LMFDB - Embedded newform 1150.2.e.e.1057.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{12} + 326x^{8} - 275x^{4} + 81 $ x^16 + 20x^12 + 326x^8 - 275*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.7
Root			$-1.06996 + 1.77707i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.e.643.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.921201 - 0.921201i) q^{3} +1.00000i q^{4} +1.30278 q^{6} +(-0.862010 + 0.862010i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.30278i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.921201 - 0.921201i) q^{3} +1.00000i q^{4} +1.30278 q^{6} +(-0.862010 + 0.862010i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.30278i q^{9} +5.24537i q^{11} +(0.921201 + 0.921201i) q^{12} +(-1.20012 + 1.20012i) q^{13} -1.21907 q^{14} -1.00000 q^{16} +(-1.98502 + 1.98502i) q^{17} +(-0.921201 + 0.921201i) q^{18} -6.83354 q^{19} +1.58817i q^{21} +(-3.70903 + 3.70903i) q^{22} +(-1.00462 - 4.68943i) q^{23} +1.30278i q^{24} -1.69722 q^{26} +(3.96372 + 3.96372i) q^{27} +(-0.862010 - 0.862010i) q^{28} -2.00000i q^{29} +6.90833 q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.83204 + 4.83204i) q^{33} -2.80724 q^{34} -1.30278 q^{36} +(1.72402 - 1.72402i) q^{37} +(-4.83204 - 4.83204i) q^{38} +2.21110i q^{39} -0.697224 q^{41} +(-1.12301 + 1.12301i) q^{42} +(3.97003 + 3.97003i) q^{43} -5.24537 q^{44} +(2.60555 - 4.02630i) q^{46} +(-3.68481 - 3.68481i) q^{47} +(-0.921201 + 0.921201i) q^{48} +5.51388i q^{49} +3.65720i q^{51} +(-1.20012 - 1.20012i) q^{52} +(7.41807 + 7.41807i) q^{53} +5.60555i q^{54} -1.21907i q^{56} +(-6.29506 + 6.29506i) q^{57} +(1.41421 - 1.41421i) q^{58} +10.6056i q^{59} +5.24537i q^{61} +(4.88492 + 4.88492i) q^{62} +(-1.12301 - 1.12301i) q^{63} -1.00000i q^{64} +6.83354i q^{66} +(11.3881 - 11.3881i) q^{67} +(-1.98502 - 1.98502i) q^{68} +(-5.24537 - 3.39445i) q^{69} +0.697224 q^{71} +(-0.921201 - 0.921201i) q^{72} +(6.08504 - 6.08504i) q^{73} +2.43813 q^{74} -6.83354i q^{76} +(-4.52156 - 4.52156i) q^{77} +(-1.56349 + 1.56349i) q^{78} -10.4907 q^{79} +3.39445 q^{81} +(-0.493012 - 0.493012i) q^{82} -1.58817 q^{84} +5.61447i q^{86} +(-1.84240 - 1.84240i) q^{87} +(-3.70903 - 3.70903i) q^{88} -2.06903i q^{91} +(4.68943 - 1.00462i) q^{92} +(6.36396 - 6.36396i) q^{93} -5.21110i q^{94} -1.30278 q^{96} +(9.40308 - 9.40308i) q^{97} +(-3.89890 + 3.89890i) q^{98} -6.83354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{6}+O(q^{10}) $ 16 * q - 8 * q^6	$ 16 q - 8 q^{6} - 16 q^{16} - 56 q^{26} + 24 q^{31} + 8 q^{36} - 40 q^{41} - 16 q^{46} + 40 q^{71} + 112 q^{81} + 8 q^{96}+O(q^{100}) $ 16 * q - 8 * q^6 - 16 * q^16 - 56 * q^26 + 24 * q^31 + 8 * q^36 - 40 * q^41 - 16 * q^46 + 40 * q^71 + 112 * q^81 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.921201	−	0.921201i	0.531856	−	0.531856i	−0.389268	−	0.921124i	$-0.627272\pi$
$3$	0.921201	−	0.921201i	0.531856	−	0.531856i	0.921124	+	0.389268i	$0.127272\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	1.30278			0.531856
$7$	−0.862010	+	0.862010i	−0.325809	+	0.325809i	−0.850990	−	0.525181i	$-0.823998\pi$
$7$	−0.862010	+	0.862010i	−0.325809	+	0.325809i	0.525181	+	0.850990i	$0.323998\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.30278i			0.434259i
$10$		0			0
$11$			5.24537i			1.58154i	0.612115	+	0.790769i	$0.290319\pi$
$11$			5.24537i			1.58154i	−0.612115	+	0.790769i	$0.709681\pi$
$12$	0.921201	+	0.921201i	0.265928	+	0.265928i
$13$	−1.20012	+	1.20012i	−0.332853	+	0.332853i	−0.853669	−	0.520816i	$-0.825628\pi$
$13$	−1.20012	+	1.20012i	−0.332853	+	0.332853i	0.520816	+	0.853669i	$0.325628\pi$
$14$	−1.21907			−0.325809
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.98502	+	1.98502i	−0.481437	+	0.481437i	−0.905590	−	0.424153i	$-0.860572\pi$
$17$	−1.98502	+	1.98502i	−0.481437	+	0.481437i	0.424153	+	0.905590i	$0.360572\pi$
$18$	−0.921201	+	0.921201i	−0.217129	+	0.217129i
$19$	−6.83354			−1.56772			−0.783860	−	0.620937i	$-0.786752\pi$
$19$	−6.83354			−1.56772			−0.783860	+	0.620937i	$0.786752\pi$
$20$		0			0
$21$			1.58817i			0.346567i
$22$	−3.70903	+	3.70903i	−0.790769	+	0.790769i
$23$	−1.00462	−	4.68943i	−0.209478	−	0.977813i
$23$	−1.00462	−	4.68943i	−0.209478	−	0.977813i
$24$			1.30278i			0.265928i
$25$		0			0
$26$	−1.69722			−0.332853
$27$	3.96372	+	3.96372i	0.762819	+	0.762819i
$28$	−0.862010	−	0.862010i	−0.162905	−	0.162905i
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	6.90833			1.24077			0.620386	−	0.784297i	$-0.286976\pi$
$31$	6.90833			1.24077			0.620386	+	0.784297i	$0.286976\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.83204	+	4.83204i	0.841150	+	0.841150i
$34$	−2.80724			−0.481437
$35$		0			0
$36$	−1.30278			−0.217129
$37$	1.72402	−	1.72402i	0.283427	−	0.283427i	−0.551047	−	0.834474i	$-0.685772\pi$
$37$	1.72402	−	1.72402i	0.283427	−	0.283427i	0.834474	+	0.551047i	$0.185772\pi$
$38$	−4.83204	−	4.83204i	−0.783860	−	0.783860i
$39$			2.21110i			0.354060i
$40$		0			0
$41$	−0.697224			−0.108888			−0.0544441	−	0.998517i	$-0.517339\pi$
$41$	−0.697224			−0.108888			−0.0544441	+	0.998517i	$0.517339\pi$
$42$	−1.12301	+	1.12301i	−0.173283	+	0.173283i
$43$	3.97003	+	3.97003i	0.605424	+	0.605424i	0.941747	−	0.336323i	$-0.109183\pi$
$43$	3.97003	+	3.97003i	0.605424	+	0.605424i	−0.336323	+	0.941747i	$0.609183\pi$
$44$	−5.24537			−0.790769
$45$		0			0
$46$	2.60555	−	4.02630i	0.384168	−	0.593646i
$47$	−3.68481	−	3.68481i	−0.537484	−	0.537484i	0.385305	−	0.922789i	$-0.374096\pi$
$47$	−3.68481	−	3.68481i	−0.537484	−	0.537484i	−0.922789	+	0.385305i	$0.874096\pi$
$48$	−0.921201	+	0.921201i	−0.132964	+	0.132964i
$49$			5.51388i			0.787697i
$50$		0			0
$51$			3.65720i			0.512110i
$52$	−1.20012	−	1.20012i	−0.166427	−	0.166427i
$53$	7.41807	+	7.41807i	1.01895	+	1.01895i	0.999817	+	0.0191333i	$0.00609068\pi$
$53$	7.41807	+	7.41807i	1.01895	+	1.01895i	0.0191333	+	0.999817i	$0.493909\pi$
$54$			5.60555i			0.762819i
$55$		0			0
$56$		−	1.21907i		−	0.162905i
$57$	−6.29506	+	6.29506i	−0.833802	+	0.833802i
$58$	1.41421	−	1.41421i	0.185695	−	0.185695i
$59$			10.6056i			1.38073i	0.723464	+	0.690363i	$0.242549\pi$
$59$			10.6056i			1.38073i	−0.723464	+	0.690363i	$0.757451\pi$
$60$		0			0
$61$			5.24537i			0.671600i	0.941933	+	0.335800i	$0.109007\pi$
$61$			5.24537i			0.671600i	−0.941933	+	0.335800i	$0.890993\pi$
$62$	4.88492	+	4.88492i	0.620386	+	0.620386i
$63$	−1.12301	−	1.12301i	−0.141485	−	0.141485i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			6.83354i			0.841150i
$67$	11.3881	−	11.3881i	1.39128	−	1.39128i	0.568806	−	0.822471i	$-0.307405\pi$
$67$	11.3881	−	11.3881i	1.39128	−	1.39128i	0.822471	−	0.568806i	$-0.192595\pi$
$68$	−1.98502	−	1.98502i	−0.240718	−	0.240718i
$69$	−5.24537	−	3.39445i	−0.631468	−	0.408644i
$70$		0			0
$71$	0.697224			0.0827453			0.0413727	−	0.999144i	$-0.486827\pi$
$71$	0.697224			0.0827453			0.0413727	+	0.999144i	$0.486827\pi$
$72$	−0.921201	−	0.921201i	−0.108565	−	0.108565i
$73$	6.08504	−	6.08504i	0.712200	−	0.712200i	−0.254795	−	0.966995i	$-0.582008\pi$
$73$	6.08504	−	6.08504i	0.712200	−	0.712200i	0.966995	+	0.254795i	$0.0820079\pi$
$74$	2.43813			0.283427
$75$		0			0
$76$		−	6.83354i		−	0.783860i
$77$	−4.52156	−	4.52156i	−0.515279	−	0.515279i
$78$	−1.56349	+	1.56349i	−0.177030	+	0.177030i
$79$	−10.4907			−1.18030			−0.590150	−	0.807294i	$-0.700931\pi$
$79$	−10.4907			−1.18030			−0.590150	+	0.807294i	$0.700931\pi$
$80$		0			0
$81$	3.39445			0.377161
$82$	−0.493012	−	0.493012i	−0.0544441	−	0.0544441i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	−1.58817			−0.173283
$85$		0			0
$86$			5.61447i			0.605424i
$87$	−1.84240	−	1.84240i	−0.197526	−	0.197526i
$88$	−3.70903	−	3.70903i	−0.395384	−	0.395384i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$		−	2.06903i		−	0.216893i
$92$	4.68943	−	1.00462i	0.488907	−	0.104739i
$93$	6.36396	−	6.36396i	0.659912	−	0.659912i
$94$		−	5.21110i		−	0.537484i
$95$		0			0
$96$	−1.30278			−0.132964
$97$	9.40308	−	9.40308i	0.954739	−	0.954739i	−0.0442805	−	0.999019i	$-0.514100\pi$
$97$	9.40308	−	9.40308i	0.954739	−	0.954739i	0.999019	+	0.0442805i	$0.0140995\pi$
$98$	−3.89890	+	3.89890i	−0.393848	+	0.393848i
$99$	−6.83354			−0.686796
$100$		0			0
$101$	3.81665			0.379771			0.189886	−	0.981806i	$-0.439188\pi$
$101$	3.81665			0.379771			0.189886	+	0.981806i	$0.439188\pi$
$102$	−2.58603	+	2.58603i	−0.256055	+	0.256055i
$103$	5.43305	+	5.43305i	0.535335	+	0.535335i	0.922155	−	0.386820i	$-0.126427\pi$
$103$	5.43305	+	5.43305i	0.535335	+	0.535335i	−0.386820	+	0.922155i	$0.626427\pi$
$104$		−	1.69722i		−	0.166427i
$105$		0			0
$106$			10.4907i			1.01895i
$107$	9.14209	−	9.14209i	0.883799	−	0.883799i	−0.110119	−	0.993918i	$-0.535123\pi$
$107$	9.14209	−	9.14209i	0.883799	−	0.883799i	0.993918	+	0.110119i	$0.0351233\pi$
$108$	−3.96372	+	3.96372i	−0.381409	+	0.381409i
$109$	−3.65720			−0.350296			−0.175148	−	0.984542i	$-0.556040\pi$
$109$	−3.65720			−0.350296			−0.175148	+	0.984542i	$0.556040\pi$
$110$		0			0
$111$		−	3.17634i		−	0.301485i
$112$	0.862010	−	0.862010i	0.0814523	−	0.0814523i
$113$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$113$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$114$	−8.90257			−0.833802
$115$		0			0
$116$	2.00000			0.185695
$117$	−1.56349	−	1.56349i	−0.144544	−	0.144544i
$118$	−7.49926	+	7.49926i	−0.690363	+	0.690363i
$119$		−	3.42221i		−	0.313713i
$120$		0			0
$121$	−16.5139			−1.50126
$122$	−3.70903	+	3.70903i	−0.335800	+	0.335800i
$123$	−0.642284	+	0.642284i	−0.0579128	+	0.0579128i
$124$			6.90833i			0.620386i
$125$		0			0
$126$		−	1.58817i		−	0.141485i
$127$	−9.76985	−	9.76985i	−0.866934	−	0.866934i	0.125198	−	0.992132i	$-0.460043\pi$
$127$	−9.76985	−	9.76985i	−0.866934	−	0.866934i	−0.992132	+	0.125198i	$0.960043\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	7.31440			0.643997
$130$		0			0
$131$	6.60555			0.577130			0.288565	−	0.957460i	$-0.406822\pi$
$131$	6.60555			0.577130			0.288565	+	0.957460i	$0.406822\pi$
$132$	−4.83204	+	4.83204i	−0.420575	+	0.420575i
$133$	5.89058	−	5.89058i	0.510778	−	0.510778i
$134$	16.1052			1.39128
$135$		0			0
$136$		−	2.80724i		−	0.240718i
$137$	−6.55606	+	6.55606i	−0.560122	+	0.560122i	−0.929342	−	0.369220i	$-0.879625\pi$
$137$	−6.55606	+	6.55606i	−0.560122	+	0.560122i	0.369220	+	0.929342i	$0.379625\pi$
$138$	−1.30880	−	6.10927i	−0.111412	−	0.520056i
$139$			3.39445i			0.287913i	0.989584	+	0.143957i	$0.0459826\pi$
$139$			3.39445i			0.287913i	−0.989584	+	0.143957i	$0.954017\pi$
$140$		0			0
$141$	−6.78890			−0.571728
$142$	0.493012	+	0.493012i	0.0413727	+	0.0413727i
$143$	−6.29506	−	6.29506i	−0.526420	−	0.526420i
$144$		−	1.30278i		−	0.108565i
$145$		0			0
$146$	8.60555			0.712200
$147$	5.07939	+	5.07939i	0.418941	+	0.418941i
$148$	1.72402	+	1.72402i	0.141714	+	0.141714i
$149$	17.3243			1.41926			0.709630	−	0.704575i	$-0.248862\pi$
$149$	17.3243			1.41926			0.709630	+	0.704575i	$0.248862\pi$
$150$		0			0
$151$	4.69722			0.382255			0.191127	−	0.981565i	$-0.438786\pi$
$151$	4.69722			0.382255			0.191127	+	0.981565i	$0.438786\pi$
$152$	4.83204	−	4.83204i	0.391930	−	0.391930i
$153$	−2.58603	−	2.58603i	−0.209068	−	0.209068i
$154$		−	6.39445i		−	0.515279i
$155$		0			0
$156$	−2.21110			−0.177030
$157$	3.97003	−	3.97003i	0.316843	−	0.316843i	−0.530710	−	0.847553i	$-0.678075\pi$
$157$	3.97003	−	3.97003i	0.316843	−	0.316843i	0.847553	+	0.530710i	$0.178075\pi$
$158$	−7.41807	−	7.41807i	−0.590150	−	0.590150i
$159$	13.6671			1.08387
$160$		0			0
$161$	4.90833	+	3.17634i	0.386830	+	0.250331i
$162$	2.40024	+	2.40024i	0.188580	+	0.188580i
$163$	−12.8124	+	12.8124i	−1.00354	+	1.00354i	−0.00354868	+	0.999994i	$0.501130\pi$
$163$	−12.8124	+	12.8124i	−1.00354	+	1.00354i	−0.999994	+	0.00354868i	$0.998870\pi$
$164$		−	0.697224i		−	0.0544441i
$165$		0			0
$166$		0			0
$167$	−12.7279	−	12.7279i	−0.984916	−	0.984916i	0.0149717	−	0.999888i	$-0.495234\pi$
$167$	−12.7279	−	12.7279i	−0.984916	−	0.984916i	−0.999888	+	0.0149717i	$0.995234\pi$
$168$	−1.12301	−	1.12301i	−0.0866417	−	0.0866417i
$169$			10.1194i			0.778418i
$170$		0			0
$171$		−	8.90257i		−	0.680796i
$172$	−3.97003	+	3.97003i	−0.302712	+	0.302712i
$173$	−7.56408	+	7.56408i	−0.575086	+	0.575086i	−0.933545	−	0.358459i	$-0.883302\pi$
$173$	−7.56408	+	7.56408i	−0.575086	+	0.575086i	0.358459	+	0.933545i	$0.383302\pi$
$174$		−	2.60555i		−	0.197526i
$175$		0			0
$176$		−	5.24537i		−	0.395384i
$177$	9.76985	+	9.76985i	0.734347	+	0.734347i
$178$		0			0
$179$		−	17.6333i		−	1.31798i	−0.752154	−	0.658988i	$-0.770985\pi$
$179$		−	17.6333i		−	1.31798i	0.752154	−	0.658988i	$-0.229015\pi$
$180$		0			0
$181$		−	17.3243i		−	1.28770i	−0.765150	−	0.643851i	$-0.777335\pi$
$181$		−	17.3243i		−	1.28770i	0.765150	−	0.643851i	$-0.222665\pi$
$182$	1.46302	−	1.46302i	0.108447	−	0.108447i
$183$	4.83204	+	4.83204i	0.357195	+	0.357195i
$184$	4.02630	+	2.60555i	0.296823	+	0.192084i
$185$		0			0
$186$	9.00000			0.659912
$187$	−10.4121	−	10.4121i	−0.761411	−	0.761411i
$188$	3.68481	−	3.68481i	0.268742	−	0.268742i
$189$	−6.83354			−0.497067
$190$		0			0
$191$			20.9815i			1.51817i	0.650994	+	0.759083i	$0.274352\pi$
$191$			20.9815i			1.51817i	−0.650994	+	0.759083i	$0.725648\pi$
$192$	−0.921201	−	0.921201i	−0.0664820	−	0.0664820i
$193$	−1.84240	+	1.84240i	−0.132619	+	0.132619i	−0.770300	−	0.637681i	$-0.779894\pi$
$193$	−1.84240	+	1.84240i	−0.132619	+	0.132619i	0.637681	+	0.770300i	$0.279894\pi$
$194$	13.2980			0.954739
$195$		0			0
$196$	−5.51388			−0.393848
$197$	14.9337	+	14.9337i	1.06398	+	1.06398i	0.997808	+	0.0661733i	$0.0210790\pi$
$197$	14.9337	+	14.9337i	1.06398	+	1.06398i	0.0661733	+	0.997808i	$0.478921\pi$
$198$	−4.83204	−	4.83204i	−0.343398	−	0.343398i
$199$	3.17634			0.225165			0.112582	−	0.993642i	$-0.464088\pi$
$199$	3.17634			0.225165			0.112582	+	0.993642i	$0.464088\pi$
$200$		0			0
$201$		−	20.9815i		−	1.47992i
$202$	2.69878	+	2.69878i	0.189886	+	0.189886i
$203$	1.72402	+	1.72402i	0.121002	+	0.121002i
$204$	−3.65720			−0.256055
$205$		0			0
$206$			7.68350i			0.535335i
$207$	6.10927	−	1.30880i	0.424624	−	0.0909677i
$208$	1.20012	−	1.20012i	0.0832133	−	0.0832133i
$209$		−	35.8444i		−	2.47941i
$210$		0			0
$211$	−28.4222			−1.95667			−0.978333	−	0.207039i	$-0.933617\pi$
$211$	−28.4222			−1.95667			−0.978333	+	0.207039i	$0.933617\pi$
$212$	−7.41807	+	7.41807i	−0.509475	+	0.509475i
$213$	0.642284	−	0.642284i	0.0440086	−	0.0440086i
$214$	12.9289			0.883799
$215$		0			0
$216$	−5.60555			−0.381409
$217$	−5.95505	+	5.95505i	−0.404255	+	0.404255i
$218$	−2.58603	−	2.58603i	−0.175148	−	0.175148i
$219$		−	11.2111i		−	0.757576i
$220$		0			0
$221$		−	4.76451i		−	0.320496i
$222$	2.24601	−	2.24601i	0.150742	−	0.150742i
$223$	9.76985	−	9.76985i	0.654238	−	0.654238i	−0.299773	−	0.954011i	$-0.596911\pi$
$223$	9.76985	−	9.76985i	0.654238	−	0.654238i	0.954011	+	0.299773i	$0.0969110\pi$
$224$	1.21907			0.0814523
$225$		0			0
$226$		0			0
$227$	−5.17206	+	5.17206i	−0.343282	+	0.343282i	−0.857600	−	0.514318i	$-0.828045\pi$
$227$	−5.17206	+	5.17206i	−0.343282	+	0.343282i	0.514318	+	0.857600i	$0.328045\pi$
$228$	−6.29506	−	6.29506i	−0.416901	−	0.416901i
$229$	20.9815			1.38649			0.693247	−	0.720700i	$-0.256179\pi$
$229$	20.9815			1.38649			0.693247	+	0.720700i	$0.256179\pi$
$230$		0			0
$231$	−8.33053			−0.548109
$232$	1.41421	+	1.41421i	0.0928477	+	0.0928477i
$233$	−2.40024	+	2.40024i	−0.157245	+	0.157245i	−0.781345	−	0.624100i	$-0.785466\pi$
$233$	−2.40024	+	2.40024i	−0.157245	+	0.157245i	0.624100	+	0.781345i	$0.285466\pi$
$234$		−	2.21110i		−	0.144544i
$235$		0			0
$236$	−10.6056			−0.690363
$237$	−9.66408	+	9.66408i	−0.627749	+	0.627749i
$238$	2.41986	−	2.41986i	0.156857	−	0.156857i
$239$			14.4222i			0.932895i	0.884549	+	0.466447i	$0.154466\pi$
$239$			14.4222i			0.932895i	−0.884549	+	0.466447i	$0.845534\pi$
$240$		0			0
$241$		−	3.17634i		−	0.204606i	−0.994753	−	0.102303i	$-0.967379\pi$
$241$		−	3.17634i		−	0.204606i	0.994753	−	0.102303i	$-0.0326211\pi$
$242$	−11.6771	−	11.6771i	−0.750631	−	0.750631i
$243$	−8.76420	+	8.76420i	−0.562224	+	0.562224i
$244$	−5.24537			−0.335800
$245$		0			0
$246$	−0.908327			−0.0579128
$247$	8.20106	−	8.20106i	0.521821	−	0.521821i
$248$	−4.88492	+	4.88492i	−0.310193	+	0.310193i
$249$		0			0
$250$		0			0
$251$		−	14.1479i		−	0.893010i	−0.894781	−	0.446505i	$-0.852669\pi$
$251$		−	14.1479i		−	0.893010i	0.894781	−	0.446505i	$-0.147331\pi$
$252$	1.12301	−	1.12301i	0.0707427	−	0.0707427i
$253$	24.5978	−	5.26961i	1.54645	−	0.331298i
$254$		−	13.8167i		−	0.866934i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.2971	+	15.2971i	0.954204	+	0.954204i	0.998996	−	0.0447920i	$-0.0142625\pi$
$257$	15.2971	+	15.2971i	0.954204	+	0.954204i	−0.0447920	+	0.998996i	$0.514263\pi$
$258$	5.17206	+	5.17206i	0.321998	+	0.321998i
$259$			2.97224i			0.184686i
$260$		0			0
$261$	2.60555			0.161280
$262$	4.67083	+	4.67083i	0.288565	+	0.288565i
$263$	−13.3731	−	13.3731i	−0.824622	−	0.824622i	0.162145	−	0.986767i	$-0.448159\pi$
$263$	−13.3731	−	13.3731i	−0.824622	−	0.824622i	−0.986767	+	0.162145i	$0.948159\pi$
$264$	−6.83354			−0.420575
$265$		0			0
$266$	8.33053			0.510778
$267$		0			0
$268$	11.3881	+	11.3881i	0.695639	+	0.695639i
$269$		−	6.42221i		−	0.391569i	−0.980647	−	0.195784i	$-0.937275\pi$
$269$		−	6.42221i		−	0.391569i	0.980647	−	0.195784i	$-0.0627253\pi$
$270$		0			0
$271$	−8.11943			−0.493220			−0.246610	−	0.969115i	$-0.579317\pi$
$271$	−8.11943			−0.493220			−0.246610	+	0.969115i	$0.579317\pi$
$272$	1.98502	−	1.98502i	0.120359	−	0.120359i
$273$	−1.90599	−	1.90599i	−0.115356	−	0.115356i
$274$	−9.27167			−0.560122
$275$		0			0
$276$	3.39445	−	5.24537i	0.204322	−	0.315734i
$277$	12.7279	+	12.7279i	0.764747	+	0.764747i	0.977176	−	0.212430i	$-0.0681376\pi$
$277$	12.7279	+	12.7279i	0.764747	+	0.764747i	−0.212430	+	0.977176i	$0.568138\pi$
$278$	−2.40024	+	2.40024i	−0.143957	+	0.143957i
$279$			9.00000i			0.538816i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−4.80048	−	4.80048i	−0.285864	−	0.285864i
$283$	−9.14209	−	9.14209i	−0.543441	−	0.543441i	0.381095	−	0.924536i	$-0.375547\pi$
$283$	−9.14209	−	9.14209i	−0.543441	−	0.543441i	−0.924536	+	0.381095i	$0.875547\pi$
$284$			0.697224i			0.0413727i
$285$		0			0
$286$		−	8.90257i		−	0.526420i
$287$	0.601014	−	0.601014i	0.0354767	−	0.0354767i
$288$	0.921201	−	0.921201i	0.0542823	−	0.0542823i
$289$			9.11943i			0.536437i
$290$		0			0
$291$		−	17.3243i		−	1.01557i
$292$	6.08504	+	6.08504i	0.356100	+	0.356100i
$293$	15.3581	+	15.3581i	0.897232	+	0.897232i	0.995190	−	0.0979589i	$-0.0312314\pi$
$293$	15.3581	+	15.3581i	0.897232	+	0.897232i	−0.0979589	+	0.995190i	$0.531231\pi$
$294$			7.18335i			0.418941i
$295$		0			0
$296$			2.43813i			0.141714i
$297$	−20.7912	+	20.7912i	−1.20643	+	1.20643i
$298$	12.2501	+	12.2501i	0.709630	+	0.709630i
$299$	6.83354	+	4.42221i	0.395194	+	0.255743i
$300$		0			0
$301$	−6.84441			−0.394505
$302$	3.32144	+	3.32144i	0.191127	+	0.191127i
$303$	3.51591	−	3.51591i	0.201984	−	0.201984i
$304$	6.83354			0.391930
$305$		0			0
$306$		−	3.65720i		−	0.209068i
$307$	−14.2070	−	14.2070i	−0.810834	−	0.810834i	0.173925	−	0.984759i	$-0.444355\pi$
$307$	−14.2070	−	14.2070i	−0.810834	−	0.810834i	−0.984759	+	0.173925i	$0.944355\pi$
$308$	4.52156	−	4.52156i	0.257640	−	0.257640i
$309$	10.0099			0.569442
$310$		0			0
$311$	30.4222			1.72508			0.862542	−	0.505985i	$-0.168871\pi$
$311$	30.4222			1.72508			0.862542	+	0.505985i	$0.168871\pi$
$312$	−1.56349	−	1.56349i	−0.0885149	−	0.0885149i
$313$	3.10802	+	3.10802i	0.175676	+	0.175676i	0.789468	−	0.613792i	$-0.210357\pi$
$313$	3.10802	+	3.10802i	0.175676	+	0.175676i	−0.613792	+	0.789468i	$0.710357\pi$
$314$	5.61447			0.316843
$315$		0			0
$316$		−	10.4907i		−	0.590150i
$317$	−12.0856	−	12.0856i	−0.678797	−	0.678797i	0.280931	−	0.959728i	$-0.409357\pi$
$317$	−12.0856	−	12.0856i	−0.678797	−	0.678797i	−0.959728	+	0.280931i	$0.909357\pi$
$318$	9.66408	+	9.66408i	0.541935	+	0.541935i
$319$	10.4907			0.587368
$320$		0			0
$321$		−	16.8434i		−	0.940108i
$322$	1.22470	+	5.71672i	0.0682499	+	0.318580i
$323$	13.5647	−	13.5647i	0.754759	−	0.754759i
$324$			3.39445i			0.188580i
$325$		0			0
$326$	−18.1194			−1.00354
$327$	−3.36902	+	3.36902i	−0.186307	+	0.186307i
$328$	0.493012	−	0.493012i	0.0272220	−	0.0272220i
$329$	6.35268			0.350234
$330$		0			0
$331$	−2.18335			−0.120008			−0.0600038	−	0.998198i	$-0.519111\pi$
$331$	−2.18335			−0.120008			−0.0600038	+	0.998198i	$0.519111\pi$
$332$		0			0
$333$	2.24601	+	2.24601i	0.123081	+	0.123081i
$334$		−	18.0000i		−	0.984916i
$335$		0			0
$336$		−	1.58817i		−	0.0866417i
$337$	−16.2201	+	16.2201i	−0.883567	+	0.883567i	−0.993895	−	0.110328i	$-0.964810\pi$
$337$	−16.2201	+	16.2201i	−0.883567	+	0.883567i	0.110328	+	0.993895i	$0.464810\pi$
$338$	−7.15552	+	7.15552i	−0.389209	+	0.389209i
$339$		0			0
$340$		0			0
$341$			36.2367i			1.96233i
$342$	6.29506	−	6.29506i	0.340398	−	0.340398i
$343$	−10.7871	−	10.7871i	−0.582448	−	0.582448i
$344$	−5.61447			−0.302712
$345$		0			0
$346$	−10.6972			−0.575086
$347$	11.2489	+	11.2489i	0.603872	+	0.603872i	0.941338	−	0.337466i	$-0.109570\pi$
$347$	11.2489	+	11.2489i	0.603872	+	0.603872i	−0.337466	+	0.941338i	$0.609570\pi$
$348$	1.84240	−	1.84240i	0.0987632	−	0.0987632i
$349$		−	14.4222i		−	0.772003i	−0.922498	−	0.386001i	$-0.873856\pi$
$349$		−	14.4222i		−	0.772003i	0.922498	−	0.386001i	$-0.126144\pi$
$350$		0			0
$351$	−9.51388			−0.507813
$352$	3.70903	−	3.70903i	0.197692	−	0.197692i
$353$	−5.52721	+	5.52721i	−0.294184	+	0.294184i	−0.838730	−	0.544547i	$-0.816702\pi$
$353$	−5.52721	+	5.52721i	−0.294184	+	0.294184i	0.544547	+	0.838730i	$0.316702\pi$
$354$			13.8167i			0.734347i
$355$		0			0
$356$		0			0
$357$	−3.15254	−	3.15254i	−0.166850	−	0.166850i
$358$	12.4686	−	12.4686i	0.658988	−	0.658988i
$359$	24.1578			1.27500			0.637500	−	0.770450i	$-0.279969\pi$
$359$	24.1578			1.27500			0.637500	+	0.770450i	$0.279969\pi$
$360$		0			0
$361$	27.6972			1.45775
$362$	12.2501	−	12.2501i	0.643851	−	0.643851i
$363$	−15.2126	+	15.2126i	−0.798455	+	0.798455i
$364$	2.06903			0.108447
$365$		0			0
$366$			6.83354i			0.357195i
$367$	23.9782	−	23.9782i	1.25165	−	1.25165i	0.296675	−	0.954979i	$-0.404122\pi$
$367$	23.9782	−	23.9782i	1.25165	−	1.25165i	0.954979	−	0.296675i	$-0.0958777\pi$
$368$	1.00462	+	4.68943i	0.0523695	+	0.244453i
$369$		−	0.908327i		−	0.0472856i
$370$		0			0
$371$	−12.7889			−0.663966
$372$	6.36396	+	6.36396i	0.329956	+	0.329956i
$373$	3.44804	+	3.44804i	0.178533	+	0.178533i	0.790716	−	0.612183i	$-0.209709\pi$
$373$	3.44804	+	3.44804i	0.178533	+	0.178533i	−0.612183	+	0.790716i	$0.709709\pi$
$374$		−	14.7250i		−	0.761411i
$375$		0			0
$376$	5.21110			0.268742
$377$	2.40024	+	2.40024i	0.123619	+	0.123619i
$378$	−4.83204	−	4.83204i	−0.248533	−	0.248533i
$379$	−22.0888			−1.13462			−0.567312	−	0.823503i	$-0.692017\pi$
$379$	−22.0888			−1.13462			−0.567312	+	0.823503i	$0.692017\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	−14.8361	+	14.8361i	−0.759083	+	0.759083i
$383$	5.69405	+	5.69405i	0.290952	+	0.290952i	0.837456	−	0.546504i	$-0.184042\pi$
$383$	5.69405	+	5.69405i	0.290952	+	0.290952i	−0.546504	+	0.837456i	$0.684042\pi$
$384$		−	1.30278i		−	0.0664820i
$385$		0			0
$386$	−2.60555			−0.132619
$387$	−5.17206	+	5.17206i	−0.262911	+	0.262911i
$388$	9.40308	+	9.40308i	0.477369	+	0.477369i
$389$	−11.5980			−0.588044			−0.294022	−	0.955799i	$-0.594994\pi$
$389$	−11.5980			−0.588044			−0.294022	+	0.955799i	$0.594994\pi$
$390$		0			0
$391$	11.3028	+	7.31440i	0.571606	+	0.369905i
$392$	−3.89890	−	3.89890i	−0.196924	−	0.196924i
$393$	6.08504	−	6.08504i	0.306950	−	0.306950i
$394$			21.1194i			1.06398i
$395$		0			0
$396$		−	6.83354i		−	0.343398i
$397$	−25.2614	−	25.2614i	−1.26783	−	1.26783i	−0.947206	−	0.320626i	$-0.896107\pi$
$397$	−25.2614	−	25.2614i	−1.26783	−	1.26783i	−0.320626	−	0.947206i	$-0.603893\pi$
$398$	2.24601	+	2.24601i	0.112582	+	0.112582i
$399$		−	10.8528i		−	0.543320i
$400$		0			0
$401$			24.1578i			1.20638i	0.797596	+	0.603192i	$0.206105\pi$
$401$			24.1578i			1.20638i	−0.797596	+	0.603192i	$0.793895\pi$
$402$	14.8361	−	14.8361i	0.739959	−	0.739959i
$403$	−8.29081	+	8.29081i	−0.412995	+	0.412995i
$404$			3.81665i			0.189886i
$405$		0			0
$406$			2.43813i			0.121002i
$407$	9.04312	+	9.04312i	0.448251	+	0.448251i
$408$	−2.58603	−	2.58603i	−0.128028	−	0.128028i
$409$		−	19.9361i		−	0.985776i	−0.870093	−	0.492888i	$-0.835941\pi$
$409$		−	19.9361i		−	0.985776i	0.870093	−	0.492888i	$-0.164059\pi$
$410$		0			0
$411$			12.0789i			0.595808i
$412$	−5.43305	+	5.43305i	−0.267667	+	0.267667i
$413$	−9.14209	−	9.14209i	−0.449853	−	0.449853i
$414$	5.24537	+	3.39445i	0.257796	+	0.166828i
$415$		0			0
$416$	1.69722			0.0832133
$417$	3.12697	+	3.12697i	0.153128	+	0.153128i
$418$	25.3458	−	25.3458i	1.23970	−	1.23970i
$419$	24.1578			1.18019			0.590093	−	0.807335i	$-0.299091\pi$
$419$	24.1578			1.18019			0.590093	+	0.807335i	$0.299091\pi$
$420$		0			0
$421$		−	24.6387i		−	1.20082i	−0.799694	−	0.600408i	$-0.795005\pi$
$421$		−	24.6387i		−	1.20082i	0.799694	−	0.600408i	$-0.204995\pi$
$422$	−20.0975	−	20.0975i	−0.978333	−	0.978333i
$423$	4.80048	−	4.80048i	0.233407	−	0.233407i
$424$	−10.4907			−0.509475
$425$		0			0
$426$	0.908327			0.0440086
$427$	−4.52156	−	4.52156i	−0.218814	−	0.218814i
$428$	9.14209	+	9.14209i	0.441900	+	0.441900i
$429$	−11.5980			−0.559959
$430$		0			0
$431$			24.1578i			1.16364i	0.813317	+	0.581820i	$0.197659\pi$
$431$			24.1578i			1.16364i	−0.813317	+	0.581820i	$0.802341\pi$
$432$	−3.96372	−	3.96372i	−0.190705	−	0.190705i
$433$	−1.38400	−	1.38400i	−0.0665108	−	0.0665108i	0.673069	−	0.739580i	$-0.264976\pi$
$433$	−1.38400	−	1.38400i	−0.0665108	−	0.0665108i	−0.739580	+	0.673069i	$0.764976\pi$
$434$	−8.42171			−0.404255
$435$		0			0
$436$		−	3.65720i		−	0.175148i
$437$	6.86512	+	32.0454i	0.328403	+	1.53294i
$438$	7.92745	−	7.92745i	0.378788	−	0.378788i
$439$		−	30.9083i		−	1.47517i	−0.675252	−	0.737587i	$-0.735965\pi$
$439$		−	30.9083i		−	1.47517i	0.675252	−	0.737587i	$-0.264035\pi$
$440$		0			0
$441$	−7.18335			−0.342064
$442$	3.36902	−	3.36902i	0.160248	−	0.160248i
$443$	−4.15819	+	4.15819i	−0.197562	+	0.197562i	−0.798954	−	0.601392i	$-0.794613\pi$
$443$	−4.15819	+	4.15819i	−0.197562	+	0.197562i	0.601392	+	0.798954i	$0.294613\pi$
$444$	3.17634			0.150742
$445$		0			0
$446$	13.8167			0.654238
$447$	15.9591	−	15.9591i	0.754842	−	0.754842i
$448$	0.862010	+	0.862010i	0.0407261	+	0.0407261i
$449$			0.302776i			0.0142889i	0.999974	+	0.00714443i	$0.00227416\pi$
$449$			0.302776i			0.0142889i	−0.999974	+	0.00714443i	$0.997726\pi$
$450$		0			0
$451$		−	3.65720i		−	0.172211i
$452$		0			0
$453$	4.32709	−	4.32709i	0.203304	−	0.203304i
$454$	−7.31440			−0.343282
$455$		0			0
$456$		−	8.90257i		−	0.416901i
$457$	−7.94006	+	7.94006i	−0.371420	+	0.371420i	−0.867994	−	0.496574i	$-0.834591\pi$
$457$	−7.94006	+	7.94006i	−0.371420	+	0.371420i	0.496574	+	0.867994i	$0.334591\pi$
$458$	14.8361	+	14.8361i	0.693247	+	0.693247i
$459$	−15.7361			−0.734498
$460$		0			0
$461$	35.6333			1.65961			0.829804	−	0.558055i	$-0.188452\pi$
$461$	35.6333			1.65961			0.829804	+	0.558055i	$0.188452\pi$
$462$	−5.89058	−	5.89058i	−0.274054	−	0.274054i
$463$	−20.0975	+	20.0975i	−0.934012	+	0.934012i	−0.997954	−	0.0639420i	$-0.979633\pi$
$463$	−20.0975	+	20.0975i	−0.934012	+	0.934012i	0.0639420	+	0.997954i	$0.479633\pi$
$464$			2.00000i			0.0928477i
$465$		0			0
$466$	−3.39445			−0.157245
$467$	24.5002	−	24.5002i	1.13373	−	1.13373i	0.144184	−	0.989551i	$-0.453944\pi$
$467$	24.5002	−	24.5002i	1.13373	−	1.13373i	0.989551	−	0.144184i	$-0.0460557\pi$
$468$	1.56349	−	1.56349i	0.0722721	−	0.0722721i
$469$			19.6333i			0.906582i
$470$		0			0
$471$		−	7.31440i		−	0.337030i
$472$	−7.49926	−	7.49926i	−0.345181	−	0.345181i
$473$	−20.8243	+	20.8243i	−0.957501	+	0.957501i
$474$	−13.6671			−0.627749
$475$		0			0
$476$	3.42221			0.156857
$477$	−9.66408	+	9.66408i	−0.442488	+	0.442488i
$478$	−10.1980	+	10.1980i	−0.466447	+	0.466447i
$479$	−7.31440			−0.334203			−0.167102	−	0.985940i	$-0.553441\pi$
$479$	−7.31440			−0.334203			−0.167102	+	0.985940i	$0.553441\pi$
$480$		0			0
$481$			4.13806i			0.188679i
$482$	2.24601	−	2.24601i	0.102303	−	0.102303i
$483$	7.44761	−	1.59551i	0.338878	−	0.0725982i
$484$		−	16.5139i		−	0.750631i
$485$		0			0
$486$	−12.3944			−0.562224
$487$	23.6134	+	23.6134i	1.07003	+	1.07003i	0.997356	+	0.0726712i	$0.0231524\pi$
$487$	23.6134	+	23.6134i	1.07003	+	1.07003i	0.0726712	+	0.997356i	$0.476848\pi$
$488$	−3.70903	−	3.70903i	−0.167900	−	0.167900i
$489$			23.6056i			1.06748i
$490$		0			0
$491$	23.6333			1.06656			0.533278	−	0.845940i	$-0.320960\pi$
$491$	23.6333			1.06656			0.533278	+	0.845940i	$0.320960\pi$
$492$	−0.642284	−	0.642284i	−0.0289564	−	0.0289564i
$493$	3.97003	+	3.97003i	0.178801	+	0.178801i
$494$	11.5980			0.521821
$495$		0			0
$496$	−6.90833			−0.310193
$497$	−0.601014	+	0.601014i	−0.0269592	+	0.0269592i
$498$		0			0
$499$			15.2111i			0.680942i	0.940255	+	0.340471i	$0.110587\pi$
$499$			15.2111i			0.680942i	−0.940255	+	0.340471i	$0.889413\pi$
$500$		0			0
$501$	−23.4500			−1.04767
$502$	10.0041	−	10.0041i	0.446505	−	0.446505i
$503$	−17.4222	−	17.4222i	−0.776816	−	0.776816i	0.202472	−	0.979288i	$-0.435103\pi$
$503$	−17.4222	−	17.4222i	−0.776816	−	0.776816i	−0.979288	+	0.202472i	$0.935103\pi$
$504$	1.58817			0.0707427
$505$		0			0
$506$	21.1194	+	13.6671i	0.938873	+	0.607576i
$507$	9.32203	+	9.32203i	0.414006	+	0.414006i
$508$	9.76985	−	9.76985i	0.433467	−	0.433467i
$509$			41.0278i			1.81852i	0.416225	+	0.909262i	$0.363353\pi$
$509$			41.0278i			1.81852i	−0.416225	+	0.909262i	$0.636647\pi$
$510$		0			0
$511$			10.4907i			0.464083i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−27.0862	−	27.0862i	−1.19589	−	1.19589i
$514$			21.6333i			0.954204i
$515$		0			0
$516$			7.31440i			0.321998i
$517$	19.3282	−	19.3282i	0.850052	−	0.850052i
$518$	−2.10169	+	2.10169i	−0.0923431	+	0.0923431i
$519$			13.9361i			0.611726i
$520$		0			0
$521$			37.8249i			1.65714i	0.559887	+	0.828569i	$0.310845\pi$
$521$			37.8249i			1.65714i	−0.559887	+	0.828569i	$0.689155\pi$
$522$	1.84240	+	1.84240i	0.0806398	+	0.0806398i
$523$	−27.9483	−	27.9483i	−1.22209	−	1.22209i	−0.966887	−	0.255205i	$-0.917857\pi$
$523$	−27.9483	−	27.9483i	−1.22209	−	1.22209i	−0.255205	−	0.966887i	$-0.582143\pi$
$524$			6.60555i			0.288565i
$525$		0			0
$526$		−	18.9124i		−	0.824622i
$527$	−13.7131	+	13.7131i	−0.597353	+	0.597353i
$528$	−4.83204	−	4.83204i	−0.210288	−	0.210288i
$529$	−20.9815	+	9.42221i	−0.912238	+	0.409661i
$530$		0			0
$531$	−13.8167			−0.599592
$532$	5.89058	+	5.89058i	0.255389	+	0.255389i
$533$	0.836752	−	0.836752i	0.0362438	−	0.0362438i
$534$		0			0
$535$		0			0
$536$			16.1052i			0.695639i
$537$	−16.2438	−	16.2438i	−0.700973	−	0.700973i
$538$	4.54118	−	4.54118i	0.195784	−	0.195784i
$539$	−28.9223			−1.24577
$540$		0			0
$541$	29.2111			1.25588			0.627942	−	0.778260i	$-0.283898\pi$
$541$	29.2111			1.25588			0.627942	+	0.778260i	$0.283898\pi$
$542$	−5.74130	−	5.74130i	−0.246610	−	0.246610i
$543$	−15.9591	−	15.9591i	−0.684872	−	0.684872i
$544$	2.80724			0.120359
$545$		0			0
$546$		−	2.69548i		−	0.115356i
$547$	−17.7817	−	17.7817i	−0.760293	−	0.760293i	0.216083	−	0.976375i	$-0.430672\pi$
$547$	−17.7817	−	17.7817i	−0.760293	−	0.760293i	−0.976375	+	0.216083i	$0.930672\pi$
$548$	−6.55606	−	6.55606i	−0.280061	−	0.280061i
$549$	−6.83354			−0.291648
$550$		0			0
$551$			13.6671i			0.582237i
$552$	6.10927	−	1.30880i	0.260028	−	0.0557061i
$553$	9.04312	−	9.04312i	0.384552	−	0.384552i
$554$			18.0000i			0.764747i
$555$		0			0
$556$	−3.39445			−0.143957
$557$	−22.7762	+	22.7762i	−0.965059	+	0.965059i	−0.999410	−	0.0343513i	$-0.989064\pi$
$557$	−22.7762	+	22.7762i	−0.965059	+	0.965059i	0.0343513	+	0.999410i	$0.489064\pi$
$558$	−6.36396	+	6.36396i	−0.269408	+	0.269408i
$559$	−9.52902			−0.403034
$560$		0			0
$561$	−19.1833			−0.809922
$562$		0			0
$563$	−23.2982	−	23.2982i	−0.981902	−	0.981902i	0.0179374	−	0.999839i	$-0.494290\pi$
$563$	−23.2982	−	23.2982i	−0.981902	−	0.981902i	−0.999839	+	0.0179374i	$0.994290\pi$
$564$		−	6.78890i		−	0.285864i
$565$		0			0
$566$		−	12.9289i		−	0.543441i
$567$	−2.92605	+	2.92605i	−0.122882	+	0.122882i
$568$	−0.493012	+	0.493012i	−0.0206863	+	0.0206863i
$569$	7.31440			0.306635			0.153318	−	0.988177i	$-0.451004\pi$
$569$	7.31440			0.306635			0.153318	+	0.988177i	$0.451004\pi$
$570$		0			0
$571$		−	36.7176i		−	1.53658i	−0.640100	−	0.768291i	$-0.721107\pi$
$571$		−	36.7176i		−	1.53658i	0.640100	−	0.768291i	$-0.278893\pi$
$572$	6.29506	−	6.29506i	0.263210	−	0.263210i
$573$	19.3282	+	19.3282i	0.807445	+	0.807445i
$574$	0.849962			0.0354767
$575$		0			0
$576$	1.30278			0.0542823
$577$	20.6554	+	20.6554i	0.859894	+	0.859894i	0.991325	−	0.131431i	$-0.0419572\pi$
$577$	20.6554	+	20.6554i	0.859894	+	0.859894i	−0.131431	+	0.991325i	$0.541957\pi$
$578$	−6.44841	+	6.44841i	−0.268219	+	0.268219i
$579$			3.39445i			0.141068i
$580$		0			0
$581$		0			0
$582$	12.2501	−	12.2501i	0.507783	−	0.507783i
$583$	−38.9105	+	38.9105i	−1.61151	+	1.61151i
$584$			8.60555i			0.356100i
$585$		0			0
$586$			21.7197i			0.897232i
$587$	−13.0913	−	13.0913i	−0.540335	−	0.540335i	0.383292	−	0.923627i	$-0.374790\pi$
$587$	−13.0913	−	13.0913i	−0.540335	−	0.540335i	−0.923627	+	0.383292i	$0.874790\pi$
$588$	−5.07939	+	5.07939i	−0.209471	+	0.209471i
$589$	−47.2083			−1.94518
$590$		0			0
$591$	27.5139			1.13177
$592$	−1.72402	+	1.72402i	−0.0708568	+	0.0708568i
$593$	−2.95807	+	2.95807i	−0.121473	+	0.121473i	−0.765230	−	0.643757i	$-0.777375\pi$
$593$	−2.95807	+	2.95807i	−0.121473	+	0.121473i	0.643757	+	0.765230i	$0.277375\pi$
$594$	−29.4032			−1.20643
$595$		0			0
$596$			17.3243i			0.709630i
$597$	2.92605	−	2.92605i	0.119755	−	0.119755i
$598$	1.70507	+	7.95901i	0.0697255	+	0.325468i
$599$		−	8.51388i		−	0.347868i	−0.984757	−	0.173934i	$-0.944352\pi$
$599$		−	8.51388i		−	0.347868i	0.984757	−	0.173934i	$-0.0556479\pi$
$600$		0			0
$601$	−17.5139			−0.714406			−0.357203	−	0.934027i	$-0.616270\pi$
$601$	−17.5139			−0.714406			−0.357203	+	0.934027i	$0.616270\pi$
$602$	−4.83973	−	4.83973i	−0.197253	−	0.197253i
$603$	14.8361	+	14.8361i	0.604174	+	0.604174i
$604$			4.69722i			0.191127i
$605$		0			0
$606$	4.97224			0.201984
$607$	18.8130	+	18.8130i	0.763595	+	0.763595i	0.976970	−	0.213376i	$-0.0684458\pi$
$607$	18.8130	+	18.8130i	0.763595	+	0.763595i	−0.213376	+	0.976970i	$0.568446\pi$
$608$	4.83204	+	4.83204i	0.195965	+	0.195965i
$609$	3.17634			0.128712
$610$		0			0
$611$	8.84441			0.357807
$612$	2.58603	−	2.58603i	0.104534	−	0.104534i
$613$	−6.21604	−	6.21604i	−0.251064	−	0.251064i	0.570343	−	0.821407i	$-0.306810\pi$
$613$	−6.21604	−	6.21604i	−0.251064	−	0.251064i	−0.821407	+	0.570343i	$0.806810\pi$
$614$		−	20.0917i		−	0.810834i
$615$		0			0
$616$	6.39445			0.257640
$617$	−25.2832	+	25.2832i	−1.01786	+	1.01786i	−0.0180260	+	0.999838i	$0.505738\pi$
$617$	−25.2832	+	25.2832i	−1.01786	+	1.01786i	−0.999838	+	0.0180260i	$0.994262\pi$
$618$	7.07805	+	7.07805i	0.284721	+	0.284721i
$619$	−0.480859			−0.0193274			−0.00966368	−	0.999953i	$-0.503076\pi$
$619$	−0.480859			−0.0193274			−0.00966368	+	0.999953i	$0.503076\pi$
$620$		0			0
$621$	14.6056	−	22.5696i	0.586101	−	0.905688i
$622$	21.5117	+	21.5117i	0.862542	+	0.862542i
$623$		0			0
$624$		−	2.21110i		−	0.0885149i
$625$		0			0
$626$			4.39540i			0.175676i
$627$	−33.0199	−	33.0199i	−1.31869	−	1.31869i
$628$	3.97003	+	3.97003i	0.158421	+	0.158421i
$629$			6.84441i			0.272905i
$630$		0			0
$631$		−	6.35268i		−	0.252896i	−0.991973	−	0.126448i	$-0.959642\pi$
$631$		−	6.35268i		−	0.252896i	0.991973	−	0.126448i	$-0.0403577\pi$
$632$	7.41807	−	7.41807i	0.295075	−	0.295075i
$633$	−26.1826	+	26.1826i	−1.04066	+	1.04066i
$634$		−	17.0917i		−	0.678797i
$635$		0			0
$636$			13.6671i			0.541935i
$637$	−6.61731	−	6.61731i	−0.262187	−	0.262187i
$638$	7.41807	+	7.41807i	0.293684	+	0.293684i
$639$			0.908327i			0.0359329i
$640$		0			0
$641$			24.1578i			0.954176i	0.878856	+	0.477088i	$0.158308\pi$
$641$			24.1578i			0.954176i	−0.878856	+	0.477088i	$0.841692\pi$
$642$	11.9101	−	11.9101i	0.470054	−	0.470054i
$643$	−21.0522	−	21.0522i	−0.830217	−	0.830217i	0.157329	−	0.987546i	$-0.449712\pi$
$643$	−21.0522	−	21.0522i	−0.830217	−	0.830217i	−0.987546	+	0.157329i	$0.949712\pi$
$644$	−3.17634	+	4.90833i	−0.125165	+	0.193415i
$645$		0			0
$646$	19.1833			0.754759
$647$	−16.4127	−	16.4127i	−0.645251	−	0.645251i	0.306591	−	0.951841i	$-0.400812\pi$
$647$	−16.4127	−	16.4127i	−0.645251	−	0.645251i	−0.951841	+	0.306591i	$0.900812\pi$
$648$	−2.40024	+	2.40024i	−0.0942902	+	0.0942902i
$649$	−55.6300			−2.18367
$650$		0			0
$651$			10.9716i			0.430011i
$652$	−12.8124	−	12.8124i	−0.501771	−	0.501771i
$653$	28.1094	−	28.1094i	1.10001	−	1.10001i	0.105598	−	0.994409i	$-0.466324\pi$
$653$	28.1094	−	28.1094i	1.10001	−	1.10001i	0.994409	−	0.105598i	$-0.0336757\pi$
$654$	−4.76451			−0.186307
$655$		0			0
$656$	0.697224			0.0272220
$657$	7.92745	+	7.92745i	0.309279	+	0.309279i
$658$	4.49202	+	4.49202i	0.175117	+	0.175117i
$659$	−3.17634			−0.123733			−0.0618663	−	0.998084i	$-0.519705\pi$
$659$	−3.17634			−0.123733			−0.0618663	+	0.998084i	$0.519705\pi$
$660$		0			0
$661$			26.2268i			1.02011i	0.860143	+	0.510053i	$0.170374\pi$
$661$			26.2268i			1.02011i	−0.860143	+	0.510053i	$0.829626\pi$
$662$	−1.54386	−	1.54386i	−0.0600038	−	0.0600038i
$663$	−4.38907	−	4.38907i	−0.170457	−	0.170457i
$664$		0			0
$665$		0			0
$666$			3.17634i			0.123081i
$667$	−9.37886	+	2.00924i	−0.363151	+	0.0777982i
$668$	12.7279	−	12.7279i	0.492458	−	0.492458i
$669$		−	18.0000i		−	0.695920i
$670$		0			0
$671$	−27.5139			−1.06216
$672$	1.12301	−	1.12301i	0.0433209	−	0.0433209i
$673$	−7.92745	+	7.92745i	−0.305581	+	0.305581i	−0.843192	−	0.537612i	$-0.819327\pi$
$673$	−7.92745	+	7.92745i	−0.305581	+	0.305581i	0.537612	+	0.843192i	$0.319327\pi$
$674$	−22.9387			−0.883567
$675$		0			0
$676$	−10.1194			−0.389209
$677$	14.8361	−	14.8361i	0.570199	−	0.570199i	−0.361985	−	0.932184i	$-0.617901\pi$
$677$	14.8361	−	14.8361i	0.570199	−	0.570199i	0.932184	+	0.361985i	$0.117901\pi$
$678$		0			0
$679$			16.2111i			0.622125i
$680$		0			0
$681$			9.52902i			0.365153i
$682$	−25.6232	+	25.6232i	−0.981164	+	0.981164i
$683$	26.2670	−	26.2670i	1.00508	−	1.00508i	0.00509282	−	0.999987i	$-0.498379\pi$
$683$	26.2670	−	26.2670i	1.00508	−	1.00508i	0.999987	−	0.00509282i	$-0.00162110\pi$
$684$	8.90257			0.340398
$685$		0			0
$686$		−	15.2552i		−	0.582448i
$687$	19.3282	−	19.3282i	0.737415	−	0.737415i
$688$	−3.97003	−	3.97003i	−0.151356	−	0.151356i
$689$	−17.8051			−0.678321
$690$		0			0
$691$	−4.18335			−0.159142			−0.0795710	−	0.996829i	$-0.525355\pi$
$691$	−4.18335			−0.159142			−0.0795710	+	0.996829i	$0.525355\pi$
$692$	−7.56408	−	7.56408i	−0.287543	−	0.287543i
$693$	5.89058	−	5.89058i	0.223764	−	0.223764i
$694$			15.9083i			0.603872i
$695$		0			0
$696$	2.60555			0.0987632
$697$	1.38400	−	1.38400i	0.0524228	−	0.0524228i
$698$	10.1980	−	10.1980i	0.386001	−	0.386001i
$699$			4.42221i			0.167263i
$700$		0			0
$701$			3.65720i			0.138130i	0.997612	+	0.0690652i	$0.0220017\pi$
$701$			3.65720i			0.138130i	−0.997612	+	0.0690652i	$0.977998\pi$
$702$	−6.72733	−	6.72733i	−0.253907	−	0.253907i
$703$	−11.7812	+	11.7812i	−0.444335	+	0.444335i
$704$	5.24537			0.197692
$705$		0			0
$706$	−7.81665			−0.294184
$707$	−3.28999	+	3.28999i	−0.123733	+	0.123733i
$708$	−9.76985	+	9.76985i	−0.367173	+	0.367173i
$709$	22.0888			0.829562			0.414781	−	0.909921i	$-0.363858\pi$
$709$	22.0888			0.829562			0.414781	+	0.909921i	$0.363858\pi$
$710$		0			0
$711$		−	13.6671i		−	0.512555i
$712$		0			0
$713$	−6.94026	−	32.3961i	−0.259915	−	1.21324i
$714$		−	4.45837i		−	0.166850i
$715$		0			0
$716$	17.6333			0.658988
$717$	13.2858	+	13.2858i	0.496166	+	0.496166i
$718$	17.0821	+	17.0821i	0.637500	+	0.637500i
$719$		−	13.3305i		−	0.497145i	−0.968613	−	0.248572i	$-0.920039\pi$
$719$		−	13.3305i		−	0.497145i	0.968613	−	0.248572i	$-0.0799614\pi$
$720$		0			0
$721$	−9.36669			−0.348834
$722$	19.5849	+	19.5849i	0.728874	+	0.728874i
$723$	−2.92605	−	2.92605i	−0.108821	−	0.108821i
$724$	17.3243			0.643851
$725$		0			0
$726$	−21.5139			−0.798455
$727$	−17.3431	+	17.3431i	−0.643222	+	0.643222i	−0.951346	−	0.308124i	$-0.900299\pi$
$727$	−17.3431	+	17.3431i	−0.643222	+	0.643222i	0.308124	+	0.951346i	$0.400299\pi$
$728$	1.46302	+	1.46302i	0.0542233	+	0.0542233i
$729$			26.3305i			0.975205i
$730$		0			0
$731$	−15.7611			−0.582947
$732$	−4.83204	+	4.83204i	−0.178597	+	0.178597i
$733$	30.1943	+	30.1943i	1.11525	+	1.11525i	0.992429	+	0.122822i	$0.0391945\pi$
$733$	30.1943	+	30.1943i	1.11525	+	1.11525i	0.122822	+	0.992429i	$0.460806\pi$
$734$	33.9103			1.25165
$735$		0			0
$736$	−2.60555	+	4.02630i	−0.0960419	+	0.148411i
$737$	59.7348	+	59.7348i	2.20036	+	2.20036i
$738$	0.642284	−	0.642284i	0.0236428	−	0.0236428i
$739$			37.2666i			1.37087i	0.728132	+	0.685437i	$0.240389\pi$
$739$			37.2666i			1.37087i	−0.728132	+	0.685437i	$0.759611\pi$
$740$		0			0
$741$		−	15.1097i		−	0.555067i
$742$	−9.04312	−	9.04312i	−0.331983	−	0.331983i
$743$	33.9823	+	33.9823i	1.24669	+	1.24669i	0.957173	+	0.289518i	$0.0934951\pi$
$743$	33.9823	+	33.9823i	1.24669	+	1.24669i	0.289518	+	0.957173i	$0.406505\pi$
$744$			9.00000i			0.329956i
$745$		0			0
$746$			4.87626i			0.178533i
$747$		0			0
$748$	10.4121	−	10.4121i	0.380705	−	0.380705i
$749$			15.7611i			0.575900i
$750$		0			0
$751$		−	37.8249i		−	1.38025i	−0.723690	−	0.690125i	$-0.757556\pi$
$751$		−	37.8249i		−	1.38025i	0.723690	−	0.690125i	$-0.242444\pi$
$752$	3.68481	+	3.68481i	0.134371	+	0.134371i
$753$	−13.0331	−	13.0331i	−0.474952	−	0.474952i
$754$			3.39445i			0.123619i
$755$		0			0
$756$		−	6.83354i		−	0.248533i
$757$	10.1861	−	10.1861i	0.370219	−	0.370219i	−0.497338	−	0.867557i	$-0.665689\pi$
$757$	10.1861	−	10.1861i	0.370219	−	0.370219i	0.867557	+	0.497338i	$0.165689\pi$
$758$	−15.6191	−	15.6191i	−0.567312	−	0.567312i
$759$	17.8051	−	27.5139i	0.646285	−	0.998691i
$760$		0			0
$761$	29.5139			1.06988			0.534939	−	0.844891i	$-0.320335\pi$
$761$	29.5139			1.06988			0.534939	+	0.844891i	$0.320335\pi$
$762$	−12.7279	−	12.7279i	−0.461084	−	0.461084i
$763$	3.15254	−	3.15254i	0.114130	−	0.114130i
$764$	−20.9815			−0.759083
$765$		0			0
$766$			8.05260i			0.290952i
$767$	−12.7279	−	12.7279i	−0.459579	−	0.459579i
$768$	0.921201	−	0.921201i	0.0332410	−	0.0332410i
$769$	52.4537			1.89153			0.945764	−	0.324855i	$-0.105315\pi$
$769$	52.4537			1.89153			0.945764	+	0.324855i	$0.105315\pi$
$770$		0			0
$771$	28.1833			1.01500
$772$	−1.84240	−	1.84240i	−0.0663095	−	0.0663095i
$773$	25.7022	+	25.7022i	0.924446	+	0.924446i	0.997340	−	0.0728941i	$-0.0232235\pi$
$773$	25.7022	+	25.7022i	0.924446	+	0.924446i	−0.0728941	+	0.997340i	$0.523224\pi$
$774$	−7.31440			−0.262911
$775$		0			0
$776$			13.2980i			0.477369i
$777$	2.73804	+	2.73804i	0.0982265	+	0.0982265i
$778$	−8.20106	−	8.20106i	−0.294022	−	0.294022i
$779$	4.76451			0.170706
$780$		0			0
$781$			3.65720i			0.130865i
$782$	2.82021	+	13.1643i	0.100851	+	0.470755i
$783$	7.92745	−	7.92745i	0.283304	−	0.283304i
$784$		−	5.51388i		−	0.196924i
$785$		0			0
$786$	8.60555			0.306950
$787$	13.6341	−	13.6341i	0.486004	−	0.486004i	−0.421039	−	0.907043i	$-0.638334\pi$
$787$	13.6341	−	13.6341i	0.486004	−	0.486004i	0.907043	+	0.421039i	$0.138334\pi$
$788$	−14.9337	+	14.9337i	−0.531991	+	0.531991i
$789$	−24.6387			−0.877160
$790$		0			0
$791$		0			0
$792$	4.83204	−	4.83204i	0.171699	−	0.171699i
$793$	−6.29506	−	6.29506i	−0.223544	−	0.223544i
$794$		−	35.7250i		−	1.26783i
$795$		0			0
$796$			3.17634i			0.112582i
$797$	5.69405	−	5.69405i	0.201694	−	0.201694i	−0.599032	−	0.800725i	$-0.704448\pi$
$797$	5.69405	−	5.69405i	0.201694	−	0.201694i	0.800725	+	0.599032i	$0.204448\pi$
$798$	7.67410	−	7.67410i	0.271660	−	0.271660i
$799$	14.6288			0.517529
$800$		0			0
$801$		0			0
$802$	−17.0821	+	17.0821i	−0.603192	+	0.603192i
$803$	31.9183	+	31.9183i	1.12637	+	1.12637i
$804$	20.9815			0.739959
$805$		0			0
$806$	−11.7250			−0.412995
$807$	−5.91614	−	5.91614i	−0.208258	−	0.208258i
$808$	−2.69878	+	2.69878i	−0.0949428	+	0.0949428i
$809$			27.3028i			0.959914i	0.877292	+	0.479957i	$0.159348\pi$
$809$			27.3028i			0.959914i	−0.877292	+	0.479957i	$0.840652\pi$
$810$		0			0
$811$	−45.2111			−1.58758			−0.793788	−	0.608194i	$-0.791894\pi$
$811$	−45.2111			−1.58758			−0.793788	+	0.608194i	$0.791894\pi$
$812$	−1.72402	+	1.72402i	−0.0605012	+	0.0605012i
$813$	−7.47963	+	7.47963i	−0.262322	+	0.262322i
$814$			12.7889i			0.448251i
$815$		0			0
$816$		−	3.65720i		−	0.128028i
$817$	−27.1293	−	27.1293i	−0.949136	−	0.949136i
$818$	14.0969	−	14.0969i	0.492888	−	0.492888i
$819$	2.69548			0.0941877
$820$		0			0
$821$	5.81665			0.203003			0.101501	−	0.994835i	$-0.467635\pi$
$821$	5.81665			0.203003			0.101501	+	0.994835i	$0.467635\pi$
$822$	−8.54107	+	8.54107i	−0.297904	+	0.297904i
$823$	0.557835	−	0.557835i	0.0194449	−	0.0194449i	−0.697317	−	0.716762i	$-0.745623\pi$
$823$	0.557835	−	0.557835i	0.0194449	−	0.0194449i	0.716762	+	0.697317i	$0.245623\pi$
$824$	−7.68350			−0.267667
$825$		0			0
$826$		−	12.9289i		−	0.449853i
$827$	−27.4263	+	27.4263i	−0.953705	+	0.953705i	−0.998975	−	0.0452700i	$-0.985585\pi$
$827$	−27.4263	+	27.4263i	−0.953705	+	0.953705i	0.0452700	+	0.998975i	$0.485585\pi$
$828$	1.30880	+	6.10927i	0.0454838	+	0.212312i
$829$			20.6056i			0.715660i	0.933787	+	0.357830i	$0.116483\pi$
$829$			20.6056i			0.715660i	−0.933787	+	0.357830i	$0.883517\pi$
$830$		0			0
$831$	23.4500			0.813470
$832$	1.20012	+	1.20012i	0.0416066	+	0.0416066i
$833$	−10.9451	−	10.9451i	−0.379226	−	0.379226i
$834$			4.42221i			0.153128i
$835$		0			0
$836$	35.8444			1.23970
$837$	27.3827	+	27.3827i	0.946484	+	0.946484i
$838$	17.0821	+	17.0821i	0.590093	+	0.590093i
$839$	−28.2959			−0.976882			−0.488441	−	0.872597i	$-0.662434\pi$
$839$	−28.2959			−0.976882			−0.488441	+	0.872597i	$0.662434\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	17.4222	−	17.4222i	0.600408	−	0.600408i
$843$		0			0
$844$		−	28.4222i		−	0.978333i
$845$		0			0
$846$	6.78890			0.233407
$847$	14.2351	−	14.2351i	0.489125	−	0.489125i
$848$	−7.41807	−	7.41807i	−0.254738	−	0.254738i
$849$	−16.8434			−0.578064
$850$		0			0
$851$	−9.81665	−	6.35268i	−0.336511	−	0.217767i
$852$	0.642284	+	0.642284i	0.0220043	+	0.0220043i
$853$	−0.0844494	+	0.0844494i	−0.00289149	+	0.00289149i	−0.708551	−	0.705660i	$-0.750651\pi$
$853$	−0.0844494	+	0.0844494i	−0.00289149	+	0.00289149i	0.705660	+	0.708551i	$0.250651\pi$
$854$		−	6.39445i		−	0.218814i
$855$		0			0
$856$			12.9289i			0.441900i
$857$	−28.5828	−	28.5828i	−0.976370	−	0.976370i	0.0233568	−	0.999727i	$-0.492565\pi$
$857$	−28.5828	−	28.5828i	−0.976370	−	0.976370i	−0.999727	+	0.0233568i	$0.992565\pi$
$858$	−8.20106	−	8.20106i	−0.279979	−	0.279979i
$859$		−	42.0555i		−	1.43492i	−0.696602	−	0.717458i	$-0.745306\pi$
$859$		−	42.0555i		−	1.43492i	0.696602	−	0.717458i	$-0.254694\pi$
$860$		0			0
$861$		−	1.10731i		−	0.0377370i
$862$	−17.0821	+	17.0821i	−0.581820	+	0.581820i
$863$	−17.6973	+	17.6973i	−0.602423	+	0.602423i	−0.940955	−	0.338532i	$-0.890070\pi$
$863$	−17.6973	+	17.6973i	−0.602423	+	0.602423i	0.338532	+	0.940955i	$0.390070\pi$
$864$		−	5.60555i		−	0.190705i
$865$		0			0
$866$		−	1.95727i		−	0.0665108i
$867$	8.40083	+	8.40083i	0.285307	+	0.285307i
$868$	−5.95505	−	5.95505i	−0.202127	−	0.202127i
$869$		−	55.0278i		−	1.86669i
$870$		0			0
$871$			27.3341i			0.926182i
$872$	2.58603	−	2.58603i	0.0875740	−	0.0875740i
$873$	12.2501	+	12.2501i	0.414603	+	0.414603i
$874$	−17.8051	+	27.5139i	−0.602268	+	0.930671i
$875$		0			0
$876$	11.2111			0.378788
$877$	4.60601	+	4.60601i	0.155534	+	0.155534i	0.780584	−	0.625050i	$-0.214922\pi$
$877$	4.60601	+	4.60601i	0.155534	+	0.155534i	−0.625050	+	0.780584i	$0.714922\pi$
$878$	21.8555	−	21.8555i	0.737587	−	0.737587i
$879$	28.2959			0.954396
$880$		0			0
$881$		−	55.6300i		−	1.87422i	−0.349031	−	0.937111i	$-0.613489\pi$
$881$		−	55.6300i		−	1.87422i	0.349031	−	0.937111i	$-0.386511\pi$
$882$	−5.07939	−	5.07939i	−0.171032	−	0.171032i
$883$	38.2682	−	38.2682i	1.28783	−	1.28783i	0.351724	−	0.936104i	$-0.385595\pi$
$883$	38.2682	−	38.2682i	1.28783	−	1.28783i	0.936104	−	0.351724i	$-0.114405\pi$
$884$	4.76451			0.160248
$885$		0			0
$886$	−5.88057			−0.197562
$887$	−11.4434	−	11.4434i	−0.384230	−	0.384230i	0.488393	−	0.872624i	$-0.337583\pi$
$887$	−11.4434	−	11.4434i	−0.384230	−	0.384230i	−0.872624	+	0.488393i	$0.837583\pi$
$888$	2.24601	+	2.24601i	0.0753712	+	0.0753712i
$889$	16.8434			0.564910
$890$		0			0
$891$			17.8051i			0.596494i
$892$	9.76985	+	9.76985i	0.327119	+	0.327119i
$893$	25.1803	+	25.1803i	0.842625	+	0.842625i
$894$	22.5696			0.754842
$895$		0			0
$896$			1.21907i			0.0407261i
$897$	10.3688	−	2.22132i	0.346204	−	0.0741678i
$898$	−0.214095	+	0.214095i	−0.00714443	+	0.00714443i
$899$		−	13.8167i		−	0.460811i
$900$		0			0
$901$	−29.4500			−0.981120
$902$	2.58603	−	2.58603i	0.0861054	−	0.0861054i
$903$	−6.30508	+	6.30508i	−0.209820	+	0.209820i
$904$		0			0
$905$		0			0
$906$	6.11943			0.203304
$907$	−11.3881	+	11.3881i	−0.378136	+	0.378136i	−0.870429	−	0.492294i	$-0.836159\pi$
$907$	−11.3881	+	11.3881i	−0.378136	+	0.378136i	0.492294	+	0.870429i	$0.336159\pi$
$908$	−5.17206	−	5.17206i	−0.171641	−	0.171641i
$909$			4.97224i			0.164919i
$910$		0			0
$911$			16.8434i			0.558047i	0.960284	+	0.279024i	$0.0900108\pi$
$911$			16.8434i			0.558047i	−0.960284	+	0.279024i	$0.909989\pi$
$912$	6.29506	−	6.29506i	0.208450	−	0.208450i
$913$		0			0
$914$	−11.2289			−0.371420
$915$		0			0
$916$			20.9815i			0.693247i
$917$	−5.69405	+	5.69405i	−0.188034	+	0.188034i
$918$	−11.1271	−	11.1271i	−0.367249	−	0.367249i
$919$	7.31440			0.241280			0.120640	−	0.992696i	$-0.461505\pi$
$919$	7.31440			0.241280			0.120640	+	0.992696i	$0.461505\pi$
$920$		0			0
$921$	−26.1749			−0.862494
$922$	25.1966	+	25.1966i	0.829804	+	0.829804i
$923$	−0.836752	+	0.836752i	−0.0275420	+	0.0275420i
$924$		−	8.33053i		−	0.274054i
$925$		0			0
$926$	−28.4222			−0.934012
$927$	−7.07805	+	7.07805i	−0.232474	+	0.232474i
$928$	−1.41421	+	1.41421i	−0.0464238	+	0.0464238i
$929$		−	29.6333i		−	0.972237i	−0.873893	−	0.486119i	$-0.838412\pi$
$929$		−	29.6333i		−	0.972237i	0.873893	−	0.486119i	$-0.161588\pi$
$930$		0			0
$931$		−	37.6793i		−	1.23489i
$932$	−2.40024	−	2.40024i	−0.0786224	−	0.0786224i
$933$	28.0250	−	28.0250i	0.917497	−	0.917497i
$934$	34.6485			1.13373
$935$		0			0
$936$	2.21110			0.0722721
$937$	3.10802	−	3.10802i	0.101535	−	0.101535i	−0.654515	−	0.756049i	$-0.727127\pi$
$937$	3.10802	−	3.10802i	0.101535	−	0.101535i	0.756049	+	0.654515i	$0.227127\pi$
$938$	−13.8828	+	13.8828i	−0.453291	+	0.453291i
$939$	5.72623			0.186868
$940$		0			0
$941$			53.5610i			1.74604i	0.487686	+	0.873019i	$0.337841\pi$
$941$			53.5610i			1.74604i	−0.487686	+	0.873019i	$0.662159\pi$
$942$	5.17206	−	5.17206i	0.168515	−	0.168515i
$943$	0.700447	+	3.26958i	0.0228097	+	0.106472i
$944$		−	10.6056i		−	0.345181i
$945$		0			0
$946$	−29.4500			−0.957501
$947$	22.4133	+	22.4133i	0.728335	+	0.728335i	0.970288	−	0.241953i	$-0.0777879\pi$
$947$	22.4133	+	22.4133i	0.728335	+	0.728335i	−0.241953	+	0.970288i	$0.577788\pi$
$948$	−9.66408	−	9.66408i	−0.313875	−	0.313875i
$949$			14.6056i			0.474116i
$950$		0			0
$951$	−22.2666			−0.722044
$952$	2.41986	+	2.41986i	0.0784283	+	0.0784283i
$953$	8.88109	+	8.88109i	0.287687	+	0.287687i	0.836165	−	0.548478i	$-0.184793\pi$
$953$	8.88109	+	8.88109i	0.287687	+	0.287687i	−0.548478	+	0.836165i	$0.684793\pi$
$954$	−13.6671			−0.442488
$955$		0			0
$956$	−14.4222			−0.466447
$957$	9.66408	−	9.66408i	0.312395	−	0.312395i
$958$	−5.17206	−	5.17206i	−0.167102	−	0.167102i
$959$		−	11.3028i		−	0.364986i
$960$		0			0
$961$	16.7250			0.539516
$962$	−2.92605	+	2.92605i	−0.0943396	+	0.0943396i
$963$	11.9101	+	11.9101i	0.383797	+	0.383797i
$964$	3.17634			0.102303
$965$		0			0
$966$	6.39445	+	4.13806i	0.205738	+	0.133140i
$967$	37.6259	+	37.6259i	1.20997	+	1.20997i	0.971036	+	0.238932i	$0.0767973\pi$
$967$	37.6259	+	37.6259i	1.20997	+	1.20997i	0.238932	+	0.971036i	$0.423203\pi$
$968$	11.6771	−	11.6771i	0.375315	−	0.375315i
$969$		−	24.9916i		−	0.802846i
$970$		0			0
$971$		−	11.5980i		−	0.372199i	−0.982531	−	0.186099i	$-0.940415\pi$
$971$		−	11.5980i		−	0.372199i	0.982531	−	0.186099i	$-0.0595847\pi$
$972$	−8.76420	−	8.76420i	−0.281112	−	0.281112i
$973$	−2.92605	−	2.92605i	−0.0938048	−	0.0938048i
$974$			33.3944i			1.07003i
$975$		0			0
$976$		−	5.24537i		−	0.167900i
$977$	−31.0563	+	31.0563i	−0.993578	+	0.993578i	−0.999980	−	0.00640111i	$-0.997962\pi$
$977$	−31.0563	+	31.0563i	−0.993578	+	0.993578i	0.00640111	+	0.999980i	$0.497962\pi$
$978$	−16.6916	+	16.6916i	−0.533740	+	0.533740i
$979$		0			0
$980$		0			0
$981$		−	4.76451i		−	0.152119i
$982$	16.7113	+	16.7113i	0.533278	+	0.533278i
$983$	32.1793	+	32.1793i	1.02636	+	1.02636i	0.999643	+	0.0267167i	$0.00850521\pi$
$983$	32.1793	+	32.1793i	1.02636	+	1.02636i	0.0267167	+	0.999643i	$0.491495\pi$
$984$		−	0.908327i		−	0.0289564i
$985$		0			0
$986$			5.61447i			0.178801i
$987$	5.85210	−	5.85210i	0.186274	−	0.186274i
$988$	8.20106	+	8.20106i	0.260910	+	0.260910i
$989$	14.6288	−	22.6056i	0.465169	−	0.718815i
$990$		0			0
$991$	0.513878			0.0163239			0.00816194	−	0.999967i	$-0.497402\pi$
$991$	0.513878			0.0163239			0.00816194	+	0.999967i	$0.497402\pi$
$992$	−4.88492	−	4.88492i	−0.155097	−	0.155097i
$993$	−2.01130	+	2.01130i	−0.0638267	+	0.0638267i
$994$	−0.849962			−0.0269592
$995$		0			0
$996$		0			0
$997$	−31.1520	−	31.1520i	−0.986592	−	0.986592i	0.0133191	−	0.999911i	$-0.495760\pi$
$997$	−31.1520	−	31.1520i	−0.986592	−	0.986592i	−0.999911	+	0.0133191i	$0.995760\pi$
$998$	−10.7559	+	10.7559i	−0.340471	+	0.340471i
$999$	13.6671			0.432407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.e.1057.7	yes	16
5.2	odd	4	inner	1150.2.e.e.643.1	✓	16
5.3	odd	4	inner	1150.2.e.e.643.8	yes	16
5.4	even	2	inner	1150.2.e.e.1057.2	yes	16
23.22	odd	2	inner	1150.2.e.e.1057.8	yes	16
115.22	even	4	inner	1150.2.e.e.643.2	yes	16
115.68	even	4	inner	1150.2.e.e.643.7	yes	16
115.114	odd	2	inner	1150.2.e.e.1057.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.e.e.643.1	✓	16	5.2	odd	4	inner
1150.2.e.e.643.2	yes	16	115.22	even	4	inner
1150.2.e.e.643.7	yes	16	115.68	even	4	inner
1150.2.e.e.643.8	yes	16	5.3	odd	4	inner
1150.2.e.e.1057.1	yes	16	115.114	odd	2	inner
1150.2.e.e.1057.2	yes	16	5.4	even	2	inner
1150.2.e.e.1057.7	yes	16	1.1	even	1	trivial
1150.2.e.e.1057.8	yes	16	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.921201 - 0.921201i) q^{3} +1.00000i q^{4} +1.30278 q^{6} +(-0.862010 + 0.862010i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.30278i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.921201 - 0.921201i) q^{3} +1.00000i q^{4} +1.30278 q^{6} +(-0.862010 + 0.862010i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.30278i q^{9} +5.24537i q^{11} +(0.921201 + 0.921201i) q^{12} +(-1.20012 + 1.20012i) q^{13} -1.21907 q^{14} -1.00000 q^{16} +(-1.98502 + 1.98502i) q^{17} +(-0.921201 + 0.921201i) q^{18} -6.83354 q^{19} +1.58817i q^{21} +(-3.70903 + 3.70903i) q^{22} +(-1.00462 - 4.68943i) q^{23} +1.30278i q^{24} -1.69722 q^{26} +(3.96372 + 3.96372i) q^{27} +(-0.862010 - 0.862010i) q^{28} -2.00000i q^{29} +6.90833 q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.83204 + 4.83204i) q^{33} -2.80724 q^{34} -1.30278 q^{36} +(1.72402 - 1.72402i) q^{37} +(-4.83204 - 4.83204i) q^{38} +2.21110i q^{39} -0.697224 q^{41} +(-1.12301 + 1.12301i) q^{42} +(3.97003 + 3.97003i) q^{43} -5.24537 q^{44} +(2.60555 - 4.02630i) q^{46} +(-3.68481 - 3.68481i) q^{47} +(-0.921201 + 0.921201i) q^{48} +5.51388i q^{49} +3.65720i q^{51} +(-1.20012 - 1.20012i) q^{52} +(7.41807 + 7.41807i) q^{53} +5.60555i q^{54} -1.21907i q^{56} +(-6.29506 + 6.29506i) q^{57} +(1.41421 - 1.41421i) q^{58} +10.6056i q^{59} +5.24537i q^{61} +(4.88492 + 4.88492i) q^{62} +(-1.12301 - 1.12301i) q^{63} -1.00000i q^{64} +6.83354i q^{66} +(11.3881 - 11.3881i) q^{67} +(-1.98502 - 1.98502i) q^{68} +(-5.24537 - 3.39445i) q^{69} +0.697224 q^{71} +(-0.921201 - 0.921201i) q^{72} +(6.08504 - 6.08504i) q^{73} +2.43813 q^{74} -6.83354i q^{76} +(-4.52156 - 4.52156i) q^{77} +(-1.56349 + 1.56349i) q^{78} -10.4907 q^{79} +3.39445 q^{81} +(-0.493012 - 0.493012i) q^{82} -1.58817 q^{84} +5.61447i q^{86} +(-1.84240 - 1.84240i) q^{87} +(-3.70903 - 3.70903i) q^{88} -2.06903i q^{91} +(4.68943 - 1.00462i) q^{92} +(6.36396 - 6.36396i) q^{93} -5.21110i q^{94} -1.30278 q^{96} +(9.40308 - 9.40308i) q^{97} +(-3.89890 + 3.89890i) q^{98} -6.83354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{6}+O(q^{10}) \) 16 * q - 8 * q^6	\( 16 q - 8 q^{6} - 16 q^{16} - 56 q^{26} + 24 q^{31} + 8 q^{36} - 40 q^{41} - 16 q^{46} + 40 q^{71} + 112 q^{81} + 8 q^{96}+O(q^{100}) \) 16 * q - 8 * q^6 - 16 * q^16 - 56 * q^26 + 24 * q^31 + 8 * q^36 - 40 * q^41 - 16 * q^46 + 40 * q^71 + 112 * q^81 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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