LMFDB - Embedded newform 1050.3.l.a.43.4

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$0.323042 - 0.323042i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.a.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +2.50755 q^{11} +(2.44949 - 2.44949i) q^{12} +(-9.25290 - 9.25290i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-10.6127 + 10.6127i) q^{17} +(-3.00000 - 3.00000i) q^{18} -28.8752i q^{19} +4.58258 q^{21} +(-2.50755 + 2.50755i) q^{22} +(8.08621 + 8.08621i) q^{23} +4.89898i q^{24} +18.5058 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -34.8903i q^{29} -37.6757 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.07111 + 3.07111i) q^{33} -21.2254i q^{34} +6.00000 q^{36} +(-12.2773 + 12.2773i) q^{37} +(28.8752 + 28.8752i) q^{38} -22.6649i q^{39} -37.0116 q^{41} +(-4.58258 + 4.58258i) q^{42} +(23.0808 + 23.0808i) q^{43} -5.01510i q^{44} -16.1724 q^{46} +(4.22570 - 4.22570i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} -25.9957 q^{51} +(-18.5058 + 18.5058i) q^{52} +(-23.0151 - 23.0151i) q^{53} -7.34847i q^{54} +7.48331 q^{56} +(35.3648 - 35.3648i) q^{57} +(34.8903 + 34.8903i) q^{58} -35.1268i q^{59} -73.3353 q^{61} +(37.6757 - 37.6757i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} -6.14222 q^{66} +(43.6725 - 43.6725i) q^{67} +(21.2254 + 21.2254i) q^{68} +19.8071i q^{69} -38.9584 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-67.6174 - 67.6174i) q^{73} -24.5546i q^{74} -57.7504 q^{76} +(4.69120 - 4.69120i) q^{77} +(22.6649 + 22.6649i) q^{78} -84.2839i q^{79} -9.00000 q^{81} +(37.0116 - 37.0116i) q^{82} +(-17.0303 - 17.0303i) q^{83} -9.16515i q^{84} -46.1615 q^{86} +(42.7317 - 42.7317i) q^{87} +(5.01510 + 5.01510i) q^{88} -96.4314i q^{89} -34.6212 q^{91} +(16.1724 - 16.1724i) q^{92} +(-46.1431 - 46.1431i) q^{93} +8.45139i q^{94} +9.79796 q^{96} +(-98.7241 + 98.7241i) q^{97} +(7.00000 + 7.00000i) q^{98} +7.52265i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 32 q^{11} - 40 q^{13} - 32 q^{16} + 40 q^{17} - 24 q^{18} + 32 q^{22} + 8 q^{23} + 80 q^{26} + 96 q^{31} + 32 q^{32} + 72 q^{33} + 48 q^{36} - 112 q^{37} + 24 q^{38} - 160 q^{41} + 64 q^{43} - 16 q^{46} - 64 q^{47} + 24 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{57} - 32 q^{58} - 128 q^{61} - 96 q^{62} - 144 q^{66} + 304 q^{67} - 80 q^{68} + 240 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{76} + 56 q^{77} + 120 q^{78} - 72 q^{81} + 160 q^{82} - 64 q^{83} - 128 q^{86} + 96 q^{87} - 64 q^{88} + 56 q^{91} + 16 q^{92} - 144 q^{93} - 272 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 32 * q^11 - 40 * q^13 - 32 * q^16 + 40 * q^17 - 24 * q^18 + 32 * q^22 + 8 * q^23 + 80 * q^26 + 96 * q^31 + 32 * q^32 + 72 * q^33 + 48 * q^36 - 112 * q^37 + 24 * q^38 - 160 * q^41 + 64 * q^43 - 16 * q^46 - 64 * q^47 + 24 * q^51 - 80 * q^52 - 80 * q^53 - 48 * q^57 - 32 * q^58 - 128 * q^61 - 96 * q^62 - 144 * q^66 + 304 * q^67 - 80 * q^68 + 240 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^76 + 56 * q^77 + 120 * q^78 - 72 * q^81 + 160 * q^82 - 64 * q^83 - 128 * q^86 + 96 * q^87 - 64 * q^88 + 56 * q^91 + 16 * q^92 - 144 * q^93 - 272 * 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
$11$	2.50755			0.227959			0.113980	−	0.993483i	$-0.463640\pi$
$11$	2.50755			0.227959			0.113980	+	0.993483i	$0.463640\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−9.25290	−	9.25290i	−0.711761	−	0.711761i	0.255142	−	0.966904i	$-0.417878\pi$
$13$	−9.25290	−	9.25290i	−0.711761	−	0.711761i	−0.966904	+	0.255142i	$0.917878\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−10.6127	+	10.6127i	−0.624277	+	0.624277i	−0.946622	−	0.322345i	$-0.895529\pi$
$17$	−10.6127	+	10.6127i	−0.624277	+	0.624277i	0.322345	+	0.946622i	$0.395529\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	28.8752i		−	1.51975i	−0.650071	−	0.759874i	$-0.725261\pi$
$19$		−	28.8752i		−	1.51975i	0.650071	−	0.759874i	$-0.274739\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	−2.50755	+	2.50755i	−0.113980	+	0.113980i
$23$	8.08621	+	8.08621i	0.351574	+	0.351574i	0.860695	−	0.509121i	$-0.170029\pi$
$23$	8.08621	+	8.08621i	0.351574	+	0.351574i	−0.509121	+	0.860695i	$0.670029\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	18.5058			0.711761
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	34.8903i		−	1.20311i	−0.798830	−	0.601557i	$-0.794547\pi$
$29$		−	34.8903i		−	1.20311i	0.798830	−	0.601557i	$-0.205453\pi$
$30$		0			0
$31$	−37.6757			−1.21535			−0.607673	−	0.794188i	$-0.707897\pi$
$31$	−37.6757			−1.21535			−0.607673	+	0.794188i	$0.707897\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	3.07111	+	3.07111i	0.0930639	+	0.0930639i
$34$		−	21.2254i		−	0.624277i
$35$		0			0
$36$	6.00000			0.166667
$37$	−12.2773	+	12.2773i	−0.331819	+	0.331819i	−0.853277	−	0.521458i	$-0.825388\pi$
$37$	−12.2773	+	12.2773i	−0.331819	+	0.331819i	0.521458	+	0.853277i	$0.325388\pi$
$38$	28.8752	+	28.8752i	0.759874	+	0.759874i
$39$		−	22.6649i		−	0.581151i
$40$		0			0
$41$	−37.0116			−0.902722			−0.451361	−	0.892342i	$-0.649061\pi$
$41$	−37.0116			−0.902722			−0.451361	+	0.892342i	$0.649061\pi$
$42$	−4.58258	+	4.58258i	−0.109109	+	0.109109i
$43$	23.0808	+	23.0808i	0.536762	+	0.536762i	0.922576	−	0.385814i	$-0.126080\pi$
$43$	23.0808	+	23.0808i	0.536762	+	0.536762i	−0.385814	+	0.922576i	$0.626080\pi$
$44$		−	5.01510i		−	0.113980i
$45$		0			0
$46$	−16.1724			−0.351574
$47$	4.22570	−	4.22570i	0.0899084	−	0.0899084i	−0.660722	−	0.750631i	$-0.729750\pi$
$47$	4.22570	−	4.22570i	0.0899084	−	0.0899084i	0.750631	+	0.660722i	$0.229750\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	−25.9957			−0.509720
$52$	−18.5058	+	18.5058i	−0.355881	+	0.355881i
$53$	−23.0151	−	23.0151i	−0.434247	−	0.434247i	0.455823	−	0.890070i	$-0.349345\pi$
$53$	−23.0151	−	23.0151i	−0.434247	−	0.434247i	−0.890070	+	0.455823i	$0.849345\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	35.3648	−	35.3648i	0.620434	−	0.620434i
$58$	34.8903	+	34.8903i	0.601557	+	0.601557i
$59$		−	35.1268i		−	0.595370i	−0.954664	−	0.297685i	$-0.903786\pi$
$59$		−	35.1268i		−	0.595370i	0.954664	−	0.297685i	$-0.0962145\pi$
$60$		0			0
$61$	−73.3353			−1.20222			−0.601109	−	0.799167i	$-0.705274\pi$
$61$	−73.3353			−1.20222			−0.601109	+	0.799167i	$0.705274\pi$
$62$	37.6757	−	37.6757i	0.607673	−	0.607673i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−6.14222			−0.0930639
$67$	43.6725	−	43.6725i	0.651828	−	0.651828i	−0.301605	−	0.953433i	$-0.597522\pi$
$67$	43.6725	−	43.6725i	0.651828	−	0.651828i	0.953433	+	0.301605i	$0.0975224\pi$
$68$	21.2254	+	21.2254i	0.312139	+	0.312139i
$69$			19.8071i			0.287059i
$70$		0			0
$71$	−38.9584			−0.548710			−0.274355	−	0.961628i	$-0.588464\pi$
$71$	−38.9584			−0.548710			−0.274355	+	0.961628i	$0.588464\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−67.6174	−	67.6174i	−0.926265	−	0.926265i	0.0711969	−	0.997462i	$-0.477318\pi$
$73$	−67.6174	−	67.6174i	−0.926265	−	0.926265i	−0.997462	+	0.0711969i	$0.977318\pi$
$74$		−	24.5546i		−	0.331819i
$75$		0			0
$76$	−57.7504			−0.759874
$77$	4.69120	−	4.69120i	0.0609247	−	0.0609247i
$78$	22.6649	+	22.6649i	0.290575	+	0.290575i
$79$		−	84.2839i		−	1.06688i	−0.845836	−	0.533442i	$-0.820898\pi$
$79$		−	84.2839i		−	1.06688i	0.845836	−	0.533442i	$-0.179102\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	37.0116	−	37.0116i	0.451361	−	0.451361i
$83$	−17.0303	−	17.0303i	−0.205184	−	0.205184i	0.597033	−	0.802217i	$-0.296346\pi$
$83$	−17.0303	−	17.0303i	−0.205184	−	0.205184i	−0.802217	+	0.597033i	$0.796346\pi$
$84$		−	9.16515i		−	0.109109i
$85$		0			0
$86$	−46.1615			−0.536762
$87$	42.7317	−	42.7317i	0.491169	−	0.491169i
$88$	5.01510	+	5.01510i	0.0569898	+	0.0569898i
$89$		−	96.4314i		−	1.08350i	−0.840540	−	0.541749i	$-0.817762\pi$
$89$		−	96.4314i		−	1.08350i	0.840540	−	0.541749i	$-0.182238\pi$
$90$		0			0
$91$	−34.6212			−0.380452
$92$	16.1724	−	16.1724i	0.175787	−	0.175787i
$93$	−46.1431	−	46.1431i	−0.496163	−	0.496163i
$94$			8.45139i			0.0899084i
$95$		0			0
$96$	9.79796			0.102062
$97$	−98.7241	+	98.7241i	−1.01777	+	1.01777i	−0.0179348	+	0.999839i	$0.505709\pi$
$97$	−98.7241	+	98.7241i	−1.01777	+	1.01777i	−0.999839	+	0.0179348i	$0.994291\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$			7.52265i			0.0759864i
$100$		0			0
$101$	114.896			1.13759			0.568794	−	0.822480i	$-0.307410\pi$
$101$	114.896			1.13759			0.568794	+	0.822480i	$0.307410\pi$
$102$	25.9957	−	25.9957i	0.254860	−	0.254860i
$103$	12.7795	+	12.7795i	0.124073	+	0.124073i	0.766417	−	0.642344i	$-0.222038\pi$
$103$	12.7795	+	12.7795i	0.124073	+	0.124073i	−0.642344	+	0.766417i	$0.722038\pi$
$104$		−	37.0116i		−	0.355881i
$105$		0			0
$106$	46.0302			0.434247
$107$	67.8422	−	67.8422i	0.634039	−	0.634039i	−0.315039	−	0.949079i	$-0.602018\pi$
$107$	67.8422	−	67.8422i	0.634039	−	0.634039i	0.949079	+	0.315039i	$0.102018\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	34.3485i		−	0.315123i	−0.987509	−	0.157562i	$-0.949637\pi$
$109$		−	34.3485i		−	0.315123i	0.987509	−	0.157562i	$-0.0503633\pi$
$110$		0			0
$111$	−30.0731			−0.270929
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	149.014	+	149.014i	1.31871	+	1.31871i	0.914802	+	0.403904i	$0.132347\pi$
$113$	149.014	+	149.014i	1.31871	+	1.31871i	0.403904	+	0.914802i	$0.367653\pi$
$114$			70.7295i			0.620434i
$115$		0			0
$116$	−69.7806			−0.601557
$117$	27.7587	−	27.7587i	0.237254	−	0.237254i
$118$	35.1268	+	35.1268i	0.297685	+	0.297685i
$119$			39.7091i			0.333690i
$120$		0			0
$121$	−114.712			−0.948035
$122$	73.3353	−	73.3353i	0.601109	−	0.601109i
$123$	−45.3297	−	45.3297i	−0.368535	−	0.368535i
$124$			75.3514i			0.607673i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	−39.5381	+	39.5381i	−0.311323	+	0.311323i	−0.845422	−	0.534099i	$-0.820651\pi$
$127$	−39.5381	+	39.5381i	−0.311323	+	0.311323i	0.534099	+	0.845422i	$0.320651\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			56.5361i			0.438264i
$130$		0			0
$131$	193.872			1.47994			0.739969	−	0.672641i	$-0.234840\pi$
$131$	193.872			1.47994			0.739969	+	0.672641i	$0.234840\pi$
$132$	6.14222	−	6.14222i	0.0465320	−	0.0465320i
$133$	−54.0205	−	54.0205i	−0.406170	−	0.406170i
$134$			87.3450i			0.651828i
$135$		0			0
$136$	−42.4509			−0.312139
$137$	135.948	−	135.948i	0.992318	−	0.992318i	−0.00765271	−	0.999971i	$-0.502436\pi$
$137$	135.948	−	135.948i	0.992318	−	0.992318i	0.999971	+	0.00765271i	$0.00243596\pi$
$138$	−19.8071	−	19.8071i	−0.143530	−	0.143530i
$139$		−	201.392i		−	1.44886i	−0.689347	−	0.724432i	$-0.742102\pi$
$139$		−	201.392i		−	1.44886i	0.689347	−	0.724432i	$-0.257898\pi$
$140$		0			0
$141$	10.3508			0.0734099
$142$	38.9584	−	38.9584i	0.274355	−	0.274355i
$143$	−23.2021	−	23.2021i	−0.162252	−	0.162252i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	135.235			0.926265
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	24.5546	+	24.5546i	0.165909	+	0.165909i
$149$		−	46.2575i		−	0.310453i	−0.987879	−	0.155226i	$-0.950389\pi$
$149$		−	46.2575i		−	0.310453i	0.987879	−	0.155226i	$-0.0496107\pi$
$150$		0			0
$151$	−237.335			−1.57175			−0.785877	−	0.618383i	$-0.787788\pi$
$151$	−237.335			−1.57175			−0.785877	+	0.618383i	$0.787788\pi$
$152$	57.7504	−	57.7504i	0.379937	−	0.379937i
$153$	−31.8381	−	31.8381i	−0.208092	−	0.208092i
$154$			9.38240i			0.0609247i
$155$		0			0
$156$	−45.3297			−0.290575
$157$	109.177	−	109.177i	0.695395	−	0.695395i	−0.268019	−	0.963414i	$-0.586369\pi$
$157$	109.177	−	109.177i	0.695395	−	0.695395i	0.963414	+	0.268019i	$0.0863690\pi$
$158$	84.2839	+	84.2839i	0.533442	+	0.533442i
$159$		−	56.3753i		−	0.354561i
$160$		0			0
$161$	30.2558			0.187924
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	59.0069	+	59.0069i	0.362006	+	0.362006i	0.864551	−	0.502545i	$-0.167603\pi$
$163$	59.0069	+	59.0069i	0.362006	+	0.362006i	−0.502545	+	0.864551i	$0.667603\pi$
$164$			74.0232i			0.451361i
$165$		0			0
$166$	34.0606			0.205184
$167$	−92.4048	+	92.4048i	−0.553322	+	0.553322i	−0.927398	−	0.374076i	$-0.877960\pi$
$167$	−92.4048	+	92.4048i	−0.553322	+	0.553322i	0.374076	+	0.927398i	$0.377960\pi$
$168$	9.16515	+	9.16515i	0.0545545	+	0.0545545i
$169$			2.23216i			0.0132080i
$170$		0			0
$171$	86.6256			0.506582
$172$	46.1615	−	46.1615i	0.268381	−	0.268381i
$173$	−91.4094	−	91.4094i	−0.528378	−	0.528378i	0.391710	−	0.920089i	$-0.371883\pi$
$173$	−91.4094	−	91.4094i	−0.528378	−	0.528378i	−0.920089	+	0.391710i	$0.871883\pi$
$174$			85.4634i			0.491169i
$175$		0			0
$176$	−10.0302			−0.0569898
$177$	43.0214	−	43.0214i	0.243059	−	0.243059i
$178$	96.4314	+	96.4314i	0.541749	+	0.541749i
$179$		−	211.508i		−	1.18161i	−0.806816	−	0.590803i	$-0.798811\pi$
$179$		−	211.508i		−	1.18161i	0.806816	−	0.590803i	$-0.201189\pi$
$180$		0			0
$181$	254.380			1.40541			0.702707	−	0.711479i	$-0.251974\pi$
$181$	254.380			1.40541			0.702707	+	0.711479i	$0.251974\pi$
$182$	34.6212	−	34.6212i	0.190226	−	0.190226i
$183$	−89.8170	−	89.8170i	−0.490803	−	0.490803i
$184$			32.3448i			0.175787i
$185$		0			0
$186$	92.2863			0.496163
$187$	−26.6119	+	26.6119i	−0.142310	+	0.142310i
$188$	−8.45139	−	8.45139i	−0.0449542	−	0.0449542i
$189$			13.7477i			0.0727393i
$190$		0			0
$191$	99.9218			0.523151			0.261575	−	0.965183i	$-0.415758\pi$
$191$	99.9218			0.523151			0.261575	+	0.965183i	$0.415758\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	102.878	+	102.878i	0.533045	+	0.533045i	0.921477	−	0.388432i	$-0.126983\pi$
$193$	102.878	+	102.878i	0.533045	+	0.533045i	−0.388432	+	0.921477i	$0.626983\pi$
$194$		−	197.448i		−	1.01777i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−62.9510	+	62.9510i	−0.319548	+	0.319548i	−0.848594	−	0.529045i	$-0.822550\pi$
$197$	−62.9510	+	62.9510i	−0.319548	+	0.319548i	0.529045	+	0.848594i	$0.322550\pi$
$198$	−7.52265	−	7.52265i	−0.0379932	−	0.0379932i
$199$		−	14.4025i		−	0.0723742i	−0.999345	−	0.0361871i	$-0.988479\pi$
$199$		−	14.4025i		−	0.0723742i	0.999345	−	0.0361871i	$-0.0115212\pi$
$200$		0			0
$201$	106.975			0.532215
$202$	−114.896	+	114.896i	−0.568794	+	0.568794i
$203$	−65.2738	−	65.2738i	−0.321546	−	0.321546i
$204$			51.9915i			0.254860i
$205$		0			0
$206$	−25.5590			−0.124073
$207$	−24.2586	+	24.2586i	−0.117191	+	0.117191i
$208$	37.0116	+	37.0116i	0.177940	+	0.177940i
$209$		−	72.4060i		−	0.346440i
$210$		0			0
$211$	−173.845			−0.823908			−0.411954	−	0.911205i	$-0.635154\pi$
$211$	−173.845			−0.823908			−0.411954	+	0.911205i	$0.635154\pi$
$212$	−46.0302	+	46.0302i	−0.217124	+	0.217124i
$213$	−47.7141	−	47.7141i	−0.224010	−	0.224010i
$214$			135.684i			0.634039i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−70.4848	+	70.4848i	−0.324815	+	0.324815i
$218$	34.3485	+	34.3485i	0.157562	+	0.157562i
$219$		−	165.628i		−	0.756293i
$220$		0			0
$221$	196.397			0.888673
$222$	30.0731	−	30.0731i	0.135464	−	0.135464i
$223$	−45.5732	−	45.5732i	−0.204364	−	0.204364i	0.597503	−	0.801867i	$-0.296160\pi$
$223$	−45.5732	−	45.5732i	−0.204364	−	0.204364i	−0.801867	+	0.597503i	$0.796160\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−298.027			−1.31871
$227$	−59.2172	+	59.2172i	−0.260869	+	0.260869i	−0.825407	−	0.564538i	$-0.809054\pi$
$227$	−59.2172	+	59.2172i	−0.260869	+	0.260869i	0.564538	+	0.825407i	$0.309054\pi$
$228$	−70.7295	−	70.7295i	−0.310217	−	0.310217i
$229$		−	207.044i		−	0.904124i	−0.891986	−	0.452062i	$-0.850689\pi$
$229$		−	207.044i		−	0.904124i	0.891986	−	0.452062i	$-0.149311\pi$
$230$		0			0
$231$	11.4910			0.0497448
$232$	69.7806	−	69.7806i	0.300778	−	0.300778i
$233$	−250.646	−	250.646i	−1.07573	−	1.07573i	−0.996887	−	0.0788463i	$-0.974876\pi$
$233$	−250.646	−	250.646i	−1.07573	−	1.07573i	−0.0788463	−	0.996887i	$-0.525124\pi$
$234$			55.5174i			0.237254i
$235$		0			0
$236$	−70.2536			−0.297685
$237$	103.226	−	103.226i	0.435554	−	0.435554i
$238$	−39.7091	−	39.7091i	−0.166845	−	0.166845i
$239$			318.381i			1.33214i	0.745890	+	0.666069i	$0.232024\pi$
$239$			318.381i			1.33214i	−0.745890	+	0.666069i	$0.767976\pi$
$240$		0			0
$241$	−148.889			−0.617798			−0.308899	−	0.951095i	$-0.599960\pi$
$241$	−148.889			−0.617798			−0.308899	+	0.951095i	$0.599960\pi$
$242$	114.712	−	114.712i	0.474017	−	0.474017i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			146.671i			0.601109i
$245$		0			0
$246$	90.6595			0.368535
$247$	−267.179	+	267.179i	−1.08170	+	1.08170i
$248$	−75.3514	−	75.3514i	−0.303836	−	0.303836i
$249$		−	41.7156i		−	0.167532i
$250$		0			0
$251$	123.837			0.493376			0.246688	−	0.969095i	$-0.420658\pi$
$251$	123.837			0.493376			0.246688	+	0.969095i	$0.420658\pi$
$252$	11.2250	−	11.2250i	0.0445435	−	0.0445435i
$253$	20.2766	+	20.2766i	0.0801446	+	0.0801446i
$254$		−	79.0762i		−	0.311323i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−83.4383	+	83.4383i	−0.324663	+	0.324663i	−0.850553	−	0.525890i	$-0.823732\pi$
$257$	−83.4383	+	83.4383i	−0.324663	+	0.324663i	0.525890	+	0.850553i	$0.323732\pi$
$258$	−56.5361	−	56.5361i	−0.219132	−	0.219132i
$259$			45.9374i			0.177365i
$260$		0			0
$261$	104.671			0.401038
$262$	−193.872	+	193.872i	−0.739969	+	0.739969i
$263$	−160.799	−	160.799i	−0.611404	−	0.611404i	0.331908	−	0.943312i	$-0.392308\pi$
$263$	−160.799	−	160.799i	−0.611404	−	0.611404i	−0.943312	+	0.331908i	$0.892308\pi$
$264$			12.2844i			0.0465320i
$265$		0			0
$266$	108.041			0.406170
$267$	118.104	−	118.104i	0.442337	−	0.442337i
$268$	−87.3450	−	87.3450i	−0.325914	−	0.325914i
$269$			438.169i			1.62888i	0.580247	+	0.814440i	$0.302956\pi$
$269$			438.169i			1.62888i	−0.580247	+	0.814440i	$0.697044\pi$
$270$		0			0
$271$	52.2554			0.192824			0.0964121	−	0.995341i	$-0.469263\pi$
$271$	52.2554			0.192824			0.0964121	+	0.995341i	$0.469263\pi$
$272$	42.4509	−	42.4509i	0.156069	−	0.156069i
$273$	−42.4021	−	42.4021i	−0.155319	−	0.155319i
$274$			271.895i			0.992318i
$275$		0			0
$276$	39.6142			0.143530
$277$	−68.3008	+	68.3008i	−0.246573	+	0.246573i	−0.819563	−	0.572989i	$-0.805784\pi$
$277$	−68.3008	+	68.3008i	−0.246573	+	0.246573i	0.572989	+	0.819563i	$0.305784\pi$
$278$	201.392	+	201.392i	0.724432	+	0.724432i
$279$		−	113.027i		−	0.405115i
$280$		0			0
$281$	472.125			1.68016			0.840079	−	0.542464i	$-0.182508\pi$
$281$	472.125			1.68016			0.840079	+	0.542464i	$0.182508\pi$
$282$	−10.3508	+	10.3508i	−0.0367050	+	0.0367050i
$283$	162.739	+	162.739i	0.575048	+	0.575048i	0.933535	−	0.358487i	$-0.116707\pi$
$283$	162.739	+	162.739i	0.575048	+	0.575048i	−0.358487	+	0.933535i	$0.616707\pi$
$284$			77.9168i			0.274355i
$285$		0			0
$286$	46.4042			0.162252
$287$	−69.2423	+	69.2423i	−0.241262	+	0.241262i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			63.7406i			0.220556i
$290$		0			0
$291$	−241.824			−0.831009
$292$	−135.235	+	135.235i	−0.463133	+	0.463133i
$293$	−49.9066	−	49.9066i	−0.170330	−	0.170330i	0.616795	−	0.787124i	$-0.288431\pi$
$293$	−49.9066	−	49.9066i	−0.170330	−	0.170330i	−0.787124	+	0.616795i	$0.788431\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	−49.1092			−0.165909
$297$	−9.21333	+	9.21333i	−0.0310213	+	0.0310213i
$298$	46.2575	+	46.2575i	0.155226	+	0.155226i
$299$		−	149.642i		−	0.500474i
$300$		0			0
$301$	86.3603			0.286911
$302$	237.335	−	237.335i	0.785877	−	0.785877i
$303$	140.719	+	140.719i	0.464418	+	0.464418i
$304$			115.501i			0.379937i
$305$		0			0
$306$	63.6763			0.208092
$307$	−371.730	+	371.730i	−1.21085	+	1.21085i	−0.240100	+	0.970748i	$0.577180\pi$
$307$	−371.730	+	371.730i	−1.21085	+	1.21085i	−0.970748	+	0.240100i	$0.922820\pi$
$308$	−9.38240	−	9.38240i	−0.0304623	−	0.0304623i
$309$			31.3033i			0.101305i
$310$		0			0
$311$	83.4682			0.268387			0.134193	−	0.990955i	$-0.457156\pi$
$311$	83.4682			0.268387			0.134193	+	0.990955i	$0.457156\pi$
$312$	45.3297	−	45.3297i	0.145288	−	0.145288i
$313$	−44.4058	−	44.4058i	−0.141872	−	0.141872i	0.632604	−	0.774475i	$-0.281986\pi$
$313$	−44.4058	−	44.4058i	−0.141872	−	0.141872i	−0.774475	+	0.632604i	$0.781986\pi$
$314$			218.354i			0.695395i
$315$		0			0
$316$	−168.568			−0.533442
$317$	−293.697	+	293.697i	−0.926488	+	0.926488i	−0.997477	−	0.0709890i	$-0.977384\pi$
$317$	−293.697	+	293.697i	−0.926488	+	0.926488i	0.0709890	+	0.997477i	$0.477384\pi$
$318$	56.3753	+	56.3753i	0.177281	+	0.177281i
$319$		−	87.4892i		−	0.274261i
$320$		0			0
$321$	166.179			0.517691
$322$	−30.2558	+	30.2558i	−0.0939622	+	0.0939622i
$323$	306.444	+	306.444i	0.948744	+	0.948744i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−118.014			−0.362006
$327$	42.0681	−	42.0681i	0.128649	−	0.128649i
$328$	−74.0232	−	74.0232i	−0.225680	−	0.225680i
$329$		−	15.8111i		−	0.0480581i
$330$		0			0
$331$	−333.640			−1.00797			−0.503987	−	0.863711i	$-0.668134\pi$
$331$	−333.640			−1.00797			−0.503987	+	0.863711i	$0.668134\pi$
$332$	−34.0606	+	34.0606i	−0.102592	+	0.102592i
$333$	−36.8319	−	36.8319i	−0.110606	−	0.110606i
$334$		−	184.810i		−	0.553322i
$335$		0			0
$336$	−18.3303			−0.0545545
$337$	−189.426	+	189.426i	−0.562095	+	0.562095i	−0.929902	−	0.367807i	$-0.880109\pi$
$337$	−189.426	+	189.426i	−0.562095	+	0.562095i	0.367807	+	0.929902i	$0.380109\pi$
$338$	−2.23216	−	2.23216i	−0.00660401	−	0.00660401i
$339$			365.007i			1.07672i
$340$		0			0
$341$	−94.4738			−0.277049
$342$	−86.6256	+	86.6256i	−0.253291	+	0.253291i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			92.3231i			0.268381i
$345$		0			0
$346$	182.819			0.528378
$347$	114.059	−	114.059i	0.328699	−	0.328699i	−0.523392	−	0.852092i	$-0.675334\pi$
$347$	114.059	−	114.059i	0.328699	−	0.328699i	0.852092	+	0.523392i	$0.175334\pi$
$348$	−85.4634	−	85.4634i	−0.245585	−	0.245585i
$349$			231.559i			0.663492i	0.943369	+	0.331746i	$0.107638\pi$
$349$			231.559i			0.663492i	−0.943369	+	0.331746i	$0.892362\pi$
$350$		0			0
$351$	67.9946			0.193717
$352$	10.0302	−	10.0302i	0.0284949	−	0.0284949i
$353$	−292.456	−	292.456i	−0.828488	−	0.828488i	0.158819	−	0.987308i	$-0.449231\pi$
$353$	−292.456	−	292.456i	−0.828488	−	0.828488i	−0.987308	+	0.158819i	$0.949231\pi$
$354$			86.0428i			0.243059i
$355$		0			0
$356$	−192.863			−0.541749
$357$	−48.6336	+	48.6336i	−0.136228	+	0.136228i
$358$	211.508	+	211.508i	0.590803	+	0.590803i
$359$			15.2161i			0.0423848i	0.999775	+	0.0211924i	$0.00674625\pi$
$359$			15.2161i			0.0423848i	−0.999775	+	0.0211924i	$0.993254\pi$
$360$		0			0
$361$	−472.777			−1.30963
$362$	−254.380	+	254.380i	−0.702707	+	0.702707i
$363$	−140.493	−	140.493i	−0.387034	−	0.387034i
$364$			69.2423i			0.190226i
$365$		0			0
$366$	179.634			0.490803
$367$	−132.968	+	132.968i	−0.362310	+	0.362310i	−0.864663	−	0.502353i	$-0.832468\pi$
$367$	−132.968	+	132.968i	−0.362310	+	0.362310i	0.502353	+	0.864663i	$0.332468\pi$
$368$	−32.3448	−	32.3448i	−0.0878936	−	0.0878936i
$369$		−	111.035i		−	0.300907i
$370$		0			0
$371$	−86.1146			−0.232115
$372$	−92.2863	+	92.2863i	−0.248081	+	0.248081i
$373$	−190.777	−	190.777i	−0.511466	−	0.511466i	0.403510	−	0.914975i	$-0.367790\pi$
$373$	−190.777	−	190.777i	−0.511466	−	0.511466i	−0.914975	+	0.403510i	$0.867790\pi$
$374$		−	53.2238i		−	0.142310i
$375$		0			0
$376$	16.9028			0.0449542
$377$	−322.836	+	322.836i	−0.856330	+	0.856330i
$378$	−13.7477	−	13.7477i	−0.0363696	−	0.0363696i
$379$			689.689i			1.81976i	0.414872	+	0.909880i	$0.363826\pi$
$379$			689.689i			1.81976i	−0.414872	+	0.909880i	$0.636174\pi$
$380$		0			0
$381$	−96.8481			−0.254195
$382$	−99.9218	+	99.9218i	−0.261575	+	0.261575i
$383$	−150.477	−	150.477i	−0.392890	−	0.392890i	0.482826	−	0.875716i	$-0.339610\pi$
$383$	−150.477	−	150.477i	−0.392890	−	0.392890i	−0.875716	+	0.482826i	$0.839610\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−205.755			−0.533045
$387$	−69.2423	+	69.2423i	−0.178921	+	0.178921i
$388$	197.448	+	197.448i	0.508887	+	0.508887i
$389$			530.798i			1.36452i	0.731110	+	0.682259i	$0.239003\pi$
$389$			530.798i			1.36452i	−0.731110	+	0.682259i	$0.760997\pi$
$390$		0			0
$391$	−171.633			−0.438960
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	237.443	+	237.443i	0.604182	+	0.604182i
$394$		−	125.902i		−	0.319548i
$395$		0			0
$396$	15.0453			0.0379932
$397$	−18.9270	+	18.9270i	−0.0476750	+	0.0476750i	−0.730542	−	0.682867i	$-0.760733\pi$
$397$	−18.9270	+	18.9270i	−0.0476750	+	0.0476750i	0.682867	+	0.730542i	$0.260733\pi$
$398$	14.4025	+	14.4025i	0.0361871	+	0.0361871i
$399$		−	132.323i		−	0.331636i
$400$		0			0
$401$	751.656			1.87445			0.937227	−	0.348719i	$-0.113383\pi$
$401$	751.656			1.87445			0.937227	+	0.348719i	$0.113383\pi$
$402$	−106.975	+	106.975i	−0.266108	+	0.266108i
$403$	348.609	+	348.609i	0.865036	+	0.865036i
$404$		−	229.793i		−	0.568794i
$405$		0			0
$406$	130.548			0.321546
$407$	−30.7859	+	30.7859i	−0.0756411	+	0.0756411i
$408$	−51.9915	−	51.9915i	−0.127430	−	0.127430i
$409$			383.985i			0.938839i	0.882975	+	0.469419i	$0.155537\pi$
$409$			383.985i			0.938839i	−0.882975	+	0.469419i	$0.844463\pi$
$410$		0			0
$411$	333.002			0.810224
$412$	25.5590	−	25.5590i	0.0620364	−	0.0620364i
$413$	−65.7163	−	65.7163i	−0.159119	−	0.159119i
$414$		−	48.5173i		−	0.117191i
$415$		0			0
$416$	−74.0232			−0.177940
$417$	246.654	−	246.654i	0.591496	−	0.591496i
$418$	72.4060	+	72.4060i	0.173220	+	0.173220i
$419$			226.026i			0.539442i	0.962939	+	0.269721i	$0.0869315\pi$
$419$			226.026i			0.539442i	−0.962939	+	0.269721i	$0.913069\pi$
$420$		0			0
$421$	−118.376			−0.281178			−0.140589	−	0.990068i	$-0.544900\pi$
$421$	−118.376			−0.281178			−0.140589	+	0.990068i	$0.544900\pi$
$422$	173.845	−	173.845i	0.411954	−	0.411954i
$423$	12.6771	+	12.6771i	0.0299695	+	0.0299695i
$424$		−	92.0604i		−	0.217124i
$425$		0			0
$426$	95.4282			0.224010
$427$	−137.198	+	137.198i	−0.321306	+	0.321306i
$428$	−135.684	−	135.684i	−0.317020	−	0.317020i
$429$		−	56.8333i		−	0.132479i
$430$		0			0
$431$	−674.804			−1.56567			−0.782835	−	0.622229i	$-0.786227\pi$
$431$	−674.804			−1.56567			−0.782835	+	0.622229i	$0.786227\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	297.411	+	297.411i	0.686862	+	0.686862i	0.961537	−	0.274675i	$-0.0885702\pi$
$433$	297.411	+	297.411i	0.686862	+	0.686862i	−0.274675	+	0.961537i	$0.588570\pi$
$434$		−	140.970i		−	0.324815i
$435$		0			0
$436$	−68.6969			−0.157562
$437$	233.491	−	233.491i	0.534304	−	0.534304i
$438$	165.628	+	165.628i	0.378146	+	0.378146i
$439$		−	850.208i		−	1.93669i	−0.249613	−	0.968346i	$-0.580303\pi$
$439$		−	850.208i		−	1.93669i	0.249613	−	0.968346i	$-0.419697\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	−196.397	+	196.397i	−0.444336	+	0.444336i
$443$	197.026	+	197.026i	0.444755	+	0.444755i	0.893606	−	0.448851i	$-0.148167\pi$
$443$	197.026	+	197.026i	0.444755	+	0.444755i	−0.448851	+	0.893606i	$0.648167\pi$
$444$			60.1462i			0.135464i
$445$		0			0
$446$	91.1463			0.204364
$447$	56.6536	−	56.6536i	0.126742	−	0.126742i
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$			357.429i			0.796055i	0.917373	+	0.398028i	$0.130305\pi$
$449$			357.429i			0.796055i	−0.917373	+	0.398028i	$0.869695\pi$
$450$		0			0
$451$	−92.8084			−0.205784
$452$	298.027	−	298.027i	0.659353	−	0.659353i
$453$	−290.675	−	290.675i	−0.641666	−	0.641666i
$454$		−	118.434i		−	0.260869i
$455$		0			0
$456$	141.459			0.310217
$457$	361.329	−	361.329i	0.790654	−	0.790654i	−0.190946	−	0.981600i	$-0.561156\pi$
$457$	361.329	−	361.329i	0.790654	−	0.790654i	0.981600	+	0.190946i	$0.0611557\pi$
$458$	207.044	+	207.044i	0.452062	+	0.452062i
$459$		−	77.9872i		−	0.169907i
$460$		0			0
$461$	89.7743			0.194738			0.0973691	−	0.995248i	$-0.468957\pi$
$461$	89.7743			0.194738			0.0973691	+	0.995248i	$0.468957\pi$
$462$	−11.4910	+	11.4910i	−0.0248724	+	0.0248724i
$463$	450.928	+	450.928i	0.973926	+	0.973926i	0.999669	−	0.0257427i	$-0.00819507\pi$
$463$	450.928	+	450.928i	0.973926	+	0.973926i	−0.0257427	+	0.999669i	$0.508195\pi$
$464$			139.561i			0.300778i
$465$		0			0
$466$	501.292			1.07573
$467$	−324.248	+	324.248i	−0.694321	+	0.694321i	−0.963180	−	0.268859i	$-0.913353\pi$
$467$	−324.248	+	324.248i	−0.694321	+	0.694321i	0.268859	+	0.963180i	$0.413353\pi$
$468$	−55.5174	−	55.5174i	−0.118627	−	0.118627i
$469$		−	163.407i		−	0.348417i
$470$		0			0
$471$	267.428			0.567787
$472$	70.2536	−	70.2536i	0.148842	−	0.148842i
$473$	57.8762	+	57.8762i	0.122360	+	0.122360i
$474$			206.453i			0.435554i
$475$		0			0
$476$	79.4183			0.166845
$477$	69.0453	−	69.0453i	0.144749	−	0.144749i
$478$	−318.381	−	318.381i	−0.666069	−	0.666069i
$479$			825.767i			1.72394i	0.506960	+	0.861969i	$0.330769\pi$
$479$			825.767i			1.72394i	−0.506960	+	0.861969i	$0.669231\pi$
$480$		0			0
$481$	227.201			0.472351
$482$	148.889	−	148.889i	0.308899	−	0.308899i
$483$	37.0557	+	37.0557i	0.0767198	+	0.0767198i
$484$			229.424i			0.474017i
$485$		0			0
$486$	22.0454			0.0453609
$487$	−387.165	+	387.165i	−0.795001	+	0.795001i	−0.982302	−	0.187302i	$-0.940026\pi$
$487$	−387.165	+	387.165i	−0.795001	+	0.795001i	0.187302	+	0.982302i	$0.440026\pi$
$488$	−146.671	−	146.671i	−0.300554	−	0.300554i
$489$			144.537i			0.295576i
$490$		0			0
$491$	−456.555			−0.929847			−0.464924	−	0.885351i	$-0.653918\pi$
$491$	−456.555			−0.929847			−0.464924	+	0.885351i	$0.653918\pi$
$492$	−90.6595	+	90.6595i	−0.184267	+	0.184267i
$493$	370.281	+	370.281i	0.751077	+	0.751077i
$494$		−	534.358i		−	1.08170i
$495$		0			0
$496$	150.703			0.303836
$497$	−72.8845	+	72.8845i	−0.146649	+	0.146649i
$498$	41.7156	+	41.7156i	0.0837662	+	0.0837662i
$499$		−	638.363i		−	1.27929i	−0.768672	−	0.639643i	$-0.779082\pi$
$499$		−	638.363i		−	1.27929i	0.768672	−	0.639643i	$-0.220918\pi$
$500$		0			0
$501$	−226.345			−0.451786
$502$	−123.837	+	123.837i	−0.246688	+	0.246688i
$503$	−596.078	−	596.078i	−1.18505	−	1.18505i	−0.978420	−	0.206625i	$-0.933752\pi$
$503$	−596.078	−	596.078i	−1.18505	−	1.18505i	−0.206625	−	0.978420i	$-0.566248\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	−40.5532			−0.0801446
$507$	−2.73382	+	2.73382i	−0.00539215	+	0.00539215i
$508$	79.0762	+	79.0762i	0.155662	+	0.155662i
$509$			609.802i			1.19804i	0.800734	+	0.599020i	$0.204443\pi$
$509$			609.802i			1.19804i	−0.800734	+	0.599020i	$0.795557\pi$
$510$		0			0
$511$	−253.001			−0.495110
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	106.094	+	106.094i	0.206811	+	0.206811i
$514$		−	166.877i		−	0.324663i
$515$		0			0
$516$	113.072			0.219132
$517$	10.5962	−	10.5962i	0.0204955	−	0.0204955i
$518$	−45.9374	−	45.9374i	−0.0886823	−	0.0886823i
$519$		−	223.906i		−	0.431419i
$520$		0			0
$521$	650.540			1.24864			0.624319	−	0.781170i	$-0.285377\pi$
$521$	650.540			1.24864			0.624319	+	0.781170i	$0.285377\pi$
$522$	−104.671	+	104.671i	−0.200519	+	0.200519i
$523$	−598.461	−	598.461i	−1.14428	−	1.14428i	−0.987658	−	0.156627i	$-0.949938\pi$
$523$	−598.461	−	598.461i	−1.14428	−	1.14428i	−0.156627	−	0.987658i	$-0.550062\pi$
$524$		−	387.744i		−	0.739969i
$525$		0			0
$526$	321.598			0.611404
$527$	399.841	−	399.841i	0.758712	−	0.758712i
$528$	−12.2844	−	12.2844i	−0.0232660	−	0.0232660i
$529$		−	398.226i		−	0.752791i
$530$		0			0
$531$	105.380			0.198457
$532$	−108.041	+	108.041i	−0.203085	+	0.203085i
$533$	342.464	+	342.464i	0.642522	+	0.642522i
$534$			236.208i			0.442337i
$535$		0			0
$536$	174.690			0.325914
$537$	259.043	−	259.043i	0.482389	−	0.482389i
$538$	−438.169	−	438.169i	−0.814440	−	0.814440i
$539$		−	17.5529i		−	0.0325656i
$540$		0			0
$541$	418.592			0.773737			0.386869	−	0.922135i	$-0.373557\pi$
$541$	418.592			0.773737			0.386869	+	0.922135i	$0.373557\pi$
$542$	−52.2554	+	52.2554i	−0.0964121	+	0.0964121i
$543$	311.551	+	311.551i	0.573758	+	0.573758i
$544$			84.9017i			0.156069i
$545$		0			0
$546$	84.8042			0.155319
$547$	275.633	−	275.633i	0.503900	−	0.503900i	−0.408748	−	0.912648i	$-0.634034\pi$
$547$	275.633	−	275.633i	0.503900	−	0.503900i	0.912648	+	0.408748i	$0.134034\pi$
$548$	−271.895	−	271.895i	−0.496159	−	0.496159i
$549$		−	220.006i		−	0.400739i
$550$		0			0
$551$	−1007.46			−1.82843
$552$	−39.6142	+	39.6142i	−0.0717648	+	0.0717648i
$553$	−157.681	−	157.681i	−0.285137	−	0.285137i
$554$		−	136.602i		−	0.246573i
$555$		0			0
$556$	−402.784			−0.724432
$557$	586.765	−	586.765i	1.05344	−	1.05344i	0.0549497	−	0.998489i	$-0.482500\pi$
$557$	586.765	−	586.765i	1.05344	−	1.05344i	0.998489	−	0.0549497i	$-0.0174998\pi$
$558$	113.027	+	113.027i	0.202558	+	0.202558i
$559$		−	427.128i		−	0.764093i
$560$		0			0
$561$	−65.1856			−0.116195
$562$	−472.125	+	472.125i	−0.840079	+	0.840079i
$563$	90.6887	+	90.6887i	0.161081	+	0.161081i	0.783046	−	0.621964i	$-0.213665\pi$
$563$	90.6887	+	90.6887i	0.161081	+	0.161081i	−0.621964	+	0.783046i	$0.713665\pi$
$564$		−	20.7016i		−	0.0367050i
$565$		0			0
$566$	−325.477			−0.575048
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	−77.9168	−	77.9168i	−0.137177	−	0.137177i
$569$		−	647.905i		−	1.13867i	−0.822105	−	0.569336i	$-0.807200\pi$
$569$		−	647.905i		−	1.13867i	0.822105	−	0.569336i	$-0.192800\pi$
$570$		0			0
$571$	463.377			0.811519			0.405759	−	0.913980i	$-0.367007\pi$
$571$	463.377			0.811519			0.405759	+	0.913980i	$0.367007\pi$
$572$	−46.4042	+	46.4042i	−0.0811262	+	0.0811262i
$573$	122.379	+	122.379i	0.213575	+	0.213575i
$574$		−	138.485i		−	0.241262i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	537.526	−	537.526i	0.931588	−	0.931588i	−0.0662174	−	0.997805i	$-0.521093\pi$
$577$	537.526	−	537.526i	0.931588	−	0.931588i	0.997805	+	0.0662174i	$0.0210931\pi$
$578$	−63.7406	−	63.7406i	−0.110278	−	0.110278i
$579$			251.998i			0.435229i
$580$		0			0
$581$	−63.7216			−0.109676
$582$	241.824	−	241.824i	0.415504	−	0.415504i
$583$	−57.7115	−	57.7115i	−0.0989906	−	0.0989906i
$584$		−	270.470i		−	0.463133i
$585$		0			0
$586$	99.8131			0.170330
$587$	−338.268	+	338.268i	−0.576265	+	0.576265i	−0.933872	−	0.357607i	$-0.883593\pi$
$587$	−338.268	+	338.268i	−0.576265	+	0.576265i	0.357607	+	0.933872i	$0.383593\pi$
$588$	−17.1464	−	17.1464i	−0.0291606	−	0.0291606i
$589$			1087.89i			1.84702i
$590$		0			0
$591$	−154.198			−0.260910
$592$	49.1092	−	49.1092i	0.0829547	−	0.0829547i
$593$	−54.6474	−	54.6474i	−0.0921542	−	0.0921542i	0.659527	−	0.751681i	$-0.270757\pi$
$593$	−54.6474	−	54.6474i	−0.0921542	−	0.0921542i	−0.751681	+	0.659527i	$0.770757\pi$
$594$		−	18.4267i		−	0.0310213i
$595$		0			0
$596$	−92.5150			−0.155226
$597$	17.6393	−	17.6393i	0.0295466	−	0.0295466i
$598$	149.642	+	149.642i	0.250237	+	0.250237i
$599$			481.284i			0.803479i	0.915754	+	0.401739i	$0.131594\pi$
$599$			481.284i			0.803479i	−0.915754	+	0.401739i	$0.868406\pi$
$600$		0			0
$601$	901.413			1.49985			0.749927	−	0.661520i	$-0.230088\pi$
$601$	901.413			1.49985			0.749927	+	0.661520i	$0.230088\pi$
$602$	−86.3603	+	86.3603i	−0.143456	+	0.143456i
$603$	131.017	+	131.017i	0.217276	+	0.217276i
$604$			474.670i			0.785877i
$605$		0			0
$606$	−281.437			−0.464418
$607$	348.176	−	348.176i	0.573601	−	0.573601i	−0.359532	−	0.933133i	$-0.617064\pi$
$607$	348.176	−	348.176i	0.573601	−	0.573601i	0.933133	+	0.359532i	$0.117064\pi$
$608$	−115.501	−	115.501i	−0.189968	−	0.189968i
$609$		−	159.887i		−	0.262541i
$610$		0			0
$611$	−78.1999			−0.127987
$612$	−63.6763	+	63.6763i	−0.104046	+	0.104046i
$613$	−311.057	−	311.057i	−0.507434	−	0.507434i	0.406304	−	0.913738i	$-0.366817\pi$
$613$	−311.057	−	311.057i	−0.507434	−	0.507434i	−0.913738	+	0.406304i	$0.866817\pi$
$614$		−	743.461i		−	1.21085i
$615$		0			0
$616$	18.7648			0.0304623
$617$	829.657	−	829.657i	1.34466	−	1.34466i	0.453309	−	0.891353i	$-0.350243\pi$
$617$	829.657	−	829.657i	1.34466	−	1.34466i	0.891353	−	0.453309i	$-0.149757\pi$
$618$	−31.3033	−	31.3033i	−0.0506525	−	0.0506525i
$619$		−	532.670i		−	0.860533i	−0.902702	−	0.430266i	$-0.858420\pi$
$619$		−	532.670i		−	0.860533i	0.902702	−	0.430266i	$-0.141580\pi$
$620$		0			0
$621$	−59.4213			−0.0956864
$622$	−83.4682	+	83.4682i	−0.134193	+	0.134193i
$623$	−180.407	−	180.407i	−0.289577	−	0.289577i
$624$			90.6595i			0.145288i
$625$		0			0
$626$	88.8116			0.141872
$627$	88.6789	−	88.6789i	0.141434	−	0.141434i
$628$	−218.354	−	218.354i	−0.347697	−	0.347697i
$629$		−	260.591i		−	0.414294i
$630$		0			0
$631$	290.181			0.459875			0.229938	−	0.973205i	$-0.426148\pi$
$631$	290.181			0.459875			0.229938	+	0.973205i	$0.426148\pi$
$632$	168.568	−	168.568i	0.266721	−	0.266721i
$633$	−212.915	−	212.915i	−0.336359	−	0.336359i
$634$		−	587.393i		−	0.926488i
$635$		0			0
$636$	−112.751			−0.177281
$637$	−64.7703	+	64.7703i	−0.101680	+	0.101680i
$638$	87.4892	+	87.4892i	0.137130	+	0.137130i
$639$		−	116.875i		−	0.182903i
$640$		0			0
$641$	477.534			0.744982			0.372491	−	0.928036i	$-0.378504\pi$
$641$	477.534			0.744982			0.372491	+	0.928036i	$0.378504\pi$
$642$	−166.179	+	166.179i	−0.258845	+	0.258845i
$643$	168.649	+	168.649i	0.262284	+	0.262284i	0.825981	−	0.563697i	$-0.190622\pi$
$643$	168.649	+	168.649i	0.262284	+	0.262284i	−0.563697	+	0.825981i	$0.690622\pi$
$644$		−	60.5117i		−	0.0939622i
$645$		0			0
$646$	−612.888			−0.948744
$647$	−399.196	+	399.196i	−0.616996	+	0.616996i	−0.944760	−	0.327764i	$-0.893705\pi$
$647$	−399.196	+	399.196i	−0.616996	+	0.616996i	0.327764	+	0.944760i	$0.393705\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	88.0823i		−	0.135720i
$650$		0			0
$651$	−172.652			−0.265210
$652$	118.014	−	118.014i	0.181003	−	0.181003i
$653$	−397.176	−	397.176i	−0.608232	−	0.608232i	0.334251	−	0.942484i	$-0.391517\pi$
$653$	−397.176	−	397.176i	−0.608232	−	0.608232i	−0.942484	+	0.334251i	$0.891517\pi$
$654$			84.1362i			0.128649i
$655$		0			0
$656$	148.046			0.225680
$657$	202.852	−	202.852i	0.308755	−	0.308755i
$658$	15.8111	+	15.8111i	0.0240290	+	0.0240290i
$659$			829.056i			1.25805i	0.777384	+	0.629026i	$0.216546\pi$
$659$			829.056i			1.25805i	−0.777384	+	0.629026i	$0.783454\pi$
$660$		0			0
$661$	−849.463			−1.28512			−0.642559	−	0.766236i	$-0.722127\pi$
$661$	−849.463			−1.28512			−0.642559	+	0.766236i	$0.722127\pi$
$662$	333.640	−	333.640i	0.503987	−	0.503987i
$663$	240.536	+	240.536i	0.362799	+	0.362799i
$664$		−	68.1212i		−	0.102592i
$665$		0			0
$666$	73.6638			0.110606
$667$	282.130	−	282.130i	0.422984	−	0.422984i
$668$	184.810	+	184.810i	0.276661	+	0.276661i
$669$		−	111.631i		−	0.166863i
$670$		0			0
$671$	−183.892			−0.274057
$672$	18.3303	−	18.3303i	0.0272772	−	0.0272772i
$673$	182.693	+	182.693i	0.271461	+	0.271461i	0.829688	−	0.558227i	$-0.188518\pi$
$673$	182.693	+	182.693i	0.271461	+	0.271461i	−0.558227	+	0.829688i	$0.688518\pi$
$674$		−	378.852i		−	0.562095i
$675$		0			0
$676$	4.46431			0.00660401
$677$	−550.403	+	550.403i	−0.813002	+	0.813002i	−0.985083	−	0.172081i	$-0.944951\pi$
$677$	−550.403	+	550.403i	−0.813002	+	0.813002i	0.172081	+	0.985083i	$0.444951\pi$
$678$	−365.007	−	365.007i	−0.538359	−	0.538359i
$679$			369.392i			0.544023i
$680$		0			0
$681$	−145.052			−0.212998
$682$	94.4738	−	94.4738i	0.138525	−	0.138525i
$683$	445.154	+	445.154i	0.651762	+	0.651762i	0.953417	−	0.301655i	$-0.0975390\pi$
$683$	445.154	+	445.154i	0.651762	+	0.651762i	−0.301655	+	0.953417i	$0.597539\pi$
$684$		−	173.251i		−	0.253291i
$685$		0			0
$686$	26.1916			0.0381802
$687$	253.577	−	253.577i	0.369107	−	0.369107i
$688$	−92.3231	−	92.3231i	−0.134190	−	0.134190i
$689$			425.913i			0.618161i
$690$		0			0
$691$	−1171.96			−1.69604			−0.848019	−	0.529966i	$-0.822205\pi$
$691$	−1171.96			−1.69604			−0.848019	+	0.529966i	$0.822205\pi$
$692$	−182.819	+	182.819i	−0.264189	+	0.264189i
$693$	14.0736	+	14.0736i	0.0203082	+	0.0203082i
$694$			228.117i			0.328699i
$695$		0			0
$696$	170.927			0.245585
$697$	392.793	−	392.793i	0.563549	−	0.563549i
$698$	−231.559	−	231.559i	−0.331746	−	0.331746i
$699$		−	613.954i		−	0.878332i
$700$		0			0
$701$	−585.877			−0.835773			−0.417887	−	0.908499i	$-0.637229\pi$
$701$	−585.877			−0.835773			−0.417887	+	0.908499i	$0.637229\pi$
$702$	−67.9946	+	67.9946i	−0.0968584	+	0.0968584i
$703$	354.509	+	354.509i	0.504281	+	0.504281i
$704$			20.0604i			0.0284949i
$705$		0			0
$706$	584.913			0.828488
$707$	214.951	−	214.951i	0.304033	−	0.304033i
$708$	−86.0428	−	86.0428i	−0.121529	−	0.121529i
$709$		−	1206.85i		−	1.70218i	−0.525016	−	0.851092i	$-0.675941\pi$
$709$		−	1206.85i		−	1.70218i	0.525016	−	0.851092i	$-0.324059\pi$
$710$		0			0
$711$	252.852			0.355628
$712$	192.863	−	192.863i	0.270875	−	0.270875i
$713$	−304.654	−	304.654i	−0.427284	−	0.427284i
$714$		−	97.2671i		−	0.136228i
$715$		0			0
$716$	−423.015			−0.590803
$717$	−389.935	+	389.935i	−0.543843	+	0.543843i
$718$	−15.2161	−	15.2161i	−0.0211924	−	0.0211924i
$719$		−	1036.00i		−	1.44089i	−0.693513	−	0.720444i	$-0.743938\pi$
$719$		−	1036.00i		−	1.44089i	0.693513	−	0.720444i	$-0.256062\pi$
$720$		0			0
$721$	47.8165			0.0663197
$722$	472.777	−	472.777i	0.654816	−	0.654816i
$723$	−182.351	−	182.351i	−0.252215	−	0.252215i
$724$		−	508.760i		−	0.702707i
$725$		0			0
$726$	280.986			0.387034
$727$	145.807	−	145.807i	0.200559	−	0.200559i	−0.599680	−	0.800240i	$-0.704706\pi$
$727$	145.807	−	145.807i	0.200559	−	0.200559i	0.800240	+	0.599680i	$0.204706\pi$
$728$	−69.2423	−	69.2423i	−0.0951131	−	0.0951131i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−489.899			−0.670177
$732$	−179.634	+	179.634i	−0.245402	+	0.245402i
$733$	−885.048	−	885.048i	−1.20743	−	1.20743i	−0.971856	−	0.235576i	$-0.924302\pi$
$733$	−885.048	−	885.048i	−1.20743	−	1.20743i	−0.235576	−	0.971856i	$-0.575698\pi$
$734$		−	265.936i		−	0.362310i
$735$		0			0
$736$	64.6897			0.0878936
$737$	109.511	−	109.511i	0.148590	−	0.148590i
$738$	111.035	+	111.035i	0.150454	+	0.150454i
$739$			1033.14i			1.39802i	0.715110	+	0.699012i	$0.246376\pi$
$739$			1033.14i			1.39802i	−0.715110	+	0.699012i	$0.753624\pi$
$740$		0			0
$741$	−654.453			−0.883202
$742$	86.1146	−	86.1146i	0.116057	−	0.116057i
$743$	914.687	+	914.687i	1.23107	+	1.23107i	0.963552	+	0.267520i	$0.0862043\pi$
$743$	914.687	+	914.687i	1.23107	+	1.23107i	0.267520	+	0.963552i	$0.413796\pi$
$744$		−	184.573i		−	0.248081i
$745$		0			0
$746$	381.553			0.511466
$747$	51.0909	−	51.0909i	0.0683948	−	0.0683948i
$748$	53.2238	+	53.2238i	0.0711549	+	0.0711549i
$749$		−	253.842i		−	0.338908i
$750$		0			0
$751$	685.276			0.912485			0.456243	−	0.889855i	$-0.349195\pi$
$751$	685.276			0.912485			0.456243	+	0.889855i	$0.349195\pi$
$752$	−16.9028	+	16.9028i	−0.0224771	+	0.0224771i
$753$	151.669	+	151.669i	0.201420	+	0.201420i
$754$		−	645.673i		−	0.856330i
$755$		0			0
$756$	27.4955			0.0363696
$757$	994.803	−	994.803i	1.31414	−	1.31414i	0.395804	−	0.918335i	$-0.370466\pi$
$757$	994.803	−	994.803i	1.31414	−	1.31414i	0.918335	−	0.395804i	$-0.129534\pi$
$758$	−689.689	−	689.689i	−0.909880	−	0.909880i
$759$			49.6673i			0.0654378i
$760$		0			0
$761$	−747.500			−0.982260			−0.491130	−	0.871086i	$-0.663416\pi$
$761$	−747.500			−0.982260			−0.491130	+	0.871086i	$0.663416\pi$
$762$	96.8481	−	96.8481i	0.127097	−	0.127097i
$763$	−64.2601	−	64.2601i	−0.0842203	−	0.0842203i
$764$		−	199.844i		−	0.261575i
$765$		0			0
$766$	300.953			0.392890
$767$	−325.025	+	325.025i	−0.423761	+	0.423761i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	665.462i		−	0.865360i	−0.901548	−	0.432680i	$-0.857568\pi$
$769$		−	665.462i		−	0.865360i	0.901548	−	0.432680i	$-0.142432\pi$
$770$		0			0
$771$	−204.381			−0.265086
$772$	205.755	−	205.755i	0.266522	−	0.266522i
$773$	497.431	+	497.431i	0.643507	+	0.643507i	0.951416	−	0.307909i	$-0.0996291\pi$
$773$	497.431	+	497.431i	0.643507	+	0.643507i	−0.307909	+	0.951416i	$0.599629\pi$
$774$		−	138.485i		−	0.178921i
$775$		0			0
$776$	−394.896			−0.508887
$777$	−56.2616	+	56.2616i	−0.0724088	+	0.0724088i
$778$	−530.798	−	530.798i	−0.682259	−	0.682259i
$779$			1068.72i			1.37191i
$780$		0			0
$781$	−97.6902			−0.125083
$782$	171.633	−	171.633i	0.219480	−	0.219480i
$783$	128.195	+	128.195i	0.163723	+	0.163723i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	−474.887			−0.604182
$787$	941.079	−	941.079i	1.19578	−	1.19578i	0.220363	−	0.975418i	$-0.429276\pi$
$787$	941.079	−	941.079i	1.19578	−	1.19578i	0.975418	−	0.220363i	$-0.0707240\pi$
$788$	125.902	+	125.902i	0.159774	+	0.159774i
$789$		−	393.876i		−	0.499209i
$790$		0			0
$791$	557.558			0.704878
$792$	−15.0453	+	15.0453i	−0.0189966	+	0.0189966i
$793$	678.564	+	678.564i	0.855692	+	0.855692i
$794$		−	37.8539i		−	0.0476750i
$795$		0			0
$796$	−28.8049			−0.0361871
$797$	447.860	−	447.860i	0.561932	−	0.561932i	−0.367924	−	0.929856i	$-0.619931\pi$
$797$	447.860	−	447.860i	0.561932	−	0.561932i	0.929856	+	0.367924i	$0.119931\pi$
$798$	132.323	+	132.323i	0.165818	+	0.165818i
$799$			89.6922i			0.112256i
$800$		0			0
$801$	289.294			0.361166
$802$	−751.656	+	751.656i	−0.937227	+	0.937227i
$803$	−169.554	−	169.554i	−0.211151	−	0.211151i
$804$		−	213.951i		−	0.266108i
$805$		0			0
$806$	−697.219			−0.865036
$807$	−536.645	+	536.645i	−0.664988	+	0.664988i
$808$	229.793	+	229.793i	0.284397	+	0.284397i
$809$		−	720.108i		−	0.890121i	−0.895501	−	0.445060i	$-0.853182\pi$
$809$		−	720.108i		−	0.890121i	0.895501	−	0.445060i	$-0.146818\pi$
$810$		0			0
$811$	312.110			0.384846			0.192423	−	0.981312i	$-0.438365\pi$
$811$	312.110			0.384846			0.192423	+	0.981312i	$0.438365\pi$
$812$	−130.548	+	130.548i	−0.160773	+	0.160773i
$813$	63.9995	+	63.9995i	0.0787202	+	0.0787202i
$814$		−	61.5719i		−	0.0756411i
$815$		0			0
$816$	103.983			0.127430
$817$	666.462	−	666.462i	0.815743	−	0.815743i
$818$	−383.985	−	383.985i	−0.469419	−	0.469419i
$819$		−	103.863i		−	0.126817i
$820$		0			0
$821$	1635.61			1.99222			0.996110	−	0.0881241i	$-0.0280872\pi$
$821$	1635.61			1.99222			0.996110	+	0.0881241i	$0.0280872\pi$
$822$	−333.002	+	333.002i	−0.405112	+	0.405112i
$823$	445.484	+	445.484i	0.541293	+	0.541293i	0.923908	−	0.382615i	$-0.124976\pi$
$823$	445.484	+	445.484i	0.541293	+	0.541293i	−0.382615	+	0.923908i	$0.624976\pi$
$824$			51.1180i			0.0620364i
$825$		0			0
$826$	131.433			0.159119
$827$	−1045.75	+	1045.75i	−1.26451	+	1.26451i	−0.315626	+	0.948884i	$0.602215\pi$
$827$	−1045.75	+	1045.75i	−1.26451	+	1.26451i	−0.948884	+	0.315626i	$0.897785\pi$
$828$	48.5173	+	48.5173i	0.0585957	+	0.0585957i
$829$		−	636.907i		−	0.768284i	−0.923274	−	0.384142i	$-0.874497\pi$
$829$		−	636.907i		−	0.768284i	0.923274	−	0.384142i	$-0.125503\pi$
$830$		0			0
$831$	−167.302			−0.201326
$832$	74.0232	−	74.0232i	0.0889702	−	0.0889702i
$833$	74.2890	+	74.2890i	0.0891825	+	0.0891825i
$834$			493.308i			0.591496i
$835$		0			0
$836$	−144.812			−0.173220
$837$	138.429	−	138.429i	0.165388	−	0.165388i
$838$	−226.026	−	226.026i	−0.269721	−	0.269721i
$839$		−	1338.90i		−	1.59583i	−0.602771	−	0.797914i	$-0.705937\pi$
$839$		−	1338.90i		−	1.59583i	0.602771	−	0.797914i	$-0.294063\pi$
$840$		0			0
$841$	−376.333			−0.447483
$842$	118.376	−	118.376i	0.140589	−	0.140589i
$843$	578.232	+	578.232i	0.685922	+	0.685922i
$844$			347.689i			0.411954i
$845$		0			0
$846$	−25.3542			−0.0299695
$847$	−214.607	+	214.607i	−0.253373	+	0.253373i
$848$	92.0604	+	92.0604i	0.108562	+	0.108562i
$849$			398.627i			0.469525i
$850$		0			0
$851$	−198.554			−0.233318
$852$	−95.4282	+	95.4282i	−0.112005	+	0.112005i
$853$	−207.083	−	207.083i	−0.242770	−	0.242770i	0.575225	−	0.817995i	$-0.304915\pi$
$853$	−207.083	−	207.083i	−0.242770	−	0.242770i	−0.817995	+	0.575225i	$0.804915\pi$
$854$		−	274.396i		−	0.321306i
$855$		0			0
$856$	271.369			0.317020
$857$	937.379	−	937.379i	1.09379	−	1.09379i	0.0986710	−	0.995120i	$-0.468541\pi$
$857$	937.379	−	937.379i	1.09379	−	1.09379i	0.995120	−	0.0986710i	$-0.0314591\pi$
$858$	56.8333	+	56.8333i	0.0662393	+	0.0662393i
$859$			1035.98i			1.20603i	0.797729	+	0.603016i	$0.206035\pi$
$859$			1035.98i			1.20603i	−0.797729	+	0.603016i	$0.793965\pi$
$860$		0			0
$861$	−169.608			−0.196990
$862$	674.804	−	674.804i	0.782835	−	0.782835i
$863$	932.668	+	932.668i	1.08073	+	1.08073i	0.996442	+	0.0842859i	$0.0268609\pi$
$863$	932.668	+	932.668i	1.08073	+	1.08073i	0.0842859	+	0.996442i	$0.473139\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	−594.823			−0.686862
$867$	−78.0660	+	78.0660i	−0.0900415	+	0.0900415i
$868$	140.970	+	140.970i	0.162407	+	0.162407i
$869$		−	211.346i		−	0.243206i
$870$		0			0
$871$	−808.194			−0.927892
$872$	68.6969	−	68.6969i	0.0787809	−	0.0787809i
$873$	−296.172	−	296.172i	−0.339258	−	0.339258i
$874$			466.982i			0.534304i
$875$		0			0
$876$	−331.256			−0.378146
$877$	99.5858	−	99.5858i	0.113553	−	0.113553i	−0.648047	−	0.761600i	$-0.724414\pi$
$877$	99.5858	−	99.5858i	0.113553	−	0.113553i	0.761600	+	0.648047i	$0.224414\pi$
$878$	850.208	+	850.208i	0.968346	+	0.968346i
$879$		−	122.246i		−	0.139074i
$880$		0			0
$881$	552.941			0.627629			0.313815	−	0.949484i	$-0.398393\pi$
$881$	552.941			0.627629			0.313815	+	0.949484i	$0.398393\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	1075.74	+	1075.74i	1.21828	+	1.21828i	0.968235	+	0.250040i	$0.0804439\pi$
$883$	1075.74	+	1075.74i	1.21828	+	1.21828i	0.250040	+	0.968235i	$0.419556\pi$
$884$		−	392.793i		−	0.444336i
$885$		0			0
$886$	−394.053			−0.444755
$887$	−867.409	+	867.409i	−0.977914	+	0.977914i	−0.999761	−	0.0218477i	$-0.993045\pi$
$887$	−867.409	+	867.409i	−0.977914	+	0.977914i	0.0218477	+	0.999761i	$0.493045\pi$
$888$	−60.1462	−	60.1462i	−0.0677322	−	0.0677322i
$889$			147.938i			0.166409i
$890$		0			0
$891$	−22.5680			−0.0253288
$892$	−91.1463	+	91.1463i	−0.102182	+	0.102182i
$893$	−122.018	−	122.018i	−0.136638	−	0.136638i
$894$			113.307i			0.126742i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	183.273	−	183.273i	0.204318	−	0.204318i
$898$	−357.429	−	357.429i	−0.398028	−	0.398028i
$899$			1314.52i			1.46220i
$900$		0			0
$901$	488.505			0.542181
$902$	92.8084	−	92.8084i	0.102892	−	0.102892i
$903$	105.769	+	105.769i	0.117131	+	0.117131i
$904$			596.055i			0.659353i
$905$		0			0
$906$	581.349			0.641666
$907$	100.803	−	100.803i	0.111139	−	0.111139i	−0.649350	−	0.760489i	$-0.724959\pi$
$907$	100.803	−	100.803i	0.111139	−	0.111139i	0.760489	+	0.649350i	$0.224959\pi$
$908$	118.434	+	118.434i	0.130434	+	0.130434i
$909$			344.689i			0.379196i
$910$		0			0
$911$	−655.096			−0.719095			−0.359548	−	0.933127i	$-0.617069\pi$
$911$	−655.096			−0.719095			−0.359548	+	0.933127i	$0.617069\pi$
$912$	−141.459	+	141.459i	−0.155109	+	0.155109i
$913$	−42.7044	−	42.7044i	−0.0467737	−	0.0467737i
$914$			722.658i			0.790654i
$915$		0			0
$916$	−414.089			−0.452062
$917$	362.701	−	362.701i	0.395530	−	0.395530i
$918$	77.9872	+	77.9872i	0.0849534	+	0.0849534i
$919$		−	1006.68i		−	1.09540i	−0.836673	−	0.547702i	$-0.815503\pi$
$919$		−	1006.68i		−	1.09540i	0.836673	−	0.547702i	$-0.184497\pi$
$920$		0			0
$921$	−910.550			−0.988654
$922$	−89.7743	+	89.7743i	−0.0973691	+	0.0973691i
$923$	360.478	+	360.478i	0.390550	+	0.390550i
$924$		−	22.9821i		−	0.0248724i
$925$		0			0
$926$	−901.855			−0.973926
$927$	−38.3385	+	38.3385i	−0.0413576	+	0.0413576i
$928$	−139.561	−	139.561i	−0.150389	−	0.150389i
$929$			230.933i			0.248582i	0.992246	+	0.124291i	$0.0396656\pi$
$929$			230.933i			0.248582i	−0.992246	+	0.124291i	$0.960334\pi$
$930$		0			0
$931$	−202.126			−0.217107
$932$	−501.292	+	501.292i	−0.537867	+	0.537867i
$933$	102.227	+	102.227i	0.109568	+	0.109568i
$934$		−	648.496i		−	0.694321i
$935$		0			0
$936$	111.035			0.118627
$937$	−116.924	+	116.924i	−0.124786	+	0.124786i	−0.766742	−	0.641956i	$-0.778123\pi$
$937$	−116.924	+	116.924i	−0.124786	+	0.124786i	0.641956	+	0.766742i	$0.278123\pi$
$938$	163.407	+	163.407i	0.174208	+	0.174208i
$939$		−	108.772i		−	0.115838i
$940$		0			0
$941$	−35.5538			−0.0377830			−0.0188915	−	0.999822i	$-0.506014\pi$
$941$	−35.5538			−0.0377830			−0.0188915	+	0.999822i	$0.506014\pi$
$942$	−267.428	+	267.428i	−0.283894	+	0.283894i
$943$	−299.284	−	299.284i	−0.317374	−	0.317374i
$944$			140.507i			0.148842i
$945$		0			0
$946$	−115.752			−0.122360
$947$	−607.150	+	607.150i	−0.641130	+	0.641130i	−0.950833	−	0.309703i	$-0.899770\pi$
$947$	−607.150	+	607.150i	−0.641130	+	0.641130i	0.309703	+	0.950833i	$0.399770\pi$
$948$	−206.453	−	206.453i	−0.217777	−	0.217777i
$949$			1251.31i			1.31856i
$950$		0			0
$951$	−719.407			−0.756474
$952$	−79.4183	+	79.4183i	−0.0834226	+	0.0834226i
$953$	934.907	+	934.907i	0.981014	+	0.981014i	0.999823	−	0.0188086i	$-0.00598732\pi$
$953$	934.907	+	934.907i	0.981014	+	0.981014i	−0.0188086	+	0.999823i	$0.505987\pi$
$954$			138.091i			0.144749i
$955$		0			0
$956$	636.762			0.666069
$957$	107.152	−	107.152i	0.111967	−	0.111967i
$958$	−825.767	−	825.767i	−0.861969	−	0.861969i
$959$		−	508.669i		−	0.530416i
$960$		0			0
$961$	458.459			0.477064
$962$	−227.201	+	227.201i	−0.236176	+	0.236176i
$963$	203.527	+	203.527i	0.211346	+	0.211346i
$964$			297.779i			0.308899i
$965$		0			0
$966$	−74.1114			−0.0767198
$967$	−400.279	+	400.279i	−0.413939	+	0.413939i	−0.883108	−	0.469169i	$-0.844553\pi$
$967$	−400.279	+	400.279i	−0.413939	+	0.413939i	0.469169	+	0.883108i	$0.344553\pi$
$968$	−229.424	−	229.424i	−0.237009	−	0.237009i
$969$			750.632i			0.774646i
$970$		0			0
$971$	−304.499			−0.313593			−0.156797	−	0.987631i	$-0.550117\pi$
$971$	−304.499			−0.313593			−0.156797	+	0.987631i	$0.550117\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−376.770	−	376.770i	−0.387225	−	0.387225i
$974$		−	774.331i		−	0.795001i
$975$		0			0
$976$	293.341			0.300554
$977$	−1212.78	+	1212.78i	−1.24133	+	1.24133i	−0.281879	+	0.959450i	$0.590958\pi$
$977$	−1212.78	+	1212.78i	−1.24133	+	1.24133i	−0.959450	+	0.281879i	$0.909042\pi$
$978$	−144.537	−	144.537i	−0.147788	−	0.147788i
$979$		−	241.807i		−	0.246993i
$980$		0			0
$981$	103.045			0.105041
$982$	456.555	−	456.555i	0.464924	−	0.464924i
$983$	−1209.04	−	1209.04i	−1.22994	−	1.22994i	−0.963984	−	0.265960i	$-0.914311\pi$
$983$	−1209.04	−	1209.04i	−1.22994	−	1.22994i	−0.265960	−	0.963984i	$-0.585689\pi$
$984$		−	181.319i		−	0.184267i
$985$		0			0
$986$	−740.562			−0.751077
$987$	19.3646	−	19.3646i	0.0196196	−	0.0196196i
$988$	534.358	+	534.358i	0.540849	+	0.540849i
$989$			373.272i			0.377424i
$990$		0			0
$991$	702.456			0.708835			0.354418	−	0.935087i	$-0.384679\pi$
$991$	702.456			0.708835			0.354418	+	0.935087i	$0.384679\pi$
$992$	−150.703	+	150.703i	−0.151918	+	0.151918i
$993$	−408.624	−	408.624i	−0.411504	−	0.411504i
$994$		−	145.769i		−	0.146649i
$995$		0			0
$996$	−83.4311			−0.0837662
$997$	1280.10	−	1280.10i	1.28395	−	1.28395i	0.345550	−	0.938401i	$-0.387693\pi$
$997$	1280.10	−	1280.10i	1.28395	−	1.28395i	0.938401	−	0.345550i	$-0.112307\pi$
$998$	638.363	+	638.363i	0.639643	+	0.639643i
$999$		−	90.2193i		−	0.0903096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.a.43.4	✓	8
5.2	odd	4	inner	1050.3.l.a.757.4	yes	8
5.3	odd	4		1050.3.l.e.757.1	yes	8
5.4	even	2		1050.3.l.e.43.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.l.a.43.4	✓	8	1.1	even	1	trivial
1050.3.l.a.757.4	yes	8	5.2	odd	4	inner
1050.3.l.e.43.1	yes	8	5.4	even	2
1050.3.l.e.757.1	yes	8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +2.50755 q^{11} +(2.44949 - 2.44949i) q^{12} +(-9.25290 - 9.25290i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-10.6127 + 10.6127i) q^{17} +(-3.00000 - 3.00000i) q^{18} -28.8752i q^{19} +4.58258 q^{21} +(-2.50755 + 2.50755i) q^{22} +(8.08621 + 8.08621i) q^{23} +4.89898i q^{24} +18.5058 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -34.8903i q^{29} -37.6757 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.07111 + 3.07111i) q^{33} -21.2254i q^{34} +6.00000 q^{36} +(-12.2773 + 12.2773i) q^{37} +(28.8752 + 28.8752i) q^{38} -22.6649i q^{39} -37.0116 q^{41} +(-4.58258 + 4.58258i) q^{42} +(23.0808 + 23.0808i) q^{43} -5.01510i q^{44} -16.1724 q^{46} +(4.22570 - 4.22570i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} -25.9957 q^{51} +(-18.5058 + 18.5058i) q^{52} +(-23.0151 - 23.0151i) q^{53} -7.34847i q^{54} +7.48331 q^{56} +(35.3648 - 35.3648i) q^{57} +(34.8903 + 34.8903i) q^{58} -35.1268i q^{59} -73.3353 q^{61} +(37.6757 - 37.6757i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} -6.14222 q^{66} +(43.6725 - 43.6725i) q^{67} +(21.2254 + 21.2254i) q^{68} +19.8071i q^{69} -38.9584 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-67.6174 - 67.6174i) q^{73} -24.5546i q^{74} -57.7504 q^{76} +(4.69120 - 4.69120i) q^{77} +(22.6649 + 22.6649i) q^{78} -84.2839i q^{79} -9.00000 q^{81} +(37.0116 - 37.0116i) q^{82} +(-17.0303 - 17.0303i) q^{83} -9.16515i q^{84} -46.1615 q^{86} +(42.7317 - 42.7317i) q^{87} +(5.01510 + 5.01510i) q^{88} -96.4314i q^{89} -34.6212 q^{91} +(16.1724 - 16.1724i) q^{92} +(-46.1431 - 46.1431i) q^{93} +8.45139i q^{94} +9.79796 q^{96} +(-98.7241 + 98.7241i) q^{97} +(7.00000 + 7.00000i) q^{98} +7.52265i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 32 q^{11} - 40 q^{13} - 32 q^{16} + 40 q^{17} - 24 q^{18} + 32 q^{22} + 8 q^{23} + 80 q^{26} + 96 q^{31} + 32 q^{32} + 72 q^{33} + 48 q^{36} - 112 q^{37} + 24 q^{38} - 160 q^{41} + 64 q^{43} - 16 q^{46} - 64 q^{47} + 24 q^{51} - 80 q^{52} - 80 q^{53} - 48 q^{57} - 32 q^{58} - 128 q^{61} - 96 q^{62} - 144 q^{66} + 304 q^{67} - 80 q^{68} + 240 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{76} + 56 q^{77} + 120 q^{78} - 72 q^{81} + 160 q^{82} - 64 q^{83} - 128 q^{86} + 96 q^{87} - 64 q^{88} + 56 q^{91} + 16 q^{92} - 144 q^{93} - 272 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 32 * q^11 - 40 * q^13 - 32 * q^16 + 40 * q^17 - 24 * q^18 + 32 * q^22 + 8 * q^23 + 80 * q^26 + 96 * q^31 + 32 * q^32 + 72 * q^33 + 48 * q^36 - 112 * q^37 + 24 * q^38 - 160 * q^41 + 64 * q^43 - 16 * q^46 - 64 * q^47 + 24 * q^51 - 80 * q^52 - 80 * q^53 - 48 * q^57 - 32 * q^58 - 128 * q^61 - 96 * q^62 - 144 * q^66 + 304 * q^67 - 80 * q^68 + 240 * q^71 - 48 * q^72 - 24 * q^73 - 48 * q^76 + 56 * q^77 + 120 * q^78 - 72 * q^81 + 160 * q^82 - 64 * q^83 - 128 * q^86 + 96 * q^87 - 64 * q^88 + 56 * q^91 + 16 * q^92 - 144 * q^93 - 272 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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