LMFDB - Embedded newform 1050.3.l.h.43.6

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.6
Root			$0.170157 + 0.170157i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.h.757.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} -5.74922 q^{11} +(2.44949 - 2.44949i) q^{12} +(-15.0034 - 15.0034i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(4.78821 - 4.78821i) q^{17} +(3.00000 + 3.00000i) q^{18} +17.4017i q^{19} -4.58258 q^{21} +(-5.74922 + 5.74922i) q^{22} +(-13.2261 - 13.2261i) q^{23} -4.89898i q^{24} -30.0069 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} +37.7271i q^{29} -27.0130 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-7.04132 - 7.04132i) q^{33} -9.57642i q^{34} +6.00000 q^{36} +(-11.3640 + 11.3640i) q^{37} +(17.4017 + 17.4017i) q^{38} -36.7508i q^{39} -53.0897 q^{41} +(-4.58258 + 4.58258i) q^{42} +(-37.1052 - 37.1052i) q^{43} +11.4984i q^{44} -26.4522 q^{46} +(9.39190 - 9.39190i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +11.7287 q^{51} +(-30.0069 + 30.0069i) q^{52} +(-43.8996 - 43.8996i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(-21.3126 + 21.3126i) q^{57} +(37.7271 + 37.7271i) q^{58} -62.9694i q^{59} -1.67492 q^{61} +(-27.0130 + 27.0130i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} -14.0826 q^{66} +(-28.4909 + 28.4909i) q^{67} +(-9.57642 - 9.57642i) q^{68} -32.3972i q^{69} +47.2039 q^{71} +(6.00000 - 6.00000i) q^{72} +(31.2071 + 31.2071i) q^{73} +22.7281i q^{74} +34.8033 q^{76} +(10.7558 - 10.7558i) q^{77} +(-36.7508 - 36.7508i) q^{78} -107.134i q^{79} -9.00000 q^{81} +(-53.0897 + 53.0897i) q^{82} +(-18.2365 - 18.2365i) q^{83} +9.16515i q^{84} -74.2105 q^{86} +(-46.2061 + 46.2061i) q^{87} +(11.4984 + 11.4984i) q^{88} +174.675i q^{89} +56.1378 q^{91} +(-26.4522 + 26.4522i) q^{92} +(-33.0840 - 33.0840i) q^{93} -18.7838i q^{94} -9.79796 q^{96} +(91.5084 - 91.5084i) q^{97} +(-7.00000 - 7.00000i) q^{98} -17.2477i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 - 32 * q^8	$ 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 - 32 * q^8 + 8 * q^11 + 32 * q^13 - 64 * q^16 - 56 * q^17 + 48 * q^18 + 8 * q^22 - 24 * q^23 + 64 * q^26 - 112 * q^31 - 64 * q^32 - 24 * q^33 + 96 * q^36 + 152 * q^37 - 48 * q^46 - 80 * q^47 - 72 * q^51 + 64 * q^52 - 48 * q^53 - 24 * q^57 - 96 * q^58 + 96 * q^61 - 112 * q^62 - 48 * q^66 + 80 * q^67 + 112 * q^68 + 536 * q^71 + 96 * q^72 + 168 * q^77 + 48 * q^78 - 144 * q^81 + 256 * q^83 + 144 * q^87 - 16 * q^88 - 48 * q^92 - 192 * q^93 - 688 * q^97 - 112 * 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
$11$	−5.74922			−0.522656			−0.261328	−	0.965250i	$-0.584160\pi$
$11$	−5.74922			−0.522656			−0.261328	+	0.965250i	$0.584160\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−15.0034	−	15.0034i	−1.15411	−	1.15411i	−0.985720	−	0.168391i	$-0.946143\pi$
$13$	−15.0034	−	15.0034i	−1.15411	−	1.15411i	−0.168391	−	0.985720i	$-0.553857\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	4.78821	−	4.78821i	0.281659	−	0.281659i	−0.552111	−	0.833771i	$-0.686178\pi$
$17$	4.78821	−	4.78821i	0.281659	−	0.281659i	0.833771	+	0.552111i	$0.186178\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			17.4017i			0.915877i	0.888984	+	0.457938i	$0.151412\pi$
$19$			17.4017i			0.915877i	−0.888984	+	0.457938i	$0.848588\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	−5.74922	+	5.74922i	−0.261328	+	0.261328i
$23$	−13.2261	−	13.2261i	−0.575048	−	0.575048i	0.358487	−	0.933535i	$-0.383293\pi$
$23$	−13.2261	−	13.2261i	−0.575048	−	0.575048i	−0.933535	+	0.358487i	$0.883293\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$	−30.0069			−1.15411
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	3.74166	+	3.74166i	0.133631	+	0.133631i
$29$			37.7271i			1.30093i	0.759534	+	0.650467i	$0.225427\pi$
$29$			37.7271i			1.30093i	−0.759534	+	0.650467i	$0.774573\pi$
$30$		0			0
$31$	−27.0130			−0.871386			−0.435693	−	0.900095i	$-0.643497\pi$
$31$	−27.0130			−0.871386			−0.435693	+	0.900095i	$0.643497\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−7.04132	−	7.04132i	−0.213373	−	0.213373i
$34$		−	9.57642i		−	0.281659i
$35$		0			0
$36$	6.00000			0.166667
$37$	−11.3640	+	11.3640i	−0.307136	+	0.307136i	−0.843798	−	0.536661i	$-0.819685\pi$
$37$	−11.3640	+	11.3640i	−0.307136	+	0.307136i	0.536661	+	0.843798i	$0.319685\pi$
$38$	17.4017	+	17.4017i	0.457938	+	0.457938i
$39$		−	36.7508i		−	0.942328i
$40$		0			0
$41$	−53.0897			−1.29487			−0.647435	−	0.762121i	$-0.724158\pi$
$41$	−53.0897			−1.29487			−0.647435	+	0.762121i	$0.724158\pi$
$42$	−4.58258	+	4.58258i	−0.109109	+	0.109109i
$43$	−37.1052	−	37.1052i	−0.862912	−	0.862912i	0.128763	−	0.991675i	$-0.458899\pi$
$43$	−37.1052	−	37.1052i	−0.862912	−	0.862912i	−0.991675	+	0.128763i	$0.958899\pi$
$44$			11.4984i			0.261328i
$45$		0			0
$46$	−26.4522			−0.575048
$47$	9.39190	−	9.39190i	0.199828	−	0.199828i	−0.600098	−	0.799926i	$-0.704872\pi$
$47$	9.39190	−	9.39190i	0.199828	−	0.199828i	0.799926	+	0.600098i	$0.204872\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	11.7287			0.229974
$52$	−30.0069	+	30.0069i	−0.577056	+	0.577056i
$53$	−43.8996	−	43.8996i	−0.828294	−	0.828294i	0.158987	−	0.987281i	$-0.449177\pi$
$53$	−43.8996	−	43.8996i	−0.828294	−	0.828294i	−0.987281	+	0.158987i	$0.949177\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	−21.3126	+	21.3126i	−0.373905	+	0.373905i
$58$	37.7271	+	37.7271i	0.650467	+	0.650467i
$59$		−	62.9694i		−	1.06728i	−0.845713	−	0.533639i	$-0.820824\pi$
$59$		−	62.9694i		−	1.06728i	0.845713	−	0.533639i	$-0.179176\pi$
$60$		0			0
$61$	−1.67492			−0.0274577			−0.0137288	−	0.999906i	$-0.504370\pi$
$61$	−1.67492			−0.0274577			−0.0137288	+	0.999906i	$0.504370\pi$
$62$	−27.0130	+	27.0130i	−0.435693	+	0.435693i
$63$	−5.61249	−	5.61249i	−0.0890871	−	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−14.0826			−0.213373
$67$	−28.4909	+	28.4909i	−0.425238	+	0.425238i	−0.887003	−	0.461765i	$-0.847216\pi$
$67$	−28.4909	+	28.4909i	−0.425238	+	0.425238i	0.461765	+	0.887003i	$0.347216\pi$
$68$	−9.57642	−	9.57642i	−0.140830	−	0.140830i
$69$		−	32.3972i		−	0.469525i
$70$		0			0
$71$	47.2039			0.664844			0.332422	−	0.943131i	$-0.392134\pi$
$71$	47.2039			0.664844			0.332422	+	0.943131i	$0.392134\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	31.2071	+	31.2071i	0.427495	+	0.427495i	0.887774	−	0.460279i	$-0.152251\pi$
$73$	31.2071	+	31.2071i	0.427495	+	0.427495i	−0.460279	+	0.887774i	$0.652251\pi$
$74$			22.7281i			0.307136i
$75$		0			0
$76$	34.8033			0.457938
$77$	10.7558	−	10.7558i	0.139686	−	0.139686i
$78$	−36.7508	−	36.7508i	−0.471164	−	0.471164i
$79$		−	107.134i		−	1.35612i	−0.735006	−	0.678061i	$-0.762821\pi$
$79$		−	107.134i		−	1.35612i	0.735006	−	0.678061i	$-0.237179\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−53.0897	+	53.0897i	−0.647435	+	0.647435i
$83$	−18.2365	−	18.2365i	−0.219716	−	0.219716i	0.588662	−	0.808379i	$-0.299655\pi$
$83$	−18.2365	−	18.2365i	−0.219716	−	0.219716i	−0.808379	+	0.588662i	$0.799655\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	−74.2105			−0.862912
$87$	−46.2061	+	46.2061i	−0.531104	+	0.531104i
$88$	11.4984	+	11.4984i	0.130664	+	0.130664i
$89$			174.675i			1.96265i	0.192368	+	0.981323i	$0.438383\pi$
$89$			174.675i			1.96265i	−0.192368	+	0.981323i	$0.561617\pi$
$90$		0			0
$91$	56.1378			0.616898
$92$	−26.4522	+	26.4522i	−0.287524	+	0.287524i
$93$	−33.0840	−	33.0840i	−0.355742	−	0.355742i
$94$		−	18.7838i		−	0.199828i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	91.5084	−	91.5084i	0.943385	−	0.943385i	−0.0550959	−	0.998481i	$-0.517546\pi$
$97$	91.5084	−	91.5084i	0.943385	−	0.943385i	0.998481	+	0.0550959i	$0.0175465\pi$
$98$	−7.00000	−	7.00000i	−0.0714286	−	0.0714286i
$99$		−	17.2477i		−	0.174219i
$100$		0			0
$101$	−182.855			−1.81045			−0.905223	−	0.424937i	$-0.860296\pi$
$101$	−182.855			−1.81045			−0.905223	+	0.424937i	$0.860296\pi$
$102$	11.7287	−	11.7287i	0.114987	−	0.114987i
$103$	46.6226	+	46.6226i	0.452647	+	0.452647i	0.896232	−	0.443586i	$-0.146294\pi$
$103$	46.6226	+	46.6226i	0.452647	+	0.452647i	−0.443586	+	0.896232i	$0.646294\pi$
$104$			60.0138i			0.577056i
$105$		0			0
$106$	−87.7991			−0.828294
$107$	−57.5651	+	57.5651i	−0.537992	+	0.537992i	−0.922939	−	0.384947i	$-0.874220\pi$
$107$	−57.5651	+	57.5651i	−0.537992	+	0.537992i	0.384947	+	0.922939i	$0.374220\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			205.254i			1.88307i	0.336920	+	0.941533i	$0.390615\pi$
$109$			205.254i			1.88307i	−0.336920	+	0.941533i	$0.609385\pi$
$110$		0			0
$111$	−27.8361			−0.250776
$112$	7.48331	−	7.48331i	0.0668153	−	0.0668153i
$113$	−32.6037	−	32.6037i	−0.288528	−	0.288528i	0.547970	−	0.836498i	$-0.315401\pi$
$113$	−32.6037	−	32.6037i	−0.288528	−	0.288528i	−0.836498	+	0.547970i	$0.815401\pi$
$114$			42.6252i			0.373905i
$115$		0			0
$116$	75.4542			0.650467
$117$	45.0103	−	45.0103i	0.384704	−	0.384704i
$118$	−62.9694	−	62.9694i	−0.533639	−	0.533639i
$119$			17.9158i			0.150553i
$120$		0			0
$121$	−87.9465			−0.726831
$122$	−1.67492	+	1.67492i	−0.0137288	+	0.0137288i
$123$	−65.0213	−	65.0213i	−0.528629	−	0.528629i
$124$			54.0259i			0.435693i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	103.735	−	103.735i	0.816814	−	0.816814i	−0.168831	−	0.985645i	$-0.553999\pi$
$127$	103.735	−	103.735i	0.816814	−	0.816814i	0.985645	+	0.168831i	$0.0539991\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	90.8889i		−	0.704565i
$130$		0			0
$131$	157.999			1.20610			0.603049	−	0.797704i	$-0.293952\pi$
$131$	157.999			1.20610			0.603049	+	0.797704i	$0.293952\pi$
$132$	−14.0826	+	14.0826i	−0.106687	+	0.106687i
$133$	−32.5555	−	32.5555i	−0.244778	−	0.244778i
$134$			56.9819i			0.425238i
$135$		0			0
$136$	−19.1528			−0.140830
$137$	36.9574	−	36.9574i	0.269762	−	0.269762i	−0.559242	−	0.829004i	$-0.688908\pi$
$137$	36.9574	−	36.9574i	0.269762	−	0.269762i	0.829004	+	0.559242i	$0.188908\pi$
$138$	−32.3972	−	32.3972i	−0.234762	−	0.234762i
$139$			132.183i			0.950960i	0.879727	+	0.475480i	$0.157726\pi$
$139$			132.183i			0.950960i	−0.879727	+	0.475480i	$0.842274\pi$
$140$		0			0
$141$	23.0054			0.163159
$142$	47.2039	−	47.2039i	0.332422	−	0.332422i
$143$	86.2581	+	86.2581i	0.603203	+	0.603203i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	62.4143			0.427495
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	22.7281	+	22.7281i	0.153568	+	0.153568i
$149$		−	255.329i		−	1.71362i	−0.515634	−	0.856809i	$-0.672444\pi$
$149$		−	255.329i		−	1.71362i	0.515634	−	0.856809i	$-0.327556\pi$
$150$		0			0
$151$	−210.524			−1.39420			−0.697098	−	0.716976i	$-0.745526\pi$
$151$	−210.524			−1.39420			−0.697098	+	0.716976i	$0.745526\pi$
$152$	34.8033	−	34.8033i	0.228969	−	0.228969i
$153$	14.3646	+	14.3646i	0.0938865	+	0.0938865i
$154$		−	21.5116i		−	0.139686i
$155$		0			0
$156$	−73.5016			−0.471164
$157$	181.671	−	181.671i	1.15714	−	1.15714i	0.172052	−	0.985088i	$-0.444960\pi$
$157$	181.671	−	181.671i	1.15714	−	1.15714i	0.985088	−	0.172052i	$-0.0550398\pi$
$158$	−107.134	−	107.134i	−0.678061	−	0.678061i
$159$		−	107.532i		−	0.676299i
$160$		0			0
$161$	49.4876			0.307376
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−155.563	−	155.563i	−0.954376	−	0.954376i	0.0446274	−	0.999004i	$-0.485790\pi$
$163$	−155.563	−	155.563i	−0.954376	−	0.954376i	−0.999004	+	0.0446274i	$0.985790\pi$
$164$			106.179i			0.647435i
$165$		0			0
$166$	−36.4729			−0.219716
$167$	−76.0788	+	76.0788i	−0.455562	+	0.455562i	−0.897195	−	0.441634i	$-0.854399\pi$
$167$	−76.0788	+	76.0788i	−0.455562	+	0.455562i	0.441634	+	0.897195i	$0.354399\pi$
$168$	9.16515	+	9.16515i	0.0545545	+	0.0545545i
$169$			281.207i			1.66395i
$170$		0			0
$171$	−52.2050			−0.305292
$172$	−74.2105	+	74.2105i	−0.431456	+	0.431456i
$173$	−28.9323	−	28.9323i	−0.167239	−	0.167239i	0.618526	−	0.785765i	$-0.287730\pi$
$173$	−28.9323	−	28.9323i	−0.167239	−	0.167239i	−0.785765	+	0.618526i	$0.787730\pi$
$174$			92.4121i			0.531104i
$175$		0			0
$176$	22.9969			0.130664
$177$	77.1214	−	77.1214i	0.435714	−	0.435714i
$178$	174.675	+	174.675i	0.981323	+	0.981323i
$179$			126.849i			0.708653i	0.935122	+	0.354327i	$0.115290\pi$
$179$			126.849i			0.708653i	−0.935122	+	0.354327i	$0.884710\pi$
$180$		0			0
$181$	307.681			1.69989			0.849947	−	0.526867i	$-0.176634\pi$
$181$	307.681			1.69989			0.849947	+	0.526867i	$0.176634\pi$
$182$	56.1378	−	56.1378i	0.308449	−	0.308449i
$183$	−2.05135	−	2.05135i	−0.0112096	−	0.0112096i
$184$			52.9044i			0.287524i
$185$		0			0
$186$	−66.1680			−0.355742
$187$	−27.5285	+	27.5285i	−0.147211	+	0.147211i
$188$	−18.7838	−	18.7838i	−0.0999139	−	0.0999139i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	71.4969			0.374329			0.187165	−	0.982329i	$-0.440070\pi$
$191$	71.4969			0.374329			0.187165	+	0.982329i	$0.440070\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	155.347	+	155.347i	0.804908	+	0.804908i	0.983858	−	0.178950i	$-0.0572701\pi$
$193$	155.347	+	155.347i	0.804908	+	0.804908i	−0.178950	+	0.983858i	$0.557270\pi$
$194$		−	183.017i		−	0.943385i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−190.520	+	190.520i	−0.967107	+	0.967107i	−0.999476	−	0.0323691i	$-0.989695\pi$
$197$	−190.520	+	190.520i	−0.967107	+	0.967107i	0.0323691	+	0.999476i	$0.489695\pi$
$198$	−17.2477	−	17.2477i	−0.0871093	−	0.0871093i
$199$		−	173.246i		−	0.870582i	−0.900290	−	0.435291i	$-0.856646\pi$
$199$		−	173.246i		−	0.870582i	0.900290	−	0.435291i	$-0.143354\pi$
$200$		0			0
$201$	−69.7883			−0.347205
$202$	−182.855	+	182.855i	−0.905223	+	0.905223i
$203$	−70.5809	−	70.5809i	−0.347689	−	0.347689i
$204$		−	23.4573i		−	0.114987i
$205$		0			0
$206$	93.2452			0.452647
$207$	39.6783	−	39.6783i	0.191683	−	0.191683i
$208$	60.0138	+	60.0138i	0.288528	+	0.288528i
$209$		−	100.046i		−	0.478689i
$210$		0			0
$211$	53.9193			0.255542			0.127771	−	0.991804i	$-0.459218\pi$
$211$	53.9193			0.255542			0.127771	+	0.991804i	$0.459218\pi$
$212$	−87.7991	+	87.7991i	−0.414147	+	0.414147i
$213$	57.8128	+	57.8128i	0.271422	+	0.271422i
$214$			115.130i			0.537992i
$215$		0			0
$216$	14.6969			0.0680414
$217$	50.5366	−	50.5366i	0.232888	−	0.232888i
$218$	205.254	+	205.254i	0.941533	+	0.941533i
$219$			76.4415i			0.349048i
$220$		0			0
$221$	−143.679			−0.650133
$222$	−27.8361	+	27.8361i	−0.125388	+	0.125388i
$223$	146.512	+	146.512i	0.657006	+	0.657006i	0.954671	−	0.297664i	$-0.0962076\pi$
$223$	146.512	+	146.512i	0.657006	+	0.657006i	−0.297664	+	0.954671i	$0.596208\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−65.2073			−0.288528
$227$	−162.897	+	162.897i	−0.717607	+	0.717607i	−0.968115	−	0.250508i	$-0.919402\pi$
$227$	−162.897	+	162.897i	−0.717607	+	0.717607i	0.250508	+	0.968115i	$0.419402\pi$
$228$	42.6252	+	42.6252i	0.186953	+	0.186953i
$229$		−	176.209i		−	0.769470i	−0.923027	−	0.384735i	$-0.874293\pi$
$229$		−	176.209i		−	0.769470i	0.923027	−	0.384735i	$-0.125707\pi$
$230$		0			0
$231$	26.3462			0.114053
$232$	75.4542	−	75.4542i	0.325234	−	0.325234i
$233$	18.3615	+	18.3615i	0.0788049	+	0.0788049i	0.745411	−	0.666606i	$-0.232253\pi$
$233$	18.3615	+	18.3615i	0.0788049	+	0.0788049i	−0.666606	+	0.745411i	$0.732253\pi$
$234$		−	90.0207i		−	0.384704i
$235$		0			0
$236$	−125.939			−0.533639
$237$	131.211	−	131.211i	0.553634	−	0.553634i
$238$	17.9158	+	17.9158i	0.0752767	+	0.0752767i
$239$		−	275.093i		−	1.15102i	−0.817795	−	0.575509i	$-0.804804\pi$
$239$		−	275.093i		−	1.15102i	0.817795	−	0.575509i	$-0.195196\pi$
$240$		0			0
$241$	338.925			1.40633			0.703164	−	0.711028i	$-0.251770\pi$
$241$	338.925			1.40633			0.703164	+	0.711028i	$0.251770\pi$
$242$	−87.9465	+	87.9465i	−0.363415	+	0.363415i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			3.34984i			0.0137288i
$245$		0			0
$246$	−130.043			−0.528629
$247$	261.085	−	261.085i	1.05702	−	1.05702i
$248$	54.0259	+	54.0259i	0.217846	+	0.217846i
$249$		−	44.6700i		−	0.179398i
$250$		0			0
$251$	72.1187			0.287326			0.143663	−	0.989627i	$-0.454112\pi$
$251$	72.1187			0.287326			0.143663	+	0.989627i	$0.454112\pi$
$252$	−11.2250	+	11.2250i	−0.0445435	+	0.0445435i
$253$	76.0397	+	76.0397i	0.300552	+	0.300552i
$254$		−	207.471i		−	0.816814i
$255$		0			0
$256$	16.0000			0.0625000
$257$	12.2256	−	12.2256i	0.0475703	−	0.0475703i	−0.682921	−	0.730492i	$-0.739291\pi$
$257$	12.2256	−	12.2256i	0.0475703	−	0.0475703i	0.730492	+	0.682921i	$0.239291\pi$
$258$	−90.8889	−	90.8889i	−0.352282	−	0.352282i
$259$		−	42.5204i		−	0.164171i
$260$		0			0
$261$	−113.181			−0.433645
$262$	157.999	−	157.999i	0.603049	−	0.603049i
$263$	−275.733	−	275.733i	−1.04842	−	1.04842i	−0.998767	−	0.0496495i	$-0.984190\pi$
$263$	−275.733	−	275.733i	−1.04842	−	1.04842i	−0.0496495	−	0.998767i	$-0.515810\pi$
$264$			28.1653i			0.106687i
$265$		0			0
$266$	−65.1110			−0.244778
$267$	−213.933	+	213.933i	−0.801247	+	0.801247i
$268$	56.9819	+	56.9819i	0.212619	+	0.212619i
$269$			275.988i			1.02598i	0.858395	+	0.512989i	$0.171462\pi$
$269$			275.988i			1.02598i	−0.858395	+	0.512989i	$0.828538\pi$
$270$		0			0
$271$	295.698			1.09114			0.545568	−	0.838067i	$-0.316314\pi$
$271$	295.698			1.09114			0.545568	+	0.838067i	$0.316314\pi$
$272$	−19.1528	+	19.1528i	−0.0704149	+	0.0704149i
$273$	68.7544	+	68.7544i	0.251848	+	0.251848i
$274$		−	73.9148i		−	0.269762i
$275$		0			0
$276$	−64.7944			−0.234762
$277$	21.4676	−	21.4676i	0.0775005	−	0.0775005i	−0.667294	−	0.744794i	$-0.732548\pi$
$277$	21.4676	−	21.4676i	0.0775005	−	0.0775005i	0.744794	+	0.667294i	$0.232548\pi$
$278$	132.183	+	132.183i	0.475480	+	0.475480i
$279$		−	81.0389i		−	0.290462i
$280$		0			0
$281$	74.2011			0.264061			0.132030	−	0.991246i	$-0.457850\pi$
$281$	74.2011			0.264061			0.132030	+	0.991246i	$0.457850\pi$
$282$	23.0054	−	23.0054i	0.0815793	−	0.0815793i
$283$	322.473	+	322.473i	1.13948	+	1.13948i	0.988543	+	0.150937i	$0.0482289\pi$
$283$	322.473	+	322.473i	1.13948	+	1.13948i	0.150937	+	0.988543i	$0.451771\pi$
$284$		−	94.4079i		−	0.332422i
$285$		0			0
$286$	172.516			0.603203
$287$	99.3217	−	99.3217i	0.346069	−	0.346069i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$			243.146i			0.841336i
$290$		0			0
$291$	224.149			0.770271
$292$	62.4143	−	62.4143i	0.213747	−	0.213747i
$293$	145.754	+	145.754i	0.497456	+	0.497456i	0.910645	−	0.413189i	$-0.135585\pi$
$293$	145.754	+	145.754i	0.497456	+	0.497456i	−0.413189	+	0.910645i	$0.635585\pi$
$294$		−	17.1464i		−	0.0583212i
$295$		0			0
$296$	45.4562			0.153568
$297$	21.1240	−	21.1240i	0.0711245	−	0.0711245i
$298$	−255.329	−	255.329i	−0.856809	−	0.856809i
$299$			396.874i			1.32734i
$300$		0			0
$301$	138.835			0.461246
$302$	−210.524	+	210.524i	−0.697098	+	0.697098i
$303$	−223.951	−	223.951i	−0.739111	−	0.739111i
$304$		−	69.6066i		−	0.228969i
$305$		0			0
$306$	28.7293			0.0938865
$307$	308.104	−	308.104i	1.00360	−	1.00360i	0.00360237	−	0.999994i	$-0.498853\pi$
$307$	308.104	−	308.104i	1.00360	−	1.00360i	0.999994	−	0.00360237i	$-0.00114667\pi$
$308$	−21.5116	−	21.5116i	−0.0698429	−	0.0698429i
$309$			114.202i			0.369584i
$310$		0			0
$311$	−29.1191			−0.0936304			−0.0468152	−	0.998904i	$-0.514907\pi$
$311$	−29.1191			−0.0936304			−0.0468152	+	0.998904i	$0.514907\pi$
$312$	−73.5016	+	73.5016i	−0.235582	+	0.235582i
$313$	−12.1714	−	12.1714i	−0.0388863	−	0.0388863i	0.687396	−	0.726283i	$-0.258754\pi$
$313$	−12.1714	−	12.1714i	−0.0388863	−	0.0388863i	−0.726283	+	0.687396i	$0.758754\pi$
$314$		−	363.342i		−	1.15714i
$315$		0			0
$316$	−214.267			−0.678061
$317$	−219.192	+	219.192i	−0.691456	+	0.691456i	−0.962552	−	0.271096i	$-0.912614\pi$
$317$	−219.192	+	219.192i	−0.691456	+	0.691456i	0.271096	+	0.962552i	$0.412614\pi$
$318$	−107.532	−	107.532i	−0.338150	−	0.338150i
$319$		−	216.901i		−	0.679941i
$320$		0			0
$321$	−141.005			−0.439269
$322$	49.4876	−	49.4876i	0.153688	−	0.153688i
$323$	83.3228	+	83.3228i	0.257965	+	0.257965i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−311.127			−0.954376
$327$	−251.384	+	251.384i	−0.768759	+	0.768759i
$328$	106.179	+	106.179i	0.323718	+	0.323718i
$329$			35.1413i			0.106812i
$330$		0			0
$331$	276.111			0.834171			0.417086	−	0.908867i	$-0.363052\pi$
$331$	276.111			0.834171			0.417086	+	0.908867i	$0.363052\pi$
$332$	−36.4729	+	36.4729i	−0.109858	+	0.109858i
$333$	−34.0921	−	34.0921i	−0.102379	−	0.102379i
$334$			152.158i			0.455562i
$335$		0			0
$336$	18.3303			0.0545545
$337$	−276.393	+	276.393i	−0.820157	+	0.820157i	−0.986130	−	0.165973i	$-0.946923\pi$
$337$	−276.393	+	276.393i	−0.820157	+	0.820157i	0.165973	+	0.986130i	$0.446923\pi$
$338$	281.207	+	281.207i	0.831973	+	0.831973i
$339$		−	79.8623i		−	0.235582i
$340$		0			0
$341$	155.303			0.455435
$342$	−52.2050	+	52.2050i	−0.152646	+	0.152646i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$			148.421i			0.431456i
$345$		0			0
$346$	−57.8647			−0.167239
$347$	158.084	−	158.084i	0.455573	−	0.455573i	−0.441626	−	0.897199i	$-0.645598\pi$
$347$	158.084	−	158.084i	0.455573	−	0.455573i	0.897199	+	0.441626i	$0.145598\pi$
$348$	92.4121	+	92.4121i	0.265552	+	0.265552i
$349$		−	452.412i		−	1.29631i	−0.761508	−	0.648155i	$-0.775541\pi$
$349$		−	452.412i		−	1.29631i	0.761508	−	0.648155i	$-0.224459\pi$
$350$		0			0
$351$	110.252			0.314109
$352$	22.9969	−	22.9969i	0.0653320	−	0.0653320i
$353$	−481.681	−	481.681i	−1.36453	−	1.36453i	−0.868039	−	0.496495i	$-0.834620\pi$
$353$	−481.681	−	481.681i	−1.36453	−	1.36453i	−0.496495	−	0.868039i	$-0.665380\pi$
$354$		−	154.243i		−	0.435714i
$355$		0			0
$356$	349.351			0.981323
$357$	−21.9423	+	21.9423i	−0.0614631	+	0.0614631i
$358$	126.849	+	126.849i	0.354327	+	0.354327i
$359$		−	485.514i		−	1.35241i	−0.736716	−	0.676203i	$-0.763624\pi$
$359$		−	485.514i		−	1.35241i	0.736716	−	0.676203i	$-0.236376\pi$
$360$		0			0
$361$	58.1823			0.161170
$362$	307.681	−	307.681i	0.849947	−	0.849947i
$363$	−107.712	−	107.712i	−0.296727	−	0.296727i
$364$		−	112.276i		−	0.308449i
$365$		0			0
$366$	−4.10270			−0.0112096
$367$	−205.331	+	205.331i	−0.559486	+	0.559486i	−0.929161	−	0.369675i	$-0.879469\pi$
$367$	−205.331	+	205.331i	−0.559486	+	0.559486i	0.369675	+	0.929161i	$0.379469\pi$
$368$	52.9044	+	52.9044i	0.143762	+	0.143762i
$369$		−	159.269i		−	0.431623i
$370$		0			0
$371$	164.257			0.442742
$372$	−66.1680	+	66.1680i	−0.177871	+	0.177871i
$373$	24.9803	+	24.9803i	0.0669714	+	0.0669714i	0.739799	−	0.672828i	$-0.234921\pi$
$373$	24.9803	+	24.9803i	0.0669714	+	0.0669714i	−0.672828	+	0.739799i	$0.734921\pi$
$374$			55.0569i			0.147211i
$375$		0			0
$376$	−37.5676			−0.0999139
$377$	566.037	−	566.037i	1.50142	−	1.50142i
$378$	−13.7477	−	13.7477i	−0.0363696	−	0.0363696i
$379$			356.423i			0.940429i	0.882552	+	0.470215i	$0.155823\pi$
$379$			356.423i			0.940429i	−0.882552	+	0.470215i	$0.844177\pi$
$380$		0			0
$381$	254.099			0.666926
$382$	71.4969	−	71.4969i	0.187165	−	0.187165i
$383$	−480.677	−	480.677i	−1.25503	−	1.25503i	−0.953436	−	0.301596i	$-0.902481\pi$
$383$	−480.677	−	480.677i	−1.25503	−	1.25503i	−0.301596	−	0.953436i	$-0.597519\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	310.695			0.804908
$387$	111.316	−	111.316i	0.287637	−	0.287637i
$388$	−183.017	−	183.017i	−0.471693	−	0.471693i
$389$			169.784i			0.436461i	0.975897	+	0.218231i	$0.0700285\pi$
$389$			169.784i			0.436461i	−0.975897	+	0.218231i	$0.929971\pi$
$390$		0			0
$391$	−126.659			−0.323935
$392$	−14.0000	+	14.0000i	−0.0357143	+	0.0357143i
$393$	193.508	+	193.508i	0.492387	+	0.492387i
$394$			381.040i			0.967107i
$395$		0			0
$396$	−34.4953			−0.0871093
$397$	66.1208	−	66.1208i	0.166551	−	0.166551i	−0.618910	−	0.785462i	$-0.712426\pi$
$397$	66.1208	−	66.1208i	0.166551	−	0.166551i	0.785462	+	0.618910i	$0.212426\pi$
$398$	−173.246	−	173.246i	−0.435291	−	0.435291i
$399$		−	79.7444i		−	0.199861i
$400$		0			0
$401$	−213.860			−0.533318			−0.266659	−	0.963791i	$-0.585920\pi$
$401$	−213.860			−0.533318			−0.266659	+	0.963791i	$0.585920\pi$
$402$	−69.7883	+	69.7883i	−0.173603	+	0.173603i
$403$	405.288	+	405.288i	1.00568	+	1.00568i
$404$			365.710i			0.905223i
$405$		0			0
$406$	−141.162			−0.347689
$407$	65.3344	−	65.3344i	0.160527	−	0.160527i
$408$	−23.4573	−	23.4573i	−0.0574935	−	0.0574935i
$409$			300.366i			0.734391i	0.930144	+	0.367196i	$0.119682\pi$
$409$			300.366i			0.734391i	−0.930144	+	0.367196i	$0.880318\pi$
$410$		0			0
$411$	90.5267			0.220260
$412$	93.2452	−	93.2452i	0.226323	−	0.226323i
$413$	117.805	+	117.805i	0.285242	+	0.285242i
$414$		−	79.3566i		−	0.191683i
$415$		0			0
$416$	120.028			0.288528
$417$	−161.891	+	161.891i	−0.388228	+	0.388228i
$418$	−100.046	−	100.046i	−0.239344	−	0.239344i
$419$		−	696.907i		−	1.66326i	−0.555328	−	0.831632i	$-0.687407\pi$
$419$		−	696.907i		−	1.66326i	0.555328	−	0.831632i	$-0.312593\pi$
$420$		0			0
$421$	−114.980			−0.273111			−0.136555	−	0.990632i	$-0.543603\pi$
$421$	−114.980			−0.273111			−0.136555	+	0.990632i	$0.543603\pi$
$422$	53.9193	−	53.9193i	0.127771	−	0.127771i
$423$	28.1757	+	28.1757i	0.0666092	+	0.0666092i
$424$			175.598i			0.414147i
$425$		0			0
$426$	115.626			0.271422
$427$	3.13349	−	3.13349i	0.00733838	−	0.00733838i
$428$	115.130	+	115.130i	0.268996	+	0.268996i
$429$			211.288i			0.492513i
$430$		0			0
$431$	−724.694			−1.68143			−0.840713	−	0.541481i	$-0.817864\pi$
$431$	−724.694			−1.68143			−0.840713	+	0.541481i	$0.817864\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−100.327	−	100.327i	−0.231703	−	0.231703i	0.581700	−	0.813403i	$-0.302388\pi$
$433$	−100.327	−	100.327i	−0.231703	−	0.231703i	−0.813403	+	0.581700i	$0.802388\pi$
$434$		−	101.073i		−	0.232888i
$435$		0			0
$436$	410.509			0.941533
$437$	230.156	−	230.156i	0.526673	−	0.526673i
$438$	76.4415	+	76.4415i	0.174524	+	0.174524i
$439$		−	685.890i		−	1.56239i	−0.624286	−	0.781195i	$-0.714610\pi$
$439$		−	685.890i		−	1.56239i	0.624286	−	0.781195i	$-0.285390\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	−143.679	+	143.679i	−0.325066	+	0.325066i
$443$	−339.752	−	339.752i	−0.766935	−	0.766935i	0.210631	−	0.977566i	$-0.432448\pi$
$443$	−339.752	−	339.752i	−0.766935	−	0.766935i	−0.977566	+	0.210631i	$0.932448\pi$
$444$			55.6722i			0.125388i
$445$		0			0
$446$	293.025			0.657006
$447$	312.713	−	312.713i	0.699581	−	0.699581i
$448$	−14.9666	−	14.9666i	−0.0334077	−	0.0334077i
$449$		−	226.637i		−	0.504758i	−0.967628	−	0.252379i	$-0.918787\pi$
$449$		−	226.637i		−	0.504758i	0.967628	−	0.252379i	$-0.0812130\pi$
$450$		0			0
$451$	305.224			0.676772
$452$	−65.2073	+	65.2073i	−0.144264	+	0.144264i
$453$	−257.838	−	257.838i	−0.569178	−	0.569178i
$454$			325.794i			0.717607i
$455$		0			0
$456$	85.2504			0.186953
$457$	266.282	−	266.282i	0.582675	−	0.582675i	−0.352963	−	0.935637i	$-0.614826\pi$
$457$	266.282	−	266.282i	0.582675	−	0.582675i	0.935637	+	0.352963i	$0.114826\pi$
$458$	−176.209	−	176.209i	−0.384735	−	0.384735i
$459$			35.1860i			0.0766580i
$460$		0			0
$461$	−121.199			−0.262905			−0.131453	−	0.991322i	$-0.541964\pi$
$461$	−121.199			−0.262905			−0.131453	+	0.991322i	$0.541964\pi$
$462$	26.3462	−	26.3462i	0.0570265	−	0.0570265i
$463$	565.604	+	565.604i	1.22161	+	1.22161i	0.967061	+	0.254547i	$0.0819262\pi$
$463$	565.604	+	565.604i	1.22161	+	1.22161i	0.254547	+	0.967061i	$0.418074\pi$
$464$		−	150.908i		−	0.325234i
$465$		0			0
$466$	36.7231			0.0788049
$467$	279.536	−	279.536i	0.598578	−	0.598578i	−0.341356	−	0.939934i	$-0.610886\pi$
$467$	279.536	−	279.536i	0.598578	−	0.598578i	0.939934	+	0.341356i	$0.110886\pi$
$468$	−90.0207	−	90.0207i	−0.192352	−	0.192352i
$469$		−	106.603i		−	0.227299i
$470$		0			0
$471$	445.001			0.944801
$472$	−125.939	+	125.939i	−0.266819	+	0.266819i
$473$	213.326	+	213.326i	0.451006	+	0.451006i
$474$		−	262.423i		−	0.553634i
$475$		0			0
$476$	35.8317			0.0752767
$477$	131.699	−	131.699i	0.276098	−	0.276098i
$478$	−275.093	−	275.093i	−0.575509	−	0.575509i
$479$		−	101.987i		−	0.212916i	−0.994317	−	0.106458i	$-0.966049\pi$
$479$		−	101.987i		−	0.212916i	0.994317	−	0.106458i	$-0.0339510\pi$
$480$		0			0
$481$	341.000			0.708939
$482$	338.925	−	338.925i	0.703164	−	0.703164i
$483$	60.6096	+	60.6096i	0.125486	+	0.125486i
$484$			175.893i			0.363415i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	−250.272	+	250.272i	−0.513907	+	0.513907i	−0.915721	−	0.401815i	$-0.868380\pi$
$487$	−250.272	+	250.272i	−0.513907	+	0.513907i	0.401815	+	0.915721i	$0.368380\pi$
$488$	3.34984	+	3.34984i	0.00686442	+	0.00686442i
$489$		−	381.051i		−	0.779245i
$490$		0			0
$491$	−648.021			−1.31980			−0.659899	−	0.751355i	$-0.729401\pi$
$491$	−648.021			−1.31980			−0.659899	+	0.751355i	$0.729401\pi$
$492$	−130.043	+	130.043i	−0.264314	+	0.264314i
$493$	180.645	+	180.645i	0.366421	+	0.366421i
$494$		−	522.170i		−	1.05702i
$495$		0			0
$496$	108.052			0.217846
$497$	−88.3105	+	88.3105i	−0.177687	+	0.177687i
$498$	−44.6700	−	44.6700i	−0.0896989	−	0.0896989i
$499$		−	377.798i		−	0.757110i	−0.925579	−	0.378555i	$-0.876421\pi$
$499$		−	377.798i		−	0.757110i	0.925579	−	0.378555i	$-0.123579\pi$
$500$		0			0
$501$	−186.354			−0.371965
$502$	72.1187	−	72.1187i	0.143663	−	0.143663i
$503$	221.145	+	221.145i	0.439651	+	0.439651i	0.891895	−	0.452243i	$-0.149376\pi$
$503$	221.145	+	221.145i	0.439651	+	0.439651i	−0.452243	+	0.891895i	$0.649376\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	152.079			0.300552
$507$	−344.407	+	344.407i	−0.679303	+	0.679303i
$508$	−207.471	−	207.471i	−0.408407	−	0.408407i
$509$			586.753i			1.15276i	0.817183	+	0.576378i	$0.195535\pi$
$509$			586.753i			1.15276i	−0.817183	+	0.576378i	$0.804465\pi$
$510$		0			0
$511$	−116.766			−0.228506
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−63.9378	−	63.9378i	−0.124635	−	0.124635i
$514$		−	24.4511i		−	0.0475703i
$515$		0			0
$516$	−181.778			−0.352282
$517$	−53.9961	+	53.9961i	−0.104441	+	0.104441i
$518$	−42.5204	−	42.5204i	−0.0820857	−	0.0820857i
$519$		−	70.8694i		−	0.136550i
$520$		0			0
$521$	−466.427			−0.895253			−0.447626	−	0.894221i	$-0.647731\pi$
$521$	−466.427			−0.895253			−0.447626	+	0.894221i	$0.647731\pi$
$522$	−113.181	+	113.181i	−0.216822	+	0.216822i
$523$	−303.656	−	303.656i	−0.580604	−	0.580604i	0.354465	−	0.935069i	$-0.384663\pi$
$523$	−303.656	−	303.656i	−0.580604	−	0.580604i	−0.935069	+	0.354465i	$0.884663\pi$
$524$		−	315.998i		−	0.603049i
$525$		0			0
$526$	−551.467			−1.04842
$527$	−129.344	+	129.344i	−0.245434	+	0.245434i
$528$	28.1653	+	28.1653i	0.0533434	+	0.0533434i
$529$		−	179.140i		−	0.338639i
$530$		0			0
$531$	188.908			0.355759
$532$	−65.1110	+	65.1110i	−0.122389	+	0.122389i
$533$	796.528	+	796.528i	1.49442	+	1.49442i
$534$			427.866i			0.801247i
$535$		0			0
$536$	113.964			0.212619
$537$	−155.358	+	155.358i	−0.289307	+	0.289307i
$538$	275.988	+	275.988i	0.512989	+	0.512989i
$539$			40.2445i			0.0746652i
$540$		0			0
$541$	465.245			0.859973			0.429986	−	0.902835i	$-0.358518\pi$
$541$	465.245			0.859973			0.429986	+	0.902835i	$0.358518\pi$
$542$	295.698	−	295.698i	0.545568	−	0.545568i
$543$	376.831	+	376.831i	0.693979	+	0.693979i
$544$			38.3057i			0.0704149i
$545$		0			0
$546$	137.509			0.251848
$547$	−492.529	+	492.529i	−0.900419	+	0.900419i	−0.995472	−	0.0950533i	$-0.969698\pi$
$547$	−492.529	+	492.529i	−0.900419	+	0.900419i	0.0950533	+	0.995472i	$0.469698\pi$
$548$	−73.9148	−	73.9148i	−0.134881	−	0.134881i
$549$		−	5.02476i		−	0.00915257i
$550$		0			0
$551$	−656.514			−1.19150
$552$	−64.7944	+	64.7944i	−0.117381	+	0.117381i
$553$	200.429	+	200.429i	0.362439	+	0.362439i
$554$		−	42.9353i		−	0.0775005i
$555$		0			0
$556$	264.367			0.475480
$557$	−395.342	+	395.342i	−0.709771	+	0.709771i	−0.966487	−	0.256716i	$-0.917359\pi$
$557$	−395.342	+	395.342i	−0.709771	+	0.709771i	0.256716	+	0.966487i	$0.417359\pi$
$558$	−81.0389	−	81.0389i	−0.145231	−	0.145231i
$559$			1113.41i			1.99179i
$560$		0			0
$561$	−67.4307			−0.120197
$562$	74.2011	−	74.2011i	0.132030	−	0.132030i
$563$	−447.005	−	447.005i	−0.793971	−	0.793971i	0.188167	−	0.982137i	$-0.439746\pi$
$563$	−447.005	−	447.005i	−0.793971	−	0.793971i	−0.982137	+	0.188167i	$0.939746\pi$
$564$		−	46.0107i		−	0.0815793i
$565$		0			0
$566$	644.946			1.13948
$567$	16.8375	−	16.8375i	0.0296957	−	0.0296957i
$568$	−94.4079	−	94.4079i	−0.166211	−	0.166211i
$569$			39.2969i			0.0690631i	0.999404	+	0.0345316i	$0.0109939\pi$
$569$			39.2969i			0.0690631i	−0.999404	+	0.0345316i	$0.989006\pi$
$570$		0			0
$571$	−824.326			−1.44365			−0.721826	−	0.692074i	$-0.756697\pi$
$571$	−824.326			−1.44365			−0.721826	+	0.692074i	$0.756697\pi$
$572$	172.516	−	172.516i	0.301602	−	0.301602i
$573$	87.5654	+	87.5654i	0.152819	+	0.152819i
$574$		−	198.643i		−	0.346069i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−645.287	+	645.287i	−1.11835	+	1.11835i	−0.126365	+	0.991984i	$0.540331\pi$
$577$	−645.287	+	645.287i	−1.11835	+	1.11835i	−0.991984	+	0.126365i	$0.959669\pi$
$578$	243.146	+	243.146i	0.420668	+	0.420668i
$579$			380.522i			0.657205i
$580$		0			0
$581$	68.2346			0.117443
$582$	224.149	−	224.149i	0.385135	−	0.385135i
$583$	252.388	+	252.388i	0.432913	+	0.432913i
$584$		−	124.829i		−	0.213747i
$585$		0			0
$586$	291.509			0.497456
$587$	−512.978	+	512.978i	−0.873898	+	0.873898i	−0.992895	−	0.118997i	$-0.962032\pi$
$587$	−512.978	+	512.978i	−0.873898	+	0.873898i	0.118997	+	0.992895i	$0.462032\pi$
$588$	−17.1464	−	17.1464i	−0.0291606	−	0.0291606i
$589$		−	470.070i		−	0.798082i
$590$		0			0
$591$	−466.677			−0.789639
$592$	45.4562	−	45.4562i	0.0767841	−	0.0767841i
$593$	379.753	+	379.753i	0.640393	+	0.640393i	0.950652	−	0.310259i	$-0.100416\pi$
$593$	379.753	+	379.753i	0.640393	+	0.640393i	−0.310259	+	0.950652i	$0.600416\pi$
$594$		−	42.2479i		−	0.0711245i
$595$		0			0
$596$	−510.658			−0.856809
$597$	212.182	−	212.182i	0.355414	−	0.355414i
$598$	396.874	+	396.874i	0.663669	+	0.663669i
$599$			167.160i			0.279065i	0.990218	+	0.139532i	$0.0445599\pi$
$599$			167.160i			0.279065i	−0.990218	+	0.139532i	$0.955440\pi$
$600$		0			0
$601$	649.442			1.08060			0.540302	−	0.841472i	$-0.318310\pi$
$601$	649.442			1.08060			0.540302	+	0.841472i	$0.318310\pi$
$602$	138.835	−	138.835i	0.230623	−	0.230623i
$603$	−85.4728	−	85.4728i	−0.141746	−	0.141746i
$604$			421.047i			0.697098i
$605$		0			0
$606$	−447.901			−0.739111
$607$	342.997	−	342.997i	0.565069	−	0.565069i	−0.365674	−	0.930743i	$-0.619161\pi$
$607$	342.997	−	342.997i	0.565069	−	0.565069i	0.930743	+	0.365674i	$0.119161\pi$
$608$	−69.6066	−	69.6066i	−0.114485	−	0.114485i
$609$		−	172.887i		−	0.283887i
$610$		0			0
$611$	−281.822			−0.461247
$612$	28.7293	−	28.7293i	0.0469432	−	0.0469432i
$613$	311.569	+	311.569i	0.508270	+	0.508270i	0.913995	−	0.405725i	$-0.132981\pi$
$613$	311.569	+	311.569i	0.508270	+	0.508270i	−0.405725	+	0.913995i	$0.632981\pi$
$614$		−	616.208i		−	1.00360i
$615$		0			0
$616$	−43.0232			−0.0698429
$617$	−442.165	+	442.165i	−0.716636	+	0.716636i	−0.967915	−	0.251279i	$-0.919149\pi$
$617$	−442.165	+	442.165i	−0.716636	+	0.716636i	0.251279	+	0.967915i	$0.419149\pi$
$618$	114.202	+	114.202i	0.184792	+	0.184792i
$619$			375.146i			0.606052i	0.952982	+	0.303026i	$0.0979968\pi$
$619$			375.146i			0.606052i	−0.952982	+	0.303026i	$0.902003\pi$
$620$		0			0
$621$	97.1916			0.156508
$622$	−29.1191	+	29.1191i	−0.0468152	+	0.0468152i
$623$	−326.788	−	326.788i	−0.524539	−	0.524539i
$624$			147.003i			0.235582i
$625$		0			0
$626$	−24.3428			−0.0388863
$627$	122.531	−	122.531i	0.195424	−	0.195424i
$628$	−363.342	−	363.342i	−0.578570	−	0.578570i
$629$			108.827i			0.173016i
$630$		0			0
$631$	−973.951			−1.54350			−0.771752	−	0.635924i	$-0.780619\pi$
$631$	−973.951			−1.54350			−0.771752	+	0.635924i	$0.780619\pi$
$632$	−214.267	+	214.267i	−0.339030	+	0.339030i
$633$	66.0374	+	66.0374i	0.104324	+	0.104324i
$634$			438.383i			0.691456i
$635$		0			0
$636$	−215.063			−0.338150
$637$	−105.024	+	105.024i	−0.164873	+	0.164873i
$638$	−216.901	−	216.901i	−0.339971	−	0.339971i
$639$			141.612i			0.221615i
$640$		0			0
$641$	487.398			0.760371			0.380185	−	0.924910i	$-0.375860\pi$
$641$	487.398			0.760371			0.380185	+	0.924910i	$0.375860\pi$
$642$	−141.005	+	141.005i	−0.219634	+	0.219634i
$643$	−554.739	−	554.739i	−0.862736	−	0.862736i	0.128919	−	0.991655i	$-0.458849\pi$
$643$	−554.739	−	554.739i	−0.862736	−	0.862736i	−0.991655	+	0.128919i	$0.958849\pi$
$644$		−	98.9751i		−	0.153688i
$645$		0			0
$646$	166.646			0.257965
$647$	−337.971	+	337.971i	−0.522367	+	0.522367i	−0.918285	−	0.395919i	$-0.870426\pi$
$647$	−337.971	+	337.971i	−0.522367	+	0.522367i	0.395919	+	0.918285i	$0.370426\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			362.025i			0.557819i
$650$		0			0
$651$	123.789			0.190152
$652$	−311.127	+	311.127i	−0.477188	+	0.477188i
$653$	−379.091	−	379.091i	−0.580537	−	0.580537i	0.354514	−	0.935051i	$-0.384646\pi$
$653$	−379.091	−	379.091i	−0.580537	−	0.580537i	−0.935051	+	0.354514i	$0.884646\pi$
$654$			502.768i			0.768759i
$655$		0			0
$656$	212.359			0.323718
$657$	−93.6214	+	93.6214i	−0.142498	+	0.142498i
$658$	35.1413	+	35.1413i	0.0534062	+	0.0534062i
$659$			932.566i			1.41512i	0.706652	+	0.707561i	$0.250205\pi$
$659$			932.566i			1.41512i	−0.706652	+	0.707561i	$0.749795\pi$
$660$		0			0
$661$	435.268			0.658500			0.329250	−	0.944243i	$-0.393204\pi$
$661$	435.268			0.658500			0.329250	+	0.944243i	$0.393204\pi$
$662$	276.111	−	276.111i	0.417086	−	0.417086i
$663$	−175.971	−	175.971i	−0.265416	−	0.265416i
$664$			72.9459i			0.109858i
$665$		0			0
$666$	−68.1843			−0.102379
$667$	498.983	−	498.983i	0.748100	−	0.748100i
$668$	152.158	+	152.158i	0.227781	+	0.227781i
$669$			358.881i			0.536443i
$670$		0			0
$671$	9.62948			0.0143509
$672$	18.3303	−	18.3303i	0.0272772	−	0.0272772i
$673$	−268.394	−	268.394i	−0.398803	−	0.398803i	0.479008	−	0.877811i	$-0.340997\pi$
$673$	−268.394	−	268.394i	−0.398803	−	0.398803i	−0.877811	+	0.479008i	$0.840997\pi$
$674$			552.786i			0.820157i
$675$		0			0
$676$	562.414			0.831973
$677$	317.565	−	317.565i	0.469076	−	0.469076i	−0.432539	−	0.901615i	$-0.642382\pi$
$677$	317.565	−	317.565i	0.469076	−	0.469076i	0.901615	+	0.432539i	$0.142382\pi$
$678$	−79.8623	−	79.8623i	−0.117791	−	0.117791i
$679$			342.393i			0.504261i
$680$		0			0
$681$	−399.014			−0.585924
$682$	155.303	−	155.303i	0.227718	−	0.227718i
$683$	−750.781	−	750.781i	−1.09924	−	1.09924i	−0.994500	−	0.104741i	$-0.966599\pi$
$683$	−750.781	−	750.781i	−1.09924	−	1.09924i	−0.104741	−	0.994500i	$-0.533401\pi$
$684$			104.410i			0.152646i
$685$		0			0
$686$	26.1916			0.0381802
$687$	215.811	−	215.811i	0.314135	−	0.314135i
$688$	148.421	+	148.421i	0.215728	+	0.215728i
$689$			1317.29i			1.91189i
$690$		0			0
$691$	−630.352			−0.912231			−0.456116	−	0.889921i	$-0.650760\pi$
$691$	−630.352			−0.912231			−0.456116	+	0.889921i	$0.650760\pi$
$692$	−57.8647	+	57.8647i	−0.0836194	+	0.0836194i
$693$	32.2674	+	32.2674i	0.0465619	+	0.0465619i
$694$		−	316.168i		−	0.455573i
$695$		0			0
$696$	184.824			0.265552
$697$	−254.205	+	254.205i	−0.364712	+	0.364712i
$698$	−452.412	−	452.412i	−0.648155	−	0.648155i
$699$			44.9764i			0.0643440i
$700$		0			0
$701$	−1143.23			−1.63085			−0.815425	−	0.578863i	$-0.803497\pi$
$701$	−1143.23			−1.63085			−0.815425	+	0.578863i	$0.803497\pi$
$702$	110.252	−	110.252i	0.157055	−	0.157055i
$703$	−197.753	−	197.753i	−0.281299	−	0.281299i
$704$		−	45.9937i		−	0.0653320i
$705$		0			0
$706$	−963.362			−1.36453
$707$	342.090	−	342.090i	0.483862	−	0.483862i
$708$	−154.243	−	154.243i	−0.217857	−	0.217857i
$709$		−	120.909i		−	0.170535i	−0.996358	−	0.0852674i	$-0.972826\pi$
$709$		−	120.909i		−	0.170535i	0.996358	−	0.0852674i	$-0.0271745\pi$
$710$		0			0
$711$	321.401			0.452040
$712$	349.351	−	349.351i	0.490661	−	0.490661i
$713$	357.276	+	357.276i	0.501089	+	0.501089i
$714$			43.8847i			0.0614631i
$715$		0			0
$716$	253.698			0.354327
$717$	336.919	−	336.919i	0.469901	−	0.469901i
$718$	−485.514	−	485.514i	−0.676203	−	0.676203i
$719$			157.658i			0.219274i	0.993972	+	0.109637i	$0.0349688\pi$
$719$			157.658i			0.219274i	−0.993972	+	0.109637i	$0.965031\pi$
$720$		0			0
$721$	−174.446			−0.241950
$722$	58.1823	−	58.1823i	0.0805849	−	0.0805849i
$723$	415.097	+	415.097i	0.574131	+	0.574131i
$724$		−	615.362i		−	0.849947i
$725$		0			0
$726$	−215.424			−0.296727
$727$	−45.5944	+	45.5944i	−0.0627159	+	0.0627159i	−0.737769	−	0.675053i	$-0.764121\pi$
$727$	−45.5944	+	45.5944i	−0.0627159	+	0.0627159i	0.675053	+	0.737769i	$0.264121\pi$
$728$	−112.276	−	112.276i	−0.154225	−	0.154225i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−355.335			−0.486095
$732$	−4.10270	+	4.10270i	−0.00560478	+	0.00560478i
$733$	−5.02444	−	5.02444i	−0.00685462	−	0.00685462i	0.703671	−	0.710526i	$-0.251543\pi$
$733$	−5.02444	−	5.02444i	−0.00685462	−	0.00685462i	−0.710526	+	0.703671i	$0.751543\pi$
$734$			410.663i			0.559486i
$735$		0			0
$736$	105.809			0.143762
$737$	163.801	−	163.801i	0.222253	−	0.222253i
$738$	−159.269	−	159.269i	−0.215812	−	0.215812i
$739$			1207.29i			1.63368i	0.576865	+	0.816839i	$0.304276\pi$
$739$			1207.29i			1.63368i	−0.576865	+	0.816839i	$0.695724\pi$
$740$		0			0
$741$	639.525			0.863056
$742$	164.257	−	164.257i	0.221371	−	0.221371i
$743$	162.402	+	162.402i	0.218577	+	0.218577i	0.807898	−	0.589322i	$-0.200605\pi$
$743$	162.402	+	162.402i	0.218577	+	0.218577i	−0.589322	+	0.807898i	$0.700605\pi$
$744$			132.336i			0.177871i
$745$		0			0
$746$	49.9606			0.0669714
$747$	54.7094	−	54.7094i	0.0732388	−	0.0732388i
$748$	55.0569	+	55.0569i	0.0736055	+	0.0736055i
$749$		−	215.389i		−	0.287569i
$750$		0			0
$751$	−1054.43			−1.40404			−0.702020	−	0.712157i	$-0.747718\pi$
$751$	−1054.43			−1.40404			−0.702020	+	0.712157i	$0.747718\pi$
$752$	−37.5676	+	37.5676i	−0.0499569	+	0.0499569i
$753$	88.3270	+	88.3270i	0.117300	+	0.117300i
$754$		−	1132.07i		−	1.50142i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	−166.416	+	166.416i	−0.219836	+	0.219836i	−0.808429	−	0.588593i	$-0.799682\pi$
$757$	−166.416	+	166.416i	−0.219836	+	0.219836i	0.588593	+	0.808429i	$0.299682\pi$
$758$	356.423	+	356.423i	0.470215	+	0.470215i
$759$			186.259i			0.245400i
$760$		0			0
$761$	1422.52			1.86928			0.934640	−	0.355596i	$-0.115722\pi$
$761$	1422.52			1.86928			0.934640	+	0.355596i	$0.115722\pi$
$762$	254.099	−	254.099i	0.333463	−	0.333463i
$763$	−383.996	−	383.996i	−0.503271	−	0.503271i
$764$		−	142.994i		−	0.187165i
$765$		0			0
$766$	−961.354			−1.25503
$767$	−944.758	+	944.758i	−1.23176	+	1.23176i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$			502.250i			0.653121i	0.945176	+	0.326560i	$0.105890\pi$
$769$			502.250i			0.653121i	−0.945176	+	0.326560i	$0.894110\pi$
$770$		0			0
$771$	29.9464			0.0388410
$772$	310.695	−	310.695i	0.402454	−	0.402454i
$773$	339.873	+	339.873i	0.439681	+	0.439681i	0.891904	−	0.452224i	$-0.149369\pi$
$773$	339.873	+	339.873i	0.439681	+	0.439681i	−0.452224	+	0.891904i	$0.649369\pi$
$774$		−	222.631i		−	0.287637i
$775$		0			0
$776$	−366.033			−0.471693
$777$	52.0766	−	52.0766i	0.0670227	−	0.0670227i
$778$	169.784	+	169.784i	0.218231	+	0.218231i
$779$		−	923.848i		−	1.18594i
$780$		0			0
$781$	−271.386			−0.347485
$782$	−126.659	+	126.659i	−0.161968	+	0.161968i
$783$	−138.618	−	138.618i	−0.177035	−	0.177035i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	387.017			0.492387
$787$	−752.550	+	752.550i	−0.956227	+	0.956227i	−0.999081	−	0.0428547i	$-0.986355\pi$
$787$	−752.550	+	752.550i	−0.956227	+	0.956227i	0.0428547	+	0.999081i	$0.486355\pi$
$788$	381.040	+	381.040i	0.483553	+	0.483553i
$789$		−	675.406i		−	0.856028i
$790$		0			0
$791$	121.992			0.154225
$792$	−34.4953	+	34.4953i	−0.0435547	+	0.0435547i
$793$	25.1296	+	25.1296i	0.0316892	+	0.0316892i
$794$		−	132.242i		−	0.166551i
$795$		0			0
$796$	−346.492			−0.435291
$797$	182.962	−	182.962i	0.229564	−	0.229564i	−0.582947	−	0.812511i	$-0.698100\pi$
$797$	182.962	−	182.962i	0.229564	−	0.229564i	0.812511	+	0.582947i	$0.198100\pi$
$798$	−79.7444	−	79.7444i	−0.0999303	−	0.0999303i
$799$		−	89.9408i		−	0.112567i
$800$		0			0
$801$	−524.026			−0.654215
$802$	−213.860	+	213.860i	−0.266659	+	0.266659i
$803$	−179.417	−	179.417i	−0.223433	−	0.223433i
$804$			139.577i			0.173603i
$805$		0			0
$806$	810.575			1.00568
$807$	−338.015	+	338.015i	−0.418853	+	0.418853i
$808$	365.710	+	365.710i	0.452611	+	0.452611i
$809$			508.611i			0.628690i	0.949309	+	0.314345i	$0.101785\pi$
$809$			508.611i			0.628690i	−0.949309	+	0.314345i	$0.898215\pi$
$810$		0			0
$811$	−768.233			−0.947267			−0.473633	−	0.880722i	$-0.657058\pi$
$811$	−768.233			−0.947267			−0.473633	+	0.880722i	$0.657058\pi$
$812$	−141.162	+	141.162i	−0.173845	+	0.173845i
$813$	362.154	+	362.154i	0.445454	+	0.445454i
$814$		−	130.669i		−	0.160527i
$815$		0			0
$816$	−46.9147			−0.0574935
$817$	645.693	−	645.693i	0.790321	−	0.790321i
$818$	300.366	+	300.366i	0.367196	+	0.367196i
$819$			168.413i			0.205633i
$820$		0			0
$821$	103.940			0.126602			0.0633011	−	0.997994i	$-0.479837\pi$
$821$	103.940			0.126602			0.0633011	+	0.997994i	$0.479837\pi$
$822$	90.5267	−	90.5267i	0.110130	−	0.110130i
$823$	−353.698	−	353.698i	−0.429767	−	0.429767i	0.458782	−	0.888549i	$-0.348286\pi$
$823$	−353.698	−	353.698i	−0.429767	−	0.429767i	−0.888549	+	0.458782i	$0.848286\pi$
$824$		−	186.490i		−	0.226323i
$825$		0			0
$826$	235.610			0.285242
$827$	−57.1544	+	57.1544i	−0.0691105	+	0.0691105i	−0.740817	−	0.671707i	$-0.765562\pi$
$827$	−57.1544	+	57.1544i	−0.0691105	+	0.0691105i	0.671707	+	0.740817i	$0.265562\pi$
$828$	−79.3566	−	79.3566i	−0.0958413	−	0.0958413i
$829$			260.205i			0.313878i	0.987608	+	0.156939i	$0.0501626\pi$
$829$			260.205i			0.313878i	−0.987608	+	0.156939i	$0.949837\pi$
$830$		0			0
$831$	52.5848			0.0632789
$832$	120.028	−	120.028i	0.144264	−	0.144264i
$833$	−33.5175	−	33.5175i	−0.0402371	−	0.0402371i
$834$			323.782i			0.388228i
$835$		0			0
$836$	−200.092			−0.239344
$837$	99.2520	−	99.2520i	0.118581	−	0.118581i
$838$	−696.907	−	696.907i	−0.831632	−	0.831632i
$839$		−	742.004i		−	0.884391i	−0.896919	−	0.442196i	$-0.854200\pi$
$839$		−	742.004i		−	0.884391i	0.896919	−	0.442196i	$-0.145800\pi$
$840$		0			0
$841$	−582.334			−0.692430
$842$	−114.980	+	114.980i	−0.136555	+	0.136555i
$843$	90.8774	+	90.8774i	0.107802	+	0.107802i
$844$		−	107.839i		−	0.127771i
$845$		0			0
$846$	56.3514			0.0666092
$847$	164.533	−	164.533i	0.194254	−	0.194254i
$848$	175.598	+	175.598i	0.207073	+	0.207073i
$849$			789.894i			0.930382i
$850$		0			0
$851$	300.604			0.353236
$852$	115.626	−	115.626i	0.135711	−	0.135711i
$853$	−876.382	−	876.382i	−1.02741	−	1.02741i	−0.999614	−	0.0277980i	$-0.991150\pi$
$853$	−876.382	−	876.382i	−1.02741	−	1.02741i	−0.0277980	−	0.999614i	$-0.508850\pi$
$854$		−	6.26698i		−	0.00733838i
$855$		0			0
$856$	230.261			0.268996
$857$	−953.370	+	953.370i	−1.11245	+	1.11245i	−0.119632	+	0.992818i	$0.538172\pi$
$857$	−953.370	+	953.370i	−1.11245	+	1.11245i	−0.992818	+	0.119632i	$0.961828\pi$
$858$	211.288	+	211.288i	0.246257	+	0.246257i
$859$		−	808.979i		−	0.941768i	−0.882195	−	0.470884i	$-0.843935\pi$
$859$		−	808.979i		−	0.941768i	0.882195	−	0.470884i	$-0.156065\pi$
$860$		0			0
$861$	243.287			0.282564
$862$	−724.694	+	724.694i	−0.840713	+	0.840713i
$863$	−315.788	−	315.788i	−0.365919	−	0.365919i	0.500068	−	0.865986i	$-0.333308\pi$
$863$	−315.788	−	315.788i	−0.365919	−	0.365919i	−0.865986	+	0.500068i	$0.833308\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$	−200.655			−0.231703
$867$	−297.792	+	297.792i	−0.343474	+	0.343474i
$868$	−101.073	−	101.073i	−0.116444	−	0.116444i
$869$			615.934i			0.708785i
$870$		0			0
$871$	854.925			0.981544
$872$	410.509	−	410.509i	0.470767	−	0.470767i
$873$	274.525	+	274.525i	0.314462	+	0.314462i
$874$		−	460.312i		−	0.526673i
$875$		0			0
$876$	152.883			0.174524
$877$	291.014	−	291.014i	0.331829	−	0.331829i	−0.521452	−	0.853281i	$-0.674609\pi$
$877$	291.014	−	291.014i	0.331829	−	0.331829i	0.853281	+	0.521452i	$0.174609\pi$
$878$	−685.890	−	685.890i	−0.781195	−	0.781195i
$879$			357.024i			0.406171i
$880$		0			0
$881$	368.877			0.418702			0.209351	−	0.977841i	$-0.432865\pi$
$881$	368.877			0.418702			0.209351	+	0.977841i	$0.432865\pi$
$882$	21.0000	−	21.0000i	0.0238095	−	0.0238095i
$883$	−1221.90	−	1221.90i	−1.38380	−	1.38380i	−0.837758	−	0.546042i	$-0.816134\pi$
$883$	−1221.90	−	1221.90i	−1.38380	−	1.38380i	−0.546042	−	0.837758i	$-0.683866\pi$
$884$			287.359i			0.325066i
$885$		0			0
$886$	−679.505			−0.766935
$887$	−67.8606	+	67.8606i	−0.0765058	+	0.0765058i	−0.744324	−	0.667818i	$-0.767228\pi$
$887$	−67.8606	+	67.8606i	−0.0765058	+	0.0765058i	0.667818	+	0.744324i	$0.267228\pi$
$888$	55.6722	+	55.6722i	0.0626940	+	0.0626940i
$889$			388.142i			0.436606i
$890$		0			0
$891$	51.7430			0.0580729
$892$	293.025	−	293.025i	0.328503	−	0.328503i
$893$	163.435	+	163.435i	0.183018	+	0.183018i
$894$		−	625.426i		−	0.699581i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	−486.070	+	486.070i	−0.541884	+	0.541884i
$898$	−226.637	−	226.637i	−0.252379	−	0.252379i
$899$		−	1019.12i		−	1.13362i
$900$		0			0
$901$	−420.401			−0.466594
$902$	305.224	−	305.224i	0.338386	−	0.338386i
$903$	170.038	+	170.038i	0.188303	+	0.188303i
$904$			130.415i			0.144264i
$905$		0			0
$906$	−515.675			−0.569178
$907$	144.428	−	144.428i	0.159237	−	0.159237i	−0.622991	−	0.782229i	$-0.714083\pi$
$907$	144.428	−	144.428i	0.159237	−	0.159237i	0.782229	+	0.622991i	$0.214083\pi$
$908$	325.794	+	325.794i	0.358804	+	0.358804i
$909$		−	548.565i		−	0.603482i
$910$		0			0
$911$	423.332			0.464689			0.232345	−	0.972634i	$-0.425360\pi$
$911$	423.332			0.464689			0.232345	+	0.972634i	$0.425360\pi$
$912$	85.2504	−	85.2504i	0.0934763	−	0.0934763i
$913$	104.845	+	104.845i	0.114836	+	0.114836i
$914$		−	532.565i		−	0.582675i
$915$		0			0
$916$	−352.417			−0.384735
$917$	−295.589	+	295.589i	−0.322343	+	0.322343i
$918$	35.1860	+	35.1860i	0.0383290	+	0.0383290i
$919$		−	1289.08i		−	1.40269i	−0.712820	−	0.701347i	$-0.752582\pi$
$919$		−	1289.08i		−	1.40269i	0.712820	−	0.701347i	$-0.247418\pi$
$920$		0			0
$921$	754.697			0.819433
$922$	−121.199	+	121.199i	−0.131453	+	0.131453i
$923$	−708.222	−	708.222i	−0.767304	−	0.767304i
$924$		−	52.6924i		−	0.0570265i
$925$		0			0
$926$	1131.21			1.22161
$927$	−139.868	+	139.868i	−0.150882	+	0.150882i
$928$	−150.908	−	150.908i	−0.162617	−	0.162617i
$929$		−	749.538i		−	0.806823i	−0.915019	−	0.403411i	$-0.867824\pi$
$929$		−	749.538i		−	0.806823i	0.915019	−	0.403411i	$-0.132176\pi$
$930$		0			0
$931$	121.812			0.130840
$932$	36.7231	−	36.7231i	0.0394025	−	0.0394025i
$933$	−35.6634	−	35.6634i	−0.0382245	−	0.0382245i
$934$		−	559.072i		−	0.598578i
$935$		0			0
$936$	−180.041			−0.192352
$937$	208.580	−	208.580i	0.222605	−	0.222605i	−0.586990	−	0.809594i	$-0.699687\pi$
$937$	208.580	−	208.580i	0.222605	−	0.222605i	0.809594	+	0.586990i	$0.199687\pi$
$938$	−106.603	−	106.603i	−0.113650	−	0.113650i
$939$		−	29.8138i		−	0.0317506i
$940$		0			0
$941$	−1017.80			−1.08161			−0.540807	−	0.841147i	$-0.681881\pi$
$941$	−1017.80			−1.08161			−0.540807	+	0.841147i	$0.681881\pi$
$942$	445.001	−	445.001i	0.472400	−	0.472400i
$943$	702.170	+	702.170i	0.744613	+	0.744613i
$944$			251.877i			0.266819i
$945$		0			0
$946$	426.652			0.451006
$947$	−288.192	+	288.192i	−0.304321	+	0.304321i	−0.842702	−	0.538381i	$-0.819036\pi$
$947$	−288.192	+	288.192i	−0.304321	+	0.304321i	0.538381	+	0.842702i	$0.319036\pi$
$948$	−262.423	−	262.423i	−0.276817	−	0.276817i
$949$		−	936.429i		−	0.986753i
$950$		0			0
$951$	−536.907			−0.564571
$952$	35.8317	−	35.8317i	0.0376383	−	0.0376383i
$953$	450.504	+	450.504i	0.472722	+	0.472722i	0.902794	−	0.430072i	$-0.141512\pi$
$953$	450.504	+	450.504i	0.472722	+	0.472722i	−0.430072	+	0.902794i	$0.641512\pi$
$954$		−	263.397i		−	0.276098i
$955$		0			0
$956$	−550.187			−0.575509
$957$	265.649	−	265.649i	0.277585	−	0.277585i
$958$	−101.987	−	101.987i	−0.106458	−	0.106458i
$959$			138.282i			0.144194i
$960$		0			0
$961$	−231.300			−0.240687
$962$	341.000	−	341.000i	0.354470	−	0.354470i
$963$	−172.695	−	172.695i	−0.179331	−	0.179331i
$964$		−	677.850i		−	0.703164i
$965$		0			0
$966$	121.219			0.125486
$967$	−824.848	+	824.848i	−0.852997	+	0.852997i	−0.990501	−	0.137505i	$-0.956092\pi$
$967$	−824.848	+	824.848i	−0.852997	+	0.852997i	0.137505	+	0.990501i	$0.456092\pi$
$968$	175.893	+	175.893i	0.181708	+	0.181708i
$969$			204.098i			0.210628i
$970$		0			0
$971$	−770.810			−0.793831			−0.396916	−	0.917855i	$-0.629919\pi$
$971$	−770.810			−0.793831			−0.396916	+	0.917855i	$0.629919\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−247.293	−	247.293i	−0.254155	−	0.254155i
$974$			500.545i			0.513907i
$975$		0			0
$976$	6.69968			0.00686442
$977$	−126.844	+	126.844i	−0.129830	+	0.129830i	−0.769036	−	0.639206i	$-0.779263\pi$
$977$	−126.844	+	126.844i	−0.129830	+	0.129830i	0.639206	+	0.769036i	$0.279263\pi$
$978$	−381.051	−	381.051i	−0.389623	−	0.389623i
$979$		−	1004.25i		−	1.02579i
$980$		0			0
$981$	−615.763			−0.627689
$982$	−648.021	+	648.021i	−0.659899	+	0.659899i
$983$	1168.93	+	1168.93i	1.18914	+	1.18914i	0.977305	+	0.211839i	$0.0679451\pi$
$983$	1168.93	+	1168.93i	1.18914	+	1.18914i	0.211839	+	0.977305i	$0.432055\pi$
$984$			260.085i			0.264314i
$985$		0			0
$986$	361.291			0.366421
$987$	−43.0391	+	43.0391i	−0.0436060	+	0.0436060i
$988$	−522.170	−	522.170i	−0.528512	−	0.528512i
$989$			981.515i			0.992432i
$990$		0			0
$991$	1475.28			1.48868			0.744339	−	0.667802i	$-0.232765\pi$
$991$	1475.28			1.48868			0.744339	+	0.667802i	$0.232765\pi$
$992$	108.052	−	108.052i	0.108923	−	0.108923i
$993$	338.165	+	338.165i	0.340549	+	0.340549i
$994$			176.621i			0.177687i
$995$		0			0
$996$	−89.3401			−0.0896989
$997$	997.648	−	997.648i	1.00065	−	1.00065i	0.000649790	−	1.00000i	$-0.499793\pi$
$997$	997.648	−	997.648i	1.00065	−	1.00065i	1.00000		0.000649790i	$-0.000206835\pi$
$998$	−377.798	−	377.798i	−0.378555	−	0.378555i
$999$		−	83.5084i		−	0.0835919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.h.43.6		16
5.2	odd	4	inner	1050.3.l.h.757.6		16
5.3	odd	4		210.3.l.b.127.1	yes	16
5.4	even	2		210.3.l.b.43.1	✓	16
15.8	even	4		630.3.o.f.127.8		16
15.14	odd	2		630.3.o.f.253.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.1	✓	16	5.4	even	2
210.3.l.b.127.1	yes	16	5.3	odd	4
630.3.o.f.127.8		16	15.8	even	4
630.3.o.f.253.8		16	15.14	odd	2
1050.3.l.h.43.6		16	1.1	even	1	trivial
1050.3.l.h.757.6		16	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} -5.74922 q^{11} +(2.44949 - 2.44949i) q^{12} +(-15.0034 - 15.0034i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(4.78821 - 4.78821i) q^{17} +(3.00000 + 3.00000i) q^{18} +17.4017i q^{19} -4.58258 q^{21} +(-5.74922 + 5.74922i) q^{22} +(-13.2261 - 13.2261i) q^{23} -4.89898i q^{24} -30.0069 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} +37.7271i q^{29} -27.0130 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-7.04132 - 7.04132i) q^{33} -9.57642i q^{34} +6.00000 q^{36} +(-11.3640 + 11.3640i) q^{37} +(17.4017 + 17.4017i) q^{38} -36.7508i q^{39} -53.0897 q^{41} +(-4.58258 + 4.58258i) q^{42} +(-37.1052 - 37.1052i) q^{43} +11.4984i q^{44} -26.4522 q^{46} +(9.39190 - 9.39190i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +11.7287 q^{51} +(-30.0069 + 30.0069i) q^{52} +(-43.8996 - 43.8996i) q^{53} +7.34847i q^{54} +7.48331 q^{56} +(-21.3126 + 21.3126i) q^{57} +(37.7271 + 37.7271i) q^{58} -62.9694i q^{59} -1.67492 q^{61} +(-27.0130 + 27.0130i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} -14.0826 q^{66} +(-28.4909 + 28.4909i) q^{67} +(-9.57642 - 9.57642i) q^{68} -32.3972i q^{69} +47.2039 q^{71} +(6.00000 - 6.00000i) q^{72} +(31.2071 + 31.2071i) q^{73} +22.7281i q^{74} +34.8033 q^{76} +(10.7558 - 10.7558i) q^{77} +(-36.7508 - 36.7508i) q^{78} -107.134i q^{79} -9.00000 q^{81} +(-53.0897 + 53.0897i) q^{82} +(-18.2365 - 18.2365i) q^{83} +9.16515i q^{84} -74.2105 q^{86} +(-46.2061 + 46.2061i) q^{87} +(11.4984 + 11.4984i) q^{88} +174.675i q^{89} +56.1378 q^{91} +(-26.4522 + 26.4522i) q^{92} +(-33.0840 - 33.0840i) q^{93} -18.7838i q^{94} -9.79796 q^{96} +(91.5084 - 91.5084i) q^{97} +(-7.00000 - 7.00000i) q^{98} -17.2477i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 - 32 * q^8	\( 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 - 32 * q^8 + 8 * q^11 + 32 * q^13 - 64 * q^16 - 56 * q^17 + 48 * q^18 + 8 * q^22 - 24 * q^23 + 64 * q^26 - 112 * q^31 - 64 * q^32 - 24 * q^33 + 96 * q^36 + 152 * q^37 - 48 * q^46 - 80 * q^47 - 72 * q^51 + 64 * q^52 - 48 * q^53 - 24 * q^57 - 96 * q^58 + 96 * q^61 - 112 * q^62 - 48 * q^66 + 80 * q^67 + 112 * q^68 + 536 * q^71 + 96 * q^72 + 168 * q^77 + 48 * q^78 - 144 * q^81 + 256 * q^83 + 144 * q^87 - 16 * q^88 - 48 * q^92 - 192 * q^93 - 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more