LMFDB - Embedded newform 231.2.g.a.197.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(197,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("231.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.g (of order $2$, degree $1$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.21
Character	$\chi$	$=$	231.197
Dual form			231.2.g.a.197.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30127 q^{2} +(-0.220342 - 1.71798i) q^{3} +3.29586 q^{4} +1.52521i q^{5} +(-0.507068 - 3.95354i) q^{6} -1.00000i q^{7} +2.98213 q^{8} +(-2.90290 + 0.757087i) q^{9} +O(q^{10})$	\(q+2.30127 q^{2} +(-0.220342 - 1.71798i) q^{3} +3.29586 q^{4} +1.52521i q^{5} +(-0.507068 - 3.95354i) q^{6} -1.00000i q^{7} +2.98213 q^{8} +(-2.90290 + 0.757087i) q^{9} +3.50993i q^{10} +(2.56112 + 2.10729i) q^{11} +(-0.726218 - 5.66222i) q^{12} -2.11441i q^{13} -2.30127i q^{14} +(2.62028 - 0.336069i) q^{15} +0.270983 q^{16} -7.10985 q^{17} +(-6.68036 + 1.74226i) q^{18} -1.02488i q^{19} +5.02689i q^{20} +(-1.71798 + 0.220342i) q^{21} +(5.89383 + 4.84946i) q^{22} +7.02437i q^{23} +(-0.657091 - 5.12324i) q^{24} +2.67372 q^{25} -4.86583i q^{26} +(1.94029 + 4.82030i) q^{27} -3.29586i q^{28} -0.896606 q^{29} +(6.02999 - 0.773388i) q^{30} -2.10128 q^{31} -5.34066 q^{32} +(3.05596 - 4.86427i) q^{33} -16.3617 q^{34} +1.52521 q^{35} +(-9.56755 + 2.49525i) q^{36} +6.44151 q^{37} -2.35853i q^{38} +(-3.63251 + 0.465894i) q^{39} +4.54839i q^{40} +4.95013 q^{41} +(-3.95354 + 0.507068i) q^{42} -4.22582i q^{43} +(8.44109 + 6.94535i) q^{44} +(-1.15472 - 4.42754i) q^{45} +16.1650i q^{46} +1.52278i q^{47} +(-0.0597090 - 0.465542i) q^{48} -1.00000 q^{49} +6.15297 q^{50} +(1.56660 + 12.2146i) q^{51} -6.96880i q^{52} -12.9241i q^{53} +(4.46514 + 11.0928i) q^{54} +(-3.21407 + 3.90625i) q^{55} -2.98213i q^{56} +(-1.76072 + 0.225824i) q^{57} -2.06334 q^{58} +4.69907i q^{59} +(8.63609 - 1.10764i) q^{60} -1.83082i q^{61} -4.83562 q^{62} +(0.757087 + 2.90290i) q^{63} -12.8323 q^{64} +3.22492 q^{65} +(7.03260 - 11.1940i) q^{66} -11.5985 q^{67} -23.4331 q^{68} +(12.0677 - 1.54777i) q^{69} +3.50993 q^{70} -7.36880i q^{71} +(-8.65683 + 2.25774i) q^{72} -13.2481i q^{73} +14.8237 q^{74} +(-0.589135 - 4.59340i) q^{75} -3.37786i q^{76} +(2.10729 - 2.56112i) q^{77} +(-8.35939 + 1.07215i) q^{78} -9.00843i q^{79} +0.413307i q^{80} +(7.85364 - 4.39549i) q^{81} +11.3916 q^{82} +10.2668 q^{83} +(-5.66222 + 0.726218i) q^{84} -10.8440i q^{85} -9.72478i q^{86} +(0.197560 + 1.54035i) q^{87} +(7.63759 + 6.28423i) q^{88} +14.6773i q^{89} +(-2.65733 - 10.1890i) q^{90} -2.11441 q^{91} +23.1513i q^{92} +(0.463001 + 3.60995i) q^{93} +3.50434i q^{94} +1.56316 q^{95} +(1.17677 + 9.17514i) q^{96} -2.68418 q^{97} -2.30127 q^{98} +(-9.03006 - 4.17827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	2.30127			1.62725			0.813623	−	0.581392i	$-0.197492\pi$
$2$	2.30127			1.62725			0.813623	+	0.581392i	$0.197492\pi$
$3$	−0.220342	−	1.71798i	−0.127215	−	0.991875i
$3$	−0.220342	−	1.71798i	−0.127215	−	0.991875i
$4$	3.29586			1.64793
$5$			1.52521i			0.682096i	0.940046	+	0.341048i	$0.110782\pi$
$5$			1.52521i			0.682096i	−0.940046	+	0.341048i	$0.889218\pi$
$6$	−0.507068	−	3.95354i	−0.207010	−	1.61403i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.98213			1.05434
$9$	−2.90290	+	0.757087i	−0.967633	+	0.252362i
$10$			3.50993i			1.10994i
$11$	2.56112	+	2.10729i	0.772206	+	0.635373i
$11$	2.56112	+	2.10729i	0.772206	+	0.635373i
$12$	−0.726218	−	5.66222i	−0.209641	−	1.63454i
$13$		−	2.11441i		−	0.586431i	−0.956046	−	0.293216i	$-0.905275\pi$
$13$		−	2.11441i		−	0.586431i	0.956046	−	0.293216i	$-0.0947254\pi$
$14$		−	2.30127i		−	0.615041i
$15$	2.62028	−	0.336069i	0.676554	−	0.0867727i
$16$	0.270983			0.0677457
$17$	−7.10985			−1.72439			−0.862196	−	0.506574i	$-0.830912\pi$
$17$	−7.10985			−1.72439			−0.862196	+	0.506574i	$0.830912\pi$
$18$	−6.68036	+	1.74226i	−1.57458	+	0.410656i
$19$		−	1.02488i		−	0.235123i	−0.993066	−	0.117562i	$-0.962492\pi$
$19$		−	1.02488i		−	0.235123i	0.993066	−	0.117562i	$-0.0375078\pi$
$20$			5.02689i			1.12405i
$21$	−1.71798	+	0.220342i	−0.374894	+	0.0480827i
$22$	5.89383	+	4.84946i	1.25657	+	1.03391i
$23$			7.02437i			1.46468i	0.680938	+	0.732341i	$0.261572\pi$
$23$			7.02437i			1.46468i	−0.680938	+	0.732341i	$0.738428\pi$
$24$	−0.657091	−	5.12324i	−0.134128	−	1.04578i
$25$	2.67372			0.534745
$26$		−	4.86583i		−	0.954268i
$27$	1.94029	+	4.82030i	0.373409	+	0.927667i
$28$		−	3.29586i		−	0.622859i
$29$	−0.896606			−0.166496			−0.0832478	−	0.996529i	$-0.526529\pi$
$29$	−0.896606			−0.166496			−0.0832478	+	0.996529i	$0.526529\pi$
$30$	6.02999	−	0.773388i	1.10092	−	0.141201i
$31$	−2.10128			−0.377401			−0.188701	−	0.982035i	$-0.560428\pi$
$31$	−2.10128			−0.377401			−0.188701	+	0.982035i	$0.560428\pi$
$32$	−5.34066			−0.944105
$33$	3.05596	−	4.86427i	0.531975	−	0.846760i
$34$	−16.3617			−2.80601
$35$	1.52521			0.257808
$36$	−9.56755	+	2.49525i	−1.59459	+	0.415876i
$37$	6.44151			1.05898			0.529489	−	0.848317i	$-0.322384\pi$
$37$	6.44151			1.05898			0.529489	+	0.848317i	$0.322384\pi$
$38$		−	2.35853i		−	0.382604i
$39$	−3.63251	+	0.465894i	−0.581667	+	0.0746027i
$40$			4.54839i			0.719164i
$41$	4.95013			0.773081			0.386540	−	0.922273i	$-0.373670\pi$
$41$	4.95013			0.773081			0.386540	+	0.922273i	$0.373670\pi$
$42$	−3.95354	+	0.507068i	−0.610044	+	0.0782424i
$43$		−	4.22582i		−	0.644432i	−0.946666	−	0.322216i	$-0.895572\pi$
$43$		−	4.22582i		−	0.644432i	0.946666	−	0.322216i	$-0.104428\pi$
$44$	8.44109	+	6.94535i	1.27254	+	1.04705i
$45$	−1.15472	−	4.42754i	−0.172135	−	0.660019i
$46$			16.1650i			2.38340i
$47$			1.52278i			0.222120i	0.993814	+	0.111060i	$0.0354247\pi$
$47$			1.52278i			0.222120i	−0.993814	+	0.111060i	$0.964575\pi$
$48$	−0.0597090	−	0.465542i	−0.00861825	−	0.0671953i
$49$	−1.00000			−0.142857
$50$	6.15297			0.870161
$51$	1.56660	+	12.2146i	0.219368	+	1.71038i
$52$		−	6.96880i		−	0.966398i
$53$		−	12.9241i		−	1.77526i	−0.460556	−	0.887631i	$-0.652350\pi$
$53$		−	12.9241i		−	1.77526i	0.460556	−	0.887631i	$-0.347650\pi$
$54$	4.46514	+	11.0928i	0.607629	+	1.50954i
$55$	−3.21407	+	3.90625i	−0.433385	+	0.526719i
$56$		−	2.98213i		−	0.398504i
$57$	−1.76072	+	0.225824i	−0.233213	+	0.0299112i
$58$	−2.06334			−0.270929
$59$			4.69907i			0.611767i	0.952069	+	0.305884i	$0.0989518\pi$
$59$			4.69907i			0.611767i	−0.952069	+	0.305884i	$0.901048\pi$
$60$	8.63609	−	1.10764i	1.11492	−	0.142995i
$61$		−	1.83082i		−	0.234413i	−0.993108	−	0.117206i	$-0.962606\pi$
$61$		−	1.83082i		−	0.234413i	0.993108	−	0.117206i	$-0.0373939\pi$
$62$	−4.83562			−0.614125
$63$	0.757087	+	2.90290i	0.0953840	+	0.365731i
$64$	−12.8323			−1.60404
$65$	3.22492			0.400003
$66$	7.03260	−	11.1940i	0.865654	−	1.37789i
$67$	−11.5985			−1.41698			−0.708489	−	0.705722i	$-0.750623\pi$
$67$	−11.5985			−1.41698			−0.708489	+	0.705722i	$0.750623\pi$
$68$	−23.4331			−2.84168
$69$	12.0677	−	1.54777i	1.45278	−	0.186329i
$70$	3.50993			0.419517
$71$		−	7.36880i		−	0.874515i	−0.899336	−	0.437258i	$-0.855950\pi$
$71$		−	7.36880i		−	0.874515i	0.899336	−	0.437258i	$-0.144050\pi$
$72$	−8.65683	+	2.25774i	−1.02022	+	0.266077i
$73$		−	13.2481i		−	1.55057i	−0.631610	−	0.775286i	$-0.717606\pi$
$73$		−	13.2481i		−	1.55057i	0.631610	−	0.775286i	$-0.282394\pi$
$74$	14.8237			1.72322
$75$	−0.589135	−	4.59340i	−0.0680274	−	0.530400i
$76$		−	3.37786i		−	0.387467i
$77$	2.10729	−	2.56112i	0.240148	−	0.291866i
$78$	−8.35939	+	1.07215i	−0.946515	+	0.121397i
$79$		−	9.00843i		−	1.01353i	−0.862085	−	0.506764i	$-0.830842\pi$
$79$		−	9.00843i		−	1.01353i	0.862085	−	0.506764i	$-0.169158\pi$
$80$			0.413307i			0.0462091i
$81$	7.85364	−	4.39549i	0.872626	−	0.488388i
$82$	11.3916			1.25799
$83$	10.2668			1.12692			0.563462	−	0.826142i	$-0.309469\pi$
$83$	10.2668			1.12692			0.563462	+	0.826142i	$0.309469\pi$
$84$	−5.66222	+	0.726218i	−0.617799	+	0.0792369i
$85$		−	10.8440i		−	1.17620i
$86$		−	9.72478i		−	1.04865i
$87$	0.197560	+	1.54035i	0.0211807	+	0.165143i
$88$	7.63759	+	6.28423i	0.814170	+	0.669901i
$89$			14.6773i			1.55580i	0.628391	+	0.777898i	$0.283714\pi$
$89$			14.6773i			1.55580i	−0.628391	+	0.777898i	$0.716286\pi$
$90$	−2.65733	−	10.1890i	−0.280107	−	1.07401i
$91$	−2.11441			−0.221650
$92$			23.1513i			2.41369i
$93$	0.463001	+	3.60995i	0.0480110	+	0.374335i
$94$			3.50434i			0.361445i
$95$	1.56316			0.160377
$96$	1.17677	+	9.17514i	0.120104	+	0.936434i
$97$	−2.68418			−0.272537			−0.136268	−	0.990672i	$-0.543511\pi$
$97$	−2.68418			−0.272537			−0.136268	+	0.990672i	$0.543511\pi$
$98$	−2.30127			−0.232464
$99$	−9.03006	−	4.17827i	−0.907556	−	0.419932i
$100$	8.81222			0.881222
$101$	−0.233074			−0.0231918			−0.0115959	−	0.999933i	$-0.503691\pi$
$101$	−0.233074			−0.0231918			−0.0115959	+	0.999933i	$0.503691\pi$
$102$	3.60518	+	28.1091i	0.356966	+	2.78321i
$103$	11.0143			1.08527			0.542634	−	0.839969i	$-0.317427\pi$
$103$	11.0143			1.08527			0.542634	+	0.839969i	$0.317427\pi$
$104$		−	6.30545i		−	0.618300i
$105$	−0.336069	−	2.62028i	−0.0327970	−	0.255714i
$106$		−	29.7419i		−	2.88879i
$107$	−6.04114			−0.584020			−0.292010	−	0.956415i	$-0.594324\pi$
$107$	−6.04114			−0.584020			−0.292010	+	0.956415i	$0.594324\pi$
$108$	6.39493	+	15.8870i	0.615353	+	1.52873i
$109$			3.42334i			0.327896i	0.986469	+	0.163948i	$0.0524229\pi$
$109$			3.42334i			0.327896i	−0.986469	+	0.163948i	$0.947577\pi$
$110$	−7.39646	+	8.98935i	−0.705225	+	0.857101i
$111$	−1.41934	−	11.0664i	−0.134718	−	1.05037i
$112$		−	0.270983i		−	0.0256055i
$113$		−	13.6987i		−	1.28867i	−0.764745	−	0.644334i	$-0.777135\pi$
$113$		−	13.6987i		−	1.28867i	0.764745	−	0.644334i	$-0.222865\pi$
$114$	−4.05190	+	0.519684i	−0.379495	+	0.0486729i
$115$	−10.7137			−0.999054
$116$	−2.95509			−0.274373
$117$	1.60079	+	6.13791i	0.147993	+	0.567450i
$118$			10.8139i			0.995496i
$119$			7.10985i			0.651759i
$120$	7.81404	−	1.00220i	0.713321	−	0.0914883i
$121$	2.11863	+	10.7940i	0.192603	+	0.981277i
$122$		−	4.21323i		−	0.381448i
$123$	−1.09072	−	8.50422i	−0.0983473	−	0.766799i
$124$	−6.92553			−0.621931
$125$			11.7041i			1.04684i
$126$	1.74226	+	6.68036i	0.155213	+	0.595134i
$127$			15.5245i			1.37758i	0.724962	+	0.688789i	$0.241857\pi$
$127$			15.5245i			1.37758i	−0.724962	+	0.688789i	$0.758143\pi$
$128$	−18.8493			−1.66606
$129$	−7.25987	+	0.931129i	−0.639196	+	0.0819813i
$130$	7.42143			0.650903
$131$	20.2985			1.77349			0.886743	−	0.462262i	$-0.152962\pi$
$131$	20.2985			1.77349			0.886743	+	0.462262i	$0.152962\pi$
$132$	10.0720	−	16.0320i	0.876657	−	1.39540i
$133$	−1.02488			−0.0888683
$134$	−26.6912			−2.30577
$135$	−7.35198	+	2.95936i	−0.632758	+	0.254701i
$136$	−21.2025			−1.81810
$137$			0.547576i			0.0467825i	0.999726	+	0.0233913i	$0.00744635\pi$
$137$			0.547576i			0.0467825i	−0.999726	+	0.0233913i	$0.992554\pi$
$138$	27.7711	−	3.56183i	2.36403	−	0.303204i
$139$			15.8142i			1.34134i	0.741756	+	0.670670i	$0.233993\pi$
$139$			15.8142i			1.34134i	−0.741756	+	0.670670i	$0.766007\pi$
$140$	5.02689			0.424850
$141$	2.61611	−	0.335533i	0.220316	−	0.0282570i
$142$		−	16.9576i		−	1.42305i
$143$	4.45568	−	5.41524i	0.372603	−	0.452845i
$144$	−0.786635	+	0.205158i	−0.0655529	+	0.0170965i
$145$		−	1.36752i		−	0.113566i
$146$		−	30.4875i		−	2.52316i
$147$	0.220342	+	1.71798i	0.0181735	+	0.141696i
$148$	21.2303			1.74512
$149$	−5.48221			−0.449121			−0.224560	−	0.974460i	$-0.572095\pi$
$149$	−5.48221			−0.449121			−0.224560	+	0.974460i	$0.572095\pi$
$150$	−1.35576	−	10.5707i	−0.110697	−	0.863091i
$151$			5.82393i			0.473945i	0.971516	+	0.236973i	$0.0761551\pi$
$151$			5.82393i			0.473945i	−0.971516	+	0.236973i	$0.923845\pi$
$152$		−	3.05633i		−	0.247901i
$153$	20.6392	−	5.38278i	1.66858	−	0.435172i
$154$	4.84946	−	5.89383i	0.390781	−	0.474938i
$155$		−	3.20490i		−	0.257424i
$156$	−11.9722	+	1.53552i	−0.958547	+	0.122940i
$157$	5.26407			0.420119			0.210059	−	0.977689i	$-0.432634\pi$
$157$	5.26407			0.420119			0.210059	+	0.977689i	$0.432634\pi$
$158$		−	20.7309i		−	1.64926i
$159$	−22.2033	+	2.84773i	−1.76084	+	0.225839i
$160$		−	8.14565i		−	0.643970i
$161$	7.02437			0.553598
$162$	18.0734	−	10.1152i	1.41998	−	0.794728i
$163$	9.28903			0.727573			0.363786	−	0.931482i	$-0.381484\pi$
$163$	9.28903			0.727573			0.363786	+	0.931482i	$0.381484\pi$
$164$	16.3149			1.27398
$165$	7.41905	+	4.66099i	0.577572	+	0.362858i
$166$	23.6267			1.83378
$167$	−18.4830			−1.43025			−0.715127	−	0.698994i	$-0.753631\pi$
$167$	−18.4830			−1.43025			−0.715127	+	0.698994i	$0.753631\pi$
$168$	−5.12324	+	0.657091i	−0.395267	+	0.0506956i
$169$	8.52928			0.656098
$170$		−	24.9551i		−	1.91397i
$171$	0.775923	+	2.97512i	0.0593363	+	0.227513i
$172$		−	13.9277i		−	1.06198i
$173$	−13.4014			−1.01889			−0.509444	−	0.860504i	$-0.670149\pi$
$173$	−13.4014			−1.01889			−0.509444	+	0.860504i	$0.670149\pi$
$174$	0.454641	+	3.54477i	0.0344662	+	0.268728i
$175$		−	2.67372i		−	0.202114i
$176$	0.694018	+	0.571040i	0.0523136	+	0.0430438i
$177$	8.07290	−	1.03541i	0.606797	−	0.0778258i
$178$			33.7766i			2.53166i
$179$			12.7007i			0.949292i	0.880177	+	0.474646i	$0.157424\pi$
$179$			12.7007i			0.949292i	−0.880177	+	0.474646i	$0.842576\pi$
$180$	−3.80580	−	14.5926i	−0.283667	−	1.08767i
$181$	−13.5816			−1.00951			−0.504757	−	0.863261i	$-0.668418\pi$
$181$	−13.5816			−1.00951			−0.504757	+	0.863261i	$0.668418\pi$
$182$	−4.86583			−0.360679
$183$	−3.14531	+	0.403408i	−0.232508	+	0.0298208i
$184$			20.9476i			1.54428i
$185$			9.82468i			0.722325i
$186$	1.06549	+	8.30749i	0.0781257	+	0.609135i
$187$	−18.2092	−	14.9825i	−1.33159	−	1.09563i
$188$			5.01888i			0.366039i
$189$	4.82030	−	1.94029i	0.350625	−	0.141135i
$190$	3.59726			0.260973
$191$		−	12.8031i		−	0.926400i	−0.886254	−	0.463200i	$-0.846701\pi$
$191$		−	12.8031i		−	0.926400i	0.886254	−	0.463200i	$-0.153299\pi$
$192$	2.82750	+	22.0456i	0.204057	+	1.59100i
$193$			10.6052i			0.763380i	0.924290	+	0.381690i	$0.124658\pi$
$193$			10.6052i			0.763380i	−0.924290	+	0.381690i	$0.875342\pi$
$194$	−6.17702			−0.443484
$195$	−0.710588	−	5.54035i	−0.0508862	−	0.396753i
$196$	−3.29586			−0.235419
$197$	2.72344			0.194037			0.0970185	−	0.995283i	$-0.469069\pi$
$197$	2.72344			0.194037			0.0970185	+	0.995283i	$0.469069\pi$
$198$	−20.7807	−	9.61534i	−1.47682	−	0.683333i
$199$	17.8466			1.26511			0.632557	−	0.774514i	$-0.282005\pi$
$199$	17.8466			1.26511			0.632557	+	0.774514i	$0.282005\pi$
$200$	7.97340			0.563805
$201$	2.55563	+	19.9259i	0.180261	+	1.40547i
$202$	−0.536368			−0.0377387
$203$			0.896606i			0.0629294i
$204$	5.16331	+	40.2575i	0.361504	+	2.81859i
$205$			7.55001i			0.527315i
$206$	25.3469			1.76600
$207$	−5.31806	−	20.3910i	−0.369631	−	1.41727i
$208$		−	0.572968i		−	0.0397282i
$209$	2.15972	−	2.62483i	0.149391	−	0.181564i
$210$	−0.773388	−	6.02999i	−0.0533688	−	0.416109i
$211$			20.2305i			1.39272i	0.717691	+	0.696362i	$0.245199\pi$
$211$			20.2305i			1.39272i	−0.717691	+	0.696362i	$0.754801\pi$
$212$		−	42.5960i		−	2.92551i
$213$	−12.6594	+	1.62366i	−0.867410	+	0.111251i
$214$	−13.9023			−0.950344
$215$	6.44529			0.439565
$216$	5.78621	+	14.3748i	0.393702	+	0.978079i
$217$			2.10128i			0.142644i
$218$			7.87803i			0.533568i
$219$	−22.7599	+	2.91912i	−1.53797	+	0.197256i
$220$	−10.5931	+	12.8745i	−0.714189	+	0.867996i
$221$			15.0331i			1.01124i
$222$	−3.26629	−	25.4668i	−0.219219	−	1.70922i
$223$	−9.10609			−0.609789			−0.304894	−	0.952386i	$-0.598621\pi$
$223$	−9.10609			−0.609789			−0.304894	+	0.952386i	$0.598621\pi$
$224$			5.34066i			0.356838i
$225$	−7.76155	+	2.02424i	−0.517436	+	0.134949i
$226$		−	31.5245i		−	2.09698i
$227$	−3.65538			−0.242616			−0.121308	−	0.992615i	$-0.538709\pi$
$227$	−3.65538			−0.242616			−0.121308	+	0.992615i	$0.538709\pi$
$228$	−5.80309	+	0.744286i	−0.384319	+	0.0492916i
$229$	−17.4304			−1.15183			−0.575917	−	0.817508i	$-0.695355\pi$
$229$	−17.4304			−1.15183			−0.575917	+	0.817508i	$0.695355\pi$
$230$	−24.6551			−1.62571
$231$	−4.86427	−	3.05596i	−0.320045	−	0.201067i
$232$	−2.67380			−0.175543
$233$	19.1495			1.25453			0.627263	−	0.778807i	$-0.284175\pi$
$233$	19.1495			1.25453			0.627263	+	0.778807i	$0.284175\pi$
$234$	3.68386	+	14.1250i	0.240821	+	0.923381i
$235$	−2.32257			−0.151508
$236$			15.4875i			1.00815i
$237$	−15.4763	+	1.98494i	−1.00529	+	0.128936i
$238$			16.3617i			1.06057i
$239$	−20.6362			−1.33484			−0.667421	−	0.744681i	$-0.732602\pi$
$239$	−20.6362			−1.33484			−0.667421	+	0.744681i	$0.732602\pi$
$240$	0.710052	−	0.0910690i	0.0458336	−	0.00587848i
$241$		−	25.2963i		−	1.62948i	−0.579829	−	0.814738i	$-0.696881\pi$
$241$		−	25.2963i		−	1.62948i	0.579829	−	0.814738i	$-0.303119\pi$
$242$	4.87555	+	24.8401i	0.313412	+	1.59678i
$243$	−9.28185	−	12.5239i	−0.595431	−	0.803406i
$244$		−	6.03414i		−	0.386296i
$245$		−	1.52521i		−	0.0974423i
$246$	−2.51005	−	19.5705i	−0.160035	−	1.24777i
$247$	−2.16701			−0.137884
$248$	−6.26630			−0.397910
$249$	−2.26221	−	17.6381i	−0.143361	−	1.11777i
$250$			26.9343i			1.70347i
$251$			27.4991i			1.73573i	0.496802	+	0.867864i	$0.334508\pi$
$251$			27.4991i			1.73573i	−0.496802	+	0.867864i	$0.665492\pi$
$252$	2.49525	+	9.56755i	0.157186	+	0.602699i
$253$	−14.8024	+	17.9902i	−0.930619	+	1.13104i
$254$			35.7261i			2.24166i
$255$	−18.6298	+	2.38940i	−1.16665	+	0.149630i
$256$	−17.7128			−1.10705
$257$		−	8.04711i		−	0.501965i	−0.967992	−	0.250983i	$-0.919246\pi$
$257$		−	8.04711i		−	0.501965i	0.967992	−	0.250983i	$-0.0807537\pi$
$258$	−16.7070	+	2.14278i	−1.04013	+	0.133404i
$259$		−	6.44151i		−	0.400256i
$260$	10.6289			0.659177
$261$	2.60276	−	0.678809i	0.161107	−	0.0420172i
$262$	46.7124			2.88590
$263$	−9.16747			−0.565290			−0.282645	−	0.959225i	$-0.591212\pi$
$263$	−9.16747			−0.565290			−0.282645	+	0.959225i	$0.591212\pi$
$264$	9.11329	−	14.5059i	0.560884	−	0.892776i
$265$	19.7120			1.21090
$266$	−2.35853			−0.144611
$267$	25.2154	−	3.23404i	1.54315	−	0.197920i
$268$	−38.2269			−2.33508
$269$		−	8.69055i		−	0.529872i	−0.964266	−	0.264936i	$-0.914649\pi$
$269$		−	8.69055i		−	0.529872i	0.964266	−	0.264936i	$-0.0853509\pi$
$270$	−16.9189	+	6.81029i	−1.02965	+	0.414461i
$271$			19.7852i			1.20187i	0.799299	+	0.600933i	$0.205204\pi$
$271$			19.7852i			1.20187i	−0.799299	+	0.600933i	$0.794796\pi$
$272$	−1.92665			−0.116820
$273$	0.465894	+	3.63251i	0.0281972	+	0.219849i
$274$			1.26012i			0.0761267i
$275$	6.84771	+	5.63432i	0.412933	+	0.339762i
$276$	39.7735	−	5.10122i	2.39408	−	0.307058i
$277$		−	22.2802i		−	1.33869i	−0.742952	−	0.669345i	$-0.766575\pi$
$277$		−	22.2802i		−	1.33869i	0.742952	−	0.669345i	$-0.233425\pi$
$278$			36.3927i			2.18269i
$279$	6.09980	−	1.59085i	0.365186	−	0.0952418i
$280$	4.54839			0.271818
$281$	−18.0748			−1.07825			−0.539126	−	0.842225i	$-0.681245\pi$
$281$	−18.0748			−1.07825			−0.539126	+	0.842225i	$0.681245\pi$
$282$	6.02037	−	0.772154i	0.358508	−	0.0459811i
$283$		−	1.92131i		−	0.114210i	−0.998368	−	0.0571050i	$-0.981813\pi$
$283$		−	1.92131i		−	0.114210i	0.998368	−	0.0571050i	$-0.0181870\pi$
$284$		−	24.2865i		−	1.44114i
$285$	−0.344431	−	2.68547i	−0.0204023	−	0.159074i
$286$	10.2537	−	12.4620i	0.606316	−	0.736891i
$287$		−	4.95013i		−	0.292197i
$288$	15.5034	−	4.04335i	0.913547	−	0.238256i
$289$	33.5500			1.97353
$290$		−	3.14703i		−	0.184800i
$291$	0.591438	+	4.61135i	0.0346707	+	0.270322i
$292$		−	43.6639i		−	2.55524i
$293$	−22.7016			−1.32624			−0.663119	−	0.748514i	$-0.730768\pi$
$293$	−22.7016			−1.32624			−0.663119	+	0.748514i	$0.730768\pi$
$294$	0.507068	+	3.95354i	0.0295728	+	0.230575i
$295$	−7.16709			−0.417284
$296$	19.2095			1.11653
$297$	−5.18847	+	16.4341i	−0.301066	+	0.953603i
$298$	−12.6161			−0.730830
$299$	14.8524			0.858935
$300$	−1.94171	−	15.1392i	−0.112104	−	0.874063i
$301$	−4.22582			−0.243572
$302$			13.4025i			0.771225i
$303$	0.0513562	+	0.400416i	0.00295033	+	0.0230033i
$304$		−	0.277725i		−	0.0159286i
$305$	2.79240			0.159892
$306$	47.4964	−	12.3872i	2.71519	−	0.708132i
$307$			14.7302i			0.840698i	0.907362	+	0.420349i	$0.138092\pi$
$307$			14.7302i			0.840698i	−0.907362	+	0.420349i	$0.861908\pi$
$308$	6.94535	−	8.44109i	0.395748	−	0.480975i
$309$	−2.42691	−	18.9223i	−0.138062	−	1.07645i
$310$		−	7.37536i		−	0.418892i
$311$		−	12.4448i		−	0.705679i	−0.935684	−	0.352840i	$-0.885216\pi$
$311$		−	12.4448i		−	0.705679i	0.935684	−	0.352840i	$-0.114784\pi$
$312$	−10.8326	+	1.38936i	−0.613276	+	0.0786569i
$313$	8.09140			0.457353			0.228676	−	0.973502i	$-0.426560\pi$
$313$	8.09140			0.457353			0.228676	+	0.973502i	$0.426560\pi$
$314$	12.1141			0.683637
$315$	−4.42754	+	1.15472i	−0.249464	+	0.0650611i
$316$		−	29.6906i		−	1.67022i
$317$		−	0.498677i		−	0.0280085i	−0.999902	−	0.0140042i	$-0.995542\pi$
$317$		−	0.498677i		−	0.0280085i	0.999902	−	0.0140042i	$-0.00445783\pi$
$318$	−51.0959	+	6.55340i	−2.86532	+	0.367496i
$319$	−2.29631	−	1.88941i	−0.128569	−	0.105787i
$320$		−	19.5720i		−	1.09411i
$321$	1.33112	+	10.3786i	0.0742959	+	0.579274i
$322$	16.1650			0.900840
$323$			7.28674i			0.405445i
$324$	25.8845	−	14.4869i	1.43803	−	0.804830i
$325$		−	5.65334i		−	0.313591i
$326$	21.3766			1.18394
$327$	5.88122	−	0.754306i	0.325232	−	0.0417132i
$328$	14.7620			0.815092
$329$	1.52278			0.0839536
$330$	17.0733	+	10.7262i	0.939852	+	0.590459i
$331$	−1.42980			−0.0785887			−0.0392944	−	0.999228i	$-0.512511\pi$
$331$	−1.42980			−0.0785887			−0.0392944	+	0.999228i	$0.512511\pi$
$332$	33.8379			1.85709
$333$	−18.6991	+	4.87679i	−1.02470	+	0.267246i
$334$	−42.5344			−2.32738
$335$		−	17.6901i		−	0.966516i
$336$	−0.465542	+	0.0597090i	−0.0253974	+	0.00325739i
$337$		−	33.0147i		−	1.79843i	−0.437510	−	0.899214i	$-0.644139\pi$
$337$		−	33.0147i		−	1.79843i	0.437510	−	0.899214i	$-0.355861\pi$
$338$	19.6282			1.06763
$339$	−23.5341	+	3.01841i	−1.27820	+	0.163938i
$340$		−	35.7405i		−	1.93830i
$341$	−5.38162	−	4.42801i	−0.291431	−	0.239790i
$342$	1.78561	+	6.84657i	0.0965548	+	0.370220i
$343$			1.00000i			0.0539949i
$344$		−	12.6020i		−	0.679453i
$345$	2.36067	+	18.4058i	0.127094	+	0.990937i
$346$	−30.8403			−1.65798
$347$	−5.43521			−0.291777			−0.145889	−	0.989301i	$-0.546604\pi$
$347$	−5.43521			−0.291777			−0.145889	+	0.989301i	$0.546604\pi$
$348$	0.651132	+	5.07678i	0.0349043	+	0.272144i
$349$			34.0398i			1.82211i	0.412289	+	0.911053i	$0.364729\pi$
$349$			34.0398i			1.82211i	−0.412289	+	0.911053i	$0.635271\pi$
$350$		−	6.15297i		−	0.328890i
$351$	10.1921	−	4.10257i	0.544013	−	0.218979i
$352$	−13.6781	−	11.2543i	−0.729043	−	0.599858i
$353$		−	7.63300i		−	0.406264i	−0.979151	−	0.203132i	$-0.934888\pi$
$353$		−	7.63300i		−	0.406264i	0.979151	−	0.203132i	$-0.0651120\pi$
$354$	18.5780	−	2.38275i	0.987408	−	0.126642i
$355$	11.2390			0.596504
$356$			48.3745i			2.56384i
$357$	12.2146	−	1.56660i	0.646464	−	0.0829134i
$358$			29.2277i			1.54473i
$359$	21.8234			1.15180			0.575898	−	0.817521i	$-0.304652\pi$
$359$	21.8234			1.15180			0.575898	+	0.817521i	$0.304652\pi$
$360$	−3.44353	−	13.2035i	−0.181490	−	0.695886i
$361$	17.9496			0.944717
$362$	−31.2550			−1.64273
$363$	18.0771	−	6.01815i	0.948802	−	0.315871i
$364$	−6.96880			−0.365264
$365$	20.2062			1.05764
$366$	−7.23823	+	0.928353i	−0.378348	+	0.0485258i
$367$	1.88794			0.0985498			0.0492749	−	0.998785i	$-0.484309\pi$
$367$	1.88794			0.0985498			0.0492749	+	0.998785i	$0.484309\pi$
$368$			1.90348i			0.0992259i
$369$	−14.3697	+	3.74768i	−0.748058	+	0.195096i
$370$			22.6093i			1.17540i
$371$	−12.9241			−0.670986
$372$	1.52599	+	11.8979i	0.0791188	+	0.616878i
$373$			31.1495i			1.61286i	0.591329	+	0.806430i	$0.298603\pi$
$373$			31.1495i			1.61286i	−0.591329	+	0.806430i	$0.701397\pi$
$374$	−41.9043	−	34.4789i	−2.16682	−	1.78286i
$375$	20.1073	−	2.57890i	1.03834	−	0.133174i
$376$			4.54114i			0.234191i
$377$			1.89579i			0.0976382i
$378$	11.0928	−	4.46514i	0.570553	−	0.229662i
$379$	2.50428			0.128636			0.0643182	−	0.997929i	$-0.479513\pi$
$379$	2.50428			0.128636			0.0643182	+	0.997929i	$0.479513\pi$
$380$	5.15196			0.264290
$381$	26.6708	−	3.42071i	1.36638	−	0.175248i
$382$		−	29.4634i		−	1.50748i
$383$		−	5.76914i		−	0.294789i	−0.989078	−	0.147395i	$-0.952911\pi$
$383$		−	5.76914i		−	0.294789i	0.989078	−	0.147395i	$-0.0470887\pi$
$384$	4.15330	+	32.3827i	0.211947	+	1.65252i
$385$	3.90625	+	3.21407i	0.199081	+	0.163804i
$386$			24.4055i			1.24221i
$387$	3.19932	+	12.2671i	0.162630	+	0.623574i
$388$	−8.84667			−0.449122
$389$		−	26.4135i		−	1.33922i	−0.742715	−	0.669608i	$-0.766462\pi$
$389$		−	26.4135i		−	1.33922i	0.742715	−	0.669608i	$-0.233538\pi$
$390$	−1.63526	−	12.7499i	−0.0828045	−	0.645614i
$391$		−	49.9422i		−	2.52569i
$392$	−2.98213			−0.150620
$393$	−4.47262	−	34.8723i	−0.225614	−	1.75908i
$394$	6.26738			0.315746
$395$	13.7398			0.691324
$396$	−29.7618	−	13.7710i	−1.49559	−	0.692019i
$397$	11.1210			0.558145			0.279073	−	0.960270i	$-0.409973\pi$
$397$	11.1210			0.558145			0.279073	+	0.960270i	$0.409973\pi$
$398$	41.0700			2.05865
$399$	0.225824	+	1.76072i	0.0113054	+	0.0881463i
$400$	0.724533			0.0362266
$401$		−	5.92253i		−	0.295757i	−0.989006	−	0.147878i	$-0.952756\pi$
$401$		−	5.92253i		−	0.295757i	0.989006	−	0.147878i	$-0.0472444\pi$
$402$	5.88122	+	45.8550i	0.293328	+	2.28704i
$403$			4.44296i			0.221320i
$404$	−0.768181			−0.0382184
$405$	6.70407	+	11.9785i	0.333128	+	0.595215i
$406$			2.06334i			0.102402i
$407$	16.4975	+	13.5742i	0.817749	+	0.672846i
$408$	4.67182	+	36.4255i	0.231289	+	1.80333i
$409$		−	3.99012i		−	0.197299i	−0.995122	−	0.0986494i	$-0.968548\pi$
$409$		−	3.99012i		−	0.197299i	0.995122	−	0.0986494i	$-0.0314522\pi$
$410$			17.3746i			0.858072i
$411$	0.940723	−	0.120654i	0.0464024	−	0.00595143i
$412$	36.3015			1.78845
$413$	4.69907			0.231226
$414$	−12.2383	−	46.9253i	−0.601480	−	2.30625i
$415$			15.6590i			0.768671i
$416$			11.2923i			0.553652i
$417$	27.1684	−	3.48453i	1.33044	−	0.170638i
$418$	4.97011	−	6.04046i	0.243096	−	0.295449i
$419$			30.1554i			1.47319i	0.676336	+	0.736593i	$0.263567\pi$
$419$			30.1554i			1.47319i	−0.676336	+	0.736593i	$0.736433\pi$
$420$	−1.10764	−	8.63609i	−0.0540472	−	0.421398i
$421$	−19.9842			−0.973968			−0.486984	−	0.873411i	$-0.661903\pi$
$421$	−19.9842			−0.973968			−0.486984	+	0.873411i	$0.661903\pi$
$422$			46.5559i			2.26630i
$423$	−1.15288	−	4.42048i	−0.0560549	−	0.214931i
$424$		−	38.5414i		−	1.87174i
$425$	−19.0098			−0.922110
$426$	−29.1328	+	3.73648i	−1.41149	+	0.181033i
$427$	−1.83082			−0.0885997
$428$	−19.9108			−0.962424
$429$	−10.2850	−	6.46155i	−0.496567	−	0.311967i
$430$	14.8324			0.715280
$431$	−29.4972			−1.42083			−0.710414	−	0.703784i	$-0.751492\pi$
$431$	−29.4972			−1.42083			−0.710414	+	0.703784i	$0.751492\pi$
$432$	0.525785	+	1.30622i	0.0252969	+	0.0628454i
$433$	31.0547			1.49239			0.746197	−	0.665725i	$-0.231878\pi$
$433$	31.0547			1.49239			0.746197	+	0.665725i	$0.231878\pi$
$434$			4.83562i			0.232117i
$435$	−2.34936	+	0.301322i	−0.112643	+	0.0144473i
$436$			11.2828i			0.540350i
$437$	7.19913			0.344381
$438$	−52.3769	+	6.71769i	−2.50266	+	0.320984i
$439$		−	9.26372i		−	0.442133i	−0.975259	−	0.221067i	$-0.929046\pi$
$439$		−	9.26372i		−	0.442133i	0.975259	−	0.221067i	$-0.0709538\pi$
$440$	−9.58479	+	11.6490i	−0.456937	+	0.555342i
$441$	2.90290	−	0.757087i	0.138233	−	0.0360518i
$442$			34.5953i			1.64553i
$443$			11.2221i			0.533178i	0.963810	+	0.266589i	$0.0858966\pi$
$443$			11.2221i			0.533178i	−0.963810	+	0.266589i	$0.914103\pi$
$444$	−4.67795	−	36.4733i	−0.222005	−	1.73094i
$445$	−22.3861			−1.06120
$446$	−20.9556			−0.992277
$447$	1.20796	+	9.41833i	0.0571348	+	0.445472i
$448$			12.8323i			0.606269i
$449$			5.68959i			0.268508i	0.990947	+	0.134254i	$0.0428639\pi$
$449$			5.68959i			0.268508i	−0.990947	+	0.134254i	$0.957136\pi$
$450$	−17.8614	+	4.65833i	−0.841997	+	0.219596i
$451$	12.6779	+	10.4314i	0.596977	+	0.491194i
$452$		−	45.1491i		−	2.12363i
$453$	10.0054	−	1.28326i	0.470094	−	0.0602928i
$454$	−8.41203			−0.394796
$455$		−	3.22492i		−	0.151187i
$456$	−5.25070	+	0.673439i	−0.245887	+	0.0315367i
$457$		−	10.7329i		−	0.502062i	−0.967979	−	0.251031i	$-0.919230\pi$
$457$		−	10.7329i		−	0.502062i	0.967979	−	0.251031i	$-0.0807695\pi$
$458$	−40.1121			−1.87432
$459$	−13.7952	−	34.2716i	−0.643904	−	1.59966i
$460$	−35.3108			−1.64637
$461$	5.07909			0.236557			0.118278	−	0.992980i	$-0.462263\pi$
$461$	5.07909			0.236557			0.118278	+	0.992980i	$0.462263\pi$
$462$	−11.1940	−	7.03260i	−0.520793	−	0.327186i
$463$	6.23754			0.289883			0.144941	−	0.989440i	$-0.453701\pi$
$463$	6.23754			0.289883			0.144941	+	0.989440i	$0.453701\pi$
$464$	−0.242965			−0.0112794
$465$	−5.50595	+	0.706176i	−0.255332	+	0.0327481i
$466$	44.0683			2.04142
$467$		−	17.2105i		−	0.796406i	−0.917297	−	0.398203i	$-0.869634\pi$
$467$		−	17.2105i		−	0.796406i	0.917297	−	0.398203i	$-0.130366\pi$
$468$	5.27599	+	20.2297i	0.243883	+	0.935119i
$469$			11.5985i			0.535567i
$470$	−5.34486			−0.246540
$471$	−1.15990	−	9.04356i	−0.0534453	−	0.416705i
$472$			14.0133i			0.645013i
$473$	8.90505	−	10.8228i	0.409455	−	0.497634i
$474$	−35.6152	+	4.56789i	−1.63586	+	0.209810i
$475$		−	2.74024i		−	0.125731i
$476$			23.4331i			1.07405i
$477$	9.78467	+	37.5173i	0.448009	+	1.71780i
$478$	−47.4894			−2.17212
$479$	−1.76460			−0.0806267			−0.0403133	−	0.999187i	$-0.512836\pi$
$479$	−1.76460			−0.0806267			−0.0403133	+	0.999187i	$0.512836\pi$
$480$	−13.9941	+	1.79483i	−0.638738	+	0.0819225i
$481$		−	13.6200i		−	0.621018i
$482$		−	58.2137i		−	2.65156i
$483$	−1.54777	−	12.0677i	−0.0704258	−	0.549100i
$484$	6.98271	+	35.5757i	0.317396	+	1.61708i
$485$		−	4.09394i		−	0.185896i
$486$	−21.3601	−	28.8208i	−0.968913	−	1.30734i
$487$	0.582031			0.0263743			0.0131872	−	0.999913i	$-0.495802\pi$
$487$	0.582031			0.0263743			0.0131872	+	0.999913i	$0.495802\pi$
$488$		−	5.45976i		−	0.247152i
$489$	−2.04677	−	15.9583i	−0.0925580	−	0.721661i
$490$		−	3.50993i		−	0.158563i
$491$	36.0481			1.62683			0.813415	−	0.581684i	$-0.197606\pi$
$491$	36.0481			1.62683			0.813415	+	0.581684i	$0.197606\pi$
$492$	−3.59488	−	28.0287i	−0.162070	−	1.26363i
$493$	6.37474			0.287104
$494$	−4.98689			−0.224371
$495$	6.37276	−	13.7728i	0.286434	−	0.619040i
$496$	−0.569411			−0.0255673
$497$	−7.36880			−0.330536
$498$	−5.20596	−	40.5901i	−0.233284	−	1.81888i
$499$	−18.7776			−0.840601			−0.420300	−	0.907385i	$-0.638075\pi$
$499$	−18.7776			−0.840601			−0.420300	+	0.907385i	$0.638075\pi$
$500$			38.5750i			1.72513i
$501$	4.07258	+	31.7533i	0.181950	+	1.41863i
$502$			63.2830i			2.82446i
$503$	1.34937			0.0601655			0.0300827	−	0.999547i	$-0.490423\pi$
$503$	1.34937			0.0601655			0.0300827	+	0.999547i	$0.490423\pi$
$504$	2.25774	+	8.65683i	0.100568	+	0.385606i
$505$		−	0.355488i		−	0.0158190i
$506$	−34.0644	+	41.4004i	−1.51435	+	1.84047i
$507$	−1.87936	−	14.6531i	−0.0834654	−	0.650768i
$508$			51.1666i			2.27015i
$509$		−	10.8779i		−	0.482156i	−0.970506	−	0.241078i	$-0.922499\pi$
$509$		−	10.8779i		−	0.482156i	0.970506	−	0.241078i	$-0.0775010\pi$
$510$	−42.8723	+	5.49867i	−1.89842	+	0.243485i
$511$	−13.2481			−0.586061
$512$	−3.06344			−0.135386
$513$	4.94022	−	1.98856i	0.218116	−	0.0877973i
$514$		−	18.5186i		−	0.816821i
$515$			16.7991i			0.740258i
$516$	−23.9275	+	3.06887i	−1.05335	+	0.135100i
$517$	−3.20895	+	3.90002i	−0.141129	+	0.171523i
$518$		−	14.8237i		−	0.651315i
$519$	2.95289	+	23.0233i	0.129618	+	1.01061i
$520$	9.61716			0.421740
$521$		−	13.5457i		−	0.593447i	−0.954963	−	0.296723i	$-0.904106\pi$
$521$		−	13.5457i		−	0.593447i	0.954963	−	0.296723i	$-0.0958939\pi$
$522$	5.98965	−	1.56213i	0.262160	−	0.0683724i
$523$		−	16.6391i		−	0.727576i	−0.931482	−	0.363788i	$-0.881483\pi$
$523$		−	16.6391i		−	0.727576i	0.931482	−	0.363788i	$-0.118517\pi$
$524$	66.9010			2.92258
$525$	−4.59340	+	0.589135i	−0.200472	+	0.0257119i
$526$	−21.0968			−0.919866
$527$	14.9398			0.650788
$528$	0.828113	−	1.31813i	0.0360390	−	0.0573644i
$529$	−26.3417			−1.14529
$530$	45.3627			1.97043
$531$	−3.55761	−	13.6409i	−0.154387	−	0.591966i
$532$	−3.37786			−0.146449
$533$		−	10.4666i		−	0.453359i
$534$	58.0274	−	7.44242i	2.51109	−	0.322065i
$535$		−	9.21404i		−	0.398358i
$536$	−34.5882			−1.49398
$537$	21.8195	−	2.79850i	0.941579	−	0.120764i
$538$		−	19.9993i		−	0.862233i
$539$	−2.56112	−	2.10729i	−0.110315	−	0.0907675i
$540$	−24.2311	+	9.75364i	−1.04274	+	0.419730i
$541$			11.0867i			0.476654i	0.971185	+	0.238327i	$0.0765989\pi$
$541$			11.0867i			0.476654i	−0.971185	+	0.238327i	$0.923401\pi$
$542$			45.5312i			1.95573i
$543$	2.99261	+	23.3329i	0.128425	+	1.00131i
$544$	37.9713			1.62801
$545$	−5.22132			−0.223657
$546$	1.07215	+	8.35939i	0.0458838	+	0.357749i
$547$			30.6009i			1.30840i	0.756321	+	0.654201i	$0.226995\pi$
$547$			30.6009i			1.30840i	−0.756321	+	0.654201i	$0.773005\pi$
$548$			1.80473i			0.0770944i
$549$	1.38609	+	5.31469i	0.0591570	+	0.226826i
$550$	15.7585	+	12.9661i	0.671943	+	0.552877i
$551$			0.918913i			0.0391470i
$552$	35.9875	−	4.61565i	1.53173	−	0.196455i
$553$	−9.00843			−0.383078
$554$		−	51.2729i		−	2.17838i
$555$	16.8786	−	2.16480i	0.716456	−	0.0918904i
$556$			52.1213i			2.21043i
$557$	10.5555			0.447251			0.223625	−	0.974675i	$-0.428211\pi$
$557$	10.5555			0.447251			0.223625	+	0.974675i	$0.428211\pi$
$558$	14.0373	−	3.66099i	0.594247	−	0.154982i
$559$	−8.93512			−0.377915
$560$	0.413307			0.0174654
$561$	−21.7274	+	34.5842i	−0.917333	+	1.46015i
$562$	−41.5951			−1.75458
$563$	6.33993			0.267196			0.133598	−	0.991036i	$-0.457347\pi$
$563$	6.33993			0.267196			0.133598	+	0.991036i	$0.457347\pi$
$564$	8.62232	−	1.10587i	0.363065	−	0.0465656i
$565$	20.8935			0.878995
$566$		−	4.42146i		−	0.185848i
$567$	−4.39549	−	7.85364i	−0.184593	−	0.329822i
$568$		−	21.9747i		−	0.922040i
$569$	−35.0699			−1.47021			−0.735103	−	0.677956i	$-0.762866\pi$
$569$	−35.0699			−1.47021			−0.735103	+	0.677956i	$0.762866\pi$
$570$	−0.792629	−	6.18001i	−0.0331996	−	0.258852i
$571$			23.7378i			0.993398i	0.867923	+	0.496699i	$0.165455\pi$
$571$			23.7378i			0.993398i	−0.867923	+	0.496699i	$0.834545\pi$
$572$	14.6853	−	17.8479i	0.614023	−	0.746258i
$573$	−21.9954	+	2.82107i	−0.918873	+	0.117852i
$574$		−	11.3916i		−	0.475476i
$575$			18.7812i			0.783231i
$576$	37.2508	−	9.71516i	1.55212	−	0.404798i
$577$	21.3165			0.887419			0.443710	−	0.896171i	$-0.353662\pi$
$577$	21.3165			0.887419			0.443710	+	0.896171i	$0.353662\pi$
$578$	77.2077			3.21142
$579$	18.2195	−	2.33678i	0.757177	−	0.0971132i
$580$		−	4.50714i		−	0.187149i
$581$		−	10.2668i		−	0.425937i
$582$	1.36106	+	10.6120i	0.0564178	+	0.439881i
$583$	27.2349	−	33.1001i	1.12795	−	1.37087i
$584$		−	39.5076i		−	1.63484i
$585$	−9.36163	+	2.44155i	−0.387056	+	0.100946i
$586$	−52.2425			−2.15812
$587$		−	38.7501i		−	1.59939i	−0.600408	−	0.799694i	$-0.704995\pi$
$587$		−	38.7501i		−	1.59939i	0.600408	−	0.799694i	$-0.295005\pi$
$588$	0.726218	+	5.66222i	0.0299487	+	0.233506i
$589$			2.15356i			0.0887359i
$590$	−16.4934			−0.679024
$591$	−0.600089	−	4.67881i	−0.0246844	−	0.192460i
$592$	1.74554			0.0717412
$593$	3.29293			0.135224			0.0676122	−	0.997712i	$-0.478462\pi$
$593$	3.29293			0.135224			0.0676122	+	0.997712i	$0.478462\pi$
$594$	−11.9401	+	37.8194i	−0.489908	+	1.55175i
$595$	−10.8440			−0.444562
$596$	−18.0686			−0.740120
$597$	−3.93237	−	30.6601i	−0.160941	−	1.25484i
$598$	34.1794			1.39770
$599$			33.3112i			1.36106i	0.732720	+	0.680530i	$0.238251\pi$
$599$			33.3112i			1.36106i	−0.732720	+	0.680530i	$0.761749\pi$
$600$	−1.75688	−	13.6981i	−0.0717243	−	0.559224i
$601$		−	20.4925i		−	0.835907i	−0.908469	−	0.417953i	$-0.862748\pi$
$601$		−	20.4925i		−	0.835907i	0.908469	−	0.417953i	$-0.137252\pi$
$602$	−9.72478			−0.396352
$603$	33.6692	−	8.78105i	1.37111	−	0.357592i
$604$			19.1949i			0.781029i
$605$	−16.4632	+	3.23136i	−0.669325	+	0.131374i
$606$	0.118185	+	0.921468i	0.00480092	+	0.0374321i
$607$		−	37.9070i		−	1.53860i	−0.638890	−	0.769298i	$-0.720606\pi$
$607$		−	37.9070i		−	1.53860i	0.638890	−	0.769298i	$-0.279394\pi$
$608$			5.47353i			0.221981i
$609$	1.54035	−	0.197560i	0.0624181	−	0.00800555i
$610$	6.42607			0.260184
$611$	3.21978			0.130258
$612$	68.0239	−	17.7409i	2.74970	−	0.717133i
$613$		−	16.8709i		−	0.681410i	−0.940170	−	0.340705i	$-0.889334\pi$
$613$		−	16.8709i		−	0.681410i	0.940170	−	0.340705i	$-0.110666\pi$
$614$			33.8983i			1.36802i
$615$	12.9707	−	1.66359i	0.523031	−	0.0670823i
$616$	6.28423	−	7.63759i	0.253199	−	0.307727i
$617$			3.35194i			0.134944i	0.997721	+	0.0674721i	$0.0214934\pi$
$617$			3.35194i			0.134944i	−0.997721	+	0.0674721i	$0.978507\pi$
$618$	−5.58499	−	43.5453i	−0.224661	−	1.75165i
$619$	27.7492			1.11534			0.557668	−	0.830064i	$-0.311696\pi$
$619$	27.7492			1.11534			0.557668	+	0.830064i	$0.311696\pi$
$620$		−	10.5629i		−	0.424217i
$621$	−33.8595	+	13.6293i	−1.35874	+	0.546926i
$622$		−	28.6389i		−	1.14831i
$623$	14.6773			0.588035
$624$	−0.984347	+	0.126249i	−0.0394054	+	0.00505401i
$625$	−4.48259			−0.179304
$626$	18.6205			0.744226
$627$	−4.98529	−	3.13199i	−0.199093	−	0.125080i
$628$	17.3497			0.692327
$629$	−45.7982			−1.82609
$630$	−10.1890	+	2.65733i	−0.405939	+	0.105870i
$631$	18.9136			0.752938			0.376469	−	0.926429i	$-0.377138\pi$
$631$	18.9136			0.752938			0.376469	+	0.926429i	$0.377138\pi$
$632$		−	26.8644i		−	1.06861i
$633$	34.7555	−	4.45763i	1.38141	−	0.177175i
$634$		−	1.14759i		−	0.0455767i
$635$	−23.6782			−0.939640
$636$	−73.1791	+	9.38572i	−2.90174	+	0.372168i
$637$			2.11441i			0.0837759i
$638$	−5.28444	−	4.34805i	−0.209213	−	0.172141i
$639$	5.57882	+	21.3909i	0.220695	+	0.846210i
$640$		−	28.7492i		−	1.13641i
$641$		−	19.0921i		−	0.754094i	−0.926194	−	0.377047i	$-0.876940\pi$
$641$		−	19.0921i		−	0.754094i	0.926194	−	0.377047i	$-0.123060\pi$
$642$	3.06327	+	23.8839i	0.120898	+	0.942622i
$643$	37.0654			1.46172			0.730858	−	0.682530i	$-0.239120\pi$
$643$	37.0654			1.46172			0.730858	+	0.682530i	$0.239120\pi$
$644$	23.1513			0.912291
$645$	−1.42017	−	11.0729i	−0.0559191	−	0.435993i
$646$			16.7688i			0.659759i
$647$			7.51779i			0.295555i	0.989021	+	0.147777i	$0.0472119\pi$
$647$			7.51779i			0.295555i	−0.989021	+	0.147777i	$0.952788\pi$
$648$	23.4206	−	13.1080i	0.920048	−	0.514929i
$649$	−9.90232	+	12.0349i	−0.388700	+	0.472410i
$650$		−	13.0099i		−	0.510290i
$651$	3.60995	−	0.463001i	0.141485	−	0.0181465i
$652$	30.6154			1.19899
$653$		−	17.0541i		−	0.667377i	−0.942683	−	0.333688i	$-0.891707\pi$
$653$		−	17.0541i		−	0.667377i	0.942683	−	0.333688i	$-0.108293\pi$
$654$	13.5343	−	1.73587i	0.529233	−	0.0678777i
$655$			30.9595i			1.20969i
$656$	1.34140			0.0523729
$657$	10.0300	+	38.4579i	0.391306	+	1.50038i
$658$	3.50434			0.136613
$659$	−27.6598			−1.07747			−0.538736	−	0.842474i	$-0.681098\pi$
$659$	−27.6598			−1.07747			−0.538736	+	0.842474i	$0.681098\pi$
$660$	24.4522	+	15.3620i	0.951799	+	0.597965i
$661$	−36.4567			−1.41800			−0.709001	−	0.705207i	$-0.750854\pi$
$661$	−36.4567			−1.41800			−0.709001	+	0.705207i	$0.750854\pi$
$662$	−3.29035			−0.127883
$663$	25.8266	−	3.31244i	1.00302	−	0.128644i
$664$	30.6169			1.18817
$665$		−	1.56316i		−	0.0606167i
$666$	−43.0317	+	11.2228i	−1.66744	+	0.434876i
$667$		−	6.29809i		−	0.243863i
$668$	−60.9173			−2.35696
$669$	2.00646	+	15.6441i	0.0775742	+	0.604834i
$670$		−	40.7099i		−	1.57276i
$671$	3.85808	−	4.68895i	0.148940	−	0.181015i
$672$	9.17514	−	1.17677i	0.353939	−	0.0453951i
$673$			12.9704i			0.499974i	0.968249	+	0.249987i	$0.0804264\pi$
$673$			12.9704i			0.499974i	−0.968249	+	0.249987i	$0.919574\pi$
$674$		−	75.9760i		−	2.92648i
$675$	5.18780	+	12.8881i	0.199679	+	0.496065i
$676$	28.1113			1.08120
$677$	−26.7892			−1.02959			−0.514796	−	0.857312i	$-0.672132\pi$
$677$	−26.7892			−1.02959			−0.514796	+	0.857312i	$0.672132\pi$
$678$	−54.1584	+	6.94619i	−2.07994	+	0.266767i
$679$			2.68418i			0.103009i
$680$		−	32.3384i		−	1.24012i
$681$	0.805436	+	6.27987i	0.0308644	+	0.240645i
$682$	−12.3846	−	10.1901i	−0.474230	−	0.390198i
$683$		−	10.4206i		−	0.398732i	−0.979925	−	0.199366i	$-0.936112\pi$
$683$		−	10.4206i		−	0.398732i	0.979925	−	0.199366i	$-0.0638883\pi$
$684$	2.55734	+	9.80559i	0.0977822	+	0.374926i
$685$	−0.835170			−0.0319102
$686$			2.30127i			0.0878631i
$687$	3.84066	+	29.9451i	0.146530	+	1.14247i
$688$		−	1.14513i		−	0.0436575i
$689$	−27.3268			−1.04107
$690$	5.43256	+	42.3569i	0.206814	+	1.61250i
$691$	−34.5687			−1.31506			−0.657529	−	0.753430i	$-0.728398\pi$
$691$	−34.5687			−1.31506			−0.657529	+	0.753430i	$0.728398\pi$
$692$	−44.1691			−1.67906
$693$	−4.17827	+	9.03006i	−0.158719	+	0.343024i
$694$	−12.5079			−0.474793
$695$	−24.1200			−0.914922
$696$	0.589151	+	4.59353i	0.0223317	+	0.174117i
$697$	−35.1947			−1.33309
$698$			78.3348i			2.96502i
$699$	−4.21945	−	32.8985i	−0.159594	−	1.24433i
$700$		−	8.81222i		−	0.333071i
$701$	6.97185			0.263323			0.131662	−	0.991295i	$-0.457969\pi$
$701$	6.97185			0.263323			0.131662	+	0.991295i	$0.457969\pi$
$702$	23.4548	−	9.44113i	0.885243	−	0.356333i
$703$		−	6.60177i		−	0.248991i
$704$	−32.8650	−	27.0414i	−1.23865	−	1.01916i
$705$	0.511760	+	3.99012i	0.0192740	+	0.150277i
$706$		−	17.5656i		−	0.661091i
$707$			0.233074i			0.00876566i
$708$	26.6072	−	3.41255i	0.999959	−	0.128252i
$709$	14.5366			0.545935			0.272967	−	0.962023i	$-0.411995\pi$
$709$	14.5366			0.545935			0.272967	+	0.962023i	$0.411995\pi$
$710$	25.8640			0.970659
$711$	6.82017	+	26.1506i	0.255776	+	0.980723i
$712$			43.7698i			1.64034i
$713$		−	14.7602i		−	0.552773i
$714$	28.1091	−	3.60518i	1.05196	−	0.134921i
$715$	8.25940	+	6.79586i	0.308884	+	0.254151i
$716$			41.8596i			1.56437i
$717$	4.54702	+	35.4525i	0.169812	+	1.32400i
$718$	50.2217			1.87426
$719$			0.447212i			0.0166782i	0.999965	+	0.00833910i	$0.00265445\pi$
$719$			0.447212i			0.0166782i	−0.999965	+	0.00833910i	$0.997346\pi$
$720$	−0.312909	−	1.19979i	−0.0116614	−	0.0447134i
$721$		−	11.0143i		−	0.410193i
$722$	41.3070			1.53729
$723$	−43.4585	+	5.57384i	−1.61624	+	0.207294i
$724$	−44.7632			−1.66361
$725$	−2.39728			−0.0890326
$726$	41.6004	−	13.8494i	1.54394	−	0.514000i
$727$	−30.2094			−1.12040			−0.560202	−	0.828356i	$-0.689276\pi$
$727$	−30.2094			−1.12040			−0.560202	+	0.828356i	$0.689276\pi$
$728$	−6.30545			−0.233695
$729$	−19.4705	+	18.7056i	−0.721131	+	0.692799i
$730$	46.5000			1.72104
$731$			30.0450i			1.11125i
$732$	−10.3665	+	1.32958i	−0.383158	+	0.0491426i
$733$		−	5.09771i		−	0.188288i	−0.995559	−	0.0941440i	$-0.969989\pi$
$733$		−	5.09771i		−	0.188288i	0.995559	−	0.0941440i	$-0.0300114\pi$
$734$	4.34467			0.160365
$735$	−2.62028	+	0.336069i	−0.0966506	+	0.0123961i
$736$		−	37.5148i		−	1.38281i
$737$	−29.7050	−	24.4414i	−1.09420	−	0.900309i
$738$	−33.0687	+	8.62444i	−1.21727	+	0.317470i
$739$		−	28.0688i		−	1.03253i	−0.856430	−	0.516264i	$-0.827322\pi$
$739$		−	28.0688i		−	1.03253i	0.856430	−	0.516264i	$-0.172678\pi$
$740$			32.3808i			1.19034i
$741$	0.477485	+	3.72288i	0.0175409	+	0.136763i
$742$	−29.7419			−1.09186
$743$	13.8994			0.509918			0.254959	−	0.966952i	$-0.417938\pi$
$743$	13.8994			0.509918			0.254959	+	0.966952i	$0.417938\pi$
$744$	1.38073	+	10.7654i	0.0506201	+	0.394677i
$745$		−	8.36155i		−	0.306343i
$746$			71.6835i			2.62452i
$747$	−29.8034	+	7.77284i	−1.09045	+	0.284393i
$748$	−60.0149	−	49.3804i	−2.19436	−	1.80553i
$749$			6.04114i			0.220739i
$750$	46.2725	−	5.93476i	1.68963	−	0.216707i
$751$	−34.1032			−1.24444			−0.622221	−	0.782841i	$-0.713770\pi$
$751$	−34.1032			−1.24444			−0.622221	+	0.782841i	$0.713770\pi$
$752$			0.412647i			0.0150477i
$753$	47.2429	−	6.05922i	1.72163	−	0.220810i
$754$			4.36273i			0.158881i
$755$	−8.88274			−0.323276
$756$	15.8870	−	6.39493i	0.577806	−	0.232581i
$757$	−49.8718			−1.81262			−0.906310	−	0.422614i	$-0.861113\pi$
$757$	−49.8718			−1.81262			−0.906310	+	0.422614i	$0.861113\pi$
$758$	5.76304			0.209323
$759$	34.1684	+	21.4662i	1.24023	+	0.779174i
$760$	4.66155			0.169092
$761$	32.5848			1.18120			0.590599	−	0.806965i	$-0.298892\pi$
$761$	32.5848			1.18120			0.590599	+	0.806965i	$0.298892\pi$
$762$	61.3767	−	7.87199i	2.22344	−	0.285172i
$763$	3.42334			0.123933
$764$		−	42.1972i		−	1.52664i
$765$	8.20989	+	31.4792i	0.296829	+	1.13813i
$766$		−	13.2764i		−	0.479695i
$767$	9.93576			0.358759
$768$	3.90288	+	30.4302i	0.140833	+	1.09806i
$769$		−	16.3887i		−	0.590990i	−0.955344	−	0.295495i	$-0.904515\pi$
$769$		−	16.3887i		−	0.590990i	0.955344	−	0.295495i	$-0.0954846\pi$
$770$	8.98935	+	7.39646i	0.323954	+	0.266550i
$771$	−13.8248	+	1.77312i	−0.497887	+	0.0638574i
$772$			34.9533i			1.25800i
$773$			51.1623i			1.84018i	0.391707	+	0.920090i	$0.371885\pi$
$773$			51.1623i			1.84018i	−0.391707	+	0.920090i	$0.628115\pi$
$774$	7.36251	+	28.2300i	0.264640	+	1.01471i
$775$	−5.61824			−0.201813
$776$	−8.00457			−0.287347
$777$	−11.0664	+	1.41934i	−0.397004	+	0.0509185i
$778$		−	60.7846i		−	2.17923i
$779$		−	5.07329i		−	0.181769i
$780$	−2.34200	−	18.2602i	−0.0838570	−	0.653821i
$781$	15.5282	−	18.8723i	0.555643	−	0.675306i
$782$		−	114.931i		−	4.10991i
$783$	−1.73968	−	4.32191i	−0.0621710	−	0.154452i
$784$	−0.270983			−0.00967795
$785$			8.02883i			0.286561i
$786$	−10.2927	−	80.2508i	−0.367129	−	2.86245i
$787$		−	22.5504i		−	0.803836i	−0.915676	−	0.401918i	$-0.868344\pi$
$787$		−	22.5504i		−	0.803836i	0.915676	−	0.401918i	$-0.131656\pi$
$788$	8.97608			0.319760
$789$	2.01998	+	15.7495i	0.0719133	+	0.560697i
$790$	31.6190			1.12495
$791$	−13.6987			−0.487070
$792$	−26.9289	−	12.4602i	−0.956875	−	0.442753i
$793$	−3.87111			−0.137467
$794$	25.5924			0.908240
$795$	−4.34339	−	33.8648i	−0.154044	−	1.20106i
$796$	58.8201			2.08482
$797$			0.210776i			0.00746606i	0.999993	+	0.00373303i	$0.00118826\pi$
$797$			0.210776i			0.00746606i	−0.999993	+	0.00373303i	$0.998812\pi$
$798$	0.519684	+	4.05190i	0.0183966	+	0.143436i
$799$		−	10.8267i		−	0.383023i
$800$	−14.2795			−0.504855
$801$	−11.1120	−	42.6068i	−0.392624	−	1.50544i
$802$		−	13.6294i		−	0.481269i
$803$	27.9176	−	33.9299i	0.985192	−	1.19736i
$804$	8.42302	+	65.6731i	0.297057	+	2.31611i
$805$			10.7137i			0.377607i
$806$			10.2245i			0.360142i
$807$	−14.9302	+	1.91490i	−0.525567	+	0.0674076i
$808$	−0.695059			−0.0244521
$809$	−23.3047			−0.819348			−0.409674	−	0.912232i	$-0.634358\pi$
$809$	−23.3047			−0.819348			−0.409674	+	0.912232i	$0.634358\pi$
$810$	15.4279	+	27.5658i	0.542081	+	0.968562i
$811$		−	15.6969i		−	0.551193i	−0.961273	−	0.275596i	$-0.911125\pi$
$811$		−	15.6969i		−	0.551193i	0.961273	−	0.275596i	$-0.0888753\pi$
$812$			2.95509i			0.103703i
$813$	33.9906	−	4.35952i	1.19210	−	0.152895i
$814$	37.9652	+	31.2379i	1.33068	+	1.09489i
$815$			14.1678i			0.496275i
$816$	0.424522	+	3.30994i	0.0148612	+	0.115871i
$817$	−4.33096			−0.151521
$818$		−	9.18236i		−	0.321054i
$819$	6.13791	−	1.60079i	0.214476	−	0.0559362i
$820$			24.8838i			0.868979i
$821$	7.86846			0.274611			0.137306	−	0.990529i	$-0.456156\pi$
$821$	7.86846			0.274611			0.137306	+	0.990529i	$0.456156\pi$
$822$	2.16486	−	0.277658i	0.0755082	−	0.00968444i
$823$	28.5087			0.993750			0.496875	−	0.867822i	$-0.334481\pi$
$823$	28.5087			0.993750			0.496875	+	0.867822i	$0.334481\pi$
$824$	32.8460			1.14425
$825$	8.17079	−	13.0057i	0.284471	−	0.452801i
$826$	10.8139			0.376262
$827$	21.2120			0.737614			0.368807	−	0.929506i	$-0.379766\pi$
$827$	21.2120			0.737614			0.368807	+	0.929506i	$0.379766\pi$
$828$	−17.5276	−	67.2060i	−0.609126	−	2.33557i
$829$	−50.6840			−1.76033			−0.880164	−	0.474670i	$-0.842567\pi$
$829$	−50.6840			−1.76033			−0.880164	+	0.474670i	$0.842567\pi$
$830$			36.0357i			1.25082i
$831$	−38.2770	+	4.90928i	−1.32781	+	0.170301i
$832$			27.1327i			0.940657i
$833$	7.10985			0.246342
$834$	62.5219	−	8.01886i	2.16496	−	0.277670i
$835$		−	28.1905i		−	0.975571i
$836$	7.11814	−	8.65109i	0.246186	−	0.299204i
$837$	−4.07710	−	10.1288i	−0.140925	−	0.350102i
$838$			69.3957i			2.39724i
$839$			29.3639i			1.01375i	0.862019	+	0.506877i	$0.169200\pi$
$839$			29.3639i			1.01375i	−0.862019	+	0.506877i	$0.830800\pi$
$840$	−1.00220	−	7.81404i	−0.0345793	−	0.269610i
$841$	−28.1961			−0.972279
$842$	−45.9890			−1.58489
$843$	3.98265	+	31.0521i	0.137170	+	1.06949i
$844$			66.6768i			2.29511i
$845$			13.0090i			0.447522i
$846$	−2.65309	−	10.1727i	−0.0912151	−	0.349746i
$847$	10.7940	−	2.11863i	0.370888	−	0.0727970i
$848$		−	3.50221i		−	0.120266i
$849$	−3.30077	+	0.423346i	−0.113282	+	0.0145292i
$850$	−43.7467			−1.50050
$851$			45.2476i			1.55107i
$852$	−41.7238	+	5.35136i	−1.42943	+	0.183334i
$853$			27.8921i			0.955008i	0.878630	+	0.477504i	$0.158458\pi$
$853$			27.8921i			0.955008i	−0.878630	+	0.477504i	$0.841542\pi$
$854$	−4.21323			−0.144174
$855$	−4.53769	+	1.18345i	−0.155186	+	0.0404731i
$856$	−18.0155			−0.615757
$857$	51.2142			1.74944			0.874721	−	0.484626i	$-0.161044\pi$
$857$	51.2142			1.74944			0.874721	+	0.484626i	$0.161044\pi$
$858$	−23.6687	−	14.8698i	−0.808036	−	0.507646i
$859$	21.5349			0.734760			0.367380	−	0.930071i	$-0.380255\pi$
$859$	21.5349			0.734760			0.367380	+	0.930071i	$0.380255\pi$
$860$	21.2428			0.724373
$861$	−8.50422	+	1.09072i	−0.289823	+	0.0371718i
$862$	−67.8811			−2.31204
$863$		−	30.0207i		−	1.02192i	−0.859606	−	0.510958i	$-0.829291\pi$
$863$		−	30.0207i		−	1.02192i	0.859606	−	0.510958i	$-0.170709\pi$
$864$	−10.3624	−	25.7436i	−0.352537	−	0.875814i
$865$		−	20.4400i		−	0.694980i
$866$	71.4654			2.42849
$867$	−7.39249	−	57.6382i	−0.251062	−	1.95749i
$868$			6.92553i			0.235068i
$869$	18.9834	−	23.0716i	0.643968	−	0.782652i
$870$	−5.40653	+	0.693424i	−0.183298	+	0.0235093i
$871$			24.5239i			0.830960i
$872$			10.2088i			0.345715i
$873$	7.79189	−	2.03215i	0.263715	−	0.0687780i
$874$	16.5672			0.560393
$875$	11.7041			0.395670
$876$	−75.0136	+	9.62101i	−2.53448	+	0.325064i
$877$		−	20.7640i		−	0.701150i	−0.936535	−	0.350575i	$-0.885986\pi$
$877$		−	20.7640i		−	0.701150i	0.936535	−	0.350575i	$-0.114014\pi$
$878$		−	21.3183i		−	0.719459i
$879$	5.00212	+	39.0008i	0.168717	+	1.31546i
$880$	−0.870958	+	1.05853i	−0.0293600	+	0.0356829i
$881$		−	11.1938i		−	0.377130i	−0.982061	−	0.188565i	$-0.939616\pi$
$881$		−	11.1938i		−	0.377130i	0.982061	−	0.188565i	$-0.0603836\pi$
$882$	6.68036	−	1.74226i	0.224940	−	0.0586651i
$883$	0.515028			0.0173321			0.00866603	−	0.999962i	$-0.497241\pi$
$883$	0.515028			0.0173321			0.00866603	+	0.999962i	$0.497241\pi$
$884$			49.5471i			1.66645i
$885$	1.57921	+	12.3129i	0.0530847	+	0.413894i
$886$			25.8251i			0.867612i
$887$	5.23367			0.175729			0.0878647	−	0.996132i	$-0.471996\pi$
$887$	5.23367			0.175729			0.0878647	+	0.996132i	$0.471996\pi$
$888$	−4.23266	−	33.0014i	−0.142039	−	1.10746i
$889$	15.5245			0.520675
$890$	−51.5165			−1.72684
$891$	29.3767	+	5.29255i	0.984156	+	0.177307i
$892$	−30.0124			−1.00489
$893$	1.56067			0.0522257
$894$	2.77986	+	21.6741i	0.0929724	+	0.724892i
$895$	−19.3712			−0.647509
$896$			18.8493i			0.629711i
$897$	−3.27261	−	25.5161i	−0.109269	−	0.851957i
$898$			13.0933i			0.436929i
$899$	1.88402			0.0628356
$900$	−25.5810	+	6.67162i	−0.852700	+	0.222387i
$901$			91.8884i			3.06125i
$902$	29.1752	+	24.0055i	0.971429	+	0.799294i
$903$	0.931129	+	7.25987i	0.0309860	+	0.241593i
$904$		−	40.8514i		−	1.35870i
$905$		−	20.7149i		−	0.688586i
$906$	23.0251	−	2.95313i	0.764959	−	0.0981113i
$907$	7.81415			0.259465			0.129732	−	0.991549i	$-0.458588\pi$
$907$	7.81415			0.259465			0.129732	+	0.991549i	$0.458588\pi$
$908$	−12.0476			−0.399815
$909$	0.676591	−	0.176458i	0.0224411	−	0.00585273i
$910$		−	7.42143i		−	0.246018i
$911$		−	28.4517i		−	0.942647i	−0.881960	−	0.471324i	$-0.843776\pi$
$911$		−	28.4517i		−	0.942647i	0.881960	−	0.471324i	$-0.156224\pi$
$912$	−0.477125	+	0.0611945i	−0.0157992	+	0.00202635i
$913$	26.2944	+	21.6351i	0.870217	+	0.716017i
$914$		−	24.6992i		−	0.816978i
$915$	−0.615284	−	4.79728i	−0.0203406	−	0.158593i
$916$	−57.4482			−1.89814
$917$		−	20.2985i		−	0.670315i
$918$	−31.7465	−	78.8684i	−1.04779	−	2.60304i
$919$			12.5715i			0.414694i	0.978267	+	0.207347i	$0.0664829\pi$
$919$			12.5715i			0.414694i	−0.978267	+	0.207347i	$0.933517\pi$
$920$	−31.9496			−1.05335
$921$	25.3062	−	3.24569i	0.833868	−	0.106949i
$922$	11.6884			0.384936
$923$	−15.5806			−0.512843
$924$	−16.0320	−	10.0720i	−0.527413	−	0.331345i
$925$	17.2228			0.566283
$926$	14.3543			0.471711
$927$	−31.9733	+	8.33876i	−1.05014	+	0.273881i
$928$	4.78847			0.157189
$929$		−	9.67422i		−	0.317401i	−0.987327	−	0.158700i	$-0.949270\pi$
$929$		−	9.67422i		−	0.317401i	0.987327	−	0.158700i	$-0.0507304\pi$
$930$	−12.6707	+	1.62510i	−0.415489	+	0.0532893i
$931$			1.02488i			0.0335891i
$932$	63.1142			2.06737
$933$	−21.3799	+	2.74212i	−0.699946	+	0.0897729i
$934$		−	39.6060i		−	1.29595i
$935$	22.8516	−	27.7729i	0.747327	−	0.908269i
$936$	4.77377	+	18.3041i	0.156036	+	0.598287i
$937$			43.7790i			1.43020i	0.699023	+	0.715099i	$0.253618\pi$
$937$			43.7790i			1.43020i	−0.699023	+	0.715099i	$0.746382\pi$
$938$			26.6912i			0.871500i
$939$	−1.78288	−	13.9008i	−0.0581821	−	0.453637i
$940$	−7.65486			−0.249674
$941$	−48.1998			−1.57127			−0.785634	−	0.618691i	$-0.787663\pi$
$941$	−48.1998			−1.57127			−0.785634	+	0.618691i	$0.787663\pi$
$942$	−2.66924	−	20.8117i	−0.0869687	−	0.678082i
$943$			34.7715i			1.13232i
$944$			1.27337i			0.0414446i
$945$	2.95936	+	7.35198i	0.0962679	+	0.239160i
$946$	20.4930	−	24.9063i	0.666284	−	0.809773i
$947$			10.6255i			0.345283i	0.984985	+	0.172641i	$0.0552302\pi$
$947$			10.6255i			0.345283i	−0.984985	+	0.172641i	$0.944770\pi$
$948$	−51.0077	+	6.54209i	−1.65665	+	0.212477i
$949$	−28.0119			−0.909304
$950$		−	6.30605i		−	0.204595i
$951$	−0.856716	+	0.109880i	−0.0277809	+	0.00356309i
$952$			21.2025i			0.687178i
$953$	1.99258			0.0645461			0.0322730	−	0.999479i	$-0.489725\pi$
$953$	1.99258			0.0645461			0.0322730	+	0.999479i	$0.489725\pi$
$954$	22.5172	+	86.3377i	0.729021	+	2.79529i
$955$	19.5275			0.631894
$956$	−68.0139			−2.19973
$957$	−2.73999	+	4.36133i	−0.0885714	+	0.140982i
$958$	−4.06083			−0.131199
$959$	0.547576			0.0176821
$960$	−33.6242	+	4.31254i	−1.08522	+	0.139187i
$961$	−26.5846			−0.857568
$962$		−	31.3433i		−	1.01055i
$963$	17.5368	−	4.57367i	0.565116	−	0.147385i
$964$		−	83.3731i		−	2.68527i
$965$	−16.1752			−0.520698
$966$	−3.56183	−	27.7711i	−0.114600	−	0.893521i
$967$		−	20.5468i		−	0.660739i	−0.943852	−	0.330370i	$-0.892827\pi$
$967$		−	20.5468i		−	0.660739i	0.943852	−	0.330370i	$-0.107173\pi$
$968$	6.31804	+	32.1893i	0.203069	+	1.03460i
$969$	12.5185	−	1.60558i	0.402151	−	0.0515786i
$970$		−	9.42128i		−	0.302499i
$971$		−	11.6969i		−	0.375372i	−0.982229	−	0.187686i	$-0.939901\pi$
$971$		−	11.6969i		−	0.375372i	0.982229	−	0.187686i	$-0.0600987\pi$
$972$	−30.5917	−	41.2769i	−0.981229	−	1.32396i
$973$	15.8142			0.506979
$974$	1.33941			0.0429175
$975$	−9.71232	+	1.24567i	−0.311043	+	0.0398934i
$976$		−	0.496121i		−	0.0158805i
$977$			38.1637i			1.22096i	0.792030	+	0.610482i	$0.209024\pi$
$977$			38.1637i			1.22096i	−0.792030	+	0.610482i	$0.790976\pi$
$978$	−4.71017	−	36.7245i	−0.150615	−	1.17432i
$979$	−30.9295	+	37.5904i	−0.988510	+	1.20139i
$980$		−	5.02689i		−	0.160578i
$981$	−2.59176	−	9.93759i	−0.0827486	−	0.317283i
$982$	82.9567			2.64725
$983$		−	16.1654i		−	0.515596i	−0.966199	−	0.257798i	$-0.917003\pi$
$983$		−	16.1654i		−	0.515596i	0.966199	−	0.257798i	$-0.0829969\pi$
$984$	−3.25268	−	25.3607i	−0.103692	−	0.808470i
$985$			4.15383i			0.132352i
$986$	14.6700			0.467188
$987$	−0.335533	−	2.61611i	−0.0106801	−	0.0832715i
$988$	−7.14218			−0.227223
$989$	29.6837			0.943888
$990$	14.6655	−	31.6949i	0.466099	−	1.00733i
$991$	36.1450			1.14818			0.574092	−	0.818791i	$-0.305355\pi$
$991$	36.1450			1.14818			0.574092	+	0.818791i	$0.305355\pi$
$992$	11.2222			0.356306
$993$	0.315045	+	2.45636i	0.00999765	+	0.0779502i
$994$	−16.9576			−0.537863
$995$			27.2199i			0.862930i
$996$	−7.45592	−	58.1327i	−0.236250	−	1.84201i
$997$		−	41.8625i		−	1.32580i	−0.748709	−	0.662899i	$-0.769326\pi$
$997$		−	41.8625i		−	1.32580i	0.748709	−	0.662899i	$-0.230674\pi$
$998$	−43.2124			−1.36786
$999$	12.4984	+	31.0500i	0.395432	+	0.982379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.g.a.197.21	yes	24
3.2	odd	2	inner	231.2.g.a.197.4	yes	24
11.10	odd	2	inner	231.2.g.a.197.3	✓	24
33.32	even	2	inner	231.2.g.a.197.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.g.a.197.3	✓	24	11.10	odd	2	inner
231.2.g.a.197.4	yes	24	3.2	odd	2	inner
231.2.g.a.197.21	yes	24	1.1	even	1	trivial
231.2.g.a.197.22	yes	24	33.32	even	2	inner

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.30127 q^{2} +(-0.220342 - 1.71798i) q^{3} +3.29586 q^{4} +1.52521i q^{5} +(-0.507068 - 3.95354i) q^{6} -1.00000i q^{7} +2.98213 q^{8} +(-2.90290 + 0.757087i) q^{9} +O(q^{10})\)	\(q+2.30127 q^{2} +(-0.220342 - 1.71798i) q^{3} +3.29586 q^{4} +1.52521i q^{5} +(-0.507068 - 3.95354i) q^{6} -1.00000i q^{7} +2.98213 q^{8} +(-2.90290 + 0.757087i) q^{9} +3.50993i q^{10} +(2.56112 + 2.10729i) q^{11} +(-0.726218 - 5.66222i) q^{12} -2.11441i q^{13} -2.30127i q^{14} +(2.62028 - 0.336069i) q^{15} +0.270983 q^{16} -7.10985 q^{17} +(-6.68036 + 1.74226i) q^{18} -1.02488i q^{19} +5.02689i q^{20} +(-1.71798 + 0.220342i) q^{21} +(5.89383 + 4.84946i) q^{22} +7.02437i q^{23} +(-0.657091 - 5.12324i) q^{24} +2.67372 q^{25} -4.86583i q^{26} +(1.94029 + 4.82030i) q^{27} -3.29586i q^{28} -0.896606 q^{29} +(6.02999 - 0.773388i) q^{30} -2.10128 q^{31} -5.34066 q^{32} +(3.05596 - 4.86427i) q^{33} -16.3617 q^{34} +1.52521 q^{35} +(-9.56755 + 2.49525i) q^{36} +6.44151 q^{37} -2.35853i q^{38} +(-3.63251 + 0.465894i) q^{39} +4.54839i q^{40} +4.95013 q^{41} +(-3.95354 + 0.507068i) q^{42} -4.22582i q^{43} +(8.44109 + 6.94535i) q^{44} +(-1.15472 - 4.42754i) q^{45} +16.1650i q^{46} +1.52278i q^{47} +(-0.0597090 - 0.465542i) q^{48} -1.00000 q^{49} +6.15297 q^{50} +(1.56660 + 12.2146i) q^{51} -6.96880i q^{52} -12.9241i q^{53} +(4.46514 + 11.0928i) q^{54} +(-3.21407 + 3.90625i) q^{55} -2.98213i q^{56} +(-1.76072 + 0.225824i) q^{57} -2.06334 q^{58} +4.69907i q^{59} +(8.63609 - 1.10764i) q^{60} -1.83082i q^{61} -4.83562 q^{62} +(0.757087 + 2.90290i) q^{63} -12.8323 q^{64} +3.22492 q^{65} +(7.03260 - 11.1940i) q^{66} -11.5985 q^{67} -23.4331 q^{68} +(12.0677 - 1.54777i) q^{69} +3.50993 q^{70} -7.36880i q^{71} +(-8.65683 + 2.25774i) q^{72} -13.2481i q^{73} +14.8237 q^{74} +(-0.589135 - 4.59340i) q^{75} -3.37786i q^{76} +(2.10729 - 2.56112i) q^{77} +(-8.35939 + 1.07215i) q^{78} -9.00843i q^{79} +0.413307i q^{80} +(7.85364 - 4.39549i) q^{81} +11.3916 q^{82} +10.2668 q^{83} +(-5.66222 + 0.726218i) q^{84} -10.8440i q^{85} -9.72478i q^{86} +(0.197560 + 1.54035i) q^{87} +(7.63759 + 6.28423i) q^{88} +14.6773i q^{89} +(-2.65733 - 10.1890i) q^{90} -2.11441 q^{91} +23.1513i q^{92} +(0.463001 + 3.60995i) q^{93} +3.50434i q^{94} +1.56316 q^{95} +(1.17677 + 9.17514i) q^{96} -2.68418 q^{97} -2.30127 q^{98} +(-9.03006 - 4.17827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

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