LMFDB - Embedded newform 525.2.n.a.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
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			316.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	525.316
Dual form			525.2.n.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +2.23607 q^{5} +(0.500000 - 1.53884i) q^{6} -1.00000 q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +2.23607 q^{5} +(0.500000 - 1.53884i) q^{6} -1.00000 q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.92705 + 2.12663i) q^{10} +(0.618034 + 0.449028i) q^{11} +(0.500000 - 0.363271i) q^{12} +(2.80902 - 2.04087i) q^{13} +(-1.30902 - 0.951057i) q^{14} +(-0.690983 - 2.12663i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.454915 - 1.40008i) q^{17} -1.61803 q^{18} +(-1.11803 + 3.44095i) q^{19} +(0.427051 + 1.31433i) q^{20} +(0.309017 + 0.951057i) q^{21} +(0.381966 + 1.17557i) q^{22} +(0.309017 + 0.224514i) q^{23} -2.23607 q^{24} +5.00000 q^{25} +5.61803 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.190983 - 0.587785i) q^{28} +(-2.07295 - 6.37988i) q^{29} +(1.11803 - 3.44095i) q^{30} +(-1.19098 + 3.66547i) q^{31} +3.38197 q^{32} +(0.236068 - 0.726543i) q^{33} +(1.92705 - 1.40008i) q^{34} -2.23607 q^{35} +(-0.500000 - 0.363271i) q^{36} +(-0.927051 + 0.673542i) q^{37} +(-4.73607 + 3.44095i) q^{38} +(-2.80902 - 2.04087i) q^{39} +(1.54508 - 4.75528i) q^{40} +(-4.11803 + 2.99193i) q^{41} +(-0.500000 + 1.53884i) q^{42} +1.00000 q^{43} +(-0.145898 + 0.449028i) q^{44} +(-1.80902 + 1.31433i) q^{45} +(0.190983 + 0.587785i) q^{46} +(3.70820 + 11.4127i) q^{47} +(-3.92705 - 2.85317i) q^{48} +1.00000 q^{49} +(6.54508 + 4.75528i) q^{50} -1.47214 q^{51} +(1.73607 + 1.26133i) q^{52} +(1.26393 + 3.88998i) q^{53} +(0.500000 + 1.53884i) q^{54} +(1.38197 + 1.00406i) q^{55} +(-0.690983 + 2.12663i) q^{56} +3.61803 q^{57} +(3.35410 - 10.3229i) q^{58} +(-8.35410 + 6.06961i) q^{59} +(1.11803 - 0.812299i) q^{60} +(-0.236068 - 0.171513i) q^{61} +(-5.04508 + 3.66547i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(6.28115 - 4.56352i) q^{65} +(1.00000 - 0.726543i) q^{66} +(-1.78115 + 5.48183i) q^{67} +0.909830 q^{68} +(0.118034 - 0.363271i) q^{69} +(-2.92705 - 2.12663i) q^{70} +(0.454915 + 1.40008i) q^{71} +(0.690983 + 2.12663i) q^{72} +(-11.3992 - 8.28199i) q^{73} -1.85410 q^{74} +(-1.54508 - 4.75528i) q^{75} -2.23607 q^{76} +(-0.618034 - 0.449028i) q^{77} +(-1.73607 - 5.34307i) q^{78} +(-2.33688 - 7.19218i) q^{79} +(8.78115 - 6.37988i) q^{80} +(0.309017 - 0.951057i) q^{81} -8.23607 q^{82} +(-4.00000 + 12.3107i) q^{83} +(-0.500000 + 0.363271i) q^{84} +(1.01722 - 3.13068i) q^{85} +(1.30902 + 0.951057i) q^{86} +(-5.42705 + 3.94298i) q^{87} +(1.38197 - 1.00406i) q^{88} +(-3.61803 - 2.62866i) q^{89} -3.61803 q^{90} +(-2.80902 + 2.04087i) q^{91} +(-0.0729490 + 0.224514i) q^{92} +3.85410 q^{93} +(-6.00000 + 18.4661i) q^{94} +(-2.50000 + 7.69421i) q^{95} +(-1.04508 - 3.21644i) q^{96} +(3.54508 + 10.9106i) q^{97} +(1.30902 + 0.951057i) q^{98} -0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 2 q^{11} + 2 q^{12} + 9 q^{13} - 3 q^{14} - 5 q^{15} + 9 q^{16} + 13 q^{17} - 2 q^{18} - 5 q^{20} - q^{21} + 6 q^{22} - q^{23} + 20 q^{25} + 18 q^{26} + q^{27} - 3 q^{28} - 15 q^{29} - 7 q^{31} + 18 q^{32} - 8 q^{33} + q^{34} - 2 q^{36} + 3 q^{37} - 10 q^{38} - 9 q^{39} - 5 q^{40} - 12 q^{41} - 2 q^{42} + 4 q^{43} - 14 q^{44} - 5 q^{45} + 3 q^{46} - 12 q^{47} - 9 q^{48} + 4 q^{49} + 15 q^{50} + 12 q^{51} - 2 q^{52} + 14 q^{53} + 2 q^{54} + 10 q^{55} - 5 q^{56} + 10 q^{57} - 20 q^{59} + 8 q^{61} - 9 q^{62} + q^{63} - 7 q^{64} + 5 q^{65} + 4 q^{66} + 13 q^{67} + 26 q^{68} - 4 q^{69} - 5 q^{70} + 13 q^{71} + 5 q^{72} - 21 q^{73} + 6 q^{74} + 5 q^{75} + 2 q^{77} + 2 q^{78} - 25 q^{79} + 15 q^{80} - q^{81} - 24 q^{82} - 16 q^{83} - 2 q^{84} - 25 q^{85} + 3 q^{86} - 15 q^{87} + 10 q^{88} - 10 q^{89} - 10 q^{90} - 9 q^{91} - 7 q^{92} + 2 q^{93} - 24 q^{94} - 10 q^{95} + 7 q^{96} + 3 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9 + 5 * q^10 - 2 * q^11 + 2 * q^12 + 9 * q^13 - 3 * q^14 - 5 * q^15 + 9 * q^16 + 13 * q^17 - 2 * q^18 - 5 * q^20 - q^21 + 6 * q^22 - q^23 + 20 * q^25 + 18 * q^26 + q^27 - 3 * q^28 - 15 * q^29 - 7 * q^31 + 18 * q^32 - 8 * q^33 + q^34 - 2 * q^36 + 3 * q^37 - 10 * q^38 - 9 * q^39 - 5 * q^40 - 12 * q^41 - 2 * q^42 + 4 * q^43 - 14 * q^44 - 5 * q^45 + 3 * q^46 - 12 * q^47 - 9 * q^48 + 4 * q^49 + 15 * q^50 + 12 * q^51 - 2 * q^52 + 14 * q^53 + 2 * q^54 + 10 * q^55 - 5 * q^56 + 10 * q^57 - 20 * q^59 + 8 * q^61 - 9 * q^62 + q^63 - 7 * q^64 + 5 * q^65 + 4 * q^66 + 13 * q^67 + 26 * q^68 - 4 * q^69 - 5 * q^70 + 13 * q^71 + 5 * q^72 - 21 * q^73 + 6 * q^74 + 5 * q^75 + 2 * q^77 + 2 * q^78 - 25 * q^79 + 15 * q^80 - q^81 - 24 * q^82 - 16 * q^83 - 2 * q^84 - 25 * q^85 + 3 * q^86 - 15 * q^87 + 10 * q^88 - 10 * q^89 - 10 * q^90 - 9 * q^91 - 7 * q^92 + 2 * q^93 - 24 * q^94 - 10 * q^95 + 7 * q^96 + 3 * q^97 + 3 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	2.23607			1.00000
$5$	2.23607			1.00000
$6$	0.500000	−	1.53884i	0.204124	−	0.628230i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	2.92705	+	2.12663i	0.925615	+	0.672499i
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	0.677046	−	0.735940i	$-0.263260\pi$
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	−0.490702	+	0.871327i	$0.663260\pi$
$12$	0.500000	−	0.363271i	0.144338	−	0.104867i
$13$	2.80902	−	2.04087i	0.779081	−	0.566036i	−0.125622	−	0.992078i	$-0.540093\pi$
$13$	2.80902	−	2.04087i	0.779081	−	0.566036i	0.904703	+	0.426043i	$0.140093\pi$
$14$	−1.30902	−	0.951057i	−0.349850	−	0.254181i
$15$	−0.690983	−	2.12663i	−0.178411	−	0.549093i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	0.454915	−	1.40008i	0.110333	−	0.339570i	−0.880612	−	0.473838i	$-0.842868\pi$
$17$	0.454915	−	1.40008i	0.110333	−	0.339570i	0.990945	+	0.134268i	$0.0428682\pi$
$18$	−1.61803			−0.381374
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	0.737037	+	0.675852i	$0.236224\pi$
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	−0.993532	+	0.113557i	$0.963776\pi$
$20$	0.427051	+	1.31433i	0.0954915	+	0.293893i
$21$	0.309017	+	0.951057i	0.0674330	+	0.207538i
$22$	0.381966	+	1.17557i	0.0814354	+	0.250632i
$23$	0.309017	+	0.224514i	0.0644345	+	0.0468144i	0.619536	−	0.784968i	$-0.287321\pi$
$23$	0.309017	+	0.224514i	0.0644345	+	0.0468144i	−0.555102	+	0.831782i	$0.687321\pi$
$24$	−2.23607			−0.456435
$25$	5.00000			1.00000
$26$	5.61803			1.10179
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.190983	−	0.587785i	−0.0360924	−	0.111081i
$29$	−2.07295	−	6.37988i	−0.384937	−	1.18471i	−0.936526	−	0.350598i	$-0.885978\pi$
$29$	−2.07295	−	6.37988i	−0.384937	−	1.18471i	0.551589	−	0.834116i	$-0.314022\pi$
$30$	1.11803	−	3.44095i	0.204124	−	0.628230i
$31$	−1.19098	+	3.66547i	−0.213907	+	0.658338i	0.785323	+	0.619087i	$0.212497\pi$
$31$	−1.19098	+	3.66547i	−0.213907	+	0.658338i	−0.999229	+	0.0392508i	$0.987503\pi$
$32$	3.38197			0.597853
$33$	0.236068	−	0.726543i	0.0410942	−	0.126475i
$34$	1.92705	−	1.40008i	0.330487	−	0.240113i
$35$	−2.23607			−0.377964
$36$	−0.500000	−	0.363271i	−0.0833333	−	0.0605452i
$37$	−0.927051	+	0.673542i	−0.152406	+	0.110730i	−0.661375	−	0.750055i	$-0.730027\pi$
$37$	−0.927051	+	0.673542i	−0.152406	+	0.110730i	0.508969	+	0.860785i	$0.330027\pi$
$38$	−4.73607	+	3.44095i	−0.768292	+	0.558197i
$39$	−2.80902	−	2.04087i	−0.449803	−	0.326801i
$40$	1.54508	−	4.75528i	0.244299	−	0.751876i
$41$	−4.11803	+	2.99193i	−0.643129	+	0.467260i	−0.860924	−	0.508734i	$-0.830114\pi$
$41$	−4.11803	+	2.99193i	−0.643129	+	0.467260i	0.217795	+	0.975995i	$0.430114\pi$
$42$	−0.500000	+	1.53884i	−0.0771517	+	0.237448i
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−0.145898	+	0.449028i	−0.0219950	+	0.0676935i
$45$	−1.80902	+	1.31433i	−0.269672	+	0.195928i
$46$	0.190983	+	0.587785i	0.0281589	+	0.0866642i
$47$	3.70820	+	11.4127i	0.540897	+	1.66471i	0.730550	+	0.682859i	$0.239264\pi$
$47$	3.70820	+	11.4127i	0.540897	+	1.66471i	−0.189653	+	0.981851i	$0.560736\pi$
$48$	−3.92705	−	2.85317i	−0.566821	−	0.411820i
$49$	1.00000			0.142857
$50$	6.54508	+	4.75528i	0.925615	+	0.672499i
$51$	−1.47214			−0.206140
$52$	1.73607	+	1.26133i	0.240749	+	0.174915i
$53$	1.26393	+	3.88998i	0.173614	+	0.534330i	0.999567	−	0.0294087i	$-0.00936242\pi$
$53$	1.26393	+	3.88998i	0.173614	+	0.534330i	−0.825953	+	0.563739i	$0.809362\pi$
$54$	0.500000	+	1.53884i	0.0680414	+	0.209410i
$55$	1.38197	+	1.00406i	0.186344	+	0.135387i
$56$	−0.690983	+	2.12663i	−0.0923365	+	0.284182i
$57$	3.61803			0.479220
$58$	3.35410	−	10.3229i	0.440415	−	1.35546i
$59$	−8.35410	+	6.06961i	−1.08761	+	0.790196i	−0.978994	−	0.203888i	$-0.934642\pi$
$59$	−8.35410	+	6.06961i	−1.08761	+	0.790196i	−0.108617	+	0.994084i	$0.534642\pi$
$60$	1.11803	−	0.812299i	0.144338	−	0.104867i
$61$	−0.236068	−	0.171513i	−0.0302254	−	0.0219600i	0.572570	−	0.819856i	$-0.305946\pi$
$61$	−0.236068	−	0.171513i	−0.0302254	−	0.0219600i	−0.602795	+	0.797896i	$0.705946\pi$
$62$	−5.04508	+	3.66547i	−0.640726	+	0.465515i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	6.28115	−	4.56352i	0.779081	−	0.566036i
$66$	1.00000	−	0.726543i	0.123091	−	0.0894312i
$67$	−1.78115	+	5.48183i	−0.217602	+	0.669712i	0.781356	+	0.624085i	$0.214528\pi$
$67$	−1.78115	+	5.48183i	−0.217602	+	0.669712i	−0.998959	+	0.0456261i	$0.985472\pi$
$68$	0.909830			0.110333
$69$	0.118034	−	0.363271i	0.0142096	−	0.0437327i
$70$	−2.92705	−	2.12663i	−0.349850	−	0.254181i
$71$	0.454915	+	1.40008i	0.0539885	+	0.166159i	0.974415	−	0.224756i	$-0.0721585\pi$
$71$	0.454915	+	1.40008i	0.0539885	+	0.166159i	−0.920427	+	0.390915i	$0.872158\pi$
$72$	0.690983	+	2.12663i	0.0814331	+	0.250625i
$73$	−11.3992	−	8.28199i	−1.33417	−	0.969334i	−0.999637	−	0.0269515i	$-0.991420\pi$
$73$	−11.3992	−	8.28199i	−1.33417	−	0.969334i	−0.334537	−	0.942383i	$-0.608580\pi$
$74$	−1.85410			−0.215535
$75$	−1.54508	−	4.75528i	−0.178411	−	0.549093i
$76$	−2.23607			−0.256495
$77$	−0.618034	−	0.449028i	−0.0704315	−	0.0511715i
$78$	−1.73607	−	5.34307i	−0.196571	−	0.604983i
$79$	−2.33688	−	7.19218i	−0.262920	−	0.809184i	−0.992165	−	0.124932i	$-0.960129\pi$
$79$	−2.33688	−	7.19218i	−0.262920	−	0.809184i	0.729246	−	0.684252i	$-0.239871\pi$
$80$	8.78115	−	6.37988i	0.981763	−	0.713292i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−8.23607			−0.909522
$83$	−4.00000	+	12.3107i	−0.439057	+	1.35128i	0.449814	+	0.893122i	$0.351490\pi$
$83$	−4.00000	+	12.3107i	−0.439057	+	1.35128i	−0.888871	+	0.458157i	$0.848510\pi$
$84$	−0.500000	+	0.363271i	−0.0545545	+	0.0396361i
$85$	1.01722	−	3.13068i	0.110333	−	0.339570i
$86$	1.30902	+	0.951057i	0.141155	+	0.102555i
$87$	−5.42705	+	3.94298i	−0.581841	+	0.422732i
$88$	1.38197	−	1.00406i	0.147318	−	0.107033i
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	0.379280	−	0.925282i	$-0.376172\pi$
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	−0.762791	+	0.646645i	$0.776172\pi$
$90$	−3.61803			−0.381374
$91$	−2.80902	+	2.04087i	−0.294465	+	0.213941i
$92$	−0.0729490	+	0.224514i	−0.00760546	+	0.0234072i
$93$	3.85410			0.399652
$94$	−6.00000	+	18.4661i	−0.618853	+	1.90463i
$95$	−2.50000	+	7.69421i	−0.256495	+	0.789409i
$96$	−1.04508	−	3.21644i	−0.106664	−	0.328277i
$97$	3.54508	+	10.9106i	0.359949	+	1.10781i	0.953084	+	0.302706i	$0.0978899\pi$
$97$	3.54508	+	10.9106i	0.359949	+	1.10781i	−0.593135	+	0.805103i	$0.702110\pi$
$98$	1.30902	+	0.951057i	0.132231	+	0.0960712i
$99$	−0.763932			−0.0767781
$100$	0.954915	+	2.93893i	0.0954915	+	0.293893i
$101$	−19.1803			−1.90852			−0.954258	−	0.298986i	$-0.903352\pi$
$101$	−19.1803			−1.90852			−0.954258	+	0.298986i	$0.903352\pi$
$102$	−1.92705	−	1.40008i	−0.190806	−	0.138629i
$103$	−3.04508	−	9.37181i	−0.300041	−	0.923432i	−0.981481	−	0.191558i	$-0.938646\pi$
$103$	−3.04508	−	9.37181i	−0.300041	−	0.923432i	0.681440	−	0.731874i	$-0.261354\pi$
$104$	−2.39919	−	7.38394i	−0.235260	−	0.724055i
$105$	0.690983	+	2.12663i	0.0674330	+	0.207538i
$106$	−2.04508	+	6.29412i	−0.198636	+	0.611339i
$107$	18.7082			1.80859			0.904295	−	0.426908i	$-0.140397\pi$
$107$	18.7082			1.80859			0.904295	+	0.426908i	$0.140397\pi$
$108$	−0.190983	+	0.587785i	−0.0183773	+	0.0565597i
$109$	6.11803	−	4.44501i	0.586001	−	0.425755i	−0.254881	−	0.966972i	$-0.582036\pi$
$109$	6.11803	−	4.44501i	0.586001	−	0.425755i	0.840883	+	0.541217i	$0.182036\pi$
$110$	0.854102	+	2.62866i	0.0814354	+	0.250632i
$111$	0.927051	+	0.673542i	0.0879918	+	0.0639298i
$112$	−3.92705	+	2.85317i	−0.371071	+	0.269599i
$113$	−8.73607	+	6.34712i	−0.821820	+	0.597087i	−0.917233	−	0.398350i	$-0.869583\pi$
$113$	−8.73607	+	6.34712i	−0.821820	+	0.597087i	0.0954131	+	0.995438i	$0.469583\pi$
$114$	4.73607	+	3.44095i	0.443573	+	0.322275i
$115$	0.690983	+	0.502029i	0.0644345	+	0.0468144i
$116$	3.35410	−	2.43690i	0.311421	−	0.226260i
$117$	−1.07295	+	3.30220i	−0.0991942	+	0.305288i
$118$	−16.7082			−1.53811
$119$	−0.454915	+	1.40008i	−0.0417020	+	0.128346i
$120$	−5.00000			−0.456435
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	−0.145898	−	0.449028i	−0.0132090	−	0.0406531i
$123$	4.11803	+	2.99193i	0.371311	+	0.269773i
$124$	−2.38197			−0.213907
$125$	11.1803			1.00000
$126$	1.61803			0.144146
$127$	−9.70820	−	7.05342i	−0.861464	−	0.625890i	0.0668190	−	0.997765i	$-0.478715\pi$
$127$	−9.70820	−	7.05342i	−0.861464	−	0.625890i	−0.928283	+	0.371875i	$0.878715\pi$
$128$	−4.20820	−	12.9515i	−0.371956	−	1.14476i
$129$	−0.309017	−	0.951057i	−0.0272074	−	0.0837359i
$130$	12.5623			1.10179
$131$	−2.20820	+	6.79615i	−0.192932	+	0.593783i	0.807063	+	0.590466i	$0.201056\pi$
$131$	−2.20820	+	6.79615i	−0.192932	+	0.593783i	−0.999994	+	0.00331706i	$0.998944\pi$
$132$	0.472136			0.0410942
$133$	1.11803	−	3.44095i	0.0969458	−	0.298369i
$134$	−7.54508	+	5.48183i	−0.651796	+	0.473558i
$135$	1.80902	+	1.31433i	0.155695	+	0.113119i
$136$	−2.66312	−	1.93487i	−0.228361	−	0.165914i
$137$	4.50000	−	3.26944i	0.384461	−	0.279327i	−0.378721	−	0.925511i	$-0.623636\pi$
$137$	4.50000	−	3.26944i	0.384461	−	0.279327i	0.763182	+	0.646184i	$0.223636\pi$
$138$	0.500000	−	0.363271i	0.0425628	−	0.0309237i
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	0.882717	−	0.469905i	$-0.155712\pi$
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	−0.174131	+	0.984722i	$0.555712\pi$
$140$	−0.427051	−	1.31433i	−0.0360924	−	0.111081i
$141$	9.70820	−	7.05342i	0.817578	−	0.594005i
$142$	−0.736068	+	2.26538i	−0.0617695	+	0.190107i
$143$	2.65248			0.221811
$144$	−1.50000	+	4.61653i	−0.125000	+	0.384710i
$145$	−4.63525	−	14.2658i	−0.384937	−	1.18471i
$146$	−7.04508	−	21.6825i	−0.583055	−	1.79446i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	−0.572949	−	0.416272i	−0.0470961	−	0.0342173i
$149$	10.3262			0.845958			0.422979	−	0.906139i	$-0.360984\pi$
$149$	10.3262			0.845958			0.422979	+	0.906139i	$0.360984\pi$
$150$	2.50000	−	7.69421i	0.204124	−	0.628230i
$151$	4.56231			0.371275			0.185638	−	0.982618i	$-0.440565\pi$
$151$	4.56231			0.371275			0.185638	+	0.982618i	$0.440565\pi$
$152$	6.54508	+	4.75528i	0.530876	+	0.385704i
$153$	0.454915	+	1.40008i	0.0367777	+	0.113190i
$154$	−0.381966	−	1.17557i	−0.0307797	−	0.0947302i
$155$	−2.66312	+	8.19624i	−0.213907	+	0.658338i
$156$	0.663119	−	2.04087i	0.0530920	−	0.163400i
$157$	11.1459			0.889540			0.444770	−	0.895645i	$-0.353286\pi$
$157$	11.1459			0.889540			0.444770	+	0.895645i	$0.353286\pi$
$158$	3.78115	−	11.6372i	0.300812	−	0.925805i
$159$	3.30902	−	2.40414i	0.262422	−	0.190661i
$160$	7.56231			0.597853
$161$	−0.309017	−	0.224514i	−0.0243540	−	0.0176942i
$162$	1.30902	−	0.951057i	0.102846	−	0.0747221i
$163$	5.04508	−	3.66547i	0.395162	−	0.287102i	−0.372406	−	0.928070i	$-0.621467\pi$
$163$	5.04508	−	3.66547i	0.395162	−	0.287102i	0.767567	+	0.640968i	$0.221467\pi$
$164$	−2.54508	−	1.84911i	−0.198738	−	0.144391i
$165$	0.527864	−	1.62460i	0.0410942	−	0.126475i
$166$	−16.9443	+	12.3107i	−1.31513	+	0.955498i
$167$	1.83688	−	5.65334i	0.142142	−	0.437468i	−0.854490	−	0.519467i	$-0.826130\pi$
$167$	1.83688	−	5.65334i	0.142142	−	0.437468i	0.996632	+	0.0819989i	$0.0261304\pi$
$168$	2.23607			0.172516
$169$	−0.291796	+	0.898056i	−0.0224459	+	0.0690812i
$170$	4.30902	−	3.13068i	0.330487	−	0.240113i
$171$	−1.11803	−	3.44095i	−0.0854982	−	0.263136i
$172$	0.190983	+	0.587785i	0.0145623	+	0.0448182i
$173$	16.3262	+	11.8617i	1.24126	+	0.901829i	0.997682	−	0.0680522i	$-0.0216784\pi$
$173$	16.3262	+	11.8617i	1.24126	+	0.901829i	0.243579	+	0.969881i	$0.421678\pi$
$174$	−10.8541			−0.822847
$175$	−5.00000			−0.377964
$176$	3.70820			0.279516
$177$	8.35410	+	6.06961i	0.627933	+	0.456220i
$178$	−2.23607	−	6.88191i	−0.167600	−	0.515821i
$179$	−2.76393	−	8.50651i	−0.206586	−	0.635806i	−0.999645	−	0.0266609i	$-0.991513\pi$
$179$	−2.76393	−	8.50651i	−0.206586	−	0.635806i	0.793059	−	0.609145i	$-0.208487\pi$
$180$	−1.11803	−	0.812299i	−0.0833333	−	0.0605452i
$181$	4.92705	−	15.1639i	0.366225	−	1.12712i	−0.582986	−	0.812482i	$-0.698116\pi$
$181$	4.92705	−	15.1639i	0.366225	−	1.12712i	0.949211	−	0.314642i	$-0.101884\pi$
$182$	−5.61803			−0.416436
$183$	−0.0901699	+	0.277515i	−0.00666555	+	0.0205145i
$184$	0.690983	−	0.502029i	0.0509399	−	0.0370100i
$185$	−2.07295	+	1.50609i	−0.152406	+	0.110730i
$186$	5.04508	+	3.66547i	0.369924	+	0.268765i
$187$	0.909830	−	0.661030i	0.0665334	−	0.0483393i
$188$	−6.00000	+	4.35926i	−0.437595	+	0.317931i
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	−10.5902	+	7.69421i	−0.768292	+	0.558197i
$191$	−18.0623	+	13.1230i	−1.30694	+	0.949549i	−0.999998	−	0.00217790i	$-0.999307\pi$
$191$	−18.0623	+	13.1230i	−1.30694	+	0.949549i	−0.306945	+	0.951727i	$0.599307\pi$
$192$	−1.30902	+	4.02874i	−0.0944702	+	0.290749i
$193$	14.4164			1.03772			0.518858	−	0.854861i	$-0.326357\pi$
$193$	14.4164			1.03772			0.518858	+	0.854861i	$0.326357\pi$
$194$	−5.73607	+	17.6538i	−0.411826	+	1.26747i
$195$	−6.28115	−	4.56352i	−0.449803	−	0.326801i
$196$	0.190983	+	0.587785i	0.0136416	+	0.0419847i
$197$	2.26393	+	6.96767i	0.161298	+	0.496426i	0.998744	−	0.0500944i	$-0.0159522\pi$
$197$	2.26393	+	6.96767i	0.161298	+	0.496426i	−0.837446	+	0.546520i	$0.815952\pi$
$198$	−1.00000	−	0.726543i	−0.0710669	−	0.0516331i
$199$	1.70820			0.121091			0.0605457	−	0.998165i	$-0.480716\pi$
$199$	1.70820			0.121091			0.0605457	+	0.998165i	$0.480716\pi$
$200$	3.45492	−	10.6331i	0.244299	−	0.751876i
$201$	5.76393			0.406556
$202$	−25.1074	−	18.2416i	−1.76655	−	1.28347i
$203$	2.07295	+	6.37988i	0.145492	+	0.447780i
$204$	−0.281153	−	0.865300i	−0.0196846	−	0.0605831i
$205$	−9.20820	+	6.69015i	−0.643129	+	0.467260i
$206$	4.92705	−	15.1639i	0.343284	−	1.05652i
$207$	−0.381966			−0.0265485
$208$	5.20820	−	16.0292i	0.361124	−	1.11143i
$209$	−2.23607	+	1.62460i	−0.154672	+	0.112376i
$210$	−1.11803	+	3.44095i	−0.0771517	+	0.237448i
$211$	−5.66312	−	4.11450i	−0.389865	−	0.283254i	0.375535	−	0.926808i	$-0.377459\pi$
$211$	−5.66312	−	4.11450i	−0.389865	−	0.283254i	−0.765400	+	0.643555i	$0.777459\pi$
$212$	−2.04508	+	1.48584i	−0.140457	+	0.102048i
$213$	1.19098	−	0.865300i	0.0816048	−	0.0592894i
$214$	24.4894	+	17.7926i	1.67406	+	1.21627i
$215$	2.23607			0.152499
$216$	1.80902	−	1.31433i	0.123088	−	0.0894287i
$217$	1.19098	−	3.66547i	0.0808492	−	0.248828i
$218$	12.2361			0.828731
$219$	−4.35410	+	13.4005i	−0.294223	+	0.905525i
$220$	−0.326238	+	1.00406i	−0.0219950	+	0.0676935i
$221$	−1.57953	−	4.86128i	−0.106250	−	0.327005i
$222$	0.572949	+	1.76336i	0.0384538	+	0.118349i
$223$	18.5623	+	13.4863i	1.24302	+	0.903110i	0.997796	−	0.0663557i	$-0.0211372\pi$
$223$	18.5623	+	13.4863i	1.24302	+	0.903110i	0.245228	+	0.969465i	$0.421137\pi$
$224$	−3.38197			−0.225967
$225$	−4.04508	+	2.93893i	−0.269672	+	0.195928i
$226$	−17.4721			−1.16223
$227$	11.6353	+	8.45351i	0.772259	+	0.561079i	0.902646	−	0.430384i	$-0.141622\pi$
$227$	11.6353	+	8.45351i	0.772259	+	0.561079i	−0.130387	+	0.991463i	$0.541622\pi$
$228$	0.690983	+	2.12663i	0.0457615	+	0.140839i
$229$	−3.51722	−	10.8249i	−0.232425	−	0.715329i	−0.997453	−	0.0713322i	$-0.977275\pi$
$229$	−3.51722	−	10.8249i	−0.232425	−	0.715329i	0.765028	−	0.643997i	$-0.222725\pi$
$230$	0.427051	+	1.31433i	0.0281589	+	0.0866642i
$231$	−0.236068	+	0.726543i	−0.0155321	+	0.0478030i
$232$	−15.0000			−0.984798
$233$	2.74671	−	8.45351i	0.179943	−	0.553808i	−0.819882	−	0.572533i	$-0.805961\pi$
$233$	2.74671	−	8.45351i	0.179943	−	0.553808i	0.999825	+	0.0187254i	$0.00596082\pi$
$234$	−4.54508	+	3.30220i	−0.297121	+	0.215871i
$235$	8.29180	+	25.5195i	0.540897	+	1.66471i
$236$	−5.16312	−	3.75123i	−0.336090	−	0.244184i
$237$	−6.11803	+	4.44501i	−0.397409	+	0.288735i
$238$	−1.92705	+	1.40008i	−0.124912	+	0.0907540i
$239$	−3.61803	−	2.62866i	−0.234031	−	0.170034i	0.464589	−	0.885527i	$-0.346202\pi$
$239$	−3.61803	−	2.62866i	−0.234031	−	0.170034i	−0.698620	+	0.715493i	$0.746202\pi$
$240$	−8.78115	−	6.37988i	−0.566821	−	0.411820i
$241$	−21.5172	+	15.6332i	−1.38605	+	1.00702i	−0.389760	+	0.920916i	$0.627442\pi$
$241$	−21.5172	+	15.6332i	−1.38605	+	1.00702i	−0.996286	+	0.0861049i	$0.972558\pi$
$242$	5.20820	−	16.0292i	0.334796	−	1.03040i
$243$	−1.00000			−0.0641500
$244$	0.0557281	−	0.171513i	0.00356763	−	0.0109800i
$245$	2.23607			0.142857
$246$	2.54508	+	7.83297i	0.162269	+	0.499412i
$247$	3.88197	+	11.9475i	0.247004	+	0.760199i
$248$	6.97214	+	5.06555i	0.442731	+	0.321663i
$249$	12.9443			0.820310
$250$	14.6353	+	10.6331i	0.925615	+	0.672499i
$251$	−7.14590			−0.451045			−0.225523	−	0.974238i	$-0.572409\pi$
$251$	−7.14590			−0.451045			−0.225523	+	0.974238i	$0.572409\pi$
$252$	0.500000	+	0.363271i	0.0314970	+	0.0228839i
$253$	0.0901699	+	0.277515i	0.00566894	+	0.0174472i
$254$	−6.00000	−	18.4661i	−0.376473	−	1.15867i
$255$	−3.29180			−0.206140
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	19.2361			1.19991			0.599956	−	0.800033i	$-0.295185\pi$
$257$	19.2361			1.19991			0.599956	+	0.800033i	$0.295185\pi$
$258$	0.500000	−	1.53884i	0.0311286	−	0.0958041i
$259$	0.927051	−	0.673542i	0.0576041	−	0.0418519i
$260$	3.88197	+	2.82041i	0.240749	+	0.174915i
$261$	5.42705	+	3.94298i	0.335926	+	0.244065i
$262$	−9.35410	+	6.79615i	−0.577898	+	0.419868i
$263$	−9.75329	+	7.08618i	−0.601414	+	0.436953i	−0.846380	−	0.532579i	$-0.821223\pi$
$263$	−9.75329	+	7.08618i	−0.601414	+	0.436953i	0.244967	+	0.969531i	$0.421223\pi$
$264$	−1.38197	−	1.00406i	−0.0850541	−	0.0617954i
$265$	2.82624	+	8.69827i	0.173614	+	0.534330i
$266$	4.73607	−	3.44095i	0.290387	−	0.210978i
$267$	−1.38197	+	4.25325i	−0.0845749	+	0.260295i
$268$	−3.56231			−0.217602
$269$	−5.79180	+	17.8253i	−0.353132	+	1.08683i	0.603953	+	0.797020i	$0.293592\pi$
$269$	−5.79180	+	17.8253i	−0.353132	+	1.08683i	−0.957085	+	0.289808i	$0.906408\pi$
$270$	1.11803	+	3.44095i	0.0680414	+	0.209410i
$271$	−2.20820	−	6.79615i	−0.134139	−	0.412837i	0.861316	−	0.508069i	$-0.169641\pi$
$271$	−2.20820	−	6.79615i	−0.134139	−	0.412837i	−0.995455	+	0.0952323i	$0.969641\pi$
$272$	−2.20820	−	6.79615i	−0.133892	−	0.412077i
$273$	2.80902	+	2.04087i	0.170009	+	0.123519i
$274$	9.00000			0.543710
$275$	3.09017	+	2.24514i	0.186344	+	0.135387i
$276$	0.236068			0.0142096
$277$	−13.4894	−	9.80059i	−0.810497	−	0.588860i	0.103478	−	0.994632i	$-0.467003\pi$
$277$	−13.4894	−	9.80059i	−0.810497	−	0.588860i	−0.913975	+	0.405771i	$0.867003\pi$
$278$	5.16312	+	15.8904i	0.309663	+	0.953046i
$279$	−1.19098	−	3.66547i	−0.0713023	−	0.219446i
$280$	−1.54508	+	4.75528i	−0.0923365	+	0.284182i
$281$	1.57295	−	4.84104i	0.0938343	−	0.288792i	−0.893114	−	0.449831i	$-0.851484\pi$
$281$	1.57295	−	4.84104i	0.0938343	−	0.288792i	0.986948	+	0.161038i	$0.0514843\pi$
$282$	19.4164			1.15623
$283$	9.84346	−	30.2951i	0.585133	−	1.80085i	−0.0136032	−	0.999907i	$-0.504330\pi$
$283$	9.84346	−	30.2951i	0.585133	−	1.80085i	0.598736	−	0.800946i	$-0.295670\pi$
$284$	−0.736068	+	0.534785i	−0.0436776	+	0.0317336i
$285$	8.09017			0.479220
$286$	3.47214	+	2.52265i	0.205312	+	0.149168i
$287$	4.11803	−	2.99193i	0.243080	−	0.176608i
$288$	−2.73607	+	1.98787i	−0.161224	+	0.117136i
$289$	12.0000	+	8.71851i	0.705882	+	0.512854i
$290$	7.50000	−	23.0826i	0.440415	−	1.35546i
$291$	9.28115	−	6.74315i	0.544071	−	0.395291i
$292$	2.69098	−	8.28199i	0.157478	−	0.484667i
$293$	−22.4164			−1.30958			−0.654790	−	0.755811i	$-0.727243\pi$
$293$	−22.4164			−1.30958			−0.654790	+	0.755811i	$0.727243\pi$
$294$	0.500000	−	1.53884i	0.0291606	−	0.0897471i
$295$	−18.6803	+	13.5721i	−1.08761	+	0.790196i
$296$	0.791796	+	2.43690i	0.0460222	+	0.141642i
$297$	0.236068	+	0.726543i	0.0136981	+	0.0421583i
$298$	13.5172	+	9.82084i	0.783032	+	0.568906i
$299$	1.32624			0.0766983
$300$	2.50000	−	1.81636i	0.144338	−	0.104867i
$301$	−1.00000			−0.0576390
$302$	5.97214	+	4.33901i	0.343658	+	0.249682i
$303$	5.92705	+	18.2416i	0.340500	+	1.04795i
$304$	5.42705	+	16.7027i	0.311263	+	0.957968i
$305$	−0.527864	−	0.383516i	−0.0302254	−	0.0219600i
$306$	−0.736068	+	2.26538i	−0.0420782	+	0.129503i
$307$	8.38197			0.478384			0.239192	−	0.970972i	$-0.423117\pi$
$307$	8.38197			0.478384			0.239192	+	0.970972i	$0.423117\pi$
$308$	0.145898	−	0.449028i	0.00831331	−	0.0255857i
$309$	−7.97214	+	5.79210i	−0.453519	+	0.329501i
$310$	−11.2812	+	8.19624i	−0.640726	+	0.465515i
$311$	−17.4721	−	12.6942i	−0.990754	−	0.719825i	−0.0306679	−	0.999530i	$-0.509763\pi$
$311$	−17.4721	−	12.6942i	−0.990754	−	0.719825i	−0.960086	+	0.279705i	$0.909763\pi$
$312$	−6.28115	+	4.56352i	−0.355600	+	0.258359i
$313$	14.6803	−	10.6659i	0.829782	−	0.602872i	−0.0897157	−	0.995967i	$-0.528596\pi$
$313$	14.6803	−	10.6659i	0.829782	−	0.602872i	0.919498	+	0.393096i	$0.128596\pi$
$314$	14.5902	+	10.6004i	0.823371	+	0.598214i
$315$	1.80902	−	1.31433i	0.101927	−	0.0740540i
$316$	3.78115	−	2.74717i	0.212706	−	0.154540i
$317$	−3.69098	+	11.3597i	−0.207306	+	0.638023i	0.792305	+	0.610126i	$0.208881\pi$
$317$	−3.69098	+	11.3597i	−0.207306	+	0.638023i	−0.999611	+	0.0278972i	$0.991119\pi$
$318$	6.61803			0.371121
$319$	1.58359	−	4.87380i	0.0886641	−	0.272880i
$320$	−7.66312	−	5.56758i	−0.428381	−	0.311237i
$321$	−5.78115	−	17.7926i	−0.322672	−	0.993084i
$322$	−0.190983	−	0.587785i	−0.0106431	−	0.0327560i
$323$	4.30902	+	3.13068i	0.239760	+	0.174196i
$324$	0.618034			0.0343352
$325$	14.0451	−	10.2044i	0.779081	−	0.566036i
$326$	10.0902			0.558843
$327$	−6.11803	−	4.44501i	−0.338328	−	0.245810i
$328$	3.51722	+	10.8249i	0.194206	+	0.597705i
$329$	−3.70820	−	11.4127i	−0.204440	−	0.629201i
$330$	2.23607	−	1.62460i	0.123091	−	0.0894312i
$331$	−4.01722	+	12.3637i	−0.220806	+	0.679572i	0.777884	+	0.628408i	$0.216293\pi$
$331$	−4.01722	+	12.3637i	−0.220806	+	0.679572i	−0.998690	+	0.0511642i	$0.983707\pi$
$332$	−8.00000			−0.439057
$333$	0.354102	−	1.08981i	0.0194047	−	0.0597214i
$334$	7.78115	−	5.65334i	0.425766	−	0.309337i
$335$	−3.98278	+	12.2577i	−0.217602	+	0.669712i
$336$	3.92705	+	2.85317i	0.214238	+	0.155653i
$337$	13.2812	−	9.64932i	0.723471	−	0.525632i	−0.164021	−	0.986457i	$-0.552446\pi$
$337$	13.2812	−	9.64932i	0.723471	−	0.525632i	0.887491	+	0.460825i	$0.152446\pi$
$338$	−1.23607	+	0.898056i	−0.0672332	+	0.0488478i
$339$	8.73607	+	6.34712i	0.474478	+	0.344729i
$340$	2.03444			0.110333
$341$	−2.38197	+	1.73060i	−0.128991	+	0.0937172i
$342$	1.80902	−	5.56758i	0.0978204	−	0.301060i
$343$	−1.00000			−0.0539949
$344$	0.690983	−	2.12663i	0.0372553	−	0.114660i
$345$	0.263932	−	0.812299i	0.0142096	−	0.0437327i
$346$	10.0902	+	31.0543i	0.542451	+	1.66949i
$347$	−10.0729	−	31.0013i	−0.540744	−	1.66424i	−0.730899	−	0.682486i	$-0.760899\pi$
$347$	−10.0729	−	31.0013i	−0.540744	−	1.66424i	0.190155	−	0.981754i	$-0.439101\pi$
$348$	−3.35410	−	2.43690i	−0.179799	−	0.130631i
$349$	25.3262			1.35568			0.677841	−	0.735208i	$-0.262916\pi$
$349$	25.3262			1.35568			0.677841	+	0.735208i	$0.262916\pi$
$350$	−6.54508	−	4.75528i	−0.349850	−	0.254181i
$351$	3.47214			0.185329
$352$	2.09017	+	1.51860i	0.111406	+	0.0809415i
$353$	−4.48936	−	13.8168i	−0.238944	−	0.735395i	−0.996574	−	0.0827100i	$-0.973642\pi$
$353$	−4.48936	−	13.8168i	−0.238944	−	0.735395i	0.757629	−	0.652685i	$-0.226358\pi$
$354$	5.16312	+	15.8904i	0.274417	+	0.844568i
$355$	1.01722	+	3.13068i	0.0539885	+	0.166159i
$356$	0.854102	−	2.62866i	0.0452673	−	0.139318i
$357$	1.47214			0.0779137
$358$	4.47214	−	13.7638i	0.236360	−	0.727440i
$359$	14.2082	−	10.3229i	0.749880	−	0.544820i	−0.145909	−	0.989298i	$-0.546611\pi$
$359$	14.2082	−	10.3229i	0.749880	−	0.544820i	0.895790	+	0.444478i	$0.146611\pi$
$360$	1.54508	+	4.75528i	0.0814331	+	0.250625i
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$	20.8713	−	15.1639i	1.09697	−	0.796997i
$363$	−8.42705	+	6.12261i	−0.442305	+	0.321354i
$364$	−1.73607	−	1.26133i	−0.0909947	−	0.0661115i
$365$	−25.4894	−	18.5191i	−1.33417	−	0.969334i
$366$	−0.381966	+	0.277515i	−0.0199657	+	0.0145059i
$367$	11.0451	−	33.9933i	0.576549	−	1.77443i	−0.0542953	−	0.998525i	$-0.517291\pi$
$367$	11.0451	−	33.9933i	0.576549	−	1.77443i	0.630844	−	0.775910i	$-0.282709\pi$
$368$	1.85410			0.0966517
$369$	1.57295	−	4.84104i	0.0818845	−	0.252014i
$370$	−4.14590			−0.215535
$371$	−1.26393	−	3.88998i	−0.0656201	−	0.201958i
$372$	0.736068	+	2.26538i	0.0381633	+	0.117455i
$373$	−2.78115	−	2.02063i	−0.144003	−	0.104624i	0.513451	−	0.858119i	$-0.328367\pi$
$373$	−2.78115	−	2.02063i	−0.144003	−	0.104624i	−0.657454	+	0.753495i	$0.728367\pi$
$374$	1.81966			0.0940924
$375$	−3.45492	−	10.6331i	−0.178411	−	0.549093i
$376$	26.8328			1.38380
$377$	−18.8435	−	13.6906i	−0.970488	−	0.705100i
$378$	−0.500000	−	1.53884i	−0.0257172	−	0.0791495i
$379$	−11.3435	−	34.9116i	−0.582674	−	1.79329i	−0.608416	−	0.793619i	$-0.708195\pi$
$379$	−11.3435	−	34.9116i	−0.582674	−	1.79329i	0.0257412	−	0.999669i	$-0.491805\pi$
$380$	−5.00000			−0.256495
$381$	−3.70820	+	11.4127i	−0.189977	+	0.584689i
$382$	−36.1246			−1.84830
$383$	1.26393	−	3.88998i	0.0645839	−	0.198769i	−0.913558	−	0.406710i	$-0.866676\pi$
$383$	1.26393	−	3.88998i	0.0645839	−	0.198769i	0.978141	+	0.207941i	$0.0666761\pi$
$384$	−11.0172	+	8.00448i	−0.562220	+	0.408477i
$385$	−1.38197	−	1.00406i	−0.0704315	−	0.0511715i
$386$	18.8713	+	13.7108i	0.960525	+	0.697862i
$387$	−0.809017	+	0.587785i	−0.0411246	+	0.0298788i
$388$	−5.73607	+	4.16750i	−0.291205	+	0.211573i
$389$	−21.4443	−	15.5802i	−1.08727	−	0.789946i	−0.108332	−	0.994115i	$-0.534551\pi$
$389$	−21.4443	−	15.5802i	−1.08727	−	0.789946i	−0.978936	+	0.204169i	$0.934551\pi$
$390$	−3.88197	−	11.9475i	−0.196571	−	0.604983i
$391$	0.454915	−	0.330515i	0.0230060	−	0.0167149i
$392$	0.690983	−	2.12663i	0.0348999	−	0.107411i
$393$	7.14590			0.360463
$394$	−3.66312	+	11.2739i	−0.184545	+	0.567972i
$395$	−5.22542	−	16.0822i	−0.262920	−	0.809184i
$396$	−0.145898	−	0.449028i	−0.00733165	−	0.0225645i
$397$	5.78115	+	17.7926i	0.290148	+	0.892983i	0.984808	+	0.173645i	$0.0555546\pi$
$397$	5.78115	+	17.7926i	0.290148	+	0.892983i	−0.694661	+	0.719338i	$0.744445\pi$
$398$	2.23607	+	1.62460i	0.112084	+	0.0814338i
$399$	−3.61803			−0.181128
$400$	19.6353	−	14.2658i	0.981763	−	0.713292i
$401$	−32.7984			−1.63787			−0.818936	−	0.573884i	$-0.805436\pi$
$401$	−32.7984			−1.63787			−0.818936	+	0.573884i	$0.805436\pi$
$402$	7.54508	+	5.48183i	0.376315	+	0.273409i
$403$	4.13525	+	12.7270i	0.205992	+	0.633977i
$404$	−3.66312	−	11.2739i	−0.182247	−	0.560899i
$405$	0.690983	−	2.12663i	0.0343352	−	0.105673i
$406$	−3.35410	+	10.3229i	−0.166461	+	0.512315i
$407$	−0.875388			−0.0433914
$408$	−1.01722	+	3.13068i	−0.0503599	+	0.154992i
$409$	2.66312	−	1.93487i	0.131683	−	0.0956731i	−0.519994	−	0.854170i	$-0.674066\pi$
$409$	2.66312	−	1.93487i	0.131683	−	0.0956731i	0.651677	+	0.758497i	$0.274066\pi$
$410$	−18.4164			−0.909522
$411$	−4.50000	−	3.26944i	−0.221969	−	0.161270i
$412$	4.92705	−	3.57971i	0.242738	−	0.176360i
$413$	8.35410	−	6.06961i	0.411078	−	0.298666i
$414$	−0.500000	−	0.363271i	−0.0245737	−	0.0178538i
$415$	−8.94427	+	27.5276i	−0.439057	+	1.35128i
$416$	9.50000	−	6.90215i	0.465776	−	0.338406i
$417$	3.19098	−	9.82084i	0.156263	−	0.480928i
$418$	−4.47214			−0.218739
$419$	−3.98278	+	12.2577i	−0.194571	+	0.598829i	0.805410	+	0.592718i	$0.201945\pi$
$419$	−3.98278	+	12.2577i	−0.194571	+	0.598829i	−0.999981	+	0.00611116i	$0.998055\pi$
$420$	−1.11803	+	0.812299i	−0.0545545	+	0.0396361i
$421$	5.25329	+	16.1680i	0.256030	+	0.787978i	0.993625	+	0.112735i	$0.0359612\pi$
$421$	5.25329	+	16.1680i	0.256030	+	0.787978i	−0.737595	+	0.675243i	$0.764039\pi$
$422$	−3.50000	−	10.7719i	−0.170377	−	0.524368i
$423$	−9.70820	−	7.05342i	−0.472029	−	0.342949i
$424$	9.14590			0.444164
$425$	2.27458	−	7.00042i	0.110333	−	0.339570i
$426$	2.38197			0.115407
$427$	0.236068	+	0.171513i	0.0114241	+	0.00830012i
$428$	3.57295	+	10.9964i	0.172705	+	0.531531i
$429$	−0.819660	−	2.52265i	−0.0395736	−	0.121795i
$430$	2.92705	+	2.12663i	0.141155	+	0.102555i
$431$	6.10739	−	18.7966i	0.294183	−	0.905401i	−0.689312	−	0.724465i	$-0.742087\pi$
$431$	6.10739	−	18.7966i	0.294183	−	0.905401i	0.983495	−	0.180937i	$-0.0579129\pi$
$432$	4.85410			0.233543
$433$	2.01722	−	6.20837i	0.0969415	−	0.298355i	−0.890813	−	0.454369i	$-0.849865\pi$
$433$	2.01722	−	6.20837i	0.0969415	−	0.298355i	0.987755	+	0.156014i	$0.0498646\pi$
$434$	5.04508	−	3.66547i	0.242172	−	0.175948i
$435$	−12.1353	+	8.81678i	−0.581841	+	0.422732i
$436$	3.78115	+	2.74717i	0.181084	+	0.131566i
$437$	−1.11803	+	0.812299i	−0.0534828	+	0.0388575i
$438$	−18.4443	+	13.4005i	−0.881301	+	0.640303i
$439$	4.20820	+	3.05744i	0.200847	+	0.145924i	0.683663	−	0.729798i	$-0.260386\pi$
$439$	4.20820	+	3.05744i	0.200847	+	0.145924i	−0.482816	+	0.875722i	$0.660386\pi$
$440$	3.09017	−	2.24514i	0.147318	−	0.107033i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	2.55573	−	7.86572i	0.121564	−	0.374134i
$443$	−28.7984			−1.36825			−0.684126	−	0.729364i	$-0.739816\pi$
$443$	−28.7984			−1.36825			−0.684126	+	0.729364i	$0.739816\pi$
$444$	−0.218847	+	0.673542i	−0.0103860	+	0.0319649i
$445$	−8.09017	−	5.87785i	−0.383511	−	0.278637i
$446$	11.4721	+	35.3076i	0.543221	+	1.67186i
$447$	−3.19098	−	9.82084i	−0.150928	−	0.464510i
$448$	3.42705	+	2.48990i	0.161913	+	0.117637i
$449$	28.0902			1.32566			0.662829	−	0.748771i	$-0.269356\pi$
$449$	28.0902			1.32566			0.662829	+	0.748771i	$0.269356\pi$
$450$	−8.09017			−0.381374
$451$	−3.88854			−0.183104
$452$	−5.39919	−	3.92274i	−0.253956	−	0.184510i
$453$	−1.40983	−	4.33901i	−0.0662396	−	0.203865i
$454$	7.19098	+	22.1316i	0.337490	+	1.03869i
$455$	−6.28115	+	4.56352i	−0.294465	+	0.213941i
$456$	2.50000	−	7.69421i	0.117073	−	0.360314i
$457$	28.5066			1.33348			0.666741	−	0.745290i	$-0.267689\pi$
$457$	28.5066			1.33348			0.666741	+	0.745290i	$0.267689\pi$
$458$	5.69098	−	17.5150i	0.265922	−	0.818424i
$459$	1.19098	−	0.865300i	0.0555903	−	0.0403887i
$460$	−0.163119	+	0.502029i	−0.00760546	+	0.0234072i
$461$	14.5623	+	10.5801i	0.678234	+	0.492766i	0.872771	−	0.488129i	$-0.162320\pi$
$461$	14.5623	+	10.5801i	0.678234	+	0.492766i	−0.194537	+	0.980895i	$0.562320\pi$
$462$	−1.00000	+	0.726543i	−0.0465242	+	0.0338018i
$463$	−6.92705	+	5.03280i	−0.321927	+	0.233894i	−0.736997	−	0.675896i	$-0.763757\pi$
$463$	−6.92705	+	5.03280i	−0.321927	+	0.233894i	0.415070	+	0.909789i	$0.363757\pi$
$464$	−26.3435	−	19.1396i	−1.22296	−	0.888536i
$465$	8.61803			0.399652
$466$	11.6353	−	8.45351i	0.538993	−	0.391601i
$467$	1.47214	−	4.53077i	0.0681223	−	0.209659i	−0.911200	−	0.411964i	$-0.864843\pi$
$467$	1.47214	−	4.53077i	0.0681223	−	0.209659i	0.979323	+	0.202305i	$0.0648431\pi$
$468$	−2.14590			−0.0991942
$469$	1.78115	−	5.48183i	0.0822460	−	0.253127i
$470$	−13.4164	+	41.2915i	−0.618853	+	1.90463i
$471$	−3.44427	−	10.6004i	−0.158704	−	0.488440i
$472$	7.13525	+	21.9601i	0.328427	+	1.01079i
$473$	0.618034	+	0.449028i	0.0284172	+	0.0206463i
$474$	−12.2361			−0.562021
$475$	−5.59017	+	17.2048i	−0.256495	+	0.789409i
$476$	−0.909830			−0.0417020
$477$	−3.30902	−	2.40414i	−0.151509	−	0.110078i
$478$	−2.23607	−	6.88191i	−0.102275	−	0.314771i
$479$	0.954915	+	2.93893i	0.0436312	+	0.134283i	0.970499	−	0.241104i	$-0.0775097\pi$
$479$	0.954915	+	2.93893i	0.0436312	+	0.134283i	−0.926868	+	0.375387i	$0.877510\pi$
$480$	−2.33688	−	7.19218i	−0.106664	−	0.328277i
$481$	−1.22949	+	3.78398i	−0.0560599	+	0.172535i
$482$	−43.0344			−1.96017
$483$	−0.118034	+	0.363271i	−0.00537073	+	0.0165294i
$484$	5.20820	−	3.78398i	0.236737	−	0.171999i
$485$	7.92705	+	24.3970i	0.359949	+	1.10781i
$486$	−1.30902	−	0.951057i	−0.0593782	−	0.0431408i
$487$	−8.42705	+	6.12261i	−0.381866	+	0.277442i	−0.762114	−	0.647443i	$-0.775839\pi$
$487$	−8.42705	+	6.12261i	−0.381866	+	0.277442i	0.380248	+	0.924885i	$0.375839\pi$
$488$	−0.527864	+	0.383516i	−0.0238953	+	0.0173609i
$489$	−5.04508	−	3.66547i	−0.228147	−	0.165758i
$490$	2.92705	+	2.12663i	0.132231	+	0.0960712i
$491$	0.354102	−	0.257270i	0.0159804	−	0.0116104i	−0.579766	−	0.814783i	$-0.696856\pi$
$491$	0.354102	−	0.257270i	0.0159804	−	0.0116104i	0.595747	+	0.803172i	$0.296856\pi$
$492$	−0.972136	+	2.99193i	−0.0438273	+	0.134886i
$493$	−9.87539			−0.444765
$494$	−6.28115	+	19.3314i	−0.282602	+	0.869761i
$495$	−1.70820			−0.0767781
$496$	5.78115	+	17.7926i	0.259581	+	0.798909i
$497$	−0.454915	−	1.40008i	−0.0204057	−	0.0628024i
$498$	16.9443	+	12.3107i	0.759291	+	0.551657i
$499$	−40.3262			−1.80525			−0.902625	−	0.430427i	$-0.858363\pi$
$499$	−40.3262			−1.80525			−0.902625	+	0.430427i	$0.858363\pi$
$500$	2.13525	+	6.57164i	0.0954915	+	0.293893i
$501$	−5.94427			−0.265570
$502$	−9.35410	−	6.79615i	−0.417494	−	0.303327i
$503$	4.41641	+	13.5923i	0.196918	+	0.606051i	0.999949	+	0.0101137i	$0.00321933\pi$
$503$	4.41641	+	13.5923i	0.196918	+	0.606051i	−0.803031	+	0.595937i	$0.796781\pi$
$504$	−0.690983	−	2.12663i	−0.0307788	−	0.0947275i
$505$	−42.8885			−1.90852
$506$	−0.145898	+	0.449028i	−0.00648596	+	0.0199617i
$507$	0.944272			0.0419366
$508$	2.29180	−	7.05342i	0.101682	−	0.312945i
$509$	−1.64590	+	1.19581i	−0.0729531	+	0.0530036i	−0.623664	−	0.781692i	$-0.714357\pi$
$509$	−1.64590	+	1.19581i	−0.0729531	+	0.0530036i	0.550711	+	0.834696i	$0.314357\pi$
$510$	−4.30902	−	3.13068i	−0.190806	−	0.138629i
$511$	11.3992	+	8.28199i	0.504270	+	0.366374i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$	−2.92705	+	2.12663i	−0.129232	+	0.0938929i
$514$	25.1803	+	18.2946i	1.11066	+	0.806940i
$515$	−6.80902	−	20.9560i	−0.300041	−	0.923432i
$516$	0.500000	−	0.363271i	0.0220113	−	0.0159921i
$517$	−2.83282	+	8.71851i	−0.124587	+	0.383440i
$518$	1.85410			0.0814646
$519$	6.23607	−	19.1926i	0.273733	−	0.842464i
$520$	−5.36475	−	16.5110i	−0.235260	−	0.724055i
$521$	−7.47214	−	22.9969i	−0.327360	−	1.00751i	−0.970364	−	0.241648i	$-0.922312\pi$
$521$	−7.47214	−	22.9969i	−0.327360	−	1.00751i	0.643004	−	0.765863i	$-0.277688\pi$
$522$	3.35410	+	10.3229i	0.146805	+	0.451820i
$523$	−13.4721	−	9.78808i	−0.589095	−	0.428003i	0.252896	−	0.967493i	$-0.418617\pi$
$523$	−13.4721	−	9.78808i	−0.589095	−	0.428003i	−0.841992	+	0.539491i	$0.818617\pi$
$524$	−4.41641			−0.192932
$525$	1.54508	+	4.75528i	0.0674330	+	0.207538i
$526$	−19.5066			−0.850527
$527$	4.59017	+	3.33495i	0.199951	+	0.145273i
$528$	−1.14590	−	3.52671i	−0.0498688	−	0.153480i
$529$	−7.06231	−	21.7355i	−0.307057	−	0.945024i
$530$	−4.57295	+	14.0741i	−0.198636	+	0.611339i
$531$	3.19098	−	9.82084i	0.138477	−	0.426188i
$532$	2.23607			0.0969458
$533$	−5.46149	+	16.8087i	−0.236564	+	0.728068i
$534$	−5.85410	+	4.25325i	−0.253332	+	0.184056i
$535$	41.8328			1.80859
$536$	10.4271	+	7.57570i	0.450380	+	0.327220i
$537$	−7.23607	+	5.25731i	−0.312259	+	0.226870i
$538$	−24.5344	+	17.8253i	−1.05775	+	0.768504i
$539$	0.618034	+	0.449028i	0.0266206	+	0.0193410i
$540$	−0.427051	+	1.31433i	−0.0183773	+	0.0565597i
$541$	−23.7533	+	17.2578i	−1.02123	+	0.741970i	−0.966535	−	0.256533i	$-0.917420\pi$
$541$	−23.7533	+	17.2578i	−1.02123	+	0.741970i	−0.0546982	+	0.998503i	$0.517420\pi$
$542$	3.57295	−	10.9964i	0.153471	−	0.472336i
$543$	−15.9443			−0.684234
$544$	1.53851	−	4.73504i	0.0659630	−	0.203013i
$545$	13.6803	−	9.93935i	0.586001	−	0.425755i
$546$	1.73607	+	5.34307i	0.0742969	+	0.228662i
$547$	−2.47214	−	7.60845i	−0.105701	−	0.325314i	0.884193	−	0.467121i	$-0.154709\pi$
$547$	−2.47214	−	7.60845i	−0.105701	−	0.325314i	−0.989894	+	0.141807i	$0.954709\pi$
$548$	2.78115	+	2.02063i	0.118805	+	0.0863169i
$549$	0.291796			0.0124536
$550$	1.90983	+	5.87785i	0.0814354	+	0.250632i
$551$	24.2705			1.03396
$552$	−0.690983	−	0.502029i	−0.0294102	−	0.0213678i
$553$	2.33688	+	7.19218i	0.0993743	+	0.305843i
$554$	−8.33688	−	25.6583i	−0.354200	−	1.09012i
$555$	2.07295	+	1.50609i	0.0879918	+	0.0639298i
$556$	−1.97214	+	6.06961i	−0.0836372	+	0.257409i
$557$	17.1246			0.725593			0.362797	−	0.931868i	$-0.381822\pi$
$557$	17.1246			0.725593			0.362797	+	0.931868i	$0.381822\pi$
$558$	1.92705	−	5.93085i	0.0815786	−	0.251073i
$559$	2.80902	−	2.04087i	0.118809	−	0.0863196i
$560$	−8.78115	+	6.37988i	−0.371071	+	0.269599i
$561$	−0.909830	−	0.661030i	−0.0384131	−	0.0279087i
$562$	6.66312	−	4.84104i	0.281067	−	0.204207i
$563$	−31.4615	+	22.8581i	−1.32594	+	0.963355i	−0.326106	+	0.945333i	$0.605737\pi$
$563$	−31.4615	+	22.8581i	−1.32594	+	0.963355i	−0.999838	+	0.0180215i	$0.994263\pi$
$564$	6.00000	+	4.35926i	0.252646	+	0.183558i
$565$	−19.5344	+	14.1926i	−0.821820	+	0.597087i
$566$	41.6976	−	30.2951i	1.75268	−	1.27340i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	3.29180			0.138121
$569$	1.64590	−	5.06555i	0.0689996	−	0.212359i	−0.910611	−	0.413265i	$-0.864388\pi$
$569$	1.64590	−	5.06555i	0.0689996	−	0.212359i	0.979611	+	0.200906i	$0.0643884\pi$
$570$	10.5902	+	7.69421i	0.443573	+	0.322275i
$571$	1.40983	+	4.33901i	0.0589996	+	0.181582i	0.976213	−	0.216815i	$-0.0695668\pi$
$571$	1.40983	+	4.33901i	0.0589996	+	0.181582i	−0.917213	+	0.398397i	$0.869567\pi$
$572$	0.506578	+	1.55909i	0.0211811	+	0.0651887i
$573$	18.0623	+	13.1230i	0.754564	+	0.548223i
$574$	8.23607			0.343767
$575$	1.54508	+	1.12257i	0.0644345	+	0.0468144i
$576$	4.23607			0.176503
$577$	−22.5344	−	16.3722i	−0.938121	−	0.681585i	0.00984657	−	0.999952i	$-0.496866\pi$
$577$	−22.5344	−	16.3722i	−0.938121	−	0.681585i	−0.947968	+	0.318367i	$0.896866\pi$
$578$	7.41641	+	22.8254i	0.308482	+	0.949410i
$579$	−4.45492	−	13.7108i	−0.185140	−	0.569802i
$580$	7.50000	−	5.44907i	0.311421	−	0.226260i
$581$	4.00000	−	12.3107i	0.165948	−	0.510735i
$582$	18.5623			0.769432
$583$	−0.965558	+	2.97168i	−0.0399893	+	0.123075i
$584$	−25.4894	+	18.5191i	−1.05476	+	0.766326i
$585$	−2.39919	+	7.38394i	−0.0991942	+	0.305288i
$586$	−29.3435	−	21.3193i	−1.21217	−	0.880691i
$587$	−19.7082	+	14.3188i	−0.813445	+	0.591002i	−0.914827	−	0.403845i	$-0.867673\pi$
$587$	−19.7082	+	14.3188i	−0.813445	+	0.591002i	0.101383	+	0.994848i	$0.467673\pi$
$588$	0.500000	−	0.363271i	0.0206197	−	0.0149811i
$589$	−11.2812	−	8.19624i	−0.464832	−	0.337720i
$590$	−37.3607			−1.53811
$591$	5.92705	−	4.30625i	0.243806	−	0.177136i
$592$	−1.71885	+	5.29007i	−0.0706442	+	0.217420i
$593$	−41.8885			−1.72016			−0.860078	−	0.510162i	$-0.829585\pi$
$593$	−41.8885			−1.72016			−0.860078	+	0.510162i	$0.829585\pi$
$594$	−0.381966	+	1.17557i	−0.0156723	+	0.0482342i
$595$	−1.01722	+	3.13068i	−0.0417020	+	0.128346i
$596$	1.97214	+	6.06961i	0.0807818	+	0.248621i
$597$	−0.527864	−	1.62460i	−0.0216040	−	0.0664904i
$598$	1.73607	+	1.26133i	0.0709931	+	0.0515795i
$599$	11.1803			0.456816			0.228408	−	0.973565i	$-0.426648\pi$
$599$	11.1803			0.456816			0.228408	+	0.973565i	$0.426648\pi$
$600$	−11.1803			−0.456435
$601$	31.2705			1.27555			0.637775	−	0.770222i	$-0.279855\pi$
$601$	31.2705			1.27555			0.637775	+	0.770222i	$0.279855\pi$
$602$	−1.30902	−	0.951057i	−0.0533515	−	0.0387622i
$603$	−1.78115	−	5.48183i	−0.0725342	−	0.223237i
$604$	0.871323	+	2.68166i	0.0354536	+	0.109115i
$605$	−7.19756	−	22.1518i	−0.292622	−	0.900599i
$606$	−9.59017	+	29.5155i	−0.389574	+	1.19899i
$607$	−31.2918			−1.27009			−0.635047	−	0.772473i	$-0.719019\pi$
$607$	−31.2918			−1.27009			−0.635047	+	0.772473i	$0.719019\pi$
$608$	−3.78115	+	11.6372i	−0.153346	+	0.471950i
$609$	5.42705	−	3.94298i	0.219915	−	0.159778i
$610$	−0.326238	−	1.00406i	−0.0132090	−	0.0406531i
$611$	33.7082	+	24.4904i	1.36369	+	0.990777i
$612$	−0.736068	+	0.534785i	−0.0297538	+	0.0216174i
$613$	−24.5902	+	17.8658i	−0.993188	+	0.721593i	−0.960617	−	0.277876i	$-0.910369\pi$
$613$	−24.5902	+	17.8658i	−0.993188	+	0.721593i	−0.0325708	+	0.999469i	$0.510369\pi$
$614$	10.9721	+	7.97172i	0.442799	+	0.321713i
$615$	9.20820	+	6.69015i	0.371311	+	0.269773i
$616$	−1.38197	+	1.00406i	−0.0556810	+	0.0404546i
$617$	−7.47214	+	22.9969i	−0.300817	+	0.925819i	0.680388	+	0.732852i	$0.261811\pi$
$617$	−7.47214	+	22.9969i	−0.300817	+	0.925819i	−0.981205	+	0.192967i	$0.938189\pi$
$618$	−15.9443			−0.641373
$619$	9.83688	−	30.2748i	0.395378	−	1.21685i	−0.533289	−	0.845933i	$-0.679044\pi$
$619$	9.83688	−	30.2748i	0.395378	−	1.21685i	0.928667	−	0.370914i	$-0.120956\pi$
$620$	−5.32624			−0.213907
$621$	0.118034	+	0.363271i	0.00473654	+	0.0145776i
$622$	−10.7984	−	33.2340i	−0.432975	−	1.33256i
$623$	3.61803	+	2.62866i	0.144953	+	0.105315i
$624$	−16.8541			−0.674704
$625$	25.0000			1.00000
$626$	29.3607			1.17349
$627$	2.23607	+	1.62460i	0.0893000	+	0.0648802i
$628$	2.12868	+	6.55139i	0.0849435	+	0.261429i
$629$	0.521286	+	1.60435i	0.0207850	+	0.0639698i
$630$	3.61803			0.144146
$631$	−7.37132	+	22.6866i	−0.293448	+	0.903139i	0.690291	+	0.723532i	$0.257483\pi$
$631$	−7.37132	+	22.6866i	−0.293448	+	0.903139i	−0.983738	+	0.179607i	$0.942517\pi$
$632$	−16.9098			−0.672637
$633$	−2.16312	+	6.65740i	−0.0859763	+	0.264608i
$634$	−15.6353	+	11.3597i	−0.620955	+	0.451150i
$635$	−21.7082	−	15.7719i	−0.861464	−	0.625890i
$636$	2.04508	+	1.48584i	0.0810929	+	0.0589174i
$637$	2.80902	−	2.04087i	0.111297	−	0.0808622i
$638$	6.70820	−	4.87380i	0.265580	−	0.192955i
$639$	−1.19098	−	0.865300i	−0.0471146	−	0.0342307i
$640$	−9.40983	−	28.9605i	−0.371956	−	1.14476i
$641$	4.33688	−	3.15093i	0.171297	−	0.124454i	−0.498834	−	0.866698i	$-0.666238\pi$
$641$	4.33688	−	3.15093i	0.171297	−	0.124454i	0.670130	+	0.742243i	$0.266238\pi$
$642$	9.35410	−	28.7890i	0.369177	−	1.13621i
$643$	−46.8885			−1.84910			−0.924552	−	0.381056i	$-0.875560\pi$
$643$	−46.8885			−1.84910			−0.924552	+	0.381056i	$0.875560\pi$
$644$	0.0729490	−	0.224514i	0.00287459	−	0.00884709i
$645$	−0.690983	−	2.12663i	−0.0272074	−	0.0837359i
$646$	2.66312	+	8.19624i	0.104779	+	0.322477i
$647$	−3.59017	−	11.0494i	−0.141144	−	0.434397i	0.855351	−	0.518049i	$-0.173342\pi$
$647$	−3.59017	−	11.0494i	−0.141144	−	0.434397i	−0.996495	+	0.0836521i	$0.973342\pi$
$648$	−1.80902	−	1.31433i	−0.0710649	−	0.0516317i
$649$	−7.88854			−0.309652
$650$	28.0902			1.10179
$651$	−3.85410			−0.151054
$652$	3.11803	+	2.26538i	0.122112	+	0.0887193i
$653$	−12.4549	−	38.3323i	−0.487398	−	1.50006i	−0.828477	−	0.560023i	$-0.810792\pi$
$653$	−12.4549	−	38.3323i	−0.487398	−	1.50006i	0.341078	−	0.940035i	$-0.389208\pi$
$654$	−3.78115	−	11.6372i	−0.147855	−	0.455050i
$655$	−4.93769	+	15.1967i	−0.192932	+	0.593783i
$656$	−7.63525	+	23.4989i	−0.298107	+	0.917478i
$657$	14.0902			0.549710
$658$	6.00000	−	18.4661i	0.233904	−	0.719884i
$659$	29.9615	−	21.7683i	1.16713	−	0.847973i	0.176471	−	0.984306i	$-0.443532\pi$
$659$	29.9615	−	21.7683i	1.16713	−	0.847973i	0.990663	+	0.136333i	$0.0435318\pi$
$660$	1.05573			0.0410942
$661$	−21.3541	−	15.5147i	−0.830578	−	0.603450i	0.0891446	−	0.996019i	$-0.471587\pi$
$661$	−21.3541	−	15.5147i	−0.830578	−	0.603450i	−0.919723	+	0.392568i	$0.871587\pi$
$662$	−17.0172	+	12.3637i	−0.661393	+	0.480530i
$663$	−4.13525	+	3.00444i	−0.160600	+	0.116683i
$664$	23.4164	+	17.0130i	0.908733	+	0.660233i
$665$	2.50000	−	7.69421i	0.0969458	−	0.298369i
$666$	1.50000	−	1.08981i	0.0581238	−	0.0422294i
$667$	0.791796	−	2.43690i	0.0306585	−	0.0943571i
$668$	3.67376			0.142142
$669$	7.09017	−	21.8213i	0.274122	−	0.843660i
$670$	−16.8713	+	12.2577i	−0.651796	+	0.473558i
$671$	−0.0688837	−	0.212002i	−0.00265923	−	0.00818426i
$672$	1.04508	+	3.21644i	0.0403150	+	0.124077i
$673$	30.2705	+	21.9928i	1.16684	+	0.847761i	0.990628	−	0.136591i	$-0.0436146\pi$
$673$	30.2705	+	21.9928i	1.16684	+	0.847761i	0.176215	+	0.984352i	$0.443615\pi$
$674$	26.5623			1.02314
$675$	4.04508	+	2.93893i	0.155695	+	0.113119i
$676$	−0.583592			−0.0224459
$677$	34.7254	+	25.2295i	1.33461	+	0.969648i	0.999624	+	0.0274241i	$0.00873045\pi$
$677$	34.7254	+	25.2295i	1.33461	+	0.969648i	0.334983	+	0.942224i	$0.391270\pi$
$678$	5.39919	+	16.6170i	0.207355	+	0.638172i
$679$	−3.54508	−	10.9106i	−0.136048	−	0.418712i
$680$	−5.95492	−	4.32650i	−0.228361	−	0.165914i
$681$	4.44427	−	13.6781i	0.170305	−	0.524144i
$682$	−4.76393			−0.182420
$683$	−10.1803	+	31.3319i	−0.389540	+	1.19888i	0.543593	+	0.839349i	$0.317064\pi$
$683$	−10.1803	+	31.3319i	−0.389540	+	1.19888i	−0.933133	+	0.359532i	$0.882936\pi$
$684$	1.80902	−	1.31433i	0.0691695	−	0.0502546i
$685$	10.0623	−	7.31069i	0.384461	−	0.279327i
$686$	−1.30902	−	0.951057i	−0.0499785	−	0.0363115i
$687$	−9.20820	+	6.69015i	−0.351315	+	0.255245i
$688$	3.92705	−	2.85317i	0.149717	−	0.108776i
$689$	11.4894	+	8.34751i	0.437710	+	0.318015i
$690$	1.11803	−	0.812299i	0.0425628	−	0.0309237i
$691$	1.47214	−	1.06957i	0.0560027	−	0.0406883i	−0.559432	−	0.828876i	$-0.688981\pi$
$691$	1.47214	−	1.06957i	0.0560027	−	0.0406883i	0.615434	+	0.788188i	$0.288981\pi$
$692$	−3.85410	+	11.8617i	−0.146511	+	0.450914i
$693$	0.763932			0.0290194
$694$	16.2984	−	50.1612i	0.618678	−	1.90409i
$695$	18.6803	+	13.5721i	0.708586	+	0.514818i
$696$	4.63525	+	14.2658i	0.175699	+	0.540746i
$697$	2.31559	+	7.12667i	0.0877094	+	0.269942i
$698$	33.1525	+	24.0867i	1.25484	+	0.911694i
$699$	−8.88854			−0.336196
$700$	−0.954915	−	2.93893i	−0.0360924	−	0.111081i
$701$	3.18034			0.120120			0.0600599	−	0.998195i	$-0.480871\pi$
$701$	3.18034			0.120120			0.0600599	+	0.998195i	$0.480871\pi$
$702$	4.54508	+	3.30220i	0.171543	+	0.124633i
$703$	−1.28115	−	3.94298i	−0.0483196	−	0.148712i
$704$	−1.00000	−	3.07768i	−0.0376889	−	0.115995i
$705$	21.7082	−	15.7719i	0.817578	−	0.594005i
$706$	7.26393	−	22.3561i	0.273382	−	0.841382i
$707$	19.1803			0.721351
$708$	−1.97214	+	6.06961i	−0.0741174	+	0.228110i
$709$	33.8435	−	24.5887i	1.27102	−	0.923448i	0.271775	−	0.962361i	$-0.412389\pi$
$709$	33.8435	−	24.5887i	1.27102	−	0.923448i	0.999243	+	0.0389123i	$0.0123893\pi$
$710$	−1.64590	+	5.06555i	−0.0617695	+	0.190107i
$711$	6.11803	+	4.44501i	0.229444	+	0.166701i
$712$	−8.09017	+	5.87785i	−0.303192	+	0.220282i
$713$	−1.19098	+	0.865300i	−0.0446027	+	0.0324057i
$714$	1.92705	+	1.40008i	0.0721181	+	0.0523968i
$715$	5.93112			0.221811
$716$	4.47214	−	3.24920i	0.167132	−	0.121428i
$717$	−1.38197	+	4.25325i	−0.0516105	+	0.158841i
$718$	28.4164			1.06049
$719$	−13.0279	+	40.0956i	−0.485857	+	1.49532i	0.344878	+	0.938648i	$0.387920\pi$
$719$	−13.0279	+	40.0956i	−0.485857	+	1.49532i	−0.830735	+	0.556668i	$0.812080\pi$
$720$	−3.35410	+	10.3229i	−0.125000	+	0.384710i
$721$	3.04508	+	9.37181i	0.113405	+	0.349024i
$722$	2.95492	+	9.09429i	0.109971	+	0.338455i
$723$	21.5172	+	15.6332i	0.800234	+	0.581404i
$724$	9.85410			0.366225
$725$	−10.3647	−	31.8994i	−0.384937	−	1.18471i
$726$	−16.8541			−0.625514
$727$	−19.2812	−	14.0086i	−0.715098	−	0.519549i	0.169716	−	0.985493i	$-0.445715\pi$
$727$	−19.2812	−	14.0086i	−0.715098	−	0.519549i	−0.884814	+	0.465944i	$0.845715\pi$
$728$	2.39919	+	7.38394i	0.0889198	+	0.273667i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−15.7533	−	48.4836i	−0.583055	−	1.79446i
$731$	0.454915	−	1.40008i	0.0168256	−	0.0517840i
$732$	−0.180340			−0.00666555
$733$	12.6459	−	38.9201i	0.467087	−	1.43755i	−0.389252	−	0.921131i	$-0.627266\pi$
$733$	12.6459	−	38.9201i	0.467087	−	1.43755i	0.856339	−	0.516414i	$-0.172734\pi$
$734$	46.7877	−	33.9933i	1.72697	−	1.25471i
$735$	−0.690983	−	2.12663i	−0.0254873	−	0.0784418i
$736$	1.04508	+	0.759299i	0.0385223	+	0.0279881i
$737$	−3.56231	+	2.58817i	−0.131219	+	0.0953363i
$738$	6.66312	−	4.84104i	0.245273	−	0.178201i
$739$	−41.3435	−	30.0378i	−1.52084	−	1.10496i	−0.961067	−	0.276314i	$-0.910887\pi$
$739$	−41.3435	−	30.0378i	−1.52084	−	1.10496i	−0.559776	−	0.828644i	$-0.689113\pi$
$740$	−1.28115	−	0.930812i	−0.0470961	−	0.0342173i
$741$	10.1631	−	7.38394i	0.373352	−	0.271256i
$742$	2.04508	−	6.29412i	0.0750774	−	0.231065i
$743$	36.6525			1.34465			0.672324	−	0.740257i	$-0.265296\pi$
$743$	36.6525			1.34465			0.672324	+	0.740257i	$0.265296\pi$
$744$	2.66312	−	8.19624i	0.0976347	−	0.300489i
$745$	23.0902			0.845958
$746$	−1.71885	−	5.29007i	−0.0629315	−	0.193683i
$747$	−4.00000	−	12.3107i	−0.146352	−	0.450426i
$748$	0.562306	+	0.408539i	0.0205599	+	0.0149377i
$749$	−18.7082			−0.683583
$750$	5.59017	−	17.2048i	0.204124	−	0.628230i
$751$	14.3607			0.524029			0.262014	−	0.965064i	$-0.415613\pi$
$751$	14.3607			0.524029			0.262014	+	0.965064i	$0.415613\pi$
$752$	47.1246	+	34.2380i	1.71846	+	1.24853i
$753$	2.20820	+	6.79615i	0.0804714	+	0.247666i
$754$	−11.6459	−	35.8424i	−0.424119	−	1.30530i
$755$	10.2016			0.371275
$756$	0.190983	−	0.587785i	0.00694598	−	0.0213775i
$757$	25.2148			0.916447			0.458223	−	0.888837i	$-0.348486\pi$
$757$	25.2148			0.916447			0.458223	+	0.888837i	$0.348486\pi$
$758$	18.3541	−	56.4881i	0.666651	−	2.05174i
$759$	0.236068	−	0.171513i	0.00856872	−	0.00622554i
$760$	14.6353	+	10.6331i	0.530876	+	0.385704i
$761$	−0.399187	−	0.290026i	−0.0144705	−	0.0105134i	0.580526	−	0.814241i	$-0.302847\pi$
$761$	−0.399187	−	0.290026i	−0.0144705	−	0.0105134i	−0.594997	+	0.803728i	$0.702847\pi$
$762$	−15.7082	+	11.4127i	−0.569048	+	0.413438i
$763$	−6.11803	+	4.44501i	−0.221488	+	0.160920i
$764$	−11.1631	−	8.11048i	−0.403867	−	0.293427i
$765$	1.01722	+	3.13068i	0.0367777	+	0.113190i
$766$	5.35410	−	3.88998i	0.193452	−	0.140551i
$767$	−11.0795	+	34.0993i	−0.400059	+	1.23125i
$768$	−13.5623			−0.489388
$769$	−11.5066	+	35.4136i	−0.414938	+	1.27705i	0.497369	+	0.867539i	$0.334300\pi$
$769$	−11.5066	+	35.4136i	−0.414938	+	1.27705i	−0.912307	+	0.409508i	$0.865700\pi$
$770$	−0.854102	−	2.62866i	−0.0307797	−	0.0947302i
$771$	−5.94427	−	18.2946i	−0.214078	−	0.658863i
$772$	2.75329	+	8.47375i	0.0990930	+	0.304977i
$773$	11.4271	+	8.30224i	0.411002	+	0.298611i	0.774008	−	0.633176i	$-0.218249\pi$
$773$	11.4271	+	8.30224i	0.411002	+	0.298611i	−0.363005	+	0.931787i	$0.618249\pi$
$774$	−1.61803			−0.0581590
$775$	−5.95492	+	18.3273i	−0.213907	+	0.658338i
$776$	25.6525			0.920870
$777$	−0.927051	−	0.673542i	−0.0332578	−	0.0241632i
$778$	−13.2533	−	40.7894i	−0.475153	−	1.46237i
$779$	−5.69098	−	17.5150i	−0.203901	−	0.627542i
$780$	1.48278	−	4.56352i	0.0530920	−	0.163400i
$781$	−0.347524	+	1.06957i	−0.0124354	+	0.0382722i
$782$	0.909830			0.0325355
$783$	2.07295	−	6.37988i	0.0740812	−	0.227998i
$784$	3.92705	−	2.85317i	0.140252	−	0.101899i
$785$	24.9230			0.889540
$786$	9.35410	+	6.79615i	0.333650	+	0.242411i
$787$	3.21885	−	2.33863i	0.114740	−	0.0833631i	−0.528936	−	0.848662i	$-0.677409\pi$
$787$	3.21885	−	2.33863i	0.114740	−	0.0833631i	0.643675	+	0.765299i	$0.277409\pi$
$788$	−3.66312	+	2.66141i	−0.130493	+	0.0948089i
$789$	9.75329	+	7.08618i	0.347226	+	0.252275i
$790$	8.45492	−	26.0216i	0.300812	−	0.925805i
$791$	8.73607	−	6.34712i	0.310619	−	0.225678i
$792$	−0.527864	+	1.62460i	−0.0187568	+	0.0577276i
$793$	−1.01316			−0.0359782
$794$	−9.35410	+	28.7890i	−0.331965	+	1.02168i
$795$	7.39919	−	5.37582i	0.262422	−	0.190661i
$796$	0.326238	+	1.00406i	0.0115632	+	0.0355879i
$797$	0.0516628	+	0.159002i	0.00182999	+	0.00563213i	0.951967	−	0.306200i	$-0.0990575\pi$
$797$	0.0516628	+	0.159002i	0.00182999	+	0.00563213i	−0.950137	+	0.311832i	$0.899057\pi$
$798$	−4.73607	−	3.44095i	−0.167655	−	0.121808i
$799$	17.6656			0.624965
$800$	16.9098			0.597853
$801$	4.47214			0.158015
$802$	−42.9336	−	31.1931i	−1.51604	−	1.10147i
$803$	−3.32624	−	10.2371i	−0.117380	−	0.361260i
$804$	1.10081	+	3.38795i	0.0388227	+	0.119484i
$805$	−0.690983	−	0.502029i	−0.0243540	−	0.0176942i
$806$	−6.69098	+	20.5927i	−0.235680	+	0.725348i
$807$	18.7426			0.659772
$808$	−13.2533	+	40.7894i	−0.466249	+	1.43497i
$809$	22.0344	−	16.0090i	0.774690	−	0.562845i	−0.128691	−	0.991685i	$-0.541077\pi$
$809$	22.0344	−	16.0090i	0.774690	−	0.562845i	0.903381	+	0.428840i	$0.141077\pi$
$810$	2.92705	−	2.12663i	0.102846	−	0.0747221i
$811$	−15.2361	−	11.0697i	−0.535011	−	0.388708i	0.287218	−	0.957865i	$-0.407270\pi$
$811$	−15.2361	−	11.0697i	−0.535011	−	0.388708i	−0.822229	+	0.569157i	$0.807270\pi$
$812$	−3.35410	+	2.43690i	−0.117706	+	0.0855183i
$813$	−5.78115	+	4.20025i	−0.202754	+	0.147309i
$814$	−1.14590	−	0.832544i	−0.0401637	−	0.0291806i
$815$	11.2812	−	8.19624i	0.395162	−	0.287102i
$816$	−5.78115	+	4.20025i	−0.202381	+	0.147038i
$817$	−1.11803	+	3.44095i	−0.0391151	+	0.120384i
$818$	5.32624			0.186228
$819$	1.07295	−	3.30220i	0.0374919	−	0.115388i
$820$	−5.69098	−	4.13474i	−0.198738	−	0.144391i
$821$	13.1180	+	40.3732i	0.457823	+	1.40903i	0.867789	+	0.496932i	$0.165540\pi$
$821$	13.1180	+	40.3732i	0.457823	+	1.40903i	−0.409967	+	0.912100i	$0.634460\pi$
$822$	−2.78115	−	8.55951i	−0.0970038	−	0.298547i
$823$	2.48278	+	1.80384i	0.0865442	+	0.0628781i	0.630216	−	0.776420i	$-0.282966\pi$
$823$	2.48278	+	1.80384i	0.0865442	+	0.0628781i	−0.543672	+	0.839298i	$0.682966\pi$
$824$	−22.0344			−0.767606
$825$	1.18034	−	3.63271i	0.0410942	−	0.126475i
$826$	16.7082			0.581353
$827$	−10.6631	−	7.74721i	−0.370793	−	0.269397i	0.386747	−	0.922186i	$-0.373599\pi$
$827$	−10.6631	−	7.74721i	−0.370793	−	0.269397i	−0.757540	+	0.652789i	$0.773599\pi$
$828$	−0.0729490	−	0.224514i	−0.00253515	−	0.00780240i
$829$	−0.326238	−	1.00406i	−0.0113307	−	0.0348723i	0.945231	−	0.326401i	$-0.105836\pi$
$829$	−0.326238	−	1.00406i	−0.0113307	−	0.0348723i	−0.956562	+	0.291529i	$0.905836\pi$
$830$	−37.8885	+	27.5276i	−1.31513	+	0.955498i
$831$	−5.15248	+	15.8577i	−0.178737	+	0.550097i
$832$	−14.7082			−0.509915
$833$	0.454915	−	1.40008i	0.0157619	−	0.0485101i
$834$	13.5172	−	9.82084i	0.468063	−	0.340068i
$835$	4.10739	−	12.6412i	0.142142	−	0.437468i
$836$	−1.38197	−	1.00406i	−0.0477963	−	0.0347260i
$837$	−3.11803	+	2.26538i	−0.107775	+	0.0783031i
$838$	−16.8713	+	12.2577i	−0.582810	+	0.423436i
$839$	27.2984	+	19.8334i	0.942445	+	0.684726i	0.949008	−	0.315252i	$-0.102089\pi$
$839$	27.2984	+	19.8334i	0.942445	+	0.684726i	−0.00656332	+	0.999978i	$0.502089\pi$
$840$	5.00000			0.172516
$841$	−12.9443	+	9.40456i	−0.446354	+	0.324295i
$842$	−8.50000	+	26.1603i	−0.292929	+	0.901544i
$843$	−5.09017			−0.175315
$844$	1.33688	−	4.11450i	0.0460173	−	0.141627i
$845$	−0.652476	+	2.00811i	−0.0224459	+	0.0690812i
$846$	−6.00000	−	18.4661i	−0.206284	−	0.634878i
$847$	3.21885	+	9.90659i	0.110601	+	0.340395i
$848$	16.0623	+	11.6699i	0.551582	+	0.400748i
$849$	−31.8541			−1.09323
$850$	9.63525	−	7.00042i	0.330487	−	0.240113i
$851$	−0.437694			−0.0150040
$852$	0.736068	+	0.534785i	0.0252173	+	0.0183214i
$853$	−0.746711	−	2.29814i	−0.0255669	−	0.0786868i	0.937459	−	0.348096i	$-0.113172\pi$
$853$	−0.746711	−	2.29814i	−0.0255669	−	0.0786868i	−0.963026	+	0.269409i	$0.913172\pi$
$854$	0.145898	+	0.449028i	0.00499253	+	0.0153654i
$855$	−2.50000	−	7.69421i	−0.0854982	−	0.263136i
$856$	12.9271	−	39.7854i	0.441838	−	1.35984i
$857$	12.6525			0.432200			0.216100	−	0.976371i	$-0.430666\pi$
$857$	12.6525			0.432200			0.216100	+	0.976371i	$0.430666\pi$
$858$	1.32624	−	4.08174i	0.0452770	−	0.139348i
$859$	17.9894	−	13.0700i	0.613789	−	0.445944i	−0.236958	−	0.971520i	$-0.576150\pi$
$859$	17.9894	−	13.0700i	0.613789	−	0.445944i	0.850747	+	0.525576i	$0.176150\pi$
$860$	0.427051	+	1.31433i	0.0145623	+	0.0448182i
$861$	−4.11803	−	2.99193i	−0.140342	−	0.101965i
$862$	25.8713	−	18.7966i	0.881181	−	0.640215i
$863$	21.6525	−	15.7314i	0.737059	−	0.535505i	−0.154730	−	0.987957i	$-0.549451\pi$
$863$	21.6525	−	15.7314i	0.737059	−	0.535505i	0.891789	+	0.452452i	$0.149451\pi$
$864$	2.73607	+	1.98787i	0.0930829	+	0.0676287i
$865$	36.5066	+	26.5236i	1.24126	+	0.901829i
$866$	8.54508	−	6.20837i	0.290374	−	0.210969i
$867$	4.58359	−	14.1068i	0.155667	−	0.479094i
$868$	2.38197			0.0808492
$869$	1.78522	−	5.49434i	0.0605594	−	0.186383i
$870$	−24.2705			−0.822847
$871$	6.18441	+	19.0336i	0.209551	+	0.644930i
$872$	−5.22542	−	16.0822i	−0.176955	−	0.544612i
$873$	−9.28115	−	6.74315i	−0.314119	−	0.228221i
$874$	−2.23607			−0.0756361
$875$	−11.1803			−0.377964
$876$	−8.70820			−0.294223
$877$	35.5795	+	25.8500i	1.20144	+	0.872894i	0.994425	−	0.105445i	$-0.0336267\pi$
$877$	35.5795	+	25.8500i	1.20144	+	0.872894i	0.207010	+	0.978339i	$0.433627\pi$
$878$	2.60081	+	8.00448i	0.0877732	+	0.270138i
$879$	6.92705	+	21.3193i	0.233644	+	0.719081i
$880$	8.29180			0.279516
$881$	−2.83688	+	8.73102i	−0.0955770	+	0.294156i	−0.987404	−	0.158222i	$-0.949424\pi$
$881$	−2.83688	+	8.73102i	−0.0955770	+	0.294156i	0.891827	+	0.452377i	$0.149424\pi$
$882$	−1.61803			−0.0544820
$883$	−16.1976	+	49.8510i	−0.545091	+	1.67762i	0.175681	+	0.984447i	$0.443787\pi$
$883$	−16.1976	+	49.8510i	−0.545091	+	1.67762i	−0.720773	+	0.693172i	$0.756213\pi$
$884$	2.55573	−	1.85685i	0.0859584	−	0.0624525i
$885$	18.6803	+	13.5721i	0.627933	+	0.456220i
$886$	−37.6976	−	27.3889i	−1.26647	−	0.920147i
$887$	−25.4615	+	18.4989i	−0.854913	+	0.621131i	−0.926496	−	0.376304i	$-0.877195\pi$
$887$	−25.4615	+	18.4989i	−0.854913	+	0.621131i	0.0715831	+	0.997435i	$0.477195\pi$
$888$	2.07295	−	1.50609i	0.0695636	−	0.0505409i
$889$	9.70820	+	7.05342i	0.325603	+	0.236564i
$890$	−5.00000	−	15.3884i	−0.167600	−	0.515821i
$891$	0.618034	−	0.449028i	0.0207049	−	0.0150430i
$892$	−4.38197	+	13.4863i	−0.146719	+	0.451555i
$893$	−43.4164			−1.45287
$894$	5.16312	−	15.8904i	0.172681	−	0.531456i
$895$	−6.18034	−	19.0211i	−0.206586	−	0.635806i
$896$	4.20820	+	12.9515i	0.140586	+	0.432680i
$897$	−0.409830	−	1.26133i	−0.0136838	−	0.0421145i
$898$	36.7705	+	26.7153i	1.22705	+	0.891502i
$899$	25.8541			0.862283
$900$	−2.50000	−	1.81636i	−0.0833333	−	0.0605452i
$901$	6.02129			0.200598
$902$	−5.09017	−	3.69822i	−0.169484	−	0.123137i
$903$	0.309017	+	0.951057i	0.0102834	+	0.0316492i
$904$	7.46149	+	22.9641i	0.248166	+	0.763775i
$905$	11.0172	−	33.9075i	0.366225	−	1.12712i
$906$	2.28115	−	7.02067i	0.0757862	−	0.233246i
$907$	−43.2492			−1.43607			−0.718033	−	0.696009i	$-0.754958\pi$
$907$	−43.2492			−1.43607			−0.718033	+	0.696009i	$0.754958\pi$
$908$	−2.74671	+	8.45351i	−0.0911528	+	0.280540i
$909$	15.5172	−	11.2739i	0.514674	−	0.373932i
$910$	−12.5623			−0.416436
$911$	40.4164	+	29.3642i	1.33906	+	0.972881i	0.999478	+	0.0323025i	$0.0102840\pi$
$911$	40.4164	+	29.3642i	1.33906	+	0.972881i	0.339577	+	0.940578i	$0.389716\pi$
$912$	14.2082	−	10.3229i	0.470481	−	0.341824i
$913$	−8.00000	+	5.81234i	−0.264761	+	0.192360i
$914$	37.3156	+	27.1114i	1.23429	+	0.896764i
$915$	−0.201626	+	0.620541i	−0.00666555	+	0.0205145i
$916$	5.69098	−	4.13474i	0.188035	−	0.136616i
$917$	2.20820	−	6.79615i	0.0729213	−	0.224429i
$918$	2.38197			0.0786166
$919$	0.527864	−	1.62460i	0.0174126	−	0.0535906i	−0.941973	−	0.335690i	$-0.891031\pi$
$919$	0.527864	−	1.62460i	0.0174126	−	0.0535906i	0.959385	+	0.282099i	$0.0910307\pi$
$920$	1.54508	−	1.12257i	0.0509399	−	0.0370100i
$921$	−2.59017	−	7.97172i	−0.0853490	−	0.262677i
$922$	9.00000	+	27.6992i	0.296399	+	0.912223i
$923$	4.13525	+	3.00444i	0.136114	+	0.0988923i
$924$	−0.472136			−0.0155321
$925$	−4.63525	+	3.36771i	−0.152406	+	0.110730i
$926$	−13.8541			−0.455274
$927$	7.97214	+	5.79210i	0.261839	+	0.190237i
$928$	−7.01064	−	21.5765i	−0.230136	−	0.708285i
$929$	11.1418	+	34.2910i	0.365552	+	1.12505i	0.949635	+	0.313359i	$0.101454\pi$
$929$	11.1418	+	34.2910i	0.365552	+	1.12505i	−0.584083	+	0.811694i	$0.698546\pi$
$930$	11.2812	+	8.19624i	0.369924	+	0.268765i
$931$	−1.11803	+	3.44095i	−0.0366421	+	0.112773i
$932$	5.49342			0.179943
$933$	−6.67376	+	20.5397i	−0.218489	+	0.672440i
$934$	6.23607	−	4.53077i	0.204050	−	0.148251i
$935$	2.03444	−	1.47811i	0.0665334	−	0.0483393i
$936$	6.28115	+	4.56352i	0.205306	+	0.149163i
$937$	42.6525	−	30.9888i	1.39340	−	1.01236i	0.397912	−	0.917423i	$-0.369735\pi$
$937$	42.6525	−	30.9888i	1.39340	−	1.01236i	0.995483	−	0.0949378i	$-0.0302652\pi$
$938$	7.54508	−	5.48183i	0.246356	−	0.178988i
$939$	−14.6803	−	10.6659i	−0.479075	−	0.348068i
$940$	−13.4164	+	9.74759i	−0.437595	+	0.317931i
$941$	−23.7533	+	17.2578i	−0.774335	+	0.562587i	−0.903274	−	0.429065i	$-0.858843\pi$
$941$	−23.7533	+	17.2578i	−0.774335	+	0.562587i	0.128938	+	0.991653i	$0.458843\pi$
$942$	5.57295	−	17.1518i	0.181576	−	0.558835i
$943$	−1.94427			−0.0633142
$944$	−15.4894	+	47.6713i	−0.504136	+	1.55157i
$945$	−1.80902	−	1.31433i	−0.0588473	−	0.0427551i
$946$	0.381966	+	1.17557i	0.0124188	+	0.0382211i
$947$	−9.87132	−	30.3808i	−0.320775	−	0.987244i	−0.973312	−	0.229487i	$-0.926295\pi$
$947$	−9.87132	−	30.3808i	−0.320775	−	0.987244i	0.652537	−	0.757757i	$-0.273705\pi$
$948$	−3.78115	−	2.74717i	−0.122806	−	0.0892239i
$949$	−48.9230			−1.58811
$950$	−23.6803	+	17.2048i	−0.768292	+	0.558197i
$951$	11.9443			0.387320
$952$	2.66312	+	1.93487i	0.0863122	+	0.0627095i
$953$	−14.8156	−	45.5977i	−0.479924	−	1.47705i	−0.839200	−	0.543823i	$-0.816976\pi$
$953$	−14.8156	−	45.5977i	−0.479924	−	1.47705i	0.359276	−	0.933232i	$-0.383024\pi$
$954$	−2.04508	−	6.29412i	−0.0662121	−	0.203780i
$955$	−40.3885	+	29.3440i	−1.30694	+	0.949549i
$956$	0.854102	−	2.62866i	0.0276236	−	0.0850168i
$957$	−5.12461			−0.165655
$958$	−1.54508	+	4.75528i	−0.0499194	+	0.153636i
$959$	−4.50000	+	3.26944i	−0.145313	+	0.105576i
$960$	−2.92705	+	9.00854i	−0.0944702	+	0.290749i
$961$	13.0623	+	9.49032i	0.421365	+	0.306139i
$962$	−5.20820	+	3.78398i	−0.167919	+	0.122000i
$963$	−15.1353	+	10.9964i	−0.487727	+	0.354354i
$964$	−13.2984	−	9.66183i	−0.428312	−	0.311187i
$965$	32.2361			1.03772
$966$	−0.500000	+	0.363271i	−0.0160872	+	0.0116881i
$967$	1.00658	−	3.09793i	0.0323694	−	0.0996226i	−0.933567	−	0.358404i	$-0.883321\pi$
$967$	1.00658	−	3.09793i	0.0323694	−	0.0996226i	0.965936	+	0.258782i	$0.0833210\pi$
$968$	−23.2918			−0.748627
$969$	1.64590	−	5.06555i	0.0528739	−	0.162729i
$970$	−12.8262	+	39.4751i	−0.411826	+	1.26747i
$971$	−13.1631	−	40.5119i	−0.422425	−	1.30009i	−0.905439	−	0.424477i	$-0.860458\pi$
$971$	−13.1631	−	40.5119i	−0.422425	−	1.30009i	0.483014	−	0.875612i	$-0.339542\pi$
$972$	−0.190983	−	0.587785i	−0.00612578	−	0.0188532i
$973$	−8.35410	−	6.06961i	−0.267820	−	0.194583i
$974$	−16.8541			−0.540040
$975$	−14.0451	−	10.2044i	−0.449803	−	0.326801i
$976$	−1.41641			−0.0453381
$977$	4.50000	+	3.26944i	0.143968	+	0.104599i	0.657438	−	0.753509i	$-0.271640\pi$
$977$	4.50000	+	3.26944i	0.143968	+	0.104599i	−0.513470	+	0.858108i	$0.671640\pi$
$978$	−3.11803	−	9.59632i	−0.0997037	−	0.306857i
$979$	−1.05573	−	3.24920i	−0.0337412	−	0.103845i
$980$	0.427051	+	1.31433i	0.0136416	+	0.0419847i
$981$	−2.33688	+	7.19218i	−0.0746109	+	0.229629i
$982$	0.708204			0.0225997
$983$	0.697561	−	2.14687i	0.0222487	−	0.0684746i	−0.939316	−	0.343054i	$-0.888539\pi$
$983$	0.697561	−	2.14687i	0.0222487	−	0.0684746i	0.961564	+	0.274579i	$0.0885386\pi$
$984$	9.20820	−	6.69015i	0.293547	−	0.213274i
$985$	5.06231	+	15.5802i	0.161298	+	0.496426i
$986$	−12.9271	−	9.39205i	−0.411681	−	0.299104i
$987$	−9.70820	+	7.05342i	−0.309016	+	0.224513i
$988$	−6.28115	+	4.56352i	−0.199830	+	0.145185i
$989$	0.309017	+	0.224514i	0.00982617	+	0.00713913i
$990$	−2.23607	−	1.62460i	−0.0710669	−	0.0516331i
$991$	23.2426	−	16.8868i	0.738327	−	0.536426i	−0.153860	−	0.988093i	$-0.549170\pi$
$991$	23.2426	−	16.8868i	0.738327	−	0.536426i	0.892187	+	0.451667i	$0.149170\pi$
$992$	−4.02786	+	12.3965i	−0.127885	+	0.393589i
$993$	13.0000			0.412543
$994$	0.736068	−	2.26538i	0.0233467	−	0.0718536i
$995$	3.81966			0.121091
$996$	2.47214	+	7.60845i	0.0783326	+	0.241083i
$997$	−1.57953	−	4.86128i	−0.0500241	−	0.153958i	0.922924	−	0.384982i	$-0.125792\pi$
$997$	−1.57953	−	4.86128i	−0.0500241	−	0.153958i	−0.972948	+	0.231024i	$0.925792\pi$
$998$	−52.7877	−	38.3525i	−1.67097	−	1.21403i
$999$	−1.14590			−0.0362546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.a.316.1	yes	4
25.11	even	5	inner	525.2.n.a.211.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.a.211.1	✓	4	25.11	even	5	inner
525.2.n.a.316.1	yes	4	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +2.23607 q^{5} +(0.500000 - 1.53884i) q^{6} -1.00000 q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +2.23607 q^{5} +(0.500000 - 1.53884i) q^{6} -1.00000 q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.92705 + 2.12663i) q^{10} +(0.618034 + 0.449028i) q^{11} +(0.500000 - 0.363271i) q^{12} +(2.80902 - 2.04087i) q^{13} +(-1.30902 - 0.951057i) q^{14} +(-0.690983 - 2.12663i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.454915 - 1.40008i) q^{17} -1.61803 q^{18} +(-1.11803 + 3.44095i) q^{19} +(0.427051 + 1.31433i) q^{20} +(0.309017 + 0.951057i) q^{21} +(0.381966 + 1.17557i) q^{22} +(0.309017 + 0.224514i) q^{23} -2.23607 q^{24} +5.00000 q^{25} +5.61803 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.190983 - 0.587785i) q^{28} +(-2.07295 - 6.37988i) q^{29} +(1.11803 - 3.44095i) q^{30} +(-1.19098 + 3.66547i) q^{31} +3.38197 q^{32} +(0.236068 - 0.726543i) q^{33} +(1.92705 - 1.40008i) q^{34} -2.23607 q^{35} +(-0.500000 - 0.363271i) q^{36} +(-0.927051 + 0.673542i) q^{37} +(-4.73607 + 3.44095i) q^{38} +(-2.80902 - 2.04087i) q^{39} +(1.54508 - 4.75528i) q^{40} +(-4.11803 + 2.99193i) q^{41} +(-0.500000 + 1.53884i) q^{42} +1.00000 q^{43} +(-0.145898 + 0.449028i) q^{44} +(-1.80902 + 1.31433i) q^{45} +(0.190983 + 0.587785i) q^{46} +(3.70820 + 11.4127i) q^{47} +(-3.92705 - 2.85317i) q^{48} +1.00000 q^{49} +(6.54508 + 4.75528i) q^{50} -1.47214 q^{51} +(1.73607 + 1.26133i) q^{52} +(1.26393 + 3.88998i) q^{53} +(0.500000 + 1.53884i) q^{54} +(1.38197 + 1.00406i) q^{55} +(-0.690983 + 2.12663i) q^{56} +3.61803 q^{57} +(3.35410 - 10.3229i) q^{58} +(-8.35410 + 6.06961i) q^{59} +(1.11803 - 0.812299i) q^{60} +(-0.236068 - 0.171513i) q^{61} +(-5.04508 + 3.66547i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(6.28115 - 4.56352i) q^{65} +(1.00000 - 0.726543i) q^{66} +(-1.78115 + 5.48183i) q^{67} +0.909830 q^{68} +(0.118034 - 0.363271i) q^{69} +(-2.92705 - 2.12663i) q^{70} +(0.454915 + 1.40008i) q^{71} +(0.690983 + 2.12663i) q^{72} +(-11.3992 - 8.28199i) q^{73} -1.85410 q^{74} +(-1.54508 - 4.75528i) q^{75} -2.23607 q^{76} +(-0.618034 - 0.449028i) q^{77} +(-1.73607 - 5.34307i) q^{78} +(-2.33688 - 7.19218i) q^{79} +(8.78115 - 6.37988i) q^{80} +(0.309017 - 0.951057i) q^{81} -8.23607 q^{82} +(-4.00000 + 12.3107i) q^{83} +(-0.500000 + 0.363271i) q^{84} +(1.01722 - 3.13068i) q^{85} +(1.30902 + 0.951057i) q^{86} +(-5.42705 + 3.94298i) q^{87} +(1.38197 - 1.00406i) q^{88} +(-3.61803 - 2.62866i) q^{89} -3.61803 q^{90} +(-2.80902 + 2.04087i) q^{91} +(-0.0729490 + 0.224514i) q^{92} +3.85410 q^{93} +(-6.00000 + 18.4661i) q^{94} +(-2.50000 + 7.69421i) q^{95} +(-1.04508 - 3.21644i) q^{96} +(3.54508 + 10.9106i) q^{97} +(1.30902 + 0.951057i) q^{98} -0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 2 q^{11} + 2 q^{12} + 9 q^{13} - 3 q^{14} - 5 q^{15} + 9 q^{16} + 13 q^{17} - 2 q^{18} - 5 q^{20} - q^{21} + 6 q^{22} - q^{23} + 20 q^{25} + 18 q^{26} + q^{27} - 3 q^{28} - 15 q^{29} - 7 q^{31} + 18 q^{32} - 8 q^{33} + q^{34} - 2 q^{36} + 3 q^{37} - 10 q^{38} - 9 q^{39} - 5 q^{40} - 12 q^{41} - 2 q^{42} + 4 q^{43} - 14 q^{44} - 5 q^{45} + 3 q^{46} - 12 q^{47} - 9 q^{48} + 4 q^{49} + 15 q^{50} + 12 q^{51} - 2 q^{52} + 14 q^{53} + 2 q^{54} + 10 q^{55} - 5 q^{56} + 10 q^{57} - 20 q^{59} + 8 q^{61} - 9 q^{62} + q^{63} - 7 q^{64} + 5 q^{65} + 4 q^{66} + 13 q^{67} + 26 q^{68} - 4 q^{69} - 5 q^{70} + 13 q^{71} + 5 q^{72} - 21 q^{73} + 6 q^{74} + 5 q^{75} + 2 q^{77} + 2 q^{78} - 25 q^{79} + 15 q^{80} - q^{81} - 24 q^{82} - 16 q^{83} - 2 q^{84} - 25 q^{85} + 3 q^{86} - 15 q^{87} + 10 q^{88} - 10 q^{89} - 10 q^{90} - 9 q^{91} - 7 q^{92} + 2 q^{93} - 24 q^{94} - 10 q^{95} + 7 q^{96} + 3 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9 + 5 * q^10 - 2 * q^11 + 2 * q^12 + 9 * q^13 - 3 * q^14 - 5 * q^15 + 9 * q^16 + 13 * q^17 - 2 * q^18 - 5 * q^20 - q^21 + 6 * q^22 - q^23 + 20 * q^25 + 18 * q^26 + q^27 - 3 * q^28 - 15 * q^29 - 7 * q^31 + 18 * q^32 - 8 * q^33 + q^34 - 2 * q^36 + 3 * q^37 - 10 * q^38 - 9 * q^39 - 5 * q^40 - 12 * q^41 - 2 * q^42 + 4 * q^43 - 14 * q^44 - 5 * q^45 + 3 * q^46 - 12 * q^47 - 9 * q^48 + 4 * q^49 + 15 * q^50 + 12 * q^51 - 2 * q^52 + 14 * q^53 + 2 * q^54 + 10 * q^55 - 5 * q^56 + 10 * q^57 - 20 * q^59 + 8 * q^61 - 9 * q^62 + q^63 - 7 * q^64 + 5 * q^65 + 4 * q^66 + 13 * q^67 + 26 * q^68 - 4 * q^69 - 5 * q^70 + 13 * q^71 + 5 * q^72 - 21 * q^73 + 6 * q^74 + 5 * q^75 + 2 * q^77 + 2 * q^78 - 25 * q^79 + 15 * q^80 - q^81 - 24 * q^82 - 16 * q^83 - 2 * q^84 - 25 * q^85 + 3 * q^86 - 15 * q^87 + 10 * q^88 - 10 * q^89 - 10 * q^90 - 9 * q^91 - 7 * q^92 + 2 * q^93 - 24 * q^94 - 10 * q^95 + 7 * q^96 + 3 * q^97 + 3 * q^98 - 12 * q^99

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