LMFDB - Embedded newform 300.3.c.a.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.c (of order $2$, degree $1$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.a.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +1.73205i q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 - 1.73205i) q^{6} +10.3923i q^{7} +8.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +1.73205i q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 - 1.73205i) q^{6} +10.3923i q^{7} +8.00000 q^{8} -3.00000 q^{9} -10.3923i q^{11} +(-6.00000 - 3.46410i) q^{12} -18.0000 q^{13} +(18.0000 - 10.3923i) q^{14} +(-8.00000 - 13.8564i) q^{16} -10.0000 q^{17} +(3.00000 + 5.19615i) q^{18} -13.8564i q^{19} -18.0000 q^{21} +(-18.0000 + 10.3923i) q^{22} +6.92820i q^{23} +13.8564i q^{24} +(18.0000 + 31.1769i) q^{26} -5.19615i q^{27} +(-36.0000 - 20.7846i) q^{28} -36.0000 q^{29} +6.92820i q^{31} +(-16.0000 + 27.7128i) q^{32} +18.0000 q^{33} +(10.0000 + 17.3205i) q^{34} +(6.00000 - 10.3923i) q^{36} -54.0000 q^{37} +(-24.0000 + 13.8564i) q^{38} -31.1769i q^{39} +18.0000 q^{41} +(18.0000 + 31.1769i) q^{42} +20.7846i q^{43} +(36.0000 + 20.7846i) q^{44} +(12.0000 - 6.92820i) q^{46} +(24.0000 - 13.8564i) q^{48} -59.0000 q^{49} -17.3205i q^{51} +(36.0000 - 62.3538i) q^{52} +26.0000 q^{53} +(-9.00000 + 5.19615i) q^{54} +83.1384i q^{56} +24.0000 q^{57} +(36.0000 + 62.3538i) q^{58} +31.1769i q^{59} -74.0000 q^{61} +(12.0000 - 6.92820i) q^{62} -31.1769i q^{63} +64.0000 q^{64} +(-18.0000 - 31.1769i) q^{66} +41.5692i q^{67} +(20.0000 - 34.6410i) q^{68} -12.0000 q^{69} +103.923i q^{71} -24.0000 q^{72} -36.0000 q^{73} +(54.0000 + 93.5307i) q^{74} +(48.0000 + 27.7128i) q^{76} +108.000 q^{77} +(-54.0000 + 31.1769i) q^{78} -90.0666i q^{79} +9.00000 q^{81} +(-18.0000 - 31.1769i) q^{82} -90.0666i q^{83} +(36.0000 - 62.3538i) q^{84} +(36.0000 - 20.7846i) q^{86} -62.3538i q^{87} -83.1384i q^{88} -18.0000 q^{89} -187.061i q^{91} +(-24.0000 - 13.8564i) q^{92} -12.0000 q^{93} +(-48.0000 - 27.7128i) q^{96} +72.0000 q^{97} +(59.0000 + 102.191i) q^{98} +31.1769i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 6 q^{6} + 16 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^6 + 16 * q^8 - 6 * q^9	$ 2 q - 2 q^{2} - 4 q^{4} + 6 q^{6} + 16 q^{8} - 6 q^{9} - 12 q^{12} - 36 q^{13} + 36 q^{14} - 16 q^{16} - 20 q^{17} + 6 q^{18} - 36 q^{21} - 36 q^{22} + 36 q^{26} - 72 q^{28} - 72 q^{29} - 32 q^{32} + 36 q^{33} + 20 q^{34} + 12 q^{36} - 108 q^{37} - 48 q^{38} + 36 q^{41} + 36 q^{42} + 72 q^{44} + 24 q^{46} + 48 q^{48} - 118 q^{49} + 72 q^{52} + 52 q^{53} - 18 q^{54} + 48 q^{57} + 72 q^{58} - 148 q^{61} + 24 q^{62} + 128 q^{64} - 36 q^{66} + 40 q^{68} - 24 q^{69} - 48 q^{72} - 72 q^{73} + 108 q^{74} + 96 q^{76} + 216 q^{77} - 108 q^{78} + 18 q^{81} - 36 q^{82} + 72 q^{84} + 72 q^{86} - 36 q^{89} - 48 q^{92} - 24 q^{93} - 96 q^{96} + 144 q^{97} + 118 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^6 + 16 * q^8 - 6 * q^9 - 12 * q^12 - 36 * q^13 + 36 * q^14 - 16 * q^16 - 20 * q^17 + 6 * q^18 - 36 * q^21 - 36 * q^22 + 36 * q^26 - 72 * q^28 - 72 * q^29 - 32 * q^32 + 36 * q^33 + 20 * q^34 + 12 * q^36 - 108 * q^37 - 48 * q^38 + 36 * q^41 + 36 * q^42 + 72 * q^44 + 24 * q^46 + 48 * q^48 - 118 * q^49 + 72 * q^52 + 52 * q^53 - 18 * q^54 + 48 * q^57 + 72 * q^58 - 148 * q^61 + 24 * q^62 + 128 * q^64 - 36 * q^66 + 40 * q^68 - 24 * q^69 - 48 * q^72 - 72 * q^73 + 108 * q^74 + 96 * q^76 + 216 * q^77 - 108 * q^78 + 18 * q^81 - 36 * q^82 + 72 * q^84 + 72 * q^86 - 36 * q^89 - 48 * q^92 - 24 * q^93 - 96 * q^96 + 144 * q^97 + 118 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$	3.00000	−	1.73205i	0.500000	−	0.288675i
$7$			10.3923i			1.48461i	0.670059	+	0.742307i	$0.266269\pi$
$7$			10.3923i			1.48461i	−0.670059	+	0.742307i	$0.733731\pi$
$8$	8.00000			1.00000
$9$	−3.00000			−0.333333
$10$		0			0
$11$		−	10.3923i		−	0.944755i	−0.881396	−	0.472377i	$-0.843396\pi$
$11$		−	10.3923i		−	0.944755i	0.881396	−	0.472377i	$-0.156604\pi$
$12$	−6.00000	−	3.46410i	−0.500000	−	0.288675i
$13$	−18.0000			−1.38462			−0.692308	−	0.721602i	$-0.743406\pi$
$13$	−18.0000			−1.38462			−0.692308	+	0.721602i	$0.743406\pi$
$14$	18.0000	−	10.3923i	1.28571	−	0.742307i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	−10.0000			−0.588235			−0.294118	−	0.955769i	$-0.595026\pi$
$17$	−10.0000			−0.588235			−0.294118	+	0.955769i	$0.595026\pi$
$18$	3.00000	+	5.19615i	0.166667	+	0.288675i
$19$		−	13.8564i		−	0.729285i	−0.931148	−	0.364642i	$-0.881191\pi$
$19$		−	13.8564i		−	0.729285i	0.931148	−	0.364642i	$-0.118809\pi$
$20$		0			0
$21$	−18.0000			−0.857143
$22$	−18.0000	+	10.3923i	−0.818182	+	0.472377i
$23$			6.92820i			0.301226i	0.988593	+	0.150613i	$0.0481248\pi$
$23$			6.92820i			0.301226i	−0.988593	+	0.150613i	$0.951875\pi$
$24$			13.8564i			0.577350i
$25$		0			0
$26$	18.0000	+	31.1769i	0.692308	+	1.19911i
$27$		−	5.19615i		−	0.192450i
$28$	−36.0000	−	20.7846i	−1.28571	−	0.742307i
$29$	−36.0000			−1.24138			−0.620690	−	0.784056i	$-0.713147\pi$
$29$	−36.0000			−1.24138			−0.620690	+	0.784056i	$0.713147\pi$
$30$		0			0
$31$			6.92820i			0.223490i	0.993737	+	0.111745i	$0.0356441\pi$
$31$			6.92820i			0.223490i	−0.993737	+	0.111745i	$0.964356\pi$
$32$	−16.0000	+	27.7128i	−0.500000	+	0.866025i
$33$	18.0000			0.545455
$34$	10.0000	+	17.3205i	0.294118	+	0.509427i
$35$		0			0
$36$	6.00000	−	10.3923i	0.166667	−	0.288675i
$37$	−54.0000			−1.45946			−0.729730	−	0.683736i	$-0.760354\pi$
$37$	−54.0000			−1.45946			−0.729730	+	0.683736i	$0.760354\pi$
$38$	−24.0000	+	13.8564i	−0.631579	+	0.364642i
$39$		−	31.1769i		−	0.799408i
$40$		0			0
$41$	18.0000			0.439024			0.219512	−	0.975610i	$-0.429553\pi$
$41$	18.0000			0.439024			0.219512	+	0.975610i	$0.429553\pi$
$42$	18.0000	+	31.1769i	0.428571	+	0.742307i
$43$			20.7846i			0.483363i	0.970356	+	0.241682i	$0.0776989\pi$
$43$			20.7846i			0.483363i	−0.970356	+	0.241682i	$0.922301\pi$
$44$	36.0000	+	20.7846i	0.818182	+	0.472377i
$45$		0			0
$46$	12.0000	−	6.92820i	0.260870	−	0.150613i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	24.0000	−	13.8564i	0.500000	−	0.288675i
$49$	−59.0000			−1.20408
$50$		0			0
$51$		−	17.3205i		−	0.339618i
$52$	36.0000	−	62.3538i	0.692308	−	1.19911i
$53$	26.0000			0.490566			0.245283	−	0.969452i	$-0.421119\pi$
$53$	26.0000			0.490566			0.245283	+	0.969452i	$0.421119\pi$
$54$	−9.00000	+	5.19615i	−0.166667	+	0.0962250i
$55$		0			0
$56$			83.1384i			1.48461i
$57$	24.0000			0.421053
$58$	36.0000	+	62.3538i	0.620690	+	1.07507i
$59$			31.1769i			0.528422i	0.964465	+	0.264211i	$0.0851116\pi$
$59$			31.1769i			0.528422i	−0.964465	+	0.264211i	$0.914888\pi$
$60$		0			0
$61$	−74.0000			−1.21311			−0.606557	−	0.795040i	$-0.707450\pi$
$61$	−74.0000			−1.21311			−0.606557	+	0.795040i	$0.707450\pi$
$62$	12.0000	−	6.92820i	0.193548	−	0.111745i
$63$		−	31.1769i		−	0.494872i
$64$	64.0000			1.00000
$65$		0			0
$66$	−18.0000	−	31.1769i	−0.272727	−	0.472377i
$67$			41.5692i			0.620436i	0.950665	+	0.310218i	$0.100402\pi$
$67$			41.5692i			0.620436i	−0.950665	+	0.310218i	$0.899598\pi$
$68$	20.0000	−	34.6410i	0.294118	−	0.509427i
$69$	−12.0000			−0.173913
$70$		0			0
$71$			103.923i			1.46370i	0.681463	+	0.731852i	$0.261344\pi$
$71$			103.923i			1.46370i	−0.681463	+	0.731852i	$0.738656\pi$
$72$	−24.0000			−0.333333
$73$	−36.0000			−0.493151			−0.246575	−	0.969124i	$-0.579305\pi$
$73$	−36.0000			−0.493151			−0.246575	+	0.969124i	$0.579305\pi$
$74$	54.0000	+	93.5307i	0.729730	+	1.26393i
$75$		0			0
$76$	48.0000	+	27.7128i	0.631579	+	0.364642i
$77$	108.000			1.40260
$78$	−54.0000	+	31.1769i	−0.692308	+	0.399704i
$79$		−	90.0666i		−	1.14008i	−0.821616	−	0.570042i	$-0.806927\pi$
$79$		−	90.0666i		−	1.14008i	0.821616	−	0.570042i	$-0.193073\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−18.0000	−	31.1769i	−0.219512	−	0.380206i
$83$		−	90.0666i		−	1.08514i	−0.840011	−	0.542570i	$-0.817451\pi$
$83$		−	90.0666i		−	1.08514i	0.840011	−	0.542570i	$-0.182549\pi$
$84$	36.0000	−	62.3538i	0.428571	−	0.742307i
$85$		0			0
$86$	36.0000	−	20.7846i	0.418605	−	0.241682i
$87$		−	62.3538i		−	0.716711i
$88$		−	83.1384i		−	0.944755i
$89$	−18.0000			−0.202247			−0.101124	−	0.994874i	$-0.532244\pi$
$89$	−18.0000			−0.202247			−0.101124	+	0.994874i	$0.532244\pi$
$90$		0			0
$91$		−	187.061i		−	2.05562i
$92$	−24.0000	−	13.8564i	−0.260870	−	0.150613i
$93$	−12.0000			−0.129032
$94$		0			0
$95$		0			0
$96$	−48.0000	−	27.7128i	−0.500000	−	0.288675i
$97$	72.0000			0.742268			0.371134	−	0.928579i	$-0.378969\pi$
$97$	72.0000			0.742268			0.371134	+	0.928579i	$0.378969\pi$
$98$	59.0000	+	102.191i	0.602041	+	1.04277i
$99$			31.1769i			0.314918i
$100$		0			0
$101$	36.0000			0.356436			0.178218	−	0.983991i	$-0.442967\pi$
$101$	36.0000			0.356436			0.178218	+	0.983991i	$0.442967\pi$
$102$	−30.0000	+	17.3205i	−0.294118	+	0.169809i
$103$			10.3923i			0.100896i	0.998727	+	0.0504481i	$0.0160649\pi$
$103$			10.3923i			0.100896i	−0.998727	+	0.0504481i	$0.983935\pi$
$104$	−144.000			−1.38462
$105$		0			0
$106$	−26.0000	−	45.0333i	−0.245283	−	0.424843i
$107$		−	187.061i		−	1.74824i	−0.485712	−	0.874119i	$-0.661439\pi$
$107$		−	187.061i		−	1.74824i	0.485712	−	0.874119i	$-0.338561\pi$
$108$	18.0000	+	10.3923i	0.166667	+	0.0962250i
$109$	−26.0000			−0.238532			−0.119266	−	0.992862i	$-0.538054\pi$
$109$	−26.0000			−0.238532			−0.119266	+	0.992862i	$0.538054\pi$
$110$		0			0
$111$		−	93.5307i		−	0.842619i
$112$	144.000	−	83.1384i	1.28571	−	0.742307i
$113$	10.0000			0.0884956			0.0442478	−	0.999021i	$-0.485911\pi$
$113$	10.0000			0.0884956			0.0442478	+	0.999021i	$0.485911\pi$
$114$	−24.0000	−	41.5692i	−0.210526	−	0.364642i
$115$		0			0
$116$	72.0000	−	124.708i	0.620690	−	1.07507i
$117$	54.0000			0.461538
$118$	54.0000	−	31.1769i	0.457627	−	0.264211i
$119$		−	103.923i		−	0.873303i
$120$		0			0
$121$	13.0000			0.107438
$122$	74.0000	+	128.172i	0.606557	+	1.05059i
$123$			31.1769i			0.253471i
$124$	−24.0000	−	13.8564i	−0.193548	−	0.111745i
$125$		0			0
$126$	−54.0000	+	31.1769i	−0.428571	+	0.247436i
$127$			218.238i			1.71841i	0.511629	+	0.859206i	$0.329042\pi$
$127$			218.238i			1.71841i	−0.511629	+	0.859206i	$0.670958\pi$
$128$	−64.0000	−	110.851i	−0.500000	−	0.866025i
$129$	−36.0000			−0.279070
$130$		0			0
$131$			135.100i			1.03130i	0.856800	+	0.515649i	$0.172449\pi$
$131$			135.100i			1.03130i	−0.856800	+	0.515649i	$0.827551\pi$
$132$	−36.0000	+	62.3538i	−0.272727	+	0.472377i
$133$	144.000			1.08271
$134$	72.0000	−	41.5692i	0.537313	−	0.310218i
$135$		0			0
$136$	−80.0000			−0.588235
$137$	−110.000			−0.802920			−0.401460	−	0.915877i	$-0.631497\pi$
$137$	−110.000			−0.802920			−0.401460	+	0.915877i	$0.631497\pi$
$138$	12.0000	+	20.7846i	0.0869565	+	0.150613i
$139$			187.061i			1.34577i	0.739749	+	0.672883i	$0.234944\pi$
$139$			187.061i			1.34577i	−0.739749	+	0.672883i	$0.765056\pi$
$140$		0			0
$141$		0			0
$142$	180.000	−	103.923i	1.26761	−	0.731852i
$143$			187.061i			1.30812i
$144$	24.0000	+	41.5692i	0.166667	+	0.288675i
$145$		0			0
$146$	36.0000	+	62.3538i	0.246575	+	0.427081i
$147$		−	102.191i		−	0.695177i
$148$	108.000	−	187.061i	0.729730	−	1.26393i
$149$	288.000			1.93289			0.966443	−	0.256881i	$-0.0826950\pi$
$149$	288.000			1.93289			0.966443	+	0.256881i	$0.0826950\pi$
$150$		0			0
$151$			187.061i			1.23882i	0.785069	+	0.619409i	$0.212628\pi$
$151$			187.061i			1.23882i	−0.785069	+	0.619409i	$0.787372\pi$
$152$		−	110.851i		−	0.729285i
$153$	30.0000			0.196078
$154$	−108.000	−	187.061i	−0.701299	−	1.21468i
$155$		0			0
$156$	108.000	+	62.3538i	0.692308	+	0.399704i
$157$	−234.000			−1.49045			−0.745223	−	0.666815i	$-0.767657\pi$
$157$	−234.000			−1.49045			−0.745223	+	0.666815i	$0.767657\pi$
$158$	−156.000	+	90.0666i	−0.987342	+	0.570042i
$159$			45.0333i			0.283228i
$160$		0			0
$161$	−72.0000			−0.447205
$162$	−9.00000	−	15.5885i	−0.0555556	−	0.0962250i
$163$			124.708i			0.765078i	0.923939	+	0.382539i	$0.124950\pi$
$163$			124.708i			0.765078i	−0.923939	+	0.382539i	$0.875050\pi$
$164$	−36.0000	+	62.3538i	−0.219512	+	0.380206i
$165$		0			0
$166$	−156.000	+	90.0666i	−0.939759	+	0.542570i
$167$			131.636i			0.788239i	0.919059	+	0.394119i	$0.128950\pi$
$167$			131.636i			0.788239i	−0.919059	+	0.394119i	$0.871050\pi$
$168$	−144.000			−0.857143
$169$	155.000			0.917160
$170$		0			0
$171$			41.5692i			0.243095i
$172$	−72.0000	−	41.5692i	−0.418605	−	0.241682i
$173$	−146.000			−0.843931			−0.421965	−	0.906612i	$-0.638660\pi$
$173$	−146.000			−0.843931			−0.421965	+	0.906612i	$0.638660\pi$
$174$	−108.000	+	62.3538i	−0.620690	+	0.358355i
$175$		0			0
$176$	−144.000	+	83.1384i	−0.818182	+	0.472377i
$177$	−54.0000			−0.305085
$178$	18.0000	+	31.1769i	0.101124	+	0.175151i
$179$			72.7461i			0.406403i	0.979137	+	0.203201i	$0.0651346\pi$
$179$			72.7461i			0.406403i	−0.979137	+	0.203201i	$0.934865\pi$
$180$		0			0
$181$	262.000			1.44751			0.723757	−	0.690055i	$-0.242414\pi$
$181$	262.000			1.44751			0.723757	+	0.690055i	$0.242414\pi$
$182$	−324.000	+	187.061i	−1.78022	+	1.02781i
$183$		−	128.172i		−	0.700392i
$184$			55.4256i			0.301226i
$185$		0			0
$186$	12.0000	+	20.7846i	0.0645161	+	0.111745i
$187$			103.923i			0.555738i
$188$		0			0
$189$	54.0000			0.285714
$190$		0			0
$191$		−	187.061i		−	0.979380i	−0.871897	−	0.489690i	$-0.837110\pi$
$191$		−	187.061i		−	0.979380i	0.871897	−	0.489690i	$-0.162890\pi$
$192$			110.851i			0.577350i
$193$	−180.000			−0.932642			−0.466321	−	0.884615i	$-0.654421\pi$
$193$	−180.000			−0.932642			−0.466321	+	0.884615i	$0.654421\pi$
$194$	−72.0000	−	124.708i	−0.371134	−	0.642823i
$195$		0			0
$196$	118.000	−	204.382i	0.602041	−	1.04277i
$197$	154.000			0.781726			0.390863	−	0.920449i	$-0.372177\pi$
$197$	154.000			0.781726			0.390863	+	0.920449i	$0.372177\pi$
$198$	54.0000	−	31.1769i	0.272727	−	0.157459i
$199$			187.061i			0.940007i	0.882664	+	0.470004i	$0.155747\pi$
$199$			187.061i			0.940007i	−0.882664	+	0.470004i	$0.844253\pi$
$200$		0			0
$201$	−72.0000			−0.358209
$202$	−36.0000	−	62.3538i	−0.178218	−	0.308682i
$203$		−	374.123i		−	1.84297i
$204$	60.0000	+	34.6410i	0.294118	+	0.169809i
$205$		0			0
$206$	18.0000	−	10.3923i	0.0873786	−	0.0504481i
$207$		−	20.7846i		−	0.100409i
$208$	144.000	+	249.415i	0.692308	+	1.19911i
$209$	−144.000			−0.688995
$210$		0			0
$211$			242.487i			1.14923i	0.818425	+	0.574614i	$0.194848\pi$
$211$			242.487i			1.14923i	−0.818425	+	0.574614i	$0.805152\pi$
$212$	−52.0000	+	90.0666i	−0.245283	+	0.424843i
$213$	−180.000			−0.845070
$214$	−324.000	+	187.061i	−1.51402	+	0.874119i
$215$		0			0
$216$		−	41.5692i		−	0.192450i
$217$	−72.0000			−0.331797
$218$	26.0000	+	45.0333i	0.119266	+	0.206575i
$219$		−	62.3538i		−	0.284721i
$220$		0			0
$221$	180.000			0.814480
$222$	−162.000	+	93.5307i	−0.729730	+	0.421310i
$223$			93.5307i			0.419420i	0.977764	+	0.209710i	$0.0672521\pi$
$223$			93.5307i			0.419420i	−0.977764	+	0.209710i	$0.932748\pi$
$224$	−288.000	−	166.277i	−1.28571	−	0.742307i
$225$		0			0
$226$	−10.0000	−	17.3205i	−0.0442478	−	0.0766394i
$227$		−	214.774i		−	0.946142i	−0.881024	−	0.473071i	$-0.843145\pi$
$227$		−	214.774i		−	0.946142i	0.881024	−	0.473071i	$-0.156855\pi$
$228$	−48.0000	+	83.1384i	−0.210526	+	0.364642i
$229$	338.000			1.47598			0.737991	−	0.674810i	$-0.235775\pi$
$229$	338.000			1.47598			0.737991	+	0.674810i	$0.235775\pi$
$230$		0			0
$231$			187.061i			0.809790i
$232$	−288.000			−1.24138
$233$	182.000			0.781116			0.390558	−	0.920578i	$-0.372282\pi$
$233$	182.000			0.781116			0.390558	+	0.920578i	$0.372282\pi$
$234$	−54.0000	−	93.5307i	−0.230769	−	0.399704i
$235$		0			0
$236$	−108.000	−	62.3538i	−0.457627	−	0.264211i
$237$	156.000			0.658228
$238$	−180.000	+	103.923i	−0.756303	+	0.436651i
$239$			353.338i			1.47840i	0.673484	+	0.739202i	$0.264797\pi$
$239$			353.338i			1.47840i	−0.673484	+	0.739202i	$0.735203\pi$
$240$		0			0
$241$	−106.000			−0.439834			−0.219917	−	0.975519i	$-0.570579\pi$
$241$	−106.000			−0.439834			−0.219917	+	0.975519i	$0.570579\pi$
$242$	−13.0000	−	22.5167i	−0.0537190	−	0.0930441i
$243$			15.5885i			0.0641500i
$244$	148.000	−	256.344i	0.606557	−	1.05059i
$245$		0			0
$246$	54.0000	−	31.1769i	0.219512	−	0.126735i
$247$			249.415i			1.00978i
$248$			55.4256i			0.223490i
$249$	156.000			0.626506
$250$		0			0
$251$		−	322.161i		−	1.28351i	−0.766909	−	0.641756i	$-0.778206\pi$
$251$		−	322.161i		−	1.28351i	0.766909	−	0.641756i	$-0.221794\pi$
$252$	108.000	+	62.3538i	0.428571	+	0.247436i
$253$	72.0000			0.284585
$254$	378.000	−	218.238i	1.48819	−	0.859206i
$255$		0			0
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	−14.0000			−0.0544747			−0.0272374	−	0.999629i	$-0.508671\pi$
$257$	−14.0000			−0.0544747			−0.0272374	+	0.999629i	$0.508671\pi$
$258$	36.0000	+	62.3538i	0.139535	+	0.241682i
$259$		−	561.184i		−	2.16674i
$260$		0			0
$261$	108.000			0.413793
$262$	234.000	−	135.100i	0.893130	−	0.515649i
$263$			187.061i			0.711260i	0.934627	+	0.355630i	$0.115734\pi$
$263$			187.061i			0.711260i	−0.934627	+	0.355630i	$0.884266\pi$
$264$	144.000			0.545455
$265$		0			0
$266$	−144.000	−	249.415i	−0.541353	−	0.937652i
$267$		−	31.1769i		−	0.116767i
$268$	−144.000	−	83.1384i	−0.537313	−	0.310218i
$269$	−108.000			−0.401487			−0.200743	−	0.979644i	$-0.564336\pi$
$269$	−108.000			−0.401487			−0.200743	+	0.979644i	$0.564336\pi$
$270$		0			0
$271$		−	325.626i		−	1.20157i	−0.799411	−	0.600785i	$-0.794855\pi$
$271$		−	325.626i		−	1.20157i	0.799411	−	0.600785i	$-0.205145\pi$
$272$	80.0000	+	138.564i	0.294118	+	0.509427i
$273$	324.000			1.18681
$274$	110.000	+	190.526i	0.401460	+	0.695349i
$275$		0			0
$276$	24.0000	−	41.5692i	0.0869565	−	0.150613i
$277$	−270.000			−0.974729			−0.487365	−	0.873199i	$-0.662042\pi$
$277$	−270.000			−0.974729			−0.487365	+	0.873199i	$0.662042\pi$
$278$	324.000	−	187.061i	1.16547	−	0.672883i
$279$		−	20.7846i		−	0.0744968i
$280$		0			0
$281$	−234.000			−0.832740			−0.416370	−	0.909195i	$-0.636698\pi$
$281$	−234.000			−0.832740			−0.416370	+	0.909195i	$0.636698\pi$
$282$		0			0
$283$		−	83.1384i		−	0.293775i	−0.989153	−	0.146888i	$-0.953074\pi$
$283$		−	83.1384i		−	0.293775i	0.989153	−	0.146888i	$-0.0469256\pi$
$284$	−360.000	−	207.846i	−1.26761	−	0.731852i
$285$		0			0
$286$	324.000	−	187.061i	1.13287	−	0.654061i
$287$			187.061i			0.651782i
$288$	48.0000	−	83.1384i	0.166667	−	0.288675i
$289$	−189.000			−0.653979
$290$		0			0
$291$			124.708i			0.428549i
$292$	72.0000	−	124.708i	0.246575	−	0.427081i
$293$	58.0000			0.197952			0.0989761	−	0.995090i	$-0.468443\pi$
$293$	58.0000			0.197952			0.0989761	+	0.995090i	$0.468443\pi$
$294$	−177.000	+	102.191i	−0.602041	+	0.347588i
$295$		0			0
$296$	−432.000			−1.45946
$297$	−54.0000			−0.181818
$298$	−288.000	−	498.831i	−0.966443	−	1.67393i
$299$		−	124.708i		−	0.417082i
$300$		0			0
$301$	−216.000			−0.717608
$302$	324.000	−	187.061i	1.07285	−	0.619409i
$303$			62.3538i			0.205788i
$304$	−192.000	+	110.851i	−0.631579	+	0.364642i
$305$		0			0
$306$	−30.0000	−	51.9615i	−0.0980392	−	0.169809i
$307$		−	270.200i		−	0.880130i	−0.897966	−	0.440065i	$-0.854955\pi$
$307$		−	270.200i		−	0.880130i	0.897966	−	0.440065i	$-0.145045\pi$
$308$	−216.000	+	374.123i	−0.701299	+	1.21468i
$309$	−18.0000			−0.0582524
$310$		0			0
$311$		−	270.200i		−	0.868810i	−0.900718	−	0.434405i	$-0.856959\pi$
$311$		−	270.200i		−	0.868810i	0.900718	−	0.434405i	$-0.143041\pi$
$312$		−	249.415i		−	0.799408i
$313$	−468.000			−1.49521			−0.747604	−	0.664145i	$-0.768796\pi$
$313$	−468.000			−1.49521			−0.747604	+	0.664145i	$0.768796\pi$
$314$	234.000	+	405.300i	0.745223	+	1.29076i
$315$		0			0
$316$	312.000	+	180.133i	0.987342	+	0.570042i
$317$	−250.000			−0.788644			−0.394322	−	0.918972i	$-0.629020\pi$
$317$	−250.000			−0.788644			−0.394322	+	0.918972i	$0.629020\pi$
$318$	78.0000	−	45.0333i	0.245283	−	0.141614i
$319$			374.123i			1.17280i
$320$		0			0
$321$	324.000			1.00935
$322$	72.0000	+	124.708i	0.223602	+	0.387291i
$323$			138.564i			0.428991i
$324$	−18.0000	+	31.1769i	−0.0555556	+	0.0962250i
$325$		0			0
$326$	216.000	−	124.708i	0.662577	−	0.382539i
$327$		−	45.0333i		−	0.137717i
$328$	144.000			0.439024
$329$		0			0
$330$		0			0
$331$			374.123i			1.13028i	0.824995	+	0.565140i	$0.191178\pi$
$331$			374.123i			1.13028i	−0.824995	+	0.565140i	$0.808822\pi$
$332$	312.000	+	180.133i	0.939759	+	0.542570i
$333$	162.000			0.486486
$334$	228.000	−	131.636i	0.682635	−	0.394119i
$335$		0			0
$336$	144.000	+	249.415i	0.428571	+	0.742307i
$337$	468.000			1.38872			0.694362	−	0.719626i	$-0.255687\pi$
$337$	468.000			1.38872			0.694362	+	0.719626i	$0.255687\pi$
$338$	−155.000	−	268.468i	−0.458580	−	0.794284i
$339$			17.3205i			0.0510929i
$340$		0			0
$341$	72.0000			0.211144
$342$	72.0000	−	41.5692i	0.210526	−	0.121547i
$343$		−	103.923i		−	0.302983i
$344$			166.277i			0.483363i
$345$		0			0
$346$	146.000	+	252.879i	0.421965	+	0.730865i
$347$		−	561.184i		−	1.61725i	−0.588327	−	0.808623i	$-0.700213\pi$
$347$		−	561.184i		−	1.61725i	0.588327	−	0.808623i	$-0.299787\pi$
$348$	216.000	+	124.708i	0.620690	+	0.358355i
$349$	−434.000			−1.24355			−0.621777	−	0.783195i	$-0.713589\pi$
$349$	−434.000			−1.24355			−0.621777	+	0.783195i	$0.713589\pi$
$350$		0			0
$351$			93.5307i			0.266469i
$352$	288.000	+	166.277i	0.818182	+	0.472377i
$353$	158.000			0.447592			0.223796	−	0.974636i	$-0.428155\pi$
$353$	158.000			0.447592			0.223796	+	0.974636i	$0.428155\pi$
$354$	54.0000	+	93.5307i	0.152542	+	0.264211i
$355$		0			0
$356$	36.0000	−	62.3538i	0.101124	−	0.175151i
$357$	180.000			0.504202
$358$	126.000	−	72.7461i	0.351955	−	0.203201i
$359$		−	457.261i		−	1.27371i	−0.770984	−	0.636854i	$-0.780235\pi$
$359$		−	457.261i		−	1.27371i	0.770984	−	0.636854i	$-0.219765\pi$
$360$		0			0
$361$	169.000			0.468144
$362$	−262.000	−	453.797i	−0.723757	−	1.25358i
$363$			22.5167i			0.0620294i
$364$	648.000	+	374.123i	1.78022	+	1.02781i
$365$		0			0
$366$	−222.000	+	128.172i	−0.606557	+	0.350196i
$367$			218.238i			0.594655i	0.954776	+	0.297328i	$0.0960953\pi$
$367$			218.238i			0.594655i	−0.954776	+	0.297328i	$0.903905\pi$
$368$	96.0000	−	55.4256i	0.260870	−	0.150613i
$369$	−54.0000			−0.146341
$370$		0			0
$371$			270.200i			0.728302i
$372$	24.0000	−	41.5692i	0.0645161	−	0.111745i
$373$	270.000			0.723861			0.361930	−	0.932205i	$-0.382118\pi$
$373$	270.000			0.723861			0.361930	+	0.932205i	$0.382118\pi$
$374$	180.000	−	103.923i	0.481283	−	0.277869i
$375$		0			0
$376$		0			0
$377$	648.000			1.71883
$378$	−54.0000	−	93.5307i	−0.142857	−	0.247436i
$379$			325.626i			0.859170i	0.903026	+	0.429585i	$0.141340\pi$
$379$			325.626i			0.859170i	−0.903026	+	0.429585i	$0.858660\pi$
$380$		0			0
$381$	−378.000			−0.992126
$382$	−324.000	+	187.061i	−0.848168	+	0.489690i
$383$		−	55.4256i		−	0.144714i	−0.997379	−	0.0723572i	$-0.976948\pi$
$383$		−	55.4256i		−	0.144714i	0.997379	−	0.0723572i	$-0.0230522\pi$
$384$	192.000	−	110.851i	0.500000	−	0.288675i
$385$		0			0
$386$	180.000	+	311.769i	0.466321	+	0.807692i
$387$		−	62.3538i		−	0.161121i
$388$	−144.000	+	249.415i	−0.371134	+	0.642823i
$389$	−288.000			−0.740360			−0.370180	−	0.928960i	$-0.620704\pi$
$389$	−288.000			−0.740360			−0.370180	+	0.928960i	$0.620704\pi$
$390$		0			0
$391$		−	69.2820i		−	0.177192i
$392$	−472.000			−1.20408
$393$	−234.000			−0.595420
$394$	−154.000	−	266.736i	−0.390863	−	0.676994i
$395$		0			0
$396$	−108.000	−	62.3538i	−0.272727	−	0.157459i
$397$	306.000			0.770781			0.385390	−	0.922754i	$-0.374067\pi$
$397$	306.000			0.770781			0.385390	+	0.922754i	$0.374067\pi$
$398$	324.000	−	187.061i	0.814070	−	0.470004i
$399$			249.415i			0.625101i
$400$		0			0
$401$	−450.000			−1.12219			−0.561097	−	0.827750i	$-0.689621\pi$
$401$	−450.000			−1.12219			−0.561097	+	0.827750i	$0.689621\pi$
$402$	72.0000	+	124.708i	0.179104	+	0.310218i
$403$		−	124.708i		−	0.309448i
$404$	−72.0000	+	124.708i	−0.178218	+	0.308682i
$405$		0			0
$406$	−648.000	+	374.123i	−1.59606	+	0.921485i
$407$			561.184i			1.37883i
$408$		−	138.564i		−	0.339618i
$409$	−50.0000			−0.122249			−0.0611247	−	0.998130i	$-0.519469\pi$
$409$	−50.0000			−0.122249			−0.0611247	+	0.998130i	$0.519469\pi$
$410$		0			0
$411$		−	190.526i		−	0.463566i
$412$	−36.0000	−	20.7846i	−0.0873786	−	0.0504481i
$413$	−324.000			−0.784504
$414$	−36.0000	+	20.7846i	−0.0869565	+	0.0502044i
$415$		0			0
$416$	288.000	−	498.831i	0.692308	−	1.19911i
$417$	−324.000			−0.776978
$418$	144.000	+	249.415i	0.344498	+	0.596687i
$419$		−	737.854i		−	1.76099i	−0.474058	−	0.880494i	$-0.657211\pi$
$419$		−	737.854i		−	1.76099i	0.474058	−	0.880494i	$-0.342789\pi$
$420$		0			0
$421$	−286.000			−0.679335			−0.339667	−	0.940546i	$-0.610315\pi$
$421$	−286.000			−0.679335			−0.339667	+	0.940546i	$0.610315\pi$
$422$	420.000	−	242.487i	0.995261	−	0.574614i
$423$		0			0
$424$	208.000			0.490566
$425$		0			0
$426$	180.000	+	311.769i	0.422535	+	0.731852i
$427$		−	769.031i		−	1.80101i
$428$	648.000	+	374.123i	1.51402	+	0.874119i
$429$	−324.000			−0.755245
$430$		0			0
$431$			124.708i			0.289345i	0.989480	+	0.144672i	$0.0462128\pi$
$431$			124.708i			0.289345i	−0.989480	+	0.144672i	$0.953787\pi$
$432$	−72.0000	+	41.5692i	−0.166667	+	0.0962250i
$433$	36.0000			0.0831409			0.0415704	−	0.999136i	$-0.486764\pi$
$433$	36.0000			0.0831409			0.0415704	+	0.999136i	$0.486764\pi$
$434$	72.0000	+	124.708i	0.165899	+	0.287345i
$435$		0			0
$436$	52.0000	−	90.0666i	0.119266	−	0.206575i
$437$	96.0000			0.219680
$438$	−108.000	+	62.3538i	−0.246575	+	0.142360i
$439$		−	782.887i		−	1.78334i	−0.452684	−	0.891671i	$-0.649534\pi$
$439$		−	782.887i		−	1.78334i	0.452684	−	0.891671i	$-0.350466\pi$
$440$		0			0
$441$	177.000			0.401361
$442$	−180.000	−	311.769i	−0.407240	−	0.705360i
$443$		−	214.774i		−	0.484818i	−0.970174	−	0.242409i	$-0.922062\pi$
$443$		−	214.774i		−	0.484818i	0.970174	−	0.242409i	$-0.0779376\pi$
$444$	324.000	+	187.061i	0.729730	+	0.421310i
$445$		0			0
$446$	162.000	−	93.5307i	0.363229	−	0.209710i
$447$			498.831i			1.11595i
$448$			665.108i			1.48461i
$449$	54.0000			0.120267			0.0601336	−	0.998190i	$-0.480847\pi$
$449$	54.0000			0.120267			0.0601336	+	0.998190i	$0.480847\pi$
$450$		0			0
$451$		−	187.061i		−	0.414770i
$452$	−20.0000	+	34.6410i	−0.0442478	+	0.0766394i
$453$	−324.000			−0.715232
$454$	−372.000	+	214.774i	−0.819383	+	0.473071i
$455$		0			0
$456$	192.000			0.421053
$457$	−288.000			−0.630197			−0.315098	−	0.949059i	$-0.602038\pi$
$457$	−288.000			−0.630197			−0.315098	+	0.949059i	$0.602038\pi$
$458$	−338.000	−	585.433i	−0.737991	−	1.27824i
$459$			51.9615i			0.113206i
$460$		0			0
$461$	−288.000			−0.624729			−0.312364	−	0.949962i	$-0.601121\pi$
$461$	−288.000			−0.624729			−0.312364	+	0.949962i	$0.601121\pi$
$462$	324.000	−	187.061i	0.701299	−	0.404895i
$463$			405.300i			0.875378i	0.899126	+	0.437689i	$0.144203\pi$
$463$			405.300i			0.875378i	−0.899126	+	0.437689i	$0.855797\pi$
$464$	288.000	+	498.831i	0.620690	+	1.07507i
$465$		0			0
$466$	−182.000	−	315.233i	−0.390558	−	0.676466i
$467$			575.041i			1.23135i	0.788000	+	0.615675i	$0.211117\pi$
$467$			575.041i			1.23135i	−0.788000	+	0.615675i	$0.788883\pi$
$468$	−108.000	+	187.061i	−0.230769	+	0.399704i
$469$	−432.000			−0.921109
$470$		0			0
$471$		−	405.300i		−	0.860509i
$472$			249.415i			0.528422i
$473$	216.000			0.456660
$474$	−156.000	−	270.200i	−0.329114	−	0.570042i
$475$		0			0
$476$	360.000	+	207.846i	0.756303	+	0.436651i
$477$	−78.0000			−0.163522
$478$	612.000	−	353.338i	1.28033	−	0.739202i
$479$			145.492i			0.303742i	0.988400	+	0.151871i	$0.0485298\pi$
$479$			145.492i			0.303742i	−0.988400	+	0.151871i	$0.951470\pi$
$480$		0			0
$481$	972.000			2.02079
$482$	106.000	+	183.597i	0.219917	+	0.380907i
$483$		−	124.708i		−	0.258194i
$484$	−26.0000	+	45.0333i	−0.0537190	+	0.0930441i
$485$		0			0
$486$	27.0000	−	15.5885i	0.0555556	−	0.0320750i
$487$		−	259.808i		−	0.533486i	−0.963768	−	0.266743i	$-0.914053\pi$
$487$		−	259.808i		−	0.533486i	0.963768	−	0.266743i	$-0.0859475\pi$
$488$	−592.000			−1.21311
$489$	−216.000			−0.441718
$490$		0			0
$491$		−	72.7461i		−	0.148159i	−0.997252	−	0.0740796i	$-0.976398\pi$
$491$		−	72.7461i		−	0.148159i	0.997252	−	0.0740796i	$-0.0236019\pi$
$492$	−108.000	−	62.3538i	−0.219512	−	0.126735i
$493$	360.000			0.730223
$494$	432.000	−	249.415i	0.874494	−	0.504889i
$495$		0			0
$496$	96.0000	−	55.4256i	0.193548	−	0.111745i
$497$	−1080.00			−2.17304
$498$	−156.000	−	270.200i	−0.313253	−	0.542570i
$499$			443.405i			0.888587i	0.895881	+	0.444294i	$0.146545\pi$
$499$			443.405i			0.888587i	−0.895881	+	0.444294i	$0.853455\pi$
$500$		0			0
$501$	−228.000			−0.455090
$502$	−558.000	+	322.161i	−1.11155	+	0.641756i
$503$			110.851i			0.220380i	0.993911	+	0.110190i	$0.0351460\pi$
$503$			110.851i			0.220380i	−0.993911	+	0.110190i	$0.964854\pi$
$504$		−	249.415i		−	0.494872i
$505$		0			0
$506$	−72.0000	−	124.708i	−0.142292	−	0.246458i
$507$			268.468i			0.529522i
$508$	−756.000	−	436.477i	−1.48819	−	0.859206i
$509$	−252.000			−0.495088			−0.247544	−	0.968877i	$-0.579624\pi$
$509$	−252.000			−0.495088			−0.247544	+	0.968877i	$0.579624\pi$
$510$		0			0
$511$		−	374.123i		−	0.732139i
$512$	512.000			1.00000
$513$	−72.0000			−0.140351
$514$	14.0000	+	24.2487i	0.0272374	+	0.0471765i
$515$		0			0
$516$	72.0000	−	124.708i	0.139535	−	0.241682i
$517$		0			0
$518$	−972.000	+	561.184i	−1.87645	+	1.08337i
$519$		−	252.879i		−	0.487244i
$520$		0			0
$521$	54.0000			0.103647			0.0518234	−	0.998656i	$-0.483497\pi$
$521$	54.0000			0.103647			0.0518234	+	0.998656i	$0.483497\pi$
$522$	−108.000	−	187.061i	−0.206897	−	0.358355i
$523$		−	623.538i		−	1.19223i	−0.802898	−	0.596117i	$-0.796709\pi$
$523$		−	623.538i		−	1.19223i	0.802898	−	0.596117i	$-0.203291\pi$
$524$	−468.000	−	270.200i	−0.893130	−	0.515649i
$525$		0			0
$526$	324.000	−	187.061i	0.615970	−	0.355630i
$527$		−	69.2820i		−	0.131465i
$528$	−144.000	−	249.415i	−0.272727	−	0.472377i
$529$	481.000			0.909263
$530$		0			0
$531$		−	93.5307i		−	0.176141i
$532$	−288.000	+	498.831i	−0.541353	+	0.937652i
$533$	−324.000			−0.607880
$534$	−54.0000	+	31.1769i	−0.101124	+	0.0583837i
$535$		0			0
$536$			332.554i			0.620436i
$537$	−126.000			−0.234637
$538$	108.000	+	187.061i	0.200743	+	0.347698i
$539$			613.146i			1.13756i
$540$		0			0
$541$	−650.000			−1.20148			−0.600739	−	0.799445i	$-0.705127\pi$
$541$	−650.000			−1.20148			−0.600739	+	0.799445i	$0.705127\pi$
$542$	−564.000	+	325.626i	−1.04059	+	0.600785i
$543$			453.797i			0.835722i
$544$	160.000	−	277.128i	0.294118	−	0.509427i
$545$		0			0
$546$	−324.000	−	561.184i	−0.593407	−	1.02781i
$547$		−	685.892i		−	1.25392i	−0.779053	−	0.626958i	$-0.784300\pi$
$547$		−	685.892i		−	1.25392i	0.779053	−	0.626958i	$-0.215700\pi$
$548$	220.000	−	381.051i	0.401460	−	0.695349i
$549$	222.000			0.404372
$550$		0			0
$551$			498.831i			0.905319i
$552$	−96.0000			−0.173913
$553$	936.000			1.69259
$554$	270.000	+	467.654i	0.487365	+	0.844140i
$555$		0			0
$556$	−648.000	−	374.123i	−1.16547	−	0.672883i
$557$	−574.000			−1.03052			−0.515260	−	0.857034i	$-0.672305\pi$
$557$	−574.000			−1.03052			−0.515260	+	0.857034i	$0.672305\pi$
$558$	−36.0000	+	20.7846i	−0.0645161	+	0.0372484i
$559$		−	374.123i		−	0.669272i
$560$		0			0
$561$	−180.000			−0.320856
$562$	234.000	+	405.300i	0.416370	+	0.721174i
$563$			561.184i			0.996775i	0.866954	+	0.498388i	$0.166074\pi$
$563$			561.184i			0.996775i	−0.866954	+	0.498388i	$0.833926\pi$
$564$		0			0
$565$		0			0
$566$	−144.000	+	83.1384i	−0.254417	+	0.146888i
$567$			93.5307i			0.164957i
$568$			831.384i			1.46370i
$569$	198.000			0.347979			0.173989	−	0.984748i	$-0.444334\pi$
$569$	198.000			0.347979			0.173989	+	0.984748i	$0.444334\pi$
$570$		0			0
$571$		−	180.133i		−	0.315470i	−0.987481	−	0.157735i	$-0.949581\pi$
$571$		−	180.133i		−	0.315470i	0.987481	−	0.157735i	$-0.0504192\pi$
$572$	−648.000	−	374.123i	−1.13287	−	0.654061i
$573$	324.000			0.565445
$574$	324.000	−	187.061i	0.564460	−	0.325891i
$575$		0			0
$576$	−192.000			−0.333333
$577$	504.000			0.873484			0.436742	−	0.899587i	$-0.356132\pi$
$577$	504.000			0.873484			0.436742	+	0.899587i	$0.356132\pi$
$578$	189.000	+	327.358i	0.326990	+	0.566363i
$579$		−	311.769i		−	0.538461i
$580$		0			0
$581$	936.000			1.61102
$582$	216.000	−	124.708i	0.371134	−	0.214274i
$583$		−	270.200i		−	0.463465i
$584$	−288.000			−0.493151
$585$		0			0
$586$	−58.0000	−	100.459i	−0.0989761	−	0.171432i
$587$		−	408.764i		−	0.696361i	−0.937427	−	0.348181i	$-0.886800\pi$
$587$		−	408.764i		−	0.696361i	0.937427	−	0.348181i	$-0.113200\pi$
$588$	354.000	+	204.382i	0.602041	+	0.347588i
$589$	96.0000			0.162988
$590$		0			0
$591$			266.736i			0.451330i
$592$	432.000	+	748.246i	0.729730	+	1.26393i
$593$	−998.000			−1.68297			−0.841484	−	0.540282i	$-0.818318\pi$
$593$	−998.000			−1.68297			−0.841484	+	0.540282i	$0.818318\pi$
$594$	54.0000	+	93.5307i	0.0909091	+	0.157459i
$595$		0			0
$596$	−576.000	+	997.661i	−0.966443	+	1.67393i
$597$	−324.000			−0.542714
$598$	−216.000	+	124.708i	−0.361204	+	0.208541i
$599$			540.400i			0.902170i	0.892481	+	0.451085i	$0.148963\pi$
$599$			540.400i			0.902170i	−0.892481	+	0.451085i	$0.851037\pi$
$600$		0			0
$601$	−614.000			−1.02163			−0.510815	−	0.859690i	$-0.670656\pi$
$601$	−614.000			−1.02163			−0.510815	+	0.859690i	$0.670656\pi$
$602$	216.000	+	374.123i	0.358804	+	0.621467i
$603$		−	124.708i		−	0.206812i
$604$	−648.000	−	374.123i	−1.07285	−	0.619409i
$605$		0			0
$606$	108.000	−	62.3538i	0.178218	−	0.102894i
$607$			654.715i			1.07861i	0.842111	+	0.539304i	$0.181313\pi$
$607$			654.715i			1.07861i	−0.842111	+	0.539304i	$0.818687\pi$
$608$	384.000	+	221.703i	0.631579	+	0.364642i
$609$	648.000			1.06404
$610$		0			0
$611$		0			0
$612$	−60.0000	+	103.923i	−0.0980392	+	0.169809i
$613$	−414.000			−0.675367			−0.337684	−	0.941260i	$-0.609643\pi$
$613$	−414.000			−0.675367			−0.337684	+	0.941260i	$0.609643\pi$
$614$	−468.000	+	270.200i	−0.762215	+	0.440065i
$615$		0			0
$616$	864.000			1.40260
$617$	−58.0000			−0.0940032			−0.0470016	−	0.998895i	$-0.514967\pi$
$617$	−58.0000			−0.0940032			−0.0470016	+	0.998895i	$0.514967\pi$
$618$	18.0000	+	31.1769i	0.0291262	+	0.0504481i
$619$		−	187.061i		−	0.302199i	−0.988519	−	0.151100i	$-0.951719\pi$
$619$		−	187.061i		−	0.302199i	0.988519	−	0.151100i	$-0.0482815\pi$
$620$		0			0
$621$	36.0000			0.0579710
$622$	−468.000	+	270.200i	−0.752412	+	0.434405i
$623$		−	187.061i		−	0.300259i
$624$	−432.000	+	249.415i	−0.692308	+	0.399704i
$625$		0			0
$626$	468.000	+	810.600i	0.747604	+	1.29489i
$627$		−	249.415i		−	0.397792i
$628$	468.000	−	810.600i	0.745223	−	1.29076i
$629$	540.000			0.858506
$630$		0			0
$631$			824.456i			1.30659i	0.757105	+	0.653293i	$0.226613\pi$
$631$			824.456i			1.30659i	−0.757105	+	0.653293i	$0.773387\pi$
$632$		−	720.533i		−	1.14008i
$633$	−420.000			−0.663507
$634$	250.000	+	433.013i	0.394322	+	0.682985i
$635$		0			0
$636$	−156.000	−	90.0666i	−0.245283	−	0.141614i
$637$	1062.00			1.66719
$638$	648.000	−	374.123i	1.01567	−	0.586400i
$639$		−	311.769i		−	0.487902i
$640$		0			0
$641$	810.000			1.26365			0.631825	−	0.775111i	$-0.282306\pi$
$641$	810.000			1.26365			0.631825	+	0.775111i	$0.282306\pi$
$642$	−324.000	−	561.184i	−0.504673	−	0.874119i
$643$		−	415.692i		−	0.646489i	−0.946316	−	0.323244i	$-0.895226\pi$
$643$		−	415.692i		−	0.646489i	0.946316	−	0.323244i	$-0.104774\pi$
$644$	144.000	−	249.415i	0.223602	−	0.387291i
$645$		0			0
$646$	240.000	−	138.564i	0.371517	−	0.214495i
$647$			983.805i			1.52056i	0.649593	+	0.760282i	$0.274939\pi$
$647$			983.805i			1.52056i	−0.649593	+	0.760282i	$0.725061\pi$
$648$	72.0000			0.111111
$649$	324.000			0.499230
$650$		0			0
$651$		−	124.708i		−	0.191563i
$652$	−432.000	−	249.415i	−0.662577	−	0.382539i
$653$	950.000			1.45482			0.727412	−	0.686201i	$-0.240723\pi$
$653$	950.000			1.45482			0.727412	+	0.686201i	$0.240723\pi$
$654$	−78.0000	+	45.0333i	−0.119266	+	0.0688583i
$655$		0			0
$656$	−144.000	−	249.415i	−0.219512	−	0.380206i
$657$	108.000			0.164384
$658$		0			0
$659$			1132.76i			1.71891i	0.511212	+	0.859455i	$0.329197\pi$
$659$			1132.76i			1.71891i	−0.511212	+	0.859455i	$0.670803\pi$
$660$		0			0
$661$	−242.000			−0.366112			−0.183056	−	0.983102i	$-0.558599\pi$
$661$	−242.000			−0.366112			−0.183056	+	0.983102i	$0.558599\pi$
$662$	648.000	−	374.123i	0.978852	−	0.565140i
$663$			311.769i			0.470240i
$664$		−	720.533i		−	1.08514i
$665$		0			0
$666$	−162.000	−	280.592i	−0.243243	−	0.421310i
$667$		−	249.415i		−	0.373936i
$668$	−456.000	−	263.272i	−0.682635	−	0.394119i
$669$	−162.000			−0.242152
$670$		0			0
$671$			769.031i			1.14610i
$672$	288.000	−	498.831i	0.428571	−	0.742307i
$673$	−324.000			−0.481426			−0.240713	−	0.970596i	$-0.577381\pi$
$673$	−324.000			−0.481426			−0.240713	+	0.970596i	$0.577381\pi$
$674$	−468.000	−	810.600i	−0.694362	−	1.20267i
$675$		0			0
$676$	−310.000	+	536.936i	−0.458580	+	0.794284i
$677$	806.000			1.19055			0.595273	−	0.803523i	$-0.297044\pi$
$677$	806.000			1.19055			0.595273	+	0.803523i	$0.297044\pi$
$678$	30.0000	−	17.3205i	0.0442478	−	0.0255465i
$679$			748.246i			1.10198i
$680$		0			0
$681$	372.000			0.546256
$682$	−72.0000	−	124.708i	−0.105572	−	0.182856i
$683$			575.041i			0.841934i	0.907076	+	0.420967i	$0.138309\pi$
$683$			575.041i			0.841934i	−0.907076	+	0.420967i	$0.861691\pi$
$684$	−144.000	−	83.1384i	−0.210526	−	0.121547i
$685$		0			0
$686$	−180.000	+	103.923i	−0.262391	+	0.151491i
$687$			585.433i			0.852159i
$688$	288.000	−	166.277i	0.418605	−	0.241682i
$689$	−468.000			−0.679245
$690$		0			0
$691$		−	775.959i		−	1.12295i	−0.827494	−	0.561475i	$-0.810234\pi$
$691$		−	775.959i		−	1.12295i	0.827494	−	0.561475i	$-0.189766\pi$
$692$	292.000	−	505.759i	0.421965	−	0.730865i
$693$	−324.000			−0.467532
$694$	−972.000	+	561.184i	−1.40058	+	0.808623i
$695$		0			0
$696$		−	498.831i		−	0.716711i
$697$	−180.000			−0.258250
$698$	434.000	+	751.710i	0.621777	+	1.07695i
$699$			315.233i			0.450977i
$700$		0			0
$701$	756.000			1.07846			0.539230	−	0.842159i	$-0.318715\pi$
$701$	756.000			1.07846			0.539230	+	0.842159i	$0.318715\pi$
$702$	162.000	−	93.5307i	0.230769	−	0.133235i
$703$			748.246i			1.06436i
$704$		−	665.108i		−	0.944755i
$705$		0			0
$706$	−158.000	−	273.664i	−0.223796	−	0.387626i
$707$			374.123i			0.529170i
$708$	108.000	−	187.061i	0.152542	−	0.264211i
$709$	−310.000			−0.437236			−0.218618	−	0.975811i	$-0.570155\pi$
$709$	−310.000			−0.437236			−0.218618	+	0.975811i	$0.570155\pi$
$710$		0			0
$711$			270.200i			0.380028i
$712$	−144.000			−0.202247
$713$	−48.0000			−0.0673212
$714$	−180.000	−	311.769i	−0.252101	−	0.436651i
$715$		0			0
$716$	−252.000	−	145.492i	−0.351955	−	0.203201i
$717$	−612.000			−0.853556
$718$	−792.000	+	457.261i	−1.10306	+	0.636854i
$719$		−	83.1384i		−	0.115631i	−0.998327	−	0.0578153i	$-0.981587\pi$
$719$		−	83.1384i		−	0.115631i	0.998327	−	0.0578153i	$-0.0184135\pi$
$720$		0			0
$721$	−108.000			−0.149792
$722$	−169.000	−	292.717i	−0.234072	−	0.405425i
$723$		−	183.597i		−	0.253938i
$724$	−524.000	+	907.595i	−0.723757	+	1.25358i
$725$		0			0
$726$	39.0000	−	22.5167i	0.0537190	−	0.0310147i
$727$		−	1091.19i		−	1.50095i	−0.660898	−	0.750476i	$-0.729824\pi$
$727$		−	1091.19i		−	1.50095i	0.660898	−	0.750476i	$-0.270176\pi$
$728$		−	1496.49i		−	2.05562i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	207.846i		−	0.284331i
$732$	444.000	+	256.344i	0.606557	+	0.350196i
$733$	−1206.00			−1.64529			−0.822647	−	0.568553i	$-0.807503\pi$
$733$	−1206.00			−1.64529			−0.822647	+	0.568553i	$0.807503\pi$
$734$	378.000	−	218.238i	0.514986	−	0.297328i
$735$		0			0
$736$	−192.000	−	110.851i	−0.260870	−	0.150613i
$737$	432.000			0.586160
$738$	54.0000	+	93.5307i	0.0731707	+	0.126735i
$739$		−	484.974i		−	0.656257i	−0.944633	−	0.328129i	$-0.893582\pi$
$739$		−	484.974i		−	0.656257i	0.944633	−	0.328129i	$-0.106418\pi$
$740$		0			0
$741$	−432.000			−0.582996
$742$	468.000	−	270.200i	0.630728	−	0.364151i
$743$		−	1122.37i		−	1.51059i	−0.655385	−	0.755295i	$-0.727493\pi$
$743$		−	1122.37i		−	1.51059i	0.655385	−	0.755295i	$-0.272507\pi$
$744$	−96.0000			−0.129032
$745$		0			0
$746$	−270.000	−	467.654i	−0.361930	−	0.626882i
$747$			270.200i			0.361713i
$748$	−360.000	−	207.846i	−0.481283	−	0.277869i
$749$	1944.00			2.59546
$750$		0			0
$751$			242.487i			0.322886i	0.986882	+	0.161443i	$0.0516147\pi$
$751$			242.487i			0.322886i	−0.986882	+	0.161443i	$0.948385\pi$
$752$		0			0
$753$	558.000			0.741036
$754$	−648.000	−	1122.37i	−0.859416	−	1.48855i
$755$		0			0
$756$	−108.000	+	187.061i	−0.142857	+	0.247436i
$757$	−846.000			−1.11757			−0.558785	−	0.829313i	$-0.688732\pi$
$757$	−846.000			−1.11757			−0.558785	+	0.829313i	$0.688732\pi$
$758$	564.000	−	325.626i	0.744063	−	0.429585i
$759$			124.708i			0.164305i
$760$		0			0
$761$	−1458.00			−1.91590			−0.957950	−	0.286935i	$-0.907364\pi$
$761$	−1458.00			−1.91590			−0.957950	+	0.286935i	$0.907364\pi$
$762$	378.000	+	654.715i	0.496063	+	0.859206i
$763$		−	270.200i		−	0.354128i
$764$	648.000	+	374.123i	0.848168	+	0.489690i
$765$		0			0
$766$	−96.0000	+	55.4256i	−0.125326	+	0.0723572i
$767$		−	561.184i		−	0.731662i
$768$	−384.000	−	221.703i	−0.500000	−	0.288675i
$769$	1282.00			1.66710			0.833550	−	0.552444i	$-0.186305\pi$
$769$	1282.00			1.66710			0.833550	+	0.552444i	$0.186305\pi$
$770$		0			0
$771$		−	24.2487i		−	0.0314510i
$772$	360.000	−	623.538i	0.466321	−	0.807692i
$773$	422.000			0.545925			0.272962	−	0.962025i	$-0.411997\pi$
$773$	422.000			0.545925			0.272962	+	0.962025i	$0.411997\pi$
$774$	−108.000	+	62.3538i	−0.139535	+	0.0805605i
$775$		0			0
$776$	576.000			0.742268
$777$	972.000			1.25097
$778$	288.000	+	498.831i	0.370180	+	0.641170i
$779$		−	249.415i		−	0.320174i
$780$		0			0
$781$	1080.00			1.38284
$782$	−120.000	+	69.2820i	−0.153453	+	0.0885959i
$783$			187.061i			0.238904i
$784$	472.000	+	817.528i	0.602041	+	1.04277i
$785$		0			0
$786$	234.000	+	405.300i	0.297710	+	0.515649i
$787$		−	1205.51i		−	1.53178i	−0.642974	−	0.765888i	$-0.722300\pi$
$787$		−	1205.51i		−	1.53178i	0.642974	−	0.765888i	$-0.277700\pi$
$788$	−308.000	+	533.472i	−0.390863	+	0.676994i
$789$	−324.000			−0.410646
$790$		0			0
$791$			103.923i			0.131382i
$792$			249.415i			0.314918i
$793$	1332.00			1.67970
$794$	−306.000	−	530.008i	−0.385390	−	0.667516i
$795$		0			0
$796$	−648.000	−	374.123i	−0.814070	−	0.470004i
$797$	94.0000			0.117942			0.0589711	−	0.998260i	$-0.481218\pi$
$797$	94.0000			0.117942			0.0589711	+	0.998260i	$0.481218\pi$
$798$	432.000	−	249.415i	0.541353	−	0.312551i
$799$		0			0
$800$		0			0
$801$	54.0000			0.0674157
$802$	450.000	+	779.423i	0.561097	+	0.971849i
$803$			374.123i			0.465907i
$804$	144.000	−	249.415i	0.179104	−	0.310218i
$805$		0			0
$806$	−216.000	+	124.708i	−0.267990	+	0.154724i
$807$		−	187.061i		−	0.231799i
$808$	288.000			0.356436
$809$	−270.000			−0.333745			−0.166873	−	0.985978i	$-0.553367\pi$
$809$	−270.000			−0.333745			−0.166873	+	0.985978i	$0.553367\pi$
$810$		0			0
$811$			187.061i			0.230655i	0.993328	+	0.115328i	$0.0367918\pi$
$811$			187.061i			0.230655i	−0.993328	+	0.115328i	$0.963208\pi$
$812$	1296.00	+	748.246i	1.59606	+	0.921485i
$813$	564.000			0.693727
$814$	972.000	−	561.184i	1.19410	−	0.689416i
$815$		0			0
$816$	−240.000	+	138.564i	−0.294118	+	0.169809i
$817$	288.000			0.352509
$818$	50.0000	+	86.6025i	0.0611247	+	0.105871i
$819$			561.184i			0.685207i
$820$		0			0
$821$	1188.00			1.44702			0.723508	−	0.690316i	$-0.242529\pi$
$821$	1188.00			1.44702			0.723508	+	0.690316i	$0.242529\pi$
$822$	−330.000	+	190.526i	−0.401460	+	0.231783i
$823$		−	384.515i		−	0.467212i	−0.972331	−	0.233606i	$-0.924947\pi$
$823$		−	384.515i		−	0.467212i	0.972331	−	0.233606i	$-0.0750525\pi$
$824$			83.1384i			0.100896i
$825$		0			0
$826$	324.000	+	561.184i	0.392252	+	0.679400i
$827$		−	450.333i		−	0.544538i	−0.962221	−	0.272269i	$-0.912226\pi$
$827$		−	450.333i		−	0.544538i	0.962221	−	0.272269i	$-0.0877741\pi$
$828$	72.0000	+	41.5692i	0.0869565	+	0.0502044i
$829$	718.000			0.866104			0.433052	−	0.901369i	$-0.357437\pi$
$829$	718.000			0.866104			0.433052	+	0.901369i	$0.357437\pi$
$830$		0			0
$831$		−	467.654i		−	0.562760i
$832$	−1152.00			−1.38462
$833$	590.000			0.708283
$834$	324.000	+	561.184i	0.388489	+	0.672883i
$835$		0			0
$836$	288.000	−	498.831i	0.344498	−	0.596687i
$837$	36.0000			0.0430108
$838$	−1278.00	+	737.854i	−1.52506	+	0.880494i
$839$		−	914.523i		−	1.09002i	−0.838431	−	0.545008i	$-0.816527\pi$
$839$		−	914.523i		−	1.09002i	0.838431	−	0.545008i	$-0.183473\pi$
$840$		0			0
$841$	455.000			0.541023
$842$	286.000	+	495.367i	0.339667	+	0.588321i
$843$		−	405.300i		−	0.480783i
$844$	−840.000	−	484.974i	−0.995261	−	0.574614i
$845$		0			0
$846$		0			0
$847$			135.100i			0.159504i
$848$	−208.000	−	360.267i	−0.245283	−	0.424843i
$849$	144.000			0.169611
$850$		0			0
$851$		−	374.123i		−	0.439627i
$852$	360.000	−	623.538i	0.422535	−	0.731852i
$853$	666.000			0.780774			0.390387	−	0.920651i	$-0.372341\pi$
$853$	666.000			0.780774			0.390387	+	0.920651i	$0.372341\pi$
$854$	−1332.00	+	769.031i	−1.55972	+	0.900504i
$855$		0			0
$856$		−	1496.49i		−	1.74824i
$857$	182.000			0.212369			0.106184	−	0.994346i	$-0.466137\pi$
$857$	182.000			0.212369			0.106184	+	0.994346i	$0.466137\pi$
$858$	324.000	+	561.184i	0.377622	+	0.654061i
$859$			990.733i			1.15336i	0.816971	+	0.576678i	$0.195651\pi$
$859$			990.733i			1.15336i	−0.816971	+	0.576678i	$0.804349\pi$
$860$		0			0
$861$	−324.000			−0.376307
$862$	216.000	−	124.708i	0.250580	−	0.144672i
$863$			1170.87i			1.35674i	0.734721	+	0.678370i	$0.237313\pi$
$863$			1170.87i			1.35674i	−0.734721	+	0.678370i	$0.762687\pi$
$864$	144.000	+	83.1384i	0.166667	+	0.0962250i
$865$		0			0
$866$	−36.0000	−	62.3538i	−0.0415704	−	0.0720021i
$867$		−	327.358i		−	0.377575i
$868$	144.000	−	249.415i	0.165899	−	0.287345i
$869$	−936.000			−1.07710
$870$		0			0
$871$		−	748.246i		−	0.859065i
$872$	−208.000			−0.238532
$873$	−216.000			−0.247423
$874$	−96.0000	−	166.277i	−0.109840	−	0.190248i
$875$		0			0
$876$	216.000	+	124.708i	0.246575	+	0.142360i
$877$	774.000			0.882554			0.441277	−	0.897371i	$-0.354526\pi$
$877$	774.000			0.882554			0.441277	+	0.897371i	$0.354526\pi$
$878$	−1356.00	+	782.887i	−1.54442	+	0.891671i
$879$			100.459i			0.114288i
$880$		0			0
$881$	−1602.00			−1.81839			−0.909194	−	0.416373i	$-0.863301\pi$
$881$	−1602.00			−1.81839			−0.909194	+	0.416373i	$0.863301\pi$
$882$	−177.000	−	306.573i	−0.200680	−	0.347588i
$883$			415.692i			0.470773i	0.971902	+	0.235386i	$0.0756355\pi$
$883$			415.692i			0.470773i	−0.971902	+	0.235386i	$0.924364\pi$
$884$	−360.000	+	623.538i	−0.407240	+	0.705360i
$885$		0			0
$886$	−372.000	+	214.774i	−0.419865	+	0.242409i
$887$		−	367.195i		−	0.413974i	−0.978344	−	0.206987i	$-0.933634\pi$
$887$		−	367.195i		−	0.413974i	0.978344	−	0.206987i	$-0.0663658\pi$
$888$		−	748.246i		−	0.842619i
$889$	−2268.00			−2.55118
$890$		0			0
$891$		−	93.5307i		−	0.104973i
$892$	−324.000	−	187.061i	−0.363229	−	0.209710i
$893$		0			0
$894$	864.000	−	498.831i	0.966443	−	0.557976i
$895$		0			0
$896$	1152.00	−	665.108i	1.28571	−	0.742307i
$897$	216.000			0.240803
$898$	−54.0000	−	93.5307i	−0.0601336	−	0.104155i
$899$		−	249.415i		−	0.277436i
$900$		0			0
$901$	−260.000			−0.288568
$902$	−324.000	+	187.061i	−0.359202	+	0.207385i
$903$		−	374.123i		−	0.414311i
$904$	80.0000			0.0884956
$905$		0			0
$906$	324.000	+	561.184i	0.357616	+	0.619409i
$907$			1434.14i			1.58119i	0.612340	+	0.790594i	$0.290228\pi$
$907$			1434.14i			1.58119i	−0.612340	+	0.790594i	$0.709772\pi$
$908$	744.000	+	429.549i	0.819383	+	0.473071i
$909$	−108.000			−0.118812
$910$		0			0
$911$		−	1080.80i		−	1.18639i	−0.805059	−	0.593194i	$-0.797867\pi$
$911$		−	1080.80i		−	1.18639i	0.805059	−	0.593194i	$-0.202133\pi$
$912$	−192.000	−	332.554i	−0.210526	−	0.364642i
$913$	−936.000			−1.02519
$914$	288.000	+	498.831i	0.315098	+	0.545767i
$915$		0			0
$916$	−676.000	+	1170.87i	−0.737991	+	1.27824i
$917$	−1404.00			−1.53108
$918$	90.0000	−	51.9615i	0.0980392	−	0.0566030i
$919$			187.061i			0.203549i	0.994807	+	0.101774i	$0.0324520\pi$
$919$			187.061i			0.203549i	−0.994807	+	0.101774i	$0.967548\pi$
$920$		0			0
$921$	468.000			0.508143
$922$	288.000	+	498.831i	0.312364	+	0.541031i
$923$		−	1870.61i		−	2.02667i
$924$	−648.000	−	374.123i	−0.701299	−	0.404895i
$925$		0			0
$926$	702.000	−	405.300i	0.758099	−	0.437689i
$927$		−	31.1769i		−	0.0336321i
$928$	576.000	−	997.661i	0.620690	−	1.07507i
$929$	54.0000			0.0581270			0.0290635	−	0.999578i	$-0.490747\pi$
$929$	54.0000			0.0581270			0.0290635	+	0.999578i	$0.490747\pi$
$930$		0			0
$931$			817.528i			0.878118i
$932$	−364.000	+	630.466i	−0.390558	+	0.676466i
$933$	468.000			0.501608
$934$	996.000	−	575.041i	1.06638	−	0.615675i
$935$		0			0
$936$	432.000			0.461538
$937$	−936.000			−0.998933			−0.499466	−	0.866333i	$-0.666471\pi$
$937$	−936.000			−0.998933			−0.499466	+	0.866333i	$0.666471\pi$
$938$	432.000	+	748.246i	0.460554	+	0.797704i
$939$		−	810.600i		−	0.863259i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	−702.000	+	405.300i	−0.745223	+	0.430255i
$943$			124.708i			0.132246i
$944$	432.000	−	249.415i	0.457627	−	0.264211i
$945$		0			0
$946$	−216.000	−	374.123i	−0.228330	−	0.395479i
$947$			1032.30i			1.09008i	0.838411	+	0.545038i	$0.183485\pi$
$947$			1032.30i			1.09008i	−0.838411	+	0.545038i	$0.816515\pi$
$948$	−312.000	+	540.400i	−0.329114	+	0.570042i
$949$	648.000			0.682824
$950$		0			0
$951$		−	433.013i		−	0.455324i
$952$		−	831.384i		−	0.873303i
$953$	−1550.00			−1.62644			−0.813221	−	0.581954i	$-0.802288\pi$
$953$	−1550.00			−1.62644			−0.813221	+	0.581954i	$0.802288\pi$
$954$	78.0000	+	135.100i	0.0817610	+	0.141614i
$955$		0			0
$956$	−1224.00	−	706.677i	−1.28033	−	0.739202i
$957$	−648.000			−0.677116
$958$	252.000	−	145.492i	0.263048	−	0.151871i
$959$		−	1143.15i		−	1.19203i
$960$		0			0
$961$	913.000			0.950052
$962$	−972.000	−	1683.55i	−1.01040	−	1.75006i
$963$			561.184i			0.582746i
$964$	212.000	−	367.195i	0.219917	−	0.380907i
$965$		0			0
$966$	−216.000	+	124.708i	−0.223602	+	0.129097i
$967$			1215.90i			1.25739i	0.777650	+	0.628697i	$0.216411\pi$
$967$			1215.90i			1.25739i	−0.777650	+	0.628697i	$0.783589\pi$
$968$	104.000			0.107438
$969$	−240.000			−0.247678
$970$		0			0
$971$			1839.44i			1.89437i	0.320681	+	0.947187i	$0.396088\pi$
$971$			1839.44i			1.89437i	−0.320681	+	0.947187i	$0.603912\pi$
$972$	−54.0000	−	31.1769i	−0.0555556	−	0.0320750i
$973$	−1944.00			−1.99794
$974$	−450.000	+	259.808i	−0.462012	+	0.266743i
$975$		0			0
$976$	592.000	+	1025.37i	0.606557	+	1.05059i
$977$	206.000			0.210850			0.105425	−	0.994427i	$-0.466380\pi$
$977$	206.000			0.210850			0.105425	+	0.994427i	$0.466380\pi$
$978$	216.000	+	374.123i	0.220859	+	0.382539i
$979$			187.061i			0.191074i
$980$		0			0
$981$	78.0000			0.0795107
$982$	−126.000	+	72.7461i	−0.128310	+	0.0740796i
$983$		−	720.533i		−	0.732994i	−0.930419	−	0.366497i	$-0.880557\pi$
$983$		−	720.533i		−	0.732994i	0.930419	−	0.366497i	$-0.119443\pi$
$984$			249.415i			0.253471i
$985$		0			0
$986$	−360.000	−	623.538i	−0.365112	−	0.632392i
$987$		0			0
$988$	−864.000	−	498.831i	−0.874494	−	0.504889i
$989$	−144.000			−0.145602
$990$		0			0
$991$			1323.29i			1.33530i	0.744473	+	0.667652i	$0.232701\pi$
$991$			1323.29i			1.33530i	−0.744473	+	0.667652i	$0.767299\pi$
$992$	−192.000	−	110.851i	−0.193548	−	0.111745i
$993$	−648.000			−0.652568
$994$	1080.00	+	1870.61i	1.08652	+	1.88191i
$995$		0			0
$996$	−312.000	+	540.400i	−0.313253	+	0.542570i
$997$	198.000			0.198596			0.0992979	−	0.995058i	$-0.468340\pi$
$997$	198.000			0.198596			0.0992979	+	0.995058i	$0.468340\pi$
$998$	768.000	−	443.405i	0.769539	−	0.444294i
$999$			280.592i			0.280873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.a.151.1		2
3.2	odd	2		900.3.c.j.451.2		2
4.3	odd	2	inner	300.3.c.a.151.2		2
5.2	odd	4		60.3.f.a.19.3	yes	4
5.3	odd	4		60.3.f.a.19.2	yes	4
5.4	even	2		300.3.c.c.151.2		2
12.11	even	2		900.3.c.j.451.1		2
15.2	even	4		180.3.f.e.19.2		4
15.8	even	4		180.3.f.e.19.3		4
15.14	odd	2		900.3.c.f.451.1		2
20.3	even	4		60.3.f.a.19.4	yes	4
20.7	even	4		60.3.f.a.19.1	✓	4
20.19	odd	2		300.3.c.c.151.1		2
40.3	even	4		960.3.j.b.319.2		4
40.13	odd	4		960.3.j.b.319.4		4
40.27	even	4		960.3.j.b.319.3		4
40.37	odd	4		960.3.j.b.319.1		4
60.23	odd	4		180.3.f.e.19.1		4
60.47	odd	4		180.3.f.e.19.4		4
60.59	even	2		900.3.c.f.451.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.a.19.1	✓	4	20.7	even	4
60.3.f.a.19.2	yes	4	5.3	odd	4
60.3.f.a.19.3	yes	4	5.2	odd	4
60.3.f.a.19.4	yes	4	20.3	even	4
180.3.f.e.19.1		4	60.23	odd	4
180.3.f.e.19.2		4	15.2	even	4
180.3.f.e.19.3		4	15.8	even	4
180.3.f.e.19.4		4	60.47	odd	4
300.3.c.a.151.1		2	1.1	even	1	trivial
300.3.c.a.151.2		2	4.3	odd	2	inner
300.3.c.c.151.1		2	20.19	odd	2
300.3.c.c.151.2		2	5.4	even	2
900.3.c.f.451.1		2	15.14	odd	2
900.3.c.f.451.2		2	60.59	even	2
900.3.c.j.451.1		2	12.11	even	2
900.3.c.j.451.2		2	3.2	odd	2
960.3.j.b.319.1		4	40.37	odd	4
960.3.j.b.319.2		4	40.3	even	4
960.3.j.b.319.3		4	40.27	even	4
960.3.j.b.319.4		4	40.13	odd	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +1.73205i q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 - 1.73205i) q^{6} +10.3923i q^{7} +8.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +1.73205i q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 - 1.73205i) q^{6} +10.3923i q^{7} +8.00000 q^{8} -3.00000 q^{9} -10.3923i q^{11} +(-6.00000 - 3.46410i) q^{12} -18.0000 q^{13} +(18.0000 - 10.3923i) q^{14} +(-8.00000 - 13.8564i) q^{16} -10.0000 q^{17} +(3.00000 + 5.19615i) q^{18} -13.8564i q^{19} -18.0000 q^{21} +(-18.0000 + 10.3923i) q^{22} +6.92820i q^{23} +13.8564i q^{24} +(18.0000 + 31.1769i) q^{26} -5.19615i q^{27} +(-36.0000 - 20.7846i) q^{28} -36.0000 q^{29} +6.92820i q^{31} +(-16.0000 + 27.7128i) q^{32} +18.0000 q^{33} +(10.0000 + 17.3205i) q^{34} +(6.00000 - 10.3923i) q^{36} -54.0000 q^{37} +(-24.0000 + 13.8564i) q^{38} -31.1769i q^{39} +18.0000 q^{41} +(18.0000 + 31.1769i) q^{42} +20.7846i q^{43} +(36.0000 + 20.7846i) q^{44} +(12.0000 - 6.92820i) q^{46} +(24.0000 - 13.8564i) q^{48} -59.0000 q^{49} -17.3205i q^{51} +(36.0000 - 62.3538i) q^{52} +26.0000 q^{53} +(-9.00000 + 5.19615i) q^{54} +83.1384i q^{56} +24.0000 q^{57} +(36.0000 + 62.3538i) q^{58} +31.1769i q^{59} -74.0000 q^{61} +(12.0000 - 6.92820i) q^{62} -31.1769i q^{63} +64.0000 q^{64} +(-18.0000 - 31.1769i) q^{66} +41.5692i q^{67} +(20.0000 - 34.6410i) q^{68} -12.0000 q^{69} +103.923i q^{71} -24.0000 q^{72} -36.0000 q^{73} +(54.0000 + 93.5307i) q^{74} +(48.0000 + 27.7128i) q^{76} +108.000 q^{77} +(-54.0000 + 31.1769i) q^{78} -90.0666i q^{79} +9.00000 q^{81} +(-18.0000 - 31.1769i) q^{82} -90.0666i q^{83} +(36.0000 - 62.3538i) q^{84} +(36.0000 - 20.7846i) q^{86} -62.3538i q^{87} -83.1384i q^{88} -18.0000 q^{89} -187.061i q^{91} +(-24.0000 - 13.8564i) q^{92} -12.0000 q^{93} +(-48.0000 - 27.7128i) q^{96} +72.0000 q^{97} +(59.0000 + 102.191i) q^{98} +31.1769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 6 q^{6} + 16 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^6 + 16 * q^8 - 6 * q^9	\( 2 q - 2 q^{2} - 4 q^{4} + 6 q^{6} + 16 q^{8} - 6 q^{9} - 12 q^{12} - 36 q^{13} + 36 q^{14} - 16 q^{16} - 20 q^{17} + 6 q^{18} - 36 q^{21} - 36 q^{22} + 36 q^{26} - 72 q^{28} - 72 q^{29} - 32 q^{32} + 36 q^{33} + 20 q^{34} + 12 q^{36} - 108 q^{37} - 48 q^{38} + 36 q^{41} + 36 q^{42} + 72 q^{44} + 24 q^{46} + 48 q^{48} - 118 q^{49} + 72 q^{52} + 52 q^{53} - 18 q^{54} + 48 q^{57} + 72 q^{58} - 148 q^{61} + 24 q^{62} + 128 q^{64} - 36 q^{66} + 40 q^{68} - 24 q^{69} - 48 q^{72} - 72 q^{73} + 108 q^{74} + 96 q^{76} + 216 q^{77} - 108 q^{78} + 18 q^{81} - 36 q^{82} + 72 q^{84} + 72 q^{86} - 36 q^{89} - 48 q^{92} - 24 q^{93} - 96 q^{96} + 144 q^{97} + 118 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 6 * q^6 + 16 * q^8 - 6 * q^9 - 12 * q^12 - 36 * q^13 + 36 * q^14 - 16 * q^16 - 20 * q^17 + 6 * q^18 - 36 * q^21 - 36 * q^22 + 36 * q^26 - 72 * q^28 - 72 * q^29 - 32 * q^32 + 36 * q^33 + 20 * q^34 + 12 * q^36 - 108 * q^37 - 48 * q^38 + 36 * q^41 + 36 * q^42 + 72 * q^44 + 24 * q^46 + 48 * q^48 - 118 * q^49 + 72 * q^52 + 52 * q^53 - 18 * q^54 + 48 * q^57 + 72 * q^58 - 148 * q^61 + 24 * q^62 + 128 * q^64 - 36 * q^66 + 40 * q^68 - 24 * q^69 - 48 * q^72 - 72 * q^73 + 108 * q^74 + 96 * q^76 + 216 * q^77 - 108 * q^78 + 18 * q^81 - 36 * q^82 + 72 * q^84 + 72 * q^86 - 36 * q^89 - 48 * q^92 - 24 * q^93 - 96 * q^96 + 144 * q^97 + 118 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more