LMFDB - Embedded newform 134.2.c.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [134,2,Mod(29,134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("134.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 134 = 2 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	134.c (of order $3$, degree $2$, 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:	$1.06999538709$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	134.37
Dual form			134.2.c.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.79129 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.895644 + 1.55130i) q^{6} +(-1.39564 + 2.41733i) q^{7} +1.00000 q^{8} +0.208712 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.79129 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.895644 + 1.55130i) q^{6} +(-1.39564 + 2.41733i) q^{7} +1.00000 q^{8} +0.208712 q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.895644 - 1.55130i) q^{12} +(0.395644 + 0.685275i) q^{13} +2.79129 q^{14} +1.79129 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.29129 - 3.96863i) q^{17} +(-0.104356 - 0.180750i) q^{18} +(1.79129 + 3.10260i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.50000 - 4.33013i) q^{21} +5.00000 q^{22} +(-3.79129 - 6.56670i) q^{23} -1.79129 q^{24} -4.00000 q^{25} +(0.395644 - 0.685275i) q^{26} +5.00000 q^{27} +(-1.39564 - 2.41733i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.895644 - 1.55130i) q^{30} +(-2.10436 + 3.64485i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.47822 - 7.75650i) q^{33} +(-2.29129 + 3.96863i) q^{34} +(1.39564 - 2.41733i) q^{35} +(-0.104356 + 0.180750i) q^{36} +(1.39564 + 2.41733i) q^{37} +(1.79129 - 3.10260i) q^{38} +(-0.708712 - 1.22753i) q^{39} -1.00000 q^{40} +(1.29129 - 2.23658i) q^{41} -5.00000 q^{42} -1.37386 q^{43} +(-2.50000 - 4.33013i) q^{44} -0.208712 q^{45} +(-3.79129 + 6.56670i) q^{46} +(-4.58258 + 7.93725i) q^{47} +(0.895644 + 1.55130i) q^{48} +(-0.395644 - 0.685275i) q^{49} +(2.00000 + 3.46410i) q^{50} +(4.10436 + 7.10895i) q^{51} -0.791288 q^{52} +8.37386 q^{53} +(-2.50000 - 4.33013i) q^{54} +(2.50000 - 4.33013i) q^{55} +(-1.39564 + 2.41733i) q^{56} +(-3.20871 - 5.55765i) q^{57} -1.00000 q^{58} +8.58258 q^{59} +(-0.895644 + 1.55130i) q^{60} +(4.68693 + 8.11800i) q^{61} +4.20871 q^{62} +(-0.291288 + 0.504525i) q^{63} +1.00000 q^{64} +(-0.395644 - 0.685275i) q^{65} -8.95644 q^{66} +(-7.87386 + 2.23658i) q^{67} +4.58258 q^{68} +(6.79129 + 11.7629i) q^{69} -2.79129 q^{70} +(-6.97822 + 12.0866i) q^{71} +0.208712 q^{72} +(1.39564 - 2.41733i) q^{74} +7.16515 q^{75} -3.58258 q^{76} +(-6.97822 - 12.0866i) q^{77} +(-0.708712 + 1.22753i) q^{78} +(1.31307 - 2.27430i) q^{79} +(0.500000 + 0.866025i) q^{80} -9.58258 q^{81} -2.58258 q^{82} +(-6.00000 - 10.3923i) q^{83} +(2.50000 + 4.33013i) q^{84} +(2.29129 + 3.96863i) q^{85} +(0.686932 + 1.18980i) q^{86} +(-0.895644 + 1.55130i) q^{87} +(-2.50000 + 4.33013i) q^{88} -2.20871 q^{89} +(0.104356 + 0.180750i) q^{90} -2.20871 q^{91} +7.58258 q^{92} +(3.76951 - 6.52898i) q^{93} +9.16515 q^{94} +(-1.79129 - 3.10260i) q^{95} +(0.895644 - 1.55130i) q^{96} +(7.39564 + 12.8096i) q^{97} +(-0.395644 + 0.685275i) q^{98} +(-0.521780 + 0.903750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} - q^{6} - q^{7} + 4 q^{8} + 10 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 - q^6 - q^7 + 4 * q^8 + 10 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} - q^{6} - q^{7} + 4 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 5 q^{18} - 2 q^{19} + 2 q^{20} + 10 q^{21} + 20 q^{22} - 6 q^{23} + 2 q^{24} - 16 q^{25} - 3 q^{26} + 20 q^{27} - q^{28} + 2 q^{29} + q^{30} - 13 q^{31} - 2 q^{32} - 5 q^{33} + q^{35} - 5 q^{36} + q^{37} - 2 q^{38} - 12 q^{39} - 4 q^{40} - 4 q^{41} - 20 q^{42} + 22 q^{43} - 10 q^{44} - 10 q^{45} - 6 q^{46} - q^{48} + 3 q^{49} + 8 q^{50} + 21 q^{51} + 6 q^{52} + 6 q^{53} - 10 q^{54} + 10 q^{55} - q^{56} - 22 q^{57} - 4 q^{58} + 16 q^{59} + q^{60} + 5 q^{61} + 26 q^{62} + 8 q^{63} + 4 q^{64} + 3 q^{65} + 10 q^{66} - 4 q^{67} + 18 q^{69} - 2 q^{70} - 5 q^{71} + 10 q^{72} + q^{74} - 8 q^{75} + 4 q^{76} - 5 q^{77} - 12 q^{78} + 19 q^{79} + 2 q^{80} - 20 q^{81} + 8 q^{82} - 24 q^{83} + 10 q^{84} - 11 q^{86} + q^{87} - 10 q^{88} - 18 q^{89} + 5 q^{90} - 18 q^{91} + 12 q^{92} - 17 q^{93} + 2 q^{95} - q^{96} + 25 q^{97} + 3 q^{98} - 25 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 - q^6 - q^7 + 4 * q^8 + 10 * q^9 + 2 * q^10 - 10 * q^11 - q^12 - 3 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 5 * q^18 - 2 * q^19 + 2 * q^20 + 10 * q^21 + 20 * q^22 - 6 * q^23 + 2 * q^24 - 16 * q^25 - 3 * q^26 + 20 * q^27 - q^28 + 2 * q^29 + q^30 - 13 * q^31 - 2 * q^32 - 5 * q^33 + q^35 - 5 * q^36 + q^37 - 2 * q^38 - 12 * q^39 - 4 * q^40 - 4 * q^41 - 20 * q^42 + 22 * q^43 - 10 * q^44 - 10 * q^45 - 6 * q^46 - q^48 + 3 * q^49 + 8 * q^50 + 21 * q^51 + 6 * q^52 + 6 * q^53 - 10 * q^54 + 10 * q^55 - q^56 - 22 * q^57 - 4 * q^58 + 16 * q^59 + q^60 + 5 * q^61 + 26 * q^62 + 8 * q^63 + 4 * q^64 + 3 * q^65 + 10 * q^66 - 4 * q^67 + 18 * q^69 - 2 * q^70 - 5 * q^71 + 10 * q^72 + q^74 - 8 * q^75 + 4 * q^76 - 5 * q^77 - 12 * q^78 + 19 * q^79 + 2 * q^80 - 20 * q^81 + 8 * q^82 - 24 * q^83 + 10 * q^84 - 11 * q^86 + q^87 - 10 * q^88 - 18 * q^89 + 5 * q^90 - 18 * q^91 + 12 * q^92 - 17 * q^93 + 2 * q^95 - q^96 + 25 * q^97 + 3 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/134\mathbb{Z}\right)^\times$.

$n$	$69$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.79129			−1.03420			−0.517100	−	0.855925i	$-0.672989\pi$
$3$	−1.79129			−1.03420			−0.517100	+	0.855925i	$0.672989\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$	0.895644	+	1.55130i	0.365645	+	0.633316i
$7$	−1.39564	+	2.41733i	−0.527504	+	0.913663i	0.471982	+	0.881608i	$0.343539\pi$
$7$	−1.39564	+	2.41733i	−0.527504	+	0.913663i	−0.999486	+	0.0320554i	$0.989795\pi$
$8$	1.00000			0.353553
$9$	0.208712			0.0695707
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	0.895644	−	1.55130i	0.258550	−	0.447822i
$13$	0.395644	+	0.685275i	0.109732	+	0.190061i	0.915662	−	0.401950i	$-0.131667\pi$
$13$	0.395644	+	0.685275i	0.109732	+	0.190061i	−0.805930	+	0.592011i	$0.798334\pi$
$14$	2.79129			0.746003
$15$	1.79129			0.462509
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.29129	−	3.96863i	−0.555719	−	0.962533i	−0.997847	−	0.0655816i	$-0.979110\pi$
$17$	−2.29129	−	3.96863i	−0.555719	−	0.962533i	0.442128	−	0.896952i	$-0.354224\pi$
$18$	−0.104356	−	0.180750i	−0.0245970	−	0.0426032i
$19$	1.79129	+	3.10260i	0.410950	+	0.711786i	0.994994	−	0.0999362i	$-0.0318639\pi$
$19$	1.79129	+	3.10260i	0.410950	+	0.711786i	−0.584044	+	0.811722i	$0.698531\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	2.50000	−	4.33013i	0.545545	−	0.944911i
$22$	5.00000			1.06600
$23$	−3.79129	−	6.56670i	−0.790538	−	1.36925i	−0.925634	−	0.378420i	$-0.876468\pi$
$23$	−3.79129	−	6.56670i	−0.790538	−	1.36925i	0.135096	−	0.990833i	$-0.456866\pi$
$24$	−1.79129			−0.365645
$25$	−4.00000			−0.800000
$26$	0.395644	−	0.685275i	0.0775922	−	0.134394i
$27$	5.00000			0.962250
$28$	−1.39564	−	2.41733i	−0.263752	−	0.456832i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	−0.895644	−	1.55130i	−0.163521	−	0.283227i
$31$	−2.10436	+	3.64485i	−0.377954	+	0.654635i	−0.990764	−	0.135595i	$-0.956705\pi$
$31$	−2.10436	+	3.64485i	−0.377954	+	0.654635i	0.612811	+	0.790230i	$0.290039\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.47822	−	7.75650i	0.779558	−	1.35023i
$34$	−2.29129	+	3.96863i	−0.392953	+	0.680614i
$35$	1.39564	−	2.41733i	0.235907	−	0.408603i
$36$	−0.104356	+	0.180750i	−0.0173927	+	0.0301250i
$37$	1.39564	+	2.41733i	0.229442	+	0.397406i	0.957643	−	0.287958i	$-0.0929764\pi$
$37$	1.39564	+	2.41733i	0.229442	+	0.397406i	−0.728201	+	0.685364i	$0.759643\pi$
$38$	1.79129	−	3.10260i	0.290585	−	0.503308i
$39$	−0.708712	−	1.22753i	−0.113485	−	0.196561i
$40$	−1.00000			−0.158114
$41$	1.29129	−	2.23658i	0.201665	−	0.349295i	−0.747400	−	0.664375i	$-0.768698\pi$
$41$	1.29129	−	2.23658i	0.201665	−	0.349295i	0.949065	+	0.315080i	$0.102031\pi$
$42$	−5.00000			−0.771517
$43$	−1.37386			−0.209512			−0.104756	−	0.994498i	$-0.533406\pi$
$43$	−1.37386			−0.209512			−0.104756	+	0.994498i	$0.533406\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$	−0.208712			−0.0311130
$46$	−3.79129	+	6.56670i	−0.558995	+	0.968208i
$47$	−4.58258	+	7.93725i	−0.668437	+	1.15777i	0.309904	+	0.950768i	$0.399703\pi$
$47$	−4.58258	+	7.93725i	−0.668437	+	1.15777i	−0.978341	+	0.207000i	$0.933630\pi$
$48$	0.895644	+	1.55130i	0.129275	+	0.223911i
$49$	−0.395644	−	0.685275i	−0.0565206	−	0.0978965i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	4.10436	+	7.10895i	0.574725	+	0.995453i
$52$	−0.791288			−0.109732
$53$	8.37386			1.15024			0.575119	−	0.818070i	$-0.304956\pi$
$53$	8.37386			1.15024			0.575119	+	0.818070i	$0.304956\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$	2.50000	−	4.33013i	0.337100	−	0.583874i
$56$	−1.39564	+	2.41733i	−0.186501	+	0.323029i
$57$	−3.20871	−	5.55765i	−0.425004	−	0.736129i
$58$	−1.00000			−0.131306
$59$	8.58258			1.11736			0.558678	−	0.829385i	$-0.311309\pi$
$59$	8.58258			1.11736			0.558678	+	0.829385i	$0.311309\pi$
$60$	−0.895644	+	1.55130i	−0.115627	+	0.200272i
$61$	4.68693	+	8.11800i	0.600100	+	1.03940i	0.992805	+	0.119739i	$0.0382059\pi$
$61$	4.68693	+	8.11800i	0.600100	+	1.03940i	−0.392705	+	0.919664i	$0.628461\pi$
$62$	4.20871			0.534507
$63$	−0.291288	+	0.504525i	−0.0366988	+	0.0635642i
$64$	1.00000			0.125000
$65$	−0.395644	−	0.685275i	−0.0490736	−	0.0849979i
$66$	−8.95644			−1.10246
$67$	−7.87386	+	2.23658i	−0.961946	+	0.273241i
$67$	−7.87386	+	2.23658i	−0.961946	+	0.273241i
$68$	4.58258			0.555719
$69$	6.79129	+	11.7629i	0.817575	+	1.41608i
$70$	−2.79129			−0.333623
$71$	−6.97822	+	12.0866i	−0.828162	+	1.43442i	0.0713160	+	0.997454i	$0.477280\pi$
$71$	−6.97822	+	12.0866i	−0.828162	+	1.43442i	−0.899478	+	0.436965i	$0.856053\pi$
$72$	0.208712			0.0245970
$73$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$73$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$74$	1.39564	−	2.41733i	0.162240	−	0.281008i
$75$	7.16515			0.827360
$76$	−3.58258			−0.410950
$77$	−6.97822	−	12.0866i	−0.795242	−	1.37740i
$78$	−0.708712	+	1.22753i	−0.0802458	+	0.138990i
$79$	1.31307	−	2.27430i	0.147732	−	0.255879i	−0.782657	−	0.622453i	$-0.786136\pi$
$79$	1.31307	−	2.27430i	0.147732	−	0.255879i	0.930389	+	0.366574i	$0.119469\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−9.58258			−1.06473
$82$	−2.58258			−0.285198
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$	2.50000	+	4.33013i	0.272772	+	0.472456i
$85$	2.29129	+	3.96863i	0.248525	+	0.430458i
$86$	0.686932	+	1.18980i	0.0740738	+	0.128300i
$87$	−0.895644	+	1.55130i	−0.0960231	+	0.166317i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−2.20871			−0.234123			−0.117062	−	0.993125i	$-0.537347\pi$
$89$	−2.20871			−0.234123			−0.117062	+	0.993125i	$0.537347\pi$
$90$	0.104356	+	0.180750i	0.0110001	+	0.0190527i
$91$	−2.20871			−0.231536
$92$	7.58258			0.790538
$93$	3.76951	−	6.52898i	0.390880	−	0.677024i
$94$	9.16515			0.945313
$95$	−1.79129	−	3.10260i	−0.183782	−	0.318320i
$96$	0.895644	−	1.55130i	0.0914113	−	0.158329i
$97$	7.39564	+	12.8096i	0.750914	+	1.30062i	0.947380	+	0.320110i	$0.103720\pi$
$97$	7.39564	+	12.8096i	0.750914	+	1.30062i	−0.196466	+	0.980511i	$0.562947\pi$
$98$	−0.395644	+	0.685275i	−0.0399661	+	0.0692233i
$99$	−0.521780	+	0.903750i	−0.0524409	+	0.0908303i
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−6.08258	+	10.5353i	−0.605239	+	1.04830i	0.386775	+	0.922174i	$0.373589\pi$
$101$	−6.08258	+	10.5353i	−0.605239	+	1.04830i	−0.992014	+	0.126130i	$0.959744\pi$
$102$	4.10436	−	7.10895i	0.406392	−	0.703891i
$103$	7.47822	−	12.9527i	0.736851	−	1.27626i	−0.217056	−	0.976159i	$-0.569645\pi$
$103$	7.47822	−	12.9527i	0.736851	−	1.27626i	0.953907	−	0.300104i	$-0.0970214\pi$
$104$	0.395644	+	0.685275i	0.0387961	+	0.0671968i
$105$	−2.50000	+	4.33013i	−0.243975	+	0.422577i
$106$	−4.18693	−	7.25198i	−0.406671	−	0.704374i
$107$	−11.9564			−1.15587			−0.577936	−	0.816082i	$-0.696142\pi$
$107$	−11.9564			−1.15587			−0.577936	+	0.816082i	$0.696142\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	−8.74773			−0.837880			−0.418940	−	0.908014i	$-0.637598\pi$
$109$	−8.74773			−0.837880			−0.418940	+	0.908014i	$0.637598\pi$
$110$	−5.00000			−0.476731
$111$	−2.50000	−	4.33013i	−0.237289	−	0.410997i
$112$	2.79129			0.263752
$113$	5.68693	−	9.85005i	0.534982	−	0.926615i	−0.464183	−	0.885739i	$-0.653652\pi$
$113$	5.68693	−	9.85005i	0.534982	−	0.926615i	0.999164	−	0.0408757i	$-0.0130148\pi$
$114$	−3.20871	+	5.55765i	−0.300523	+	0.520522i
$115$	3.79129	+	6.56670i	0.353539	+	0.612348i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	0.0825757	+	0.143025i	0.00763413	+	0.0132227i
$118$	−4.29129	−	7.43273i	−0.395045	−	0.684238i
$119$	12.7913			1.17258
$120$	1.79129			0.163521
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	4.68693	−	8.11800i	0.424335	−	0.734970i
$123$	−2.31307	+	4.00635i	−0.208562	+	0.361241i
$124$	−2.10436	−	3.64485i	−0.188977	−	0.327317i
$125$	9.00000			0.804984
$126$	0.582576			0.0519000
$127$	9.66515	−	16.7405i	0.857644	−	1.48548i	−0.0165272	−	0.999863i	$-0.505261\pi$
$127$	9.66515	−	16.7405i	0.857644	−	1.48548i	0.874171	−	0.485619i	$-0.161406\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.46099			0.216678
$130$	−0.395644	+	0.685275i	−0.0347003	+	0.0601026i
$131$	10.5826			0.924604			0.462302	−	0.886723i	$-0.347024\pi$
$131$	10.5826			0.924604			0.462302	+	0.886723i	$0.347024\pi$
$132$	4.47822	+	7.75650i	0.389779	+	0.675117i
$133$	−10.0000			−0.867110
$134$	5.87386	+	5.70068i	0.507425	+	0.492464i
$135$	−5.00000			−0.430331
$136$	−2.29129	−	3.96863i	−0.196476	−	0.340307i
$137$	−20.5826			−1.75849			−0.879244	−	0.476372i	$-0.841952\pi$
$137$	−20.5826			−1.75849			−0.879244	+	0.476372i	$0.841952\pi$
$138$	6.79129	−	11.7629i	0.578113	−	1.00132i
$139$	3.62614			0.307565			0.153782	−	0.988105i	$-0.450855\pi$
$139$	3.62614			0.307565			0.153782	+	0.988105i	$0.450855\pi$
$140$	1.39564	+	2.41733i	0.117953	+	0.204301i
$141$	8.20871	−	14.2179i	0.691298	−	1.19736i
$142$	13.9564			1.17120
$143$	−3.95644			−0.330854
$144$	−0.104356	−	0.180750i	−0.00869634	−	0.0150625i
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$		0			0
$147$	0.708712	+	1.22753i	0.0584536	+	0.101245i
$148$	−2.79129			−0.229442
$149$	8.53901			0.699543			0.349772	−	0.936835i	$-0.386259\pi$
$149$	8.53901			0.699543			0.349772	+	0.936835i	$0.386259\pi$
$150$	−3.58258	−	6.20520i	−0.292516	−	0.506653i
$151$	0.895644	+	1.55130i	0.0728865	+	0.126243i	0.900165	−	0.435549i	$-0.143446\pi$
$151$	0.895644	+	1.55130i	0.0728865	+	0.126243i	−0.827279	+	0.561792i	$0.810112\pi$
$152$	1.79129	+	3.10260i	0.145293	+	0.251654i
$153$	−0.478220	−	0.828301i	−0.0386618	−	0.0669641i
$154$	−6.97822	+	12.0866i	−0.562321	+	0.973968i
$155$	2.10436	−	3.64485i	0.169026	−	0.292762i
$156$	1.41742			0.113485
$157$	2.29129	+	3.96863i	0.182865	+	0.316731i	0.942855	−	0.333204i	$-0.108130\pi$
$157$	2.29129	+	3.96863i	0.182865	+	0.316731i	−0.759990	+	0.649935i	$0.774796\pi$
$158$	−2.62614			−0.208924
$159$	−15.0000			−1.18958
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	21.1652			1.66805
$162$	4.79129	+	8.29875i	0.376439	+	0.652012i
$163$	−9.79129	+	16.9590i	−0.766913	+	1.32833i	0.172316	+	0.985042i	$0.444875\pi$
$163$	−9.79129	+	16.9590i	−0.766913	+	1.32833i	−0.939229	+	0.343290i	$0.888459\pi$
$164$	1.29129	+	2.23658i	0.100833	+	0.174647i
$165$	−4.47822	+	7.75650i	−0.348629	+	0.603843i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−10.2913	+	17.8250i	−0.796364	+	1.37934i	0.125606	+	0.992080i	$0.459913\pi$
$167$	−10.2913	+	17.8250i	−0.796364	+	1.37934i	−0.921970	+	0.387262i	$0.873421\pi$
$168$	2.50000	−	4.33013i	0.192879	−	0.334077i
$169$	6.18693	−	10.7161i	0.475918	−	0.824314i
$170$	2.29129	−	3.96863i	0.175734	−	0.304380i
$171$	0.373864	+	0.647551i	0.0285901	+	0.0495194i
$172$	0.686932	−	1.18980i	0.0523781	−	0.0907215i
$173$	8.79129	+	15.2270i	0.668389	+	1.15768i	0.978354	+	0.206936i	$0.0663493\pi$
$173$	8.79129	+	15.2270i	0.668389	+	1.15768i	−0.309965	+	0.950748i	$0.600317\pi$
$174$	1.79129			0.135797
$175$	5.58258	−	9.66930i	0.422003	−	0.730931i
$176$	5.00000			0.376889
$177$	−15.3739			−1.15557
$178$	1.10436	+	1.91280i	0.0827750	+	0.143370i
$179$	−15.7477			−1.17704			−0.588520	−	0.808483i	$-0.700289\pi$
$179$	−15.7477			−1.17704			−0.588520	+	0.808483i	$0.700289\pi$
$180$	0.104356	−	0.180750i	0.00777824	−	0.0134723i
$181$	−10.2913	+	17.8250i	−0.764945	+	1.32492i	0.175330	+	0.984510i	$0.443901\pi$
$181$	−10.2913	+	17.8250i	−0.764945	+	1.32492i	−0.940275	+	0.340415i	$0.889433\pi$
$182$	1.10436	+	1.91280i	0.0818603	+	0.141786i
$183$	−8.39564	−	14.5417i	−0.620624	−	1.07495i
$184$	−3.79129	−	6.56670i	−0.279497	−	0.484104i
$185$	−1.39564	−	2.41733i	−0.102610	−	0.177725i
$186$	−7.53901			−0.552787
$187$	22.9129			1.67556
$188$	−4.58258	−	7.93725i	−0.334219	−	0.578884i
$189$	−6.97822	+	12.0866i	−0.507591	+	0.879173i
$190$	−1.79129	+	3.10260i	−0.129954	+	0.225086i
$191$	7.18693	+	12.4481i	0.520028	+	0.900715i	0.999729	+	0.0232830i	$0.00741188\pi$
$191$	7.18693	+	12.4481i	0.520028	+	0.900715i	−0.479701	+	0.877432i	$0.659255\pi$
$192$	−1.79129			−0.129275
$193$	−12.3739			−0.890690			−0.445345	−	0.895359i	$-0.646919\pi$
$193$	−12.3739			−0.890690			−0.445345	+	0.895359i	$0.646919\pi$
$194$	7.39564	−	12.8096i	0.530976	−	0.919678i
$195$	0.708712	+	1.22753i	0.0507519	+	0.0879049i
$196$	0.791288			0.0565206
$197$	−8.79129	+	15.2270i	−0.626353	+	1.08488i	0.361924	+	0.932208i	$0.382120\pi$
$197$	−8.79129	+	15.2270i	−0.626353	+	1.08488i	−0.988277	+	0.152668i	$0.951213\pi$
$198$	1.04356			0.0741626
$199$	−5.79129	−	10.0308i	−0.410534	−	0.711065i	0.584415	−	0.811455i	$-0.301324\pi$
$199$	−5.79129	−	10.0308i	−0.410534	−	0.711065i	−0.994948	+	0.100390i	$0.967991\pi$
$200$	−4.00000			−0.282843
$201$	14.1044	−	4.00635i	0.994845	−	0.282586i
$202$	12.1652			0.855937
$203$	1.39564	+	2.41733i	0.0979550	+	0.169663i
$204$	−8.20871			−0.574725
$205$	−1.29129	+	2.23658i	−0.0901875	+	0.156209i
$206$	−14.9564			−1.04206
$207$	−0.791288	−	1.37055i	−0.0549983	−	0.0952599i
$208$	0.395644	−	0.685275i	0.0274330	−	0.0475153i
$209$	−17.9129			−1.23906
$210$	5.00000			0.345033
$211$	−11.0826	−	19.1956i	−0.762956	−	1.32148i	−0.941320	−	0.337514i	$-0.890414\pi$
$211$	−11.0826	−	19.1956i	−0.762956	−	1.32148i	0.178365	−	0.983964i	$-0.442919\pi$
$212$	−4.18693	+	7.25198i	−0.287560	+	0.498068i
$213$	12.5000	−	21.6506i	0.856486	−	1.48348i
$214$	5.97822	+	10.3546i	0.408663	+	0.707825i
$215$	1.37386			0.0936967
$216$	5.00000			0.340207
$217$	−5.87386	−	10.1738i	−0.398744	−	0.690645i
$218$	4.37386	+	7.57575i	0.296235	+	0.513095i
$219$		0			0
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$	1.81307	−	3.14033i	0.121960	−	0.211241i
$222$	−2.50000	+	4.33013i	−0.167789	+	0.290619i
$223$	25.3303			1.69624			0.848121	−	0.529802i	$-0.177734\pi$
$223$	25.3303			1.69624			0.848121	+	0.529802i	$0.177734\pi$
$224$	−1.39564	−	2.41733i	−0.0932504	−	0.161514i
$225$	−0.834849			−0.0556566
$226$	−11.3739			−0.756578
$227$	−6.56080	+	11.3636i	−0.435455	+	0.754231i	−0.997333	−	0.0729898i	$-0.976746\pi$
$227$	−6.56080	+	11.3636i	−0.435455	+	0.754231i	0.561877	+	0.827221i	$0.310079\pi$
$228$	6.41742			0.425004
$229$	−4.47822	−	7.75650i	−0.295929	−	0.512564i	0.679272	−	0.733887i	$-0.262296\pi$
$229$	−4.47822	−	7.75650i	−0.295929	−	0.512564i	−0.975201	+	0.221323i	$0.928963\pi$
$230$	3.79129	−	6.56670i	0.249990	−	0.432996i
$231$	12.5000	+	21.6506i	0.822440	+	1.42451i
$232$	0.500000	−	0.866025i	0.0328266	−	0.0568574i
$233$	−8.10436	+	14.0372i	−0.530934	+	0.919605i	0.468414	+	0.883509i	$0.344825\pi$
$233$	−8.10436	+	14.0372i	−0.530934	+	0.919605i	−0.999348	+	0.0360958i	$0.988508\pi$
$234$	0.0825757	−	0.143025i	0.00539814	−	0.00934986i
$235$	4.58258	−	7.93725i	0.298934	−	0.517769i
$236$	−4.29129	+	7.43273i	−0.279339	+	0.483829i
$237$	−2.35208	+	4.07393i	−0.152784	+	0.264630i
$238$	−6.39564	−	11.0776i	−0.414568	−	0.718053i
$239$	−1.31307	+	2.27430i	−0.0849353	+	0.147112i	−0.905364	−	0.424637i	$-0.860402\pi$
$239$	−1.31307	+	2.27430i	−0.0849353	+	0.147112i	0.820428	+	0.571749i	$0.193735\pi$
$240$	−0.895644	−	1.55130i	−0.0578136	−	0.100136i
$241$	14.3739			0.925902			0.462951	−	0.886384i	$-0.346791\pi$
$241$	14.3739			0.925902			0.462951	+	0.886384i	$0.346791\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$	2.16515			0.138895
$244$	−9.37386			−0.600100
$245$	0.395644	+	0.685275i	0.0252768	+	0.0437806i
$246$	4.62614			0.294952
$247$	−1.41742	+	2.45505i	−0.0901885	+	0.156211i
$248$	−2.10436	+	3.64485i	−0.133627	+	0.231448i
$249$	10.7477	+	18.6156i	0.681110	+	1.17972i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−8.29129	−	14.3609i	−0.523341	−	0.906454i	−0.999631	−	0.0271655i	$-0.991352\pi$
$251$	−8.29129	−	14.3609i	−0.523341	−	0.906454i	0.476290	−	0.879289i	$-0.341981\pi$
$252$	−0.291288	−	0.504525i	−0.0183494	−	0.0317821i
$253$	37.9129			2.38356
$254$	−19.3303			−1.21289
$255$	−4.10436	−	7.10895i	−0.257025	−	0.445180i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.18693	−	8.98403i	0.323552	−	0.560408i	−0.657666	−	0.753309i	$-0.728456\pi$
$257$	5.18693	−	8.98403i	0.323552	−	0.560408i	0.981218	+	0.192901i	$0.0617896\pi$
$258$	−1.23049	−	2.13128i	−0.0766071	−	0.132687i
$259$	−7.79129			−0.484127
$260$	0.791288			0.0490736
$261$	0.104356	−	0.180750i	0.00645948	−	0.0111881i
$262$	−5.29129	−	9.16478i	−0.326897	−	0.566202i
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$	4.47822	−	7.75650i	0.275615	−	0.477380i
$265$	−8.37386			−0.514402
$266$	5.00000	+	8.66025i	0.306570	+	0.530994i
$267$	3.95644			0.242130
$268$	2.00000	−	7.93725i	0.122169	−	0.484845i
$269$	10.7477			0.655300			0.327650	−	0.944799i	$-0.393743\pi$
$269$	10.7477			0.655300			0.327650	+	0.944799i	$0.393743\pi$
$270$	2.50000	+	4.33013i	0.152145	+	0.263523i
$271$	15.1652			0.921217			0.460609	−	0.887603i	$-0.347631\pi$
$271$	15.1652			0.921217			0.460609	+	0.887603i	$0.347631\pi$
$272$	−2.29129	+	3.96863i	−0.138930	+	0.240633i
$273$	3.95644			0.239455
$274$	10.2913	+	17.8250i	0.621719	+	1.07685i
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$	−13.5826			−0.817575
$277$	14.1652			0.851101			0.425551	−	0.904935i	$-0.360080\pi$
$277$	14.1652			0.851101			0.425551	+	0.904935i	$0.360080\pi$
$278$	−1.81307	−	3.14033i	−0.108741	−	0.188344i
$279$	−0.439205	+	0.760725i	−0.0262945	+	0.0455434i
$280$	1.39564	−	2.41733i	0.0834057	−	0.144463i
$281$	−2.26951	−	3.93090i	−0.135387	−	0.234498i	0.790358	−	0.612645i	$-0.209895\pi$
$281$	−2.26951	−	3.93090i	−0.135387	−	0.234498i	−0.925745	+	0.378147i	$0.876561\pi$
$282$	−16.4174			−0.977643
$283$	9.79129			0.582032			0.291016	−	0.956718i	$-0.406007\pi$
$283$	9.79129			0.582032			0.291016	+	0.956718i	$0.406007\pi$
$284$	−6.97822	−	12.0866i	−0.414081	−	0.717210i
$285$	3.20871	+	5.55765i	0.190068	+	0.329207i
$286$	1.97822	+	3.42638i	0.116975	+	0.202606i
$287$	3.60436	+	6.24293i	0.212758	+	0.368508i
$288$	−0.104356	+	0.180750i	−0.00614924	+	0.0106508i
$289$	−2.00000	+	3.46410i	−0.117647	+	0.203771i
$290$	1.00000			0.0587220
$291$	−13.2477	−	22.9457i	−0.776596	−	1.34510i
$292$		0			0
$293$	−10.6261			−0.620786			−0.310393	−	0.950608i	$-0.600461\pi$
$293$	−10.6261			−0.620786			−0.310393	+	0.950608i	$0.600461\pi$
$294$	0.708712	−	1.22753i	0.0413329	−	0.0715907i
$295$	−8.58258			−0.499697
$296$	1.39564	+	2.41733i	0.0811202	+	0.140504i
$297$	−12.5000	+	21.6506i	−0.725324	+	1.25630i
$298$	−4.26951	−	7.39500i	−0.247326	−	0.428381i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$	−3.58258	+	6.20520i	−0.206840	+	0.358258i
$301$	1.91742	−	3.32108i	0.110518	−	0.191424i
$302$	0.895644	−	1.55130i	0.0515385	−	0.0892673i
$303$	10.8956	−	18.8718i	0.625938	−	1.08416i
$304$	1.79129	−	3.10260i	0.102737	−	0.177946i
$305$	−4.68693	−	8.11800i	−0.268373	−	0.464836i
$306$	−0.478220	+	0.828301i	−0.0273380	+	0.0473508i
$307$	−13.6044	−	23.5634i	−0.776442	−	1.34484i	−0.933981	−	0.357324i	$-0.883689\pi$
$307$	−13.6044	−	23.5634i	−0.776442	−	1.34484i	0.157539	−	0.987513i	$-0.449644\pi$
$308$	13.9564			0.795242
$309$	−13.3956	+	23.2019i	−0.762052	+	1.31991i
$310$	−4.20871			−0.239039
$311$	−7.83485			−0.444274			−0.222137	−	0.975016i	$-0.571303\pi$
$311$	−7.83485			−0.444274			−0.222137	+	0.975016i	$0.571303\pi$
$312$	−0.708712	−	1.22753i	−0.0401229	−	0.0694949i
$313$	−29.9564			−1.69324			−0.846619	−	0.532199i	$-0.821366\pi$
$313$	−29.9564			−1.69324			−0.846619	+	0.532199i	$0.821366\pi$
$314$	2.29129	−	3.96863i	0.129305	−	0.223963i
$315$	0.291288	−	0.504525i	0.0164122	−	0.0284268i
$316$	1.31307	+	2.27430i	0.0738659	+	0.127939i
$317$	6.70871	+	11.6198i	0.376799	+	0.652635i	0.990595	−	0.136830i	$-0.0436915\pi$
$317$	6.70871	+	11.6198i	0.376799	+	0.652635i	−0.613796	+	0.789465i	$0.710358\pi$
$318$	7.50000	+	12.9904i	0.420579	+	0.728464i
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$	−1.00000			−0.0559017
$321$	21.4174			1.19540
$322$	−10.5826	−	18.3296i	−0.589744	−	1.02147i
$323$	8.20871	−	14.2179i	0.456745	−	0.791105i
$324$	4.79129	−	8.29875i	0.266183	−	0.461042i
$325$	−1.58258	−	2.74110i	−0.0877855	−	0.152049i
$326$	19.5826			1.08458
$327$	15.6697			0.866536
$328$	1.29129	−	2.23658i	0.0712994	−	0.123494i
$329$	−12.7913	−	22.1552i	−0.705207	−	1.22145i
$330$	8.95644			0.493036
$331$	8.79129	−	15.2270i	0.483213	−	0.836949i	−0.516601	−	0.856226i	$-0.672803\pi$
$331$	8.79129	−	15.2270i	0.483213	−	0.836949i	0.999814	+	0.0192768i	$0.00613638\pi$
$332$	12.0000			0.658586
$333$	0.291288	+	0.504525i	0.0159625	+	0.0276478i
$334$	20.5826			1.12623
$335$	7.87386	−	2.23658i	0.430195	−	0.122197i
$336$	−5.00000			−0.272772
$337$	14.3739	+	24.8963i	0.782994	+	1.35619i	0.930190	+	0.367078i	$0.119642\pi$
$337$	14.3739	+	24.8963i	0.782994	+	1.35619i	−0.147196	+	0.989107i	$0.547025\pi$
$338$	−12.3739			−0.673049
$339$	−10.1869	+	17.6443i	−0.553278	+	0.958306i
$340$	−4.58258			−0.248525
$341$	−10.5218	−	18.2243i	−0.569786	−	0.986899i
$342$	0.373864	−	0.647551i	0.0202162	−	0.0350155i
$343$	−17.3303			−0.935748
$344$	−1.37386			−0.0740738
$345$	−6.79129	−	11.7629i	−0.365631	−	0.633291i
$346$	8.79129	−	15.2270i	0.472623	−	0.818606i
$347$	6.18693	−	10.7161i	0.332132	−	0.575269i	−0.650798	−	0.759251i	$-0.725565\pi$
$347$	6.18693	−	10.7161i	0.332132	−	0.575269i	0.982930	+	0.183982i	$0.0588988\pi$
$348$	−0.895644	−	1.55130i	−0.0480116	−	0.0831585i
$349$	−9.41742			−0.504103			−0.252052	−	0.967714i	$-0.581105\pi$
$349$	−9.41742			−0.504103			−0.252052	+	0.967714i	$0.581105\pi$
$350$	−11.1652			−0.596802
$351$	1.97822	+	3.42638i	0.105590	+	0.182886i
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	−8.68693	−	15.0462i	−0.462359	−	0.800829i	0.536719	−	0.843761i	$-0.319663\pi$
$353$	−8.68693	−	15.0462i	−0.462359	−	0.800829i	−0.999078	+	0.0429321i	$0.986330\pi$
$354$	7.68693	+	13.3142i	0.408556	+	0.707639i
$355$	6.97822	−	12.0866i	0.370365	−	0.641492i
$356$	1.10436	−	1.91280i	0.0585308	−	0.101378i
$357$	−22.9129			−1.21268
$358$	7.87386	+	13.6379i	0.416147	+	0.720787i
$359$	−0.373864			−0.0197318			−0.00986588	−	0.999951i	$-0.503140\pi$
$359$	−0.373864			−0.0197318			−0.00986588	+	0.999951i	$0.503140\pi$
$360$	−0.208712			−0.0110001
$361$	3.08258	−	5.33918i	0.162241	−	0.281009i
$362$	20.5826			1.08180
$363$	12.5390	+	21.7182i	0.658128	+	1.13991i
$364$	1.10436	−	1.91280i	0.0578840	−	0.100258i
$365$		0			0
$366$	−8.39564	+	14.5417i	−0.438847	+	0.760106i
$367$	−8.97822	+	15.5507i	−0.468659	+	0.811742i	−0.999358	−	0.0358187i	$-0.988596\pi$
$367$	−8.97822	+	15.5507i	−0.468659	+	0.811742i	0.530699	+	0.847560i	$0.321929\pi$
$368$	−3.79129	+	6.56670i	−0.197635	+	0.342313i
$369$	0.269507	−	0.466801i	0.0140300	−	0.0243007i
$370$	−1.39564	+	2.41733i	−0.0725561	+	0.125671i
$371$	−11.6869	+	20.2424i	−0.606755	+	1.05093i
$372$	3.76951	+	6.52898i	0.195440	+	0.338512i
$373$	−13.7695	+	23.8495i	−0.712958	+	1.23488i	0.250784	+	0.968043i	$0.419312\pi$
$373$	−13.7695	+	23.8495i	−0.712958	+	1.23488i	−0.963742	+	0.266836i	$0.914022\pi$
$374$	−11.4564	−	19.8431i	−0.592398	−	1.02606i
$375$	−16.1216			−0.832515
$376$	−4.58258	+	7.93725i	−0.236328	+	0.409333i
$377$	0.791288			0.0407534
$378$	13.9564			0.717842
$379$	−14.1044	−	24.4295i	−0.724492	−	1.25486i	−0.959183	−	0.282787i	$-0.908741\pi$
$379$	−14.1044	−	24.4295i	−0.724492	−	1.25486i	0.234691	−	0.972070i	$-0.424592\pi$
$380$	3.58258			0.183782
$381$	−17.3131	+	29.9871i	−0.886975	+	1.53629i
$382$	7.18693	−	12.4481i	0.367715	−	0.636902i
$383$	10.6044	+	18.3673i	0.541857	+	0.938524i	0.998797	+	0.0490269i	$0.0156120\pi$
$383$	10.6044	+	18.3673i	0.541857	+	0.938524i	−0.456940	+	0.889497i	$0.651055\pi$
$384$	0.895644	+	1.55130i	0.0457056	+	0.0791645i
$385$	6.97822	+	12.0866i	0.355643	+	0.615992i
$386$	6.18693	+	10.7161i	0.314907	+	0.545434i
$387$	−0.286742			−0.0145759
$388$	−14.7913			−0.750914
$389$	0.895644	+	1.55130i	0.0454109	+	0.0786541i	0.887837	−	0.460157i	$-0.152207\pi$
$389$	0.895644	+	1.55130i	0.0454109	+	0.0786541i	−0.842427	+	0.538811i	$0.818874\pi$
$390$	0.708712	−	1.22753i	0.0358870	−	0.0621582i
$391$	−17.3739	+	30.0924i	−0.878634	+	1.52184i
$392$	−0.395644	−	0.685275i	−0.0199830	−	0.0346116i
$393$	−18.9564			−0.956226
$394$	17.5826			0.885797
$395$	−1.31307	+	2.27430i	−0.0660676	+	0.114432i
$396$	−0.521780	−	0.903750i	−0.0262205	−	0.0454152i
$397$	25.5390			1.28177			0.640883	−	0.767638i	$-0.278568\pi$
$397$	25.5390			1.28177			0.640883	+	0.767638i	$0.278568\pi$
$398$	−5.79129	+	10.0308i	−0.290291	+	0.502799i
$399$	17.9129			0.896766
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$	−10.5218	−	10.2116i	−0.524779	−	0.509306i
$403$	−3.33030			−0.165894
$404$	−6.08258	−	10.5353i	−0.302619	−	0.524152i
$405$	9.58258			0.476162
$406$	1.39564	−	2.41733i	0.0692646	−	0.119970i
$407$	−13.9564			−0.691795
$408$	4.10436	+	7.10895i	0.203196	+	0.351946i
$409$	−5.95644	+	10.3169i	−0.294527	+	0.510136i	−0.974875	−	0.222754i	$-0.928495\pi$
$409$	−5.95644	+	10.3169i	−0.294527	+	0.510136i	0.680348	+	0.732889i	$0.261829\pi$
$410$	2.58258			0.127544
$411$	36.8693			1.81863
$412$	7.47822	+	12.9527i	0.368425	+	0.638132i
$413$	−11.9782	+	20.7469i	−0.589410	+	1.02089i
$414$	−0.791288	+	1.37055i	−0.0388897	+	0.0673589i
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	−0.791288			−0.0387961
$417$	−6.49545			−0.318084
$418$	8.95644	+	15.5130i	0.438074	+	0.758766i
$419$	2.81307	+	4.87238i	0.137427	+	0.238031i	0.926522	−	0.376240i	$-0.122783\pi$
$419$	2.81307	+	4.87238i	0.137427	+	0.238031i	−0.789095	+	0.614272i	$0.789450\pi$
$420$	−2.50000	−	4.33013i	−0.121988	−	0.211289i
$421$	−4.68693	−	8.11800i	−0.228427	−	0.395647i	0.728915	−	0.684604i	$-0.240025\pi$
$421$	−4.68693	−	8.11800i	−0.228427	−	0.395647i	−0.957342	+	0.288957i	$0.906692\pi$
$422$	−11.0826	+	19.1956i	−0.539491	+	0.934426i
$423$	−0.956439	+	1.65660i	−0.0465037	+	0.0805467i
$424$	8.37386			0.406671
$425$	9.16515	+	15.8745i	0.444575	+	0.770027i
$426$	−25.0000			−1.21125
$427$	−26.1652			−1.26622
$428$	5.97822	−	10.3546i	0.288968	−	0.500508i
$429$	7.08712			0.342169
$430$	−0.686932	−	1.18980i	−0.0331268	−	0.0573773i
$431$	−12.1434	+	21.0329i	−0.584926	+	1.01312i	0.409959	+	0.912104i	$0.365543\pi$
$431$	−12.1434	+	21.0329i	−0.584926	+	1.01312i	−0.994885	+	0.101017i	$0.967790\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	9.37386	−	16.2360i	0.450479	−	0.780253i	−0.547937	−	0.836520i	$-0.684587\pi$
$433$	9.37386	−	16.2360i	0.450479	−	0.780253i	0.998416	+	0.0562671i	$0.0179198\pi$
$434$	−5.87386	+	10.1738i	−0.281954	+	0.488359i
$435$	0.895644	−	1.55130i	0.0429428	−	0.0743792i
$436$	4.37386	−	7.57575i	0.209470	−	0.362813i
$437$	13.5826	−	23.5257i	0.649743	−	1.12539i
$438$		0			0
$439$	−6.76951	−	11.7251i	−0.323091	−	0.559610i	0.658033	−	0.752989i	$-0.271389\pi$
$439$	−6.76951	−	11.7251i	−0.323091	−	0.559610i	−0.981124	+	0.193379i	$0.938055\pi$
$440$	2.50000	−	4.33013i	0.119183	−	0.206431i
$441$	−0.0825757	−	0.143025i	−0.00393218	−	0.00681073i
$442$	−3.62614			−0.172478
$443$	−6.29129	+	10.8968i	−0.298908	+	0.517724i	−0.975886	−	0.218279i	$-0.929956\pi$
$443$	−6.29129	+	10.8968i	−0.298908	+	0.517724i	0.676978	+	0.736003i	$0.263289\pi$
$444$	5.00000			0.237289
$445$	2.20871			0.104703
$446$	−12.6652	−	21.9367i	−0.599712	−	1.03873i
$447$	−15.2958			−0.723468
$448$	−1.39564	+	2.41733i	−0.0659380	+	0.114208i
$449$	15.5826	−	26.9898i	0.735387	−	1.27373i	−0.219166	−	0.975688i	$-0.570334\pi$
$449$	15.5826	−	26.9898i	0.735387	−	1.27373i	0.954553	−	0.298040i	$-0.0963330\pi$
$450$	0.417424	+	0.723000i	0.0196776	+	0.0340826i
$451$	6.45644	+	11.1829i	0.304022	+	0.526581i
$452$	5.68693	+	9.85005i	0.267491	+	0.463308i
$453$	−1.60436	−	2.77883i	−0.0753792	−	0.130561i
$454$	13.1216			0.615827
$455$	2.20871			0.103546
$456$	−3.20871	−	5.55765i	−0.150262	−	0.260261i
$457$	5.89564	−	10.2116i	0.275787	−	0.477676i	−0.694547	−	0.719448i	$-0.744395\pi$
$457$	5.89564	−	10.2116i	0.275787	−	0.477676i	0.970333	+	0.241771i	$0.0777284\pi$
$458$	−4.47822	+	7.75650i	−0.209253	+	0.362438i
$459$	−11.4564	−	19.8431i	−0.534741	−	0.926198i
$460$	−7.58258			−0.353539
$461$	30.1652			1.40493			0.702466	−	0.711718i	$-0.252082\pi$
$461$	30.1652			1.40493			0.702466	+	0.711718i	$0.252082\pi$
$462$	12.5000	−	21.6506i	0.581553	−	1.00728i
$463$	−4.08258	−	7.07123i	−0.189733	−	0.328628i	0.755428	−	0.655232i	$-0.227429\pi$
$463$	−4.08258	−	7.07123i	−0.189733	−	0.328628i	−0.945161	+	0.326604i	$0.894096\pi$
$464$	−1.00000			−0.0464238
$465$	−3.76951	+	6.52898i	−0.174807	+	0.302774i
$466$	16.2087			0.750854
$467$	8.18693	+	14.1802i	0.378846	+	0.656181i	0.990895	−	0.134640i	$-0.0429877\pi$
$467$	8.18693	+	14.1802i	0.378846	+	0.656181i	−0.612049	+	0.790820i	$0.709654\pi$
$468$	−0.165151			−0.00763413
$469$	5.58258	−	22.1552i	0.257779	−	1.02303i
$470$	−9.16515			−0.422757
$471$	−4.10436	−	7.10895i	−0.189119	−	0.327563i
$472$	8.58258			0.395045
$473$	3.43466	−	5.94900i	0.157926	−	0.273535i
$474$	4.70417			0.216070
$475$	−7.16515	−	12.4104i	−0.328760	−	0.569428i
$476$	−6.39564	+	11.0776i	−0.293144	+	0.507740i
$477$	1.74773			0.0800229
$478$	2.62614			0.120117
$479$	2.16515	+	3.75015i	0.0989283	+	0.171349i	0.911241	−	0.411873i	$-0.135125\pi$
$479$	2.16515	+	3.75015i	0.0989283	+	0.171349i	−0.812313	+	0.583222i	$0.801792\pi$
$480$	−0.895644	+	1.55130i	−0.0408804	+	0.0708069i
$481$	−1.10436	+	1.91280i	−0.0503543	+	0.0872162i
$482$	−7.18693	−	12.4481i	−0.327356	−	0.566997i
$483$	−37.9129			−1.72510
$484$	14.0000			0.636364
$485$	−7.39564	−	12.8096i	−0.335819	−	0.581655i
$486$	−1.08258	−	1.87508i	−0.0491066	−	0.0850552i
$487$	−2.95644	−	5.12070i	−0.133969	−	0.232041i	0.791234	−	0.611513i	$-0.209439\pi$
$487$	−2.95644	−	5.12070i	−0.133969	−	0.232041i	−0.925203	+	0.379472i	$0.876106\pi$
$488$	4.68693	+	8.11800i	0.212167	+	0.367485i
$489$	17.5390	−	30.3785i	0.793142	−	1.37376i
$490$	0.395644	−	0.685275i	0.0178734	−	0.0309576i
$491$	16.9564			0.765233			0.382617	−	0.923907i	$-0.375023\pi$
$491$	16.9564			0.765233			0.382617	+	0.923907i	$0.375023\pi$
$492$	−2.31307	−	4.00635i	−0.104281	−	0.180620i
$493$	−4.58258			−0.206389
$494$	2.83485			0.127546
$495$	0.521780	−	0.903750i	0.0234523	−	0.0406205i
$496$	4.20871			0.188977
$497$	−19.4782	−	33.7373i	−0.873718	−	1.51332i
$498$	10.7477	−	18.6156i	0.481617	−	0.834185i
$499$	10.8131	+	18.7288i	0.484059	+	0.838415i	0.999832	−	0.0183098i	$-0.00582852\pi$
$499$	10.8131	+	18.7288i	0.484059	+	0.838415i	−0.515773	+	0.856725i	$0.672495\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	18.4347	−	31.9298i	0.823600	−	1.42652i
$502$	−8.29129	+	14.3609i	−0.370058	+	0.640960i
$503$	−11.3739	+	19.7001i	−0.507136	+	0.878384i	0.492830	+	0.870125i	$0.335962\pi$
$503$	−11.3739	+	19.7001i	−0.507136	+	0.878384i	−0.999966	+	0.00825907i	$0.997371\pi$
$504$	−0.291288	+	0.504525i	−0.0129750	+	0.0224733i
$505$	6.08258	−	10.5353i	0.270671	−	0.468816i
$506$	−18.9564	−	32.8335i	−0.842717	−	1.45963i
$507$	−11.0826	+	19.1956i	−0.492194	+	0.852506i
$508$	9.66515	+	16.7405i	0.428822	+	0.742741i
$509$	6.95644			0.308339			0.154169	−	0.988044i	$-0.450730\pi$
$509$	6.95644			0.308339			0.154169	+	0.988044i	$0.450730\pi$
$510$	−4.10436	+	7.10895i	−0.181744	+	0.314790i
$511$		0			0
$512$	1.00000			0.0441942
$513$	8.95644	+	15.5130i	0.395436	+	0.684916i
$514$	−10.3739			−0.457572
$515$	−7.47822	+	12.9527i	−0.329530	+	0.570762i
$516$	−1.23049	+	2.13128i	−0.0541694	+	0.0938242i
$517$	−22.9129	−	39.6863i	−1.00771	−	1.74540i
$518$	3.89564	+	6.74745i	0.171165	+	0.296466i
$519$	−15.7477	−	27.2759i	−0.691248	−	1.19728i
$520$	−0.395644	−	0.685275i	−0.0173501	−	0.0300513i
$521$	25.7042			1.12612			0.563060	−	0.826416i	$-0.309624\pi$
$521$	25.7042			1.12612			0.563060	+	0.826416i	$0.309624\pi$
$522$	−0.208712			−0.00913508
$523$	13.3739	+	23.1642i	0.584798	+	1.01290i	0.994901	+	0.100861i	$0.0321596\pi$
$523$	13.3739	+	23.1642i	0.584798	+	1.01290i	−0.410102	+	0.912040i	$0.634507\pi$
$524$	−5.29129	+	9.16478i	−0.231151	+	0.400365i
$525$	−10.0000	+	17.3205i	−0.436436	+	0.755929i
$526$	−6.00000	−	10.3923i	−0.261612	−	0.453126i
$527$	19.2867			0.840144
$528$	−8.95644			−0.389779
$529$	−17.2477	+	29.8739i	−0.749901	+	1.29887i
$530$	4.18693	+	7.25198i	0.181869	+	0.315006i
$531$	1.79129			0.0777353
$532$	5.00000	−	8.66025i	0.216777	−	0.375470i
$533$	2.04356			0.0885164
$534$	−1.97822	−	3.42638i	−0.0856059	−	0.148274i
$535$	11.9564			0.516922
$536$	−7.87386	+	2.23658i	−0.340099	+	0.0966054i
$537$	28.2087			1.21730
$538$	−5.37386	−	9.30780i	−0.231684	−	0.401288i
$539$	3.95644			0.170416
$540$	2.50000	−	4.33013i	0.107583	−	0.186339i
$541$	0.330303			0.0142008			0.00710041	−	0.999975i	$-0.497740\pi$
$541$	0.330303			0.0142008			0.00710041	+	0.999975i	$0.497740\pi$
$542$	−7.58258	−	13.1334i	−0.325700	−	0.564128i
$543$	18.4347	−	31.9298i	0.791107	−	1.37024i
$544$	4.58258			0.196476
$545$	8.74773			0.374711
$546$	−1.97822	−	3.42638i	−0.0846600	−	0.146635i
$547$	−18.0826	+	31.3199i	−0.773155	+	1.33914i	0.162670	+	0.986680i	$0.447989\pi$
$547$	−18.0826	+	31.3199i	−0.773155	+	1.33914i	−0.935826	+	0.352463i	$0.885344\pi$
$548$	10.2913	−	17.8250i	0.439622	−	0.761448i
$549$	0.978220	+	1.69433i	0.0417494	+	0.0723121i
$550$	−20.0000			−0.852803
$551$	3.58258			0.152623
$552$	6.79129	+	11.7629i	0.289056	+	0.500660i
$553$	3.66515	+	6.34823i	0.155858	+	0.269954i
$554$	−7.08258	−	12.2674i	−0.300910	−	0.521191i
$555$	2.50000	+	4.33013i	0.106119	+	0.183804i
$556$	−1.81307	+	3.14033i	−0.0768912	+	0.133179i
$557$	17.6434	−	30.5592i	0.747574	−	1.29484i	−0.201409	−	0.979507i	$-0.564552\pi$
$557$	17.6434	−	30.5592i	0.747574	−	1.29484i	0.948983	−	0.315328i	$-0.102115\pi$
$558$	0.878409			0.0371860
$559$	−0.543561	−	0.941475i	−0.0229902	−	0.0398201i
$560$	−2.79129			−0.117953
$561$	−41.0436			−1.73286
$562$	−2.26951	+	3.93090i	−0.0957334	+	0.165815i
$563$	−7.58258			−0.319567			−0.159784	−	0.987152i	$-0.551080\pi$
$563$	−7.58258			−0.319567			−0.159784	+	0.987152i	$0.551080\pi$
$564$	8.20871	+	14.2179i	0.345649	+	0.598682i
$565$	−5.68693	+	9.85005i	−0.239251	+	0.414395i
$566$	−4.89564	−	8.47950i	−0.205779	−	0.356420i
$567$	13.3739	−	23.1642i	0.561649	−	0.972805i
$568$	−6.97822	+	12.0866i	−0.292800	+	0.507144i
$569$	−20.0390	+	34.7086i	−0.840079	+	1.45506i	0.0497478	+	0.998762i	$0.484158\pi$
$569$	−20.0390	+	34.7086i	−0.840079	+	1.45506i	−0.889827	+	0.456298i	$0.849175\pi$
$570$	3.20871	−	5.55765i	0.134398	−	0.232784i
$571$	−17.4564	+	30.2354i	−0.730529	+	1.26531i	0.226128	+	0.974098i	$0.427393\pi$
$571$	−17.4564	+	30.2354i	−0.730529	+	1.26531i	−0.956657	+	0.291216i	$0.905940\pi$
$572$	1.97822	−	3.42638i	0.0827135	−	0.143264i
$573$	−12.8739	−	22.2982i	−0.537813	−	0.931520i
$574$	3.60436	−	6.24293i	0.150443	−	0.260575i
$575$	15.1652	+	26.2668i	0.632431	+	1.09540i
$576$	0.208712			0.00869634
$577$	17.0826	−	29.5879i	0.711157	−	1.23176i	−0.253266	−	0.967397i	$-0.581505\pi$
$577$	17.0826	−	29.5879i	0.711157	−	1.23176i	0.964423	−	0.264363i	$-0.0851618\pi$
$578$	4.00000			0.166378
$579$	22.1652			0.921152
$580$	−0.500000	−	0.866025i	−0.0207614	−	0.0359597i
$581$	33.4955			1.38963
$582$	−13.2477	+	22.9457i	−0.549136	+	0.951131i
$583$	−20.9347	+	36.2599i	−0.867025	+	1.50173i
$584$		0			0
$585$	−0.0825757	−	0.143025i	−0.00341408	−	0.00591337i
$586$	5.31307	+	9.20250i	0.219481	+	0.380152i
$587$	−3.83485	−	6.64215i	−0.158281	−	0.274151i	0.775968	−	0.630773i	$-0.217262\pi$
$587$	−3.83485	−	6.64215i	−0.158281	−	0.274151i	−0.934249	+	0.356622i	$0.883929\pi$
$588$	−1.41742			−0.0584536
$589$	−15.0780			−0.621279
$590$	4.29129	+	7.43273i	0.176670	+	0.306001i
$591$	15.7477	−	27.2759i	0.647775	−	1.12198i
$592$	1.39564	−	2.41733i	0.0573606	−	0.0993515i
$593$	1.31307	+	2.27430i	0.0539212	+	0.0933943i	0.891726	−	0.452575i	$-0.149495\pi$
$593$	1.31307	+	2.27430i	0.0539212	+	0.0933943i	−0.837805	+	0.545970i	$0.816161\pi$
$594$	25.0000			1.02576
$595$	−12.7913			−0.524392
$596$	−4.26951	+	7.39500i	−0.174886	+	0.302911i
$597$	10.3739	+	17.9681i	0.424574	+	0.735384i
$598$	−6.00000			−0.245358
$599$	22.8303	−	39.5432i	0.932821	−	1.61569i	0.154347	−	0.988017i	$-0.450673\pi$
$599$	22.8303	−	39.5432i	0.932821	−	1.61569i	0.778474	−	0.627676i	$-0.215994\pi$
$600$	7.16515			0.292516
$601$	−15.7695	−	27.3136i	−0.643252	−	1.11414i	−0.984702	−	0.174245i	$-0.944252\pi$
$601$	−15.7695	−	27.3136i	−0.643252	−	1.11414i	0.341451	−	0.939900i	$-0.389082\pi$
$602$	−3.83485			−0.156297
$603$	−1.64337	+	0.466801i	−0.0669232	+	0.0190096i
$604$	−1.79129			−0.0728865
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	−21.7913			−0.885211
$607$	10.5000	−	18.1865i	0.426182	−	0.738169i	−0.570348	−	0.821403i	$-0.693192\pi$
$607$	10.5000	−	18.1865i	0.426182	−	0.738169i	0.996530	+	0.0832344i	$0.0265250\pi$
$608$	−3.58258			−0.145293
$609$	−2.50000	−	4.33013i	−0.101305	−	0.175466i
$610$	−4.68693	+	8.11800i	−0.189768	+	0.328688i
$611$	−7.25227			−0.293396
$612$	0.956439			0.0386618
$613$	4.87386	+	8.44178i	0.196853	+	0.340960i	0.947507	−	0.319736i	$-0.103594\pi$
$613$	4.87386	+	8.44178i	0.196853	+	0.340960i	−0.750653	+	0.660697i	$0.770261\pi$
$614$	−13.6044	+	23.5634i	−0.549027	+	0.950943i
$615$	2.31307	−	4.00635i	0.0932719	−	0.161552i
$616$	−6.97822	−	12.0866i	−0.281160	−	0.486984i
$617$	17.2087			0.692797			0.346398	−	0.938088i	$-0.387405\pi$
$617$	17.2087			0.692797			0.346398	+	0.938088i	$0.387405\pi$
$618$	26.7913			1.07770
$619$	12.0608	+	20.8899i	0.484764	+	0.839636i	0.999847	−	0.0175042i	$-0.00557205\pi$
$619$	12.0608	+	20.8899i	0.484764	+	0.839636i	−0.515082	+	0.857141i	$0.672239\pi$
$620$	2.10436	+	3.64485i	0.0845130	+	0.146381i
$621$	−18.9564	−	32.8335i	−0.760696	−	1.31756i
$622$	3.91742	+	6.78518i	0.157074	+	0.272061i
$623$	3.08258	−	5.33918i	0.123501	−	0.213910i
$624$	−0.708712	+	1.22753i	−0.0283712	+	0.0491403i
$625$	11.0000			0.440000
$626$	14.9782	+	25.9430i	0.598650	+	1.03689i
$627$	32.0871			1.28144
$628$	−4.58258			−0.182865
$629$	6.39564	−	11.0776i	0.255011	−	0.441692i
$630$	−0.582576			−0.0232104
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	0.995795	+	0.0916122i	$0.0292020\pi$
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	−0.418559	+	0.908190i	$0.637465\pi$
$632$	1.31307	−	2.27430i	0.0522310	−	0.0904668i
$633$	19.8521	+	34.3848i	0.789049	+	1.36667i
$634$	6.70871	−	11.6198i	0.266437	−	0.461482i
$635$	−9.66515	+	16.7405i	−0.383550	+	0.664328i
$636$	7.50000	−	12.9904i	0.297394	−	0.515102i
$637$	0.313068	−	0.542250i	0.0124042	−	0.0214847i
$638$	2.50000	−	4.33013i	0.0989759	−	0.171431i
$639$	−1.45644	+	2.52263i	−0.0576158	+	0.0997936i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	3.76951	−	6.52898i	0.148887	−	0.257879i	−0.781930	−	0.623367i	$-0.785764\pi$
$641$	3.76951	−	6.52898i	0.148887	−	0.257879i	0.930816	+	0.365488i	$0.119098\pi$
$642$	−10.7087	−	18.5480i	−0.422639	−	0.732032i
$643$	20.7477			0.818210			0.409105	−	0.912487i	$-0.365841\pi$
$643$	20.7477			0.818210			0.409105	+	0.912487i	$0.365841\pi$
$644$	−10.5826	+	18.3296i	−0.417012	+	0.722286i
$645$	−2.46099			−0.0969012
$646$	−16.4174			−0.645935
$647$	4.70871	+	8.15573i	0.185119	+	0.320635i	0.943616	−	0.331041i	$-0.107400\pi$
$647$	4.70871	+	8.15573i	0.185119	+	0.320635i	−0.758498	+	0.651675i	$0.774066\pi$
$648$	−9.58258			−0.376439
$649$	−21.4564	+	37.1636i	−0.842239	+	1.45880i
$650$	−1.58258	+	2.74110i	−0.0620737	+	0.107515i
$651$	10.5218	+	18.2243i	0.412381	+	0.714265i
$652$	−9.79129	−	16.9590i	−0.383456	−	0.664166i
$653$	−11.8739	−	20.5661i	−0.464660	−	0.804815i	0.534526	−	0.845152i	$-0.320490\pi$
$653$	−11.8739	−	20.5661i	−0.464660	−	0.804815i	−0.999186	+	0.0403370i	$0.987157\pi$
$654$	−7.83485	−	13.5704i	−0.306367	−	0.530643i
$655$	−10.5826			−0.413495
$656$	−2.58258			−0.100833
$657$		0			0
$658$	−12.7913	+	22.1552i	−0.498656	+	0.863698i
$659$	−6.97822	+	12.0866i	−0.271833	+	0.470828i	−0.969331	−	0.245758i	$-0.920963\pi$
$659$	−6.97822	+	12.0866i	−0.271833	+	0.470828i	0.697498	+	0.716586i	$0.254296\pi$
$660$	−4.47822	−	7.75650i	−0.174314	−	0.301922i
$661$	−9.74773			−0.379143			−0.189571	−	0.981867i	$-0.560710\pi$
$661$	−9.74773			−0.379143			−0.189571	+	0.981867i	$0.560710\pi$
$662$	−17.5826			−0.683366
$663$	−3.24773	+	5.62523i	−0.126131	+	0.218466i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	10.0000			0.387783
$666$	0.291288	−	0.504525i	0.0112872	−	0.0195500i
$667$	−7.58258			−0.293599
$668$	−10.2913	−	17.8250i	−0.398182	−	0.689671i
$669$	−45.3739			−1.75425
$670$	−5.87386	−	5.70068i	−0.226927	−	0.220236i
$671$	−46.8693			−1.80937
$672$	2.50000	+	4.33013i	0.0964396	+	0.167038i
$673$	−15.1216			−0.582894			−0.291447	−	0.956587i	$-0.594137\pi$
$673$	−15.1216			−0.582894			−0.291447	+	0.956587i	$0.594137\pi$
$674$	14.3739	−	24.8963i	0.553661	−	0.958968i
$675$	−20.0000			−0.769800
$676$	6.18693	+	10.7161i	0.237959	+	0.412157i
$677$	−16.6434	+	28.8272i	−0.639657	+	1.10792i	0.345851	+	0.938289i	$0.387590\pi$
$677$	−16.6434	+	28.8272i	−0.639657	+	1.10792i	−0.985508	+	0.169629i	$0.945743\pi$
$678$	20.3739			0.782454
$679$	−41.2867			−1.58444
$680$	2.29129	+	3.96863i	0.0878669	+	0.152190i
$681$	11.7523	−	20.3555i	0.450348	−	0.780026i
$682$	−10.5218	+	18.2243i	−0.402900	+	0.697843i
$683$	18.2695	+	31.6437i	0.699063	+	1.21081i	0.968792	+	0.247877i	$0.0797328\pi$
$683$	18.2695	+	31.6437i	0.699063	+	1.21081i	−0.269728	+	0.962936i	$0.586934\pi$
$684$	−0.747727			−0.0285901
$685$	20.5826			0.786420
$686$	8.66515	+	15.0085i	0.330837	+	0.573027i
$687$	8.02178	+	13.8941i	0.306050	+	0.530094i
$688$	0.686932	+	1.18980i	0.0261890	+	0.0453607i
$689$	3.31307	+	5.73840i	0.126218	+	0.218616i
$690$	−6.79129	+	11.7629i	−0.258540	+	0.447804i
$691$	11.9347	−	20.6714i	0.454016	−	0.786378i	−0.544615	−	0.838686i	$-0.683324\pi$
$691$	11.9347	−	20.6714i	0.454016	−	0.786378i	0.998631	+	0.0523076i	$0.0166576\pi$
$692$	−17.5826			−0.668389
$693$	−1.45644	−	2.52263i	−0.0553256	−	0.0958267i
$694$	−12.3739			−0.469705
$695$	−3.62614			−0.137547
$696$	−0.895644	+	1.55130i	−0.0339493	+	0.0588019i
$697$	−11.8348			−0.448277
$698$	4.70871	+	8.15573i	0.178227	+	0.308699i
$699$	14.5172	−	25.1446i	0.549092	−	0.951056i
$700$	5.58258	+	9.66930i	0.211002	+	0.365465i
$701$	1.58258	−	2.74110i	0.0597731	−	0.103530i	−0.834590	−	0.550871i	$-0.814296\pi$
$701$	1.58258	−	2.74110i	0.0597731	−	0.103530i	0.894363	+	0.447341i	$0.147629\pi$
$702$	1.97822	−	3.42638i	0.0746631	−	0.129320i
$703$	−5.00000	+	8.66025i	−0.188579	+	0.326628i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	−8.20871	+	14.2179i	−0.309158	+	0.535477i
$706$	−8.68693	+	15.0462i	−0.326937	+	0.566271i
$707$	−16.9782	−	29.4071i	−0.638532	−	1.10597i
$708$	7.68693	−	13.3142i	0.288893	−	0.500377i
$709$	19.8521	+	34.3848i	0.745561	+	1.29135i	0.949932	+	0.312456i	$0.101152\pi$
$709$	19.8521	+	34.3848i	0.745561	+	1.29135i	−0.204372	+	0.978893i	$0.565515\pi$
$710$	−13.9564			−0.523776
$711$	0.274053	−	0.474674i	0.0102778	−	0.0178017i
$712$	−2.20871			−0.0827750
$713$	31.9129			1.19515
$714$	11.4564	+	19.8431i	0.428746	+	0.742611i
$715$	3.95644			0.147962
$716$	7.87386	−	13.6379i	0.294260	−	0.509673i
$717$	2.35208	−	4.07393i	0.0878402	−	0.152144i
$718$	0.186932	+	0.323775i	0.00697623	+	0.0120832i
$719$	−13.8956	−	24.0680i	−0.518220	−	0.897583i	−0.999776	−	0.0211681i	$-0.993261\pi$
$719$	−13.8956	−	24.0680i	−0.518220	−	0.897583i	0.481556	−	0.876415i	$-0.340072\pi$
$720$	0.104356	+	0.180750i	0.00388912	+	0.00673616i
$721$	20.8739	+	36.1546i	0.777383	+	1.34647i
$722$	−6.16515			−0.229443
$723$	−25.7477			−0.957568
$724$	−10.2913	−	17.8250i	−0.382473	−	0.662462i
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$	12.5390	−	21.7182i	0.465366	−	0.806038i
$727$	−0.686932	−	1.18980i	−0.0254769	−	0.0441273i	0.853006	−	0.521901i	$-0.174777\pi$
$727$	−0.686932	−	1.18980i	−0.0254769	−	0.0441273i	−0.878483	+	0.477774i	$0.841444\pi$
$728$	−2.20871			−0.0818603
$729$	24.8693			0.921086
$730$		0			0
$731$	3.14792	+	5.45235i	0.116430	+	0.201663i
$732$	16.7913			0.620624
$733$	−10.9782	+	19.0148i	−0.405490	+	0.702329i	−0.994378	−	0.105885i	$-0.966232\pi$
$733$	−10.9782	+	19.0148i	−0.405490	+	0.702329i	0.588889	+	0.808214i	$0.299566\pi$
$734$	17.9564			0.662784
$735$	−0.708712	−	1.22753i	−0.0261412	−	0.0452780i
$736$	7.58258			0.279497
$737$	10.0000	−	39.6863i	0.368355	−	1.46186i
$738$	−0.539015			−0.0198414
$739$	5.73049	+	9.92550i	0.210800	+	0.365116i	0.951965	−	0.306207i	$-0.0990599\pi$
$739$	5.73049	+	9.92550i	0.210800	+	0.365116i	−0.741165	+	0.671322i	$0.765727\pi$
$740$	2.79129			0.102610
$741$	2.53901	−	4.39770i	0.0932730	−	0.161554i
$742$	23.3739			0.858082
$743$	−20.5000	−	35.5070i	−0.752072	−	1.30263i	−0.946817	−	0.321773i	$-0.895721\pi$
$743$	−20.5000	−	35.5070i	−0.752072	−	1.30263i	0.194745	−	0.980854i	$-0.437612\pi$
$744$	3.76951	−	6.52898i	0.138197	−	0.239364i
$745$	−8.53901			−0.312845
$746$	27.5390			1.00827
$747$	−1.25227	−	2.16900i	−0.0458183	−	0.0793596i
$748$	−11.4564	+	19.8431i	−0.418889	+	0.725537i
$749$	16.6869	−	28.9026i	0.609727	−	1.05608i
$750$	8.06080	+	13.9617i	0.294339	+	0.509809i
$751$	20.1216			0.734247			0.367124	−	0.930172i	$-0.380343\pi$
$751$	20.1216			0.734247			0.367124	+	0.930172i	$0.380343\pi$
$752$	9.16515			0.334219
$753$	14.8521	+	25.7246i	0.541240	+	0.937455i
$754$	−0.395644	−	0.685275i	−0.0144085	−	0.0249563i
$755$	−0.895644	−	1.55130i	−0.0325958	−	0.0564576i
$756$	−6.97822	−	12.0866i	−0.253795	−	0.439587i
$757$	−6.24773	+	10.8214i	−0.227078	+	0.393310i	−0.956941	−	0.290283i	$-0.906250\pi$
$757$	−6.24773	+	10.8214i	−0.227078	+	0.393310i	0.729863	+	0.683593i	$0.239584\pi$
$758$	−14.1044	+	24.4295i	−0.512293	+	0.887318i
$759$	−67.9129			−2.46508
$760$	−1.79129	−	3.10260i	−0.0649768	−	0.112543i
$761$	−31.1652			−1.12974			−0.564868	−	0.825181i	$-0.691073\pi$
$761$	−31.1652			−1.12974			−0.564868	+	0.825181i	$0.691073\pi$
$762$	34.6261			1.25437
$763$	12.2087	−	21.1461i	0.441985	−	0.765541i
$764$	−14.3739			−0.520028
$765$	0.478220	+	0.828301i	0.0172901	+	0.0299473i
$766$	10.6044	−	18.3673i	0.383151	−	0.663637i
$767$	3.39564	+	5.88143i	0.122610	+	0.212366i
$768$	0.895644	−	1.55130i	0.0323188	−	0.0559777i
$769$	−17.1652	+	29.7309i	−0.618991	+	1.07212i	0.370679	+	0.928761i	$0.379125\pi$
$769$	−17.1652	+	29.7309i	−0.618991	+	1.07212i	−0.989670	+	0.143363i	$0.954208\pi$
$770$	6.97822	−	12.0866i	0.251478	−	0.435572i
$771$	−9.29129	+	16.0930i	−0.334618	+	0.579575i
$772$	6.18693	−	10.7161i	0.222673	−	0.385680i
$773$	7.79129	−	13.4949i	0.280233	−	0.485378i	−0.691209	−	0.722655i	$-0.742922\pi$
$773$	7.79129	−	13.4949i	0.280233	−	0.485378i	0.971442	+	0.237277i	$0.0762549\pi$
$774$	0.143371	+	0.248326i	0.00515336	+	0.00892589i
$775$	8.41742	−	14.5794i	0.302363	−	0.523708i
$776$	7.39564	+	12.8096i	0.265488	+	0.459839i
$777$	13.9564			0.500684
$778$	0.895644	−	1.55130i	0.0321104	−	0.0556168i
$779$	9.25227			0.331497
$780$	−1.41742			−0.0507519
$781$	−34.8911	−	60.4332i	−1.24850	−	2.16247i
$782$	34.7477			1.24258
$783$	2.50000	−	4.33013i	0.0893427	−	0.154746i
$784$	−0.395644	+	0.685275i	−0.0141301	+	0.0244741i
$785$	−2.29129	−	3.96863i	−0.0817796	−	0.141646i
$786$	9.47822	+	16.4168i	0.338077	+	0.585566i
$787$	−16.1652	−	27.9989i	−0.576225	−	0.998052i	−0.995907	−	0.0903804i	$-0.971192\pi$
$787$	−16.1652	−	27.9989i	−0.576225	−	0.998052i	0.419682	−	0.907671i	$-0.362142\pi$
$788$	−8.79129	−	15.2270i	−0.313177	−	0.542438i
$789$	−21.4955			−0.765258
$790$	2.62614			0.0934337
$791$	15.8739	+	27.4943i	0.564410	+	0.977586i
$792$	−0.521780	+	0.903750i	−0.0185407	+	0.0321134i
$793$	−3.70871	+	6.42368i	−0.131700	+	0.228111i
$794$	−12.7695	−	22.1174i	−0.453173	−	0.784918i
$795$	15.0000			0.531995
$796$	11.5826			0.410534
$797$	1.54356	−	2.67353i	0.0546757	−	0.0947011i	−0.837392	−	0.546603i	$-0.815921\pi$
$797$	1.54356	−	2.67353i	0.0546757	−	0.0947011i	0.892068	+	0.451902i	$0.149254\pi$
$798$	−8.95644	−	15.5130i	−0.317055	−	0.549155i
$799$	42.0000			1.48585
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−0.460985			−0.0162881
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$		0			0
$804$	−3.58258	+	14.2179i	−0.126348	+	0.501427i
$805$	−21.1652			−0.745974
$806$	1.66515	+	2.88413i	0.0586525	+	0.101589i
$807$	−19.2523			−0.677712
$808$	−6.08258	+	10.5353i	−0.213984	+	0.370632i
$809$	41.6606			1.46471			0.732354	−	0.680924i	$-0.238421\pi$
$809$	41.6606			1.46471			0.732354	+	0.680924i	$0.238421\pi$
$810$	−4.79129	−	8.29875i	−0.168349	−	0.291588i
$811$	15.7695	−	27.3136i	0.553742	−	0.959110i	−0.444258	−	0.895899i	$-0.646533\pi$
$811$	15.7695	−	27.3136i	0.553742	−	0.959110i	0.998000	−	0.0632109i	$-0.0201341\pi$
$812$	−2.79129			−0.0979550
$813$	−27.1652			−0.952723
$814$	6.97822	+	12.0866i	0.244586	+	0.423636i
$815$	9.79129	−	16.9590i	0.342974	−	0.594048i
$816$	4.10436	−	7.10895i	0.143681	−	0.248863i
$817$	−2.46099	−	4.26255i	−0.0860990	−	0.149128i
$818$	11.9129			0.416524
$819$	−0.460985			−0.0161081
$820$	−1.29129	−	2.23658i	−0.0450937	−	0.0781046i
$821$	−6.68693	−	11.5821i	−0.233376	−	0.404218i	0.725424	−	0.688302i	$-0.241644\pi$
$821$	−6.68693	−	11.5821i	−0.233376	−	0.404218i	−0.958799	+	0.284084i	$0.908310\pi$
$822$	−18.4347	−	31.9298i	−0.642983	−	1.11368i
$823$	−0.917424	−	1.58903i	−0.0319794	−	0.0553899i	0.849593	−	0.527439i	$-0.176848\pi$
$823$	−0.917424	−	1.58903i	−0.0319794	−	0.0553899i	−0.881572	+	0.472049i	$0.843514\pi$
$824$	7.47822	−	12.9527i	0.260516	−	0.451227i
$825$	−17.9129	+	31.0260i	−0.623646	+	1.08019i
$826$	23.9564			0.833551
$827$	6.89564	+	11.9436i	0.239785	+	0.415320i	0.960653	−	0.277753i	$-0.0895897\pi$
$827$	6.89564	+	11.9436i	0.239785	+	0.415320i	−0.720867	+	0.693073i	$0.756256\pi$
$828$	1.58258			0.0549983
$829$	10.7477			0.373284			0.186642	−	0.982428i	$-0.440240\pi$
$829$	10.7477			0.373284			0.186642	+	0.982428i	$0.440240\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$	−25.3739			−0.880210
$832$	0.395644	+	0.685275i	0.0137165	+	0.0237576i
$833$	−1.81307	+	3.14033i	−0.0628191	+	0.108806i
$834$	3.24773	+	5.62523i	0.112460	+	0.194786i
$835$	10.2913	−	17.8250i	0.356145	−	0.616861i
$836$	8.95644	−	15.5130i	0.309765	−	0.536529i
$837$	−10.5218	+	18.2243i	−0.363686	+	0.629923i
$838$	2.81307	−	4.87238i	0.0971758	−	0.168313i
$839$	−9.08258	+	15.7315i	−0.313565	+	0.543111i	−0.979131	−	0.203228i	$-0.934857\pi$
$839$	−9.08258	+	15.7315i	−0.313565	+	0.543111i	0.665566	+	0.746339i	$0.268190\pi$
$840$	−2.50000	+	4.33013i	−0.0862582	+	0.149404i
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−4.68693	+	8.11800i	−0.161522	+	0.279765i
$843$	4.06534	+	7.04138i	0.140018	+	0.242518i
$844$	22.1652			0.762956
$845$	−6.18693	+	10.7161i	−0.212837	+	0.368644i
$846$	1.91288			0.0657661
$847$	39.0780			1.34274
$848$	−4.18693	−	7.25198i	−0.143780	−	0.249034i
$849$	−17.5390			−0.601937
$850$	9.16515	−	15.8745i	0.314362	−	0.544491i
$851$	10.5826	−	18.3296i	0.362766	−	0.628329i
$852$	12.5000	+	21.6506i	0.428243	+	0.741739i
$853$	−20.2259	−	35.0324i	−0.692523	−	1.19949i	−0.971009	−	0.239045i	$-0.923166\pi$
$853$	−20.2259	−	35.0324i	−0.692523	−	1.19949i	0.278485	−	0.960440i	$-0.410168\pi$
$854$	13.0826	+	22.6597i	0.447677	+	0.775398i
$855$	−0.373864	−	0.647551i	−0.0127859	−	0.0221458i
$856$	−11.9564			−0.408663
$857$	8.58258			0.293175			0.146588	−	0.989198i	$-0.453171\pi$
$857$	8.58258			0.293175			0.146588	+	0.989198i	$0.453171\pi$
$858$	−3.54356	−	6.13763i	−0.120975	−	0.209535i
$859$	17.8521	−	30.9207i	0.609105	−	1.05500i	−0.382283	−	0.924045i	$-0.624862\pi$
$859$	17.8521	−	30.9207i	0.609105	−	1.05500i	0.991388	−	0.130956i	$-0.0418046\pi$
$860$	−0.686932	+	1.18980i	−0.0234242	+	0.0405719i
$861$	−6.45644	−	11.1829i	−0.220035	−	0.381112i
$862$	24.2867			0.827210
$863$	−33.6606			−1.14582			−0.572910	−	0.819618i	$-0.694186\pi$
$863$	−33.6606			−1.14582			−0.572910	+	0.819618i	$0.694186\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	−8.79129	−	15.2270i	−0.298913	−	0.517732i
$866$	−18.7477			−0.637074
$867$	3.58258	−	6.20520i	0.121671	−	0.210740i
$868$	11.7477			0.398744
$869$	6.56534	+	11.3715i	0.222714	+	0.385752i
$870$	−1.79129			−0.0607303
$871$	−4.64792	−	4.51088i	−0.157489	−	0.152845i
$872$	−8.74773			−0.296235
$873$	1.54356	+	2.67353i	0.0522416	+	0.0904851i
$874$	−27.1652			−0.918875
$875$	−12.5608	+	21.7559i	−0.424632	+	0.735485i
$876$		0			0
$877$	13.5826	+	23.5257i	0.458651	+	0.794407i	0.998890	−	0.0471048i	$-0.0149995\pi$
$877$	13.5826	+	23.5257i	0.458651	+	0.794407i	−0.540239	+	0.841512i	$0.681666\pi$
$878$	−6.76951	+	11.7251i	−0.228460	+	0.395704i
$879$	19.0345			0.642017
$880$	−5.00000			−0.168550
$881$	−12.3956	−	21.4699i	−0.417620	−	0.723339i	0.578080	−	0.815980i	$-0.303802\pi$
$881$	−12.3956	−	21.4699i	−0.417620	−	0.723339i	−0.995700	+	0.0926415i	$0.970469\pi$
$882$	−0.0825757	+	0.143025i	−0.00278047	+	0.00481591i
$883$	−23.8739	+	41.3507i	−0.803419	+	1.39156i	0.113933	+	0.993488i	$0.463655\pi$
$883$	−23.8739	+	41.3507i	−0.803419	+	1.39156i	−0.917353	+	0.398075i	$0.869678\pi$
$884$	1.81307	+	3.14033i	0.0609801	+	0.105621i
$885$	15.3739			0.516787
$886$	12.5826			0.422720
$887$	−2.79129	−	4.83465i	−0.0937223	−	0.162332i	0.815352	−	0.578965i	$-0.196543\pi$
$887$	−2.79129	−	4.83465i	−0.0937223	−	0.162332i	−0.909075	+	0.416633i	$0.863210\pi$
$888$	−2.50000	−	4.33013i	−0.0838945	−	0.145310i
$889$	26.9782	+	46.7276i	0.904820	+	1.56719i
$890$	−1.10436	−	1.91280i	−0.0370181	−	0.0641172i
$891$	23.9564	−	41.4938i	0.802571	−	1.39009i
$892$	−12.6652	+	21.9367i	−0.424061	+	0.734495i
$893$	−32.8348			−1.09878
$894$	7.64792	+	13.2466i	0.255785	+	0.443032i
$895$	15.7477			0.526388
$896$	2.79129			0.0932504
$897$	−5.37386	+	9.30780i	−0.179428	+	0.310779i
$898$	−31.1652			−1.03999
$899$	2.10436	+	3.64485i	0.0701842	+	0.121563i
$900$	0.417424	−	0.723000i	0.0139141	−	0.0241000i
$901$	−19.1869	−	33.2327i	−0.639209	−	1.10714i
$902$	6.45644	−	11.1829i	0.214976	−	0.372349i
$903$	−3.43466	+	5.94900i	−0.114298	+	0.197970i
$904$	5.68693	−	9.85005i	0.189145	−	0.327608i
$905$	10.2913	−	17.8250i	0.342094	−	0.592524i
$906$	−1.60436	+	2.77883i	−0.0533012	+	0.0923203i
$907$	14.7477	−	25.5438i	0.489690	−	0.848168i	−0.510239	−	0.860032i	$-0.670443\pi$
$907$	14.7477	−	25.5438i	0.489690	−	0.848168i	0.999930	+	0.0118641i	$0.00377653\pi$
$908$	−6.56080	−	11.3636i	−0.217728	−	0.377115i
$909$	−1.26951	+	2.19885i	−0.0421069	+	0.0729313i
$910$	−1.10436	−	1.91280i	−0.0366090	−	0.0634087i
$911$	−12.9564			−0.429266			−0.214633	−	0.976695i	$-0.568856\pi$
$911$	−12.9564			−0.429266			−0.214633	+	0.976695i	$0.568856\pi$
$912$	−3.20871	+	5.55765i	−0.106251	+	0.184032i
$913$	60.0000			1.98571
$914$	−11.7913			−0.390021
$915$	8.39564	+	14.5417i	0.277551	+	0.480733i
$916$	8.95644			0.295929
$917$	−14.7695	+	25.5815i	−0.487732	+	0.844777i
$918$	−11.4564	+	19.8431i	−0.378119	+	0.654921i
$919$	7.66515	+	13.2764i	0.252850	+	0.437949i	0.964309	−	0.264778i	$-0.0852987\pi$
$919$	7.66515	+	13.2764i	0.252850	+	0.437949i	−0.711459	+	0.702727i	$0.751965\pi$
$920$	3.79129	+	6.56670i	0.124995	+	0.216498i
$921$	24.3693	+	42.2089i	0.802996	+	1.39083i
$922$	−15.0826	−	26.1238i	−0.496718	−	0.860341i
$923$	−11.0436			−0.363503
$924$	−25.0000			−0.822440
$925$	−5.58258	−	9.66930i	−0.183554	−	0.317925i
$926$	−4.08258	+	7.07123i	−0.134162	+	0.232375i
$927$	1.56080	−	2.70338i	0.0512632	−	0.0887905i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	−53.1216			−1.74286			−0.871431	−	0.490517i	$-0.836808\pi$
$929$	−53.1216			−1.74286			−0.871431	+	0.490517i	$0.836808\pi$
$930$	7.53901			0.247214
$931$	1.41742	−	2.45505i	0.0464542	−	0.0804610i
$932$	−8.10436	−	14.0372i	−0.265467	−	0.459802i
$933$	14.0345			0.459468
$934$	8.18693	−	14.1802i	0.267885	−	0.463990i
$935$	−22.9129			−0.749331
$936$	0.0825757	+	0.143025i	0.00269907	+	0.00467493i
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	−21.9782	+	6.24293i	−0.717614	+	0.203839i
$939$	53.6606			1.75115
$940$	4.58258	+	7.93725i	0.149467	+	0.258885i
$941$	0.373864			0.0121876			0.00609380	−	0.999981i	$-0.498060\pi$
$941$	0.373864			0.0121876			0.00609380	+	0.999981i	$0.498060\pi$
$942$	−4.10436	+	7.10895i	−0.133727	+	0.231622i
$943$	−19.5826			−0.637696
$944$	−4.29129	−	7.43273i	−0.139670	−	0.241915i
$945$	6.97822	−	12.0866i	0.227002	−	0.393178i
$946$	−6.86932			−0.223341
$947$	−29.3303			−0.953107			−0.476553	−	0.879146i	$-0.658114\pi$
$947$	−29.3303			−0.953107			−0.476553	+	0.879146i	$0.658114\pi$
$948$	−2.35208	−	4.07393i	−0.0763921	−	0.132315i
$949$		0			0
$950$	−7.16515	+	12.4104i	−0.232468	+	0.402647i
$951$	−12.0172	−	20.8145i	−0.389686	−	0.674955i
$952$	12.7913			0.414568
$953$	−36.8258			−1.19290			−0.596452	−	0.802649i	$-0.703423\pi$
$953$	−36.8258			−1.19290			−0.596452	+	0.802649i	$0.703423\pi$
$954$	−0.873864	−	1.51358i	−0.0282924	−	0.0490038i
$955$	−7.18693	−	12.4481i	−0.232564	−	0.402812i
$956$	−1.31307	−	2.27430i	−0.0424677	−	0.0735561i
$957$	−4.47822	−	7.75650i	−0.144760	−	0.250732i
$958$	2.16515	−	3.75015i	0.0699529	−	0.121162i
$959$	28.7259	−	49.7548i	0.927609	−	1.60667i
$960$	1.79129			0.0578136
$961$	6.64337	+	11.5067i	0.214302	+	0.371182i
$962$	2.20871			0.0712117
$963$	−2.49545			−0.0804149
$964$	−7.18693	+	12.4481i	−0.231475	+	0.400927i
$965$	12.3739			0.398329
$966$	18.9564	+	32.8335i	0.609913	+	1.05640i
$967$	−15.9174	+	27.5698i	−0.511870	+	0.886585i	0.488035	+	0.872824i	$0.337714\pi$
$967$	−15.9174	+	27.5698i	−0.511870	+	0.886585i	−0.999905	+	0.0137608i	$0.995620\pi$
$968$	−7.00000	−	12.1244i	−0.224989	−	0.389692i
$969$	−14.7042	+	25.4684i	−0.472366	+	0.818162i
$970$	−7.39564	+	12.8096i	−0.237460	+	0.411292i
$971$	8.20871	−	14.2179i	0.263430	−	0.456274i	−0.703721	−	0.710476i	$-0.748479\pi$
$971$	8.20871	−	14.2179i	0.263430	−	0.456274i	0.967151	+	0.254202i	$0.0818128\pi$
$972$	−1.08258	+	1.87508i	−0.0347236	+	0.0601431i
$973$	−5.06080	+	8.76555i	−0.162242	+	0.281011i
$974$	−2.95644	+	5.12070i	−0.0947304	+	0.164078i
$975$	2.83485	+	4.91010i	0.0907878	+	0.157249i
$976$	4.68693	−	8.11800i	0.150025	−	0.259851i
$977$	14.7695	+	25.5815i	0.472518	+	0.818426i	0.999505	−	0.0314475i	$-0.0100117\pi$
$977$	14.7695	+	25.5815i	0.472518	+	0.818426i	−0.526987	+	0.849873i	$0.676678\pi$
$978$	−35.0780			−1.12167
$979$	5.52178	−	9.56400i	0.176477	−	0.305667i
$980$	−0.791288			−0.0252768
$981$	−1.82576			−0.0582919
$982$	−8.47822	−	14.6847i	−0.270551	−	0.468608i
$983$	38.0436			1.21340			0.606701	−	0.794930i	$-0.292493\pi$
$983$	38.0436			1.21340			0.606701	+	0.794930i	$0.292493\pi$
$984$	−2.31307	+	4.00635i	−0.0737379	+	0.127718i
$985$	8.79129	−	15.2270i	0.280114	−	0.485171i
$986$	2.29129	+	3.96863i	0.0729695	+	0.126387i
$987$	22.9129	+	39.6863i	0.729325	+	1.26323i
$988$	−1.41742	−	2.45505i	−0.0450943	−	0.0781056i
$989$	5.20871	+	9.02175i	0.165627	+	0.286875i
$990$	−1.04356			−0.0331665
$991$	−8.74773			−0.277881			−0.138940	−	0.990301i	$-0.544370\pi$
$991$	−8.74773			−0.277881			−0.138940	+	0.990301i	$0.544370\pi$
$992$	−2.10436	−	3.64485i	−0.0668134	−	0.115724i
$993$	−15.7477	+	27.2759i	−0.499739	+	0.865573i
$994$	−19.4782	+	33.7373i	−0.617812	+	1.07008i
$995$	5.79129	+	10.0308i	0.183596	+	0.317998i
$996$	−21.4955			−0.681110
$997$	33.6606			1.06604			0.533021	−	0.846102i	$-0.321057\pi$
$997$	33.6606			1.06604			0.533021	+	0.846102i	$0.321057\pi$
$998$	10.8131	−	18.7288i	0.342282	−	0.592849i
$999$	6.97822	+	12.0866i	0.220781	+	0.382404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	134.2.c.b.37.1	yes	4
3.2	odd	2		1206.2.h.c.37.1		4
4.3	odd	2		1072.2.i.c.305.2		4
67.29	even	3	inner	134.2.c.b.29.1	✓	4
67.30	odd	6		8978.2.a.c.1.2		2
67.37	even	3		8978.2.a.f.1.1		2
201.29	odd	6		1206.2.h.c.163.1		4
268.163	odd	6		1072.2.i.c.833.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
134.2.c.b.29.1	✓	4	67.29	even	3	inner
134.2.c.b.37.1	yes	4	1.1	even	1	trivial
1072.2.i.c.305.2		4	4.3	odd	2
1072.2.i.c.833.2		4	268.163	odd	6
1206.2.h.c.37.1		4	3.2	odd	2
1206.2.h.c.163.1		4	201.29	odd	6
8978.2.a.c.1.2		2	67.30	odd	6
8978.2.a.f.1.1		2	67.37	even	3

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:	\( N \)	\(=\)	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	134.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.79129 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.895644 + 1.55130i) q^{6} +(-1.39564 + 2.41733i) q^{7} +1.00000 q^{8} +0.208712 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.79129 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.895644 + 1.55130i) q^{6} +(-1.39564 + 2.41733i) q^{7} +1.00000 q^{8} +0.208712 q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.895644 - 1.55130i) q^{12} +(0.395644 + 0.685275i) q^{13} +2.79129 q^{14} +1.79129 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.29129 - 3.96863i) q^{17} +(-0.104356 - 0.180750i) q^{18} +(1.79129 + 3.10260i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.50000 - 4.33013i) q^{21} +5.00000 q^{22} +(-3.79129 - 6.56670i) q^{23} -1.79129 q^{24} -4.00000 q^{25} +(0.395644 - 0.685275i) q^{26} +5.00000 q^{27} +(-1.39564 - 2.41733i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.895644 - 1.55130i) q^{30} +(-2.10436 + 3.64485i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.47822 - 7.75650i) q^{33} +(-2.29129 + 3.96863i) q^{34} +(1.39564 - 2.41733i) q^{35} +(-0.104356 + 0.180750i) q^{36} +(1.39564 + 2.41733i) q^{37} +(1.79129 - 3.10260i) q^{38} +(-0.708712 - 1.22753i) q^{39} -1.00000 q^{40} +(1.29129 - 2.23658i) q^{41} -5.00000 q^{42} -1.37386 q^{43} +(-2.50000 - 4.33013i) q^{44} -0.208712 q^{45} +(-3.79129 + 6.56670i) q^{46} +(-4.58258 + 7.93725i) q^{47} +(0.895644 + 1.55130i) q^{48} +(-0.395644 - 0.685275i) q^{49} +(2.00000 + 3.46410i) q^{50} +(4.10436 + 7.10895i) q^{51} -0.791288 q^{52} +8.37386 q^{53} +(-2.50000 - 4.33013i) q^{54} +(2.50000 - 4.33013i) q^{55} +(-1.39564 + 2.41733i) q^{56} +(-3.20871 - 5.55765i) q^{57} -1.00000 q^{58} +8.58258 q^{59} +(-0.895644 + 1.55130i) q^{60} +(4.68693 + 8.11800i) q^{61} +4.20871 q^{62} +(-0.291288 + 0.504525i) q^{63} +1.00000 q^{64} +(-0.395644 - 0.685275i) q^{65} -8.95644 q^{66} +(-7.87386 + 2.23658i) q^{67} +4.58258 q^{68} +(6.79129 + 11.7629i) q^{69} -2.79129 q^{70} +(-6.97822 + 12.0866i) q^{71} +0.208712 q^{72} +(1.39564 - 2.41733i) q^{74} +7.16515 q^{75} -3.58258 q^{76} +(-6.97822 - 12.0866i) q^{77} +(-0.708712 + 1.22753i) q^{78} +(1.31307 - 2.27430i) q^{79} +(0.500000 + 0.866025i) q^{80} -9.58258 q^{81} -2.58258 q^{82} +(-6.00000 - 10.3923i) q^{83} +(2.50000 + 4.33013i) q^{84} +(2.29129 + 3.96863i) q^{85} +(0.686932 + 1.18980i) q^{86} +(-0.895644 + 1.55130i) q^{87} +(-2.50000 + 4.33013i) q^{88} -2.20871 q^{89} +(0.104356 + 0.180750i) q^{90} -2.20871 q^{91} +7.58258 q^{92} +(3.76951 - 6.52898i) q^{93} +9.16515 q^{94} +(-1.79129 - 3.10260i) q^{95} +(0.895644 - 1.55130i) q^{96} +(7.39564 + 12.8096i) q^{97} +(-0.395644 + 0.685275i) q^{98} +(-0.521780 + 0.903750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} - q^{6} - q^{7} + 4 q^{8} + 10 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 - q^6 - q^7 + 4 * q^8 + 10 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} - q^{6} - q^{7} + 4 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 5 q^{18} - 2 q^{19} + 2 q^{20} + 10 q^{21} + 20 q^{22} - 6 q^{23} + 2 q^{24} - 16 q^{25} - 3 q^{26} + 20 q^{27} - q^{28} + 2 q^{29} + q^{30} - 13 q^{31} - 2 q^{32} - 5 q^{33} + q^{35} - 5 q^{36} + q^{37} - 2 q^{38} - 12 q^{39} - 4 q^{40} - 4 q^{41} - 20 q^{42} + 22 q^{43} - 10 q^{44} - 10 q^{45} - 6 q^{46} - q^{48} + 3 q^{49} + 8 q^{50} + 21 q^{51} + 6 q^{52} + 6 q^{53} - 10 q^{54} + 10 q^{55} - q^{56} - 22 q^{57} - 4 q^{58} + 16 q^{59} + q^{60} + 5 q^{61} + 26 q^{62} + 8 q^{63} + 4 q^{64} + 3 q^{65} + 10 q^{66} - 4 q^{67} + 18 q^{69} - 2 q^{70} - 5 q^{71} + 10 q^{72} + q^{74} - 8 q^{75} + 4 q^{76} - 5 q^{77} - 12 q^{78} + 19 q^{79} + 2 q^{80} - 20 q^{81} + 8 q^{82} - 24 q^{83} + 10 q^{84} - 11 q^{86} + q^{87} - 10 q^{88} - 18 q^{89} + 5 q^{90} - 18 q^{91} + 12 q^{92} - 17 q^{93} + 2 q^{95} - q^{96} + 25 q^{97} + 3 q^{98} - 25 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 - q^6 - q^7 + 4 * q^8 + 10 * q^9 + 2 * q^10 - 10 * q^11 - q^12 - 3 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 5 * q^18 - 2 * q^19 + 2 * q^20 + 10 * q^21 + 20 * q^22 - 6 * q^23 + 2 * q^24 - 16 * q^25 - 3 * q^26 + 20 * q^27 - q^28 + 2 * q^29 + q^30 - 13 * q^31 - 2 * q^32 - 5 * q^33 + q^35 - 5 * q^36 + q^37 - 2 * q^38 - 12 * q^39 - 4 * q^40 - 4 * q^41 - 20 * q^42 + 22 * q^43 - 10 * q^44 - 10 * q^45 - 6 * q^46 - q^48 + 3 * q^49 + 8 * q^50 + 21 * q^51 + 6 * q^52 + 6 * q^53 - 10 * q^54 + 10 * q^55 - q^56 - 22 * q^57 - 4 * q^58 + 16 * q^59 + q^60 + 5 * q^61 + 26 * q^62 + 8 * q^63 + 4 * q^64 + 3 * q^65 + 10 * q^66 - 4 * q^67 + 18 * q^69 - 2 * q^70 - 5 * q^71 + 10 * q^72 + q^74 - 8 * q^75 + 4 * q^76 - 5 * q^77 - 12 * q^78 + 19 * q^79 + 2 * q^80 - 20 * q^81 + 8 * q^82 - 24 * q^83 + 10 * q^84 - 11 * q^86 + q^87 - 10 * q^88 - 18 * q^89 + 5 * q^90 - 18 * q^91 + 12 * q^92 - 17 * q^93 + 2 * q^95 - q^96 + 25 * q^97 + 3 * q^98 - 25 * q^99

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