LMFDB - Embedded newform 165.3.l.a.98.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,3,Mod(32,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("165.32");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	165.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.49592436194$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			98.2
Root			$1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	165.98
Dual form			165.3.l.a.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58114 - 1.58114i) q^{2} -3.00000 q^{3} -1.00000i q^{4} +(-4.00000 + 3.00000i) q^{5} +(-4.74342 + 4.74342i) q^{6} +(3.16228 + 3.16228i) q^{7} +(4.74342 + 4.74342i) q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(1.58114 - 1.58114i) q^{2} -3.00000 q^{3} -1.00000i q^{4} +(-4.00000 + 3.00000i) q^{5} +(-4.74342 + 4.74342i) q^{6} +(3.16228 + 3.16228i) q^{7} +(4.74342 + 4.74342i) q^{8} +9.00000 q^{9} +(-1.58114 + 11.0680i) q^{10} +(6.32456 + 9.00000i) q^{11} +3.00000i q^{12} +(3.16228 - 3.16228i) q^{13} +10.0000 q^{14} +(12.0000 - 9.00000i) q^{15} +19.0000 q^{16} +(-22.1359 + 22.1359i) q^{17} +(14.2302 - 14.2302i) q^{18} -12.6491 q^{19} +(3.00000 + 4.00000i) q^{20} +(-9.48683 - 9.48683i) q^{21} +(24.2302 + 4.23025i) q^{22} +(-7.00000 + 7.00000i) q^{23} +(-14.2302 - 14.2302i) q^{24} +(7.00000 - 24.0000i) q^{25} -10.0000i q^{26} -27.0000 q^{27} +(3.16228 - 3.16228i) q^{28} +18.9737i q^{29} +(4.74342 - 33.2039i) q^{30} +20.0000 q^{31} +(11.0680 - 11.0680i) q^{32} +(-18.9737 - 27.0000i) q^{33} +70.0000i q^{34} +(-22.1359 - 3.16228i) q^{35} -9.00000i q^{36} +(7.00000 - 7.00000i) q^{37} +(-20.0000 + 20.0000i) q^{38} +(-9.48683 + 9.48683i) q^{39} +(-33.2039 - 4.74342i) q^{40} +69.5701 q^{41} -30.0000 q^{42} +(22.1359 - 22.1359i) q^{43} +(9.00000 - 6.32456i) q^{44} +(-36.0000 + 27.0000i) q^{45} +22.1359i q^{46} +(-43.0000 - 43.0000i) q^{47} -57.0000 q^{48} -29.0000i q^{49} +(-26.8794 - 49.0153i) q^{50} +(66.4078 - 66.4078i) q^{51} +(-3.16228 - 3.16228i) q^{52} +(17.0000 - 17.0000i) q^{53} +(-42.6907 + 42.6907i) q^{54} +(-52.2982 - 17.0263i) q^{55} +30.0000i q^{56} +37.9473 q^{57} +(30.0000 + 30.0000i) q^{58} +22.0000 q^{59} +(-9.00000 - 12.0000i) q^{60} +94.8683i q^{61} +(31.6228 - 31.6228i) q^{62} +(28.4605 + 28.4605i) q^{63} +41.0000i q^{64} +(-3.16228 + 22.1359i) q^{65} +(-72.6907 - 12.6907i) q^{66} +(-47.0000 + 47.0000i) q^{67} +(22.1359 + 22.1359i) q^{68} +(21.0000 - 21.0000i) q^{69} +(-40.0000 + 30.0000i) q^{70} -120.000i q^{71} +(42.6907 + 42.6907i) q^{72} +(22.1359 - 22.1359i) q^{73} -22.1359i q^{74} +(-21.0000 + 72.0000i) q^{75} +12.6491i q^{76} +(-8.46050 + 48.4605i) q^{77} +30.0000i q^{78} +6.32456 q^{79} +(-76.0000 + 57.0000i) q^{80} +81.0000 q^{81} +(110.000 - 110.000i) q^{82} +(-60.0833 - 60.0833i) q^{83} +(-9.48683 + 9.48683i) q^{84} +(22.1359 - 154.952i) q^{85} -70.0000i q^{86} -56.9210i q^{87} +(-12.6907 + 72.6907i) q^{88} +100.000 q^{89} +(-14.2302 + 99.6117i) q^{90} +20.0000 q^{91} +(7.00000 + 7.00000i) q^{92} -60.0000 q^{93} -135.978 q^{94} +(50.5964 - 37.9473i) q^{95} +(-33.2039 + 33.2039i) q^{96} +(43.0000 - 43.0000i) q^{97} +(-45.8530 - 45.8530i) q^{98} +(56.9210 + 81.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{3} - 16 q^{5} + 36 q^{9}+O(q^{10}) $ 4 * q - 12 * q^3 - 16 * q^5 + 36 * q^9	$ 4 q - 12 q^{3} - 16 q^{5} + 36 q^{9} + 40 q^{14} + 48 q^{15} + 76 q^{16} + 12 q^{20} + 40 q^{22} - 28 q^{23} + 28 q^{25} - 108 q^{27} + 80 q^{31} + 28 q^{37} - 80 q^{38} - 120 q^{42} + 36 q^{44} - 144 q^{45} - 172 q^{47} - 228 q^{48} + 68 q^{53} - 108 q^{55} + 120 q^{58} + 88 q^{59} - 36 q^{60} - 120 q^{66} - 188 q^{67} + 84 q^{69} - 160 q^{70} - 84 q^{75} + 80 q^{77} - 304 q^{80} + 324 q^{81} + 440 q^{82} + 120 q^{88} + 400 q^{89} + 80 q^{91} + 28 q^{92} - 240 q^{93} + 172 q^{97}+O(q^{100}) $ 4 * q - 12 * q^3 - 16 * q^5 + 36 * q^9 + 40 * q^14 + 48 * q^15 + 76 * q^16 + 12 * q^20 + 40 * q^22 - 28 * q^23 + 28 * q^25 - 108 * q^27 + 80 * q^31 + 28 * q^37 - 80 * q^38 - 120 * q^42 + 36 * q^44 - 144 * q^45 - 172 * q^47 - 228 * q^48 + 68 * q^53 - 108 * q^55 + 120 * q^58 + 88 * q^59 - 36 * q^60 - 120 * q^66 - 188 * q^67 + 84 * q^69 - 160 * q^70 - 84 * q^75 + 80 * q^77 - 304 * q^80 + 324 * q^81 + 440 * q^82 + 120 * q^88 + 400 * q^89 + 80 * q^91 + 28 * q^92 - 240 * q^93 + 172 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.58114	−	1.58114i	0.790569	−	0.790569i	−0.191017	−	0.981587i	$-0.561179\pi$
$2$	1.58114	−	1.58114i	0.790569	−	0.790569i	0.981587	+	0.191017i	$0.0611786\pi$
$3$	−3.00000			−1.00000
$3$	−3.00000			−1.00000
$4$		−	1.00000i		−	0.250000i
$5$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$5$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$6$	−4.74342	+	4.74342i	−0.790569	+	0.790569i
$7$	3.16228	+	3.16228i	0.451754	+	0.451754i	0.895936	−	0.444182i	$-0.146506\pi$
$7$	3.16228	+	3.16228i	0.451754	+	0.451754i	−0.444182	+	0.895936i	$0.646506\pi$
$8$	4.74342	+	4.74342i	0.592927	+	0.592927i
$9$	9.00000			1.00000
$10$	−1.58114	+	11.0680i	−0.158114	+	1.10680i
$11$	6.32456	+	9.00000i	0.574960	+	0.818182i
$11$	6.32456	+	9.00000i	0.574960	+	0.818182i
$12$			3.00000i			0.250000i
$13$	3.16228	−	3.16228i	0.243252	−	0.243252i	−0.574942	−	0.818194i	$-0.694975\pi$
$13$	3.16228	−	3.16228i	0.243252	−	0.243252i	0.818194	+	0.574942i	$0.194975\pi$
$14$	10.0000			0.714286
$15$	12.0000	−	9.00000i	0.800000	−	0.600000i
$16$	19.0000			1.18750
$17$	−22.1359	+	22.1359i	−1.30211	+	1.30211i	−0.375150	+	0.926964i	$0.622409\pi$
$17$	−22.1359	+	22.1359i	−1.30211	+	1.30211i	−0.926964	+	0.375150i	$0.877591\pi$
$18$	14.2302	−	14.2302i	0.790569	−	0.790569i
$19$	−12.6491			−0.665743			−0.332871	−	0.942972i	$-0.608017\pi$
$19$	−12.6491			−0.665743			−0.332871	+	0.942972i	$0.608017\pi$
$20$	3.00000	+	4.00000i	0.150000	+	0.200000i
$21$	−9.48683	−	9.48683i	−0.451754	−	0.451754i
$22$	24.2302	+	4.23025i	1.10137	+	0.192284i
$23$	−7.00000	+	7.00000i	−0.304348	+	0.304348i	−0.842712	−	0.538364i	$-0.819042\pi$
$23$	−7.00000	+	7.00000i	−0.304348	+	0.304348i	0.538364	+	0.842712i	$0.319042\pi$
$24$	−14.2302	−	14.2302i	−0.592927	−	0.592927i
$25$	7.00000	−	24.0000i	0.280000	−	0.960000i
$26$		−	10.0000i		−	0.384615i
$27$	−27.0000			−1.00000
$28$	3.16228	−	3.16228i	0.112938	−	0.112938i
$29$			18.9737i			0.654264i	0.944979	+	0.327132i	$0.106082\pi$
$29$			18.9737i			0.654264i	−0.944979	+	0.327132i	$0.893918\pi$
$30$	4.74342	−	33.2039i	0.158114	−	1.10680i
$31$	20.0000			0.645161			0.322581	−	0.946542i	$-0.395450\pi$
$31$	20.0000			0.645161			0.322581	+	0.946542i	$0.395450\pi$
$32$	11.0680	−	11.0680i	0.345874	−	0.345874i
$33$	−18.9737	−	27.0000i	−0.574960	−	0.818182i
$34$			70.0000i			2.05882i
$35$	−22.1359	−	3.16228i	−0.632456	−	0.0903508i
$36$		−	9.00000i		−	0.250000i
$37$	7.00000	−	7.00000i	0.189189	−	0.189189i	−0.606156	−	0.795346i	$-0.707289\pi$
$37$	7.00000	−	7.00000i	0.189189	−	0.189189i	0.795346	+	0.606156i	$0.207289\pi$
$38$	−20.0000	+	20.0000i	−0.526316	+	0.526316i
$39$	−9.48683	+	9.48683i	−0.243252	+	0.243252i
$40$	−33.2039	−	4.74342i	−0.830098	−	0.118585i
$41$	69.5701			1.69683			0.848416	−	0.529330i	$-0.177557\pi$
$41$	69.5701			1.69683			0.848416	+	0.529330i	$0.177557\pi$
$42$	−30.0000			−0.714286
$43$	22.1359	−	22.1359i	0.514789	−	0.514789i	−0.401201	−	0.915990i	$-0.631407\pi$
$43$	22.1359	−	22.1359i	0.514789	−	0.514789i	0.915990	+	0.401201i	$0.131407\pi$
$44$	9.00000	−	6.32456i	0.204545	−	0.143740i
$45$	−36.0000	+	27.0000i	−0.800000	+	0.600000i
$46$			22.1359i			0.481216i
$47$	−43.0000	−	43.0000i	−0.914894	−	0.914894i	0.0817585	−	0.996652i	$-0.473946\pi$
$47$	−43.0000	−	43.0000i	−0.914894	−	0.914894i	−0.996652	+	0.0817585i	$0.973946\pi$
$48$	−57.0000			−1.18750
$49$		−	29.0000i		−	0.591837i
$50$	−26.8794	−	49.0153i	−0.537587	−	0.980306i
$51$	66.4078	−	66.4078i	1.30211	−	1.30211i
$52$	−3.16228	−	3.16228i	−0.0608130	−	0.0608130i
$53$	17.0000	−	17.0000i	0.320755	−	0.320755i	−0.528302	−	0.849057i	$-0.677171\pi$
$53$	17.0000	−	17.0000i	0.320755	−	0.320755i	0.849057	+	0.528302i	$0.177171\pi$
$54$	−42.6907	+	42.6907i	−0.790569	+	0.790569i
$55$	−52.2982	−	17.0263i	−0.950877	−	0.309570i
$56$			30.0000i			0.535714i
$57$	37.9473			0.665743
$58$	30.0000	+	30.0000i	0.517241	+	0.517241i
$59$	22.0000			0.372881			0.186441	−	0.982466i	$-0.440305\pi$
$59$	22.0000			0.372881			0.186441	+	0.982466i	$0.440305\pi$
$60$	−9.00000	−	12.0000i	−0.150000	−	0.200000i
$61$			94.8683i			1.55522i	0.628748	+	0.777609i	$0.283568\pi$
$61$			94.8683i			1.55522i	−0.628748	+	0.777609i	$0.716432\pi$
$62$	31.6228	−	31.6228i	0.510045	−	0.510045i
$63$	28.4605	+	28.4605i	0.451754	+	0.451754i
$64$			41.0000i			0.640625i
$65$	−3.16228	+	22.1359i	−0.0486504	+	0.340553i
$66$	−72.6907	−	12.6907i	−1.10137	−	0.192284i
$67$	−47.0000	+	47.0000i	−0.701493	+	0.701493i	−0.964731	−	0.263238i	$-0.915209\pi$
$67$	−47.0000	+	47.0000i	−0.701493	+	0.701493i	0.263238	+	0.964731i	$0.415209\pi$
$68$	22.1359	+	22.1359i	0.325529	+	0.325529i
$69$	21.0000	−	21.0000i	0.304348	−	0.304348i
$70$	−40.0000	+	30.0000i	−0.571429	+	0.428571i
$71$		−	120.000i		−	1.69014i	−0.534655	−	0.845070i	$-0.679558\pi$
$71$		−	120.000i		−	1.69014i	0.534655	−	0.845070i	$-0.320442\pi$
$72$	42.6907	+	42.6907i	0.592927	+	0.592927i
$73$	22.1359	−	22.1359i	0.303232	−	0.303232i	−0.539045	−	0.842277i	$-0.681215\pi$
$73$	22.1359	−	22.1359i	0.303232	−	0.303232i	0.842277	+	0.539045i	$0.181215\pi$
$74$		−	22.1359i		−	0.299134i
$75$	−21.0000	+	72.0000i	−0.280000	+	0.960000i
$76$			12.6491i			0.166436i
$77$	−8.46050	+	48.4605i	−0.109877	+	0.629357i
$78$			30.0000i			0.384615i
$79$	6.32456			0.0800577			0.0400288	−	0.999199i	$-0.487255\pi$
$79$	6.32456			0.0800577			0.0400288	+	0.999199i	$0.487255\pi$
$80$	−76.0000	+	57.0000i	−0.950000	+	0.712500i
$81$	81.0000			1.00000
$82$	110.000	−	110.000i	1.34146	−	1.34146i
$83$	−60.0833	−	60.0833i	−0.723895	−	0.723895i	0.245501	−	0.969396i	$-0.421047\pi$
$83$	−60.0833	−	60.0833i	−0.723895	−	0.723895i	−0.969396	+	0.245501i	$0.921047\pi$
$84$	−9.48683	+	9.48683i	−0.112938	+	0.112938i
$85$	22.1359	−	154.952i	0.260423	−	1.82296i
$86$		−	70.0000i		−	0.813953i
$87$		−	56.9210i		−	0.654264i
$88$	−12.6907	+	72.6907i	−0.144213	+	0.826031i
$89$	100.000			1.12360			0.561798	−	0.827275i	$-0.310110\pi$
$89$	100.000			1.12360			0.561798	+	0.827275i	$0.310110\pi$
$90$	−14.2302	+	99.6117i	−0.158114	+	1.10680i
$91$	20.0000			0.219780
$92$	7.00000	+	7.00000i	0.0760870	+	0.0760870i
$93$	−60.0000			−0.645161
$94$	−135.978			−1.44657
$95$	50.5964	−	37.9473i	0.532594	−	0.399446i
$96$	−33.2039	+	33.2039i	−0.345874	+	0.345874i
$97$	43.0000	−	43.0000i	0.443299	−	0.443299i	−0.449820	−	0.893119i	$-0.648512\pi$
$97$	43.0000	−	43.0000i	0.443299	−	0.443299i	0.893119	+	0.449820i	$0.148512\pi$
$98$	−45.8530	−	45.8530i	−0.467888	−	0.467888i
$99$	56.9210	+	81.0000i	0.574960	+	0.818182i
$100$	−24.0000	−	7.00000i	−0.240000	−	0.0700000i
$101$	−139.140			−1.37763			−0.688813	−	0.724939i	$-0.741868\pi$
$101$	−139.140			−1.37763			−0.688813	+	0.724939i	$0.741868\pi$
$102$		−	210.000i		−	2.05882i
$103$	7.00000	+	7.00000i	0.0679612	+	0.0679612i	0.740270	−	0.672309i	$-0.234697\pi$
$103$	7.00000	+	7.00000i	0.0679612	+	0.0679612i	−0.672309	+	0.740270i	$0.734697\pi$
$104$	30.0000			0.288462
$105$	66.4078	+	9.48683i	0.632456	+	0.0903508i
$106$		−	53.7587i		−	0.507158i
$107$	−41.1096	+	41.1096i	−0.384202	+	0.384202i	−0.872613	−	0.488411i	$-0.837577\pi$
$107$	−41.1096	+	41.1096i	−0.384202	+	0.384202i	0.488411	+	0.872613i	$0.337577\pi$
$108$			27.0000i			0.250000i
$109$	215.035			1.97280			0.986399	−	0.164371i	$-0.0525595\pi$
$109$	215.035			1.97280			0.986399	+	0.164371i	$0.0525595\pi$
$110$	−109.612	+	55.7698i	−0.996470	+	0.506998i
$111$	−21.0000	+	21.0000i	−0.189189	+	0.189189i
$112$	60.0833	+	60.0833i	0.536458	+	0.536458i
$113$	53.0000	−	53.0000i	0.469027	−	0.469027i	−0.432573	−	0.901599i	$-0.642394\pi$
$113$	53.0000	−	53.0000i	0.469027	−	0.469027i	0.901599	+	0.432573i	$0.142394\pi$
$114$	60.0000	−	60.0000i	0.526316	−	0.526316i
$115$	7.00000	−	49.0000i	0.0608696	−	0.426087i
$116$	18.9737			0.163566
$117$	28.4605	−	28.4605i	0.243252	−	0.243252i
$118$	34.7851	−	34.7851i	0.294789	−	0.294789i
$119$	−140.000			−1.17647
$120$	99.6117	+	14.2302i	0.830098	+	0.118585i
$121$	−41.0000	+	113.842i	−0.338843	+	0.940843i
$122$	150.000	+	150.000i	1.22951	+	1.22951i
$123$	−208.710			−1.69683
$124$		−	20.0000i		−	0.161290i
$125$	44.0000	+	117.000i	0.352000	+	0.936000i
$126$	90.0000			0.714286
$127$	41.1096	+	41.1096i	0.323698	+	0.323698i	0.850184	−	0.526486i	$-0.176491\pi$
$127$	41.1096	+	41.1096i	0.323698	+	0.323698i	−0.526486	+	0.850184i	$0.676491\pi$
$128$	109.099	+	109.099i	0.852333	+	0.852333i
$129$	−66.4078	+	66.4078i	−0.514789	+	0.514789i
$130$	30.0000	+	40.0000i	0.230769	+	0.307692i
$131$	126.491			0.965581			0.482790	−	0.875736i	$-0.339623\pi$
$131$	126.491			0.965581			0.482790	+	0.875736i	$0.339623\pi$
$132$	−27.0000	+	18.9737i	−0.204545	+	0.143740i
$133$	−40.0000	−	40.0000i	−0.300752	−	0.300752i
$134$			148.627i			1.10916i
$135$	108.000	−	81.0000i	0.800000	−	0.600000i
$136$	−210.000			−1.54412
$137$	83.0000	+	83.0000i	0.605839	+	0.605839i	0.941856	−	0.336017i	$-0.109080\pi$
$137$	83.0000	+	83.0000i	0.605839	+	0.605839i	−0.336017	+	0.941856i	$0.609080\pi$
$138$		−	66.4078i		−	0.481216i
$139$	−12.6491			−0.0910008			−0.0455004	−	0.998964i	$-0.514488\pi$
$139$	−12.6491			−0.0910008			−0.0455004	+	0.998964i	$0.514488\pi$
$140$	−3.16228	+	22.1359i	−0.0225877	+	0.158114i
$141$	129.000	+	129.000i	0.914894	+	0.914894i
$142$	−189.737	−	189.737i	−1.33617	−	1.33617i
$143$	48.4605	+	8.46050i	0.338885	+	0.0591643i
$144$	171.000			1.18750
$145$	−56.9210	−	75.8947i	−0.392559	−	0.523411i
$146$		−	70.0000i		−	0.479452i
$147$			87.0000i			0.591837i
$148$	−7.00000	−	7.00000i	−0.0472973	−	0.0472973i
$149$			94.8683i			0.636700i	0.947973	+	0.318350i	$0.103129\pi$
$149$			94.8683i			0.636700i	−0.947973	+	0.318350i	$0.896871\pi$
$150$	80.6381	+	147.046i	0.537587	+	0.980306i
$151$			113.842i			0.753921i	0.926229	+	0.376960i	$0.123031\pi$
$151$			113.842i			0.753921i	−0.926229	+	0.376960i	$0.876969\pi$
$152$	−60.0000	−	60.0000i	−0.394737	−	0.394737i
$153$	−199.223	+	199.223i	−1.30211	+	1.30211i
$154$	63.2456	+	90.0000i	0.410685	+	0.584416i
$155$	−80.0000	+	60.0000i	−0.516129	+	0.387097i
$156$	9.48683	+	9.48683i	0.0608130	+	0.0608130i
$157$	67.0000	−	67.0000i	0.426752	−	0.426752i	−0.460769	−	0.887520i	$-0.652426\pi$
$157$	67.0000	−	67.0000i	0.426752	−	0.426752i	0.887520	+	0.460769i	$0.152426\pi$
$158$	10.0000	−	10.0000i	0.0632911	−	0.0632911i
$159$	−51.0000	+	51.0000i	−0.320755	+	0.320755i
$160$	−11.0680	+	77.4758i	−0.0691748	+	0.484224i
$161$	−44.2719			−0.274981
$162$	128.072	−	128.072i	0.790569	−	0.790569i
$163$	−137.000	−	137.000i	−0.840491	−	0.840491i	0.148432	−	0.988923i	$-0.452577\pi$
$163$	−137.000	−	137.000i	−0.840491	−	0.840491i	−0.988923	+	0.148432i	$0.952577\pi$
$164$		−	69.5701i		−	0.424208i
$165$	156.895	+	51.0790i	0.950877	+	0.309570i
$166$	−190.000			−1.14458
$167$	205.548	−	205.548i	1.23083	−	1.23083i	0.267180	−	0.963647i	$-0.413908\pi$
$167$	205.548	−	205.548i	1.23083	−	1.23083i	0.963647	−	0.267180i	$-0.0860918\pi$
$168$		−	90.0000i		−	0.535714i
$169$			149.000i			0.881657i
$170$	−210.000	−	280.000i	−1.23529	−	1.64706i
$171$	−113.842			−0.665743
$172$	−22.1359	−	22.1359i	−0.128697	−	0.128697i
$173$	34.7851	+	34.7851i	0.201070	+	0.201070i	0.800458	−	0.599389i	$-0.204590\pi$
$173$	34.7851	+	34.7851i	0.201070	+	0.201070i	−0.599389	+	0.800458i	$0.704590\pi$
$174$	−90.0000	−	90.0000i	−0.517241	−	0.517241i
$175$	98.0306	−	53.7587i	0.560175	−	0.307193i
$176$	120.167	+	171.000i	0.682764	+	0.971591i
$177$	−66.0000			−0.372881
$178$	158.114	−	158.114i	0.888280	−	0.888280i
$179$	−320.000			−1.78771			−0.893855	−	0.448357i	$-0.852009\pi$
$179$	−320.000			−1.78771			−0.893855	+	0.448357i	$0.852009\pi$
$180$	27.0000	+	36.0000i	0.150000	+	0.200000i
$181$	80.0000			0.441989			0.220994	−	0.975275i	$-0.429070\pi$
$181$	80.0000			0.441989			0.220994	+	0.975275i	$0.429070\pi$
$182$	31.6228	−	31.6228i	0.173752	−	0.173752i
$183$		−	284.605i		−	1.55522i
$184$	−66.4078			−0.360912
$185$	−7.00000	+	49.0000i	−0.0378378	+	0.264865i
$186$	−94.8683	+	94.8683i	−0.510045	+	0.510045i
$187$	−339.223	−	59.2235i	−1.81403	−	0.316703i
$188$	−43.0000	+	43.0000i	−0.228723	+	0.228723i
$189$	−85.3815	−	85.3815i	−0.451754	−	0.451754i
$190$	20.0000	−	140.000i	0.105263	−	0.736842i
$191$		−	258.000i		−	1.35079i	−0.737458	−	0.675393i	$-0.763974\pi$
$191$		−	258.000i		−	1.35079i	0.737458	−	0.675393i	$-0.236026\pi$
$192$		−	123.000i		−	0.640625i
$193$	79.0569	−	79.0569i	0.409621	−	0.409621i	−0.471985	−	0.881607i	$-0.656462\pi$
$193$	79.0569	−	79.0569i	0.409621	−	0.409621i	0.881607	+	0.471985i	$0.156462\pi$
$194$		−	135.978i		−	0.700917i
$195$	9.48683	−	66.4078i	0.0486504	−	0.340553i
$196$	−29.0000			−0.147959
$197$	−230.846	+	230.846i	−1.17181	+	1.17181i	−0.190030	+	0.981778i	$0.560859\pi$
$197$	−230.846	+	230.846i	−1.17181	+	1.17181i	−0.981778	+	0.190030i	$0.939141\pi$
$198$	218.072	+	38.0722i	1.10137	+	0.192284i
$199$		−	120.000i		−	0.603015i	−0.953464	−	0.301508i	$-0.902510\pi$
$199$		−	120.000i		−	0.603015i	0.953464	−	0.301508i	$-0.0974898\pi$
$200$	147.046	−	80.6381i	0.735230	−	0.403190i
$201$	141.000	−	141.000i	0.701493	−	0.701493i
$202$	−220.000	+	220.000i	−1.08911	+	1.08911i
$203$	−60.0000	+	60.0000i	−0.295567	+	0.295567i
$204$	−66.4078	−	66.4078i	−0.325529	−	0.325529i
$205$	−278.280	+	208.710i	−1.35747	+	1.01810i
$206$	22.1359			0.107456
$207$	−63.0000	+	63.0000i	−0.304348	+	0.304348i
$208$	60.0833	−	60.0833i	0.288862	−	0.288862i
$209$	−80.0000	−	113.842i	−0.382775	−	0.544699i
$210$	120.000	−	90.0000i	0.571429	−	0.428571i
$211$		−	246.658i		−	1.16899i	−0.811396	−	0.584497i	$-0.801292\pi$
$211$		−	246.658i		−	1.16899i	0.811396	−	0.584497i	$-0.198708\pi$
$212$	−17.0000	−	17.0000i	−0.0801887	−	0.0801887i
$213$			360.000i			1.69014i
$214$			130.000i			0.607477i
$215$	−22.1359	+	154.952i	−0.102958	+	0.720705i
$216$	−128.072	−	128.072i	−0.592927	−	0.592927i
$217$	63.2456	+	63.2456i	0.291454	+	0.291454i
$218$	340.000	−	340.000i	1.55963	−	1.55963i
$219$	−66.4078	+	66.4078i	−0.303232	+	0.303232i
$220$	−17.0263	+	52.2982i	−0.0773924	+	0.237719i
$221$			140.000i			0.633484i
$222$			66.4078i			0.299134i
$223$	73.0000	+	73.0000i	0.327354	+	0.327354i	0.851580	−	0.524225i	$-0.175645\pi$
$223$	73.0000	+	73.0000i	0.327354	+	0.327354i	−0.524225	+	0.851580i	$0.675645\pi$
$224$	70.0000			0.312500
$225$	63.0000	−	216.000i	0.280000	−	0.960000i
$226$		−	167.601i		−	0.741596i
$227$	−154.952	+	154.952i	−0.682606	+	0.682606i	−0.960587	−	0.277981i	$-0.910335\pi$
$227$	−154.952	+	154.952i	−0.682606	+	0.682606i	0.277981	+	0.960587i	$0.410335\pi$
$228$		−	37.9473i		−	0.166436i
$229$		−	180.000i		−	0.786026i	−0.919533	−	0.393013i	$-0.871433\pi$
$229$		−	180.000i		−	0.786026i	0.919533	−	0.393013i	$-0.128567\pi$
$230$	−66.4078	−	88.5438i	−0.288730	−	0.384973i
$231$	25.3815	−	145.381i	0.109877	−	0.629357i
$232$	−90.0000	+	90.0000i	−0.387931	+	0.387931i
$233$	−3.16228	−	3.16228i	−0.0135720	−	0.0135720i	0.700288	−	0.713860i	$-0.253055\pi$
$233$	−3.16228	−	3.16228i	−0.0135720	−	0.0135720i	−0.713860	+	0.700288i	$0.753055\pi$
$234$		−	90.0000i		−	0.384615i
$235$	301.000	+	43.0000i	1.28085	+	0.182979i
$236$		−	22.0000i		−	0.0932203i
$237$	−18.9737			−0.0800577
$238$	−221.359	+	221.359i	−0.930082	+	0.930082i
$239$		−	379.473i		−	1.58775i	−0.608078	−	0.793877i	$-0.708059\pi$
$239$		−	379.473i		−	1.58775i	0.608078	−	0.793877i	$-0.291941\pi$
$240$	228.000	−	171.000i	0.950000	−	0.712500i
$241$		−	151.789i		−	0.629831i	−0.949120	−	0.314916i	$-0.898024\pi$
$241$		−	151.789i		−	0.629831i	0.949120	−	0.314916i	$-0.101976\pi$
$242$	115.173	+	244.827i	0.475923	+	1.01168i
$243$	−243.000			−1.00000
$244$	94.8683			0.388805
$245$	87.0000	+	116.000i	0.355102	+	0.473469i
$246$	−330.000	+	330.000i	−1.34146	+	1.34146i
$247$	−40.0000	+	40.0000i	−0.161943	+	0.161943i
$248$	94.8683	+	94.8683i	0.382534	+	0.382534i
$249$	180.250	+	180.250i	0.723895	+	0.723895i
$250$	254.563	+	115.423i	1.01825	+	0.461693i
$251$		−	60.0000i		−	0.239044i	−0.992832	−	0.119522i	$-0.961864\pi$
$251$		−	60.0000i		−	0.239044i	0.992832	−	0.119522i	$-0.0381362\pi$
$252$	28.4605	−	28.4605i	0.112938	−	0.112938i
$253$	−107.272	−	18.7281i	−0.424000	−	0.0740242i
$254$	130.000			0.511811
$255$	−66.4078	+	464.855i	−0.260423	+	1.82296i
$256$	181.000			0.707031
$257$	23.0000	+	23.0000i	0.0894942	+	0.0894942i	0.750437	−	0.660942i	$-0.229843\pi$
$257$	23.0000	+	23.0000i	0.0894942	+	0.0894942i	−0.660942	+	0.750437i	$0.729843\pi$
$258$			210.000i			0.813953i
$259$	44.2719			0.170934
$260$	22.1359	+	3.16228i	0.0851382	+	0.0121626i
$261$			170.763i			0.654264i
$262$	200.000	−	200.000i	0.763359	−	0.763359i
$263$	167.601	+	167.601i	0.637265	+	0.637265i	0.949880	−	0.312615i	$-0.101205\pi$
$263$	167.601	+	167.601i	0.637265	+	0.637265i	−0.312615	+	0.949880i	$0.601205\pi$
$264$	38.0722	−	218.072i	0.144213	−	0.826031i
$265$	−17.0000	+	119.000i	−0.0641509	+	0.449057i
$266$	−126.491			−0.475530
$267$	−300.000			−1.12360
$268$	47.0000	+	47.0000i	0.175373	+	0.175373i
$269$	−182.000			−0.676580			−0.338290	−	0.941042i	$-0.609848\pi$
$269$	−182.000			−0.676580			−0.338290	+	0.941042i	$0.609848\pi$
$270$	42.6907	−	298.835i	0.158114	−	1.10680i
$271$			265.631i			0.980189i	0.871669	+	0.490095i	$0.163038\pi$
$271$			265.631i			0.980189i	−0.871669	+	0.490095i	$0.836962\pi$
$272$	−420.583	+	420.583i	−1.54626	+	1.54626i
$273$	−60.0000			−0.219780
$274$	262.469			0.957916
$275$	260.272	−	88.7893i	0.946443	−	0.322870i
$276$	−21.0000	−	21.0000i	−0.0760870	−	0.0760870i
$277$	154.952	+	154.952i	0.559392	+	0.559392i	0.929134	−	0.369742i	$-0.120554\pi$
$277$	154.952	+	154.952i	0.559392	+	0.559392i	−0.369742	+	0.929134i	$0.620554\pi$
$278$	−20.0000	+	20.0000i	−0.0719424	+	0.0719424i
$279$	180.000			0.645161
$280$	−90.0000	−	120.000i	−0.321429	−	0.428571i
$281$	335.201			1.19289			0.596444	−	0.802655i	$-0.296580\pi$
$281$	335.201			1.19289			0.596444	+	0.802655i	$0.296580\pi$
$282$	407.934			1.44657
$283$	−281.443	+	281.443i	−0.994497	+	0.994497i	−0.999985	−	0.00548773i	$-0.998253\pi$
$283$	−281.443	+	281.443i	−0.994497	+	0.994497i	0.00548773	+	0.999985i	$0.498253\pi$
$284$	−120.000			−0.422535
$285$	−151.789	+	113.842i	−0.532594	+	0.399446i
$286$	90.0000	−	63.2456i	0.314685	−	0.221138i
$287$	220.000	+	220.000i	0.766551	+	0.766551i
$288$	99.6117	−	99.6117i	0.345874	−	0.345874i
$289$		−	691.000i		−	2.39100i
$290$	−210.000	−	30.0000i	−0.724138	−	0.103448i
$291$	−129.000	+	129.000i	−0.443299	+	0.443299i
$292$	−22.1359	−	22.1359i	−0.0758080	−	0.0758080i
$293$	−230.846	−	230.846i	−0.787871	−	0.787871i	0.193274	−	0.981145i	$-0.438089\pi$
$293$	−230.846	−	230.846i	−0.787871	−	0.787871i	−0.981145	+	0.193274i	$0.938089\pi$
$294$	137.559	+	137.559i	0.467888	+	0.467888i
$295$	−88.0000	+	66.0000i	−0.298305	+	0.223729i
$296$	66.4078			0.224351
$297$	−170.763	−	243.000i	−0.574960	−	0.818182i
$298$	150.000	+	150.000i	0.503356	+	0.503356i
$299$			44.2719i			0.148067i
$300$	72.0000	+	21.0000i	0.240000	+	0.0700000i
$301$	140.000			0.465116
$302$	180.000	+	180.000i	0.596026	+	0.596026i
$303$	417.421			1.37763
$304$	−240.333			−0.790569
$305$	−284.605	−	379.473i	−0.933131	−	1.24417i
$306$			630.000i			2.05882i
$307$	154.952	+	154.952i	0.504728	+	0.504728i	0.912904	−	0.408175i	$-0.133835\pi$
$307$	154.952	+	154.952i	0.504728	+	0.504728i	−0.408175	+	0.912904i	$0.633835\pi$
$308$	48.4605	+	8.46050i	0.157339	+	0.0274692i
$309$	−21.0000	−	21.0000i	−0.0679612	−	0.0679612i
$310$	−31.6228	+	221.359i	−0.102009	+	0.714063i
$311$			240.000i			0.771704i	0.922561	+	0.385852i	$0.126092\pi$
$311$			240.000i			0.771704i	−0.922561	+	0.385852i	$0.873908\pi$
$312$	−90.0000			−0.288462
$313$	127.000	+	127.000i	0.405751	+	0.405751i	0.880254	−	0.474503i	$-0.157372\pi$
$313$	127.000	+	127.000i	0.405751	+	0.405751i	−0.474503	+	0.880254i	$0.657372\pi$
$314$		−	211.873i		−	0.674754i
$315$	−199.223	−	28.4605i	−0.632456	−	0.0903508i
$316$		−	6.32456i		−	0.0200144i
$317$	−127.000	−	127.000i	−0.400631	−	0.400631i	0.477824	−	0.878455i	$-0.341426\pi$
$317$	−127.000	−	127.000i	−0.400631	−	0.400631i	−0.878455	+	0.477824i	$0.841426\pi$
$318$			161.276i			0.507158i
$319$	−170.763	+	120.000i	−0.535307	+	0.376176i
$320$	−123.000	−	164.000i	−0.384375	−	0.512500i
$321$	123.329	−	123.329i	0.384202	−	0.384202i
$322$	−70.0000	+	70.0000i	−0.217391	+	0.217391i
$323$	280.000	−	280.000i	0.866873	−	0.866873i
$324$		−	81.0000i		−	0.250000i
$325$	−53.7587	−	98.0306i	−0.165411	−	0.301633i
$326$	−433.232			−1.32893
$327$	−645.105			−1.97280
$328$	330.000	+	330.000i	1.00610	+	1.00610i
$329$		−	271.956i		−	0.826614i
$330$	328.835	−	167.309i	0.996470	−	0.506998i
$331$	200.000			0.604230			0.302115	−	0.953272i	$-0.402307\pi$
$331$	200.000			0.604230			0.302115	+	0.953272i	$0.402307\pi$
$332$	−60.0833	+	60.0833i	−0.180974	+	0.180974i
$333$	63.0000	−	63.0000i	0.189189	−	0.189189i
$334$		−	650.000i		−	1.94611i
$335$	47.0000	−	329.000i	0.140299	−	0.982090i
$336$	−180.250	−	180.250i	−0.536458	−	0.536458i
$337$	363.662	+	363.662i	1.07912	+	1.07912i	0.996589	+	0.0825267i	$0.0262990\pi$
$337$	363.662	+	363.662i	1.07912	+	1.07912i	0.0825267	+	0.996589i	$0.473701\pi$
$338$	235.590	+	235.590i	0.697011	+	0.697011i
$339$	−159.000	+	159.000i	−0.469027	+	0.469027i
$340$	−154.952	−	22.1359i	−0.455740	−	0.0651057i
$341$	126.491	+	180.000i	0.370942	+	0.527859i
$342$	−180.000	+	180.000i	−0.526316	+	0.526316i
$343$	246.658	−	246.658i	0.719119	−	0.719119i
$344$	210.000			0.610465
$345$	−21.0000	+	147.000i	−0.0608696	+	0.426087i
$346$	110.000			0.317919
$347$	91.7061	−	91.7061i	0.264283	−	0.264283i	−0.562509	−	0.826791i	$-0.690164\pi$
$347$	91.7061	−	91.7061i	0.264283	−	0.264283i	0.826791	+	0.562509i	$0.190164\pi$
$348$	−56.9210			−0.163566
$349$	252.982			0.724877			0.362439	−	0.932008i	$-0.381944\pi$
$349$	252.982			0.724877			0.362439	+	0.932008i	$0.381944\pi$
$350$	70.0000	−	240.000i	0.200000	−	0.685714i
$351$	−85.3815	+	85.3815i	−0.243252	+	0.243252i
$352$	169.612	+	29.6117i	0.481852	+	0.0841243i
$353$	−313.000	+	313.000i	−0.886686	+	0.886686i	−0.994203	−	0.107518i	$-0.965710\pi$
$353$	−313.000	+	313.000i	−0.886686	+	0.886686i	0.107518	+	0.994203i	$0.465710\pi$
$354$	−104.355	+	104.355i	−0.294789	+	0.294789i
$355$	360.000	+	480.000i	1.01408	+	1.35211i
$356$		−	100.000i		−	0.280899i
$357$	420.000			1.17647
$358$	−505.964	+	505.964i	−1.41331	+	1.41331i
$359$			75.8947i			0.211406i	0.994398	+	0.105703i	$0.0337092\pi$
$359$			75.8947i			0.211406i	−0.994398	+	0.105703i	$0.966291\pi$
$360$	−298.835	−	42.6907i	−0.830098	−	0.118585i
$361$	−201.000			−0.556787
$362$	126.491	−	126.491i	0.349423	−	0.349423i
$363$	123.000	−	341.526i	0.338843	−	0.940843i
$364$		−	20.0000i		−	0.0549451i
$365$	−22.1359	+	154.952i	−0.0606464	+	0.424525i
$366$	−450.000	−	450.000i	−1.22951	−	1.22951i
$367$	97.0000	−	97.0000i	0.264305	−	0.264305i	−0.562495	−	0.826800i	$-0.690159\pi$
$367$	97.0000	−	97.0000i	0.264305	−	0.264305i	0.826800	+	0.562495i	$0.190159\pi$
$368$	−133.000	+	133.000i	−0.361413	+	0.361413i
$369$	626.131			1.69683
$370$	66.4078	+	88.5438i	0.179481	+	0.239307i
$371$	107.517			0.289804
$372$			60.0000i			0.161290i
$373$	230.846	−	230.846i	0.618891	−	0.618891i	−0.326356	−	0.945247i	$-0.605821\pi$
$373$	230.846	−	230.846i	0.618891	−	0.618891i	0.945247	+	0.326356i	$0.105821\pi$
$374$	−630.000	+	442.719i	−1.68449	+	1.18374i
$375$	−132.000	−	351.000i	−0.352000	−	0.936000i
$376$		−	407.934i		−	1.08493i
$377$	60.0000	+	60.0000i	0.159151	+	0.159151i
$378$	−270.000			−0.714286
$379$			60.0000i			0.158311i	0.996862	+	0.0791557i	$0.0252224\pi$
$379$			60.0000i			0.158311i	−0.996862	+	0.0791557i	$0.974778\pi$
$380$	−37.9473	−	50.5964i	−0.0998614	−	0.133149i
$381$	−123.329	−	123.329i	−0.323698	−	0.323698i
$382$	−407.934	−	407.934i	−1.06789	−	1.06789i
$383$	413.000	−	413.000i	1.07833	−	1.07833i	0.0816695	−	0.996659i	$-0.473975\pi$
$383$	413.000	−	413.000i	1.07833	−	1.07833i	0.996659	−	0.0816695i	$-0.0260252\pi$
$384$	−327.296	−	327.296i	−0.852333	−	0.852333i
$385$	−111.540	−	219.223i	−0.289713	−	0.569412i
$386$		−	250.000i		−	0.647668i
$387$	199.223	−	199.223i	0.514789	−	0.514789i
$388$	−43.0000	−	43.0000i	−0.110825	−	0.110825i
$389$	298.000			0.766067			0.383033	−	0.923734i	$-0.374879\pi$
$389$	298.000			0.766067			0.383033	+	0.923734i	$0.374879\pi$
$390$	−90.0000	−	120.000i	−0.230769	−	0.307692i
$391$		−	309.903i		−	0.792591i
$392$	137.559	−	137.559i	0.350916	−	0.350916i
$393$	−379.473			−0.965581
$394$			730.000i			1.85279i
$395$	−25.2982	+	18.9737i	−0.0640461	+	0.0480346i
$396$	81.0000	−	56.9210i	0.204545	−	0.143740i
$397$	73.0000	−	73.0000i	0.183879	−	0.183879i	−0.609165	−	0.793044i	$-0.708495\pi$
$397$	73.0000	−	73.0000i	0.183879	−	0.183879i	0.793044	+	0.609165i	$0.208495\pi$
$398$	−189.737	−	189.737i	−0.476725	−	0.476725i
$399$	120.000	+	120.000i	0.300752	+	0.300752i
$400$	133.000	−	456.000i	0.332500	−	1.14000i
$401$		−	258.000i		−	0.643392i	−0.946843	−	0.321696i	$-0.895747\pi$
$401$		−	258.000i		−	0.643392i	0.946843	−	0.321696i	$-0.104253\pi$
$402$		−	445.881i		−	1.10916i
$403$	63.2456	−	63.2456i	0.156937	−	0.156937i
$404$			139.140i			0.344406i
$405$	−324.000	+	243.000i	−0.800000	+	0.600000i
$406$			189.737i			0.467332i
$407$	107.272	+	18.7281i	0.263567	+	0.0460150i
$408$	630.000			1.54412
$409$	−638.780			−1.56181			−0.780905	−	0.624650i	$-0.785242\pi$
$409$	−638.780			−1.56181			−0.780905	+	0.624650i	$0.785242\pi$
$410$	−110.000	+	770.000i	−0.268293	+	1.87805i
$411$	−249.000	−	249.000i	−0.605839	−	0.605839i
$412$	7.00000	−	7.00000i	0.0169903	−	0.0169903i
$413$	69.5701	+	69.5701i	0.168451	+	0.168451i
$414$			199.223i			0.481216i
$415$	420.583	+	60.0833i	1.01345	+	0.144779i
$416$		−	70.0000i		−	0.168269i
$417$	37.9473			0.0910008
$418$	−306.491	−	53.5089i	−0.733232	−	0.128012i
$419$	−200.000			−0.477327			−0.238663	−	0.971102i	$-0.576709\pi$
$419$	−200.000			−0.477327			−0.238663	+	0.971102i	$0.576709\pi$
$420$	9.48683	−	66.4078i	0.0225877	−	0.158114i
$421$	−400.000			−0.950119			−0.475059	−	0.879954i	$-0.657573\pi$
$421$	−400.000			−0.950119			−0.475059	+	0.879954i	$0.657573\pi$
$422$	−390.000	−	390.000i	−0.924171	−	0.924171i
$423$	−387.000	−	387.000i	−0.914894	−	0.914894i
$424$	161.276			0.380368
$425$	376.311	+	686.214i	0.885438	+	1.61462i
$426$	569.210	+	569.210i	1.33617	+	1.33617i
$427$	−300.000	+	300.000i	−0.702576	+	0.702576i
$428$	41.1096	+	41.1096i	0.0960505	+	0.0960505i
$429$	−145.381	−	25.3815i	−0.338885	−	0.0591643i
$430$	210.000	+	280.000i	0.488372	+	0.651163i
$431$	−158.114			−0.366854			−0.183427	−	0.983033i	$-0.558719\pi$
$431$	−158.114			−0.366854			−0.183427	+	0.983033i	$0.558719\pi$
$432$	−513.000			−1.18750
$433$	193.000	+	193.000i	0.445727	+	0.445727i	0.893931	−	0.448204i	$-0.147936\pi$
$433$	193.000	+	193.000i	0.445727	+	0.445727i	−0.448204	+	0.893931i	$0.647936\pi$
$434$	200.000			0.460829
$435$	170.763	+	227.684i	0.392559	+	0.523411i
$436$		−	215.035i		−	0.493199i
$437$	88.5438	−	88.5438i	0.202617	−	0.202617i
$438$			210.000i			0.479452i
$439$	−373.149			−0.849997			−0.424999	−	0.905194i	$-0.639725\pi$
$439$	−373.149			−0.849997			−0.424999	+	0.905194i	$0.639725\pi$
$440$	−167.309	−	328.835i	−0.380248	−	0.747353i
$441$		−	261.000i		−	0.591837i
$442$	221.359	+	221.359i	0.500813	+	0.500813i
$443$	−463.000	+	463.000i	−1.04515	+	1.04515i	−0.0462152	+	0.998932i	$0.514716\pi$
$443$	−463.000	+	463.000i	−1.04515	+	1.04515i	−0.998932	+	0.0462152i	$0.985284\pi$
$444$	21.0000	+	21.0000i	0.0472973	+	0.0472973i
$445$	−400.000	+	300.000i	−0.898876	+	0.674157i
$446$	230.846			0.517593
$447$		−	284.605i		−	0.636700i
$448$	−129.653	+	129.653i	−0.289405	+	0.289405i
$449$	−260.000			−0.579065			−0.289532	−	0.957168i	$-0.593500\pi$
$449$	−260.000			−0.579065			−0.289532	+	0.957168i	$0.593500\pi$
$450$	−241.914	−	441.138i	−0.537587	−	0.980306i
$451$	440.000	+	626.131i	0.975610	+	1.38832i
$452$	−53.0000	−	53.0000i	−0.117257	−	0.117257i
$453$		−	341.526i		−	0.753921i
$454$			490.000i			1.07930i
$455$	−80.0000	+	60.0000i	−0.175824	+	0.131868i
$456$	180.000	+	180.000i	0.394737	+	0.394737i
$457$	−91.7061	−	91.7061i	−0.200670	−	0.200670i	0.599617	−	0.800287i	$-0.295320\pi$
$457$	−91.7061	−	91.7061i	−0.200670	−	0.200670i	−0.800287	+	0.599617i	$0.795320\pi$
$458$	−284.605	−	284.605i	−0.621408	−	0.621408i
$459$	597.670	−	597.670i	1.30211	−	1.30211i
$460$	−49.0000	−	7.00000i	−0.106522	−	0.0152174i
$461$	202.386			0.439015			0.219507	−	0.975611i	$-0.429555\pi$
$461$	202.386			0.439015			0.219507	+	0.975611i	$0.429555\pi$
$462$	−189.737	−	270.000i	−0.410685	−	0.584416i
$463$	−527.000	−	527.000i	−1.13823	−	1.13823i	−0.988768	−	0.149461i	$-0.952246\pi$
$463$	−527.000	−	527.000i	−1.13823	−	1.13823i	−0.149461	−	0.988768i	$-0.547754\pi$
$464$			360.500i			0.776939i
$465$	240.000	−	180.000i	0.516129	−	0.387097i
$466$	−10.0000			−0.0214592
$467$	347.000	+	347.000i	0.743041	+	0.743041i	0.973162	−	0.230121i	$-0.0739123\pi$
$467$	347.000	+	347.000i	0.743041	+	0.743041i	−0.230121	+	0.973162i	$0.573912\pi$
$468$	−28.4605	−	28.4605i	−0.0608130	−	0.0608130i
$469$	−297.254			−0.633804
$470$	543.912	−	407.934i	1.15726	−	0.867944i
$471$	−201.000	+	201.000i	−0.426752	+	0.426752i
$472$	104.355	+	104.355i	0.221091	+	0.221091i
$473$	339.223	+	59.2235i	0.717174	+	0.125208i
$474$	−30.0000	+	30.0000i	−0.0632911	+	0.0632911i
$475$	−88.5438	+	303.579i	−0.186408	+	0.639113i
$476$			140.000i			0.294118i
$477$	153.000	−	153.000i	0.320755	−	0.320755i
$478$	−600.000	−	600.000i	−1.25523	−	1.25523i
$479$			37.9473i			0.0792220i	0.999215	+	0.0396110i	$0.0126119\pi$
$479$			37.9473i			0.0792220i	−0.999215	+	0.0396110i	$0.987388\pi$
$480$	33.2039	−	232.427i	0.0691748	−	0.484224i
$481$		−	44.2719i		−	0.0920413i
$482$	−240.000	−	240.000i	−0.497925	−	0.497925i
$483$	132.816			0.274981
$484$	113.842	+	41.0000i	0.235211	+	0.0847107i
$485$	−43.0000	+	301.000i	−0.0886598	+	0.620619i
$486$	−384.217	+	384.217i	−0.790569	+	0.790569i
$487$	−257.000	+	257.000i	−0.527721	+	0.527721i	−0.919892	−	0.392171i	$-0.871724\pi$
$487$	−257.000	+	257.000i	−0.527721	+	0.527721i	0.392171	+	0.919892i	$0.371724\pi$
$488$	−450.000	+	450.000i	−0.922131	+	0.922131i
$489$	411.000	+	411.000i	0.840491	+	0.840491i
$490$	320.971	+	45.8530i	0.655043	+	0.0935776i
$491$	−101.193			−0.206095			−0.103048	−	0.994676i	$-0.532859\pi$
$491$	−101.193			−0.206095			−0.103048	+	0.994676i	$0.532859\pi$
$492$			208.710i			0.424208i
$493$	−420.000	−	420.000i	−0.851927	−	0.851927i
$494$			126.491i			0.256055i
$495$	−470.684	−	153.237i	−0.950877	−	0.309570i
$496$	380.000			0.766129
$497$	379.473	−	379.473i	0.763528	−	0.763528i
$498$	570.000			1.14458
$499$		−	540.000i		−	1.08216i	−0.840970	−	0.541082i	$-0.818015\pi$
$499$		−	540.000i		−	1.08216i	0.840970	−	0.541082i	$-0.181985\pi$
$500$	117.000	−	44.0000i	0.234000	−	0.0880000i
$501$	−616.644	+	616.644i	−1.23083	+	1.23083i
$502$	−94.8683	−	94.8683i	−0.188981	−	0.188981i
$503$	338.364	+	338.364i	0.672691	+	0.672691i	0.958336	−	0.285644i	$-0.0922076\pi$
$503$	338.364	+	338.364i	0.672691	+	0.672691i	−0.285644	+	0.958336i	$0.592208\pi$
$504$			270.000i			0.535714i
$505$	556.561	−	417.421i	1.10210	−	0.826576i
$506$	−199.223	+	140.000i	−0.393722	+	0.276680i
$507$		−	447.000i		−	0.881657i
$508$	41.1096	−	41.1096i	0.0809244	−	0.0809244i
$509$	742.000			1.45776			0.728880	−	0.684641i	$-0.240041\pi$
$509$	742.000			1.45776			0.728880	+	0.684641i	$0.240041\pi$
$510$	630.000	+	840.000i	1.23529	+	1.64706i
$511$	140.000			0.273973
$512$	−150.208	+	150.208i	−0.293375	+	0.293375i
$513$	341.526			0.665743
$514$	72.7324			0.141503
$515$	−49.0000	−	7.00000i	−0.0951456	−	0.0135922i
$516$	66.4078	+	66.4078i	0.128697	+	0.128697i
$517$	115.044	−	658.956i	0.222522	−	1.27458i
$518$	70.0000	−	70.0000i	0.135135	−	0.135135i
$519$	−104.355	−	104.355i	−0.201070	−	0.201070i
$520$	−120.000	+	90.0000i	−0.230769	+	0.173077i
$521$		−	942.000i		−	1.80806i	−0.427468	−	0.904031i	$-0.640594\pi$
$521$		−	942.000i		−	1.80806i	0.427468	−	0.904031i	$-0.359406\pi$
$522$	270.000	+	270.000i	0.517241	+	0.517241i
$523$	79.0569	−	79.0569i	0.151161	−	0.151161i	−0.627476	−	0.778636i	$-0.715912\pi$
$523$	79.0569	−	79.0569i	0.151161	−	0.151161i	0.778636	+	0.627476i	$0.215912\pi$
$524$		−	126.491i		−	0.241395i
$525$	−294.092	+	161.276i	−0.560175	+	0.307193i
$526$	530.000			1.00760
$527$	−442.719	+	442.719i	−0.840074	+	0.840074i
$528$	−360.500	−	513.000i	−0.682764	−	0.971591i
$529$			431.000i			0.814745i
$530$	161.276	+	215.035i	0.304295	+	0.405726i
$531$	198.000			0.372881
$532$	−40.0000	+	40.0000i	−0.0751880	+	0.0751880i
$533$	220.000	−	220.000i	0.412758	−	0.412758i
$534$	−474.342	+	474.342i	−0.888280	+	0.888280i
$535$	41.1096	−	287.767i	0.0768404	−	0.537883i
$536$	−445.881			−0.831868
$537$	960.000			1.78771
$538$	−287.767	+	287.767i	−0.534883	+	0.534883i
$539$	261.000	−	183.412i	0.484230	−	0.340282i
$540$	−81.0000	−	108.000i	−0.150000	−	0.200000i
$541$		−	436.394i		−	0.806644i	−0.915058	−	0.403322i	$-0.867855\pi$
$541$		−	436.394i		−	0.806644i	0.915058	−	0.403322i	$-0.132145\pi$
$542$	420.000	+	420.000i	0.774908	+	0.774908i
$543$	−240.000			−0.441989
$544$			490.000i			0.900735i
$545$	−860.140	+	645.105i	−1.57824	+	1.18368i
$546$	−94.8683	+	94.8683i	−0.173752	+	0.173752i
$547$	−528.100	−	528.100i	−0.965449	−	0.965449i	0.0339741	−	0.999423i	$-0.489184\pi$
$547$	−528.100	−	528.100i	−0.965449	−	0.965449i	−0.999423	+	0.0339741i	$0.989184\pi$
$548$	83.0000	−	83.0000i	0.151460	−	0.151460i
$549$			853.815i			1.55522i
$550$	271.138	−	551.914i	0.492978	−	1.00348i
$551$		−	240.000i		−	0.435572i
$552$	199.223			0.360912
$553$	20.0000	+	20.0000i	0.0361664	+	0.0361664i
$554$	490.000			0.884477
$555$	21.0000	−	147.000i	0.0378378	−	0.264865i
$556$			12.6491i			0.0227502i
$557$	641.942	−	641.942i	1.15250	−	1.15250i	0.166450	−	0.986050i	$-0.446770\pi$
$557$	641.942	−	641.942i	1.15250	−	1.15250i	0.986050	−	0.166450i	$-0.0532304\pi$
$558$	284.605	−	284.605i	0.510045	−	0.510045i
$559$		−	140.000i		−	0.250447i
$560$	−420.583	−	60.0833i	−0.751041	−	0.107292i
$561$	1017.67	+	177.670i	1.81403	+	0.316703i
$562$	530.000	−	530.000i	0.943060	−	0.943060i
$563$	−117.004	−	117.004i	−0.207823	−	0.207823i	0.595519	−	0.803341i	$-0.296947\pi$
$563$	−117.004	−	117.004i	−0.207823	−	0.207823i	−0.803341	+	0.595519i	$0.796947\pi$
$564$	129.000	−	129.000i	0.228723	−	0.228723i
$565$	−53.0000	+	371.000i	−0.0938053	+	0.656637i
$566$			890.000i			1.57244i
$567$	256.144	+	256.144i	0.451754	+	0.451754i
$568$	569.210	−	569.210i	1.00213	−	1.00213i
$569$			607.157i			1.06706i	0.845781	+	0.533530i	$0.179135\pi$
$569$			607.157i			1.06706i	−0.845781	+	0.533530i	$0.820865\pi$
$570$	−60.0000	+	420.000i	−0.105263	+	0.736842i
$571$			512.289i			0.897179i	0.893738	+	0.448589i	$0.148073\pi$
$571$			512.289i			0.897179i	−0.893738	+	0.448589i	$0.851927\pi$
$572$	8.46050	−	48.4605i	0.0147911	−	0.0847212i
$573$			774.000i			1.35079i
$574$	695.701			1.21202
$575$	119.000	+	217.000i	0.206957	+	0.377391i
$576$			369.000i			0.640625i
$577$	43.0000	−	43.0000i	0.0745234	−	0.0745234i	−0.668863	−	0.743386i	$-0.733219\pi$
$577$	43.0000	−	43.0000i	0.0745234	−	0.0745234i	0.743386	+	0.668863i	$0.233219\pi$
$578$	−1092.57	−	1092.57i	−1.89025	−	1.89025i
$579$	−237.171	+	237.171i	−0.409621	+	0.409621i
$580$	−75.8947	+	56.9210i	−0.130853	+	0.0981397i
$581$		−	380.000i		−	0.654045i
$582$			407.934i			0.700917i
$583$	260.517	+	45.4826i	0.446857	+	0.0780147i
$584$	210.000			0.359589
$585$	−28.4605	+	199.223i	−0.0486504	+	0.340553i
$586$	−730.000			−1.24573
$587$	−553.000	−	553.000i	−0.942078	−	0.942078i	0.0563336	−	0.998412i	$-0.482059\pi$
$587$	−553.000	−	553.000i	−0.942078	−	0.942078i	−0.998412	+	0.0563336i	$0.982059\pi$
$588$	87.0000			0.147959
$589$	−252.982			−0.429511
$590$	−34.7851	+	243.495i	−0.0589577	+	0.412704i
$591$	692.539	−	692.539i	1.17181	−	1.17181i
$592$	133.000	−	133.000i	0.224662	−	0.224662i
$593$	−363.662	−	363.662i	−0.613258	−	0.613258i	0.330536	−	0.943794i	$-0.392771\pi$
$593$	−363.662	−	363.662i	−0.613258	−	0.613258i	−0.943794	+	0.330536i	$0.892771\pi$
$594$	−654.217	−	114.217i	−1.10137	−	0.192284i
$595$	560.000	−	420.000i	0.941176	−	0.705882i
$596$	94.8683			0.159175
$597$			360.000i			0.603015i
$598$	70.0000	+	70.0000i	0.117057	+	0.117057i
$599$	−860.000			−1.43573			−0.717863	−	0.696184i	$-0.754880\pi$
$599$	−860.000			−1.43573			−0.717863	+	0.696184i	$0.754880\pi$
$600$	−441.138	+	241.914i	−0.735230	+	0.403190i
$601$			75.8947i			0.126281i	0.998005	+	0.0631403i	$0.0201116\pi$
$601$			75.8947i			0.126281i	−0.998005	+	0.0631403i	$0.979888\pi$
$602$	221.359	−	221.359i	0.367707	−	0.367707i
$603$	−423.000	+	423.000i	−0.701493	+	0.701493i
$604$	113.842			0.188480
$605$	−177.526	−	578.368i	−0.293431	−	0.955980i
$606$	660.000	−	660.000i	1.08911	−	1.08911i
$607$	325.715	+	325.715i	0.536597	+	0.536597i	0.922528	−	0.385930i	$-0.126120\pi$
$607$	325.715	+	325.715i	0.536597	+	0.536597i	−0.385930	+	0.922528i	$0.626120\pi$
$608$	−140.000	+	140.000i	−0.230263	+	0.230263i
$609$	180.000	−	180.000i	0.295567	−	0.295567i
$610$	−1050.00	−	150.000i	−1.72131	−	0.245902i
$611$	−271.956			−0.445100
$612$	199.223	+	199.223i	0.325529	+	0.325529i
$613$	−110.680	+	110.680i	−0.180554	+	0.180554i	−0.791597	−	0.611043i	$-0.790750\pi$
$613$	−110.680	+	110.680i	−0.180554	+	0.180554i	0.611043	+	0.791597i	$0.290750\pi$
$614$	490.000			0.798046
$615$	834.841	−	626.131i	1.35747	−	1.01810i
$616$	−270.000	+	189.737i	−0.438312	+	0.308014i
$617$	−757.000	−	757.000i	−1.22690	−	1.22690i	−0.965129	−	0.261776i	$-0.915692\pi$
$617$	−757.000	−	757.000i	−1.22690	−	1.22690i	−0.261776	−	0.965129i	$-0.584308\pi$
$618$	−66.4078			−0.107456
$619$			162.000i			0.261712i	0.991401	+	0.130856i	$0.0417726\pi$
$619$			162.000i			0.261712i	−0.991401	+	0.130856i	$0.958227\pi$
$620$	60.0000	+	80.0000i	0.0967742	+	0.129032i
$621$	189.000	−	189.000i	0.304348	−	0.304348i
$622$	379.473	+	379.473i	0.610086	+	0.610086i
$623$	316.228	+	316.228i	0.507589	+	0.507589i
$624$	−180.250	+	180.250i	−0.288862	+	0.288862i
$625$	−527.000	−	336.000i	−0.843200	−	0.537600i
$626$	401.609			0.641548
$627$	240.000	+	341.526i	0.382775	+	0.544699i
$628$	−67.0000	−	67.0000i	−0.106688	−	0.106688i
$629$			309.903i			0.492692i
$630$	−360.000	+	270.000i	−0.571429	+	0.428571i
$631$	158.000			0.250396			0.125198	−	0.992132i	$-0.460043\pi$
$631$	158.000			0.250396			0.125198	+	0.992132i	$0.460043\pi$
$632$	30.0000	+	30.0000i	0.0474684	+	0.0474684i
$633$			739.973i			1.16899i
$634$	−401.609			−0.633453
$635$	−287.767	−	41.1096i	−0.453177	−	0.0647395i
$636$	51.0000	+	51.0000i	0.0801887	+	0.0801887i
$637$	−91.7061	−	91.7061i	−0.143966	−	0.143966i
$638$	−80.2633	+	459.737i	−0.125805	+	0.720590i
$639$		−	1080.00i		−	1.69014i
$640$	−763.690	−	109.099i	−1.19327	−	0.170467i
$641$			942.000i			1.46958i	0.678295	+	0.734789i	$0.262719\pi$
$641$			942.000i			1.46958i	−0.678295	+	0.734789i	$0.737281\pi$
$642$		−	390.000i		−	0.607477i
$643$	757.000	+	757.000i	1.17729	+	1.17729i	0.980431	+	0.196863i	$0.0630754\pi$
$643$	757.000	+	757.000i	1.17729	+	1.17729i	0.196863	+	0.980431i	$0.436925\pi$
$644$			44.2719i			0.0687452i
$645$	66.4078	−	464.855i	0.102958	−	0.720705i
$646$		−	885.438i		−	1.37065i
$647$	257.000	+	257.000i	0.397218	+	0.397218i	0.877251	−	0.480033i	$-0.159375\pi$
$647$	257.000	+	257.000i	0.397218	+	0.397218i	−0.480033	+	0.877251i	$0.659375\pi$
$648$	384.217	+	384.217i	0.592927	+	0.592927i
$649$	139.140	+	198.000i	0.214392	+	0.305085i
$650$	−240.000	−	70.0000i	−0.369231	−	0.107692i
$651$	−189.737	−	189.737i	−0.291454	−	0.291454i
$652$	−137.000	+	137.000i	−0.210123	+	0.210123i
$653$	263.000	−	263.000i	0.402757	−	0.402757i	−0.476447	−	0.879203i	$-0.658076\pi$
$653$	263.000	−	263.000i	0.402757	−	0.402757i	0.879203	+	0.476447i	$0.158076\pi$
$654$	−1020.00	+	1020.00i	−1.55963	+	1.55963i
$655$	−505.964	+	379.473i	−0.772465	+	0.579349i
$656$	1321.83			2.01499
$657$	199.223	−	199.223i	0.303232	−	0.303232i
$658$	−430.000	−	430.000i	−0.653495	−	0.653495i
$659$		−	398.447i		−	0.604624i	−0.953209	−	0.302312i	$-0.902242\pi$
$659$		−	398.447i		−	0.604624i	0.953209	−	0.302312i	$-0.0977584\pi$
$660$	51.0790	−	156.895i	0.0773924	−	0.237719i
$661$	−1078.00			−1.63086			−0.815431	−	0.578854i	$-0.803500\pi$
$661$	−1078.00			−1.63086			−0.815431	+	0.578854i	$0.803500\pi$
$662$	316.228	−	316.228i	0.477685	−	0.477685i
$663$		−	420.000i		−	0.633484i
$664$		−	570.000i		−	0.858434i
$665$	280.000	+	40.0000i	0.421053	+	0.0601504i
$666$		−	199.223i		−	0.299134i
$667$	−132.816	−	132.816i	−0.199124	−	0.199124i
$668$	−205.548	−	205.548i	−0.307707	−	0.307707i
$669$	−219.000	−	219.000i	−0.327354	−	0.327354i
$670$	−445.881	−	594.508i	−0.665494	−	0.887326i
$671$	−853.815	+	600.000i	−1.27245	+	0.894188i
$672$	−210.000			−0.312500
$673$	−357.337	+	357.337i	−0.530962	+	0.530962i	−0.920859	−	0.389897i	$-0.872511\pi$
$673$	−357.337	+	357.337i	−0.530962	+	0.530962i	0.389897	+	0.920859i	$0.372511\pi$
$674$	1150.00			1.70623
$675$	−189.000	+	648.000i	−0.280000	+	0.960000i
$676$	149.000			0.220414
$677$	110.680	−	110.680i	0.163486	−	0.163486i	−0.620623	−	0.784109i	$-0.713120\pi$
$677$	110.680	−	110.680i	0.163486	−	0.163486i	0.784109	+	0.620623i	$0.213120\pi$
$678$			502.802i			0.741596i
$679$	271.956			0.400524
$680$	840.000	−	630.000i	1.23529	−	0.926471i
$681$	464.855	−	464.855i	0.682606	−	0.682606i
$682$	484.605	+	84.6050i	0.710565	+	0.124054i
$683$	−397.000	+	397.000i	−0.581259	+	0.581259i	−0.935249	−	0.353990i	$-0.884825\pi$
$683$	−397.000	+	397.000i	−0.581259	+	0.581259i	0.353990	+	0.935249i	$0.384825\pi$
$684$			113.842i			0.166436i
$685$	−581.000	−	83.0000i	−0.848175	−	0.121168i
$686$		−	780.000i		−	1.13703i
$687$			540.000i			0.786026i
$688$	420.583	−	420.583i	0.611312	−	0.611312i
$689$		−	107.517i		−	0.156049i
$690$	199.223	+	265.631i	0.288730	+	0.384973i
$691$	362.000			0.523878			0.261939	−	0.965084i	$-0.415638\pi$
$691$	362.000			0.523878			0.261939	+	0.965084i	$0.415638\pi$
$692$	34.7851	−	34.7851i	0.0502674	−	0.0502674i
$693$	−76.1445	+	436.144i	−0.109877	+	0.629357i
$694$		−	290.000i		−	0.417867i
$695$	50.5964	−	37.9473i	0.0728006	−	0.0546005i
$696$	270.000	−	270.000i	0.387931	−	0.387931i
$697$	−1540.00	+	1540.00i	−2.20947	+	2.20947i
$698$	400.000	−	400.000i	0.573066	−	0.573066i
$699$	9.48683	+	9.48683i	0.0135720	+	0.0135720i
$700$	−53.7587	−	98.0306i	−0.0767982	−	0.140044i
$701$	−25.2982			−0.0360888			−0.0180444	−	0.999837i	$-0.505744\pi$
$701$	−25.2982			−0.0360888			−0.0180444	+	0.999837i	$0.505744\pi$
$702$			270.000i			0.384615i
$703$	−88.5438	+	88.5438i	−0.125951	+	0.125951i
$704$	−369.000	+	259.307i	−0.524148	+	0.368333i
$705$	−903.000	−	129.000i	−1.28085	−	0.182979i
$706$			989.793i			1.40197i
$707$	−440.000	−	440.000i	−0.622348	−	0.622348i
$708$			66.0000i			0.0932203i
$709$			1038.00i			1.46403i	0.681286	+	0.732017i	$0.261421\pi$
$709$			1038.00i			1.46403i	−0.681286	+	0.732017i	$0.738579\pi$
$710$	1328.16	+	189.737i	1.87064	+	0.267235i
$711$	56.9210			0.0800577
$712$	474.342	+	474.342i	0.666210	+	0.666210i
$713$	−140.000	+	140.000i	−0.196353	+	0.196353i
$714$	664.078	−	664.078i	0.930082	−	0.930082i
$715$	−219.223	+	111.540i	−0.306606	+	0.155999i
$716$			320.000i			0.446927i
$717$			1138.42i			1.58775i
$718$	120.000	+	120.000i	0.167131	+	0.167131i
$719$	940.000			1.30737			0.653686	−	0.756766i	$-0.273222\pi$
$719$	940.000			1.30737			0.653686	+	0.756766i	$0.273222\pi$
$720$	−684.000	+	513.000i	−0.950000	+	0.712500i
$721$			44.2719i			0.0614034i
$722$	−317.809	+	317.809i	−0.440179	+	0.440179i
$723$			455.368i			0.629831i
$724$		−	80.0000i		−	0.110497i
$725$	455.368	+	132.816i	0.628094	+	0.183194i
$726$	−345.520	−	734.480i	−0.475923	−	1.01168i
$727$	517.000	−	517.000i	0.711142	−	0.711142i	−0.255632	−	0.966774i	$-0.582284\pi$
$727$	517.000	−	517.000i	0.711142	−	0.711142i	0.966774	+	0.255632i	$0.0822837\pi$
$728$	94.8683	+	94.8683i	0.130314	+	0.130314i
$729$	729.000			1.00000
$730$	210.000	+	280.000i	0.287671	+	0.383562i
$731$			980.000i			1.34063i
$732$	−284.605			−0.388805
$733$	629.293	−	629.293i	0.858517	−	0.858517i	−0.132646	−	0.991163i	$-0.542347\pi$
$733$	629.293	−	629.293i	0.858517	−	0.858517i	0.991163	+	0.132646i	$0.0423474\pi$
$734$		−	306.741i		−	0.417903i
$735$	−261.000	−	348.000i	−0.355102	−	0.473469i
$736$			154.952i			0.210532i
$737$	−720.254	−	125.746i	−0.977278	−	0.170619i
$738$	990.000	−	990.000i	1.34146	−	1.34146i
$739$	−885.438			−1.19816			−0.599078	−	0.800690i	$-0.704466\pi$
$739$	−885.438			−1.19816			−0.599078	+	0.800690i	$0.704466\pi$
$740$	49.0000	+	7.00000i	0.0662162	+	0.00945946i
$741$	120.000	−	120.000i	0.161943	−	0.161943i
$742$	170.000	−	170.000i	0.229111	−	0.229111i
$743$	−41.1096	−	41.1096i	−0.0553292	−	0.0553292i	0.678901	−	0.734230i	$-0.262457\pi$
$743$	−41.1096	−	41.1096i	−0.0553292	−	0.0553292i	−0.734230	+	0.678901i	$0.762457\pi$
$744$	−284.605	−	284.605i	−0.382534	−	0.382534i
$745$	−284.605	−	379.473i	−0.382020	−	0.509360i
$746$		−	730.000i		−	0.978552i
$747$	−540.749	−	540.749i	−0.723895	−	0.723895i
$748$	−59.2235	+	339.223i	−0.0791758	+	0.453507i
$749$	−260.000			−0.347130
$750$	−763.690	−	346.269i	−1.01825	−	0.461693i
$751$	−922.000			−1.22770			−0.613848	−	0.789424i	$-0.710379\pi$
$751$	−922.000			−1.22770			−0.613848	+	0.789424i	$0.710379\pi$
$752$	−817.000	−	817.000i	−1.08644	−	1.08644i
$753$			180.000i			0.239044i
$754$	189.737			0.251640
$755$	−341.526	−	455.368i	−0.452352	−	0.603136i
$756$	−85.3815	+	85.3815i	−0.112938	+	0.112938i
$757$	607.000	−	607.000i	0.801849	−	0.801849i	−0.181535	−	0.983384i	$-0.558107\pi$
$757$	607.000	−	607.000i	0.801849	−	0.801849i	0.983384	+	0.181535i	$0.0581066\pi$
$758$	94.8683	+	94.8683i	0.125156	+	0.125156i
$759$	321.816	+	56.1843i	0.424000	+	0.0740242i
$760$	420.000	+	60.0000i	0.552632	+	0.0789474i
$761$	−1144.74			−1.50426			−0.752132	−	0.659013i	$-0.770974\pi$
$761$	−1144.74			−1.50426			−0.752132	+	0.659013i	$0.770974\pi$
$762$	−390.000			−0.511811
$763$	680.000	+	680.000i	0.891219	+	0.891219i
$764$	−258.000			−0.337696
$765$	199.223	−	1394.56i	0.260423	−	1.82296i
$766$		−	1306.02i		−	1.70499i
$767$	69.5701	−	69.5701i	0.0907042	−	0.0907042i
$768$	−543.000			−0.707031

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	165.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58114 - 1.58114i) q^{2} -3.00000 q^{3} -1.00000i q^{4} +(-4.00000 + 3.00000i) q^{5} +(-4.74342 + 4.74342i) q^{6} +(3.16228 + 3.16228i) q^{7} +(4.74342 + 4.74342i) q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(1.58114 - 1.58114i) q^{2} -3.00000 q^{3} -1.00000i q^{4} +(-4.00000 + 3.00000i) q^{5} +(-4.74342 + 4.74342i) q^{6} +(3.16228 + 3.16228i) q^{7} +(4.74342 + 4.74342i) q^{8} +9.00000 q^{9} +(-1.58114 + 11.0680i) q^{10} +(6.32456 + 9.00000i) q^{11} +3.00000i q^{12} +(3.16228 - 3.16228i) q^{13} +10.0000 q^{14} +(12.0000 - 9.00000i) q^{15} +19.0000 q^{16} +(-22.1359 + 22.1359i) q^{17} +(14.2302 - 14.2302i) q^{18} -12.6491 q^{19} +(3.00000 + 4.00000i) q^{20} +(-9.48683 - 9.48683i) q^{21} +(24.2302 + 4.23025i) q^{22} +(-7.00000 + 7.00000i) q^{23} +(-14.2302 - 14.2302i) q^{24} +(7.00000 - 24.0000i) q^{25} -10.0000i q^{26} -27.0000 q^{27} +(3.16228 - 3.16228i) q^{28} +18.9737i q^{29} +(4.74342 - 33.2039i) q^{30} +20.0000 q^{31} +(11.0680 - 11.0680i) q^{32} +(-18.9737 - 27.0000i) q^{33} +70.0000i q^{34} +(-22.1359 - 3.16228i) q^{35} -9.00000i q^{36} +(7.00000 - 7.00000i) q^{37} +(-20.0000 + 20.0000i) q^{38} +(-9.48683 + 9.48683i) q^{39} +(-33.2039 - 4.74342i) q^{40} +69.5701 q^{41} -30.0000 q^{42} +(22.1359 - 22.1359i) q^{43} +(9.00000 - 6.32456i) q^{44} +(-36.0000 + 27.0000i) q^{45} +22.1359i q^{46} +(-43.0000 - 43.0000i) q^{47} -57.0000 q^{48} -29.0000i q^{49} +(-26.8794 - 49.0153i) q^{50} +(66.4078 - 66.4078i) q^{51} +(-3.16228 - 3.16228i) q^{52} +(17.0000 - 17.0000i) q^{53} +(-42.6907 + 42.6907i) q^{54} +(-52.2982 - 17.0263i) q^{55} +30.0000i q^{56} +37.9473 q^{57} +(30.0000 + 30.0000i) q^{58} +22.0000 q^{59} +(-9.00000 - 12.0000i) q^{60} +94.8683i q^{61} +(31.6228 - 31.6228i) q^{62} +(28.4605 + 28.4605i) q^{63} +41.0000i q^{64} +(-3.16228 + 22.1359i) q^{65} +(-72.6907 - 12.6907i) q^{66} +(-47.0000 + 47.0000i) q^{67} +(22.1359 + 22.1359i) q^{68} +(21.0000 - 21.0000i) q^{69} +(-40.0000 + 30.0000i) q^{70} -120.000i q^{71} +(42.6907 + 42.6907i) q^{72} +(22.1359 - 22.1359i) q^{73} -22.1359i q^{74} +(-21.0000 + 72.0000i) q^{75} +12.6491i q^{76} +(-8.46050 + 48.4605i) q^{77} +30.0000i q^{78} +6.32456 q^{79} +(-76.0000 + 57.0000i) q^{80} +81.0000 q^{81} +(110.000 - 110.000i) q^{82} +(-60.0833 - 60.0833i) q^{83} +(-9.48683 + 9.48683i) q^{84} +(22.1359 - 154.952i) q^{85} -70.0000i q^{86} -56.9210i q^{87} +(-12.6907 + 72.6907i) q^{88} +100.000 q^{89} +(-14.2302 + 99.6117i) q^{90} +20.0000 q^{91} +(7.00000 + 7.00000i) q^{92} -60.0000 q^{93} -135.978 q^{94} +(50.5964 - 37.9473i) q^{95} +(-33.2039 + 33.2039i) q^{96} +(43.0000 - 43.0000i) q^{97} +(-45.8530 - 45.8530i) q^{98} +(56.9210 + 81.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{3} - 16 q^{5} + 36 q^{9}+O(q^{10}) \) 4 * q - 12 * q^3 - 16 * q^5 + 36 * q^9	\( 4 q - 12 q^{3} - 16 q^{5} + 36 q^{9} + 40 q^{14} + 48 q^{15} + 76 q^{16} + 12 q^{20} + 40 q^{22} - 28 q^{23} + 28 q^{25} - 108 q^{27} + 80 q^{31} + 28 q^{37} - 80 q^{38} - 120 q^{42} + 36 q^{44} - 144 q^{45} - 172 q^{47} - 228 q^{48} + 68 q^{53} - 108 q^{55} + 120 q^{58} + 88 q^{59} - 36 q^{60} - 120 q^{66} - 188 q^{67} + 84 q^{69} - 160 q^{70} - 84 q^{75} + 80 q^{77} - 304 q^{80} + 324 q^{81} + 440 q^{82} + 120 q^{88} + 400 q^{89} + 80 q^{91} + 28 q^{92} - 240 q^{93} + 172 q^{97}+O(q^{100}) \) 4 * q - 12 * q^3 - 16 * q^5 + 36 * q^9 + 40 * q^14 + 48 * q^15 + 76 * q^16 + 12 * q^20 + 40 * q^22 - 28 * q^23 + 28 * q^25 - 108 * q^27 + 80 * q^31 + 28 * q^37 - 80 * q^38 - 120 * q^42 + 36 * q^44 - 144 * q^45 - 172 * q^47 - 228 * q^48 + 68 * q^53 - 108 * q^55 + 120 * q^58 + 88 * q^59 - 36 * q^60 - 120 * q^66 - 188 * q^67 + 84 * q^69 - 160 * q^70 - 84 * q^75 + 80 * q^77 - 304 * q^80 + 324 * q^81 + 440 * q^82 + 120 * q^88 + 400 * q^89 + 80 * q^91 + 28 * q^92 - 240 * q^93 + 172 * q^97

Introduction

L-functions

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