LMFDB - Embedded newform 88.2.i.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(9,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("88.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.i (of order $5$, degree $4$, 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:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$-0.390899 - 1.20306i$ of defining polynomial
Character	$\chi$	$=$	88.25
Dual form			88.2.i.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.632489 - 1.94660i) q^{3} +(0.132489 + 0.0962586i) q^{5} +(1.08188 - 3.32969i) q^{7} +(-0.962157 + 0.699048i) q^{9} +(-0.605270 + 3.26093i) q^{11} +(-2.17926 + 1.58333i) q^{13} +(0.103579 - 0.318785i) q^{15} +(6.12970 + 4.45349i) q^{17} +(1.42705 + 4.39201i) q^{19} -7.16586 q^{21} -0.706114 q^{23} +(-1.53680 - 4.72978i) q^{25} +(-2.99831 - 2.17840i) q^{27} +(-0.317950 + 0.978551i) q^{29} +(-4.36856 + 3.17394i) q^{31} +(6.73055 - 0.884280i) q^{33} +(0.463848 - 0.337006i) q^{35} +(3.58293 - 11.0271i) q^{37} +(4.46047 + 3.24072i) q^{39} +(-0.0867577 - 0.267013i) q^{41} +4.31175 q^{43} -0.194764 q^{45} +(1.80113 + 5.54330i) q^{47} +(-4.25326 - 3.09017i) q^{49} +(4.79220 - 14.7489i) q^{51} +(-7.98659 + 5.80260i) q^{53} +(-0.394084 + 0.373773i) q^{55} +(7.64689 - 5.55579i) q^{57} +(-0.954915 + 2.93893i) q^{59} +(-5.60801 - 4.07446i) q^{61} +(1.28667 + 3.95998i) q^{63} -0.441137 q^{65} +1.91665 q^{67} +(0.446609 + 1.37452i) q^{69} +(-9.84407 - 7.15214i) q^{71} +(-3.51550 + 10.8196i) q^{73} +(-8.23497 + 5.98306i) q^{75} +(10.2031 + 5.54330i) q^{77} +(1.39747 - 1.01532i) q^{79} +(-3.44661 + 10.6076i) q^{81} +(-3.81006 - 2.76817i) q^{83} +(0.383429 + 1.18007i) q^{85} +2.10595 q^{87} +6.31175 q^{89} +(2.91429 + 8.96925i) q^{91} +(8.94146 + 6.49635i) q^{93} +(-0.233701 + 0.719257i) q^{95} +(-5.66755 + 4.11771i) q^{97} +(-1.69718 - 3.56064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9} + 7 q^{11} + 7 q^{13} - 13 q^{15} + q^{17} - 2 q^{19} - 2 q^{21} - 4 q^{23} - 33 q^{25} - 22 q^{27} + 17 q^{29} - 13 q^{31} + 16 q^{33} + 11 q^{35} + q^{37}+ \cdots - 27 q^{99}+O(q^{100}) $ 8 * q - q^3 - 3 * q^5 + 7 * q^7 - 13 * q^9 + 7 * q^11 + 7 * q^13 - 13 * q^15 + q^17 - 2 * q^19 - 2 * q^21 - 4 * q^23 - 33 * q^25 - 22 * q^27 + 17 * q^29 - 13 * q^31 + 16 * q^33 + 11 * q^35 + q^37 + 39 * q^39 + 9 * q^41 + 6 * q^43 + 44 * q^45 - q^47 + 3 * q^49 + 38 * q^51 - 33 * q^53 + 13 * q^55 - 6 * q^57 - 30 * q^59 - 9 * q^61 - 10 * q^63 - 10 * q^65 - 10 * q^67 - 38 * q^69 - 25 * q^71 - 7 * q^73 - 6 * q^75 - 7 * q^77 - q^79 + 14 * q^81 + 39 * q^85 - 6 * q^87 + 22 * q^89 + 7 * q^91 - 5 * q^93 + 7 * q^95 + 8 * q^97 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.632489	−	1.94660i	−0.365167	−	1.12387i	−0.949876	−	0.312626i	$-0.898791\pi$
$3$	−0.632489	−	1.94660i	−0.365167	−	1.12387i	0.584709	−	0.811243i	$-0.301209\pi$
$4$		0			0
$5$	0.132489	+	0.0962586i	0.0592507	+	0.0430481i	0.617016	−	0.786950i	$-0.288341\pi$
$5$	0.132489	+	0.0962586i	0.0592507	+	0.0430481i	−0.557766	+	0.829998i	$0.688341\pi$
$6$		0			0
$7$	1.08188	−	3.32969i	0.408913	−	1.25851i	−0.508670	−	0.860962i	$-0.669863\pi$
$7$	1.08188	−	3.32969i	0.408913	−	1.25851i	0.917583	−	0.397544i	$-0.130137\pi$
$8$		0			0
$9$	−0.962157	+	0.699048i	−0.320719	+	0.233016i
$10$		0			0
$11$	−0.605270	+	3.26093i	−0.182496	+	0.983207i
$11$	−0.605270	+	3.26093i	−0.182496	+	0.983207i
$12$		0			0
$13$	−2.17926	+	1.58333i	−0.604419	+	0.439136i	−0.847445	−	0.530884i	$-0.821860\pi$
$13$	−2.17926	+	1.58333i	−0.604419	+	0.439136i	0.243025	+	0.970020i	$0.421860\pi$
$14$		0			0
$15$	0.103579	−	0.318785i	0.0267441	−	0.0823098i
$16$		0			0
$17$	6.12970	+	4.45349i	1.48667	+	1.08013i	0.975330	+	0.220753i	$0.0708513\pi$
$17$	6.12970	+	4.45349i	1.48667	+	1.08013i	0.511342	+	0.859378i	$0.329149\pi$
$18$		0			0
$19$	1.42705	+	4.39201i	0.327388	+	1.00760i	0.970351	+	0.241699i	$0.0777048\pi$
$19$	1.42705	+	4.39201i	0.327388	+	1.00760i	−0.642963	+	0.765897i	$0.722295\pi$
$20$		0			0
$21$	−7.16586			−1.56372
$22$		0			0
$23$	−0.706114			−0.147235			−0.0736174	−	0.997287i	$-0.523454\pi$
$23$	−0.706114			−0.147235			−0.0736174	+	0.997287i	$0.523454\pi$
$24$		0			0
$25$	−1.53680	−	4.72978i	−0.307359	−	0.945955i
$26$		0			0
$27$	−2.99831	−	2.17840i	−0.577025	−	0.419233i
$28$		0			0
$29$	−0.317950	+	0.978551i	−0.0590419	+	0.181712i	−0.976228	−	0.216748i	$-0.930455\pi$
$29$	−0.317950	+	0.978551i	−0.0590419	+	0.181712i	0.917186	+	0.398460i	$0.130455\pi$
$30$		0			0
$31$	−4.36856	+	3.17394i	−0.784616	+	0.570057i	−0.906361	−	0.422505i	$-0.861151\pi$
$31$	−4.36856	+	3.17394i	−0.784616	+	0.570057i	0.121745	+	0.992561i	$0.461151\pi$
$32$		0			0
$33$	6.73055	−	0.884280i	1.17164	−	0.153933i
$34$		0			0
$35$	0.463848	−	0.337006i	0.0784047	−	0.0569643i
$36$		0			0
$37$	3.58293	−	11.0271i	0.589030	−	1.81285i	0.00658248	−	0.999978i	$-0.497905\pi$
$37$	3.58293	−	11.0271i	0.589030	−	1.81285i	0.582447	−	0.812869i	$-0.302095\pi$
$38$		0			0
$39$	4.46047	+	3.24072i	0.714246	+	0.518930i
$40$		0			0
$41$	−0.0867577	−	0.267013i	−0.0135493	−	0.0417004i	0.944053	−	0.329793i	$-0.106979\pi$
$41$	−0.0867577	−	0.267013i	−0.0135493	−	0.0417004i	−0.957603	+	0.288093i	$0.906979\pi$
$42$		0			0
$43$	4.31175			0.657536			0.328768	−	0.944411i	$-0.393367\pi$
$43$	4.31175			0.657536			0.328768	+	0.944411i	$0.393367\pi$
$44$		0			0
$45$	−0.194764			−0.0290337
$46$		0			0
$47$	1.80113	+	5.54330i	0.262722	+	0.808574i	0.992210	+	0.124580i	$0.0397584\pi$
$47$	1.80113	+	5.54330i	0.262722	+	0.808574i	−0.729488	+	0.683994i	$0.760242\pi$
$48$		0			0
$49$	−4.25326	−	3.09017i	−0.607608	−	0.441453i
$50$		0			0
$51$	4.79220	−	14.7489i	0.671042	−	2.06525i
$52$		0			0
$53$	−7.98659	+	5.80260i	−1.09704	+	0.797048i	−0.980575	−	0.196146i	$-0.937157\pi$
$53$	−7.98659	+	5.80260i	−1.09704	+	0.797048i	−0.116468	+	0.993194i	$0.537157\pi$
$54$		0			0
$55$	−0.394084	+	0.373773i	−0.0531382	+	0.0503996i
$56$		0			0
$57$	7.64689	−	5.55579i	1.01286	−	0.735883i
$58$		0			0
$59$	−0.954915	+	2.93893i	−0.124319	+	0.382616i	−0.993776	−	0.111393i	$-0.964469\pi$
$59$	−0.954915	+	2.93893i	−0.124319	+	0.382616i	0.869457	+	0.494008i	$0.164469\pi$
$60$		0			0
$61$	−5.60801	−	4.07446i	−0.718032	−	0.521681i	0.167723	−	0.985834i	$-0.446359\pi$
$61$	−5.60801	−	4.07446i	−0.718032	−	0.521681i	−0.885755	+	0.464154i	$0.846359\pi$
$62$		0			0
$63$	1.28667	+	3.95998i	0.162106	+	0.498910i
$64$		0			0
$65$	−0.441137			−0.0547163
$66$		0			0
$67$	1.91665			0.234157			0.117078	−	0.993123i	$-0.462647\pi$
$67$	1.91665			0.234157			0.117078	+	0.993123i	$0.462647\pi$
$68$		0			0
$69$	0.446609	+	1.37452i	0.0537654	+	0.165473i
$70$		0			0
$71$	−9.84407	−	7.15214i	−1.16828	−	0.848803i	−0.177475	−	0.984125i	$-0.556793\pi$
$71$	−9.84407	−	7.15214i	−1.16828	−	0.848803i	−0.990802	+	0.135323i	$0.956793\pi$
$72$		0			0
$73$	−3.51550	+	10.8196i	−0.411458	+	1.26634i	0.503923	+	0.863749i	$0.331890\pi$
$73$	−3.51550	+	10.8196i	−0.411458	+	1.26634i	−0.915381	+	0.402589i	$0.868110\pi$
$74$		0			0
$75$	−8.23497	+	5.98306i	−0.950893	+	0.690864i
$76$		0			0
$77$	10.2031	+	5.54330i	1.16275	+	0.631718i
$78$		0			0
$79$	1.39747	−	1.01532i	0.157227	−	0.114232i	−0.506390	−	0.862305i	$-0.669020\pi$
$79$	1.39747	−	1.01532i	0.157227	−	0.114232i	0.663617	+	0.748072i	$0.269020\pi$
$80$		0			0
$81$	−3.44661	+	10.6076i	−0.382957	+	1.17862i
$82$		0			0
$83$	−3.81006	−	2.76817i	−0.418209	−	0.303846i	0.358708	−	0.933450i	$-0.383217\pi$
$83$	−3.81006	−	2.76817i	−0.418209	−	0.303846i	−0.776917	+	0.629603i	$0.783217\pi$
$84$		0			0
$85$	0.383429	+	1.18007i	0.0415887	+	0.127997i
$86$		0			0
$87$	2.10595			0.225781
$88$		0			0
$89$	6.31175			0.669044			0.334522	−	0.942388i	$-0.391425\pi$
$89$	6.31175			0.669044			0.334522	+	0.942388i	$0.391425\pi$
$90$		0			0
$91$	2.91429	+	8.96925i	0.305500	+	0.940233i
$92$		0			0
$93$	8.94146	+	6.49635i	0.927186	+	0.673640i
$94$		0			0
$95$	−0.233701	+	0.719257i	−0.0239772	+	0.0737942i
$96$		0			0
$97$	−5.66755	+	4.11771i	−0.575452	+	0.418090i	−0.837082	−	0.547078i	$-0.815740\pi$
$97$	−5.66755	+	4.11771i	−0.575452	+	0.418090i	0.261630	+	0.965168i	$0.415740\pi$
$98$		0			0
$99$	−1.69718	−	3.56064i	−0.170573	−	0.357858i
$100$		0			0
$101$	−3.25495	+	2.36486i	−0.323880	+	0.235312i	−0.737829	−	0.674988i	$-0.764149\pi$
$101$	−3.25495	+	2.36486i	−0.323880	+	0.235312i	0.413950	+	0.910300i	$0.364149\pi$
$102$		0			0
$103$	4.65523	−	14.3273i	0.458694	−	1.41171i	−0.408050	−	0.912960i	$-0.633791\pi$
$103$	4.65523	−	14.3273i	0.458694	−	1.41171i	0.866744	−	0.498754i	$-0.166209\pi$
$104$		0			0
$105$	−0.949394	−	0.689775i	−0.0926514	−	0.0673151i
$106$		0			0
$107$	−0.160353	−	0.493515i	−0.0155019	−	0.0477099i	0.943006	−	0.332775i	$-0.107985\pi$
$107$	−0.160353	−	0.493515i	−0.0155019	−	0.0477099i	−0.958508	+	0.285065i	$0.907985\pi$
$108$		0			0
$109$	−0.285032			−0.0273011			−0.0136506	−	0.999907i	$-0.504345\pi$
$109$	−0.285032			−0.0273011			−0.0136506	+	0.999907i	$0.504345\pi$
$110$		0			0
$111$	−23.7315			−2.25250
$112$		0			0
$113$	−3.57504	−	11.0028i	−0.336311	−	1.03506i	−0.966072	−	0.258271i	$-0.916847\pi$
$113$	−3.57504	−	11.0028i	−0.336311	−	1.03506i	0.629761	−	0.776789i	$-0.283153\pi$
$114$		0			0
$115$	−0.0935520	−	0.0679695i	−0.00872377	−	0.00633819i
$116$		0			0
$117$	0.989973	−	3.04682i	0.0915230	−	0.281679i
$118$		0			0
$119$	21.4604	−	15.5919i	1.96727	−	1.42930i
$120$		0			0
$121$	−10.2673	−	3.94749i	−0.933390	−	0.358862i
$122$		0			0
$123$	−0.464894	+	0.337765i	−0.0419180	+	0.0304552i
$124$		0			0
$125$	0.504704	−	1.55332i	0.0451421	−	0.138933i
$126$		0			0
$127$	13.8495	+	10.0623i	1.22895	+	0.892883i	0.996811	−	0.0797996i	$-0.0254280\pi$
$127$	13.8495	+	10.0623i	1.22895	+	0.892883i	0.232138	+	0.972683i	$0.425428\pi$
$128$		0			0
$129$	−2.72713	−	8.39326i	−0.240111	−	0.738985i
$130$		0			0
$131$	5.02344			0.438900			0.219450	−	0.975624i	$-0.429574\pi$
$131$	5.02344			0.438900			0.219450	+	0.975624i	$0.429574\pi$
$132$		0			0
$133$	16.1679			1.40194
$134$		0			0
$135$	−0.187552	−	0.577226i	−0.0161419	−	0.0496797i
$136$		0			0
$137$	−2.43148	−	1.76657i	−0.207735	−	0.150928i	0.479053	−	0.877786i	$-0.340980\pi$
$137$	−2.43148	−	1.76657i	−0.207735	−	0.150928i	−0.686788	+	0.726857i	$0.740980\pi$
$138$		0			0
$139$	−1.65652	+	5.09825i	−0.140504	+	0.432428i	−0.996406	−	0.0847114i	$-0.973003\pi$
$139$	−1.65652	+	5.09825i	−0.140504	+	0.432428i	0.855901	+	0.517140i	$0.173003\pi$
$140$		0			0
$141$	9.65140	−	7.01215i	0.812795	−	0.590530i
$142$		0			0
$143$	−3.84407	−	8.06477i	−0.321458	−	0.674410i
$144$		0			0
$145$	−0.136319	+	0.0990413i	−0.0113207	+	0.00822493i
$146$		0			0
$147$	−3.32519	+	10.2339i	−0.274257	+	0.844077i
$148$		0			0
$149$	−4.70922	−	3.42145i	−0.385794	−	0.280296i	0.377936	−	0.925832i	$-0.376634\pi$
$149$	−4.70922	−	3.42145i	−0.385794	−	0.280296i	−0.763730	+	0.645536i	$0.776634\pi$
$150$		0			0
$151$	1.12657	+	3.46722i	0.0916788	+	0.282158i	0.986374	−	0.164519i	$-0.0526072\pi$
$151$	1.12657	+	3.46722i	0.0916788	+	0.282158i	−0.894695	+	0.446677i	$0.852607\pi$
$152$		0			0
$153$	−9.01094			−0.728492
$154$		0			0
$155$	−0.884303			−0.0710289
$156$		0			0
$157$	0.0448569	+	0.138055i	0.00357997	+	0.0110180i	0.952831	−	0.303503i	$-0.0981562\pi$
$157$	0.0448569	+	0.138055i	0.00357997	+	0.0110180i	−0.949251	+	0.314521i	$0.898156\pi$
$158$		0			0
$159$	16.3468	+	11.8766i	1.29638	+	0.941877i
$160$		0			0
$161$	−0.763932	+	2.35114i	−0.0602063	+	0.185296i
$162$		0			0
$163$	11.6809	−	8.48668i	0.914919	−	0.664728i	−0.0273349	−	0.999626i	$-0.508702\pi$
$163$	11.6809	−	8.48668i	0.914919	−	0.664728i	0.942254	+	0.334899i	$0.108702\pi$
$164$		0			0
$165$	0.976840	+	0.530716i	0.0760469	+	0.0413162i
$166$		0			0
$167$	−14.1091	+	10.2508i	−1.09179	+	0.793233i	−0.979701	−	0.200465i	$-0.935755\pi$
$167$	−14.1091	+	10.2508i	−1.09179	+	0.793233i	−0.112090	+	0.993698i	$0.535755\pi$
$168$		0			0
$169$	−1.77496	+	5.46275i	−0.136535	+	0.420212i
$170$		0			0
$171$	−4.44328	−	3.22823i	−0.339786	−	0.246869i
$172$		0			0
$173$	−5.63736	−	17.3500i	−0.428601	−	1.31910i	−0.899504	−	0.436913i	$-0.856072\pi$
$173$	−5.63736	−	17.3500i	−0.428601	−	1.31910i	0.470903	−	0.882185i	$-0.343928\pi$
$174$		0			0
$175$	−17.4113			−1.31617
$176$		0			0
$177$	6.32489			0.475408
$178$		0			0
$179$	−2.82688	−	8.70025i	−0.211291	−	0.650288i	−0.999396	−	0.0347466i	$-0.988938\pi$
$179$	−2.82688	−	8.70025i	−0.211291	−	0.650288i	0.788105	−	0.615541i	$-0.211062\pi$
$180$		0			0
$181$	13.4621	+	9.78079i	1.00063	+	0.727001i	0.962223	−	0.272261i	$-0.0877716\pi$
$181$	13.4621	+	9.78079i	1.00063	+	0.727001i	0.0384073	+	0.999262i	$0.487772\pi$
$182$		0			0
$183$	−4.38433	+	13.4936i	−0.324099	+	0.997475i
$184$		0			0
$185$	1.53615	−	1.11608i	0.112940	−	0.0820558i
$186$		0			0
$187$	−18.2326	+	17.2930i	−1.33330	+	1.26459i
$188$		0			0
$189$	−10.4972	+	7.62667i	−0.763560	+	0.554759i
$190$		0			0
$191$	−2.37239	+	7.30146i	−0.171660	+	0.528315i	−0.999465	−	0.0327007i	$-0.989589\pi$
$191$	−2.37239	+	7.30146i	−0.171660	+	0.528315i	0.827805	+	0.561015i	$0.189589\pi$
$192$		0			0
$193$	−15.9130	−	11.5615i	−1.14544	−	0.832213i	−0.157574	−	0.987507i	$-0.550367\pi$
$193$	−15.9130	−	11.5615i	−1.14544	−	0.832213i	−0.987868	+	0.155294i	$0.950367\pi$
$194$		0			0
$195$	0.279014	+	0.858716i	0.0199806	+	0.0614940i
$196$		0			0
$197$	22.7460			1.62059			0.810294	−	0.586024i	$-0.199308\pi$
$197$	22.7460			1.62059			0.810294	+	0.586024i	$0.199308\pi$
$198$		0			0
$199$	6.85748			0.486114			0.243057	−	0.970012i	$-0.421850\pi$
$199$	6.85748			0.486114			0.243057	+	0.970012i	$0.421850\pi$
$200$		0			0
$201$	−1.21226	−	3.73096i	−0.0855064	−	0.263162i
$202$		0			0
$203$	2.91429	+	2.11735i	0.204543	+	0.148609i
$204$		0			0
$205$	0.0142079	−	0.0437273i	0.000992320	−	0.00305405i
$206$		0			0
$207$	0.679393	−	0.493608i	0.0472210	−	0.0343081i
$208$		0			0
$209$	−15.1858	+	1.99516i	−1.05042	+	0.138008i
$210$		0			0
$211$	9.30563	−	6.76094i	0.640626	−	0.465442i	−0.219439	−	0.975626i	$-0.570423\pi$
$211$	9.30563	−	6.76094i	0.640626	−	0.465442i	0.860065	+	0.510184i	$0.170423\pi$
$212$		0			0
$213$	−7.69609	+	23.6861i	−0.527327	+	1.62295i
$214$		0			0
$215$	0.571258	+	0.415043i	0.0389595	+	0.0283057i
$216$		0			0
$217$	5.84198	+	17.9798i	0.396580	+	1.22055i
$218$		0			0
$219$	23.2849			1.57345
$220$		0			0
$221$	−20.4096			−1.37290
$222$		0			0
$223$	5.02745	+	15.4729i	0.336663	+	1.03614i	0.965897	+	0.258926i	$0.0833685\pi$
$223$	5.02745	+	15.4729i	0.336663	+	1.03614i	−0.629235	+	0.777215i	$0.716632\pi$
$224$		0			0
$225$	4.78498	+	3.47649i	0.318999	+	0.231766i
$226$		0			0
$227$	1.91835	−	5.90406i	0.127325	−	0.391866i	−0.866992	−	0.498321i	$-0.833950\pi$
$227$	1.91835	−	5.90406i	0.127325	−	0.391866i	0.994318	+	0.106455i	$0.0339500\pi$
$228$		0			0
$229$	16.6982	−	12.1319i	1.10345	−	0.801701i	0.121827	−	0.992551i	$-0.461125\pi$
$229$	16.6982	−	12.1319i	1.10345	−	0.801701i	0.981619	+	0.190850i	$0.0611246\pi$
$230$		0			0
$231$	4.33728	−	23.3673i	0.285372	−	1.53746i
$232$		0			0
$233$	8.31111	−	6.03837i	0.544479	−	0.395587i	−0.281267	−	0.959630i	$-0.590755\pi$
$233$	8.31111	−	6.03837i	0.544479	−	0.395587i	0.825746	+	0.564043i	$0.190755\pi$
$234$		0			0
$235$	−0.294962	+	0.907799i	−0.0192412	+	0.0592182i
$236$		0			0
$237$	−2.86030	−	2.07813i	−0.185796	−	0.134989i
$238$		0			0
$239$	−6.19330	−	19.0610i	−0.400611	−	1.23295i	−0.924505	−	0.381171i	$-0.875521\pi$
$239$	−6.19330	−	19.0610i	−0.400611	−	1.23295i	0.523893	−	0.851784i	$-0.324479\pi$
$240$		0			0
$241$	−6.87625			−0.442938			−0.221469	−	0.975167i	$-0.571085\pi$
$241$	−6.87625			−0.442938			−0.221469	+	0.975167i	$0.571085\pi$
$242$		0			0
$243$	11.7103			0.751216
$244$		0			0
$245$	−0.266052	−	0.818825i	−0.0169975	−	0.0523128i
$246$		0			0
$247$	−10.0639	−	7.31186i	−0.640352	−	0.465243i
$248$		0			0
$249$	−2.97870	+	9.16750i	−0.188768	+	0.580967i
$250$		0			0
$251$	−4.20817	+	3.05742i	−0.265618	+	0.192982i	−0.712620	−	0.701550i	$-0.752492\pi$
$251$	−4.20817	+	3.05742i	−0.265618	+	0.192982i	0.447002	+	0.894533i	$0.352492\pi$
$252$		0			0
$253$	0.427390	−	2.30259i	0.0268698	−	0.144762i
$254$		0			0
$255$	2.05462	−	1.49277i	0.128665	−	0.0934806i
$256$		0			0
$257$	5.74683	−	17.6869i	0.358478	−	1.10328i	−0.595488	−	0.803364i	$-0.703041\pi$
$257$	5.74683	−	17.6869i	0.358478	−	1.10328i	0.953965	−	0.299916i	$-0.0969588\pi$
$258$		0			0
$259$	−32.8406	−	23.8601i	−2.04062	−	1.48259i
$260$		0			0
$261$	−0.378136	−	1.16378i	−0.0234060	−	0.0720363i
$262$		0			0
$263$	1.27857			0.0788397			0.0394199	−	0.999223i	$-0.487449\pi$
$263$	1.27857			0.0788397			0.0394199	+	0.999223i	$0.487449\pi$
$264$		0			0
$265$	−1.61668			−0.0993120
$266$		0			0
$267$	−3.99211	−	12.2865i	−0.244313	−	0.751919i
$268$		0			0
$269$	−2.17926	−	1.58333i	−0.132872	−	0.0965372i	0.519364	−	0.854553i	$-0.326169\pi$
$269$	−2.17926	−	1.58333i	−0.132872	−	0.0965372i	−0.652236	+	0.758016i	$0.726169\pi$
$270$		0			0
$271$	−3.20991	+	9.87910i	−0.194988	+	0.600112i	0.804988	+	0.593291i	$0.202171\pi$
$271$	−3.20991	+	9.87910i	−0.194988	+	0.600112i	−0.999977	+	0.00682189i	$0.997829\pi$
$272$		0			0
$273$	15.6163	−	11.3459i	0.945141	−	0.686685i
$274$		0			0
$275$	16.3536	−	2.14859i	0.986161	−	0.129565i
$276$		0			0
$277$	5.91429	−	4.29698i	0.355355	−	0.258181i	−0.395757	−	0.918355i	$-0.629518\pi$
$277$	5.91429	−	4.29698i	0.355355	−	0.258181i	0.751112	+	0.660175i	$0.229518\pi$
$278$		0			0
$279$	1.98450	−	6.10766i	0.118809	−	0.365656i
$280$		0			0
$281$	13.5472	+	9.84260i	0.808157	+	0.587160i	0.913296	−	0.407297i	$-0.133529\pi$
$281$	13.5472	+	9.84260i	0.808157	+	0.587160i	−0.105139	+	0.994458i	$0.533529\pi$
$282$		0			0
$283$	−6.32816	−	19.4761i	−0.376170	−	1.15773i	−0.942686	−	0.333681i	$-0.891709\pi$
$283$	−6.32816	−	19.4761i	−0.376170	−	1.15773i	0.566516	−	0.824051i	$-0.308291\pi$
$284$		0			0
$285$	1.54792			0.0916908
$286$		0			0
$287$	−0.982932			−0.0580206
$288$		0			0
$289$	12.4864	+	38.4292i	0.734494	+	2.26054i
$290$		0			0
$291$	11.6002	+	8.42804i	0.680016	+	0.494060i
$292$		0			0
$293$	−5.76665	+	17.7479i	−0.336891	+	1.03684i	0.628892	+	0.777493i	$0.283509\pi$
$293$	−5.76665	+	17.7479i	−0.336891	+	1.03684i	−0.965783	+	0.259352i	$0.916491\pi$
$294$		0			0
$295$	−0.409412	+	0.297455i	−0.0238369	+	0.0173185i
$296$		0			0
$297$	8.91839	−	8.45875i	0.517497	−	0.490826i
$298$		0			0
$299$	1.53881	−	1.11801i	0.0889916	−	0.0646562i
$300$		0			0
$301$	4.66481	−	14.3568i	0.268875	−	0.827513i
$302$		0			0
$303$	6.66215	+	4.84034i	0.382731	+	0.278070i
$304$		0			0
$305$	−0.350795	−	1.07964i	−0.0200865	−	0.0618199i
$306$		0			0
$307$	−16.2802			−0.929160			−0.464580	−	0.885531i	$-0.653795\pi$
$307$	−16.2802			−0.929160			−0.464580	+	0.885531i	$0.653795\pi$
$308$		0			0
$309$	−30.8339			−1.75408
$310$		0			0
$311$	3.22987	+	9.94052i	0.183149	+	0.563675i	0.999912	−	0.0132990i	$-0.00423333\pi$
$311$	3.22987	+	9.94052i	0.183149	+	0.563675i	−0.816762	+	0.576974i	$0.804233\pi$
$312$		0			0
$313$	−6.81457	−	4.95107i	−0.385182	−	0.279851i	0.378296	−	0.925685i	$-0.376510\pi$
$313$	−6.81457	−	4.95107i	−0.385182	−	0.279851i	−0.763478	+	0.645833i	$0.776510\pi$
$314$		0			0
$315$	−0.210712	+	0.648505i	−0.0118723	+	0.0365391i
$316$		0			0
$317$	−17.3685	+	12.6189i	−0.975510	+	0.708749i	−0.956701	−	0.291074i	$-0.905988\pi$
$317$	−17.3685	+	12.6189i	−0.975510	+	0.708749i	−0.0188092	+	0.999823i	$0.505988\pi$
$318$		0			0
$319$	−2.99854	−	1.62910i	−0.167886	−	0.0912121i
$320$		0			0
$321$	−0.859254	+	0.624285i	−0.0479589	+	0.0348442i
$322$		0			0
$323$	−10.8124	+	33.2771i	−0.601617	+	1.85159i
$324$		0			0
$325$	10.8379	+	7.87418i	0.601177	+	0.436781i
$326$		0			0
$327$	0.180279	+	0.554843i	0.00996948	+	0.0306829i
$328$		0			0
$329$	20.4061			1.12502
$330$		0			0
$331$	21.5452			1.18423			0.592117	−	0.805852i	$-0.298292\pi$
$331$	21.5452			1.18423			0.592117	+	0.805852i	$0.298292\pi$
$332$		0			0
$333$	4.26115	+	13.1145i	0.233509	+	0.718668i
$334$		0			0
$335$	0.253935	+	0.184494i	0.0138739	+	0.0100800i
$336$		0			0
$337$	3.46278	−	10.6574i	0.188630	−	0.580543i	−0.811362	−	0.584544i	$-0.801273\pi$
$337$	3.46278	−	10.6574i	0.188630	−	0.580543i	0.999992	+	0.00400074i	$0.00127348\pi$
$338$		0			0
$339$	−19.1570	+	13.9183i	−1.04046	+	0.755940i
$340$		0			0
$341$	−7.70584	−	16.1666i	−0.417294	−	0.875473i
$342$		0			0
$343$	4.93598	−	3.58620i	0.266518	−	0.193637i
$344$		0			0
$345$	−0.0731388	+	0.225098i	−0.00393766	+	0.0121189i
$346$		0			0
$347$	−10.1421	−	7.36867i	−0.544456	−	0.395571i	0.281281	−	0.959625i	$-0.409241\pi$
$347$	−10.1421	−	7.36867i	−0.544456	−	0.395571i	−0.825737	+	0.564055i	$0.809241\pi$
$348$		0			0
$349$	4.96963	+	15.2949i	0.266018	+	0.818719i	0.991457	+	0.130433i	$0.0416368\pi$
$349$	4.96963	+	15.2949i	0.266018	+	0.818719i	−0.725439	+	0.688286i	$0.758363\pi$
$350$		0			0
$351$	9.98323			0.532865
$352$		0			0
$353$	−16.9450			−0.901892			−0.450946	−	0.892551i	$-0.648913\pi$
$353$	−16.9450			−0.901892			−0.450946	+	0.892551i	$0.648913\pi$
$354$		0			0
$355$	−0.615773	−	1.89515i	−0.0326818	−	0.100584i
$356$		0			0
$357$	−43.9246	−	31.9131i	−2.32473	−	1.68902i
$358$		0			0
$359$	−7.62469	+	23.4664i	−0.402416	+	1.23851i	0.520618	+	0.853789i	$0.325701\pi$
$359$	−7.62469	+	23.4664i	−0.402416	+	1.23851i	−0.923034	+	0.384718i	$0.874299\pi$
$360$		0			0
$361$	−1.88197	+	1.36733i	−0.0990508	+	0.0719646i
$362$		0			0
$363$	−1.19023	+	22.4831i	−0.0624708	+	1.18005i
$364$		0			0
$365$	−1.50724	+	1.09508i	−0.0788927	+	0.0573189i
$366$		0			0
$367$	9.56377	−	29.4343i	0.499225	−	1.53646i	−0.311043	−	0.950396i	$-0.600678\pi$
$367$	9.56377	−	29.4343i	0.499225	−	1.53646i	0.810268	−	0.586060i	$-0.199322\pi$
$368$		0			0
$369$	0.270129	+	0.196260i	0.0140624	+	0.0102169i
$370$		0			0
$371$	10.6803	+	32.8706i	0.554494	+	1.70656i
$372$		0			0
$373$	−16.6908			−0.864217			−0.432108	−	0.901822i	$-0.642230\pi$
$373$	−16.6908			−0.864217			−0.432108	+	0.901822i	$0.642230\pi$
$374$		0			0
$375$	−3.34291			−0.172627
$376$		0			0
$377$	−0.856469	−	2.63594i	−0.0441104	−	0.135758i
$378$		0			0
$379$	13.4370	+	9.76252i	0.690210	+	0.501467i	0.876729	−	0.480985i	$-0.159721\pi$
$379$	13.4370	+	9.76252i	0.690210	+	0.501467i	−0.186519	+	0.982451i	$0.559721\pi$
$380$		0			0
$381$	10.8276	−	33.3238i	0.554713	−	1.70723i
$382$		0			0
$383$	−2.20817	+	1.60433i	−0.112832	+	0.0819775i	−0.642771	−	0.766059i	$-0.722215\pi$
$383$	−2.20817	+	1.60433i	−0.112832	+	0.0819775i	0.529938	+	0.848036i	$0.322215\pi$
$384$		0			0
$385$	0.818197	+	1.71656i	0.0416992	+	0.0874838i
$386$		0			0
$387$	−4.14859	+	3.01412i	−0.210884	+	0.153217i
$388$		0			0
$389$	−4.71908	+	14.5238i	−0.239267	+	0.736387i	0.757260	+	0.653113i	$0.226538\pi$
$389$	−4.71908	+	14.5238i	−0.239267	+	0.736387i	−0.996527	+	0.0832735i	$0.973462\pi$
$390$		0			0
$391$	−4.32827	−	3.14467i	−0.218890	−	0.159033i
$392$		0			0
$393$	−3.17727	−	9.77862i	−0.160272	−	0.493266i
$394$		0			0
$395$	0.282881			0.0142333
$396$		0			0
$397$	21.4810			1.07810			0.539050	−	0.842274i	$-0.318783\pi$
$397$	21.4810			1.07810			0.539050	+	0.842274i	$0.318783\pi$
$398$		0			0
$399$	−10.2260	−	31.4725i	−0.511942	−	1.57560i
$400$		0			0
$401$	28.9448	+	21.0296i	1.44544	+	1.05017i	0.986871	+	0.161509i	$0.0516360\pi$
$401$	28.9448	+	21.0296i	1.44544	+	1.05017i	0.458564	+	0.888661i	$0.348364\pi$
$402$		0			0
$403$	4.49485	−	13.8337i	0.223904	−	0.689107i
$404$		0			0
$405$	−1.47771	+	1.07362i	−0.0734278	+	0.0533484i
$406$		0			0
$407$	33.7900	+	18.3581i	1.67491	+	0.909975i
$408$		0			0
$409$	−8.54327	+	6.20705i	−0.422437	+	0.306919i	−0.778618	−	0.627499i	$-0.784079\pi$
$409$	−8.54327	+	6.20705i	−0.422437	+	0.306919i	0.356180	+	0.934417i	$0.384079\pi$
$410$		0			0
$411$	−1.90093	+	5.85045i	−0.0937658	+	0.288581i
$412$		0			0
$413$	8.75261	+	6.35915i	0.430688	+	0.312913i
$414$		0			0
$415$	−0.238329	−	0.733502i	−0.0116991	−	0.0360062i
$416$		0			0
$417$	10.9720			0.537301
$418$		0			0
$419$	29.9952			1.46536			0.732680	−	0.680573i	$-0.238269\pi$
$419$	29.9952			1.46536			0.732680	+	0.680573i	$0.238269\pi$
$420$		0			0
$421$	−6.55267	−	20.1670i	−0.319357	−	0.982881i	−0.973924	−	0.226876i	$-0.927149\pi$
$421$	−6.55267	−	20.1670i	−0.319357	−	0.982881i	0.654566	−	0.756005i	$-0.272851\pi$
$422$		0			0
$423$	−5.60801	−	4.07446i	−0.272671	−	0.198107i
$424$		0			0
$425$	11.6439	−	35.8362i	0.564812	−	1.73831i
$426$		0			0
$427$	−19.6339	+	14.2649i	−0.950150	+	0.690325i
$428$		0			0
$429$	−13.2675	+	12.5837i	−0.640563	+	0.607549i
$430$		0			0
$431$	10.8875	−	7.91021i	0.524431	−	0.381021i	−0.293840	−	0.955855i	$-0.594933\pi$
$431$	10.8875	−	7.91021i	0.524431	−	0.381021i	0.818270	+	0.574833i	$0.194933\pi$
$432$		0			0
$433$	9.24458	−	28.4519i	0.444266	−	1.36731i	−0.439020	−	0.898477i	$-0.644674\pi$
$433$	9.24458	−	28.4519i	0.444266	−	1.36731i	0.883286	−	0.468834i	$-0.155326\pi$
$434$		0			0
$435$	0.279014	+	0.202715i	0.0133777	+	0.00971946i
$436$		0			0
$437$	−1.00766	−	3.10126i	−0.0482029	−	0.148353i
$438$		0			0
$439$	−33.1644			−1.58285			−0.791425	−	0.611266i	$-0.790661\pi$
$439$	−33.1644			−1.58285			−0.791425	+	0.611266i	$0.790661\pi$
$440$		0			0
$441$	6.25248			0.297737
$442$		0			0
$443$	−8.59675	−	26.4581i	−0.408444	−	1.25706i	−0.917985	−	0.396615i	$-0.870185\pi$
$443$	−8.59675	−	26.4581i	−0.408444	−	1.25706i	0.509541	−	0.860447i	$-0.329815\pi$
$444$		0			0
$445$	0.836235	+	0.607560i	0.0396413	+	0.0288011i
$446$		0			0
$447$	−3.68166	+	11.3310i	−0.174137	+	0.535937i
$448$		0			0
$449$	5.90249	−	4.28841i	0.278556	−	0.202383i	−0.439731	−	0.898129i	$-0.644926\pi$
$449$	5.90249	−	4.28841i	0.278556	−	0.202383i	0.718287	+	0.695747i	$0.244926\pi$
$450$		0			0
$451$	0.923221	−	0.121296i	0.0434728	−	0.00571159i
$452$		0			0
$453$	6.03675	−	4.38595i	0.283631	−	0.206070i
$454$		0			0
$455$	−0.477258	+	1.46885i	−0.0223742	+	0.0688607i
$456$		0			0
$457$	13.0495	+	9.48103i	0.610430	+	0.443504i	0.849566	−	0.527483i	$-0.176864\pi$
$457$	13.0495	+	9.48103i	0.610430	+	0.443504i	−0.239135	+	0.970986i	$0.576864\pi$
$458$		0			0
$459$	−8.67727	−	26.7059i	−0.405020	−	1.24652i
$460$		0			0
$461$	−14.4253			−0.671851			−0.335926	−	0.941888i	$-0.609049\pi$
$461$	−14.4253			−0.671851			−0.335926	+	0.941888i	$0.609049\pi$
$462$		0			0
$463$	−19.7906			−0.919748			−0.459874	−	0.887984i	$-0.652105\pi$
$463$	−19.7906			−0.919748			−0.459874	+	0.887984i	$0.652105\pi$
$464$		0			0
$465$	0.559312	+	1.72138i	0.0259374	+	0.0798273i
$466$		0			0
$467$	−30.5957	−	22.2291i	−1.41580	−	1.02864i	−0.992447	−	0.122673i	$-0.960853\pi$
$467$	−30.5957	−	22.2291i	−1.41580	−	1.02864i	−0.423352	−	0.905965i	$-0.639147\pi$
$468$		0			0
$469$	2.07359	−	6.38187i	0.0957497	−	0.294687i
$470$		0			0
$471$	0.240367	−	0.174637i	0.0110755	−	0.00804685i
$472$		0			0
$473$	−2.60978	+	14.0603i	−0.119998	+	0.646494i
$474$		0			0
$475$	18.5801	−	13.4993i	0.852515	−	0.619389i
$476$		0			0
$477$	3.62806	−	11.1660i	0.166118	−	0.511257i
$478$		0			0
$479$	31.0120	+	22.5316i	1.41698	+	1.02949i	0.992262	+	0.124165i	$0.0396253\pi$
$479$	31.0120	+	22.5316i	1.41698	+	1.02949i	0.424714	+	0.905328i	$0.360375\pi$
$480$		0			0
$481$	9.65140	+	29.7040i	0.440066	+	1.35438i
$482$		0			0
$483$	5.05991			0.230234
$484$		0			0
$485$	−1.14725			−0.0520940
$486$		0			0
$487$	−3.54083	−	10.8975i	−0.160450	−	0.493815i	0.838222	−	0.545329i	$-0.183595\pi$
$487$	−3.54083	−	10.8975i	−0.160450	−	0.493815i	−0.998672	+	0.0515142i	$0.983595\pi$
$488$		0			0
$489$	−23.9082	−	17.3703i	−1.08117	−	0.785513i
$490$		0			0
$491$	7.56701	−	23.2889i	0.341494	−	1.05101i	−0.621939	−	0.783065i	$-0.713655\pi$
$491$	7.56701	−	23.2889i	0.341494	−	1.05101i	0.963434	−	0.267946i	$-0.0863450\pi$
$492$		0			0
$493$	−6.30691	+	4.58224i	−0.284049	+	0.206374i
$494$		0			0
$495$	0.117885	−	0.635112i	0.00529854	−	0.0285462i
$496$		0			0
$497$	−34.4645	+	25.0400i	−1.54595	+	1.12320i
$498$		0			0
$499$	4.69978	−	14.4644i	0.210391	−	0.647516i	−0.789058	−	0.614319i	$-0.789431\pi$
$499$	4.69978	−	14.4644i	0.210391	−	0.647516i	0.999449	−	0.0331977i	$-0.0105691\pi$
$500$		0			0
$501$	28.8781	+	20.9811i	1.29018	+	0.937368i
$502$		0			0
$503$	8.23196	+	25.3354i	0.367045	+	1.12965i	0.948691	+	0.316206i	$0.102409\pi$
$503$	8.23196	+	25.3354i	0.367045	+	1.12965i	−0.581646	+	0.813442i	$0.697591\pi$
$504$		0			0
$505$	−0.658882			−0.0293198
$506$		0			0
$507$	11.7564			0.522121
$508$		0			0
$509$	4.72544	+	14.5434i	0.209452	+	0.644626i	0.999501	+	0.0315827i	$0.0100548\pi$
$509$	4.72544	+	14.5434i	0.209452	+	0.644626i	−0.790050	+	0.613043i	$0.789945\pi$
$510$		0			0
$511$	32.2226	+	23.4111i	1.42544	+	1.03564i
$512$		0			0
$513$	5.28881	−	16.2773i	0.233507	−	0.718660i
$514$		0			0
$515$	1.99589	−	1.45010i	0.0879496	−	0.0638991i
$516$		0			0
$517$	−19.1665	+	2.51815i	−0.842941	+	0.110748i
$518$		0			0
$519$	−30.2080	+	21.9474i	−1.32598	+	0.963383i
$520$		0			0
$521$	−10.7044	+	32.9446i	−0.468967	+	1.44333i	0.384958	+	0.922934i	$0.374216\pi$
$521$	−10.7044	+	32.9446i	−0.468967	+	1.44333i	−0.853925	+	0.520397i	$0.825784\pi$
$522$		0			0
$523$	13.5192	+	9.82230i	0.591155	+	0.429499i	0.842728	−	0.538339i	$-0.180948\pi$
$523$	13.5192	+	9.82230i	0.591155	+	0.429499i	−0.251574	+	0.967838i	$0.580948\pi$
$524$		0			0
$525$	11.0125	+	33.8929i	0.480624	+	1.47921i
$526$		0			0
$527$	−40.9131			−1.78220
$528$		0			0
$529$	−22.5014			−0.978322
$530$		0			0
$531$	−1.13567	−	3.49524i	−0.0492840	−	0.151681i
$532$		0			0
$533$	0.611837	+	0.444525i	0.0265016	+	0.0192545i
$534$		0			0
$535$	0.0262601	−	0.0808204i	0.00113532	−	0.00349417i
$536$		0			0
$537$	−15.1479	+	11.0056i	−0.653682	+	0.474928i
$538$		0			0
$539$	12.6512	−	11.9992i	0.544926	−	0.516841i
$540$		0			0
$541$	10.4552	−	7.59614i	0.449504	−	0.326583i	−0.339896	−	0.940463i	$-0.610392\pi$
$541$	10.4552	−	7.59614i	0.449504	−	0.326583i	0.789400	+	0.613880i	$0.210392\pi$
$542$		0			0
$543$	10.5247	−	32.3916i	0.451656	−	1.39006i
$544$		0			0
$545$	−0.0377635	−	0.0274368i	−0.00161761	−	0.00117526i
$546$		0			0
$547$	1.61370	+	4.96645i	0.0689968	+	0.212350i	0.979610	−	0.200910i	$-0.0643899\pi$
$547$	1.61370	+	4.96645i	0.0689968	+	0.212350i	−0.910613	+	0.413260i	$0.864390\pi$
$548$		0			0
$549$	8.24403			0.351846
$550$		0			0
$551$	−4.75154			−0.202422
$552$		0			0
$553$	−1.86880	−	5.75159i	−0.0794696	−	0.244582i
$554$		0			0
$555$	−3.14416	−	2.28436i	−0.133462	−	0.0969659i
$556$		0			0
$557$	−3.64711	+	11.2247i	−0.154533	+	0.475604i	−0.998113	−	0.0613991i	$-0.980444\pi$
$557$	−3.64711	+	11.2247i	−0.154533	+	0.475604i	0.843580	+	0.537003i	$0.180444\pi$
$558$		0			0
$559$	−9.39645	+	6.82692i	−0.397428	+	0.288748i
$560$		0			0
$561$	45.1944	+	24.5541i	1.90811	+	1.03667i
$562$		0			0
$563$	−29.8190	+	21.6648i	−1.25672	+	0.913061i	−0.998592	−	0.0530501i	$-0.983106\pi$
$563$	−29.8190	+	21.6648i	−1.25672	+	0.913061i	−0.258128	+	0.966111i	$0.583106\pi$
$564$		0			0
$565$	0.585466	−	1.80188i	0.0246307	−	0.0758056i
$566$		0			0
$567$	31.5911	+	22.9523i	1.32670	+	0.963906i
$568$		0			0
$569$	−8.33266	−	25.6453i	−0.349323	−	1.07511i	−0.959228	−	0.282632i	$-0.908792\pi$
$569$	−8.33266	−	25.6453i	−0.349323	−	1.07511i	0.609905	−	0.792475i	$-0.291208\pi$
$570$		0			0
$571$	−14.3565			−0.600801			−0.300400	−	0.953813i	$-0.597120\pi$
$571$	−14.3565			−0.600801			−0.300400	+	0.953813i	$0.597120\pi$
$572$		0			0
$573$	15.7135			0.656442
$574$		0			0
$575$	1.08515	+	3.33976i	0.0452540	+	0.139278i
$576$		0			0
$577$	−8.57084	−	6.22708i	−0.356809	−	0.259237i	0.394911	−	0.918719i	$-0.370775\pi$
$577$	−8.57084	−	6.22708i	−0.356809	−	0.259237i	−0.751720	+	0.659483i	$0.770775\pi$
$578$		0			0
$579$	−12.4408	+	38.2887i	−0.517020	+	1.59123i
$580$		0			0
$581$	−13.3392	+	9.69150i	−0.553403	+	0.402071i
$582$		0			0
$583$	−14.0878	−	29.5558i	−0.583457	−	1.22408i
$584$		0			0
$585$	0.424443	−	0.308376i	0.0175486	−	0.0127498i
$586$		0			0
$587$	6.17859	−	19.0157i	0.255018	−	0.784864i	−0.738809	−	0.673915i	$-0.764611\pi$
$587$	6.17859	−	19.0157i	0.255018	−	0.784864i	0.993826	−	0.110948i	$-0.0353888\pi$
$588$		0			0
$589$	−20.1741	−	14.6574i	−0.831261	−	0.603947i
$590$		0			0
$591$	−14.3866	−	44.2774i	−0.591786	−	1.82133i
$592$		0			0
$593$	12.8414			0.527334			0.263667	−	0.964614i	$-0.415068\pi$
$593$	12.8414			0.527334			0.263667	+	0.964614i	$0.415068\pi$
$594$		0			0
$595$	4.34410			0.178091
$596$		0			0
$597$	−4.33728	−	13.3488i	−0.177513	−	0.546329i
$598$		0			0
$599$	−14.8097	−	10.7599i	−0.605108	−	0.439636i	0.242581	−	0.970131i	$-0.422006\pi$
$599$	−14.8097	−	10.7599i	−0.605108	−	0.439636i	−0.847688	+	0.530495i	$0.822006\pi$
$600$		0			0
$601$	4.98290	−	15.3358i	0.203257	−	0.625560i	−0.796524	−	0.604607i	$-0.793330\pi$
$601$	4.98290	−	15.3358i	0.203257	−	0.625560i	0.999780	−	0.0209527i	$-0.00666995\pi$
$602$		0			0
$603$	−1.84412	+	1.33983i	−0.0750985	+	0.0545623i
$604$		0			0
$605$	−0.980320	−	1.51131i	−0.0398557	−	0.0614436i
$606$		0			0
$607$	8.08900	−	5.87700i	0.328322	−	0.238540i	−0.411396	−	0.911457i	$-0.634959\pi$
$607$	8.08900	−	5.87700i	0.328322	−	0.238540i	0.739718	+	0.672917i	$0.234959\pi$
$608$		0			0
$609$	2.27839	−	7.01215i	0.0923249	−	0.284147i
$610$		0			0
$611$	−12.7020	−	9.22855i	−0.513868	−	0.373347i
$612$		0			0
$613$	12.3469	+	37.9997i	0.498685	+	1.53479i	0.811134	+	0.584860i	$0.198851\pi$
$613$	12.3469	+	37.9997i	0.498685	+	1.53479i	−0.312449	+	0.949934i	$0.601149\pi$
$614$		0			0
$615$	−0.0941059			−0.00379471
$616$		0			0
$617$	−28.5485			−1.14932			−0.574660	−	0.818392i	$-0.694866\pi$
$617$	−28.5485			−1.14932			−0.574660	+	0.818392i	$0.694866\pi$
$618$		0			0
$619$	4.02429	+	12.3855i	0.161750	+	0.497815i	0.998782	−	0.0493385i	$-0.0157113\pi$
$619$	4.02429	+	12.3855i	0.161750	+	0.497815i	−0.837032	+	0.547154i	$0.815711\pi$
$620$		0			0
$621$	2.11715	+	1.53820i	0.0849582	+	0.0617257i
$622$		0			0
$623$	6.82857	−	21.0162i	0.273581	−	0.841996i
$624$		0			0
$625$	−19.9006	+	14.4586i	−0.796022	+	0.578344i
$626$		0			0
$627$	13.4886	+	28.2987i	0.538683	+	1.13014i
$628$		0			0
$629$	71.0714	−	51.6364i	2.83380	−	2.05888i
$630$		0			0
$631$	−6.00401	+	18.4784i	−0.239016	+	0.735615i	0.757547	+	0.652780i	$0.226397\pi$
$631$	−6.00401	+	18.4784i	−0.239016	+	0.735615i	−0.996563	+	0.0828350i	$0.973603\pi$
$632$		0			0
$633$	−19.0466	−	13.8381i	−0.757032	−	0.550016i
$634$		0			0
$635$	0.866325	+	2.66628i	0.0343791	+	0.105808i
$636$		0			0
$637$	14.1617			0.561108
$638$		0			0
$639$	14.4712			0.572473
$640$		0			0
$641$	−4.50108	−	13.8529i	−0.177782	−	0.547156i	0.821968	−	0.569534i	$-0.192876\pi$
$641$	−4.50108	−	13.8529i	−0.177782	−	0.547156i	−0.999750	+	0.0223779i	$0.992876\pi$
$642$		0			0
$643$	2.92158	+	2.12265i	0.115216	+	0.0837092i	0.643901	−	0.765109i	$-0.277315\pi$
$643$	2.92158	+	2.12265i	0.115216	+	0.0837092i	−0.528685	+	0.848818i	$0.677315\pi$
$644$		0			0
$645$	0.446609	−	1.37452i	0.0175852	−	0.0541217i
$646$		0			0
$647$	5.38652	−	3.91354i	0.211766	−	0.153857i	−0.476846	−	0.878987i	$-0.658220\pi$
$647$	5.38652	−	3.91354i	0.211766	−	0.153857i	0.688612	+	0.725130i	$0.258220\pi$
$648$		0			0
$649$	−9.00564	−	4.89275i	−0.353502	−	0.192057i
$650$		0			0
$651$	31.3044	−	22.7440i	1.22692	−	0.891408i
$652$		0			0
$653$	0.814815	−	2.50774i	0.0318862	−	0.0981356i	−0.933847	−	0.357673i	$-0.883570\pi$
$653$	0.814815	−	2.50774i	0.0318862	−	0.0981356i	0.965733	+	0.259538i	$0.0835702\pi$
$654$		0			0
$655$	0.665548	+	0.483549i	0.0260051	+	0.0188938i
$656$		0			0
$657$	−4.18096	−	12.8677i	−0.163115	−	0.502015i
$658$		0			0
$659$	18.2059			0.709200			0.354600	−	0.935018i	$-0.384617\pi$
$659$	18.2059			0.709200			0.354600	+	0.935018i	$0.384617\pi$
$660$		0			0
$661$	37.6750			1.46539			0.732693	−	0.680559i	$-0.238263\pi$
$661$	37.6750			1.46539			0.732693	+	0.680559i	$0.238263\pi$
$662$		0			0
$663$	12.9088	+	39.7293i	0.501337	+	1.54296i
$664$		0			0
$665$	2.14207	+	1.55630i	0.0830658	+	0.0603509i
$666$		0			0
$667$	0.224509	−	0.690968i	0.00869303	−	0.0267544i
$668$		0			0
$669$	26.9397	−	19.5728i	1.04155	−	0.756730i
$670$		0			0
$671$	16.6809	−	15.8212i	0.643958	−	0.610769i
$672$		0			0
$673$	−13.9996	+	10.1713i	−0.539644	+	0.392074i	−0.823953	−	0.566658i	$-0.808236\pi$
$673$	−13.9996	+	10.1713i	−0.539644	+	0.392074i	0.284309	+	0.958733i	$0.408236\pi$
$674$		0			0
$675$	−5.69555	+	17.5291i	−0.219222	+	0.674695i
$676$		0			0
$677$	−7.77933	−	5.65202i	−0.298984	−	0.217225i	0.428171	−	0.903698i	$-0.359158\pi$
$677$	−7.77933	−	5.65202i	−0.298984	−	0.217225i	−0.727155	+	0.686473i	$0.759158\pi$
$678$		0			0
$679$	7.57910	+	23.3261i	0.290859	+	0.895172i
$680$		0			0
$681$	−12.7062			−0.486902
$682$		0			0
$683$	−33.2554			−1.27248			−0.636241	−	0.771491i	$-0.719511\pi$
$683$	−33.2554			−1.27248			−0.636241	+	0.771491i	$0.719511\pi$
$684$		0			0
$685$	−0.152095	−	0.468101i	−0.00581126	−	0.0178852i
$686$		0			0
$687$	−34.1774	−	24.8314i	−1.30395	−	0.947375i
$688$		0			0
$689$	8.21748	−	25.2908i	0.313061	−	0.963502i
$690$		0			0
$691$	−13.7945	+	10.0223i	−0.524768	+	0.381266i	−0.818397	−	0.574653i	$-0.805137\pi$
$691$	−13.7945	+	10.0223i	−0.524768	+	0.381266i	0.293629	+	0.955919i	$0.405137\pi$
$692$		0			0
$693$	−13.6920	+	1.79889i	−0.520115	+	0.0683344i
$694$		0			0
$695$	−0.710221	+	0.516006i	−0.0269402	+	0.0195732i
$696$		0			0
$697$	0.657340	−	2.02308i	0.0248985	−	0.0766297i
$698$		0			0
$699$	−17.0110	−	12.3592i	−0.643414	−	0.467468i
$700$		0			0
$701$	−11.3166	−	34.8289i	−0.427422	−	1.31547i	−0.900656	−	0.434533i	$-0.856913\pi$
$701$	−11.3166	−	34.8289i	−0.427422	−	1.31547i	0.473234	−	0.880937i	$-0.343087\pi$
$702$		0			0
$703$	53.5442			2.01946
$704$		0			0
$705$	1.95368			0.0735798
$706$		0			0
$707$	4.35278	+	13.3965i	0.163703	+	0.503826i
$708$		0			0
$709$	−15.8194	−	11.4935i	−0.594112	−	0.431647i	0.249672	−	0.968330i	$-0.419677\pi$
$709$	−15.8194	−	11.4935i	−0.594112	−	0.431647i	−0.843784	+	0.536683i	$0.819677\pi$
$710$		0			0
$711$	−0.634826	+	1.95379i	−0.0238078	+	0.0732729i
$712$		0			0
$713$	3.08470	−	2.24116i	0.115523	−	0.0839323i
$714$		0			0
$715$	0.267007	−	1.43851i	0.00998549	−	0.0537974i
$716$		0			0
$717$	−33.1870	+	24.1118i	−1.23939	+	0.900470i
$718$		0			0
$719$	1.09209	−	3.36110i	0.0407280	−	0.125348i	−0.928625	−	0.371019i	$-0.879008\pi$
$719$	1.09209	−	3.36110i	0.0407280	−	0.125348i	0.969353	+	0.245671i	$0.0790084\pi$
$720$		0			0
$721$	−42.6692	−	31.0010i	−1.58908	−	1.15454i
$722$		0			0
$723$	4.34915	+	13.3853i	0.161747	+	0.497805i
$724$		0			0
$725$	5.11695			0.190039
$726$		0			0
$727$	5.02836			0.186491			0.0932457	−	0.995643i	$-0.470276\pi$
$727$	5.02836			0.186491			0.0932457	+	0.995643i	$0.470276\pi$
$728$		0			0
$729$	2.93320	+	9.02746i	0.108637	+	0.334350i
$730$		0			0
$731$	26.4298	+	19.2024i	0.977540	+	0.710225i
$732$		0			0
$733$	−3.52505	+	10.8490i	−0.130201	+	0.400716i	−0.994813	−	0.101724i	$-0.967564\pi$
$733$	−3.52505	+	10.8490i	−0.130201	+	0.400716i	0.864612	+	0.502440i	$0.167564\pi$
$734$		0			0
$735$	−1.42565	+	1.03580i	−0.0525859	+	0.0382059i
$736$		0			0
$737$	−1.16009	+	6.25007i	−0.0427326	+	0.230224i
$738$		0			0
$739$	−3.65966	+	2.65890i	−0.134623	+	0.0978091i	−0.653059	−	0.757307i	$-0.726514\pi$
$739$	−3.65966	+	2.65890i	−0.134623	+	0.0978091i	0.518436	+	0.855116i	$0.326514\pi$
$740$		0			0
$741$	−7.86796	+	24.2151i	−0.289037	+	0.889564i
$742$		0			0
$743$	−19.5365	−	14.1941i	−0.716725	−	0.520731i	0.168611	−	0.985683i	$-0.446072\pi$
$743$	−19.5365	−	14.1941i	−0.716725	−	0.520731i	−0.885336	+	0.464952i	$0.846072\pi$
$744$		0			0
$745$	−0.294574	−	0.906605i	−0.0107924	−	0.0332155i
$746$		0			0
$747$	5.60097			0.204929
$748$		0			0
$749$	−1.81673			−0.0663820
$750$		0			0
$751$	4.56162	+	14.0392i	0.166456	+	0.512298i	0.999141	−	0.0414489i	$-0.0131974\pi$
$751$	4.56162	+	14.0392i	0.166456	+	0.512298i	−0.832685	+	0.553747i	$0.813197\pi$
$752$		0			0
$753$	8.61319	+	6.25785i	0.313882	+	0.228049i
$754$		0			0
$755$	−0.184492	+	0.567809i	−0.00671436	+	0.0206647i
$756$		0			0
$757$	−10.2060	+	7.41508i	−0.370943	+	0.269506i	−0.757602	−	0.652717i	$-0.773629\pi$
$757$	−10.2060	+	7.41508i	−0.370943	+	0.269506i	0.386659	+	0.922223i	$0.373629\pi$
$758$		0			0
$759$	−4.75253	+	0.624402i	−0.172506	+	0.0226644i
$760$		0			0
$761$	20.0141	−	14.5411i	0.725509	−	0.527113i	−0.162630	−	0.986687i	$-0.551998\pi$
$761$	20.0141	−	14.5411i	0.725509	−	0.527113i	0.888140	+	0.459574i	$0.151998\pi$
$762$		0			0
$763$	−0.308371	+	0.949069i	−0.0111638	+	0.0343586i
$764$		0			0
$765$	−1.19385	−	0.867381i	−0.0431636	−	0.0313602i
$766$		0			0
$767$	−2.57227	−	7.91664i	−0.0928794	−	0.285853i
$768$		0			0
$769$	−5.37741			−0.193914			−0.0969571	−	0.995289i	$-0.530911\pi$
$769$	−5.37741			−0.193914			−0.0969571	+	0.995289i	$0.530911\pi$
$770$		0			0
$771$	−38.0642			−1.37085
$772$		0			0
$773$	5.02699	+	15.4715i	0.180808	+	0.556471i	0.999851	−	0.0172619i	$-0.00549490\pi$
$773$	5.02699	+	15.4715i	0.180808	+	0.556471i	−0.819043	+	0.573733i	$0.805495\pi$
$774$		0			0
$775$	21.7256	+	15.7846i	0.780407	+	0.566999i
$776$		0			0
$777$	−25.6747	+	79.0187i	−0.921076	+	2.83478i
$778$		0			0
$779$	1.04892	−	0.762081i	0.0375813	−	0.0273044i
$780$		0			0
$781$	29.2809	−	27.7718i	1.04775	−	0.993754i
$782$		0			0
$783$	3.08499	−	2.24137i	0.110248	−	0.0801002i
$784$		0			0
$785$	−0.00734599	+	0.0226086i	−0.000262190	+	0.000806937i
$786$		0			0
$787$	15.0196	+	10.9124i	0.535392	+	0.388985i	0.822371	−	0.568952i	$-0.192651\pi$
$787$	15.0196	+	10.9124i	0.535392	+	0.388985i	−0.286979	+	0.957937i	$0.592651\pi$
$788$		0			0
$789$	−0.808678	−	2.48886i	−0.0287897	−	0.0886056i
$790$		0			0
$791$	−40.5038			−1.44015
$792$		0			0
$793$	18.6725			0.663081
$794$		0			0
$795$	1.02253	+	3.14703i	0.0362655	+	0.111614i
$796$		0			0
$797$	26.0278	+	18.9103i	0.921952	+	0.669837i	0.944009	−	0.329919i	$-0.107022\pi$
$797$	26.0278	+	18.9103i	0.921952	+	0.669837i	−0.0220572	+	0.999757i	$0.507022\pi$
$798$		0			0
$799$	−13.6467	+	42.0001i	−0.482784	+	1.48586i
$800$		0			0
$801$	−6.07290	+	4.41222i	−0.214575	+	0.155898i
$802$		0			0
$803$	−33.1541	−	18.0126i	−1.16998	−	0.635650i
$804$		0			0
$805$	−0.327530	+	0.237964i	−0.0115439	+	0.00838714i
$806$		0			0
$807$	−1.70375	+	5.24359i	−0.0599747	+	0.184583i
$808$		0			0
$809$	23.4124	+	17.0101i	0.823138	+	0.598045i	0.917610	−	0.397483i	$-0.130116\pi$
$809$	23.4124	+	17.0101i	0.823138	+	0.598045i	−0.0944717	+	0.995528i	$0.530116\pi$
$810$		0			0
$811$	3.10198	+	9.54691i	0.108925	+	0.335237i	0.990632	−	0.136561i	$-0.0436050\pi$
$811$	3.10198	+	9.54691i	0.108925	+	0.335237i	−0.881706	+	0.471799i	$0.843605\pi$
$812$		0			0
$813$	21.2609			0.745652
$814$		0			0
$815$	2.36450			0.0828249
$816$		0			0
$817$	6.15309	+	18.9373i	0.215269	+	0.662531i
$818$		0			0
$819$	−9.07395	−	6.59261i	−0.317069	−	0.230364i
$820$		0			0
$821$	−9.27874	+	28.5570i	−0.323830	+	0.996647i	0.648136	+	0.761525i	$0.275549\pi$
$821$	−9.27874	+	28.5570i	−0.323830	+	0.996647i	−0.971966	+	0.235122i	$0.924451\pi$
$822$		0			0
$823$	24.7215	−	17.9612i	0.861738	−	0.626089i	−0.0666193	−	0.997778i	$-0.521221\pi$
$823$	24.7215	−	17.9612i	0.861738	−	0.626089i	0.928357	+	0.371689i	$0.121221\pi$
$824$		0			0
$825$	−14.5259	−	30.4750i	−0.505728	−	1.06100i
$826$		0			0
$827$	4.75466	−	3.45446i	0.165336	−	0.120123i	−0.502041	−	0.864844i	$-0.667417\pi$
$827$	4.75466	−	3.45446i	0.165336	−	0.120123i	0.667376	+	0.744721i	$0.267417\pi$
$828$		0			0
$829$	−3.23670	+	9.96152i	−0.112415	+	0.345978i	−0.991399	−	0.130873i	$-0.958222\pi$
$829$	−3.23670	+	9.96152i	−0.112415	+	0.345978i	0.878984	+	0.476851i	$0.158222\pi$
$830$		0			0
$831$	−12.1052	−	8.79496i	−0.419925	−	0.305094i
$832$		0			0
$833$	−12.3092	−	37.8837i	−0.426487	−	1.31259i
$834$		0			0
$835$	−2.85602			−0.0988366
$836$		0			0
$837$	20.0124			0.691730
$838$		0			0
$839$	−10.3026	−	31.7082i	−0.355686	−	1.09469i	−0.955610	−	0.294633i	$-0.904803\pi$
$839$	−10.3026	−	31.7082i	−0.355686	−	1.09469i	0.599924	−	0.800057i	$-0.295197\pi$
$840$		0			0
$841$	22.6050	+	16.4235i	0.779484	+	0.566328i
$842$		0			0
$843$	10.5912	−	32.5963i	0.364779	−	1.12267i
$844$		0			0
$845$	−0.760998	+	0.552897i	−0.0261791	+	0.0190203i
$846$		0			0
$847$	−24.2519	+	29.9162i	−0.833306	+	1.02793i
$848$		0			0
$849$	−33.9096	+	24.6368i	−1.16377	+	0.845532i
$850$		0			0
$851$	−2.52995	+	7.78640i	−0.0867257	+	0.266914i
$852$		0			0
$853$	22.4071	+	16.2797i	0.767205	+	0.557407i	0.901112	−	0.433587i	$-0.142752\pi$
$853$	22.4071	+	16.2797i	0.767205	+	0.557407i	−0.133907	+	0.990994i	$0.542752\pi$
$854$		0			0
$855$	−0.277939	−	0.855407i	−0.00950530	−	0.0292543i
$856$		0			0
$857$	−2.13818			−0.0730387			−0.0365194	−	0.999333i	$-0.511627\pi$
$857$	−2.13818			−0.0730387			−0.0365194	+	0.999333i	$0.511627\pi$
$858$		0			0
$859$	−6.06982			−0.207099			−0.103550	−	0.994624i	$-0.533020\pi$
$859$	−6.06982			−0.207099			−0.103550	+	0.994624i	$0.533020\pi$
$860$		0			0
$861$	0.621693	+	1.91337i	0.0211872	+	0.0652076i
$862$		0			0
$863$	−24.1070	−	17.5148i	−0.820613	−	0.596210i	0.0962753	−	0.995355i	$-0.469307\pi$
$863$	−24.1070	−	17.5148i	−0.820613	−	0.596210i	−0.916888	+	0.399145i	$0.869307\pi$
$864$		0			0
$865$	0.923202	−	2.84132i	0.0313898	−	0.0966079i
$866$		0			0
$867$	66.9087	−	48.6120i	2.27234	−	1.65095i
$868$		0			0
$869$	2.46503	+	5.17158i	0.0836206	+	0.175434i
$870$		0			0
$871$	−4.17690	+	3.03469i	−0.141529	+	0.102827i
$872$		0			0
$873$	2.57459	−	7.92378i	0.0871367	−	0.268179i
$874$		0			0
$875$	−4.62604	−	3.36102i	−0.156389	−	0.113623i
$876$		0			0
$877$	−11.4515	−	35.2440i	−0.386688	−	1.19010i	−0.935248	−	0.353993i	$-0.884824\pi$
$877$	−11.4515	−	35.2440i	−0.386688	−	1.19010i	0.548560	−	0.836111i	$-0.315176\pi$
$878$		0			0
$879$	38.1954			1.28830
$880$		0			0
$881$	−10.6956			−0.360345			−0.180172	−	0.983635i	$-0.557666\pi$
$881$	−10.6956			−0.360345			−0.180172	+	0.983635i	$0.557666\pi$
$882$		0			0
$883$	−4.97395	−	15.3082i	−0.167387	−	0.515163i	0.831818	−	0.555049i	$-0.187301\pi$
$883$	−4.97395	−	15.3082i	−0.167387	−	0.515163i	−0.999204	+	0.0398858i	$0.987301\pi$
$884$		0			0
$885$	0.837975	+	0.608825i	0.0281682	+	0.0204654i
$886$		0			0
$887$	8.12229	−	24.9978i	0.272720	−	0.839345i	−0.717094	−	0.696977i	$-0.754528\pi$
$887$	8.12229	−	24.9978i	0.272720	−	0.839345i	0.989814	−	0.142369i	$-0.0454719\pi$
$888$		0			0
$889$	48.4879	−	35.2285i	1.62623	−	1.18153i
$890$		0			0
$891$	−32.5044	−	17.6596i	−1.08894	−	0.591619i
$892$		0			0
$893$	−21.7760	+	15.8212i	−0.728704	+	0.529435i
$894$		0			0
$895$	0.462944	−	1.42480i	0.0154745	−	0.0476257i
$896$		0			0
$897$	−3.14960	−	2.28832i	−0.105162	−	0.0764046i
$898$		0			0
$899$	−1.71688	−	5.28401i	−0.0572611	−	0.176232i
$900$		0			0
$901$	−74.7972			−2.49186
$902$		0			0
$903$	−30.8974			−1.02820
$904$		0			0
$905$	0.842090	+	2.59169i	0.0279920	+	0.0861506i
$906$		0			0
$907$	5.33332	+	3.87489i	0.177090	+	0.128663i	0.672799	−	0.739825i	$-0.265092\pi$
$907$	5.33332	+	3.87489i	0.177090	+	0.128663i	−0.495709	+	0.868489i	$0.665092\pi$
$908$		0			0
$909$	1.47862	−	4.55073i	0.0490428	−	0.150938i
$910$		0			0
$911$	35.7326	−	25.9613i	1.18387	−	0.860135i	0.191271	−	0.981537i	$-0.438739\pi$
$911$	35.7326	−	25.9613i	1.18387	−	0.860135i	0.992603	+	0.121402i	$0.0387391\pi$
$912$		0			0
$913$	11.3329	−	10.7488i	0.375065	−	0.355735i
$914$		0			0
$915$	−1.87975	+	1.36572i	−0.0621425	+	0.0451492i
$916$		0			0
$917$	5.43477	−	16.7265i	0.179472	−	0.552358i
$918$		0			0
$919$	−25.4641	−	18.5008i	−0.839983	−	0.610284i	0.0823828	−	0.996601i	$-0.473747\pi$
$919$	−25.4641	−	18.5008i	−0.839983	−	0.610284i	−0.922366	+	0.386317i	$0.873747\pi$
$920$		0			0
$921$	10.2970	+	31.6910i	0.339299	+	1.04425i
$922$		0			0
$923$	32.7770			1.07887
$924$		0			0
$925$	−57.6620			−1.89592
$926$		0			0
$927$	5.53643	+	17.0394i	0.181840	+	0.559646i
$928$		0			0
$929$	26.2675	+	19.0845i	0.861810	+	0.626142i	0.928377	−	0.371640i	$-0.121204\pi$
$929$	26.2675	+	19.0845i	0.861810	+	0.626142i	−0.0665666	+	0.997782i	$0.521204\pi$
$930$		0			0
$931$	7.50246	−	23.0902i	0.245883	−	0.756751i
$932$		0			0
$933$	17.3074	−	12.5745i	0.566617	−	0.411672i
$934$		0			0
$935$	−4.08021	+	0.536071i	−0.133437	+	0.0175314i
$936$		0			0
$937$	23.4691	−	17.0513i	0.766701	−	0.557041i	−0.134257	−	0.990947i	$-0.542865\pi$
$937$	23.4691	−	17.0513i	0.766701	−	0.557041i	0.900958	+	0.433905i	$0.142865\pi$
$938$		0			0
$939$	−5.32762	+	16.3967i	−0.173860	+	0.535087i
$940$		0			0
$941$	−4.76511	−	3.46205i	−0.155338	−	0.112860i	0.507401	−	0.861710i	$-0.330606\pi$
$941$	−4.76511	−	3.46205i	−0.155338	−	0.112860i	−0.662739	+	0.748850i	$0.730606\pi$
$942$		0			0
$943$	0.0612608	+	0.188541i	0.00199493	+	0.00613975i
$944$		0			0
$945$	−2.12489			−0.0691228
$946$		0			0
$947$	52.2319			1.69731			0.848655	−	0.528947i	$-0.177413\pi$
$947$	52.2319			1.69731			0.848655	+	0.528947i	$0.177413\pi$
$948$		0			0
$949$	−9.46977	−	29.1450i	−0.307402	−	0.946085i
$950$		0			0
$951$	35.5493	+	25.8281i	1.15277	+	0.837534i
$952$		0			0
$953$	−11.8723	+	36.5391i	−0.384581	+	1.18362i	0.552203	+	0.833710i	$0.313787\pi$
$953$	−11.8723	+	36.5391i	−0.384581	+	1.18362i	−0.936784	+	0.349909i	$0.886213\pi$
$954$		0			0
$955$	−1.01714	+	0.738997i	−0.0329139	+	0.0239134i
$956$		0			0
$957$	−1.27467	+	6.86734i	−0.0412041	+	0.221990i
$958$		0			0
$959$	−8.51271	+	6.18485i	−0.274890	+	0.199719i
$960$		0			0
$961$	−0.569149	+	1.75166i	−0.0183596	+	0.0565052i
$962$		0			0
$963$	0.499275	+	0.362745i	0.0160889	+	0.0116893i
$964$		0			0
$965$	−0.995400	−	3.06352i	−0.0320430	−	0.0986183i
$966$		0			0
$967$	50.8436			1.63502			0.817509	−	0.575915i	$-0.195354\pi$
$967$	50.8436			1.63502			0.817509	+	0.575915i	$0.195354\pi$
$968$		0			0
$969$	71.6159			2.30063
$970$		0			0
$971$	−2.44121	−	7.51327i	−0.0783422	−	0.241112i	0.904214	−	0.427080i	$-0.140458\pi$
$971$	−2.44121	−	7.51327i	−0.0783422	−	0.241112i	−0.982556	+	0.185968i	$0.940458\pi$
$972$		0			0
$973$	15.1834	+	11.0314i	0.486759	+	0.353651i
$974$		0			0
$975$	8.47304	−	26.0773i	0.271354	−	0.835143i
$976$		0			0
$977$	12.9596	−	9.41571i	0.414615	−	0.301235i	−0.360853	−	0.932623i	$-0.617514\pi$
$977$	12.9596	−	9.41571i	0.414615	−	0.301235i	0.775467	+	0.631388i	$0.217514\pi$
$978$		0			0
$979$	−3.82032	+	20.5822i	−0.122098	+	0.657809i
$980$		0			0
$981$	0.274246	−	0.199251i	0.00875599	−	0.00636160i
$982$		0			0
$983$	−18.0716	+	55.6186i	−0.576394	+	1.77396i	0.0549895	+	0.998487i	$0.482487\pi$
$983$	−18.0716	+	55.6186i	−0.576394	+	1.77396i	−0.631383	+	0.775471i	$0.717513\pi$
$984$		0			0
$985$	3.01359	+	2.18950i	0.0960209	+	0.0697633i
$986$		0			0
$987$	−12.9066	−	39.7225i	−0.410822	−	1.26438i
$988$		0			0
$989$	−3.04459			−0.0968123
$990$		0			0
$991$	−17.1741			−0.545552			−0.272776	−	0.962078i	$-0.587942\pi$
$991$	−17.1741			−0.545552			−0.272776	+	0.962078i	$0.587942\pi$
$992$		0			0
$993$	−13.6271	−	41.9400i	−0.432443	−	1.33092i
$994$		0			0
$995$	0.908538	+	0.660092i	0.0288026	+	0.0209263i
$996$		0			0
$997$	−12.8382	+	39.5118i	−0.406588	+	1.25135i	0.512973	+	0.858405i	$0.328544\pi$
$997$	−12.8382	+	39.5118i	−0.406588	+	1.25135i	−0.919562	+	0.392946i	$0.871456\pi$
$998$		0			0
$999$	−34.7642	+	25.2577i	−1.09989	+	0.799117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.i.b.25.1	✓	8
3.2	odd	2		792.2.r.g.289.1		8
4.3	odd	2		176.2.m.d.113.2		8
8.3	odd	2		704.2.m.i.641.1		8
8.5	even	2		704.2.m.l.641.2		8
11.2	odd	10		968.2.a.m.1.1		4
11.3	even	5		968.2.i.s.753.2		8
11.4	even	5	inner	88.2.i.b.81.1	yes	8
11.5	even	5		968.2.i.s.9.2		8
11.6	odd	10		968.2.i.t.9.2		8
11.7	odd	10		968.2.i.p.81.1		8
11.8	odd	10		968.2.i.t.753.2		8
11.9	even	5		968.2.a.n.1.1		4
11.10	odd	2		968.2.i.p.729.1		8
33.2	even	10		8712.2.a.cd.1.3		4
33.20	odd	10		8712.2.a.ce.1.3		4
33.26	odd	10		792.2.r.g.433.1		8
44.15	odd	10		176.2.m.d.81.2		8
44.31	odd	10		1936.2.a.bb.1.4		4
44.35	even	10		1936.2.a.bc.1.4		4
88.13	odd	10		7744.2.a.dh.1.4		4
88.35	even	10		7744.2.a.ds.1.1		4
88.37	even	10		704.2.m.l.257.2		8
88.53	even	10		7744.2.a.di.1.4		4
88.59	odd	10		704.2.m.i.257.1		8
88.75	odd	10		7744.2.a.dr.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.25.1	✓	8	1.1	even	1	trivial
88.2.i.b.81.1	yes	8	11.4	even	5	inner
176.2.m.d.81.2		8	44.15	odd	10
176.2.m.d.113.2		8	4.3	odd	2
704.2.m.i.257.1		8	88.59	odd	10
704.2.m.i.641.1		8	8.3	odd	2
704.2.m.l.257.2		8	88.37	even	10
704.2.m.l.641.2		8	8.5	even	2
792.2.r.g.289.1		8	3.2	odd	2
792.2.r.g.433.1		8	33.26	odd	10
968.2.a.m.1.1		4	11.2	odd	10
968.2.a.n.1.1		4	11.9	even	5
968.2.i.p.81.1		8	11.7	odd	10
968.2.i.p.729.1		8	11.10	odd	2
968.2.i.s.9.2		8	11.5	even	5
968.2.i.s.753.2		8	11.3	even	5
968.2.i.t.9.2		8	11.6	odd	10
968.2.i.t.753.2		8	11.8	odd	10
1936.2.a.bb.1.4		4	44.31	odd	10
1936.2.a.bc.1.4		4	44.35	even	10
7744.2.a.dh.1.4		4	88.13	odd	10
7744.2.a.di.1.4		4	88.53	even	10
7744.2.a.dr.1.1		4	88.75	odd	10
7744.2.a.ds.1.1		4	88.35	even	10
8712.2.a.cd.1.3		4	33.2	even	10
8712.2.a.ce.1.3		4	33.20	odd	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.632489 - 1.94660i) q^{3} +(0.132489 + 0.0962586i) q^{5} +(1.08188 - 3.32969i) q^{7} +(-0.962157 + 0.699048i) q^{9} +(-0.605270 + 3.26093i) q^{11} +(-2.17926 + 1.58333i) q^{13} +(0.103579 - 0.318785i) q^{15} +(6.12970 + 4.45349i) q^{17} +(1.42705 + 4.39201i) q^{19} -7.16586 q^{21} -0.706114 q^{23} +(-1.53680 - 4.72978i) q^{25} +(-2.99831 - 2.17840i) q^{27} +(-0.317950 + 0.978551i) q^{29} +(-4.36856 + 3.17394i) q^{31} +(6.73055 - 0.884280i) q^{33} +(0.463848 - 0.337006i) q^{35} +(3.58293 - 11.0271i) q^{37} +(4.46047 + 3.24072i) q^{39} +(-0.0867577 - 0.267013i) q^{41} +4.31175 q^{43} -0.194764 q^{45} +(1.80113 + 5.54330i) q^{47} +(-4.25326 - 3.09017i) q^{49} +(4.79220 - 14.7489i) q^{51} +(-7.98659 + 5.80260i) q^{53} +(-0.394084 + 0.373773i) q^{55} +(7.64689 - 5.55579i) q^{57} +(-0.954915 + 2.93893i) q^{59} +(-5.60801 - 4.07446i) q^{61} +(1.28667 + 3.95998i) q^{63} -0.441137 q^{65} +1.91665 q^{67} +(0.446609 + 1.37452i) q^{69} +(-9.84407 - 7.15214i) q^{71} +(-3.51550 + 10.8196i) q^{73} +(-8.23497 + 5.98306i) q^{75} +(10.2031 + 5.54330i) q^{77} +(1.39747 - 1.01532i) q^{79} +(-3.44661 + 10.6076i) q^{81} +(-3.81006 - 2.76817i) q^{83} +(0.383429 + 1.18007i) q^{85} +2.10595 q^{87} +6.31175 q^{89} +(2.91429 + 8.96925i) q^{91} +(8.94146 + 6.49635i) q^{93} +(-0.233701 + 0.719257i) q^{95} +(-5.66755 + 4.11771i) q^{97} +(-1.69718 - 3.56064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9} + 7 q^{11} + 7 q^{13} - 13 q^{15} + q^{17} - 2 q^{19} - 2 q^{21} - 4 q^{23} - 33 q^{25} - 22 q^{27} + 17 q^{29} - 13 q^{31} + 16 q^{33} + 11 q^{35} + q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 8 * q - q^3 - 3 * q^5 + 7 * q^7 - 13 * q^9 + 7 * q^11 + 7 * q^13 - 13 * q^15 + q^17 - 2 * q^19 - 2 * q^21 - 4 * q^23 - 33 * q^25 - 22 * q^27 + 17 * q^29 - 13 * q^31 + 16 * q^33 + 11 * q^35 + q^37 + 39 * q^39 + 9 * q^41 + 6 * q^43 + 44 * q^45 - q^47 + 3 * q^49 + 38 * q^51 - 33 * q^53 + 13 * q^55 - 6 * q^57 - 30 * q^59 - 9 * q^61 - 10 * q^63 - 10 * q^65 - 10 * q^67 - 38 * q^69 - 25 * q^71 - 7 * q^73 - 6 * q^75 - 7 * q^77 - q^79 + 14 * q^81 + 39 * q^85 - 6 * q^87 + 22 * q^89 + 7 * q^91 - 5 * q^93 + 7 * q^95 + 8 * q^97 - 27 * q^99

Introduction

L-functions

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