LMFDB - Embedded newform 1050.3.l.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(43,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1050.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$0.323042 - 0.323042i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.b.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +19.5717 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-8.03207 - 8.03207i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(2.19659 - 2.19659i) q^{17} +(-3.00000 - 3.00000i) q^{18} +8.25097i q^{19} -4.58258 q^{21} +(-19.5717 + 19.5717i) q^{22} +(17.9068 + 17.9068i) q^{23} -4.89898i q^{24} +16.0641 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -19.7495i q^{29} +30.0043 q^{31} +(4.00000 - 4.00000i) q^{32} +(-23.9703 - 23.9703i) q^{33} +4.39319i q^{34} +6.00000 q^{36} +(-37.2346 + 37.2346i) q^{37} +(-8.25097 - 8.25097i) q^{38} +19.6745i q^{39} -80.8620 q^{41} +(4.58258 - 4.58258i) q^{42} +(13.6780 + 13.6780i) q^{43} -39.1434i q^{44} -35.8136 q^{46} +(8.17549 - 8.17549i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} -5.38053 q^{51} +(-16.0641 + 16.0641i) q^{52} +(38.8560 + 38.8560i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(10.1053 - 10.1053i) q^{57} +(19.7495 + 19.7495i) q^{58} -74.3773i q^{59} +97.8414 q^{61} +(-30.0043 + 30.0043i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +47.9406 q^{66} +(67.1712 - 67.1712i) q^{67} +(-4.39319 - 4.39319i) q^{68} -43.8625i q^{69} -13.3793 q^{71} +(-6.00000 + 6.00000i) q^{72} +(48.2738 + 48.2738i) q^{73} -74.4691i q^{74} +16.5019 q^{76} +(36.6153 - 36.6153i) q^{77} +(-19.6745 - 19.6745i) q^{78} +40.2089i q^{79} -9.00000 q^{81} +(80.8620 - 80.8620i) q^{82} +(-34.4137 - 34.4137i) q^{83} +9.16515i q^{84} -27.3560 q^{86} +(-24.1881 + 24.1881i) q^{87} +(39.1434 + 39.1434i) q^{88} -157.941i q^{89} -30.0532 q^{91} +(35.8136 - 35.8136i) q^{92} +(-36.7476 - 36.7476i) q^{93} +16.3510i q^{94} -9.79796 q^{96} +(73.2856 - 73.2856i) q^{97} +(7.00000 + 7.00000i) q^{98} +58.7150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	2.44949			0.408248
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	19.5717			1.77924			0.889622	−	0.456698i	$-0.150968\pi$
$11$	19.5717			1.77924			0.889622	+	0.456698i	$0.150968\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−8.03207	−	8.03207i	−0.617851	−	0.617851i	0.327129	−	0.944980i	$-0.393919\pi$
$13$	−8.03207	−	8.03207i	−0.617851	−	0.617851i	−0.944980	+	0.327129i	$0.893919\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	2.19659	−	2.19659i	0.129211	−	0.129211i	−0.639543	−	0.768755i	$-0.720877\pi$
$17$	2.19659	−	2.19659i	0.129211	−	0.129211i	0.768755	+	0.639543i	$0.220877\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			8.25097i			0.434261i	0.976143	+	0.217131i	$0.0696698\pi$
$19$			8.25097i			0.434261i	−0.976143	+	0.217131i	$0.930330\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	−19.5717	+	19.5717i	−0.889622	+	0.889622i
$23$	17.9068	+	17.9068i	0.778557	+	0.778557i	0.979585	−	0.201028i	$-0.0644284\pi$
$23$	17.9068	+	17.9068i	0.778557	+	0.778557i	−0.201028	+	0.979585i	$0.564428\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$	16.0641			0.617851
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	19.7495i		−	0.681017i	−0.940241	−	0.340508i	$-0.889401\pi$
$29$		−	19.7495i		−	0.681017i	0.940241	−	0.340508i	$-0.110599\pi$
$30$		0			0
$31$	30.0043			0.967881			0.483940	−	0.875101i	$-0.339205\pi$
$31$	30.0043			0.967881			0.483940	+	0.875101i	$0.339205\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−23.9703	−	23.9703i	−0.726373	−	0.726373i
$34$			4.39319i			0.129211i
$35$		0			0
$36$	6.00000			0.166667
$37$	−37.2346	+	37.2346i	−1.00634	+	1.00634i	−0.00635971	+	0.999980i	$0.502024\pi$
$37$	−37.2346	+	37.2346i	−1.00634	+	1.00634i	−0.999980	+	0.00635971i	$0.997976\pi$
$38$	−8.25097	−	8.25097i	−0.217131	−	0.217131i
$39$			19.6745i			0.504473i
$40$		0			0
$41$	−80.8620			−1.97224			−0.986122	−	0.166023i	$-0.946907\pi$
$41$	−80.8620			−1.97224			−0.986122	+	0.166023i	$0.946907\pi$
$42$	4.58258	−	4.58258i	0.109109	−	0.109109i
$43$	13.6780	+	13.6780i	0.318093	+	0.318093i	0.848034	−	0.529942i	$-0.177786\pi$
$43$	13.6780	+	13.6780i	0.318093	+	0.318093i	−0.529942	+	0.848034i	$0.677786\pi$
$44$		−	39.1434i		−	0.889622i
$45$		0			0
$46$	−35.8136			−0.778557
$47$	8.17549	−	8.17549i	0.173947	−	0.173947i	−0.614764	−	0.788711i	$-0.710749\pi$
$47$	8.17549	−	8.17549i	0.173947	−	0.173947i	0.788711	+	0.614764i	$0.210749\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	−5.38053			−0.105501
$52$	−16.0641	+	16.0641i	−0.308926	+	0.308926i
$53$	38.8560	+	38.8560i	0.733132	+	0.733132i	0.971239	−	0.238107i	$-0.0765268\pi$
$53$	38.8560	+	38.8560i	0.733132	+	0.733132i	−0.238107	+	0.971239i	$0.576527\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	10.1053	−	10.1053i	0.177287	−	0.177287i
$58$	19.7495	+	19.7495i	0.340508	+	0.340508i
$59$		−	74.3773i		−	1.26063i	−0.776339	−	0.630316i	$-0.782925\pi$
$59$		−	74.3773i		−	1.26063i	0.776339	−	0.630316i	$-0.217075\pi$
$60$		0			0
$61$	97.8414			1.60396			0.801979	−	0.597352i	$-0.203781\pi$
$61$	97.8414			1.60396			0.801979	+	0.597352i	$0.203781\pi$
$62$	−30.0043	+	30.0043i	−0.483940	+	0.483940i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	47.9406			0.726373
$67$	67.1712	−	67.1712i	1.00255	−	1.00255i	0.00255792	−	0.999997i	$-0.499186\pi$
$67$	67.1712	−	67.1712i	1.00255	−	1.00255i	0.999997	−	0.00255792i	$-0.000814213\pi$
$68$	−4.39319	−	4.39319i	−0.0646057	−	0.0646057i
$69$		−	43.8625i		−	0.635689i
$70$		0			0
$71$	−13.3793			−0.188441			−0.0942203	−	0.995551i	$-0.530036\pi$
$71$	−13.3793			−0.188441			−0.0942203	+	0.995551i	$0.530036\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	48.2738	+	48.2738i	0.661285	+	0.661285i	0.955683	−	0.294398i	$-0.0951190\pi$
$73$	48.2738	+	48.2738i	0.661285	+	0.661285i	−0.294398	+	0.955683i	$0.595119\pi$
$74$		−	74.4691i		−	1.00634i
$75$		0			0
$76$	16.5019			0.217131
$77$	36.6153	−	36.6153i	0.475523	−	0.475523i
$78$	−19.6745	−	19.6745i	−0.252237	−	0.252237i
$79$			40.2089i			0.508973i	0.967076	+	0.254487i	$0.0819065\pi$
$79$			40.2089i			0.508973i	−0.967076	+	0.254487i	$0.918094\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	80.8620	−	80.8620i	0.986122	−	0.986122i
$83$	−34.4137	−	34.4137i	−0.414623	−	0.414623i	0.468722	−	0.883346i	$-0.344715\pi$
$83$	−34.4137	−	34.4137i	−0.414623	−	0.414623i	−0.883346	+	0.468722i	$0.844715\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	−27.3560			−0.318093
$87$	−24.1881	+	24.1881i	−0.278024	+	0.278024i
$88$	39.1434	+	39.1434i	0.444811	+	0.444811i
$89$		−	157.941i		−	1.77462i	−0.461176	−	0.887309i	$-0.652572\pi$
$89$		−	157.941i		−	1.77462i	0.461176	−	0.887309i	$-0.347428\pi$
$90$		0			0
$91$	−30.0532			−0.330255
$92$	35.8136	−	35.8136i	0.389278	−	0.389278i
$93$	−36.7476	−	36.7476i	−0.395136	−	0.395136i
$94$			16.3510i			0.173947i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	73.2856	−	73.2856i	0.755522	−	0.755522i	−0.219982	−	0.975504i	$-0.570600\pi$
$97$	73.2856	−	73.2856i	0.755522	−	0.755522i	0.975504	+	0.219982i	$0.0705999\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$			58.7150i			0.593081i
$100$		0			0
$101$	121.236			1.20035			0.600176	−	0.799868i	$-0.295097\pi$
$101$	121.236			1.20035			0.600176	+	0.799868i	$0.295097\pi$
$102$	5.38053	−	5.38053i	0.0527503	−	0.0527503i
$103$	−23.5614	−	23.5614i	−0.228751	−	0.228751i	0.583419	−	0.812171i	$-0.301714\pi$
$103$	−23.5614	−	23.5614i	−0.228751	−	0.228751i	−0.812171	+	0.583419i	$0.801714\pi$
$104$		−	32.1283i		−	0.308926i
$105$		0			0
$106$	−77.7120			−0.733132
$107$	14.4314	−	14.4314i	0.134873	−	0.134873i	−0.636447	−	0.771320i	$-0.719597\pi$
$107$	14.4314	−	14.4314i	0.134873	−	0.134873i	0.771320	+	0.636447i	$0.219597\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			34.6374i			0.317775i	0.987297	+	0.158887i	$0.0507907\pi$
$109$			34.6374i			0.317775i	−0.987297	+	0.158887i	$0.949209\pi$
$110$		0			0
$111$	91.2057			0.821673
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	19.9430	+	19.9430i	0.176486	+	0.176486i	0.789822	−	0.613336i	$-0.210173\pi$
$113$	19.9430	+	19.9430i	0.176486	+	0.176486i	−0.613336	+	0.789822i	$0.710173\pi$
$114$			20.2107i			0.177287i
$115$		0			0
$116$	−39.4990			−0.340508
$117$	24.0962	−	24.0962i	0.205950	−	0.205950i
$118$	74.3773	+	74.3773i	0.630316	+	0.630316i
$119$		−	8.21890i		−	0.0690664i
$120$		0			0
$121$	262.051			2.16571
$122$	−97.8414	+	97.8414i	−0.801979	+	0.801979i
$123$	99.0353	+	99.0353i	0.805165	+	0.805165i
$124$		−	60.0086i		−	0.483940i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	−13.8950	+	13.8950i	−0.109410	+	0.109410i	−0.759692	−	0.650283i	$-0.774650\pi$
$127$	−13.8950	+	13.8950i	−0.109410	+	0.109410i	0.650283	+	0.759692i	$0.274650\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	33.5041i		−	0.259722i
$130$		0			0
$131$	161.799			1.23511			0.617554	−	0.786528i	$-0.288124\pi$
$131$	161.799			1.23511			0.617554	+	0.786528i	$0.288124\pi$
$132$	−47.9406	+	47.9406i	−0.363187	+	0.363187i
$133$	15.4361	+	15.4361i	0.116061	+	0.116061i
$134$			134.342i			1.00255i
$135$		0			0
$136$	8.78638			0.0646057
$137$	35.8023	−	35.8023i	0.261331	−	0.261331i	−0.564264	−	0.825595i	$-0.690840\pi$
$137$	35.8023	−	35.8023i	0.261331	−	0.261331i	0.825595	+	0.564264i	$0.190840\pi$
$138$	43.8625	+	43.8625i	0.317845	+	0.317845i
$139$			89.7460i			0.645654i	0.946458	+	0.322827i	$0.104633\pi$
$139$			89.7460i			0.645654i	−0.946458	+	0.322827i	$0.895367\pi$
$140$		0			0
$141$	−20.0258			−0.142027
$142$	13.3793	−	13.3793i	0.0942203	−	0.0942203i
$143$	−157.201	−	157.201i	−1.09931	−	1.09931i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	−96.5477			−0.661285
$147$	−8.57321	+	8.57321i	−0.0583212	+	0.0583212i
$148$	74.4691	+	74.4691i	0.503170	+	0.503170i
$149$		−	293.641i		−	1.97075i	−0.170408	−	0.985374i	$-0.554509\pi$
$149$		−	293.641i		−	1.97075i	0.170408	−	0.985374i	$-0.445491\pi$
$150$		0			0
$151$	231.725			1.53461			0.767303	−	0.641285i	$-0.221598\pi$
$151$	231.725			1.53461			0.767303	+	0.641285i	$0.221598\pi$
$152$	−16.5019	+	16.5019i	−0.108565	+	0.108565i
$153$	6.58978	+	6.58978i	0.0430705	+	0.0430705i
$154$			73.2305i			0.475523i
$155$		0			0
$156$	39.3489			0.252237
$157$	−62.8204	+	62.8204i	−0.400130	+	0.400130i	−0.878279	−	0.478149i	$-0.841308\pi$
$157$	−62.8204	+	62.8204i	−0.400130	+	0.400130i	0.478149	+	0.878279i	$0.341308\pi$
$158$	−40.2089	−	40.2089i	−0.254487	−	0.254487i
$159$		−	95.1774i		−	0.598600i
$160$		0			0
$161$	67.0011			0.416156
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−97.0117	−	97.0117i	−0.595164	−	0.595164i	0.343858	−	0.939022i	$-0.388266\pi$
$163$	−97.0117	−	97.0117i	−0.595164	−	0.595164i	−0.939022	+	0.343858i	$0.888266\pi$
$164$			161.724i			0.986122i
$165$		0			0
$166$	68.8275			0.414623
$167$	135.497	−	135.497i	0.811362	−	0.811362i	−0.173476	−	0.984838i	$-0.555500\pi$
$167$	135.497	−	135.497i	0.811362	−	0.811362i	0.984838	+	0.173476i	$0.0554999\pi$
$168$	−9.16515	−	9.16515i	−0.0545545	−	0.0545545i
$169$		−	39.9718i		−	0.236520i
$170$		0			0
$171$	−24.7529			−0.144754
$172$	27.3560	−	27.3560i	0.159046	−	0.159046i
$173$	66.1772	+	66.1772i	0.382527	+	0.382527i	0.872012	−	0.489485i	$-0.162815\pi$
$173$	66.1772	+	66.1772i	0.382527	+	0.382527i	−0.489485	+	0.872012i	$0.662815\pi$
$174$		−	48.3762i		−	0.278024i
$175$		0			0
$176$	−78.2867			−0.444811
$177$	−91.0932	+	91.0932i	−0.514651	+	0.514651i
$178$	157.941	+	157.941i	0.887309	+	0.887309i
$179$			274.045i			1.53098i	0.643450	+	0.765488i	$0.277503\pi$
$179$			274.045i			1.53098i	−0.643450	+	0.765488i	$0.722497\pi$
$180$		0			0
$181$	−36.0493			−0.199167			−0.0995836	−	0.995029i	$-0.531751\pi$
$181$	−36.0493			−0.199167			−0.0995836	+	0.995029i	$0.531751\pi$
$182$	30.0532	−	30.0532i	0.165128	−	0.165128i
$183$	−119.831	−	119.831i	−0.654813	−	0.654813i
$184$			71.6272i			0.389278i
$185$		0			0
$186$	73.4952			0.395136
$187$	42.9910	−	42.9910i	0.229899	−	0.229899i
$188$	−16.3510	−	16.3510i	−0.0869733	−	0.0869733i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	133.194			0.697352			0.348676	−	0.937243i	$-0.386631\pi$
$191$	133.194			0.697352			0.348676	+	0.937243i	$0.386631\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	236.565	+	236.565i	1.22573	+	1.22573i	0.965566	+	0.260160i	$0.0837753\pi$
$193$	236.565	+	236.565i	1.22573	+	1.22573i	0.260160	+	0.965566i	$0.416225\pi$
$194$			146.571i			0.755522i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	203.011	−	203.011i	1.03051	−	1.03051i	0.0309909	−	0.999520i	$-0.490134\pi$
$197$	203.011	−	203.011i	1.03051	−	1.03051i	0.999520	−	0.0309909i	$-0.00986629\pi$
$198$	−58.7150	−	58.7150i	−0.296541	−	0.296541i
$199$			102.932i			0.517244i	0.965979	+	0.258622i	$0.0832684\pi$
$199$			102.932i			0.517244i	−0.965979	+	0.258622i	$0.916732\pi$
$200$		0			0
$201$	−164.535			−0.818582
$202$	−121.236	+	121.236i	−0.600176	+	0.600176i
$203$	−36.9479	−	36.9479i	−0.182009	−	0.182009i
$204$			10.7611i			0.0527503i
$205$		0			0
$206$	47.1228			0.228751
$207$	−53.7204	+	53.7204i	−0.259519	+	0.259519i
$208$	32.1283	+	32.1283i	0.154463	+	0.154463i
$209$			161.485i			0.772657i
$210$		0			0
$211$	−216.191			−1.02460			−0.512301	−	0.858806i	$-0.671207\pi$
$211$	−216.191			−1.02460			−0.512301	+	0.858806i	$0.671207\pi$
$212$	77.7120	−	77.7120i	0.366566	−	0.366566i
$213$	16.3862	+	16.3862i	0.0769306	+	0.0769306i
$214$			28.8629i			0.134873i
$215$		0			0
$216$	14.6969			0.0680414
$217$	56.1329	−	56.1329i	0.258677	−	0.258677i
$218$	−34.6374	−	34.6374i	−0.158887	−	0.158887i
$219$		−	118.246i		−	0.539937i
$220$		0			0
$221$	−35.2864			−0.159667
$222$	−91.2057	+	91.2057i	−0.410836	+	0.410836i
$223$	−143.253	−	143.253i	−0.642390	−	0.642390i	0.308752	−	0.951142i	$-0.400089\pi$
$223$	−143.253	−	143.253i	−0.642390	−	0.642390i	−0.951142	+	0.308752i	$0.900089\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−39.8859			−0.176486
$227$	−226.766	+	226.766i	−0.998969	+	0.998969i	−0.999999	−	0.00103000i	$-0.999672\pi$
$227$	−226.766	+	226.766i	−0.998969	+	0.998969i	0.00103000	+	0.999999i	$0.499672\pi$
$228$	−20.2107	−	20.2107i	−0.0886433	−	0.0886433i
$229$		−	48.9068i		−	0.213567i	−0.994282	−	0.106783i	$-0.965945\pi$
$229$		−	48.9068i		−	0.213567i	0.994282	−	0.106783i	$-0.0340552\pi$
$230$		0			0
$231$	−89.6887			−0.388263
$232$	39.4990	−	39.4990i	0.170254	−	0.170254i
$233$	122.967	+	122.967i	0.527755	+	0.527755i	0.919902	−	0.392147i	$-0.128268\pi$
$233$	122.967	+	122.967i	0.527755	+	0.527755i	−0.392147	+	0.919902i	$0.628268\pi$
$234$			48.1924i			0.205950i
$235$		0			0
$236$	−148.755			−0.630316
$237$	49.2456	−	49.2456i	0.207787	−	0.207787i
$238$	8.21890	+	8.21890i	0.0345332	+	0.0345332i
$239$		−	359.392i		−	1.50373i	−0.659317	−	0.751865i	$-0.729154\pi$
$239$		−	359.392i		−	1.50373i	0.659317	−	0.751865i	$-0.270846\pi$
$240$		0			0
$241$	−96.4510			−0.400212			−0.200106	−	0.979774i	$-0.564129\pi$
$241$	−96.4510			−0.400212			−0.200106	+	0.979774i	$0.564129\pi$
$242$	−262.051	+	262.051i	−1.08285	+	1.08285i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	195.683i		−	0.801979i
$245$		0			0
$246$	−198.071			−0.805165
$247$	66.2723	−	66.2723i	0.268309	−	0.268309i
$248$	60.0086	+	60.0086i	0.241970	+	0.241970i
$249$			84.2961i			0.338539i
$250$		0			0
$251$	−290.502			−1.15738			−0.578690	−	0.815548i	$-0.696436\pi$
$251$	−290.502			−1.15738			−0.578690	+	0.815548i	$0.696436\pi$
$252$	11.2250	−	11.2250i	0.0445435	−	0.0445435i
$253$	350.466	+	350.466i	1.38524	+	1.38524i
$254$		−	27.7901i		−	0.109410i
$255$		0			0
$256$	16.0000			0.0625000
$257$	225.583	−	225.583i	0.877755	−	0.877755i	−0.115547	−	0.993302i	$-0.536862\pi$
$257$	225.583	−	225.583i	0.877755	−	0.877755i	0.993302	+	0.115547i	$0.0368620\pi$
$258$	33.5041	+	33.5041i	0.129861	+	0.129861i
$259$			139.319i			0.537911i
$260$		0			0
$261$	59.2485			0.227006
$262$	−161.799	+	161.799i	−0.617554	+	0.617554i
$263$	−245.931	−	245.931i	−0.935097	−	0.935097i	0.0629214	−	0.998018i	$-0.479958\pi$
$263$	−245.931	−	245.931i	−0.935097	−	0.935097i	−0.998018	+	0.0629214i	$0.979958\pi$
$264$		−	95.8813i		−	0.363187i
$265$		0			0
$266$	−30.8723			−0.116061
$267$	−193.437	+	193.437i	−0.724485	+	0.724485i
$268$	−134.342	−	134.342i	−0.501277	−	0.501277i
$269$			306.198i			1.13828i	0.822240	+	0.569142i	$0.192724\pi$
$269$			306.198i			1.13828i	−0.822240	+	0.569142i	$0.807276\pi$
$270$		0			0
$271$	−370.284			−1.36636			−0.683180	−	0.730250i	$-0.739404\pi$
$271$	−370.284			−1.36636			−0.683180	+	0.730250i	$0.739404\pi$
$272$	−8.78638	+	8.78638i	−0.0323029	+	0.0323029i
$273$	36.8075	+	36.8075i	0.134826	+	0.134826i
$274$			71.6046i			0.261331i
$275$		0			0
$276$	−87.7251			−0.317845
$277$	161.817	−	161.817i	0.584176	−	0.584176i	−0.351872	−	0.936048i	$-0.614455\pi$
$277$	161.817	−	161.817i	0.584176	−	0.584176i	0.936048	+	0.351872i	$0.114455\pi$
$278$	−89.7460	−	89.7460i	−0.322827	−	0.322827i
$279$			90.0129i			0.322627i
$280$		0			0
$281$	−235.757			−0.838994			−0.419497	−	0.907757i	$-0.637793\pi$
$281$	−235.757			−0.838994			−0.419497	+	0.907757i	$0.637793\pi$
$282$	20.0258	−	20.0258i	0.0710134	−	0.0710134i
$283$	−2.26750	−	2.26750i	−0.00801238	−	0.00801238i	0.703089	−	0.711102i	$-0.251803\pi$
$283$	−2.26750	−	2.26750i	−0.00801238	−	0.00801238i	−0.711102	+	0.703089i	$0.751803\pi$
$284$			26.7586i			0.0942203i
$285$		0			0
$286$	314.402			1.09931
$287$	−151.279	+	151.279i	−0.527104	+	0.527104i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			279.350i			0.966609i
$290$		0			0
$291$	−179.512			−0.616881
$292$	96.5477	−	96.5477i	0.330643	−	0.330643i
$293$	−199.403	−	199.403i	−0.680556	−	0.680556i	0.279570	−	0.960125i	$-0.409808\pi$
$293$	−199.403	−	199.403i	−0.680556	−	0.680556i	−0.960125	+	0.279570i	$0.909808\pi$
$294$		−	17.1464i		−	0.0583212i
$295$		0			0
$296$	−148.938			−0.503170
$297$	71.9110	−	71.9110i	0.242124	−	0.242124i
$298$	293.641	+	293.641i	0.985374	+	0.985374i
$299$		−	287.657i		−	0.962065i
$300$		0			0
$301$	51.1783			0.170028
$302$	−231.725	+	231.725i	−0.767303	+	0.767303i
$303$	−148.483	−	148.483i	−0.490042	−	0.490042i
$304$		−	33.0039i		−	0.108565i
$305$		0			0
$306$	−13.1796			−0.0430705
$307$	381.514	−	381.514i	1.24272	−	1.24272i	0.283847	−	0.958870i	$-0.408389\pi$
$307$	381.514	−	381.514i	1.24272	−	1.24272i	0.958870	−	0.283847i	$-0.0916108\pi$
$308$	−73.2305	−	73.2305i	−0.237761	−	0.237761i
$309$			57.7134i			0.186775i
$310$		0			0
$311$	−388.702			−1.24985			−0.624923	−	0.780686i	$-0.714870\pi$
$311$	−388.702			−1.24985			−0.624923	+	0.780686i	$0.714870\pi$
$312$	−39.3489	+	39.3489i	−0.126118	+	0.126118i
$313$	50.5806	+	50.5806i	0.161599	+	0.161599i	0.783275	−	0.621675i	$-0.213548\pi$
$313$	50.5806	+	50.5806i	0.161599	+	0.161599i	−0.621675	+	0.783275i	$0.713548\pi$
$314$		−	125.641i		−	0.400130i
$315$		0			0
$316$	80.4178			0.254487
$317$	−54.9675	+	54.9675i	−0.173399	+	0.173399i	−0.788471	−	0.615072i	$-0.789127\pi$
$317$	−54.9675	+	54.9675i	−0.173399	+	0.173399i	0.615072	+	0.788471i	$0.289127\pi$
$318$	95.1774	+	95.1774i	0.299300	+	0.299300i
$319$		−	386.531i		−	1.21169i
$320$		0			0
$321$	−35.3497			−0.110124
$322$	−67.0011	+	67.0011i	−0.208078	+	0.208078i
$323$	18.1240	+	18.1240i	0.0561115	+	0.0561115i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	194.023			0.595164
$327$	42.4220	−	42.4220i	0.129731	−	0.129731i
$328$	−161.724	−	161.724i	−0.493061	−	0.493061i
$329$		−	30.5899i		−	0.0929783i
$330$		0			0
$331$	195.576			0.590865			0.295433	−	0.955364i	$-0.404536\pi$
$331$	195.576			0.590865			0.295433	+	0.955364i	$0.404536\pi$
$332$	−68.8275	+	68.8275i	−0.207312	+	0.207312i
$333$	−111.704	−	111.704i	−0.335446	−	0.335446i
$334$			270.995i			0.811362i
$335$		0			0
$336$	18.3303			0.0545545
$337$	−420.206	+	420.206i	−1.24690	+	1.24690i	−0.289822	+	0.957081i	$0.593596\pi$
$337$	−420.206	+	420.206i	−1.24690	+	1.24690i	−0.957081	+	0.289822i	$0.906404\pi$
$338$	39.9718	+	39.9718i	0.118260	+	0.118260i
$339$		−	48.8501i		−	0.144101i
$340$		0			0
$341$	587.235			1.72210
$342$	24.7529	−	24.7529i	0.0723769	−	0.0723769i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			54.7119i			0.159046i
$345$		0			0
$346$	−132.354			−0.382527
$347$	−21.4182	+	21.4182i	−0.0617238	+	0.0617238i	−0.737295	−	0.675571i	$-0.763897\pi$
$347$	−21.4182	+	21.4182i	−0.0617238	+	0.0617238i	0.675571	+	0.737295i	$0.263897\pi$
$348$	48.3762	+	48.3762i	0.139012	+	0.139012i
$349$			244.156i			0.699588i	0.936827	+	0.349794i	$0.113748\pi$
$349$			244.156i			0.699588i	−0.936827	+	0.349794i	$0.886252\pi$
$350$		0			0
$351$	−59.0234			−0.168158
$352$	78.2867	−	78.2867i	0.222405	−	0.222405i
$353$	−228.969	−	228.969i	−0.648637	−	0.648637i	0.304026	−	0.952664i	$-0.401669\pi$
$353$	−228.969	−	228.969i	−0.648637	−	0.648637i	−0.952664	+	0.304026i	$0.901669\pi$
$354$		−	182.186i		−	0.514651i
$355$		0			0
$356$	−315.882			−0.887309
$357$	−10.0661	+	10.0661i	−0.0281962	+	0.0281962i
$358$	−274.045	−	274.045i	−0.765488	−	0.765488i
$359$		−	165.483i		−	0.460956i	−0.973078	−	0.230478i	$-0.925971\pi$
$359$		−	165.483i		−	0.460956i	0.973078	−	0.230478i	$-0.0740290\pi$
$360$		0			0
$361$	292.922			0.811417
$362$	36.0493	−	36.0493i	0.0995836	−	0.0995836i
$363$	−320.945	−	320.945i	−0.884147	−	0.884147i
$364$			60.1065i			0.165128i
$365$		0			0
$366$	239.662			0.654813
$367$	225.601	−	225.601i	0.614715	−	0.614715i	−0.329456	−	0.944171i	$-0.606865\pi$
$367$	225.601	−	225.601i	0.614715	−	0.614715i	0.944171	+	0.329456i	$0.106865\pi$
$368$	−71.6272	−	71.6272i	−0.194639	−	0.194639i
$369$		−	242.586i		−	0.657415i
$370$		0			0
$371$	145.386			0.391876
$372$	−73.4952	+	73.4952i	−0.197568	+	0.197568i
$373$	−279.406	−	279.406i	−0.749078	−	0.749078i	0.225228	−	0.974306i	$-0.427687\pi$
$373$	−279.406	−	279.406i	−0.749078	−	0.749078i	−0.974306	+	0.225228i	$0.927687\pi$
$374$			85.9821i			0.229899i
$375$		0			0
$376$	32.7020			0.0869733
$377$	−158.629	+	158.629i	−0.420767	+	0.420767i
$378$	13.7477	+	13.7477i	0.0363696	+	0.0363696i
$379$			746.946i			1.97083i	0.170158	+	0.985417i	$0.445572\pi$
$379$			746.946i			1.97083i	−0.170158	+	0.985417i	$0.554428\pi$
$380$		0			0
$381$	34.0357			0.0893327
$382$	−133.194	+	133.194i	−0.348676	+	0.348676i
$383$	−359.176	−	359.176i	−0.937797	−	0.937797i	0.0603788	−	0.998176i	$-0.480769\pi$
$383$	−359.176	−	359.176i	−0.937797	−	0.937797i	−0.998176	+	0.0603788i	$0.980769\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−473.130			−1.22573
$387$	−41.0339	+	41.0339i	−0.106031	+	0.106031i
$388$	−146.571	−	146.571i	−0.377761	−	0.377761i
$389$		−	476.719i		−	1.22550i	−0.790278	−	0.612749i	$-0.790064\pi$
$389$		−	476.719i		−	1.22550i	0.790278	−	0.612749i	$-0.209936\pi$
$390$		0			0
$391$	78.6680			0.201197
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	−198.163	−	198.163i	−0.504231	−	0.504231i
$394$			406.021i			1.03051i
$395$		0			0
$396$	117.430			0.296541
$397$	137.315	−	137.315i	0.345883	−	0.345883i	−0.512691	−	0.858573i	$-0.671351\pi$
$397$	137.315	−	137.315i	0.345883	−	0.345883i	0.858573	+	0.512691i	$0.171351\pi$
$398$	−102.932	−	102.932i	−0.258622	−	0.258622i
$399$		−	37.8107i		−	0.0947636i
$400$		0			0
$401$	−691.294			−1.72392			−0.861962	−	0.506973i	$-0.830765\pi$
$401$	−691.294			−1.72392			−0.861962	+	0.506973i	$0.830765\pi$
$402$	164.535	−	164.535i	0.409291	−	0.409291i
$403$	−240.997	−	240.997i	−0.598006	−	0.598006i
$404$		−	242.471i		−	0.600176i
$405$		0			0
$406$	73.8958			0.182009
$407$	−728.743	+	728.743i	−1.79052	+	1.79052i
$408$	−10.7611	−	10.7611i	−0.0263752	−	0.0263752i
$409$			146.348i			0.357818i	0.983866	+	0.178909i	$0.0572568\pi$
$409$			146.348i			0.357818i	−0.983866	+	0.178909i	$0.942743\pi$
$410$		0			0
$411$	−87.6974			−0.213376
$412$	−47.1228	+	47.1228i	−0.114376	+	0.114376i
$413$	−139.147	−	139.147i	−0.336918	−	0.336918i
$414$		−	107.441i		−	0.259519i
$415$		0			0
$416$	−64.2565			−0.154463
$417$	109.916	−	109.916i	0.263587	−	0.263587i
$418$	−161.485	−	161.485i	−0.386329	−	0.386329i
$419$		−	19.1814i		−	0.0457790i	−0.999738	−	0.0228895i	$-0.992713\pi$
$419$		−	19.1814i		−	0.0457790i	0.999738	−	0.0228895i	$-0.00728659\pi$
$420$		0			0
$421$	−343.060			−0.814870			−0.407435	−	0.913234i	$-0.633577\pi$
$421$	−343.060			−0.814870			−0.407435	+	0.913234i	$0.633577\pi$
$422$	216.191	−	216.191i	0.512301	−	0.512301i
$423$	24.5265	+	24.5265i	0.0579822	+	0.0579822i
$424$			155.424i			0.366566i
$425$		0			0
$426$	−32.7724			−0.0769306
$427$	183.045	−	183.045i	0.428676	−	0.428676i
$428$	−28.8629	−	28.8629i	−0.0674366	−	0.0674366i
$429$			385.062i			0.897581i
$430$		0			0
$431$	251.794			0.584210			0.292105	−	0.956386i	$-0.405644\pi$
$431$	251.794			0.584210			0.292105	+	0.956386i	$0.405644\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	125.195	+	125.195i	0.289133	+	0.289133i	0.836737	−	0.547604i	$-0.184460\pi$
$433$	125.195	+	125.195i	0.289133	+	0.289133i	−0.547604	+	0.836737i	$0.684460\pi$
$434$			112.266i			0.258677i
$435$		0			0
$436$	69.2749			0.158887
$437$	−147.749	+	147.749i	−0.338097	+	0.338097i
$438$	118.246	+	118.246i	0.269969	+	0.269969i
$439$		−	37.5609i		−	0.0855601i	−0.999085	−	0.0427801i	$-0.986379\pi$
$439$		−	37.5609i		−	0.0855601i	0.999085	−	0.0427801i	$-0.0136215\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	35.2864	−	35.2864i	0.0798334	−	0.0798334i
$443$	583.967	+	583.967i	1.31821	+	1.31821i	0.915192	+	0.403019i	$0.132039\pi$
$443$	583.967	+	583.967i	1.31821	+	1.31821i	0.403019	+	0.915192i	$0.367961\pi$
$444$		−	182.411i		−	0.410836i
$445$		0			0
$446$	286.506			0.642390
$447$	−359.636	+	359.636i	−0.804554	+	0.804554i
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$			595.556i			1.32640i	0.748440	+	0.663202i	$0.230803\pi$
$449$			595.556i			1.32640i	−0.748440	+	0.663202i	$0.769197\pi$
$450$		0			0
$451$	−1582.61			−3.50910
$452$	39.8859	−	39.8859i	0.0882432	−	0.0882432i
$453$	−283.805	−	283.805i	−0.626500	−	0.626500i
$454$		−	453.532i		−	0.998969i
$455$		0			0
$456$	40.4213			0.0886433
$457$	−300.505	+	300.505i	−0.657560	+	0.657560i	−0.954802	−	0.297242i	$-0.903933\pi$
$457$	−300.505	+	300.505i	−0.657560	+	0.657560i	0.297242	+	0.954802i	$0.403933\pi$
$458$	48.9068	+	48.9068i	0.106783	+	0.106783i
$459$		−	16.1416i		−	0.0351669i
$460$		0			0
$461$	565.424			1.22652			0.613258	−	0.789883i	$-0.289859\pi$
$461$	565.424			1.22652			0.613258	+	0.789883i	$0.289859\pi$
$462$	89.6887	−	89.6887i	0.194131	−	0.194131i
$463$	247.619	+	247.619i	0.534815	+	0.534815i	0.922001	−	0.387186i	$-0.126553\pi$
$463$	247.619	+	247.619i	0.534815	+	0.534815i	−0.387186	+	0.922001i	$0.626553\pi$
$464$			78.9979i			0.170254i
$465$		0			0
$466$	−245.934			−0.527755
$467$	310.936	−	310.936i	0.665816	−	0.665816i	−0.290929	−	0.956745i	$-0.593964\pi$
$467$	310.936	−	310.936i	0.665816	−	0.665816i	0.956745	+	0.290929i	$0.0939643\pi$
$468$	−48.1924	−	48.1924i	−0.102975	−	0.102975i
$469$		−	251.331i		−	0.535888i
$470$		0			0
$471$	153.878			0.326705
$472$	148.755	−	148.755i	0.315158	−	0.315158i
$473$	267.701	+	267.701i	0.565964	+	0.565964i
$474$			98.4912i			0.207787i
$475$		0			0
$476$	−16.4378			−0.0345332
$477$	−116.568	+	116.568i	−0.244377	+	0.244377i
$478$	359.392	+	359.392i	0.751865	+	0.751865i
$479$		−	337.547i		−	0.704692i	−0.935870	−	0.352346i	$-0.885384\pi$
$479$		−	337.547i		−	0.704692i	0.935870	−	0.352346i	$-0.114616\pi$
$480$		0			0
$481$	598.141			1.24354
$482$	96.4510	−	96.4510i	0.200106	−	0.200106i
$483$	−82.0593	−	82.0593i	−0.169895	−	0.169895i
$484$		−	524.101i		−	1.08285i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	−153.784	+	153.784i	−0.315778	+	0.315778i	−0.847143	−	0.531365i	$-0.821679\pi$
$487$	−153.784	+	153.784i	−0.315778	+	0.315778i	0.531365	+	0.847143i	$0.321679\pi$
$488$	195.683	+	195.683i	0.400989	+	0.400989i
$489$			237.629i			0.485949i
$490$		0			0
$491$	320.910			0.653585			0.326792	−	0.945096i	$-0.394032\pi$
$491$	320.910			0.653585			0.326792	+	0.945096i	$0.394032\pi$
$492$	198.071	−	198.071i	0.402583	−	0.402583i
$493$	−43.3816	−	43.3816i	−0.0879951	−	0.0879951i
$494$			132.545i			0.268309i
$495$		0			0
$496$	−120.017			−0.241970
$497$	−25.0304	+	25.0304i	−0.0503629	+	0.0503629i
$498$	−84.2961	−	84.2961i	−0.169269	−	0.169269i
$499$		−	284.928i		−	0.570997i	−0.958379	−	0.285499i	$-0.907841\pi$
$499$		−	284.928i		−	0.570997i	0.958379	−	0.285499i	$-0.0921592\pi$
$500$		0			0
$501$	−331.900			−0.662474
$502$	290.502	−	290.502i	0.578690	−	0.578690i
$503$	548.564	+	548.564i	1.09058	+	1.09058i	0.995466	+	0.0951181i	$0.0303229\pi$
$503$	548.564	+	548.564i	1.09058	+	1.09058i	0.0951181	+	0.995466i	$0.469677\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	−700.933			−1.38524
$507$	−48.9553	+	48.9553i	−0.0965588	+	0.0965588i
$508$	27.7901	+	27.7901i	0.0547049	+	0.0547049i
$509$			558.480i			1.09721i	0.836081	+	0.548606i	$0.184841\pi$
$509$			558.480i			1.09721i	−0.836081	+	0.548606i	$0.815159\pi$
$510$		0			0
$511$	180.624			0.353472
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	30.3160	+	30.3160i	0.0590955	+	0.0590955i
$514$			451.166i			0.877755i
$515$		0			0
$516$	−67.0081			−0.129861
$517$	160.008	−	160.008i	0.309493	−	0.309493i
$518$	−139.319	−	139.319i	−0.268956	−	0.268956i
$519$		−	162.100i		−	0.312332i
$520$		0			0
$521$	455.328			0.873949			0.436975	−	0.899474i	$-0.356050\pi$
$521$	455.328			0.873949			0.436975	+	0.899474i	$0.356050\pi$
$522$	−59.2485	+	59.2485i	−0.113503	+	0.113503i
$523$	−37.6920	−	37.6920i	−0.0720687	−	0.0720687i	0.670154	−	0.742222i	$-0.266228\pi$
$523$	−37.6920	−	37.6920i	−0.0720687	−	0.0720687i	−0.742222	+	0.670154i	$0.766228\pi$
$524$		−	323.598i		−	0.617554i
$525$		0			0
$526$	491.861			0.935097
$527$	65.9073	−	65.9073i	0.125061	−	0.125061i
$528$	95.8813	+	95.8813i	0.181593	+	0.181593i
$529$			112.308i			0.212302i
$530$		0			0
$531$	223.132			0.420211
$532$	30.8723	−	30.8723i	0.0580306	−	0.0580306i
$533$	649.489	+	649.489i	1.21855	+	1.21855i
$534$		−	386.875i		−	0.724485i
$535$		0			0
$536$	268.685			0.501277
$537$	335.635	−	335.635i	0.625019	−	0.625019i
$538$	−306.198	−	306.198i	−0.569142	−	0.569142i
$539$		−	137.002i		−	0.254178i
$540$		0			0
$541$	122.456			0.226352			0.113176	−	0.993575i	$-0.463898\pi$
$541$	122.456			0.226352			0.113176	+	0.993575i	$0.463898\pi$
$542$	370.284	−	370.284i	0.683180	−	0.683180i
$543$	44.1512	+	44.1512i	0.0813097	+	0.0813097i
$544$		−	17.5728i		−	0.0323029i
$545$		0			0
$546$	−73.6151			−0.134826
$547$	−630.975	+	630.975i	−1.15352	+	1.15352i	−0.167676	+	0.985842i	$0.553626\pi$
$547$	−630.975	+	630.975i	−1.15352	+	1.15352i	−0.985842	+	0.167676i	$0.946374\pi$
$548$	−71.6046	−	71.6046i	−0.130665	−	0.130665i
$549$			293.524i			0.534653i
$550$		0			0
$551$	162.952			0.295739
$552$	87.7251	−	87.7251i	0.158922	−	0.158922i
$553$	75.2239	+	75.2239i	0.136029	+	0.136029i
$554$			323.634i			0.584176i
$555$		0			0
$556$	179.492			0.322827
$557$	−89.6207	+	89.6207i	−0.160899	+	0.160899i	−0.782965	−	0.622066i	$-0.786294\pi$
$557$	−89.6207	+	89.6207i	−0.160899	+	0.160899i	0.622066	+	0.782965i	$0.286294\pi$
$558$	−90.0129	−	90.0129i	−0.161313	−	0.161313i
$559$		−	219.725i		−	0.393068i
$560$		0			0
$561$	−105.306			−0.187711
$562$	235.757	−	235.757i	0.419497	−	0.419497i
$563$	268.774	+	268.774i	0.477396	+	0.477396i	0.904298	−	0.426902i	$-0.140395\pi$
$563$	268.774	+	268.774i	0.477396	+	0.477396i	−0.426902	+	0.904298i	$0.640395\pi$
$564$			40.0516i			0.0710134i
$565$		0			0
$566$	4.53501			0.00801238
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	−26.7586	−	26.7586i	−0.0471102	−	0.0471102i
$569$			373.315i			0.656089i	0.944662	+	0.328045i	$0.106390\pi$
$569$			373.315i			0.656089i	−0.944662	+	0.328045i	$0.893610\pi$
$570$		0			0
$571$	93.3963			0.163566			0.0817831	−	0.996650i	$-0.473939\pi$
$571$	93.3963			0.163566			0.0817831	+	0.996650i	$0.473939\pi$
$572$	−314.402	+	314.402i	−0.549654	+	0.549654i
$573$	−163.129	−	163.129i	−0.284693	−	0.284693i
$574$		−	302.558i		−	0.527104i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	356.401	−	356.401i	0.617679	−	0.617679i	−0.327257	−	0.944936i	$-0.606124\pi$
$577$	356.401	−	356.401i	0.617679	−	0.617679i	0.944936	+	0.327257i	$0.106124\pi$
$578$	−279.350	−	279.350i	−0.483304	−	0.483304i
$579$		−	579.464i		−	1.00080i
$580$		0			0
$581$	−128.764			−0.221626
$582$	179.512	−	179.512i	0.308441	−	0.308441i
$583$	760.478	+	760.478i	1.30442	+	1.30442i
$584$			193.095i			0.330643i
$585$		0			0
$586$	398.806			0.680556
$587$	213.286	−	213.286i	0.363349	−	0.363349i	−0.501695	−	0.865044i	$-0.667290\pi$
$587$	213.286	−	213.286i	0.363349	−	0.363349i	0.865044	+	0.501695i	$0.167290\pi$
$588$	17.1464	+	17.1464i	0.0291606	+	0.0291606i
$589$			247.565i			0.420313i
$590$		0			0
$591$	−497.272			−0.841408
$592$	148.938	−	148.938i	0.251585	−	0.251585i
$593$	−118.172	−	118.172i	−0.199279	−	0.199279i	0.600412	−	0.799691i	$-0.295003\pi$
$593$	−118.172	−	118.172i	−0.199279	−	0.199279i	−0.799691	+	0.600412i	$0.795003\pi$
$594$			143.822i			0.242124i
$595$		0			0
$596$	−587.283			−0.985374
$597$	126.065	−	126.065i	0.211164	−	0.211164i
$598$	287.657	+	287.657i	0.481032	+	0.481032i
$599$		−	210.890i		−	0.352071i	−0.984384	−	0.176035i	$-0.943673\pi$
$599$		−	210.890i		−	0.352071i	0.984384	−	0.176035i	$-0.0563273\pi$
$600$		0			0
$601$	−238.143			−0.396244			−0.198122	−	0.980177i	$-0.563484\pi$
$601$	−238.143			−0.396244			−0.198122	+	0.980177i	$0.563484\pi$
$602$	−51.1783	+	51.1783i	−0.0850138	+	0.0850138i
$603$	201.513	+	201.513i	0.334185	+	0.334185i
$604$		−	463.451i		−	0.767303i
$605$		0			0
$606$	296.965			0.490042
$607$	−617.412	+	617.412i	−1.01715	+	1.01715i	−0.0173035	+	0.999850i	$0.505508\pi$
$607$	−617.412	+	617.412i	−1.01715	+	1.01715i	−0.999850	+	0.0173035i	$0.994492\pi$
$608$	33.0039	+	33.0039i	0.0542827	+	0.0542827i
$609$			90.5035i			0.148610i
$610$		0			0
$611$	−131.332			−0.214946
$612$	13.1796	−	13.1796i	0.0215352	−	0.0215352i
$613$	765.627	+	765.627i	1.24898	+	1.24898i	0.956169	+	0.292816i	$0.0945922\pi$
$613$	765.627	+	765.627i	1.24898	+	1.24898i	0.292816	+	0.956169i	$0.405408\pi$
$614$			763.028i			1.24272i
$615$		0			0
$616$	146.461			0.237761
$617$	−42.0185	+	42.0185i	−0.0681012	+	0.0681012i	−0.740337	−	0.672236i	$-0.765334\pi$
$617$	−42.0185	+	42.0185i	−0.0681012	+	0.0681012i	0.672236	+	0.740337i	$0.265334\pi$
$618$	−57.7134	−	57.7134i	−0.0933874	−	0.0933874i
$619$			564.440i			0.911858i	0.890016	+	0.455929i	$0.150693\pi$
$619$			564.440i			0.911858i	−0.890016	+	0.455929i	$0.849307\pi$
$620$		0			0
$621$	131.588			0.211896
$622$	388.702	−	388.702i	0.624923	−	0.624923i
$623$	−295.480	−	295.480i	−0.474287	−	0.474287i
$624$		−	78.6978i		−	0.126118i
$625$		0			0
$626$	−101.161			−0.161599
$627$	197.778	−	197.778i	0.315436	−	0.315436i
$628$	125.641	+	125.641i	0.200065	+	0.200065i
$629$			163.578i			0.260061i
$630$		0			0
$631$	498.286			0.789676			0.394838	−	0.918751i	$-0.370801\pi$
$631$	498.286			0.789676			0.394838	+	0.918751i	$0.370801\pi$
$632$	−80.4178	+	80.4178i	−0.127243	+	0.127243i
$633$	264.779	+	264.779i	0.418292	+	0.418292i
$634$		−	109.935i		−	0.173399i
$635$		0			0
$636$	−190.355			−0.299300
$637$	−56.2245	+	56.2245i	−0.0882645	+	0.0882645i
$638$	386.531	+	386.531i	0.605847	+	0.605847i
$639$		−	40.1379i		−	0.0628136i
$640$		0			0
$641$	145.183			0.226494			0.113247	−	0.993567i	$-0.463875\pi$
$641$	145.183			0.226494			0.113247	+	0.993567i	$0.463875\pi$
$642$	35.3497	−	35.3497i	0.0550618	−	0.0550618i
$643$	−646.724	−	646.724i	−1.00579	−	1.00579i	−0.999983	−	0.00580843i	$-0.998151\pi$
$643$	−646.724	−	646.724i	−1.00579	−	1.00579i	−0.00580843	−	0.999983i	$-0.501849\pi$
$644$		−	134.002i		−	0.208078i
$645$		0			0
$646$	−36.2481			−0.0561115
$647$	−190.030	+	190.030i	−0.293710	+	0.293710i	−0.838544	−	0.544834i	$-0.816593\pi$
$647$	−190.030	+	190.030i	−0.293710	+	0.293710i	0.544834	+	0.838544i	$0.316593\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	1455.69i		−	2.24297i
$650$		0			0
$651$	−137.497			−0.211209
$652$	−194.023	+	194.023i	−0.297582	+	0.297582i
$653$	−416.099	−	416.099i	−0.637212	−	0.637212i	0.312655	−	0.949867i	$-0.398782\pi$
$653$	−416.099	−	416.099i	−0.637212	−	0.637212i	−0.949867	+	0.312655i	$0.898782\pi$
$654$			84.8441i			0.129731i
$655$		0			0
$656$	323.448			0.493061
$657$	−144.822	+	144.822i	−0.220428	+	0.220428i
$658$	30.5899	+	30.5899i	0.0464892	+	0.0464892i
$659$			615.296i			0.933682i	0.884341	+	0.466841i	$0.154608\pi$
$659$			615.296i			0.933682i	−0.884341	+	0.466841i	$0.845392\pi$
$660$		0			0
$661$	−455.425			−0.688994			−0.344497	−	0.938787i	$-0.611951\pi$
$661$	−455.425			−0.688994			−0.344497	+	0.938787i	$0.611951\pi$
$662$	−195.576	+	195.576i	−0.295433	+	0.295433i
$663$	43.2168	+	43.2168i	0.0651837	+	0.0651837i
$664$		−	137.655i		−	0.207312i
$665$		0			0
$666$	223.407			0.335446
$667$	353.650	−	353.650i	0.530210	−	0.530210i
$668$	−270.995	−	270.995i	−0.405681	−	0.405681i
$669$			350.897i			0.524509i
$670$		0			0
$671$	1914.92			2.85383
$672$	−18.3303	+	18.3303i	−0.0272772	+	0.0272772i
$673$	−156.161	−	156.161i	−0.232037	−	0.232037i	0.581505	−	0.813543i	$-0.302464\pi$
$673$	−156.161	−	156.161i	−0.232037	−	0.232037i	−0.813543	+	0.581505i	$0.802464\pi$
$674$		−	840.412i		−	1.24690i
$675$		0			0
$676$	−79.9437			−0.118260
$677$	567.709	−	567.709i	0.838566	−	0.838566i	−0.150104	−	0.988670i	$-0.547961\pi$
$677$	567.709	−	567.709i	0.838566	−	0.838566i	0.988670	+	0.150104i	$0.0479610\pi$
$678$	48.8501	+	48.8501i	0.0720503	+	0.0720503i
$679$		−	274.210i		−	0.403843i
$680$		0			0
$681$	555.461			0.815655
$682$	−587.235	+	587.235i	−0.861048	+	0.861048i
$683$	124.523	+	124.523i	0.182317	+	0.182317i	0.792365	−	0.610047i	$-0.208850\pi$
$683$	124.523	+	124.523i	0.182317	+	0.182317i	−0.610047	+	0.792365i	$0.708850\pi$
$684$			49.5058i			0.0723769i
$685$		0			0
$686$	26.1916			0.0381802
$687$	−59.8984	+	59.8984i	−0.0871883	+	0.0871883i
$688$	−54.7119	−	54.7119i	−0.0795231	−	0.0795231i
$689$		−	624.188i		−	0.905934i
$690$		0			0
$691$	−1214.16			−1.75710			−0.878551	−	0.477648i	$-0.841489\pi$
$691$	−1214.16			−1.75710			−0.878551	+	0.477648i	$0.841489\pi$
$692$	132.354	−	132.354i	0.191263	−	0.191263i
$693$	109.846	+	109.846i	0.158508	+	0.158508i
$694$		−	42.8363i		−	0.0617238i
$695$		0			0
$696$	−96.7523			−0.139012
$697$	−177.621	+	177.621i	−0.254836	+	0.254836i
$698$	−244.156	−	244.156i	−0.349794	−	0.349794i
$699$		−	301.206i		−	0.430910i
$700$		0			0
$701$	−788.147			−1.12432			−0.562159	−	0.827029i	$-0.690029\pi$
$701$	−788.147			−1.12432			−0.562159	+	0.827029i	$0.690029\pi$
$702$	59.0234	−	59.0234i	0.0840789	−	0.0840789i
$703$	−307.221	−	307.221i	−0.437014	−	0.437014i
$704$			156.573i			0.222405i
$705$		0			0
$706$	457.938			0.648637
$707$	226.811	−	226.811i	0.320808	−	0.320808i
$708$	182.186	+	182.186i	0.257325	+	0.257325i
$709$			1230.75i			1.73589i	0.496660	+	0.867945i	$0.334560\pi$
$709$			1230.75i			1.73589i	−0.496660	+	0.867945i	$0.665440\pi$
$710$		0			0
$711$	−120.627			−0.169658
$712$	315.882	−	315.882i	0.443654	−	0.443654i
$713$	537.281	+	537.281i	0.753550	+	0.753550i
$714$		−	20.1321i		−	0.0281962i
$715$		0			0
$716$	548.090			0.765488
$717$	−440.163	+	440.163i	−0.613895	+	0.613895i
$718$	165.483	+	165.483i	0.230478	+	0.230478i
$719$			251.624i			0.349963i	0.984572	+	0.174982i	$0.0559866\pi$
$719$			251.624i			0.349963i	−0.984572	+	0.174982i	$0.944013\pi$
$720$		0			0
$721$	−88.1587			−0.122273
$722$	−292.922	+	292.922i	−0.405708	+	0.405708i
$723$	118.128	+	118.128i	0.163386	+	0.163386i
$724$			72.0985i			0.0995836i
$725$		0			0
$726$	641.891			0.884147
$727$	−254.322	+	254.322i	−0.349824	+	0.349824i	−0.860044	−	0.510220i	$-0.829564\pi$
$727$	−254.322	+	254.322i	−0.349824	+	0.349824i	0.510220	+	0.860044i	$0.329564\pi$
$728$	−60.1065	−	60.1065i	−0.0825638	−	0.0825638i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	60.0899			0.0822024
$732$	−239.662	+	239.662i	−0.327406	+	0.327406i
$733$	27.6831	+	27.6831i	0.0377668	+	0.0377668i	0.725738	−	0.687971i	$-0.241498\pi$
$733$	27.6831	+	27.6831i	0.0377668	+	0.0377668i	−0.687971	+	0.725738i	$0.741498\pi$
$734$			451.201i			0.614715i
$735$		0			0
$736$	143.254			0.194639
$737$	1314.65	−	1314.65i	1.78379	−	1.78379i
$738$	242.586	+	242.586i	0.328707	+	0.328707i
$739$		−	434.621i		−	0.588121i	−0.955787	−	0.294060i	$-0.904993\pi$
$739$		−	434.621i		−	0.588121i	0.955787	−	0.294060i	$-0.0950066\pi$
$740$		0			0
$741$	−162.333			−0.219073
$742$	−145.386	+	145.386i	−0.195938	+	0.195938i
$743$	−126.704	−	126.704i	−0.170530	−	0.170530i	0.616682	−	0.787212i	$-0.288476\pi$
$743$	−126.704	−	126.704i	−0.170530	−	0.170530i	−0.787212	+	0.616682i	$0.788476\pi$
$744$		−	146.990i		−	0.197568i
$745$		0			0
$746$	558.812			0.749078
$747$	103.241	−	103.241i	0.138208	−	0.138208i
$748$	−85.9821	−	85.9821i	−0.114949	−	0.114949i
$749$		−	53.9975i		−	0.0720928i
$750$		0			0
$751$	735.755			0.979701			0.489851	−	0.871806i	$-0.337051\pi$
$751$	735.755			0.979701			0.489851	+	0.871806i	$0.337051\pi$
$752$	−32.7020	+	32.7020i	−0.0434866	+	0.0434866i
$753$	355.791	+	355.791i	0.472498	+	0.472498i
$754$		−	317.258i		−	0.420767i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	255.322	−	255.322i	0.337281	−	0.337281i	−0.518062	−	0.855343i	$-0.673346\pi$
$757$	255.322	−	255.322i	0.337281	−	0.337281i	0.855343	+	0.518062i	$0.173346\pi$
$758$	−746.946	−	746.946i	−0.985417	−	0.985417i
$759$		−	858.464i		−	1.13105i
$760$		0			0
$761$	783.231			1.02921			0.514606	−	0.857427i	$-0.327938\pi$
$761$	783.231			1.02921			0.514606	+	0.857427i	$0.327938\pi$
$762$	−34.0357	+	34.0357i	−0.0446663	+	0.0446663i
$763$	64.8007	+	64.8007i	0.0849289	+	0.0849289i
$764$		−	266.389i		−	0.348676i
$765$		0			0
$766$	718.352			0.937797
$767$	−597.403	+	597.403i	−0.778883	+	0.778883i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			186.068i			0.241961i	0.992655	+	0.120980i	$0.0386038\pi$
$769$			186.068i			0.241961i	−0.992655	+	0.120980i	$0.961396\pi$
$770$		0			0
$771$	−552.564			−0.716684
$772$	473.130	−	473.130i	0.612863	−	0.612863i
$773$	333.576	+	333.576i	0.431534	+	0.431534i	0.889150	−	0.457616i	$-0.151297\pi$
$773$	333.576	+	333.576i	0.431534	+	0.431534i	−0.457616	+	0.889150i	$0.651297\pi$
$774$		−	82.0679i		−	0.106031i
$775$		0			0
$776$	293.143			0.377761
$777$	170.630	−	170.630i	0.219601	−	0.219601i
$778$	476.719	+	476.719i	0.612749	+	0.612749i
$779$		−	667.190i		−	0.856469i
$780$		0			0
$781$	−261.855			−0.335282
$782$	−78.6680	+	78.6680i	−0.100598	+	0.100598i
$783$	−72.5642	−	72.5642i	−0.0926746	−	0.0926746i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	396.326			0.504231
$787$	−431.752	+	431.752i	−0.548605	+	0.548605i	−0.926037	−	0.377432i	$-0.876807\pi$
$787$	−431.752	+	431.752i	−0.548605	+	0.548605i	0.377432	+	0.926037i	$0.376807\pi$
$788$	−406.021	−	406.021i	−0.515255	−	0.515255i
$789$			602.404i			0.763504i
$790$		0			0
$791$	74.6197			0.0943360
$792$	−117.430	+	117.430i	−0.148270	+	0.148270i
$793$	−785.869	−	785.869i	−0.991007	−	0.991007i
$794$			274.631i			0.345883i
$795$		0			0
$796$	205.863			0.258622
$797$	67.9296	−	67.9296i	0.0852316	−	0.0852316i	−0.663206	−	0.748437i	$-0.730805\pi$
$797$	67.9296	−	67.9296i	0.0852316	−	0.0852316i	0.748437	+	0.663206i	$0.230805\pi$
$798$	37.8107	+	37.8107i	0.0473818	+	0.0473818i
$799$		−	35.9165i		−	0.0449518i
$800$		0			0
$801$	473.823			0.591539
$802$	691.294	−	691.294i	0.861962	−	0.861962i
$803$	944.800	+	944.800i	1.17659	+	1.17659i
$804$			329.070i			0.409291i
$805$		0			0
$806$	481.993			0.598006
$807$	375.015	−	375.015i	0.464702	−	0.464702i
$808$	242.471	+	242.471i	0.300088	+	0.300088i
$809$		−	375.281i		−	0.463883i	−0.972730	−	0.231941i	$-0.925492\pi$
$809$		−	375.281i		−	0.463883i	0.972730	−	0.231941i	$-0.0745078\pi$
$810$		0			0
$811$	283.093			0.349066			0.174533	−	0.984651i	$-0.444158\pi$
$811$	283.093			0.349066			0.174533	+	0.984651i	$0.444158\pi$
$812$	−73.8958	+	73.8958i	−0.0910047	+	0.0910047i
$813$	453.503	+	453.503i	0.557814	+	0.557814i
$814$		−	1457.49i		−	1.79052i
$815$		0			0
$816$	21.5221			0.0263752
$817$	−112.857	+	112.857i	−0.138135	+	0.138135i
$818$	−146.348	−	146.348i	−0.178909	−	0.178909i
$819$		−	90.1597i		−	0.110085i
$820$		0			0
$821$	1325.60			1.61462			0.807308	−	0.590131i	$-0.200924\pi$
$821$	1325.60			1.61462			0.807308	+	0.590131i	$0.200924\pi$
$822$	87.6974	−	87.6974i	0.106688	−	0.106688i
$823$	−794.494	−	794.494i	−0.965363	−	0.965363i	0.0340566	−	0.999420i	$-0.489157\pi$
$823$	−794.494	−	794.494i	−0.965363	−	0.965363i	−0.999420	+	0.0340566i	$0.989157\pi$
$824$		−	94.2456i		−	0.114376i
$825$		0			0
$826$	278.294			0.336918
$827$	−361.128	+	361.128i	−0.436672	+	0.436672i	−0.890890	−	0.454218i	$-0.849919\pi$
$827$	−361.128	+	361.128i	−0.436672	+	0.436672i	0.454218	+	0.890890i	$0.349919\pi$
$828$	107.441	+	107.441i	0.129759	+	0.129759i
$829$		−	195.726i		−	0.236099i	−0.993008	−	0.118049i	$-0.962336\pi$
$829$		−	195.726i		−	0.236099i	0.993008	−	0.118049i	$-0.0376641\pi$
$830$		0			0
$831$	−396.368			−0.476978
$832$	64.2565	−	64.2565i	0.0772314	−	0.0772314i
$833$	−15.3762	−	15.3762i	−0.0184588	−	0.0184588i
$834$			219.832i			0.263587i
$835$		0			0
$836$	322.971			0.386329
$837$	110.243	−	110.243i	0.131712	−	0.131712i
$838$	19.1814	+	19.1814i	0.0228895	+	0.0228895i
$839$			10.5401i			0.0125627i	0.999980	+	0.00628133i	$0.00199942\pi$
$839$			10.5401i			0.0125627i	−0.999980	+	0.00628133i	$0.998001\pi$
$840$		0			0
$841$	450.958			0.536216
$842$	343.060	−	343.060i	0.407435	−	0.407435i
$843$	288.742	+	288.742i	0.342518	+	0.342518i
$844$			432.382i			0.512301i
$845$		0			0
$846$	−49.0529			−0.0579822
$847$	490.252	−	490.252i	0.578810	−	0.578810i
$848$	−155.424	−	155.424i	−0.183283	−	0.183283i
$849$			5.55423i			0.00654208i
$850$		0			0
$851$	−1333.50			−1.56699
$852$	32.7724	−	32.7724i	0.0384653	−	0.0384653i
$853$	950.696	+	950.696i	1.11453	+	1.11453i	0.992530	+	0.122002i	$0.0389315\pi$
$853$	950.696	+	950.696i	1.11453	+	1.11453i	0.122002	+	0.992530i	$0.461068\pi$
$854$			366.089i			0.428676i
$855$		0			0
$856$	57.7258			0.0674366
$857$	−628.392	+	628.392i	−0.733246	+	0.733246i	−0.971261	−	0.238016i	$-0.923503\pi$
$857$	−628.392	+	628.392i	−0.733246	+	0.733246i	0.238016	+	0.971261i	$0.423503\pi$
$858$	−385.062	−	385.062i	−0.448791	−	0.448791i
$859$			832.998i			0.969730i	0.874589	+	0.484865i	$0.161131\pi$
$859$			832.998i			0.969730i	−0.874589	+	0.484865i	$0.838869\pi$
$860$		0			0
$861$	370.556			0.430379
$862$	−251.794	+	251.794i	−0.292105	+	0.292105i
$863$	−802.913	−	802.913i	−0.930374	−	0.930374i	0.0673547	−	0.997729i	$-0.478544\pi$
$863$	−802.913	−	802.913i	−0.930374	−	0.930374i	−0.997729	+	0.0673547i	$0.978544\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$	−250.389			−0.289133
$867$	342.132	−	342.132i	0.394616	−	0.394616i
$868$	−112.266	−	112.266i	−0.129339	−	0.129339i
$869$			786.955i			0.905587i
$870$		0			0
$871$	−1079.05			−1.23886
$872$	−69.2749	+	69.2749i	−0.0794437	+	0.0794437i
$873$	219.857	+	219.857i	0.251841	+	0.251841i
$874$		−	295.497i		−	0.338097i
$875$		0			0
$876$	−236.493			−0.269969
$877$	−483.085	+	483.085i	−0.550838	+	0.550838i	−0.926683	−	0.375845i	$-0.877353\pi$
$877$	−483.085	+	483.085i	−0.550838	+	0.550838i	0.375845	+	0.926683i	$0.377353\pi$
$878$	37.5609	+	37.5609i	0.0427801	+	0.0427801i
$879$			488.435i			0.555671i
$880$		0			0
$881$	−1190.88			−1.35174			−0.675868	−	0.737023i	$-0.736231\pi$
$881$	−1190.88			−1.35174			−0.675868	+	0.737023i	$0.736231\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	52.9133	+	52.9133i	0.0599245	+	0.0599245i	0.736434	−	0.676509i	$-0.236508\pi$
$883$	52.9133	+	52.9133i	0.0599245	+	0.0599245i	−0.676509	+	0.736434i	$0.736508\pi$
$884$			70.5727i			0.0798334i
$885$		0			0
$886$	−1167.93			−1.31821
$887$	393.366	−	393.366i	0.443479	−	0.443479i	−0.449700	−	0.893180i	$-0.648469\pi$
$887$	393.366	−	393.366i	0.443479	−	0.443479i	0.893180	+	0.449700i	$0.148469\pi$
$888$	182.411	+	182.411i	0.205418	+	0.205418i
$889$			51.9905i			0.0584820i
$890$		0			0
$891$	−176.145			−0.197694
$892$	−286.506	+	286.506i	−0.321195	+	0.321195i
$893$	67.4557	+	67.4557i	0.0755383	+	0.0755383i
$894$		−	719.271i		−	0.804554i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	−352.307	+	352.307i	−0.392761	+	0.392761i
$898$	−595.556	−	595.556i	−0.663202	−	0.663202i
$899$		−	592.570i		−	0.659143i
$900$		0			0
$901$	170.702			0.189458
$902$	1582.61	−	1582.61i	1.75455	−	1.75455i
$903$	−62.6804	−	62.6804i	−0.0694135	−	0.0694135i
$904$			79.7719i			0.0882432i
$905$		0			0
$906$	567.609			0.626500
$907$	−715.081	+	715.081i	−0.788403	+	0.788403i	−0.981232	−	0.192829i	$-0.938234\pi$
$907$	−715.081	+	715.081i	−0.788403	+	0.788403i	0.192829	+	0.981232i	$0.438234\pi$
$908$	453.532	+	453.532i	0.499485	+	0.499485i
$909$			363.707i			0.400118i
$910$		0			0
$911$	−1440.70			−1.58145			−0.790727	−	0.612169i	$-0.790297\pi$
$911$	−1440.70			−1.58145			−0.790727	+	0.612169i	$0.790297\pi$
$912$	−40.4213	+	40.4213i	−0.0443216	+	0.0443216i
$913$	−673.535	−	673.535i	−0.737716	−	0.737716i
$914$		−	601.010i		−	0.657560i
$915$		0			0
$916$	−97.8136			−0.106783
$917$	302.699	−	302.699i	0.330097	−	0.330097i
$918$	16.1416	+	16.1416i	0.0175834	+	0.0175834i
$919$			139.961i			0.152297i	0.997096	+	0.0761485i	$0.0242623\pi$
$919$			139.961i			0.152297i	−0.997096	+	0.0761485i	$0.975738\pi$
$920$		0			0
$921$	−934.515			−1.01467
$922$	−565.424	+	565.424i	−0.613258	+	0.613258i
$923$	107.463	+	107.463i	0.116428	+	0.116428i
$924$			179.377i			0.194131i
$925$		0			0
$926$	−495.239			−0.534815
$927$	70.6842	−	70.6842i	0.0762505	−	0.0762505i
$928$	−78.9979	−	78.9979i	−0.0851271	−	0.0851271i
$929$		−	268.303i		−	0.288808i	−0.989519	−	0.144404i	$-0.953874\pi$
$929$		−	268.303i		−	0.288808i	0.989519	−	0.144404i	$-0.0461265\pi$
$930$		0			0
$931$	57.7568			0.0620374
$932$	245.934	−	245.934i	0.263878	−	0.263878i
$933$	476.061	+	476.061i	0.510248	+	0.510248i
$934$			621.872i			0.665816i
$935$		0			0
$936$	96.3848			0.102975
$937$	750.288	−	750.288i	0.800734	−	0.800734i	−0.182476	−	0.983210i	$-0.558411\pi$
$937$	750.288	−	750.288i	0.800734	−	0.800734i	0.983210	+	0.182476i	$0.0584113\pi$
$938$	251.331	+	251.331i	0.267944	+	0.267944i
$939$		−	123.897i		−	0.131945i
$940$		0			0
$941$	858.370			0.912189			0.456095	−	0.889931i	$-0.349248\pi$
$941$	858.370			0.912189			0.456095	+	0.889931i	$0.349248\pi$
$942$	−153.878	+	153.878i	−0.163352	+	0.163352i
$943$	−1447.98	−	1447.98i	−1.53550	−	1.53550i
$944$			297.509i			0.315158i
$945$		0			0
$946$	−535.402			−0.565964
$947$	−1103.38	+	1103.38i	−1.16513	+	1.16513i	−0.181798	+	0.983336i	$0.558192\pi$
$947$	−1103.38	+	1103.38i	−1.16513	+	1.16513i	−0.983336	+	0.181798i	$0.941808\pi$
$948$	−98.4912	−	98.4912i	−0.103894	−	0.103894i
$949$		−	775.477i		−	0.817152i
$950$		0			0
$951$	134.642			0.141580
$952$	16.4378	−	16.4378i	0.0172666	−	0.0172666i
$953$	1277.56	+	1277.56i	1.34056	+	1.34056i	0.895499	+	0.445064i	$0.146819\pi$
$953$	1277.56	+	1277.56i	1.34056	+	1.34056i	0.445064	+	0.895499i	$0.353181\pi$
$954$		−	233.136i		−	0.244377i
$955$		0			0
$956$	−718.783			−0.751865
$957$	−473.401	+	473.401i	−0.494672	+	0.494672i
$958$	337.547	+	337.547i	0.352346	+	0.352346i
$959$		−	133.960i		−	0.139687i
$960$		0			0
$961$	−60.7414			−0.0632064
$962$	−598.141	+	598.141i	−0.621768	+	0.621768i
$963$	43.2943	+	43.2943i	0.0449578	+	0.0449578i
$964$			192.902i			0.200106i
$965$		0			0
$966$	164.119			0.169895
$967$	478.601	−	478.601i	0.494933	−	0.494933i	−0.414923	−	0.909857i	$-0.636192\pi$
$967$	478.601	−	478.601i	0.494933	−	0.494933i	0.909857	+	0.414923i	$0.136192\pi$
$968$	524.101	+	524.101i	0.541427	+	0.541427i
$969$		−	44.3946i		−	0.0458149i
$970$		0			0
$971$	97.1677			0.100070			0.0500349	−	0.998747i	$-0.484067\pi$
$971$	97.1677			0.100070			0.0500349	+	0.998747i	$0.484067\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	167.899	+	167.899i	0.172558	+	0.172558i
$974$		−	307.568i		−	0.315778i
$975$		0			0
$976$	−391.366			−0.400989
$977$	711.442	−	711.442i	0.728191	−	0.728191i	−0.242068	−	0.970259i	$-0.577826\pi$
$977$	711.442	−	711.442i	0.728191	−	0.728191i	0.970259	+	0.242068i	$0.0778259\pi$
$978$	−237.629	−	237.629i	−0.242975	−	0.242975i
$979$		−	3091.17i		−	3.15748i
$980$		0			0
$981$	−103.912			−0.105925
$982$	−320.910	+	320.910i	−0.326792	+	0.326792i
$983$	443.320	+	443.320i	0.450986	+	0.450986i	0.895682	−	0.444695i	$-0.146688\pi$
$983$	443.320	+	443.320i	0.450986	+	0.450986i	−0.444695	+	0.895682i	$0.646688\pi$
$984$			396.141i			0.402583i
$985$		0			0
$986$	86.7632			0.0879951
$987$	−37.4648	+	37.4648i	−0.0379583	+	0.0379583i
$988$	−132.545	−	132.545i	−0.134154	−	0.134154i
$989$			489.858i			0.495306i
$990$		0			0
$991$	1708.27			1.72378			0.861890	−	0.507095i	$-0.169281\pi$
$991$	1708.27			1.72378			0.861890	+	0.507095i	$0.169281\pi$
$992$	120.017	−	120.017i	0.120985	−	0.120985i
$993$	−239.531	−	239.531i	−0.241220	−	0.241220i
$994$		−	50.0607i		−	0.0503629i
$995$		0			0
$996$	168.592			0.169269
$997$	−1363.41	+	1363.41i	−1.36752	+	1.36752i	−0.503548	+	0.863967i	$0.667972\pi$
$997$	−1363.41	+	1363.41i	−1.36752	+	1.36752i	−0.863967	+	0.503548i	$0.832028\pi$
$998$	284.928	+	284.928i	0.285499	+	0.285499i
$999$			273.617i			0.273891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.b.43.2		8
5.2	odd	4	inner	1050.3.l.b.757.2		8
5.3	odd	4		210.3.l.a.127.3	yes	8
5.4	even	2		210.3.l.a.43.3	✓	8
15.8	even	4		630.3.o.b.127.2		8
15.14	odd	2		630.3.o.b.253.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.3	✓	8	5.4	even	2
210.3.l.a.127.3	yes	8	5.3	odd	4
630.3.o.b.127.2		8	15.8	even	4
630.3.o.b.253.2		8	15.14	odd	2
1050.3.l.b.43.2		8	1.1	even	1	trivial
1050.3.l.b.757.2		8	5.2	odd	4	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +19.5717 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-8.03207 - 8.03207i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(2.19659 - 2.19659i) q^{17} +(-3.00000 - 3.00000i) q^{18} +8.25097i q^{19} -4.58258 q^{21} +(-19.5717 + 19.5717i) q^{22} +(17.9068 + 17.9068i) q^{23} -4.89898i q^{24} +16.0641 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -19.7495i q^{29} +30.0043 q^{31} +(4.00000 - 4.00000i) q^{32} +(-23.9703 - 23.9703i) q^{33} +4.39319i q^{34} +6.00000 q^{36} +(-37.2346 + 37.2346i) q^{37} +(-8.25097 - 8.25097i) q^{38} +19.6745i q^{39} -80.8620 q^{41} +(4.58258 - 4.58258i) q^{42} +(13.6780 + 13.6780i) q^{43} -39.1434i q^{44} -35.8136 q^{46} +(8.17549 - 8.17549i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} -5.38053 q^{51} +(-16.0641 + 16.0641i) q^{52} +(38.8560 + 38.8560i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(10.1053 - 10.1053i) q^{57} +(19.7495 + 19.7495i) q^{58} -74.3773i q^{59} +97.8414 q^{61} +(-30.0043 + 30.0043i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +47.9406 q^{66} +(67.1712 - 67.1712i) q^{67} +(-4.39319 - 4.39319i) q^{68} -43.8625i q^{69} -13.3793 q^{71} +(-6.00000 + 6.00000i) q^{72} +(48.2738 + 48.2738i) q^{73} -74.4691i q^{74} +16.5019 q^{76} +(36.6153 - 36.6153i) q^{77} +(-19.6745 - 19.6745i) q^{78} +40.2089i q^{79} -9.00000 q^{81} +(80.8620 - 80.8620i) q^{82} +(-34.4137 - 34.4137i) q^{83} +9.16515i q^{84} -27.3560 q^{86} +(-24.1881 + 24.1881i) q^{87} +(39.1434 + 39.1434i) q^{88} -157.941i q^{89} -30.0532 q^{91} +(35.8136 - 35.8136i) q^{92} +(-36.7476 - 36.7476i) q^{93} +16.3510i q^{94} -9.79796 q^{96} +(73.2856 - 73.2856i) q^{97} +(7.00000 + 7.00000i) q^{98} +58.7150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more