i	−0.190881	−	0.587473i
$528$	1.11803	−	0.812299i	0.0486562	−	0.0353508i
$529$	2.42705	−	1.76336i	0.105524	−	0.0766676i
$530$	6.28115	−	19.3314i	0.272836	−	0.839702i
$531$	1.11803	+	0.812299i	0.0485185	+	0.0352508i
$532$	2.94427			0.127650
$533$	15.4164	+	11.2007i	0.667759	+	0.485155i
$534$	−3.85410	+	11.8617i	−0.166783	+	0.513306i
$535$	−6.48278	−	19.9519i	−0.280275	−	0.862598i
$536$	−3.23607	−	9.95959i	−0.139777	−	0.430189i
$537$	−0.972136	+	2.99193i	−0.0419508	+	0.129111i
$538$	0.645898	−	1.98787i	0.0278466	−	0.0857032i
$539$	−2.92705	−	9.00854i	−0.126077	−	0.388025i
$540$	−0.690983	+	2.12663i	−0.0297352	+	0.0915155i
$541$	−1.18034	+	3.63271i	−0.0507468	+	0.156183i	−0.973218	−	0.229882i	$-0.926166\pi$
$541$	−1.18034	+	3.63271i	−0.0507468	+	0.156183i	0.922472	+	0.386065i	$0.126166\pi$
$542$	−8.92705	−	6.48588i	−0.383450	−	0.278592i
$543$	−24.6525			−1.05794
$544$	2.61803	+	1.90211i	0.112247	+	0.0815524i
$545$	28.5410			1.22256
$546$	0.763932	−	0.555029i	0.0326933	−	0.0237531i
$547$	3.00000	−	2.17963i	0.128271	−	0.0931941i	−0.521800	−	0.853068i	$-0.674739\pi$
$547$	3.00000	−	2.17963i	0.128271	−	0.0931941i	0.650071	+	0.759874i	$0.274739\pi$
$548$	3.14590	+	9.68208i	0.134386	+	0.413598i
$549$	7.23607			0.308828
$550$	2.13525	−	6.57164i	0.0910476	−	0.280216i
$551$	−3.63932			−0.155040
$552$	1.38197	+	4.25325i	0.0588204	+	0.181031i
$553$	1.04508	−	0.759299i	0.0444415	−	0.0322887i
$554$	0.763932	−	0.555029i	0.0324564	−	0.0235809i
$555$	14.4721	−	10.5146i	0.614308	−	0.446321i
$556$	−1.23607	−	0.898056i	−0.0524210	−	0.0380861i
$557$	−2.67376			−0.113291			−0.0566455	−	0.998394i	$-0.518040\pi$
$557$	−2.67376			−0.113291			−0.0566455	+	0.998394i	$0.518040\pi$
$558$	−3.54508	−	2.57565i	−0.150075	−	0.109036i
$559$	4.36068	−	13.4208i	0.184437	−	0.567639i
$560$	0.854102			0.0360924
$561$	1.38197	+	4.25325i	0.0583467	+	0.179573i
$562$	−9.23607	+	28.4257i	−0.389600	+	1.19907i
$563$	−3.79180	+	11.6699i	−0.159805	+	0.491830i	−0.998616	−	0.0525933i	$-0.983251\pi$
$563$	−3.79180	+	11.6699i	−0.159805	+	0.491830i	0.838811	+	0.544423i	$0.183251\pi$
$564$	3.61803	+	11.1352i	0.152347	+	0.468875i
$565$	−33.0132			−1.38887
$566$	9.70820	−	29.8788i	0.408066	−	1.25590i
$567$	−0.309017	−	0.224514i	−0.0129775	−	0.00942870i
$568$	14.4721			0.607237
$569$	−35.4164	−	25.7315i	−1.48473	−	1.07872i	−0.975993	−	0.217801i	$-0.930111\pi$
$569$	−35.4164	−	25.7315i	−1.48473	−	1.07872i	−0.508740	−	0.860920i	$-0.669889\pi$
$570$	13.9443	−	10.1311i	0.584061	−	0.424345i
$571$	22.5623	−	16.3925i	0.944203	−	0.686004i	−0.00522561	−	0.999986i	$-0.501663\pi$
$571$	22.5623	−	16.3925i	0.944203	−	0.686004i	0.949429	+	0.313983i	$0.101663\pi$
$572$	−2.76393	+	2.00811i	−0.115566	+	0.0839635i
$573$	−5.47214	−	16.8415i	−0.228602	−	0.703564i
$574$	−2.94427			−0.122892
$575$	18.0902	+	13.1433i	0.754412	+	0.548113i
$576$	1.00000			0.0416667
$577$	−11.7361	−	36.1199i	−0.488579	−	1.50369i	−0.826730	−	0.562599i	$-0.809801\pi$
$577$	−11.7361	−	36.1199i	−0.488579	−	1.50369i	0.338151	−	0.941092i	$-0.390199\pi$
$578$	5.28115	−	3.83698i	0.219667	−	0.159597i
$579$	9.01722	−	6.55139i	0.374743	−	0.272267i
$580$	−1.05573			−0.0438367
$581$	−2.73607	−	1.98787i	−0.113511	−	0.0824707i
$582$	5.61803			0.232875
$583$	−10.1631	−	7.38394i	−0.420913	−	0.305811i
$584$	3.85410	−	11.8617i	0.159484	−	0.490841i
$585$	1.70820	−	5.25731i	0.0706255	−	0.217363i
$586$	−3.37132	−	10.3759i	−0.139268	−	0.428623i
$587$	−9.28115	+	28.5645i	−0.383074	+	1.17898i	0.554794	+	0.831988i	$0.312797\pi$
$587$	−9.28115	+	28.5645i	−0.383074	+	1.17898i	−0.937868	+	0.346993i	$0.887203\pi$
$588$	2.11803	−	6.51864i	0.0873462	−	0.268824i
$589$	10.4377	+	32.1239i	0.430078	+	1.32364i
$590$	−0.954915	−	2.93893i	−0.0393132	−	0.120994i
$591$	1.82624	−	5.62058i	0.0751214	−	0.231200i
$592$	−6.47214	−	4.70228i	−0.266003	−	0.193263i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	1.11803	+	0.812299i	0.0458735	+	0.0333290i
$595$	−0.854102	+	2.62866i	−0.0350148	+	0.107764i
$596$	−8.82624	+	6.41264i	−0.361537	+	0.262672i
$597$	−14.9721	+	10.8779i	−0.612769	+	0.445203i
$598$	−3.41641	−	10.5146i	−0.139707	−	0.429975i
$599$	−8.47214			−0.346162			−0.173081	−	0.984908i	$-0.555372\pi$
$599$	−8.47214			−0.346162			−0.173081	+	0.984908i	$0.555372\pi$
$600$	4.04508	−	2.93893i	0.165140	−	0.119981i
$601$	−41.2705			−1.68346			−0.841730	−	0.539899i	$-0.818462\pi$
$601$	−41.2705			−1.68346			−0.841730	+	0.539899i	$0.818462\pi$
$602$	0.673762	+	2.07363i	0.0274605	+	0.0845147i
$603$	8.47214	−	6.15537i	0.345012	−	0.250666i
$604$	−2.16312	+	1.57160i	−0.0880161	+	0.0639474i
$605$	16.4443	+	11.9475i	0.668555	+	0.485733i
$606$	5.35410	+	3.88998i	0.217496	+	0.158020i
$607$	−13.5623			−0.550477			−0.275239	−	0.961376i	$-0.588757\pi$
$607$	−13.5623			−0.550477			−0.275239	+	0.961376i	$0.588757\pi$
$608$	−6.23607	−	4.53077i	−0.252906	−	0.183747i
$609$	0.0557281	−	0.171513i	0.00225822	−	0.00695007i
$610$	−13.0902	−	9.51057i	−0.530005	−	0.385072i
$611$	−8.94427	−	27.5276i	−0.361847	−	1.11365i
$612$	−1.00000	+	3.07768i	−0.0404226	+	0.124408i
$613$	−9.96556	+	30.6708i	−0.402505	+	1.23878i	0.520455	+	0.853889i	$0.325762\pi$
$613$	−9.96556	+	30.6708i	−0.402505	+	1.23878i	−0.922961	+	0.384895i	$0.874238\pi$
$614$	3.09017	+	9.51057i	0.124709	+	0.383815i
$615$	−13.9443	+	10.1311i	−0.562287	+	0.408526i
$616$	0.163119	−	0.502029i	0.00657225	−	0.0202273i
$617$	−30.6525	−	22.2703i	−1.23402	−	0.896570i	−0.236837	−	0.971549i	$-0.576111\pi$
$617$	−30.6525	−	22.2703i	−1.23402	−	0.896570i	−0.997185	+	0.0749797i	$0.976111\pi$
$618$	1.32624			0.0533491
$619$	−14.0902	−	10.2371i	−0.566332	−	0.411464i	0.267439	−	0.963575i	$-0.413823\pi$
$619$	−14.0902	−	10.2371i	−0.566332	−	0.411464i	−0.833771	+	0.552111i	$0.813823\pi$
$620$	3.02786	+	9.31881i	0.121602	+	0.374252i
$621$	−3.61803	+	2.62866i	−0.145187	+	0.105484i
$622$	15.3262	−	11.1352i	0.614526	−	0.446479i
$623$	1.47214	+	4.53077i	0.0589799	+	0.181521i
$624$	−2.47214			−0.0989646
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	17.2705			0.690268
$627$	−3.29180	−	10.1311i	−0.131462	−	0.404597i
$628$	18.3262	−	13.3148i	0.731297	−	0.531318i
$629$	20.9443	−	15.2169i	0.835103	−	0.606738i
$630$	0.263932	+	0.812299i	0.0105153	+	0.0323628i
$631$	−30.3607	−	22.0583i	−1.20864	−	0.878128i	−0.213533	−	0.976936i	$-0.568497\pi$
$631$	−30.3607	−	22.0583i	−1.20864	−	0.878128i	−0.995107	+	0.0988078i	$0.968497\pi$
$632$	−3.38197			−0.134527
$633$	18.9443	+	13.7638i	0.752967	+	0.547063i
$634$	−0.135255	+	0.416272i	−0.00537166	+	0.0165323i
$635$	−20.5902	+	14.9596i	−0.817096	+	0.593655i
$636$	−2.80902	−	8.64527i	−0.111385	−	0.342807i
$637$	−5.23607	+	16.1150i	−0.207461	+	0.638498i
$638$	−0.201626	+	0.620541i	−0.00798245	+	0.0245675i
$639$	4.47214	+	13.7638i	0.176915	+	0.544488i
$640$	−1.80902	−	1.31433i	−0.0715077	−	0.0519534i
$641$	−11.1803	+	34.4095i	−0.441597	+	1.35910i	0.444576	+	0.895741i	$0.353354\pi$
$641$	−11.1803	+	34.4095i	−0.441597	+	1.35910i	−0.886173	+	0.463354i	$0.846646\pi$
$642$	−7.59017	−	5.51458i	−0.299560	−	0.217643i
$643$	−13.8885			−0.547711			−0.273855	−	0.961771i	$-0.588299\pi$
$643$	−13.8885			−0.547711			−0.273855	+	0.961771i	$0.588299\pi$
$644$	1.38197	+	1.00406i	0.0544571	+	0.0395654i
$645$	10.3262	+	7.50245i	0.406595	+	0.295409i
$646$	20.1803	−	14.6619i	0.793985	−	0.576864i
$647$	4.09017	−	2.97168i	0.160801	−	0.116829i	−0.504475	−	0.863426i	$-0.668314\pi$
$647$	4.09017	−	2.97168i	0.160801	−	0.116829i	0.665276	+	0.746598i	$0.268314\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	−1.90983			−0.0749674
$650$	−10.0000	+	7.26543i	−0.392232	+	0.284973i
$651$	−1.67376			−0.0655999
$652$	2.61803	+	8.05748i	0.102530	+	0.315555i
$653$	−2.30902	+	1.67760i	−0.0903588	+	0.0656495i	−0.632047	−	0.774930i	$-0.717785\pi$
$653$	−2.30902	+	1.67760i	−0.0903588	+	0.0656495i	0.541689	+	0.840579i	$0.317785\pi$
$654$	10.3262	−	7.50245i	0.403788	−	0.293369i
$655$	12.3607	−	38.0423i	0.482972	−	1.48643i
$656$	6.23607	+	4.53077i	0.243478	+	0.176897i
$657$	12.4721			0.486584
$658$	3.61803	+	2.62866i	0.141046	+	0.102476i
$659$	−5.68034	+	17.4823i	−0.221275	+	0.681013i	0.777374	+	0.629039i	$0.216551\pi$
$659$	−5.68034	+	17.4823i	−0.221275	+	0.681013i	−0.998648	+	0.0519743i	$0.983449\pi$
$660$	−0.954915	−	2.93893i	−0.0371700	−	0.114398i
$661$	−6.65248	−	20.4742i	−0.258751	−	0.796355i	−0.993067	−	0.117547i	$-0.962497\pi$
$661$	−6.65248	−	20.4742i	−0.258751	−	0.796355i	0.734316	−	0.678808i	$-0.237503\pi$
$662$	−5.56231	+	17.1190i	−0.216185	+	0.665350i
$663$	2.47214	−	7.60845i	0.0960098	−	0.295488i
$664$	2.73607	+	8.42075i	0.106180	+	0.326789i
$665$	2.03444	−	6.26137i	0.0788923	−	0.242805i
$666$	2.47214	−	7.60845i	0.0957933	−	0.294822i
$667$	−1.70820	−	1.24108i	−0.0661419	−	0.0480549i
$668$	−1.70820			−0.0660924
$669$	2.50000	+	1.81636i	0.0966556	+	0.0702244i
$670$	−23.4164			−0.904655
$671$	−8.09017	+	5.87785i	−0.312318	+	0.226912i
$672$	0.309017	−	0.224514i	0.0119206	−	0.00866082i
$673$	7.55573	+	23.2541i	0.291252	+	0.896381i	0.984455	+	0.175639i	$0.0561990\pi$
$673$	7.55573	+	23.2541i	0.291252	+	0.896381i	−0.693203	+	0.720743i	$0.743801\pi$
$674$	12.0902			0.465696
$675$	4.04508	+	2.93893i	0.155695	+	0.113119i
$676$	−6.88854			−0.264944
$677$	5.53444	+	17.0333i	0.212706	+	0.654641i	0.999309	+	0.0371818i	$0.0118381\pi$
$677$	5.53444	+	17.0333i	0.212706	+	0.654641i	−0.786603	+	0.617460i	$0.788162\pi$
$678$	−11.9443	+	8.67802i	−0.458717	+	0.333277i
$679$	1.73607	−	1.26133i	0.0666242	−	0.0484053i
$680$	5.85410	−	4.25325i	0.224495	−	0.163105i
$681$	9.11803	+	6.62464i	0.349404	+	0.253857i
$682$	6.05573			0.231886
$683$	3.64590	+	2.64890i	0.139506	+	0.101357i	0.655350	−	0.755326i	$-0.272521\pi$
$683$	3.64590	+	2.64890i	0.139506	+	0.101357i	−0.515843	+	0.856683i	$0.672521\pi$
$684$	2.38197	−	7.33094i	0.0910767	−	0.280305i
$685$	22.7639			0.869765
$686$	−1.63525	−	5.03280i	−0.0624343	−	0.192153i
$687$	4.47214	−	13.7638i	0.170623	−	0.525122i
$688$	1.76393	−	5.42882i	0.0672493	−	0.206972i
$689$	6.94427	+	21.3723i	0.264556	+	0.814219i
$690$	10.0000			0.380693
$691$	2.09017	−	6.43288i	0.0795138	−	0.244718i	−0.903396	−	0.428808i	$-0.858934\pi$
$691$	2.09017	−	6.43288i	0.0795138	−	0.244718i	0.982909	+	0.184090i	$0.0589337\pi$
$692$	4.92705	+	3.57971i	0.187298	+	0.136080i
$693$	0.527864			0.0200519
$694$	−0.354102	−	0.257270i	−0.0134415	−	0.00976584i
$695$	−2.76393	+	2.00811i	−0.104842	+	0.0761721i
$696$	−0.381966	+	0.277515i	−0.0144784	+	0.0105192i
$697$	−20.1803	+	14.6619i	−0.764385	+	0.555358i
$698$	2.43769	+	7.50245i	0.0922681	+	0.283972i
$699$	12.6525			0.478561
$700$	0.590170	−	1.81636i	0.0223063	−	0.0686518i
$701$	−12.8328			−0.484689			−0.242344	−	0.970190i	$-0.577916\pi$
$701$	−12.8328			−0.484689			−0.242344	+	0.970190i	$0.577916\pi$
$702$	−0.763932	−	2.35114i	−0.0288328	−	0.0887381i
$703$	−49.8885	+	36.2461i	−1.88158	+	1.36705i
$704$	−1.11803	+	0.812299i	−0.0421375	+	0.0306147i
$705$	26.1803			0.986009
$706$	7.09017	+	5.15131i	0.266842	+	0.193872i
$707$	2.52786			0.0950701
$708$	−1.11803	−	0.812299i	−0.0420183	−	0.0305281i
$709$	−9.36068	+	28.8092i	−0.351548	+	1.08195i	0.606437	+	0.795132i	$0.292598\pi$
$709$	−9.36068	+	28.8092i	−0.351548	+	1.08195i	−0.957984	+	0.286821i	$0.907402\pi$
$710$	10.0000	−	30.7768i	0.375293	−	1.15503i
$711$	−1.04508	−	3.21644i	−0.0391937	−	0.120626i
$712$	3.85410	−	11.8617i	0.144439	−	0.444536i
$713$	−6.05573	+	18.6376i	−0.226789	+	0.697984i
$714$	0.381966	+	1.17557i	0.0142947	+	0.0439946i
$715$	2.36068	+	7.26543i	0.0882844	+	0.271711i
$716$	0.972136	−	2.99193i	0.0363304	−	0.111814i
$717$	20.7984	+	15.1109i	0.776730	+	0.564327i
$718$	−0.180340			−0.00673022
$719$	35.1246	+	25.5195i	1.30993	+	0.951718i	1.00000		0.000957448i	$0.000304765\pi$
$719$	35.1246	+	25.5195i	1.30993	+	0.951718i	0.309927	+	0.950760i	$0.399695\pi$
$720$	0.690983	−	2.12663i	0.0257514	−	0.0792547i
$721$	0.409830	−	0.297759i	0.0152629	−	0.0110891i
$722$	−32.6976	+	23.7562i	−1.21688	+	0.884113i
$723$	3.26393	+	10.0453i	0.121387	+	0.373591i
$724$	24.6525			0.916202
$725$	−0.729490	+	2.24514i	−0.0270926	+	0.0833824i
$726$	9.09017			0.337368
$727$	−10.9443	−	33.6830i	−0.405901	−	1.24923i	−0.920141	−	0.391587i	$-0.871926\pi$
$727$	−10.9443	−	33.6830i	−0.405901	−	1.24923i	0.514240	−	0.857646i	$-0.328074\pi$
$728$	−0.763932	+	0.555029i	−0.0283132	+	0.0205707i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−22.5623	−	16.3925i	−0.835068	−	0.606713i
$731$	14.9443	+	10.8576i	0.552734	+	0.401585i
$732$	−7.23607			−0.267453
$733$	0.0901699	+	0.0655123i	0.00333050	+	0.00241975i	0.589449	−	0.807805i	$-0.299345\pi$
$733$	0.0901699	+	0.0655123i	0.00333050	+	0.00241975i	−0.586119	+	0.810225i	$0.699345\pi$
$734$	−8.77051	+	26.9929i	−0.323725	+	0.996324i
$735$	−12.3992	−	9.00854i	−0.457351	−	0.332285i
$736$	−1.38197	−	4.25325i	−0.0509399	−	0.156777i
$737$	−4.47214	+	13.7638i	−0.164733	+	0.506997i
$738$	−2.38197	+	7.33094i	−0.0876814	+	0.269856i
$739$	−7.97871	−	24.5560i	−0.293502	−	0.903305i	−0.983721	−	0.179705i	$-0.942486\pi$
$739$	−7.97871	−	24.5560i	−0.293502	−	0.903305i	0.690219	−	0.723601i	$-0.257514\pi$
$740$	−14.4721	+	10.5146i	−0.532006	+	0.386525i
$741$	−5.88854	+	18.1231i	−0.216321	+	0.665768i
$742$	−2.80902	−	2.04087i	−0.103122	−	0.0749227i
$743$	37.0132			1.35788			0.678940	−	0.734193i	$-0.262439\pi$
$743$	37.0132			1.35788			0.678940	+	0.734193i	$0.262439\pi$
$744$	3.54508	+	2.57565i	0.129969	+	0.0944281i
$745$	7.53851	+	23.2011i	0.276190	+	0.850024i
$746$	16.5623	−	12.0332i	0.606389	−	0.440567i
$747$	−7.16312	+	5.20431i	−0.262085	+	0.190416i
$748$	−1.38197	−	4.25325i	−0.0505297	−	0.155514i
$749$	−3.58359			−0.130942
$750$	−3.45492	−	10.6331i	−0.126156	−	0.388267i
$751$	0.201626			0.00735744			0.00367872	−	0.999993i	$-0.498829\pi$
$751$	0.201626			0.00735744			0.00367872	+	0.999993i	$0.498829\pi$
$752$	−3.61803	−	11.1352i	−0.131936	−	0.406058i
$753$	−5.30902	+	3.85723i	−0.193471	+	0.140565i
$754$	0.944272	−	0.686054i	0.0343884	−	0.0249846i
$755$	1.84752	+	5.68609i	0.0672383	+	0.206938i
$756$	0.309017	+	0.224514i	0.0112388	+	0.00816549i
$757$	23.1246			0.840478			0.420239	−	0.907413i	$-0.361946\pi$
$757$	23.1246			0.840478			0.420239	+	0.907413i	$0.361946\pi$
$758$	−1.76393	−	1.28157i	−0.0640689	−	0.0465488i
$759$	1.90983	−	5.87785i	0.0693224	−	0.213353i
$760$	−13.9443	+	10.1311i	−0.505812	+	0.367494i
$761$	−7.85410	−	24.1724i	−0.284711	−	0.876250i	−0.986485	−	0.163851i	$-0.947608\pi$
$761$	−7.85410	−	24.1724i	−0.284711	−	0.876250i	0.701774	−	0.712399i	$-0.252392\pi$
$762$	−3.51722	+	10.8249i	−0.127415	+	0.392144i
$763$	1.50658	−	4.63677i	0.0545418	−	0.167862i
$764$	5.47214	+	16.8415i	0.197975	+	0.609304i
$765$	5.85410	+	4.25325i	0.211656	+	0.153777i
$766$	−6.18034	+	19.0211i	−0.223305	+	0.687261i
$767$	2.76393	+	2.00811i	0.0997998	+	0.0725088i
$768$	−1.00000			−0.0360844
$769$	28.8713	+	20.9762i	1.04113	+	0.756423i	0.970505	−	0.241080i	$-0.0775018\pi$
$769$	28.8713	+	20.9762i	1.04113	+	0.756423i	0.0706214	+	0.997503i	$0.477502\pi$
$770$	−0.954915	−	0.693786i	−0.0344127	−	0.0250023i
$771$	−17.7984	+	12.9313i	−0.640993	+	0.465709i
$772$	−9.01722	+	6.55139i	−0.324537	+	0.235790i
$773$	−2.42705	−	7.46969i	−0.0872950	−	0.268666i	0.897874	−	0.440252i	$-0.145111\pi$
$773$	−2.42705	−	7.46969i	−0.0872950	−	0.268666i	−0.985169	+	0.171586i	$0.945111\pi$
$774$	5.70820			0.205177
$775$	21.9098			0.787024
$776$	−5.61803			−0.201676
$777$	−0.944272	−	2.90617i	−0.0338756	−	0.104258i
$778$	11.8262	−	8.59226i	0.423991	−	0.308048i
$779$	48.0689	−	34.9241i	1.72225	−	1.25129i
$780$	−1.70820	+	5.25731i	−0.0611635	+	0.188242i
$781$	−16.1803	−	11.7557i	−0.578978	−	0.420652i
$782$	14.4721			0.517523
$783$	−0.381966	−	0.277515i	−0.0136504	−	0.00991756i
$784$	−2.11803	+	6.51864i	−0.0756441	+	0.232809i
$785$	−15.6525	−	48.1734i	−0.558661	−	1.71938i
$786$	−5.52786	−	17.0130i	−0.197172	−	0.606834i
$787$	−9.29180	+	28.5972i	−0.331217	+	1.01938i	0.637339	+	0.770584i	$0.280035\pi$
$787$	−9.29180	+	28.5972i	−0.331217	+	1.01938i	−0.968556	+	0.248797i	$0.919965\pi$
$788$	−1.82624	+	5.62058i	−0.0650570	+	0.200225i
$789$	−0.527864	−	1.62460i	−0.0187925	−	0.0578372i
$790$	−2.33688	+	7.19218i	−0.0831425	+	0.255886i
$791$	−1.74265	+	5.36331i	−0.0619614	+	0.190697i
$792$	−1.11803	−	0.812299i	−0.0397276	−	0.0288638i
$793$	17.8885			0.635241
$794$	28.5066	+	20.7112i	1.01166	+	0.735014i
$795$	−20.3262			−0.720897
$796$	14.9721	−	10.8779i	0.530673	−	0.385557i
$797$	29.5344	−	21.4580i	1.04616	−	0.760082i	0.0746844	−	0.997207i	$-0.476205\pi$
$797$	29.5344	−	21.4580i	1.04616	−	0.760082i	0.971479	+	0.237125i	$0.0762051\pi$
$798$	−0.909830	−	2.80017i	−0.0322076	−	0.0991249i
$799$	37.8885			1.34040
$800$	−4.04508	+	2.93893i	−0.143015	+	0.103907i
$801$	12.4721			0.440681
$802$	3.79837	+	11.6902i	0.134125	+	0.412795i
$803$	−13.9443	+	10.1311i	−0.492083	+	0.357519i
$804$	−8.47214	+	6.15537i	−0.298789	+	0.217083i
$805$	3.09017	−	2.24514i	0.108914	−	0.0791308i
$806$	−8.76393	−	6.36737i	−0.308696	−	0.224281i
$807$	−2.09017			−0.0735775
$808$	−5.35410	−	3.88998i	−0.188357	−	0.136849i
$809$	7.05573	−	21.7153i	0.248066	−	0.763469i	−0.747051	−	0.664767i	$-0.768531\pi$
$809$	7.05573	−	21.7153i	0.248066	−	0.763469i	0.995117	−	0.0987023i	$-0.0314692\pi$
$810$	2.23607			0.0785674
$811$	2.38197	+	7.33094i	0.0836421	+	0.257424i	0.984128	−	0.177462i	$-0.0567887\pi$
$811$	2.38197	+	7.33094i	0.0836421	+	0.257424i	−0.900486	+	0.434886i	$0.856789\pi$
$812$	−0.0557281	+	0.171513i	−0.00195567	+	0.00601894i
$813$	−3.40983	+	10.4944i	−0.119588	+	0.368054i
$814$	3.41641	+	10.5146i	0.119745	+	0.368537i
$815$	18.9443			0.663589
$816$	1.00000	−	3.07768i	0.0350070	−	0.107740i
$817$	−35.5967	−	25.8626i	−1.24537	−	0.904816i
$818$	−18.7984			−0.657270
$819$	−0.763932	−	0.555029i	−0.0266939	−	0.0193943i
$820$	13.9443	−	10.1311i	0.486955	−	0.353794i
$821$	27.4336	−	19.9317i	0.957440	−	0.695621i	0.00488541	−	0.999988i	$-0.498445\pi$
$821$	27.4336	−	19.9317i	0.957440	−	0.695621i	0.952555	+	0.304367i	$0.0984449\pi$
$822$	8.23607	−	5.98385i	0.287266	−	0.208711i
$823$	9.89919	+	30.4666i	0.345064	+	1.06200i	0.961550	+	0.274631i	$0.0885559\pi$
$823$	9.89919	+	30.4666i	0.345064	+	1.06200i	−0.616486	+	0.787366i	$0.711444\pi$
$824$	−1.32624			−0.0462017
$825$	−6.90983			−0.240569
$826$	−0.527864			−0.0183667
$827$	−13.3197	−	40.9937i	−0.463170	−	1.42549i	−0.861270	−	0.508148i	$-0.830330\pi$
$827$	−13.3197	−	40.9937i	−0.463170	−	1.42549i	0.398100	−	0.917342i	$-0.369670\pi$
$828$	3.61803	−	2.62866i	0.125735	−	0.0913521i
$829$	8.00000	−	5.81234i	0.277851	−	0.201871i	−0.440128	−	0.897935i	$-0.645067\pi$
$829$	8.00000	−	5.81234i	0.277851	−	0.201871i	0.717980	+	0.696064i	$0.245067\pi$
$830$	19.7984			0.687212
$831$	−0.763932	−	0.555029i	−0.0265005	−	0.0192537i
$832$	2.47214			0.0857059
$833$	−17.9443	−	13.0373i	−0.621732	−	0.451715i
$834$	−0.472136	+	1.45309i	−0.0163487	+	0.0503162i
$835$	−1.18034	+	3.63271i	−0.0408473	+	0.125715i
$836$	3.29180	+	10.1311i	0.113849	+	0.350392i
$837$	−1.35410	+	4.16750i	−0.0468046	+	0.144050i
$838$	2.50000	−	7.69421i	0.0863611	−	0.265792i
$839$	−11.8541	−	36.4832i	−0.409249	−	1.25954i	−0.917295	−	0.398209i	$-0.869632\pi$
$839$	−11.8541	−	36.4832i	−0.409249	−	1.25954i	0.508046	−	0.861330i	$-0.330368\pi$
$840$	−0.263932	−	0.812299i	−0.00910652	−	0.0280270i
$841$	−8.89261	+	27.3686i	−0.306642	+	0.943746i
$842$	22.0344	+	16.0090i	0.759357	+	0.551705i
$843$	29.8885			1.02942
$844$	−18.9443	−	13.7638i	−0.652089	−	0.473770i
$845$	−4.75987	+	14.6494i	−0.163744	+	0.503953i
$846$	9.47214	−	6.88191i	0.325659	−	0.236605i
$847$	2.80902	−	2.04087i	0.0965190	−	0.0701251i
$848$	2.80902	+	8.64527i	0.0964620	+	0.296880i
$849$	−31.4164			−1.07821
$850$	−5.00000	−	15.3884i	−0.171499	−	0.527818i
$851$	−35.7771			−1.22642
$852$	−4.47214	−	13.7638i	−0.153213	−	0.471541i
$853$	−4.52786	+	3.28969i	−0.155031	+	0.112637i	−0.662597	−	0.748977i	$-0.730546\pi$
$853$	−4.52786	+	3.28969i	−0.155031	+	0.112637i	0.507565	+	0.861613i	$0.330546\pi$
$854$	−2.23607	+	1.62460i	−0.0765167	+	0.0555926i
$855$	−13.9443	−	10.1311i	−0.476884	−	0.346477i
$856$	7.59017	+	5.51458i	0.259427	+	0.188485i
$857$	42.0689			1.43705			0.718523	−	0.695503i	$-0.244819\pi$
$857$	42.0689			1.43705			0.718523	+	0.695503i	$0.244819\pi$
$858$	2.76393	+	2.00811i	0.0943591	+	0.0685559i
$859$	−4.85410	+	14.9394i	−0.165620	+	0.509725i	−0.999081	−	0.0428520i	$-0.986356\pi$
$859$	−4.85410	+	14.9394i	−0.165620	+	0.509725i	0.833462	+	0.552577i	$0.186356\pi$
$860$	−10.3262	−	7.50245i	−0.352122	−	0.255831i
$861$	0.909830	+	2.80017i	0.0310069	+	0.0954295i
$862$	−11.3820	+	35.0301i	−0.387671	+	1.19313i
$863$	3.76393	−	11.5842i	0.128126	−	0.394330i	−0.866332	−	0.499469i	$-0.833529\pi$
$863$	3.76393	−	11.5842i	0.128126	−	0.394330i	0.994458	+	0.105138i	$0.0335285\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	11.0172	−	8.00448i	0.374597	−	0.272160i
$866$	−6.95492	+	21.4050i	−0.236338	+	0.727372i
$867$	−5.28115	−	3.83698i	−0.179357	−	0.130311i
$868$	1.67376			0.0568112
$869$	3.78115	+	2.74717i	0.128267	+	0.0931913i
$870$	0.326238	+	1.00406i	0.0110605	+	0.0340407i
$871$	20.9443	−	15.2169i	0.709670	−	0.515605i
$872$	−10.3262	+	7.50245i	−0.349691	+	0.254065i
$873$	−1.73607	−	5.34307i	−0.0587570	−	0.180835i
$874$	−34.4721			−1.16604
$875$	−3.45492	−	2.51014i	−0.116797	−	0.0848583i
$876$	−12.4721			−0.421394
$877$	0.965558	+	2.97168i	0.0326046	+	0.100347i	0.966034	−	0.258413i	$-0.0831997\pi$
$877$	0.965558	+	2.97168i	0.0326046	+	0.100347i	−0.933430	+	0.358760i	$0.883200\pi$
$878$	−11.7361	+	8.52675i	−0.396073	+	0.287764i
$879$	−8.82624	+	6.41264i	−0.297702	+	0.216293i
$880$	0.954915	+	2.93893i	0.0321902	+	0.0990712i
$881$	−20.7082	−	15.0454i	−0.697677	−	0.506892i	0.181498	−	0.983391i	$-0.441905\pi$
$881$	−20.7082	−	15.0454i	−0.697677	−	0.506892i	−0.879175	+	0.476499i	$0.841905\pi$
$882$	−6.85410			−0.230790
$883$	−22.7082	−	16.4985i	−0.764192	−	0.555218i	0.136001	−	0.990709i	$-0.456575\pi$
$883$	−22.7082	−	16.4985i	−0.764192	−	0.555218i	−0.900193	+	0.435491i	$0.856575\pi$
$884$	−2.47214	+	7.60845i	−0.0831469	+	0.255900i
$885$	−2.50000	+	1.81636i	−0.0840366	+	0.0610561i
$886$	4.44427	+	13.6781i	0.149308	+	0.459523i
$887$	−1.05573	+	3.24920i	−0.0354479	+	0.109097i	−0.967215	−	0.253960i	$-0.918267\pi$
$887$	−1.05573	+	3.24920i	−0.0354479	+	0.109097i	0.931767	+	0.363057i	$0.118267\pi$
$888$	−2.47214	+	7.60845i	−0.0829595	+	0.255323i
$889$	1.34346	+	4.13474i	0.0450582	+	0.138675i
$890$	−22.5623	−	16.3925i	−0.756290	−	0.549477i
$891$	0.427051	−	1.31433i	0.0143067	−	0.0440316i
$892$	−2.50000	−	1.81636i	−0.0837062	−	0.0608161i
$893$	−90.2492			−3.02008
$894$	8.82624	+	6.41264i	0.295194	+	0.214471i
$895$	−5.69098	−	4.13474i	−0.190229	−	0.138209i
$896$	−0.309017	+	0.224514i	−0.0103235	+	0.00750049i
$897$	−8.94427	+	6.49839i	−0.298641	+	0.216975i
$898$	−4.41641	−	13.5923i	−0.147377	−	0.453581i
$899$	−2.06888			−0.0690011
$900$	−4.04508	−	2.93893i	−0.134836	−	0.0979642i
$901$	−29.4164			−0.980003
$902$	−3.29180	−	10.1311i	−0.109605	−	0.337329i
$903$	1.76393	−	1.28157i	0.0587000	−	0.0426480i
$904$	11.9443	−	8.67802i	0.397261	−	0.288627i
$905$	17.0344	−	52.4266i	0.566244	−	1.74272i
$906$	2.16312	+	1.57160i	0.0718648	+	0.0522128i
$907$	21.5279			0.714821			0.357410	−	0.933947i	$-0.383660\pi$
$907$	21.5279			0.714821			0.357410	+	0.933947i	$0.383660\pi$
$908$	−9.11803	−	6.62464i	−0.302593	−	0.219846i
$909$	2.04508	−	6.29412i	0.0678312	−	0.208763i
$910$	0.652476	+	2.00811i	0.0216294	+	0.0665683i
$911$	−1.29180	−	3.97574i	−0.0427991	−	0.131722i	0.927374	−	0.374136i	$-0.122061\pi$
$911$	−1.29180	−	3.97574i	−0.0427991	−	0.131722i	−0.970173	+	0.242414i	$0.922061\pi$
$912$	−2.38197	+	7.33094i	−0.0788748	+	0.242752i
$913$	3.78115	−	11.6372i	0.125138	−	0.385135i
$914$	2.19098	+	6.74315i	0.0724713	+	0.223044i
$915$	−5.00000	+	15.3884i	−0.165295	+	0.508725i
$916$	−4.47214	+	13.7638i	−0.147764	+	0.454769i
$917$	−5.52786	−	4.01623i	−0.182546	−	0.132628i
$918$	3.23607			0.106806
$919$	−39.4164	−	28.6377i	−1.30023	−	0.944670i	−0.300269	−	0.953854i	$-0.597077\pi$
$919$	−39.4164	−	28.6377i	−1.30023	−	0.944670i	−0.999958	+	0.00918396i	$0.997077\pi$
$920$	−10.0000			−0.329690
$921$	8.09017	−	5.87785i	0.266580	−	0.193682i
$922$	10.1631	−	7.38394i	0.334704	−	0.243177i
$923$	11.0557	+	34.0260i	0.363904	+	1.11998i
$924$	−0.527864			−0.0173655
$925$	12.3607	+	38.0423i	0.406417	+	1.25082i
$926$	30.8328			1.01323
$927$	−0.409830	−	1.26133i	−0.0134606	−	0.0414274i
$928$	0.381966	−	0.277515i	0.0125386	−	0.00910986i
$929$	−46.1246	+	33.5115i	−1.51330	+	1.09948i	−0.548613	+	0.836077i	$0.684844\pi$
$929$	−46.1246	+	33.5115i	−1.51330	+	1.09948i	−0.964687	+	0.263400i	$0.915156\pi$
$930$	7.92705	−	5.75934i	0.259938	−	0.188856i
$931$	42.7426	+	31.0543i	1.40083	+	1.01777i
$932$	−12.6525			−0.414446
$933$	−15.3262	−	11.1352i	−0.501759	−	0.364549i
$934$	8.13525	−	25.0377i	0.266194	−	0.819260i
$935$	−10.0000			−0.327035
$936$	0.763932	+	2.35114i	0.0249699	+	0.0768494i
$937$	15.9721	−	49.1572i	0.521787	−	1.60590i	−0.248796	−	0.968556i	$-0.580035\pi$
$937$	15.9721	−	49.1572i	0.521787	−	1.60590i	0.770583	−	0.637339i	$-0.219965\pi$
$938$	−1.23607	+	3.80423i	−0.0403591	+	0.124212i
$939$	−5.33688	−	16.4252i	−0.174163	−	0.536017i
$940$	−26.1803			−0.853909
$941$	−7.59017	+	23.3601i	−0.247432	+	0.761519i	0.747794	+	0.663930i	$0.231113\pi$
$941$	−7.59017	+	23.3601i	−0.247432	+	0.761519i	−0.995227	+	0.0975885i	$0.968887\pi$
$942$	−18.3262	−	13.3148i	−0.597101	−	0.433819i
$943$	34.4721			1.12257
$944$	1.11803	+	0.812299i	0.0363889	+	0.0264381i
$945$	0.690983	−	0.502029i	0.0224777	−	0.0163310i
$946$	−6.38197	+	4.63677i	−0.207496	+	0.150754i
$947$	10.8713	−	7.89848i	0.353271	−	0.256666i	−0.396969	−	0.917832i	$-0.629938\pi$
$947$	10.8713	−	7.89848i	0.353271	−	0.256666i	0.750240	+	0.661166i	$0.229938\pi$
$948$	1.04508	+	3.21644i	0.0339428	+	0.104465i
$949$	30.8328			1.00088
$950$	11.9098	+	36.6547i	0.386406	+	1.18924i
$951$	0.437694			0.0141932
$952$	−0.381966	−	1.17557i	−0.0123796	−	0.0381005i
$953$	46.3607	−	33.6830i	1.50177	−	1.09110i	0.532100	−	0.846682i	$-0.321403\pi$
$953$	46.3607	−	33.6830i	1.50177	−	1.09110i	0.969670	−	0.244418i	$-0.0785969\pi$
$954$	−7.35410	+	5.34307i	−0.238098	+	0.172988i
$955$	39.5967			1.28132
$956$	−20.7984	−	15.1109i	−0.672667	−	0.488722i
$957$	0.652476			0.0210915
$958$	−9.00000	−	6.53888i	−0.290777	−	0.211262i
$959$	1.20163	−	3.69822i	0.0388025	−	0.119422i
$960$	−0.690983	+	2.12663i	−0.0223014	+	0.0686366i
$961$	−3.64590	−	11.2209i	−0.117610	−	0.361965i
$962$	6.11146	−	18.8091i	0.197041	−	0.606431i
$963$	−2.89919	+	8.92278i	−0.0934250	+	0.287533i
$964$	−3.26393	−	10.0453i	−0.105124	−	0.323539i
$965$	7.70163	+	23.7032i	0.247924	+	0.763032i
$966$	0.527864	−	1.62460i	0.0169837	−	0.0522706i
$967$	−17.8713	−	12.9843i	−0.574703	−	0.417546i	0.262108	−	0.965039i	$-0.415582\pi$
$967$	−17.8713	−	12.9843i	−0.574703	−	0.417546i	−0.836811	+	0.547492i	$0.815582\pi$
$968$	−9.09017			−0.292169
$969$	−20.1803	−	14.6619i	−0.648286	−	0.471007i
$970$	−3.88197	+	11.9475i	−0.124642	+	0.383610i
$971$	−30.1074	+	21.8743i	−0.966192	+	0.701980i	−0.954581	−	0.297953i	$-0.903696\pi$
$971$	−30.1074	+	21.8743i	−0.966192	+	0.701980i	−0.0116116	+	0.999933i	$0.503696\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	0.180340	+	0.555029i	0.00578143	+	0.0177934i
$974$	−6.79837			−0.217834
$975$	10.0000	+	7.26543i	0.320256	+	0.232680i
$976$	7.23607			0.231621
$977$	−1.61803	−	4.97980i	−0.0517655	−	0.159318i	0.921832	−	0.387590i	$-0.126692\pi$
$977$	−1.61803	−	4.97980i	−0.0517655	−	0.159318i	−0.973597	+	0.228272i	$0.926692\pi$
$978$	6.85410	−	4.97980i	0.219170	−	0.159236i
$979$	−13.9443	+	10.1311i	−0.445661	+	0.323792i
$980$	12.3992	+	9.00854i	0.396077	+	0.287767i
$981$	−10.3262	−	7.50245i	−0.329691	−	0.239535i
$982$	8.27051			0.263923
$983$	−14.4164	−	10.4741i	−0.459812	−	0.334073i	0.333646	−	0.942699i	$-0.391721\pi$
$983$	−14.4164	−	10.4741i	−0.459812	−	0.334073i	−0.793458	+	0.608626i	$0.791721\pi$
$984$	2.38197	−	7.33094i	0.0759343	−	0.233702i
$985$	10.6910	+	7.76745i	0.340643	+	0.247492i
$986$	0.472136	+	1.45309i	0.0150359	+	0.0462757i
$987$	1.38197	−	4.25325i	0.0439885	−	0.135383i
$988$	5.88854	−	18.1231i	0.187340	−	0.576572i
$989$	−7.88854	−	24.2784i	−0.250841	−	0.772010i
$990$	−2.50000	+	1.81636i	−0.0794552	+	0.0577276i
$991$	−8.17376	+	25.1563i	−0.259648	+	0.799115i	0.733230	+	0.679981i	$0.238012\pi$
$991$	−8.17376	+	25.1563i	−0.259648	+	0.799115i	−0.992878	+	0.119134i	$0.961988\pi$
$992$	−3.54508	−	2.57565i	−0.112557	−	0.0817771i
$993$	18.0000			0.571213
$994$	−4.47214	−	3.24920i	−0.141848	−	0.103058i
$995$	−12.7877	−	39.3566i	−0.405398	−	1.24769i
$996$	7.16312	−	5.20431i	0.226972	−	0.164905i
$997$	−35.2705	+	25.6255i	−1.11703	+	0.811569i	−0.983756	−	0.179511i	$-0.942548\pi$
$997$	−35.2705	+	25.6255i	−1.11703	+	0.811569i	−0.133272	+	0.991079i	$0.542548\pi$
$998$	−4.20163	−	12.9313i	−0.133000	−	0.409332i
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.g.a.31.1	✓	4
3.2	odd	2		450.2.h.c.181.1		4
5.2	odd	4		750.2.h.b.349.1		8
5.3	odd	4		750.2.h.b.349.2		8
5.4	even	2		750.2.g.b.151.1		4
25.2	odd	20		3750.2.c.b.1249.3		4
25.3	odd	20		750.2.h.b.649.1		8
25.4	even	10		750.2.g.b.601.1		4
25.11	even	5		3750.2.a.f.1.1		2
25.14	even	10		3750.2.a.d.1.2		2
25.21	even	5	inner	150.2.g.a.121.1	yes	4
25.22	odd	20		750.2.h.b.649.2		8
25.23	odd	20		3750.2.c.b.1249.2		4
75.71	odd	10		450.2.h.c.271.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.31.1	✓	4	1.1	even	1	trivial
150.2.g.a.121.1	yes	4	25.21	even	5	inner
450.2.h.c.181.1		4	3.2	odd	2
450.2.h.c.271.1		4	75.71	odd	10
750.2.g.b.151.1		4	5.4	even	2
750.2.g.b.601.1		4	25.4	even	10
750.2.h.b.349.1		8	5.2	odd	4
750.2.h.b.349.2		8	5.3	odd	4
750.2.h.b.649.1		8	25.3	odd	20
750.2.h.b.649.2		8	25.22	odd	20
3750.2.a.d.1.2		2	25.14	even	10
3750.2.a.f.1.1		2	25.11	even	5
3750.2.c.b.1249.2		4	25.23	odd	20
3750.2.c.b.1249.3		4	25.2	odd	20

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.690983 + 2.12663i) q^{5} +(0.809017 + 0.587785i) q^{6} +0.381966 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.690983 + 2.12663i) q^{5} +(0.809017 + 0.587785i) q^{6} +0.381966 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-1.80902 + 1.31433i) q^{10} +(0.427051 + 1.31433i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(0.763932 - 2.35114i) q^{13} +(0.118034 + 0.363271i) q^{14} +(1.80902 + 1.31433i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.61803 + 1.90211i) q^{17} +1.00000 q^{18} +(-6.23607 - 4.53077i) q^{19} +(-1.80902 - 1.31433i) q^{20} +(0.309017 - 0.224514i) q^{21} +(-1.11803 + 0.812299i) q^{22} +(-1.38197 - 4.25325i) q^{23} -1.00000 q^{24} +(-4.04508 + 2.93893i) q^{25} +2.47214 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.309017 + 0.224514i) q^{28} +(0.381966 - 0.277515i) q^{29} +(-0.690983 + 2.12663i) q^{30} +(-3.54508 - 2.57565i) q^{31} +1.00000 q^{32} +(1.11803 + 0.812299i) q^{33} +(-1.00000 + 3.07768i) q^{34} +(0.263932 + 0.812299i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.47214 - 7.60845i) q^{37} +(2.38197 - 7.33094i) q^{38} +(-0.763932 - 2.35114i) q^{39} +(0.690983 - 2.12663i) q^{40} +(-2.38197 + 7.33094i) q^{41} +(0.309017 + 0.224514i) q^{42} +5.70820 q^{43} +(-1.11803 - 0.812299i) q^{44} +2.23607 q^{45} +(3.61803 - 2.62866i) q^{46} +(9.47214 - 6.88191i) q^{47} +(-0.309017 - 0.951057i) q^{48} -6.85410 q^{49} +(-4.04508 - 2.93893i) q^{50} +3.23607 q^{51} +(0.763932 + 2.35114i) q^{52} +(-7.35410 + 5.34307i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-2.50000 + 1.81636i) q^{55} +(-0.309017 - 0.224514i) q^{56} -7.70820 q^{57} +(0.381966 + 0.277515i) q^{58} +(-0.427051 + 1.31433i) q^{59} -2.23607 q^{60} +(2.23607 + 6.88191i) q^{61} +(1.35410 - 4.16750i) q^{62} +(0.118034 - 0.363271i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.52786 q^{65} +(-0.427051 + 1.31433i) q^{66} +(8.47214 + 6.15537i) q^{67} -3.23607 q^{68} +(-3.61803 - 2.62866i) q^{69} +(-0.690983 + 0.502029i) q^{70} +(-11.7082 + 8.50651i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(3.85410 + 11.8617i) q^{73} +8.00000 q^{74} +(-1.54508 + 4.75528i) q^{75} +7.70820 q^{76} +(0.163119 + 0.502029i) q^{77} +(2.00000 - 1.45309i) q^{78} +(2.73607 - 1.98787i) q^{79} +2.23607 q^{80} +(-0.809017 - 0.587785i) q^{81} -7.70820 q^{82} +(-7.16312 - 5.20431i) q^{83} +(-0.118034 + 0.363271i) q^{84} +(-2.23607 + 6.88191i) q^{85} +(1.76393 + 5.42882i) q^{86} +(0.145898 - 0.449028i) q^{87} +(0.427051 - 1.31433i) q^{88} +(3.85410 + 11.8617i) q^{89} +(0.690983 + 2.12663i) q^{90} +(0.291796 - 0.898056i) q^{91} +(3.61803 + 2.62866i) q^{92} -4.38197 q^{93} +(9.47214 + 6.88191i) q^{94} +(5.32624 - 16.3925i) q^{95} +(0.809017 - 0.587785i) q^{96} +(4.54508 - 3.30220i) q^{97} +(-2.11803 - 6.51864i) q^{98} +1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + 5 q^{5} + q^{6} + 6 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 + 5 * q^5 + q^6 + 6 * q^7 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} + 5 q^{5} + q^{6} + 6 q^{7} - q^{8} - q^{9} - 5 q^{10} - 5 q^{11} + q^{12} + 12 q^{13} - 4 q^{14} + 5 q^{15} - q^{16} + 6 q^{17} + 4 q^{18} - 16 q^{19} - 5 q^{20} - q^{21} - 10 q^{23} - 4 q^{24} - 5 q^{25} - 8 q^{26} + q^{27} + q^{28} + 6 q^{29} - 5 q^{30} - 3 q^{31} + 4 q^{32} - 4 q^{34} + 10 q^{35} - q^{36} - 8 q^{37} + 14 q^{38} - 12 q^{39} + 5 q^{40} - 14 q^{41} - q^{42} - 4 q^{43} + 10 q^{46} + 20 q^{47} + q^{48} - 14 q^{49} - 5 q^{50} + 4 q^{51} + 12 q^{52} - 16 q^{53} + q^{54} - 10 q^{55} + q^{56} - 4 q^{57} + 6 q^{58} + 5 q^{59} - 8 q^{62} - 4 q^{63} - q^{64} + 40 q^{65} + 5 q^{66} + 16 q^{67} - 4 q^{68} - 10 q^{69} - 5 q^{70} - 20 q^{71} - q^{72} + 2 q^{73} + 32 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} + 8 q^{78} + 2 q^{79} - q^{81} - 4 q^{82} - 13 q^{83} + 4 q^{84} + 16 q^{86} + 14 q^{87} - 5 q^{88} + 2 q^{89} + 5 q^{90} + 28 q^{91} + 10 q^{92} - 22 q^{93} + 20 q^{94} - 10 q^{95} + q^{96} + 7 q^{97} - 4 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + 5 * q^5 + q^6 + 6 * q^7 - q^8 - q^9 - 5 * q^10 - 5 * q^11 + q^12 + 12 * q^13 - 4 * q^14 + 5 * q^15 - q^16 + 6 * q^17 + 4 * q^18 - 16 * q^19 - 5 * q^20 - q^21 - 10 * q^23 - 4 * q^24 - 5 * q^25 - 8 * q^26 + q^27 + q^28 + 6 * q^29 - 5 * q^30 - 3 * q^31 + 4 * q^32 - 4 * q^34 + 10 * q^35 - q^36 - 8 * q^37 + 14 * q^38 - 12 * q^39 + 5 * q^40 - 14 * q^41 - q^42 - 4 * q^43 + 10 * q^46 + 20 * q^47 + q^48 - 14 * q^49 - 5 * q^50 + 4 * q^51 + 12 * q^52 - 16 * q^53 + q^54 - 10 * q^55 + q^56 - 4 * q^57 + 6 * q^58 + 5 * q^59 - 8 * q^62 - 4 * q^63 - q^64 + 40 * q^65 + 5 * q^66 + 16 * q^67 - 4 * q^68 - 10 * q^69 - 5 * q^70 - 20 * q^71 - q^72 + 2 * q^73 + 32 * q^74 + 5 * q^75 + 4 * q^76 - 15 * q^77 + 8 * q^78 + 2 * q^79 - q^81 - 4 * q^82 - 13 * q^83 + 4 * q^84 + 16 * q^86 + 14 * q^87 - 5 * q^88 + 2 * q^89 + 5 * q^90 + 28 * q^91 + 10 * q^92 - 22 * q^93 + 20 * q^94 - 10 * q^95 + q^96 + 7 * q^97 - 4 * q^98 + 10 * q^99

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