LMFDB - Embedded newform 231.2.e.a.188.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(188,231)]

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, 1, 0]))

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

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

chi := DirichletCharacter("231.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.e (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:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.20
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.12088i q^{2} +(0.799601 - 1.53644i) q^{3} +0.743632 q^{4} -0.911250 q^{5} +(1.72216 + 0.896255i) q^{6} +(2.18571 - 1.49086i) q^{7} +3.07528i q^{8} +(-1.72128 - 2.45707i) q^{9} +O(q^{10})$	\(q+1.12088i q^{2} +(0.799601 - 1.53644i) q^{3} +0.743632 q^{4} -0.911250 q^{5} +(1.72216 + 0.896255i) q^{6} +(2.18571 - 1.49086i) q^{7} +3.07528i q^{8} +(-1.72128 - 2.45707i) q^{9} -1.02140i q^{10} -1.00000i q^{11} +(0.594609 - 1.14254i) q^{12} +0.687952i q^{13} +(1.67108 + 2.44991i) q^{14} +(-0.728636 + 1.40008i) q^{15} -1.95975 q^{16} +3.26618 q^{17} +(2.75408 - 1.92934i) q^{18} +0.717942i q^{19} -0.677635 q^{20} +(-0.542924 - 4.55030i) q^{21} +1.12088 q^{22} +0.687108i q^{23} +(4.72497 + 2.45899i) q^{24} -4.16962 q^{25} -0.771110 q^{26} +(-5.15147 + 0.679956i) q^{27} +(1.62536 - 1.10865i) q^{28} -0.255478i q^{29} +(-1.56932 - 0.816713i) q^{30} +8.80590i q^{31} +3.95392i q^{32} +(-1.53644 - 0.799601i) q^{33} +3.66099i q^{34} +(-1.99173 + 1.35855i) q^{35} +(-1.28000 - 1.82716i) q^{36} -3.81013 q^{37} -0.804725 q^{38} +(1.05699 + 0.550087i) q^{39} -2.80235i q^{40} -9.59006 q^{41} +(5.10033 - 0.608552i) q^{42} +8.59846 q^{43} -0.743632i q^{44} +(1.56851 + 2.23901i) q^{45} -0.770165 q^{46} -12.5667 q^{47} +(-1.56701 + 3.01103i) q^{48} +(2.55465 - 6.51719i) q^{49} -4.67364i q^{50} +(2.61164 - 5.01828i) q^{51} +0.511583i q^{52} -5.09030i q^{53} +(-0.762148 - 5.77417i) q^{54} +0.911250i q^{55} +(4.58482 + 6.72166i) q^{56} +(1.10307 + 0.574067i) q^{57} +0.286360 q^{58} +5.86778 q^{59} +(-0.541838 + 1.04114i) q^{60} +5.13466i q^{61} -9.87034 q^{62} +(-7.42537 - 2.80426i) q^{63} -8.35135 q^{64} -0.626896i q^{65} +(0.896255 - 1.72216i) q^{66} -8.19722 q^{67} +2.42884 q^{68} +(1.05570 + 0.549412i) q^{69} +(-1.52277 - 2.23248i) q^{70} -5.71470i q^{71} +(7.55618 - 5.29340i) q^{72} -9.05463i q^{73} -4.27069i q^{74} +(-3.33403 + 6.40636i) q^{75} +0.533885i q^{76} +(-1.49086 - 2.18571i) q^{77} +(-0.616580 + 1.18476i) q^{78} -2.48351 q^{79} +1.78582 q^{80} +(-3.07441 + 8.45860i) q^{81} -10.7493i q^{82} -3.94545 q^{83} +(-0.403736 - 3.38375i) q^{84} -2.97631 q^{85} +9.63782i q^{86} +(-0.392526 - 0.204280i) q^{87} +3.07528 q^{88} +12.1065 q^{89} +(-2.50965 + 1.75811i) q^{90} +(1.02564 + 1.50366i) q^{91} +0.510956i q^{92} +(13.5297 + 7.04121i) q^{93} -14.0858i q^{94} -0.654224i q^{95} +(6.07495 + 3.16156i) q^{96} +9.33260i q^{97} +(7.30498 + 2.86345i) q^{98} +(-2.45707 + 1.72128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

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 $

$2$			1.12088i			0.792580i	0.918125	+	0.396290i	$0.129703\pi$
$2$			1.12088i			0.792580i	−0.918125	+	0.396290i	$0.870297\pi$
$3$	0.799601	−	1.53644i	0.461650	−	0.887062i
$3$	0.799601	−	1.53644i	0.461650	−	0.887062i
$4$	0.743632			0.371816
$5$	−0.911250			−0.407523			−0.203762	−	0.979021i	$-0.565317\pi$
$5$	−0.911250			−0.407523			−0.203762	+	0.979021i	$0.565317\pi$
$6$	1.72216	+	0.896255i	0.703068	+	0.365895i
$7$	2.18571	−	1.49086i	0.826120	−	0.563494i
$7$	2.18571	−	1.49086i	0.826120	−	0.563494i
$8$			3.07528i			1.08727i
$9$	−1.72128	−	2.45707i	−0.573759	−	0.819024i
$10$		−	1.02140i		−	0.322995i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	0.594609	−	1.14254i	0.171649	−	0.329824i
$13$			0.687952i			0.190803i	0.995439	+	0.0954017i	$0.0304136\pi$
$13$			0.687952i			0.190803i	−0.995439	+	0.0954017i	$0.969586\pi$
$14$	1.67108	+	2.44991i	0.446614	+	0.654767i
$15$	−0.728636	+	1.40008i	−0.188133	+	0.361499i
$16$	−1.95975			−0.489936
$17$	3.26618			0.792166			0.396083	−	0.918215i	$-0.370369\pi$
$17$	3.26618			0.792166			0.396083	+	0.918215i	$0.370369\pi$
$18$	2.75408	−	1.92934i	0.649143	−	0.454750i
$19$			0.717942i			0.164707i	0.996603	+	0.0823536i	$0.0262437\pi$
$19$			0.717942i			0.164707i	−0.996603	+	0.0823536i	$0.973756\pi$
$20$	−0.677635			−0.151524
$21$	−0.542924	−	4.55030i	−0.118476	−	0.992957i
$22$	1.12088			0.238972
$23$			0.687108i			0.143272i	0.997431	+	0.0716360i	$0.0228220\pi$
$23$			0.687108i			0.143272i	−0.997431	+	0.0716360i	$0.977178\pi$
$24$	4.72497	+	2.45899i	0.964480	+	0.501940i
$25$	−4.16962			−0.833925
$26$	−0.771110			−0.151227
$27$	−5.15147	+	0.679956i	−0.991401	+	0.130858i
$28$	1.62536	−	1.10865i	0.307165	−	0.209516i
$29$		−	0.255478i		−	0.0474411i	−0.999719	−	0.0237205i	$-0.992449\pi$
$29$		−	0.255478i		−	0.0474411i	0.999719	−	0.0237205i	$-0.00755119\pi$
$30$	−1.56932	−	0.816713i	−0.286517	−	0.149111i
$31$			8.80590i			1.58159i	0.612083	+	0.790794i	$0.290332\pi$
$31$			8.80590i			1.58159i	−0.612083	+	0.790794i	$0.709668\pi$
$32$			3.95392i			0.698961i
$33$	−1.53644	−	0.799601i	−0.267459	−	0.139193i
$34$			3.66099i			0.627855i
$35$	−1.99173	+	1.35855i	−0.336663	+	0.229637i
$36$	−1.28000	−	1.82716i	−0.213333	−	0.304526i
$37$	−3.81013			−0.626381			−0.313190	−	0.949690i	$-0.601398\pi$
$37$	−3.81013			−0.626381			−0.313190	+	0.949690i	$0.601398\pi$
$38$	−0.804725			−0.130544
$39$	1.05699	+	0.550087i	0.169255	+	0.0880844i
$40$		−	2.80235i		−	0.443090i
$41$	−9.59006			−1.49772			−0.748858	−	0.662730i	$-0.769398\pi$
$41$	−9.59006			−1.49772			−0.748858	+	0.662730i	$0.769398\pi$
$42$	5.10033	−	0.608552i	0.786998	−	0.0939015i
$43$	8.59846			1.31125			0.655626	−	0.755086i	$-0.272405\pi$
$43$	8.59846			1.31125			0.655626	+	0.755086i	$0.272405\pi$
$44$		−	0.743632i		−	0.112107i
$45$	1.56851	+	2.23901i	0.233820	+	0.333772i
$46$	−0.770165			−0.113555
$47$	−12.5667			−1.83305			−0.916523	−	0.399982i	$-0.869016\pi$
$47$	−12.5667			−1.83305			−0.916523	+	0.399982i	$0.869016\pi$
$48$	−1.56701	+	3.01103i	−0.226179	+	0.434604i
$49$	2.55465	−	6.51719i	0.364950	−	0.931027i
$50$		−	4.67364i		−	0.660952i
$51$	2.61164	−	5.01828i	0.365703	−	0.702700i
$52$			0.511583i			0.0709438i
$53$		−	5.09030i		−	0.699206i	−0.936898	−	0.349603i	$-0.886316\pi$
$53$		−	5.09030i		−	0.699206i	0.936898	−	0.349603i	$-0.113684\pi$
$54$	−0.762148	−	5.77417i	−0.103715	−	0.785765i
$55$			0.911250i			0.122873i
$56$	4.58482	+	6.72166i	0.612672	+	0.898220i
$57$	1.10307	+	0.574067i	0.146105	+	0.0760370i
$58$	0.286360			0.0376009
$59$	5.86778			0.763920			0.381960	−	0.924179i	$-0.375249\pi$
$59$	5.86778			0.763920			0.381960	+	0.924179i	$0.375249\pi$
$60$	−0.541838	+	1.04114i	−0.0699509	+	0.134411i
$61$			5.13466i			0.657426i	0.944430	+	0.328713i	$0.106615\pi$
$61$			5.13466i			0.657426i	−0.944430	+	0.328713i	$0.893385\pi$
$62$	−9.87034			−1.25354
$63$	−7.42537	−	2.80426i	−0.935509	−	0.353303i
$64$	−8.35135			−1.04392
$65$		−	0.626896i		−	0.0777569i
$66$	0.896255	−	1.72216i	0.110321	−	0.211983i
$67$	−8.19722			−1.00145			−0.500725	−	0.865607i	$-0.666933\pi$
$67$	−8.19722			−1.00145			−0.500725	+	0.865607i	$0.666933\pi$
$68$	2.42884			0.294540
$69$	1.05570	+	0.549412i	0.127091	+	0.0661415i
$70$	−1.52277	−	2.23248i	−0.182006	−	0.266833i
$71$		−	5.71470i		−	0.678210i	−0.940748	−	0.339105i	$-0.889876\pi$
$71$		−	5.71470i		−	0.678210i	0.940748	−	0.339105i	$-0.110124\pi$
$72$	7.55618	−	5.29340i	0.890504	−	0.623834i
$73$		−	9.05463i		−	1.05976i	−0.848071	−	0.529882i	$-0.822236\pi$
$73$		−	9.05463i		−	1.05976i	0.848071	−	0.529882i	$-0.177764\pi$
$74$		−	4.27069i		−	0.496457i
$75$	−3.33403	+	6.40636i	−0.384981	+	0.739743i
$76$			0.533885i			0.0612408i
$77$	−1.49086	−	2.18571i	−0.169900	−	0.249085i
$78$	−0.616580	+	1.18476i	−0.0698140	+	0.134148i
$79$	−2.48351			−0.279417			−0.139708	−	0.990193i	$-0.544617\pi$
$79$	−2.48351			−0.279417			−0.139708	+	0.990193i	$0.544617\pi$
$80$	1.78582			0.199661
$81$	−3.07441	+	8.45860i	−0.341601	+	0.939845i
$82$		−	10.7493i		−	1.18706i
$83$	−3.94545			−0.433069			−0.216534	−	0.976275i	$-0.569475\pi$
$83$	−3.94545			−0.433069			−0.216534	+	0.976275i	$0.569475\pi$
$84$	−0.403736	−	3.38375i	−0.0440512	−	0.369197i
$85$	−2.97631			−0.322826
$86$			9.63782i			1.03927i
$87$	−0.392526	−	0.204280i	−0.0420832	−	0.0219012i
$88$	3.07528			0.327826
$89$	12.1065			1.28328			0.641642	−	0.767005i	$-0.278254\pi$
$89$	12.1065			1.28328			0.641642	+	0.767005i	$0.278254\pi$
$90$	−2.50965	+	1.75811i	−0.264541	+	0.185321i
$91$	1.02564	+	1.50366i	0.107517	+	0.157627i
$92$			0.510956i			0.0532708i
$93$	13.5297	+	7.04121i	1.40297	+	0.730139i
$94$		−	14.0858i		−	1.45284i
$95$		−	0.654224i		−	0.0671220i
$96$	6.07495	+	3.16156i	0.620022	+	0.322675i
$97$			9.33260i			0.947582i	0.880637	+	0.473791i	$0.157115\pi$
$97$			9.33260i			0.947582i	−0.880637	+	0.473791i	$0.842885\pi$
$98$	7.30498	+	2.86345i	0.737914	+	0.289252i
$99$	−2.45707	+	1.72128i	−0.246945	+	0.172995i
$100$	−3.10067			−0.310067
$101$	17.2097			1.71243			0.856215	−	0.516620i	$-0.172810\pi$
$101$	17.2097			1.71243			0.856215	+	0.516620i	$0.172810\pi$
$102$	5.62488	+	2.92733i	0.556946	+	0.289849i
$103$			10.0111i			0.986420i	0.869910	+	0.493210i	$0.164177\pi$
$103$			10.0111i			0.986420i	−0.869910	+	0.493210i	$0.835823\pi$
$104$	−2.11564			−0.207456
$105$	0.494740	+	4.14646i	0.0482816	+	0.404653i
$106$	5.70560			0.554177
$107$			2.86037i			0.276522i	0.990396	+	0.138261i	$0.0441513\pi$
$107$			2.86037i			0.276522i	−0.990396	+	0.138261i	$0.955849\pi$
$108$	−3.83080	+	0.505637i	−0.368619	+	0.0486550i
$109$	11.1607			1.06900			0.534500	−	0.845168i	$-0.320500\pi$
$109$	11.1607			1.06900			0.534500	+	0.845168i	$0.320500\pi$
$110$	−1.02140			−0.0973867
$111$	−3.04658	+	5.85402i	−0.289169	+	0.555639i
$112$	−4.28343	+	2.92172i	−0.404747	+	0.276076i
$113$			7.70520i			0.724844i	0.932014	+	0.362422i	$0.118050\pi$
$113$			7.70520i			0.724844i	−0.932014	+	0.362422i	$0.881950\pi$
$114$	−0.643459	+	1.23641i	−0.0602654	+	0.115800i
$115$		−	0.626127i		−	0.0583867i
$116$		−	0.189982i		−	0.0176394i
$117$	1.69035	−	1.18416i	0.156273	−	0.109475i
$118$			6.57707i			0.605468i
$119$	7.13892	−	4.86943i	0.654424	−	0.446380i
$120$	−4.30563	−	2.24076i	−0.393048	−	0.204552i
$121$	−1.00000			−0.0909091
$122$	−5.75533			−0.521063
$123$	−7.66822	+	14.7345i	−0.691420	+	1.32857i
$124$			6.54836i			0.588060i
$125$	8.35582			0.747367
$126$	3.14323	−	8.32294i	0.280021	−	0.741466i
$127$	−1.39511			−0.123796			−0.0618980	−	0.998082i	$-0.519715\pi$
$127$	−1.39511			−0.123796			−0.0618980	+	0.998082i	$0.519715\pi$
$128$		−	1.45301i		−	0.128429i
$129$	6.87533	−	13.2110i	0.605339	−	1.16316i
$130$	0.702674			0.0616286
$131$	−2.56073			−0.223732			−0.111866	−	0.993723i	$-0.535683\pi$
$131$	−2.56073			−0.223732			−0.111866	+	0.993723i	$0.535683\pi$
$132$	−1.14254	−	0.594609i	−0.0994457	−	0.0517541i
$133$	1.07035	+	1.56921i	0.0928114	+	0.136068i
$134$		−	9.18808i		−	0.793729i
$135$	4.69428	−	0.619610i	0.404019	−	0.0533275i
$136$			10.0444i			0.861302i
$137$		−	18.7120i		−	1.59868i	−0.600882	−	0.799338i	$-0.705184\pi$
$137$		−	18.7120i		−	1.59868i	0.600882	−	0.799338i	$-0.294816\pi$
$138$	−0.615824	+	1.18331i	−0.0524224	+	0.100730i
$139$		−	14.4827i		−	1.22841i	−0.789148	−	0.614204i	$-0.789477\pi$
$139$		−	14.4827i		−	1.22841i	0.789148	−	0.614204i	$-0.210523\pi$
$140$	−1.48111	+	1.01026i	−0.125177	+	0.0853827i
$141$	−10.0484	+	19.3080i	−0.846225	+	1.62603i
$142$	6.40548			0.537536
$143$	0.687952			0.0575294
$144$	3.37327	+	4.81524i	0.281105	+	0.401270i
$145$			0.232804i			0.0193333i
$146$	10.1491			0.839949
$147$	−7.97055	−	9.13621i	−0.657400	−	0.753542i
$148$	−2.83333			−0.232899
$149$			23.2776i			1.90697i	0.301433	+	0.953487i	$0.402535\pi$
$149$			23.2776i			1.90697i	−0.301433	+	0.953487i	$0.597465\pi$
$150$	−7.18075	−	3.73705i	−0.586306	−	0.305129i
$151$	12.8559			1.04620			0.523099	−	0.852272i	$-0.324776\pi$
$151$	12.8559			1.04620			0.523099	+	0.852272i	$0.324776\pi$
$152$	−2.20787			−0.179082
$153$	−5.62200	−	8.02525i	−0.454512	−	0.648803i
$154$	2.44991	−	1.67108i	0.197420	−	0.134659i
$155$		−	8.02438i		−	0.644534i
$156$	0.786015	+	0.409062i	0.0629316	+	0.0327512i
$157$		−	15.6447i		−	1.24858i	−0.781193	−	0.624290i	$-0.785388\pi$
$157$		−	15.6447i		−	1.24858i	0.781193	−	0.624290i	$-0.214612\pi$
$158$		−	2.78371i		−	0.221460i
$159$	−7.82092	−	4.07021i	−0.620239	−	0.322788i
$160$		−	3.60301i		−	0.284843i
$161$	1.02439	+	1.50182i	0.0807329	+	0.118360i
$162$	−9.48106	−	3.44604i	−0.744903	−	0.270747i
$163$	−11.6450			−0.912106			−0.456053	−	0.889953i	$-0.650737\pi$
$163$	−11.6450			−0.912106			−0.456053	+	0.889953i	$0.650737\pi$
$164$	−7.13148			−0.556875
$165$	1.40008	+	0.728636i	0.108996	+	0.0567243i
$166$		−	4.42236i		−	0.343242i
$167$	−4.76569			−0.368780			−0.184390	−	0.982853i	$-0.559031\pi$
$167$	−4.76569			−0.368780			−0.184390	+	0.982853i	$0.559031\pi$
$168$	13.9934	−	1.66964i	1.07962	−	0.128816i
$169$	12.5267			0.963594
$170$		−	3.33608i		−	0.255866i
$171$	1.76403	−	1.23578i	0.134899	−	0.0945022i
$172$	6.39409			0.487545
$173$	24.2047			1.84025			0.920124	−	0.391628i	$-0.128088\pi$
$173$	24.2047			1.84025			0.920124	+	0.391628i	$0.128088\pi$
$174$	0.228973	−	0.439974i	0.0173584	−	0.0333543i
$175$	−9.11358	+	6.21634i	−0.688922	+	0.469911i
$176$			1.95975i			0.147721i
$177$	4.69188	−	9.01547i	0.352663	−	0.677644i
$178$			13.5699i			1.01711i
$179$		−	17.6229i		−	1.31720i	−0.752494	−	0.658599i	$-0.771149\pi$
$179$		−	17.6229i		−	1.31720i	0.752494	−	0.658599i	$-0.228851\pi$
$180$	1.16640	+	1.66500i	0.0869381	+	0.124102i
$181$		−	7.77441i		−	0.577867i	−0.957349	−	0.288934i	$-0.906699\pi$
$181$		−	7.77441i		−	0.577867i	0.957349	−	0.288934i	$-0.0933007\pi$
$182$	−1.68542	+	1.14962i	−0.124932	+	0.0852155i
$183$	7.88909	+	4.10568i	0.583178	+	0.303501i
$184$	−2.11305			−0.155776
$185$	3.47198			0.255265
$186$	−7.89234	+	15.1652i	−0.578694	+	1.11196i
$187$		−	3.26618i		−	0.238847i
$188$	−9.34503			−0.681556
$189$	−10.2459	+	9.16633i	−0.745279	+	0.666752i
$190$	0.733306			0.0531996
$191$		−	7.45179i		−	0.539193i	−0.962973	−	0.269596i	$-0.913110\pi$
$191$		−	7.45179i		−	0.539193i	0.962973	−	0.269596i	$-0.0868903\pi$
$192$	−6.67775	+	12.8313i	−0.481925	+	0.926021i
$193$	−17.5035			−1.25993			−0.629965	−	0.776624i	$-0.716931\pi$
$193$	−17.5035			−1.25993			−0.629965	+	0.776624i	$0.716931\pi$
$194$	−10.4607			−0.751035
$195$	−0.963186	−	0.501267i	−0.0689752	−	0.0358964i
$196$	1.89972	−	4.84639i	0.135694	−	0.346171i
$197$		−	28.0261i		−	1.99678i	−0.0567462	−	0.998389i	$-0.518073\pi$
$197$		−	28.0261i		−	1.99678i	0.0567462	−	0.998389i	$-0.481927\pi$
$198$	−1.92934	−	2.75408i	−0.137112	−	0.195724i
$199$		−	2.90213i		−	0.205727i	−0.994695	−	0.102863i	$-0.967200\pi$
$199$		−	2.90213i		−	0.205727i	0.994695	−	0.102863i	$-0.0328004\pi$
$200$		−	12.8227i		−	0.906705i
$201$	−6.55450	+	12.5945i	−0.462319	+	0.888348i
$202$			19.2900i			1.35724i
$203$	−0.380883	−	0.558401i	−0.0267327	−	0.0391920i
$204$	1.94210	−	3.73176i	0.135974	−	0.261275i
$205$	8.73895			0.610355
$206$	−11.2212			−0.781817
$207$	1.68827	−	1.18270i	0.117343	−	0.0822036i
$208$		−	1.34821i		−	0.0934816i
$209$	0.717942			0.0496611
$210$	−4.64768	+	0.554543i	−0.320720	+	0.0382671i
$211$	−1.48631			−0.102322			−0.0511609	−	0.998690i	$-0.516292\pi$
$211$	−1.48631			−0.102322			−0.0511609	+	0.998690i	$0.516292\pi$
$212$		−	3.78531i		−	0.259976i
$213$	−8.78028	−	4.56948i	−0.601615	−	0.313096i
$214$	−3.20612			−0.219166
$215$	−7.83534			−0.534366
$216$	−2.09105	−	15.8422i	−0.142278	−	1.07793i
$217$	13.1284	+	19.2471i	0.891214	+	1.30658i
$218$			12.5098i			0.847269i
$219$	−13.9119	−	7.24009i	−0.940077	−	0.489240i
$220$			0.677635i			0.0456862i
$221$			2.24698i			0.151148i
$222$	−6.56164	−	3.41484i	−0.440388	−	0.229189i
$223$		−	16.3583i		−	1.09543i	−0.836664	−	0.547717i	$-0.815497\pi$
$223$		−	16.3583i		−	1.09543i	0.836664	−	0.547717i	$-0.184503\pi$
$224$	5.89476	+	8.64212i	0.393860	+	0.577426i
$225$	7.17708	+	10.2451i	0.478472	+	0.683004i
$226$	−8.63659			−0.574498
$227$	−7.72042			−0.512422			−0.256211	−	0.966621i	$-0.582474\pi$
$227$	−7.72042			−0.512422			−0.256211	+	0.966621i	$0.582474\pi$
$228$	0.820280	+	0.426895i	0.0543244	+	0.0282718i
$229$			3.07289i			0.203062i	0.994832	+	0.101531i	$0.0323742\pi$
$229$			3.07289i			0.203062i	−0.994832	+	0.101531i	$0.967626\pi$
$230$	0.701813			0.0462761
$231$	−4.55030	+	0.542924i	−0.299388	+	0.0357218i
$232$	0.785666			0.0515815
$233$			0.139538i			0.00914143i	0.999990	+	0.00457072i	$0.00145491\pi$
$233$			0.139538i			0.00914143i	−0.999990	+	0.00457072i	$0.998545\pi$
$234$	1.32729	+	1.89467i	0.0867679	+	0.123859i
$235$	11.4514			0.747009
$236$	4.36347			0.284038
$237$	−1.98582	+	3.81576i	−0.128993	+	0.247860i
$238$	5.45804	+	8.00186i	0.353792	+	0.518684i
$239$			21.9169i			1.41769i	0.705366	+	0.708843i	$0.250783\pi$
$239$			21.9169i			1.41769i	−0.705366	+	0.708843i	$0.749217\pi$
$240$	1.42794	−	2.74380i	0.0921733	−	0.177111i
$241$			8.92051i			0.574620i	0.957838	+	0.287310i	$0.0927610\pi$
$241$			8.92051i			0.574620i	−0.957838	+	0.287310i	$0.907239\pi$
$242$		−	1.12088i		−	0.0720528i
$243$	10.5378	+	11.4871i	0.676001	+	0.736901i
$244$			3.81830i			0.244442i
$245$	−2.32792	+	5.93879i	−0.148726	+	0.379415i
$246$	−16.5156	−	8.59514i	−1.05300	−	0.548006i
$247$	−0.493909			−0.0314267
$248$	−27.0806			−1.71962
$249$	−3.15478	+	6.06193i	−0.199926	+	0.384159i
$250$			9.36586i			0.592349i
$251$	20.7247			1.30813			0.654065	−	0.756439i	$-0.273062\pi$
$251$	20.7247			1.30813			0.654065	+	0.756439i	$0.273062\pi$
$252$	−5.52175	−	2.08534i	−0.347837	−	0.131364i
$253$	0.687108			0.0431981
$254$		−	1.56375i		−	0.0981182i
$255$	−2.37986	+	4.57291i	−0.149033	+	0.286367i
$256$	−15.0741			−0.942129
$257$	−21.2823			−1.32755			−0.663775	−	0.747932i	$-0.731047\pi$
$257$	−21.2823			−1.32755			−0.663775	+	0.747932i	$0.731047\pi$
$258$	14.8079	+	7.70641i	0.921900	+	0.479780i
$259$	−8.32783	+	5.68038i	−0.517466	+	0.352962i
$260$		−	0.466180i		−	0.0289113i
$261$	−0.627728	+	0.439748i	−0.0388554	+	0.0272197i
$262$		−	2.87026i		−	0.177325i
$263$			7.64499i			0.471410i	0.971825	+	0.235705i	$0.0757400\pi$
$263$			7.64499i			0.471410i	−0.971825	+	0.235705i	$0.924260\pi$
$264$	2.45899	−	4.72497i	0.151341	−	0.290802i
$265$			4.63853i			0.284943i
$266$	−1.75889	+	1.19974i	−0.107845	+	0.0735605i
$267$	9.68034	−	18.6008i	0.592427	−	1.13835i
$268$	−6.09572			−0.372355
$269$	22.2430			1.35618			0.678089	−	0.734980i	$-0.262808\pi$
$269$	22.2430			1.35618			0.678089	+	0.734980i	$0.262808\pi$
$270$	0.694507	+	5.26171i	0.0422664	+	0.320218i
$271$			21.5031i			1.30622i	0.757263	+	0.653110i	$0.226536\pi$
$271$			21.5031i			1.30622i	−0.757263	+	0.653110i	$0.773464\pi$
$272$	−6.40089			−0.388111
$273$	3.13039	−	0.373505i	0.189460	−	0.0226056i
$274$	20.9739			1.26708
$275$			4.16962i			0.251438i
$276$	0.785052	+	0.408561i	0.0472546	+	0.0245925i
$277$	−8.02374			−0.482100			−0.241050	−	0.970513i	$-0.577492\pi$
$277$	−8.02374			−0.482100			−0.241050	+	0.970513i	$0.577492\pi$
$278$	16.2333			0.973611
$279$	21.6367	−	15.1574i	1.29536	−	0.907450i
$280$	−4.17792	−	6.12511i	−0.249678	−	0.366046i
$281$		−	10.8576i		−	0.647711i	−0.946107	−	0.323855i	$-0.895021\pi$
$281$		−	10.8576i		−	0.647711i	0.946107	−	0.323855i	$-0.104979\pi$
$282$	−21.6419	−	11.2630i	−1.28876	−	0.670702i
$283$		−	27.4578i		−	1.63219i	−0.577915	−	0.816097i	$-0.696133\pi$
$283$		−	27.4578i		−	1.63219i	0.577915	−	0.816097i	$-0.303867\pi$
$284$		−	4.24964i		−	0.252170i
$285$	−1.00517	−	0.523118i	−0.0595414	−	0.0309869i
$286$			0.771110i			0.0455967i
$287$	−20.9611	+	14.2975i	−1.23729	+	0.843954i
$288$	9.71506	−	6.80579i	0.572466	−	0.401035i
$289$	−6.33205			−0.372474
$290$	−0.260945			−0.0153232
$291$	14.3390	+	7.46236i	0.840564	+	0.437451i
$292$		−	6.73332i		−	0.394038i
$293$	20.7918			1.21467			0.607336	−	0.794445i	$-0.292238\pi$
$293$	20.7918			1.21467			0.607336	+	0.794445i	$0.292238\pi$
$294$	10.2406	−	8.93402i	0.597242	−	0.521043i
$295$	−5.34701			−0.311315
$296$		−	11.7172i		−	0.681048i
$297$	0.679956	+	5.15147i	0.0394550	+	0.298919i
$298$	−26.0913			−1.51143
$299$	−0.472697			−0.0273368
$300$	−2.47930	+	4.76398i	−0.143142	+	0.275048i
$301$	18.7937	−	12.8191i	1.08325	−	0.738882i
$302$			14.4099i			0.829195i
$303$	13.7609	−	26.4416i	0.790543	−	1.51903i
$304$		−	1.40698i		−	0.0806960i
$305$		−	4.67896i		−	0.267917i
$306$	8.99532	−	6.30158i	0.514228	−	0.360237i
$307$			3.48537i			0.198921i	0.995042	+	0.0994604i	$0.0317117\pi$
$307$			3.48537i			0.198921i	−0.995042	+	0.0994604i	$0.968288\pi$
$308$	−1.10865	−	1.62536i	−0.0631715	−	0.0926137i
$309$	15.3814	+	8.00486i	0.875016	+	0.455380i
$310$	8.99435			0.510845
$311$	−22.1846			−1.25797			−0.628987	−	0.777415i	$-0.716530\pi$
$311$	−22.1846			−1.25797			−0.628987	+	0.777415i	$0.716530\pi$
$312$	−1.69167	+	3.25055i	−0.0957719	+	0.184026i
$313$		−	26.2044i		−	1.48116i	−0.671968	−	0.740580i	$-0.734551\pi$
$313$		−	26.2044i		−	1.48116i	0.671968	−	0.740580i	$-0.265449\pi$
$314$	17.5358			0.989600
$315$	6.76637	+	2.55538i	0.381242	+	0.143979i
$316$	−1.84682			−0.103892
$317$			14.6776i			0.824377i	0.911099	+	0.412188i	$0.135235\pi$
$317$			14.6776i			0.824377i	−0.911099	+	0.412188i	$0.864765\pi$
$318$	4.56220	−	8.76630i	0.255836	−	0.491590i
$319$	−0.255478			−0.0143040
$320$	7.61017			0.425421
$321$	4.39478	+	2.28715i	0.245292	+	0.127656i
$322$	−1.68336	+	1.14821i	−0.0938097	+	0.0639873i
$323$			2.34493i			0.130475i
$324$	−2.28623	+	6.29009i	−0.127013	+	0.349450i
$325$		−	2.86850i		−	0.159116i
$326$		−	13.0526i		−	0.722917i
$327$	8.92410	−	17.1477i	0.493504	−	0.948270i
$328$		−	29.4921i		−	1.62843i
$329$	−27.4672	+	18.7353i	−1.51432	+	1.03291i
$330$	−0.816713	+	1.56932i	−0.0449585	+	0.0863881i
$331$	−11.4478			−0.629227			−0.314613	−	0.949220i	$-0.601875\pi$
$331$	−11.4478			−0.629227			−0.314613	+	0.949220i	$0.601875\pi$
$332$	−2.93396			−0.161022
$333$	6.55828	+	9.36176i	0.359392	+	0.513021i
$334$		−	5.34176i		−	0.292288i
$335$	7.46971			0.408114
$336$	1.06399	+	8.91743i	0.0580456	+	0.486486i
$337$	−23.3907			−1.27417			−0.637086	−	0.770793i	$-0.719860\pi$
$337$	−23.3907			−1.27417			−0.637086	+	0.770793i	$0.719860\pi$
$338$			14.0409i			0.763726i
$339$	11.8386	+	6.16109i	0.642982	+	0.334624i
$340$	−2.21328			−0.120032
$341$	8.80590			0.476866
$342$	1.38515	+	1.97727i	0.0749006	+	0.106918i
$343$	−4.13253	−	18.0533i	−0.223136	−	0.974787i
$344$			26.4426i			1.42569i
$345$	−0.962005	−	0.500652i	−0.0517926	−	0.0269542i
$346$			27.1305i			1.45854i
$347$			5.81627i			0.312234i	0.987739	+	0.156117i	$0.0498976\pi$
$347$			5.81627i			0.312234i	−0.987739	+	0.156117i	$0.950102\pi$
$348$	−0.291895	−	0.151910i	−0.0156472	−	0.00814321i
$349$		−	6.74800i		−	0.361212i	−0.983556	−	0.180606i	$-0.942194\pi$
$349$		−	6.74800i		−	0.361212i	0.983556	−	0.180606i	$-0.0578059\pi$
$350$	−6.96776	−	10.2152i	−0.372443	−	0.546026i
$351$	−0.467777	−	3.54396i	−0.0249681	−	0.189163i
$352$	3.95392			0.210745
$353$	−0.766904			−0.0408182			−0.0204091	−	0.999792i	$-0.506497\pi$
$353$	−0.766904			−0.0408182			−0.0204091	+	0.999792i	$0.506497\pi$
$354$	10.1052	+	5.25903i	0.537088	+	0.279514i
$355$			5.20752i			0.276387i
$356$	9.00276			0.477146
$357$	−1.77329	−	14.8621i	−0.0938524	−	0.786586i
$358$	19.7531			1.04399
$359$			23.6117i			1.24618i	0.782152	+	0.623088i	$0.214122\pi$
$359$			23.6117i			1.24618i	−0.782152	+	0.623088i	$0.785878\pi$
$360$	−6.88557	+	4.82361i	−0.362901	+	0.254227i
$361$	18.4846			0.972872
$362$	8.71416			0.458006
$363$	−0.799601	+	1.53644i	−0.0419682	+	0.0806420i
$364$	0.762701	+	1.11817i	0.0399764	+	0.0586081i
$365$			8.25104i			0.431879i
$366$	−4.60197	+	8.84270i	−0.240549	+	0.462216i
$367$			20.5896i			1.07477i	0.843338	+	0.537384i	$0.180587\pi$
$367$			20.5896i			1.07477i	−0.843338	+	0.537384i	$0.819413\pi$
$368$		−	1.34656i		−	0.0701942i
$369$	16.5072	+	23.5635i	0.859328	+	1.22667i
$370$			3.89166i			0.202318i
$371$	−7.58894	−	11.1259i	−0.393998	−	0.577628i
$372$	10.0611	+	5.23607i	0.521646	+	0.271478i
$373$	22.0764			1.14307			0.571537	−	0.820576i	$-0.306347\pi$
$373$	22.0764			1.14307			0.571537	+	0.820576i	$0.306347\pi$
$374$	3.66099			0.189305
$375$	6.68132	−	12.8382i	0.345022	−	0.662961i
$376$		−	38.6462i		−	1.99302i
$377$	0.175756			0.00905192
$378$	−10.2743	−	11.4844i	−0.528455	−	0.590694i
$379$	−30.1056			−1.54642			−0.773211	−	0.634149i	$-0.781351\pi$
$379$	−30.1056			−1.54642			−0.773211	+	0.634149i	$0.781351\pi$
$380$		−	0.486503i		−	0.0249571i
$381$	−1.11553	+	2.14350i	−0.0571504	+	0.109815i
$382$	8.35255			0.427354
$383$	−16.6645			−0.851518			−0.425759	−	0.904837i	$-0.639993\pi$
$383$	−16.6645			−0.851518			−0.425759	+	0.904837i	$0.639993\pi$
$384$	−2.23246	−	1.16183i	−0.113925	−	0.0592893i
$385$	1.35855	+	1.99173i	0.0692381	+	0.101508i
$386$		−	19.6193i		−	0.998596i
$387$	−14.8003	−	21.1270i	−0.752343	−	1.07395i
$388$			6.94003i			0.352326i
$389$		−	4.42991i		−	0.224605i	−0.993674	−	0.112303i	$-0.964177\pi$
$389$		−	4.42991i		−	0.224605i	0.993674	−	0.112303i	$-0.0358226\pi$
$390$	0.561859	−	1.07961i	0.0284508	−	0.0546684i
$391$			2.24422i			0.113495i
$392$	20.0422	+	7.85625i	1.01228	+	0.396801i
$393$	−2.04756	+	3.93440i	−0.103286	+	0.198464i
$394$	31.4138			1.58261
$395$	2.26310			0.113869
$396$	−1.82716	+	1.28000i	−0.0918182	+	0.0643223i
$397$		−	17.8336i		−	0.895045i	−0.894273	−	0.447523i	$-0.852306\pi$
$397$		−	17.8336i		−	0.895045i	0.894273	−	0.447523i	$-0.147694\pi$
$398$	3.25294			0.163055
$399$	3.26685	−	0.389788i	0.163547	−	0.0195138i
$400$	8.17140			0.408570
$401$		−	0.554521i		−	0.0276914i	−0.999904	−	0.0138457i	$-0.995593\pi$
$401$		−	0.554521i		−	0.0276914i	0.999904	−	0.0138457i	$-0.00440737\pi$
$402$	−14.1169	−	7.34680i	−0.704087	−	0.366425i
$403$	−6.05804			−0.301772
$404$	12.7977			0.636709
$405$	2.80156	−	7.70790i	0.139211	−	0.383009i
$406$	0.625899	−	0.426923i	0.0310628	−	0.0211879i
$407$			3.81013i			0.188861i
$408$	15.4326	+	8.03152i	0.764028	+	0.397620i
$409$			37.5869i			1.85855i	0.369387	+	0.929276i	$0.379568\pi$
$409$			37.5869i			1.85855i	−0.369387	+	0.929276i	$0.620432\pi$
$410$			9.79529i			0.483755i
$411$	−28.7498	−	14.9621i	−1.41812	−	0.738028i
$412$			7.44455i			0.366767i
$413$	12.8253	−	8.74806i	0.631090	−	0.430464i
$414$	1.32567	+	1.89235i	0.0651529	+	0.0930039i
$415$	3.59529			0.176486
$416$	−2.72010			−0.133364
$417$	−22.2518	−	11.5804i	−1.08967	−	0.567094i
$418$			0.804725i			0.0393604i
$419$	−2.79077			−0.136338			−0.0681689	−	0.997674i	$-0.521716\pi$
$419$	−2.79077			−0.136338			−0.0681689	+	0.997674i	$0.521716\pi$
$420$	0.367904	+	3.08344i	0.0179519	+	0.150457i
$421$	−22.2982			−1.08675			−0.543374	−	0.839491i	$-0.682853\pi$
$421$	−22.2982			−1.08675			−0.543374	+	0.839491i	$0.682853\pi$
$422$		−	1.66597i		−	0.0810983i
$423$	21.6308	+	30.8774i	1.05173	+	1.50131i
$424$	15.6541			0.760229
$425$	−13.6187			−0.660606
$426$	5.12183	−	9.84162i	0.248154	−	0.476828i
$427$	7.65509	+	11.2229i	0.370456	+	0.543113i
$428$			2.12706i			0.102815i
$429$	0.550087	−	1.05699i	0.0265584	−	0.0510322i
$430$		−	8.78246i		−	0.423528i
$431$			8.80016i			0.423889i	0.977282	+	0.211944i	$0.0679796\pi$
$431$			8.80016i			0.423889i	−0.977282	+	0.211944i	$0.932020\pi$
$432$	10.0956	−	1.33254i	0.485724	−	0.0641119i
$433$		−	18.1703i		−	0.873209i	−0.899654	−	0.436604i	$-0.856181\pi$
$433$		−	18.1703i		−	0.873209i	0.899654	−	0.436604i	$-0.143819\pi$
$434$	−21.5737	+	14.7153i	−1.03557	+	0.706359i
$435$	0.357689	+	0.186151i	0.0171499	+	0.00892524i
$436$	8.29946			0.397472
$437$	−0.493304			−0.0235979
$438$	8.11526	−	15.5935i	0.387762	−	0.745087i
$439$			17.4614i			0.833389i	0.909047	+	0.416694i	$0.136811\pi$
$439$			17.4614i			0.833389i	−0.909047	+	0.416694i	$0.863189\pi$
$440$	−2.80235			−0.133597
$441$	−20.4105	+	4.94093i	−0.971927	+	0.235283i
$442$	−2.51859			−0.119797
$443$			8.88364i			0.422074i	0.977478	+	0.211037i	$0.0676841\pi$
$443$			8.88364i			0.422074i	−0.977478	+	0.211037i	$0.932316\pi$
$444$	−2.26554	+	4.35324i	−0.107518	+	0.206596i
$445$	−11.0320			−0.522968
$446$	18.3357			0.868219
$447$	35.7645	+	18.6128i	1.69161	+	0.880354i
$448$	−18.2536	+	12.4507i	−0.862403	+	0.588242i
$449$		−	20.5058i		−	0.967727i	−0.875144	−	0.483863i	$-0.839233\pi$
$449$		−	20.5058i		−	0.967727i	0.875144	−	0.483863i	$-0.160767\pi$
$450$	−11.4835	+	8.04463i	−0.541336	+	0.379227i
$451$			9.59006i			0.451579i
$452$			5.72984i			0.269509i
$453$	10.2796	−	19.7523i	0.482977	−	0.928042i
$454$		−	8.65365i		−	0.406136i
$455$	−0.934617	−	1.37021i	−0.0438155	−	0.0642365i
$456$	−1.76541	+	3.39225i	−0.0826731	+	0.158857i
$457$	−24.3127			−1.13730			−0.568651	−	0.822579i	$-0.692534\pi$
$457$	−24.3127			−1.13730			−0.568651	+	0.822579i	$0.692534\pi$
$458$	−3.44434			−0.160943
$459$	−16.8256	+	2.22086i	−0.785354	+	0.103661i
$460$		−	0.465609i		−	0.0217091i
$461$	−1.85809			−0.0865399			−0.0432700	−	0.999063i	$-0.513778\pi$
$461$	−1.85809			−0.0865399			−0.0432700	+	0.999063i	$0.513778\pi$
$462$	−0.608552	−	5.10033i	−0.0283124	−	0.237289i
$463$	2.71924			0.126374			0.0631868	−	0.998002i	$-0.479874\pi$
$463$	2.71924			0.126374			0.0631868	+	0.998002i	$0.479874\pi$
$464$			0.500672i			0.0232431i
$465$	−12.3290	−	6.41630i	−0.571742	−	0.297549i
$466$	−0.156405			−0.00724532
$467$	−33.5357			−1.55184			−0.775922	−	0.630828i	$-0.782715\pi$
$467$	−33.5357			−1.55184			−0.775922	+	0.630828i	$0.782715\pi$
$468$	1.25700	−	0.880576i	0.0581047	−	0.0407047i
$469$	−17.9167	+	12.2209i	−0.827318	+	0.564310i
$470$			12.8357i			0.592065i
$471$	−24.0370	−	12.5095i	−1.10757	−	0.576407i
$472$			18.0450i			0.830591i
$473$		−	8.59846i		−	0.395357i
$474$	−4.27700	−	2.22586i	−0.196449	−	0.102237i
$475$		−	2.99355i		−	0.137353i
$476$	5.30874	−	3.62107i	0.243325	−	0.165971i
$477$	−12.5072	+	8.76181i	−0.572667	+	0.401176i
$478$	−24.5662			−1.12363
$479$	12.0569			0.550896			0.275448	−	0.961316i	$-0.411174\pi$
$479$	12.0569			0.550896			0.275448	+	0.961316i	$0.411174\pi$
$480$	−5.53580	−	2.88097i	−0.252673	−	0.131498i
$481$		−	2.62118i		−	0.119516i
$482$	−9.99880			−0.455433
$483$	3.12655	−	0.373048i	0.142263	−	0.0169743i
$484$	−0.743632			−0.0338015
$485$		−	8.50434i		−	0.386162i
$486$	−12.8757	+	11.8116i	−0.584053	+	0.535785i
$487$	34.6685			1.57098			0.785490	−	0.618874i	$-0.212411\pi$
$487$	34.6685			1.57098			0.785490	+	0.618874i	$0.212411\pi$
$488$	−15.7905			−0.714803
$489$	−9.31134	+	17.8918i	−0.421074	+	0.809095i
$490$	−6.65666	−	2.60932i	−0.300717	−	0.117877i
$491$		−	14.7036i		−	0.663563i	−0.943356	−	0.331782i	$-0.892350\pi$
$491$		−	14.7036i		−	0.663563i	0.943356	−	0.331782i	$-0.107650\pi$
$492$	−5.70234	+	10.9571i	−0.257081	+	0.493983i
$493$		−	0.834438i		−	0.0375812i
$494$		−	0.553612i		−	0.0249082i
$495$	2.23901	−	1.56851i	0.100636	−	0.0704994i
$496$		−	17.2573i		−	0.774877i
$497$	−8.51984	−	12.4907i	−0.382167	−	0.560283i
$498$	−6.79468	−	3.53613i	−0.304477	−	0.158458i
$499$	21.7764			0.974845			0.487422	−	0.873166i	$-0.337937\pi$
$499$	21.7764			0.974845			0.487422	+	0.873166i	$0.337937\pi$
$500$	6.21366			0.277883
$501$	−3.81065	+	7.32218i	−0.170247	+	0.327131i
$502$			23.2298i			1.03680i
$503$	−13.8255			−0.616447			−0.308223	−	0.951314i	$-0.599734\pi$
$503$	−13.8255			−0.616447			−0.308223	+	0.951314i	$0.599734\pi$
$504$	8.62386	−	22.8351i	0.384137	−	1.01716i
$505$	−15.6823			−0.697855
$506$			0.770165i			0.0342380i
$507$	10.0164	−	19.2465i	0.444843	−	0.854768i
$508$	−1.03745			−0.0460293
$509$	7.82530			0.346850			0.173425	−	0.984847i	$-0.444517\pi$
$509$	7.82530			0.346850			0.173425	+	0.984847i	$0.444517\pi$
$510$	−5.12568	−	2.66753i	−0.226969	−	0.118120i
$511$	−13.4992	−	19.7908i	−0.597171	−	0.875493i
$512$		−	19.8022i		−	0.875142i
$513$	−0.488169	−	3.69846i	−0.0215532	−	0.163291i
$514$		−	23.8548i		−	1.05219i
$515$		−	9.12258i		−	0.401989i
$516$	5.11272	−	9.82412i	0.225075	−	0.432483i
$517$			12.5667i			0.552684i
$518$	−6.36701	−	9.33448i	−0.279751	−	0.410133i
$519$	19.3541	−	37.1890i	0.849550	−	1.63241i
$520$	1.92788			0.0845431
$521$	−15.1149			−0.662194			−0.331097	−	0.943597i	$-0.607419\pi$
$521$	−15.1149			−0.662194			−0.331097	+	0.943597i	$0.607419\pi$
$522$	−0.492904	−	0.703606i	−0.0215738	−	0.0307960i
$523$			26.1240i			1.14232i	0.820838	+	0.571161i	$0.193507\pi$
$523$			26.1240i			1.14232i	−0.820838	+	0.571161i	$0.806493\pi$
$524$	−1.90424			−0.0831871
$525$	2.26379	+	18.9730i	0.0987998	+	0.828051i
$526$	−8.56910			−0.373631
$527$			28.7617i			1.25288i
$528$	3.01103	+	1.56701i	0.131038	+	0.0681956i
$529$	22.5279			0.979473
$530$	−5.19923			−0.225840
$531$	−10.1001	−	14.4176i	−0.438306	−	0.625669i
$532$	0.795950	+	1.16692i	0.0345088	+	0.0505923i
$533$		−	6.59750i		−	0.285769i
$534$	20.8493	+	10.8505i	0.902236	+	0.469546i
$535$		−	2.60651i		−	0.112689i
$536$		−	25.2087i		−	1.08885i
$537$	−27.0765	−	14.0913i	−1.16844	−	0.608084i
$538$			24.9317i			1.07488i
$539$	−6.51719	−	2.55465i	−0.280715	−	0.110036i
$540$	3.49082	−	0.460762i	0.150221	−	0.0198280i
$541$	42.2372			1.81592			0.907960	−	0.419058i	$-0.137639\pi$
$541$	42.2372			1.81592			0.907960	+	0.419058i	$0.137639\pi$
$542$	−24.1023			−1.03528
$543$	−11.9449	−	6.21642i	−0.512604	−	0.266772i
$544$			12.9142i			0.553693i
$545$	−10.1702			−0.435643
$546$	0.418654	+	3.50878i	0.0179167	+	0.150162i
$547$	−2.48045			−0.106056			−0.0530282	−	0.998593i	$-0.516887\pi$
$547$	−2.48045			−0.106056			−0.0530282	+	0.998593i	$0.516887\pi$
$548$		−	13.9149i		−	0.594414i
$549$	12.6162	−	8.83818i	0.538448	−	0.377204i
$550$	−4.67364			−0.199285
$551$	0.183418			0.00781388
$552$	−1.68960	+	3.24657i	−0.0719140	+	0.138183i
$553$	−5.42823	+	3.70258i	−0.230832	+	0.157450i
$554$		−	8.99364i		−	0.382103i
$555$	2.77620	−	5.33447i	0.117843	−	0.226436i
$556$		−	10.7698i		−	0.456742i
$557$			32.4525i			1.37506i	0.726158	+	0.687528i	$0.241304\pi$
$557$			32.4525i			1.37506i	−0.726158	+	0.687528i	$0.758696\pi$
$558$	16.9896	+	24.2522i	0.719227	+	1.02668i
$559$			5.91532i			0.250191i
$560$	3.90328	−	2.66241i	0.164944	−	0.112507i
$561$	−5.01828	−	2.61164i	−0.211872	−	0.110264i
$562$	12.1701			0.513363
$563$	−5.47185			−0.230611			−0.115305	−	0.993330i	$-0.536785\pi$
$563$	−5.47185			−0.230611			−0.115305	+	0.993330i	$0.536785\pi$
$564$	−7.47229	+	14.3580i	−0.314640	+	0.604583i
$565$		−	7.02137i		−	0.295391i
$566$	30.7768			1.29365
$567$	5.89086	+	23.0716i	0.247393	+	0.968915i
$568$	17.5743			0.737401
$569$		−	27.6510i		−	1.15919i	−0.814905	−	0.579594i	$-0.803211\pi$
$569$		−	27.6510i		−	1.15919i	0.814905	−	0.579594i	$-0.196789\pi$
$570$	0.586352	−	1.12668i	0.0245596	−	0.0471914i
$571$	2.47380			0.103525			0.0517626	−	0.998659i	$-0.483516\pi$
$571$	2.47380			0.103525			0.0517626	+	0.998659i	$0.483516\pi$
$572$	0.511583			0.0213904
$573$	−11.4492	−	5.95846i	−0.478297	−	0.248918i
$574$	−16.0257	−	23.4948i	−0.668901	−	0.980655i
$575$		−	2.86498i		−	0.119478i
$576$	14.3750	+	20.5199i	0.598958	+	0.854995i
$577$			16.9184i			0.704323i	0.935939	+	0.352161i	$0.114553\pi$
$577$			16.9184i			0.704323i	−0.935939	+	0.352161i	$0.885447\pi$
$578$		−	7.09746i		−	0.295215i
$579$	−13.9958	+	26.8930i	−0.581646	+	1.11764i
$580$			0.173121i			0.00718845i
$581$	−8.62360	+	5.88212i	−0.357767	+	0.244032i
$582$	−8.36439	+	16.0722i	−0.346715	+	0.666215i
$583$	−5.09030			−0.210819
$584$	27.8455			1.15226
$585$	−1.54033	+	1.07906i	−0.0636848	+	0.0446137i
$586$			23.3051i			0.962725i
$587$	20.9582			0.865039			0.432519	−	0.901625i	$-0.357625\pi$
$587$	20.9582			0.865039			0.432519	+	0.901625i	$0.357625\pi$
$588$	−5.92716	−	6.79398i	−0.244432	−	0.280179i
$589$	−6.32213			−0.260499
$590$		−	5.99335i		−	0.246742i
$591$	−43.0603	−	22.4097i	−1.77127	−	0.921812i
$592$	7.46688			0.306887
$593$	21.8317			0.896521			0.448260	−	0.893903i	$-0.352044\pi$
$593$	21.8317			0.896521			0.448260	+	0.893903i	$0.352044\pi$
$594$	−5.77417	+	0.762148i	−0.236917	+	0.0312713i
$595$	−6.50535	+	4.43727i	−0.266693	+	0.181910i
$596$			17.3100i			0.709044i
$597$	−4.45894	−	2.32055i	−0.182492	−	0.0949737i
$598$		−	0.529836i		−	0.0216666i
$599$			40.4129i			1.65123i	0.564236	+	0.825613i	$0.309171\pi$
$599$			40.4129i			1.65123i	−0.564236	+	0.825613i	$0.690829\pi$
$600$	−19.7013	−	10.2531i	−0.804304	−	0.418580i
$601$			16.2442i			0.662614i	0.943523	+	0.331307i	$0.107490\pi$
$601$			16.2442i			0.662614i	−0.943523	+	0.331307i	$0.892510\pi$
$602$	14.3687	+	21.0655i	0.585624	+	0.858564i
$603$	14.1097	+	20.1412i	0.574591	+	0.820211i
$604$	9.56005			0.388993
$605$	0.911250			0.0370476
$606$	29.6378	+	15.4243i	1.20395	+	0.626569i
$607$		−	32.8202i		−	1.33213i	−0.745894	−	0.666065i	$-0.767977\pi$
$607$		−	32.8202i		−	1.33213i	0.745894	−	0.666065i	$-0.232023\pi$
$608$	−2.83868			−0.115124
$609$	−1.16250	+	0.138705i	−0.0471069	+	0.00562061i
$610$	5.24455			0.212346
$611$		−	8.64530i		−	0.349752i
$612$	−4.18070	−	5.96783i	−0.168995	−	0.241235i
$613$	−0.463359			−0.0187149			−0.00935744	−	0.999956i	$-0.502979\pi$
$613$	−0.463359			−0.0187149			−0.00935744	+	0.999956i	$0.502979\pi$
$614$	−3.90668			−0.157661
$615$	6.98767	−	13.4268i	0.281770	−	0.541422i
$616$	6.72166	−	4.58482i	0.270823	−	0.184728i
$617$		−	23.3771i		−	0.941128i	−0.882366	−	0.470564i	$-0.844050\pi$
$617$		−	23.3771i		−	0.941128i	0.882366	−	0.470564i	$-0.155950\pi$
$618$	−8.97247	+	17.2406i	−0.360926	+	0.693520i
$619$		−	34.7406i		−	1.39634i	−0.715930	−	0.698172i	$-0.753997\pi$
$619$		−	34.7406i		−	1.39634i	0.715930	−	0.698172i	$-0.246003\pi$
$620$		−	5.96719i		−	0.239648i
$621$	−0.467203	−	3.53962i	−0.0187482	−	0.142040i
$622$		−	24.8663i		−	0.997046i
$623$	26.4612	−	18.0491i	1.06015	−	0.723122i
$624$	−2.07144	−	1.07803i	−0.0829240	−	0.0431558i
$625$	13.2339			0.529355
$626$	29.3719			1.17394
$627$	0.574067	−	1.10307i	0.0229260	−	0.0440525i
$628$		−	11.6339i		−	0.464242i
$629$	−12.4446			−0.496197
$630$	−2.86427	+	7.58428i	−0.114115	+	0.302165i
$631$	34.0797			1.35669			0.678345	−	0.734743i	$-0.262697\pi$
$631$	34.0797			1.35669			0.678345	+	0.734743i	$0.262697\pi$
$632$		−	7.63749i		−	0.303803i
$633$	−1.18846	+	2.28362i	−0.0472369	+	0.0907658i
$634$	−16.4518			−0.653385
$635$	1.27129			0.0504497
$636$	−5.81589	−	3.02674i	−0.230615	−	0.120018i
$637$	4.48351	+	1.75747i	0.177643	+	0.0696337i
$638$		−	0.286360i		−	0.0113371i
$639$	−14.0414	+	9.83658i	−0.555471	+	0.389129i
$640$			1.32406i			0.0523379i
$641$		−	32.5233i		−	1.28459i	−0.766456	−	0.642297i	$-0.777982\pi$
$641$		−	32.5233i		−	1.28459i	0.766456	−	0.642297i	$-0.222018\pi$
$642$	−2.56362	+	4.92601i	−0.101178	+	0.194414i
$643$			28.8060i			1.13600i	0.823029	+	0.567999i	$0.192282\pi$
$643$			28.8060i			1.13600i	−0.823029	+	0.567999i	$0.807718\pi$
$644$	0.761766	+	1.11680i	0.0300178	+	0.0440081i
$645$	−6.26515	+	12.0385i	−0.246690	+	0.474016i
$646$	−2.62838			−0.103412
$647$	−10.1544			−0.399211			−0.199606	−	0.979876i	$-0.563966\pi$
$647$	−10.1544			−0.399211			−0.199606	+	0.979876i	$0.563966\pi$
$648$	−26.0126	−	9.45467i	−1.02187	−	0.371414i
$649$		−	5.86778i		−	0.230330i
$650$	3.21524			0.126112
$651$	40.0695	−	4.78094i	1.57045	−	0.187380i
$652$	−8.65959			−0.339136
$653$			8.73458i			0.341810i	0.985287	+	0.170905i	$0.0546692\pi$
$653$			8.73458i			0.341810i	−0.985287	+	0.170905i	$0.945331\pi$
$654$	19.2205	+	10.0028i	0.751581	+	0.391142i
$655$	2.33346			0.0911759
$656$	18.7941			0.733786
$657$	−22.2479	+	15.5855i	−0.867973	+	0.608050i
$658$	−21.0000	−	30.7874i	−0.818664	−	1.20022i
$659$			7.73635i			0.301366i	0.988582	+	0.150683i	$0.0481472\pi$
$659$			7.73635i			0.301366i	−0.988582	+	0.150683i	$0.951853\pi$
$660$	1.04114	+	0.541838i	0.0405265	+	0.0210910i
$661$		−	29.9735i		−	1.16583i	−0.812532	−	0.582917i	$-0.801911\pi$
$661$		−	29.9735i		−	1.16583i	0.812532	−	0.582917i	$-0.198089\pi$
$662$		−	12.8316i		−	0.498713i
$663$	3.45234	+	1.79668i	0.134078	+	0.0697774i
$664$		−	12.1333i		−	0.470865i
$665$	−0.975360	−	1.42994i	−0.0378228	−	0.0554509i
$666$	−10.4934	+	7.35103i	−0.406610	+	0.284847i
$667$	0.175541			0.00679698
$668$	−3.54392			−0.137118
$669$	−25.1335	−	13.0801i	−0.971718	−	0.505707i
$670$			8.37264i			0.323463i
$671$	5.13466			0.198222
$672$	17.9915	−	2.14668i	0.694038	−	0.0828099i
$673$	−11.5118			−0.443748			−0.221874	−	0.975075i	$-0.571217\pi$
$673$	−11.5118			−0.443748			−0.221874	+	0.975075i	$0.571217\pi$
$674$		−	26.2181i		−	1.00988i
$675$	21.4797	−	2.83516i	0.826754	−	0.109125i
$676$	9.31528			0.358280
$677$	21.9575			0.843895			0.421947	−	0.906620i	$-0.361347\pi$
$677$	21.9575			0.843895			0.421947	+	0.906620i	$0.361347\pi$
$678$	−6.90583	+	13.2696i	−0.265217	+	0.509615i
$679$	13.9136	+	20.3984i	0.533957	+	0.782817i
$680$		−	9.15298i		−	0.351001i
$681$	−6.17325	+	11.8619i	−0.236560	+	0.454550i
$682$			9.87034i			0.377955i
$683$			47.3873i			1.81323i	0.421964	+	0.906613i	$0.361341\pi$
$683$			47.3873i			1.81323i	−0.421964	+	0.906613i	$0.638659\pi$
$684$	1.31179	−	0.918963i	0.0501577	−	0.0351374i
$685$			17.0513i			0.651498i
$686$	20.2356	−	4.63206i	0.772597	−	0.176853i
$687$	4.72130	+	2.45709i	0.180129	+	0.0937437i
$688$	−16.8508			−0.642430
$689$	3.50188			0.133411
$690$	0.561170	−	1.07829i	0.0213634	−	0.0410498i
$691$		−	7.32735i		−	0.278746i	−0.990240	−	0.139373i	$-0.955491\pi$
$691$		−	7.32735i		−	0.278746i	0.990240	−	0.139373i	$-0.0445086\pi$
$692$	17.9994			0.684234
$693$	−2.80426	+	7.42537i	−0.106525	+	0.282067i
$694$	−6.51933			−0.247470
$695$			13.1974i			0.500605i
$696$	0.628219	−	1.20713i	0.0238126	−	0.0457560i
$697$	−31.3229			−1.18644
$698$	7.56368			0.286290
$699$	0.214391	+	0.111575i	0.00810902	+	0.00422014i
$700$	−6.77716	+	4.62267i	−0.256152	+	0.174721i
$701$		−	36.7279i		−	1.38719i	−0.720364	−	0.693596i	$-0.756025\pi$
$701$		−	36.7279i		−	1.38719i	0.720364	−	0.693596i	$-0.243975\pi$
$702$	3.97235	−	0.524321i	0.149927	−	0.0197892i
$703$		−	2.73545i		−	0.103169i
$704$			8.35135i			0.314753i
$705$	9.15658	−	17.5944i	0.344857	−	0.662644i
$706$		−	0.859606i		−	0.0323517i
$707$	37.6154	−	25.6573i	1.41467	−	0.964943i
$708$	3.48904	−	6.70420i	0.131126	−	0.251959i
$709$	−26.4285			−0.992544			−0.496272	−	0.868167i	$-0.665298\pi$
$709$	−26.4285			−0.992544			−0.496272	+	0.868167i	$0.665298\pi$
$710$	−5.83700			−0.219059
$711$	4.27481	+	6.10217i	0.160318	+	0.228849i
$712$			37.2308i			1.39528i
$713$	−6.05061			−0.226597
$714$	16.6586	−	1.98764i	0.623433	−	0.0743856i
$715$	−0.626896			−0.0234446
$716$		−	13.1050i		−	0.489756i
$717$	33.6739	+	17.5248i	1.25758	+	0.654475i
$718$	−26.4658			−0.987695
$719$	−20.9581			−0.781605			−0.390802	−	0.920475i	$-0.627802\pi$
$719$	−20.9581			−0.781605			−0.390802	+	0.920475i	$0.627802\pi$
$720$	−3.07389	−	4.38789i	−0.114557	−	0.163527i
$721$	14.9251	+	21.8813i	0.555841	+	0.814901i
$722$			20.7189i			0.771079i
$723$	13.7058	+	7.13284i	0.509724	+	0.265273i
$724$		−	5.78130i		−	0.214860i
$725$			1.06525i			0.0395623i
$726$	−1.72216	−	0.896255i	−0.0639153	−	0.0332631i
$727$		−	3.46534i		−	0.128522i	−0.997933	−	0.0642612i	$-0.979531\pi$
$727$		−	3.46534i		−	0.128522i	0.997933	−	0.0642612i	$-0.0204691\pi$
$728$	−4.62418	+	3.15414i	−0.171383	+	0.116900i
$729$	26.0753	−	7.00555i	0.965753	−	0.259465i
$730$	−9.24841			−0.342299
$731$	28.0841			1.03873
$732$	5.86658	+	3.05312i	0.216835	+	0.112846i
$733$			8.17540i			0.301965i	0.988536	+	0.150983i	$0.0482438\pi$
$733$			8.17540i			0.301965i	−0.988536	+	0.150983i	$0.951756\pi$
$734$	−23.0784			−0.851840
$735$	7.26317	+	8.32537i	0.267906	+	0.307086i
$736$	−2.71677			−0.100141
$737$			8.19722i			0.301948i
$738$	−26.4118	+	18.5025i	−0.972232	+	0.681087i
$739$	30.5363			1.12329			0.561647	−	0.827377i	$-0.310168\pi$
$739$	30.5363			1.12329			0.561647	+	0.827377i	$0.310168\pi$
$740$	2.58188			0.0949116
$741$	−0.394930	+	0.758860i	−0.0145081	+	0.0278774i
$742$	12.4708	−	8.50628i	0.457817	−	0.312275i
$743$			51.7603i			1.89890i	0.313914	+	0.949452i	$0.398360\pi$
$743$			51.7603i			1.89890i	−0.313914	+	0.949452i	$0.601640\pi$
$744$	−21.6537	+	41.6076i	−0.793862	+	1.52541i
$745$		−	21.2117i		−	0.777137i
$746$			24.7450i			0.905979i
$747$	6.79120	+	9.69425i	0.248477	+	0.354694i
$748$		−	2.42884i		−	0.0888071i
$749$	4.26442	+	6.25193i	0.155819	+	0.228441i
$750$	14.3900	+	7.48895i	0.525450	+	0.273458i
$751$	4.67882			0.170733			0.0853663	−	0.996350i	$-0.472794\pi$
$751$	4.67882			0.170733			0.0853663	+	0.996350i	$0.472794\pi$
$752$	24.6276			0.898076
$753$	16.5715	−	31.8421i	0.603897	−	1.16039i
$754$			0.197002i			0.00717438i
$755$	−11.7149			−0.426350
$756$	−7.61918	+	6.81638i	−0.277107	+	0.247909i
$757$	−1.65916			−0.0603031			−0.0301515	−	0.999545i	$-0.509599\pi$
$757$	−1.65916			−0.0603031			−0.0301515	+	0.999545i	$0.509599\pi$
$758$		−	33.7447i		−	1.22566i
$759$	0.549412	−	1.05570i	0.0199424	−	0.0383194i
$760$	2.01192			0.0729801
$761$	1.57802			0.0572030			0.0286015	−	0.999591i	$-0.490895\pi$
$761$	1.57802			0.0572030			0.0286015	+	0.999591i	$0.490895\pi$
$762$	−2.40260	−	1.25037i	−0.0870370	−	0.0452963i
$763$	24.3940	−	16.6391i	0.883123	−	0.602375i
$764$		−	5.54139i		−	0.200481i
$765$	5.12305	+	7.31301i	0.185224	+	0.264402i
$766$		−	18.6789i		−	0.674897i
$767$			4.03675i			0.145759i
$768$	−12.0532	+	23.1603i	−0.434933	+	0.835727i
$769$		−	23.8922i		−	0.861575i	−0.902453	−	0.430787i	$-0.858236\pi$
$769$		−	23.8922i		−	0.861575i	0.902453	−	0.430787i	$-0.141764\pi$
$770$	−2.23248	+	1.52277i	−0.0804531	+	0.0548768i
$771$	−17.0173	+	32.6988i	−0.612864	+	1.17762i
$772$	−13.0162			−0.468462
$773$	−3.23860			−0.116484			−0.0582422	−	0.998302i	$-0.518550\pi$
$773$	−3.23860			−0.116484			−0.0582422	+	0.998302i	$0.518550\pi$
$774$	23.6808	−	16.5894i	0.851190	−	0.596292i
$775$		−	36.7173i		−	1.31892i
$776$	−28.7003			−1.03028
$777$	2.06861	+	17.3372i	0.0742109	+	0.621969i
$778$	4.96539			0.178018
$779$		−	6.88511i		−	0.246685i
$780$	−0.716256	−	0.372758i	−0.0256461	−	0.0133469i
$781$	−5.71470			−0.204488
$782$	−2.51550			−0.0899540
$783$	0.173714	+	1.31609i	0.00620802	+	0.0470331i
$784$	−5.00646	+	12.7720i	−0.178802	+	0.456144i
$785$			14.2562i			0.508826i
$786$	−4.40998	−	2.29506i	−0.157299	−	0.0818623i
$787$		−	44.2933i		−	1.57889i	−0.613824	−	0.789443i	$-0.710370\pi$
$787$		−	44.2933i		−	1.57889i	0.613824	−	0.789443i	$-0.289630\pi$
$788$		−	20.8411i		−	0.742434i
$789$	11.7460	+	6.11294i	0.418170	+	0.217626i
$790$			2.53666i			0.0902503i
$791$	11.4874	+	16.8413i	0.408445	+	0.598809i
$792$	−5.29340	−	7.55618i	−0.188093	−	0.268497i
$793$	−3.53240			−0.125439
$794$	19.9893			0.709395
$795$	7.12682	+	3.70898i	0.252762	+	0.131544i
$796$		−	2.15812i		−	0.0764925i
$797$	−38.2431			−1.35464			−0.677320	−	0.735689i	$-0.736859\pi$
$797$	−38.2431			−1.35464			−0.677320	+	0.735689i	$0.736859\pi$
$798$	0.436905	+	3.66174i	0.0154663	+	0.129624i
$799$	−41.0452			−1.45208
$800$		−	16.4864i		−	0.582880i
$801$	−20.8386	−	29.7465i	−0.736295	−	1.05104i
$802$	0.621550			0.0219477
$803$	−9.05463			−0.319531
$804$	−4.87414	+	9.36568i	−0.171898	+	0.330302i
$805$	−0.933471	−	1.36853i	−0.0329005	−	0.0482344i
$806$		−	6.79032i		−	0.239179i
$807$	17.7855	−	34.1749i	0.626079	−	1.20301i
$808$			52.9246i			1.86188i
$809$			5.45780i			0.191886i	0.995387	+	0.0959430i	$0.0305866\pi$
$809$			5.45780i			0.191886i	−0.995387	+	0.0959430i	$0.969413\pi$
$810$	8.63962	+	3.14021i	0.303565	+	0.110336i
$811$			10.9671i			0.385107i	0.981286	+	0.192554i	$0.0616769\pi$
$811$			10.9671i			0.385107i	−0.981286	+	0.192554i	$0.938323\pi$
$812$	−0.283237	−	0.415245i	−0.00993967	−	0.0145722i
$813$	33.0381	+	17.1939i	1.15870	+	0.603016i
$814$	−4.27069			−0.149687
$815$	10.6115			0.371705
$816$	−5.11816	+	9.83456i	−0.179171	+	0.344278i
$817$			6.17319i			0.215973i
$818$	−42.1303			−1.47305
$819$	1.92919	−	5.10830i	0.0674114	−	0.178498i
$820$	6.49856			0.226940
$821$		−	20.1381i		−	0.702826i	−0.936221	−	0.351413i	$-0.885701\pi$
$821$		−	20.1381i		−	0.702826i	0.936221	−	0.351413i	$-0.114299\pi$
$822$	16.7707	−	32.2251i	0.584947	−	1.12398i
$823$	−4.46285			−0.155565			−0.0777825	−	0.996970i	$-0.524784\pi$
$823$	−4.46285			−0.155565			−0.0777825	+	0.996970i	$0.524784\pi$
$824$	−30.7868			−1.07251
$825$	6.40636	+	3.33403i	0.223041	+	0.116076i
$826$	9.80551	+	14.3756i	0.341177	+	0.500189i
$827$			30.1577i			1.04869i	0.851507	+	0.524344i	$0.175689\pi$
$827$			30.1577i			1.04869i	−0.851507	+	0.524344i	$0.824311\pi$
$828$	1.25546	−	0.879497i	0.0436301	−	0.0305646i
$829$			16.5961i			0.576405i	0.957569	+	0.288203i	$0.0930576\pi$
$829$			16.5961i			0.576405i	−0.957569	+	0.288203i	$0.906942\pi$
$830$			4.02988i			0.139879i
$831$	−6.41579	+	12.3280i	−0.222561	+	0.427653i
$832$		−	5.74533i		−	0.199183i
$833$	8.34395	−	21.2863i	0.289101	−	0.737528i
$834$	12.9802	−	24.9415i	0.449467	−	0.863654i
$835$	4.34273			0.150286
$836$	0.533885			0.0184648
$837$	−5.98763	−	45.3634i	−0.206963	−	1.56799i
$838$		−	3.12811i		−	0.108059i
$839$	19.2374			0.664148			0.332074	−	0.943253i	$-0.392252\pi$
$839$	19.2374			0.664148			0.332074	+	0.943253i	$0.392252\pi$
$840$	−12.7515	+	1.52146i	−0.439969	+	0.0524954i
$841$	28.9347			0.997749
$842$		−	24.9936i		−	0.861335i
$843$	−16.6820	−	8.68175i	−0.574560	−	0.299015i
$844$	−1.10527			−0.0380449
$845$	−11.4150			−0.392687
$846$	−34.6098	+	24.2455i	−1.18991	+	0.833578i
$847$	−2.18571	+	1.49086i	−0.0751019	+	0.0512267i
$848$			9.97569i			0.342567i
$849$	−42.1871	−	21.9552i	−1.44786	−	0.753502i
$850$		−	15.2650i		−	0.523584i
$851$		−	2.61797i		−	0.0897428i
$852$	−6.52930	−	3.39801i	−0.223690	−	0.116414i
$853$		−	5.17253i		−	0.177104i	−0.996072	−	0.0885521i	$-0.971776\pi$
$853$		−	5.17253i		−	0.177104i	0.996072	−	0.0885521i	$-0.0282240\pi$
$854$	−12.5795	+	8.58042i	−0.430461	+	0.293616i
$855$	−1.60748	+	1.12610i	−0.0549746	+	0.0385119i
$856$	−8.79643			−0.300656
$857$	−17.6200			−0.601888			−0.300944	−	0.953642i	$-0.597302\pi$
$857$	−17.6200			−0.601888			−0.300944	+	0.953642i	$0.597302\pi$
$858$	1.18476	+	0.616580i	0.0404471	+	0.0210497i
$859$			44.1080i			1.50495i	0.658623	+	0.752473i	$0.271139\pi$
$859$			44.1080i			1.50495i	−0.658623	+	0.752473i	$0.728861\pi$
$860$	−5.82662			−0.198686
$861$	5.20668	+	43.6377i	0.177443	+	1.48717i
$862$	−9.86391			−0.335966
$863$		−	2.55278i		−	0.0868977i	−0.999056	−	0.0434488i	$-0.986165\pi$
$863$		−	2.55278i		−	0.0868977i	0.999056	−	0.0434488i	$-0.0138345\pi$
$864$	−2.68849	−	20.3685i	−0.0914643	−	0.692950i
$865$	−22.0565			−0.749944
$866$	20.3667			0.692088
$867$	−5.06312	+	9.72880i	−0.171952	+	0.330407i
$868$	9.76271	+	14.3128i	0.331368	+	0.485808i
$869$			2.48351i			0.0842474i
$870$	−0.208652	+	0.400926i	−0.00707397	+	0.0135927i
$871$		−	5.63929i		−	0.191080i
$872$			34.3222i			1.16230i
$873$	22.9309	−	16.0640i	0.776093	−	0.543684i
$874$		−	0.552933i		−	0.0187032i
$875$	18.2634	−	12.4574i	0.617415	−	0.421137i
$876$	−10.3453	−	5.38397i	−0.349536	−	0.181907i
$877$	10.7088			0.361610			0.180805	−	0.983519i	$-0.442130\pi$
$877$	10.7088			0.361610			0.180805	+	0.983519i	$0.442130\pi$
$878$	−19.5721			−0.660528
$879$	16.6252	−	31.9453i	0.560753	−	1.07749i
$880$		−	1.78582i		−	0.0601999i
$881$	−39.7417			−1.33893			−0.669467	−	0.742842i	$-0.733477\pi$
$881$	−39.7417			−1.33893			−0.669467	+	0.742842i	$0.733477\pi$
$882$	−5.53818	−	22.8776i	−0.186480	−	0.770330i
$883$	41.2362			1.38771			0.693855	−	0.720115i	$-0.255911\pi$
$883$	41.2362			1.38771			0.693855	+	0.720115i	$0.255911\pi$
$884$			1.67092i			0.0561992i
$885$	−4.27548	+	8.21535i	−0.143719	+	0.276156i
$886$	−9.95747			−0.334528
$887$	32.8277			1.10225			0.551123	−	0.834424i	$-0.314200\pi$
$887$	32.8277			1.10225			0.551123	+	0.834424i	$0.314200\pi$
$888$	−18.0027	−	9.36908i	−0.604132	−	0.314406i
$889$	−3.04930	+	2.07992i	−0.102270	+	0.0697582i
$890$		−	12.3656i		−	0.414494i
$891$	8.45860	+	3.07441i	0.283374	+	0.102997i
$892$		−	12.1646i		−	0.407300i
$893$		−	9.02218i		−	0.301916i
$894$	−20.8627	+	40.0877i	−0.697752	+	1.34073i
$895$			16.0589i			0.536789i
$896$	−2.16624	−	3.17586i	−0.0723690	−	0.106098i
$897$	−0.377969	+	0.726270i	−0.0126200	+	0.0242494i
$898$	22.9845			0.767001
$899$	2.24971			0.0750322
$900$	5.33711	+	7.61856i	0.177904	+	0.253952i
$901$		−	16.6258i		−	0.553887i
$902$	−10.7493			−0.357912
$903$	−4.66831	−	39.1256i	−0.155352	−	1.30202i
$904$	−23.6956			−0.788105
$905$			7.08443i			0.235494i
$906$	22.1399	+	11.5222i	0.735548	+	0.382798i
$907$	1.96030			0.0650906			0.0325453	−	0.999470i	$-0.489639\pi$
$907$	1.96030			0.0650906			0.0325453	+	0.999470i	$0.489639\pi$
$908$	−5.74115			−0.190527
$909$	−29.6227	−	42.2855i	−0.982522	−	1.40252i
$910$	1.53584	−	1.04759i	0.0509126	−	0.0347273i
$911$		−	16.9206i		−	0.560604i	−0.959912	−	0.280302i	$-0.909565\pi$
$911$		−	16.9206i		−	0.560604i	0.959912	−	0.280302i	$-0.0904346\pi$
$912$	−2.16174	−	1.12503i	−0.0715824	−	0.0372533i
$913$			3.94545i			0.130575i
$914$		−	27.2516i		−	0.901403i
$915$	−7.18893	−	3.74130i	−0.237659	−	0.123684i
$916$			2.28510i			0.0755019i
$917$	−5.59701	+	3.81770i	−0.184829	+	0.126071i
$918$	−2.48931	−	18.8595i	−0.0821596	−	0.622456i
$919$	−37.3966			−1.23360			−0.616801	−	0.787119i	$-0.711572\pi$
$919$	−37.3966			−1.23360			−0.616801	+	0.787119i	$0.711572\pi$
$920$	1.92552			0.0634824
$921$	5.35506	+	2.78691i	0.176455	+	0.0918317i
$922$		−	2.08269i		−	0.0685899i
$923$	3.93144			0.129405
$924$	−3.38375	+	0.403736i	−0.111317	+	0.0132819i
$925$	15.8868			0.522354
$926$			3.04793i			0.100161i
$927$	24.5979	−	17.2318i	0.807902	−	0.565967i
$928$	1.01014			0.0331594
$929$	−25.4847			−0.836126			−0.418063	−	0.908418i	$-0.637291\pi$
$929$	−25.4847			−0.836126			−0.418063	+	0.908418i	$0.637291\pi$
$930$	7.19189	−	13.8193i	0.235831	−	0.453151i
$931$	4.67896	+	1.83409i	0.153347	+	0.0601098i
$932$			0.103765i			0.00339893i
$933$	−17.7388	+	34.0853i	−0.580744	+	1.11590i
$934$		−	37.5894i		−	1.22996i
$935$			2.97631i			0.0973357i
$936$	3.64161	+	5.19829i	0.119030	+	0.169911i
$937$			53.0865i			1.73426i	0.498081	+	0.867131i	$0.334038\pi$
$937$			53.0865i			1.73426i	−0.498081	+	0.867131i	$0.665962\pi$
$938$	−13.6982	−	20.0825i	−0.447261	−	0.655716i
$939$	−40.2614	−	20.9531i	−1.31388	−	0.683777i
$940$	8.51566			0.277750
$941$	−16.6313			−0.542164			−0.271082	−	0.962556i	$-0.587381\pi$
$941$	−16.6313			−0.542164			−0.271082	+	0.962556i	$0.587381\pi$
$942$	14.0216	−	26.9426i	0.456849	−	0.877837i
$943$		−	6.58941i		−	0.214581i
$944$	−11.4994			−0.374272
$945$	9.33657	−	8.35282i	0.303719	−	0.271717i
$946$	9.63782			0.313353
$947$			38.5573i			1.25294i	0.779444	+	0.626472i	$0.215502\pi$
$947$			38.5573i			1.25294i	−0.779444	+	0.626472i	$0.784498\pi$
$948$	−1.47672	+	2.83752i	−0.0479616	+	0.0921585i
$949$	6.22915			0.202207
$950$	3.35540			0.108864
$951$	22.5512	+	11.7362i	0.731273	+	0.380573i
$952$	14.9749	+	21.9542i	0.485338	+	0.711539i
$953$		−	22.1094i		−	0.716194i	−0.933684	−	0.358097i	$-0.883426\pi$
$953$		−	22.1094i		−	0.716194i	0.933684	−	0.358097i	$-0.116574\pi$
$954$	−9.82092	−	14.0191i	−0.317964	−	0.453884i
$955$			6.79045i			0.219734i
$956$			16.2981i			0.527119i
$957$	−0.204280	+	0.392526i	−0.00660345	+	0.0126886i
$958$			13.5144i			0.436629i
$959$	−27.8971	−	40.8990i	−0.900844	−	1.32070i
$960$	6.08510	−	11.6925i	0.196396	−	0.377375i
$961$	−46.5440			−1.50142
$962$	2.93803			0.0947258
$963$	7.02813	−	4.92349i	0.226478	−	0.158657i
$964$			6.63358i			0.213653i
$965$	15.9501			0.513451
$966$	0.418141	+	3.50448i	0.0134535	+	0.112755i
$967$	−36.8465			−1.18490			−0.592451	−	0.805606i	$-0.701840\pi$
$967$	−36.8465			−1.18490			−0.592451	+	0.805606i	$0.701840\pi$
$968$		−	3.07528i		−	0.0988432i
$969$	3.60283	+	1.87501i	0.115740	+	0.0602339i
$970$	9.53232			0.306064
$971$	−22.0977			−0.709149			−0.354574	−	0.935028i	$-0.615374\pi$
$971$	−22.0977			−0.709149			−0.354574	+	0.935028i	$0.615374\pi$
$972$	7.83626	+	8.54222i	0.251348	+	0.273992i
$973$	−21.5917	−	31.6550i	−0.692200	−	1.01481i
$974$			38.8592i			1.24513i
$975$	−4.40727	−	2.29365i	−0.141146	−	0.0734557i
$976$		−	10.0626i		−	0.322097i
$977$			26.9989i			0.863772i	0.901928	+	0.431886i	$0.142152\pi$
$977$			26.9989i			0.863772i	−0.901928	+	0.431886i	$0.857848\pi$
$978$	−20.0545	−	10.4369i	−0.641273	−	0.333735i
$979$		−	12.1065i		−	0.386924i
$980$	−1.73112	+	4.41628i	−0.0552986	+	0.141073i
$981$	−19.2106	−	27.4226i	−0.613349	−	0.875538i
$982$	16.4809			0.525927
$983$	−6.31875			−0.201537			−0.100768	−	0.994910i	$-0.532130\pi$
$983$	−6.31875			−0.201537			−0.100768	+	0.994910i	$0.532130\pi$
$984$	−45.3128	−	23.5819i	−1.44452	−	0.751764i
$985$			25.5388i			0.813734i
$986$	0.935303			0.0297861
$987$	6.82278	+	57.1824i	0.217171	+	1.82014i
$988$	−0.367287			−0.0116850
$989$			5.90807i			0.187866i
$990$	1.75811	+	2.50965i	0.0558765	+	0.0797621i
$991$	−23.6178			−0.750243			−0.375122	−	0.926976i	$-0.622399\pi$
$991$	−23.6178			−0.750243			−0.375122	+	0.926976i	$0.622399\pi$
$992$	−34.8178			−1.10547
$993$	−9.15365	+	17.5888i	−0.290482	+	0.558163i
$994$	14.0005	−	9.54971i	0.444070	−	0.302898i
$995$			2.64457i			0.0838384i
$996$	−2.34600	+	4.50785i	−0.0743358	+	0.142837i
$997$		−	20.4875i		−	0.648846i	−0.945912	−	0.324423i	$-0.894830\pi$
$997$		−	20.4875i		−	0.648846i	0.945912	−	0.324423i	$-0.105170\pi$
$998$			24.4087i			0.772643i
$999$	19.6278	−	2.59072i	0.620995	−	0.0819667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.e.a.188.20	yes	28
3.2	odd	2	inner	231.2.e.a.188.9	✓	28
7.6	odd	2	inner	231.2.e.a.188.19	yes	28
21.20	even	2	inner	231.2.e.a.188.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.e.a.188.9	✓	28	3.2	odd	2	inner
231.2.e.a.188.10	yes	28	21.20	even	2	inner
231.2.e.a.188.19	yes	28	7.6	odd	2	inner
231.2.e.a.188.20	yes	28	1.1	even	1	trivial

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.12088i q^{2} +(0.799601 - 1.53644i) q^{3} +0.743632 q^{4} -0.911250 q^{5} +(1.72216 + 0.896255i) q^{6} +(2.18571 - 1.49086i) q^{7} +3.07528i q^{8} +(-1.72128 - 2.45707i) q^{9} +O(q^{10})\)	\(q+1.12088i q^{2} +(0.799601 - 1.53644i) q^{3} +0.743632 q^{4} -0.911250 q^{5} +(1.72216 + 0.896255i) q^{6} +(2.18571 - 1.49086i) q^{7} +3.07528i q^{8} +(-1.72128 - 2.45707i) q^{9} -1.02140i q^{10} -1.00000i q^{11} +(0.594609 - 1.14254i) q^{12} +0.687952i q^{13} +(1.67108 + 2.44991i) q^{14} +(-0.728636 + 1.40008i) q^{15} -1.95975 q^{16} +3.26618 q^{17} +(2.75408 - 1.92934i) q^{18} +0.717942i q^{19} -0.677635 q^{20} +(-0.542924 - 4.55030i) q^{21} +1.12088 q^{22} +0.687108i q^{23} +(4.72497 + 2.45899i) q^{24} -4.16962 q^{25} -0.771110 q^{26} +(-5.15147 + 0.679956i) q^{27} +(1.62536 - 1.10865i) q^{28} -0.255478i q^{29} +(-1.56932 - 0.816713i) q^{30} +8.80590i q^{31} +3.95392i q^{32} +(-1.53644 - 0.799601i) q^{33} +3.66099i q^{34} +(-1.99173 + 1.35855i) q^{35} +(-1.28000 - 1.82716i) q^{36} -3.81013 q^{37} -0.804725 q^{38} +(1.05699 + 0.550087i) q^{39} -2.80235i q^{40} -9.59006 q^{41} +(5.10033 - 0.608552i) q^{42} +8.59846 q^{43} -0.743632i q^{44} +(1.56851 + 2.23901i) q^{45} -0.770165 q^{46} -12.5667 q^{47} +(-1.56701 + 3.01103i) q^{48} +(2.55465 - 6.51719i) q^{49} -4.67364i q^{50} +(2.61164 - 5.01828i) q^{51} +0.511583i q^{52} -5.09030i q^{53} +(-0.762148 - 5.77417i) q^{54} +0.911250i q^{55} +(4.58482 + 6.72166i) q^{56} +(1.10307 + 0.574067i) q^{57} +0.286360 q^{58} +5.86778 q^{59} +(-0.541838 + 1.04114i) q^{60} +5.13466i q^{61} -9.87034 q^{62} +(-7.42537 - 2.80426i) q^{63} -8.35135 q^{64} -0.626896i q^{65} +(0.896255 - 1.72216i) q^{66} -8.19722 q^{67} +2.42884 q^{68} +(1.05570 + 0.549412i) q^{69} +(-1.52277 - 2.23248i) q^{70} -5.71470i q^{71} +(7.55618 - 5.29340i) q^{72} -9.05463i q^{73} -4.27069i q^{74} +(-3.33403 + 6.40636i) q^{75} +0.533885i q^{76} +(-1.49086 - 2.18571i) q^{77} +(-0.616580 + 1.18476i) q^{78} -2.48351 q^{79} +1.78582 q^{80} +(-3.07441 + 8.45860i) q^{81} -10.7493i q^{82} -3.94545 q^{83} +(-0.403736 - 3.38375i) q^{84} -2.97631 q^{85} +9.63782i q^{86} +(-0.392526 - 0.204280i) q^{87} +3.07528 q^{88} +12.1065 q^{89} +(-2.50965 + 1.75811i) q^{90} +(1.02564 + 1.50366i) q^{91} +0.510956i q^{92} +(13.5297 + 7.04121i) q^{93} -14.0858i q^{94} -0.654224i q^{95} +(6.07495 + 3.16156i) q^{96} +9.33260i q^{97} +(7.30498 + 2.86345i) q^{98} +(-2.45707 + 1.72128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more