LMFDB - Embedded newform 92.2.e.a.81.1

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			81.1
Root			$1.82483 + 2.10597i$ of defining polynomial
Character	$\chi$	$=$	92.81
Dual form			92.2.e.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396574 + 2.75823i) q^{3} +(-1.50454 + 0.441774i) q^{5} +(-0.107929 - 0.124557i) q^{7} +(-4.57211 - 1.34249i) q^{9} +O(q^{10})$	\(q+(-0.396574 + 2.75823i) q^{3} +(-1.50454 + 0.441774i) q^{5} +(-0.107929 - 0.124557i) q^{7} +(-4.57211 - 1.34249i) q^{9} +(5.36013 + 3.44475i) q^{11} +(2.99118 - 3.45201i) q^{13} +(-0.621853 - 4.32508i) q^{15} +(-0.232983 - 0.510162i) q^{17} +(1.75854 - 3.85066i) q^{19} +(0.386358 - 0.248297i) q^{21} +(-2.40635 + 4.14843i) q^{23} +(-2.13778 + 1.37387i) q^{25} +(2.04330 - 4.47420i) q^{27} +(-2.34087 - 5.12579i) q^{29} +(-1.27395 - 8.86051i) q^{31} +(-11.6271 + 13.4184i) q^{33} +(0.217410 + 0.139721i) q^{35} +(5.69427 + 1.67199i) q^{37} +(8.33521 + 9.61935i) q^{39} +(3.37652 - 0.991436i) q^{41} +(-1.17188 + 8.15062i) q^{43} +7.47201 q^{45} -5.52419 q^{47} +(0.992338 - 6.90186i) q^{49} +(1.49954 - 0.440305i) q^{51} +(1.22835 + 1.41760i) q^{53} +(-9.58636 - 2.81481i) q^{55} +(9.92362 + 6.37752i) q^{57} +(-4.03623 + 4.65806i) q^{59} +(-0.202144 - 1.40594i) q^{61} +(0.326246 + 0.714380i) q^{63} +(-2.97536 + 6.51512i) q^{65} +(-6.36535 + 4.09076i) q^{67} +(-10.4880 - 8.28245i) q^{69} +(-1.68406 + 1.08228i) q^{71} +(4.50073 - 9.85523i) q^{73} +(-2.94166 - 6.44134i) q^{75} +(-0.149447 - 1.03943i) q^{77} +(5.70639 - 6.58552i) q^{79} +(-0.495456 - 0.318410i) q^{81} +(0.778972 + 0.228727i) q^{83} +(0.575909 + 0.664635i) q^{85} +(15.0665 - 4.42391i) q^{87} +(0.923336 - 6.42194i) q^{89} -0.752805 q^{91} +24.9446 q^{93} +(-0.944675 + 6.57036i) q^{95} +(-7.25803 + 2.13115i) q^{97} +(-19.8825 - 22.9457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

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
$3$	−0.396574	+	2.75823i	−0.228962	+	1.59247i	0.473531	+	0.880777i	$0.342979\pi$
$3$	−0.396574	+	2.75823i	−0.228962	+	1.59247i	−0.702493	+	0.711690i	$0.747930\pi$
$4$		0			0
$5$	−1.50454	+	0.441774i	−0.672853	+	0.197567i	−0.600273	−	0.799795i	$-0.704941\pi$
$5$	−1.50454	+	0.441774i	−0.672853	+	0.197567i	−0.0725797	+	0.997363i	$0.523123\pi$
$6$		0			0
$7$	−0.107929	−	0.124557i	−0.0407933	−	0.0470780i	0.734986	−	0.678082i	$-0.237189\pi$
$7$	−0.107929	−	0.124557i	−0.0407933	−	0.0470780i	−0.775780	+	0.631004i	$0.782643\pi$
$8$		0			0
$9$	−4.57211	−	1.34249i	−1.52404	−	0.447497i
$10$		0			0
$11$	5.36013	+	3.44475i	1.61614	+	1.03863i	0.958417	+	0.285371i	$0.0921169\pi$
$11$	5.36013	+	3.44475i	1.61614	+	1.03863i	0.657724	+	0.753259i	$0.271519\pi$
$12$		0			0
$13$	2.99118	−	3.45201i	0.829604	−	0.957414i	−0.170003	−	0.985444i	$-0.554378\pi$
$13$	2.99118	−	3.45201i	0.829604	−	0.957414i	0.999607	+	0.0280295i	$0.00892324\pi$
$14$		0			0
$15$	−0.621853	−	4.32508i	−0.160562	−	1.11673i
$16$		0			0
$17$	−0.232983	−	0.510162i	−0.0565067	−	0.123732i	0.879272	−	0.476319i	$-0.158029\pi$
$17$	−0.232983	−	0.510162i	−0.0565067	−	0.123732i	−0.935779	+	0.352587i	$0.885302\pi$
$18$		0			0
$19$	1.75854	−	3.85066i	0.403436	−	0.883401i	−0.593474	−	0.804853i	$-0.702244\pi$
$19$	1.75854	−	3.85066i	0.403436	−	0.883401i	0.996910	−	0.0785484i	$-0.0250285\pi$
$20$		0			0
$21$	0.386358	−	0.248297i	0.0843103	−	0.0541830i
$22$		0			0
$23$	−2.40635	+	4.14843i	−0.501760	+	0.865007i
$23$	−2.40635	+	4.14843i	−0.501760	+	0.865007i
$24$		0			0
$25$	−2.13778	+	1.37387i	−0.427556	+	0.274773i
$26$		0			0
$27$	2.04330	−	4.47420i	0.393233	−	0.861061i
$28$		0			0
$29$	−2.34087	−	5.12579i	−0.434689	−	0.951836i	−0.992543	−	0.121897i	$-0.961102\pi$
$29$	−2.34087	−	5.12579i	−0.434689	−	0.951836i	0.557854	−	0.829939i	$-0.311625\pi$
$30$		0			0
$31$	−1.27395	−	8.86051i	−0.228808	−	1.59139i	−0.703142	−	0.711049i	$-0.748220\pi$
$31$	−1.27395	−	8.86051i	−0.228808	−	1.59139i	0.474334	−	0.880345i	$-0.342689\pi$
$32$		0			0
$33$	−11.6271	+	13.4184i	−2.02402	+	2.33584i
$34$		0			0
$35$	0.217410	+	0.139721i	0.0367490	+	0.0236171i
$36$		0			0
$37$	5.69427	+	1.67199i	0.936132	+	0.274873i	0.714002	−	0.700144i	$-0.246881\pi$
$37$	5.69427	+	1.67199i	0.936132	+	0.274873i	0.222130	+	0.975017i	$0.428699\pi$
$38$		0			0
$39$	8.33521	+	9.61935i	1.33470	+	1.54033i
$40$		0			0
$41$	3.37652	−	0.991436i	0.527324	−	0.154836i	−0.00722474	−	0.999974i	$-0.502300\pi$
$41$	3.37652	−	0.991436i	0.527324	−	0.154836i	0.534549	+	0.845138i	$0.320482\pi$
$42$		0			0
$43$	−1.17188	+	8.15062i	−0.178710	+	1.24296i	0.681041	+	0.732245i	$0.261527\pi$
$43$	−1.17188	+	8.15062i	−0.178710	+	1.24296i	−0.859752	+	0.510712i	$0.829382\pi$
$44$		0			0
$45$	7.47201			1.11386
$46$		0			0
$47$	−5.52419			−0.805786			−0.402893	−	0.915247i	$-0.631995\pi$
$47$	−5.52419			−0.805786			−0.402893	+	0.915247i	$0.631995\pi$
$48$		0			0
$49$	0.992338	−	6.90186i	0.141763	−	0.985981i
$50$		0			0
$51$	1.49954	−	0.440305i	0.209978	−	0.0616550i
$52$		0			0
$53$	1.22835	+	1.41760i	0.168727	+	0.194722i	0.833816	−	0.552043i	$-0.186152\pi$
$53$	1.22835	+	1.41760i	0.168727	+	0.194722i	−0.665088	+	0.746765i	$0.731606\pi$
$54$		0			0
$55$	−9.58636	−	2.81481i	−1.29262	−	0.379549i
$56$		0			0
$57$	9.92362	+	6.37752i	1.31442	+	0.844724i
$58$		0			0
$59$	−4.03623	+	4.65806i	−0.525472	+	0.606427i	−0.954993	−	0.296630i	$-0.904137\pi$
$59$	−4.03623	+	4.65806i	−0.525472	+	0.606427i	0.429520	+	0.903057i	$0.358683\pi$
$60$		0			0
$61$	−0.202144	−	1.40594i	−0.0258819	−	0.180013i	0.972780	−	0.231732i	$-0.0744391\pi$
$61$	−0.202144	−	1.40594i	−0.0258819	−	0.180013i	−0.998662	+	0.0517189i	$0.983530\pi$
$62$		0			0
$63$	0.326246	+	0.714380i	0.0411032	+	0.0900034i
$64$		0			0
$65$	−2.97536	+	6.51512i	−0.369047	+	0.808101i
$66$		0			0
$67$	−6.36535	+	4.09076i	−0.777651	+	0.499766i	−0.868253	−	0.496121i	$-0.834757\pi$
$67$	−6.36535	+	4.09076i	−0.777651	+	0.499766i	0.0906025	+	0.995887i	$0.471121\pi$
$68$		0			0
$69$	−10.4880	−	8.28245i	−1.26261	−	0.997090i
$70$		0			0
$71$	−1.68406	+	1.08228i	−0.199861	+	0.128443i	−0.636743	−	0.771076i	$-0.719719\pi$
$71$	−1.68406	+	1.08228i	−0.199861	+	0.128443i	0.436882	+	0.899519i	$0.356083\pi$
$72$		0			0
$73$	4.50073	−	9.85523i	0.526771	−	1.15347i	−0.440041	−	0.897978i	$-0.645036\pi$
$73$	4.50073	−	9.85523i	0.526771	−	1.15347i	0.966812	−	0.255490i	$-0.0822367\pi$
$74$		0			0
$75$	−2.94166	−	6.44134i	−0.339674	−	0.743781i
$76$		0			0
$77$	−0.149447	−	1.03943i	−0.0170311	−	0.118454i
$78$		0			0
$79$	5.70639	−	6.58552i	0.642019	−	0.740929i	−0.337712	−	0.941250i	$-0.609653\pi$
$79$	5.70639	−	6.58552i	0.642019	−	0.740929i	0.979730	+	0.200320i	$0.0641983\pi$
$80$		0			0
$81$	−0.495456	−	0.318410i	−0.0550506	−	0.0353789i
$82$		0			0
$83$	0.778972	+	0.228727i	0.0855033	+	0.0251060i	0.324204	−	0.945987i	$-0.394903\pi$
$83$	0.778972	+	0.228727i	0.0855033	+	0.0251060i	−0.238701	+	0.971093i	$0.576722\pi$
$84$		0			0
$85$	0.575909	+	0.664635i	0.0624662	+	0.0720898i
$86$		0			0
$87$	15.0665	−	4.42391i	1.61529	−	0.474293i
$88$		0			0
$89$	0.923336	−	6.42194i	0.0978734	−	0.680724i	−0.880526	−	0.473999i	$-0.842810\pi$
$89$	0.923336	−	6.42194i	0.0978734	−	0.680724i	0.978399	−	0.206726i	$-0.0662808\pi$
$90$		0			0
$91$	−0.752805			−0.0789155
$92$		0			0
$93$	24.9446			2.58663
$94$		0			0
$95$	−0.944675	+	6.57036i	−0.0969216	+	0.674105i
$96$		0			0
$97$	−7.25803	+	2.13115i	−0.736941	+	0.216385i	−0.628600	−	0.777728i	$-0.716372\pi$
$97$	−7.25803	+	2.13115i	−0.736941	+	0.216385i	−0.108341	+	0.994114i	$0.534554\pi$
$98$		0			0
$99$	−19.8825	−	22.9457i	−1.99827	−	2.30613i
$100$		0			0
$101$	2.89762	+	0.850817i	0.288324	+	0.0846595i	0.422696	−	0.906271i	$-0.361084\pi$
$101$	2.89762	+	0.850817i	0.288324	+	0.0846595i	−0.134373	+	0.990931i	$0.542902\pi$
$102$		0			0
$103$	2.43490	+	1.56482i	0.239918	+	0.154186i	0.655075	−	0.755564i	$-0.272637\pi$
$103$	2.43490	+	1.56482i	0.239918	+	0.154186i	−0.415157	+	0.909750i	$0.636273\pi$
$104$		0			0
$105$	−0.471602	+	0.544258i	−0.0460236	+	0.0531141i
$106$		0			0
$107$	−2.30965	−	16.0639i	−0.223282	−	1.55296i	−0.725502	−	0.688220i	$-0.758392\pi$
$107$	−2.30965	−	16.0639i	−0.223282	−	1.55296i	0.502220	−	0.864740i	$-0.332517\pi$
$108$		0			0
$109$	4.66724	+	10.2198i	0.447041	+	0.978882i	0.990252	+	0.139287i	$0.0444809\pi$
$109$	4.66724	+	10.2198i	0.447041	+	0.978882i	−0.543211	+	0.839596i	$0.682792\pi$
$110$		0			0
$111$	−6.86993	+	15.0431i	−0.652065	+	1.42782i
$112$		0			0
$113$	−5.79608	+	3.72491i	−0.545249	+	0.350410i	−0.784089	−	0.620649i	$-0.786869\pi$
$113$	−5.79608	+	3.72491i	−0.545249	+	0.350410i	0.238839	+	0.971059i	$0.423233\pi$
$114$		0			0
$115$	1.78780	−	7.30456i	0.166713	−	0.681154i
$116$		0			0
$117$	−18.3103	+	11.7673i	−1.69279	+	1.08789i
$118$		0			0
$119$	−0.0383984	+	0.0840809i	−0.00351998	+	0.00770768i
$120$		0			0
$121$	12.2952	+	26.9227i	1.11774	+	2.44751i
$122$		0			0
$123$	1.39557	+	9.70642i	0.125834	+	0.875198i
$124$		0			0
$125$	7.74375	−	8.93677i	0.692622	−	0.799329i
$126$		0			0
$127$	−5.17708	−	3.32711i	−0.459392	−	0.295233i	0.290402	−	0.956905i	$-0.406211\pi$
$127$	−5.17708	−	3.32711i	−0.459392	−	0.295233i	−0.749794	+	0.661671i	$0.769847\pi$
$128$		0			0
$129$	−22.0166	−	6.46465i	−1.93845	−	0.569181i
$130$		0			0
$131$	3.64511	+	4.20668i	0.318474	+	0.367539i	0.892304	−	0.451436i	$-0.149088\pi$
$131$	3.64511	+	4.20668i	0.318474	+	0.367539i	−0.573829	+	0.818975i	$0.694543\pi$
$132$		0			0
$133$	−0.669422	+	0.196560i	−0.0580463	+	0.0170439i
$134$		0			0
$135$	−1.09765	+	7.63431i	−0.0944706	+	0.657057i
$136$		0			0
$137$	−3.23168			−0.276101			−0.138051	−	0.990425i	$-0.544084\pi$
$137$	−3.23168			−0.276101			−0.138051	+	0.990425i	$0.544084\pi$
$138$		0			0
$139$	−4.67006			−0.396109			−0.198055	−	0.980191i	$-0.563462\pi$
$139$	−4.67006			−0.396109			−0.198055	+	0.980191i	$0.563462\pi$
$140$		0			0
$141$	2.19075	−	15.2370i	0.184495	−	1.28319i
$142$		0			0
$143$	27.9244	−	8.19935i	2.33516	−	0.685664i
$144$		0			0
$145$	5.78639	+	6.67785i	0.480533	+	0.554565i
$146$		0			0
$147$	18.6434	+	5.47420i	1.53768	+	0.451505i
$148$		0			0
$149$	2.42009	+	1.55530i	0.198262	+	0.127415i	0.636005	−	0.771685i	$-0.280586\pi$
$149$	2.42009	+	1.55530i	0.198262	+	0.127415i	−0.437743	+	0.899100i	$0.644222\pi$
$150$		0			0
$151$	−8.27575	+	9.55073i	−0.673471	+	0.777227i	−0.984915	−	0.173037i	$-0.944642\pi$
$151$	−8.27575	+	9.55073i	−0.673471	+	0.777227i	0.311444	+	0.950265i	$0.399187\pi$
$152$		0			0
$153$	0.380335	+	2.64529i	0.0307483	+	0.213859i
$154$		0			0
$155$	5.83105	+	12.7682i	0.468362	+	1.02557i
$156$		0			0
$157$	−6.63368	+	14.5257i	−0.529425	+	1.15928i	0.436321	+	0.899791i	$0.356281\pi$
$157$	−6.63368	+	14.5257i	−0.529425	+	1.15928i	−0.965746	+	0.259488i	$0.916446\pi$
$158$		0			0
$159$	−4.39719	+	2.82590i	−0.348720	+	0.224109i
$160$		0			0
$161$	0.776430	−	0.148008i	0.0611913	−	0.0116647i
$162$		0			0
$163$	0.272429	−	0.175080i	0.0213383	−	0.0137133i	−0.529928	−	0.848043i	$-0.677781\pi$
$163$	0.272429	−	0.175080i	0.0213383	−	0.0137133i	0.551266	+	0.834329i	$0.314145\pi$
$164$		0			0
$165$	11.5656	−	25.3251i	0.900381	−	1.97156i
$166$		0			0
$167$	0.343445	+	0.752039i	0.0265766	+	0.0581945i	0.922455	−	0.386105i	$-0.126180\pi$
$167$	0.343445	+	0.752039i	0.0265766	+	0.0581945i	−0.895878	+	0.444300i	$0.853453\pi$
$168$		0			0
$169$	−1.11909	−	7.78346i	−0.0860840	−	0.598727i
$170$		0			0
$171$	−13.2097	+	15.2448i	−1.01017	+	1.16580i
$172$		0			0
$173$	−15.5091	−	9.96712i	−1.17914	−	0.757786i	−0.203911	−	0.978989i	$-0.565365\pi$
$173$	−15.5091	−	9.96712i	−1.17914	−	0.757786i	−0.975228	+	0.221203i	$0.929002\pi$
$174$		0			0
$175$	0.401853	+	0.117995i	0.0303772	+	0.00891955i
$176$		0			0
$177$	−11.2473	−	12.9801i	−0.845403	−	0.975647i
$178$		0			0
$179$	15.7699	−	4.63045i	1.17869	−	0.346096i	0.367024	−	0.930212i	$-0.380377\pi$
$179$	15.7699	−	4.63045i	1.17869	−	0.346096i	0.811670	+	0.584116i	$0.198559\pi$
$180$		0			0
$181$	0.835071	−	5.80805i	0.0620703	−	0.431709i	−0.934963	−	0.354744i	$-0.884568\pi$
$181$	0.835071	−	5.80805i	0.0620703	−	0.431709i	0.997034	−	0.0769647i	$-0.0245229\pi$
$182$		0			0
$183$	3.95809			0.292590
$184$		0			0
$185$	−9.30591			−0.684184
$186$		0			0
$187$	0.508559	−	3.53710i	0.0371895	−	0.258659i
$188$		0			0
$189$	−0.777824	+	0.228390i	−0.0565783	+	0.0166129i
$190$		0			0
$191$	−12.7039	−	14.6610i	−0.919220	−	1.06084i	−0.997954	−	0.0639403i	$-0.979633\pi$
$191$	−12.7039	−	14.6610i	−0.919220	−	1.06084i	0.0787342	−	0.996896i	$-0.474912\pi$
$192$		0			0
$193$	10.7012	+	3.14215i	0.770289	+	0.226177i	0.643184	−	0.765712i	$-0.277613\pi$
$193$	10.7012	+	3.14215i	0.770289	+	0.226177i	0.127105	+	0.991889i	$0.459431\pi$
$194$		0			0
$195$	−16.7903	−	10.7905i	−1.20238	−	0.772721i
$196$		0			0
$197$	−9.25522	+	10.6811i	−0.659407	+	0.760997i	−0.982680	−	0.185309i	$-0.940671\pi$
$197$	−9.25522	+	10.6811i	−0.659407	+	0.760997i	0.323273	+	0.946306i	$0.395217\pi$
$198$		0			0
$199$	2.29107	+	15.9347i	0.162410	+	1.12958i	0.894074	+	0.447918i	$0.147835\pi$
$199$	2.29107	+	15.9347i	0.162410	+	1.12958i	−0.731665	+	0.681664i	$0.761256\pi$
$200$		0			0
$201$	−8.75894	−	19.1794i	−0.617808	−	1.35281i
$202$		0			0
$203$	−0.385804	+	0.844793i	−0.0270781	+	0.0592929i
$204$		0			0
$205$	−4.64214	+	2.98332i	−0.324221	+	0.208364i
$206$		0			0
$207$	16.5713	−	15.7365i	1.15179	−	1.09377i
$208$		0			0
$209$	22.6905	−	14.5823i	1.56954	−	1.00868i
$210$		0			0
$211$	−3.17811	+	6.95908i	−0.218790	+	0.479083i	−0.986920	−	0.161211i	$-0.948460\pi$
$211$	−3.17811	+	6.95908i	−0.218790	+	0.479083i	0.768130	+	0.640294i	$0.221187\pi$
$212$		0			0
$213$	−2.31733	−	5.07424i	−0.158781	−	0.347681i
$214$		0			0
$215$	−1.83758	−	12.7807i	−0.125322	−	0.871634i
$216$		0			0
$217$	−0.966140	+	1.11498i	−0.0655858	+	0.0756901i
$218$		0			0
$219$	25.3982	+	16.3224i	1.71625	+	1.10297i
$220$		0			0
$221$	−2.45798	−	0.721727i	−0.165341	−	0.0485486i
$222$		0			0
$223$	1.46883	+	1.69512i	0.0983599	+	0.113513i	0.802795	−	0.596255i	$-0.203345\pi$
$223$	1.46883	+	1.69512i	0.0983599	+	0.113513i	−0.704435	+	0.709768i	$0.748800\pi$
$224$		0			0
$225$	11.6186	−	3.41152i	0.774570	−	0.227434i
$226$		0			0
$227$	−2.59896	+	18.0762i	−0.172499	+	1.19976i	0.701082	+	0.713080i	$0.252701\pi$
$227$	−2.59896	+	18.0762i	−0.172499	+	1.19976i	−0.873582	+	0.486678i	$0.838209\pi$
$228$		0			0
$229$	−17.3351			−1.14554			−0.572768	−	0.819718i	$-0.694130\pi$
$229$	−17.3351			−1.14554			−0.572768	+	0.819718i	$0.694130\pi$
$230$		0			0
$231$	2.92625			0.192533
$232$		0			0
$233$	2.20289	−	15.3214i	0.144316	−	1.00374i	−0.780997	−	0.624535i	$-0.785289\pi$
$233$	2.20289	−	15.3214i	0.144316	−	1.00374i	0.925313	−	0.379205i	$-0.123802\pi$
$234$		0			0
$235$	8.31139	−	2.44044i	0.542175	−	0.159197i
$236$		0			0
$237$	15.9014	+	18.3512i	1.03291	+	1.19204i
$238$		0			0
$239$	−20.1170	−	5.90689i	−1.30126	−	0.382085i	−0.443565	−	0.896242i	$-0.646287\pi$
$239$	−20.1170	−	5.90689i	−1.30126	−	0.382085i	−0.857696	+	0.514157i	$0.828105\pi$
$240$		0			0
$241$	12.6061	+	8.10145i	0.812030	+	0.521860i	0.879521	−	0.475860i	$-0.157863\pi$
$241$	12.6061	+	8.10145i	0.812030	+	0.521860i	−0.0674909	+	0.997720i	$0.521499\pi$
$242$		0			0
$243$	10.7379	−	12.3922i	0.688838	−	0.794961i
$244$		0			0
$245$	1.55605	+	10.8225i	0.0994122	+	0.691427i
$246$		0			0
$247$	−8.03239	−	17.5885i	−0.511089	−	1.11913i
$248$		0			0
$249$	−0.939802	+	2.05788i	−0.0595575	+	0.130413i
$250$		0			0
$251$	3.34897	−	2.15225i	0.211385	−	0.135849i	−0.430664	−	0.902512i	$-0.641721\pi$
$251$	3.34897	−	2.15225i	0.211385	−	0.135849i	0.642050	+	0.766663i	$0.278084\pi$
$252$		0			0
$253$	−27.1887	+	13.9468i	−1.70934	+	0.876830i
$254$		0			0
$255$	−2.06161	+	1.32492i	−0.129103	+	0.0829695i
$256$		0			0
$257$	−9.44008	+	20.6709i	−0.588856	+	1.28942i	0.347275	+	0.937764i	$0.387107\pi$
$257$	−9.44008	+	20.6709i	−0.588856	+	1.28942i	−0.936131	+	0.351652i	$0.885620\pi$
$258$		0			0
$259$	−0.406319	−	0.889715i	−0.0252474	−	0.0552842i
$260$		0			0
$261$	3.82138	+	26.5783i	0.236537	+	1.64515i
$262$		0			0
$263$	11.8522	−	13.6781i	0.730837	−	0.843431i	−0.261729	−	0.965141i	$-0.584293\pi$
$263$	11.8522	−	13.6781i	0.730837	−	0.843431i	0.992566	+	0.121711i	$0.0388380\pi$
$264$		0			0
$265$	−2.47437	−	1.59018i	−0.151999	−	0.0976840i
$266$		0			0
$267$	17.3470	+	5.09355i	1.06162	+	0.311720i
$268$		0			0
$269$	−3.62431	−	4.18268i	−0.220978	−	0.255022i	0.634426	−	0.772984i	$-0.281237\pi$
$269$	−3.62431	−	4.18268i	−0.220978	−	0.255022i	−0.855404	+	0.517961i	$0.826691\pi$
$270$		0			0
$271$	−24.1863	+	7.10173i	−1.46921	+	0.431399i	−0.915843	−	0.401537i	$-0.868476\pi$
$271$	−24.1863	+	7.10173i	−1.46921	+	0.431399i	−0.553369	+	0.832936i	$0.686658\pi$
$272$		0			0
$273$	0.298543	−	2.07641i	0.0180687	−	0.125670i
$274$		0			0
$275$	−16.1914			−0.976378
$276$		0			0
$277$	1.48028			0.0889416			0.0444708	−	0.999011i	$-0.485840\pi$
$277$	1.48028			0.0889416			0.0444708	+	0.999011i	$0.485840\pi$
$278$		0			0
$279$	−6.07053	+	42.2214i	−0.363433	+	2.52773i
$280$		0			0
$281$	−22.6649	+	6.65501i	−1.35207	+	0.397005i	−0.875962	−	0.482380i	$-0.839772\pi$
$281$	−22.6649	+	6.65501i	−1.35207	+	0.397005i	−0.476111	+	0.879385i	$0.657954\pi$
$282$		0			0
$283$	3.39480	+	3.91780i	0.201800	+	0.232889i	0.847625	−	0.530596i	$-0.178032\pi$
$283$	3.39480	+	3.91780i	0.201800	+	0.232889i	−0.645825	+	0.763485i	$0.723486\pi$
$284$		0			0
$285$	−17.7480	−	5.21127i	−1.05130	−	0.308689i
$286$		0			0
$287$	−0.487915	−	0.313564i	−0.0288007	−	0.0185091i
$288$		0			0
$289$	10.9266	−	12.6100i	0.642744	−	0.741766i
$290$		0			0
$291$	−2.99986	−	20.8645i	−0.175855	−	1.22310i
$292$		0			0
$293$	11.9359	+	26.1360i	0.697302	+	1.52688i	0.843212	+	0.537581i	$0.180662\pi$
$293$	11.9359	+	26.1360i	0.697302	+	1.52688i	−0.145909	+	0.989298i	$0.546611\pi$
$294$		0			0
$295$	4.01488	−	8.79135i	0.233755	−	0.511852i
$296$		0			0
$297$	26.3649	−	16.9437i	1.52984	−	0.983172i
$298$		0			0
$299$	7.12256	+	20.7154i	0.411908	+	1.19801i
$300$		0			0
$301$	1.14169	−	0.733722i	0.0658061	−	0.0422910i
$302$		0			0
$303$	−3.49587	+	7.65490i	−0.200833	+	0.439762i
$304$		0			0
$305$	0.925245	+	2.02600i	0.0529794	+	0.116009i
$306$		0			0
$307$	−1.23252	−	8.57237i	−0.0703437	−	0.489251i	−0.994289	−	0.106725i	$-0.965963\pi$
$307$	−1.23252	−	8.57237i	−0.0703437	−	0.489251i	0.923945	−	0.382526i	$-0.124946\pi$
$308$		0			0
$309$	−5.28175	+	6.09546i	−0.300468	+	0.346759i
$310$		0			0
$311$	3.83317	+	2.46343i	0.217359	+	0.139688i	0.644790	−	0.764360i	$-0.276945\pi$
$311$	3.83317	+	2.46343i	0.217359	+	0.139688i	−0.427431	+	0.904048i	$0.640581\pi$
$312$		0			0
$313$	15.1964	+	4.46208i	0.858954	+	0.252212i	0.681411	−	0.731901i	$-0.261367\pi$
$313$	15.1964	+	4.46208i	0.858954	+	0.252212i	0.177543	+	0.984113i	$0.443185\pi$
$314$		0			0
$315$	−0.806447	−	0.930689i	−0.0454381	−	0.0524384i
$316$		0			0
$317$	−0.964264	+	0.283134i	−0.0541585	+	0.0159024i	−0.308700	−	0.951160i	$-0.599894\pi$
$317$	−0.964264	+	0.283134i	−0.0541585	+	0.0159024i	0.254541	+	0.967062i	$0.418076\pi$
$318$		0			0
$319$	5.10969	−	35.5386i	0.286087	−	1.98978i
$320$		0			0
$321$	45.2241			2.52416
$322$		0			0
$323$	−2.37417			−0.132102
$324$		0			0
$325$	−1.65188	+	11.4891i	−0.0916301	+	0.637301i
$326$		0			0
$327$	−30.0396	+	8.82042i	−1.66119	+	0.487770i
$328$		0			0
$329$	0.596220	+	0.688075i	0.0328707	+	0.0379348i
$330$		0			0
$331$	16.7154	+	4.90809i	0.918762	+	0.269773i	0.706725	−	0.707489i	$-0.250172\pi$
$331$	16.7154	+	4.90809i	0.918762	+	0.269773i	0.212037	+	0.977262i	$0.431990\pi$
$332$		0			0
$333$	−23.7902	−	15.2890i	−1.30369	−	0.837832i
$334$		0			0
$335$	7.76975	−	8.96677i	0.424507	−	0.489907i
$336$		0			0
$337$	−2.24527	−	15.6162i	−0.122308	−	0.850668i	−0.954931	−	0.296828i	$-0.904071\pi$
$337$	−2.24527	−	15.6162i	−0.122308	−	0.850668i	0.832623	−	0.553840i	$-0.186838\pi$
$338$		0			0
$339$	−7.97561	−	17.4642i	−0.433176	−	0.948523i
$340$		0			0
$341$	23.6937	−	51.8819i	1.28308	−	2.80956i
$342$		0			0
$343$	−1.93732	+	1.24504i	−0.104605	+	0.0672257i
$344$		0			0
$345$	19.4387	+	7.82797i	1.04654	+	0.421444i
$346$		0			0
$347$	−0.505142	+	0.324635i	−0.0271174	+	0.0174273i	−0.554129	−	0.832431i	$-0.686949\pi$
$347$	−0.505142	+	0.324635i	−0.0271174	+	0.0174273i	0.527012	+	0.849858i	$0.323312\pi$
$348$		0			0
$349$	−4.17782	+	9.14815i	−0.223634	+	0.489689i	−0.987877	−	0.155239i	$-0.950385\pi$
$349$	−4.17782	+	9.14815i	−0.223634	+	0.489689i	0.764243	+	0.644928i	$0.223113\pi$
$350$		0			0
$351$	−9.33310	−	20.4366i	−0.498164	−	1.09083i
$352$		0			0
$353$	0.146239	+	1.01711i	0.00778352	+	0.0541355i	0.993343	−	0.115194i	$-0.0367489\pi$
$353$	0.146239	+	1.01711i	0.00778352	+	0.0541355i	−0.985560	+	0.169329i	$0.945840\pi$
$354$		0			0
$355$	2.05562	−	2.37231i	0.109101	−	0.125909i
$356$		0			0
$357$	−0.216687	−	0.139256i	−0.0114683	−	0.00737022i
$358$		0			0
$359$	−10.0574	−	2.95311i	−0.530808	−	0.155859i	0.00533634	−	0.999986i	$-0.498301\pi$
$359$	−10.0574	−	2.95311i	−0.530808	−	0.155859i	−0.536144	+	0.844127i	$0.680120\pi$
$360$		0			0
$361$	0.707246	+	0.816205i	0.0372235	+	0.0429582i
$362$		0			0
$363$	−79.1349	+	23.2361i	−4.15351	+	1.21958i
$364$		0			0
$365$	−2.41777	+	16.8159i	−0.126552	+	0.880186i
$366$		0			0
$367$	−3.84260			−0.200582			−0.100291	−	0.994958i	$-0.531977\pi$
$367$	−3.84260			−0.200582			−0.100291	+	0.994958i	$0.531977\pi$
$368$		0			0
$369$	−16.7688			−0.872949
$370$		0			0
$371$	0.0439961	−	0.305999i	0.00228416	−	0.0158867i
$372$		0			0
$373$	9.08332	−	2.66710i	0.470317	−	0.138097i	−0.0379818	−	0.999278i	$-0.512093\pi$
$373$	9.08332	−	2.66710i	0.470317	−	0.138097i	0.508298	+	0.861181i	$0.330275\pi$
$374$		0			0
$375$	21.5787	+	24.9032i	1.11432	+	1.28599i
$376$		0			0
$377$	−24.6962	−	7.25147i	−1.27192	−	0.373470i
$378$		0			0
$379$	21.2475	+	13.6549i	1.09141	+	0.701407i	0.957166	−	0.289541i	$-0.0935026\pi$
$379$	21.2475	+	13.6549i	1.09141	+	0.701407i	0.134245	+	0.990948i	$0.457139\pi$
$380$		0			0
$381$	11.2300	−	12.9602i	0.575333	−	0.663969i
$382$		0			0
$383$	−0.0120526	−	0.0838277i	−0.000615859	−	0.00428340i	0.989511	−	0.144456i	$-0.0461433\pi$
$383$	−0.0120526	−	0.0838277i	−0.000615859	−	0.00428340i	−0.990127	+	0.140173i	$0.955234\pi$
$384$		0			0
$385$	0.684043	+	1.49784i	0.0348620	+	0.0763372i
$386$		0			0
$387$	16.3001	−	35.6922i	0.828581	−	1.81434i
$388$		0			0
$389$	15.9416	−	10.2450i	0.808269	−	0.519443i	−0.0700353	−	0.997545i	$-0.522311\pi$
$389$	15.9416	−	10.2450i	0.808269	−	0.519443i	0.878305	+	0.478101i	$0.158675\pi$
$390$		0			0
$391$	2.67701	+	0.261117i	0.135382	+	0.0132052i
$392$		0			0
$393$	−13.0486	+	8.38580i	−0.658213	+	0.423008i
$394$		0			0
$395$	−5.67620	+	12.4291i	−0.285601	+	0.625378i
$396$		0			0
$397$	−12.8315	−	28.0971i	−0.643994	−	1.41015i	−0.896714	−	0.442611i	$-0.854052\pi$
$397$	−12.8315	−	28.0971i	−0.643994	−	1.41015i	0.252719	−	0.967540i	$-0.418675\pi$
$398$		0			0
$399$	−0.276683	−	1.92437i	−0.0138515	−	0.0963392i
$400$		0			0
$401$	7.67174	−	8.85366i	0.383108	−	0.442131i	−0.531140	−	0.847284i	$-0.678236\pi$
$401$	7.67174	−	8.85366i	0.383108	−	0.442131i	0.914249	+	0.405153i	$0.132782\pi$
$402$		0			0
$403$	−34.3971	−	22.1057i	−1.71344	−	1.10116i
$404$		0			0
$405$	0.886100	+	0.260182i	0.0440307	+	0.0129286i
$406$		0			0
$407$	24.7624	+	28.5774i	1.22743	+	1.41653i
$408$		0			0
$409$	9.39039	−	2.75727i	0.464325	−	0.136338i	−0.0411984	−	0.999151i	$-0.513118\pi$
$409$	9.39039	−	2.75727i	0.464325	−	0.136338i	0.505523	+	0.862813i	$0.331299\pi$
$410$		0			0
$411$	1.28160	−	8.91374i	0.0632168	−	0.439682i
$412$		0			0
$413$	1.01582			0.0499852
$414$		0			0
$415$	−1.27304			−0.0624912
$416$		0			0
$417$	1.85202	−	12.8811i	0.0906940	−	0.630791i
$418$		0			0
$419$	1.73635	−	0.509839i	0.0848264	−	0.0249073i	−0.239044	−	0.971009i	$-0.576834\pi$
$419$	1.73635	−	0.509839i	0.0848264	−	0.0249073i	0.323870	+	0.946101i	$0.395016\pi$
$420$		0			0
$421$	13.6969	+	15.8070i	0.667544	+	0.770387i	0.983990	−	0.178224i	$-0.0570351\pi$
$421$	13.6969	+	15.8070i	0.667544	+	0.770387i	−0.316446	+	0.948611i	$0.602490\pi$
$422$		0			0
$423$	25.2572	+	7.41618i	1.22805	+	0.360587i
$424$		0			0
$425$	1.19896	+	0.770525i	0.0581581	+	0.0373760i
$426$		0			0
$427$	−0.153303	+	0.176921i	−0.00741883	+	0.00856179i
$428$		0			0
$429$	11.5416	+	80.2737i	0.557234	+	3.87565i
$430$		0			0
$431$	1.44972	+	3.17445i	0.0698307	+	0.152908i	0.941329	−	0.337491i	$-0.109578\pi$
$431$	1.44972	+	3.17445i	0.0698307	+	0.152908i	−0.871498	+	0.490399i	$0.836851\pi$
$432$		0			0
$433$	10.0284	−	21.9591i	0.481934	−	1.05529i	−0.499993	−	0.866029i	$-0.666664\pi$
$433$	10.0284	−	21.9591i	0.481934	−	1.05529i	0.981927	−	0.189259i	$-0.0606086\pi$
$434$		0			0
$435$	−20.7138	+	13.3119i	−0.993150	+	0.638259i
$436$		0			0
$437$	11.7425	+	16.5612i	0.561720	+	0.792230i
$438$		0			0
$439$	24.7737	−	15.9211i	1.18238	−	0.759872i	0.206561	−	0.978434i	$-0.433773\pi$
$439$	24.7737	−	15.9211i	1.18238	−	0.759872i	0.975823	+	0.218562i	$0.0701365\pi$
$440$		0			0
$441$	−13.8028	+	30.2238i	−0.657275	+	1.43923i
$442$		0			0
$443$	−4.50711	−	9.86920i	−0.214139	−	0.468900i	0.771829	−	0.635830i	$-0.219342\pi$
$443$	−4.50711	−	9.86920i	−0.214139	−	0.468900i	−0.985969	+	0.166930i	$0.946615\pi$
$444$		0			0
$445$	1.44785	+	10.0700i	0.0686345	+	0.477364i
$446$		0			0
$447$	−5.24962	+	6.05839i	−0.248299	+	0.286552i
$448$		0			0
$449$	33.0571	+	21.2445i	1.56006	+	1.00259i	0.982504	+	0.186239i	$0.0596299\pi$
$449$	33.0571	+	21.2445i	1.56006	+	1.00259i	0.577556	+	0.816351i	$0.304006\pi$
$450$		0			0
$451$	21.5139	+	6.31704i	1.01305	+	0.297458i
$452$		0			0
$453$	−23.0612	−	26.6140i	−1.08351	−	1.25044i
$454$		0			0
$455$	1.13263	−	0.332570i	0.0530985	−	0.0155911i
$456$		0			0
$457$	3.87296	−	26.9370i	0.181169	−	1.26006i	−0.672834	−	0.739794i	$-0.734923\pi$
$457$	3.87296	−	26.9370i	0.181169	−	1.26006i	0.854003	−	0.520268i	$-0.174168\pi$
$458$		0			0
$459$	−2.75862			−0.128761
$460$		0			0
$461$	−42.2854			−1.96943			−0.984713	−	0.174187i	$-0.944270\pi$
$461$	−42.2854			−1.96943			−0.984713	+	0.174187i	$0.944270\pi$
$462$		0			0
$463$	1.36587	−	9.49984i	0.0634774	−	0.441495i	−0.933154	−	0.359478i	$-0.882955\pi$
$463$	1.36587	−	9.49984i	0.0634774	−	0.441495i	0.996631	−	0.0820170i	$-0.0261362\pi$
$464$		0			0
$465$	−37.5302	+	11.0199i	−1.74042	+	0.511034i
$466$		0			0
$467$	12.0521	+	13.9089i	0.557706	+	0.643628i	0.962661	−	0.270709i	$-0.0872582\pi$
$467$	12.0521	+	13.9089i	0.557706	+	0.643628i	−0.404955	+	0.914337i	$0.632713\pi$
$468$		0			0
$469$	1.19654	+	0.351335i	0.0552509	+	0.0162231i
$470$		0			0
$471$	−37.4346	−	24.0578i	−1.72490	−	1.10852i
$472$		0			0
$473$	−34.3583	+	39.6515i	−1.57979	+	1.82318i
$474$		0			0
$475$	1.53093	+	10.6478i	0.0702439	+	0.488557i
$476$		0			0
$477$	−3.71305	−	8.13045i	−0.170009	−	0.372268i
$478$		0			0
$479$	−13.2808	+	29.0808i	−0.606814	+	1.32874i	0.317918	+	0.948118i	$0.397016\pi$
$479$	−13.2808	+	29.0808i	−0.606814	+	1.32874i	−0.924732	+	0.380619i	$0.875711\pi$
$480$		0			0
$481$	22.8043	−	14.6554i	1.03979	−	0.668230i
$482$		0			0
$483$	0.100329	+	2.20027i	0.00456512	+	0.100116i
$484$		0			0
$485$	9.97854	−	6.41282i	0.453102	−	0.291191i
$486$		0			0
$487$	−5.04515	+	11.0473i	−0.228618	+	0.500603i	−0.988826	−	0.149077i	$-0.952370\pi$
$487$	−5.04515	+	11.0473i	−0.228618	+	0.500603i	0.760208	+	0.649680i	$0.225097\pi$
$488$		0			0
$489$	0.374872	+	0.820855i	0.0169523	+	0.0371204i
$490$		0			0
$491$	−2.85041	−	19.8250i	−0.128637	−	0.894691i	−0.947284	−	0.320394i	$-0.896185\pi$
$491$	−2.85041	−	19.8250i	−0.128637	−	0.894691i	0.818647	−	0.574297i	$-0.194724\pi$
$492$		0			0
$493$	−2.06960	+	2.38845i	−0.0932101	+	0.107570i
$494$		0			0
$495$	40.0510	+	25.7392i	1.80016	+	1.15689i
$496$		0			0
$497$	0.316564	+	0.0929516i	0.0141998	+	0.00416945i
$498$		0			0
$499$	−1.73885	−	2.00674i	−0.0778418	−	0.0898342i	0.715493	−	0.698620i	$-0.246202\pi$
$499$	−1.73885	−	2.00674i	−0.0778418	−	0.0898342i	−0.793334	+	0.608786i	$0.791657\pi$
$500$		0			0
$501$	−2.21050	+	0.649062i	−0.0987579	+	0.0289979i
$502$		0			0
$503$	−1.78212	+	12.3949i	−0.0794607	+	0.552661i	0.910737	+	0.412987i	$0.135515\pi$
$503$	−1.78212	+	12.3949i	−0.0794607	+	0.552661i	−0.990198	+	0.139674i	$0.955395\pi$
$504$		0			0
$505$	−4.73546			−0.210725
$506$		0			0
$507$	21.9124			0.973164
$508$		0			0
$509$	−4.74014	+	32.9684i	−0.210103	+	1.46130i	0.562705	+	0.826657i	$0.309761\pi$
$509$	−4.74014	+	32.9684i	−0.210103	+	1.46130i	−0.772808	+	0.634640i	$0.781149\pi$
$510$		0			0
$511$	−1.71329	+	0.503069i	−0.0757917	+	0.0222545i
$512$		0			0
$513$	−13.6354	−	15.7361i	−0.602018	−	0.694766i
$514$		0			0
$515$	−4.35471	−	1.27866i	−0.191892	−	0.0563444i
$516$		0			0
$517$	−29.6104	−	19.0294i	−1.30226	−	0.836914i
$518$		0			0
$519$	33.6422	−	38.8252i	1.47673	−	1.70423i
$520$		0			0
$521$	−4.47284	−	31.1093i	−0.195959	−	1.36292i	−0.815863	−	0.578245i	$-0.803738\pi$
$521$	−4.47284	−	31.1093i	−0.195959	−	1.36292i	0.619905	−	0.784677i	$-0.287171\pi$
$522$		0			0
$523$	−13.2114	−	28.9290i	−0.577695	−	1.26498i	−0.942598	−	0.333930i	$-0.891625\pi$
$523$	−13.2114	−	28.9290i	−0.577695	−	1.26498i	0.364903	−	0.931046i	$-0.381102\pi$
$524$		0			0
$525$	−0.484821	+	1.06161i	−0.0211593	+	0.0463325i
$526$		0			0
$527$	−4.22348	+	2.71427i	−0.183978	+	0.118235i
$528$		0			0
$529$	−11.4189	−	19.9652i	−0.496474	−	0.868051i
$530$		0			0
$531$	24.7075	−	15.8785i	1.07221	−	0.689069i
$532$		0			0
$533$	6.67734	−	14.6213i	0.289228	−	0.633320i
$534$		0			0
$535$	10.5716	+	23.1486i	0.457050	+	1.00080i
$536$		0			0
$537$	6.51794	+	45.3333i	0.281270	+	1.95627i
$538$		0			0
$539$	29.0942	−	33.5765i	1.25318	−	1.44624i
$540$		0			0
$541$	−7.05888	−	4.53647i	−0.303485	−	0.195038i	0.380031	−	0.924974i	$-0.375913\pi$
$541$	−7.05888	−	4.53647i	−0.303485	−	0.195038i	−0.683515	+	0.729936i	$0.739550\pi$
$542$		0			0
$543$	15.6888	+	4.60664i	0.673270	+	0.197690i
$544$		0			0
$545$	−11.5369	−	13.3143i	−0.494188	−	0.570323i
$546$		0			0
$547$	−4.61213	+	1.35424i	−0.197200	+	0.0579033i	−0.378841	−	0.925462i	$-0.623677\pi$
$547$	−4.61213	+	1.35424i	−0.197200	+	0.0579033i	0.181641	+	0.983365i	$0.441859\pi$
$548$		0			0
$549$	−0.963243	+	6.69950i	−0.0411102	+	0.285928i
$550$		0			0
$551$	−23.8542			−1.01622
$552$		0			0
$553$	−1.43616			−0.0610716
$554$		0			0
$555$	3.69049	−	25.6679i	0.156652	−	1.08954i
$556$		0			0
$557$	44.2513	−	12.9933i	1.87499	−	0.550545i	0.877508	−	0.479562i	$-0.159204\pi$
$557$	44.2513	−	12.9933i	1.87499	−	0.550545i	0.997477	−	0.0709838i	$-0.0226139\pi$
$558$		0			0
$559$	24.6307	+	28.4253i	1.04177	+	1.20226i
$560$		0			0
$561$	9.55447	+	2.80545i	0.403390	+	0.118446i
$562$		0			0
$563$	−22.0416	−	14.1653i	−0.928942	−	0.596994i	−0.0137026	−	0.999906i	$-0.504362\pi$
$563$	−22.0416	−	14.1653i	−0.928942	−	0.596994i	−0.915239	+	0.402912i	$0.867998\pi$
$564$		0			0
$565$	7.07489	−	8.16486i	0.297643	−	0.343498i
$566$		0			0
$567$	0.0138139	+	0.0960780i	0.000580130	+	0.00403490i
$568$		0			0
$569$	6.62385	+	14.5042i	0.277686	+	0.608048i	0.996164	−	0.0875013i	$-0.0278882\pi$
$569$	6.62385	+	14.5042i	0.277686	+	0.608048i	−0.718478	+	0.695550i	$0.755161\pi$
$570$		0			0
$571$	−19.2232	+	42.0928i	−0.804464	+	1.76153i	−0.174894	+	0.984587i	$0.555958\pi$
$571$	−19.2232	+	42.0928i	−0.804464	+	1.76153i	−0.629570	+	0.776944i	$0.716769\pi$
$572$		0			0
$573$	45.4766	−	29.2260i	1.89981	−	1.22094i
$574$		0			0
$575$	−0.555135	−	12.1744i	−0.0231507	−	0.507709i
$576$		0			0
$577$	4.78677	−	3.07627i	0.199276	−	0.128067i	−0.437197	−	0.899366i	$-0.644029\pi$
$577$	4.78677	−	3.07627i	0.199276	−	0.128067i	0.636473	+	0.771299i	$0.280393\pi$
$578$		0			0
$579$	−12.9106	+	28.2703i	−0.536547	+	1.17487i
$580$		0			0
$581$	−0.0555842	−	0.121712i	−0.00230602	−	0.00504948i
$582$		0			0
$583$	1.70088	+	11.8299i	0.0704432	+	0.489943i
$584$		0			0
$585$	22.3501	−	25.7934i	0.924064	−	1.06643i
$586$		0			0
$587$	−24.0081	−	15.4291i	−0.990922	−	0.636827i	−0.0585340	−	0.998285i	$-0.518643\pi$
$587$	−24.0081	−	15.4291i	−0.990922	−	0.636827i	−0.932388	+	0.361458i	$0.882279\pi$
$588$		0			0
$589$	−36.3591	−	10.6760i	−1.49815	−	0.439896i
$590$		0			0
$591$	−25.7906	−	29.7639i	−1.06088	−	1.22432i
$592$		0			0
$593$	1.18808	−	0.348853i	0.0487888	−	0.0143257i	−0.257247	−	0.966346i	$-0.582815\pi$
$593$	1.18808	−	0.348853i	0.0487888	−	0.0143257i	0.306036	+	0.952020i	$0.400997\pi$
$594$		0			0
$595$	0.0206274	−	0.143467i	0.000845641	−	0.00588156i
$596$		0			0
$597$	−44.8603			−1.83601
$598$		0			0
$599$	−9.25426			−0.378119			−0.189059	−	0.981966i	$-0.560544\pi$
$599$	−9.25426			−0.378119			−0.189059	+	0.981966i	$0.560544\pi$
$600$		0			0
$601$	1.63080	−	11.3425i	0.0665217	−	0.462668i	−0.929148	−	0.369708i	$-0.879458\pi$
$601$	1.63080	−	11.3425i	0.0665217	−	0.462668i	0.995670	−	0.0929607i	$-0.0296331\pi$
$602$		0			0
$603$	34.5948	−	10.1580i	1.40881	−	0.413664i
$604$		0			0
$605$	−30.3923	−	35.0746i	−1.23562	−	1.42599i
$606$		0			0
$607$	11.4554	+	3.36361i	0.464960	+	0.136525i	0.505818	−	0.862640i	$-0.331191\pi$
$607$	11.4554	+	3.36361i	0.464960	+	0.136525i	−0.0408576	+	0.999165i	$0.513009\pi$
$608$		0			0
$609$	−2.17714	−	1.39916i	−0.0882220	−	0.0566969i
$610$		0			0
$611$	−16.5238	+	19.0695i	−0.668483	+	0.771471i
$612$		0			0
$613$	−3.35979	−	23.3679i	−0.135701	−	0.943820i	−0.937935	−	0.346810i	$-0.887265\pi$
$613$	−3.35979	−	23.3679i	−0.135701	−	0.943820i	0.802234	−	0.597009i	$-0.203644\pi$
$614$		0			0
$615$	−6.38774	−	13.9872i	−0.257579	−	0.564018i
$616$		0			0
$617$	−0.673991	+	1.47583i	−0.0271338	+	0.0594148i	−0.922714	−	0.385486i	$-0.874034\pi$
$617$	−0.673991	+	1.47583i	−0.0271338	+	0.0594148i	0.895580	+	0.444901i	$0.146761\pi$
$618$		0			0
$619$	−29.2199	+	18.7785i	−1.17445	+	0.754771i	−0.974357	−	0.225007i	$-0.927760\pi$
$619$	−29.2199	+	18.7785i	−1.17445	+	0.754771i	−0.200089	+	0.979778i	$0.564123\pi$
$620$		0			0
$621$	13.6440	+	19.2430i	0.547515	+	0.772195i
$622$		0			0
$623$	−0.899551	+	0.578106i	−0.0360397	+	0.0231613i
$624$		0			0
$625$	−2.42456	+	5.30904i	−0.0969824	+	0.212362i
$626$		0			0
$627$	31.2230	+	68.3688i	1.24693	+	2.73039i
$628$		0			0
$629$	−0.473684	−	3.29454i	−0.0188870	−	0.131362i
$630$		0			0
$631$	−10.5723	+	12.2011i	−0.420878	+	0.485719i	−0.926104	−	0.377268i	$-0.876864\pi$
$631$	−10.5723	+	12.2011i	−0.420878	+	0.485719i	0.505226	+	0.862987i	$0.331409\pi$
$632$		0			0
$633$	−17.9344	−	11.5258i	−0.712829	−	0.458108i
$634$		0			0
$635$	9.25898	+	2.71868i	0.367431	+	0.107888i
$636$		0			0
$637$	−20.8570	−	24.0703i	−0.826385	−	0.953699i
$638$		0			0
$639$	9.15265	−	2.68746i	0.362073	−	0.106314i
$640$		0			0
$641$	−2.17781	+	15.1470i	−0.0860182	+	0.598270i	0.900529	+	0.434795i	$0.143179\pi$
$641$	−2.17781	+	15.1470i	−0.0860182	+	0.598270i	−0.986548	+	0.163475i	$0.947730\pi$
$642$		0			0
$643$	34.0990			1.34473			0.672367	−	0.740218i	$-0.265278\pi$
$643$	34.0990			1.34473			0.672367	+	0.740218i	$0.265278\pi$
$644$		0			0
$645$	35.9808			1.41674
$646$		0			0
$647$	−3.68804	+	25.6509i	−0.144992	+	1.00844i	0.779272	+	0.626685i	$0.215589\pi$
$647$	−3.68804	+	25.6509i	−0.144992	+	1.00844i	−0.924264	+	0.381754i	$0.875320\pi$
$648$		0			0
$649$	−37.6806	+	11.0640i	−1.47909	+	0.434300i
$650$		0			0
$651$	−2.69224	−	3.10701i	−0.105517	−	0.121773i
$652$		0			0
$653$	40.3319	+	11.8425i	1.57831	+	0.463433i	0.949406	−	0.314050i	$-0.101686\pi$
$653$	40.3319	+	11.8425i	1.57831	+	0.463433i	0.628903	+	0.777484i	$0.283504\pi$
$654$		0			0
$655$	−7.34262	−	4.71882i	−0.286900	−	0.184379i
$656$		0			0
$657$	−33.8084	+	39.0170i	−1.31899	+	1.52220i
$658$		0			0
$659$	3.45698	+	24.0438i	0.134665	+	0.936614i	0.939362	+	0.342928i	$0.111419\pi$
$659$	3.45698	+	24.0438i	0.134665	+	0.936614i	−0.804697	+	0.593686i	$0.797672\pi$
$660$		0			0
$661$	11.3921	+	24.9453i	0.443103	+	0.970260i	0.991018	+	0.133726i	$0.0426942\pi$
$661$	11.3921	+	24.9453i	0.443103	+	0.970260i	−0.547916	+	0.836534i	$0.684579\pi$
$662$		0			0
$663$	2.96546	−	6.49345i	0.115169	−	0.252185i
$664$		0			0
$665$	0.920340	−	0.591467i	0.0356893	−	0.0229361i
$666$		0			0
$667$	26.8970	+	2.62354i	1.04145	+	0.101584i
$668$		0			0
$669$	−5.25803	+	3.37913i	−0.203287	+	0.130645i
$670$		0			0
$671$	3.75960	−	8.23238i	0.145138	−	0.317808i
$672$		0			0
$673$	13.5315	+	29.6298i	0.521600	+	1.14214i	0.968830	+	0.247725i	$0.0796830\pi$
$673$	13.5315	+	29.6298i	0.521600	+	1.14214i	−0.447231	+	0.894419i	$0.647590\pi$
$674$		0			0
$675$	1.77884	+	12.3721i	0.0684675	+	0.476202i
$676$		0			0
$677$	14.8524	−	17.1406i	0.570825	−	0.658767i	−0.394782	−	0.918775i	$-0.629180\pi$
$677$	14.8524	−	17.1406i	0.570825	−	0.658767i	0.965606	+	0.260008i	$0.0837252\pi$
$678$		0			0
$679$	1.04880	+	0.674023i	0.0402493	+	0.0258666i
$680$		0			0
$681$	−48.8277	−	14.3371i	−1.87108	−	0.549399i
$682$		0			0
$683$	−22.7938	−	26.3054i	−0.872180	−	1.00655i	−0.999891	−	0.0147379i	$-0.995309\pi$
$683$	−22.7938	−	26.3054i	−0.872180	−	1.00655i	0.127711	−	0.991811i	$-0.459237\pi$
$684$		0			0
$685$	4.86221	−	1.42767i	0.185775	−	0.0545486i
$686$		0			0
$687$	6.87465	−	47.8143i	0.262284	−	1.82423i
$688$		0			0
$689$	8.56777			0.326406
$690$		0			0
$691$	30.0080			1.14156			0.570778	−	0.821104i	$-0.306642\pi$
$691$	30.0080			1.14156			0.570778	+	0.821104i	$0.306642\pi$
$692$		0			0
$693$	−0.712135	+	4.95301i	−0.0270518	+	0.188149i
$694$		0			0
$695$	7.02631	−	2.06311i	0.266523	−	0.0782582i
$696$		0			0
$697$	−1.29247	−	1.49158i	−0.0489556	−	0.0564978i
$698$		0			0
$699$	41.3864	+	12.1522i	1.56538	+	0.459637i
$700$		0			0
$701$	32.0061	+	20.5691i	1.20885	+	0.776883i	0.980466	−	0.196687i	$-0.0630184\pi$
$701$	32.0061	+	20.5691i	1.20885	+	0.776883i	0.228387	+	0.973570i	$0.426655\pi$
$702$		0			0
$703$	16.4518	−	18.9864i	0.620492	−	0.716086i
$704$		0			0
$705$	3.43523	+	23.8926i	0.129378	+	0.899846i
$706$		0			0
$707$	−0.206762	−	0.452746i	−0.00777609	−	0.0170273i
$708$		0			0
$709$	−7.44057	+	16.2926i	−0.279436	+	0.611880i	−0.996358	−	0.0852740i	$-0.972823\pi$
$709$	−7.44057	+	16.2926i	−0.279436	+	0.611880i	0.716921	+	0.697154i	$0.245551\pi$
$710$		0			0
$711$	−34.9312	+	22.4489i	−1.31002	+	0.841901i
$712$		0			0
$713$	39.8228	+	16.0366i	1.49137	+	0.600577i
$714$		0			0
$715$	−38.3912	+	24.6726i	−1.43575	+	0.922701i
$716$		0			0
$717$	24.2705	−	53.1449i	0.906397	−	1.98473i
$718$		0			0
$719$	−15.2167	−	33.3200i	−0.567488	−	1.24263i	−0.948124	−	0.317901i	$-0.897022\pi$
$719$	−15.2167	−	33.3200i	−0.567488	−	1.24263i	0.380636	−	0.924725i	$-0.375705\pi$
$720$		0			0
$721$	−0.0678881	−	0.472172i	−0.00252829	−	0.0175846i
$722$		0			0
$723$	−27.3449	+	31.5578i	−1.01697	+	1.17365i
$724$		0			0
$725$	12.0464	+	7.74177i	0.447393	+	0.287522i
$726$		0			0
$727$	−25.0434	−	7.35340i	−0.928807	−	0.272722i	−0.217870	−	0.975978i	$-0.569911\pi$
$727$	−25.0434	−	7.35340i	−0.928807	−	0.272722i	−0.710937	+	0.703256i	$0.751729\pi$
$728$		0			0
$729$	28.7652	+	33.1968i	1.06538	+	1.22951i
$730$		0			0
$731$	4.43116	−	1.30111i	0.163892	−	0.0481232i
$732$		0			0
$733$	−6.26549	+	43.5775i	−0.231421	+	1.60957i	0.460542	+	0.887638i	$0.347655\pi$
$733$	−6.26549	+	43.5775i	−0.231421	+	1.60957i	−0.691963	+	0.721933i	$0.743254\pi$
$734$		0			0
$735$	−30.4682			−1.12384
$736$		0			0
$737$	−48.2107			−1.77586
$738$		0			0
$739$	1.84705	−	12.8465i	0.0679447	−	0.472566i	−0.927234	−	0.374483i	$-0.877820\pi$
$739$	1.84705	−	12.8465i	0.0679447	−	0.472566i	0.995178	−	0.0980823i	$-0.0312708\pi$
$740$		0			0
$741$	51.6986	−	15.1801i	1.89920	−	0.557654i
$742$		0			0
$743$	−31.2490	−	36.0633i	−1.14642	−	1.32303i	−0.938656	−	0.344854i	$-0.887929\pi$
$743$	−31.2490	−	36.0633i	−1.14642	−	1.32303i	−0.207759	−	0.978180i	$-0.566617\pi$
$744$		0			0
$745$	−4.32822	−	1.27088i	−0.158574	−	0.0465615i
$746$		0			0
$747$	−3.25448	−	2.09153i	−0.119075	−	0.0765249i
$748$		0			0
$749$	−1.75159	+	2.02145i	−0.0640018	+	0.0738621i
$750$		0			0
$751$	5.58886	+	38.8714i	0.203941	+	1.41844i	0.792445	+	0.609944i	$0.208808\pi$
$751$	5.58886	+	38.8714i	0.203941	+	1.41844i	−0.588504	+	0.808494i	$0.700283\pi$
$752$		0			0
$753$	4.60831	+	10.0908i	0.167936	+	0.367729i
$754$		0			0
$755$	8.23197	−	18.0255i	0.299592	−	0.656015i
$756$		0			0
$757$	−41.2157	+	26.4877i	−1.49801	+	0.962712i	−0.502857	+	0.864369i	$0.667718\pi$
$757$	−41.2157	+	26.4877i	−1.49801	+	0.962712i	−0.995153	+	0.0983430i	$0.968646\pi$
$758$		0			0
$759$	−27.6863	−	80.5237i	−1.00495	−	2.92282i
$760$		0			0
$761$	1.76994	−	1.13747i	0.0641601	−	0.0412332i	−0.508168	−	0.861258i	$-0.669677\pi$
$761$	1.76994	−	1.13747i	0.0641601	−	0.0412332i	0.572328	+	0.820025i	$0.306041\pi$
$762$		0			0
$763$	0.769218	−	1.68435i	0.0278476	−	0.0609777i
$764$		0			0
$765$	−1.74085	−	3.81193i	−0.0629406	−	0.137821i
$766$		0			0
$767$	4.00655	+	27.8662i	0.144668	+	1.00619i
$768$		0			0
$769$	21.4692	−	24.7768i	0.774201	−	0.893475i	−0.222476	−	0.974938i	$-0.571414\pi$
$769$	21.4692	−	24.7768i	0.774201	−	0.893475i	0.996676	+	0.0814630i	$0.0259592\pi$
$770$		0			0
$771$	−53.2715	−	34.2355i	−1.91853	−	1.23296i
$772$		0			0
$773$	−19.9624	−	5.86149i	−0.717998	−	0.210823i	−0.0977298	−	0.995213i	$-0.531158\pi$
$773$	−19.9624	−	5.86149i	−0.717998	−	0.210823i	−0.620268	+	0.784390i	$0.712976\pi$
$774$		0			0
$775$	14.8966	+	17.1916i	0.535101	+	0.617540i
$776$		0			0
$777$	2.61518	−	0.767886i	0.0938190	−	0.0275477i
$778$		0			0
$779$	2.12005	−	14.7453i	0.0759588	−	0.528305i
$780$		0			0
$781$	−12.7550			−0.456409
$782$		0			0
$783$	−27.7170			−0.990523
$784$		0			0
$785$	3.56357	−	24.7852i	0.127189	−	0.884621i
$786$		0			0
$787$	9.56383	−	2.80819i	0.340914	−	0.100101i	−0.106794	−	0.994281i	$-0.534059\pi$
$787$	9.56383	−	2.80819i	0.340914	−	0.100101i	0.447708	+	0.894180i	$0.352240\pi$
$788$		0			0
$789$	33.0273	+	38.1155i	1.17580	+	1.35695i
$790$		0			0
$791$	1.08953	+	0.319914i	0.0387392	+	0.0113748i
$792$		0			0
$793$	−5.45798	−	3.50763i	−0.193818	−	0.124560i
$794$		0			0
$795$	5.36736	−	6.19426i	0.190361	−	0.219688i
$796$		0			0
$797$	−1.93675	−	13.4704i	−0.0686032	−	0.477146i	−0.994942	−	0.100454i	$-0.967971\pi$
$797$	−1.93675	−	13.4704i	−0.0686032	−	0.477146i	0.926339	−	0.376692i	$-0.122938\pi$
$798$		0			0
$799$	1.28704	+	2.81823i	0.0455323	+	0.0997018i
$800$		0			0
$801$	−12.8430	+	28.1222i	−0.453785	+	0.993650i
$802$		0			0
$803$	58.0733	−	37.3214i	2.04936	−	1.31705i
$804$		0			0
$805$	−1.10279	+	0.565691i	−0.0388681	+	0.0199380i
$806$		0			0
$807$	12.9741	−	8.33796i	0.456710	−	0.293510i
$808$		0			0
$809$	−9.00153	+	19.7106i	−0.316477	+	0.692988i	−0.999293	−	0.0376027i	$-0.988028\pi$
$809$	−9.00153	+	19.7106i	−0.316477	+	0.692988i	0.682816	+	0.730591i	$0.260755\pi$
$810$		0			0
$811$	4.34697	+	9.51854i	0.152643	+	0.334241i	0.970470	−	0.241223i	$-0.0775486\pi$
$811$	4.34697	+	9.51854i	0.152643	+	0.334241i	−0.817827	+	0.575464i	$0.804821\pi$
$812$		0			0
$813$	−9.99658	−	69.5278i	−0.350596	−	2.43845i
$814$		0			0
$815$	−0.332536	+	0.383767i	−0.0116482	+	0.0134428i
$816$		0			0
$817$	29.3244	+	18.8457i	1.02593	+	0.659326i
$818$		0			0
$819$	3.44191	+	1.01063i	0.120270	+	0.0353144i
$820$		0			0
$821$	5.73260	+	6.61577i	0.200069	+	0.230892i	0.846914	−	0.531729i	$-0.178458\pi$
$821$	5.73260	+	6.61577i	0.200069	+	0.230892i	−0.646845	+	0.762621i	$0.723912\pi$
$822$		0			0
$823$	20.9526	−	6.15223i	0.730361	−	0.214453i	0.104651	−	0.994509i	$-0.466627\pi$
$823$	20.9526	−	6.15223i	0.730361	−	0.214453i	0.625710	+	0.780056i	$0.284809\pi$
$824$		0			0
$825$	6.42109	−	44.6597i	0.223554	−	1.55485i
$826$		0			0
$827$	15.2620			0.530713			0.265357	−	0.964150i	$-0.414510\pi$
$827$	15.2620			0.530713			0.265357	+	0.964150i	$0.414510\pi$
$828$		0			0
$829$	26.8540			0.932679			0.466340	−	0.884606i	$-0.345572\pi$
$829$	26.8540			0.932679			0.466340	+	0.884606i	$0.345572\pi$
$830$		0			0
$831$	−0.587042	+	4.08297i	−0.0203643	+	0.141637i
$832$		0			0
$833$	−3.75226	+	1.10176i	−0.130008	+	0.0381739i
$834$		0			0
$835$	−0.848959	−	0.979751i	−0.0293794	−	0.0339057i
$836$		0			0
$837$	−42.2468	−	12.4048i	−1.46026	−	0.428772i
$838$		0			0
$839$	1.55632	+	1.00019i	0.0537302	+	0.0345303i	0.567230	−	0.823559i	$-0.308015\pi$
$839$	1.55632	+	1.00019i	0.0537302	+	0.0345303i	−0.513500	+	0.858090i	$0.671651\pi$
$840$		0			0
$841$	−1.80312	+	2.08091i	−0.0621765	+	0.0717556i
$842$		0			0
$843$	−9.36777	−	65.1542i	−0.322643	−	2.24403i
$844$		0			0
$845$	5.12225	+	11.2162i	0.176211	+	0.385848i
$846$		0			0
$847$	2.02639	−	4.43718i	0.0696277	−	0.152463i
$848$		0			0
$849$	−12.1525	+	7.80994i	−0.417073	+	0.268036i
$850$		0			0
$851$	−20.6385	+	19.5989i	−0.707480	+	0.671840i
$852$		0			0
$853$	17.3443	−	11.1465i	0.593859	−	0.381650i	−0.208915	−	0.977934i	$-0.566993\pi$
$853$	17.3443	−	11.1465i	0.593859	−	0.381650i	0.802774	+	0.596284i	$0.203357\pi$
$854$		0			0
$855$	13.1398	−	28.7722i	0.449372	−	0.983987i
$856$		0			0
$857$	−11.3266	−	24.8017i	−0.386908	−	0.847210i	−0.998432	−	0.0559842i	$-0.982170\pi$
$857$	−11.3266	−	24.8017i	−0.386908	−	0.847210i	0.611524	−	0.791226i	$-0.290557\pi$
$858$		0			0
$859$	−2.97450	−	20.6881i	−0.101489	−	0.705869i	−0.975506	−	0.219974i	$-0.929403\pi$
$859$	−2.97450	−	20.6881i	−0.101489	−	0.705869i	0.874017	−	0.485895i	$-0.161506\pi$
$860$		0			0
$861$	1.05838	−	1.22143i	0.0360694	−	0.0416263i
$862$		0			0
$863$	34.8356	+	22.3875i	1.18582	+	0.762079i	0.976447	−	0.215757i	$-0.0692219\pi$
$863$	34.8356	+	22.3875i	1.18582	+	0.762079i	0.209371	+	0.977836i	$0.432858\pi$
$864$		0			0
$865$	27.7374	+	8.14444i	0.943100	+	0.276919i
$866$		0			0
$867$	30.4482	+	35.1391i	1.03407	+	1.19339i
$868$		0			0
$869$	53.2725	−	15.6422i	1.80714	−	0.530626i
$870$		0			0
$871$	−4.91857	+	34.2094i	−0.166659	+	1.15914i
$872$		0			0
$873$	36.0455			1.21996
$874$		0			0
$875$	−1.94891			−0.0658852
$876$		0			0
$877$	2.98600	−	20.7681i	0.100830	−	0.701288i	−0.875217	−	0.483730i	$-0.839282\pi$
$877$	2.98600	−	20.7681i	0.100830	−	0.701288i	0.976047	−	0.217558i	$-0.0698092\pi$
$878$		0			0
$879$	−76.8226	+	22.5571i	−2.59116	+	0.760834i
$880$		0			0
$881$	−17.3441	−	20.0162i	−0.584338	−	0.674362i	0.384194	−	0.923253i	$-0.374479\pi$
$881$	−17.3441	−	20.0162i	−0.584338	−	0.674362i	−0.968532	+	0.248891i	$0.919934\pi$
$882$		0			0
$883$	−24.4710	−	7.18535i	−0.823516	−	0.241806i	−0.157287	−	0.987553i	$-0.550275\pi$
$883$	−24.4710	−	7.18535i	−0.823516	−	0.241806i	−0.666229	+	0.745747i	$0.732093\pi$
$884$		0			0
$885$	22.6564	+	14.5604i	0.761587	+	0.489442i
$886$		0			0
$887$	−15.3216	+	17.6821i	−0.514449	+	0.593705i	−0.952232	−	0.305375i	$-0.901218\pi$
$887$	−15.3216	+	17.6821i	−0.514449	+	0.593705i	0.437783	+	0.899080i	$0.355764\pi$
$888$		0			0
$889$	0.144344	+	1.00393i	0.00484113	+	0.0336708i
$890$		0			0
$891$	−1.55887	−	3.41344i	−0.0522240	−	0.114355i
$892$		0			0
$893$	−9.71449	+	21.2718i	−0.325083	+	0.711832i
$894$		0			0
$895$	−21.6808	+	13.9334i	−0.724710	+	0.465743i
$896$		0			0
$897$	−59.9627	+	11.4305i	−2.00210	+	0.381652i
$898$		0			0
$899$	−42.4350	+	27.2713i	−1.41529	+	0.909549i
$900$		0			0
$901$	0.437017	−	0.956934i	0.0145592	−	0.0318801i
$902$		0			0
$903$	1.57101	+	3.44003i	0.0522800	+	0.114477i
$904$		0			0
$905$	1.30944	+	9.10737i	0.0435273	+	0.302739i
$906$		0			0
$907$	−31.3222	+	36.1477i	−1.04004	+	1.20026i	−0.0606721	+	0.998158i	$0.519324\pi$
$907$	−31.3222	+	36.1477i	−1.04004	+	1.20026i	−0.979363	+	0.202107i	$0.935221\pi$
$908$		0			0
$909$	−12.1060	−	7.78005i	−0.401531	−	0.258048i
$910$		0			0
$911$	37.7765	+	11.0922i	1.25159	+	0.367500i	0.839358	−	0.543579i	$-0.182931\pi$
$911$	37.7765	+	11.0922i	1.25159	+	0.367500i	0.412232	+	0.911079i	$0.364749\pi$
$912$		0			0
$913$	3.38749	+	3.90937i	0.112109	+	0.129381i
$914$		0			0
$915$	−5.95512	+	1.74858i	−0.196870	+	0.0578063i
$916$		0			0
$917$	0.130557	−	0.908045i	0.00431138	−	0.0299863i
$918$		0			0
$919$	24.8047			0.818232			0.409116	−	0.912482i	$-0.365837\pi$
$919$	24.8047			0.818232			0.409116	+	0.912482i	$0.365837\pi$
$920$		0			0
$921$	24.1334			0.795222
$922$		0			0
$923$	−1.30129	+	9.05068i	−0.0428325	+	0.297907i
$924$		0			0
$925$	−14.4702	+	4.24883i	−0.475776	+	0.139701i
$926$		0			0
$927$	−9.03187	−	10.4233i	−0.296646	−	0.342347i
$928$		0			0
$929$	−17.1722	−	5.04220i	−0.563400	−	0.165429i	−0.0123834	−	0.999923i	$-0.503942\pi$
$929$	−17.1722	−	5.04220i	−0.563400	−	0.165429i	−0.551017	+	0.834494i	$0.685760\pi$
$930$		0			0
$931$	−24.8316	−	15.9583i	−0.813824	−	0.523013i
$932$		0			0
$933$	−8.31485	+	9.59585i	−0.272216	+	0.314154i
$934$		0			0
$935$	0.797451	+	5.54639i	0.0260794	+	0.181386i
$936$		0			0
$937$	−3.42908	−	7.50863i	−0.112023	−	0.245296i	0.845314	−	0.534270i	$-0.179413\pi$
$937$	−3.42908	−	7.50863i	−0.112023	−	0.245296i	−0.957337	+	0.288973i	$0.906686\pi$
$938$		0			0
$939$	−18.3340	+	40.1458i	−0.598307	+	1.31011i
$940$		0			0
$941$	30.4961	−	19.5986i	0.994144	−	0.638897i	0.0609008	−	0.998144i	$-0.480603\pi$
$941$	30.4961	−	19.5986i	0.994144	−	0.638897i	0.933243	+	0.359247i	$0.116966\pi$
$942$		0			0
$943$	−4.01221	+	16.3930i	−0.130655	+	0.533830i
$944$		0			0
$945$	1.06937	−	0.687244i	0.0347867	−	0.0223561i
$946$		0			0
$947$	7.76483	−	17.0026i	0.252323	−	0.552511i	−0.740506	−	0.672049i	$-0.765414\pi$
$947$	7.76483	−	17.0026i	0.252323	−	0.552511i	0.992830	+	0.119539i	$0.0381416\pi$
$948$		0			0
$949$	−20.5578	−	45.0153i	−0.667335	−	1.46126i
$950$		0			0
$951$	−0.398546	−	2.77195i	−0.0129237	−	0.0898866i
$952$		0			0
$953$	−34.0468	+	39.2921i	−1.10288	+	1.27279i	−0.143819	+	0.989604i	$0.545938\pi$
$953$	−34.0468	+	39.2921i	−1.10288	+	1.27279i	−0.959064	+	0.283190i	$0.908607\pi$
$954$		0			0
$955$	25.5904	+	16.4459i	0.828086	+	0.532178i
$956$		0			0
$957$	95.9975	+	28.1874i	3.10316	+	0.911170i
$958$		0			0
$959$	0.348792	+	0.402528i	0.0112631	+	0.0129983i
$960$		0			0
$961$	−47.1414	+	13.8420i	−1.52069	+	0.446515i
$962$		0			0
$963$	−11.0058	+	76.5467i	−0.354655	+	2.46668i
$964$		0			0
$965$	−17.4885			−0.562976
$966$		0			0
$967$	51.7211			1.66324			0.831618	−	0.555347i	$-0.187415\pi$
$967$	51.7211			1.66324			0.831618	+	0.555347i	$0.187415\pi$
$968$		0			0
$969$	0.941533	−	6.54851i	0.0302464	−	0.210368i
$970$		0			0
$971$	34.5146	−	10.1344i	1.10763	−	0.325228i	0.323747	−	0.946144i	$-0.395057\pi$
$971$	34.5146	−	10.1344i	1.10763	−	0.325228i	0.783878	+	0.620915i	$0.213239\pi$
$972$		0			0
$973$	0.504035	+	0.581687i	0.0161586	+	0.0186480i
$974$		0			0
$975$	−31.0346	−	9.11257i	−0.993901	−	0.291836i
$976$		0			0
$977$	24.9327	+	16.0233i	0.797669	+	0.512631i	0.874854	−	0.484386i	$-0.160957\pi$
$977$	24.9327	+	16.0233i	0.797669	+	0.512631i	−0.0771854	+	0.997017i	$0.524593\pi$
$978$		0			0
$979$	27.0712	−	31.2418i	0.865198	−	0.998492i
$980$		0			0
$981$	−7.61908	−	52.9919i	−0.243259	−	1.69190i
$982$		0			0
$983$	1.60274	+	3.50951i	0.0511195	+	0.111936i	0.933468	−	0.358660i	$-0.116766\pi$
$983$	1.60274	+	3.50951i	0.0511195	+	0.111936i	−0.882349	+	0.470596i	$0.844039\pi$
$984$		0			0
$985$	9.20626	−	20.1589i	0.293336	−	0.642316i
$986$		0			0
$987$	−2.13432	+	1.37164i	−0.0679361	+	0.0436599i
$988$		0			0
$989$	−30.9923	−	24.4747i	−0.985497	−	0.778251i
$990$		0			0
$991$	−15.1601	+	9.74283i	−0.481577	+	0.309491i	−0.758810	−	0.651312i	$-0.774219\pi$
$991$	−15.1601	+	9.74283i	−0.481577	+	0.309491i	0.277233	+	0.960803i	$0.410583\pi$
$992$		0			0
$993$	−20.1665	+	44.1586i	−0.639966	+	1.40133i
$994$		0			0
$995$	−10.4866	−	22.9624i	−0.332446	−	0.727956i
$996$		0			0
$997$	7.12722	+	49.5709i	0.225721	+	1.56993i	0.715836	+	0.698268i	$0.246046\pi$
$997$	7.12722	+	49.5709i	0.225721	+	1.56993i	−0.490115	+	0.871658i	$0.663045\pi$
$998$		0			0
$999$	19.1159	−	22.0609i	0.604801	−	0.697977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.81.1	yes	20
3.2	odd	2		828.2.q.a.541.2		20
4.3	odd	2		368.2.m.d.81.2		20
23.2	even	11	inner	92.2.e.a.25.1	✓	20
23.5	odd	22		2116.2.a.i.1.10		10
23.18	even	11		2116.2.a.j.1.10		10
69.2	odd	22		828.2.q.a.577.2		20
92.51	even	22		8464.2.a.cd.1.1		10
92.71	odd	22		368.2.m.d.209.2		20
92.87	odd	22		8464.2.a.ce.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.25.1	✓	20	23.2	even	11	inner
92.2.e.a.81.1	yes	20	1.1	even	1	trivial
368.2.m.d.81.2		20	4.3	odd	2
368.2.m.d.209.2		20	92.71	odd	22
828.2.q.a.541.2		20	3.2	odd	2
828.2.q.a.577.2		20	69.2	odd	22
2116.2.a.i.1.10		10	23.5	odd	22
2116.2.a.j.1.10		10	23.18	even	11
8464.2.a.cd.1.1		10	92.51	even	22
8464.2.a.ce.1.1		10	92.87	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)

\(f(q)\)	\(=\)	\(q+(-0.396574 + 2.75823i) q^{3} +(-1.50454 + 0.441774i) q^{5} +(-0.107929 - 0.124557i) q^{7} +(-4.57211 - 1.34249i) q^{9} +O(q^{10})\)	\(q+(-0.396574 + 2.75823i) q^{3} +(-1.50454 + 0.441774i) q^{5} +(-0.107929 - 0.124557i) q^{7} +(-4.57211 - 1.34249i) q^{9} +(5.36013 + 3.44475i) q^{11} +(2.99118 - 3.45201i) q^{13} +(-0.621853 - 4.32508i) q^{15} +(-0.232983 - 0.510162i) q^{17} +(1.75854 - 3.85066i) q^{19} +(0.386358 - 0.248297i) q^{21} +(-2.40635 + 4.14843i) q^{23} +(-2.13778 + 1.37387i) q^{25} +(2.04330 - 4.47420i) q^{27} +(-2.34087 - 5.12579i) q^{29} +(-1.27395 - 8.86051i) q^{31} +(-11.6271 + 13.4184i) q^{33} +(0.217410 + 0.139721i) q^{35} +(5.69427 + 1.67199i) q^{37} +(8.33521 + 9.61935i) q^{39} +(3.37652 - 0.991436i) q^{41} +(-1.17188 + 8.15062i) q^{43} +7.47201 q^{45} -5.52419 q^{47} +(0.992338 - 6.90186i) q^{49} +(1.49954 - 0.440305i) q^{51} +(1.22835 + 1.41760i) q^{53} +(-9.58636 - 2.81481i) q^{55} +(9.92362 + 6.37752i) q^{57} +(-4.03623 + 4.65806i) q^{59} +(-0.202144 - 1.40594i) q^{61} +(0.326246 + 0.714380i) q^{63} +(-2.97536 + 6.51512i) q^{65} +(-6.36535 + 4.09076i) q^{67} +(-10.4880 - 8.28245i) q^{69} +(-1.68406 + 1.08228i) q^{71} +(4.50073 - 9.85523i) q^{73} +(-2.94166 - 6.44134i) q^{75} +(-0.149447 - 1.03943i) q^{77} +(5.70639 - 6.58552i) q^{79} +(-0.495456 - 0.318410i) q^{81} +(0.778972 + 0.228727i) q^{83} +(0.575909 + 0.664635i) q^{85} +(15.0665 - 4.42391i) q^{87} +(0.923336 - 6.42194i) q^{89} -0.752805 q^{91} +24.9446 q^{93} +(-0.944675 + 6.57036i) q^{95} +(-7.25803 + 2.13115i) q^{97} +(-19.8825 - 22.9457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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Modular forms

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Database

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