LMFDB - Embedded newform 1456.2.r.p.625.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not 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:	$11.6262185343$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.3
Root			$0.597828 - 1.03547i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.p.417.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.129894 - 0.224983i) q^{3} +(-1.96625 + 3.40565i) q^{5} +(-1.12324 + 2.39548i) q^{7} +(1.46625 - 2.53963i) q^{9} +O(q^{10})$	\(q+(-0.129894 - 0.224983i) q^{3} +(-1.96625 + 3.40565i) q^{5} +(-1.12324 + 2.39548i) q^{7} +(1.46625 - 2.53963i) q^{9} +(2.25314 + 3.90255i) q^{11} +1.00000 q^{13} +1.02162 q^{15} +(1.14070 + 1.97576i) q^{17} +(-0.893841 + 1.54818i) q^{19} +(0.684846 - 0.0584481i) q^{21} +(0.870106 - 1.50707i) q^{23} +(-5.23232 - 9.06264i) q^{25} -1.54120 q^{27} +1.65110 q^{29} +(2.80262 + 4.85427i) q^{31} +(0.585339 - 1.01384i) q^{33} +(-5.94959 - 8.53550i) q^{35} +(-3.57204 + 6.18695i) q^{37} +(-0.129894 - 0.224983i) q^{39} -8.11574 q^{41} -6.81353 q^{43} +(5.76606 + 9.98711i) q^{45} +(1.77271 - 3.07043i) q^{47} +(-4.47665 - 5.38141i) q^{49} +(0.296342 - 0.513279i) q^{51} +(-1.64483 - 2.84892i) q^{53} -17.7210 q^{55} +0.464419 q^{57} +(2.25314 + 3.90255i) q^{59} +(-3.77234 + 6.53388i) q^{61} +(4.43667 + 6.36500i) q^{63} +(-1.96625 + 3.40565i) q^{65} +(-6.33263 - 10.9684i) q^{67} -0.452087 q^{69} -9.54869 q^{71} +(-0.540019 - 0.935340i) q^{73} +(-1.35930 + 2.35437i) q^{75} +(-11.8793 + 1.01384i) q^{77} +(0.395849 - 0.685630i) q^{79} +(-4.19857 - 7.27214i) q^{81} +7.14643 q^{83} -8.97166 q^{85} +(-0.214468 - 0.371470i) q^{87} +(5.63281 - 9.75631i) q^{89} +(-1.12324 + 2.39548i) q^{91} +(0.728087 - 1.26108i) q^{93} +(-3.51504 - 6.08823i) q^{95} -8.81353 q^{97} +13.2147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99}+O(q^{100}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.129894	−	0.224983i	−0.0749945	−	0.129894i	0.826089	−	0.563539i	$-0.190561\pi$
$3$	−0.129894	−	0.224983i	−0.0749945	−	0.129894i	−0.901084	+	0.433645i	$0.857227\pi$
$4$		0			0
$5$	−1.96625	+	3.40565i	−0.879336	+	1.52305i	−0.0272650	+	0.999628i	$0.508680\pi$
$5$	−1.96625	+	3.40565i	−0.879336	+	1.52305i	−0.852071	+	0.523426i	$0.824654\pi$
$6$		0			0
$7$	−1.12324	+	2.39548i	−0.424546	+	0.905406i
$7$	−1.12324	+	2.39548i	−0.424546	+	0.905406i
$8$		0			0
$9$	1.46625	−	2.53963i	0.488752	−	0.846543i
$10$		0			0
$11$	2.25314	+	3.90255i	0.679346	+	1.17666i	0.975178	+	0.221422i	$0.0710699\pi$
$11$	2.25314	+	3.90255i	0.679346	+	1.17666i	−0.295832	+	0.955240i	$0.595597\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	1.02162			0.263781
$16$		0			0
$17$	1.14070	+	1.97576i	0.276661	+	0.479192i	0.970553	−	0.240888i	$-0.0774386\pi$
$17$	1.14070	+	1.97576i	0.276661	+	0.479192i	−0.693891	+	0.720080i	$0.744105\pi$
$18$		0			0
$19$	−0.893841	+	1.54818i	−0.205061	+	0.355177i	−0.950152	−	0.311786i	$-0.899073\pi$
$19$	−0.893841	+	1.54818i	−0.205061	+	0.355177i	0.745091	+	0.666963i	$0.232406\pi$
$20$		0			0
$21$	0.684846	−	0.0584481i	0.149446	−	0.0127544i
$22$		0			0
$23$	0.870106	−	1.50707i	0.181430	−	0.314245i	−0.760938	−	0.648825i	$-0.775261\pi$
$23$	0.870106	−	1.50707i	0.181430	−	0.314245i	0.942368	+	0.334579i	$0.108594\pi$
$24$		0			0
$25$	−5.23232	−	9.06264i	−1.04646	−	1.81253i
$26$		0			0
$27$	−1.54120			−0.296604
$28$		0			0
$29$	1.65110			0.306602			0.153301	−	0.988180i	$-0.451010\pi$
$29$	1.65110			0.306602			0.153301	+	0.988180i	$0.451010\pi$
$30$		0			0
$31$	2.80262	+	4.85427i	0.503365	+	0.871853i	0.999992	+	0.00388953i	$0.00123808\pi$
$31$	2.80262	+	4.85427i	0.503365	+	0.871853i	−0.496628	+	0.867964i	$0.665429\pi$
$32$		0			0
$33$	0.585339	−	1.01384i	0.101894	−	0.176486i
$34$		0			0
$35$	−5.94959	−	8.53550i	−1.00566	−	1.44276i
$36$		0			0
$37$	−3.57204	+	6.18695i	−0.587239	+	1.01713i	0.407353	+	0.913271i	$0.366452\pi$
$37$	−3.57204	+	6.18695i	−0.587239	+	1.01713i	−0.994592	+	0.103857i	$0.966881\pi$
$38$		0			0
$39$	−0.129894	−	0.224983i	−0.0207997	−	0.0360262i
$40$		0			0
$41$	−8.11574			−1.26746			−0.633732	−	0.773552i	$-0.718478\pi$
$41$	−8.11574			−1.26746			−0.633732	+	0.773552i	$0.718478\pi$
$42$		0			0
$43$	−6.81353			−1.03905			−0.519527	−	0.854454i	$-0.673892\pi$
$43$	−6.81353			−1.03905			−0.519527	+	0.854454i	$0.673892\pi$
$44$		0			0
$45$	5.76606	+	9.98711i	0.859554	+	1.48879i
$46$		0			0
$47$	1.77271	−	3.07043i	0.258577	−	0.447868i	−0.707284	−	0.706929i	$-0.750080\pi$
$47$	1.77271	−	3.07043i	0.258577	−	0.447868i	0.965861	+	0.259061i	$0.0834131\pi$
$48$		0			0
$49$	−4.47665	−	5.38141i	−0.639522	−	0.768773i
$50$		0			0
$51$	0.296342	−	0.513279i	0.0414962	−	0.0718735i
$52$		0			0
$53$	−1.64483	−	2.84892i	−0.225934	−	0.391330i	0.730665	−	0.682736i	$-0.239210\pi$
$53$	−1.64483	−	2.84892i	−0.225934	−	0.391330i	−0.956599	+	0.291406i	$0.905877\pi$
$54$		0			0
$55$	−17.7210			−2.38949
$56$		0			0
$57$	0.464419			0.0615138
$58$		0			0
$59$	2.25314	+	3.90255i	0.293333	+	0.508068i	0.974596	−	0.223971i	$-0.0719021\pi$
$59$	2.25314	+	3.90255i	0.293333	+	0.508068i	−0.681262	+	0.732039i	$0.738569\pi$
$60$		0			0
$61$	−3.77234	+	6.53388i	−0.482998	+	0.836577i	−0.999809	−	0.0195220i	$-0.993786\pi$
$61$	−3.77234	+	6.53388i	−0.482998	+	0.836577i	0.516811	+	0.856099i	$0.327119\pi$
$62$		0			0
$63$	4.43667	+	6.36500i	0.558968	+	0.801915i
$64$		0			0
$65$	−1.96625	+	3.40565i	−0.243884	+	0.422419i
$66$		0			0
$67$	−6.33263	−	10.9684i	−0.773653	−	1.34001i	−0.935548	−	0.353199i	$-0.885094\pi$
$67$	−6.33263	−	10.9684i	−0.773653	−	1.34001i	0.161895	−	0.986808i	$-0.448239\pi$
$68$		0			0
$69$	−0.452087			−0.0544249
$70$		0			0
$71$	−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	0.832692	−	0.553737i	$-0.186799\pi$
$73$	−0.540019	−	0.935340i	−0.0632044	−	0.109473i	−0.895896	+	0.444264i	$0.853465\pi$
$74$		0			0
$75$	−1.35930	+	2.35437i	−0.156958	+	0.271859i
$76$		0			0
$77$	−11.8793	+	1.01384i	−1.35377	+	0.115537i
$78$		0			0
$79$	0.395849	−	0.685630i	0.0445365	−	0.0771394i	−0.842898	−	0.538074i	$-0.819152\pi$
$79$	0.395849	−	0.685630i	0.0445365	−	0.0771394i	0.887434	+	0.460934i	$0.152486\pi$
$80$		0			0
$81$	−4.19857	−	7.27214i	−0.466508	−	0.808016i
$82$		0			0
$83$	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			0
$87$	−0.214468	−	0.371470i	−0.0229934	−	0.0398258i
$88$		0			0
$89$	5.63281	−	9.75631i	0.597077	−	1.03417i	−0.396174	−	0.918176i	$-0.629662\pi$
$89$	5.63281	−	9.75631i	0.597077	−	1.03417i	0.993250	−	0.115992i	$-0.0370045\pi$
$90$		0			0
$91$	−1.12324	+	2.39548i	−0.117748	+	0.251115i
$92$		0			0
$93$	0.728087	−	1.26108i	0.0754991	−	0.130768i
$94$		0			0
$95$	−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	$0.647664\pi$
$98$		0			0
$99$	13.2147			1.32813
$100$		0			0
$101$	7.15855	+	12.3990i	0.712303	+	1.23374i	0.963991	+	0.265936i	$0.0856810\pi$
$101$	7.15855	+	12.3990i	0.712303	+	1.23374i	−0.251688	+	0.967808i	$0.580986\pi$
$102$		0			0
$103$	−3.74607	+	6.48839i	−0.369111	+	0.639320i	−0.989427	−	0.145033i	$-0.953671\pi$
$103$	−3.74607	+	6.48839i	−0.369111	+	0.639320i	0.620315	+	0.784352i	$0.287005\pi$
$104$		0			0
$105$	−1.14753	+	2.44727i	−0.111987	+	0.238829i
$106$		0			0
$107$	5.48919	−	9.50756i	0.530660	−	0.919130i	−0.468700	−	0.883357i	$-0.655277\pi$
$107$	5.48919	−	9.50756i	0.530660	−	0.919130i	0.999360	−	0.0357726i	$-0.0113892\pi$
$108$		0			0
$109$	6.22314	+	10.7788i	0.596068	+	1.03242i	0.993395	+	0.114744i	$0.0366046\pi$
$109$	6.22314	+	10.7788i	0.596068	+	1.03242i	−0.397327	+	0.917677i	$0.630062\pi$
$110$		0			0
$111$	1.85595			0.176159
$112$		0			0
$113$	−1.65110			−0.155323			−0.0776613	−	0.996980i	$-0.524745\pi$
$113$	−1.65110			−0.155323			−0.0776613	+	0.996980i	$0.524745\pi$
$114$		0			0
$115$	3.42170	+	5.92656i	0.319075	+	0.552654i
$116$		0			0
$117$	1.46625	−	2.53963i	0.135555	−	0.234789i
$118$		0			0
$119$	−6.01418	+	0.513279i	−0.551319	+	0.0470522i
$120$		0			0
$121$	−4.65325	+	8.05967i	−0.423023	+	0.732697i
$122$		0			0
$123$	1.05419	+	1.82591i	0.0950528	+	0.164636i
$124$		0			0
$125$	21.4897			1.92210
$126$		0			0
$127$	4.49297			0.398687			0.199343	−	0.979930i	$-0.436119\pi$
$127$	4.49297			0.398687			0.199343	+	0.979930i	$0.436119\pi$
$128$		0			0
$129$	0.885039	+	1.53293i	0.0779233	+	0.134967i
$130$		0			0
$131$	−6.32836	+	10.9610i	−0.552911	+	0.957670i	0.445151	+	0.895455i	$0.353150\pi$
$131$	−6.32836	+	10.9610i	−0.552911	+	0.957670i	−0.998063	+	0.0622152i	$0.980184\pi$
$132$		0			0
$133$	−2.70463	−	3.88016i	−0.234521	−	0.336453i
$134$		0			0
$135$	3.03039	−	5.24878i	0.260814	−	0.451743i
$136$		0			0
$137$	4.64321	+	8.04227i	0.396696	+	0.687097i	0.993316	−	0.115426i	$-0.0368234\pi$
$137$	4.64321	+	8.04227i	0.396696	+	0.687097i	−0.596620	+	0.802524i	$0.703490\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−0.921061			−0.0775673
$142$		0			0
$143$	2.25314	+	3.90255i	0.188417	+	0.326347i
$144$		0			0
$145$	−3.24649	+	5.62308i	−0.269606	+	0.466971i
$146$		0			0
$147$	−0.629237	+	1.70619i	−0.0518986	+	0.140724i
$148$		0			0
$149$	7.58243	−	13.1332i	0.621177	−	1.07591i	−0.368090	−	0.929790i	$-0.619988\pi$
$149$	7.58243	−	13.1332i	0.621177	−	1.07591i	0.989267	−	0.146120i	$-0.0466786\pi$
$150$		0			0
$151$	2.57079	+	4.45274i	0.209208	+	0.362359i	0.951465	−	0.307756i	$-0.0995780\pi$
$151$	2.57079	+	4.45274i	0.209208	+	0.362359i	−0.742257	+	0.670115i	$0.766245\pi$
$152$		0			0
$153$	6.69025			0.540875
$154$		0			0
$155$	−22.0426			−1.77051
$156$		0			0
$157$	5.36557	+	9.29344i	0.428219	+	0.741697i	0.996715	−	0.0809889i	$-0.0258078\pi$
$157$	5.36557	+	9.29344i	0.428219	+	0.741697i	−0.568496	+	0.822686i	$0.692474\pi$
$158$		0			0
$159$	−0.427307	+	0.740117i	−0.0338877	+	0.0586951i
$160$		0			0
$161$	2.63281	+	3.77712i	0.207495	+	0.297679i
$162$		0			0
$163$	1.18620	−	2.05455i	0.0929101	−	0.160925i	−0.815824	−	0.578300i	$-0.803716\pi$
$163$	1.18620	−	2.05455i	0.0929101	−	0.160925i	0.908734	+	0.417375i	$0.137050\pi$
$164$		0			0
$165$	2.30185	+	3.98692i	0.179199	+	0.310382i
$166$		0			0
$167$	−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			0
$171$	2.62120	+	4.54005i	0.200448	+	0.347186i
$172$		0			0
$173$	9.70485	−	16.8093i	0.737846	−	1.27799i	−0.215618	−	0.976478i	$-0.569176\pi$
$173$	9.70485	−	16.8093i	0.737846	−	1.27799i	0.953463	−	0.301509i	$-0.0974902\pi$
$174$		0			0
$175$	27.5865	−	2.35437i	2.08535	−	0.177974i
$176$		0			0
$177$	0.585339	−	1.01384i	0.0439968	−	0.0762046i
$178$		0			0
$179$	7.32219	+	12.6824i	0.547286	+	0.947928i	0.998459	+	0.0554912i	$0.0176725\pi$
$179$	7.32219	+	12.6824i	0.547286	+	0.947928i	−0.451173	+	0.892437i	$0.648994\pi$
$180$		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			0
$183$	1.96002			0.144889
$184$		0			0
$185$	−14.0471	−	24.3302i	−1.03276	−	1.78879i
$186$		0			0
$187$	−5.14033	+	8.90331i	−0.375898	+	0.651074i
$188$		0			0
$189$	1.73114	−	3.69191i	0.125922	−	0.268547i
$190$		0			0
$191$	6.27687	−	10.8719i	0.454179	−	0.786660i	−0.544462	−	0.838786i	$-0.683266\pi$
$191$	6.27687	−	10.8719i	0.454179	−	0.786660i	0.998641	+	0.0521252i	$0.0165995\pi$
$192$		0			0
$193$	4.68430	+	8.11344i	0.337183	+	0.584018i	0.983902	−	0.178710i	$-0.0571925\pi$
$193$	4.68430	+	8.11344i	0.337183	+	0.584018i	−0.646719	+	0.762729i	$0.723859\pi$
$194$		0			0
$195$	1.02162			0.0731598
$196$		0			0
$197$	−7.62276			−0.543099			−0.271550	−	0.962424i	$-0.587536\pi$
$197$	−7.62276			−0.543099			−0.271550	+	0.962424i	$0.587536\pi$
$198$		0			0
$199$	6.76443	+	11.7163i	0.479518	+	0.830549i	0.999724	−	0.0234914i	$-0.00747822\pi$
$199$	6.76443	+	11.7163i	0.479518	+	0.830549i	−0.520206	+	0.854041i	$0.674145\pi$
$200$		0			0
$201$	−1.64514	+	2.84947i	−0.116039	+	0.200986i
$202$		0			0
$203$	−1.85459	+	3.95518i	−0.130167	+	0.277599i
$204$		0			0
$205$	15.9576	−	27.6394i	1.11453	−	1.93042i
$206$		0			0
$207$	−2.55159	−	4.41949i	−0.177348	−	0.307176i
$208$		0			0
$209$	−8.05579			−0.557231
$210$		0			0
$211$	15.7995			1.08768			0.543840	−	0.839189i	$-0.316970\pi$
$211$	15.7995			1.08768			0.543840	+	0.839189i	$0.316970\pi$
$212$		0			0
$213$	1.24032	+	2.14830i	0.0849853	+	0.147199i
$214$		0			0
$215$	13.3971	−	23.2045i	0.913678	−	1.58254i
$216$		0			0
$217$	−14.7763	+	1.26108i	−1.00308	+	0.0856080i
$218$		0			0
$219$	−0.140291	+	0.242991i	−0.00947997	+	0.0164198i
$220$		0			0
$221$	1.14070	+	1.97576i	0.0767321	+	0.132904i
$222$		0			0
$223$	−22.4737			−1.50495			−0.752474	−	0.658622i	$-0.771139\pi$
$223$	−22.4737			−1.50495			−0.752474	+	0.658622i	$0.771139\pi$
$224$		0			0
$225$	−30.6876			−2.04584
$226$		0			0
$227$	−4.60124	−	7.96959i	−0.305395	−	0.528960i	0.671954	−	0.740593i	$-0.265455\pi$
$227$	−4.60124	−	7.96959i	−0.305395	−	0.528960i	−0.977349	+	0.211633i	$0.932122\pi$
$228$		0			0
$229$	−7.64611	+	13.2435i	−0.505269	+	0.875152i	0.494712	+	0.869057i	$0.335274\pi$
$229$	−7.64611	+	13.2435i	−0.505269	+	0.875152i	−0.999981	+	0.00609528i	$0.998060\pi$
$230$		0			0
$231$	1.77115	+	2.54095i	0.116533	+	0.167182i
$232$		0			0
$233$	4.02789	−	6.97652i	0.263876	−	0.457047i	−0.703392	−	0.710802i	$-0.748332\pi$
$233$	4.02789	−	6.97652i	0.263876	−	0.457047i	0.967269	+	0.253755i	$0.0816656\pi$
$234$		0			0
$235$	6.97121	+	12.0745i	0.454752	+	0.787653i
$236$		0			0
$237$	−0.205674			−0.0133600
$238$		0			0
$239$	−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	0.980564	+	0.196199i	$0.0628598\pi$
$241$	10.2490	+	17.7518i	0.660195	+	1.14349i	−0.320369	+	0.947293i	$0.603807\pi$
$242$		0			0
$243$	−3.40254	+	5.89337i	−0.218273	+	0.378060i
$244$		0			0
$245$	27.1295	−	4.66470i	1.73324	−	0.298017i
$246$		0			0
$247$	−0.893841	+	1.54818i	−0.0568738	+	0.0985083i
$248$		0			0
$249$	−0.928280	−	1.60783i	−0.0588273	−	0.101892i
$250$		0			0
$251$	−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			0
$255$	1.16537	+	2.01848i	0.0729781	+	0.126402i
$256$		0			0
$257$	4.49838	−	7.79142i	0.280601	−	0.486016i	−0.690932	−	0.722920i	$-0.742799\pi$
$257$	4.49838	−	7.79142i	0.280601	−	0.486016i	0.971533	+	0.236904i	$0.0761328\pi$
$258$		0			0
$259$	−10.8084	−	15.5062i	−0.671604	−	0.963508i
$260$		0			0
$261$	2.42094	−	4.19318i	0.149852	−	0.259551i
$262$		0			0
$263$	0.716961	+	1.24181i	0.0442097	+	0.0765735i	0.887284	−	0.461224i	$-0.152590\pi$
$263$	0.716961	+	1.24181i	0.0442097	+	0.0765735i	−0.843074	+	0.537798i	$0.819256\pi$
$264$		0			0
$265$	12.9366			0.794689
$266$		0			0
$267$	−2.92668			−0.179110
$268$		0			0
$269$	4.08416	+	7.07397i	0.249016	+	0.431308i	0.963253	−	0.268596i	$-0.0865596\pi$
$269$	4.08416	+	7.07397i	0.249016	+	0.431308i	−0.714237	+	0.699904i	$0.753226\pi$
$270$		0			0
$271$	−0.106159	+	0.183872i	−0.00644867	+	0.0111694i	−0.869232	−	0.494405i	$-0.835386\pi$
$271$	−0.106159	+	0.183872i	−0.00644867	+	0.0111694i	0.862783	+	0.505574i	$0.168719\pi$
$272$		0			0
$273$	0.684846	−	0.0584481i	0.0414488	−	0.00353744i
$274$		0			0
$275$	23.5783	−	40.8387i	1.42182	−	2.46267i
$276$		0			0
$277$	−11.4875	−	19.8969i	−0.690215	−	1.19549i	−0.971767	−	0.235942i	$-0.924182\pi$
$277$	−11.4875	−	19.8969i	−0.690215	−	1.19549i	0.281552	−	0.959546i	$-0.409151\pi$
$278$		0			0
$279$	16.4374			0.984081
$280$		0			0
$281$	−0.345228			−0.0205946			−0.0102973	−	0.999947i	$-0.503278\pi$
$281$	−0.345228			−0.0205946			−0.0102973	+	0.999947i	$0.503278\pi$
$282$		0			0
$283$	−14.4857	−	25.0900i	−0.861087	−	1.49145i	−0.870880	−	0.491495i	$-0.836451\pi$
$283$	−14.4857	−	25.0900i	−0.861087	−	1.49145i	0.00979277	−	0.999952i	$-0.496883\pi$
$284$		0			0
$285$	−0.913167	+	1.58165i	−0.0540913	+	0.0936889i
$286$		0			0
$287$	9.11594	−	19.4411i	0.538097	−	1.14757i
$288$		0			0
$289$	5.89759	−	10.2149i	0.346917	−	0.600878i
$290$		0			0
$291$	1.14483	+	1.98290i	0.0671109	+	0.116240i
$292$		0			0
$293$	31.5427			1.84274			0.921372	−	0.388682i	$-0.127070\pi$
$293$	31.5427			1.84274			0.921372	+	0.388682i	$0.127070\pi$
$294$		0			0
$295$	−17.7210			−1.03175
$296$		0			0
$297$	−3.47253	−	6.01460i	−0.201497	−	0.349002i
$298$		0			0
$299$	0.870106	−	1.50707i	0.0503195	−	0.0871560i
$300$		0			0
$301$	7.65325	−	16.3217i	0.441126	−	0.940766i
$302$		0			0
$303$	1.85971	−	3.22111i	0.106838	−	0.185048i
$304$		0			0
$305$	−14.8348	−	25.6945i	−0.849435	−	1.47127i
$306$		0			0
$307$	18.1941			1.03839			0.519197	−	0.854655i	$-0.326231\pi$
$307$	18.1941			1.03839			0.519197	+	0.854655i	$0.326231\pi$
$308$		0			0
$309$	1.94637			0.110725
$310$		0			0
$311$	−0.188312	−	0.326165i	−0.0106782	−	0.0184951i	0.860637	−	0.509219i	$-0.170066\pi$
$311$	−0.188312	−	0.326165i	−0.0106782	−	0.0184951i	−0.871315	+	0.490724i	$0.836732\pi$
$312$		0			0
$313$	−5.49415	+	9.51615i	−0.310548	+	0.537884i	−0.978481	−	0.206337i	$-0.933846\pi$
$313$	−5.49415	+	9.51615i	−0.310548	+	0.537884i	0.667933	+	0.744221i	$0.267179\pi$
$314$		0			0
$315$	−30.4006	+	2.59454i	−1.71288	+	0.146186i
$316$		0			0
$317$	−13.0903	+	22.6731i	−0.735225	+	1.27345i	0.219400	+	0.975635i	$0.429590\pi$
$317$	−13.0903	+	22.6731i	−0.735225	+	1.27345i	−0.954625	+	0.297812i	$0.903743\pi$
$318$		0			0
$319$	3.72016	+	6.44350i	0.208289	+	0.360767i
$320$		0			0
$321$	−2.85206			−0.159186
$322$		0			0
$323$	−4.07844			−0.226930
$324$		0			0
$325$	−5.23232	−	9.06264i	−0.290237	−	0.502705i
$326$		0			0
$327$	1.61670	−	2.80020i	0.0894037	−	0.154852i
$328$		0			0
$329$	5.36397	+	7.69534i	0.295725	+	0.424258i
$330$		0			0
$331$	−17.0466	+	29.5256i	−0.936967	+	1.62287i	−0.165878	+	0.986146i	$0.553046\pi$
$331$	−17.0466	+	29.5256i	−0.936967	+	1.62287i	−0.771089	+	0.636728i	$0.780288\pi$
$332$		0			0
$333$	10.4750	+	18.1433i	0.574028	+	0.994246i
$334$		0			0
$335$	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			0
$339$	0.214468	+	0.371470i	0.0116483	+	0.0201755i
$340$		0			0
$341$	−12.6294	+	21.8747i	−0.683918	+	1.18458i
$342$		0			0
$343$	17.9194	−	4.67910i	0.967558	−	0.252648i
$344$		0			0
$345$	0.888918	−	1.53965i	0.0478577	−	0.0828920i
$346$		0			0
$347$	14.9733	+	25.9345i	0.803809	+	1.39224i	0.917092	+	0.398675i	$0.130530\pi$
$347$	14.9733	+	25.9345i	0.803809	+	1.39224i	−0.113284	+	0.993563i	$0.536137\pi$
$348$		0			0
$349$	−13.4793			−0.721532			−0.360766	−	0.932656i	$-0.617485\pi$
$349$	−13.4793			−0.721532			−0.360766	+	0.932656i	$0.617485\pi$
$350$		0			0
$351$	−1.54120			−0.0822630
$352$		0			0
$353$	−0.0817659	−	0.141623i	−0.00435196	−	0.00753781i	0.863841	−	0.503764i	$-0.168052\pi$
$353$	−0.0817659	−	0.141623i	−0.00435196	−	0.00753781i	−0.868193	+	0.496226i	$0.834719\pi$
$354$		0			0
$355$	18.7752	−	32.5195i	0.996482	−	1.72596i
$356$		0			0
$357$	0.896686	+	1.28642i	0.0474577	+	0.0680845i
$358$		0			0
$359$	4.46065	−	7.72607i	0.235424	−	0.407766i	−0.723972	−	0.689830i	$-0.757685\pi$
$359$	4.46065	−	7.72607i	0.235424	−	0.407766i	0.959396	+	0.282063i	$0.0910188\pi$
$360$		0			0
$361$	7.90209	+	13.6868i	0.415900	+	0.720359i
$362$		0			0
$363$	2.41772			0.126898
$364$		0			0
$365$	4.24726			0.222312
$366$		0			0
$367$	18.3276	+	31.7443i	0.956693	+	1.65704i	0.730445	+	0.682971i	$0.239313\pi$
$367$	18.3276	+	31.7443i	0.956693	+	1.65704i	0.226248	+	0.974070i	$0.427354\pi$
$368$		0			0
$369$	−11.8997	+	20.6110i	−0.619476	+	1.07296i
$370$		0			0
$371$	8.67208	−	0.740117i	0.450232	−	0.0384250i
$372$		0			0
$373$	−13.5637	+	23.4930i	−0.702302	+	1.21642i	0.265355	+	0.964151i	$0.414511\pi$
$373$	−13.5637	+	23.4930i	−0.702302	+	1.21642i	−0.967656	+	0.252271i	$0.918822\pi$
$374$		0			0
$375$	−2.79139	−	4.83483i	−0.144147	−	0.249670i
$376$		0			0
$377$	1.65110			0.0850360
$378$		0			0
$379$	15.8943			0.816434			0.408217	−	0.912885i	$-0.366151\pi$
$379$	15.8943			0.816434			0.408217	+	0.912885i	$0.366151\pi$
$380$		0			0
$381$	−0.583611	−	1.01084i	−0.0298993	−	0.0517871i
$382$		0			0
$383$	0.575394	−	0.996611i	0.0294013	−	0.0509245i	−0.850950	−	0.525246i	$-0.823973\pi$
$383$	0.575394	−	0.996611i	0.0294013	−	0.0509245i	0.880352	+	0.474322i	$0.157307\pi$
$384$		0			0
$385$	19.9049	−	42.4502i	1.01445	−	2.16346i
$386$		0			0
$387$	−9.99038	+	17.3038i	−0.507839	+	0.879604i
$388$		0			0
$389$	7.15651	+	12.3954i	0.362850	+	0.628474i	0.988429	−	0.151687i	$-0.0484705\pi$
$389$	7.15651	+	12.3954i	0.362850	+	0.628474i	−0.625579	+	0.780161i	$0.715137\pi$
$390$		0			0
$391$	3.97013			0.200778
$392$		0			0
$393$	3.28807			0.165861
$394$		0			0
$395$	1.55668	+	2.69625i	0.0783251	+	0.135663i
$396$		0			0
$397$	12.9588	−	22.4453i	0.650383	−	1.12650i	−0.332647	−	0.943051i	$-0.607942\pi$
$397$	12.9588	−	22.4453i	0.650383	−	1.12650i	0.983030	−	0.183445i	$-0.0587248\pi$
$398$		0			0
$399$	−0.521656	+	1.11251i	−0.0261154	+	0.0556950i
$400$		0			0
$401$	2.14816	−	3.72072i	0.107274	−	0.185804i	−0.807391	−	0.590017i	$-0.799121\pi$
$401$	2.14816	−	3.72072i	0.107274	−	0.185804i	0.914665	+	0.404213i	$0.132455\pi$
$402$		0			0
$403$	2.80262	+	4.85427i	0.139608	+	0.241809i
$404$		0			0
$405$	33.0219			1.64087
$406$		0			0
$407$	−32.1931			−1.59575
$408$		0			0
$409$	12.3536	+	21.3970i	0.610844	+	1.05801i	0.991098	+	0.133131i	$0.0425030\pi$
$409$	12.3536	+	21.3970i	0.610844	+	1.05801i	−0.380255	+	0.924882i	$0.624164\pi$
$410$		0			0
$411$	1.20625	−	2.08929i	0.0595000	−	0.103057i
$412$		0			0
$413$	−11.8793	+	1.01384i	−0.584542	+	0.0498876i
$414$		0			0
$415$	−14.0517	+	24.3383i	−0.689771	+	1.19472i
$416$		0			0
$417$	−0.519577	−	0.899934i	−0.0254438	−	0.0440699i
$418$		0			0
$419$	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	$0.578356\pi$
$422$		0			0
$423$	−5.19850	−	9.00407i	−0.252760	−	0.437793i
$424$		0			0
$425$	11.9371	−	20.6756i	0.579032	−	1.00291i
$426$		0			0
$427$	−11.4145	−	16.3757i	−0.552388	−	0.792475i
$428$		0			0
$429$	0.585339	−	1.01384i	0.0282604	−	0.0489485i
$430$		0			0
$431$	−2.84426	−	4.92639i	−0.137003	−	0.237296i	0.789358	−	0.613933i	$-0.210414\pi$
$431$	−2.84426	−	4.92639i	−0.137003	−	0.237296i	−0.926361	+	0.376637i	$0.877080\pi$
$432$		0			0
$433$	12.2598			0.589169			0.294584	−	0.955625i	$-0.404819\pi$
$433$	12.2598			0.589169			0.294584	+	0.955625i	$0.404819\pi$
$434$		0			0
$435$	1.68680			0.0808758
$436$		0			0
$437$	1.55547	+	2.69416i	0.0744084	+	0.128879i
$438$		0			0
$439$	2.51158	−	4.35019i	0.119871	−	0.207623i	−0.799845	−	0.600206i	$-0.795085\pi$
$439$	2.51158	−	4.35019i	0.119871	−	0.207623i	0.919717	+	0.392583i	$0.128418\pi$
$440$		0			0
$441$	−20.2307	+	3.47851i	−0.963367	+	0.165643i
$442$		0			0
$443$	0.289401	−	0.501258i	0.0137499	−	0.0238155i	−0.859069	−	0.511860i	$-0.828956\pi$
$443$	0.289401	−	0.501258i	0.0137499	−	0.0238155i	0.872818	+	0.488045i	$0.162290\pi$
$444$		0			0
$445$	22.1511	+	38.3668i	1.05006	+	1.81876i
$446$		0			0
$447$	−3.93966			−0.186339
$448$		0			0
$449$	−7.36359			−0.347509			−0.173755	−	0.984789i	$-0.555590\pi$
$449$	−7.36359			−0.347509			−0.173755	+	0.984789i	$0.555590\pi$
$450$		0			0
$451$	−18.2859	−	31.6720i	−0.861048	−	1.49138i
$452$		0			0
$453$	0.667862	−	1.15677i	0.0313789	−	0.0543499i
$454$		0			0
$455$	−5.94959	−	8.53550i	−0.278921	−	0.400150i
$456$		0			0
$457$	−3.95912	+	6.85739i	−0.185200	+	0.320775i	−0.943644	−	0.330963i	$-0.892627\pi$
$457$	−3.95912	+	6.85739i	−0.185200	+	0.320775i	0.758444	+	0.651738i	$0.225960\pi$
$458$		0			0
$459$	−1.75805	−	3.04503i	−0.0820588	−	0.142130i
$460$		0			0
$461$	−9.53600			−0.444136			−0.222068	−	0.975031i	$-0.571281\pi$
$461$	−9.53600			−0.444136			−0.222068	+	0.975031i	$0.571281\pi$
$462$		0			0
$463$	−2.16049			−0.100406			−0.0502032	−	0.998739i	$-0.515987\pi$
$463$	−2.16049			−0.100406			−0.0502032	+	0.998739i	$0.515987\pi$
$464$		0			0
$465$	2.86321	+	4.95923i	0.132778	+	0.229979i
$466$		0			0
$467$	−4.05950	+	7.03126i	−0.187851	+	0.325368i	−0.944534	−	0.328415i	$-0.893486\pi$
$467$	−4.05950	+	7.03126i	−0.187851	+	0.325368i	0.756682	+	0.653783i	$0.226819\pi$
$468$		0			0
$469$	33.3877	−	2.84947i	1.54170	−	0.131576i
$470$		0			0
$471$	1.39391	−	2.41433i	0.0642281	−	0.111246i
$472$		0			0
$473$	−15.3518	−	26.5901i	−0.705878	−	1.22262i
$474$		0			0
$475$	18.7074			0.858357
$476$		0			0
$477$	−9.64694			−0.441703
$478$		0			0
$479$	7.27663	+	12.6035i	0.332478	+	0.575868i	0.982997	−	0.183621i	$-0.0587820\pi$
$479$	7.27663	+	12.6035i	0.332478	+	0.575868i	−0.650519	+	0.759490i	$0.725449\pi$
$480$		0			0
$481$	−3.57204	+	6.18695i	−0.162871	+	0.282101i
$482$		0			0
$483$	0.507803	−	1.08297i	0.0231058	−	0.0492766i
$484$		0			0
$485$	17.3297	−	30.0158i	0.786899	−	1.36295i
$486$		0			0
$487$	−16.6295	−	28.8031i	−0.753554	−	1.30519i	−0.946090	−	0.323904i	$-0.895005\pi$
$487$	−16.6295	−	28.8031i	−0.753554	−	1.30519i	0.192536	−	0.981290i	$-0.438329\pi$
$488$		0			0
$489$	−0.616320			−0.0278710
$490$		0			0
$491$	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			0
$495$	−25.9835	+	45.0047i	−1.16787	+	2.02281i
$496$		0			0
$497$	10.7255	−	22.8737i	0.481104	−	1.02603i
$498$		0			0
$499$	−5.69271	+	9.86007i	−0.254841	+	0.441397i	−0.964852	−	0.262793i	$-0.915356\pi$
$499$	−5.69271	+	9.86007i	−0.254841	+	0.441397i	0.710011	+	0.704190i	$0.248690\pi$
$500$		0			0
$501$	1.56891	+	2.71743i	0.0700938	+	0.121406i
$502$		0			0
$503$	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			0
$507$	−0.129894	−	0.224983i	−0.00576880	−	0.00999186i
$508$		0			0
$509$	−9.64188	+	16.7002i	−0.427369	+	0.740225i	−0.996638	−	0.0819263i	$-0.973893\pi$
$509$	−9.64188	+	16.7002i	−0.427369	+	0.740225i	0.569269	+	0.822151i	$0.307226\pi$
$510$		0			0
$511$	2.84716	−	0.242991i	0.125951	−	0.0107493i
$512$		0			0
$513$	1.37759	−	2.38605i	0.0608219	−	0.105347i
$514$		0			0
$515$	−14.7315	−	25.5156i	−0.649146	−	1.12435i
$516$		0			0
$517$	15.9767			0.702653
$518$		0			0
$519$	−5.04241			−0.221337
$520$		0			0
$521$	−12.5584	−	21.7518i	−0.550193	−	0.952963i	−0.998260	−	0.0589629i	$-0.981221\pi$
$521$	−12.5584	−	21.7518i	−0.550193	−	0.952963i	0.448067	−	0.894000i	$-0.352113\pi$
$522$		0			0
$523$	−14.9824	+	25.9503i	−0.655134	+	1.13473i	0.326726	+	0.945119i	$0.394054\pi$
$523$	−14.9824	+	25.9503i	−0.655134	+	1.13473i	−0.981860	+	0.189606i	$0.939279\pi$
$524$		0			0
$525$	−4.11303	−	5.90069i	−0.179507	−	0.257527i
$526$		0			0
$527$	−6.39391	+	11.0746i	−0.278523	+	0.482416i
$528$		0			0
$529$	9.98583	+	17.2960i	0.434167	+	0.751999i
$530$		0			0
$531$	13.2147			0.573469
$532$		0			0
$533$	−8.11574			−0.351532
$534$		0			0
$535$	21.5863	+	37.3886i	0.933257	+	1.61645i
$536$		0			0
$537$	1.90222	−	3.29474i	0.0820869	−	0.142179i
$538$		0			0
$539$	10.9147	−	29.5954i	0.470130	−	1.27476i
$540$		0			0
$541$	−2.54987	+	4.41650i	−0.109627	+	0.189880i	−0.915619	−	0.402046i	$-0.868299\pi$
$541$	−2.54987	+	4.41650i	−0.109627	+	0.189880i	0.805992	+	0.591926i	$0.201632\pi$
$542$		0			0
$543$	1.22702	+	2.12525i	0.0526563	+	0.0912034i
$544$		0			0
$545$	−48.9451			−2.09658
$546$		0			0
$547$	−2.92025			−0.124861			−0.0624305	−	0.998049i	$-0.519885\pi$
$547$	−2.92025			−0.124861			−0.0624305	+	0.998049i	$0.519885\pi$
$548$		0			0
$549$	11.0624	+	19.1607i	0.472132	+	0.817757i
$550$		0			0
$551$	−1.47582	+	2.55620i	−0.0628722	+	0.108898i
$552$		0			0
$553$	1.19778	+	1.71838i	0.0509348	+	0.0730728i
$554$		0			0
$555$	−3.64927	+	6.32071i	−0.154903	+	0.268299i
$556$		0			0
$557$	−12.9937	−	22.5058i	−0.550561	−	0.953600i	−0.998234	−	0.0594024i	$-0.981080\pi$
$557$	−12.9937	−	22.5058i	−0.550561	−	0.953600i	0.447673	−	0.894197i	$-0.352253\pi$
$558$		0			0
$559$	−6.81353			−0.288182
$560$		0			0
$561$	2.67079			0.112761
$562$		0			0
$563$	1.82534	+	3.16159i	0.0769291	+	0.133245i	0.901924	−	0.431896i	$-0.142155\pi$
$563$	1.82534	+	3.16159i	0.0769291	+	0.133245i	−0.824994	+	0.565141i	$0.808822\pi$
$564$		0			0
$565$	3.24649	−	5.62308i	0.136581	−	0.236565i
$566$		0			0
$567$	22.1363	−	1.88922i	0.929637	−	0.0793397i
$568$		0			0
$569$	12.6766	−	21.9566i	0.531432	−	0.920468i	−0.467895	−	0.883784i	$-0.654987\pi$
$569$	12.6766	−	21.9566i	0.531432	−	0.920468i	0.999327	−	0.0366835i	$-0.0116793\pi$
$570$		0			0
$571$	13.8626	+	24.0108i	0.580133	+	1.00482i	0.995463	+	0.0951493i	$0.0303329\pi$
$571$	13.8626	+	24.0108i	0.580133	+	1.00482i	−0.415330	+	0.909671i	$0.636334\pi$
$572$		0			0
$573$	−3.26132			−0.136244
$574$		0			0
$575$	−18.2107			−0.759438
$576$		0			0
$577$	−19.7877	−	34.2733i	−0.823773	−	1.42682i	−0.902854	−	0.429948i	$-0.858532\pi$
$577$	−19.7877	−	34.2733i	−0.823773	−	1.42682i	0.0790809	−	0.996868i	$-0.474801\pi$
$578$		0			0
$579$	1.21693	−	2.10778i	0.0505737	−	0.0875963i
$580$		0			0
$581$	−8.02717	+	17.1191i	−0.333023	+	0.710221i
$582$		0			0
$583$	7.41204	−	12.8380i	0.306975	−	0.531697i
$584$		0			0
$585$	5.76606	+	9.98711i	0.238397	+	0.412916i
$586$		0			0
$587$	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
$590$		0			0
$591$	0.990153	+	1.71500i	0.0407295	+	0.0705455i
$592$		0			0
$593$	5.96149	−	10.3256i	0.244809	−	0.424021i	−0.717269	−	0.696796i	$-0.754608\pi$
$593$	5.96149	−	10.3256i	0.244809	−	0.424021i	0.962078	+	0.272775i	$0.0879415\pi$
$594$		0			0
$595$	10.0774	−	21.4914i	0.413131	−	0.881063i
$596$		0			0
$597$	1.75732	−	3.04377i	0.0719224	−	0.124573i
$598$		0			0
$599$	−17.8079	−	30.8442i	−0.727611	−	1.26026i	−0.957890	−	0.287135i	$-0.907297\pi$
$599$	−17.8079	−	30.8442i	−0.727611	−	1.26026i	0.230279	−	0.973125i	$-0.426036\pi$
$600$		0			0
$601$	38.9252			1.58779			0.793896	−	0.608054i	$-0.208050\pi$
$601$	38.9252			1.58779			0.793896	+	0.608054i	$0.208050\pi$
$602$		0			0
$603$	−37.1410			−1.51250
$604$		0			0
$605$	−18.2990	−	31.6947i	−0.743959	−	1.28857i
$606$		0			0
$607$	−6.84828	+	11.8616i	−0.277963	+	0.481446i	−0.970878	−	0.239573i	$-0.922993\pi$
$607$	−6.84828	+	11.8616i	−0.277963	+	0.481446i	0.692915	+	0.721019i	$0.256326\pi$
$608$		0			0
$609$	1.13075	−	0.0965037i	0.0458203	−	0.00391053i
$610$		0			0
$611$	1.77271	−	3.07043i	0.0717163	−	0.124216i
$612$		0			0
$613$	−1.58056	−	2.73761i	−0.0638382	−	0.110571i	0.832340	−	0.554266i	$-0.187001\pi$
$613$	−1.58056	−	2.73761i	−0.0638382	−	0.110571i	−0.896178	+	0.443695i	$0.853667\pi$
$614$		0			0
$615$	−8.29120			−0.334334
$616$		0			0
$617$	20.9297			0.842597			0.421299	−	0.906922i	$-0.361574\pi$
$617$	20.9297			0.842597			0.421299	+	0.906922i	$0.361574\pi$
$618$		0			0
$619$	15.4772	+	26.8073i	0.622082	+	1.07748i	0.989097	+	0.147262i	$0.0470461\pi$
$619$	15.4772	+	26.8073i	0.622082	+	1.07748i	−0.367016	+	0.930215i	$0.619621\pi$
$620$		0			0
$621$	−1.34100	+	2.32269i	−0.0538127	+	0.0932063i
$622$		0			0
$623$	17.0440	+	24.4520i	0.682855	+	0.979648i
$624$		0			0
$625$	−16.0927	+	27.8734i	−0.643708	+	1.11494i
$626$		0			0
$627$	1.04640	+	1.81242i	0.0417892	+	0.0723810i
$628$		0			0
$629$	−16.2986			−0.649866
$630$		0			0
$631$	15.1218			0.601988			0.300994	−	0.953626i	$-0.402682\pi$
$631$	15.1218			0.601988			0.300994	+	0.953626i	$0.402682\pi$
$632$		0			0
$633$	−2.05226	−	3.55462i	−0.0815700	−	0.141283i
$634$		0			0
$635$	−8.83433	+	15.3015i	−0.350580	+	0.607222i
$636$		0			0
$637$	−4.47665	−	5.38141i	−0.177371	−	0.213219i
$638$		0			0
$639$	−14.0008	+	24.2501i	−0.553864	+	0.959320i
$640$		0			0
$641$	23.6207	+	40.9123i	0.932962	+	1.61594i	0.778229	+	0.627981i	$0.216118\pi$
$641$	23.6207	+	40.9123i	0.932962	+	1.61594i	0.154733	+	0.987956i	$0.450548\pi$
$642$		0			0
$643$	−39.9249			−1.57448			−0.787241	−	0.616645i	$-0.788491\pi$
$643$	−39.9249			−1.57448			−0.787241	+	0.616645i	$0.788491\pi$
$644$		0			0
$645$	−6.96085			−0.274083
$646$		0			0
$647$	−14.9139	−	25.8317i	−0.586327	−	1.01555i	−0.994709	−	0.102736i	$-0.967240\pi$
$647$	−14.9139	−	25.8317i	−0.586327	−	1.01555i	0.408382	−	0.912811i	$-0.366093\pi$
$648$		0			0
$649$	−10.1533	+	17.5859i	−0.398550	+	0.690309i
$650$		0			0
$651$	2.20308	+	3.16062i	0.0863456	+	0.123875i
$652$		0			0
$653$	−12.5774	+	21.7848i	−0.492194	+	0.852504i	−0.999960	−	0.00899079i	$-0.997138\pi$
$653$	−12.5774	+	21.7848i	−0.492194	+	0.852504i	0.507766	+	0.861495i	$0.330471\pi$
$654$		0			0
$655$	−24.8863	−	43.1044i	−0.972390	−	1.68423i
$656$		0			0
$657$	−3.16722			−0.123565
$658$		0			0
$659$	−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	0.941516	−	0.336969i	$-0.109402\pi$
$661$	4.60037	+	7.96808i	0.178934	+	0.309922i	−0.762582	+	0.646892i	$0.776069\pi$
$662$		0			0
$663$	0.296342	−	0.513279i	0.0115090	−	0.0199341i
$664$		0			0
$665$	18.5325	−	1.58165i	0.718659	−	0.0613338i
$666$		0			0
$667$	1.43663	−	2.48832i	0.0556266	−	0.0963482i
$668$		0			0
$669$	2.91920	+	5.05620i	0.112863	+	0.195484i
$670$		0			0
$671$	−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	$0.391397\pi$
$674$		0			0
$675$	8.06403	+	13.9673i	0.310385	+	0.537602i
$676$		0			0
$677$	−24.9913	+	43.2861i	−0.960492	+	1.66362i	−0.239225	+	0.970964i	$0.576893\pi$
$677$	−24.9913	+	43.2861i	−0.960492	+	1.66362i	−0.721267	+	0.692657i	$0.756440\pi$
$678$		0			0
$679$	9.89974	−	21.1126i	0.379917	−	0.810229i
$680$		0			0
$681$	−1.19535	+	2.07041i	−0.0458059	+	0.0793382i
$682$		0			0
$683$	16.8077	+	29.1117i	0.643128	+	1.11393i	0.984731	+	0.174086i	$0.0556969\pi$
$683$	16.8077	+	29.1117i	0.643128	+	1.11393i	−0.341603	+	0.939844i	$0.610970\pi$
$684$		0			0
$685$	−36.5189			−1.39532
$686$		0			0
$687$	3.97274			0.151570
$688$		0			0
$689$	−1.64483	−	2.84892i	−0.0626629	−	0.108535i
$690$		0			0
$691$	−7.56545	+	13.1038i	−0.287803	+	0.498490i	−0.973285	−	0.229600i	$-0.926258\pi$
$691$	−7.56545	+	13.1038i	−0.287803	+	0.498490i	0.685482	+	0.728090i	$0.259592\pi$
$692$		0			0
$693$	−14.8433	+	31.6555i	−0.563851	+	1.20249i
$694$		0			0
$695$	−7.86502	+	13.6226i	−0.298337	+	0.516735i
$696$		0			0
$697$	−9.25766	−	16.0347i	−0.350659	−	0.607359i
$698$		0			0
$699$	−2.09280			−0.0791570
$700$		0			0
$701$	2.02467			0.0764705			0.0382353	−	0.999269i	$-0.487826\pi$
$701$	2.02467			0.0764705			0.0382353	+	0.999269i	$0.487826\pi$
$702$		0			0
$703$	−6.38567	−	11.0603i	−0.240840	−	0.417147i
$704$		0			0
$705$	1.81104	−	3.13681i	0.0682077	−	0.118139i
$706$		0			0
$707$	−37.7423	+	3.22111i	−1.41945	+	0.121142i
$708$		0			0
$709$	15.2276	−	26.3751i	0.571886	−	0.990536i	−0.424486	−	0.905434i	$-0.639545\pi$
$709$	15.2276	−	26.3751i	0.571886	−	0.990536i	0.996372	−	0.0851015i	$-0.0271215\pi$
$710$		0			0
$711$	−1.16083	−	2.01062i	−0.0435346	−	0.0754041i
$712$		0			0
$713$	9.75429			0.365301
$714$		0			0
$715$	−17.7210			−0.662727
$716$		0			0
$717$	2.82206	+	4.88795i	0.105392	+	0.182544i
$718$		0			0
$719$	−12.2123	+	21.1523i	−0.455442	+	0.788848i	−0.998713	−	0.0507089i	$-0.983852\pi$
$719$	−12.2123	+	21.1523i	−0.455442	+	0.788848i	0.543272	+	0.839557i	$0.317185\pi$
$720$		0			0
$721$	−11.3351	−	16.2617i	−0.422139	−	0.605616i
$722$		0			0
$723$	2.66257	−	4.61170i	0.0990220	−	0.171511i
$724$		0			0
$725$	−8.63908	−	14.9633i	−0.320848	−	0.555724i
$726$		0			0
$727$	3.09307			0.114716			0.0573578	−	0.998354i	$-0.481732\pi$
$727$	3.09307			0.114716			0.0573578	+	0.998354i	$0.481732\pi$
$728$		0			0
$729$	−23.4236			−0.867539
$730$		0			0
$731$	−7.77223	−	13.4619i	−0.287466	−	0.497906i
$732$		0			0
$733$	4.20713	−	7.28697i	0.155394	−	0.269150i	−0.777808	−	0.628501i	$-0.783669\pi$
$733$	4.20713	−	7.28697i	0.155394	−	0.269150i	0.933202	+	0.359351i	$0.117002\pi$
$734$		0			0
$735$	−4.57344	−	5.49776i	−0.168694	−	0.202788i
$736$		0			0
$737$	28.5365	−	49.4267i	1.05116	−	1.82066i
$738$		0			0
$739$	−3.61379	−	6.25927i	−0.132936	−	0.230251i	0.791871	−	0.610688i	$-0.209107\pi$
$739$	−3.61379	−	6.25927i	−0.132936	−	0.230251i	−0.924807	+	0.380437i	$0.875774\pi$
$740$		0			0
$741$	0.464419			0.0170609
$742$		0			0
$743$	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
$746$		0			0
$747$	10.4785	−	18.1493i	0.383388	−	0.664047i
$748$		0			0
$749$	16.6095	+	23.8285i	0.606897	+	0.870676i
$750$		0			0
$751$	14.6221	−	25.3262i	0.533568	−	0.924168i	−0.465663	−	0.884962i	$-0.654184\pi$
$751$	14.6221	−	25.3262i	0.533568	−	0.924168i	0.999231	−	0.0392053i	$-0.0124826\pi$
$752$		0			0
$753$	0.338856	+	0.586916i	0.0123486	+	0.0213884i
$754$		0			0
$755$	−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	$0.631298\pi$
$758$		0			0
$759$	−1.01861	−	1.76429i	−0.0369733	−	0.0640397i
$760$		0			0
$761$	−8.90805	+	15.4292i	−0.322917	+	0.559308i	−0.981089	−	0.193560i	$-0.937997\pi$
$761$	−8.90805	+	15.4292i	−0.322917	+	0.559308i	0.658172	+	0.752868i	$0.271330\pi$
$762$		0			0
$763$	−32.8105	+	2.80020i	−1.18782	+	0.101374i
$764$		0			0
$765$	−13.1547	+	22.7847i	−0.475611	+	0.823782i
$766$		0			0
$767$	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	$0.565352\pi$
$770$		0			0
$771$	−2.33725			−0.0841741
$772$		0			0
$773$	0.964104	+	1.66988i	0.0346764	+	0.0600613i	0.882843	−	0.469669i	$-0.155627\pi$
$773$	0.964104	+	1.66988i	0.0346764	+	0.0600613i	−0.848166	+	0.529730i	$0.822293\pi$
$774$		0			0
$775$	29.3284	−	50.7982i	1.05351	−	1.82472i
$776$		0			0
$777$	−2.08468	+	4.44588i	−0.0747875	+	0.159495i
$778$		0			0
$779$	7.25418	−	12.5646i	0.259908	−	0.450174i
$780$		0			0
$781$	−21.5145	−	37.2642i	−0.769849	−	1.33342i
$782$		0			0
$783$	−2.54467			−0.0909392
$784$		0			0
$785$	−42.2003			−1.50619
$786$		0			0
$787$	2.76577	+	4.79046i	0.0985892	+	0.170761i	0.911101	−	0.412183i	$-0.135234\pi$
$787$	2.76577	+	4.79046i	0.0985892	+	0.170761i	−0.812512	+	0.582945i	$0.801900\pi$
$788$		0			0
$789$	0.186258	−	0.322609i	0.00663097	−	0.0114852i
$790$		0			0
$791$	1.85459	−	3.95518i	0.0659415	−	0.140630i
$792$		0			0
$793$	−3.77234	+	6.53388i	−0.133960	+	0.232025i
$794$		0			0
$795$	−1.68039	−	2.91052i	−0.0595973	−	0.103225i
$796$		0			0
$797$	−13.8038			−0.488955			−0.244477	−	0.969655i	$-0.578616\pi$
$797$	−13.8038			−0.488955			−0.244477	+	0.969655i	$0.578616\pi$
$798$		0			0
$799$	8.08857			0.286153
$800$		0			0
$801$	−16.5183	−	28.6105i	−0.583644	−	1.01090i
$802$		0			0
$803$	2.43347	−	4.21490i	0.0858754	−	0.148741i
$804$		0			0
$805$	−18.0404	+	1.53965i	−0.635839	+	0.0542656i
$806$		0			0
$807$	1.06102	−	1.83774i	0.0373496	−	0.0646914i
$808$		0			0
$809$	−14.1498	−	24.5082i	−0.497480	−	0.861661i	0.502515	−	0.864568i	$-0.332408\pi$
$809$	−14.1498	−	24.5082i	−0.497480	−	0.861661i	−0.999996	+	0.00290700i	$0.999075\pi$
$810$		0			0
$811$	12.2124			0.428837			0.214418	−	0.976742i	$-0.431214\pi$
$811$	12.2124			0.428837			0.214418	+	0.976742i	$0.431214\pi$
$812$		0			0
$813$	0.0551575			0.00193446
$814$		0			0
$815$	4.66473	+	8.07955i	0.163398	+	0.283014i
$816$		0			0
$817$	6.09022	−	10.5486i	0.213070	−	0.369048i
$818$		0			0
$819$	4.43667	+	6.36500i	0.155030	+	0.222411i
$820$		0			0
$821$	20.7005	−	35.8544i	0.722453	−	1.25133i	−0.237560	−	0.971373i	$-0.576348\pi$
$821$	20.7005	−	35.8544i	0.722453	−	1.25133i	0.960014	−	0.279953i	$-0.0903189\pi$
$822$		0			0
$823$	23.5876	+	40.8550i	0.822213	+	1.42411i	0.904031	+	0.427467i	$0.140594\pi$
$823$	23.5876	+	40.8550i	0.822213	+	1.42411i	−0.0818184	+	0.996647i	$0.526073\pi$
$824$		0			0
$825$	−12.2507			−0.426515
$826$		0			0
$827$	−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	0.871501	−	0.490393i	$-0.163147\pi$
$829$	0.318376	+	0.551444i	0.0110577	+	0.0191524i	−0.860444	+	0.509546i	$0.829813\pi$
$830$		0			0
$831$	−2.98431	+	5.16898i	−0.103525	+	0.179310i
$832$		0			0
$833$	5.52583	−	14.9834i	0.191459	−	0.519143i
$834$		0			0
$835$	23.7492	−	41.1348i	0.821874	−	1.42353i
$836$		0			0
$837$	−4.31938	−	7.48139i	−0.149300	−	0.258595i
$838$		0			0
$839$	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			0
$843$	0.0448431	+	0.0776705i	0.00154448	+	0.00267511i
$844$		0			0
$845$	−1.96625	+	3.40565i	−0.0676412	+	0.117158i
$846$		0			0
$847$	−14.0800	−	20.1997i	−0.483796	−	0.694071i
$848$		0			0
$849$	−3.76323	+	6.51810i	−0.129154	+	0.223701i
$850$		0			0
$851$	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	$0.463146\pi$
$854$		0			0
$855$	−20.6158			−0.705045
$856$		0			0
$857$	22.5134	+	38.9943i	0.769043	+	1.33202i	0.938082	+	0.346412i	$0.112600\pi$
$857$	22.5134	+	38.9943i	0.769043	+	1.33202i	−0.169040	+	0.985609i	$0.554067\pi$
$858$		0			0
$859$	−18.3635	+	31.8065i	−0.626554	+	1.08522i	0.361684	+	0.932301i	$0.382202\pi$
$859$	−18.3635	+	31.8065i	−0.626554	+	1.08522i	−0.988238	+	0.152923i	$0.951131\pi$
$860$		0			0
$861$	−5.55803	+	0.474349i	−0.189417	+	0.0161658i
$862$		0			0
$863$	−21.7137	+	37.6093i	−0.739144	+	1.28024i	0.213737	+	0.976891i	$0.431437\pi$
$863$	−21.7137	+	37.6093i	−0.739144	+	1.28024i	−0.952881	+	0.303344i	$0.901897\pi$
$864$		0			0
$865$	38.1644	+	66.1027i	1.29763	+	2.24756i
$866$		0			0
$867$	−3.06425			−0.104067
$868$		0			0
$869$	3.56761			0.121023
$870$		0			0
$871$	−6.33263	−	10.9684i	−0.214573	−	0.371651i
$872$		0			0
$873$	−12.9229	+	22.3831i	−0.437373	+	0.757553i
$874$		0			0
$875$	−24.1382	+	51.4782i	−0.816020	+	1.74028i
$876$		0			0
$877$	−20.0040	+	34.6480i	−0.675488	+	1.16998i	0.300838	+	0.953675i	$0.402734\pi$
$877$	−20.0040	+	34.6480i	−0.675488	+	1.16998i	−0.976326	+	0.216304i	$0.930600\pi$
$878$		0			0
$879$	−4.09721	−	7.09658i	−0.138196	−	0.239362i
$880$		0			0
$881$	35.4308			1.19370			0.596848	−	0.802355i	$-0.296420\pi$
$881$	35.4308			1.19370			0.596848	+	0.802355i	$0.296420\pi$
$882$		0			0
$883$	−22.6654			−0.762751			−0.381375	−	0.924420i	$-0.624549\pi$
$883$	−22.6654			−0.762751			−0.381375	+	0.924420i	$0.624549\pi$
$884$		0			0
$885$	2.30185	+	3.98692i	0.0773759	+	0.134019i
$886$		0			0
$887$	22.3440	−	38.7010i	0.750240	−	1.29945i	−0.197467	−	0.980310i	$-0.563271\pi$
$887$	22.3440	−	38.7010i	0.750240	−	1.29945i	0.947706	−	0.319144i	$-0.103395\pi$
$888$		0			0
$889$	−5.04670	+	10.7628i	−0.169261	+	0.360974i
$890$		0			0
$891$	18.9199	−	32.7703i	0.633841	−	1.09784i
$892$		0			0
$893$	3.16905	+	5.48896i	0.106048	+	0.183681i
$894$		0			0
$895$	−57.5892			−1.92499
$896$		0			0
$897$	−0.452087			−0.0150947
$898$		0			0
$899$	4.62740	+	8.01489i	0.154332	+	0.267312i
$900$		0			0
$901$	3.75252	−	6.49956i	0.125015	−	0.216532i
$902$		0			0
$903$	−4.66622	+	0.398238i	−0.155282	+	0.0132525i
$904$		0			0
$905$	18.5738	−	32.1707i	0.617413	−	1.06939i
$906$		0			0
$907$	27.2374	+	47.1766i	0.904403	+	1.56647i	0.821717	+	0.569896i	$0.193017\pi$
$907$	27.2374	+	47.1766i	0.904403	+	1.56647i	0.0826860	+	0.996576i	$0.473650\pi$
$908$		0			0
$909$	41.9851			1.39256
$910$		0			0
$911$	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			0
$915$	−3.85390	+	6.67514i	−0.127406	+	0.220673i
$916$		0			0
$917$	−19.1487	−	27.4714i	−0.632345	−	0.907184i
$918$		0			0
$919$	−24.1440	+	41.8186i	−0.796437	+	1.37947i	0.125486	+	0.992095i	$0.459951\pi$
$919$	−24.1440	+	41.8186i	−0.796437	+	1.37947i	−0.921923	+	0.387374i	$0.873382\pi$
$920$		0			0
$921$	−2.36331	−	4.09337i	−0.0778737	−	0.134881i
$922$		0			0
$923$	−9.54869			−0.314299
$924$		0			0
$925$	74.7601			2.45810
$926$		0			0
$927$	10.9854	+	19.0273i	0.360808	+	0.624937i
$928$		0			0
$929$	−21.6577	+	37.5122i	−0.710566	+	1.23074i	0.254079	+	0.967183i	$0.418228\pi$
$929$	−21.6577	+	37.5122i	−0.710566	+	1.23074i	−0.964645	+	0.263553i	$0.915106\pi$
$930$		0			0
$931$	12.3328	−	2.12053i	0.404191	−	0.0694975i
$932$		0			0
$933$	−0.0489212	+	0.0847339i	−0.00160161	+	0.00277406i
$934$		0			0
$935$	−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	$0.708020\pi$
$938$		0			0
$939$	2.85463			0.0931574
$940$		0			0
$941$	−7.98754	−	13.8348i	−0.260386	−	0.451002i	0.705958	−	0.708253i	$-0.250517\pi$
$941$	−7.98754	−	13.8348i	−0.260386	−	0.451002i	−0.966345	+	0.257251i	$0.917183\pi$
$942$		0			0
$943$	−7.06155	+	12.2310i	−0.229956	+	0.398295i
$944$		0			0
$945$	9.16950	+	13.1549i	0.298284	+	0.427929i
$946$		0			0
$947$	13.8786	−	24.0384i	0.450994	−	0.781144i	−0.547454	−	0.836836i	$-0.684403\pi$
$947$	13.8786	−	24.0384i	0.450994	−	0.781144i	0.998448	+	0.0556912i	$0.0177363\pi$
$948$		0			0
$949$	−0.540019	−	0.935340i	−0.0175298	−	0.0303624i
$950$		0			0
$951$	6.80142			0.220551
$952$		0			0
$953$	12.0303			0.389700			0.194850	−	0.980833i	$-0.437578\pi$
$953$	12.0303			0.389700			0.194850	+	0.980833i	$0.437578\pi$
$954$		0			0
$955$	24.6839	+	42.7537i	0.798751	+	1.38348i
$956$		0			0
$957$	0.966454	−	1.67395i	0.0312410	−	0.0541110i
$958$		0			0
$959$	−24.4805	+	2.08929i	−0.790518	+	0.0674666i
$960$		0			0
$961$	−0.209310	+	0.362536i	−0.00675194	+	0.0116947i
$962$		0			0
$963$	−16.0971	−	27.8810i	−0.518722	−	0.898453i
$964$		0			0
$965$	−36.8421			−1.18599
$966$		0			0
$967$	−5.40788			−0.173906			−0.0869528	−	0.996212i	$-0.527713\pi$
$967$	−5.40788			−0.173906			−0.0869528	+	0.996212i	$0.527713\pi$
$968$		0			0
$969$	0.529765	+	0.917580i	0.0170185	+	0.0294769i
$970$		0			0
$971$	21.1376	−	36.6114i	0.678338	−	1.17492i	−0.297143	−	0.954833i	$-0.596034\pi$
$971$	21.1376	−	36.6114i	0.678338	−	1.17492i	0.975481	−	0.220083i	$-0.0706329\pi$
$972$		0			0
$973$	−4.49297	+	9.58192i	−0.144038	+	0.307182i
$974$		0			0
$975$	−1.35930	+	2.35437i	−0.0435323	+	0.0754001i
$976$		0			0
$977$	5.41508	+	9.37920i	0.173244	+	0.300067i	0.939552	−	0.342406i	$-0.111242\pi$
$977$	5.41508	+	9.37920i	0.173244	+	0.300067i	−0.766308	+	0.642473i	$0.777908\pi$
$978$		0			0
$979$	50.7660			1.62249
$980$		0			0
$981$	36.4988			1.16532
$982$		0			0
$983$	10.7805	+	18.6723i	0.343844	+	0.595555i	0.985143	−	0.171736i	$-0.0549375\pi$
$983$	10.7805	+	18.6723i	0.343844	+	0.595555i	−0.641299	+	0.767291i	$0.721604\pi$
$984$		0			0
$985$	14.9883	−	25.9605i	0.477567	−	0.827170i
$986$		0			0
$987$	1.03458	−	2.20638i	0.0329309	−	0.0702300i
$988$		0			0
$989$	−5.92850	+	10.2685i	−0.188515	+	0.326518i
$990$		0			0
$991$	4.31312	+	7.47054i	0.137011	+	0.237310i	0.926364	−	0.376630i	$-0.122917\pi$
$991$	4.31312	+	7.47054i	0.137011	+	0.237310i	−0.789353	+	0.613940i	$0.789584\pi$
$992$		0			0
$993$	8.85703			0.281069
$994$		0			0
$995$	−53.2024			−1.68663
$996$		0			0
$997$	−10.8484	−	18.7899i	−0.343571	−	0.595082i	0.641522	−	0.767105i	$-0.278303\pi$
$997$	−10.8484	−	18.7899i	−0.343571	−	0.595082i	−0.985093	+	0.172022i	$0.944970\pi$
$998$		0			0
$999$	5.50521	−	9.53531i	0.174177	−	0.301684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.p.625.3		10
4.3	odd	2		91.2.e.c.79.4	yes	10
7.4	even	3	inner	1456.2.r.p.417.3		10
12.11	even	2		819.2.j.h.352.2		10
28.3	even	6		637.2.e.m.508.4		10
28.11	odd	6		91.2.e.c.53.4	✓	10
28.19	even	6		637.2.a.k.1.2		5
28.23	odd	6		637.2.a.l.1.2		5
28.27	even	2		637.2.e.m.79.4		10
52.51	odd	2		1183.2.e.f.170.2		10
84.11	even	6		819.2.j.h.235.2		10
84.23	even	6		5733.2.a.bl.1.4		5
84.47	odd	6		5733.2.a.bm.1.4		5
364.51	odd	6		8281.2.a.bw.1.4		5
364.103	even	6		8281.2.a.bx.1.4		5
364.207	odd	6		1183.2.e.f.508.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.4	✓	10	28.11	odd	6
91.2.e.c.79.4	yes	10	4.3	odd	2
637.2.a.k.1.2		5	28.19	even	6
637.2.a.l.1.2		5	28.23	odd	6
637.2.e.m.79.4		10	28.27	even	2
637.2.e.m.508.4		10	28.3	even	6
819.2.j.h.235.2		10	84.11	even	6
819.2.j.h.352.2		10	12.11	even	2
1183.2.e.f.170.2		10	52.51	odd	2
1183.2.e.f.508.2		10	364.207	odd	6
1456.2.r.p.417.3		10	7.4	even	3	inner
1456.2.r.p.625.3		10	1.1	even	1	trivial
5733.2.a.bl.1.4		5	84.23	even	6
5733.2.a.bm.1.4		5	84.47	odd	6
8281.2.a.bw.1.4		5	364.51	odd	6
8281.2.a.bx.1.4		5	364.103	even	6

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.129894 - 0.224983i) q^{3} +(-1.96625 + 3.40565i) q^{5} +(-1.12324 + 2.39548i) q^{7} +(1.46625 - 2.53963i) q^{9} +O(q^{10})\)	\(q+(-0.129894 - 0.224983i) q^{3} +(-1.96625 + 3.40565i) q^{5} +(-1.12324 + 2.39548i) q^{7} +(1.46625 - 2.53963i) q^{9} +(2.25314 + 3.90255i) q^{11} +1.00000 q^{13} +1.02162 q^{15} +(1.14070 + 1.97576i) q^{17} +(-0.893841 + 1.54818i) q^{19} +(0.684846 - 0.0584481i) q^{21} +(0.870106 - 1.50707i) q^{23} +(-5.23232 - 9.06264i) q^{25} -1.54120 q^{27} +1.65110 q^{29} +(2.80262 + 4.85427i) q^{31} +(0.585339 - 1.01384i) q^{33} +(-5.94959 - 8.53550i) q^{35} +(-3.57204 + 6.18695i) q^{37} +(-0.129894 - 0.224983i) q^{39} -8.11574 q^{41} -6.81353 q^{43} +(5.76606 + 9.98711i) q^{45} +(1.77271 - 3.07043i) q^{47} +(-4.47665 - 5.38141i) q^{49} +(0.296342 - 0.513279i) q^{51} +(-1.64483 - 2.84892i) q^{53} -17.7210 q^{55} +0.464419 q^{57} +(2.25314 + 3.90255i) q^{59} +(-3.77234 + 6.53388i) q^{61} +(4.43667 + 6.36500i) q^{63} +(-1.96625 + 3.40565i) q^{65} +(-6.33263 - 10.9684i) q^{67} -0.452087 q^{69} -9.54869 q^{71} +(-0.540019 - 0.935340i) q^{73} +(-1.35930 + 2.35437i) q^{75} +(-11.8793 + 1.01384i) q^{77} +(0.395849 - 0.685630i) q^{79} +(-4.19857 - 7.27214i) q^{81} +7.14643 q^{83} -8.97166 q^{85} +(-0.214468 - 0.371470i) q^{87} +(5.63281 - 9.75631i) q^{89} +(-1.12324 + 2.39548i) q^{91} +(0.728087 - 1.26108i) q^{93} +(-3.51504 - 6.08823i) q^{95} -8.81353 q^{97} +13.2147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99}+O(q^{100}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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