LMFDB - Embedded newform 819.2.j.h.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("819.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$819 = 3^{2} \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	819.j (of order $3$ , 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4$ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$3$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.2
Root			$0.597828 + 1.03547i$ of defining polynomial
Character	$\chi$	$=$	819.235
Dual form			819.2.j.h.352.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0978281 - 0.169443i) q^{2} +(0.980859 - 1.69890i) q^{4} +(1.96625 + 3.40565i) q^{5} +(1.12324 + 2.39548i) q^{7} -0.775135 q^{8} +(0.384710 - 0.666337i) q^{10} +(2.25314 - 3.90255i) q^{11} +1.00000 q^{13} +(0.296013 - 0.424671i) q^{14} +(-1.88589 - 3.26645i) q^{16} +(-1.14070 + 1.97576i) q^{17} +(0.893841 + 1.54818i) q^{19} +7.71448 q^{20} -0.881681 q^{22} +(0.870106 + 1.50707i) q^{23} +(-5.23232 + 9.06264i) q^{25} +(-0.0978281 - 0.169443i) q^{26} +(5.17142 + 0.441354i) q^{28} -1.65110 q^{29} +(-2.80262 + 4.85427i) q^{31} +(-1.14412 + 1.98168i) q^{32} +0.446372 q^{34} +(-5.94959 + 8.53550i) q^{35} +(-3.57204 - 6.18695i) q^{37} +(0.174886 - 0.302911i) q^{38} +(-1.52411 - 2.63984i) q^{40} +8.11574 q^{41} +6.81353 q^{43} +(-4.42002 - 7.65570i) q^{44} +(0.170242 - 0.294867i) q^{46} +(1.77271 + 3.07043i) q^{47} +(-4.47665 + 5.38141i) q^{49} +2.04747 q^{50} +(0.980859 - 1.69890i) q^{52} +(1.64483 - 2.84892i) q^{53} +17.7210 q^{55} +(-0.870665 - 1.85682i) q^{56} +(0.161524 + 0.279768i) q^{58} +(2.25314 - 3.90255i) q^{59} +(-3.77234 - 6.53388i) q^{61} +1.09670 q^{62} -7.09585 q^{64} +(1.96625 + 3.40565i) q^{65} +(6.33263 - 10.9684i) q^{67} +(2.23774 + 3.87588i) q^{68} +(2.02832 + 0.173107i) q^{70} -9.54869 q^{71} +(-0.540019 + 0.935340i) q^{73} +(-0.698891 + 1.21052i) q^{74} +3.50693 q^{76} +(11.8793 + 1.01384i) q^{77} +(-0.395849 - 0.685630i) q^{79} +(7.41628 - 12.8454i) q^{80} +(-0.793947 - 1.37516i) q^{82} +7.14643 q^{83} -8.97166 q^{85} +(-0.666555 - 1.15451i) q^{86} +(-1.74649 + 3.02500i) q^{88} +(-5.63281 - 9.75631i) q^{89} +(1.12324 + 2.39548i) q^{91} +3.41381 q^{92} +(0.346843 - 0.600749i) q^{94} +(-3.51504 + 6.08823i) q^{95} -8.81353 q^{97} +(1.34979 + 0.232085i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28}+ \cdots + 7 q^{98}+O(q^{100})$ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$ .

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	−0.0978281	−	0.169443i	−0.0691749	−	0.119815i	0.829363	−	0.558710i	$-0.188703\pi$
$2$	−0.0978281	−	0.169443i	−0.0691749	−	0.119815i	−0.898538	+	0.438895i	$0.855370\pi$
$3$		0			0
$3$		0			0
$4$	0.980859	−	1.69890i	0.490430	−	0.849449i
$5$	1.96625	+	3.40565i	0.879336	+	1.52305i	0.852071	+	0.523426i	$0.175346\pi$
$5$	1.96625	+	3.40565i	0.879336	+	1.52305i	0.0272650	+	0.999628i	$0.491320\pi$
$6$		0			0
$7$	1.12324	+	2.39548i	0.424546	+	0.905406i
$7$	1.12324	+	2.39548i	0.424546	+	0.905406i
$8$	−0.775135			−0.274052
$9$		0			0
$10$	0.384710	−	0.666337i	0.121656	−	0.210714i
$11$	2.25314	−	3.90255i	0.679346	−	1.17666i	−0.295832	−	0.955240i	$-0.595597\pi$
$11$	2.25314	−	3.90255i	0.679346	−	1.17666i	0.975178	−	0.221422i	$-0.0710699\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	0.296013	−	0.424671i	0.0791129	−	0.113498i
$15$		0			0
$16$	−1.88589	−	3.26645i	−0.471472	−	0.816614i
$17$	−1.14070	+	1.97576i	−0.276661	+	0.479192i	−0.970553	−	0.240888i	$-0.922561\pi$
$17$	−1.14070	+	1.97576i	−0.276661	+	0.479192i	0.693891	+	0.720080i	$0.255895\pi$
$18$		0			0
$19$	0.893841	+	1.54818i	0.205061	+	0.355177i	0.950152	−	0.311786i	$-0.100927\pi$
$19$	0.893841	+	1.54818i	0.205061	+	0.355177i	−0.745091	+	0.666963i	$0.767594\pi$
$20$	7.71448			1.72501
$21$		0			0
$22$	−0.881681			−0.187975
$23$	0.870106	+	1.50707i	0.181430	+	0.314245i	0.942368	−	0.334579i	$-0.108594\pi$
$23$	0.870106	+	1.50707i	0.181430	+	0.314245i	−0.760938	+	0.648825i	$0.775261\pi$
$24$		0			0
$25$	−5.23232	+	9.06264i	−1.04646	+	1.81253i
$26$	−0.0978281	−	0.169443i	−0.0191857	−	0.0332306i
$27$		0			0
$28$	5.17142	+	0.441354i	0.977307	+	0.0834081i
$29$	−1.65110			−0.306602			−0.153301	−	0.988180i	$-0.548990\pi$
$29$	−1.65110			−0.306602			−0.153301	+	0.988180i	$0.548990\pi$
$30$		0			0
$31$	−2.80262	+	4.85427i	−0.503365	+	0.871853i	0.496628	+	0.867964i	$0.334571\pi$
$31$	−2.80262	+	4.85427i	−0.503365	+	0.871853i	−0.999992	+	0.00388953i	$0.998762\pi$
$32$	−1.14412	+	1.98168i	−0.202254	+	0.350314i
$33$		0			0
$34$	0.446372			0.0765522
$35$	−5.94959	+	8.53550i	−1.00566	+	1.44276i
$36$		0			0
$37$	−3.57204	−	6.18695i	−0.587239	−	1.01713i	−0.994592	−	0.103857i	$-0.966881\pi$
$37$	−3.57204	−	6.18695i	−0.587239	−	1.01713i	0.407353	−	0.913271i	$-0.366452\pi$
$38$	0.174886	−	0.302911i	0.0283702	−	0.0491386i
$39$		0			0
$40$	−1.52411	−	2.63984i	−0.240983	−	0.417396i
$41$	8.11574			1.26746			0.633732	−	0.773552i	$-0.281522\pi$
$41$	8.11574			1.26746			0.633732	+	0.773552i	$0.281522\pi$
$42$		0			0
$43$	6.81353			1.03905			0.519527	−	0.854454i	$-0.326108\pi$
$43$	6.81353			1.03905			0.519527	+	0.854454i	$0.326108\pi$
$44$	−4.42002	−	7.65570i	−0.666343	−	1.15414i
$45$		0			0
$46$	0.170242	−	0.294867i	0.0251008	−	0.0434758i
$47$	1.77271	+	3.07043i	0.258577	+	0.447868i	0.965861	−	0.259061i	$-0.0834131\pi$
$47$	1.77271	+	3.07043i	0.258577	+	0.447868i	−0.707284	+	0.706929i	$0.750080\pi$
$48$		0			0
$49$	−4.47665	+	5.38141i	−0.639522	+	0.768773i
$50$	2.04747			0.289556
$51$		0			0
$52$	0.980859	−	1.69890i	0.136021	−	0.235595i
$53$	1.64483	−	2.84892i	0.225934	−	0.391330i	−0.730665	−	0.682736i	$-0.760790\pi$
$53$	1.64483	−	2.84892i	0.225934	−	0.391330i	0.956599	+	0.291406i	$0.0941232\pi$
$54$		0			0
$55$	17.7210			2.38949
$56$	−0.870665	−	1.85682i	−0.116347	−	0.248128i
$57$		0			0
$58$	0.161524	+	0.279768i	0.0212092	+	0.0367353i
$59$	2.25314	−	3.90255i	0.293333	−	0.508068i	−0.681262	−	0.732039i	$-0.738569\pi$
$59$	2.25314	−	3.90255i	0.293333	−	0.508068i	0.974596	+	0.223971i	$0.0719021\pi$
$60$		0			0
$61$	−3.77234	−	6.53388i	−0.482998	−	0.836577i	0.516811	−	0.856099i	$-0.327119\pi$
$61$	−3.77234	−	6.53388i	−0.482998	−	0.836577i	−0.999809	+	0.0195220i	$0.993786\pi$
$62$	1.09670			0.139281
$63$		0			0
$64$	−7.09585			−0.886981
$65$	1.96625	+	3.40565i	0.243884	+	0.422419i
$66$		0			0
$67$	6.33263	−	10.9684i	0.773653	−	1.34001i	−0.161895	−	0.986808i	$-0.551761\pi$
$67$	6.33263	−	10.9684i	0.773653	−	1.34001i	0.935548	−	0.353199i	$-0.114906\pi$
$68$	2.23774	+	3.87588i	0.271366	+	0.470020i
$69$		0			0
$70$	2.02832	+	0.173107i	0.242431	+	0.0206902i
$71$	−9.54869			−1.13322			−0.566610	−	0.823986i	$-0.691746\pi$
$71$	−9.54869			−1.13322			−0.566610	+	0.823986i	$0.691746\pi$
$72$		0			0
$73$	−0.540019	+	0.935340i	−0.0632044	+	0.109473i	−0.895896	−	0.444264i	$-0.853465\pi$
$73$	−0.540019	+	0.935340i	−0.0632044	+	0.109473i	0.832692	+	0.553737i	$0.186799\pi$
$74$	−0.698891	+	1.21052i	−0.0812445	+	0.140720i
$75$		0			0
$76$	3.50693			0.402273
$77$	11.8793	+	1.01384i	1.35377	+	0.115537i
$78$		0			0
$79$	−0.395849	−	0.685630i	−0.0445365	−	0.0771394i	0.842898	−	0.538074i	$-0.180848\pi$
$79$	−0.395849	−	0.685630i	−0.0445365	−	0.0771394i	−0.887434	+	0.460934i	$0.847514\pi$
$80$	7.41628	−	12.8454i	0.829165	−	1.43616i
$81$		0			0
$82$	−0.793947	−	1.37516i	−0.0876768	−	0.151861i
$83$	7.14643			0.784422			0.392211	−	0.919875i	$-0.371710\pi$
$83$	7.14643			0.784422			0.392211	+	0.919875i	$0.371710\pi$
$84$		0			0
$85$	−8.97166			−0.973114
$86$	−0.666555	−	1.15451i	−0.0718765	−	0.124494i
$87$		0			0
$88$	−1.74649	+	3.02500i	−0.186176	+	0.322466i
$89$	−5.63281	−	9.75631i	−0.597077	−	1.03417i	−0.993250	−	0.115992i	$-0.962995\pi$
$89$	−5.63281	−	9.75631i	−0.597077	−	1.03417i	0.396174	−	0.918176i	$-0.370338\pi$
$90$		0			0
$91$	1.12324	+	2.39548i	0.117748	+	0.251115i
$92$	3.41381			0.355914
$93$		0			0
$94$	0.346843	−	0.600749i	0.0357741	−	0.0619625i
$95$	−3.51504	+	6.08823i	−0.360636	+	0.624639i
$96$		0			0
$97$	−8.81353			−0.894879			−0.447439	−	0.894314i	$-0.647664\pi$
$97$	−8.81353			−0.894879			−0.447439	+	0.894314i	$0.647664\pi$
$98$	1.34979	+	0.232085i	0.136349	+	0.0234441i
$99$		0			0
$100$	10.2643	+	17.7783i	1.02643	+	1.77783i
$101$	−7.15855	+	12.3990i	−0.712303	+	1.23374i	0.251688	+	0.967808i	$0.419014\pi$
$101$	−7.15855	+	12.3990i	−0.712303	+	1.23374i	−0.963991	+	0.265936i	$0.914319\pi$
$102$		0			0
$103$	3.74607	+	6.48839i	0.369111	+	0.639320i	0.989427	−	0.145033i	$-0.0463287\pi$
$103$	3.74607	+	6.48839i	0.369111	+	0.639320i	−0.620315	+	0.784352i	$0.712995\pi$
$104$	−0.775135			−0.0760082
$105$		0			0
$106$	−0.643641			−0.0625160
$107$	5.48919	+	9.50756i	0.530660	+	0.919130i	0.999360	+	0.0357726i	$0.0113892\pi$
$107$	5.48919	+	9.50756i	0.530660	+	0.919130i	−0.468700	+	0.883357i	$0.655277\pi$
$108$		0			0
$109$	6.22314	−	10.7788i	0.596068	−	1.03242i	−0.397327	−	0.917677i	$-0.630062\pi$
$109$	6.22314	−	10.7788i	0.596068	−	1.03242i	0.993395	−	0.114744i	$-0.0366046\pi$
$110$	−1.73361	−	3.00270i	−0.165293	−	0.286296i
$111$		0			0
$112$	5.70642	−	8.18663i	0.539206	−	0.773564i
$113$	1.65110			0.155323			0.0776613	−	0.996980i	$-0.475255\pi$
$113$	1.65110			0.155323			0.0776613	+	0.996980i	$0.475255\pi$
$114$		0			0
$115$	−3.42170	+	5.92656i	−0.319075	+	0.552654i
$116$	−1.61950	+	2.80505i	−0.150367	+	0.260443i
$117$		0			0
$118$	−0.881681			−0.0811653
$119$	−6.01418	−	0.513279i	−0.551319	−	0.0470522i
$120$		0			0
$121$	−4.65325	−	8.05967i	−0.423023	−	0.732697i
$122$	−0.738081	+	1.27839i	−0.0668227	+	0.115740i
$123$		0			0
$124$	5.49794	+	9.52272i	0.493730	+	0.855165i
$125$	−21.4897			−1.92210
$126$		0			0
$127$	−4.49297			−0.398687			−0.199343	−	0.979930i	$-0.563881\pi$
$127$	−4.49297			−0.398687			−0.199343	+	0.979930i	$0.563881\pi$
$128$	2.98242	+	5.16569i	0.263611	+	0.456587i
$129$		0			0
$130$	0.384710	−	0.666337i	0.0337413	−	0.0584417i
$131$	−6.32836	−	10.9610i	−0.552911	−	0.957670i	−0.998063	−	0.0622152i	$-0.980184\pi$
$131$	−6.32836	−	10.9610i	−0.552911	−	0.957670i	0.445151	−	0.895455i	$-0.353150\pi$
$132$		0			0
$133$	−2.70463	+	3.88016i	−0.234521	+	0.336453i
$134$	−2.47804			−0.214070
$135$		0			0
$136$	0.884200	−	1.53148i	0.0758195	−	0.131323i
$137$	−4.64321	+	8.04227i	−0.396696	+	0.687097i	−0.993316	−	0.115426i	$-0.963177\pi$
$137$	−4.64321	+	8.04227i	−0.396696	+	0.687097i	0.596620	+	0.802524i	$0.296510\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	8.66523	+	18.4799i	0.732346	+	1.56183i
$141$		0			0
$142$	0.934130	+	1.61796i	0.0783905	+	0.135776i
$143$	2.25314	−	3.90255i	0.188417	−	0.326347i
$144$		0			0
$145$	−3.24649	−	5.62308i	−0.269606	−	0.466971i
$146$	0.211316			0.0174887
$147$		0			0
$148$	−14.0147			−1.15200
$149$	−7.58243	−	13.1332i	−0.621177	−	1.07591i	−0.989267	−	0.146120i	$-0.953321\pi$
$149$	−7.58243	−	13.1332i	−0.621177	−	1.07591i	0.368090	−	0.929790i	$-0.380012\pi$
$150$		0			0
$151$	−2.57079	+	4.45274i	−0.209208	+	0.362359i	−0.951465	−	0.307756i	$-0.900422\pi$
$151$	−2.57079	+	4.45274i	−0.209208	+	0.362359i	0.742257	+	0.670115i	$0.233755\pi$
$152$	−0.692848	−	1.20005i	−0.0561974	−	0.0973367i
$153$		0			0
$154$	−0.990341	−	2.11205i	−0.0798040	−	0.170194i
$155$	−22.0426			−1.77051
$156$		0			0
$157$	5.36557	−	9.29344i	0.428219	−	0.741697i	−0.568496	−	0.822686i	$-0.692474\pi$
$157$	5.36557	−	9.29344i	0.428219	−	0.741697i	0.996715	+	0.0809889i	$0.0258078\pi$
$158$	−0.0774503	+	0.134148i	−0.00616162	+	0.0106722i
$159$		0			0
$160$	−8.99853			−0.711397
$161$	−2.63281	+	3.77712i	−0.207495	+	0.297679i
$162$		0			0
$163$	−1.18620	−	2.05455i	−0.0929101	−	0.160925i	0.815824	−	0.578300i	$-0.196284\pi$
$163$	−1.18620	−	2.05455i	−0.0929101	−	0.160925i	−0.908734	+	0.417375i	$0.862950\pi$
$164$	7.96039	−	13.7878i	0.621602	−	1.07665i
$165$		0			0
$166$	−0.699122	−	1.21091i	−0.0542624	−	0.0939852i
$167$	−12.0784			−0.934653			−0.467327	−	0.884085i	$-0.654783\pi$
$167$	−12.0784			−0.934653			−0.467327	+	0.884085i	$0.654783\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	0.877681	+	1.52019i	0.0673151	+	0.116593i
$171$		0			0
$172$	6.68312	−	11.5755i	0.509583	−	0.882624i
$173$	−9.70485	−	16.8093i	−0.737846	−	1.27799i	−0.953463	−	0.301509i	$-0.902510\pi$
$173$	−9.70485	−	16.8093i	−0.737846	−	1.27799i	0.215618	−	0.976478i	$-0.430824\pi$
$174$		0			0
$175$	−27.5865	−	2.35437i	−2.08535	−	0.177974i
$176$	−16.9967			−1.28117
$177$		0			0
$178$	−1.10209	+	1.90888i	−0.0826055	+	0.143077i
$179$	7.32219	−	12.6824i	0.547286	−	0.947928i	−0.451173	−	0.892437i	$-0.648994\pi$
$179$	7.32219	−	12.6824i	0.547286	−	0.947928i	0.998459	−	0.0554912i	$-0.0176725\pi$
$180$		0			0
$181$	−9.44627			−0.702136			−0.351068	−	0.936350i	$-0.614181\pi$
$181$	−9.44627			−0.702136			−0.351068	+	0.936350i	$0.614181\pi$
$182$	0.296013	−	0.424671i	0.0219420	−	0.0314787i
$183$		0			0
$184$	−0.674450	−	1.16818i	−0.0497211	−	0.0861194i
$185$	14.0471	−	24.3302i	1.03276	−	1.78879i
$186$		0			0
$187$	5.14033	+	8.90331i	0.375898	+	0.651074i
$188$	6.95513			0.507255
$189$		0			0
$190$	1.37548			0.0997878
$191$	6.27687	+	10.8719i	0.454179	+	0.786660i	0.998641	−	0.0521252i	$-0.0165995\pi$
$191$	6.27687	+	10.8719i	0.454179	+	0.786660i	−0.544462	+	0.838786i	$0.683266\pi$
$192$		0			0
$193$	4.68430	−	8.11344i	0.337183	−	0.584018i	−0.646719	−	0.762729i	$-0.723859\pi$
$193$	4.68430	−	8.11344i	0.337183	−	0.584018i	0.983902	+	0.178710i	$0.0571925\pi$
$194$	0.862212	+	1.49339i	0.0619032	+	0.107219i
$195$		0			0
$196$	4.75151	+	12.8838i	0.339393	+	0.920270i
$197$	7.62276			0.543099			0.271550	−	0.962424i	$-0.412464\pi$
$197$	7.62276			0.543099			0.271550	+	0.962424i	$0.412464\pi$
$198$		0			0
$199$	−6.76443	+	11.7163i	−0.479518	+	0.830549i	−0.999724	−	0.0234914i	$-0.992522\pi$
$199$	−6.76443	+	11.7163i	−0.479518	+	0.830549i	0.520206	+	0.854041i	$0.325855\pi$
$200$	4.05575	−	7.02477i	0.286785	−	0.496726i
$201$		0			0
$202$	2.80123			0.197094
$203$	−1.85459	−	3.95518i	−0.130167	−	0.277599i
$204$		0			0
$205$	15.9576	+	27.6394i	1.11453	+	1.93042i
$206$	0.732942	−	1.26949i	0.0510665	−	0.0884498i
$207$		0			0
$208$	−1.88589	−	3.26645i	−0.130763	−	0.226488i
$209$	8.05579			0.557231
$210$		0			0
$211$	−15.7995			−1.08768			−0.543840	−	0.839189i	$-0.683030\pi$
$211$	−15.7995			−1.08768			−0.543840	+	0.839189i	$0.683030\pi$
$212$	−3.22669	−	5.58879i	−0.221610	−	0.383839i
$213$		0			0
$214$	1.07399	−	1.86021i	0.0734167	−	0.127162i
$215$	13.3971	+	23.2045i	0.913678	+	1.58254i
$216$		0			0
$217$	−14.7763	−	1.26108i	−1.00308	−	0.0856080i
$218$	−2.43519			−0.164932
$219$		0			0
$220$	17.3818	−	30.1061i	1.17188	−	2.02975i
$221$	−1.14070	+	1.97576i	−0.0767321	+	0.132904i
$222$		0			0
$223$	22.4737			1.50495			0.752474	−	0.658622i	$-0.228861\pi$
$223$	22.4737			1.50495			0.752474	+	0.658622i	$0.228861\pi$
$224$	−6.03219	−	0.514816i	−0.403043	−	0.0343976i
$225$		0			0
$226$	−0.161524	−	0.279768i	−0.0107444	−	0.0186099i
$227$	−4.60124	+	7.96959i	−0.305395	+	0.528960i	−0.977349	−	0.211633i	$-0.932122\pi$
$227$	−4.60124	+	7.96959i	−0.305395	+	0.528960i	0.671954	+	0.740593i	$0.265455\pi$
$228$		0			0
$229$	−7.64611	−	13.2435i	−0.505269	−	0.875152i	−0.999981	−	0.00609528i	$-0.998060\pi$
$229$	−7.64611	−	13.2435i	−0.505269	−	0.875152i	0.494712	−	0.869057i	$-0.335274\pi$
$230$	1.33895			0.0882880
$231$		0			0
$232$	1.27983			0.0840247
$233$	−4.02789	−	6.97652i	−0.263876	−	0.457047i	0.703392	−	0.710802i	$-0.251668\pi$
$233$	−4.02789	−	6.97652i	−0.263876	−	0.457047i	−0.967269	+	0.253755i	$0.918334\pi$
$234$		0			0
$235$	−6.97121	+	12.0745i	−0.454752	+	0.787653i
$236$	−4.42002	−	7.65570i	−0.287719	−	0.498344i
$237$		0			0
$238$	0.501384	+	1.06928i	0.0324999	+	0.0693108i
$239$	−21.7258			−1.40533			−0.702663	−	0.711523i	$-0.748006\pi$
$239$	−21.7258			−1.40533			−0.702663	+	0.711523i	$0.748006\pi$
$240$		0			0
$241$	10.2490	−	17.7518i	0.660195	−	1.14349i	−0.320369	−	0.947293i	$-0.603807\pi$
$241$	10.2490	−	17.7518i	0.660195	−	1.14349i	0.980564	−	0.196199i	$-0.0628598\pi$
$242$	−0.910438	+	1.57692i	−0.0585252	+	0.101369i
$243$		0			0
$244$	−14.8005			−0.947507
$245$	−27.1295	−	4.66470i	−1.73324	−	0.298017i
$246$		0			0
$247$	0.893841	+	1.54818i	0.0568738	+	0.0985083i
$248$	2.17241	−	3.76272i	0.137948	−	0.238933i
$249$		0			0
$250$	2.10230	+	3.64129i	0.132961	+	0.230295i
$251$	−2.60871			−0.164660			−0.0823301	−	0.996605i	$-0.526236\pi$
$251$	−2.60871			−0.164660			−0.0823301	+	0.996605i	$0.526236\pi$
$252$		0			0
$253$	7.84187			0.493014
$254$	0.439539	+	0.761304i	0.0275791	+	0.0477685i
$255$		0			0
$256$	−6.51232	+	11.2797i	−0.407020	+	0.704979i
$257$	−4.49838	−	7.79142i	−0.280601	−	0.486016i	0.690932	−	0.722920i	$-0.257201\pi$
$257$	−4.49838	−	7.79142i	−0.280601	−	0.486016i	−0.971533	+	0.236904i	$0.923867\pi$
$258$		0			0
$259$	10.8084	−	15.5062i	0.671604	−	0.963508i
$260$	7.71448			0.478432
$261$		0			0
$262$	−1.23818	+	2.14460i	−0.0764952	+	0.132494i
$263$	0.716961	−	1.24181i	0.0442097	−	0.0765735i	−0.843074	−	0.537798i	$-0.819256\pi$
$263$	0.716961	−	1.24181i	0.0442097	−	0.0765735i	0.887284	+	0.461224i	$0.152590\pi$
$264$		0			0
$265$	12.9366			0.794689
$266$	0.922056	+	0.0786927i	0.0565349	+	0.00482496i
$267$		0			0
$268$	−12.4228	−	21.5170i	−0.758845	−	1.31436i
$269$	−4.08416	+	7.07397i	−0.249016	+	0.431308i	−0.963253	−	0.268596i	$-0.913440\pi$
$269$	−4.08416	+	7.07397i	−0.249016	+	0.431308i	0.714237	+	0.699904i	$0.246774\pi$
$270$		0			0
$271$	0.106159	+	0.183872i	0.00644867	+	0.0111694i	0.869232	−	0.494405i	$-0.164614\pi$
$271$	0.106159	+	0.183872i	0.00644867	+	0.0111694i	−0.862783	+	0.505574i	$0.831281\pi$
$272$	8.60497			0.521753
$273$		0			0
$274$	1.81695			0.109766
$275$	23.5783	+	40.8387i	1.42182	+	2.46267i
$276$		0			0
$277$	−11.4875	+	19.8969i	−0.690215	+	1.19549i	0.281552	+	0.959546i	$0.409151\pi$
$277$	−11.4875	+	19.8969i	−0.690215	+	1.19549i	−0.971767	+	0.235942i	$0.924182\pi$
$278$	0.391313	+	0.677773i	0.0234694	+	0.0406501i
$279$		0			0
$280$	4.61174	−	6.61617i	0.275604	−	0.395392i
$281$	0.345228			0.0205946			0.0102973	−	0.999947i	$-0.496722\pi$
$281$	0.345228			0.0205946			0.0102973	+	0.999947i	$0.496722\pi$
$282$		0			0
$283$	14.4857	−	25.0900i	0.861087	−	1.49145i	−0.00979277	−	0.999952i	$-0.503117\pi$
$283$	14.4857	−	25.0900i	0.861087	−	1.49145i	0.870880	−	0.491495i	$-0.163549\pi$
$284$	−9.36592	+	16.2222i	−0.555765	+	0.962613i
$285$		0			0
$286$	−0.881681			−0.0521349
$287$	9.11594	+	19.4411i	0.538097	+	1.14757i
$288$		0			0
$289$	5.89759	+	10.2149i	0.346917	+	0.600878i
$290$	−0.635195	+	1.10019i	−0.0372999	+	0.0646054i
$291$		0			0
$292$	1.05937	+	1.83487i	0.0619947	+	0.107378i
$293$	−31.5427			−1.84274			−0.921372	−	0.388682i	$-0.872930\pi$
$293$	−31.5427			−1.84274			−0.921372	+	0.388682i	$0.872930\pi$
$294$		0			0
$295$	17.7210			1.03175
$296$	2.76881	+	4.79572i	0.160934	+	0.278746i
$297$		0			0
$298$	−1.48355	+	2.56958i	−0.0859398	+	0.148852i
$299$	0.870106	+	1.50707i	0.0503195	+	0.0871560i
$300$		0			0
$301$	7.65325	+	16.3217i	0.441126	+	0.940766i
$302$	1.00598			0.0578879
$303$		0			0
$304$	3.37137	−	5.83939i	0.193361	−	0.334912i
$305$	14.8348	−	25.6945i	0.849435	−	1.47127i
$306$		0			0
$307$	−18.1941			−1.03839			−0.519197	−	0.854655i	$-0.673769\pi$
$307$	−18.1941			−1.03839			−0.519197	+	0.854655i	$0.673769\pi$
$308$	13.3743	−	19.1873i	0.762073	−	1.09330i
$309$		0			0
$310$	2.15639	+	3.73498i	0.122475	+	0.212132i
$311$	−0.188312	+	0.326165i	−0.0106782	+	0.0184951i	−0.871315	−	0.490724i	$-0.836732\pi$
$311$	−0.188312	+	0.326165i	−0.0106782	+	0.0184951i	0.860637	+	0.509219i	$0.170066\pi$
$312$		0			0
$313$	−5.49415	−	9.51615i	−0.310548	−	0.537884i	0.667933	−	0.744221i	$-0.267179\pi$
$313$	−5.49415	−	9.51615i	−0.310548	−	0.537884i	−0.978481	+	0.206337i	$0.933846\pi$
$314$	−2.09961			−0.118488
$315$		0			0
$316$	−1.55309			−0.0873680
$317$	13.0903	+	22.6731i	0.735225	+	1.27345i	0.954625	+	0.297812i	$0.0962568\pi$
$317$	13.0903	+	22.6731i	0.735225	+	1.27345i	−0.219400	+	0.975635i	$0.570410\pi$
$318$		0			0
$319$	−3.72016	+	6.44350i	−0.208289	+	0.360767i
$320$	−13.9522	−	24.1660i	−0.779954	−	1.35092i
$321$		0			0
$322$	0.897571	+	0.0766031i	0.0500197	+	0.00426892i
$323$	−4.07844			−0.226930
$324$		0			0
$325$	−5.23232	+	9.06264i	−0.290237	+	0.502705i
$326$	−0.232087	+	0.401986i	−0.0128541	+	0.0222639i
$327$		0			0
$328$	−6.29079			−0.347351
$329$	−5.36397	+	7.69534i	−0.295725	+	0.424258i
$330$		0			0
$331$	17.0466	+	29.5256i	0.936967	+	1.62287i	0.771089	+	0.636728i	$0.219712\pi$
$331$	17.0466	+	29.5256i	0.936967	+	1.62287i	0.165878	+	0.986146i	$0.446954\pi$
$332$	7.00964	−	12.1411i	0.384704	−	0.666327i
$333$		0			0
$334$	1.18161	+	2.04660i	0.0646546	+	0.111985i
$335$	49.8062			2.72120
$336$		0			0
$337$	14.7532			0.803657			0.401829	−	0.915715i	$-0.368375\pi$
$337$	14.7532			0.803657			0.401829	+	0.915715i	$0.368375\pi$
$338$	−0.0978281	−	0.169443i	−0.00532115	−	0.00921650i
$339$		0			0
$340$	−8.79994	+	15.2419i	−0.477244	+	0.826610i
$341$	12.6294	+	21.8747i	0.683918	+	1.18458i
$342$		0			0
$343$	−17.9194	−	4.67910i	−0.967558	−	0.252648i
$344$	−5.28141			−0.284754
$345$		0			0
$346$	−1.89881	+	3.28884i	−0.102081	+	0.176809i
$347$	14.9733	−	25.9345i	0.803809	−	1.39224i	−0.113284	−	0.993563i	$-0.536137\pi$
$347$	14.9733	−	25.9345i	0.803809	−	1.39224i	0.917092	−	0.398675i	$-0.130530\pi$
$348$		0			0
$349$	−13.4793			−0.721532			−0.360766	−	0.932656i	$-0.617485\pi$
$349$	−13.4793			−0.721532			−0.360766	+	0.932656i	$0.617485\pi$
$350$	2.29981	+	4.90468i	0.122930	+	0.262166i
$351$		0			0
$352$	5.15572	+	8.92997i	0.274801	+	0.475969i
$353$	0.0817659	−	0.141623i	0.00435196	−	0.00753781i	−0.863841	−	0.503764i	$-0.831948\pi$
$353$	0.0817659	−	0.141623i	0.00435196	−	0.00753781i	0.868193	+	0.496226i	$0.165281\pi$
$354$		0			0
$355$	−18.7752	−	32.5195i	−0.996482	−	1.72596i
$356$	−22.1000			−1.17130
$357$		0			0
$358$	−2.86527			−0.151434
$359$	4.46065	+	7.72607i	0.235424	+	0.407766i	0.959396	−	0.282063i	$-0.0910188\pi$
$359$	4.46065	+	7.72607i	0.235424	+	0.407766i	−0.723972	+	0.689830i	$0.757685\pi$
$360$		0			0
$361$	7.90209	−	13.6868i	0.415900	−	0.720359i
$362$	0.924111	+	1.60061i	0.0485702	+	0.0841261i
$363$		0			0
$364$	5.17142	+	0.441354i	0.271056	+	0.0231332i
$365$	−4.24726			−0.222312
$366$		0			0
$367$	−18.3276	+	31.7443i	−0.956693	+	1.65704i	−0.226248	+	0.974070i	$0.572646\pi$
$367$	−18.3276	+	31.7443i	−0.956693	+	1.65704i	−0.730445	+	0.682971i	$0.760687\pi$
$368$	3.28185	−	5.68432i	0.171078	−	0.296316i
$369$		0			0
$370$	−5.49679			−0.285765
$371$	8.67208	+	0.740117i	0.450232	+	0.0384250i
$372$		0			0
$373$	−13.5637	−	23.4930i	−0.702302	−	1.21642i	−0.967656	−	0.252271i	$-0.918822\pi$
$373$	−13.5637	−	23.4930i	−0.702302	−	1.21642i	0.265355	−	0.964151i	$-0.414511\pi$
$374$	1.00574	−	1.74199i	0.0520054	−	0.0900761i
$375$		0			0
$376$	−1.37409	−	2.38000i	−0.0708634	−	0.122739i
$377$	−1.65110			−0.0850360
$378$		0			0
$379$	−15.8943			−0.816434			−0.408217	−	0.912885i	$-0.633849\pi$
$379$	−15.8943			−0.816434			−0.408217	+	0.912885i	$0.633849\pi$
$380$	6.89552	+	11.9434i	0.353733	+	0.612683i
$381$		0			0
$382$	1.22811	−	2.12715i	0.0628355	−	0.108834i
$383$	0.575394	+	0.996611i	0.0294013	+	0.0509245i	0.880352	−	0.474322i	$-0.157307\pi$
$383$	0.575394	+	0.996611i	0.0294013	+	0.0509245i	−0.850950	+	0.525246i	$0.823973\pi$
$384$		0			0
$385$	19.9049	+	42.4502i	1.01445	+	2.16346i
$386$	−1.83302			−0.0932985
$387$		0			0
$388$	−8.64484	+	14.9733i	−0.438875	+	0.760154i
$389$	−7.15651	+	12.3954i	−0.362850	+	0.628474i	−0.988429	−	0.151687i	$-0.951529\pi$
$389$	−7.15651	+	12.3954i	−0.362850	+	0.628474i	0.625579	+	0.780161i	$0.284863\pi$
$390$		0			0
$391$	−3.97013			−0.200778
$392$	3.47001	−	4.17132i	0.175262	−	0.210684i
$393$		0			0
$394$	−0.745721	−	1.29163i	−0.0375689	−	0.0650712i
$395$	1.55668	−	2.69625i	0.0783251	−	0.135663i
$396$		0			0
$397$	12.9588	+	22.4453i	0.650383	+	1.12650i	0.983030	+	0.183445i	$0.0587248\pi$
$397$	12.9588	+	22.4453i	0.650383	+	1.12650i	−0.332647	+	0.943051i	$0.607942\pi$
$398$	2.64701			0.132682
$399$		0			0
$400$	39.4703			1.97351
$401$	−2.14816	−	3.72072i	−0.107274	−	0.185804i	0.807391	−	0.590017i	$-0.200879\pi$
$401$	−2.14816	−	3.72072i	−0.107274	−	0.185804i	−0.914665	+	0.404213i	$0.867545\pi$
$402$		0			0
$403$	−2.80262	+	4.85427i	−0.139608	+	0.241809i
$404$	14.0431	+	24.3233i	0.698669	+	1.21013i
$405$		0			0
$406$	−0.488748	+	0.701175i	−0.0242562	+	0.0347987i
$407$	−32.1931			−1.59575
$408$		0			0
$409$	12.3536	−	21.3970i	0.610844	−	1.05801i	−0.380255	−	0.924882i	$-0.624164\pi$
$409$	12.3536	−	21.3970i	0.610844	−	1.05801i	0.991098	−	0.133131i	$-0.0425030\pi$
$410$	3.12221	−	5.40782i	0.154195	−	0.267073i
$411$		0			0
$412$	14.6975			0.724093
$413$	11.8793	+	1.01384i	0.584542	+	0.0498876i
$414$		0			0
$415$	14.0517	+	24.3383i	0.689771	+	1.19472i
$416$	−1.14412	+	1.98168i	−0.0560951	+	0.0971596i
$417$		0			0
$418$	−0.788083	−	1.36500i	−0.0385464	−	0.0667643i
$419$	24.9293			1.21787			0.608937	−	0.793218i	$-0.291596\pi$
$419$	24.9293			1.21787			0.608937	+	0.793218i	$0.291596\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	1.54563	+	2.67712i	0.0752402	+	0.130320i
$423$		0			0
$424$	−1.27496	+	2.20830i	−0.0619177	+	0.107245i
$425$	−11.9371	−	20.6756i	−0.579032	−	1.00291i
$426$		0			0
$427$	11.4145	−	16.3757i	0.552388	−	0.792475i
$428$	21.5365			1.04101
$429$		0			0
$430$	2.62124	−	4.54011i	0.126407	−	0.218944i
$431$	−2.84426	+	4.92639i	−0.137003	+	0.237296i	−0.926361	−	0.376637i	$-0.877080\pi$
$431$	−2.84426	+	4.92639i	−0.137003	+	0.237296i	0.789358	+	0.613933i	$0.210414\pi$
$432$		0			0
$433$	12.2598			0.589169			0.294584	−	0.955625i	$-0.404819\pi$
$433$	12.2598			0.589169			0.294584	+	0.955625i	$0.404819\pi$
$434$	1.23186	+	2.62712i	0.0591311	+	0.126106i
$435$		0			0
$436$	−12.2080	−	21.1450i	−0.584659	−	1.01266i
$437$	−1.55547	+	2.69416i	−0.0744084	+	0.128879i
$438$		0			0
$439$	−2.51158	−	4.35019i	−0.119871	−	0.207623i	0.799845	−	0.600206i	$-0.204915\pi$
$439$	−2.51158	−	4.35019i	−0.119871	−	0.207623i	−0.919717	+	0.392583i	$0.871582\pi$
$440$	−13.7361			−0.654845
$441$		0			0
$442$	0.446372			0.0212317
$443$	0.289401	+	0.501258i	0.0137499	+	0.0238155i	0.872818	−	0.488045i	$-0.162290\pi$
$443$	0.289401	+	0.501258i	0.0137499	+	0.0238155i	−0.859069	+	0.511860i	$0.828956\pi$
$444$		0			0
$445$	22.1511	−	38.3668i	1.05006	−	1.81876i
$446$	−2.19856	−	3.80801i	−0.104105	−	0.180315i
$447$		0			0
$448$	−7.97036	−	16.9980i	−0.376564	−	0.803078i
$449$	7.36359			0.347509			0.173755	−	0.984789i	$-0.444410\pi$
$449$	7.36359			0.347509			0.173755	+	0.984789i	$0.444410\pi$
$450$		0			0
$451$	18.2859	−	31.6720i	0.861048	−	1.49138i
$452$	1.61950	−	2.80505i	0.0761748	−	0.131939i
$453$		0			0
$454$	1.80052			0.0845028
$455$	−5.94959	+	8.53550i	−0.278921	+	0.400150i
$456$		0			0
$457$	−3.95912	−	6.85739i	−0.185200	−	0.320775i	0.758444	−	0.651738i	$-0.225960\pi$
$457$	−3.95912	−	6.85739i	−0.185200	−	0.320775i	−0.943644	+	0.330963i	$0.892627\pi$
$458$	−1.49601	+	2.59117i	−0.0699040	+	0.121077i
$459$		0			0
$460$	6.71241	+	11.6262i	0.312968	+	0.542076i
$461$	9.53600			0.444136			0.222068	−	0.975031i	$-0.428719\pi$
$461$	9.53600			0.444136			0.222068	+	0.975031i	$0.428719\pi$
$462$		0			0
$463$	2.16049			0.100406			0.0502032	−	0.998739i	$-0.484013\pi$
$463$	2.16049			0.100406			0.0502032	+	0.998739i	$0.484013\pi$
$464$	3.11379	+	5.39325i	0.144554	+	0.250375i
$465$		0			0
$466$	−0.788083	+	1.36500i	−0.0365072	+	0.0632324i
$467$	−4.05950	−	7.03126i	−0.187851	−	0.325368i	0.756682	−	0.653783i	$-0.226819\pi$
$467$	−4.05950	−	7.03126i	−0.187851	−	0.325368i	−0.944534	+	0.328415i	$0.893486\pi$
$468$		0			0
$469$	33.3877	+	2.84947i	1.54170	+	0.131576i
$470$	2.72792			0.125830
$471$		0			0
$472$	−1.74649	+	3.02500i	−0.0803885	+	0.139237i
$473$	15.3518	−	26.5901i	0.705878	−	1.22262i
$474$		0			0
$475$	−18.7074			−0.858357
$476$	−6.77107	+	9.71402i	−0.310352	+	0.445241i
$477$		0			0
$478$	2.12540	+	3.68129i	0.0972133	+	0.168378i
$479$	7.27663	−	12.6035i	0.332478	−	0.575868i	−0.650519	−	0.759490i	$-0.725449\pi$
$479$	7.27663	−	12.6035i	0.332478	−	0.575868i	0.982997	+	0.183621i	$0.0587820\pi$
$480$		0			0
$481$	−3.57204	−	6.18695i	−0.162871	−	0.282101i
$482$	−4.01056			−0.182676
$483$		0			0
$484$	−18.2567			−0.829852
$485$	−17.3297	−	30.0158i	−0.786899	−	1.36295i
$486$		0			0
$487$	16.6295	−	28.8031i	0.753554	−	1.30519i	−0.192536	−	0.981290i	$-0.561671\pi$
$487$	16.6295	−	28.8031i	0.753554	−	1.30519i	0.946090	−	0.323904i	$-0.104995\pi$
$488$	2.92407	+	5.06464i	0.132366	+	0.229265i
$489$		0			0
$490$	1.86362	+	5.05324i	0.0841899	+	0.228282i
$491$	22.5563			1.01795			0.508977	−	0.860780i	$-0.330024\pi$
$491$	22.5563			1.01795			0.508977	+	0.860780i	$0.330024\pi$
$492$		0			0
$493$	1.88342	−	3.26218i	0.0848249	−	0.146921i
$494$	0.174886	−	0.302911i	0.00786848	−	0.0136286i
$495$		0			0
$496$	21.1417			0.949290
$497$	−10.7255	−	22.8737i	−0.481104	−	1.02603i
$498$		0			0
$499$	5.69271	+	9.86007i	0.254841	+	0.441397i	0.964852	−	0.262793i	$-0.0846436\pi$
$499$	5.69271	+	9.86007i	0.254841	+	0.441397i	−0.710011	+	0.704190i	$0.751310\pi$
$500$	−21.0784	+	36.5089i	−0.942655	+	1.63273i
$501$		0			0
$502$	0.255205	+	0.442028i	0.0113904	+	0.0197287i
$503$	8.81825			0.393186			0.196593	−	0.980485i	$-0.437012\pi$
$503$	8.81825			0.393186			0.196593	+	0.980485i	$0.437012\pi$
$504$		0			0
$505$	−56.3022			−2.50541
$506$	−0.767156	−	1.32875i	−0.0341042	−	0.0590702i
$507$		0			0
$508$	−4.40697	+	7.63310i	−0.195528	+	0.338664i
$509$	9.64188	+	16.7002i	0.427369	+	0.740225i	0.996638	−	0.0819263i	$-0.0261072\pi$
$509$	9.64188	+	16.7002i	0.427369	+	0.740225i	−0.569269	+	0.822151i	$0.692774\pi$
$510$		0			0
$511$	−2.84716	−	0.242991i	−0.125951	−	0.0107493i
$512$	14.4780			0.639844
$513$		0			0
$514$	−0.880136	+	1.52444i	−0.0388211	+	0.0672402i
$515$	−14.7315	+	25.5156i	−0.649146	+	1.12435i
$516$		0			0
$517$	15.9767			0.702653
$518$	−3.68479	−	0.314478i	−0.161900	−	0.0138174i
$519$		0			0
$520$	−1.52411	−	2.63984i	−0.0668368	−	0.115765i
$521$	12.5584	−	21.7518i	0.550193	−	0.952963i	−0.448067	−	0.894000i	$-0.647887\pi$
$521$	12.5584	−	21.7518i	0.550193	−	0.952963i	0.998260	−	0.0589629i	$-0.0187794\pi$
$522$		0			0
$523$	14.9824	+	25.9503i	0.655134	+	1.13473i	0.981860	+	0.189606i	$0.0607212\pi$
$523$	14.9824	+	25.9503i	0.655134	+	1.13473i	−0.326726	+	0.945119i	$0.605946\pi$
$524$	−24.8289			−1.08466
$525$		0			0
$526$	−0.280556			−0.0122328
$527$	−6.39391	−	11.0746i	−0.278523	−	0.482416i
$528$		0			0
$529$	9.98583	−	17.2960i	0.434167	−	0.751999i
$530$	−1.26556	−	2.19202i	−0.0549726	−	0.0952153i
$531$		0			0
$532$	3.93913	+	8.40078i	0.170783	+	0.364220i
$533$	8.11574			0.351532
$534$		0			0
$535$	−21.5863	+	37.3886i	−0.933257	+	1.61645i
$536$	−4.90864	+	8.50201i	−0.212021	+	0.367231i
$537$		0			0
$538$	1.59818			0.0689026
$539$	10.9147	+	29.5954i	0.470130	+	1.27476i
$540$		0			0
$541$	−2.54987	−	4.41650i	−0.109627	−	0.189880i	0.805992	−	0.591926i	$-0.201632\pi$
$541$	−2.54987	−	4.41650i	−0.109627	−	0.189880i	−0.915619	+	0.402046i	$0.868299\pi$
$542$	0.0207706	−	0.0359757i	0.000892173	−	0.00154529i
$543$		0			0
$544$	−2.61021	−	4.52101i	−0.111912	−	0.193837i
$545$	48.9451			2.09658
$546$		0			0
$547$	2.92025			0.124861			0.0624305	−	0.998049i	$-0.480115\pi$
$547$	2.92025			0.124861			0.0624305	+	0.998049i	$0.480115\pi$
$548$	9.10867	+	15.7767i	0.389103	+	0.673946i
$549$		0			0
$550$	4.61323	−	7.99035i	0.196709	−	0.340710i
$551$	−1.47582	−	2.55620i	−0.0628722	−	0.108898i
$552$		0			0
$553$	1.19778	−	1.71838i	0.0509348	−	0.0730728i
$554$	4.49519			0.190982
$555$		0			0
$556$	−3.92344	+	6.79559i	−0.166391	+	0.288197i
$557$	12.9937	−	22.5058i	0.550561	−	0.953600i	−0.447673	−	0.894197i	$-0.647747\pi$
$557$	12.9937	−	22.5058i	0.550561	−	0.953600i	0.998234	−	0.0594024i	$-0.0189195\pi$
$558$		0			0
$559$	6.81353			0.288182
$560$	39.1011	+	3.33708i	1.65232	+	0.141017i
$561$		0			0
$562$	−0.0337730	−	0.0584965i	−0.00142463	−	0.00246753i
$563$	1.82534	−	3.16159i	0.0769291	−	0.133245i	−0.824994	−	0.565141i	$-0.808822\pi$
$563$	1.82534	−	3.16159i	0.0769291	−	0.133245i	0.901924	+	0.431896i	$0.142155\pi$
$564$		0			0
$565$	3.24649	+	5.62308i	0.136581	+	0.236565i
$566$	−5.66845			−0.238263
$567$		0			0
$568$	7.40152			0.310561
$569$	−12.6766	−	21.9566i	−0.531432	−	0.920468i	−0.999327	−	0.0366835i	$-0.988321\pi$
$569$	−12.6766	−	21.9566i	−0.531432	−	0.920468i	0.467895	−	0.883784i	$-0.345013\pi$
$570$		0			0
$571$	−13.8626	+	24.0108i	−0.580133	+	1.00482i	0.415330	+	0.909671i	$0.363666\pi$
$571$	−13.8626	+	24.0108i	−0.580133	+	1.00482i	−0.995463	+	0.0951493i	$0.969667\pi$
$572$	−4.42002	−	7.65570i	−0.184810	−	0.320101i
$573$		0			0
$574$	2.40237	−	3.44652i	0.100273	−	0.143855i
$575$	−18.2107			−0.759438
$576$		0			0
$577$	−19.7877	+	34.2733i	−0.823773	+	1.42682i	0.0790809	+	0.996868i	$0.474801\pi$
$577$	−19.7877	+	34.2733i	−0.823773	+	1.42682i	−0.902854	+	0.429948i	$0.858532\pi$
$578$	1.15390	−	1.99861i	0.0479959	−	0.0831313i
$579$		0			0
$580$	−12.7374			−0.528891
$581$	8.02717	+	17.1191i	0.333023	+	0.710221i
$582$		0			0
$583$	−7.41204	−	12.8380i	−0.306975	−	0.531697i
$584$	0.418588	−	0.725015i	0.0173213	−	0.0300013i
$585$		0			0
$586$	3.08576	+	5.34470i	0.127472	+	0.220787i
$587$	8.24177			0.340174			0.170087	−	0.985429i	$-0.445595\pi$
$587$	8.24177			0.340174			0.170087	+	0.985429i	$0.445595\pi$
$588$		0			0
$589$	−10.0204			−0.412882
$590$	−1.73361	−	3.00270i	−0.0713716	−	0.123619i
$591$		0			0
$592$	−13.4729	+	23.3358i	−0.553734	+	0.959095i
$593$	−5.96149	−	10.3256i	−0.244809	−	0.424021i	0.717269	−	0.696796i	$-0.245392\pi$
$593$	−5.96149	−	10.3256i	−0.244809	−	0.424021i	−0.962078	+	0.272775i	$0.912059\pi$
$594$		0			0
$595$	−10.0774	−	21.4914i	−0.413131	−	0.881063i
$596$	−29.7492			−1.21857
$597$		0			0
$598$	0.170242	−	0.294867i	0.00696170	−	0.0120580i
$599$	−17.8079	+	30.8442i	−0.727611	+	1.26026i	0.230279	+	0.973125i	$0.426036\pi$
$599$	−17.8079	+	30.8442i	−0.727611	+	1.26026i	−0.957890	+	0.287135i	$0.907297\pi$
$600$		0			0
$601$	38.9252			1.58779			0.793896	−	0.608054i	$-0.208050\pi$
$601$	38.9252			1.58779			0.793896	+	0.608054i	$0.208050\pi$
$602$	2.01690	−	2.89351i	0.0822026	−	0.117931i
$603$		0			0
$604$	5.04317	+	8.73503i	0.205204	+	0.355423i
$605$	18.2990	−	31.6947i	0.743959	−	1.28857i
$606$		0			0
$607$	6.84828	+	11.8616i	0.277963	+	0.481446i	0.970878	−	0.239573i	$-0.0770074\pi$
$607$	6.84828	+	11.8616i	0.277963	+	0.481446i	−0.692915	+	0.721019i	$0.743674\pi$
$608$	−4.09065			−0.165898
$609$		0			0
$610$	−5.80502			−0.235039
$611$	1.77271	+	3.07043i	0.0717163	+	0.124216i
$612$		0			0
$613$	−1.58056	+	2.73761i	−0.0638382	+	0.110571i	−0.896178	−	0.443695i	$-0.853667\pi$
$613$	−1.58056	+	2.73761i	−0.0638382	+	0.110571i	0.832340	+	0.554266i	$0.187001\pi$
$614$	1.77990	+	3.08287i	0.0718308	+	0.124415i
$615$		0			0
$616$	−9.20806	−	0.785860i	−0.371003	−	0.0316632i
$617$	−20.9297			−0.842597			−0.421299	−	0.906922i	$-0.638426\pi$
$617$	−20.9297			−0.842597			−0.421299	+	0.906922i	$0.638426\pi$
$618$		0			0
$619$	−15.4772	+	26.8073i	−0.622082	+	1.07748i	0.367016	+	0.930215i	$0.380379\pi$
$619$	−15.4772	+	26.8073i	−0.622082	+	1.07748i	−0.989097	+	0.147262i	$0.952954\pi$
$620$	−21.6207	+	37.4482i	−0.868309	+	1.50396i
$621$		0			0
$622$	0.0736887			0.00295465
$623$	17.0440	−	24.4520i	0.682855	−	0.979648i
$624$		0			0
$625$	−16.0927	−	27.8734i	−0.643708	−	1.11494i
$626$	−1.07496	+	1.86189i	−0.0429642	+	0.0744162i
$627$		0			0
$628$	−10.5257	−	18.2311i	−0.420023	−	0.727501i
$629$	16.2986			0.649866
$630$		0			0
$631$	−15.1218			−0.601988			−0.300994	−	0.953626i	$-0.597318\pi$
$631$	−15.1218			−0.601988			−0.300994	+	0.953626i	$0.597318\pi$
$632$	0.306836	+	0.531456i	0.0122053	+	0.0211402i
$633$		0			0
$634$	2.56120	−	4.43613i	0.101718	−	0.176181i
$635$	−8.83433	−	15.3015i	−0.350580	−	0.607222i
$636$		0			0
$637$	−4.47665	+	5.38141i	−0.177371	+	0.213219i
$638$	1.45574			0.0576335
$639$		0			0
$640$	−11.7284	+	20.3141i	−0.463605	+	0.802987i
$641$	−23.6207	+	40.9123i	−0.932962	+	1.61594i	−0.154733	+	0.987956i	$0.549452\pi$
$641$	−23.6207	+	40.9123i	−0.932962	+	1.61594i	−0.778229	+	0.627981i	$0.783882\pi$
$642$		0			0
$643$	39.9249			1.57448			0.787241	−	0.616645i	$-0.211509\pi$
$643$	39.9249			1.57448			0.787241	+	0.616645i	$0.211509\pi$
$644$	3.83453	+	8.17770i	0.151102	+	0.322247i
$645$		0			0
$646$	0.398986	+	0.691064i	0.0156979	+	0.0271895i
$647$	−14.9139	+	25.8317i	−0.586327	+	1.01555i	0.408382	+	0.912811i	$0.366093\pi$
$647$	−14.9139	+	25.8317i	−0.586327	+	1.01555i	−0.994709	+	0.102736i	$0.967240\pi$
$648$		0			0
$649$	−10.1533	−	17.5859i	−0.398550	−	0.690309i
$650$	2.04747			0.0803084
$651$		0			0
$652$	−4.65397			−0.182263
$653$	12.5774	+	21.7848i	0.492194	+	0.852504i	0.999960	−	0.00899079i	$-0.00286189\pi$
$653$	12.5774	+	21.7848i	0.492194	+	0.852504i	−0.507766	+	0.861495i	$0.669529\pi$
$654$		0			0
$655$	24.8863	−	43.1044i	0.972390	−	1.68423i
$656$	−15.3054	−	26.5097i	−0.597574	−	1.03503i
$657$		0			0
$658$	1.82867	+	0.156068i	0.0712890	+	0.00608415i
$659$	−17.3155			−0.674517			−0.337258	−	0.941412i	$-0.609500\pi$
$659$	−17.3155			−0.674517			−0.337258	+	0.941412i	$0.609500\pi$
$660$		0			0
$661$	4.60037	−	7.96808i	0.178934	−	0.309922i	−0.762582	−	0.646892i	$-0.776069\pi$
$661$	4.60037	−	7.96808i	0.178934	−	0.309922i	0.941516	+	0.336969i	$0.109402\pi$
$662$	3.33528	−	5.77687i	0.129629	−	0.224524i
$663$		0			0
$664$	−5.53945			−0.214972
$665$	−18.5325	−	1.58165i	−0.718659	−	0.0613338i
$666$		0			0
$667$	−1.43663	−	2.48832i	−0.0556266	−	0.0963482i
$668$	−11.8472	+	20.5199i	−0.458382	+	0.793940i
$669$		0			0
$670$	−4.87245	−	8.43933i	−0.188239	−	0.326040i
$671$	−33.9984			−1.31249
$672$		0			0
$673$	17.3609			0.669212			0.334606	−	0.942358i	$-0.391397\pi$
$673$	17.3609			0.669212			0.334606	+	0.942358i	$0.391397\pi$
$674$	−1.44328	−	2.49983i	−0.0555930	−	0.0962898i
$675$		0			0
$676$	0.980859	−	1.69890i	0.0377254	−	0.0653422i
$677$	24.9913	+	43.2861i	0.960492	+	1.66362i	0.721267	+	0.692657i	$0.243560\pi$
$677$	24.9913	+	43.2861i	0.960492	+	1.66362i	0.239225	+	0.970964i	$0.423107\pi$
$678$		0			0
$679$	−9.89974	−	21.1126i	−0.379917	−	0.810229i
$680$	6.95425			0.266683
$681$		0			0
$682$	2.47101	−	4.27992i	0.0946200	−	0.163887i
$683$	16.8077	−	29.1117i	0.643128	−	1.11393i	−0.341603	−	0.939844i	$-0.610970\pi$
$683$	16.8077	−	29.1117i	0.643128	−	1.11393i	0.984731	−	0.174086i	$-0.0556969\pi$
$684$		0			0
$685$	−36.5189			−1.39532
$686$	0.960183	+	3.49408i	0.0366599	+	0.133404i
$687$		0			0
$688$	−12.8496	−	22.2561i	−0.489885	−	0.848506i
$689$	1.64483	−	2.84892i	0.0626629	−	0.108535i
$690$		0			0
$691$	7.56545	+	13.1038i	0.287803	+	0.498490i	0.973285	−	0.229600i	$-0.0737417\pi$
$691$	7.56545	+	13.1038i	0.287803	+	0.498490i	−0.685482	+	0.728090i	$0.740408\pi$
$692$	−38.0764			−1.44745
$693$		0			0
$694$	−5.85924			−0.222414
$695$	−7.86502	−	13.6226i	−0.298337	−	0.516735i
$696$		0			0
$697$	−9.25766	+	16.0347i	−0.350659	+	0.607359i
$698$	1.31866	+	2.28398i	0.0499119	+	0.0864500i
$699$		0			0
$700$	−31.0583	+	44.5574i	−1.17390	+	1.68411i
$701$	−2.02467			−0.0764705			−0.0382353	−	0.999269i	$-0.512174\pi$
$701$	−2.02467			−0.0764705			−0.0382353	+	0.999269i	$0.512174\pi$
$702$		0			0
$703$	6.38567	−	11.0603i	0.240840	−	0.417147i
$704$	−15.9879	+	27.6919i	−0.602567	+	1.04368i
$705$		0			0
$706$	−0.0319960			−0.00120419
$707$	−37.7423	−	3.22111i	−1.41945	−	0.121142i
$708$		0			0
$709$	15.2276	+	26.3751i	0.571886	+	0.990536i	0.996372	+	0.0851015i	$0.0271215\pi$
$709$	15.2276	+	26.3751i	0.571886	+	0.990536i	−0.424486	+	0.905434i	$0.639545\pi$
$710$	−3.67348	+	6.36265i	−0.137863	+	0.238786i
$711$		0			0
$712$	4.36619	+	7.56246i	0.163630	+	0.283415i
$713$	−9.75429			−0.365301
$714$		0			0
$715$	17.7210			0.662727
$716$	−14.3641	−	24.8793i	−0.536811	−	0.929784i
$717$		0			0
$718$	0.872754	−	1.51165i	0.0325709	−	0.0564144i
$719$	−12.2123	−	21.1523i	−0.455442	−	0.788848i	0.543272	−	0.839557i	$-0.317185\pi$
$719$	−12.2123	−	21.1523i	−0.455442	−	0.788848i	−0.998713	+	0.0507089i	$0.983852\pi$
$720$		0			0
$721$	−11.3351	+	16.2617i	−0.422139	+	0.605616i
$722$	−3.09219			−0.115079
$723$		0			0
$724$	−9.26547	+	16.0483i	−0.344348	+	0.596429i
$725$	8.63908	−	14.9633i	0.320848	−	0.555724i
$726$		0			0
$727$	−3.09307			−0.114716			−0.0573578	−	0.998354i	$-0.518268\pi$
$727$	−3.09307			−0.114716			−0.0573578	+	0.998354i	$0.518268\pi$
$728$	−0.870665	−	1.85682i	−0.0322690	−	0.0688184i
$729$		0			0
$730$	0.415501	+	0.719670i	0.0153784	+	0.0266362i
$731$	−7.77223	+	13.4619i	−0.287466	+	0.497906i
$732$		0			0
$733$	4.20713	+	7.28697i	0.155394	+	0.269150i	0.933202	−	0.359351i	$-0.117002\pi$
$733$	4.20713	+	7.28697i	0.155394	+	0.269150i	−0.777808	+	0.628501i	$0.783669\pi$
$734$	7.17182			0.264717
$735$		0			0
$736$	−3.98203			−0.146779
$737$	−28.5365	−	49.4267i	−1.05116	−	1.82066i
$738$		0			0
$739$	3.61379	−	6.25927i	0.132936	−	0.230251i	−0.791871	−	0.610688i	$-0.790893\pi$
$739$	3.61379	−	6.25927i	0.132936	−	0.230251i	0.924807	+	0.380437i	$0.124226\pi$
$740$	−27.5564	−	47.7291i	−1.01299	−	1.75456i
$741$		0			0
$742$	−0.722966	−	1.54183i	−0.0265409	−	0.0566024i
$743$	53.9092			1.97774			0.988869	−	0.148791i	$-0.0475383\pi$
$743$	53.9092			1.97774			0.988869	+	0.148791i	$0.0475383\pi$
$744$		0			0
$745$	29.8180	−	51.6463i	1.09245	−	1.89217i
$746$	−2.65382	+	4.59656i	−0.0971634	+	0.168292i
$747$		0			0
$748$	20.1678			0.737406
$749$	−16.6095	+	23.8285i	−0.606897	+	0.870676i
$750$		0			0
$751$	−14.6221	−	25.3262i	−0.533568	−	0.924168i	−0.999231	−	0.0392053i	$-0.987517\pi$
$751$	−14.6221	−	25.3262i	−0.533568	−	0.924168i	0.465663	−	0.884962i	$-0.345816\pi$
$752$	6.68628	−	11.5810i	0.243824	−	0.422315i
$753$		0			0
$754$	0.161524	+	0.279768i	0.00588236	+	0.0101885i
$755$	−20.2193			−0.735857
$756$		0			0
$757$	−22.0597			−0.801773			−0.400887	−	0.916128i	$-0.631298\pi$
$757$	−22.0597			−0.801773			−0.400887	+	0.916128i	$0.631298\pi$
$758$	1.55491	+	2.69318i	0.0564768	+	0.0978206i
$759$		0			0
$760$	2.72463	−	4.71920i	0.0988328	−	0.171183i
$761$	8.90805	+	15.4292i	0.322917	+	0.559308i	0.981089	−	0.193560i	$-0.0620033\pi$
$761$	8.90805	+	15.4292i	0.322917	+	0.559308i	−0.658172	+	0.752868i	$0.728670\pi$
$762$		0			0
$763$	32.8105	+	2.80020i	1.18782	+	0.101374i
$764$	24.6269			0.890971
$765$		0			0
$766$	0.112579	−	0.194993i	0.00406766	−	0.00704539i
$767$	2.25314	−	3.90255i	0.0813561	−	0.140913i
$768$		0			0
$769$	−11.3069			−0.407738			−0.203869	−	0.978998i	$-0.565352\pi$
$769$	−11.3069			−0.407738			−0.203869	+	0.978998i	$0.565352\pi$
$770$	5.24564	−	7.52559i	0.189040	−	0.271203i
$771$		0			0
$772$	−9.18927	−	15.9163i	−0.330729	−	0.572840i
$773$	−0.964104	+	1.66988i	−0.0346764	+	0.0600613i	−0.882843	−	0.469669i	$-0.844373\pi$
$773$	−0.964104	+	1.66988i	−0.0346764	+	0.0600613i	0.848166	+	0.529730i	$0.177707\pi$
$774$		0			0
$775$	−29.3284	−	50.7982i	−1.05351	−	1.82472i
$776$	6.83168			0.245243
$777$		0			0
$778$	2.80043			0.100400
$779$	7.25418	+	12.5646i	0.259908	+	0.450174i
$780$		0			0
$781$	−21.5145	+	37.2642i	−0.769849	+	1.33342i
$782$	0.388391	+	0.672713i	0.0138888	+	0.0240562i
$783$		0			0
$784$	26.0206	+	4.47404i	0.929307	+	0.159787i
$785$	42.2003			1.50619
$786$		0			0
$787$	−2.76577	+	4.79046i	−0.0985892	+	0.170761i	−0.911101	−	0.412183i	$-0.864766\pi$
$787$	−2.76577	+	4.79046i	−0.0985892	+	0.170761i	0.812512	+	0.582945i	$0.198100\pi$
$788$	7.47686	−	12.9503i	0.266352	−	0.461335i
$789$		0			0
$790$	−0.609148			−0.0216725
$791$	1.85459	+	3.95518i	0.0659415	+	0.140630i
$792$		0			0
$793$	−3.77234	−	6.53388i	−0.133960	−	0.232025i
$794$	2.53547	−	4.39156i	0.0899804	−	0.155851i
$795$		0			0
$796$	13.2699	+	22.9842i	0.470340	+	0.814652i
$797$	13.8038			0.488955			0.244477	−	0.969655i	$-0.421384\pi$
$797$	13.8038			0.488955			0.244477	+	0.969655i	$0.421384\pi$
$798$		0			0
$799$	−8.08857			−0.286153
$800$	−11.9728	−	20.7375i	−0.423303	−	0.733182i
$801$		0			0
$802$	−0.420300	+	0.727982i	−0.0148413	+	0.0257059i
$803$	2.43347	+	4.21490i	0.0858754	+	0.148741i
$804$		0			0
$805$	−18.0404	−	1.53965i	−0.635839	−	0.0542656i
$806$	1.09670			0.0386296
$807$		0			0
$808$	5.54885	−	9.61088i	0.195208	−	0.338110i
$809$	14.1498	−	24.5082i	0.497480	−	0.861661i	−0.502515	−	0.864568i	$-0.667592\pi$
$809$	14.1498	−	24.5082i	0.497480	−	0.861661i	0.999996	+	0.00290700i	$0.000925329\pi$
$810$		0			0
$811$	−12.2124			−0.428837			−0.214418	−	0.976742i	$-0.568786\pi$
$811$	−12.2124			−0.428837			−0.214418	+	0.976742i	$0.568786\pi$
$812$	−8.53854	−	0.728720i	−0.299644	−	0.0255731i
$813$		0			0
$814$	3.14940	+	5.45491i	0.110386	+	0.191195i
$815$	4.66473	−	8.07955i	0.163398	−	0.283014i
$816$		0			0
$817$	6.09022	+	10.5486i	0.213070	+	0.369048i
$818$	−4.83410			−0.169020
$819$		0			0
$820$	62.6087			2.18639
$821$	−20.7005	−	35.8544i	−0.722453	−	1.25133i	−0.960014	−	0.279953i	$-0.909681\pi$
$821$	−20.7005	−	35.8544i	−0.722453	−	1.25133i	0.237560	−	0.971373i	$-0.423652\pi$
$822$		0			0
$823$	−23.5876	+	40.8550i	−0.822213	+	1.42411i	0.0818184	+	0.996647i	$0.473927\pi$
$823$	−23.5876	+	40.8550i	−0.822213	+	1.42411i	−0.904031	+	0.427467i	$0.859406\pi$
$824$	−2.90371	−	5.02938i	−0.101156	−	0.175207i
$825$		0			0
$826$	−0.990341	−	2.11205i	−0.0344584	−	0.0734876i
$827$	−21.1124			−0.734150			−0.367075	−	0.930191i	$-0.619641\pi$
$827$	−21.1124			−0.734150			−0.367075	+	0.930191i	$0.619641\pi$
$828$		0			0
$829$	0.318376	−	0.551444i	0.0110577	−	0.0191524i	−0.860444	−	0.509546i	$-0.829813\pi$
$829$	0.318376	−	0.551444i	0.0110577	−	0.0191524i	0.871501	+	0.490393i	$0.163147\pi$
$830$	2.74930	−	4.76193i	0.0954297	−	0.165289i
$831$		0			0
$832$	−7.09585			−0.246004
$833$	−5.52583	−	14.9834i	−0.191459	−	0.519143i
$834$		0			0
$835$	−23.7492	−	41.1348i	−0.821874	−	1.42353i
$836$	7.90160	−	13.6860i	0.273282	−	0.473339i
$837$		0			0
$838$	−2.43878	−	4.22410i	−0.0842464	−	0.145919i
$839$	26.9432			0.930183			0.465092	−	0.885263i	$-0.346021\pi$
$839$	26.9432			0.930183			0.465092	+	0.885263i	$0.346021\pi$
$840$		0			0
$841$	−26.2739			−0.905995
$842$	0.978281	+	1.69443i	0.0337138	+	0.0583940i
$843$		0			0
$844$	−15.4971	+	26.8417i	−0.533431	+	0.923929i
$845$	1.96625	+	3.40565i	0.0676412	+	0.117158i
$846$		0			0
$847$	14.0800	−	20.1997i	0.483796	−	0.694071i
$848$	−12.4078			−0.426087
$849$		0			0
$850$	−2.33556	+	4.04531i	−0.0801090	+	0.138753i
$851$	6.21610	−	10.7666i	0.213085	−	0.369074i
$852$		0			0
$853$	6.74784			0.231042			0.115521	−	0.993305i	$-0.463146\pi$
$853$	6.74784			0.231042			0.115521	+	0.993305i	$0.463146\pi$
$854$	−3.89141	−	0.332112i	−0.133161	−	0.0113646i
$855$		0			0
$856$	−4.25486	−	7.36964i	−0.145428	−	0.251889i
$857$	−22.5134	+	38.9943i	−0.769043	+	1.33202i	0.169040	+	0.985609i	$0.445933\pi$
$857$	−22.5134	+	38.9943i	−0.769043	+	1.33202i	−0.938082	+	0.346412i	$0.887400\pi$
$858$		0			0
$859$	18.3635	+	31.8065i	0.626554	+	1.08522i	0.988238	+	0.152923i	$0.0488687\pi$
$859$	18.3635	+	31.8065i	0.626554	+	1.08522i	−0.361684	+	0.932301i	$0.617798\pi$
$860$	52.5629			1.79238
$861$		0			0
$862$	1.11299			0.0379087
$863$	−21.7137	−	37.6093i	−0.739144	−	1.28024i	−0.952881	−	0.303344i	$-0.901897\pi$
$863$	−21.7137	−	37.6093i	−0.739144	−	1.28024i	0.213737	−	0.976891i	$-0.431437\pi$
$864$		0			0
$865$	38.1644	−	66.1027i	1.29763	−	2.24756i
$866$	−1.19935	−	2.07734i	−0.0407557	−	0.0705910i
$867$		0			0
$868$	−16.6360	+	23.8665i	−0.564661	+	0.810083i
$869$	−3.56761			−0.121023
$870$		0			0
$871$	6.33263	−	10.9684i	0.214573	−	0.371651i
$872$	−4.82377	+	8.35502i	−0.163354	+	0.282937i
$873$		0			0
$874$	0.608676			0.0205888
$875$	−24.1382	−	51.4782i	−0.816020	−	1.74028i
$876$		0			0
$877$	−20.0040	−	34.6480i	−0.675488	−	1.16998i	−0.976326	−	0.216304i	$-0.930600\pi$
$877$	−20.0040	−	34.6480i	−0.675488	−	1.16998i	0.300838	−	0.953675i	$-0.402734\pi$
$878$	−0.491407	+	0.851142i	−0.0165842	+	0.0287247i
$879$		0			0
$880$	−33.4198	−	57.8847i	−1.12658	−	1.95129i
$881$	−35.4308			−1.19370			−0.596848	−	0.802355i	$-0.703580\pi$
$881$	−35.4308			−1.19370			−0.596848	+	0.802355i	$0.703580\pi$
$882$		0			0
$883$	22.6654			0.762751			0.381375	−	0.924420i	$-0.375451\pi$
$883$	22.6654			0.762751			0.381375	+	0.924420i	$0.375451\pi$
$884$	2.23774	+	3.87588i	0.0752634	+	0.130360i
$885$		0			0
$886$	0.0566232	−	0.0980742i	0.00190229	−	0.00329487i
$887$	22.3440	+	38.7010i	0.750240	+	1.29945i	0.947706	+	0.319144i	$0.103395\pi$
$887$	22.3440	+	38.7010i	0.750240	+	1.29945i	−0.197467	+	0.980310i	$0.563271\pi$
$888$		0			0
$889$	−5.04670	−	10.7628i	−0.169261	−	0.360974i
$890$	−8.66800			−0.290552
$891$		0			0
$892$	22.0435	−	38.1804i	0.738071	−	1.27838i
$893$	−3.16905	+	5.48896i	−0.106048	+	0.183681i
$894$		0			0
$895$	57.5892			1.92499
$896$	−9.02434	+	12.9466i	−0.301482	+	0.432517i
$897$		0			0
$898$	−0.720366	−	1.24771i	−0.0240389	−	0.0416366i
$899$	4.62740	−	8.01489i	0.154332	−	0.267312i
$900$		0			0
$901$	3.75252	+	6.49956i	0.125015	+	0.216532i
$902$	−7.15549			−0.238252
$903$		0			0
$904$	−1.27983			−0.0425664
$905$	−18.5738	−	32.1707i	−0.617413	−	1.06939i
$906$		0			0
$907$	−27.2374	+	47.1766i	−0.904403	+	1.56647i	−0.0826860	+	0.996576i	$0.526350\pi$
$907$	−27.2374	+	47.1766i	−0.904403	+	1.56647i	−0.821717	+	0.569896i	$0.806983\pi$
$908$	9.02635	+	15.6341i	0.299550	+	0.518836i
$909$		0			0
$910$	2.02832	+	0.173107i	0.0672382	+	0.00573843i
$911$	27.4793			0.910431			0.455215	−	0.890381i	$-0.349562\pi$
$911$	27.4793			0.910431			0.455215	+	0.890381i	$0.349562\pi$
$912$		0			0
$913$	16.1019	−	27.8893i	0.532895	−	0.923000i
$914$	−0.774626	+	1.34169i	−0.0256224	+	0.0443792i
$915$		0			0
$916$	−29.9990			−0.991196
$917$	19.1487	−	27.4714i	0.632345	−	0.907184i
$918$		0			0
$919$	24.1440	+	41.8186i	0.796437	+	1.37947i	0.921923	+	0.387374i	$0.126618\pi$
$919$	24.1440	+	41.8186i	0.796437	+	1.37947i	−0.125486	+	0.992095i	$0.540049\pi$
$920$	2.65228	−	4.59388i	0.0874431	−	0.151456i
$921$		0			0
$922$	−0.932889	−	1.61581i	−0.0307231	−	0.0532139i
$923$	−9.54869			−0.314299
$924$		0			0
$925$	74.7601			2.45810
$926$	−0.211356	−	0.366080i	−0.00694560	−	0.0120301i
$927$		0			0
$928$	1.88906	−	3.27195i	0.0620114	−	0.107407i
$929$	21.6577	+	37.5122i	0.710566	+	1.23074i	0.964645	+	0.263553i	$0.0848943\pi$
$929$	21.6577	+	37.5122i	0.710566	+	1.23074i	−0.254079	+	0.967183i	$0.581772\pi$
$930$		0			0
$931$	−12.3328	−	2.12053i	−0.404191	−	0.0694975i
$932$	−15.8032			−0.517651
$933$		0			0
$934$	−0.794266	+	1.37571i	−0.0259892	+	0.0450146i
$935$	−20.2144	+	35.0123i	−0.661081	+	1.14503i
$936$		0			0
$937$	−37.2211			−1.21596			−0.607980	−	0.793952i	$-0.708020\pi$
$937$	−37.2211			−1.21596			−0.607980	+	0.793952i	$0.708020\pi$
$938$	−2.78344	−	5.93609i	−0.0908824	−	0.193820i
$939$		0			0
$940$	13.6756	+	23.6868i	0.446048	+	0.772577i
$941$	7.98754	−	13.8348i	0.260386	−	0.451002i	−0.705958	−	0.708253i	$-0.749483\pi$
$941$	7.98754	−	13.8348i	0.260386	−	0.451002i	0.966345	+	0.257251i	$0.0828167\pi$
$942$		0			0
$943$	7.06155	+	12.2310i	0.229956	+	0.398295i
$944$	−16.9967			−0.553194
$945$		0			0
$946$	−6.00736			−0.195316
$947$	13.8786	+	24.0384i	0.450994	+	0.781144i	0.998448	−	0.0556912i	$-0.0177363\pi$
$947$	13.8786	+	24.0384i	0.450994	+	0.781144i	−0.547454	+	0.836836i	$0.684403\pi$
$948$		0			0
$949$	−0.540019	+	0.935340i	−0.0175298	+	0.0303624i
$950$	1.83011	+	3.16985i	0.0593768	+	0.102844i
$951$		0			0
$952$	4.66180	+	0.397861i	0.151090	+	0.0128947i
$953$	−12.0303			−0.389700			−0.194850	−	0.980833i	$-0.562422\pi$
$953$	−12.0303			−0.389700			−0.194850	+	0.980833i	$0.562422\pi$
$954$		0			0
$955$	−24.6839	+	42.7537i	−0.798751	+	1.38348i
$956$	−21.3100	+	36.9099i	−0.689213	+	1.19375i
$957$		0			0
$958$	−2.84744			−0.0919965
$959$	−24.4805	−	2.08929i	−0.790518	−	0.0674666i
$960$		0			0
$961$	−0.209310	−	0.362536i	−0.00675194	−	0.0116947i
$962$	−0.698891	+	1.21052i	−0.0225332	+	0.0390286i
$963$		0			0
$964$	−20.1056	−	34.8240i	−0.647559	−	1.12160i
$965$	36.8421			1.18599
$966$		0			0
$967$	5.40788			0.173906			0.0869528	−	0.996212i	$-0.472287\pi$
$967$	5.40788			0.173906			0.0869528	+	0.996212i	$0.472287\pi$
$968$	3.60690	+	6.24733i	0.115930	+	0.200797i
$969$		0			0
$970$	−3.39066	+	5.87279i	−0.108867	+	0.188564i
$971$	21.1376	+	36.6114i	0.678338	+	1.17492i	0.975481	+	0.220083i	$0.0706329\pi$
$971$	21.1376	+	36.6114i	0.678338	+	1.17492i	−0.297143	+	0.954833i	$0.596034\pi$
$972$		0			0
$973$	−4.49297	−	9.58192i	−0.144038	−	0.307182i
$974$	−6.50733			−0.208508
$975$		0			0
$976$	−14.2284	+	24.6443i	−0.455440	+	0.788846i
$977$	−5.41508	+	9.37920i	−0.173244	+	0.300067i	−0.939552	−	0.342406i	$-0.888758\pi$
$977$	−5.41508	+	9.37920i	−0.173244	+	0.300067i	0.766308	+	0.642473i	$0.222092\pi$
$978$		0			0
$979$	−50.7660			−1.62249
$980$	−34.5350	+	41.5148i	−1.10318	+	1.32614i
$981$		0			0
$982$	−2.20664	−	3.82202i	−0.0704169	−	0.121966i
$983$	10.7805	−	18.6723i	0.343844	−	0.595555i	−0.641299	−	0.767291i	$-0.721604\pi$
$983$	10.7805	−	18.6723i	0.343844	−	0.595555i	0.985143	+	0.171736i	$0.0549375\pi$
$984$		0			0
$985$	14.9883	+	25.9605i	0.477567	+	0.827170i
$986$	−0.737005			−0.0234710
$987$		0			0
$988$	3.50693			0.111570
$989$	5.92850	+	10.2685i	0.188515	+	0.326518i
$990$		0			0
$991$	−4.31312	+	7.47054i	−0.137011	+	0.237310i	−0.926364	−	0.376630i	$-0.877083\pi$
$991$	−4.31312	+	7.47054i	−0.137011	+	0.237310i	0.789353	+	0.613940i	$0.210416\pi$
$992$	−6.41306	−	11.1078i	−0.203615	−	0.352671i
$993$		0			0
$994$	−2.82654	+	4.05505i	−0.0896524	+	0.128618i
$995$	−53.2024			−1.68663
$996$		0			0
$997$	−10.8484	+	18.7899i	−0.343571	+	0.595082i	−0.985093	−	0.172022i	$-0.944970\pi$
$997$	−10.8484	+	18.7899i	−0.343571	+	0.595082i	0.641522	+	0.767105i	$0.278303\pi$
$998$	1.11381	−	1.92918i	0.0352572	−	0.0610672i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.h.235.2		10
3.2	odd	2		91.2.e.c.53.4	✓	10
7.2	even	3	inner	819.2.j.h.352.2		10
7.3	odd	6		5733.2.a.bm.1.4		5
7.4	even	3		5733.2.a.bl.1.4		5
12.11	even	2		1456.2.r.p.417.3		10
21.2	odd	6		91.2.e.c.79.4	yes	10
21.5	even	6		637.2.e.m.79.4		10
21.11	odd	6		637.2.a.l.1.2		5
21.17	even	6		637.2.a.k.1.2		5
21.20	even	2		637.2.e.m.508.4		10
39.38	odd	2		1183.2.e.f.508.2		10
84.23	even	6		1456.2.r.p.625.3		10
273.38	even	6		8281.2.a.bx.1.4		5
273.116	odd	6		8281.2.a.bw.1.4		5
273.233	odd	6		1183.2.e.f.170.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.4	✓	10	3.2	odd	2
91.2.e.c.79.4	yes	10	21.2	odd	6
637.2.a.k.1.2		5	21.17	even	6
637.2.a.l.1.2		5	21.11	odd	6
637.2.e.m.79.4		10	21.5	even	6
637.2.e.m.508.4		10	21.20	even	2
819.2.j.h.235.2		10	1.1	even	1	trivial
819.2.j.h.352.2		10	7.2	even	3	inner
1183.2.e.f.170.2		10	273.233	odd	6
1183.2.e.f.508.2		10	39.38	odd	2
1456.2.r.p.417.3		10	12.11	even	2
1456.2.r.p.625.3		10	84.23	even	6
5733.2.a.bl.1.4		5	7.4	even	3
5733.2.a.bm.1.4		5	7.3	odd	6
8281.2.a.bw.1.4		5	273.116	odd	6
8281.2.a.bx.1.4		5	273.38	even	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	819.2.j.h.235.2

Level	$819$
Weight	$2$
Character	819.235
Analytic conductor	$6.540$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$