LMFDB - Embedded newform 289.3.e.o.214.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([15]))

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

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

chi := DirichletCharacter("289.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{16})$
Coefficient field:	16.0.3954223417733761003417501696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 214358881 $ x^16 + 214358881
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			214.2
Root			$-0.647041 + 3.25290i$ of defining polynomial
Character	$\chi$	$=$	289.214
Dual form			289.3.e.o.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 + 0.923880i) q^{2} +(3.89994 + 2.60586i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-4.60029 + 0.915055i) q^{5} +(-3.89994 + 2.60586i) q^{6} +(9.20058 + 1.83011i) q^{7} +(-6.46716 + 2.67878i) q^{8} +(4.97488 + 12.0104i) q^{9} +O(q^{10})$	\(q+(-0.382683 + 0.923880i) q^{2} +(3.89994 + 2.60586i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-4.60029 + 0.915055i) q^{5} +(-3.89994 + 2.60586i) q^{6} +(9.20058 + 1.83011i) q^{7} +(-6.46716 + 2.67878i) q^{8} +(4.97488 + 12.0104i) q^{9} +(0.915055 - 4.60029i) q^{10} +(-2.60586 - 3.89994i) q^{11} +(2.74516 + 13.8009i) q^{12} +(7.07107 - 7.07107i) q^{13} +(-5.21171 + 7.79988i) q^{14} +(-20.3253 - 8.41904i) q^{15} +5.00000i q^{16} -13.0000 q^{18} +(-6.88830 + 16.6298i) q^{19} +(-11.6998 - 7.81757i) q^{20} +(31.1127 + 31.1127i) q^{21} +(4.60029 - 0.915055i) q^{22} +(7.79988 - 5.21171i) q^{23} +(-32.2020 - 6.40538i) q^{24} +(-2.77164 + 1.14805i) q^{25} +(3.82683 + 9.23880i) q^{26} +(-3.66022 + 18.4012i) q^{27} +(15.6351 + 23.3996i) q^{28} +(-10.0656 - 50.6032i) q^{29} +(15.5563 - 15.5563i) q^{30} +(20.8468 - 31.1995i) q^{31} +(-30.4880 - 12.6286i) q^{32} -22.0000i q^{33} -44.0000 q^{35} +(-14.9247 + 36.0313i) q^{36} +(3.89994 + 2.60586i) q^{37} +(-12.7279 - 12.7279i) q^{38} +(46.0029 - 9.15055i) q^{39} +(27.2996 - 18.2410i) q^{40} +(9.20058 + 1.83011i) q^{41} +(-40.6507 + 16.8381i) q^{42} +(14.5420 + 35.1074i) q^{43} +(2.74516 - 13.8009i) q^{44} +(-33.8761 - 50.6992i) q^{45} +(1.83011 + 9.20058i) q^{46} +(-41.0122 + 41.0122i) q^{47} +(-13.0293 + 19.4997i) q^{48} +(36.0313 + 14.9247i) q^{49} -3.00000i q^{50} +30.0000 q^{52} +(-6.88830 + 16.6298i) q^{53} +(-15.5998 - 10.4234i) q^{54} +(15.5563 + 15.5563i) q^{55} +(-64.4041 + 12.8108i) q^{56} +(-70.1989 + 46.9054i) q^{57} +(50.6032 + 10.0656i) q^{58} +(68.3671 - 28.3186i) q^{59} +(-25.2571 - 60.9760i) q^{60} +(4.57527 - 23.0015i) q^{61} +(20.8468 + 31.1995i) q^{62} +(23.7914 + 119.608i) q^{63} +(9.19239 - 9.19239i) q^{64} +(-26.0586 + 38.9994i) q^{65} +(20.3253 + 8.41904i) q^{66} -34.0000i q^{67} +44.0000 q^{69} +(16.8381 - 40.6507i) q^{70} +(70.1989 + 46.9054i) q^{71} +(-64.3467 - 64.3467i) q^{72} +(-82.8052 + 16.4710i) q^{73} +(-3.89994 + 2.60586i) q^{74} +(-13.8009 - 2.74516i) q^{75} +(-49.8895 + 20.6649i) q^{76} +(-16.8381 - 40.6507i) q^{77} +(-9.15055 + 46.0029i) q^{78} +(41.6937 + 62.3990i) q^{79} +(-4.57527 - 23.0015i) q^{80} +(20.5061 - 20.5061i) q^{81} +(-5.21171 + 7.79988i) q^{82} +(53.5850 + 22.1956i) q^{83} +132.000i q^{84} -38.0000 q^{86} +(92.6094 - 223.579i) q^{87} +(27.2996 + 18.2410i) q^{88} +(-55.1543 - 55.1543i) q^{89} +(59.8038 - 11.8957i) q^{90} +(77.9988 - 52.1171i) q^{91} +(27.6017 + 5.49033i) q^{92} +(162.603 - 67.3523i) q^{93} +(-22.1956 - 53.5850i) q^{94} +(16.4710 - 82.8052i) q^{95} +(-85.9932 - 128.698i) q^{96} +(-25.6215 - 128.808i) q^{97} +(-27.5772 + 27.5772i) q^{98} +(33.8761 - 50.6992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 208 q^{18} - 704 q^{35} + 480 q^{52} + 704 q^{69} - 608 q^{86}+O(q^{100}) $ 16 * q - 208 * q^18 - 704 * q^35 + 480 * q^52 + 704 * q^69 - 608 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	−0.382683	+	0.923880i	−0.191342	+	0.461940i	−0.990213	−	0.139562i	$-0.955431\pi$
$2$	−0.382683	+	0.923880i	−0.191342	+	0.461940i	0.798872	+	0.601502i	$0.205431\pi$
$3$	3.89994	+	2.60586i	1.29998	+	0.868618i	0.996449	−	0.0842032i	$-0.0268345\pi$
$3$	3.89994	+	2.60586i	1.29998	+	0.868618i	0.303531	+	0.952822i	$0.401834\pi$
$4$	2.12132	+	2.12132i	0.530330	+	0.530330i
$5$	−4.60029	+	0.915055i	−0.920058	+	0.183011i	−0.632328	−	0.774701i	$-0.717901\pi$
$5$	−4.60029	+	0.915055i	−0.920058	+	0.183011i	−0.287730	+	0.957712i	$0.592901\pi$
$6$	−3.89994	+	2.60586i	−0.649990	+	0.434309i
$7$	9.20058	+	1.83011i	1.31437	+	0.261444i	0.802001	−	0.597322i	$-0.203769\pi$
$7$	9.20058	+	1.83011i	1.31437	+	0.261444i	0.512367	+	0.858766i	$0.328769\pi$
$8$	−6.46716	+	2.67878i	−0.808395	+	0.334848i
$9$	4.97488	+	12.0104i	0.552765	+	1.33449i
$10$	0.915055	−	4.60029i	0.0915055	−	0.460029i
$11$	−2.60586	−	3.89994i	−0.236896	−	0.354540i	0.693905	−	0.720067i	$-0.255889\pi$
$11$	−2.60586	−	3.89994i	−0.236896	−	0.354540i	−0.930801	+	0.365527i	$0.880889\pi$
$12$	2.74516	+	13.8009i	0.228764	+	1.15007i
$13$	7.07107	−	7.07107i	0.543928	−	0.543928i	−0.380750	−	0.924678i	$-0.624334\pi$
$13$	7.07107	−	7.07107i	0.543928	−	0.543928i	0.924678	+	0.380750i	$0.124334\pi$
$14$	−5.21171	+	7.79988i	−0.372265	+	0.557134i
$15$	−20.3253	−	8.41904i	−1.35502	−	0.561269i
$16$			5.00000i			0.312500i
$17$		0			0
$17$		0			0
$18$	−13.0000			−0.722222
$19$	−6.88830	+	16.6298i	−0.362542	+	0.875254i	0.632385	+	0.774654i	$0.282076\pi$
$19$	−6.88830	+	16.6298i	−0.362542	+	0.875254i	−0.994927	+	0.100600i	$0.967924\pi$
$20$	−11.6998	−	7.81757i	−0.584991	−	0.390878i
$21$	31.1127	+	31.1127i	1.48156	+	1.48156i
$22$	4.60029	−	0.915055i	0.209104	−	0.0415934i
$23$	7.79988	−	5.21171i	0.339125	−	0.226596i	−0.374333	−	0.927295i	$-0.622128\pi$
$23$	7.79988	−	5.21171i	0.339125	−	0.226596i	0.713458	+	0.700698i	$0.247128\pi$
$24$	−32.2020	−	6.40538i	−1.34175	−	0.266891i
$25$	−2.77164	+	1.14805i	−0.110866	+	0.0459220i
$26$	3.82683	+	9.23880i	0.147186	+	0.355338i
$27$	−3.66022	+	18.4012i	−0.135564	+	0.681525i
$28$	15.6351	+	23.3996i	0.558398	+	0.835701i
$29$	−10.0656	−	50.6032i	−0.347090	−	1.74494i	−0.621583	−	0.783349i	$-0.713510\pi$
$29$	−10.0656	−	50.6032i	−0.347090	−	1.74494i	0.274493	−	0.961589i	$-0.411490\pi$
$30$	15.5563	−	15.5563i	0.518545	−	0.518545i
$31$	20.8468	−	31.1995i	0.672479	−	1.00644i	−0.325662	−	0.945486i	$-0.605587\pi$
$31$	20.8468	−	31.1995i	0.672479	−	1.00644i	0.998141	−	0.0609494i	$-0.0194128\pi$
$32$	−30.4880	−	12.6286i	−0.952751	−	0.394642i
$33$		−	22.0000i		−	0.666667i
$34$		0			0
$35$	−44.0000			−1.25714
$36$	−14.9247	+	36.0313i	−0.414574	+	1.00087i
$37$	3.89994	+	2.60586i	0.105404	+	0.0704285i	0.607155	−	0.794583i	$-0.292311\pi$
$37$	3.89994	+	2.60586i	0.105404	+	0.0704285i	−0.501751	+	0.865012i	$0.667311\pi$
$38$	−12.7279	−	12.7279i	−0.334945	−	0.334945i
$39$	46.0029	−	9.15055i	1.17956	−	0.234629i
$40$	27.2996	−	18.2410i	0.682489	−	0.456025i
$41$	9.20058	+	1.83011i	0.224404	+	0.0446368i	0.306012	−	0.952028i	$-0.401005\pi$
$41$	9.20058	+	1.83011i	0.224404	+	0.0446368i	−0.0816073	+	0.996665i	$0.526005\pi$
$42$	−40.6507	+	16.8381i	−0.967874	+	0.400906i
$43$	14.5420	+	35.1074i	0.338185	+	0.816452i	0.997890	+	0.0649267i	$0.0206814\pi$
$43$	14.5420	+	35.1074i	0.338185	+	0.816452i	−0.659705	+	0.751525i	$0.729319\pi$
$44$	2.74516	−	13.8009i	0.0623901	−	0.313656i
$45$	−33.8761	−	50.6992i	−0.752803	−	1.12665i
$46$	1.83011	+	9.20058i	0.0397850	+	0.200013i
$47$	−41.0122	+	41.0122i	−0.872600	+	0.872600i	−0.992755	−	0.120155i	$-0.961661\pi$
$47$	−41.0122	+	41.0122i	−0.872600	+	0.872600i	0.120155	+	0.992755i	$0.461661\pi$
$48$	−13.0293	+	19.4997i	−0.271443	+	0.406244i
$49$	36.0313	+	14.9247i	0.735333	+	0.304585i
$50$		−	3.00000i		−	0.0600000i
$51$		0			0
$52$	30.0000			0.576923
$53$	−6.88830	+	16.6298i	−0.129968	+	0.313770i	−0.975446	−	0.220240i	$-0.929316\pi$
$53$	−6.88830	+	16.6298i	−0.129968	+	0.313770i	0.845478	+	0.534011i	$0.179316\pi$
$54$	−15.5998	−	10.4234i	−0.288884	−	0.193026i
$55$	15.5563	+	15.5563i	0.282843	+	0.282843i
$56$	−64.4041	+	12.8108i	−1.15007	+	0.228764i
$57$	−70.1989	+	46.9054i	−1.23156	+	0.822902i
$58$	50.6032	+	10.0656i	0.872469	+	0.173545i
$59$	68.3671	−	28.3186i	1.15876	−	0.479976i	0.281301	−	0.959620i	$-0.409234\pi$
$59$	68.3671	−	28.3186i	1.15876	−	0.479976i	0.877463	+	0.479644i	$0.159234\pi$
$60$	−25.2571	−	60.9760i	−0.420952	−	1.01627i
$61$	4.57527	−	23.0015i	0.0750045	−	0.377073i	−0.924991	−	0.379988i	$-0.875928\pi$
$61$	4.57527	−	23.0015i	0.0750045	−	0.377073i	0.999996	+	0.00291536i	$0.000927988\pi$
$62$	20.8468	+	31.1995i	0.336239	+	0.503218i
$63$	23.7914	+	119.608i	0.377642	+	1.89853i
$64$	9.19239	−	9.19239i	0.143631	−	0.143631i
$65$	−26.0586	+	38.9994i	−0.400901	+	0.599990i
$66$	20.3253	+	8.41904i	0.307960	+	0.127561i
$67$		−	34.0000i		−	0.507463i	−0.967275	−	0.253731i	$-0.918342\pi$
$67$		−	34.0000i		−	0.507463i	0.967275	−	0.253731i	$-0.0816579\pi$
$68$		0			0
$69$	44.0000			0.637681
$70$	16.8381	−	40.6507i	0.240544	−	0.580724i
$71$	70.1989	+	46.9054i	0.988717	+	0.660639i	0.941065	−	0.338225i	$-0.109826\pi$
$71$	70.1989	+	46.9054i	0.988717	+	0.660639i	0.0476513	+	0.998864i	$0.484826\pi$
$72$	−64.3467	−	64.3467i	−0.893704	−	0.893704i
$73$	−82.8052	+	16.4710i	−1.13432	+	0.225630i	−0.726323	−	0.687354i	$-0.758772\pi$
$73$	−82.8052	+	16.4710i	−1.13432	+	0.225630i	−0.407996	+	0.912984i	$0.633772\pi$
$74$	−3.89994	+	2.60586i	−0.0527019	+	0.0352143i
$75$	−13.8009	−	2.74516i	−0.184012	−	0.0366022i
$76$	−49.8895	+	20.6649i	−0.656441	+	0.271907i
$77$	−16.8381	−	40.6507i	−0.218676	−	0.527931i
$78$	−9.15055	+	46.0029i	−0.117315	+	0.589781i
$79$	41.6937	+	62.3990i	0.527768	+	0.789861i	0.995575	−	0.0939698i	$-0.0299557\pi$
$79$	41.6937	+	62.3990i	0.527768	+	0.789861i	−0.467807	+	0.883831i	$0.654956\pi$
$80$	−4.57527	−	23.0015i	−0.0571909	−	0.287518i
$81$	20.5061	−	20.5061i	0.253162	−	0.253162i
$82$	−5.21171	+	7.79988i	−0.0635574	+	0.0951204i
$83$	53.5850	+	22.1956i	0.645603	+	0.267417i	0.681366	−	0.731943i	$-0.261386\pi$
$83$	53.5850	+	22.1956i	0.645603	+	0.267417i	−0.0357634	+	0.999360i	$0.511386\pi$
$84$			132.000i			1.57143i
$85$		0			0
$86$	−38.0000			−0.441860
$87$	92.6094	−	223.579i	1.06448	−	2.56987i
$88$	27.2996	+	18.2410i	0.310222	+	0.207284i
$89$	−55.1543	−	55.1543i	−0.619712	−	0.619712i	0.325746	−	0.945457i	$-0.394385\pi$
$89$	−55.1543	−	55.1543i	−0.619712	−	0.619712i	−0.945457	+	0.325746i	$0.894385\pi$
$90$	59.8038	−	11.8957i	0.664486	−	0.132175i
$91$	77.9988	−	52.1171i	0.857129	−	0.572715i
$92$	27.6017	+	5.49033i	0.300019	+	0.0596775i
$93$	162.603	−	67.3523i	1.74842	−	0.724218i
$94$	−22.1956	−	53.5850i	−0.236124	−	0.570053i
$95$	16.4710	−	82.8052i	0.173379	−	0.871634i
$96$	−85.9932	−	128.698i	−0.895763	−	1.34060i
$97$	−25.6215	−	128.808i	−0.264140	−	1.32792i	−0.853941	−	0.520370i	$-0.825794\pi$
$97$	−25.6215	−	128.808i	−0.264140	−	1.32792i	0.589801	−	0.807549i	$-0.299206\pi$
$98$	−27.5772	+	27.5772i	−0.281400	+	0.281400i
$99$	33.8761	−	50.6992i	0.342183	−	0.512113i
$100$	−8.31492	−	3.44415i	−0.0831492	−	0.0344415i
$101$		−	34.0000i		−	0.336634i	−0.985733	−	0.168317i	$-0.946167\pi$
$101$		−	34.0000i		−	0.336634i	0.985733	−	0.168317i	$-0.0538332\pi$
$102$		0			0
$103$	172.000			1.66990			0.834951	−	0.550324i	$-0.185496\pi$
$103$	172.000			1.66990			0.834951	+	0.550324i	$0.185496\pi$
$104$	−26.7878	+	64.6716i	−0.257575	+	0.621842i
$105$	−171.597	−	114.658i	−1.63426	−	1.09198i
$106$	−12.7279	−	12.7279i	−0.120075	−	0.120075i
$107$	151.810	−	30.1968i	1.41878	−	0.282213i	0.574672	−	0.818384i	$-0.305130\pi$
$107$	151.810	−	30.1968i	1.41878	−	0.282213i	0.844109	+	0.536171i	$0.180130\pi$
$108$	−46.7993	+	31.2703i	−0.433326	+	0.289539i
$109$	−69.0044	−	13.7258i	−0.633068	−	0.125925i	−0.131883	−	0.991265i	$-0.542102\pi$
$109$	−69.0044	−	13.7258i	−0.633068	−	0.125925i	−0.501185	+	0.865340i	$0.667102\pi$
$110$	−20.3253	+	8.41904i	−0.184776	+	0.0765367i
$111$	8.41904	+	20.3253i	0.0758472	+	0.183111i
$112$	−9.15055	+	46.0029i	−0.0817013	+	0.410740i
$113$	41.6937	+	62.3990i	0.368971	+	0.552204i	0.968775	−	0.247943i	$-0.0797547\pi$
$113$	41.6937	+	62.3990i	0.368971	+	0.552204i	−0.599804	+	0.800147i	$0.704755\pi$
$114$	−16.4710	−	82.8052i	−0.144482	−	0.726362i
$115$	−31.1127	+	31.1127i	−0.270545	+	0.270545i
$116$	85.9932	−	128.698i	0.741321	−	1.10947i
$117$	120.104	+	49.7488i	1.02653	+	0.425204i
$118$			74.0000i			0.627119i
$119$		0			0
$120$	154.000			1.28333
$121$	37.8857	−	91.4641i	0.313105	−	0.755901i
$122$	19.4997	+	13.0293i	0.159834	+	0.106797i
$123$	31.1127	+	31.1127i	0.252949	+	0.252949i
$124$	110.407	−	21.9613i	0.890379	−	0.177107i
$125$	109.198	−	72.9640i	0.873586	−	0.583712i
$126$	−119.608	−	23.7914i	−0.949266	−	0.188821i
$127$	−88.6924	+	36.7376i	−0.698366	+	0.289273i	−0.703481	−	0.710714i	$-0.748372\pi$
$127$	−88.6924	+	36.7376i	−0.698366	+	0.289273i	0.00511503	+	0.999987i	$0.498372\pi$
$128$	−45.5393	−	109.942i	−0.355776	−	0.858919i
$129$	−34.7721	+	174.811i	−0.269551	+	1.35512i
$130$	−26.0586	−	38.9994i	−0.200450	−	0.299995i
$131$	21.0463	+	105.807i	0.160658	+	0.807685i	0.974114	+	0.226057i	$0.0725837\pi$
$131$	21.0463	+	105.807i	0.160658	+	0.807685i	−0.813456	+	0.581627i	$0.802416\pi$
$132$	46.6690	−	46.6690i	0.353553	−	0.353553i
$133$	−93.8108	+	140.398i	−0.705344	+	1.05562i
$134$	31.4119	+	13.0112i	0.234417	+	0.0970988i
$135$		−	88.0000i		−	0.651852i
$136$		0			0
$137$	−236.000			−1.72263			−0.861314	−	0.508073i	$-0.830358\pi$
$137$	−236.000			−1.72263			−0.861314	+	0.508073i	$0.830358\pi$
$138$	−16.8381	+	40.6507i	−0.122015	+	0.294570i
$139$	3.89994	+	2.60586i	0.0280571	+	0.0187472i	0.569520	−	0.821978i	$-0.307129\pi$
$139$	3.89994	+	2.60586i	0.0280571	+	0.0187472i	−0.541463	+	0.840725i	$0.682129\pi$
$140$	−93.3381	−	93.3381i	−0.666701	−	0.666701i
$141$	−266.817	+	53.0732i	−1.89232	+	0.376405i
$142$	−70.1989	+	46.9054i	−0.494358	+	0.330320i
$143$	−46.0029	−	9.15055i	−0.321699	−	0.0639898i
$144$	−60.0522	+	24.8744i	−0.417029	+	0.172739i
$145$	92.6094	+	223.579i	0.638685	+	1.54192i
$146$	16.4710	−	82.8052i	0.112815	−	0.567159i
$147$	101.628	+	152.098i	0.691349	+	1.03468i
$148$	2.74516	+	13.8009i	0.0185484	+	0.0932491i
$149$	−41.0122	+	41.0122i	−0.275250	+	0.275250i	−0.831209	−	0.555960i	$-0.812351\pi$
$149$	−41.0122	+	41.0122i	−0.275250	+	0.275250i	0.555960	+	0.831209i	$0.312351\pi$
$150$	7.81757	−	11.6998i	0.0521171	−	0.0779988i
$151$	−40.6507	−	16.8381i	−0.269210	−	0.111510i	0.243995	−	0.969776i	$-0.421542\pi$
$151$	−40.6507	−	16.8381i	−0.269210	−	0.111510i	−0.513205	+	0.858266i	$0.671542\pi$
$152$		−	126.000i		−	0.828947i
$153$		0			0
$154$	44.0000			0.285714
$155$	−67.3523	+	162.603i	−0.434531	+	1.04905i
$156$	116.998	+	78.1757i	0.749988	+	0.501126i
$157$	41.0122	+	41.0122i	0.261224	+	0.261224i	0.825551	−	0.564327i	$-0.190864\pi$
$157$	41.0122	+	41.0122i	0.261224	+	0.261224i	−0.564327	+	0.825551i	$0.690864\pi$
$158$	−73.6047	+	14.6409i	−0.465852	+	0.0926638i
$159$	−70.1989	+	46.9054i	−0.441502	+	0.295002i
$160$	151.810	+	30.1968i	0.948810	+	0.188730i
$161$	81.3014	−	33.6761i	0.504978	−	0.209169i
$162$	11.0978	+	26.7925i	0.0685051	+	0.165386i
$163$	35.6871	−	179.411i	0.218939	−	1.10068i	−0.702358	−	0.711824i	$-0.747869\pi$
$163$	35.6871	−	179.411i	0.218939	−	1.10068i	0.921297	−	0.388859i	$-0.127131\pi$
$164$	15.6351	+	23.3996i	0.0953362	+	0.142681i
$165$	20.1312	+	101.206i	0.122007	+	0.613372i
$166$	−41.0122	+	41.0122i	−0.247061	+	0.247061i
$167$	−67.7522	+	101.398i	−0.405702	+	0.607176i	−0.976916	−	0.213625i	$-0.931473\pi$
$167$	−67.7522	+	101.398i	−0.405702	+	0.607176i	0.571214	+	0.820801i	$0.306473\pi$
$168$	−284.555	−	117.866i	−1.69378	−	0.701586i
$169$			69.0000i			0.408284i
$170$		0			0
$171$	−234.000			−1.36842
$172$	−43.6259	+	105.322i	−0.253639	+	0.612339i
$173$	3.89994	+	2.60586i	0.0225430	+	0.0150627i	0.566791	−	0.823862i	$-0.308185\pi$
$173$	3.89994	+	2.60586i	0.0225430	+	0.0150627i	−0.544248	+	0.838925i	$0.683185\pi$
$174$	171.120	+	171.120i	0.983447	+	0.983447i
$175$	−27.6017	+	5.49033i	−0.157724	+	0.0313733i
$176$	19.4997	−	13.0293i	0.110794	−	0.0740300i
$177$	340.422	+	67.7140i	1.92329	+	0.382565i
$178$	72.0626	−	29.8493i	0.404846	−	0.167693i
$179$	−89.5479	−	216.188i	−0.500268	−	1.20775i	−0.949338	−	0.314257i	$-0.898245\pi$
$179$	−89.5479	−	216.188i	−0.500268	−	1.20775i	0.449070	−	0.893496i	$-0.351755\pi$
$180$	35.6871	−	179.411i	0.198262	−	0.996730i
$181$	−179.804	−	269.096i	−0.993392	−	1.48672i	−0.869201	−	0.494458i	$-0.835366\pi$
$181$	−179.804	−	269.096i	−0.993392	−	1.48672i	−0.124191	−	0.992258i	$-0.539634\pi$
$182$	18.3011	+	92.0058i	0.100555	+	0.505526i
$183$	77.7817	−	77.7817i	0.425037	−	0.425037i
$184$	−36.4820	+	54.5991i	−0.198272	+	0.296734i
$185$	−20.3253	−	8.41904i	−0.109867	−	0.0455083i
$186$			176.000i			0.946237i
$187$		0			0
$188$	−174.000			−0.925532
$189$	−67.3523	+	162.603i	−0.356361	+	0.860332i
$190$	70.1989	+	46.9054i	0.369468	+	0.246871i
$191$	137.179	+	137.179i	0.718213	+	0.718213i	0.968239	−	0.250026i	$-0.0804392\pi$
$191$	137.179	+	137.179i	0.718213	+	0.718213i	−0.250026	+	0.968239i	$0.580439\pi$
$192$	59.8038	−	11.8957i	0.311478	−	0.0619568i
$193$	−124.798	+	83.3874i	−0.646622	+	0.432059i	−0.835160	−	0.550007i	$-0.814625\pi$
$193$	−124.798	+	83.3874i	−0.646622	+	0.432059i	0.188538	+	0.982066i	$0.439625\pi$
$194$	128.808	+	25.6215i	0.663959	+	0.132070i
$195$	−203.253	+	84.1904i	−1.04233	+	0.431745i
$196$	44.7740	+	108.094i	0.228439	+	0.551500i
$197$	−57.6484	+	289.818i	−0.292632	+	1.47116i	0.502423	+	0.864622i	$0.332442\pi$
$197$	−57.6484	+	289.818i	−0.292632	+	1.47116i	−0.795055	+	0.606537i	$0.792558\pi$
$198$	33.8761	+	50.6992i	0.171092	+	0.256057i
$199$	5.49033	+	27.6017i	0.0275896	+	0.138702i	0.992125	−	0.125251i	$-0.0399736\pi$
$199$	5.49033	+	27.6017i	0.0275896	+	0.138702i	−0.964536	+	0.263953i	$0.914974\pi$
$200$	14.8492	−	14.8492i	0.0742462	−	0.0742462i
$201$	88.5991	−	132.598i	0.440791	−	0.659691i
$202$	31.4119	+	13.0112i	0.155504	+	0.0644121i
$203$		−	484.000i		−	2.38424i
$204$		0			0
$205$	−44.0000			−0.214634
$206$	−65.8216	+	158.907i	−0.319522	+	0.771395i
$207$	101.398	+	67.7522i	0.489847	+	0.327306i
$208$	35.3553	+	35.3553i	0.169978	+	0.169978i
$209$	82.8052	−	16.4710i	0.396197	−	0.0788085i
$210$	171.597	−	114.658i	0.817130	−	0.545989i
$211$	−381.824	−	75.9495i	−1.80959	−	0.359950i	−0.829503	−	0.558503i	$-0.811376\pi$
$211$	−381.824	−	75.9495i	−1.80959	−	0.359950i	−0.980090	+	0.198552i	$0.936376\pi$
$212$	−49.8895	+	20.6649i	−0.235328	+	0.0974760i
$213$	151.543	+	365.856i	0.711468	+	1.71764i
$214$	−30.1968	+	151.810i	−0.141107	+	0.709391i
$215$	−99.0225	−	148.198i	−0.460570	−	0.689291i
$216$	−25.6215	−	128.808i	−0.118618	−	0.596334i
$217$	248.902	−	248.902i	1.14701	−	1.14701i
$218$	39.0878	−	58.4991i	0.179302	−	0.268344i
$219$	−365.856	−	151.543i	−1.67058	−	0.691976i
$220$			66.0000i			0.300000i
$221$		0			0
$222$	−22.0000			−0.0990991
$223$	45.1566	−	109.018i	0.202496	−	0.488869i	−0.789709	−	0.613481i	$-0.789769\pi$
$223$	45.1566	−	109.018i	0.202496	−	0.488869i	0.992206	+	0.124612i	$0.0397687\pi$
$224$	−257.396	−	171.986i	−1.14909	−	0.767797i
$225$	−27.5772	−	27.5772i	−0.122565	−	0.122565i
$226$	−73.6047	+	14.6409i	−0.325684	+	0.0647826i
$227$	−191.097	+	127.687i	−0.841837	+	0.562497i	−0.900040	−	0.435807i	$-0.856463\pi$
$227$	−191.097	+	127.687i	−0.841837	+	0.562497i	0.0582031	+	0.998305i	$0.481463\pi$
$228$	−248.416	−	49.4130i	−1.08954	−	0.216723i
$229$	−120.104	+	49.7488i	−0.524473	+	0.217244i	−0.629181	−	0.777259i	$-0.716609\pi$
$229$	−120.104	+	49.7488i	−0.524473	+	0.217244i	0.104707	+	0.994503i	$0.466609\pi$
$230$	−16.8381	−	40.6507i	−0.0732090	−	0.176742i
$231$	40.2624	−	202.413i	0.174296	−	0.876246i
$232$	200.651	+	300.295i	0.864874	+	1.29438i
$233$	−56.7334	−	285.218i	−0.243491	−	1.22411i	−0.888118	−	0.459615i	$-0.847987\pi$
$233$	−56.7334	−	285.218i	−0.243491	−	1.22411i	0.644627	−	0.764497i	$-0.277013\pi$
$234$	−91.9239	+	91.9239i	−0.392837	+	0.392837i
$235$	151.140	−	226.196i	0.643147	−	0.962538i
$236$	205.101	+	84.9557i	0.869073	+	0.359982i
$237$			352.000i			1.48523i
$238$		0			0
$239$	70.0000			0.292887			0.146444	−	0.989219i	$-0.453217\pi$
$239$	70.0000			0.292887			0.146444	+	0.989219i	$0.453217\pi$
$240$	42.0952	−	101.627i	0.175397	−	0.423445i
$241$	−62.3990	−	41.6937i	−0.258917	−	0.173003i	0.419336	−	0.907831i	$-0.362263\pi$
$241$	−62.3990	−	41.6937i	−0.258917	−	0.173003i	−0.678253	+	0.734828i	$0.737263\pi$
$242$	70.0036	+	70.0036i	0.289271	+	0.289271i
$243$	299.019	−	59.4786i	1.23053	−	0.244768i
$244$	58.4991	−	39.0878i	0.239750	−	0.160196i
$245$	−179.411	−	35.6871i	−0.732291	−	0.145662i
$246$	−40.6507	+	16.8381i	−0.165247	+	0.0684474i
$247$	68.8830	+	166.298i	0.278879	+	0.673273i
$248$	−51.2431	+	257.616i	−0.206625	+	1.03878i
$249$	151.140	+	226.196i	0.606986	+	0.908419i
$250$	25.6215	+	128.808i	0.102486	+	0.515233i
$251$	−281.428	+	281.428i	−1.12123	+	1.12123i	−0.129672	+	0.991557i	$0.541392\pi$
$251$	−281.428	+	281.428i	−1.12123	+	1.12123i	−0.991557	+	0.129672i	$0.958608\pi$
$252$	−203.257	+	304.195i	−0.806574	+	1.20712i
$253$	−40.6507	−	16.8381i	−0.160675	−	0.0665536i
$254$		−	96.0000i		−	0.377953i
$255$		0			0
$256$	171.000			0.667969
$257$	−150.012	+	362.161i	−0.583704	+	1.40919i	0.305728	+	0.952119i	$0.401100\pi$
$257$	−150.012	+	362.161i	−0.583704	+	1.40919i	−0.889432	+	0.457067i	$0.848900\pi$
$258$	−148.198	−	99.0225i	−0.574409	−	0.383808i
$259$	31.1127	+	31.1127i	0.120126	+	0.120126i
$260$	−138.009	+	27.4516i	−0.530803	+	0.105583i
$261$	557.691	−	372.637i	2.13675	−	1.42773i
$262$	−105.807	−	21.0463i	−0.403842	−	0.0803292i
$263$	−25.8686	+	10.7151i	−0.0983598	+	0.0407420i	−0.431321	−	0.902199i	$-0.641952\pi$
$263$	−25.8686	+	10.7151i	−0.0983598	+	0.0407420i	0.332961	+	0.942941i	$0.391952\pi$
$264$	58.9332	+	142.277i	0.223232	+	0.538930i
$265$	16.4710	−	82.8052i	0.0621547	−	0.312473i
$266$	−93.8108	−	140.398i	−0.352672	−	0.527811i
$267$	−71.3743	−	358.823i	−0.267319	−	1.34391i
$268$	72.1249	−	72.1249i	0.269123	−	0.269123i
$269$	−23.4527	+	35.0994i	−0.0871848	+	0.130481i	−0.872499	−	0.488617i	$-0.837502\pi$
$269$	−23.4527	+	35.0994i	−0.0871848	+	0.130481i	0.785314	+	0.619098i	$0.212502\pi$
$270$	81.3014	+	33.6761i	0.301116	+	0.124726i
$271$			306.000i			1.12915i	0.825381	+	0.564576i	$0.190960\pi$
$271$			306.000i			1.12915i	−0.825381	+	0.564576i	$0.809040\pi$
$272$		0			0
$273$	440.000			1.61172
$274$	90.3133	−	218.036i	0.329611	−	0.795750i
$275$	11.6998	+	7.81757i	0.0425448	+	0.0284275i
$276$	93.3381	+	93.3381i	0.338182	+	0.338182i
$277$	308.219	−	61.3087i	1.11271	−	0.221331i	0.395687	−	0.918385i	$-0.370506\pi$
$277$	308.219	−	61.3087i	1.11271	−	0.221331i	0.717018	+	0.697054i	$0.245506\pi$
$278$	−3.89994	+	2.60586i	−0.0140286	+	0.00937358i
$279$	478.430	+	95.1657i	1.71480	+	0.341096i
$280$	284.555	−	117.866i	1.01627	−	0.420952i
$281$	−154.604	−	373.247i	−0.550193	−	1.32828i	−0.917334	−	0.398117i	$-0.869664\pi$
$281$	−154.604	−	373.247i	−0.550193	−	1.32828i	0.367142	−	0.930165i	$-0.380336\pi$
$282$	53.0732	−	266.817i	0.188203	−	0.946159i
$283$	−91.2049	−	136.498i	−0.322279	−	0.482325i	0.634588	−	0.772850i	$-0.281170\pi$
$283$	−91.2049	−	136.498i	−0.322279	−	0.482325i	−0.956867	+	0.290526i	$0.906170\pi$
$284$	49.4130	+	248.416i	0.173989	+	0.874703i
$285$	280.014	−	280.014i	0.982506	−	0.982506i
$286$	26.0586	−	38.9994i	0.0911138	−	0.136361i
$287$	81.3014	+	33.6761i	0.283280	+	0.117338i
$288$		−	429.000i		−	1.48958i
$289$		0			0
$290$	−242.000			−0.834483
$291$	235.733	−	569.110i	0.810079	−	1.95570i
$292$	−210.597	−	140.716i	−0.721221	−	0.481905i
$293$	−295.571	−	295.571i	−1.00877	−	1.00877i	−0.999961	−	0.00881233i	$-0.997195\pi$
$293$	−295.571	−	295.571i	−1.00877	−	1.00877i	−0.00881233	−	0.999961i	$-0.502805\pi$
$294$	−179.411	+	35.6871i	−0.610243	+	0.121385i
$295$	−288.595	+	192.833i	−0.978290	+	0.653672i
$296$	−32.2020	−	6.40538i	−0.108791	−	0.0216398i
$297$	81.3014	−	33.6761i	0.273742	−	0.113388i
$298$	−22.1956	−	53.5850i	−0.0744820	−	0.179815i
$299$	18.3011	−	92.0058i	0.0612077	−	0.307712i
$300$	−23.4527	−	35.0994i	−0.0781757	−	0.116998i
$301$	69.5442	+	349.622i	0.231044	+	1.16154i
$302$	31.1127	−	31.1127i	0.103022	−	0.103022i
$303$	88.5991	−	132.598i	0.292406	−	0.437617i
$304$	−83.1492	−	34.4415i	−0.273517	−	0.113294i
$305$			110.000i			0.360656i
$306$		0			0
$307$	−66.0000			−0.214984			−0.107492	−	0.994206i	$-0.534282\pi$
$307$	−66.0000			−0.214984			−0.107492	+	0.994206i	$0.534282\pi$
$308$	50.5142	−	121.952i	0.164007	−	0.395948i
$309$	670.789	+	448.207i	2.17084	+	1.45051i
$310$	−124.451	−	124.451i	−0.401454	−	0.401454i
$311$	−395.625	+	78.6947i	−1.27211	+	0.253038i	−0.784556	−	0.620058i	$-0.787109\pi$
$311$	−395.625	+	78.6947i	−1.27211	+	0.253038i	−0.487550	+	0.873095i	$0.662109\pi$
$312$	−272.996	+	182.410i	−0.874986	+	0.584647i
$313$	322.020	+	64.0538i	1.02882	+	0.204645i	0.680513	−	0.732736i	$-0.261757\pi$
$313$	322.020	+	64.0538i	1.02882	+	0.204645i	0.348306	+	0.937381i	$0.386757\pi$
$314$	−53.5850	+	22.1956i	−0.170653	+	0.0706867i
$315$	−218.895	−	528.459i	−0.694905	−	1.67765i
$316$	−43.9226	+	220.814i	−0.138996	+	0.698778i
$317$	−91.2049	−	136.498i	−0.287713	−	0.430593i	0.659256	−	0.751919i	$-0.270871\pi$
$317$	−91.2049	−	136.498i	−0.287713	−	0.430593i	−0.946969	+	0.321326i	$0.895871\pi$
$318$	−16.4710	−	82.8052i	−0.0517956	−	0.260394i
$319$	−171.120	+	171.120i	−0.536426	+	0.536426i
$320$	−33.8761	+	50.6992i	−0.105863	+	0.158435i
$321$	670.737	+	277.828i	2.08952	+	0.865508i
$322$			88.0000i			0.273292i
$323$		0			0
$324$	87.0000			0.268519
$325$	−11.4805	+	27.7164i	−0.0353246	+	0.0852812i
$326$	152.098	+	101.628i	0.466557	+	0.311743i
$327$	−233.345	−	233.345i	−0.713594	−	0.713594i
$328$	−64.4041	+	12.8108i	−0.196354	+	0.0390572i
$329$	−452.393	+	302.279i	−1.37505	+	0.918782i
$330$	−101.206	−	20.1312i	−0.306686	−	0.0610036i
$331$	−120.104	+	49.7488i	−0.362853	+	0.150299i	−0.556659	−	0.830741i	$-0.687917\pi$
$331$	−120.104	+	49.7488i	−0.362853	+	0.150299i	0.193806	+	0.981040i	$0.437917\pi$
$332$	66.5869	+	160.755i	0.200563	+	0.484202i
$333$	−11.8957	+	59.8038i	−0.0357229	+	0.179591i
$334$	−67.7522	−	101.398i	−0.202851	−	0.303588i
$335$	31.1119	+	156.410i	0.0928712	+	0.466895i
$336$	−155.563	+	155.563i	−0.462987	+	0.462987i
$337$	20.8468	−	31.1995i	0.0618601	−	0.0925801i	−0.799250	−	0.600999i	$-0.794770\pi$
$337$	20.8468	−	31.1995i	0.0618601	−	0.0925801i	0.861110	+	0.508419i	$0.169770\pi$
$338$	−63.7477	−	26.4052i	−0.188603	−	0.0781218i
$339$			352.000i			1.03835i
$340$		0			0
$341$	−176.000			−0.516129
$342$	89.5479	−	216.188i	0.261836	−	0.632128i
$343$	−77.9988	−	52.1171i	−0.227402	−	0.151945i
$344$	−188.090	−	188.090i	−0.546774	−	0.546774i
$345$	−202.413	+	40.2624i	−0.586704	+	0.116703i
$346$	−3.89994	+	2.60586i	−0.0112715	+	0.00753137i
$347$	87.4055	+	17.3860i	0.251889	+	0.0501039i	0.319420	−	0.947613i	$-0.396512\pi$
$347$	87.4055	+	17.3860i	0.251889	+	0.0501039i	−0.0675306	+	0.997717i	$0.521512\pi$
$348$	670.737	−	277.828i	1.92740	−	0.798357i
$349$	−193.638	−	467.483i	−0.554836	−	1.33949i	−0.913809	−	0.406145i	$-0.866873\pi$
$349$	−193.638	−	467.483i	−0.554836	−	1.33949i	0.358973	−	0.933348i	$-0.383127\pi$
$350$	5.49033	−	27.6017i	0.0156867	−	0.0788621i
$351$	104.234	+	155.998i	0.296964	+	0.444437i
$352$	30.1968	+	151.810i	0.0857864	+	0.431277i
$353$	−209.304	+	209.304i	−0.592928	+	0.592928i	−0.938421	−	0.345493i	$-0.887712\pi$
$353$	−209.304	+	209.304i	−0.592928	+	0.592928i	0.345493	+	0.938421i	$0.387712\pi$
$354$	−192.833	+	288.595i	−0.544727	+	0.815241i
$355$	−365.856	−	151.543i	−1.03058	−	0.426881i
$356$		−	234.000i		−	0.657303i
$357$		0			0
$358$	234.000			0.653631
$359$	−84.9557	+	205.101i	−0.236645	+	0.571313i	−0.996932	−	0.0782754i	$-0.975059\pi$
$359$	−84.9557	+	205.101i	−0.236645	+	0.571313i	0.760286	+	0.649588i	$0.225059\pi$
$360$	354.894	+	237.133i	0.985818	+	0.658702i
$361$	26.1630	+	26.1630i	0.0724735	+	0.0724735i
$362$	317.420	−	63.1388i	0.876851	−	0.174417i
$363$	386.094	−	257.980i	1.06362	−	0.710688i
$364$	276.017	+	54.9033i	0.758290	+	0.150833i
$365$	365.856	−	151.543i	1.00235	−	0.415185i
$366$	42.0952	+	101.627i	0.115014	+	0.277669i
$367$	−73.2044	+	368.023i	−0.199467	+	1.00279i	0.743204	+	0.669065i	$0.233305\pi$
$367$	−73.2044	+	368.023i	−0.199467	+	1.00279i	−0.942671	+	0.333723i	$0.891695\pi$
$368$	26.0586	+	38.9994i	0.0708113	+	0.105977i
$369$	23.7914	+	119.608i	0.0644754	+	0.324140i
$370$	15.5563	−	15.5563i	0.0420442	−	0.0420442i
$371$	−93.8108	+	140.398i	−0.252859	+	0.378431i
$372$	487.808	+	202.057i	1.31131	+	0.543164i
$373$		−	170.000i		−	0.455764i	−0.973689	−	0.227882i	$-0.926820\pi$
$373$		−	170.000i		−	0.455764i	0.973689	−	0.227882i	$-0.0731801\pi$
$374$		0			0
$375$	616.000			1.64267
$376$	155.369	−	375.095i	0.413217	−	0.997593i
$377$	−428.993	−	286.644i	−1.13791	−	0.760329i
$378$	−124.451	−	124.451i	−0.329235	−	0.329235i
$379$	−317.420	+	63.1388i	−0.837520	+	0.166593i	−0.595174	−	0.803597i	$-0.702917\pi$
$379$	−317.420	+	63.1388i	−0.837520	+	0.166593i	−0.242346	+	0.970190i	$0.577917\pi$
$380$	210.597	−	140.716i	0.554202	−	0.370306i
$381$	−441.628	−	87.8453i	−1.15913	−	0.230565i
$382$	−179.233	+	74.2406i	−0.469195	+	0.194347i
$383$	−24.4917	−	59.1283i	−0.0639471	−	0.154382i	0.888676	−	0.458536i	$-0.151626\pi$
$383$	−24.4917	−	59.1283i	−0.0639471	−	0.154382i	−0.952623	+	0.304154i	$0.901626\pi$
$384$	108.892	−	547.435i	0.283572	−	1.42561i
$385$	114.658	+	171.597i	0.297812	+	0.445707i
$386$	−29.2818	−	147.209i	−0.0758595	−	0.381371i
$387$	−349.311	+	349.311i	−0.902612	+	0.902612i
$388$	218.892	−	327.595i	0.564154	−	0.844317i
$389$	430.528	+	178.330i	1.10676	+	0.458433i	0.859819	−	0.510599i	$-0.170576\pi$
$389$	430.528	+	178.330i	1.10676	+	0.458433i	0.246936	+	0.969032i	$0.420576\pi$
$390$		−	220.000i		−	0.564103i
$391$		0			0
$392$	−273.000			−0.696429
$393$	−193.638	+	467.483i	−0.492717	+	1.18952i
$394$	−245.696	−	164.169i	−0.623594	−	0.416672i
$395$	−248.902	−	248.902i	−0.630131	−	0.630131i
$396$	179.411	−	35.6871i	0.453059	−	0.0901190i
$397$	339.295	−	226.709i	0.854646	−	0.571056i	−0.0492604	−	0.998786i	$-0.515686\pi$
$397$	339.295	−	226.709i	0.854646	−	0.571056i	0.903907	+	0.427730i	$0.140686\pi$
$398$	−27.6017	−	5.49033i	−0.0693511	−	0.0137948i
$399$	−731.713	+	303.085i	−1.83387	+	0.759612i
$400$	−5.74025	−	13.8582i	−0.0143506	−	0.0346455i
$401$	113.467	−	570.436i	0.282960	−	1.42253i	−0.533827	−	0.845594i	$-0.679247\pi$
$401$	113.467	−	570.436i	0.282960	−	1.42253i	0.816787	−	0.576940i	$-0.195753\pi$
$402$	88.5991	+	132.598i	0.220396	+	0.329846i
$403$	−73.2044	−	368.023i	−0.181649	−	0.913209i
$404$	72.1249	−	72.1249i	0.178527	−	0.178527i
$405$	−75.5698	+	113.098i	−0.186592	+	0.279255i
$406$	447.158	+	185.219i	1.10137	+	0.456204i
$407$		−	22.0000i		−	0.0540541i
$408$		0			0
$409$	−100.000			−0.244499			−0.122249	−	0.992499i	$-0.539011\pi$
$409$	−100.000			−0.244499			−0.122249	+	0.992499i	$0.539011\pi$
$410$	16.8381	−	40.6507i	0.0410685	−	0.0991480i
$411$	−920.385	−	614.982i	−2.23938	−	1.49631i
$412$	364.867	+	364.867i	0.885600	+	0.885600i
$413$	680.843	−	135.428i	1.64853	−	0.327913i
$414$	−101.398	+	67.7522i	−0.244924	+	0.163653i
$415$	−266.817	−	53.0732i	−0.642932	−	0.127887i
$416$	−304.880	+	126.286i	−0.732885	+	0.303571i
$417$	8.41904	+	20.3253i	0.0201895	+	0.0487418i
$418$	−16.4710	+	82.8052i	−0.0394043	+	0.198099i
$419$	−2.60586	−	3.89994i	−0.00621923	−	0.00930773i	0.828347	−	0.560215i	$-0.189282\pi$
$419$	−2.60586	−	3.89994i	−0.00621923	−	0.00930773i	−0.834566	+	0.550908i	$0.814282\pi$
$420$	−120.787	−	607.238i	−0.287589	−	1.44581i
$421$	439.820	−	439.820i	1.04470	−	1.04470i	0.0457512	−	0.998953i	$-0.485432\pi$
$421$	439.820	−	439.820i	1.04470	−	1.04470i	0.998953	−	0.0457512i	$-0.0145681\pi$
$422$	216.286	−	323.695i	0.512526	−	0.767049i
$423$	−696.605	−	288.543i	−1.64682	−	0.682135i
$424$		−	126.000i		−	0.297170i
$425$		0			0
$426$	−396.000			−0.929577
$427$	84.1904	−	203.253i	0.197167	−	0.476004i
$428$	386.094	+	257.980i	0.902089	+	0.602756i
$429$	−155.563	−	155.563i	−0.362619	−	0.362619i
$430$	174.811	−	34.7721i	0.406537	−	0.0808653i
$431$	140.398	−	93.8108i	0.325749	−	0.217658i	−0.381932	−	0.924190i	$-0.624741\pi$
$431$	140.398	−	93.8108i	0.325749	−	0.217658i	0.707681	+	0.706532i	$0.249741\pi$
$432$	−92.0058	−	18.3011i	−0.212976	−	0.0423636i
$433$	382.486	−	158.431i	0.883340	−	0.365891i	0.105549	−	0.994414i	$-0.466340\pi$
$433$	382.486	−	158.431i	0.883340	−	0.365891i	0.777791	+	0.628523i	$0.216340\pi$
$434$	134.705	+	325.206i	0.310379	+	0.749322i
$435$	−221.443	+	1113.27i	−0.509065	+	2.55924i
$436$	−117.263	−	175.497i	−0.268953	−	0.402517i
$437$	32.9420	+	165.610i	0.0753821	+	0.378971i
$438$	280.014	−	280.014i	0.639302	−	0.639302i
$439$	−244.950	+	366.594i	−0.557974	+	0.835066i	−0.998019	−	0.0629089i	$-0.979962\pi$
$439$	−244.950	+	366.594i	−0.557974	+	0.835066i	0.440046	+	0.897975i	$0.354962\pi$
$440$	−142.277	−	58.9332i	−0.323358	−	0.133939i
$441$			507.000i			1.14966i
$442$		0			0
$443$	478.000			1.07901			0.539503	−	0.841983i	$-0.318612\pi$
$443$	478.000			1.07901			0.539503	+	0.841983i	$0.318612\pi$
$444$	−25.2571	+	60.9760i	−0.0568854	+	0.137333i
$445$	304.195	+	203.257i	0.683585	+	0.456757i
$446$	83.4386	+	83.4386i	0.187082	+	0.187082i
$447$	−266.817	+	53.0732i	−0.596906	+	0.118732i
$448$	101.398	−	67.7522i	0.226336	−	0.151233i
$449$	−772.849	−	153.729i	−1.72127	−	0.342381i	−0.767071	−	0.641563i	$-0.778286\pi$
$449$	−772.849	−	153.729i	−1.72127	−	0.342381i	−0.954196	+	0.299181i	$0.903286\pi$
$450$	36.0313	−	14.9247i	0.0800696	−	0.0331659i
$451$	−16.8381	−	40.6507i	−0.0373350	−	0.0901346i
$452$	−43.9226	+	220.814i	−0.0971740	+	0.488526i
$453$	−114.658	−	171.597i	−0.253107	−	0.378802i
$454$	−44.8377	−	225.414i	−0.0987614	−	0.496507i
$455$	−311.127	+	311.127i	−0.683796	+	0.683796i
$456$	328.338	−	491.392i	0.720039	−	1.07761i
$457$	−386.182	−	159.962i	−0.845036	−	0.350026i	−0.0821990	−	0.996616i	$-0.526194\pi$
$457$	−386.182	−	159.962i	−0.845036	−	0.350026i	−0.762837	+	0.646590i	$0.776194\pi$
$458$		−	130.000i		−	0.283843i
$459$		0			0
$460$	−132.000			−0.286957
$461$	−137.001	+	330.749i	−0.297181	+	0.717460i	0.702800	+	0.711387i	$0.251933\pi$
$461$	−137.001	+	330.749i	−0.297181	+	0.717460i	−0.999982	+	0.00607217i	$0.998067\pi$
$462$	171.597	+	114.658i	0.371423	+	0.248177i
$463$	209.304	+	209.304i	0.452060	+	0.452060i	0.896038	−	0.443978i	$-0.146433\pi$
$463$	209.304	+	209.304i	0.452060	+	0.452060i	−0.443978	+	0.896038i	$0.646433\pi$
$464$	253.016	−	50.3280i	0.545293	−	0.108466i
$465$	−686.389	+	458.631i	−1.47611	+	0.986302i
$466$	285.218	+	56.7334i	0.612056	+	0.121745i
$467$	131.191	−	54.3410i	0.280923	−	0.116362i	−0.237773	−	0.971321i	$-0.576418\pi$
$467$	131.191	−	54.3410i	0.280923	−	0.116362i	0.518696	+	0.854959i	$0.326418\pi$
$468$	149.247	+	360.313i	0.318903	+	0.769900i
$469$	62.2237	−	312.820i	0.132673	−	0.666993i
$470$	151.140	+	226.196i	0.321574	+	0.481269i
$471$	53.0732	+	266.817i	0.112682	+	0.566490i
$472$	−366.281	+	366.281i	−0.776020	+	0.776020i
$473$	99.0225	−	148.198i	0.209350	−	0.313314i
$474$	−325.206	−	134.705i	−0.686088	−	0.284187i
$475$		−	54.0000i		−	0.113684i
$476$		0			0
$477$	−234.000			−0.490566
$478$	−26.7878	+	64.6716i	−0.0560415	+	0.135296i
$479$	202.797	+	135.504i	0.423375	+	0.282890i	0.748951	−	0.662626i	$-0.230558\pi$
$479$	202.797	+	135.504i	0.423375	+	0.282890i	−0.325575	+	0.945516i	$0.605558\pi$
$480$	513.360	+	513.360i	1.06950	+	1.06950i
$481$	46.0029	−	9.15055i	0.0956401	−	0.0190240i
$482$	62.3990	−	41.6937i	0.129459	−	0.0865014i
$483$	404.826	+	80.5248i	0.838148	+	0.166718i
$484$	274.392	−	113.657i	0.566926	−	0.234828i
$485$	235.733	+	569.110i	0.486047	+	1.17342i
$486$	−59.4786	+	299.019i	−0.122384	+	0.615265i
$487$	−46.9054	−	70.1989i	−0.0963150	−	0.144146i	0.780183	−	0.625552i	$-0.215126\pi$
$487$	−46.9054	−	70.1989i	−0.0963150	−	0.144146i	−0.876498	+	0.481406i	$0.840126\pi$
$488$	32.0269	+	161.010i	0.0656289	+	0.329939i
$489$	606.698	−	606.698i	1.24069	−	1.24069i
$490$	101.628	−	152.098i	0.207405	−	0.310403i
$491$	−386.182	−	159.962i	−0.786521	−	0.325788i	−0.0469769	−	0.998896i	$-0.514959\pi$
$491$	−386.182	−	159.962i	−0.786521	−	0.325788i	−0.739544	+	0.673108i	$0.764959\pi$
$492$			132.000i			0.268293i
$493$		0			0
$494$	−180.000			−0.364372
$495$	−109.447	+	264.230i	−0.221106	+	0.533797i
$496$	155.998	+	104.234i	0.314511	+	0.210150i
$497$	560.029	+	560.029i	1.12682	+	1.12682i
$498$	−266.817	+	53.0732i	−0.535777	+	0.106573i
$499$	206.697	−	138.110i	0.414222	−	0.276774i	−0.330948	−	0.943649i	$-0.607368\pi$
$499$	206.697	−	138.110i	0.414222	−	0.276774i	0.745170	+	0.666875i	$0.232368\pi$
$500$	386.424	+	76.8646i	0.772849	+	0.153729i
$501$	−528.459	+	218.895i	−1.05481	+	0.436916i
$502$	−152.308	−	367.704i	−0.303402	−	0.732478i
$503$	82.3549	−	414.026i	0.163727	−	0.823114i	−0.808395	−	0.588640i	$-0.799663\pi$
$503$	82.3549	−	414.026i	0.163727	−	0.823114i	0.972123	−	0.234473i	$-0.0753366\pi$
$504$	−474.266	−	709.789i	−0.941003	−	1.40831i
$505$	31.1119	+	156.410i	0.0616076	+	0.309723i
$506$	31.1127	−	31.1127i	0.0614875	−	0.0614875i
$507$	−179.804	+	269.096i	−0.354643	+	0.530761i
$508$	−266.077	−	110.213i	−0.523774	−	0.216954i
$509$			850.000i			1.66994i	0.550295	+	0.834971i	$0.314515\pi$
$509$			850.000i			1.66994i	−0.550295	+	0.834971i	$0.685485\pi$
$510$		0			0
$511$	−792.000			−1.54990
$512$	116.718	−	281.783i	0.227966	−	0.550358i
$513$	−280.796	−	187.622i	−0.547360	−	0.365734i
$514$	−277.186	−	277.186i	−0.539272	−	0.539272i
$515$	−791.250	+	157.389i	−1.53641	+	0.305611i
$516$	−444.593	+	297.068i	−0.861614	+	0.575712i
$517$	266.817	+	53.0732i	0.516087	+	0.102656i
$518$	−40.6507	+	16.8381i	−0.0784763	+	0.0325059i
$519$	8.41904	+	20.3253i	0.0162216	+	0.0391625i
$520$	64.0538	−	322.020i	0.123180	−	0.619270i
$521$	484.689	+	725.389i	0.930305	+	1.39230i	0.919814	+	0.392355i	$0.128340\pi$
$521$	484.689	+	725.389i	0.930305	+	1.39230i	0.0104917	+	0.999945i	$0.496660\pi$
$522$	130.853	+	657.842i	0.250676	+	1.26023i
$523$	632.153	−	632.153i	1.20871	−	1.20871i	0.237260	−	0.971446i	$-0.423751\pi$
$523$	632.153	−	632.153i	1.20871	−	1.20871i	0.971446	−	0.237260i	$-0.0762494\pi$
$524$	−179.804	+	269.096i	−0.343137	+	0.513541i
$525$	−121.952	−	50.5142i	−0.232290	−	0.0962175i
$526$		−	28.0000i		−	0.0532319i
$527$		0			0
$528$	110.000			0.208333
$529$	−168.763	+	407.431i	−0.319023	+	0.770191i
$530$	70.1989	+	46.9054i	0.132451	+	0.0885007i
$531$	680.237	+	680.237i	1.28105	+	1.28105i
$532$	−496.831	+	98.8259i	−0.933894	+	0.185763i
$533$	77.9988	−	52.1171i	0.146339	−	0.0977807i
$534$	358.823	+	71.3743i	0.671953	+	0.133660i
$535$	−670.737	+	277.828i	−1.25371	+	0.519305i
$536$	91.0787	+	219.883i	0.169923	+	0.410230i
$537$	214.123	−	1076.47i	0.398739	−	2.00460i
$538$	−23.4527	−	35.0994i	−0.0435924	−	0.0652406i
$539$	−35.6871	−	179.411i	−0.0662099	−	0.332860i
$540$	186.676	−	186.676i	0.345697	−	0.345697i
$541$	−466.448	+	698.089i	−0.862196	+	1.29037i	0.0933822	+	0.995630i	$0.470232\pi$
$541$	−466.448	+	698.089i	−0.862196	+	1.29037i	−0.955578	+	0.294737i	$0.904768\pi$
$542$	−282.707	−	117.101i	−0.521600	−	0.216054i
$543$		−	1518.00i		−	2.79558i
$544$		0			0
$545$	330.000			0.605505
$546$	−168.381	+	406.507i	−0.308390	+	0.744518i
$547$	534.292	+	357.002i	0.976767	+	0.652655i	0.938015	−	0.346594i	$-0.112662\pi$
$547$	534.292	+	357.002i	0.976767	+	0.652655i	0.0387517	+	0.999249i	$0.487662\pi$
$548$	−500.632	−	500.632i	−0.913561	−	0.913561i
$549$	299.019	−	59.4786i	0.544661	−	0.108340i
$550$	−11.6998	+	7.81757i	−0.0212724	+	0.0142138i
$551$	910.858	+	181.181i	1.65310	+	0.328822i
$552$	−284.555	+	117.866i	−0.515498	+	0.213526i
$553$	269.409	+	650.411i	0.487177	+	1.17615i
$554$	−61.3087	+	308.219i	−0.110665	+	0.556353i
$555$	−57.3288	−	85.7986i	−0.103295	−	0.154592i
$556$	2.74516	+	13.8009i	0.00493735	+	0.0248217i
$557$	−233.345	+	233.345i	−0.418932	+	0.418932i	−0.884836	−	0.465903i	$-0.845729\pi$
$557$	−233.345	+	233.345i	−0.418932	+	0.418932i	0.465903	+	0.884836i	$0.345729\pi$
$558$	−271.009	+	405.594i	−0.485679	+	0.726870i
$559$	351.074	+	145.420i	0.628040	+	0.260143i
$560$		−	220.000i		−	0.392857i
$561$		0			0
$562$	404.000			0.718861
$563$	97.2016	−	234.665i	0.172649	−	0.416812i	−0.813742	−	0.581226i	$-0.802573\pi$
$563$	97.2016	−	234.665i	0.172649	−	0.416812i	0.986391	+	0.164414i	$0.0525732\pi$
$564$	−678.589	−	453.419i	−1.20317	−	0.803934i
$565$	−248.902	−	248.902i	−0.440534	−	0.440534i
$566$	161.010	−	32.0269i	0.284470	−	0.0565847i
$567$	226.196	−	151.140i	0.398935	−	0.266560i
$568$	−579.637	−	115.297i	−1.02049	−	0.202987i
$569$	−57.2805	+	23.7264i	−0.100669	+	0.0416984i	−0.432449	−	0.901658i	$-0.642351\pi$
$569$	−57.2805	+	23.7264i	−0.100669	+	0.0416984i	0.331781	+	0.943357i	$0.392351\pi$
$570$	151.543	+	365.856i	0.265864	+	0.641853i
$571$	−26.5366	+	133.408i	−0.0464739	+	0.233640i	−0.997040	−	0.0768815i	$-0.975504\pi$
$571$	−26.5366	+	133.408i	−0.0464739	+	0.233640i	0.950566	+	0.310522i	$0.100504\pi$
$572$	−78.1757	−	116.998i	−0.136671	−	0.204542i
$573$	177.521	+	892.456i	0.309809	+	1.55752i
$574$	−62.2254	+	62.2254i	−0.108407	+	0.108407i
$575$	−15.6351	+	23.3996i	−0.0271915	+	0.0406950i
$576$	156.136	+	64.6735i	0.271069	+	0.112280i
$577$			408.000i			0.707106i	0.935415	+	0.353553i	$0.115027\pi$
$577$			408.000i			0.707106i	−0.935415	+	0.353553i	$0.884973\pi$
$578$		0			0
$579$	−704.000			−1.21589
$580$	−277.828	+	670.737i	−0.479014	+	1.15644i
$581$	452.393	+	302.279i	0.778645	+	0.520274i
$582$	435.578	+	435.578i	0.748415	+	0.748415i
$583$	82.8052	−	16.4710i	0.142033	−	0.0282521i
$584$	491.392	−	328.338i	0.841425	−	0.562222i
$585$	−598.038	−	118.957i	−1.02229	−	0.203345i
$586$	386.182	−	159.962i	0.659013	−	0.272972i
$587$	−141.593	−	341.835i	−0.241214	−	0.582343i	0.756190	−	0.654353i	$-0.227059\pi$
$587$	−141.593	−	341.835i	−0.241214	−	0.582343i	−0.997404	+	0.0720095i	$0.977059\pi$
$588$	−107.061	+	538.234i	−0.182077	+	0.915364i
$589$	375.243	+	561.591i	0.637085	+	0.953465i
$590$	−67.7140	−	340.422i	−0.114770	−	0.576986i
$591$	−980.050	+	980.050i	−1.65829	+	1.65829i
$592$	−13.0293	+	19.4997i	−0.0220089	+	0.0329387i
$593$	−197.710	−	81.8943i	−0.333407	−	0.138102i	0.209699	−	0.977766i	$-0.432752\pi$
$593$	−197.710	−	81.8943i	−0.333407	−	0.138102i	−0.543106	+	0.839664i	$0.682752\pi$
$594$			88.0000i			0.148148i
$595$		0			0
$596$	−174.000			−0.291946
$597$	−50.5142	+	121.952i	−0.0846134	+	0.204275i
$598$	77.9988	+	52.1171i	0.130433	+	0.0871524i
$599$	353.553	+	353.553i	0.590239	+	0.590239i	0.937696	−	0.347457i	$-0.112955\pi$
$599$	353.553	+	353.553i	0.590239	+	0.590239i	−0.347457	+	0.937696i	$0.612955\pi$
$600$	96.6061	−	19.2161i	0.161010	−	0.0320269i
$601$	−522.592	+	349.185i	−0.869537	+	0.581006i	−0.908336	−	0.418241i	$-0.862647\pi$
$601$	−522.592	+	349.185i	−0.869537	+	0.581006i	0.0387991	+	0.999247i	$0.487647\pi$
$602$	−349.622	−	69.5442i	−0.580768	−	0.115522i
$603$	408.355	−	169.146i	0.677205	−	0.280508i
$604$	−50.5142	−	121.952i	−0.0836328	−	0.201907i
$605$	−90.5904	+	455.429i	−0.149736	+	0.752775i
$606$	88.5991	+	132.598i	0.146203	+	0.218808i
$607$	−150.069	−	754.448i	−0.247231	−	1.24291i	−0.882385	−	0.470527i	$-0.844064\pi$
$607$	−150.069	−	754.448i	−0.247231	−	1.24291i	0.635155	−	0.772385i	$-0.280936\pi$
$608$	420.021	−	420.021i	0.690825	−	0.690825i
$609$	1261.23	−	1887.57i	2.07099	−	3.09946i
$610$	−101.627	−	42.0952i	−0.166601	−	0.0690085i
$611$			580.000i			0.949264i
$612$		0			0
$613$	−66.0000			−0.107667			−0.0538336	−	0.998550i	$-0.517144\pi$
$613$	−66.0000			−0.107667			−0.0538336	+	0.998550i	$0.517144\pi$
$614$	25.2571	−	60.9760i	0.0411354	−	0.0993095i
$615$	−171.597	−	114.658i	−0.279020	−	0.186435i
$616$	217.789	+	217.789i	0.353553	+	0.353553i
$617$	−395.625	+	78.6947i	−0.641207	+	0.127544i	−0.504977	−	0.863133i	$-0.668499\pi$
$617$	−395.625	+	78.6947i	−0.641207	+	0.127544i	−0.136231	+	0.990677i	$0.543499\pi$
$618$	−670.789	+	448.207i	−1.08542	+	0.725254i
$619$	−694.644	−	138.173i	−1.12220	−	0.223220i	−0.401091	−	0.916038i	$-0.631369\pi$
$619$	−694.644	−	138.173i	−1.12220	−	0.223220i	−0.721112	+	0.692818i	$0.756369\pi$
$620$	−487.808	+	202.057i	−0.786788	+	0.325898i
$621$	67.3523	+	162.603i	0.108458	+	0.261840i
$622$	78.6947	−	395.625i	0.126519	−	0.636053i
$623$	−406.513	−	608.390i	−0.652510	−	0.976550i
$624$	45.7527	+	230.015i	0.0733217	+	0.368613i
$625$	−382.545	+	382.545i	−0.612072	+	0.612072i
$626$	−182.410	+	272.996i	−0.291390	+	0.436095i
$627$	365.856	+	151.543i	0.583503	+	0.241695i
$628$			174.000i			0.277070i
$629$		0			0
$630$	572.000			0.907937
$631$	−6.88830	+	16.6298i	−0.0109165	+	0.0263547i	−0.929244	−	0.369467i	$-0.879540\pi$
$631$	−6.88830	+	16.6298i	−0.0109165	+	0.0263547i	0.918327	+	0.395822i	$0.129540\pi$
$632$	−436.793	−	291.856i	−0.691128	−	0.461797i
$633$	−1291.18	−	1291.18i	−2.03977	−	2.03977i
$634$	161.010	−	32.0269i	0.253959	−	0.0505156i
$635$	374.394	−	250.162i	0.589597	−	0.393956i
$636$	−248.416	−	49.4130i	−0.390591	−	0.0776933i
$637$	360.313	−	149.247i	0.565641	−	0.234296i
$638$	−92.6094	−	223.579i	−0.145156	−	0.350437i
$639$	−214.123	+	1076.47i	−0.335090	+	1.68461i
$640$	310.097	+	464.093i	0.484526	+	0.725145i
$641$	−212.293	−	1067.27i	−0.331190	−	1.66500i	−0.684132	−	0.729359i	$-0.739819\pi$
$641$	−212.293	−	1067.27i	−0.331190	−	1.66500i	0.352942	−	0.935645i	$-0.385181\pi$
$642$	−513.360	+	513.360i	−0.799625	+	0.799625i
$643$	65.1464	−	97.4985i	0.101316	−	0.151631i	−0.777348	−	0.629071i	$-0.783435\pi$
$643$	65.1464	−	97.4985i	0.101316	−	0.151631i	0.878664	+	0.477441i	$0.158435\pi$
$644$	243.904	+	101.028i	0.378733	+	0.156876i
$645$		−	836.000i		−	1.29612i
$646$		0			0
$647$	546.000			0.843895			0.421947	−	0.906620i	$-0.361347\pi$
$647$	546.000			0.843895			0.421947	+	0.906620i	$0.361347\pi$
$648$	−77.6847	+	187.548i	−0.119884	+	0.289425i
$649$	−288.595	−	192.833i	−0.444677	−	0.297124i
$650$	−21.2132	−	21.2132i	−0.0326357	−	0.0326357i
$651$	1619.30	−	322.099i	2.48741	−	0.494776i
$652$	456.293	−	304.885i	0.699836	−	0.467615i
$653$	556.635	+	110.722i	0.852428	+	0.169558i	0.601920	−	0.798556i	$-0.294403\pi$
$653$	556.635	+	110.722i	0.852428	+	0.169558i	0.250507	+	0.968115i	$0.419403\pi$
$654$	304.880	−	126.286i	0.466178	−	0.193097i
$655$	−193.638	−	467.483i	−0.295630	−	0.713715i
$656$	−9.15055	+	46.0029i	−0.0139490	+	0.0701264i
$657$	−609.770	−	912.586i	−0.928113	−	1.38902i
$658$	−106.146	−	533.634i	−0.161317	−	0.810994i
$659$	824.487	−	824.487i	1.25112	−	1.25112i	0.295898	−	0.955220i	$-0.404381\pi$
$659$	824.487	−	824.487i	1.25112	−	1.25112i	0.955220	−	0.295898i	$-0.0956189\pi$
$660$	−171.986	+	257.396i	−0.260586	+	0.389994i
$661$	618.999	+	256.398i	0.936459	+	0.387894i	0.798125	−	0.602492i	$-0.205825\pi$
$661$	618.999	+	256.398i	0.936459	+	0.387894i	0.138334	+	0.990386i	$0.455825\pi$
$662$		−	130.000i		−	0.196375i
$663$		0			0
$664$	−406.000			−0.611446
$665$	303.085	−	731.713i	0.455767	−	1.10032i
$666$	−50.6992	−	33.8761i	−0.0761249	−	0.0508650i
$667$	−342.240	−	342.240i	−0.513103	−	0.513103i
$668$	−358.823	+	71.3743i	−0.537160	+	0.106848i
$669$	460.193	−	307.491i	0.687881	−	0.459628i
$670$	−156.410	−	31.1119i	−0.233448	−	0.0464356i
$671$	−101.627	+	42.0952i	−0.151456	+	0.0627350i
$672$	−555.656	−	1341.47i	−0.826870	−	1.99624i
$673$	113.467	−	570.436i	0.168598	−	0.847602i	−0.800196	−	0.599738i	$-0.795271\pi$
$673$	113.467	−	570.436i	0.168598	−	0.847602i	0.968795	−	0.247864i	$-0.0797286\pi$
$674$	20.8468	+	31.1995i	0.0309300	+	0.0462901i
$675$	−10.9807	−	55.2035i	−0.0162676	−	0.0817829i
$676$	−146.371	+	146.371i	−0.216525	+	0.216525i
$677$	330.944	−	495.292i	0.488838	−	0.731598i	−0.502262	−	0.864716i	$-0.667499\pi$
$677$	330.944	−	495.292i	0.488838	−	0.731598i	0.991100	+	0.133117i	$0.0424986\pi$
$678$	−325.206	−	134.705i	−0.479654	−	0.198679i
$679$		−	1232.00i		−	1.81443i
$680$		0			0
$681$	−1078.00			−1.58297
$682$	67.3523	−	162.603i	0.0987570	−	0.238421i
$683$	3.89994	+	2.60586i	0.00571001	+	0.00381531i	0.558422	−	0.829557i	$-0.311407\pi$
$683$	3.89994	+	2.60586i	0.00571001	+	0.00381531i	−0.552712	+	0.833372i	$0.686407\pi$
$684$	−496.389	−	496.389i	−0.725715	−	0.725715i
$685$	1085.67	−	215.953i	1.58492	−	0.315260i
$686$	77.9988	−	52.1171i	0.113701	−	0.0759725i
$687$	−598.038	−	118.957i	−0.870506	−	0.173154i
$688$	−175.537	+	72.7099i	−0.255141	+	0.105683i
$689$	68.8830	+	166.298i	0.0999754	+	0.241362i
$690$	40.2624	−	202.413i	0.0583513	−	0.293352i
$691$	−91.2049	−	136.498i	−0.131990	−	0.197537i	0.759588	−	0.650405i	$-0.225401\pi$
$691$	−91.2049	−	136.498i	−0.131990	−	0.197537i	−0.891577	+	0.452868i	$0.850401\pi$
$692$	2.74516	+	13.8009i	0.00396700	+	0.0199435i
$693$	404.465	−	404.465i	0.583644	−	0.583644i
$694$	−49.5113	+	74.0988i	−0.0713419	+	0.106771i
$695$	−20.3253	−	8.41904i	−0.0292451	−	0.0121137i
$696$			1694.00i			2.43391i
$697$		0			0
$698$	506.000			0.724928
$699$	521.980	−	1260.17i	0.746753	−	1.80282i
$700$	−70.1989	−	46.9054i	−0.100284	−	0.0670077i
$701$	666.095	+	666.095i	0.950206	+	0.950206i	0.998818	−	0.0486115i	$-0.0154796\pi$
$701$	666.095	+	666.095i	0.950206	+	0.950206i	−0.0486115	+	0.998818i	$0.515480\pi$
$702$	−184.012	+	36.6022i	−0.262125	+	0.0521399i
$703$	−70.1989	+	46.9054i	−0.0998562	+	0.0667218i
$704$	−59.8038	−	11.8957i	−0.0849486	−	0.0168973i
$705$	1178.87	−	488.304i	1.67216	−	0.692630i
$706$	−113.274	−	273.468i	−0.160445	−	0.387349i
$707$	62.2237	−	312.820i	0.0880109	−	0.442461i
$708$	578.500	+	865.786i	0.817090	+	1.22286i
$709$	21.0463	+	105.807i	0.0296844	+	0.149234i	0.992785	−	0.119908i	$-0.0382600\pi$
$709$	21.0463	+	105.807i	0.0296844	+	0.149234i	−0.963101	+	0.269142i	$0.913260\pi$
$710$	280.014	−	280.014i	0.394386	−	0.394386i
$711$	−542.018	+	811.187i	−0.762332	+	1.14091i
$712$	504.438	+	208.945i	0.708481	+	0.293462i
$713$		−	352.000i		−	0.493689i
$714$		0			0
$715$	220.000			0.307692
$716$	268.644	−	648.563i	0.375201	−	0.905815i
$717$	272.996	+	182.410i	0.380747	+	0.254407i
$718$	−156.978	−	156.978i	−0.218632	−	0.218632i
$719$	−552.035	+	109.807i	−0.767781	+	0.152721i	−0.563416	−	0.826173i	$-0.690513\pi$
$719$	−552.035	+	109.807i	−0.767781	+	0.152721i	−0.204366	+	0.978895i	$0.565513\pi$
$720$	253.496	−	169.381i	0.352078	−	0.235251i
$721$	1582.50	+	314.779i	2.19487	+	0.436586i
$722$	−34.1835	+	14.1593i	−0.0473456	+	0.0196112i
$723$	−134.705	−	325.206i	−0.186313	−	0.449800i
$724$	189.416	−	952.260i	0.261625	−	1.31528i
$725$	85.9932	+	128.698i	0.118611	+	0.177514i
$726$	90.5904	+	455.429i	0.124780	+	0.627312i
$727$	−473.762	+	473.762i	−0.651666	+	0.651666i	−0.953394	−	0.301728i	$-0.902437\pi$
$727$	−473.762	+	473.762i	−0.651666	+	0.651666i	0.301728	+	0.953394i	$0.402437\pi$
$728$	−364.820	+	545.991i	−0.501126	+	0.749988i
$729$	1080.02	+	447.357i	1.48150	+	0.613658i
$730$			396.000i			0.542466i
$731$		0			0
$732$	330.000			0.450820
$733$	−32.9108	+	79.4536i	−0.0448987	+	0.108395i	−0.944738	−	0.327827i	$-0.893684\pi$
$733$	−32.9108	+	79.4536i	−0.0448987	+	0.108395i	0.899839	+	0.436222i	$0.143684\pi$
$734$	−311.995	−	208.468i	−0.425061	−	0.284017i
$735$	−606.698	−	606.698i	−0.825439	−	0.825439i
$736$	−303.619	+	60.3936i	−0.412526	+	0.0820565i
$737$	−132.598	+	88.5991i	−0.179916	+	0.120216i
$738$	−119.608	−	23.7914i	−0.162070	−	0.0322377i
$739$	194.015	−	80.3635i	0.262537	−	0.108746i	−0.247533	−	0.968880i	$-0.579620\pi$
$739$	194.015	−	80.3635i	0.262537	−	0.108746i	0.510069	+	0.860133i	$0.329620\pi$
$740$	−25.2571	−	60.9760i	−0.0341312	−	0.0824001i
$741$	−164.710	+	828.052i	−0.222280	+	1.11748i
$742$	−93.8108	−	140.398i	−0.126430	−	0.189215i
$743$	129.938	+	653.241i	0.174883	+	0.879194i	0.964193	+	0.265200i	$0.0854381\pi$
$743$	129.938	+	653.241i	0.174883	+	0.879194i	−0.789311	+	0.613994i	$0.789562\pi$
$744$	−871.156	+	871.156i	−1.17091	+	1.17091i
$745$	151.140	−	226.196i	0.202872	−	0.303619i
$746$	157.060	+	65.0562i	0.210536	+	0.0872067i
$747$			754.000i			1.00937i
$748$		0			0
$749$	1452.00			1.93858
$750$	−235.733	+	569.110i	−0.314311	+	0.758813i
$751$	202.797	+	135.504i	0.270036	+	0.180432i	0.683214	−	0.730218i	$-0.260581\pi$
$751$	202.797	+	135.504i	0.270036	+	0.180432i	−0.413179	+	0.910650i	$0.635581\pi$
$752$	−205.061	−	205.061i	−0.272687	−	0.272687i
$753$	−1830.92	+	364.192i	−2.43149	+	0.483654i
$754$	428.993	−	286.644i	0.568956	−	0.380165i
$755$	202.413	+	40.2624i	0.268096	+	0.0533277i
$756$	−487.808	+	202.057i	−0.645249	+	0.267271i
$757$	66.5869	+	160.755i	0.0879616	+	0.212358i	0.961739	−	0.273969i	$-0.0883365\pi$
$757$	66.5869	+	160.755i	0.0879616	+	0.212358i	−0.873777	+	0.486327i	$0.838336\pi$
$758$	63.1388	−	317.420i	0.0832965	−	0.418760i
$759$	−114.658	−	171.597i	−0.151064	−	0.226083i
$760$	115.297	+	579.637i	0.151706	+	0.762680i
$761$	31.1127	−	31.1127i	0.0408840	−	0.0408840i	−0.686369	−	0.727253i	$-0.740797\pi$
$761$	31.1127	−	31.1127i	0.0408840	−	0.0408840i	0.727253	+	0.686369i	$0.240797\pi$
$762$	250.162	−	374.394i	0.328297	−	0.491331i
$763$	−609.760	−	252.571i	−0.799162	−	0.331024i
$764$			582.000i			0.761780i
$765$		0			0
$766$	64.0000			0.0835509
$767$	283.186	−	683.671i	0.369212	−	0.891357i
$768$	666.889	+	445.601i	0.868346	+	0.580210i
$769$	−175.362	−	175.362i	−0.228040	−	0.228040i	0.583834	−	0.811873i	$-0.301552\pi$
$769$	−175.362	−	175.362i	−0.228040	−	0.228040i	−0.811873	+	0.583834i	$0.801552\pi$
$770$	−202.413	+	40.2624i	−0.262874	+	0.0522888i
$771$	−1528.78	+	1021.50i	−1.98285	+	1.32490i
$772$	−441.628	−	87.8453i	−0.572057	−	0.113789i
$773$	947.900	−	392.633i	1.22626	−	0.507934i	0.326867	−	0.945071i	$-0.394007\pi$
$773$	947.900	−	392.633i	1.22626	−	0.507934i	0.899395	+	0.437136i	$0.144007\pi$
$774$	−189.046	−	456.396i	−0.244245	−	0.589660i
$775$	−21.9613	+	110.407i	−0.0283372	+	0.142461i
$776$	510.748	+	764.388i	0.658180	+	0.985036i
$777$	40.2624	+	202.413i	0.0518178	+	0.260506i
$778$	−329.512	+	329.512i	−0.423537	+	0.423537i
$779$	−93.8108	+	140.398i	−0.120425	+	0.180228i
$780$	−609.760	−	252.571i	−0.781744	−	0.323809i
$781$		−	396.000i		−	0.507042i
$782$		0			0
$783$	968.000			1.23627
$784$	−74.6233	+	180.157i	−0.0951827	+	0.229791i
$785$	−226.196	−	151.140i	−0.288148	−	0.192535i
$786$	−357.796	−	357.796i	−0.455211	−	0.455211i
$787$	−943.060	+	187.586i	−1.19830	+	0.238356i	−0.753605	−	0.657328i	$-0.771687\pi$
$787$	−943.060	+	187.586i	−1.19830	+	0.238356i	−0.444692	+	0.895684i	$0.646687\pi$
$788$	−737.088	+	492.507i	−0.935391	+	0.625008i
$789$	−128.808	−	25.6215i	−0.163255	−	0.0324734i
$790$	325.206	−	134.705i	0.411653	−	0.170512i
$791$	269.409	+	650.411i	0.340593	+	0.822264i
$792$	−83.2700	+	418.626i	−0.105139	+	0.528569i
$793$	−130.293	−	194.997i	−0.164304	−	0.245898i
$794$	79.6098	+	400.225i	0.100264	+	0.504062i
$795$	280.014	−	280.014i	0.352219	−	0.352219i
$796$	−46.9054	+	70.1989i	−0.0589264	+	0.0881896i
$797$	618.999	+	256.398i	0.776662	+	0.321704i	0.735567	−	0.677452i	$-0.236916\pi$
$797$	618.999	+	256.398i	0.776662	+	0.321704i	0.0410942	+	0.999155i	$0.486916\pi$
$798$		−	792.000i		−	0.992481i
$799$		0			0
$800$	99.0000			0.123750
$801$	388.041	−	936.814i	0.484446	−	1.16956i
$802$	483.592	+	323.126i	0.602983	+	0.402900i
$803$	280.014	+	280.014i	0.348710	+	0.348710i
$804$	469.230	−	93.3356i	0.583619	−	0.116089i
$805$	−343.195	+	229.315i	−0.426329	+	0.284864i
$806$	368.023	+	73.2044i	0.456605	+	0.0908243i
$807$	−182.928	+	75.7713i	−0.226677	+	0.0938926i
$808$	91.0787	+	219.883i	0.112721	+	0.272133i
$809$	−104.316	+	524.433i	−0.128945	+	0.648249i	0.861208	+	0.508253i	$0.169709\pi$
$809$	−104.316	+	524.433i	−0.128945	+	0.648249i	−0.990152	+	0.139995i	$0.955291\pi$
$810$	−75.5698	−	113.098i	−0.0932961	−	0.139627i
$811$	52.1581	+	262.217i	0.0643133	+	0.323325i	0.999527	−	0.0307594i	$-0.00979256\pi$
$811$	52.1581	+	262.217i	0.0643133	+	0.323325i	−0.935213	+	0.354084i	$0.884793\pi$
$812$	1026.72	−	1026.72i	1.26443	−	1.26443i
$813$	−797.392	+	1193.38i	−0.980802	+	1.46787i
$814$	20.3253	+	8.41904i	0.0249697	+	0.0103428i
$815$			858.000i			1.05276i
$816$		0			0
$817$	−684.000			−0.837209
$818$	38.2683	−	92.3880i	0.0467828	−	0.112944i
$819$	1013.98	+	677.522i	1.23808	+	0.827256i
$820$	−93.3381	−	93.3381i	−0.113827	−	0.113827i
$821$	933.859	−	185.756i	1.13747	−	0.226256i	0.409791	−	0.912179i	$-0.365601\pi$
$821$	933.859	−	185.756i	1.13747	−	0.226256i	0.727674	+	0.685923i	$0.240601\pi$
$822$	920.385	−	614.982i	1.11969	−	0.748153i
$823$	9.20058	+	1.83011i	0.0111793	+	0.00222371i	0.200677	−	0.979657i	$-0.435686\pi$
$823$	9.20058	+	1.83011i	0.0111793	+	0.00222371i	−0.189497	+	0.981881i	$0.560686\pi$
$824$	−1112.35	+	460.751i	−1.34994	+	0.559164i
$825$	25.2571	+	60.9760i	0.0306147	+	0.0739104i
$826$	−135.428	+	680.843i	−0.163957	+	0.824265i
$827$	−445.601	−	666.889i	−0.538817	−	0.806396i	0.457760	−	0.889076i	$-0.348652\pi$
$827$	−445.601	−	666.889i	−0.538817	−	0.806396i	−0.996576	+	0.0826801i	$0.973652\pi$
$828$	71.3743	+	358.823i	0.0862008	+	0.433361i
$829$	−666.095	+	666.095i	−0.803492	+	0.803492i	−0.983640	−	0.180148i	$-0.942342\pi$
$829$	−666.095	+	666.095i	−0.803492	+	0.803492i	0.180148	+	0.983640i	$0.442342\pi$
$830$	151.140	−	226.196i	0.182096	−	0.272526i
$831$	1361.80	+	564.075i	1.63875	+	0.678791i
$832$		−	130.000i		−	0.156250i
$833$		0			0
$834$	−22.0000			−0.0263789
$835$	218.895	−	528.459i	0.262150	−	0.632885i
$836$	210.597	+	140.716i	0.251910	+	0.168321i
$837$	497.803	+	497.803i	0.594747	+	0.594747i
$838$	4.60029	−	0.915055i	0.00548961	−	0.00109195i
$839$	7.79988	−	5.21171i	0.00929663	−	0.00621181i	−0.550913	−	0.834563i	$-0.685720\pi$
$839$	7.79988	−	5.21171i	0.00929663	−	0.00621181i	0.560210	+	0.828351i	$0.310720\pi$
$840$	1416.89	+	281.837i	1.68677	+	0.335520i
$841$	−1682.38	+	696.867i	−2.00046	+	0.828617i
$842$	238.029	+	574.653i	0.282695	+	0.682486i
$843$	369.682	−	1858.52i	0.438532	−	2.20465i
$844$	−648.858	−	971.085i	−0.768789	−	1.15057i
$845$	−63.1388	−	317.420i	−0.0747204	−	0.375645i
$846$	533.159	−	533.159i	0.630211	−	0.630211i
$847$	515.959	−	772.188i	0.609161	−	0.911674i
$848$	−83.1492	−	34.4415i	−0.0980533	−	0.0406150i
$849$		−	770.000i		−	0.906949i
$850$		0			0
$851$	44.0000			0.0517039
$852$	−454.628	+	1097.57i	−0.533601	+	1.28823i
$853$	−791.687	−	528.989i	−0.928121	−	0.620151i	−0.00307091	−	0.999995i	$-0.500978\pi$
$853$	−791.687	−	528.989i	−0.928121	−	0.620151i	−0.925050	+	0.379844i	$0.875978\pi$
$854$	155.563	+	155.563i	0.182159	+	0.182159i
$855$	1076.47	−	214.123i	1.25903	−	0.250436i
$856$	−900.886	+	601.953i	−1.05244	+	0.703216i
$857$	−616.439	−	122.617i	−0.719299	−	0.143077i	−0.178149	−	0.984004i	$-0.557011\pi$
$857$	−616.439	−	122.617i	−0.719299	−	0.143077i	−0.541150	+	0.840926i	$0.682011\pi$
$858$	203.253	−	84.1904i	0.236892	−	0.0981240i
$859$	352.834	+	851.817i	0.410750	+	0.991638i	0.984937	+	0.172914i	$0.0553182\pi$
$859$	352.834	+	851.817i	0.410750	+	0.991638i	−0.574187	+	0.818724i	$0.694682\pi$
$860$	104.316	−	524.433i	0.121298	−	0.609806i
$861$	229.315	+	343.195i	0.266336	+	0.398600i
$862$	32.9420	+	165.610i	0.0382157	+	0.192124i
$863$	−113.137	+	113.137i	−0.131097	+	0.131097i	−0.769611	−	0.638513i	$-0.779550\pi$
$863$	−113.137	+	113.137i	−0.131097	+	0.131097i	0.638513	+	0.769611i	$0.279550\pi$
$864$	343.973	−	514.792i	0.398117	−	0.595824i
$865$	−20.3253	−	8.41904i	−0.0234975	−	0.00973299i
$866$			414.000i			0.478060i
$867$		0			0
$868$	1056.00			1.21659
$869$	134.705	−	325.206i	0.155011	−	0.374230i
$870$	−943.785	−	630.617i	−1.08481	−	0.724847i
$871$	−240.416	−	240.416i	−0.276023	−	0.276023i
$872$	483.031	−	96.0807i	0.553934	−	0.110184i
$873$	1419.58	−	948.531i	1.62609	−	1.08652i
$874$	−165.610	−	32.9420i	−0.189486	−	0.0376910i
$875$	1138.22	−	471.466i	1.30082	−	0.538818i
$876$	−454.628	−	1097.57i	−0.518982	−	1.25293i
$877$	−213.208	+	1071.87i	−0.243110	+	1.22220i	0.645581	+	0.763692i	$0.276615\pi$
$877$	−213.208	+	1071.87i	−0.243110	+	1.22220i	−0.888691	+	0.458506i	$0.848385\pi$
$878$	−244.950	−	366.594i	−0.278987	−	0.417533i
$879$	−382.493	−	1922.92i	−0.435145	−	2.18762i
$880$	−77.7817	+	77.7817i	−0.0883883	+	0.0883883i
$881$	20.8468	−	31.1995i	0.0236627	−	0.0354137i	−0.819450	−	0.573151i	$-0.805721\pi$
$881$	20.8468	−	31.1995i	0.0236627	−	0.0354137i	0.843112	+	0.537737i	$0.180721\pi$
$882$	−468.407	−	194.021i	−0.531074	−	0.219978i
$883$		−	646.000i		−	0.731597i	−0.930694	−	0.365798i	$-0.880796\pi$
$883$		−	646.000i		−	0.731597i	0.930694	−	0.365798i	$-0.119204\pi$
$884$		0			0
$885$	−1628.00			−1.83955
$886$	−182.923	+	441.614i	−0.206459	+	0.498436i
$887$	−194.997	−	130.293i	−0.219839	−	0.146892i	0.440775	−	0.897618i	$-0.354704\pi$
$887$	−194.997	−	130.293i	−0.219839	−	0.146892i	−0.660613	+	0.750726i	$0.729704\pi$
$888$	−108.894	−	108.894i	−0.122629	−	0.122629i
$889$	−883.256	+	175.691i	−0.993539	+	0.197627i
$890$	−304.195	+	203.257i	−0.341792	+	0.228378i
$891$	−133.408	−	26.5366i	−0.149729	−	0.0297829i
$892$	327.053	−	135.470i	0.366652	−	0.151872i
$893$	−399.522	−	964.530i	−0.447393	−	1.08010i
$894$	53.0732	−	266.817i	0.0593660	−	0.298453i
$895$	609.770	+	912.586i	0.681307	+	1.01965i
$896$	−217.783	−	1094.87i	−0.243061	−	1.22195i
$897$	311.127	−	311.127i	0.346853	−	0.346853i
$898$	437.784	−	655.190i	0.487510	−	0.729610i
$899$	−1788.63	−	740.875i	−1.98958	−	0.824110i
$900$		−	117.000i		−	0.130000i
$901$		0			0
$902$	44.0000			0.0487805
$903$	−639.847	+	1544.73i	−0.708579	+	1.71066i
$904$	−436.793	−	291.856i	−0.483178	−	0.322849i
$905$	1073.39	+	1073.39i	1.18606	+	1.18606i
$906$	202.413	−	40.2624i	0.223414	−	0.0444397i
$907$	1002.28	−	669.705i	1.10505	−	0.738374i	0.137365	−	0.990520i	$-0.456137\pi$
$907$	1002.28	−	669.705i	1.10505	−	0.738374i	0.967689	+	0.252147i	$0.0811366\pi$
$908$	−676.243	−	134.513i	−0.744761	−	0.148142i
$909$	408.355	−	169.146i	0.449235	−	0.186079i
$910$	−168.381	−	406.507i	−0.185034	−	0.446711i
$911$	113.467	−	570.436i	0.124552	−	0.626165i	−0.867197	−	0.497966i	$-0.834080\pi$
$911$	113.467	−	570.436i	0.124552	−	0.626165i	0.991748	−	0.128199i	$-0.0409195\pi$
$912$	−234.527	−	350.994i	−0.257157	−	0.384862i
$913$	−53.0732	−	266.817i	−0.0581305	−	0.292242i
$914$	295.571	−	295.571i	0.323381	−	0.323381i
$915$	−286.644	+	428.993i	−0.313272	+	0.468845i
$916$	−360.313	−	149.247i	−0.393355	−	0.162933i
$917$			1012.00i			1.10360i
$918$		0			0
$919$	−1086.00			−1.18172			−0.590860	−	0.806774i	$-0.701211\pi$
$919$	−1086.00			−1.18172			−0.590860	+	0.806774i	$0.701211\pi$
$920$	117.866	−	284.555i	0.128116	−	0.309299i
$921$	−257.396	−	171.986i	−0.279474	−	0.186739i
$922$	−253.144	−	253.144i	−0.274560	−	0.274560i
$923$	828.052	−	164.710i	0.897131	−	0.178451i
$924$	514.792	−	343.973i	0.557134	−	0.372265i
$925$	−13.8009	−	2.74516i	−0.0149199	−	0.00296775i
$926$	−273.468	+	113.274i	−0.295322	+	0.122326i
$927$	855.680	+	2065.79i	0.923064	+	2.22847i
$928$	−332.165	+	1669.91i	−0.357936	+	1.79947i
$929$	396.090	+	592.791i	0.426362	+	0.638095i	0.981003	−	0.193994i	$-0.0621444\pi$
$929$	396.090	+	592.791i	0.426362	+	0.638095i	−0.554641	+	0.832090i	$0.687144\pi$
$930$	−161.050	−	809.651i	−0.173172	−	0.870593i
$931$	−496.389	+	496.389i	−0.533178	+	0.533178i
$932$	484.689	−	725.389i	0.520053	−	0.778314i
$933$	−1747.98	−	724.037i	−1.87350	−	0.776031i
$934$			142.000i			0.152034i
$935$		0			0
$936$	−910.000			−0.972222
$937$	−488.304	+	1178.87i	−0.521136	+	1.25813i	0.416063	+	0.909336i	$0.363410\pi$
$937$	−488.304	+	1178.87i	−0.521136	+	1.25813i	−0.937198	+	0.348797i	$0.886590\pi$
$938$	265.196	+	177.198i	0.282725	+	0.188911i
$939$	1088.94	+	1088.94i	1.15969	+	1.15969i
$940$	800.451	−	159.220i	0.851543	−	0.169382i
$941$	471.893	−	315.309i	0.501480	−	0.335078i	−0.278967	−	0.960301i	$-0.589992\pi$
$941$	471.893	−	315.309i	0.501480	−	0.335078i	0.780446	+	0.625223i	$0.214992\pi$
$942$	−266.817	−	53.0732i	−0.283245	−	0.0563409i
$943$	81.3014	−	33.6761i	0.0862157	−	0.0357117i
$944$	141.593	+	341.835i	0.149992	+	0.362114i
$945$	161.050	−	809.651i	0.170423	−	0.856774i
$946$	99.0225	+	148.198i	0.104675	+	0.156657i
$947$	363.277	+	1826.32i	0.383608	+	1.92853i	0.371067	+	0.928606i	$0.378992\pi$
$947$	363.277	+	1826.32i	0.383608	+	1.92853i	0.0125407	+	0.999921i	$0.496008\pi$
$948$	−746.705	+	746.705i	−0.787663	+	0.787663i
$949$	−469.054	+	701.989i	−0.494261	+	0.739714i
$950$	49.8895	+	20.6649i	0.0525153	+	0.0217525i
$951$		−	770.000i		−	0.809674i
$952$		0			0
$953$	750.000			0.786988			0.393494	−	0.919327i	$-0.371266\pi$
$953$	750.000			0.786988			0.393494	+	0.919327i	$0.371266\pi$
$954$	89.5479	−	216.188i	0.0938657	−	0.226612i
$955$	−756.588	−	505.536i	−0.792239	−	0.529357i
$956$	148.492	+	148.492i	0.155327	+	0.155327i
$957$	−1113.27	+	221.443i	−1.16329	+	0.231393i
$958$	−202.797	+	135.504i	−0.211688	+	0.141445i
$959$	−2171.34	−	431.906i	−2.26417	−	0.450371i
$960$	−264.230	+	109.447i	−0.275239	+	0.114008i
$961$	−171.059	−	412.974i	−0.178002	−	0.429734i
$962$	−9.15055	+	46.0029i	−0.00951200	+	0.0478201i
$963$	1117.91	+	1673.07i	1.16086	+	1.73736i
$964$	−43.9226	−	220.814i	−0.0455629	−	0.229060i
$965$	497.803	−	497.803i	0.515858	−	0.515858i
$966$	−229.315	+	343.195i	−0.237386	+	0.355274i
$967$	1687.00	+	698.780i	1.74458	+	0.722627i	0.998380	+	0.0568993i	$0.0181214\pi$
$967$	1687.00	+	698.780i	1.74458	+	0.722627i	0.746195	+	0.665727i	$0.231879\pi$
$968$			693.000i			0.715909i
$969$		0			0
$970$	−616.000			−0.635052
$971$	−163.023	+	393.573i	−0.167892	+	0.405327i	−0.985323	−	0.170699i	$-0.945397\pi$
$971$	−163.023	+	393.573i	−0.167892	+	0.405327i	0.817431	+	0.576026i	$0.195397\pi$
$972$	760.488	+	508.142i	0.782395	+	0.522780i
$973$	31.1127	+	31.1127i	0.0319761	+	0.0319761i
$974$	82.8052	−	16.4710i	0.0850156	−	0.0169107i
$975$	−116.998	+	78.1757i	−0.119998	+	0.0801802i
$976$	115.007	+	22.8764i	0.117835	+	0.0234389i
$977$	−245.752	+	101.794i	−0.251537	+	0.104190i	−0.504890	−	0.863184i	$-0.668467\pi$
$977$	−245.752	+	101.794i	−0.251537	+	0.104190i	0.253352	+	0.967374i	$0.418467\pi$
$978$	328.342	+	792.689i	0.335728	+	0.810520i
$979$	−71.3743	+	358.823i	−0.0729053	+	0.366520i
$980$	−304.885	−	456.293i	−0.311107	−	0.465605i
$981$	−178.436	−	897.057i	−0.181892	−	0.914431i
$982$	295.571	−	295.571i	0.300988	−	0.300988i
$983$	463.842	−	694.189i	0.471864	−	0.706194i	−0.516839	−	0.856083i	$-0.672891\pi$
$983$	463.842	−	694.189i	0.471864	−	0.706194i	0.988703	+	0.149888i	$0.0478914\pi$
$984$	−284.555	−	117.866i	−0.289182	−	0.119783i
$985$		−	1386.00i		−	1.40711i
$986$		0			0
$987$	−2552.00			−2.58561
$988$	−206.649	+	498.895i	−0.209159	+	0.504954i
$989$	296.395	+	198.045i	0.299692	+	0.200248i
$990$	−202.233	−	202.233i	−0.204275	−	0.204275i
$991$	699.244	−	139.088i	0.705595	−	0.140351i	0.170765	−	0.985312i	$-0.445376\pi$
$991$	699.244	−	139.088i	0.705595	−	0.140351i	0.534829	+	0.844960i	$0.320376\pi$
$992$	−1029.58	+	687.946i	−1.03789	+	0.693494i
$993$	−598.038	−	118.957i	−0.602254	−	0.119796i
$994$	−731.713	+	303.085i	−0.736129	+	0.304915i
$995$	−50.5142	−	121.952i	−0.0507681	−	0.122565i
$996$	−159.220	+	800.451i	−0.159859	+	0.803665i
$997$	−268.403	−	401.694i	−0.269211	−	0.402902i	0.672091	−	0.740468i	$-0.265396\pi$
$997$	−268.403	−	401.694i	−0.269211	−	0.402902i	−0.941302	+	0.337566i	$0.890396\pi$
$998$	48.4979	+	243.815i	0.0485951	+	0.244304i
$999$	−62.2254	+	62.2254i	−0.0622877	+	0.0622877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.o.214.2	yes	16
17.2	even	8	inner	289.3.e.o.40.2	yes	16
17.3	odd	16	inner	289.3.e.o.158.2	yes	16
17.4	even	4	inner	289.3.e.o.75.2	yes	16
17.5	odd	16	inner	289.3.e.o.131.1	yes	16
17.6	odd	16	inner	289.3.e.o.224.2	yes	16
17.7	odd	16	inner	289.3.e.o.65.2	yes	16
17.8	even	8	inner	289.3.e.o.249.1	yes	16
17.9	even	8	inner	289.3.e.o.249.2	yes	16
17.10	odd	16	inner	289.3.e.o.65.1	yes	16
17.11	odd	16	inner	289.3.e.o.224.1	yes	16
17.12	odd	16	inner	289.3.e.o.131.2	yes	16
17.13	even	4	inner	289.3.e.o.75.1	yes	16
17.14	odd	16	inner	289.3.e.o.158.1	yes	16
17.15	even	8	inner	289.3.e.o.40.1	✓	16
17.16	even	2	inner	289.3.e.o.214.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.o.40.1	✓	16	17.15	even	8	inner
289.3.e.o.40.2	yes	16	17.2	even	8	inner
289.3.e.o.65.1	yes	16	17.10	odd	16	inner
289.3.e.o.65.2	yes	16	17.7	odd	16	inner
289.3.e.o.75.1	yes	16	17.13	even	4	inner
289.3.e.o.75.2	yes	16	17.4	even	4	inner
289.3.e.o.131.1	yes	16	17.5	odd	16	inner
289.3.e.o.131.2	yes	16	17.12	odd	16	inner
289.3.e.o.158.1	yes	16	17.14	odd	16	inner
289.3.e.o.158.2	yes	16	17.3	odd	16	inner
289.3.e.o.214.1	yes	16	17.16	even	2	inner
289.3.e.o.214.2	yes	16	1.1	even	1	trivial
289.3.e.o.224.1	yes	16	17.11	odd	16	inner
289.3.e.o.224.2	yes	16	17.6	odd	16	inner
289.3.e.o.249.1	yes	16	17.8	even	8	inner
289.3.e.o.249.2	yes	16	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(3.89994 + 2.60586i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-4.60029 + 0.915055i) q^{5} +(-3.89994 + 2.60586i) q^{6} +(9.20058 + 1.83011i) q^{7} +(-6.46716 + 2.67878i) q^{8} +(4.97488 + 12.0104i) q^{9} +O(q^{10})\)	\(q+(-0.382683 + 0.923880i) q^{2} +(3.89994 + 2.60586i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-4.60029 + 0.915055i) q^{5} +(-3.89994 + 2.60586i) q^{6} +(9.20058 + 1.83011i) q^{7} +(-6.46716 + 2.67878i) q^{8} +(4.97488 + 12.0104i) q^{9} +(0.915055 - 4.60029i) q^{10} +(-2.60586 - 3.89994i) q^{11} +(2.74516 + 13.8009i) q^{12} +(7.07107 - 7.07107i) q^{13} +(-5.21171 + 7.79988i) q^{14} +(-20.3253 - 8.41904i) q^{15} +5.00000i q^{16} -13.0000 q^{18} +(-6.88830 + 16.6298i) q^{19} +(-11.6998 - 7.81757i) q^{20} +(31.1127 + 31.1127i) q^{21} +(4.60029 - 0.915055i) q^{22} +(7.79988 - 5.21171i) q^{23} +(-32.2020 - 6.40538i) q^{24} +(-2.77164 + 1.14805i) q^{25} +(3.82683 + 9.23880i) q^{26} +(-3.66022 + 18.4012i) q^{27} +(15.6351 + 23.3996i) q^{28} +(-10.0656 - 50.6032i) q^{29} +(15.5563 - 15.5563i) q^{30} +(20.8468 - 31.1995i) q^{31} +(-30.4880 - 12.6286i) q^{32} -22.0000i q^{33} -44.0000 q^{35} +(-14.9247 + 36.0313i) q^{36} +(3.89994 + 2.60586i) q^{37} +(-12.7279 - 12.7279i) q^{38} +(46.0029 - 9.15055i) q^{39} +(27.2996 - 18.2410i) q^{40} +(9.20058 + 1.83011i) q^{41} +(-40.6507 + 16.8381i) q^{42} +(14.5420 + 35.1074i) q^{43} +(2.74516 - 13.8009i) q^{44} +(-33.8761 - 50.6992i) q^{45} +(1.83011 + 9.20058i) q^{46} +(-41.0122 + 41.0122i) q^{47} +(-13.0293 + 19.4997i) q^{48} +(36.0313 + 14.9247i) q^{49} -3.00000i q^{50} +30.0000 q^{52} +(-6.88830 + 16.6298i) q^{53} +(-15.5998 - 10.4234i) q^{54} +(15.5563 + 15.5563i) q^{55} +(-64.4041 + 12.8108i) q^{56} +(-70.1989 + 46.9054i) q^{57} +(50.6032 + 10.0656i) q^{58} +(68.3671 - 28.3186i) q^{59} +(-25.2571 - 60.9760i) q^{60} +(4.57527 - 23.0015i) q^{61} +(20.8468 + 31.1995i) q^{62} +(23.7914 + 119.608i) q^{63} +(9.19239 - 9.19239i) q^{64} +(-26.0586 + 38.9994i) q^{65} +(20.3253 + 8.41904i) q^{66} -34.0000i q^{67} +44.0000 q^{69} +(16.8381 - 40.6507i) q^{70} +(70.1989 + 46.9054i) q^{71} +(-64.3467 - 64.3467i) q^{72} +(-82.8052 + 16.4710i) q^{73} +(-3.89994 + 2.60586i) q^{74} +(-13.8009 - 2.74516i) q^{75} +(-49.8895 + 20.6649i) q^{76} +(-16.8381 - 40.6507i) q^{77} +(-9.15055 + 46.0029i) q^{78} +(41.6937 + 62.3990i) q^{79} +(-4.57527 - 23.0015i) q^{80} +(20.5061 - 20.5061i) q^{81} +(-5.21171 + 7.79988i) q^{82} +(53.5850 + 22.1956i) q^{83} +132.000i q^{84} -38.0000 q^{86} +(92.6094 - 223.579i) q^{87} +(27.2996 + 18.2410i) q^{88} +(-55.1543 - 55.1543i) q^{89} +(59.8038 - 11.8957i) q^{90} +(77.9988 - 52.1171i) q^{91} +(27.6017 + 5.49033i) q^{92} +(162.603 - 67.3523i) q^{93} +(-22.1956 - 53.5850i) q^{94} +(16.4710 - 82.8052i) q^{95} +(-85.9932 - 128.698i) q^{96} +(-25.6215 - 128.808i) q^{97} +(-27.5772 + 27.5772i) q^{98} +(33.8761 - 50.6992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 208 q^{18} - 704 q^{35} + 480 q^{52} + 704 q^{69} - 608 q^{86}+O(q^{100}) \) 16 * q - 208 * q^18 - 704 * q^35 + 480 * q^52 + 704 * q^69 - 608 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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