LMFDB - Embedded newform 1050.3.l.e.757.1

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			757.1
Root			$0.323042 + 0.323042i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.e.43.1

$q$-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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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	$-0.582122\pi$
$13$	9.25290	−	9.25290i	0.711761	−	0.711761i	0.966904	+	0.255142i	$0.0821223\pi$
$14$		−	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	$-0.104471\pi$
$17$	10.6127	+	10.6127i	0.624277	+	0.624277i	−0.322345	+	0.946622i	$0.604471\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			28.8752i			1.51975i	0.650071	+	0.759874i	$0.274739\pi$
$19$			28.8752i			1.51975i	−0.650071	+	0.759874i	$0.725261\pi$
$20$		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	$-0.829971\pi$
$23$	−8.08621	+	8.08621i	−0.351574	+	0.351574i	0.509121	+	0.860695i	$0.329971\pi$
$24$		−	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	$0.205453\pi$
$29$			34.8903i			1.20311i	−0.798830	+	0.601557i	$0.794547\pi$
$30$		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	$-0.174612\pi$
$37$	12.2773	+	12.2773i	0.331819	+	0.331819i	−0.521458	+	0.853277i	$0.674612\pi$
$38$	−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	$-0.873920\pi$
$43$	−23.0808	+	23.0808i	−0.536762	+	0.536762i	0.385814	+	0.922576i	$0.373920\pi$
$44$			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	$-0.270250\pi$
$47$	−4.22570	−	4.22570i	−0.0899084	−	0.0899084i	−0.750631	+	0.660722i	$0.770250\pi$
$48$	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	$-0.650655\pi$
$53$	23.0151	−	23.0151i	0.434247	−	0.434247i	0.890070	+	0.455823i	$0.150655\pi$
$54$			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	$0.0962145\pi$
$59$			35.1268i			0.595370i	−0.954664	+	0.297685i	$0.903786\pi$
$60$		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	$-0.402478\pi$
$67$	−43.6725	−	43.6725i	−0.651828	−	0.651828i	−0.953433	+	0.301605i	$0.902478\pi$
$68$	−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	$-0.522682\pi$
$73$	67.6174	−	67.6174i	0.926265	−	0.926265i	0.997462	+	0.0711969i	$0.0226819\pi$
$74$			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	$0.179102\pi$
$79$			84.2839i			1.06688i	−0.845836	+	0.533442i	$0.820898\pi$
$80$		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	$-0.703654\pi$
$83$	17.0303	−	17.0303i	0.205184	−	0.205184i	0.802217	+	0.597033i	$0.203654\pi$
$84$			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	$0.182238\pi$
$89$			96.4314i			1.08350i	−0.840540	+	0.541749i	$0.817762\pi$
$90$		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	0.999839	+	0.0179348i	$0.00570914\pi$
$97$	98.7241	+	98.7241i	1.01777	+	1.01777i	0.0179348	+	0.999839i	$0.494291\pi$
$98$	−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	$-0.777962\pi$
$103$	−12.7795	+	12.7795i	−0.124073	+	0.124073i	0.642344	+	0.766417i	$0.277962\pi$
$104$			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	$-0.397982\pi$
$107$	−67.8422	−	67.8422i	−0.634039	−	0.634039i	−0.949079	+	0.315039i	$0.897982\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			34.3485i			0.315123i	0.987509	+	0.157562i	$0.0503633\pi$
$109$			34.3485i			0.315123i	−0.987509	+	0.157562i	$0.949637\pi$
$110$		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	−0.403904	+	0.914802i	$0.632347\pi$
$113$	−149.014	+	149.014i	−1.31871	+	1.31871i	−0.914802	+	0.403904i	$0.867653\pi$
$114$		−	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	$-0.179349\pi$
$127$	39.5381	+	39.5381i	0.311323	+	0.311323i	−0.534099	+	0.845422i	$0.679349\pi$
$128$	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	$-0.497564\pi$
$137$	−135.948	−	135.948i	−0.992318	−	0.992318i	−0.999971	+	0.00765271i	$0.997564\pi$
$138$	19.8071	−	19.8071i	0.143530	−	0.143530i
$139$			201.392i			1.44886i	0.689347	+	0.724432i	$0.257898\pi$
$139$			201.392i			1.44886i	−0.689347	+	0.724432i	$0.742102\pi$
$140$		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	$0.0496107\pi$
$149$			46.2575i			0.310453i	−0.987879	+	0.155226i	$0.950389\pi$
$150$		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	$-0.413631\pi$
$157$	−109.177	−	109.177i	−0.695395	−	0.695395i	−0.963414	+	0.268019i	$0.913631\pi$
$158$	−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	$-0.832397\pi$
$163$	−59.0069	+	59.0069i	−0.362006	+	0.362006i	0.502545	+	0.864551i	$0.332397\pi$
$164$		−	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	$-0.122040\pi$
$167$	92.4048	+	92.4048i	0.553322	+	0.553322i	−0.374076	+	0.927398i	$0.622040\pi$
$168$	−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	$-0.628117\pi$
$173$	91.4094	−	91.4094i	0.528378	−	0.528378i	0.920089	+	0.391710i	$0.128117\pi$
$174$		−	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	$0.201189\pi$
$179$			211.508i			1.18161i	−0.806816	+	0.590803i	$0.798811\pi$
$180$		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	$-0.873017\pi$
$193$	−102.878	+	102.878i	−0.533045	+	0.533045i	0.388432	+	0.921477i	$0.373017\pi$
$194$			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	$-0.177450\pi$
$197$	62.9510	+	62.9510i	0.319548	+	0.319548i	−0.529045	+	0.848594i	$0.677450\pi$
$198$	7.52265	−	7.52265i	0.0379932	−	0.0379932i
$199$			14.4025i			0.0723742i	0.999345	+	0.0361871i	$0.0115212\pi$
$199$			14.4025i			0.0723742i	−0.999345	+	0.0361871i	$0.988479\pi$
$200$		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	$-0.703840\pi$
$223$	45.5732	−	45.5732i	0.204364	−	0.204364i	0.801867	+	0.597503i	$0.203840\pi$
$224$			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	$-0.190946\pi$
$227$	59.2172	+	59.2172i	0.260869	+	0.260869i	−0.564538	+	0.825407i	$0.690946\pi$
$228$	70.7295	−	70.7295i	0.310217	−	0.310217i
$229$			207.044i			0.904124i	0.891986	+	0.452062i	$0.149311\pi$
$229$			207.044i			0.904124i	−0.891986	+	0.452062i	$0.850689\pi$
$230$		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	0.0788463	−	0.996887i	$-0.474876\pi$
$233$	250.646	−	250.646i	1.07573	−	1.07573i	0.996887	−	0.0788463i	$-0.0251236\pi$
$234$		−	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	$-0.767976\pi$
$239$		−	318.381i		−	1.33214i	0.745890	−	0.666069i	$-0.232024\pi$
$240$		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	$-0.176268\pi$
$257$	83.4383	+	83.4383i	0.324663	+	0.324663i	−0.525890	+	0.850553i	$0.676268\pi$
$258$	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	$-0.607692\pi$
$263$	160.799	−	160.799i	0.611404	−	0.611404i	0.943312	+	0.331908i	$0.107692\pi$
$264$		−	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	$-0.697044\pi$
$269$		−	438.169i		−	1.62888i	0.580247	−	0.814440i	$-0.302956\pi$
$270$		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	$-0.194216\pi$
$277$	68.3008	+	68.3008i	0.246573	+	0.246573i	−0.572989	+	0.819563i	$0.694216\pi$
$278$	−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	$-0.883293\pi$
$283$	−162.739	+	162.739i	−0.575048	+	0.575048i	0.358487	+	0.933535i	$0.383293\pi$
$284$		−	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	$-0.711569\pi$
$293$	49.9066	−	49.9066i	0.170330	−	0.170330i	0.787124	+	0.616795i	$0.211569\pi$
$294$		−	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	0.970748	+	0.240100i	$0.0771804\pi$
$307$	371.730	+	371.730i	1.21085	+	1.21085i	0.240100	+	0.970748i	$0.422820\pi$
$308$	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	$-0.718014\pi$
$313$	44.4058	−	44.4058i	0.141872	−	0.141872i	0.774475	+	0.632604i	$0.218014\pi$
$314$		−	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	$-0.0226155\pi$
$317$	293.697	+	293.697i	0.926488	+	0.926488i	−0.0709890	+	0.997477i	$0.522616\pi$
$318$	−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	$-0.119891\pi$
$337$	189.426	+	189.426i	0.562095	+	0.562095i	−0.367807	+	0.929902i	$0.619891\pi$
$338$	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	$-0.324666\pi$
$347$	−114.059	−	114.059i	−0.328699	−	0.328699i	−0.852092	+	0.523392i	$0.824666\pi$
$348$	85.4634	−	85.4634i	0.245585	−	0.245585i
$349$		−	231.559i		−	0.663492i	−0.943369	−	0.331746i	$-0.892362\pi$
$349$		−	231.559i		−	0.663492i	0.943369	−	0.331746i	$-0.107638\pi$
$350$		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	$-0.550769\pi$
$353$	292.456	−	292.456i	0.828488	−	0.828488i	0.987308	+	0.158819i	$0.0507687\pi$
$354$		−	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	$-0.993254\pi$
$359$		−	15.2161i		−	0.0423848i	0.999775	−	0.0211924i	$-0.00674625\pi$
$360$		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	$-0.167532\pi$
$367$	132.968	+	132.968i	0.362310	+	0.362310i	−0.502353	+	0.864663i	$0.667532\pi$
$368$	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	$-0.632210\pi$
$373$	190.777	−	190.777i	0.511466	−	0.511466i	0.914975	+	0.403510i	$0.132210\pi$
$374$			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	$-0.636174\pi$
$379$		−	689.689i		−	1.81976i	0.414872	−	0.909880i	$-0.363826\pi$
$380$		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	$-0.660390\pi$
$383$	150.477	−	150.477i	0.392890	−	0.392890i	0.875716	+	0.482826i	$0.160390\pi$
$384$			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	$-0.760997\pi$
$389$		−	530.798i		−	1.36452i	0.731110	−	0.682259i	$-0.239003\pi$
$390$		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	$-0.239267\pi$
$397$	18.9270	+	18.9270i	0.0476750	+	0.0476750i	−0.682867	+	0.730542i	$0.739267\pi$
$398$	−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	$-0.844463\pi$
$409$		−	383.985i		−	0.938839i	0.882975	−	0.469419i	$-0.155537\pi$
$410$		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	$-0.913069\pi$
$419$		−	226.026i		−	0.539442i	0.962939	−	0.269721i	$-0.0869315\pi$
$420$		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	$-0.911430\pi$
$433$	−297.411	+	297.411i	−0.686862	+	0.686862i	0.274675	+	0.961537i	$0.411430\pi$
$434$			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	$0.419697\pi$
$439$			850.208i			1.93669i	−0.249613	+	0.968346i	$0.580303\pi$
$440$		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	$-0.851833\pi$
$443$	−197.026	+	197.026i	−0.444755	+	0.444755i	0.448851	+	0.893606i	$0.351833\pi$
$444$		−	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	$-0.869695\pi$
$449$		−	357.429i		−	0.796055i	0.917373	−	0.398028i	$-0.130305\pi$
$450$		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	$-0.438844\pi$
$457$	−361.329	−	361.329i	−0.790654	−	0.790654i	−0.981600	+	0.190946i	$0.938844\pi$
$458$	−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	$-0.991805\pi$
$463$	−450.928	+	450.928i	−0.973926	+	0.973926i	0.0257427	+	0.999669i	$0.491805\pi$
$464$		−	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	$-0.0866465\pi$
$467$	324.248	+	324.248i	0.694321	+	0.694321i	−0.268859	+	0.963180i	$0.586647\pi$
$468$	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	$-0.669231\pi$
$479$		−	825.767i		−	1.72394i	0.506960	−	0.861969i	$-0.330769\pi$
$480$		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	$-0.0599741\pi$
$487$	387.165	+	387.165i	0.795001	+	0.795001i	−0.187302	+	0.982302i	$0.559974\pi$
$488$	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	$0.220918\pi$
$499$			638.363i			1.27929i	−0.768672	+	0.639643i	$0.779082\pi$
$500$		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	0.206625	−	0.978420i	$-0.433752\pi$
$503$	596.078	−	596.078i	1.18505	−	1.18505i	0.978420	−	0.206625i	$-0.0662481\pi$
$504$		−	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	$-0.795557\pi$
$509$		−	609.802i		−	1.19804i	0.800734	−	0.599020i	$-0.204443\pi$
$510$		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	0.156627	−	0.987658i	$-0.449938\pi$
$523$	598.461	−	598.461i	1.14428	−	1.14428i	0.987658	−	0.156627i	$-0.0500620\pi$
$524$			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	$-0.365966\pi$
$547$	−275.633	−	275.633i	−0.503900	−	0.503900i	−0.912648	+	0.408748i	$0.865966\pi$
$548$	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	−0.998489	−	0.0549497i	$-0.982500\pi$
$557$	−586.765	−	586.765i	−1.05344	−	1.05344i	−0.0549497	−	0.998489i	$-0.517500\pi$
$558$	−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	$-0.786335\pi$
$563$	−90.6887	+	90.6887i	−0.161081	+	0.161081i	0.621964	+	0.783046i	$0.286335\pi$
$564$			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	$0.192800\pi$
$569$			647.905i			1.13867i	−0.822105	+	0.569336i	$0.807200\pi$
$570$		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	$-0.478907\pi$
$577$	−537.526	−	537.526i	−0.931588	−	0.931588i	−0.997805	+	0.0662174i	$0.978907\pi$
$578$	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	$-0.116407\pi$
$587$	338.268	+	338.268i	0.576265	+	0.576265i	−0.357607	+	0.933872i	$0.616407\pi$
$588$	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	$-0.729243\pi$
$593$	54.6474	−	54.6474i	0.0921542	−	0.0921542i	0.751681	+	0.659527i	$0.229243\pi$
$594$			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	$-0.868406\pi$
$599$		−	481.284i		−	0.803479i	0.915754	−	0.401739i	$-0.131594\pi$
$600$		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	$-0.382936\pi$
$607$	−348.176	−	348.176i	−0.573601	−	0.573601i	−0.933133	+	0.359532i	$0.882936\pi$
$608$	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	$-0.633183\pi$
$613$	311.057	−	311.057i	0.507434	−	0.507434i	0.913738	+	0.406304i	$0.133183\pi$
$614$			743.461i			1.21085i
$615$		0			0
$616$	18.7648			0.0304623
$617$	−829.657	−	829.657i	−1.34466	−	1.34466i	−0.891353	−	0.453309i	$-0.850243\pi$
$617$	−829.657	−	829.657i	−1.34466	−	1.34466i	−0.453309	−	0.891353i	$-0.649757\pi$
$618$	31.3033	−	31.3033i	0.0506525	−	0.0506525i
$619$			532.670i			0.860533i	0.902702	+	0.430266i	$0.141580\pi$
$619$			532.670i			0.860533i	−0.902702	+	0.430266i	$0.858420\pi$
$620$		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	$-0.809378\pi$
$643$	−168.649	+	168.649i	−0.262284	+	0.262284i	0.563697	+	0.825981i	$0.309378\pi$
$644$			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	$-0.106295\pi$
$647$	399.196	+	399.196i	0.616996	+	0.616996i	−0.327764	+	0.944760i	$0.606295\pi$
$648$	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	$-0.608483\pi$
$653$	397.176	−	397.176i	0.608232	−	0.608232i	0.942484	+	0.334251i	$0.108483\pi$
$654$		−	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	$-0.783454\pi$
$659$		−	829.056i		−	1.25805i	0.777384	−	0.629026i	$-0.216546\pi$
$660$		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	$-0.811482\pi$
$673$	−182.693	+	182.693i	−0.271461	+	0.271461i	0.558227	+	0.829688i	$0.311482\pi$
$674$			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	$-0.0550489\pi$
$677$	550.403	+	550.403i	0.813002	+	0.813002i	−0.172081	+	0.985083i	$0.555049\pi$
$678$	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	$-0.902461\pi$
$683$	−445.154	+	445.154i	−0.651762	+	0.651762i	0.301655	+	0.953417i	$0.402461\pi$
$684$			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	$0.324059\pi$
$709$			1206.85i			1.70218i	−0.525016	+	0.851092i	$0.675941\pi$
$710$		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	$0.256062\pi$
$719$			1036.00i			1.44089i	−0.693513	+	0.720444i	$0.743938\pi$
$720$		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	$-0.295294\pi$
$727$	−145.807	−	145.807i	−0.200559	−	0.200559i	−0.800240	+	0.599680i	$0.795294\pi$
$728$	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	0.235576	−	0.971856i	$-0.424302\pi$
$733$	885.048	−	885.048i	1.20743	−	1.20743i	0.971856	−	0.235576i	$-0.0756976\pi$
$734$			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	$-0.753624\pi$
$739$		−	1033.14i		−	1.39802i	0.715110	−	0.699012i	$-0.246376\pi$
$740$		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	−0.267520	+	0.963552i	$0.586204\pi$
$743$	−914.687	+	914.687i	−1.23107	+	1.23107i	−0.963552	+	0.267520i	$0.913796\pi$
$744$			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	−0.918335	−	0.395804i	$-0.870466\pi$
$757$	−994.803	−	994.803i	−1.31414	−	1.31414i	−0.395804	−	0.918335i	$-0.629534\pi$
$758$	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	$0.142432\pi$
$769$			665.462i			0.865360i	−0.901548	+	0.432680i	$0.857568\pi$
$770$		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	$-0.900371\pi$
$773$	−497.431	+	497.431i	−0.643507	+	0.643507i	0.307909	+	0.951416i	$0.400371\pi$
$774$			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	−0.975418	−	0.220363i	$-0.929276\pi$
$787$	−941.079	−	941.079i	−1.19578	−	1.19578i	−0.220363	−	0.975418i	$-0.570724\pi$
$788$	−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	$-0.380069\pi$
$797$	−447.860	−	447.860i	−0.561932	−	0.561932i	−0.929856	+	0.367924i	$0.880069\pi$
$798$	−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	$0.146818\pi$
$809$			720.108i			0.890121i	−0.895501	+	0.445060i	$0.853182\pi$
$810$		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	$-0.875024\pi$
$823$	−445.484	+	445.484i	−0.541293	+	0.541293i	0.382615	+	0.923908i	$0.375024\pi$
$824$		−	51.1180i		−	0.0620364i
$825$		0			0
$826$	131.433			0.159119
$827$	1045.75	+	1045.75i	1.26451	+	1.26451i	0.948884	+	0.315626i	$0.102215\pi$
$827$	1045.75	+	1045.75i	1.26451	+	1.26451i	0.315626	+	0.948884i	$0.397785\pi$
$828$	−48.5173	+	48.5173i	−0.0585957	+	0.0585957i
$829$			636.907i			0.768284i	0.923274	+	0.384142i	$0.125503\pi$
$829$			636.907i			0.768284i	−0.923274	+	0.384142i	$0.874497\pi$
$830$		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	$0.294063\pi$
$839$			1338.90i			1.59583i	−0.602771	+	0.797914i	$0.705937\pi$
$840$		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	$-0.695085\pi$
$853$	207.083	−	207.083i	0.242770	−	0.242770i	0.817995	+	0.575225i	$0.195085\pi$
$854$			274.396i			0.321306i
$855$		0			0
$856$	271.369			0.317020
$857$	−937.379	−	937.379i	−1.09379	−	1.09379i	−0.995120	−	0.0986710i	$-0.968541\pi$
$857$	−937.379	−	937.379i	−1.09379	−	1.09379i	−0.0986710	−	0.995120i	$-0.531459\pi$
$858$	−56.8333	+	56.8333i	−0.0662393	+	0.0662393i
$859$		−	1035.98i		−	1.20603i	−0.797729	−	0.603016i	$-0.793965\pi$
$859$		−	1035.98i		−	1.20603i	0.797729	−	0.603016i	$-0.206035\pi$
$860$		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	−0.0842859	+	0.996442i	$0.526861\pi$
$863$	−932.668	+	932.668i	−1.08073	+	1.08073i	−0.996442	+	0.0842859i	$0.973139\pi$
$864$		−	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	$-0.275586\pi$
$877$	−99.5858	−	99.5858i	−0.113553	−	0.113553i	−0.761600	+	0.648047i	$0.775586\pi$
$878$	−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	−0.250040	+	0.968235i	$0.580444\pi$
$883$	−1075.74	+	1075.74i	−1.21828	+	1.21828i	−0.968235	+	0.250040i	$0.919556\pi$
$884$			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	$-0.00695490\pi$
$887$	867.409	+	867.409i	0.977914	+	0.977914i	−0.0218477	+	0.999761i	$0.506955\pi$
$888$	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	$-0.275041\pi$
$907$	−100.803	−	100.803i	−0.111139	−	0.111139i	−0.760489	+	0.649350i	$0.775041\pi$
$908$	−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	$0.184497\pi$
$919$			1006.68i			1.09540i	−0.836673	+	0.547702i	$0.815503\pi$
$920$		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	$-0.960334\pi$
$929$		−	230.933i		−	0.248582i	0.992246	−	0.124291i	$-0.0396656\pi$
$930$		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	$-0.221877\pi$
$937$	116.924	+	116.924i	0.124786	+	0.124786i	−0.641956	+	0.766742i	$0.721877\pi$
$938$	−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	$-0.100230\pi$
$947$	607.150	+	607.150i	0.641130	+	0.641130i	−0.309703	+	0.950833i	$0.600230\pi$
$948$	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	$-0.994013\pi$
$953$	−934.907	+	934.907i	−0.981014	+	0.981014i	0.0188086	+	0.999823i	$0.494013\pi$
$954$		−	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	$-0.155447\pi$
$967$	400.279	+	400.279i	0.413939	+	0.413939i	−0.469169	+	0.883108i	$0.655447\pi$
$968$	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	0.959450	+	0.281879i	$0.0909578\pi$
$977$	1212.78	+	1212.78i	1.24133	+	1.24133i	0.281879	+	0.959450i	$0.409042\pi$
$978$	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	0.265960	−	0.963984i	$-0.414311\pi$
$983$	1209.04	−	1209.04i	1.22994	−	1.22994i	0.963984	−	0.265960i	$-0.0856889\pi$
$984$			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	−0.938401	−	0.345550i	$-0.887693\pi$
$997$	−1280.10	−	1280.10i	−1.28395	−	1.28395i	−0.345550	−	0.938401i	$-0.612307\pi$
$998$	−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.e.757.1	yes	8
5.2	odd	4		1050.3.l.a.43.4	✓	8
5.3	odd	4	inner	1050.3.l.e.43.1	yes	8
5.4	even	2		1050.3.l.a.757.4	yes	8

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

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

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Database

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