LMFDB - Embedded newform 92.2.e.a.13.1

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			13.1
Root			$-0.420431 - 0.123450i$ of defining polynomial
Character	$\chi$	$=$	92.13
Dual form			92.2.e.a.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.368621 - 0.236898i) q^{3} +(0.781296 - 1.71080i) q^{5} +(4.72847 + 1.38840i) q^{7} +(-1.16648 - 2.55425i) q^{9} +O(q^{10})$	\(q+(-0.368621 - 0.236898i) q^{3} +(0.781296 - 1.71080i) q^{5} +(4.72847 + 1.38840i) q^{7} +(-1.16648 - 2.55425i) q^{9} +(-2.86466 + 3.30599i) q^{11} +(-3.72299 + 1.09317i) q^{13} +(-0.693287 + 0.445548i) q^{15} +(-0.170460 - 1.18558i) q^{17} +(-0.220090 + 1.53076i) q^{19} +(-1.41410 - 1.63196i) q^{21} +(-4.25781 - 2.20705i) q^{23} +(0.957892 + 1.10547i) q^{25} +(-0.362184 + 2.51905i) q^{27} +(0.772612 + 5.37364i) q^{29} +(-2.63810 + 1.69540i) q^{31} +(1.83915 - 0.540024i) q^{33} +(6.06962 - 7.00471i) q^{35} +(-1.08028 - 2.36547i) q^{37} +(1.63134 + 0.479005i) q^{39} +(4.38557 - 9.60306i) q^{41} +(4.09254 + 2.63012i) q^{43} -5.28117 q^{45} -2.40483 q^{47} +(14.5420 + 9.34557i) q^{49} +(-0.218025 + 0.477409i) q^{51} +(-10.1568 - 2.98231i) q^{53} +(3.41774 + 7.48381i) q^{55} +(0.443765 - 0.512132i) q^{57} +(5.25467 - 1.54291i) q^{59} +(8.58911 - 5.51989i) q^{61} +(-1.96936 - 13.6972i) q^{63} +(-1.03857 + 7.22338i) q^{65} +(-6.95204 - 8.02308i) q^{67} +(1.04667 + 1.82223i) q^{69} +(0.461121 + 0.532163i) q^{71} +(-0.964609 + 6.70901i) q^{73} +(-0.0912159 - 0.634420i) q^{75} +(-18.1355 + 11.6550i) q^{77} +(-1.13462 + 0.333154i) q^{79} +(-4.78628 + 5.52366i) q^{81} +(-2.80407 - 6.14005i) q^{83} +(-2.16146 - 0.634662i) q^{85} +(0.988203 - 2.16386i) q^{87} +(9.29920 + 5.97623i) q^{89} -19.1218 q^{91} +1.37410 q^{93} +(2.44687 + 1.57251i) q^{95} +(3.84506 - 8.41951i) q^{97} +(11.7859 + 3.46065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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
$3$	−0.368621	−	0.236898i	−0.212823	−	0.136773i	0.429887	−	0.902883i	$-0.358554\pi$
$3$	−0.368621	−	0.236898i	−0.212823	−	0.136773i	−0.642710	+	0.766110i	$0.722190\pi$
$4$		0			0
$5$	0.781296	−	1.71080i	0.349406	−	0.765093i	−0.650578	−	0.759440i	$-0.725473\pi$
$5$	0.781296	−	1.71080i	0.349406	−	0.765093i	0.999984	−	0.00565324i	$-0.00179949\pi$
$6$		0			0
$7$	4.72847	+	1.38840i	1.78719	+	0.524767i	0.996203	−	0.0870608i	$-0.0277474\pi$
$7$	4.72847	+	1.38840i	1.78719	+	0.524767i	0.790991	+	0.611828i	$0.209566\pi$
$8$		0			0
$9$	−1.16648	−	2.55425i	−0.388828	−	0.851415i
$10$		0			0
$11$	−2.86466	+	3.30599i	−0.863727	+	0.996794i	0.136255	+	0.990674i	$0.456493\pi$
$11$	−2.86466	+	3.30599i	−0.863727	+	0.996794i	−0.999981	+	0.00611985i	$0.998052\pi$
$12$		0			0
$13$	−3.72299	+	1.09317i	−1.03257	+	0.303190i	−0.753756	−	0.657154i	$-0.771760\pi$
$13$	−3.72299	+	1.09317i	−1.03257	+	0.303190i	−0.278816	+	0.960345i	$0.589942\pi$
$14$		0			0
$15$	−0.693287	+	0.445548i	−0.179006	+	0.115040i
$16$		0			0
$17$	−0.170460	−	1.18558i	−0.0413426	−	0.287544i	−0.999996	−	0.00296653i	$-0.999056\pi$
$17$	−0.170460	−	1.18558i	−0.0413426	−	0.287544i	0.958653	−	0.284578i	$-0.0918534\pi$
$18$		0			0
$19$	−0.220090	+	1.53076i	−0.0504922	+	0.351181i	0.948876	+	0.315648i	$0.102222\pi$
$19$	−0.220090	+	1.53076i	−0.0504922	+	0.351181i	−0.999369	+	0.0355329i	$0.988687\pi$
$20$		0			0
$21$	−1.41410	−	1.63196i	−0.308582	−	0.356123i
$22$		0			0
$23$	−4.25781	−	2.20705i	−0.887815	−	0.460201i
$23$	−4.25781	−	2.20705i	−0.887815	−	0.460201i
$24$		0			0
$25$	0.957892	+	1.10547i	0.191578	+	0.221093i
$26$		0			0
$27$	−0.362184	+	2.51905i	−0.0697024	+	0.484790i
$28$		0			0
$29$	0.772612	+	5.37364i	0.143471	+	0.997859i	0.926613	+	0.376017i	$0.122707\pi$
$29$	0.772612	+	5.37364i	0.143471	+	0.997859i	−0.783142	+	0.621843i	$0.786384\pi$
$30$		0			0
$31$	−2.63810	+	1.69540i	−0.473817	+	0.304504i	−0.755668	−	0.654954i	$-0.772688\pi$
$31$	−2.63810	+	1.69540i	−0.473817	+	0.304504i	0.281851	+	0.959458i	$0.409051\pi$
$32$		0			0
$33$	1.83915	−	0.540024i	0.320156	−	0.0940062i
$34$		0			0
$35$	6.06962	−	7.00471i	1.02595	−	1.18401i
$36$		0			0
$37$	−1.08028	−	2.36547i	−0.177596	−	0.388882i	0.799809	−	0.600254i	$-0.204934\pi$
$37$	−1.08028	−	2.36547i	−0.177596	−	0.388882i	−0.977406	+	0.211373i	$0.932207\pi$
$38$		0			0
$39$	1.63134	+	0.479005i	0.261224	+	0.0767022i
$40$		0			0
$41$	4.38557	−	9.60306i	0.684911	−	1.49975i	−0.172443	−	0.985019i	$-0.555166\pi$
$41$	4.38557	−	9.60306i	0.684911	−	1.49975i	0.857354	−	0.514727i	$-0.172107\pi$
$42$		0			0
$43$	4.09254	+	2.63012i	0.624107	+	0.401089i	0.814123	−	0.580692i	$-0.197218\pi$
$43$	4.09254	+	2.63012i	0.624107	+	0.401089i	−0.190017	+	0.981781i	$0.560854\pi$
$44$		0			0
$45$	−5.28117			−0.787270
$46$		0			0
$47$	−2.40483			−0.350781			−0.175391	−	0.984499i	$-0.556119\pi$
$47$	−2.40483			−0.350781			−0.175391	+	0.984499i	$0.556119\pi$
$48$		0			0
$49$	14.5420	+	9.34557i	2.07743	+	1.33508i
$50$		0			0
$51$	−0.218025	+	0.477409i	−0.0305297	+	0.0668506i
$52$		0			0
$53$	−10.1568	−	2.98231i	−1.39514	−	0.409651i	−0.504130	−	0.863628i	$-0.668187\pi$
$53$	−10.1568	−	2.98231i	−1.39514	−	0.409651i	−0.891014	+	0.453977i	$0.850005\pi$
$54$		0			0
$55$	3.41774	+	7.48381i	0.460848	+	1.00912i
$56$		0			0
$57$	0.443765	−	0.512132i	0.0587781	−	0.0678335i
$58$		0			0
$59$	5.25467	−	1.54291i	0.684100	−	0.200870i	0.0788275	−	0.996888i	$-0.474882\pi$
$59$	5.25467	−	1.54291i	0.684100	−	0.200870i	0.605272	+	0.796018i	$0.293064\pi$
$60$		0			0
$61$	8.58911	−	5.51989i	1.09972	−	0.706749i	0.140693	−	0.990053i	$-0.455067\pi$
$61$	8.58911	−	5.51989i	1.09972	−	0.706749i	0.959030	+	0.283304i	$0.0914305\pi$
$62$		0			0
$63$	−1.96936	−	13.6972i	−0.248116	−	1.72569i
$64$		0			0
$65$	−1.03857	+	7.22338i	−0.128818	+	0.895950i
$66$		0			0
$67$	−6.95204	−	8.02308i	−0.849327	−	0.980175i	0.150638	−	0.988589i	$-0.451867\pi$
$67$	−6.95204	−	8.02308i	−0.849327	−	0.980175i	−0.999965	+	0.00841372i	$0.997322\pi$
$68$		0			0
$69$	1.04667	+	1.82223i	0.126004	+	0.219371i
$70$		0			0
$71$	0.461121	+	0.532163i	0.0547250	+	0.0631561i	0.782452	−	0.622711i	$-0.213969\pi$
$71$	0.461121	+	0.532163i	0.0547250	+	0.0631561i	−0.727727	+	0.685867i	$0.759423\pi$
$72$		0			0
$73$	−0.964609	+	6.70901i	−0.112899	+	0.785230i	0.852176	+	0.523255i	$0.175283\pi$
$73$	−0.964609	+	6.70901i	−0.112899	+	0.785230i	−0.965075	+	0.261974i	$0.915626\pi$
$74$		0			0
$75$	−0.0912159	−	0.634420i	−0.0105327	−	0.0732565i
$76$		0			0
$77$	−18.1355	+	11.6550i	−2.06673	+	1.32821i
$78$		0			0
$79$	−1.13462	+	0.333154i	−0.127655	+	0.0374828i	−0.344936	−	0.938626i	$-0.612099\pi$
$79$	−1.13462	+	0.333154i	−0.127655	+	0.0374828i	0.217281	+	0.976109i	$0.430281\pi$
$80$		0			0
$81$	−4.78628	+	5.52366i	−0.531809	+	0.613740i
$82$		0			0
$83$	−2.80407	−	6.14005i	−0.307786	−	0.673958i	0.691018	−	0.722837i	$-0.257162\pi$
$83$	−2.80407	−	6.14005i	−0.307786	−	0.673958i	−0.998805	+	0.0488792i	$0.984435\pi$
$84$		0			0
$85$	−2.16146	−	0.634662i	−0.234443	−	0.0688388i
$86$		0			0
$87$	0.988203	−	2.16386i	0.105947	−	0.231991i
$88$		0			0
$89$	9.29920	+	5.97623i	0.985713	+	0.633479i	0.930999	−	0.365023i	$-0.118939\pi$
$89$	9.29920	+	5.97623i	0.985713	+	0.633479i	0.0547144	+	0.998502i	$0.482575\pi$
$90$		0			0
$91$	−19.1218			−2.00451
$92$		0			0
$93$	1.37410			0.142487
$94$		0			0
$95$	2.44687	+	1.57251i	0.251044	+	0.161336i
$96$		0			0
$97$	3.84506	−	8.41951i	0.390407	−	0.854872i	−0.607747	−	0.794131i	$-0.707926\pi$
$97$	3.84506	−	8.41951i	0.390407	−	0.854872i	0.998154	−	0.0607409i	$-0.0193464\pi$
$98$		0			0
$99$	11.7859	+	3.46065i	1.18453	+	0.347808i
$100$		0			0
$101$	1.68544	+	3.69059i	0.167707	+	0.367228i	0.974761	−	0.223250i	$-0.0716666\pi$
$101$	1.68544	+	3.69059i	0.167707	+	0.367228i	−0.807054	+	0.590478i	$0.798939\pi$
$102$		0			0
$103$	−4.25438	+	4.90982i	−0.419197	+	0.483779i	−0.925592	−	0.378522i	$-0.876432\pi$
$103$	−4.25438	+	4.90982i	−0.419197	+	0.483779i	0.506395	+	0.862302i	$0.330978\pi$
$104$		0			0
$105$	−3.89679	+	1.14420i	−0.380288	+	0.111662i
$106$		0			0
$107$	−1.61218	+	1.03608i	−0.155855	+	0.100162i	−0.616244	−	0.787555i	$-0.711346\pi$
$107$	−1.61218	+	1.03608i	−0.155855	+	0.100162i	0.460389	+	0.887717i	$0.347710\pi$
$108$		0			0
$109$	−1.90076	−	13.2201i	−0.182060	−	1.26625i	−0.851882	−	0.523733i	$-0.824539\pi$
$109$	−1.90076	−	13.2201i	−0.182060	−	1.26625i	0.669822	−	0.742522i	$-0.266370\pi$
$110$		0			0
$111$	−0.162164	+	1.12788i	−0.0153920	+	0.107053i
$112$		0			0
$113$	−3.82059	−	4.40920i	−0.359411	−	0.414782i	0.547031	−	0.837112i	$-0.315758\pi$
$113$	−3.82059	−	4.40920i	−0.359411	−	0.414782i	−0.906442	+	0.422330i	$0.861212\pi$
$114$		0			0
$115$	−7.10242	+	5.55990i	−0.662304	+	0.518464i
$116$		0			0
$117$	7.13503	+	8.23427i	0.659634	+	0.761258i
$118$		0			0
$119$	0.840043	−	5.84262i	0.0770066	−	0.535592i
$120$		0			0
$121$	−1.15785	−	8.05302i	−0.105259	−	0.732093i
$122$		0			0
$123$	−3.89156	+	2.50095i	−0.350890	+	0.225503i
$124$		0			0
$125$	11.6625	−	3.42442i	1.04313	−	0.306290i
$126$		0			0
$127$	8.93614	−	10.3129i	0.792955	−	0.915118i	−0.205018	−	0.978758i	$-0.565725\pi$
$127$	8.93614	−	10.3129i	0.792955	−	0.915118i	0.997973	+	0.0636398i	$0.0202709\pi$
$128$		0			0
$129$	−0.885525	−	1.93903i	−0.0779662	−	0.170722i
$130$		0			0
$131$	16.0487	+	4.71232i	1.40218	+	0.411718i	0.893433	−	0.449197i	$-0.148290\pi$
$131$	16.0487	+	4.71232i	1.40218	+	0.411718i	0.508749	+	0.860915i	$0.330108\pi$
$132$		0			0
$133$	−3.16601	+	6.93259i	−0.274528	+	0.601132i
$134$		0			0
$135$	4.02661	+	2.58774i	0.346555	+	0.222718i
$136$		0			0
$137$	15.3511			1.31154			0.655768	−	0.754963i	$-0.272345\pi$
$137$	15.3511			1.31154			0.655768	+	0.754963i	$0.272345\pi$
$138$		0			0
$139$	9.33601			0.791870			0.395935	−	0.918278i	$-0.370420\pi$
$139$	9.33601			0.791870			0.395935	+	0.918278i	$0.370420\pi$
$140$		0			0
$141$	0.886472	+	0.569701i	0.0746544	+	0.0479774i
$142$		0			0
$143$	7.05109	−	15.4397i	0.589642	−	1.29113i
$144$		0			0
$145$	9.79685	+	2.87662i	0.813585	+	0.238890i
$146$		0			0
$147$	−3.14653	−	6.88994i	−0.259521	−	0.568272i
$148$		0			0
$149$	−13.3736	+	15.4339i	−1.09561	+	1.26440i	−0.133699	+	0.991022i	$0.542685\pi$
$149$	−13.3736	+	15.4339i	−1.09561	+	1.26440i	−0.961908	+	0.273375i	$0.911860\pi$
$150$		0			0
$151$	−17.1954	+	5.04901i	−1.39934	+	0.410883i	−0.892457	−	0.451133i	$-0.851020\pi$
$151$	−17.1954	+	5.04901i	−1.39934	+	0.410883i	−0.506882	+	0.862016i	$0.669202\pi$
$152$		0			0
$153$	−2.82941	+	1.81835i	−0.228744	+	0.147005i
$154$		0			0
$155$	0.839360	+	5.83788i	0.0674190	+	0.468909i
$156$		0			0
$157$	1.85221	−	12.8824i	0.147823	−	1.02813i	−0.771952	−	0.635681i	$-0.780719\pi$
$157$	1.85221	−	12.8824i	0.147823	−	1.02813i	0.919774	−	0.392448i	$-0.128372\pi$
$158$		0			0
$159$	3.03750	+	3.50546i	0.240890	+	0.278001i
$160$		0			0
$161$	−17.0687	−	16.3475i	−1.34520	−	1.28836i
$162$		0			0
$163$	−4.19935	−	4.84631i	−0.328919	−	0.379593i	0.567070	−	0.823670i	$-0.308077\pi$
$163$	−4.19935	−	4.84631i	−0.328919	−	0.379593i	−0.895988	+	0.444077i	$0.853532\pi$
$164$		0			0
$165$	0.513050	−	3.56834i	0.0399409	−	0.277795i
$166$		0			0
$167$	3.51397	+	24.4402i	0.271919	+	1.89124i	0.428446	+	0.903567i	$0.359061\pi$
$167$	3.51397	+	24.4402i	0.271919	+	1.89124i	−0.156527	+	0.987674i	$0.550030\pi$
$168$		0			0
$169$	1.72935	−	1.11138i	0.133027	−	0.0854911i
$170$		0			0
$171$	4.16668	−	1.22345i	0.318634	−	0.0935593i
$172$		0			0
$173$	5.17919	−	5.97710i	0.393766	−	0.454430i	−0.523902	−	0.851779i	$-0.675524\pi$
$173$	5.17919	−	5.97710i	0.393766	−	0.454430i	0.917668	+	0.397348i	$0.130070\pi$
$174$		0			0
$175$	2.99453	+	6.55710i	0.226365	+	0.495671i
$176$		0			0
$177$	−2.30249	−	0.676073i	−0.173066	−	0.0508167i
$178$		0			0
$179$	1.49842	−	3.28107i	0.111997	−	0.245239i	−0.845331	−	0.534243i	$-0.820597\pi$
$179$	1.49842	−	3.28107i	0.111997	−	0.245239i	0.957328	+	0.289004i	$0.0933240\pi$
$180$		0			0
$181$	−0.707821	−	0.454889i	−0.0526119	−	0.0338116i	0.514070	−	0.857748i	$-0.328137\pi$
$181$	−0.707821	−	0.454889i	−0.0526119	−	0.0338116i	−0.566682	+	0.823936i	$0.691773\pi$
$182$		0			0
$183$	−4.47378			−0.330711
$184$		0			0
$185$	−4.89087			−0.359584
$186$		0			0
$187$	4.40781	+	2.83273i	0.322331	+	0.207150i
$188$		0			0
$189$	−5.21003	+	11.4084i	−0.378974	+	0.829837i
$190$		0			0
$191$	−10.2099	−	2.99788i	−0.738759	−	0.216919i	−0.109361	−	0.994002i	$-0.534880\pi$
$191$	−10.2099	−	2.99788i	−0.738759	−	0.216919i	−0.629398	+	0.777083i	$0.716699\pi$
$192$		0			0
$193$	−5.62373	−	12.3142i	−0.404805	−	0.886399i	−0.996760	−	0.0804281i	$-0.974371\pi$
$193$	−5.62373	−	12.3142i	−0.404805	−	0.886399i	0.591956	−	0.805970i	$-0.298356\pi$
$194$		0			0
$195$	2.09404	−	2.41665i	0.149957	−	0.173060i
$196$		0			0
$197$	6.29705	−	1.84898i	0.448646	−	0.131734i	−0.0496017	−	0.998769i	$-0.515795\pi$
$197$	6.29705	−	1.84898i	0.448646	−	0.131734i	0.498248	+	0.867035i	$0.333977\pi$
$198$		0			0
$199$	−14.7385	+	9.47187i	−1.04479	+	0.671443i	−0.946166	−	0.323682i	$-0.895079\pi$
$199$	−14.7385	+	9.47187i	−1.04479	+	0.671443i	−0.0986200	+	0.995125i	$0.531443\pi$
$200$		0			0
$201$	0.662012	+	4.60440i	0.0466947	+	0.324769i
$202$		0			0
$203$	−3.80751	+	26.4818i	−0.267234	+	1.85866i
$204$		0			0
$205$	−13.0025	−	15.0057i	−0.908133	−	1.04804i
$206$		0			0
$207$	−0.670664	+	13.4500i	−0.0466144	+	0.934838i
$208$		0			0
$209$	−4.43020	−	5.11273i	−0.306444	−	0.353655i
$210$		0			0
$211$	0.413560	−	2.87637i	0.0284706	−	0.198017i	−0.970622	−	0.240610i	$-0.922653\pi$
$211$	0.413560	−	2.87637i	0.0284706	−	0.198017i	0.999093	+	0.0425924i	$0.0135617\pi$
$212$		0			0
$213$	−0.0439106	−	0.305405i	−0.00300870	−	0.0209260i
$214$		0			0
$215$	7.69709	−	4.94662i	0.524937	−	0.337357i
$216$		0			0
$217$	−14.8281	+	4.35392i	−1.00660	+	0.295563i
$218$		0			0
$219$	1.94493	−	2.24456i	0.131426	−	0.151674i
$220$		0			0
$221$	1.93065	+	4.22754i	0.129870	+	0.284375i
$222$		0			0
$223$	−8.98602	−	2.63853i	−0.601748	−	0.176689i	−0.0333512	−	0.999444i	$-0.510618\pi$
$223$	−8.98602	−	2.63853i	−0.601748	−	0.176689i	−0.568397	+	0.822755i	$0.692436\pi$
$224$		0			0
$225$	1.70627	−	3.73620i	0.113751	−	0.249080i
$226$		0			0
$227$	−15.5483	−	9.99227i	−1.03197	−	0.663210i	−0.0889855	−	0.996033i	$-0.528362\pi$
$227$	−15.5483	−	9.99227i	−1.03197	−	0.663210i	−0.942989	+	0.332823i	$0.891999\pi$
$228$		0			0
$229$	7.98568			0.527709			0.263854	−	0.964563i	$-0.415006\pi$
$229$	7.98568			0.527709			0.263854	+	0.964563i	$0.415006\pi$
$230$		0			0
$231$	9.44616			0.621512
$232$		0			0
$233$	−4.03131	−	2.59077i	−0.264100	−	0.169727i	0.401889	−	0.915688i	$-0.368354\pi$
$233$	−4.03131	−	2.59077i	−0.264100	−	0.169727i	−0.665989	+	0.745962i	$0.731990\pi$
$234$		0			0
$235$	−1.87889	+	4.11419i	−0.122565	+	0.268380i
$236$		0			0
$237$	0.497167	+	0.145982i	0.0322945	+	0.00948252i
$238$		0			0
$239$	4.35978	+	9.54659i	0.282011	+	0.617517i	0.996633	−	0.0819934i	$-0.0261286\pi$
$239$	4.35978	+	9.54659i	0.282011	+	0.617517i	−0.714622	+	0.699511i	$0.753401\pi$
$240$		0			0
$241$	−0.200330	+	0.231193i	−0.0129044	+	0.0148924i	−0.762165	−	0.647383i	$-0.775864\pi$
$241$	−0.200330	+	0.231193i	−0.0129044	+	0.0148924i	0.749261	+	0.662275i	$0.230409\pi$
$242$		0			0
$243$	10.3984	−	3.05326i	0.667061	−	0.195867i
$244$		0			0
$245$	27.3500	−	17.5768i	1.74733	−	1.12294i
$246$		0			0
$247$	−0.853987	−	5.93961i	−0.0543379	−	0.377929i
$248$		0			0
$249$	−0.420929	+	2.92763i	−0.0266753	+	0.185531i
$250$		0			0
$251$	9.59046	+	11.0680i	0.605345	+	0.698605i	0.972855	−	0.231414i	$-0.0743353\pi$
$251$	9.59046	+	11.0680i	0.605345	+	0.698605i	−0.367511	+	0.930019i	$0.619790\pi$
$252$		0			0
$253$	19.4936	−	7.75385i	1.22555	−	0.487481i
$254$		0			0
$255$	0.646409	+	0.745995i	0.0404797	+	0.0467161i
$256$		0			0
$257$	−3.87846	+	26.9753i	−0.241932	+	1.68267i	0.400473	+	0.916309i	$0.368846\pi$
$257$	−3.87846	+	26.9753i	−0.241932	+	1.68267i	−0.642405	+	0.766365i	$0.722063\pi$
$258$		0			0
$259$	−1.82382	−	12.6849i	−0.113327	−	0.788203i
$260$		0			0
$261$	12.8243	−	8.24171i	0.793807	−	0.510149i
$262$		0			0
$263$	−7.56887	+	2.22242i	−0.466717	+	0.137040i	−0.506631	−	0.862163i	$-0.669110\pi$
$263$	−7.56887	+	2.22242i	−0.466717	+	0.137040i	0.0399148	+	0.999203i	$0.487291\pi$
$264$		0			0
$265$	−13.0376	+	15.0462i	−0.800893	+	0.924280i
$266$		0			0
$267$	−2.01212	−	4.40592i	−0.123140	−	0.269638i
$268$		0			0
$269$	−3.92411	−	1.15222i	−0.239257	−	0.0702523i	0.159906	−	0.987132i	$-0.448881\pi$
$269$	−3.92411	−	1.15222i	−0.239257	−	0.0702523i	−0.399163	+	0.916880i	$0.630699\pi$
$270$		0			0
$271$	9.94666	−	21.7801i	0.604216	−	1.32305i	−0.322244	−	0.946657i	$-0.604437\pi$
$271$	9.94666	−	21.7801i	0.604216	−	1.32305i	0.926460	−	0.376393i	$-0.122836\pi$
$272$		0			0
$273$	7.04869	+	4.52992i	0.426606	+	0.274163i
$274$		0			0
$275$	−6.39869			−0.385856
$276$		0			0
$277$	−6.86931			−0.412737			−0.206368	−	0.978474i	$-0.566165\pi$
$277$	−6.86931			−0.412737			−0.206368	+	0.978474i	$0.566165\pi$
$278$		0			0
$279$	7.40778	+	4.76069i	0.443492	+	0.285015i
$280$		0			0
$281$	−5.09904	+	11.1653i	−0.304183	+	0.666069i	−0.998566	−	0.0535373i	$-0.982950\pi$
$281$	−5.09904	+	11.1653i	−0.304183	+	0.666069i	0.694382	+	0.719606i	$0.255678\pi$
$282$		0			0
$283$	−2.44911	−	0.719124i	−0.145585	−	0.0427475i	0.208128	−	0.978102i	$-0.433263\pi$
$283$	−2.44911	−	0.719124i	−0.145585	−	0.0427475i	−0.353713	+	0.935354i	$0.615081\pi$
$284$		0			0
$285$	−0.529443	−	1.15932i	−0.0313615	−	0.0686721i
$286$		0			0
$287$	34.0700	−	39.3188i	2.01109	−	2.32092i
$288$		0			0
$289$	14.9348	−	4.38527i	0.878521	−	0.257957i
$290$		0			0
$291$	−3.41194	+	2.19272i	−0.200011	+	0.128539i
$292$		0			0
$293$	0.943729	+	6.56378i	0.0551333	+	0.383460i	0.998641	+	0.0521107i	$0.0165949\pi$
$293$	0.943729	+	6.56378i	0.0551333	+	0.383460i	−0.943508	+	0.331350i	$0.892496\pi$
$294$		0			0
$295$	1.46584	−	10.1952i	0.0853447	−	0.593585i
$296$		0			0
$297$	−7.29041	−	8.41358i	−0.423032	−	0.488205i
$298$		0			0
$299$	18.2645	+	3.56230i	1.05626	+	0.206013i
$300$		0			0
$301$	15.6998	+	18.1185i	0.904921	+	1.04433i
$302$		0			0
$303$	0.253008	−	1.75971i	0.0145349	−	0.101092i
$304$		0			0
$305$	−2.73278	−	19.0069i	−0.156479	−	1.08833i
$306$		0			0
$307$	−3.69823	+	2.37671i	−0.211069	+	0.135646i	−0.641904	−	0.766785i	$-0.721855\pi$
$307$	−3.69823	+	2.37671i	−0.211069	+	0.135646i	0.430835	+	0.902431i	$0.358219\pi$
$308$		0			0
$309$	2.73138	−	0.802006i	0.155383	−	0.0456245i
$310$		0			0
$311$	−11.0320	+	12.7317i	−0.625570	+	0.721946i	−0.976755	−	0.214360i	$-0.931233\pi$
$311$	−11.0320	+	12.7317i	−0.625570	+	0.721946i	0.351185	+	0.936306i	$0.385779\pi$
$312$		0			0
$313$	2.67930	+	5.86686i	0.151443	+	0.331614i	0.970114	−	0.242648i	$-0.0780161\pi$
$313$	2.67930	+	5.86686i	0.151443	+	0.331614i	−0.818671	+	0.574263i	$0.805289\pi$
$314$		0			0
$315$	−24.9719	−	7.33240i	−1.40700	−	0.413134i
$316$		0			0
$317$	−12.7314	+	27.8778i	−0.715064	+	1.56577i	0.105630	+	0.994406i	$0.466314\pi$
$317$	−12.7314	+	27.8778i	−0.715064	+	1.56577i	−0.820694	+	0.571367i	$0.806413\pi$
$318$		0			0
$319$	−19.9785	−	12.8394i	−1.11858	−	0.718867i
$320$		0			0
$321$	0.839728			0.0468690
$322$		0			0
$323$	1.85235			0.103068
$324$		0			0
$325$	−4.77468	−	3.06850i	−0.264852	−	0.170210i
$326$		0			0
$327$	−2.43115	+	5.32348i	−0.134443	+	0.294389i
$328$		0			0
$329$	−11.3712	−	3.33888i	−0.626914	−	0.184079i
$330$		0			0
$331$	12.6296	+	27.6549i	0.694184	+	1.52005i	0.846884	+	0.531778i	$0.178476\pi$
$331$	12.6296	+	27.6549i	0.694184	+	1.52005i	−0.152700	+	0.988273i	$0.548797\pi$
$332$		0			0
$333$	−4.78187	+	5.51858i	−0.262045	+	0.302416i
$334$		0			0
$335$	−19.1575	+	5.62514i	−1.04669	+	0.307334i
$336$		0			0
$337$	−18.2067	+	11.7007i	−0.991781	+	0.637379i	−0.932616	−	0.360869i	$-0.882480\pi$
$337$	−18.2067	+	11.7007i	−0.991781	+	0.637379i	−0.0591647	+	0.998248i	$0.518844\pi$
$338$		0			0
$339$	0.363818	+	2.53041i	0.0197599	+	0.137433i
$340$		0			0
$341$	1.95226	−	13.5783i	0.105721	−	0.735306i
$342$		0			0
$343$	33.1954	+	38.3096i	1.79238	+	2.06852i
$344$		0			0
$345$	3.93523	−	0.366945i	0.211866	−	0.0197557i
$346$		0			0
$347$	−12.7458	−	14.7094i	−0.684229	−	0.789642i	0.302303	−	0.953212i	$-0.402245\pi$
$347$	−12.7458	−	14.7094i	−0.684229	−	0.789642i	−0.986532	+	0.163569i	$0.947699\pi$
$348$		0			0
$349$	3.04180	−	21.1562i	0.162824	−	1.13247i	−0.730454	−	0.682962i	$-0.760692\pi$
$349$	3.04180	−	21.1562i	0.162824	−	1.13247i	0.893278	−	0.449504i	$-0.148399\pi$
$350$		0			0
$351$	−1.40533	−	9.77431i	−0.0750112	−	0.521714i
$352$		0			0
$353$	4.94762	−	3.17964i	0.263335	−	0.169235i	−0.402310	−	0.915503i	$-0.631793\pi$
$353$	4.94762	−	3.17964i	0.263335	−	0.169235i	0.665645	+	0.746268i	$0.268156\pi$
$354$		0			0
$355$	1.27070	−	0.373110i	0.0674415	−	0.0198026i
$356$		0			0
$357$	−1.69376	+	1.95471i	−0.0896435	+	0.103454i
$358$		0			0
$359$	−11.7559	−	25.7417i	−0.620450	−	1.35860i	−0.915191	−	0.403020i	$-0.867961\pi$
$359$	−11.7559	−	25.7417i	−0.620450	−	1.35860i	0.294741	−	0.955577i	$-0.404767\pi$
$360$		0			0
$361$	15.9356	+	4.67911i	0.838714	+	0.246269i
$362$		0			0
$363$	−1.48094	+	3.24280i	−0.0777291	+	0.170203i
$364$		0			0
$365$	10.7241	+	6.89197i	0.561326	+	0.360742i
$366$		0			0
$367$	7.82639			0.408534			0.204267	−	0.978915i	$-0.434519\pi$
$367$	7.82639			0.408534			0.204267	+	0.978915i	$0.434519\pi$
$368$		0			0
$369$	−29.6443			−1.54322
$370$		0			0
$371$	−43.8855	−	28.2035i	−2.27842	−	1.46425i
$372$		0			0
$373$	−5.01953	+	10.9912i	−0.259901	+	0.569105i	−0.993930	−	0.110014i	$-0.964910\pi$
$373$	−5.01953	+	10.9912i	−0.259901	+	0.569105i	0.734029	+	0.679118i	$0.237638\pi$
$374$		0			0
$375$	−5.11028	−	1.50051i	−0.263894	−	0.0774862i
$376$		0			0
$377$	−8.75072	−	19.1614i	−0.450685	−	0.986863i
$378$		0			0
$379$	−5.29294	+	6.10838i	−0.271880	+	0.313766i	−0.875227	−	0.483713i	$-0.839288\pi$
$379$	−5.29294	+	6.10838i	−0.271880	+	0.313766i	0.603347	+	0.797479i	$0.293833\pi$
$380$		0			0
$381$	−5.73714	+	1.68458i	−0.293923	+	0.0863035i
$382$		0			0
$383$	1.34988	−	0.867513i	0.0689755	−	0.0443279i	−0.505699	−	0.862710i	$-0.668765\pi$
$383$	1.34988	−	0.867513i	0.0689755	−	0.0443279i	0.574674	+	0.818382i	$0.305129\pi$
$384$		0			0
$385$	5.77014	+	40.1322i	0.294073	+	2.04533i
$386$		0			0
$387$	1.94408	−	13.5213i	0.0988229	−	0.687329i
$388$		0			0
$389$	11.4321	+	13.1934i	0.579632	+	0.668930i	0.967525	−	0.252774i	$-0.0813428\pi$
$389$	11.4321	+	13.1934i	0.579632	+	0.668930i	−0.387894	+	0.921704i	$0.626797\pi$
$390$		0			0
$391$	−1.89083	+	5.42417i	−0.0956235	+	0.274312i
$392$		0			0
$393$	−4.79954	−	5.53897i	−0.242105	−	0.279404i
$394$		0			0
$395$	−0.316513	+	2.20140i	−0.0159255	+	0.110764i
$396$		0			0
$397$	2.43126	+	16.9098i	0.122021	+	0.848677i	0.955261	+	0.295765i	$0.0955744\pi$
$397$	2.43126	+	16.9098i	0.122021	+	0.848677i	−0.833239	+	0.552912i	$0.813516\pi$
$398$		0			0
$399$	2.80937	−	1.80547i	0.140645	−	0.0903868i
$400$		0			0
$401$	1.01219	−	0.297205i	0.0505463	−	0.0148417i	−0.256362	−	0.966581i	$-0.582524\pi$
$401$	1.01219	−	0.297205i	0.0505463	−	0.0148417i	0.306908	+	0.951739i	$0.400706\pi$
$402$		0			0
$403$	7.96826	−	9.19587i	0.396927	−	0.458079i
$404$		0			0
$405$	5.71037	+	12.5040i	0.283751	+	0.621328i
$406$		0			0
$407$	10.9149	+	3.20489i	0.541029	+	0.158861i
$408$		0			0
$409$	−8.51568	+	18.6467i	−0.421073	+	0.922022i	0.573619	+	0.819123i	$0.305539\pi$
$409$	−8.51568	+	18.6467i	−0.421073	+	0.922022i	−0.994692	+	0.102899i	$0.967188\pi$
$410$		0			0
$411$	−5.65874	−	3.63665i	−0.279125	−	0.179383i
$412$		0			0
$413$	26.9887			1.32803
$414$		0			0
$415$	−12.6952			−0.623183
$416$		0			0
$417$	−3.44145	−	2.21168i	−0.168528	−	0.108307i
$418$		0			0
$419$	7.76828	−	17.0102i	0.379505	−	0.831000i	−0.619438	−	0.785045i	$-0.712640\pi$
$419$	7.76828	−	17.0102i	0.379505	−	0.831000i	0.998944	−	0.0459551i	$-0.0146331\pi$
$420$		0			0
$421$	−1.92934	−	0.566505i	−0.0940303	−	0.0276098i	0.234379	−	0.972145i	$-0.424694\pi$
$421$	−1.92934	−	0.566505i	−0.0940303	−	0.0276098i	−0.328409	+	0.944536i	$0.606513\pi$
$422$		0			0
$423$	2.80520	+	6.14254i	0.136394	+	0.298660i
$424$		0			0
$425$	1.14733	−	1.32409i	0.0556537	−	0.0642278i
$426$		0			0
$427$	48.2772	−	14.1755i	2.33630	−	0.685999i
$428$		0			0
$429$	−6.25682	+	4.02101i	−0.302082	+	0.194136i
$430$		0			0
$431$	2.08461	+	14.4988i	0.100412	+	0.698383i	0.976387	+	0.216027i	$0.0693099\pi$
$431$	2.08461	+	14.4988i	0.100412	+	0.698383i	−0.875975	+	0.482356i	$0.839781\pi$
$432$		0			0
$433$	5.18739	−	36.0791i	0.249290	−	1.73385i	−0.353043	−	0.935607i	$-0.614853\pi$
$433$	5.18739	−	36.0791i	0.249290	−	1.73385i	0.602333	−	0.798245i	$-0.294238\pi$
$434$		0			0
$435$	−2.92986	−	3.38124i	−0.140476	−	0.162118i
$436$		0			0
$437$	4.31557	−	6.03195i	0.206442	−	0.288547i
$438$		0			0
$439$	−12.9843	−	14.9846i	−0.619705	−	0.715178i	0.355946	−	0.934507i	$-0.384159\pi$
$439$	−12.9843	−	14.9846i	−0.619705	−	0.715178i	−0.975651	+	0.219328i	$0.929613\pi$
$440$		0			0
$441$	6.90787	−	48.0453i	0.328946	−	2.28787i
$442$		0			0
$443$	−0.130477	−	0.907490i	−0.00619917	−	0.0431161i	0.986487	−	0.163839i	$-0.0523878\pi$
$443$	−0.130477	−	0.907490i	−0.00619917	−	0.0431161i	−0.992686	+	0.120723i	$0.961479\pi$
$444$		0			0
$445$	17.4896	−	11.2399i	0.829085	−	0.532820i
$446$		0			0
$447$	8.58604	−	2.52109i	0.406106	−	0.119243i
$448$		0			0
$449$	−18.1257	+	20.9182i	−0.855404	+	0.987189i	−0.999997	−	0.00230182i	$-0.999267\pi$
$449$	−18.1257	+	20.9182i	−0.855404	+	0.987189i	0.144593	+	0.989491i	$0.453813\pi$
$450$		0			0
$451$	19.1845	+	42.0081i	0.903362	+	1.97809i
$452$		0			0
$453$	7.53466	+	2.21238i	0.354009	+	0.103947i
$454$		0			0
$455$	−14.9398	+	32.7136i	−0.700388	+	1.53364i
$456$		0			0
$457$	0.915093	+	0.588094i	0.0428062	+	0.0275099i	0.561869	−	0.827226i	$-0.310083\pi$
$457$	0.915093	+	0.588094i	0.0428062	+	0.0275099i	−0.519063	+	0.854736i	$0.673719\pi$
$458$		0			0
$459$	3.04826			0.142280
$460$		0			0
$461$	26.7366			1.24525			0.622624	−	0.782521i	$-0.286066\pi$
$461$	26.7366			1.24525			0.622624	+	0.782521i	$0.286066\pi$
$462$		0			0
$463$	−17.7874	−	11.4312i	−0.826649	−	0.531255i	0.0575626	−	0.998342i	$-0.481667\pi$
$463$	−17.7874	−	11.4312i	−0.826649	−	0.531255i	−0.884211	+	0.467087i	$0.845303\pi$
$464$		0			0
$465$	1.07358	−	2.35080i	0.0497859	−	0.109016i
$466$		0			0
$467$	24.0957	+	7.07515i	1.11502	+	0.327399i	0.786803	−	0.617204i	$-0.211735\pi$
$467$	24.0957	+	7.07515i	1.11502	+	0.327399i	0.328215	+	0.944603i	$0.393553\pi$
$468$		0			0
$469$	−21.7332	−	47.5891i	−1.00355	−	2.19746i
$470$		0			0
$471$	−3.73458	+	4.30994i	−0.172081	+	0.198592i
$472$		0			0
$473$	−20.4189	+	5.99552i	−0.938861	+	0.275674i
$474$		0			0
$475$	−1.90303	+	1.22300i	−0.0873170	+	0.0561152i
$476$		0			0
$477$	4.23021	+	29.4218i	0.193688	+	1.34713i
$478$		0			0
$479$	0.465539	−	3.23790i	0.0212710	−	0.147943i	−0.976418	−	0.215888i	$-0.930735\pi$
$479$	0.465539	−	3.23790i	0.0212710	−	0.147943i	0.997689	+	0.0679453i	$0.0216443\pi$
$480$		0			0
$481$	6.60772	+	7.62571i	0.301286	+	0.347703i
$482$		0			0
$483$	2.41917	+	10.0696i	0.110076	+	0.458181i
$484$		0			0
$485$	−11.4000	−	13.1563i	−0.517646	−	0.597395i
$486$		0			0
$487$	1.07399	−	7.46975i	0.0486670	−	0.338487i	−0.950912	−	0.309462i	$-0.899851\pi$
$487$	1.07399	−	7.46975i	0.0486670	−	0.338487i	0.999579	−	0.0290243i	$-0.00924001\pi$
$488$		0			0
$489$	0.399886	+	2.78127i	0.0180835	+	0.125773i
$490$		0			0
$491$	25.8706	−	16.6260i	1.16753	−	0.750323i	0.194473	−	0.980908i	$-0.437700\pi$
$491$	25.8706	−	16.6260i	1.16753	−	0.750323i	0.973052	+	0.230585i	$0.0740640\pi$
$492$		0			0
$493$	6.23915	−	1.83198i	0.280997	−	0.0825082i
$494$		0			0
$495$	15.1287	−	17.4595i	0.679987	−	0.784746i
$496$		0			0
$497$	1.44154	+	3.15654i	0.0646620	+	0.141590i
$498$		0			0
$499$	10.8788	+	3.19429i	0.487000	+	0.142996i	0.516009	−	0.856583i	$-0.327417\pi$
$499$	10.8788	+	3.19429i	0.487000	+	0.142996i	−0.0290090	+	0.999579i	$0.509235\pi$
$500$		0			0
$501$	4.49452	−	9.84162i	0.200800	−	0.439691i
$502$		0			0
$503$	0.248763	+	0.159871i	0.0110918	+	0.00712828i	0.546175	−	0.837671i	$-0.316083\pi$
$503$	0.248763	+	0.159871i	0.0110918	+	0.00712828i	−0.535083	+	0.844799i	$0.679720\pi$
$504$		0			0
$505$	7.63069			0.339561
$506$		0			0
$507$	−0.900758			−0.0400041
$508$		0			0
$509$	−27.5602	−	17.7118i	−1.22158	−	0.785064i	−0.239024	−	0.971014i	$-0.576827\pi$
$509$	−27.5602	−	17.7118i	−1.22158	−	0.785064i	−0.982559	+	0.185950i	$0.940464\pi$
$510$		0			0
$511$	−13.8759	+	30.3841i	−0.613835	+	1.34411i
$512$		0			0
$513$	−3.77635	−	1.10884i	−0.166730	−	0.0489563i
$514$		0			0
$515$	5.07579	+	11.1144i	0.223666	+	0.489760i
$516$		0			0
$517$	6.88903	−	7.95036i	0.302979	−	0.349656i
$518$		0			0
$519$	−3.32512	+	0.976343i	−0.145956	+	0.0428567i
$520$		0			0
$521$	27.1264	−	17.4331i	1.18843	−	0.763758i	0.211513	−	0.977375i	$-0.432161\pi$
$521$	27.1264	−	17.4331i	1.18843	−	0.763758i	0.976917	+	0.213617i	$0.0685246\pi$
$522$		0			0
$523$	−0.486415	−	3.38309i	−0.0212695	−	0.147932i	0.976419	−	0.215883i	$-0.0692630\pi$
$523$	−0.486415	−	3.38309i	−0.0212695	−	0.147932i	−0.997689	+	0.0679508i	$0.978354\pi$
$524$		0			0
$525$	0.449520	−	3.12648i	0.0196187	−	0.136451i
$526$		0			0
$527$	2.45972	+	2.83867i	0.107147	+	0.123654i
$528$		0			0
$529$	13.2579	+	18.7944i	0.576431	+	0.817146i
$530$		0			0
$531$	−10.0705	−	11.6219i	−0.437021	−	0.504349i
$532$		0			0
$533$	−5.82967	+	40.5463i	−0.252511	+	1.75625i
$534$		0			0
$535$	0.512944	+	3.56760i	0.0221765	+	0.154241i
$536$		0			0
$537$	−1.32963	+	0.854500i	−0.0573777	+	0.0368744i
$538$		0			0
$539$	−72.5542	+	21.3038i	−3.12513	+	0.917621i
$540$		0			0
$541$	−20.3348	+	23.4676i	−0.874261	+	1.00895i	0.125597	+	0.992081i	$0.459916\pi$
$541$	−20.3348	+	23.4676i	−0.874261	+	1.00895i	−0.999858	+	0.0168698i	$0.994630\pi$
$542$		0			0
$543$	0.153155	+	0.335363i	0.00657251	+	0.0143918i
$544$		0			0
$545$	−24.1020	−	7.07698i	−1.03242	−	0.303145i
$546$		0			0
$547$	−1.67952	+	3.67764i	−0.0718111	+	0.157244i	−0.942133	−	0.335238i	$-0.891183\pi$
$547$	−1.67952	+	3.67764i	−0.0718111	+	0.157244i	0.870322	+	0.492483i	$0.163910\pi$
$548$		0			0
$549$	−24.1182	−	15.4998i	−1.02934	−	0.661517i
$550$		0			0
$551$	−8.39581			−0.357674
$552$		0			0
$553$	−5.82756			−0.247813
$554$		0			0
$555$	1.80287	+	1.15864i	0.0765277	+	0.0491814i
$556$		0			0
$557$	6.65168	−	14.5652i	0.281841	−	0.617145i	−0.714774	−	0.699355i	$-0.753471\pi$
$557$	6.65168	−	14.5652i	0.281841	−	0.617145i	0.996615	+	0.0822100i	$0.0261978\pi$
$558$		0			0
$559$	−18.1117	−	5.31806i	−0.766041	−	0.224930i
$560$		0			0
$561$	−0.953742	−	2.08840i	−0.0402670	−	0.0881724i
$562$		0			0
$563$	15.7618	−	18.1901i	0.664282	−	0.766622i	−0.319189	−	0.947691i	$-0.603410\pi$
$563$	15.7618	−	18.1901i	0.664282	−	0.766622i	0.983470	+	0.181069i	$0.0579559\pi$
$564$		0			0
$565$	−10.5283	+	3.09138i	−0.442927	+	0.130055i
$566$		0			0
$567$	−30.3008	+	19.4732i	−1.27252	+	0.817796i
$568$		0			0
$569$	−3.07405	−	21.3805i	−0.128871	−	0.896315i	−0.946989	−	0.321266i	$-0.895892\pi$
$569$	−3.07405	−	21.3805i	−0.128871	−	0.896315i	0.818118	−	0.575050i	$-0.195017\pi$
$570$		0			0
$571$	−4.76443	+	33.1373i	−0.199385	+	1.38675i	0.606689	+	0.794939i	$0.292497\pi$
$571$	−4.76443	+	33.1373i	−0.199385	+	1.38675i	−0.806074	+	0.591815i	$0.798412\pi$
$572$		0			0
$573$	3.05337	+	3.52378i	0.127556	+	0.147208i
$574$		0			0
$575$	−1.63871	−	6.82098i	−0.0683389	−	0.284454i
$576$		0			0
$577$	14.4595	+	16.6872i	0.601958	+	0.694697i	0.972177	−	0.234248i	$-0.0752628\pi$
$577$	14.4595	+	16.6872i	0.601958	+	0.694697i	−0.370219	+	0.928945i	$0.620717\pi$
$578$		0			0
$579$	−0.844199	+	5.87153i	−0.0350837	+	0.244013i
$580$		0			0
$581$	−4.73408	−	32.9262i	−0.196403	−	1.36601i
$582$		0			0
$583$	38.9552	−	25.0350i	1.61336	−	1.03684i
$584$		0			0
$585$	19.6618	−	5.77321i	0.812913	−	0.238693i
$586$		0			0
$587$	−21.0521	+	24.2955i	−0.868915	+	1.00278i	0.131020	+	0.991380i	$0.458175\pi$
$587$	−21.0521	+	24.2955i	−0.868915	+	1.00278i	−0.999935	+	0.0114017i	$0.996371\pi$
$588$		0			0
$589$	−2.01464	−	4.41145i	−0.0830119	−	0.181771i
$590$		0			0
$591$	−2.75924	−	0.810186i	−0.113500	−	0.0333266i
$592$		0			0
$593$	1.32781	−	2.90751i	0.0545268	−	0.119397i	−0.880408	−	0.474218i	$-0.842731\pi$
$593$	1.32781	−	2.90751i	0.0545268	−	0.119397i	0.934934	+	0.354821i	$0.115458\pi$
$594$		0			0
$595$	−9.33924	−	6.00196i	−0.382871	−	0.246056i
$596$		0			0
$597$	7.67679			0.314190
$598$		0			0
$599$	25.8422			1.05588			0.527942	−	0.849280i	$-0.322964\pi$
$599$	25.8422			1.05588			0.527942	+	0.849280i	$0.322964\pi$
$600$		0			0
$601$	20.8313	+	13.3874i	0.849725	+	0.546085i	0.891489	−	0.453043i	$-0.149661\pi$
$601$	20.8313	+	13.3874i	0.849725	+	0.546085i	−0.0417643	+	0.999127i	$0.513298\pi$
$602$		0			0
$603$	−12.3835	+	27.1160i	−0.504294	+	1.10425i
$604$		0			0
$605$	−14.6817	−	4.31095i	−0.596897	−	0.175265i
$606$		0			0
$607$	6.09301	+	13.3418i	0.247308	+	0.541528i	0.992053	−	0.125820i	$-0.0401563\pi$
$607$	6.09301	+	13.3418i	0.247308	+	0.541528i	−0.744745	+	0.667349i	$0.767429\pi$
$608$		0			0
$609$	7.67701	−	8.85974i	0.311088	−	0.359015i
$610$		0			0
$611$	8.95318	−	2.62889i	0.362207	−	0.106354i
$612$		0			0
$613$	−20.3237	+	13.0613i	−0.820867	+	0.527539i	−0.882364	−	0.470568i	$-0.844049\pi$
$613$	−20.3237	+	13.0613i	−0.820867	+	0.527539i	0.0614967	+	0.998107i	$0.480413\pi$
$614$		0			0
$615$	1.23817	+	8.61166i	0.0499278	+	0.347256i
$616$		0			0
$617$	0.991474	−	6.89585i	0.0399152	−	0.277617i	−0.960083	−	0.279717i	$-0.909759\pi$
$617$	0.991474	−	6.89585i	0.0399152	−	0.277617i	0.999998	+	0.00210023i	$0.000668525\pi$
$618$		0			0
$619$	−10.1549	−	11.7194i	−0.408160	−	0.471042i	0.514034	−	0.857770i	$-0.328151\pi$
$619$	−10.1549	−	11.7194i	−0.408160	−	0.471042i	−0.922194	+	0.386728i	$0.873605\pi$
$620$		0			0
$621$	7.10176	−	9.92626i	0.284984	−	0.398327i
$622$		0			0
$623$	35.6736	+	41.1695i	1.42923	+	1.64942i
$624$		0			0
$625$	2.21252	−	15.3884i	0.0885009	−	0.615538i
$626$		0			0
$627$	0.421869	+	2.93416i	0.0168478	+	0.117179i
$628$		0			0
$629$	−2.62030	+	1.68397i	−0.104478	+	0.0671442i
$630$		0			0
$631$	27.0925	−	7.95506i	1.07853	−	0.316686i	0.306242	−	0.951954i	$-0.400928\pi$
$631$	27.0925	−	7.95506i	1.07853	−	0.316686i	0.772292	+	0.635268i	$0.219110\pi$
$632$		0			0
$633$	−0.833853	+	0.962318i	−0.0331427	+	0.0382487i
$634$		0			0
$635$	−10.6615	−	23.3453i	−0.423087	−	0.926432i
$636$		0			0
$637$	−64.3560	−	18.8966i	−2.54988	−	0.748711i
$638$		0			0
$639$	0.821382	−	1.79858i	0.0324934	−	0.0711506i
$640$		0			0
$641$	−8.94192	−	5.74662i	−0.353185	−	0.226978i	0.352003	−	0.935999i	$-0.385501\pi$
$641$	−8.94192	−	5.74662i	−0.353185	−	0.226978i	−0.705187	+	0.709021i	$0.749137\pi$
$642$		0			0
$643$	3.25974			0.128551			0.0642757	−	0.997932i	$-0.479526\pi$
$643$	3.25974			0.128551			0.0642757	+	0.997932i	$0.479526\pi$
$644$		0			0
$645$	−4.00915			−0.157860
$646$		0			0
$647$	−13.6085	−	8.74564i	−0.535005	−	0.343827i	0.245078	−	0.969503i	$-0.421187\pi$
$647$	−13.6085	−	8.74564i	−0.535005	−	0.343827i	−0.780082	+	0.625677i	$0.784823\pi$
$648$		0			0
$649$	−9.95198	+	21.7918i	−0.390650	+	0.855403i
$650$		0			0
$651$	6.49737	+	1.90780i	0.254652	+	0.0747726i
$652$		0			0
$653$	7.69174	+	16.8426i	0.301001	+	0.659100i	0.998337	−	0.0576440i	$-0.0183588\pi$
$653$	7.69174	+	16.8426i	0.301001	+	0.659100i	−0.697336	+	0.716744i	$0.745632\pi$
$654$		0			0
$655$	20.6006	−	23.7744i	0.804933	−	0.928942i
$656$		0			0
$657$	18.2616	−	5.36210i	0.712455	−	0.209196i
$658$		0			0
$659$	25.1248	−	16.1467i	0.978724	−	0.628988i	0.0496051	−	0.998769i	$-0.484204\pi$
$659$	25.1248	−	16.1467i	0.978724	−	0.628988i	0.929119	+	0.369781i	$0.120567\pi$
$660$		0			0
$661$	−1.53664	−	10.6876i	−0.0597685	−	0.415699i	−0.997637	−	0.0687078i	$-0.978112\pi$
$661$	−1.53664	−	10.6876i	−0.0597685	−	0.415699i	0.937868	−	0.346991i	$-0.112797\pi$
$662$		0			0
$663$	0.289818	−	2.01573i	0.0112556	−	0.0782844i
$664$		0			0
$665$	9.38669	+	10.8328i	0.364000	+	0.420078i
$666$		0			0
$667$	8.57022	−	24.5851i	0.331840	−	0.951940i
$668$		0			0
$669$	2.68737	+	3.10139i	0.103900	+	0.119907i
$670$		0			0
$671$	−6.35617	+	44.2081i	−0.245377	+	1.70664i
$672$		0			0
$673$	−1.42944	−	9.94197i	−0.0551008	−	0.383235i	−0.998647	−	0.0519947i	$-0.983442\pi$
$673$	−1.42944	−	9.94197i	−0.0551008	−	0.383235i	0.943547	−	0.331240i	$-0.107467\pi$
$674$		0			0
$675$	−3.13165	+	2.01259i	−0.120537	+	0.0774647i
$676$		0			0
$677$	−6.79281	+	1.99455i	−0.261069	+	0.0766567i	−0.409648	−	0.912244i	$-0.634348\pi$
$677$	−6.79281	+	1.99455i	−0.261069	+	0.0766567i	0.148579	+	0.988901i	$0.452530\pi$
$678$		0			0
$679$	29.8709	−	34.4729i	1.14634	−	1.32295i
$680$		0			0
$681$	3.36426	+	7.36671i	0.128919	+	0.282293i
$682$		0			0
$683$	29.3356	+	8.61372i	1.12250	+	0.329595i	0.789754	−	0.613423i	$-0.210208\pi$
$683$	29.3356	+	8.61372i	1.12250	+	0.329595i	0.332742	+	0.943018i	$0.392026\pi$
$684$		0			0
$685$	11.9938	−	26.2627i	0.458259	−	1.00345i
$686$		0			0
$687$	−2.94369	−	1.89179i	−0.112309	−	0.0721764i
$688$		0			0
$689$	41.0738			1.56479
$690$		0			0
$691$	−38.7392			−1.47371			−0.736854	−	0.676052i	$-0.763690\pi$
$691$	−38.7392			−1.47371			−0.736854	+	0.676052i	$0.763690\pi$
$692$		0			0
$693$	50.9244	+	32.7272i	1.93446	+	1.24320i
$694$		0			0
$695$	7.29419	−	15.9720i	0.276684	−	0.605854i
$696$		0			0
$697$	−12.1327	−	3.56249i	−0.459559	−	0.134939i
$698$		0			0
$699$	0.872276	+	1.91002i	0.0329925	+	0.0722436i
$700$		0			0
$701$	6.49305	−	7.49338i	0.245239	−	0.283021i	−0.619763	−	0.784789i	$-0.712771\pi$
$701$	6.49305	−	7.49338i	0.245239	−	0.283021i	0.865002	+	0.501768i	$0.167317\pi$
$702$		0			0
$703$	3.85874	−	1.13303i	0.145535	−	0.0427330i
$704$		0			0
$705$	1.66724	−	1.07147i	0.0627919	−	0.0403539i
$706$		0			0
$707$	2.84551	+	19.7909i	0.107016	+	0.744315i
$708$		0			0
$709$	−6.17957	+	42.9799i	−0.232079	+	1.61414i	0.457007	+	0.889463i	$0.348922\pi$
$709$	−6.17957	+	42.9799i	−0.232079	+	1.61414i	−0.689085	+	0.724680i	$0.741988\pi$
$710$		0			0
$711$	2.17447	+	2.50948i	0.0815491	+	0.0941127i
$712$		0			0
$713$	14.9744	−	1.39630i	0.560795	−	0.0522920i
$714$		0			0
$715$	−20.9053	−	24.1260i	−0.781814	−	0.902261i
$716$		0			0
$717$	0.654463	−	4.55189i	0.0244414	−	0.169993i
$718$		0			0
$719$	−2.66577	−	18.5408i	−0.0994163	−	0.691455i	−0.977188	−	0.212376i	$-0.931880\pi$
$719$	−2.66577	−	18.5408i	−0.0994163	−	0.691455i	0.877772	−	0.479079i	$-0.159029\pi$
$720$		0			0
$721$	−26.9335	+	17.3091i	−1.00306	+	0.644626i
$722$		0			0
$723$	0.128615	−	0.0377647i	0.00478324	−	0.00140449i
$724$		0			0
$725$	−5.20029	+	6.00146i	−0.193134	+	0.222889i
$726$		0			0
$727$	−12.2504	−	26.8247i	−0.454343	−	0.994872i	−0.988741	−	0.149639i	$-0.952189\pi$
$727$	−12.2504	−	26.8247i	−0.454343	−	0.994872i	0.534398	−	0.845233i	$-0.320538\pi$
$728$		0			0
$729$	16.4820	+	4.83954i	0.610443	+	0.179242i
$730$		0			0
$731$	2.42059	−	5.30035i	0.0895286	−	0.196040i
$732$		0			0
$733$	−18.0771	−	11.6174i	−0.667693	−	0.429100i	0.162400	−	0.986725i	$-0.448076\pi$
$733$	−18.0771	−	11.6174i	−0.667693	−	0.429100i	−0.830093	+	0.557625i	$0.811713\pi$
$734$		0			0
$735$	−14.2457			−0.525460
$736$		0			0
$737$	46.4394			1.71062
$738$		0			0
$739$	−7.12581	−	4.57948i	−0.262127	−	0.168459i	0.402976	−	0.915211i	$-0.367976\pi$
$739$	−7.12581	−	4.57948i	−0.262127	−	0.168459i	−0.665103	+	0.746752i	$0.731612\pi$
$740$		0			0
$741$	−1.09229	+	2.39177i	−0.0401261	+	0.0878639i
$742$		0			0
$743$	−14.0803	−	4.13436i	−0.516557	−	0.151675i	0.0130549	−	0.999915i	$-0.495844\pi$
$743$	−14.0803	−	4.13436i	−0.516557	−	0.151675i	−0.529612	+	0.848240i	$0.677663\pi$
$744$		0			0
$745$	15.9556	+	34.9380i	0.584569	+	1.28003i
$746$		0			0
$747$	−12.4123	+	14.3245i	−0.454142	+	0.524108i
$748$		0			0
$749$	−9.06164	+	2.66074i	−0.331105	+	0.0972212i
$750$		0			0
$751$	−20.5806	+	13.2264i	−0.750998	+	0.482637i	−0.859294	−	0.511482i	$-0.829097\pi$
$751$	−20.5806	+	13.2264i	−0.750998	+	0.482637i	0.108296	+	0.994119i	$0.465460\pi$
$752$		0			0
$753$	−0.913258	−	6.35185i	−0.0332810	−	0.231474i
$754$		0			0
$755$	−4.79682	+	33.3626i	−0.174574	+	1.21419i
$756$		0			0
$757$	−9.25536	−	10.6813i	−0.336392	−	0.388217i	0.562201	−	0.827001i	$-0.309955\pi$
$757$	−9.25536	−	10.6813i	−0.336392	−	0.388217i	−0.898593	+	0.438784i	$0.855409\pi$
$758$		0			0
$759$	−9.02263	−	1.75978i	−0.327501	−	0.0638758i
$760$		0			0
$761$	−1.37866	−	1.59106i	−0.0499765	−	0.0576759i	0.730211	−	0.683222i	$-0.239422\pi$
$761$	−1.37866	−	1.59106i	−0.0499765	−	0.0576759i	−0.780187	+	0.625546i	$0.784876\pi$
$762$		0			0
$763$	9.36713	−	65.1498i	0.339113	−	2.35858i
$764$		0			0
$765$	0.900228	+	6.26123i	0.0325478	+	0.226375i
$766$		0			0
$767$	−17.8764	+	11.4885i	−0.645481	+	0.414825i
$768$		0			0
$769$	25.1904	−	7.39656i	0.908388	−	0.266727i	0.206026	−	0.978547i	$-0.433947\pi$
$769$	25.1904	−	7.39656i	0.908388	−	0.266727i	0.702362	+	0.711820i	$0.252129\pi$
$770$		0			0
$771$	7.82008	−	9.02486i	0.281633	−	0.325022i
$772$		0			0
$773$	7.38626	+	16.1737i	0.265665	+	0.581726i	0.994708	−	0.102742i	$-0.0327617\pi$
$773$	7.38626	+	16.1737i	0.265665	+	0.581726i	−0.729043	+	0.684468i	$0.760034\pi$
$774$		0			0
$775$	−4.40123	−	1.29232i	−0.158097	−	0.0464214i
$776$		0			0
$777$	−2.33274	+	5.10799i	−0.0836865	+	0.183248i
$778$		0			0
$779$	13.7348	+	8.82681i	0.492100	+	0.316253i
$780$		0			0
$781$	−3.08028			−0.110221
$782$		0			0
$783$	−13.8163			−0.493753
$784$		0			0
$785$	−20.5921	−	13.2337i	−0.734964	−	0.472333i
$786$		0			0
$787$	13.1874	−	28.8765i	0.470082	−	1.02934i	−0.514991	−	0.857196i	$-0.672205\pi$
$787$	13.1874	−	28.8765i	0.470082	−	1.02934i	0.985073	−	0.172140i	$-0.0550681\pi$
$788$		0			0
$789$	3.31653	+	0.973821i	0.118072	+	0.0346689i
$790$		0			0
$791$	−11.9438	−	26.1533i	−0.424673	−	0.929903i
$792$		0			0
$793$	−25.9430	+	29.9398i	−0.921264	+	1.06320i
$794$		0			0
$795$	8.37034	−	2.45775i	0.296865	−	0.0871675i
$796$		0			0
$797$	−7.25548	+	4.66282i	−0.257002	+	0.165165i	−0.662798	−	0.748799i	$-0.730631\pi$
$797$	−7.25548	+	4.66282i	−0.257002	+	0.165165i	0.405795	+	0.913964i	$0.366995\pi$
$798$		0			0
$799$	0.409928	+	2.85111i	0.0145022	+	0.100865i
$800$		0			0
$801$	4.41739	−	30.7236i	0.156081	−	1.08557i
$802$		0			0
$803$	−19.4166	−	22.4080i	−0.685198	−	0.790761i
$804$		0			0
$805$	−41.3030	+	16.4288i	−1.45574	+	0.579040i
$806$		0			0
$807$	1.17355	+	1.35435i	0.0413109	+	0.0476753i
$808$		0			0
$809$	−3.59346	+	24.9931i	−0.126339	+	0.878710i	0.823799	+	0.566882i	$0.191850\pi$
$809$	−3.59346	+	24.9931i	−0.126339	+	0.878710i	−0.950138	+	0.311828i	$0.899059\pi$
$810$		0			0
$811$	3.24877	+	22.5957i	0.114080	+	0.793442i	0.963880	+	0.266337i	$0.0858134\pi$
$811$	3.24877	+	22.5957i	0.114080	+	0.793442i	−0.849800	+	0.527105i	$0.823278\pi$
$812$		0			0
$813$	−8.82622	+	5.67227i	−0.309549	+	0.198935i
$814$		0			0
$815$	−11.5720	+	3.39785i	−0.405350	+	0.119021i
$816$		0			0
$817$	−4.92681	+	5.68585i	−0.172367	+	0.198923i
$818$		0			0
$819$	22.3053	+	48.8418i	0.779410	+	1.70667i
$820$		0			0
$821$	16.3969	+	4.81455i	0.572254	+	0.168029i	0.555041	−	0.831823i	$-0.312702\pi$
$821$	16.3969	+	4.81455i	0.572254	+	0.168029i	0.0172130	+	0.999852i	$0.494521\pi$
$822$		0			0
$823$	−6.15836	+	13.4849i	−0.214667	+	0.470055i	−0.986078	−	0.166282i	$-0.946824\pi$
$823$	−6.15836	+	13.4849i	−0.214667	+	0.470055i	0.771411	+	0.636337i	$0.219551\pi$
$824$		0			0
$825$	2.35869	+	1.51584i	0.0821190	+	0.0527747i
$826$		0			0
$827$	−35.6981			−1.24135			−0.620673	−	0.784070i	$-0.713141\pi$
$827$	−35.6981			−1.24135			−0.620673	+	0.784070i	$0.713141\pi$
$828$		0			0
$829$	−48.6807			−1.69075			−0.845376	−	0.534172i	$-0.820623\pi$
$829$	−48.6807			−1.69075			−0.845376	+	0.534172i	$0.820623\pi$
$830$		0			0
$831$	2.53217	+	1.62733i	0.0878399	+	0.0564513i
$832$		0			0
$833$	8.60105	−	18.8337i	0.298009	−	0.652548i
$834$		0			0
$835$	44.5578	+	13.0833i	1.54199	+	0.452768i
$836$		0			0
$837$	−3.31532	−	7.25955i	−0.114594	−	0.250927i
$838$		0			0
$839$	−26.1538	+	30.1831i	−0.902930	+	1.04204i	0.0959815	+	0.995383i	$0.469401\pi$
$839$	−26.1538	+	30.1831i	−0.902930	+	1.04204i	−0.998911	+	0.0466532i	$0.985144\pi$
$840$		0			0
$841$	−0.453748	+	0.133232i	−0.0156465	+	0.00459422i
$842$		0			0
$843$	4.52466	−	2.90782i	0.155838	−	0.100151i
$844$		0			0
$845$	−0.550223	−	3.82689i	−0.0189283	−	0.131649i
$846$		0			0
$847$	5.70599	−	39.6861i	0.196060	−	1.36363i
$848$		0			0
$849$	0.732434	+	0.845274i	0.0251371	+	0.0290097i
$850$		0			0
$851$	−0.621098	+	12.4560i	−0.0212910	+	0.426985i
$852$		0			0
$853$	−12.9783	−	14.9777i	−0.444368	−	0.512828i	0.488738	−	0.872431i	$-0.337458\pi$
$853$	−12.9783	−	14.9777i	−0.444368	−	0.512828i	−0.933105	+	0.359603i	$0.882912\pi$
$854$		0			0
$855$	1.16234	−	8.08422i	0.0397510	−	0.276475i
$856$		0			0
$857$	7.96630	+	55.4068i	0.272124	+	1.89266i	0.426243	+	0.904609i	$0.359837\pi$
$857$	7.96630	+	55.4068i	0.272124	+	1.89266i	−0.154119	+	0.988052i	$0.549254\pi$
$858$		0			0
$859$	−22.2351	+	14.2896i	−0.758650	+	0.487555i	−0.861886	−	0.507102i	$-0.830717\pi$
$859$	−22.2351	+	14.2896i	−0.758650	+	0.487555i	0.103236	+	0.994657i	$0.467080\pi$
$860$		0			0
$861$	−21.8734	+	6.42262i	−0.745445	+	0.218882i
$862$		0			0
$863$	3.75417	−	4.33254i	0.127793	−	0.147481i	−0.688247	−	0.725477i	$-0.741619\pi$
$863$	3.75417	−	4.33254i	0.127793	−	0.147481i	0.816040	+	0.577995i	$0.196165\pi$
$864$		0			0
$865$	−6.17914	−	13.5304i	−0.210097	−	0.460049i
$866$		0			0
$867$	−6.54415	−	1.92154i	−0.222251	−	0.0652588i
$868$		0			0
$869$	2.14889	−	4.70541i	0.0728961	−	0.159620i
$870$		0			0
$871$	34.6530	+	22.2701i	1.17417	+	0.754594i
$872$		0			0
$873$	−25.9907			−0.879652
$874$		0			0
$875$	59.9003			2.02500
$876$		0			0
$877$	13.4023	+	8.61310i	0.452562	+	0.290844i	0.746997	−	0.664828i	$-0.231495\pi$
$877$	13.4023	+	8.61310i	0.452562	+	0.290844i	−0.294435	+	0.955672i	$0.595131\pi$
$878$		0			0
$879$	1.20707	−	2.64311i	0.0407134	−	0.0891500i
$880$		0			0
$881$	−12.1413	−	3.56502i	−0.409052	−	0.120108i	0.0707316	−	0.997495i	$-0.477467\pi$
$881$	−12.1413	−	3.56502i	−0.409052	−	0.120108i	−0.479783	+	0.877387i	$0.659285\pi$
$882$		0			0
$883$	−21.1509	−	46.3141i	−0.711786	−	1.55859i	−0.825070	−	0.565031i	$-0.808864\pi$
$883$	−21.1509	−	46.3141i	−0.711786	−	1.55859i	0.113284	−	0.993563i	$-0.463863\pi$
$884$		0			0
$885$	−2.95555	+	3.41089i	−0.0993498	+	0.114656i
$886$		0			0
$887$	−36.6085	+	10.7492i	−1.22919	+	0.360923i	−0.830945	−	0.556355i	$-0.812200\pi$
$887$	−36.6085	+	10.7492i	−1.22919	+	0.360923i	−0.398247	+	0.917278i	$0.630381\pi$
$888$		0			0
$889$	56.5727	−	36.3571i	1.89739	−	1.21938i
$890$		0			0
$891$	−4.55012	−	31.6468i	−0.152435	−	1.06021i
$892$		0			0
$893$	0.529281	−	3.68123i	0.0177117	−	0.123188i
$894$		0			0
$895$	−4.44255	−	5.12698i	−0.148498	−	0.171376i
$896$		0			0
$897$	−5.88875	−	5.63995i	−0.196620	−	0.188313i
$898$		0			0
$899$	−11.1487	−	12.8663i	−0.371831	−	0.429115i
$900$		0			0
$901$	−1.80442	+	12.5500i	−0.0601139	+	0.418102i
$902$		0			0
$903$	−1.49502	−	10.3981i	−0.0497512	−	0.346028i
$904$		0			0
$905$	−1.33124	+	0.855536i	−0.0442519	+	0.0284390i
$906$		0			0
$907$	50.1722	−	14.7319i	1.66594	−	0.489164i	0.693139	−	0.720804i	$-0.256227\pi$
$907$	50.1722	−	14.7319i	1.66594	−	0.489164i	0.972802	+	0.231639i	$0.0744089\pi$
$908$		0			0
$909$	7.46064	−	8.61004i	0.247454	−	0.285577i
$910$		0			0
$911$	−18.2870	−	40.0430i	−0.605876	−	1.32668i	−0.925359	−	0.379091i	$-0.876237\pi$
$911$	−18.2870	−	40.0430i	−0.605876	−	1.32668i	0.319484	−	0.947592i	$-0.396491\pi$
$912$		0			0
$913$	28.3316	+	8.31892i	0.937640	+	0.275316i
$914$		0			0
$915$	−3.49534	+	7.65373i	−0.115552	+	0.253025i
$916$		0			0
$917$	69.3432	+	44.5642i	2.28991	+	1.47164i
$918$		0			0
$919$	3.28315			0.108301			0.0541506	−	0.998533i	$-0.482755\pi$
$919$	3.28315			0.108301			0.0541506	+	0.998533i	$0.482755\pi$
$920$		0			0
$921$	1.92628			0.0634730
$922$		0			0
$923$	−2.29849	−	1.47715i	−0.0756559	−	0.0486211i
$924$		0			0
$925$	1.58016	−	3.46008i	0.0519555	−	0.113767i
$926$		0			0
$927$	17.5036	+	5.13951i	0.574892	+	0.168804i
$928$		0			0
$929$	2.83159	+	6.20032i	0.0929015	+	0.203426i	0.950378	−	0.311097i	$-0.100696\pi$
$929$	2.83159	+	6.20032i	0.0929015	+	0.203426i	−0.857477	+	0.514523i	$0.827969\pi$
$930$		0			0
$931$	−17.5064	+	20.2035i	−0.573749	+	0.662142i
$932$		0			0
$933$	7.08274	−	2.07968i	0.231878	−	0.0680857i
$934$		0			0
$935$	8.29003	−	5.32768i	0.271113	−	0.174234i
$936$		0			0
$937$	−5.62857	−	39.1475i	−0.183877	−	1.27889i	−0.847487	−	0.530816i	$-0.821886\pi$
$937$	−5.62857	−	39.1475i	−0.183877	−	1.27889i	0.663610	−	0.748079i	$-0.269023\pi$
$938$		0			0
$939$	0.402201	−	2.79737i	0.0131253	−	0.0912886i
$940$		0			0
$941$	−1.78856	−	2.06411i	−0.0583055	−	0.0672882i	0.725848	−	0.687856i	$-0.241448\pi$
$941$	−1.78856	−	2.06411i	−0.0583055	−	0.0672882i	−0.784153	+	0.620567i	$0.786902\pi$
$942$		0			0
$943$	−39.8673	+	31.2089i	−1.29826	+	1.01630i
$944$		0			0
$945$	15.4469	+	17.8266i	0.502487	+	0.579900i
$946$		0			0
$947$	−0.370338	+	2.57576i	−0.0120344	+	0.0837010i	−0.994954	−	0.100337i	$-0.968008\pi$
$947$	−0.370338	+	2.57576i	−0.0120344	+	0.0837010i	0.982919	+	0.184038i	$0.0589170\pi$
$948$		0			0
$949$	−3.74284	−	26.0320i	−0.121498	−	0.845036i
$950$		0			0
$951$	11.2972	−	7.26029i	0.366338	−	0.235431i
$952$		0			0
$953$	−21.8091	+	6.40372i	−0.706465	+	0.207437i	−0.615179	−	0.788388i	$-0.710916\pi$
$953$	−21.8091	+	6.40372i	−0.706465	+	0.207437i	−0.0912867	+	0.995825i	$0.529098\pi$
$954$		0			0
$955$	−13.1057	+	15.1248i	−0.424090	+	0.489426i
$956$		0			0
$957$	4.32285	+	9.46572i	0.139738	+	0.305983i
$958$		0			0
$959$	72.5873	+	21.3136i	2.34397	+	0.688251i
$960$		0			0
$961$	−8.79268	+	19.2533i	−0.283635	+	0.621074i
$962$		0			0
$963$	4.52699	+	2.90932i	0.145880	+	0.0937516i
$964$		0			0
$965$	−25.4610			−0.819618
$966$		0			0
$967$	23.9400			0.769858			0.384929	−	0.922946i	$-0.374226\pi$
$967$	23.9400			0.769858			0.384929	+	0.922946i	$0.374226\pi$
$968$		0			0
$969$	−0.682815	−	0.438818i	−0.0219352	−	0.0140969i
$970$		0			0
$971$	21.2660	−	46.5659i	0.682457	−	1.49437i	−0.177562	−	0.984110i	$-0.556821\pi$
$971$	21.2660	−	46.5659i	0.682457	−	1.49437i	0.860019	−	0.510262i	$-0.170452\pi$
$972$		0			0
$973$	44.1451	+	12.9622i	1.41523	+	0.415548i
$974$		0			0
$975$	1.03312	+	2.26223i	0.0330865	+	0.0724492i
$976$		0			0
$977$	3.82983	−	4.41985i	0.122527	−	0.141404i	−0.691172	−	0.722691i	$-0.742905\pi$
$977$	3.82983	−	4.41985i	0.122527	−	0.141404i	0.813699	+	0.581287i	$0.197451\pi$
$978$		0			0
$979$	−46.3964	+	13.6232i	−1.48283	+	0.435400i
$980$		0			0
$981$	−31.5501	+	20.2760i	−1.00732	+	0.647364i
$982$		0			0
$983$	−5.25276	−	36.5338i	−0.167537	−	1.16525i	−0.883954	−	0.467574i	$-0.845128\pi$
$983$	−5.25276	−	36.5338i	−0.167537	−	1.16525i	0.716417	−	0.697673i	$-0.245781\pi$
$984$		0			0
$985$	1.75662	−	12.2176i	0.0559707	−	0.389285i
$986$		0			0
$987$	3.40068	+	3.92459i	0.108245	+	0.124921i
$988$		0			0
$989$	−11.6205	−	20.2310i	−0.369510	−	0.643307i
$990$		0			0
$991$	25.7157	+	29.6775i	0.816885	+	0.942736i	0.999179	−	0.0405085i	$-0.0128978\pi$
$991$	25.7157	+	29.6775i	0.816885	+	0.942736i	−0.182294	+	0.983244i	$0.558352\pi$
$992$		0			0
$993$	1.89587	−	13.1861i	0.0601637	−	0.418448i
$994$		0			0
$995$	4.68933	+	32.6150i	0.148662	+	1.03396i
$996$		0			0
$997$	25.8118	−	16.5882i	0.817468	−	0.525354i	−0.0638053	−	0.997962i	$-0.520324\pi$
$997$	25.8118	−	16.5882i	0.817468	−	0.525354i	0.881273	+	0.472608i	$0.156687\pi$
$998$		0			0
$999$	6.34999	−	1.86453i	0.200905	−	0.0589910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.13.1	✓	20
3.2	odd	2		828.2.q.a.289.1		20
4.3	odd	2		368.2.m.d.289.2		20
23.4	even	11		2116.2.a.j.1.5		10
23.16	even	11	inner	92.2.e.a.85.1	yes	20
23.19	odd	22		2116.2.a.i.1.5		10
69.62	odd	22		828.2.q.a.361.1		20
92.19	even	22		8464.2.a.cd.1.6		10
92.27	odd	22		8464.2.a.ce.1.6		10
92.39	odd	22		368.2.m.d.177.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.13.1	✓	20	1.1	even	1	trivial
92.2.e.a.85.1	yes	20	23.16	even	11	inner
368.2.m.d.177.2		20	92.39	odd	22
368.2.m.d.289.2		20	4.3	odd	2
828.2.q.a.289.1		20	3.2	odd	2
828.2.q.a.361.1		20	69.62	odd	22
2116.2.a.i.1.5		10	23.19	odd	22
2116.2.a.j.1.5		10	23.4	even	11
8464.2.a.cd.1.6		10	92.19	even	22
8464.2.a.ce.1.6		10	92.27	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)

\(f(q)\)	\(=\)	\(q+(-0.368621 - 0.236898i) q^{3} +(0.781296 - 1.71080i) q^{5} +(4.72847 + 1.38840i) q^{7} +(-1.16648 - 2.55425i) q^{9} +O(q^{10})\)	\(q+(-0.368621 - 0.236898i) q^{3} +(0.781296 - 1.71080i) q^{5} +(4.72847 + 1.38840i) q^{7} +(-1.16648 - 2.55425i) q^{9} +(-2.86466 + 3.30599i) q^{11} +(-3.72299 + 1.09317i) q^{13} +(-0.693287 + 0.445548i) q^{15} +(-0.170460 - 1.18558i) q^{17} +(-0.220090 + 1.53076i) q^{19} +(-1.41410 - 1.63196i) q^{21} +(-4.25781 - 2.20705i) q^{23} +(0.957892 + 1.10547i) q^{25} +(-0.362184 + 2.51905i) q^{27} +(0.772612 + 5.37364i) q^{29} +(-2.63810 + 1.69540i) q^{31} +(1.83915 - 0.540024i) q^{33} +(6.06962 - 7.00471i) q^{35} +(-1.08028 - 2.36547i) q^{37} +(1.63134 + 0.479005i) q^{39} +(4.38557 - 9.60306i) q^{41} +(4.09254 + 2.63012i) q^{43} -5.28117 q^{45} -2.40483 q^{47} +(14.5420 + 9.34557i) q^{49} +(-0.218025 + 0.477409i) q^{51} +(-10.1568 - 2.98231i) q^{53} +(3.41774 + 7.48381i) q^{55} +(0.443765 - 0.512132i) q^{57} +(5.25467 - 1.54291i) q^{59} +(8.58911 - 5.51989i) q^{61} +(-1.96936 - 13.6972i) q^{63} +(-1.03857 + 7.22338i) q^{65} +(-6.95204 - 8.02308i) q^{67} +(1.04667 + 1.82223i) q^{69} +(0.461121 + 0.532163i) q^{71} +(-0.964609 + 6.70901i) q^{73} +(-0.0912159 - 0.634420i) q^{75} +(-18.1355 + 11.6550i) q^{77} +(-1.13462 + 0.333154i) q^{79} +(-4.78628 + 5.52366i) q^{81} +(-2.80407 - 6.14005i) q^{83} +(-2.16146 - 0.634662i) q^{85} +(0.988203 - 2.16386i) q^{87} +(9.29920 + 5.97623i) q^{89} -19.1218 q^{91} +1.37410 q^{93} +(2.44687 + 1.57251i) q^{95} +(3.84506 - 8.41951i) q^{97} +(11.7859 + 3.46065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 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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