LMFDB - Embedded newform 150.3.f.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(7,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("150.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.f (of order $4$, 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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	150.7
Dual form			150.3.f.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-0.898979 - 0.898979i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-0.898979 - 0.898979i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} -13.7980 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-12.7980 + 12.7980i) q^{13} +1.79796i q^{14} -4.00000 q^{16} +(-15.8990 - 15.8990i) q^{17} +(-3.00000 + 3.00000i) q^{18} +25.7980i q^{19} +2.20204 q^{21} +(13.7980 + 13.7980i) q^{22} +(-10.6969 + 10.6969i) q^{23} +4.89898i q^{24} +25.5959 q^{26} +(3.67423 + 3.67423i) q^{27} +(1.79796 - 1.79796i) q^{28} -25.7980i q^{29} -39.5959 q^{31} +(4.00000 + 4.00000i) q^{32} +(16.8990 - 16.8990i) q^{33} +31.7980i q^{34} +6.00000 q^{36} +(27.0000 + 27.0000i) q^{37} +(25.7980 - 25.7980i) q^{38} -31.3485i q^{39} +17.7980 q^{41} +(-2.20204 - 2.20204i) q^{42} +(12.4949 - 12.4949i) q^{43} -27.5959i q^{44} +21.3939 q^{46} +(-9.30306 - 9.30306i) q^{47} +(4.89898 - 4.89898i) q^{48} -47.3837i q^{49} +38.9444 q^{51} +(-25.5959 - 25.5959i) q^{52} +(19.0908 - 19.0908i) q^{53} -7.34847i q^{54} -3.59592 q^{56} +(-31.5959 - 31.5959i) q^{57} +(-25.7980 + 25.7980i) q^{58} +20.0000i q^{59} +15.1918 q^{61} +(39.5959 + 39.5959i) q^{62} +(-2.69694 + 2.69694i) q^{63} -8.00000i q^{64} -33.7980 q^{66} +(48.0908 + 48.0908i) q^{67} +(31.7980 - 31.7980i) q^{68} -26.2020i q^{69} +6.20204 q^{71} +(-6.00000 - 6.00000i) q^{72} +(37.2020 - 37.2020i) q^{73} -54.0000i q^{74} -51.5959 q^{76} +(12.4041 + 12.4041i) q^{77} +(-31.3485 + 31.3485i) q^{78} +115.373i q^{79} -9.00000 q^{81} +(-17.7980 - 17.7980i) q^{82} +(-82.2929 + 82.2929i) q^{83} +4.40408i q^{84} -24.9898 q^{86} +(31.5959 + 31.5959i) q^{87} +(-27.5959 + 27.5959i) q^{88} +117.394i q^{89} +23.0102 q^{91} +(-21.3939 - 21.3939i) q^{92} +(48.4949 - 48.4949i) q^{93} +18.6061i q^{94} -9.79796 q^{96} +(-81.9898 - 81.9898i) q^{97} +(-47.3837 + 47.3837i) q^{98} +41.3939i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8	$ 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8} - 16 q^{11} - 12 q^{13} - 16 q^{16} - 44 q^{17} - 12 q^{18} + 48 q^{21} + 16 q^{22} + 16 q^{23} + 24 q^{26} - 32 q^{28} - 80 q^{31} + 16 q^{32} + 48 q^{33} + 24 q^{36} + 108 q^{37} + 64 q^{38} + 32 q^{41} - 48 q^{42} - 48 q^{43} - 32 q^{46} - 96 q^{47} + 48 q^{51} - 24 q^{52} - 100 q^{53} + 64 q^{56} - 48 q^{57} - 64 q^{58} - 96 q^{61} + 80 q^{62} + 48 q^{63} - 96 q^{66} + 16 q^{67} + 88 q^{68} + 64 q^{71} - 24 q^{72} + 188 q^{73} - 128 q^{76} + 128 q^{77} - 96 q^{78} - 36 q^{81} - 32 q^{82} - 192 q^{83} + 96 q^{86} + 48 q^{87} - 32 q^{88} + 288 q^{91} + 32 q^{92} + 96 q^{93} - 132 q^{97} + 124 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8 - 16 * q^11 - 12 * q^13 - 16 * q^16 - 44 * q^17 - 12 * q^18 + 48 * q^21 + 16 * q^22 + 16 * q^23 + 24 * q^26 - 32 * q^28 - 80 * q^31 + 16 * q^32 + 48 * q^33 + 24 * q^36 + 108 * q^37 + 64 * q^38 + 32 * q^41 - 48 * q^42 - 48 * q^43 - 32 * q^46 - 96 * q^47 + 48 * q^51 - 24 * q^52 - 100 * q^53 + 64 * q^56 - 48 * q^57 - 64 * q^58 - 96 * q^61 + 80 * q^62 + 48 * q^63 - 96 * q^66 + 16 * q^67 + 88 * q^68 + 64 * q^71 - 24 * q^72 + 188 * q^73 - 128 * q^76 + 128 * q^77 - 96 * q^78 - 36 * q^81 - 32 * q^82 - 192 * q^83 + 96 * q^86 + 48 * q^87 - 32 * q^88 + 288 * q^91 + 32 * q^92 + 96 * q^93 - 132 * q^97 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.44949			0.408248
$7$	−0.898979	−	0.898979i	−0.128426	−	0.128426i	0.639972	−	0.768398i	$-0.278946\pi$
$7$	−0.898979	−	0.898979i	−0.128426	−	0.128426i	−0.768398	+	0.639972i	$0.778946\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−13.7980			−1.25436			−0.627180	−	0.778874i	$-0.715791\pi$
$11$	−13.7980			−1.25436			−0.627180	+	0.778874i	$0.715791\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−12.7980	+	12.7980i	−0.984458	+	0.984458i	−0.999881	−	0.0154227i	$-0.995091\pi$
$13$	−12.7980	+	12.7980i	−0.984458	+	0.984458i	0.0154227	+	0.999881i	$0.495091\pi$
$14$			1.79796i			0.128426i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−15.8990	−	15.8990i	−0.935234	−	0.935234i	0.0627925	−	0.998027i	$-0.479999\pi$
$17$	−15.8990	−	15.8990i	−0.935234	−	0.935234i	−0.998027	+	0.0627925i	$0.979999\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			25.7980i			1.35779i	0.734237	+	0.678894i	$0.237540\pi$
$19$			25.7980i			1.35779i	−0.734237	+	0.678894i	$0.762460\pi$
$20$		0			0
$21$	2.20204			0.104859
$22$	13.7980	+	13.7980i	0.627180	+	0.627180i
$23$	−10.6969	+	10.6969i	−0.465084	+	0.465084i	−0.900318	−	0.435233i	$-0.856666\pi$
$23$	−10.6969	+	10.6969i	−0.465084	+	0.465084i	0.435233	+	0.900318i	$0.356666\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	25.5959			0.984458
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	1.79796	−	1.79796i	0.0642128	−	0.0642128i
$29$		−	25.7980i		−	0.889585i	−0.895634	−	0.444792i	$-0.853277\pi$
$29$		−	25.7980i		−	0.889585i	0.895634	−	0.444792i	$-0.146723\pi$
$30$		0			0
$31$	−39.5959			−1.27729			−0.638644	−	0.769502i	$-0.720504\pi$
$31$	−39.5959			−1.27729			−0.638644	+	0.769502i	$0.720504\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	16.8990	−	16.8990i	0.512090	−	0.512090i
$34$			31.7980i			0.935234i
$35$		0			0
$36$	6.00000			0.166667
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	0.970566	−	0.240836i	$-0.0774216\pi$
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	−0.240836	+	0.970566i	$0.577422\pi$
$38$	25.7980	−	25.7980i	0.678894	−	0.678894i
$39$		−	31.3485i		−	0.803807i
$40$		0			0
$41$	17.7980			0.434097			0.217048	−	0.976161i	$-0.430357\pi$
$41$	17.7980			0.434097			0.217048	+	0.976161i	$0.430357\pi$
$42$	−2.20204	−	2.20204i	−0.0524295	−	0.0524295i
$43$	12.4949	−	12.4949i	0.290579	−	0.290579i	−0.546730	−	0.837309i	$-0.684128\pi$
$43$	12.4949	−	12.4949i	0.290579	−	0.290579i	0.837309	+	0.546730i	$0.184128\pi$
$44$		−	27.5959i		−	0.627180i
$45$		0			0
$46$	21.3939			0.465084
$47$	−9.30306	−	9.30306i	−0.197937	−	0.197937i	0.601178	−	0.799115i	$-0.294698\pi$
$47$	−9.30306	−	9.30306i	−0.197937	−	0.197937i	−0.799115	+	0.601178i	$0.794698\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	47.3837i		−	0.967014i
$50$		0			0
$51$	38.9444			0.763615
$52$	−25.5959	−	25.5959i	−0.492229	−	0.492229i
$53$	19.0908	−	19.0908i	0.360204	−	0.360204i	−0.503684	−	0.863888i	$-0.668022\pi$
$53$	19.0908	−	19.0908i	0.360204	−	0.360204i	0.863888	+	0.503684i	$0.168022\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−3.59592			−0.0642128
$57$	−31.5959	−	31.5959i	−0.554314	−	0.554314i
$58$	−25.7980	+	25.7980i	−0.444792	+	0.444792i
$59$			20.0000i			0.338983i	0.985532	+	0.169492i	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$		0			0
$61$	15.1918			0.249046			0.124523	−	0.992217i	$-0.460260\pi$
$61$	15.1918			0.249046			0.124523	+	0.992217i	$0.460260\pi$
$62$	39.5959	+	39.5959i	0.638644	+	0.638644i
$63$	−2.69694	+	2.69694i	−0.0428085	+	0.0428085i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−33.7980			−0.512090
$67$	48.0908	+	48.0908i	0.717773	+	0.717773i	0.968149	−	0.250375i	$-0.0805541\pi$
$67$	48.0908	+	48.0908i	0.717773	+	0.717773i	−0.250375	+	0.968149i	$0.580554\pi$
$68$	31.7980	−	31.7980i	0.467617	−	0.467617i
$69$		−	26.2020i		−	0.379740i
$70$		0			0
$71$	6.20204			0.0873527			0.0436763	−	0.999046i	$-0.486093\pi$
$71$	6.20204			0.0873527			0.0436763	+	0.999046i	$0.486093\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	37.2020	−	37.2020i	0.509617	−	0.509617i	−0.404792	−	0.914409i	$-0.632656\pi$
$73$	37.2020	−	37.2020i	0.509617	−	0.509617i	0.914409	+	0.404792i	$0.132656\pi$
$74$		−	54.0000i		−	0.729730i
$75$		0			0
$76$	−51.5959			−0.678894
$77$	12.4041	+	12.4041i	0.161092	+	0.161092i
$78$	−31.3485	+	31.3485i	−0.401903	+	0.401903i
$79$			115.373i			1.46042i	0.683221	+	0.730212i	$0.260579\pi$
$79$			115.373i			1.46042i	−0.683221	+	0.730212i	$0.739421\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−17.7980	−	17.7980i	−0.217048	−	0.217048i
$83$	−82.2929	+	82.2929i	−0.991480	+	0.991480i	−0.999964	−	0.00848381i	$-0.997299\pi$
$83$	−82.2929	+	82.2929i	−0.991480	+	0.991480i	0.00848381	+	0.999964i	$0.497299\pi$
$84$			4.40408i			0.0524295i
$85$		0			0
$86$	−24.9898			−0.290579
$87$	31.5959	+	31.5959i	0.363171	+	0.363171i
$88$	−27.5959	+	27.5959i	−0.313590	+	0.313590i
$89$			117.394i			1.31903i	0.751690	+	0.659516i	$0.229239\pi$
$89$			117.394i			1.31903i	−0.751690	+	0.659516i	$0.770761\pi$
$90$		0			0
$91$	23.0102			0.252859
$92$	−21.3939	−	21.3939i	−0.232542	−	0.232542i
$93$	48.4949	−	48.4949i	0.521451	−	0.521451i
$94$			18.6061i			0.197937i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	−81.9898	−	81.9898i	−0.845256	−	0.845256i	0.144281	−	0.989537i	$-0.453913\pi$
$97$	−81.9898	−	81.9898i	−0.845256	−	0.845256i	−0.989537	+	0.144281i	$0.953913\pi$
$98$	−47.3837	+	47.3837i	−0.483507	+	0.483507i
$99$			41.3939i			0.418120i
$100$		0			0
$101$	28.3837			0.281026			0.140513	−	0.990079i	$-0.455125\pi$
$101$	28.3837			0.281026			0.140513	+	0.990079i	$0.455125\pi$
$102$	−38.9444	−	38.9444i	−0.381808	−	0.381808i
$103$	−16.4949	+	16.4949i	−0.160145	+	0.160145i	−0.782631	−	0.622486i	$-0.786123\pi$
$103$	−16.4949	+	16.4949i	−0.160145	+	0.160145i	0.622486	+	0.782631i	$0.286123\pi$
$104$			51.1918i			0.492229i
$105$		0			0
$106$	−38.1816			−0.360204
$107$	−15.1010	−	15.1010i	−0.141131	−	0.141131i	0.633011	−	0.774142i	$-0.281819\pi$
$107$	−15.1010	−	15.1010i	−0.141131	−	0.141131i	−0.774142	+	0.633011i	$0.781819\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	130.000i		−	1.19266i	−0.802739	−	0.596330i	$-0.796625\pi$
$109$		−	130.000i		−	1.19266i	0.802739	−	0.596330i	$-0.203375\pi$
$110$		0			0
$111$	−66.1362			−0.595822
$112$	3.59592	+	3.59592i	0.0321064	+	0.0321064i
$113$	−77.2929	+	77.2929i	−0.684008	+	0.684008i	−0.960901	−	0.276893i	$-0.910695\pi$
$113$	−77.2929	+	77.2929i	−0.684008	+	0.684008i	0.276893	+	0.960901i	$0.410695\pi$
$114$			63.1918i			0.554314i
$115$		0			0
$116$	51.5959			0.444792
$117$	38.3939	+	38.3939i	0.328153	+	0.328153i
$118$	20.0000	−	20.0000i	0.169492	−	0.169492i
$119$			28.5857i			0.240216i
$120$		0			0
$121$	69.3837			0.573419
$122$	−15.1918	−	15.1918i	−0.124523	−	0.124523i
$123$	−21.7980	+	21.7980i	−0.177219	+	0.177219i
$124$		−	79.1918i		−	0.638644i
$125$		0			0
$126$	5.39388			0.0428085
$127$	−18.2929	−	18.2929i	−0.144038	−	0.144038i	0.631411	−	0.775449i	$-0.282476\pi$
$127$	−18.2929	−	18.2929i	−0.144038	−	0.144038i	−0.775449	+	0.631411i	$0.782476\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			30.6061i			0.237257i
$130$		0			0
$131$	−133.798			−1.02136			−0.510679	−	0.859771i	$-0.670606\pi$
$131$	−133.798			−1.02136			−0.510679	+	0.859771i	$0.670606\pi$
$132$	33.7980	+	33.7980i	0.256045	+	0.256045i
$133$	23.1918	−	23.1918i	0.174375	−	0.174375i
$134$		−	96.1816i		−	0.717773i
$135$		0			0
$136$	−63.5959			−0.467617
$137$	−25.8990	−	25.8990i	−0.189044	−	0.189044i	0.606239	−	0.795283i	$-0.292678\pi$
$137$	−25.8990	−	25.8990i	−0.189044	−	0.189044i	−0.795283	+	0.606239i	$0.792678\pi$
$138$	−26.2020	+	26.2020i	−0.189870	+	0.189870i
$139$		−	54.2020i		−	0.389943i	−0.980809	−	0.194971i	$-0.937539\pi$
$139$		−	54.2020i		−	0.389943i	0.980809	−	0.194971i	$-0.0624614\pi$
$140$		0			0
$141$	22.7878			0.161615
$142$	−6.20204	−	6.20204i	−0.0436763	−	0.0436763i
$143$	176.586	−	176.586i	1.23487	−	1.23487i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	−74.4041			−0.509617
$147$	58.0329	+	58.0329i	0.394782	+	0.394782i
$148$	−54.0000	+	54.0000i	−0.364865	+	0.364865i
$149$		−	42.7673i		−	0.287029i	−0.989648	−	0.143515i	$-0.954160\pi$
$149$		−	42.7673i		−	0.287029i	0.989648	−	0.143515i	$-0.0458404\pi$
$150$		0			0
$151$	178.384			1.18135			0.590674	−	0.806910i	$-0.298862\pi$
$151$	178.384			1.18135			0.590674	+	0.806910i	$0.298862\pi$
$152$	51.5959	+	51.5959i	0.339447	+	0.339447i
$153$	−47.6969	+	47.6969i	−0.311745	+	0.311745i
$154$		−	24.8082i		−	0.161092i
$155$		0			0
$156$	62.6969			0.401903
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	0.196970	−	0.980410i	$-0.436890\pi$
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	−0.980410	+	0.196970i	$0.936890\pi$
$158$	115.373	−	115.373i	0.730212	−	0.730212i
$159$			46.7628i			0.294105i
$160$		0			0
$161$	19.2327			0.119457
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	63.5051	−	63.5051i	0.389602	−	0.389602i	−0.484944	−	0.874545i	$-0.661160\pi$
$163$	63.5051	−	63.5051i	0.389602	−	0.389602i	0.874545	+	0.484944i	$0.161160\pi$
$164$			35.5959i			0.217048i
$165$		0			0
$166$	164.586			0.991480
$167$	48.6765	+	48.6765i	0.291476	+	0.291476i	0.837663	−	0.546187i	$-0.183921\pi$
$167$	48.6765	+	48.6765i	0.291476	+	0.291476i	−0.546187	+	0.837663i	$0.683921\pi$
$168$	4.40408	−	4.40408i	0.0262148	−	0.0262148i
$169$		−	158.576i		−	0.938317i
$170$		0			0
$171$	77.3939			0.452596
$172$	24.9898	+	24.9898i	0.145290	+	0.145290i
$173$	−35.1112	+	35.1112i	−0.202955	+	0.202955i	−0.801265	−	0.598310i	$-0.795839\pi$
$173$	−35.1112	+	35.1112i	−0.202955	+	0.202955i	0.598310	+	0.801265i	$0.295839\pi$
$174$		−	63.1918i		−	0.363171i
$175$		0			0
$176$	55.1918			0.313590
$177$	−24.4949	−	24.4949i	−0.138389	−	0.138389i
$178$	117.394	−	117.394i	0.659516	−	0.659516i
$179$			141.171i			0.788667i	0.918967	+	0.394334i	$0.129025\pi$
$179$			141.171i			0.788667i	−0.918967	+	0.394334i	$0.870975\pi$
$180$		0			0
$181$	58.8082			0.324907			0.162453	−	0.986716i	$-0.448059\pi$
$181$	58.8082			0.324907			0.162453	+	0.986716i	$0.448059\pi$
$182$	−23.0102	−	23.0102i	−0.126430	−	0.126430i
$183$	−18.6061	+	18.6061i	−0.101673	+	0.101673i
$184$			42.7878i			0.232542i
$185$		0			0
$186$	−96.9898			−0.521451
$187$	219.373	+	219.373i	1.17312	+	1.17312i
$188$	18.6061	−	18.6061i	0.0989687	−	0.0989687i
$189$		−	6.60612i		−	0.0349530i
$190$		0			0
$191$	−325.394			−1.70363			−0.851816	−	0.523840i	$-0.824499\pi$
$191$	−325.394			−1.70363			−0.851816	+	0.523840i	$0.824499\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	39.3837	−	39.3837i	0.204060	−	0.204060i	−0.597677	−	0.801737i	$-0.703909\pi$
$193$	39.3837	−	39.3837i	0.204060	−	0.204060i	0.801737	+	0.597677i	$0.203909\pi$
$194$			163.980i			0.845256i
$195$		0			0
$196$	94.7673			0.483507
$197$	119.313	+	119.313i	0.605651	+	0.605651i	0.941807	−	0.336155i	$-0.109127\pi$
$197$	119.313	+	119.313i	0.605651	+	0.605651i	−0.336155	+	0.941807i	$0.609127\pi$
$198$	41.3939	−	41.3939i	0.209060	−	0.209060i
$199$		−	178.565i		−	0.897313i	−0.893704	−	0.448657i	$-0.851903\pi$
$199$		−	178.565i		−	0.897313i	0.893704	−	0.448657i	$-0.148097\pi$
$200$		0			0
$201$	−117.798			−0.586059
$202$	−28.3837	−	28.3837i	−0.140513	−	0.140513i
$203$	−23.1918	+	23.1918i	−0.114245	+	0.114245i
$204$			77.8888i			0.381808i
$205$		0			0
$206$	32.9898			0.160145
$207$	32.0908	+	32.0908i	0.155028	+	0.155028i
$208$	51.1918	−	51.1918i	0.246115	−	0.246115i
$209$		−	355.959i		−	1.70315i
$210$		0			0
$211$	−318.747			−1.51065			−0.755324	−	0.655351i	$-0.772521\pi$
$211$	−318.747			−1.51065			−0.755324	+	0.655351i	$0.772521\pi$
$212$	38.1816	+	38.1816i	0.180102	+	0.180102i
$213$	−7.59592	+	7.59592i	−0.0356616	+	0.0356616i
$214$			30.2020i			0.141131i
$215$		0			0
$216$	14.6969			0.0680414
$217$	35.5959	+	35.5959i	0.164036	+	0.164036i
$218$	−130.000	+	130.000i	−0.596330	+	0.596330i
$219$			91.1260i			0.416101i
$220$		0			0
$221$	406.949			1.84140
$222$	66.1362	+	66.1362i	0.297911	+	0.297911i
$223$	−208.677	+	208.677i	−0.935769	+	0.935769i	−0.998058	−	0.0622890i	$-0.980160\pi$
$223$	−208.677	+	208.677i	−0.935769	+	0.935769i	0.0622890	+	0.998058i	$0.480160\pi$
$224$		−	7.19184i		−	0.0321064i
$225$		0			0
$226$	154.586			0.684008
$227$	−242.070	−	242.070i	−1.06639	−	1.06639i	−0.997634	−	0.0687559i	$-0.978097\pi$
$227$	−242.070	−	242.070i	−1.06639	−	1.06639i	−0.0687559	−	0.997634i	$-0.521903\pi$
$228$	63.1918	−	63.1918i	0.277157	−	0.277157i
$229$			413.939i			1.80759i	0.427963	+	0.903796i	$0.359231\pi$
$229$			413.939i			1.80759i	−0.427963	+	0.903796i	$0.640769\pi$
$230$		0			0
$231$	−30.3837			−0.131531
$232$	−51.5959	−	51.5959i	−0.222396	−	0.222396i
$233$	−64.2622	+	64.2622i	−0.275804	+	0.275804i	−0.831431	−	0.555628i	$-0.812478\pi$
$233$	−64.2622	+	64.2622i	−0.275804	+	0.275804i	0.555628	+	0.831431i	$0.312478\pi$
$234$		−	76.7878i		−	0.328153i
$235$		0			0
$236$	−40.0000			−0.169492
$237$	−141.303	−	141.303i	−0.596215	−	0.596215i
$238$	28.5857	−	28.5857i	0.120108	−	0.120108i
$239$		−	154.788i		−	0.647648i	−0.946117	−	0.323824i	$-0.895032\pi$
$239$		−	154.788i		−	0.647648i	0.946117	−	0.323824i	$-0.104968\pi$
$240$		0			0
$241$	−421.939			−1.75078			−0.875392	−	0.483414i	$-0.839396\pi$
$241$	−421.939			−1.75078			−0.875392	+	0.483414i	$0.839396\pi$
$242$	−69.3837	−	69.3837i	−0.286709	−	0.286709i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			30.3837i			0.124523i
$245$		0			0
$246$	43.5959			0.177219
$247$	−330.161	−	330.161i	−1.33669	−	1.33669i
$248$	−79.1918	+	79.1918i	−0.319322	+	0.319322i
$249$		−	201.576i		−	0.809540i
$250$		0			0
$251$	392.586			1.56409			0.782043	−	0.623224i	$-0.214178\pi$
$251$	392.586			1.56409			0.782043	+	0.623224i	$0.214178\pi$
$252$	−5.39388	−	5.39388i	−0.0214043	−	0.0214043i
$253$	147.596	−	147.596i	0.583383	−	0.583383i
$254$			36.5857i			0.144038i
$255$		0			0
$256$	16.0000			0.0625000
$257$	123.515	+	123.515i	0.480604	+	0.480604i	0.905325	−	0.424720i	$-0.139628\pi$
$257$	123.515	+	123.515i	0.480604	+	0.480604i	−0.424720	+	0.905325i	$0.639628\pi$
$258$	30.6061	−	30.6061i	0.118628	−	0.118628i
$259$		−	48.5449i		−	0.187432i
$260$		0			0
$261$	−77.3939			−0.296528
$262$	133.798	+	133.798i	0.510679	+	0.510679i
$263$	−30.6969	+	30.6969i	−0.116718	+	0.116718i	−0.763054	−	0.646335i	$-0.776301\pi$
$263$	−30.6969	+	30.6969i	−0.116718	+	0.116718i	0.646335	+	0.763054i	$0.276301\pi$
$264$		−	67.5959i		−	0.256045i
$265$		0			0
$266$	−46.3837			−0.174375
$267$	−143.778	−	143.778i	−0.538493	−	0.538493i
$268$	−96.1816	+	96.1816i	−0.358887	+	0.358887i
$269$			429.151i			1.59536i	0.603083	+	0.797678i	$0.293939\pi$
$269$			429.151i			1.59536i	−0.603083	+	0.797678i	$0.706061\pi$
$270$		0			0
$271$	220.727			0.814489			0.407245	−	0.913319i	$-0.366490\pi$
$271$	220.727			0.814489			0.407245	+	0.913319i	$0.366490\pi$
$272$	63.5959	+	63.5959i	0.233809	+	0.233809i
$273$	−28.1816	+	28.1816i	−0.103229	+	0.103229i
$274$			51.7980i			0.189044i
$275$		0			0
$276$	52.4041			0.189870
$277$	45.9898	+	45.9898i	0.166028	+	0.166028i	0.785231	−	0.619203i	$-0.212544\pi$
$277$	45.9898	+	45.9898i	0.166028	+	0.166028i	−0.619203	+	0.785231i	$0.712544\pi$
$278$	−54.2020	+	54.2020i	−0.194971	+	0.194971i
$279$			118.788i			0.425763i
$280$		0			0
$281$	−482.524			−1.71717			−0.858584	−	0.512672i	$-0.828656\pi$
$281$	−482.524			−1.71717			−0.858584	+	0.512672i	$0.828656\pi$
$282$	−22.7878	−	22.7878i	−0.0808076	−	0.0808076i
$283$	−271.283	+	271.283i	−0.958596	+	0.958596i	−0.999176	−	0.0405803i	$-0.987079\pi$
$283$	−271.283	+	271.283i	−0.958596	+	0.958596i	0.0405803	+	0.999176i	$0.487079\pi$
$284$			12.4041i			0.0436763i
$285$		0			0
$286$	−353.171			−1.23487
$287$	−16.0000	−	16.0000i	−0.0557491	−	0.0557491i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			216.555i			0.749326i
$290$		0			0
$291$	200.833			0.690148
$292$	74.4041	+	74.4041i	0.254809	+	0.254809i
$293$	149.091	−	149.091i	0.508842	−	0.508842i	−0.405329	−	0.914171i	$-0.632843\pi$
$293$	149.091	−	149.091i	0.508842	−	0.508842i	0.914171	+	0.405329i	$0.132843\pi$
$294$		−	116.066i		−	0.394782i
$295$		0			0
$296$	108.000			0.364865
$297$	−50.6969	−	50.6969i	−0.170697	−	0.170697i
$298$	−42.7673	+	42.7673i	−0.143515	+	0.143515i
$299$		−	273.798i		−	0.915712i
$300$		0			0
$301$	−22.4653			−0.0746356
$302$	−178.384	−	178.384i	−0.590674	−	0.590674i
$303$	−34.7628	+	34.7628i	−0.114729	+	0.114729i
$304$		−	103.192i		−	0.339447i
$305$		0			0
$306$	95.3939			0.311745
$307$	230.697	+	230.697i	0.751456	+	0.751456i	0.974751	−	0.223295i	$-0.0716813\pi$
$307$	230.697	+	230.697i	0.751456	+	0.751456i	−0.223295	+	0.974751i	$0.571681\pi$
$308$	−24.8082	+	24.8082i	−0.0805460	+	0.0805460i
$309$		−	40.4041i		−	0.130758i
$310$		0			0
$311$	−47.7367			−0.153494			−0.0767472	−	0.997051i	$-0.524453\pi$
$311$	−47.7367			−0.153494			−0.0767472	+	0.997051i	$0.524453\pi$
$312$	−62.6969	−	62.6969i	−0.200952	−	0.200952i
$313$	−219.767	+	219.767i	−0.702132	+	0.702132i	−0.964868	−	0.262736i	$-0.915375\pi$
$313$	−219.767	+	219.767i	−0.702132	+	0.702132i	0.262736	+	0.964868i	$0.415375\pi$
$314$			246.000i			0.783439i
$315$		0			0
$316$	−230.747			−0.730212
$317$	332.828	+	332.828i	1.04993	+	1.04993i	0.998686	+	0.0512429i	$0.0163183\pi$
$317$	332.828	+	332.828i	1.04993	+	1.04993i	0.0512429	+	0.998686i	$0.483682\pi$
$318$	46.7628	−	46.7628i	0.147053	−	0.147053i
$319$			355.959i			1.11586i
$320$		0			0
$321$	36.9898			0.115233
$322$	−19.2327	−	19.2327i	−0.0597287	−	0.0597287i
$323$	410.161	−	410.161i	1.26985	−	1.26985i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	−127.010			−0.389602
$327$	159.217	+	159.217i	0.486902	+	0.486902i
$328$	35.5959	−	35.5959i	0.108524	−	0.108524i
$329$			16.7265i			0.0508405i
$330$		0			0
$331$	209.980			0.634379			0.317190	−	0.948362i	$-0.397261\pi$
$331$	209.980			0.634379			0.317190	+	0.948362i	$0.397261\pi$
$332$	−164.586	−	164.586i	−0.495740	−	0.495740i
$333$	81.0000	−	81.0000i	0.243243	−	0.243243i
$334$		−	97.3531i		−	0.291476i
$335$		0			0
$336$	−8.80816			−0.0262148
$337$	−88.3735	−	88.3735i	−0.262236	−	0.262236i	0.563726	−	0.825962i	$-0.309367\pi$
$337$	−88.3735	−	88.3735i	−0.262236	−	0.262236i	−0.825962	+	0.563726i	$0.809367\pi$
$338$	−158.576	+	158.576i	−0.469158	+	0.469158i
$339$		−	189.328i		−	0.558490i
$340$		0			0
$341$	546.343			1.60218
$342$	−77.3939	−	77.3939i	−0.226298	−	0.226298i
$343$	−86.6469	+	86.6469i	−0.252615	+	0.252615i
$344$		−	49.9796i		−	0.145290i
$345$		0			0
$346$	70.2225			0.202955
$347$	−212.495	−	212.495i	−0.612377	−	0.612377i	0.331188	−	0.943565i	$-0.392551\pi$
$347$	−212.495	−	212.495i	−0.612377	−	0.612377i	−0.943565	+	0.331188i	$0.892551\pi$
$348$	−63.1918	+	63.1918i	−0.181586	+	0.181586i
$349$			280.000i			0.802292i	0.916014	+	0.401146i	$0.131388\pi$
$349$			280.000i			0.802292i	−0.916014	+	0.401146i	$0.868612\pi$
$350$		0			0
$351$	−94.0454			−0.267936
$352$	−55.1918	−	55.1918i	−0.156795	−	0.156795i
$353$	−212.505	+	212.505i	−0.601997	+	0.601997i	−0.940842	−	0.338845i	$-0.889964\pi$
$353$	−212.505	+	212.505i	−0.601997	+	0.601997i	0.338845	+	0.940842i	$0.389964\pi$
$354$			48.9898i			0.138389i
$355$		0			0
$356$	−234.788			−0.659516
$357$	−35.0102	−	35.0102i	−0.0980678	−	0.0980678i
$358$	141.171	−	141.171i	0.394334	−	0.394334i
$359$		−	633.090i		−	1.76348i	−0.471734	−	0.881741i	$-0.656372\pi$
$359$		−	633.090i		−	1.76348i	0.471734	−	0.881741i	$-0.343628\pi$
$360$		0			0
$361$	−304.535			−0.843586
$362$	−58.8082	−	58.8082i	−0.162453	−	0.162453i
$363$	−84.9773	+	84.9773i	−0.234097	+	0.234097i
$364$			46.0204i			0.126430i
$365$		0			0
$366$	37.2122			0.101673
$367$	267.505	+	267.505i	0.728897	+	0.728897i	0.970400	−	0.241503i	$-0.0776405\pi$
$367$	267.505	+	267.505i	0.728897	+	0.728897i	−0.241503	+	0.970400i	$0.577640\pi$
$368$	42.7878	−	42.7878i	0.116271	−	0.116271i
$369$		−	53.3939i		−	0.144699i
$370$		0			0
$371$	−34.3245			−0.0925189
$372$	96.9898	+	96.9898i	0.260725	+	0.260725i
$373$	376.939	−	376.939i	1.01056	−	1.01056i	0.0106161	−	0.999944i	$-0.496621\pi$
$373$	376.939	−	376.939i	1.01056	−	1.01056i	0.999944	−	0.0106161i	$-0.00337926\pi$
$374$		−	438.747i		−	1.17312i
$375$		0			0
$376$	−37.2122			−0.0989687
$377$	330.161	+	330.161i	0.875759	+	0.875759i
$378$	−6.60612	+	6.60612i	−0.0174765	+	0.0174765i
$379$			167.818i			0.442793i	0.975184	+	0.221396i	$0.0710614\pi$
$379$			167.818i			0.442793i	−0.975184	+	0.221396i	$0.928939\pi$
$380$		0			0
$381$	44.8082			0.117607
$382$	325.394	+	325.394i	0.851816	+	0.851816i
$383$	478.293	−	478.293i	1.24881	−	1.24881i	0.292559	−	0.956248i	$-0.405493\pi$
$383$	478.293	−	478.293i	1.24881	−	1.24881i	0.956248	−	0.292559i	$-0.0945068\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−78.7673			−0.204060
$387$	−37.4847	−	37.4847i	−0.0968597	−	0.0968597i
$388$	163.980	−	163.980i	0.422628	−	0.422628i
$389$			169.151i			0.434836i	0.976079	+	0.217418i	$0.0697634\pi$
$389$			169.151i			0.434836i	−0.976079	+	0.217418i	$0.930237\pi$
$390$		0			0
$391$	340.141			0.869925
$392$	−94.7673	−	94.7673i	−0.241753	−	0.241753i
$393$	163.868	−	163.868i	0.416968	−	0.416968i
$394$		−	238.627i		−	0.605651i
$395$		0			0
$396$	−82.7878			−0.209060
$397$	69.3429	+	69.3429i	0.174667	+	0.174667i	0.789026	−	0.614359i	$-0.210585\pi$
$397$	69.3429	+	69.3429i	0.174667	+	0.174667i	−0.614359	+	0.789026i	$0.710585\pi$
$398$	−178.565	+	178.565i	−0.448657	+	0.448657i
$399$			56.8082i			0.142376i
$400$		0			0
$401$	414.767			1.03433			0.517166	−	0.855885i	$-0.326987\pi$
$401$	414.767			1.03433			0.517166	+	0.855885i	$0.326987\pi$
$402$	117.798	+	117.798i	0.293030	+	0.293030i
$403$	506.747	−	506.747i	1.25744	−	1.25744i
$404$			56.7673i			0.140513i
$405$		0			0
$406$	46.3837			0.114245
$407$	−372.545	−	372.545i	−0.915344	−	0.915344i
$408$	77.8888	−	77.8888i	0.190904	−	0.190904i
$409$		−	605.110i		−	1.47949i	−0.672889	−	0.739744i	$-0.734947\pi$
$409$		−	605.110i		−	1.47949i	0.672889	−	0.739744i	$-0.265053\pi$
$410$		0			0
$411$	63.4393			0.154353
$412$	−32.9898	−	32.9898i	−0.0800723	−	0.0800723i
$413$	17.9796	−	17.9796i	0.0435341	−	0.0435341i
$414$		−	64.1816i		−	0.155028i
$415$		0			0
$416$	−102.384			−0.246115
$417$	66.3837	+	66.3837i	0.159193	+	0.159193i
$418$	−355.959	+	355.959i	−0.851577	+	0.851577i
$419$		−	15.9592i		−	0.0380887i	−0.999819	−	0.0190444i	$-0.993938\pi$
$419$		−	15.9592i		−	0.0380887i	0.999819	−	0.0190444i	$-0.00606238\pi$
$420$		0			0
$421$	433.171			1.02891			0.514455	−	0.857517i	$-0.327994\pi$
$421$	433.171			1.02891			0.514455	+	0.857517i	$0.327994\pi$
$422$	318.747	+	318.747i	0.755324	+	0.755324i
$423$	−27.9092	+	27.9092i	−0.0659792	+	0.0659792i
$424$		−	76.3633i		−	0.180102i
$425$		0			0
$426$	15.1918			0.0356616
$427$	−13.6571	−	13.6571i	−0.0319840	−	0.0319840i
$428$	30.2020	−	30.2020i	0.0705655	−	0.0705655i
$429$			432.545i			1.00826i
$430$		0			0
$431$	24.1816			0.0561059			0.0280529	−	0.999606i	$-0.491069\pi$
$431$	24.1816			0.0561059			0.0280529	+	0.999606i	$0.491069\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−528.918	+	528.918i	−1.22152	+	1.22152i	−0.254429	+	0.967091i	$0.581888\pi$
$433$	−528.918	+	528.918i	−1.22152	+	1.22152i	−0.967091	+	0.254429i	$0.918112\pi$
$434$		−	71.1918i		−	0.164036i
$435$		0			0
$436$	260.000			0.596330
$437$	−275.959	−	275.959i	−0.631486	−	0.631486i
$438$	91.1260	−	91.1260i	0.208050	−	0.208050i
$439$		−	44.6265i		−	0.101655i	−0.998707	−	0.0508275i	$-0.983814\pi$
$439$		−	44.6265i		−	0.101655i	0.998707	−	0.0508275i	$-0.0161859\pi$
$440$		0			0
$441$	−142.151			−0.322338
$442$	−406.949	−	406.949i	−0.920699	−	0.920699i
$443$	−311.283	+	311.283i	−0.702670	+	0.702670i	−0.964983	−	0.262313i	$-0.915515\pi$
$443$	−311.283	+	311.283i	−0.702670	+	0.702670i	0.262313	+	0.964983i	$0.415515\pi$
$444$		−	132.272i		−	0.297911i
$445$		0			0
$446$	417.353			0.935769
$447$	52.3791	+	52.3791i	0.117179	+	0.117179i
$448$	−7.19184	+	7.19184i	−0.0160532	+	0.0160532i
$449$			141.273i			0.314640i	0.987548	+	0.157320i	$0.0502855\pi$
$449$			141.273i			0.314640i	−0.987548	+	0.157320i	$0.949715\pi$
$450$		0			0
$451$	−245.576			−0.544513
$452$	−154.586	−	154.586i	−0.342004	−	0.342004i
$453$	−218.474	+	218.474i	−0.482284	+	0.482284i
$454$			484.141i			1.06639i
$455$		0			0
$456$	−126.384			−0.277157
$457$	−20.3939	−	20.3939i	−0.0446256	−	0.0446256i	0.684442	−	0.729067i	$-0.260046\pi$
$457$	−20.3939	−	20.3939i	−0.0446256	−	0.0446256i	−0.729067	+	0.684442i	$0.760046\pi$
$458$	413.939	−	413.939i	0.903796	−	0.903796i
$459$		−	116.833i		−	0.254538i
$460$		0			0
$461$	−626.727			−1.35949			−0.679747	−	0.733447i	$-0.737910\pi$
$461$	−626.727			−1.35949			−0.679747	+	0.733447i	$0.737910\pi$
$462$	30.3837	+	30.3837i	0.0657655	+	0.0657655i
$463$	314.515	−	314.515i	0.679299	−	0.679299i	−0.280543	−	0.959842i	$-0.590514\pi$
$463$	314.515	−	314.515i	0.679299	−	0.679299i	0.959842	+	0.280543i	$0.0905145\pi$
$464$			103.192i			0.222396i
$465$		0			0
$466$	128.524			0.275804
$467$	−46.6969	−	46.6969i	−0.0999934	−	0.0999934i	0.655340	−	0.755334i	$-0.272525\pi$
$467$	−46.6969	−	46.6969i	−0.0999934	−	0.0999934i	−0.755334	+	0.655340i	$0.772525\pi$
$468$	−76.7878	+	76.7878i	−0.164076	+	0.164076i
$469$		−	86.4653i		−	0.184361i
$470$		0			0
$471$	301.287			0.639676
$472$	40.0000	+	40.0000i	0.0847458	+	0.0847458i
$473$	−172.404	+	172.404i	−0.364491	+	0.364491i
$474$			282.606i			0.596215i
$475$		0			0
$476$	−57.1714			−0.120108
$477$	−57.2724	−	57.2724i	−0.120068	−	0.120068i
$478$	−154.788	+	154.788i	−0.323824	+	0.323824i
$479$		−	71.2735i		−	0.148796i	−0.997229	−	0.0743982i	$-0.976296\pi$
$479$		−	71.2735i		−	0.148796i	0.997229	−	0.0743982i	$-0.0237036\pi$
$480$		0			0
$481$	−691.090			−1.43678
$482$	421.939	+	421.939i	0.875392	+	0.875392i
$483$	−23.5551	+	23.5551i	−0.0487683	+	0.0487683i
$484$			138.767i			0.286709i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	−295.423	−	295.423i	−0.606619	−	0.606619i	0.335442	−	0.942061i	$-0.391114\pi$
$487$	−295.423	−	295.423i	−0.606619	−	0.606619i	−0.942061	+	0.335442i	$0.891114\pi$
$488$	30.3837	−	30.3837i	0.0622616	−	0.0622616i
$489$			155.555i			0.318109i
$490$		0			0
$491$	−910.080			−1.85352			−0.926761	−	0.375651i	$-0.877419\pi$
$491$	−910.080			−1.85352			−0.926761	+	0.375651i	$0.877419\pi$
$492$	−43.5959	−	43.5959i	−0.0886096	−	0.0886096i
$493$	−410.161	+	410.161i	−0.831970	+	0.831970i
$494$			660.322i			1.33669i
$495$		0			0
$496$	158.384			0.319322
$497$	−5.57551	−	5.57551i	−0.0112183	−	0.0112183i
$498$	−201.576	+	201.576i	−0.404770	+	0.404770i
$499$		−	970.161i		−	1.94421i	−0.234544	−	0.972105i	$-0.575360\pi$
$499$		−	970.161i		−	1.94421i	0.234544	−	0.972105i	$-0.424640\pi$
$500$		0			0
$501$	−119.233			−0.237989
$502$	−392.586	−	392.586i	−0.782043	−	0.782043i
$503$	−276.817	+	276.817i	−0.550333	+	0.550333i	−0.926537	−	0.376204i	$-0.877229\pi$
$503$	−276.817	+	276.817i	−0.550333	+	0.550333i	0.376204	+	0.926537i	$0.377229\pi$
$504$			10.7878i			0.0214043i
$505$		0			0
$506$	−295.192			−0.583383
$507$	194.215	+	194.215i	0.383066	+	0.383066i
$508$	36.5857	−	36.5857i	0.0720191	−	0.0720191i
$509$			900.059i			1.76829i	0.467213	+	0.884145i	$0.345258\pi$
$509$			900.059i			1.76829i	−0.467213	+	0.884145i	$0.654742\pi$
$510$		0			0
$511$	−66.8877			−0.130896
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−94.7878	+	94.7878i	−0.184771	+	0.184771i
$514$		−	247.031i		−	0.480604i
$515$		0			0
$516$	−61.2122			−0.118628
$517$	128.363	+	128.363i	0.248285	+	0.248285i
$518$	−48.5449	+	48.5449i	−0.0937160	+	0.0937160i
$519$		−	86.0046i		−	0.165712i
$520$		0			0
$521$	−239.494			−0.459681			−0.229841	−	0.973228i	$-0.573820\pi$
$521$	−239.494			−0.459681			−0.229841	+	0.973228i	$0.573820\pi$
$522$	77.3939	+	77.3939i	0.148264	+	0.148264i
$523$	−12.7173	+	12.7173i	−0.0243162	+	0.0243162i	−0.719160	−	0.694844i	$-0.755473\pi$
$523$	−12.7173	+	12.7173i	−0.0243162	+	0.0243162i	0.694844	+	0.719160i	$0.255473\pi$
$524$		−	267.596i		−	0.510679i
$525$		0			0
$526$	61.3939			0.116718
$527$	629.535	+	629.535i	1.19456	+	1.19456i
$528$	−67.5959	+	67.5959i	−0.128023	+	0.128023i
$529$			300.151i			0.567393i
$530$		0			0
$531$	60.0000			0.112994
$532$	46.3837	+	46.3837i	0.0871874	+	0.0871874i
$533$	−227.778	+	227.778i	−0.427350	+	0.427350i
$534$			287.555i			0.538493i
$535$		0			0
$536$	192.363			0.358887
$537$	−172.899	−	172.899i	−0.321972	−	0.321972i
$538$	429.151	−	429.151i	0.797678	−	0.797678i
$539$			653.798i			1.21298i
$540$		0			0
$541$	477.110			0.881904			0.440952	−	0.897531i	$-0.354641\pi$
$541$	477.110			0.881904			0.440952	+	0.897531i	$0.354641\pi$
$542$	−220.727	−	220.727i	−0.407245	−	0.407245i
$543$	−72.0250	+	72.0250i	−0.132643	+	0.132643i
$544$		−	127.192i		−	0.233809i
$545$		0			0
$546$	56.3633			0.103229
$547$	−720.372	−	720.372i	−1.31695	−	1.31695i	−0.916177	−	0.400775i	$-0.868741\pi$
$547$	−720.372	−	720.372i	−1.31695	−	1.31695i	−0.400775	−	0.916177i	$-0.631259\pi$
$548$	51.7980	−	51.7980i	0.0945218	−	0.0945218i
$549$		−	45.5755i		−	0.0830155i
$550$		0			0
$551$	665.535			1.20787
$552$	−52.4041	−	52.4041i	−0.0949349	−	0.0949349i
$553$	103.718	−	103.718i	0.187556	−	0.187556i
$554$		−	91.9796i		−	0.166028i
$555$		0			0
$556$	108.404			0.194971
$557$	139.899	+	139.899i	0.251165	+	0.251165i	0.821448	−	0.570283i	$-0.193166\pi$
$557$	139.899	+	139.899i	0.251165	+	0.251165i	−0.570283	+	0.821448i	$0.693166\pi$
$558$	118.788	−	118.788i	0.212881	−	0.212881i
$559$			319.818i			0.572126i
$560$		0			0
$561$	−537.353			−0.957849
$562$	482.524	+	482.524i	0.858584	+	0.858584i
$563$	−461.121	+	461.121i	−0.819043	+	0.819043i	−0.985969	−	0.166926i	$-0.946616\pi$
$563$	−461.121	+	461.121i	−0.819043	+	0.819043i	0.166926	+	0.985969i	$0.446616\pi$
$564$			45.5755i			0.0808076i
$565$		0			0
$566$	542.565			0.958596
$567$	8.09082	+	8.09082i	0.0142695	+	0.0142695i
$568$	12.4041	−	12.4041i	0.0218382	−	0.0218382i
$569$		−	31.4939i		−	0.0553495i	−0.999617	−	0.0276748i	$-0.991190\pi$
$569$		−	31.4939i		−	0.0553495i	0.999617	−	0.0276748i	$-0.00881027\pi$
$570$		0			0
$571$	139.233			0.243840			0.121920	−	0.992540i	$-0.461095\pi$
$571$	139.233			0.243840			0.121920	+	0.992540i	$0.461095\pi$
$572$	353.171	+	353.171i	0.617433	+	0.617433i
$573$	398.524	−	398.524i	0.695505	−	0.695505i
$574$			32.0000i			0.0557491i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−463.000	−	463.000i	−0.802426	−	0.802426i	0.181048	−	0.983474i	$-0.442051\pi$
$577$	−463.000	−	463.000i	−0.802426	−	0.802426i	−0.983474	+	0.181048i	$0.942051\pi$
$578$	216.555	−	216.555i	0.374663	−	0.374663i
$579$			96.4699i			0.166615i
$580$		0			0
$581$	147.959			0.254663
$582$	−200.833	−	200.833i	−0.345074	−	0.345074i
$583$	−263.414	+	263.414i	−0.451826	+	0.451826i
$584$		−	148.808i		−	0.254809i
$585$		0			0
$586$	−298.182			−0.508842
$587$	−464.091	−	464.091i	−0.790615	−	0.790615i	0.190979	−	0.981594i	$-0.438834\pi$
$587$	−464.091	−	464.091i	−0.790615	−	0.790615i	−0.981594	+	0.190979i	$0.938834\pi$
$588$	−116.066	+	116.066i	−0.197391	+	0.197391i
$589$		−	1021.49i		−	1.73429i
$590$		0			0
$591$	−292.257			−0.494512
$592$	−108.000	−	108.000i	−0.182432	−	0.182432i
$593$	−120.646	+	120.646i	−0.203450	+	0.203450i	−0.801476	−	0.598026i	$-0.795952\pi$
$593$	−120.646	+	120.646i	−0.203450	+	0.203450i	0.598026	+	0.801476i	$0.295952\pi$
$594$			101.394i			0.170697i
$595$		0			0
$596$	85.5347			0.143515
$597$	218.697	+	218.697i	0.366327	+	0.366327i
$598$	−273.798	+	273.798i	−0.457856	+	0.457856i
$599$		−	157.131i		−	0.262322i	−0.991361	−	0.131161i	$-0.958130\pi$
$599$		−	157.131i		−	0.262322i	0.991361	−	0.131161i	$-0.0418704\pi$
$600$		0			0
$601$	550.302			0.915644			0.457822	−	0.889044i	$-0.348630\pi$
$601$	550.302			0.915644			0.457822	+	0.889044i	$0.348630\pi$
$602$	22.4653	+	22.4653i	0.0373178	+	0.0373178i
$603$	144.272	−	144.272i	0.239258	−	0.239258i
$604$			356.767i			0.590674i
$605$		0			0
$606$	69.5255			0.114729
$607$	182.030	+	182.030i	0.299884	+	0.299884i	0.840968	−	0.541084i	$-0.181986\pi$
$607$	182.030	+	182.030i	0.299884	+	0.299884i	−0.541084	+	0.840968i	$0.681986\pi$
$608$	−103.192	+	103.192i	−0.169723	+	0.169723i
$609$		−	56.8082i		−	0.0932811i
$610$		0			0
$611$	238.120			0.389722
$612$	−95.3939	−	95.3939i	−0.155872	−	0.155872i
$613$	788.110	−	788.110i	1.28566	−	1.28566i	0.348265	−	0.937396i	$-0.386771\pi$
$613$	788.110	−	788.110i	1.28566	−	1.28566i	0.937396	−	0.348265i	$-0.113229\pi$
$614$		−	461.394i		−	0.751456i
$615$		0			0
$616$	49.6163			0.0805460
$617$	−356.221	−	356.221i	−0.577344	−	0.577344i	0.356826	−	0.934171i	$-0.383859\pi$
$617$	−356.221	−	356.221i	−0.577344	−	0.577344i	−0.934171	+	0.356826i	$0.883859\pi$
$618$	−40.4041	+	40.4041i	−0.0653788	+	0.0653788i
$619$		−	73.8796i		−	0.119353i	−0.998218	−	0.0596766i	$-0.980993\pi$
$619$		−	73.8796i		−	0.119353i	0.998218	−	0.0596766i	$-0.0190069\pi$
$620$		0			0
$621$	−78.6061			−0.126580
$622$	47.7367	+	47.7367i	0.0767472	+	0.0767472i
$623$	105.535	−	105.535i	0.169398	−	0.169398i
$624$			125.394i			0.200952i
$625$		0			0
$626$	439.535			0.702132
$627$	435.959	+	435.959i	0.695310	+	0.695310i
$628$	246.000	−	246.000i	0.391720	−	0.391720i
$629$		−	858.545i		−	1.36494i
$630$		0			0
$631$	−45.9796			−0.0728678			−0.0364339	−	0.999336i	$-0.511600\pi$
$631$	−45.9796			−0.0728678			−0.0364339	+	0.999336i	$0.511600\pi$
$632$	230.747	+	230.747i	0.365106	+	0.365106i
$633$	390.384	−	390.384i	0.616720	−	0.616720i
$634$		−	665.655i		−	1.04993i
$635$		0			0
$636$	−93.5255			−0.147053
$637$	606.414	+	606.414i	0.951985	+	0.951985i
$638$	355.959	−	355.959i	0.557930	−	0.557930i
$639$		−	18.6061i		−	0.0291176i
$640$		0			0
$641$	−789.757			−1.23207			−0.616035	−	0.787719i	$-0.711262\pi$
$641$	−789.757			−1.23207			−0.616035	+	0.787719i	$0.711262\pi$
$642$	−36.9898	−	36.9898i	−0.0576165	−	0.0576165i
$643$	530.474	−	530.474i	0.824999	−	0.824999i	−0.161821	−	0.986820i	$-0.551737\pi$
$643$	530.474	−	530.474i	0.824999	−	0.824999i	0.986820	+	0.161821i	$0.0517367\pi$
$644$			38.4653i			0.0597287i
$645$		0			0
$646$	−820.322			−1.26985
$647$	135.323	+	135.323i	0.209155	+	0.209155i	0.803908	−	0.594753i	$-0.202750\pi$
$647$	135.323	+	135.323i	0.209155	+	0.209155i	−0.594753	+	0.803908i	$0.702750\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	275.959i		−	0.425207i
$650$		0			0
$651$	−87.1918			−0.133935
$652$	127.010	+	127.010i	0.194801	+	0.194801i
$653$	49.8377	−	49.8377i	0.0763212	−	0.0763212i	−0.667916	−	0.744237i	$-0.732813\pi$
$653$	49.8377	−	49.8377i	0.0763212	−	0.0763212i	0.744237	+	0.667916i	$0.232813\pi$
$654$		−	318.434i		−	0.486902i
$655$		0			0
$656$	−71.1918			−0.108524
$657$	−111.606	−	111.606i	−0.169872	−	0.169872i
$658$	16.7265	−	16.7265i	0.0254202	−	0.0254202i
$659$		−	209.576i		−	0.318020i	−0.987277	−	0.159010i	$-0.949170\pi$
$659$		−	209.576i		−	0.318020i	0.987277	−	0.159010i	$-0.0508303\pi$
$660$		0			0
$661$	−119.273			−0.180444			−0.0902220	−	0.995922i	$-0.528758\pi$
$661$	−119.273			−0.180444			−0.0902220	+	0.995922i	$0.528758\pi$
$662$	−209.980	−	209.980i	−0.317190	−	0.317190i
$663$	−498.409	+	498.409i	−0.751748	+	0.751748i
$664$			329.171i			0.495740i
$665$		0			0
$666$	−162.000			−0.243243
$667$	275.959	+	275.959i	0.413732	+	0.413732i
$668$	−97.3531	+	97.3531i	−0.145738	+	0.145738i
$669$		−	511.151i		−	0.764052i
$670$		0			0
$671$	−209.616			−0.312394
$672$	8.80816	+	8.80816i	0.0131074	+	0.0131074i
$673$	468.857	−	468.857i	0.696667	−	0.696667i	−0.267023	−	0.963690i	$-0.586040\pi$
$673$	468.857	−	468.857i	0.696667	−	0.696667i	0.963690	+	0.267023i	$0.0860399\pi$
$674$			176.747i			0.262236i
$675$		0			0
$676$	317.151			0.469158
$677$	654.160	+	654.160i	0.966263	+	0.966263i	0.999449	−	0.0331860i	$-0.0105654\pi$
$677$	654.160	+	654.160i	0.966263	+	0.966263i	−0.0331860	+	0.999449i	$0.510565\pi$
$678$	−189.328	+	189.328i	−0.279245	+	0.279245i
$679$			147.414i			0.217105i
$680$		0			0
$681$	592.949			0.870703
$682$	−546.343	−	546.343i	−0.801089	−	0.801089i
$683$	−286.070	+	286.070i	−0.418844	+	0.418844i	−0.884805	−	0.465961i	$-0.845709\pi$
$683$	−286.070	+	286.070i	−0.418844	+	0.418844i	0.465961	+	0.884805i	$0.345709\pi$
$684$			154.788i			0.226298i
$685$		0			0
$686$	173.294			0.252615
$687$	−506.969	−	506.969i	−0.737947	−	0.737947i
$688$	−49.9796	+	49.9796i	−0.0726448	+	0.0726448i
$689$			488.647i			0.709212i
$690$		0			0
$691$	738.706			1.06904			0.534520	−	0.845156i	$-0.320493\pi$
$691$	738.706			1.06904			0.534520	+	0.845156i	$0.320493\pi$
$692$	−70.2225	−	70.2225i	−0.101478	−	0.101478i
$693$	37.2122	−	37.2122i	0.0536973	−	0.0536973i
$694$			424.990i			0.612377i
$695$		0			0
$696$	126.384			0.181586
$697$	−282.969	−	282.969i	−0.405982	−	0.405982i
$698$	280.000	−	280.000i	0.401146	−	0.401146i
$699$		−	157.410i		−	0.225193i
$700$		0			0
$701$	475.778			0.678713			0.339356	−	0.940658i	$-0.389791\pi$
$701$	475.778			0.678713			0.339356	+	0.940658i	$0.389791\pi$
$702$	94.0454	+	94.0454i	0.133968	+	0.133968i
$703$	−696.545	+	696.545i	−0.990818	+	0.990818i
$704$			110.384i			0.156795i
$705$		0			0
$706$	425.010			0.601997
$707$	−25.5163	−	25.5163i	−0.0360910	−	0.0360910i
$708$	48.9898	−	48.9898i	0.0691946	−	0.0691946i
$709$			504.363i			0.711373i	0.934605	+	0.355686i	$0.115753\pi$
$709$			504.363i			0.711373i	−0.934605	+	0.355686i	$0.884247\pi$
$710$		0			0
$711$	346.120			0.486808
$712$	234.788	+	234.788i	0.329758	+	0.329758i
$713$	423.555	−	423.555i	0.594046	−	0.594046i
$714$			70.0204i			0.0980678i
$715$		0			0
$716$	−282.343			−0.394334
$717$	189.576	+	189.576i	0.264401	+	0.264401i
$718$	−633.090	+	633.090i	−0.881741	+	0.881741i
$719$			481.816i			0.670120i	0.942197	+	0.335060i	$0.108757\pi$
$719$			481.816i			0.670120i	−0.942197	+	0.335060i	$0.891243\pi$
$720$		0			0
$721$	29.6571			0.0411334
$722$	304.535	+	304.535i	0.421793	+	0.421793i
$723$	516.767	−	516.767i	0.714754	−	0.714754i
$724$			117.616i			0.162453i
$725$		0			0
$726$	169.955			0.234097
$727$	782.352	+	782.352i	1.07614	+	1.07614i	0.996852	+	0.0792856i	$0.0252639\pi$
$727$	782.352	+	782.352i	1.07614	+	1.07614i	0.0792856	+	0.996852i	$0.474736\pi$
$728$	46.0204	−	46.0204i	0.0632148	−	0.0632148i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−397.312			−0.543519
$732$	−37.2122	−	37.2122i	−0.0508364	−	0.0508364i
$733$	−537.586	+	537.586i	−0.733405	+	0.733405i	−0.971293	−	0.237888i	$-0.923545\pi$
$733$	−537.586	+	537.586i	−0.733405	+	0.733405i	0.237888	+	0.971293i	$0.423545\pi$
$734$		−	535.010i		−	0.728897i
$735$		0			0
$736$	−85.5755			−0.116271
$737$	−663.555	−	663.555i	−0.900346	−	0.900346i
$738$	−53.3939	+	53.3939i	−0.0723494	+	0.0723494i
$739$			833.353i			1.12768i	0.825885	+	0.563838i	$0.190676\pi$
$739$			833.353i			1.12768i	−0.825885	+	0.563838i	$0.809324\pi$
$740$		0			0
$741$	808.727			1.09140
$742$	34.3245	+	34.3245i	0.0462594	+	0.0462594i
$743$	991.383	−	991.383i	1.33430	−	1.33430i	0.432813	−	0.901484i	$-0.357521\pi$
$743$	991.383	−	991.383i	1.33430	−	1.33430i	0.901484	−	0.432813i	$-0.142479\pi$
$744$		−	193.980i		−	0.260725i
$745$		0			0
$746$	−753.878			−1.01056
$747$	246.879	+	246.879i	0.330493	+	0.330493i
$748$	−438.747	+	438.747i	−0.586560	+	0.586560i
$749$			27.1510i			0.0362497i
$750$		0			0
$751$	−1276.73			−1.70004			−0.850018	−	0.526754i	$-0.823409\pi$
$751$	−1276.73			−1.70004			−0.850018	+	0.526754i	$0.823409\pi$
$752$	37.2122	+	37.2122i	0.0494844	+	0.0494844i
$753$	−480.817	+	480.817i	−0.638536	+	0.638536i
$754$		−	660.322i		−	0.875759i
$755$		0			0
$756$	13.2122			0.0174765
$757$	36.0918	+	36.0918i	0.0476775	+	0.0476775i	0.730544	−	0.682866i	$-0.239267\pi$
$757$	36.0918	+	36.0918i	0.0476775	+	0.0476775i	−0.682866	+	0.730544i	$0.739267\pi$
$758$	167.818	−	167.818i	0.221396	−	0.221396i
$759$			361.535i			0.476330i
$760$		0			0
$761$	716.261			0.941211			0.470605	−	0.882344i	$-0.344036\pi$
$761$	716.261			0.941211			0.470605	+	0.882344i	$0.344036\pi$
$762$	−44.8082	−	44.8082i	−0.0588034	−	0.0588034i
$763$	−116.867	+	116.867i	−0.153168	+	0.153168i
$764$		−	650.788i		−	0.851816i
$765$		0			0
$766$	−956.586			−1.24881
$767$	−255.959	−	255.959i	−0.333715	−	0.333715i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			389.576i			0.506600i	0.967388	+	0.253300i	$0.0815160\pi$
$769$			389.576i			0.506600i	−0.967388	+	0.253300i	$0.918484\pi$
$770$		0			0
$771$	−302.549			−0.392412
$772$	78.7673	+	78.7673i	0.102030	+	0.102030i
$773$	409.677	−	409.677i	0.529983	−	0.529983i	−0.390585	−	0.920567i	$-0.627727\pi$
$773$	409.677	−	409.677i	0.529983	−	0.529983i	0.920567	+	0.390585i	$0.127727\pi$
$774$			74.9694i			0.0968597i
$775$		0			0
$776$	−327.959			−0.422628
$777$	59.4551	+	59.4551i	0.0765188	+	0.0765188i
$778$	169.151	−	169.151i	0.217418	−	0.217418i
$779$			459.151i			0.589411i
$780$		0			0
$781$	−85.5755			−0.109572
$782$	−340.141	−	340.141i	−0.434963	−	0.434963i
$783$	94.7878	−	94.7878i	0.121057	−	0.121057i
$784$			189.535i			0.241753i
$785$		0			0
$786$	−327.737			−0.416968
$787$	383.142	+	383.142i	0.486838	+	0.486838i	0.907307	−	0.420469i	$-0.138134\pi$
$787$	383.142	+	383.142i	0.486838	+	0.486838i	−0.420469	+	0.907307i	$0.638134\pi$
$788$	−238.627	+	238.627i	−0.302826	+	0.302826i
$789$		−	75.1918i		−	0.0953002i
$790$		0			0
$791$	138.969			0.175688
$792$	82.7878	+	82.7878i	0.104530	+	0.104530i
$793$	−194.424	+	194.424i	−0.245176	+	0.245176i
$794$		−	138.686i		−	0.174667i
$795$		0			0
$796$	357.131			0.448657
$797$	−563.191	−	563.191i	−0.706638	−	0.706638i	0.259188	−	0.965827i	$-0.416545\pi$
$797$	−563.191	−	563.191i	−0.706638	−	0.706638i	−0.965827	+	0.259188i	$0.916545\pi$
$798$	56.8082	−	56.8082i	0.0711882	−	0.0711882i
$799$			295.818i			0.370236i
$800$		0			0
$801$	352.182			0.439677
$802$	−414.767	−	414.767i	−0.517166	−	0.517166i
$803$	−513.312	+	513.312i	−0.639243	+	0.639243i
$804$		−	235.596i		−	0.293030i
$805$		0			0
$806$	−1013.49			−1.25744
$807$	−525.601	−	525.601i	−0.651302	−	0.651302i
$808$	56.7673	−	56.7673i	0.0702566	−	0.0702566i
$809$		−	770.161i		−	0.951992i	−0.879448	−	0.475996i	$-0.842088\pi$
$809$		−	770.161i		−	0.951992i	0.879448	−	0.475996i	$-0.157912\pi$
$810$		0			0
$811$	13.4939			0.0166386			0.00831928	−	0.999965i	$-0.497352\pi$
$811$	13.4939			0.0166386			0.00831928	+	0.999965i	$0.497352\pi$
$812$	−46.3837	−	46.3837i	−0.0571227	−	0.0571227i
$813$	−270.334	+	270.334i	−0.332514	+	0.332514i
$814$			745.090i			0.915344i
$815$		0			0
$816$	−155.778			−0.190904
$817$	322.343	+	322.343i	0.394544	+	0.394544i
$818$	−605.110	+	605.110i	−0.739744	+	0.739744i
$819$		−	69.0306i		−	0.0842865i
$820$		0			0
$821$	741.312			0.902938			0.451469	−	0.892287i	$-0.350900\pi$
$821$	741.312			0.902938			0.451469	+	0.892287i	$0.350900\pi$
$822$	−63.4393	−	63.4393i	−0.0771767	−	0.0771767i
$823$	196.272	−	196.272i	0.238484	−	0.238484i	−0.577738	−	0.816222i	$-0.696064\pi$
$823$	196.272	−	196.272i	0.238484	−	0.238484i	0.816222	+	0.577738i	$0.196064\pi$
$824$			65.9796i			0.0800723i
$825$		0			0
$826$	−35.9592			−0.0435341
$827$	20.5357	+	20.5357i	0.0248316	+	0.0248316i	0.719414	−	0.694582i	$-0.244411\pi$
$827$	20.5357	+	20.5357i	0.0248316	+	0.0248316i	−0.694582	+	0.719414i	$0.744411\pi$
$828$	−64.1816	+	64.1816i	−0.0775140	+	0.0775140i
$829$			264.465i			0.319017i	0.987197	+	0.159509i	$0.0509910\pi$
$829$			264.465i			0.319017i	−0.987197	+	0.159509i	$0.949009\pi$
$830$		0			0
$831$	−112.652			−0.135561
$832$	102.384	+	102.384i	0.123057	+	0.123057i
$833$	−753.352	+	753.352i	−0.904384	+	0.904384i
$834$		−	132.767i		−	0.159193i
$835$		0			0
$836$	711.918			0.851577
$837$	−145.485	−	145.485i	−0.173817	−	0.173817i
$838$	−15.9592	+	15.9592i	−0.0190444	+	0.0190444i
$839$			353.090i			0.420846i	0.977610	+	0.210423i	$0.0674841\pi$
$839$			353.090i			0.420846i	−0.977610	+	0.210423i	$0.932516\pi$
$840$		0			0
$841$	175.465			0.208639
$842$	−433.171	−	433.171i	−0.514455	−	0.514455i
$843$	590.969	−	590.969i	0.701031	−	0.701031i
$844$		−	637.494i		−	0.755324i
$845$		0			0
$846$	55.8184			0.0659792
$847$	−62.3745	−	62.3745i	−0.0736417	−	0.0736417i
$848$	−76.3633	+	76.3633i	−0.0900510	+	0.0900510i
$849$		−	664.504i		−	0.782690i
$850$		0			0
$851$	−577.635			−0.678772
$852$	−15.1918	−	15.1918i	−0.0178308	−	0.0178308i
$853$	−19.4449	+	19.4449i	−0.0227959	+	0.0227959i	−0.718413	−	0.695617i	$-0.755131\pi$
$853$	−19.4449	+	19.4449i	−0.0227959	+	0.0227959i	0.695617	+	0.718413i	$0.255131\pi$
$854$			27.3143i			0.0319840i
$855$		0			0
$856$	−60.4041			−0.0705655
$857$	−602.444	−	602.444i	−0.702968	−	0.702968i	0.262078	−	0.965047i	$-0.415592\pi$
$857$	−602.444	−	602.444i	−0.702968	−	0.702968i	−0.965047	+	0.262078i	$0.915592\pi$
$858$	432.545	−	432.545i	0.504132	−	0.504132i
$859$			1099.53i			1.28001i	0.768369	+	0.640007i	$0.221069\pi$
$859$			1099.53i			1.28001i	−0.768369	+	0.640007i	$0.778931\pi$
$860$		0			0
$861$	39.1918			0.0455190
$862$	−24.1816	−	24.1816i	−0.0280529	−	0.0280529i
$863$	−694.797	+	694.797i	−0.805095	+	0.805095i	−0.983887	−	0.178792i	$-0.942781\pi$
$863$	−694.797	+	694.797i	−0.805095	+	0.805095i	0.178792	+	0.983887i	$0.442781\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	1057.84			1.22152
$867$	−265.225	−	265.225i	−0.305911	−	0.305911i
$868$	−71.1918	+	71.1918i	−0.0820182	+	0.0820182i
$869$		−	1591.92i		−	1.83190i
$870$		0			0
$871$	−1230.93			−1.41324
$872$	−260.000	−	260.000i	−0.298165	−	0.298165i
$873$	−245.969	+	245.969i	−0.281752	+	0.281752i
$874$			551.918i			0.631486i
$875$		0			0
$876$	−182.252			−0.208050
$877$	−1092.90	−	1092.90i	−1.24618	−	1.24618i	−0.957394	−	0.288783i	$-0.906749\pi$
$877$	−1092.90	−	1092.90i	−1.24618	−	1.24618i	−0.288783	−	0.957394i	$-0.593251\pi$
$878$	−44.6265	+	44.6265i	−0.0508275	+	0.0508275i
$879$			365.196i			0.415468i
$880$		0			0
$881$	138.443			0.157143			0.0785714	−	0.996908i	$-0.474964\pi$
$881$	138.443			0.157143			0.0785714	+	0.996908i	$0.474964\pi$
$882$	142.151	+	142.151i	0.161169	+	0.161169i
$883$	−1008.41	+	1008.41i	−1.14203	+	1.14203i	−0.153953	+	0.988078i	$0.549200\pi$
$883$	−1008.41	+	1008.41i	−1.14203	+	1.14203i	−0.988078	+	0.153953i	$0.950800\pi$
$884$			813.898i			0.920699i
$885$		0			0
$886$	622.565			0.702670
$887$	639.687	+	639.687i	0.721180	+	0.721180i	0.968846	−	0.247666i	$-0.0796634\pi$
$887$	639.687	+	639.687i	0.721180	+	0.721180i	−0.247666	+	0.968846i	$0.579663\pi$
$888$	−132.272	+	132.272i	−0.148955	+	0.148955i
$889$			32.8898i			0.0369964i
$890$		0			0
$891$	124.182			0.139373
$892$	−417.353	−	417.353i	−0.467885	−	0.467885i
$893$	240.000	−	240.000i	0.268757	−	0.268757i
$894$		−	104.758i		−	0.117179i
$895$		0			0
$896$	14.3837			0.0160532
$897$	335.333	+	335.333i	0.373838	+	0.373838i
$898$	141.273	−	141.273i	0.157320	−	0.157320i
$899$			1021.49i			1.13626i
$900$		0			0
$901$	−607.049			−0.673750
$902$	245.576	+	245.576i	0.272257	+	0.272257i
$903$	27.5143	−	27.5143i	0.0304699	−	0.0304699i
$904$			309.171i			0.342004i
$905$		0			0
$906$	436.949			0.482284
$907$	893.303	+	893.303i	0.984899	+	0.984899i	0.999888	−	0.0149890i	$-0.00477133\pi$
$907$	893.303	+	893.303i	0.984899	+	0.984899i	−0.0149890	+	0.999888i	$0.504771\pi$
$908$	484.141	−	484.141i	0.533195	−	0.533195i
$909$		−	85.1510i		−	0.0936755i
$910$		0			0
$911$	1045.03			1.14712			0.573562	−	0.819162i	$-0.305561\pi$
$911$	1045.03			1.14712			0.573562	+	0.819162i	$0.305561\pi$
$912$	126.384	+	126.384i	0.138579	+	0.138579i
$913$	1135.47	−	1135.47i	1.24367	−	1.24367i
$914$			40.7878i			0.0446256i
$915$		0			0
$916$	−827.878			−0.903796
$917$	120.282	+	120.282i	0.131169	+	0.131169i
$918$	−116.833	+	116.833i	−0.127269	+	0.127269i
$919$		−	803.573i		−	0.874400i	−0.899364	−	0.437200i	$-0.855970\pi$
$919$		−	803.573i		−	0.874400i	0.899364	−	0.437200i	$-0.144030\pi$
$920$		0			0
$921$	−565.090			−0.613561
$922$	626.727	+	626.727i	0.679747	+	0.679747i
$923$	−79.3735	+	79.3735i	−0.0859951	+	0.0859951i
$924$		−	60.7673i		−	0.0657655i
$925$		0			0
$926$	−629.031			−0.679299
$927$	49.4847	+	49.4847i	0.0533815	+	0.0533815i
$928$	103.192	−	103.192i	0.111198	−	0.111198i
$929$		−	1270.64i		−	1.36776i	−0.729597	−	0.683878i	$-0.760292\pi$
$929$		−	1270.64i		−	1.36776i	0.729597	−	0.683878i	$-0.239708\pi$
$930$		0			0
$931$	1222.40			1.31300
$932$	−128.524	−	128.524i	−0.137902	−	0.137902i
$933$	58.4653	−	58.4653i	0.0626638	−	0.0626638i
$934$			93.3939i			0.0999934i
$935$		0			0
$936$	153.576			0.164076
$937$	970.616	+	970.616i	1.03588	+	1.03588i	0.999332	+	0.0365445i	$0.0116351\pi$
$937$	970.616	+	970.616i	1.03588	+	1.03588i	0.0365445	+	0.999332i	$0.488365\pi$
$938$	−86.4653	+	86.4653i	−0.0921805	+	0.0921805i
$939$		−	538.318i		−	0.573288i
$940$		0			0
$941$	−431.616			−0.458678			−0.229339	−	0.973347i	$-0.573656\pi$
$941$	−431.616			−0.458678			−0.229339	+	0.973347i	$0.573656\pi$
$942$	−301.287	−	301.287i	−0.319838	−	0.319838i
$943$	−190.384	+	190.384i	−0.201891	+	0.201891i
$944$		−	80.0000i		−	0.0847458i
$945$		0			0
$946$	344.808			0.364491
$947$	721.121	+	721.121i	0.761480	+	0.761480i	0.976590	−	0.215110i	$-0.0690110\pi$
$947$	721.121	+	721.121i	0.761480	+	0.761480i	−0.215110	+	0.976590i	$0.569011\pi$
$948$	282.606	−	282.606i	0.298108	−	0.298108i
$949$			952.220i			1.00339i
$950$		0			0
$951$	−815.258			−0.857264
$952$	57.1714	+	57.1714i	0.0600540	+	0.0600540i
$953$	737.291	−	737.291i	0.773652	−	0.773652i	−0.205091	−	0.978743i	$-0.565749\pi$
$953$	737.291	−	737.291i	0.773652	−	0.773652i	0.978743	+	0.205091i	$0.0657489\pi$
$954$			114.545i			0.120068i
$955$		0			0
$956$	309.576			0.323824
$957$	−435.959	−	435.959i	−0.455548	−	0.455548i
$958$	−71.2735	+	71.2735i	−0.0743982	+	0.0743982i
$959$			46.5653i			0.0485561i
$960$		0			0
$961$	606.837			0.631464
$962$	691.090	+	691.090i	0.718389	+	0.718389i
$963$	−45.3031	+	45.3031i	−0.0470437	+	0.0470437i
$964$		−	843.878i		−	0.875392i
$965$		0			0
$966$	47.1102			0.0487683
$967$	−958.879	−	958.879i	−0.991601	−	0.991601i	0.00836361	−	0.999965i	$-0.497338\pi$
$967$	−958.879	−	958.879i	−0.991601	−	0.991601i	−0.999965	+	0.00836361i	$0.997338\pi$
$968$	138.767	−	138.767i	0.143355	−	0.143355i
$969$			1004.69i			1.03683i
$970$		0			0
$971$	−1507.86			−1.55289			−0.776444	−	0.630186i	$-0.782979\pi$
$971$	−1507.86			−1.55289			−0.776444	+	0.630186i	$0.782979\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−48.7265	+	48.7265i	−0.0500786	+	0.0500786i
$974$			590.847i			0.606619i
$975$		0			0
$976$	−60.7673			−0.0622616
$977$	373.838	+	373.838i	0.382638	+	0.382638i	0.872052	−	0.489413i	$-0.162789\pi$
$977$	373.838	+	373.838i	0.382638	+	0.382638i	−0.489413	+	0.872052i	$0.662789\pi$
$978$	155.555	−	155.555i	0.159054	−	0.159054i
$979$		−	1619.80i		−	1.65454i
$980$		0			0
$981$	−390.000			−0.397554
$982$	910.080	+	910.080i	0.926761	+	0.926761i
$983$	1319.46	−	1319.46i	1.34228	−	1.34228i	0.448501	−	0.893783i	$-0.351958\pi$
$983$	1319.46	−	1319.46i	1.34228	−	1.34228i	0.893783	−	0.448501i	$-0.148042\pi$
$984$			87.1918i			0.0886096i
$985$		0			0
$986$	820.322			0.831970
$987$	−20.4857	−	20.4857i	−0.0207555	−	0.0207555i
$988$	660.322	−	660.322i	0.668343	−	0.668343i
$989$			267.314i			0.270287i
$990$		0			0
$991$	−315.029			−0.317890			−0.158945	−	0.987287i	$-0.550809\pi$
$991$	−315.029			−0.317890			−0.158945	+	0.987287i	$0.550809\pi$
$992$	−158.384	−	158.384i	−0.159661	−	0.159661i
$993$	−257.171	+	257.171i	−0.258984	+	0.258984i
$994$			11.1510i			0.0112183i
$995$		0			0
$996$	403.151			0.404770
$997$	−1009.38	−	1009.38i	−1.01242	−	1.01242i	−0.999922	−	0.0124991i	$-0.996021\pi$
$997$	−1009.38	−	1009.38i	−1.01242	−	1.01242i	−0.0124991	−	0.999922i	$-0.503979\pi$
$998$	−970.161	+	970.161i	−0.972105	+	0.972105i
$999$			198.409i			0.198607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.f.b.7.1		4
3.2	odd	2		450.3.g.j.307.1		4
4.3	odd	2		1200.3.bg.d.1057.2		4
5.2	odd	4		30.3.f.a.13.2	yes	4
5.3	odd	4	inner	150.3.f.b.43.1		4
5.4	even	2		30.3.f.a.7.2	✓	4
15.2	even	4		90.3.g.d.73.2		4
15.8	even	4		450.3.g.j.343.1		4
15.14	odd	2		90.3.g.d.37.2		4
20.3	even	4		1200.3.bg.d.193.2		4
20.7	even	4		240.3.bg.b.193.1		4
20.19	odd	2		240.3.bg.b.97.1		4
40.19	odd	2		960.3.bg.g.577.2		4
40.27	even	4		960.3.bg.g.193.2		4
40.29	even	2		960.3.bg.e.577.1		4
40.37	odd	4		960.3.bg.e.193.1		4
60.47	odd	4		720.3.bh.i.433.2		4
60.59	even	2		720.3.bh.i.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.2	✓	4	5.4	even	2
30.3.f.a.13.2	yes	4	5.2	odd	4
90.3.g.d.37.2		4	15.14	odd	2
90.3.g.d.73.2		4	15.2	even	4
150.3.f.b.7.1		4	1.1	even	1	trivial
150.3.f.b.43.1		4	5.3	odd	4	inner
240.3.bg.b.97.1		4	20.19	odd	2
240.3.bg.b.193.1		4	20.7	even	4
450.3.g.j.307.1		4	3.2	odd	2
450.3.g.j.343.1		4	15.8	even	4
720.3.bh.i.433.2		4	60.47	odd	4
720.3.bh.i.577.2		4	60.59	even	2
960.3.bg.e.193.1		4	40.37	odd	4
960.3.bg.e.577.1		4	40.29	even	2
960.3.bg.g.193.2		4	40.27	even	4
960.3.bg.g.577.2		4	40.19	odd	2
1200.3.bg.d.193.2		4	20.3	even	4
1200.3.bg.d.1057.2		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-0.898979 - 0.898979i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-0.898979 - 0.898979i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} -13.7980 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-12.7980 + 12.7980i) q^{13} +1.79796i q^{14} -4.00000 q^{16} +(-15.8990 - 15.8990i) q^{17} +(-3.00000 + 3.00000i) q^{18} +25.7980i q^{19} +2.20204 q^{21} +(13.7980 + 13.7980i) q^{22} +(-10.6969 + 10.6969i) q^{23} +4.89898i q^{24} +25.5959 q^{26} +(3.67423 + 3.67423i) q^{27} +(1.79796 - 1.79796i) q^{28} -25.7980i q^{29} -39.5959 q^{31} +(4.00000 + 4.00000i) q^{32} +(16.8990 - 16.8990i) q^{33} +31.7980i q^{34} +6.00000 q^{36} +(27.0000 + 27.0000i) q^{37} +(25.7980 - 25.7980i) q^{38} -31.3485i q^{39} +17.7980 q^{41} +(-2.20204 - 2.20204i) q^{42} +(12.4949 - 12.4949i) q^{43} -27.5959i q^{44} +21.3939 q^{46} +(-9.30306 - 9.30306i) q^{47} +(4.89898 - 4.89898i) q^{48} -47.3837i q^{49} +38.9444 q^{51} +(-25.5959 - 25.5959i) q^{52} +(19.0908 - 19.0908i) q^{53} -7.34847i q^{54} -3.59592 q^{56} +(-31.5959 - 31.5959i) q^{57} +(-25.7980 + 25.7980i) q^{58} +20.0000i q^{59} +15.1918 q^{61} +(39.5959 + 39.5959i) q^{62} +(-2.69694 + 2.69694i) q^{63} -8.00000i q^{64} -33.7980 q^{66} +(48.0908 + 48.0908i) q^{67} +(31.7980 - 31.7980i) q^{68} -26.2020i q^{69} +6.20204 q^{71} +(-6.00000 - 6.00000i) q^{72} +(37.2020 - 37.2020i) q^{73} -54.0000i q^{74} -51.5959 q^{76} +(12.4041 + 12.4041i) q^{77} +(-31.3485 + 31.3485i) q^{78} +115.373i q^{79} -9.00000 q^{81} +(-17.7980 - 17.7980i) q^{82} +(-82.2929 + 82.2929i) q^{83} +4.40408i q^{84} -24.9898 q^{86} +(31.5959 + 31.5959i) q^{87} +(-27.5959 + 27.5959i) q^{88} +117.394i q^{89} +23.0102 q^{91} +(-21.3939 - 21.3939i) q^{92} +(48.4949 - 48.4949i) q^{93} +18.6061i q^{94} -9.79796 q^{96} +(-81.9898 - 81.9898i) q^{97} +(-47.3837 + 47.3837i) q^{98} +41.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8	\( 4 q - 4 q^{2} + 16 q^{7} + 8 q^{8} - 16 q^{11} - 12 q^{13} - 16 q^{16} - 44 q^{17} - 12 q^{18} + 48 q^{21} + 16 q^{22} + 16 q^{23} + 24 q^{26} - 32 q^{28} - 80 q^{31} + 16 q^{32} + 48 q^{33} + 24 q^{36} + 108 q^{37} + 64 q^{38} + 32 q^{41} - 48 q^{42} - 48 q^{43} - 32 q^{46} - 96 q^{47} + 48 q^{51} - 24 q^{52} - 100 q^{53} + 64 q^{56} - 48 q^{57} - 64 q^{58} - 96 q^{61} + 80 q^{62} + 48 q^{63} - 96 q^{66} + 16 q^{67} + 88 q^{68} + 64 q^{71} - 24 q^{72} + 188 q^{73} - 128 q^{76} + 128 q^{77} - 96 q^{78} - 36 q^{81} - 32 q^{82} - 192 q^{83} + 96 q^{86} + 48 q^{87} - 32 q^{88} + 288 q^{91} + 32 q^{92} + 96 q^{93} - 132 q^{97} + 124 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 16 * q^7 + 8 * q^8 - 16 * q^11 - 12 * q^13 - 16 * q^16 - 44 * q^17 - 12 * q^18 + 48 * q^21 + 16 * q^22 + 16 * q^23 + 24 * q^26 - 32 * q^28 - 80 * q^31 + 16 * q^32 + 48 * q^33 + 24 * q^36 + 108 * q^37 + 64 * q^38 + 32 * q^41 - 48 * q^42 - 48 * q^43 - 32 * q^46 - 96 * q^47 + 48 * q^51 - 24 * q^52 - 100 * q^53 + 64 * q^56 - 48 * q^57 - 64 * q^58 - 96 * q^61 + 80 * q^62 + 48 * q^63 - 96 * q^66 + 16 * q^67 + 88 * q^68 + 64 * q^71 - 24 * q^72 + 188 * q^73 - 128 * q^76 + 128 * q^77 - 96 * q^78 - 36 * q^81 - 32 * q^82 - 192 * q^83 + 96 * q^86 + 48 * q^87 - 32 * q^88 + 288 * q^91 + 32 * q^92 + 96 * q^93 - 132 * q^97 + 124 * q^98

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