LMFDB - Embedded newform 92.2.e.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 51x^18 - 200x^17 + 633x^16 - 1688x^15 + 3957x^14 - 8161x^13 + 14788x^12 - 23925x^11 + 35080x^10 - 43945x^9 + 57269x^8 - 57348x^7 + 52821x^6 - 34986x^5 + 26231x^4 + 96928x^3 + 49370x^2 + 8165*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.2
Root			$-0.967148 + 1.11615i$ of defining polynomial
Character	$\chi$	$=$	92.25
Dual form			92.2.e.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.210181 + 1.46184i) q^{3} +(0.926812 + 0.272136i) q^{5} +(-1.14874 + 1.32572i) q^{7} +(0.785668 - 0.230693i) q^{9} +O(q^{10})$	\(q+(0.210181 + 1.46184i) q^{3} +(0.926812 + 0.272136i) q^{5} +(-1.14874 + 1.32572i) q^{7} +(0.785668 - 0.230693i) q^{9} +(0.436414 - 0.280466i) q^{11} +(-2.04423 - 2.35917i) q^{13} +(-0.203022 + 1.41205i) q^{15} +(1.39464 - 3.05384i) q^{17} +(-2.90720 - 6.36588i) q^{19} +(-2.17943 - 1.40064i) q^{21} +(-1.35369 + 4.60082i) q^{23} +(-3.42135 - 2.19877i) q^{25} +(2.34292 + 5.13028i) q^{27} +(1.01343 - 2.21909i) q^{29} +(-0.253078 + 1.76020i) q^{31} +(0.501724 + 0.579020i) q^{33} +(-1.42544 + 0.916075i) q^{35} +(-4.58723 + 1.34693i) q^{37} +(3.01908 - 3.48420i) q^{39} +(12.0596 + 3.54102i) q^{41} +(-0.236292 - 1.64344i) q^{43} +0.790946 q^{45} +5.46023 q^{47} +(0.558283 + 3.88295i) q^{49} +(4.75737 + 1.39689i) q^{51} +(-8.08238 + 9.32757i) q^{53} +(0.480798 - 0.141175i) q^{55} +(8.69489 - 5.58786i) q^{57} +(-0.434046 - 0.500915i) q^{59} +(-0.685355 + 4.76675i) q^{61} +(-0.596695 + 1.30658i) q^{63} +(-1.25260 - 2.74282i) q^{65} +(-9.51795 - 6.11682i) q^{67} +(-7.01020 - 1.01188i) q^{69} +(-4.30334 - 2.76559i) q^{71} +(5.40478 + 11.8348i) q^{73} +(2.49515 - 5.46361i) q^{75} +(-0.129507 + 0.900743i) q^{77} +(-9.56521 - 11.0388i) q^{79} +(-4.94068 + 3.17518i) q^{81} +(2.91071 - 0.854661i) q^{83} +(2.12363 - 2.45080i) q^{85} +(3.45697 + 1.01506i) q^{87} +(-1.78337 - 12.4036i) q^{89} +5.47588 q^{91} -2.62633 q^{93} +(-0.962039 - 6.69113i) q^{95} +(-0.645676 - 0.189588i) q^{97} +(0.278175 - 0.321031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.210181	+	1.46184i	0.121348	+	0.843996i	0.956031	+	0.293265i	$0.0947418\pi$
$3$	0.210181	+	1.46184i	0.121348	+	0.843996i	−0.834683	+	0.550731i	$0.814349\pi$
$4$		0			0
$5$	0.926812	+	0.272136i	0.414483	+	0.121703i	0.482324	−	0.875993i	$-0.339793\pi$
$5$	0.926812	+	0.272136i	0.414483	+	0.121703i	−0.0678410	+	0.997696i	$0.521611\pi$
$6$		0			0
$7$	−1.14874	+	1.32572i	−0.434183	+	0.501074i	−0.930105	−	0.367293i	$-0.880285\pi$
$7$	−1.14874	+	1.32572i	−0.434183	+	0.501074i	0.495922	+	0.868367i	$0.334830\pi$
$8$		0			0
$9$	0.785668	−	0.230693i	0.261889	−	0.0768977i
$10$		0			0
$11$	0.436414	−	0.280466i	0.131584	−	0.0845637i	−0.473193	−	0.880959i	$-0.656899\pi$
$11$	0.436414	−	0.280466i	0.131584	−	0.0845637i	0.604777	+	0.796395i	$0.293262\pi$
$12$		0			0
$13$	−2.04423	−	2.35917i	−0.566968	−	0.654316i	0.397783	−	0.917479i	$-0.369780\pi$
$13$	−2.04423	−	2.35917i	−0.566968	−	0.654316i	−0.964751	+	0.263163i	$0.915234\pi$
$14$		0			0
$15$	−0.203022	+	1.41205i	−0.0524202	+	0.364590i
$16$		0			0
$17$	1.39464	−	3.05384i	0.338251	−	0.740666i	−0.661708	−	0.749762i	$-0.730168\pi$
$17$	1.39464	−	3.05384i	0.338251	−	0.740666i	0.999959	+	0.00909607i	$0.00289541\pi$
$18$		0			0
$19$	−2.90720	−	6.36588i	−0.666958	−	1.46043i	−0.875894	−	0.482504i	$-0.839727\pi$
$19$	−2.90720	−	6.36588i	−0.666958	−	1.46043i	0.208936	−	0.977929i	$-0.433000\pi$
$20$		0			0
$21$	−2.17943	−	1.40064i	−0.475591	−	0.305644i
$22$		0			0
$23$	−1.35369	+	4.60082i	−0.282264	+	0.959337i
$23$	−1.35369	+	4.60082i	−0.282264	+	0.959337i
$24$		0			0
$25$	−3.42135	−	2.19877i	−0.684269	−	0.439753i
$26$		0			0
$27$	2.34292	+	5.13028i	0.450895	+	0.987322i
$28$		0			0
$29$	1.01343	−	2.21909i	0.188188	−	0.412075i	−0.791896	−	0.610656i	$-0.790906\pi$
$29$	1.01343	−	2.21909i	0.188188	−	0.412075i	0.980085	+	0.198581i	$0.0636332\pi$
$30$		0			0
$31$	−0.253078	+	1.76020i	−0.0454542	+	0.316141i	0.954391	+	0.298559i	$0.0965059\pi$
$31$	−0.253078	+	1.76020i	−0.0454542	+	0.316141i	−0.999845	+	0.0175820i	$0.994403\pi$
$32$		0			0
$33$	0.501724	+	0.579020i	0.0873389	+	0.100794i
$34$		0			0
$35$	−1.42544	+	0.916075i	−0.240943	+	0.154845i
$36$		0			0
$37$	−4.58723	+	1.34693i	−0.754135	+	0.221434i	−0.636133	−	0.771579i	$-0.719467\pi$
$37$	−4.58723	+	1.34693i	−0.754135	+	0.221434i	−0.118002	+	0.993013i	$0.537649\pi$
$38$		0			0
$39$	3.01908	−	3.48420i	0.483439	−	0.557919i
$40$		0			0
$41$	12.0596	+	3.54102i	1.88339	+	0.553014i	0.995706	+	0.0925673i	$0.0295073\pi$
$41$	12.0596	+	3.54102i	1.88339	+	0.553014i	0.887687	+	0.460447i	$0.152311\pi$
$42$		0			0
$43$	−0.236292	−	1.64344i	−0.0360341	−	0.250623i	0.963840	−	0.266481i	$-0.0858610\pi$
$43$	−0.236292	−	1.64344i	−0.0360341	−	0.250623i	−0.999874	+	0.0158584i	$0.994952\pi$
$44$		0			0
$45$	0.790946			0.117907
$46$		0			0
$47$	5.46023			0.796456			0.398228	−	0.917286i	$-0.369625\pi$
$47$	5.46023			0.796456			0.398228	+	0.917286i	$0.369625\pi$
$48$		0			0
$49$	0.558283	+	3.88295i	0.0797547	+	0.554706i
$50$		0			0
$51$	4.75737	+	1.39689i	0.666165	+	0.195604i
$52$		0			0
$53$	−8.08238	+	9.32757i	−1.11020	+	1.28124i	−0.154147	+	0.988048i	$0.549263\pi$
$53$	−8.08238	+	9.32757i	−1.11020	+	1.28124i	−0.956054	+	0.293192i	$0.905282\pi$
$54$		0			0
$55$	0.480798	−	0.141175i	0.0648308	−	0.0190361i
$56$		0			0
$57$	8.69489	−	5.58786i	1.15167	−	0.740131i
$58$		0			0
$59$	−0.434046	−	0.500915i	−0.0565079	−	0.0652136i	0.726792	−	0.686858i	$-0.241010\pi$
$59$	−0.434046	−	0.500915i	−0.0565079	−	0.0652136i	−0.783300	+	0.621644i	$0.786465\pi$
$60$		0			0
$61$	−0.685355	+	4.76675i	−0.0877507	+	0.610320i	0.897732	+	0.440542i	$0.145214\pi$
$61$	−0.685355	+	4.76675i	−0.0877507	+	0.610320i	−0.985482	+	0.169777i	$0.945695\pi$
$62$		0			0
$63$	−0.596695	+	1.30658i	−0.0751765	+	0.164613i
$64$		0			0
$65$	−1.25260	−	2.74282i	−0.155366	−	0.340205i
$66$		0			0
$67$	−9.51795	−	6.11682i	−1.16280	−	0.747288i	−0.190655	−	0.981657i	$-0.561061\pi$
$67$	−9.51795	−	6.11682i	−1.16280	−	0.747288i	−0.972148	+	0.234369i	$0.924698\pi$
$68$		0			0
$69$	−7.01020	−	1.01188i	−0.843928	−	0.121816i
$70$		0			0
$71$	−4.30334	−	2.76559i	−0.510713	−	0.328215i	0.259776	−	0.965669i	$-0.416351\pi$
$71$	−4.30334	−	2.76559i	−0.510713	−	0.328215i	−0.770489	+	0.637454i	$0.779988\pi$
$72$		0			0
$73$	5.40478	+	11.8348i	0.632582	+	1.38516i	0.906005	+	0.423267i	$0.139117\pi$
$73$	5.40478	+	11.8348i	0.632582	+	1.38516i	−0.273424	+	0.961894i	$0.588156\pi$
$74$		0			0
$75$	2.49515	−	5.46361i	0.288115	−	0.630884i
$76$		0			0
$77$	−0.129507	+	0.900743i	−0.0147587	+	0.102649i
$78$		0			0
$79$	−9.56521	−	11.0388i	−1.07617	−	1.24197i	−0.968825	−	0.247744i	$-0.920311\pi$
$79$	−9.56521	−	11.0388i	−1.07617	−	1.24197i	−0.107344	−	0.994222i	$-0.534235\pi$
$80$		0			0
$81$	−4.94068	+	3.17518i	−0.548964	+	0.352798i
$82$		0			0
$83$	2.91071	−	0.854661i	0.319492	−	0.0938113i	−0.118055	−	0.993007i	$-0.537666\pi$
$83$	2.91071	−	0.854661i	0.319492	−	0.0938113i	0.437546	+	0.899196i	$0.355848\pi$
$84$		0			0
$85$	2.12363	−	2.45080i	0.230340	−	0.265827i
$86$		0			0
$87$	3.45697	+	1.01506i	0.370626	+	0.108826i
$88$		0			0
$89$	−1.78337	−	12.4036i	−0.189036	−	1.31478i	−0.834509	−	0.550994i	$-0.814249\pi$
$89$	−1.78337	−	12.4036i	−0.189036	−	1.31478i	0.645473	−	0.763783i	$-0.276660\pi$
$90$		0			0
$91$	5.47588			0.574028
$92$		0			0
$93$	−2.62633			−0.272337
$94$		0			0
$95$	−0.962039	−	6.69113i	−0.0987032	−	0.686495i
$96$		0			0
$97$	−0.645676	−	0.189588i	−0.0655585	−	0.0192497i	0.248789	−	0.968558i	$-0.419967\pi$
$97$	−0.645676	−	0.189588i	−0.0655585	−	0.0192497i	−0.314347	+	0.949308i	$0.601786\pi$
$98$		0			0
$99$	0.278175	−	0.321031i	0.0279576	−	0.0322648i
$100$		0			0
$101$	−14.2284	+	4.17782i	−1.41578	+	0.415709i	−0.898071	−	0.439851i	$-0.855031\pi$
$101$	−14.2284	+	4.17782i	−1.41578	+	0.415709i	−0.517704	+	0.855560i	$0.673213\pi$
$102$		0			0
$103$	9.56379	−	6.14627i	0.942348	−	0.605610i	0.0232883	−	0.999729i	$-0.492586\pi$
$103$	9.56379	−	6.14627i	0.942348	−	0.605610i	0.919060	+	0.394119i	$0.128950\pi$
$104$		0			0
$105$	−1.63876	−	1.89123i	−0.159927	−	0.184565i
$106$		0			0
$107$	−1.97206	+	13.7160i	−0.190646	+	1.32597i	0.639656	+	0.768661i	$0.279077\pi$
$107$	−1.97206	+	13.7160i	−0.190646	+	1.32597i	−0.830303	+	0.557313i	$0.811832\pi$
$108$		0			0
$109$	1.58189	−	3.46385i	0.151517	−	0.331777i	−0.818619	−	0.574337i	$-0.805260\pi$
$109$	1.58189	−	3.46385i	0.151517	−	0.331777i	0.970136	+	0.242560i	$0.0779872\pi$
$110$		0			0
$111$	−2.93315	−	6.42271i	−0.278402	−	0.609616i
$112$		0			0
$113$	9.78498	+	6.28843i	0.920494	+	0.591565i	0.912801	−	0.408405i	$-0.133915\pi$
$113$	9.78498	+	6.28843i	0.920494	+	0.591565i	0.00769277	+	0.999970i	$0.497551\pi$
$114$		0			0
$115$	−2.50667	+	3.89570i	−0.233748	+	0.363276i
$116$		0			0
$117$	−2.15033	−	1.38193i	−0.198798	−	0.127760i
$118$		0			0
$119$	2.44645	+	5.35697i	0.224265	+	0.491073i
$120$		0			0
$121$	−4.45777	+	9.76115i	−0.405252	+	0.887378i
$122$		0			0
$123$	−2.64171	+	18.3735i	−0.238195	+	1.65668i
$124$		0			0
$125$	−5.73536	−	6.61895i	−0.512986	−	0.592017i
$126$		0			0
$127$	3.16060	−	2.03119i	0.280458	−	0.180239i	−0.392848	−	0.919603i	$-0.628510\pi$
$127$	3.16060	−	2.03119i	0.280458	−	0.180239i	0.673306	+	0.739364i	$0.264874\pi$
$128$		0			0
$129$	2.35279	−	0.690843i	0.207152	−	0.0608253i
$130$		0			0
$131$	8.75057	−	10.0987i	0.764541	−	0.882328i	−0.231351	−	0.972870i	$-0.574315\pi$
$131$	8.75057	−	10.0987i	0.764541	−	0.882328i	0.995893	+	0.0905426i	$0.0288601\pi$
$132$		0			0
$133$	11.7790	+	3.45862i	1.02137	+	0.299900i
$134$		0			0
$135$	0.775309	+	5.39240i	0.0667280	+	0.464103i
$136$		0			0
$137$	0.928329			0.0793125			0.0396563	−	0.999213i	$-0.487374\pi$
$137$	0.928329			0.0793125			0.0396563	+	0.999213i	$0.487374\pi$
$138$		0			0
$139$	11.2717			0.956053			0.478027	−	0.878345i	$-0.341352\pi$
$139$	11.2717			0.956053			0.478027	+	0.878345i	$0.341352\pi$
$140$		0			0
$141$	1.14764	+	7.98200i	0.0966486	+	0.672206i
$142$		0			0
$143$	−1.55380	−	0.456236i	−0.129935	−	0.0381524i
$144$		0			0
$145$	1.54315	−	1.78089i	0.128152	−	0.147895i
$146$		0			0
$147$	−5.55892	+	1.63225i	−0.458492	+	0.134625i
$148$		0			0
$149$	13.4172	−	8.62268i	1.09918	−	0.706398i	0.140268	−	0.990114i	$-0.455204\pi$
$149$	13.4172	−	8.62268i	1.09918	−	0.706398i	0.958908	+	0.283716i	$0.0915672\pi$
$150$		0			0
$151$	11.6433	+	13.4370i	0.947515	+	1.09349i	0.995511	+	0.0946426i	$0.0301708\pi$
$151$	11.6433	+	13.4370i	0.947515	+	1.09349i	−0.0479968	+	0.998847i	$0.515284\pi$
$152$		0			0
$153$	0.391227	−	2.72104i	0.0316288	−	0.219983i
$154$		0			0
$155$	−0.713570	+	1.56250i	−0.0573153	+	0.125503i
$156$		0			0
$157$	2.41260	+	5.28287i	0.192547	+	0.421619i	0.981140	−	0.193296i	$-0.0619178\pi$
$157$	2.41260	+	5.28287i	0.192547	+	0.421619i	−0.788594	+	0.614915i	$0.789190\pi$
$158$		0			0
$159$	−15.3342	−	9.85470i	−1.21608	−	0.781529i
$160$		0			0
$161$	−4.54434	−	7.07975i	−0.358144	−	0.557963i
$162$		0			0
$163$	−3.22681	−	2.07375i	−0.252744	−	0.162428i	0.408134	−	0.912922i	$-0.366180\pi$
$163$	−3.22681	−	2.07375i	−0.252744	−	0.162428i	−0.660878	+	0.750493i	$0.729816\pi$
$164$		0			0
$165$	0.307431	+	0.673180i	0.0239335	+	0.0524070i
$166$		0			0
$167$	−6.00365	+	13.1462i	−0.464577	+	1.01728i	0.521844	+	0.853041i	$0.325244\pi$
$167$	−6.00365	+	13.1462i	−0.464577	+	1.01728i	−0.986420	+	0.164240i	$0.947483\pi$
$168$		0			0
$169$	0.463296	−	3.22229i	0.0356382	−	0.247869i
$170$		0			0
$171$	−3.75266	−	4.33080i	−0.286973	−	0.331185i
$172$		0			0
$173$	12.0019	−	7.71317i	0.912490	−	0.586422i	0.00202060	−	0.999998i	$-0.499357\pi$
$173$	12.0019	−	7.71317i	0.912490	−	0.586422i	0.910470	+	0.413576i	$0.135720\pi$
$174$		0			0
$175$	6.84517	−	2.00992i	0.517447	−	0.151936i
$176$		0			0
$177$	0.641032	−	0.739790i	0.0481829	−	0.0556060i
$178$		0			0
$179$	−15.0136	−	4.40840i	−1.12217	−	0.329499i	−0.332544	−	0.943088i	$-0.607907\pi$
$179$	−15.0136	−	4.40840i	−1.12217	−	0.329499i	−0.789626	+	0.613589i	$0.789725\pi$
$180$		0			0
$181$	0.601363	+	4.18257i	0.0446990	+	0.310888i	0.999889	+	0.0148951i	$0.00474144\pi$
$181$	0.601363	+	4.18257i	0.0446990	+	0.310888i	−0.955190	+	0.295993i	$0.904349\pi$
$182$		0			0
$183$	−7.11229			−0.525756
$184$		0			0
$185$	−4.61804			−0.339525
$186$		0			0
$187$	−0.247858	−	1.72389i	−0.0181252	−	0.126063i
$188$		0			0
$189$	−9.49270	−	2.78731i	−0.690492	−	0.202747i
$190$		0			0
$191$	−9.42330	+	10.8751i	−0.681846	+	0.786892i	−0.986181	−	0.165673i	$-0.947020\pi$
$191$	−9.42330	+	10.8751i	−0.681846	+	0.786892i	0.304335	+	0.952565i	$0.401566\pi$
$192$		0			0
$193$	−8.89288	+	2.61118i	−0.640123	+	0.187957i	−0.585658	−	0.810559i	$-0.699164\pi$
$193$	−8.89288	+	2.61118i	−0.640123	+	0.187957i	−0.0544655	+	0.998516i	$0.517346\pi$
$194$		0			0
$195$	3.74630	−	2.40760i	0.268278	−	0.172412i
$196$		0			0
$197$	−13.9825	−	16.1367i	−0.996215	−	1.14969i	−0.988728	−	0.149721i	$-0.952162\pi$
$197$	−13.9825	−	16.1367i	−0.996215	−	1.14969i	−0.00748628	−	0.999972i	$-0.502383\pi$
$198$		0			0
$199$	0.0166440	−	0.115762i	0.00117986	−	0.00820612i	−0.989223	−	0.146417i	$-0.953226\pi$
$199$	0.0166440	−	0.115762i	0.00117986	−	0.00820612i	0.990403	+	0.138211i	$0.0441351\pi$
$200$		0			0
$201$	6.94133	−	15.1994i	0.489604	−	1.07208i
$202$		0			0
$203$	1.77772	+	3.89267i	0.124772	+	0.273212i
$204$		0			0
$205$	10.2133	+	6.56372i	0.713331	+	0.458430i
$206$		0			0
$207$	−0.00217724	+	3.92700i	−0.000151329	+	0.272946i
$208$		0			0
$209$	−3.05416	−	1.96279i	−0.211260	−	0.135769i
$210$		0			0
$211$	−2.51034	−	5.49689i	−0.172819	−	0.378421i	0.803326	−	0.595539i	$-0.203062\pi$
$211$	−2.51034	−	5.49689i	−0.172819	−	0.378421i	−0.976145	+	0.217118i	$0.930334\pi$
$212$		0			0
$213$	3.13838	−	6.87209i	0.215038	−	0.470868i
$214$		0			0
$215$	0.228243	−	1.58747i	0.0155661	−	0.108264i
$216$		0			0
$217$	−2.04280	−	2.35752i	−0.138674	−	0.160039i
$218$		0			0
$219$	−16.1647	+	10.3884i	−1.09231	+	0.701983i
$220$		0			0
$221$	−10.0555	+	2.95256i	−0.676407	+	0.198611i
$222$		0			0
$223$	7.73402	−	8.92553i	0.517908	−	0.597698i	−0.435198	−	0.900335i	$-0.643322\pi$
$223$	7.73402	−	8.92553i	0.517908	−	0.597698i	0.953106	+	0.302637i	$0.0978670\pi$
$224$		0			0
$225$	−3.19528	−	0.938220i	−0.213019	−	0.0625480i
$226$		0			0
$227$	−1.25236	−	8.71033i	−0.0831219	−	0.578125i	−0.988234	−	0.152952i	$-0.951122\pi$
$227$	−1.25236	−	8.71033i	−0.0831219	−	0.578125i	0.905112	−	0.425174i	$-0.139787\pi$
$228$		0			0
$229$	22.9248			1.51492			0.757458	−	0.652884i	$-0.226441\pi$
$229$	22.9248			1.51492			0.757458	+	0.652884i	$0.226441\pi$
$230$		0			0
$231$	−1.34397			−0.0884265
$232$		0			0
$233$	−0.909316	−	6.32443i	−0.0595713	−	0.414327i	−0.997685	−	0.0680007i	$-0.978338\pi$
$233$	−0.909316	−	6.32443i	−0.0595713	−	0.414327i	0.938114	−	0.346327i	$-0.112571\pi$
$234$		0			0
$235$	5.06060	+	1.48593i	0.330117	+	0.0969312i
$236$		0			0
$237$	14.1266	−	16.3030i	0.917623	−	1.05899i
$238$		0			0
$239$	11.3585	−	3.33516i	0.734720	−	0.215733i	0.107095	−	0.994249i	$-0.465845\pi$
$239$	11.3585	−	3.33516i	0.734720	−	0.215733i	0.627625	+	0.778516i	$0.284027\pi$
$240$		0			0
$241$	−13.6815	+	8.79254i	−0.881300	+	0.566377i	−0.901190	−	0.433425i	$-0.857305\pi$
$241$	−13.6815	+	8.79254i	−0.881300	+	0.566377i	0.0198895	+	0.999802i	$0.493669\pi$
$242$		0			0
$243$	5.40009	+	6.23203i	0.346416	+	0.399785i
$244$		0			0
$245$	−0.539268	+	3.75069i	−0.0344525	+	0.239623i
$246$		0			0
$247$	−9.07521	+	19.8719i	−0.577442	+	1.26442i
$248$		0			0
$249$	1.86116	+	4.07537i	0.117946	+	0.258266i
$250$		0			0
$251$	2.38953	+	1.53565i	0.150826	+	0.0969297i	0.613877	−	0.789402i	$-0.289609\pi$
$251$	2.38953	+	1.53565i	0.150826	+	0.0969297i	−0.463051	+	0.886331i	$0.653245\pi$
$252$		0			0
$253$	0.699603	+	2.38752i	0.0439837	+	0.150102i
$254$		0			0
$255$	4.02904	+	2.58931i	0.252308	+	0.162149i
$256$		0			0
$257$	3.00213	+	6.57375i	0.187268	+	0.410060i	0.979858	−	0.199695i	$-0.0639952\pi$
$257$	3.00213	+	6.57375i	0.187268	+	0.410060i	−0.792590	+	0.609755i	$0.791268\pi$
$258$		0			0
$259$	3.48388	−	7.62863i	0.216478	−	0.474020i
$260$		0			0
$261$	0.284287	−	1.97726i	0.0175969	−	0.122389i
$262$		0			0
$263$	16.4597	+	18.9955i	1.01495	+	1.17131i	0.985139	+	0.171759i	$0.0549449\pi$
$263$	16.4597	+	18.9955i	1.01495	+	1.17131i	0.0298105	+	0.999556i	$0.490510\pi$
$264$		0			0
$265$	−10.0292	+	6.44539i	−0.616090	+	0.395937i
$266$		0			0
$267$	17.7573	−	5.21400i	1.08673	−	0.319092i
$268$		0			0
$269$	−14.8108	+	17.0926i	−0.903031	+	1.04215i	0.0958752	+	0.995393i	$0.469435\pi$
$269$	−14.8108	+	17.0926i	−0.903031	+	1.04215i	−0.998906	+	0.0467599i	$0.985110\pi$
$270$		0			0
$271$	−0.834682	−	0.245085i	−0.0507033	−	0.0148878i	0.256283	−	0.966602i	$-0.417502\pi$
$271$	−0.834682	−	0.245085i	−0.0507033	−	0.0148878i	−0.306986	+	0.951714i	$0.599320\pi$
$272$		0			0
$273$	1.15093	+	8.00488i	0.0696573	+	0.484477i
$274$		0			0
$275$	−2.10980			−0.127226
$276$		0			0
$277$	2.07085			0.124426			0.0622128	−	0.998063i	$-0.480184\pi$
$277$	2.07085			0.124426			0.0622128	+	0.998063i	$0.480184\pi$
$278$		0			0
$279$	0.207230	+	1.44131i	0.0124065	+	0.0862893i
$280$		0			0
$281$	1.62178	+	0.476198i	0.0967474	+	0.0284076i	0.329748	−	0.944069i	$-0.393036\pi$
$281$	1.62178	+	0.476198i	0.0967474	+	0.0284076i	−0.233001	+	0.972477i	$0.574854\pi$
$282$		0			0
$283$	−1.55734	+	1.79727i	−0.0925743	+	0.106836i	−0.800147	−	0.599805i	$-0.795245\pi$
$283$	−1.55734	+	1.79727i	−0.0925743	+	0.106836i	0.707572	+	0.706641i	$0.249790\pi$
$284$		0			0
$285$	9.57918	−	2.81270i	0.567422	−	0.166610i
$286$		0			0
$287$	−18.5477	+	11.9199i	−1.09484	+	0.703610i
$288$		0			0
$289$	3.75171	+	4.32970i	0.220689	+	0.254688i
$290$		0			0
$291$	0.141438	−	0.983726i	0.00829127	−	0.0576670i
$292$		0			0
$293$	3.58917	−	7.85918i	0.209681	−	0.459138i	−0.775346	−	0.631537i	$-0.782424\pi$
$293$	3.58917	−	7.85918i	0.209681	−	0.459138i	0.985027	+	0.172399i	$0.0551518\pi$
$294$		0			0
$295$	−0.265961	−	0.582374i	−0.0154849	−	0.0339071i
$296$		0			0
$297$	2.46135	+	1.58181i	0.142822	+	0.0917862i
$298$		0			0
$299$	13.6214	−	6.21155i	0.787744	−	0.359223i
$300$		0			0
$301$	2.45018	+	1.57463i	0.141226	+	0.0907603i
$302$		0			0
$303$	−9.09786	−	19.9215i	−0.522659	−	1.14446i
$304$		0			0
$305$	−1.93240	+	4.23137i	−0.110649	+	0.242287i
$306$		0			0
$307$	2.60364	−	18.1087i	0.148598	−	1.03352i	−0.769920	−	0.638141i	$-0.779704\pi$
$307$	2.60364	−	18.1087i	0.148598	−	1.03352i	0.918518	−	0.395380i	$-0.129387\pi$
$308$		0			0
$309$	10.9950	+	12.6889i	0.625485	+	0.721848i
$310$		0			0
$311$	25.2335	−	16.2166i	1.43086	−	0.919559i	0.431010	−	0.902347i	$-0.358157\pi$
$311$	25.2335	−	16.2166i	1.43086	−	0.919559i	0.999852	−	0.0172116i	$-0.00547889\pi$
$312$		0			0
$313$	−18.5863	+	5.45743i	−1.05056	+	0.308472i	−0.761044	−	0.648701i	$-0.775313\pi$
$313$	−18.5863	+	5.45743i	−1.05056	+	0.308472i	−0.289516	+	0.957173i	$0.593494\pi$
$314$		0			0
$315$	−0.908591	+	1.04857i	−0.0511933	+	0.0590802i
$316$		0			0
$317$	14.7242	+	4.32340i	0.826991	+	0.242826i	0.667724	−	0.744409i	$-0.267269\pi$
$317$	14.7242	+	4.32340i	0.826991	+	0.242826i	0.159267	+	0.987236i	$0.449087\pi$
$318$		0			0
$319$	−0.180107	−	1.25267i	−0.0100841	−	0.0701363i
$320$		0			0
$321$	−20.4651			−1.14225
$322$		0			0
$323$	−23.4949			−1.30729
$324$		0			0
$325$	1.80676	+	12.5663i	0.100221	+	0.697054i
$326$		0			0
$327$	5.39609	+	1.58443i	0.298404	+	0.0876195i
$328$		0			0
$329$	−6.27238	+	7.23871i	−0.345808	+	0.399083i
$330$		0			0
$331$	26.9815	−	7.92249i	1.48304	−	0.435460i	0.562727	−	0.826643i	$-0.309752\pi$
$331$	26.9815	−	7.92249i	1.48304	−	0.435460i	0.920313	+	0.391183i	$0.127934\pi$
$332$		0			0
$333$	−3.29331	+	2.11648i	−0.180472	+	0.115982i
$334$		0			0
$335$	−7.15674	−	8.25932i	−0.391015	−	0.451255i
$336$		0			0
$337$	4.16083	−	28.9392i	0.226655	−	1.57642i	−0.485397	−	0.874294i	$-0.661325\pi$
$337$	4.16083	−	28.9392i	0.226655	−	1.57642i	0.712052	−	0.702126i	$-0.247766\pi$
$338$		0			0
$339$	−7.13607	+	15.6258i	−0.387578	+	0.848678i
$340$		0			0
$341$	0.383229	+	0.839154i	0.0207530	+	0.0454428i
$342$		0			0
$343$	−16.1189	−	10.3590i	−0.870341	−	0.559334i
$344$		0			0
$345$	−6.22176	−	2.84555i	−0.334968	−	0.153199i
$346$		0			0
$347$	10.3618	+	6.65914i	0.556252	+	0.357481i	0.788365	−	0.615207i	$-0.210928\pi$
$347$	10.3618	+	6.65914i	0.556252	+	0.357481i	−0.232113	+	0.972689i	$0.574564\pi$
$348$		0			0
$349$	−5.11275	−	11.1954i	−0.273679	−	0.599274i	0.722025	−	0.691867i	$-0.243212\pi$
$349$	−5.11275	−	11.1954i	−0.273679	−	0.599274i	−0.995704	+	0.0925935i	$0.970484\pi$
$350$		0			0
$351$	7.31373	−	16.0148i	0.390378	−	0.854808i
$352$		0			0
$353$	2.88626	−	20.0744i	0.153620	−	1.06845i	−0.756466	−	0.654033i	$-0.773076\pi$
$353$	2.88626	−	20.0744i	0.153620	−	1.06845i	0.910086	−	0.414419i	$-0.136015\pi$
$354$		0			0
$355$	−3.23577	−	3.73428i	−0.171737	−	0.198195i
$356$		0			0
$357$	−7.31686	+	4.70226i	−0.387249	+	0.248870i
$358$		0			0
$359$	−7.86829	+	2.31034i	−0.415273	+	0.121935i	−0.482693	−	0.875790i	$-0.660341\pi$
$359$	−7.86829	+	2.31034i	−0.415273	+	0.121935i	0.0674204	+	0.997725i	$0.478523\pi$
$360$		0			0
$361$	−19.6303	+	22.6546i	−1.03317	+	1.19235i
$362$		0			0
$363$	−15.2062	−	4.46495i	−0.798120	−	0.234349i
$364$		0			0
$365$	1.78853	+	12.4395i	0.0936158	+	0.651112i
$366$		0			0
$367$	−26.6065			−1.38885			−0.694425	−	0.719565i	$-0.744341\pi$
$367$	−26.6065			−1.38885			−0.694425	+	0.719565i	$0.744341\pi$
$368$		0			0
$369$	10.2917			0.535766
$370$		0			0
$371$	−3.08115	−	21.4299i	−0.159966	−	1.11258i
$372$		0			0
$373$	−19.3035	−	5.66802i	−0.999498	−	0.293479i	−0.259248	−	0.965811i	$-0.583475\pi$
$373$	−19.3035	−	5.66802i	−0.999498	−	0.293479i	−0.740250	+	0.672332i	$0.765293\pi$
$374$		0			0
$375$	8.47041	−	9.77538i	0.437410	−	0.504798i
$376$		0			0
$377$	−7.30689	+	2.14550i	−0.376324	+	0.110499i
$378$		0			0
$379$	−28.4289	+	18.2701i	−1.46029	+	0.938474i	−0.461615	+	0.887080i	$0.652730\pi$
$379$	−28.4289	+	18.2701i	−1.46029	+	0.938474i	−0.998678	+	0.0513937i	$0.983634\pi$
$380$		0			0
$381$	3.63358	+	4.19338i	0.186154	+	0.214833i
$382$		0			0
$383$	3.60713	−	25.0882i	0.184316	−	1.28195i	−0.662097	−	0.749418i	$-0.730333\pi$
$383$	3.60713	−	25.0882i	0.184316	−	1.28195i	0.846413	−	0.532527i	$-0.178758\pi$
$384$		0			0
$385$	−0.365154	+	0.799576i	−0.0186100	+	0.0407501i
$386$		0			0
$387$	−0.564778	−	1.23669i	−0.0287093	−	0.0628645i
$388$		0			0
$389$	29.2499	+	18.7977i	1.48303	+	0.953083i	0.996857	+	0.0792189i	$0.0252426\pi$
$389$	29.2499	+	18.7977i	1.48303	+	0.953083i	0.486170	+	0.873865i	$0.338394\pi$
$390$		0			0
$391$	12.1623	+	10.5505i	0.615071	+	0.533560i
$392$		0			0
$393$	16.6019	+	10.6694i	0.837457	+	0.538201i
$394$		0			0
$395$	−5.86108	−	12.8340i	−0.294903	−	0.645747i
$396$		0			0
$397$	8.60673	−	18.8461i	0.431960	−	0.945860i	−0.561045	−	0.827785i	$-0.689601\pi$
$397$	8.60673	−	18.8461i	0.431960	−	0.945860i	0.993005	−	0.118074i	$-0.0376721\pi$
$398$		0			0
$399$	−2.58024	+	17.9460i	−0.129173	+	0.898421i
$400$		0			0
$401$	10.3045	+	11.8921i	0.514584	+	0.593862i	0.952266	−	0.305268i	$-0.0987460\pi$
$401$	10.3045	+	11.8921i	0.514584	+	0.593862i	−0.437682	+	0.899130i	$0.644201\pi$
$402$		0			0
$403$	4.66996	−	3.00120i	0.232627	−	0.149500i
$404$		0			0
$405$	−5.44316	+	1.59826i	−0.270473	+	0.0794180i
$406$		0			0
$407$	−1.62416	+	1.87438i	−0.0805066	+	0.0929096i
$408$		0			0
$409$	−33.6390	−	9.87730i	−1.66334	−	0.488401i	−0.691173	−	0.722689i	$-0.742906\pi$
$409$	−33.6390	−	9.87730i	−1.66334	−	0.488401i	−0.972167	+	0.234288i	$0.924724\pi$
$410$		0			0
$411$	0.195117	+	1.35707i	0.00962444	+	0.0669394i
$412$		0			0
$413$	1.16268			0.0572116
$414$		0			0
$415$	2.93026			0.143841
$416$		0			0
$417$	2.36910	+	16.4775i	0.116015	+	0.806905i
$418$		0			0
$419$	37.4554	+	10.9979i	1.82982	+	0.537282i	0.999791	−	0.0204444i	$-0.00650811\pi$
$419$	37.4554	+	10.9979i	1.82982	+	0.537282i	0.830025	+	0.557727i	$0.188326\pi$
$420$		0			0
$421$	22.9972	−	26.5402i	1.12082	−	1.29349i	0.169411	−	0.985546i	$-0.445814\pi$
$421$	22.9972	−	26.5402i	1.12082	−	1.29349i	0.951404	−	0.307944i	$-0.0996410\pi$
$422$		0			0
$423$	4.28993	−	1.25964i	0.208583	−	0.0612456i
$424$		0			0
$425$	−11.4862	+	7.38176i	−0.557164	+	0.358068i
$426$		0			0
$427$	−5.53206	−	6.38434i	−0.267715	−	0.308960i
$428$		0			0
$429$	0.340367	−	2.36730i	0.0164331	−	0.114294i
$430$		0			0
$431$	4.54066	−	9.94266i	0.218716	−	0.478921i	−0.768189	−	0.640223i	$-0.778842\pi$
$431$	4.54066	−	9.94266i	0.218716	−	0.478921i	0.986905	+	0.161302i	$0.0515693\pi$
$432$		0			0
$433$	−4.11321	−	9.00667i	−0.197668	−	0.432833i	0.784678	−	0.619903i	$-0.212828\pi$
$433$	−4.11321	−	9.00667i	−0.197668	−	0.432833i	−0.982347	+	0.187070i	$0.940101\pi$
$434$		0			0
$435$	2.92772	+	1.88153i	0.140374	+	0.0902127i
$436$		0			0
$437$	33.2237	−	4.75805i	1.58931	−	0.227608i
$438$		0			0
$439$	12.1438	+	7.80436i	0.579593	+	0.372482i	0.797346	−	0.603522i	$-0.206236\pi$
$439$	12.1438	+	7.80436i	0.579593	+	0.372482i	−0.217753	+	0.976004i	$0.569873\pi$
$440$		0			0
$441$	1.33439	+	2.92191i	0.0635425	+	0.139139i
$442$		0			0
$443$	−10.0060	+	21.9102i	−0.475401	+	1.04098i	0.508301	+	0.861179i	$0.330274\pi$
$443$	−10.0060	+	21.9102i	−0.475401	+	1.04098i	−0.983702	+	0.179804i	$0.942454\pi$
$444$		0			0
$445$	1.72262	−	11.9811i	0.0816601	−	0.567959i
$446$		0			0
$447$	15.4251	+	17.8015i	0.729580	+	0.841980i
$448$		0			0
$449$	−4.17750	+	2.68471i	−0.197148	+	0.126700i	−0.635491	−	0.772109i	$-0.719202\pi$
$449$	−4.17750	+	2.68471i	−0.197148	+	0.126700i	0.438342	+	0.898808i	$0.355566\pi$
$450$		0			0
$451$	6.25611	−	1.83696i	0.294589	−	0.0864991i
$452$		0			0
$453$	−17.1956	+	19.8448i	−0.807922	+	0.932392i
$454$		0			0
$455$	5.07511	+	1.49019i	0.237925	+	0.0698610i
$456$		0			0
$457$	2.49898	+	17.3808i	0.116897	+	0.813040i	0.960939	+	0.276761i	$0.0892612\pi$
$457$	2.49898	+	17.3808i	0.116897	+	0.813040i	−0.844041	+	0.536278i	$0.819830\pi$
$458$		0			0
$459$	18.9346			0.883791
$460$		0			0
$461$	−26.5086			−1.23463			−0.617313	−	0.786717i	$-0.711779\pi$
$461$	−26.5086			−1.23463			−0.617313	+	0.786717i	$0.711779\pi$
$462$		0			0
$463$	−3.32533	−	23.1282i	−0.154541	−	1.07486i	−0.908485	−	0.417918i	$-0.862760\pi$
$463$	−3.32533	−	23.1282i	−0.154541	−	1.07486i	0.753944	−	0.656939i	$-0.228149\pi$
$464$		0			0
$465$	−2.43411	−	0.714719i	−0.112879	−	0.0331443i
$466$		0			0
$467$	−12.8583	+	14.8393i	−0.595013	+	0.686682i	−0.970763	−	0.240039i	$-0.922840\pi$
$467$	−12.8583	+	14.8393i	−0.595013	+	0.686682i	0.375750	+	0.926721i	$0.377385\pi$
$468$		0			0
$469$	19.0428	−	5.59147i	0.879315	−	0.258190i
$470$		0			0
$471$	−7.21564	+	4.63721i	−0.332479	+	0.213671i
$472$		0			0
$473$	−0.564051	−	0.650950i	−0.0259351	−	0.0299307i
$474$		0			0
$475$	−4.05054	+	28.1721i	−0.185852	+	1.29263i
$476$		0			0
$477$	−4.19827	+	9.19292i	−0.192225	+	0.420915i
$478$		0			0
$479$	9.42917	+	20.6470i	0.430830	+	0.943386i	0.993191	+	0.116494i	$0.0371656\pi$
$479$	9.42917	+	20.6470i	0.430830	+	0.943386i	−0.562362	+	0.826891i	$0.690107\pi$
$480$		0			0
$481$	12.5550	+	8.06861i	0.572459	+	0.367897i
$482$		0			0
$483$	9.39436	−	8.13114i	0.427458	−	0.369980i
$484$		0			0
$485$	−0.546827	−	0.351424i	−0.0248301	−	0.0159573i
$486$		0			0
$487$	−5.54926	−	12.1512i	−0.251461	−	0.550623i	0.741238	−	0.671243i	$-0.234239\pi$
$487$	−5.54926	−	12.1512i	−0.251461	−	0.550623i	−0.992699	+	0.120620i	$0.961512\pi$
$488$		0			0
$489$	2.35328	−	5.15296i	0.106419	−	0.233025i
$490$		0			0
$491$	0.207720	−	1.44472i	0.00937426	−	0.0651994i	−0.984597	−	0.174837i	$-0.944060\pi$
$491$	0.207720	−	1.44472i	0.00937426	−	0.0651994i	0.993972	+	0.109638i	$0.0349691\pi$
$492$		0			0
$493$	−5.36339	−	6.18968i	−0.241555	−	0.278769i
$494$		0			0
$495$	0.345180	−	0.221834i	0.0155147	−	0.00997068i
$496$		0			0
$497$	8.60980	−	2.52807i	0.386202	−	0.113399i
$498$		0			0
$499$	−12.7402	+	14.7029i	−0.570328	+	0.658194i	−0.965497	−	0.260415i	$-0.916141\pi$
$499$	−12.7402	+	14.7029i	−0.570328	+	0.658194i	0.395169	+	0.918609i	$0.370686\pi$
$500$		0			0
$501$	−20.4795	−	6.01332i	−0.914957	−	0.268656i
$502$		0			0
$503$	−0.875808	−	6.09138i	−0.0390503	−	0.271601i	0.960936	−	0.276770i	$-0.0892639\pi$
$503$	−0.875808	−	6.09138i	−0.0390503	−	0.271601i	−0.999987	+	0.00516853i	$0.998355\pi$
$504$		0			0
$505$	−14.3240			−0.637408
$506$		0			0
$507$	4.80787			0.213525
$508$		0			0
$509$	2.75237	+	19.1431i	0.121996	+	0.848504i	0.955289	+	0.295672i	$0.0955437\pi$
$509$	2.75237	+	19.1431i	0.121996	+	0.848504i	−0.833293	+	0.552832i	$0.813547\pi$
$510$		0			0
$511$	−21.8983	−	6.42992i	−0.968723	−	0.284443i
$512$		0			0
$513$	25.8474	−	29.8295i	1.14119	−	1.31700i
$514$		0			0
$515$	10.5365	−	3.09378i	0.464292	−	0.136328i
$516$		0			0
$517$	2.38292	−	1.53141i	0.104801	−	0.0673513i
$518$		0			0
$519$	13.7980	+	15.9238i	0.605667	+	0.698977i
$520$		0			0
$521$	3.00225	−	20.8811i	0.131531	−	0.914817i	−0.812030	−	0.583616i	$-0.801637\pi$
$521$	3.00225	−	20.8811i	0.131531	−	0.914817i	0.943560	−	0.331201i	$-0.107454\pi$
$522$		0			0
$523$	−2.84292	+	6.22513i	−0.124312	+	0.272206i	−0.961548	−	0.274636i	$-0.911443\pi$
$523$	−2.84292	+	6.22513i	−0.124312	+	0.272206i	0.837236	+	0.546842i	$0.184170\pi$
$524$		0			0
$525$	4.37692	+	9.58413i	0.191025	+	0.418286i
$526$		0			0
$527$	5.02241	+	3.22771i	0.218780	+	0.140601i
$528$		0			0
$529$	−19.3350	−	12.4562i	−0.840654	−	0.541573i
$530$		0			0
$531$	−0.456573	−	0.293422i	−0.0198136	−	0.0127334i
$532$		0			0
$533$	−16.2988	−	35.6893i	−0.705978	−	1.54588i
$534$		0			0
$535$	−5.56035	+	12.1755i	−0.240395	+	0.526391i
$536$		0			0
$537$	3.28880	−	22.8741i	0.141922	−	0.987091i
$538$		0			0
$539$	1.33268	+	1.53799i	0.0574025	+	0.0662460i
$540$		0			0
$541$	12.5393	−	8.05852i	0.539107	−	0.346463i	−0.242583	−	0.970131i	$-0.577995\pi$
$541$	12.5393	−	8.05852i	0.539107	−	0.346463i	0.781689	+	0.623668i	$0.214358\pi$
$542$		0			0
$543$	−5.98787	+	1.75820i	−0.256964	+	0.0754515i
$544$		0			0
$545$	2.40875	−	2.77985i	0.103180	−	0.119076i
$546$		0			0
$547$	−35.8353	−	10.5222i	−1.53221	−	0.449897i	−0.596483	−	0.802626i	$-0.703436\pi$
$547$	−35.8353	−	10.5222i	−1.53221	−	0.449897i	−0.935725	+	0.352729i	$0.885254\pi$
$548$		0			0
$549$	0.561194	+	3.90319i	0.0239512	+	0.166584i
$550$		0			0
$551$	−17.0727			−0.727322
$552$		0			0
$553$	25.6223			1.08957
$554$		0			0
$555$	−0.970627	−	6.75086i	−0.0412008	−	0.286558i
$556$		0			0
$557$	−18.8763	−	5.54258i	−0.799815	−	0.234847i	−0.143812	−	0.989605i	$-0.545936\pi$
$557$	−18.8763	−	5.54258i	−0.799815	−	0.234847i	−0.656003	+	0.754758i	$0.727754\pi$
$558$		0			0
$559$	−3.39413	+	3.91703i	−0.143556	+	0.165673i
$560$		0			0
$561$	2.46796	−	0.724659i	0.104197	−	0.0305951i
$562$		0			0
$563$	−16.1788	+	10.3975i	−0.681857	+	0.438203i	−0.835183	−	0.549973i	$-0.814638\pi$
$563$	−16.1788	+	10.3975i	−0.681857	+	0.438203i	0.153325	+	0.988176i	$0.451002\pi$
$564$		0			0
$565$	7.35752	+	8.49104i	0.309533	+	0.357221i
$566$		0			0
$567$	1.46616	−	10.1974i	0.0615731	−	0.428250i
$568$		0			0
$569$	7.42264	−	16.2533i	0.311173	−	0.681374i	−0.687837	−	0.725866i	$-0.741439\pi$
$569$	7.42264	−	16.2533i	0.311173	−	0.681374i	0.999010	+	0.0444912i	$0.0141667\pi$
$570$		0			0
$571$	6.13161	+	13.4264i	0.256600	+	0.561876i	0.993461	−	0.114168i	$-0.0364203\pi$
$571$	6.13161	+	13.4264i	0.256600	+	0.561876i	−0.736861	+	0.676044i	$0.763693\pi$
$572$		0			0
$573$	−17.8782	−	11.4897i	−0.746874	−	0.479987i
$574$		0			0
$575$	14.7476	−	12.7645i	0.615016	−	0.532318i
$576$		0			0
$577$	−15.5628	−	10.0016i	−0.647888	−	0.416372i	0.175006	−	0.984567i	$-0.444005\pi$
$577$	−15.5628	−	10.0016i	−0.647888	−	0.416372i	−0.822894	+	0.568195i	$0.807642\pi$
$578$		0			0
$579$	−5.68626	−	12.4512i	−0.236313	−	0.517453i
$580$		0			0
$581$	−2.21061	+	4.84056i	−0.0917115	+	0.200820i
$582$		0			0
$583$	−0.911197	+	6.33751i	−0.0377379	+	0.262473i
$584$		0			0
$585$	−1.61688	−	1.86598i	−0.0668497	−	0.0771486i
$586$		0			0
$587$	−4.18945	+	2.69240i	−0.172917	+	0.111127i	−0.624237	−	0.781235i	$-0.714590\pi$
$587$	−4.18945	+	2.69240i	−0.172917	+	0.111127i	0.451319	+	0.892362i	$0.350954\pi$
$588$		0			0
$589$	11.9410	−	3.50618i	0.492019	−	0.144470i
$590$		0			0
$591$	20.6505	−	23.8319i	0.849447	−	0.980314i
$592$		0			0
$593$	20.9865	+	6.16220i	0.861813	+	0.253051i	0.682630	−	0.730765i	$-0.260836\pi$
$593$	20.9865	+	6.16220i	0.861813	+	0.253051i	0.179183	+	0.983816i	$0.442654\pi$
$594$		0			0
$595$	0.809568	+	5.63067i	0.0331891	+	0.230835i
$596$		0			0
$597$	0.172724			0.00706911
$598$		0			0
$599$	−44.8557			−1.83275			−0.916377	−	0.400316i	$-0.868900\pi$
$599$	−44.8557			−1.83275			−0.916377	+	0.400316i	$0.868900\pi$
$600$		0			0
$601$	−0.0139146	−	0.0967780i	−0.000567587	−	0.00394766i	0.989536	−	0.144288i	$-0.0460893\pi$
$601$	−0.0139146	−	0.0967780i	−0.000567587	−	0.00394766i	−0.990103	+	0.140341i	$0.955180\pi$
$602$		0			0
$603$	−8.88906	−	2.61006i	−0.361990	−	0.106290i
$604$		0			0
$605$	−6.78788	+	7.83363i	−0.275966	+	0.318482i
$606$		0			0
$607$	−34.6159	+	10.1642i	−1.40502	+	0.412550i	−0.894404	−	0.447260i	$-0.852400\pi$
$607$	−34.6159	+	10.1642i	−1.40502	+	0.412550i	−0.510614	+	0.859810i	$0.670582\pi$
$608$		0			0
$609$	−5.31683	+	3.41692i	−0.215449	+	0.138461i
$610$		0			0
$611$	−11.1620	−	12.8816i	−0.451565	−	0.521134i
$612$		0			0
$613$	4.27965	−	29.7656i	0.172853	−	1.20222i	−0.699965	−	0.714177i	$-0.746801\pi$
$613$	4.27965	−	29.7656i	0.172853	−	1.20222i	0.872818	−	0.488045i	$-0.162290\pi$
$614$		0			0
$615$	−7.44847	+	16.3099i	−0.300351	+	0.657678i
$616$		0			0
$617$	20.1029	+	44.0193i	0.809314	+	1.77215i	0.610330	+	0.792147i	$0.291037\pi$
$617$	20.1029	+	44.0193i	0.809314	+	1.77215i	0.198984	+	0.980003i	$0.436236\pi$
$618$		0			0
$619$	20.1459	+	12.9470i	0.809733	+	0.520384i	0.878778	−	0.477230i	$-0.158359\pi$
$619$	20.1459	+	12.9470i	0.809733	+	0.520384i	−0.0690459	+	0.997613i	$0.521995\pi$
$620$		0			0
$621$	−26.7751	+	3.83452i	−1.07445	+	0.153874i
$622$		0			0
$623$	18.4922	+	11.8842i	0.740876	+	0.476132i
$624$		0			0
$625$	4.93305	+	10.8019i	0.197322	+	0.432075i
$626$		0			0
$627$	2.22736	−	4.87724i	0.0889523	−	0.194778i
$628$		0			0
$629$	−2.28423	+	15.8872i	−0.0910781	+	0.633462i
$630$		0			0
$631$	20.2589	+	23.3800i	0.806495	+	0.930745i	0.998719	−	0.0506061i	$-0.0161153\pi$
$631$	20.2589	+	23.3800i	0.806495	+	0.930745i	−0.192224	+	0.981351i	$0.561570\pi$
$632$		0			0
$633$	7.50796	−	4.82507i	0.298415	−	0.191779i
$634$		0			0
$635$	3.48204	−	1.02242i	0.138180	−	0.0405735i
$636$		0			0
$637$	8.01927	−	9.25473i	0.317735	−	0.366686i
$638$		0			0
$639$	−4.01900	−	1.18008i	−0.158989	−	0.0466834i
$640$		0			0
$641$	−1.56606	−	10.8922i	−0.0618558	−	0.430217i	−0.997093	−	0.0761947i	$-0.975723\pi$
$641$	−1.56606	−	10.8922i	−0.0618558	−	0.430217i	0.935237	−	0.354022i	$-0.115186\pi$
$642$		0			0
$643$	28.9985			1.14359			0.571794	−	0.820397i	$-0.306248\pi$
$643$	28.9985			1.14359			0.571794	+	0.820397i	$0.306248\pi$
$644$		0			0
$645$	2.36860			0.0932635
$646$		0			0
$647$	−5.55195	−	38.6146i	−0.218270	−	1.51810i	−0.744423	−	0.667708i	$-0.767275\pi$
$647$	−5.55195	−	38.6146i	−0.218270	−	1.51810i	0.526154	−	0.850390i	$-0.323634\pi$
$648$		0			0
$649$	−0.329913	−	0.0968713i	−0.0129502	−	0.00380253i
$650$		0			0
$651$	3.01697	−	3.48176i	0.118244	−	0.136461i
$652$		0			0
$653$	−20.2959	+	5.95942i	−0.794240	+	0.233210i	−0.653589	−	0.756849i	$-0.726738\pi$
$653$	−20.2959	+	5.95942i	−0.794240	+	0.233210i	−0.140651	+	0.990059i	$0.544920\pi$
$654$		0			0
$655$	10.8584	−	6.97824i	0.424271	−	0.272663i
$656$		0			0
$657$	6.97657	+	8.05139i	0.272182	+	0.314115i
$658$		0			0
$659$	−3.70420	+	25.7633i	−0.144295	+	1.00360i	0.781050	+	0.624469i	$0.214685\pi$
$659$	−3.70420	+	25.7633i	−0.144295	+	1.00360i	−0.925345	+	0.379127i	$0.876225\pi$
$660$		0			0
$661$	−14.9423	+	32.7190i	−0.581187	+	1.27262i	0.359437	+	0.933169i	$0.382969\pi$
$661$	−14.9423	+	32.7190i	−0.581187	+	1.27262i	−0.940623	+	0.339452i	$0.889758\pi$
$662$		0			0
$663$	−6.42967	−	14.0790i	−0.249708	−	0.546783i
$664$		0			0
$665$	9.97567	+	6.41097i	0.386840	+	0.248607i
$666$		0			0
$667$	8.83777	+	7.66655i	0.342200	+	0.296850i
$668$		0			0
$669$	14.6733	+	9.42995i	0.567302	+	0.364583i
$670$		0			0
$671$	1.03781	+	2.27249i	0.0400643	+	0.0877286i
$672$		0			0
$673$	−4.84641	+	10.6122i	−0.186815	+	0.409068i	−0.979746	−	0.200243i	$-0.935827\pi$
$673$	−4.84641	+	10.6122i	−0.186815	+	0.409068i	0.792931	+	0.609311i	$0.208554\pi$
$674$		0			0
$675$	3.26434	−	22.7040i	0.125645	−	0.873877i
$676$		0			0
$677$	−5.15162	−	5.94529i	−0.197993	−	0.228496i	0.648068	−	0.761583i	$-0.275577\pi$
$677$	−5.15162	−	5.94529i	−0.197993	−	0.228496i	−0.846061	+	0.533087i	$0.821032\pi$
$678$		0			0
$679$	0.993053	−	0.638197i	0.0381099	−	0.0244917i
$680$		0			0
$681$	12.4699	−	3.66150i	0.477849	−	0.140309i
$682$		0			0
$683$	13.7880	−	15.9122i	0.527583	−	0.608863i	−0.427930	−	0.903812i	$-0.640757\pi$
$683$	13.7880	−	15.9122i	0.527583	−	0.608863i	0.955513	+	0.294949i	$0.0953026\pi$
$684$		0			0
$685$	0.860386	+	0.252632i	0.0328737	+	0.00965258i
$686$		0			0
$687$	4.81838	+	33.5125i	0.183833	+	1.27858i
$688$		0			0
$689$	38.5276			1.46778
$690$		0			0
$691$	−5.33705			−0.203031			−0.101516	−	0.994834i	$-0.532369\pi$
$691$	−5.33705			−0.203031			−0.101516	+	0.994834i	$0.532369\pi$
$692$		0			0
$693$	0.106045	+	0.737562i	0.00402833	+	0.0280176i
$694$		0			0
$695$	10.4467	+	3.06744i	0.396268	+	0.116355i
$696$		0			0
$697$	27.6326	−	31.8897i	1.04666	−	1.20791i
$698$		0			0
$699$	9.05421	−	2.65856i	0.342462	−	0.100556i
$700$		0			0
$701$	4.41204	−	2.83545i	0.166640	−	0.107093i	−0.454662	−	0.890664i	$-0.650240\pi$
$701$	4.41204	−	2.83545i	0.166640	−	0.107093i	0.621303	+	0.783571i	$0.286604\pi$
$702$		0			0
$703$	21.9104	+	25.2859i	0.826366	+	0.953677i
$704$		0			0
$705$	−1.10855	+	7.71013i	−0.0417504	+	0.290380i
$706$		0			0
$707$	10.8061	−	23.6620i	0.406404	−	0.889901i
$708$		0			0
$709$	−0.665926	−	1.45817i	−0.0250094	−	0.0547629i	0.896715	−	0.442608i	$-0.145947\pi$
$709$	−0.665926	−	1.45817i	−0.0250094	−	0.0547629i	−0.921724	+	0.387845i	$0.873219\pi$
$710$		0			0
$711$	−10.0617	−	6.46624i	−0.377342	−	0.242503i
$712$		0			0
$713$	−7.75576	−	3.54713i	−0.290455	−	0.132841i
$714$		0			0
$715$	−1.31592	−	0.845690i	−0.0492126	−	0.0316270i
$716$		0			0
$717$	7.26282	+	15.9034i	0.271235	+	0.593922i
$718$		0			0
$719$	−16.8993	+	37.0043i	−0.630238	+	1.38003i	0.277595	+	0.960698i	$0.410463\pi$
$719$	−16.8993	+	37.0043i	−0.630238	+	1.38003i	−0.907833	+	0.419331i	$0.862265\pi$
$720$		0			0
$721$	−2.83809	+	19.7393i	−0.105696	+	0.735131i
$722$		0			0
$723$	−15.7289	−	18.1521i	−0.584964	−	0.675085i
$724$		0			0
$725$	−8.34654	+	5.36400i	−0.309983	+	0.199214i
$726$		0			0
$727$	28.8374	−	8.46742i	1.06952	−	0.314039i	0.300841	−	0.953674i	$-0.402733\pi$
$727$	28.8374	−	8.46742i	1.06952	−	0.314039i	0.768679	+	0.639635i	$0.220914\pi$
$728$		0			0
$729$	−19.5132	+	22.5195i	−0.722713	+	0.834055i
$730$		0			0
$731$	−5.34836	−	1.57042i	−0.197816	−	0.0580841i
$732$		0			0
$733$	1.15854	+	8.05783i	0.0427917	+	0.297623i	0.999967	+	0.00811406i	$0.00258281\pi$
$733$	1.15854	+	8.05783i	0.0427917	+	0.297623i	−0.957175	+	0.289509i	$0.906508\pi$
$734$		0			0
$735$	−5.59626			−0.206421
$736$		0			0
$737$	−5.86932			−0.216199
$738$		0			0
$739$	3.06022	+	21.2843i	0.112572	+	0.782956i	0.965402	+	0.260767i	$0.0839754\pi$
$739$	3.06022	+	21.2843i	0.112572	+	0.782956i	−0.852830	+	0.522189i	$0.825116\pi$
$740$		0			0
$741$	−30.9571	−	9.08982i	−1.13724	−	0.333923i
$742$		0			0
$743$	−0.0641545	+	0.0740382i	−0.00235360	+	0.00271620i	−0.756925	−	0.653502i	$-0.773299\pi$
$743$	−0.0641545	+	0.0740382i	−0.00235360	+	0.00271620i	0.754572	+	0.656218i	$0.227845\pi$
$744$		0			0
$745$	14.7817	−	4.34031i	0.541561	−	0.159017i
$746$		0			0
$747$	2.08969	−	1.34296i	0.0764576	−	0.0491363i
$748$		0			0
$749$	−15.9181	−	18.3705i	−0.581635	−	0.671243i
$750$		0			0
$751$	1.64953	−	11.4727i	0.0601922	−	0.418646i	−0.937339	−	0.348419i	$-0.886719\pi$
$751$	1.64953	−	11.4727i	0.0601922	−	0.418646i	0.997531	−	0.0702269i	$-0.0223723\pi$
$752$		0			0
$753$	−1.74265	+	3.81588i	−0.0635058	+	0.139058i
$754$		0			0
$755$	7.13440	+	15.6222i	0.259647	+	0.568548i
$756$		0			0
$757$	−15.4162	−	9.90738i	−0.560311	−	0.360090i	0.229625	−	0.973279i	$-0.426250\pi$
$757$	−15.4162	−	9.90738i	−0.560311	−	0.360090i	−0.789936	+	0.613189i	$0.789886\pi$
$758$		0			0
$759$	−3.34314	+	1.52452i	−0.121348	+	0.0553367i
$760$		0			0
$761$	−11.8034	−	7.58561i	−0.427874	−	0.274978i	0.308929	−	0.951085i	$-0.400029\pi$
$761$	−11.8034	−	7.58561i	−0.427874	−	0.274978i	−0.736803	+	0.676107i	$0.763666\pi$
$762$		0			0
$763$	2.77490	+	6.07619i	0.100458	+	0.219973i
$764$		0			0
$765$	1.10309	−	2.41543i	0.0398822	−	0.0873299i
$766$		0			0
$767$	−0.294454	+	2.04797i	−0.0106321	+	0.0739481i
$768$		0			0
$769$	−11.2852	−	13.0238i	−0.406955	−	0.469651i	0.514864	−	0.857272i	$-0.327842\pi$
$769$	−11.2852	−	13.0238i	−0.406955	−	0.469651i	−0.921819	+	0.387621i	$0.873297\pi$
$770$		0			0
$771$	−8.97881	+	5.77033i	−0.323364	+	0.207813i
$772$		0			0
$773$	−32.9396	+	9.67193i	−1.18475	+	0.347875i	−0.814005	−	0.580858i	$-0.802717\pi$
$773$	−32.9396	+	9.67193i	−1.18475	+	0.347875i	−0.370749	+	0.928733i	$0.620899\pi$
$774$		0			0
$775$	4.73613	−	5.46579i	0.170127	−	0.196337i
$776$		0			0
$777$	11.8841	+	3.48949i	0.426340	+	0.125185i
$778$		0			0
$779$	−12.5180	−	87.0645i	−0.448503	−	3.11941i
$780$		0			0
$781$	−2.65369			−0.0949565
$782$		0			0
$783$	13.7589			0.491704
$784$		0			0
$785$	0.798369	+	5.55278i	0.0284950	+	0.198187i
$786$		0			0
$787$	10.0733	+	2.95779i	0.359075	+	0.105434i	0.456294	−	0.889829i	$-0.349177\pi$
$787$	10.0733	+	2.95779i	0.359075	+	0.105434i	−0.0972189	+	0.995263i	$0.530995\pi$
$788$		0			0
$789$	−24.3090	+	28.0540i	−0.865422	+	0.998750i
$790$		0			0
$791$	−19.5771	+	5.74834i	−0.696080	+	0.204388i
$792$		0			0
$793$	12.6466	−	8.12747i	0.449094	−	0.288615i
$794$		0			0
$795$	−11.5301	−	13.3065i	−0.408931	−	0.471931i
$796$		0			0
$797$	−5.70906	+	39.7074i	−0.202225	+	1.40651i	0.595437	+	0.803402i	$0.296979\pi$
$797$	−5.70906	+	39.7074i	−0.202225	+	1.40651i	−0.797662	+	0.603105i	$0.793930\pi$
$798$		0			0
$799$	7.61507	−	16.6747i	0.269402	−	0.589908i
$800$		0			0
$801$	−4.26255	−	9.33369i	−0.150610	−	0.329790i
$802$		0			0
$803$	5.67798	+	3.64902i	0.200372	+	0.128771i
$804$		0			0
$805$	−2.28509	−	7.79828i	−0.0805387	−	0.274853i
$806$		0			0
$807$	−28.0996	−	18.0585i	−0.989154	−	0.635691i
$808$		0			0
$809$	−6.95070	−	15.2199i	−0.244374	−	0.535103i	0.747208	−	0.664591i	$-0.231394\pi$
$809$	−6.95070	−	15.2199i	−0.244374	−	0.535103i	−0.991581	+	0.129487i	$0.958667\pi$
$810$		0			0
$811$	14.1617	−	31.0099i	0.497286	−	1.08890i	−0.480056	−	0.877238i	$-0.659384\pi$
$811$	14.1617	−	31.0099i	0.497286	−	1.08890i	0.977342	−	0.211667i	$-0.0678892\pi$
$812$		0			0
$813$	0.182841	−	1.27169i	0.00641251	−	0.0446000i
$814$		0			0
$815$	−2.42631	−	2.80011i	−0.0849898	−	0.0980834i
$816$		0			0
$817$	−9.77502	+	6.28203i	−0.341985	+	0.219780i
$818$		0			0
$819$	4.30222	−	1.26325i	0.150332	−	0.0441414i
$820$		0			0
$821$	14.7312	−	17.0008i	0.514124	−	0.593331i	−0.438026	−	0.898962i	$-0.644322\pi$
$821$	14.7312	−	17.0008i	0.514124	−	0.593331i	0.952150	+	0.305632i	$0.0988676\pi$
$822$		0			0
$823$	20.7227	+	6.08474i	0.722349	+	0.212101i	0.622185	−	0.782870i	$-0.286245\pi$
$823$	20.7227	+	6.08474i	0.722349	+	0.212101i	0.100164	+	0.994971i	$0.468063\pi$
$824$		0			0
$825$	−0.443441	−	3.08420i	−0.0154386	−	0.107378i
$826$		0			0
$827$	−45.6318			−1.58677			−0.793387	−	0.608718i	$-0.791684\pi$
$827$	−45.6318			−1.58677			−0.793387	+	0.608718i	$0.791684\pi$
$828$		0			0
$829$	13.3668			0.464249			0.232125	−	0.972686i	$-0.425432\pi$
$829$	13.3668			0.464249			0.232125	+	0.972686i	$0.425432\pi$
$830$		0			0
$831$	0.435255	+	3.02727i	0.0150988	+	0.105015i
$832$		0			0
$833$	12.6365	+	3.71041i	0.437829	+	0.128558i
$834$		0			0
$835$	−9.14181	+	10.5502i	−0.316365	+	0.365105i
$836$		0			0
$837$	−9.62325	+	2.82564i	−0.332628	+	0.0976684i
$838$		0			0
$839$	31.2442	−	20.0794i	1.07867	−	0.693220i	0.124421	−	0.992230i	$-0.460293\pi$
$839$	31.2442	−	20.0794i	1.07867	−	0.693220i	0.954250	+	0.299010i	$0.0966564\pi$
$840$		0			0
$841$	15.0936	+	17.4190i	0.520470	+	0.600654i
$842$		0			0
$843$	−0.355259	+	2.47088i	−0.0122358	+	0.0851016i
$844$		0			0
$845$	1.30629	−	2.86038i	0.0449378	−	0.0984001i
$846$		0			0
$847$	−7.81970	−	17.1228i	−0.268688	−	0.588345i
$848$		0			0
$849$	−2.95465	−	1.89884i	−0.101403	−	0.0651679i
$850$		0			0
$851$	0.0127121	−	22.9283i	0.000435765	−	0.785973i
$852$		0			0
$853$	−7.25367	−	4.66165i	−0.248361	−	0.159612i	0.410538	−	0.911844i	$-0.365341\pi$
$853$	−7.25367	−	4.66165i	−0.248361	−	0.159612i	−0.658899	+	0.752232i	$0.728977\pi$
$854$		0			0
$855$	−2.29944	−	5.03507i	−0.0786392	−	0.172196i
$856$		0			0
$857$	−0.310055	+	0.678927i	−0.0105913	+	0.0231917i	−0.914854	−	0.403785i	$-0.867694\pi$
$857$	−0.310055	+	0.678927i	−0.0105913	+	0.0231917i	0.904262	+	0.426977i	$0.140422\pi$
$858$		0			0
$859$	−4.37273	+	30.4130i	−0.149196	+	1.03768i	0.768345	+	0.640036i	$0.221080\pi$
$859$	−4.37273	+	30.4130i	−0.149196	+	1.03768i	−0.917541	+	0.397642i	$0.869829\pi$
$860$		0			0
$861$	−21.3234	−	24.6085i	−0.726700	−	0.838657i
$862$		0			0
$863$	30.6078	−	19.6705i	1.04190	−	0.669590i	0.0964463	−	0.995338i	$-0.469252\pi$
$863$	30.6078	−	19.6705i	1.04190	−	0.669590i	0.945457	+	0.325748i	$0.105616\pi$
$864$		0			0
$865$	13.2226	−	3.88250i	0.449581	−	0.132009i
$866$		0			0
$867$	−5.54081	+	6.39443i	−0.188176	+	0.217166i
$868$		0			0
$869$	−7.27041	−	2.13478i	−0.246632	−	0.0724176i
$870$		0			0
$871$	5.02630	+	34.9587i	0.170310	+	1.18453i
$872$		0			0
$873$	−0.551024			−0.0186493
$874$		0			0
$875$	15.3633			0.519374
$876$		0			0
$877$	1.92171	+	13.3658i	0.0648916	+	0.451331i	0.996200	+	0.0870988i	$0.0277596\pi$
$877$	1.92171	+	13.3658i	0.0648916	+	0.451331i	−0.931308	+	0.364233i	$0.881331\pi$
$878$		0			0
$879$	12.2433	+	3.59495i	0.412955	+	0.121255i
$880$		0			0
$881$	−19.3669	+	22.3506i	−0.652488	+	0.753011i	−0.981531	−	0.191304i	$-0.938728\pi$
$881$	−19.3669	+	22.3506i	−0.652488	+	0.753011i	0.329043	+	0.944315i	$0.393274\pi$
$882$		0			0
$883$	11.0148	−	3.23425i	0.370679	−	0.108841i	−0.0910870	−	0.995843i	$-0.529034\pi$
$883$	11.0148	−	3.23425i	0.370679	−	0.108841i	0.461766	+	0.887002i	$0.347216\pi$
$884$		0			0
$885$	0.795439	−	0.511198i	0.0267384	−	0.0171837i
$886$		0			0
$887$	−27.5712	−	31.8189i	−0.925751	−	1.06837i	−0.997480	−	0.0709499i	$-0.977397\pi$
$887$	−27.5712	−	31.8189i	−0.925751	−	1.06837i	0.0717284	−	0.997424i	$-0.477149\pi$
$888$		0			0
$889$	−0.937918	+	6.52336i	−0.0314568	+	0.218787i
$890$		0			0
$891$	−1.26565	+	2.77139i	−0.0424008	+	0.0928449i
$892$		0			0
$893$	−15.8740	−	34.7592i	−0.531203	−	1.16317i
$894$		0			0
$895$	−12.7151	−	8.17150i	−0.425019	−	0.273143i
$896$		0			0
$897$	11.9433	+	18.6068i	0.398774	+	0.621262i
$898$		0			0
$899$	3.64957	+	2.34543i	0.121720	+	0.0782246i
$900$		0			0
$901$	17.2129	+	37.6910i	0.573444	+	1.25567i
$902$		0			0
$903$	−1.78689	+	3.91273i	−0.0594638	+	0.130208i
$904$		0			0
$905$	−0.580880	+	4.04011i	−0.0193091	+	0.134298i
$906$		0			0
$907$	−16.6320	−	19.1943i	−0.552255	−	0.637336i	0.409152	−	0.912466i	$-0.365825\pi$
$907$	−16.6320	−	19.1943i	−0.552255	−	0.637336i	−0.961407	+	0.275130i	$0.911279\pi$
$908$		0			0
$909$	−10.2150	+	6.56477i	−0.338809	+	0.217740i
$910$		0			0
$911$	−42.7734	+	12.5594i	−1.41715	+	0.416112i	−0.898537	−	0.438898i	$-0.855369\pi$
$911$	−42.7734	+	12.5594i	−1.41715	+	0.416112i	−0.518611	+	0.855010i	$0.673551\pi$
$912$		0			0
$913$	1.03057	−	1.18934i	0.0341069	−	0.0393614i
$914$		0			0
$915$	−6.59175	−	1.93551i	−0.217917	−	0.0639861i
$916$		0			0
$917$	3.33588	+	23.2016i	0.110160	+	0.766183i
$918$		0			0
$919$	15.9451			0.525981			0.262991	−	0.964798i	$-0.415291\pi$
$919$	15.9451			0.525981			0.262991	+	0.964798i	$0.415291\pi$
$920$		0			0
$921$	27.0194			0.890319
$922$		0			0
$923$	2.27253	+	15.8058i	0.0748014	+	0.520255i
$924$		0			0
$925$	18.6561	+	5.47792i	0.613408	+	0.180113i
$926$		0			0
$927$	6.09606	−	7.03523i	0.200221	−	0.231067i
$928$		0			0
$929$	0.0663141	−	0.0194716i	0.00217569	−	0.000638841i	−0.280645	−	0.959812i	$-0.590548\pi$
$929$	0.0663141	−	0.0194716i	0.00217569	−	0.000638841i	0.282820	+	0.959173i	$0.408730\pi$
$930$		0			0
$931$	23.0953	−	14.8425i	0.756919	−	0.486442i
$932$		0			0
$933$	29.0097	+	33.4790i	0.949736	+	1.09605i
$934$		0			0
$935$	0.239416	−	1.66517i	0.00782972	−	0.0544569i
$936$		0			0
$937$	1.97100	−	4.31588i	0.0643897	−	0.140994i	−0.874701	−	0.484662i	$-0.838942\pi$
$937$	1.97100	−	4.31588i	0.0643897	−	0.140994i	0.939091	+	0.343669i	$0.111670\pi$
$938$		0			0
$939$	−11.8844	−	26.0232i	−0.387833	−	0.849236i
$940$		0			0
$941$	11.1562	+	7.16965i	0.363681	+	0.233724i	0.709700	−	0.704504i	$-0.248830\pi$
$941$	11.1562	+	7.16965i	0.363681	+	0.233724i	−0.346019	+	0.938228i	$0.612467\pi$
$942$		0			0
$943$	−32.6166	+	50.6906i	−1.06214	+	1.65071i
$944$		0			0
$945$	−8.03941	−	5.16662i	−0.261522	−	0.168070i
$946$		0			0
$947$	24.0061	+	52.5661i	0.780095	+	1.70817i	0.703049	+	0.711141i	$0.251821\pi$
$947$	24.0061	+	52.5661i	0.780095	+	1.70817i	0.0770457	+	0.997028i	$0.475451\pi$
$948$		0			0
$949$	16.8717	−	36.9439i	0.547679	−	1.19925i
$950$		0			0
$951$	−3.22540	+	22.4331i	−0.104591	+	0.727444i
$952$		0			0
$953$	33.3901	+	38.5342i	1.08161	+	1.24825i	0.966984	+	0.254837i	$0.0820218\pi$
$953$	33.3901	+	38.5342i	1.08161	+	1.24825i	0.114627	+	0.993409i	$0.463433\pi$
$954$		0			0
$955$	−11.6931	+	7.51471i	−0.378381	+	0.243170i
$956$		0			0
$957$	1.79336	−	0.526577i	0.0579710	−	0.0170218i
$958$		0			0
$959$	−1.06641	+	1.23070i	−0.0344361	+	0.0397414i
$960$		0			0
$961$	26.7100	+	7.84277i	0.861614	+	0.252993i
$962$		0			0
$963$	1.61480	+	11.2311i	0.0520360	+	0.361919i
$964$		0			0
$965$	−8.95262			−0.288195
$966$		0			0
$967$	1.97410			0.0634829			0.0317414	−	0.999496i	$-0.489895\pi$
$967$	1.97410			0.0634829			0.0317414	+	0.999496i	$0.489895\pi$
$968$		0			0
$969$	−4.93819	−	34.3459i	−0.158638	−	1.10335i
$970$		0			0
$971$	31.1698	+	9.15228i	1.00029	+	0.293711i	0.740573	−	0.671975i	$-0.234554\pi$
$971$	31.1698	+	9.15228i	1.00029	+	0.293711i	0.259713	+	0.965686i	$0.416372\pi$
$972$		0			0
$973$	−12.9482	+	14.9431i	−0.415102	+	0.479053i
$974$		0			0
$975$	−17.9903	+	5.28242i	−0.576149	+	0.169173i
$976$		0			0
$977$	9.46633	−	6.08364i	0.302855	−	0.194633i	−0.380383	−	0.924829i	$-0.624208\pi$
$977$	9.46633	−	6.08364i	0.302855	−	0.194633i	0.683237	+	0.730196i	$0.260571\pi$
$978$		0			0
$979$	−4.25707	−	4.91292i	−0.136056	−	0.157018i
$980$		0			0
$981$	0.443752	−	3.08637i	0.0141679	−	0.0985401i
$982$		0			0
$983$	10.8560	−	23.7713i	0.346253	−	0.758188i	−0.653746	−	0.756714i	$-0.726804\pi$
$983$	10.8560	−	23.7713i	0.346253	−	0.758188i	0.999999	−	0.00147372i	$-0.000469099\pi$
$984$		0			0
$985$	−8.56779	−	18.7608i	−0.272993	−	0.597770i
$986$		0			0
$987$	−11.9002	−	7.64780i	−0.378788	−	0.243432i
$988$		0			0
$989$	7.88105	+	1.13758i	0.250603	+	0.0361731i
$990$		0			0
$991$	15.9462	+	10.2480i	0.506549	+	0.325539i	0.768831	−	0.639452i	$-0.220839\pi$
$991$	15.9462	+	10.2480i	0.506549	+	0.325539i	−0.262282	+	0.964991i	$0.584475\pi$
$992$		0			0
$993$	17.2525	+	37.7776i	0.547490	+	1.19884i
$994$		0			0
$995$	0.0469288	−	0.102760i	0.00148774	−	0.00325770i
$996$		0			0
$997$	5.70019	−	39.6457i	0.180527	−	1.25559i	−0.674994	−	0.737824i	$-0.735854\pi$
$997$	5.70019	−	39.6457i	0.180527	−	1.25559i	0.855521	−	0.517769i	$-0.173237\pi$
$998$		0			0
$999$	−17.6576	−	20.3780i	−0.558663	−	0.644731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.25.2	✓	20
3.2	odd	2		828.2.q.a.577.1		20
4.3	odd	2		368.2.m.d.209.1		20
23.9	even	11		2116.2.a.j.1.4		10
23.12	even	11	inner	92.2.e.a.81.2	yes	20
23.14	odd	22		2116.2.a.i.1.4		10
69.35	odd	22		828.2.q.a.541.1		20
92.35	odd	22		368.2.m.d.81.1		20
92.55	odd	22		8464.2.a.ce.1.7		10
92.83	even	22		8464.2.a.cd.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.25.2	✓	20	1.1	even	1	trivial
92.2.e.a.81.2	yes	20	23.12	even	11	inner
368.2.m.d.81.1		20	92.35	odd	22
368.2.m.d.209.1		20	4.3	odd	2
828.2.q.a.541.1		20	69.35	odd	22
828.2.q.a.577.1		20	3.2	odd	2
2116.2.a.i.1.4		10	23.14	odd	22
2116.2.a.j.1.4		10	23.9	even	11
8464.2.a.cd.1.7		10	92.83	even	22
8464.2.a.ce.1.7		10	92.55	odd	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.210181 + 1.46184i) q^{3} +(0.926812 + 0.272136i) q^{5} +(-1.14874 + 1.32572i) q^{7} +(0.785668 - 0.230693i) q^{9} +O(q^{10})\)	\(q+(0.210181 + 1.46184i) q^{3} +(0.926812 + 0.272136i) q^{5} +(-1.14874 + 1.32572i) q^{7} +(0.785668 - 0.230693i) q^{9} +(0.436414 - 0.280466i) q^{11} +(-2.04423 - 2.35917i) q^{13} +(-0.203022 + 1.41205i) q^{15} +(1.39464 - 3.05384i) q^{17} +(-2.90720 - 6.36588i) q^{19} +(-2.17943 - 1.40064i) q^{21} +(-1.35369 + 4.60082i) q^{23} +(-3.42135 - 2.19877i) q^{25} +(2.34292 + 5.13028i) q^{27} +(1.01343 - 2.21909i) q^{29} +(-0.253078 + 1.76020i) q^{31} +(0.501724 + 0.579020i) q^{33} +(-1.42544 + 0.916075i) q^{35} +(-4.58723 + 1.34693i) q^{37} +(3.01908 - 3.48420i) q^{39} +(12.0596 + 3.54102i) q^{41} +(-0.236292 - 1.64344i) q^{43} +0.790946 q^{45} +5.46023 q^{47} +(0.558283 + 3.88295i) q^{49} +(4.75737 + 1.39689i) q^{51} +(-8.08238 + 9.32757i) q^{53} +(0.480798 - 0.141175i) q^{55} +(8.69489 - 5.58786i) q^{57} +(-0.434046 - 0.500915i) q^{59} +(-0.685355 + 4.76675i) q^{61} +(-0.596695 + 1.30658i) q^{63} +(-1.25260 - 2.74282i) q^{65} +(-9.51795 - 6.11682i) q^{67} +(-7.01020 - 1.01188i) q^{69} +(-4.30334 - 2.76559i) q^{71} +(5.40478 + 11.8348i) q^{73} +(2.49515 - 5.46361i) q^{75} +(-0.129507 + 0.900743i) q^{77} +(-9.56521 - 11.0388i) q^{79} +(-4.94068 + 3.17518i) q^{81} +(2.91071 - 0.854661i) q^{83} +(2.12363 - 2.45080i) q^{85} +(3.45697 + 1.01506i) q^{87} +(-1.78337 - 12.4036i) q^{89} +5.47588 q^{91} -2.62633 q^{93} +(-0.962039 - 6.69113i) q^{95} +(-0.645676 - 0.189588i) q^{97} +(0.278175 - 0.321031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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