LMFDB - Embedded newform 152.2.q.a.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(9,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	152.73
Dual form			152.2.q.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.76604 + 0.642788i) q^{3} +(0.0603074 - 0.342020i) q^{5} +(2.37939 + 4.12122i) q^{7} +(0.407604 - 0.342020i) q^{9} +(-2.37939 + 4.12122i) q^{11} +(1.76604 + 0.642788i) q^{13} +(0.113341 + 0.642788i) q^{15} +(1.17365 + 0.984808i) q^{17} +(-0.694593 - 4.30320i) q^{19} +(-6.85117 - 5.74881i) q^{21} +(-1.06031 - 6.01330i) q^{23} +(4.58512 + 1.66885i) q^{25} +(2.31908 - 4.01676i) q^{27} +(-1.52094 + 1.27622i) q^{29} +(1.68479 + 2.91815i) q^{31} +(1.55303 - 8.80769i) q^{33} +(1.55303 - 0.565258i) q^{35} -3.38919 q^{37} -3.53209 q^{39} +(4.21941 - 1.53574i) q^{41} +(0.365715 - 2.07407i) q^{43} +(-0.0923963 - 0.160035i) q^{45} +(-3.76991 + 3.16333i) q^{47} +(-7.82295 + 13.5497i) q^{49} +(-2.70574 - 0.984808i) q^{51} +(-2.18092 - 12.3686i) q^{53} +(1.26604 + 1.06234i) q^{55} +(3.99273 + 7.15317i) q^{57} +(4.33615 + 3.63846i) q^{59} +(1.73530 + 9.84137i) q^{61} +(2.37939 + 0.866025i) q^{63} +(0.326352 - 0.565258i) q^{65} +(8.11721 - 6.81115i) q^{67} +(5.73783 + 9.93821i) q^{69} +(1.99613 - 11.3206i) q^{71} +(13.7369 - 4.99984i) q^{73} -9.17024 q^{75} -22.6459 q^{77} +(-2.21941 + 0.807798i) q^{79} +(-1.79086 + 10.1565i) q^{81} +(5.76857 + 9.99146i) q^{83} +(0.407604 - 0.342020i) q^{85} +(1.86571 - 3.23151i) q^{87} +(-5.29813 - 1.92836i) q^{89} +(1.55303 + 8.80769i) q^{91} +(-4.85117 - 4.07061i) q^{93} +(-1.51367 - 0.0219501i) q^{95} +(5.86824 + 4.92404i) q^{97} +(0.439693 + 2.49362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} + 6 q^{5} + 3 q^{7} + 6 q^{9} - 3 q^{11} + 6 q^{13} - 6 q^{15} + 6 q^{17} - 15 q^{21} - 12 q^{23} + 6 q^{25} - 3 q^{27} - 6 q^{29} + 3 q^{31} - 3 q^{33} - 3 q^{35} - 12 q^{37} - 12 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 + 6 * q^5 + 3 * q^7 + 6 * q^9 - 3 * q^11 + 6 * q^13 - 6 * q^15 + 6 * q^17 - 15 * q^21 - 12 * q^23 + 6 * q^25 - 3 * q^27 - 6 * q^29 + 3 * q^31 - 3 * q^33 - 3 * q^35 - 12 * q^37 - 12 * q^39 - 6 * q^41 + 12 * q^43 + 3 * q^45 + 6 * q^47 - 6 * q^49 - 6 * q^51 - 30 * q^53 + 3 * q^55 + 6 * q^57 + 30 * q^59 + 6 * q^61 + 3 * q^63 + 3 * q^65 + 18 * q^67 + 15 * q^69 + 36 * q^71 + 6 * q^73 - 12 * q^75 - 54 * q^77 + 18 * q^79 + 21 * q^81 + 15 * q^83 + 6 * q^85 + 21 * q^87 - 18 * q^89 - 3 * q^91 - 3 * q^93 + 12 * q^95 + 30 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.76604	+	0.642788i	−1.01963	+	0.371114i	−0.797122	−	0.603818i	$-0.793645\pi$
$3$	−1.76604	+	0.642788i	−1.01963	+	0.371114i	−0.222504	+	0.974932i	$0.571423\pi$
$4$		0			0
$5$	0.0603074	−	0.342020i	0.0269703	−	0.152956i	−0.968349	−	0.249602i	$-0.919700\pi$
$5$	0.0603074	−	0.342020i	0.0269703	−	0.152956i	0.995319	+	0.0966457i	$0.0308114\pi$
$6$		0			0
$7$	2.37939	+	4.12122i	0.899323	+	1.55767i	0.828361	+	0.560194i	$0.189274\pi$
$7$	2.37939	+	4.12122i	0.899323	+	1.55767i	0.0709618	+	0.997479i	$0.477393\pi$
$8$		0			0
$9$	0.407604	−	0.342020i	0.135868	−	0.114007i
$10$		0			0
$11$	−2.37939	+	4.12122i	−0.717412	+	1.24259i	0.244610	+	0.969621i	$0.421340\pi$
$11$	−2.37939	+	4.12122i	−0.717412	+	1.24259i	−0.962022	+	0.272972i	$0.911993\pi$
$12$		0			0
$13$	1.76604	+	0.642788i	0.489813	+	0.178277i	0.575106	−	0.818079i	$-0.304961\pi$
$13$	1.76604	+	0.642788i	0.489813	+	0.178277i	−0.0852938	+	0.996356i	$0.527183\pi$
$14$		0			0
$15$	0.113341	+	0.642788i	0.0292645	+	0.165967i
$16$		0			0
$17$	1.17365	+	0.984808i	0.284651	+	0.238851i	0.773922	−	0.633281i	$-0.218292\pi$
$17$	1.17365	+	0.984808i	0.284651	+	0.238851i	−0.489270	+	0.872132i	$0.662737\pi$
$18$		0			0
$19$	−0.694593	−	4.30320i	−0.159350	−	0.987222i
$19$	−0.694593	−	4.30320i	−0.159350	−	0.987222i
$20$		0			0
$21$	−6.85117	−	5.74881i	−1.49505	−	1.25449i
$22$		0			0
$23$	−1.06031	−	6.01330i	−0.221089	−	1.25386i	−0.870021	−	0.493014i	$-0.835895\pi$
$23$	−1.06031	−	6.01330i	−0.221089	−	1.25386i	0.648932	−	0.760846i	$-0.275216\pi$
$24$		0			0
$25$	4.58512	+	1.66885i	0.917024	+	0.333770i
$26$		0			0
$27$	2.31908	−	4.01676i	0.446307	−	0.773026i
$28$		0			0
$29$	−1.52094	+	1.27622i	−0.282432	+	0.236989i	−0.772987	−	0.634421i	$-0.781238\pi$
$29$	−1.52094	+	1.27622i	−0.282432	+	0.236989i	0.490555	+	0.871410i	$0.336794\pi$
$30$		0			0
$31$	1.68479	+	2.91815i	0.302598	+	0.524115i	0.976724	−	0.214502i	$-0.0688128\pi$
$31$	1.68479	+	2.91815i	0.302598	+	0.524115i	−0.674126	+	0.738616i	$0.735479\pi$
$32$		0			0
$33$	1.55303	−	8.80769i	0.270348	−	1.53322i
$34$		0			0
$35$	1.55303	−	0.565258i	0.262511	−	0.0955460i
$36$		0			0
$37$	−3.38919			−0.557179			−0.278589	−	0.960410i	$-0.589867\pi$
$37$	−3.38919			−0.557179			−0.278589	+	0.960410i	$0.589867\pi$
$38$		0			0
$39$	−3.53209			−0.565587
$40$		0			0
$41$	4.21941	−	1.53574i	0.658961	−	0.239842i	0.00917315	−	0.999958i	$-0.497080\pi$
$41$	4.21941	−	1.53574i	0.658961	−	0.239842i	0.649788	+	0.760116i	$0.274858\pi$
$42$		0			0
$43$	0.365715	−	2.07407i	0.0557710	−	0.316293i	−0.944141	−	0.329541i	$-0.893106\pi$
$43$	0.365715	−	2.07407i	0.0557710	−	0.316293i	0.999912	+	0.0132481i	$0.00421713\pi$
$44$		0			0
$45$	−0.0923963	−	0.160035i	−0.0137736	−	0.0238566i
$46$		0			0
$47$	−3.76991	+	3.16333i	−0.549899	+	0.461420i	−0.874907	−	0.484292i	$-0.839077\pi$
$47$	−3.76991	+	3.16333i	−0.549899	+	0.461420i	0.325008	+	0.945711i	$0.394633\pi$
$48$		0			0
$49$	−7.82295	+	13.5497i	−1.11756	+	1.93568i
$50$		0			0
$51$	−2.70574	−	0.984808i	−0.378879	−	0.137901i
$52$		0			0
$53$	−2.18092	−	12.3686i	−0.299573	−	1.69896i	−0.648012	−	0.761630i	$-0.724399\pi$
$53$	−2.18092	−	12.3686i	−0.299573	−	1.69896i	0.348440	−	0.937331i	$-0.386712\pi$
$54$		0			0
$55$	1.26604	+	1.06234i	0.170713	+	0.143246i
$56$		0			0
$57$	3.99273	+	7.15317i	0.528849	+	0.947460i
$58$		0			0
$59$	4.33615	+	3.63846i	0.564519	+	0.473688i	0.879822	−	0.475303i	$-0.157662\pi$
$59$	4.33615	+	3.63846i	0.564519	+	0.473688i	−0.315303	+	0.948991i	$0.602106\pi$
$60$		0			0
$61$	1.73530	+	9.84137i	0.222182	+	1.26006i	0.867999	+	0.496566i	$0.165406\pi$
$61$	1.73530	+	9.84137i	0.222182	+	1.26006i	−0.645817	+	0.763493i	$0.723483\pi$
$62$		0			0
$63$	2.37939	+	0.866025i	0.299774	+	0.109109i
$64$		0			0
$65$	0.326352	−	0.565258i	0.0404790	−	0.0701116i
$66$		0			0
$67$	8.11721	−	6.81115i	0.991675	−	0.832114i	0.00586579	−	0.999983i	$-0.498133\pi$
$67$	8.11721	−	6.81115i	0.991675	−	0.832114i	0.985809	+	0.167869i	$0.0536884\pi$
$68$		0			0
$69$	5.73783	+	9.93821i	0.690753	+	1.19642i
$70$		0			0
$71$	1.99613	−	11.3206i	0.236897	−	1.34351i	−0.601685	−	0.798734i	$-0.705504\pi$
$71$	1.99613	−	11.3206i	0.236897	−	1.34351i	0.838582	−	0.544776i	$-0.183385\pi$
$72$		0			0
$73$	13.7369	−	4.99984i	1.60779	−	0.585187i	0.626787	−	0.779190i	$-0.284369\pi$
$73$	13.7369	−	4.99984i	1.60779	−	0.585187i	0.981001	+	0.194003i	$0.0621473\pi$
$74$		0			0
$75$	−9.17024			−1.05889
$76$		0			0
$77$	−22.6459			−2.58074
$78$		0			0
$79$	−2.21941	+	0.807798i	−0.249703	+	0.0908844i	−0.463839	−	0.885919i	$-0.653529\pi$
$79$	−2.21941	+	0.807798i	−0.249703	+	0.0908844i	0.214136	+	0.976804i	$0.431306\pi$
$80$		0			0
$81$	−1.79086	+	10.1565i	−0.198984	+	1.12850i
$82$		0			0
$83$	5.76857	+	9.99146i	0.633183	+	1.09670i	0.986897	+	0.161351i	$0.0515852\pi$
$83$	5.76857	+	9.99146i	0.633183	+	1.09670i	−0.353714	+	0.935354i	$0.615081\pi$
$84$		0			0
$85$	0.407604	−	0.342020i	0.0442108	−	0.0370973i
$86$		0			0
$87$	1.86571	−	3.23151i	0.200026	−	0.346455i
$88$		0			0
$89$	−5.29813	−	1.92836i	−0.561601	−	0.204406i	0.0455924	−	0.998960i	$-0.485482\pi$
$89$	−5.29813	−	1.92836i	−0.561601	−	0.204406i	−0.607193	+	0.794554i	$0.707705\pi$
$90$		0			0
$91$	1.55303	+	8.80769i	0.162802	+	0.923297i
$92$		0			0
$93$	−4.85117	−	4.07061i	−0.503043	−	0.422103i
$94$		0			0
$95$	−1.51367	−	0.0219501i	−0.155299	−	0.00225203i
$96$		0			0
$97$	5.86824	+	4.92404i	0.595830	+	0.499960i	0.890102	−	0.455761i	$-0.150633\pi$
$97$	5.86824	+	4.92404i	0.595830	+	0.499960i	−0.294273	+	0.955722i	$0.595077\pi$
$98$		0			0
$99$	0.439693	+	2.49362i	0.0441908	+	0.250618i
$100$		0			0
$101$	4.21941	+	1.53574i	0.419847	+	0.152812i	0.543300	−	0.839539i	$-0.317175\pi$
$101$	4.21941	+	1.53574i	0.419847	+	0.152812i	−0.123453	+	0.992350i	$0.539397\pi$
$102$		0			0
$103$	7.50774	−	13.0038i	0.739760	−	1.28130i	−0.212844	−	0.977086i	$-0.568273\pi$
$103$	7.50774	−	13.0038i	0.739760	−	1.28130i	0.952603	−	0.304215i	$-0.0983942\pi$
$104$		0			0
$105$	−2.37939	+	1.99654i	−0.232204	+	0.194842i
$106$		0			0
$107$	5.44356	+	9.42853i	0.526249	+	0.911490i	0.999532	+	0.0305799i	$0.00973539\pi$
$107$	5.44356	+	9.42853i	0.526249	+	0.911490i	−0.473283	+	0.880910i	$0.656931\pi$
$108$		0			0
$109$	−1.32888	+	7.53644i	−0.127283	+	0.721860i	0.852642	+	0.522496i	$0.174999\pi$
$109$	−1.32888	+	7.53644i	−0.127283	+	0.721860i	−0.979925	+	0.199365i	$0.936112\pi$
$110$		0			0
$111$	5.98545	−	2.17853i	0.568114	−	0.206777i
$112$		0			0
$113$	0.128356			0.0120747			0.00603734	−	0.999982i	$-0.498078\pi$
$113$	0.128356			0.0120747			0.00603734	+	0.999982i	$0.498078\pi$
$114$		0			0
$115$	−2.12061			−0.197748
$116$		0			0
$117$	0.939693	−	0.342020i	0.0868746	−	0.0316198i
$118$		0			0
$119$	−1.26604	+	7.18009i	−0.116058	+	0.658198i
$120$		0			0
$121$	−5.82295	−	10.0856i	−0.529359	−	0.916877i
$122$		0			0
$123$	−6.46451	+	5.42437i	−0.582885	+	0.489099i
$124$		0			0
$125$	1.71554	−	2.97140i	0.153442	−	0.265770i
$126$		0			0
$127$	−18.1211	−	6.59553i	−1.60799	−	0.585259i	−0.626946	−	0.779063i	$-0.715695\pi$
$127$	−18.1211	−	6.59553i	−1.60799	−	0.585259i	−0.981040	+	0.193804i	$0.937917\pi$
$128$		0			0
$129$	0.687319	+	3.89798i	0.0605150	+	0.343198i
$130$		0			0
$131$	−13.5064	−	11.3332i	−1.18006	−	0.990187i	−0.999979	−	0.00653553i	$-0.997920\pi$
$131$	−13.5064	−	11.3332i	−1.18006	−	0.990187i	−0.180081	−	0.983652i	$-0.557636\pi$
$132$		0			0
$133$	16.0817	−	13.1015i	1.39446	−	1.13605i
$134$		0			0
$135$	−1.23396	−	1.03541i	−0.106202	−	0.0891140i
$136$		0			0
$137$	−3.41266	−	19.3541i	−0.291563	−	1.65354i	−0.680853	−	0.732420i	$-0.738391\pi$
$137$	−3.41266	−	19.3541i	−0.291563	−	1.65354i	0.389290	−	0.921115i	$-0.372720\pi$
$138$		0			0
$139$	9.73695	+	3.54396i	0.825877	+	0.300595i	0.720166	−	0.693802i	$-0.244066\pi$
$139$	9.73695	+	3.54396i	0.825877	+	0.300595i	0.105712	+	0.994397i	$0.466288\pi$
$140$		0			0
$141$	4.62449	−	8.00984i	0.389452	−	0.674550i
$142$		0			0
$143$	−6.85117	+	5.74881i	−0.572923	+	0.480740i
$144$		0			0
$145$	0.344770	+	0.597159i	0.0286316	+	0.0495914i
$146$		0			0
$147$	5.10607	−	28.9579i	0.421141	−	2.38841i
$148$		0			0
$149$	0.00727396	−	0.00264750i	0.000595906	−	0.000216892i	−0.341722	−	0.939801i	$-0.611010\pi$
$149$	0.00727396	−	0.00264750i	0.000595906	−	0.000216892i	0.342318	+	0.939584i	$0.388788\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		0			0
$153$	0.815207			0.0659056
$154$		0			0
$155$	1.09967	−	0.400247i	0.0883276	−	0.0321486i
$156$		0			0
$157$	0.996130	−	5.64933i	0.0794998	−	0.450866i	−0.918909	−	0.394470i	$-0.870928\pi$
$157$	0.996130	−	5.64933i	0.0794998	−	0.450866i	0.998409	−	0.0563955i	$-0.0179608\pi$
$158$		0			0
$159$	11.8020	+	20.4417i	0.935960	+	1.62113i
$160$		0			0
$161$	22.2592	−	18.6777i	1.75427	−	1.47201i
$162$		0			0
$163$	1.29561	−	2.24406i	0.101480	−	0.175768i	−0.810815	−	0.585303i	$-0.800976\pi$
$163$	1.29561	−	2.24406i	0.101480	−	0.175768i	0.912295	+	0.409535i	$0.134309\pi$
$164$		0			0
$165$	−2.91875	−	1.06234i	−0.227224	−	0.0827029i
$166$		0			0
$167$	3.15183	+	17.8749i	0.243896	+	1.38320i	0.823043	+	0.567978i	$0.192274\pi$
$167$	3.15183	+	17.8749i	0.243896	+	1.38320i	−0.579148	+	0.815223i	$0.696615\pi$
$168$		0			0
$169$	−7.25284	−	6.08586i	−0.557911	−	0.468143i
$170$		0			0
$171$	−1.75490	−	1.51644i	−0.134201	−	0.115965i
$172$		0			0
$173$	−6.95471	−	5.83569i	−0.528757	−	0.443679i	0.338915	−	0.940817i	$-0.389940\pi$
$173$	−6.95471	−	5.83569i	−0.528757	−	0.443679i	−0.867672	+	0.497137i	$0.834384\pi$
$174$		0			0
$175$	4.03209	+	22.8671i	0.304797	+	1.72859i
$176$		0			0
$177$	−9.99660	−	3.63846i	−0.751390	−	0.273484i
$178$		0			0
$179$	−3.31521	+	5.74211i	−0.247790	+	0.429185i	−0.962912	−	0.269814i	$-0.913038\pi$
$179$	−3.31521	+	5.74211i	−0.247790	+	0.429185i	0.715122	+	0.698999i	$0.246371\pi$
$180$		0			0
$181$	−3.89053	+	3.26454i	−0.289181	+	0.242651i	−0.775824	−	0.630949i	$-0.782666\pi$
$181$	−3.89053	+	3.26454i	−0.289181	+	0.242651i	0.486643	+	0.873601i	$0.338221\pi$
$182$		0			0
$183$	−9.39053	−	16.2649i	−0.694168	−	1.20233i
$184$		0			0
$185$	−0.204393	+	1.15917i	−0.0150273	+	0.0852239i
$186$		0			0
$187$	−6.85117	+	2.49362i	−0.501007	+	0.182352i
$188$		0			0
$189$	22.0719			1.60550
$190$		0			0
$191$	8.90673			0.644468			0.322234	−	0.946660i	$-0.395566\pi$
$191$	8.90673			0.644468			0.322234	+	0.946660i	$0.395566\pi$
$192$		0			0
$193$	−18.1211	+	6.59553i	−1.30438	+	0.474757i	−0.898422	−	0.439133i	$-0.855286\pi$
$193$	−18.1211	+	6.59553i	−1.30438	+	0.474757i	−0.405962	+	0.913890i	$0.633063\pi$
$194$		0			0
$195$	−0.213011	+	1.20805i	−0.0152540	+	0.0865099i
$196$		0			0
$197$	8.95336	+	15.5077i	0.637901	+	1.10488i	0.985893	+	0.167379i	$0.0535303\pi$
$197$	8.95336	+	15.5077i	0.637901	+	1.10488i	−0.347992	+	0.937498i	$0.613136\pi$
$198$		0			0
$199$	6.68345	−	5.60808i	0.473777	−	0.397546i	−0.374393	−	0.927270i	$-0.622149\pi$
$199$	6.68345	−	5.60808i	0.473777	−	0.397546i	0.848170	+	0.529724i	$0.177704\pi$
$200$		0			0
$201$	−9.95723	+	17.2464i	−0.702329	+	1.21647i
$202$		0			0
$203$	−8.87851	−	3.23151i	−0.623149	−	0.226808i
$204$		0			0
$205$	−0.270792	−	1.53574i	−0.0189129	−	0.107261i
$206$		0			0
$207$	−2.48886	−	2.08840i	−0.172987	−	0.145154i
$208$		0			0
$209$	19.3871	+	7.37641i	1.34104	+	0.510237i
$210$		0			0
$211$	0.577382	+	0.484481i	0.0397486	+	0.0333530i	0.662446	−	0.749110i	$-0.269519\pi$
$211$	0.577382	+	0.484481i	0.0397486	+	0.0333530i	−0.622697	+	0.782463i	$0.713963\pi$
$212$		0			0
$213$	3.75150	+	21.2758i	0.257048	+	1.45779i
$214$		0			0
$215$	−0.687319	−	0.250164i	−0.0468747	−	0.0170610i
$216$		0			0
$217$	−8.01754	+	13.8868i	−0.544266	+	0.942697i
$218$		0			0
$219$	−21.0462	+	17.6599i	−1.42217	+	1.19334i
$220$		0			0
$221$	1.43969	+	2.49362i	0.0968442	+	0.167739i
$222$		0			0
$223$	−0.826819	+	4.68912i	−0.0553679	+	0.314007i	−0.999896	−	0.0144238i	$-0.995409\pi$
$223$	−0.826819	+	4.68912i	−0.0553679	+	0.314007i	0.944528	+	0.328431i	$0.106520\pi$
$224$		0			0
$225$	2.43969	−	0.887975i	0.162646	−	0.0591984i
$226$		0			0
$227$	28.4243			1.88658			0.943292	−	0.331963i	$-0.107711\pi$
$227$	28.4243			1.88658			0.943292	+	0.331963i	$0.107711\pi$
$228$		0			0
$229$	−15.6459			−1.03391			−0.516955	−	0.856013i	$-0.672935\pi$
$229$	−15.6459			−1.03391			−0.516955	+	0.856013i	$0.672935\pi$
$230$		0			0
$231$	39.9937	−	14.5565i	2.63139	−	0.957747i
$232$		0			0
$233$	0.0603074	−	0.342020i	0.00395087	−	0.0224065i	−0.982769	−	0.184840i	$-0.940823\pi$
$233$	0.0603074	−	0.342020i	0.00395087	−	0.0224065i	0.986719	+	0.162434i	$0.0519344\pi$
$234$		0			0
$235$	0.854570	+	1.48016i	0.0557460	+	0.0965549i
$236$		0			0
$237$	3.40033	−	2.85322i	0.220875	−	0.185336i
$238$		0			0
$239$	−3.20233	+	5.54660i	−0.207142	+	0.358780i	−0.950813	−	0.309765i	$-0.899749\pi$
$239$	−3.20233	+	5.54660i	−0.207142	+	0.358780i	0.743671	+	0.668545i	$0.233083\pi$
$240$		0			0
$241$	−15.4265	−	5.61478i	−0.993708	−	0.361680i	−0.206553	−	0.978435i	$-0.566224\pi$
$241$	−15.4265	−	5.61478i	−0.993708	−	0.361680i	−0.787155	+	0.616756i	$0.788447\pi$
$242$		0			0
$243$	−0.949493	−	5.38484i	−0.0609100	−	0.345438i
$244$		0			0
$245$	4.16250	+	3.49276i	0.265933	+	0.223144i
$246$		0			0
$247$	1.53936	−	8.04612i	0.0979473	−	0.511962i
$248$		0			0
$249$	−16.6099	−	13.9374i	−1.05261	−	0.883246i
$250$		0			0
$251$	0.116744	+	0.662090i	0.00736884	+	0.0417908i	0.988270	−	0.152714i	$-0.0488012\pi$
$251$	0.116744	+	0.662090i	0.00736884	+	0.0417908i	−0.980902	+	0.194504i	$0.937690\pi$
$252$		0			0
$253$	27.3050	+	9.93821i	1.71665	+	0.624810i
$254$		0			0
$255$	−0.500000	+	0.866025i	−0.0313112	+	0.0542326i
$256$		0			0
$257$	−7.15136	+	6.00070i	−0.446090	+	0.374314i	−0.837982	−	0.545697i	$-0.816265\pi$
$257$	−7.15136	+	6.00070i	−0.446090	+	0.374314i	0.391893	+	0.920011i	$0.371820\pi$
$258$		0			0
$259$	−8.06418	−	13.9676i	−0.501084	−	0.867902i
$260$		0			0
$261$	−0.183448	+	1.04039i	−0.0113552	+	0.0643984i
$262$		0			0
$263$	−10.6728	+	3.88457i	−0.658111	+	0.239533i	−0.649421	−	0.760429i	$-0.724989\pi$
$263$	−10.6728	+	3.88457i	−0.658111	+	0.239533i	−0.00869056	+	0.999962i	$0.502766\pi$
$264$		0			0
$265$	−4.36184			−0.267946
$266$		0			0
$267$	10.5963			0.648481
$268$		0			0
$269$	−17.4265	+	6.34272i	−1.06251	+	0.386723i	−0.813371	−	0.581745i	$-0.802370\pi$
$269$	−17.4265	+	6.34272i	−1.06251	+	0.386723i	−0.249140	+	0.968467i	$0.580148\pi$
$270$		0			0
$271$	3.72580	−	21.1301i	0.226326	−	1.28356i	−0.633807	−	0.773492i	$-0.718508\pi$
$271$	3.72580	−	21.1301i	0.226326	−	1.28356i	0.860133	−	0.510070i	$-0.170380\pi$
$272$		0			0
$273$	−8.40420	−	14.5565i	−0.508645	−	0.881000i
$274$		0			0
$275$	−17.7875	+	14.9254i	−1.07262	+	0.900038i
$276$		0			0
$277$	8.01754	−	13.8868i	0.481727	−	0.834376i	−0.518053	−	0.855349i	$-0.673343\pi$
$277$	8.01754	−	13.8868i	0.481727	−	0.834376i	0.999780	+	0.0209725i	$0.00667623\pi$
$278$		0			0
$279$	1.68479	+	0.613214i	0.100866	+	0.0367122i
$280$		0			0
$281$	3.25284	+	18.4478i	0.194048	+	1.10050i	0.913768	+	0.406237i	$0.133159\pi$
$281$	3.25284	+	18.4478i	0.194048	+	1.10050i	−0.719719	+	0.694265i	$0.755730\pi$
$282$		0			0
$283$	5.40033	+	4.53141i	0.321016	+	0.269365i	0.789027	−	0.614358i	$-0.210585\pi$
$283$	5.40033	+	4.53141i	0.321016	+	0.269365i	−0.468011	+	0.883723i	$0.655029\pi$
$284$		0			0
$285$	2.68732	−	0.934204i	0.159183	−	0.0553375i
$286$		0			0
$287$	16.3687	+	13.7350i	0.966214	+	0.810750i
$288$		0			0
$289$	−2.54442	−	14.4301i	−0.149671	−	0.848829i
$290$		0			0
$291$	−13.5287	−	4.92404i	−0.793066	−	0.288652i
$292$		0			0
$293$	4.13041	−	7.15409i	0.241301	−	0.417946i	−0.719784	−	0.694198i	$-0.755759\pi$
$293$	4.13041	−	7.15409i	0.241301	−	0.417946i	0.961085	+	0.276252i	$0.0890924\pi$
$294$		0			0
$295$	1.50593	−	1.26363i	0.0876786	−	0.0735711i
$296$		0			0
$297$	11.0360	+	19.1148i	0.640371	+	1.10916i
$298$		0			0
$299$	1.99273	−	11.3013i	0.115242	−	0.653572i
$300$		0			0
$301$	9.41787	−	3.42782i	0.542837	−	0.197577i
$302$		0			0
$303$	−8.43882			−0.484797
$304$		0			0
$305$	3.47060			0.198726
$306$		0			0
$307$	4.44609	−	1.61824i	0.253752	−	0.0923581i	−0.212012	−	0.977267i	$-0.568002\pi$
$307$	4.44609	−	1.61824i	0.253752	−	0.0923581i	0.465764	+	0.884909i	$0.345780\pi$
$308$		0			0
$309$	−4.90033	+	27.7912i	−0.278770	+	1.58098i
$310$		0			0
$311$	−5.62061	−	9.73519i	−0.318716	−	0.552032i	0.661505	−	0.749941i	$-0.269918\pi$
$311$	−5.62061	−	9.73519i	−0.318716	−	0.552032i	−0.980220	+	0.197909i	$0.936585\pi$
$312$		0			0
$313$	5.30200	−	4.44891i	0.299687	−	0.251467i	−0.480527	−	0.876980i	$-0.659555\pi$
$313$	5.30200	−	4.44891i	0.299687	−	0.251467i	0.780214	+	0.625513i	$0.215110\pi$
$314$		0			0
$315$	0.439693	−	0.761570i	0.0247739	−	0.0429096i
$316$		0			0
$317$	13.7369	+	4.99984i	0.771544	+	0.280819i	0.697642	−	0.716447i	$-0.254233\pi$
$317$	13.7369	+	4.99984i	0.771544	+	0.280819i	0.0739019	+	0.997266i	$0.476455\pi$
$318$		0			0
$319$	−1.64068	−	9.30477i	−0.0918606	−	0.520967i
$320$		0			0
$321$	−15.6741	−	13.1521i	−0.874844	−	0.734081i
$322$		0			0
$323$	3.42262	−	5.73448i	0.190440	−	0.319075i
$324$		0			0
$325$	7.02481	+	5.89452i	0.389667	+	0.326969i
$326$		0			0
$327$	−2.49747	−	14.1639i	−0.138111	−	0.783264i
$328$		0			0
$329$	−22.0069	−	8.00984i	−1.21328	−	0.441597i
$330$		0			0
$331$	1.83275	−	3.17441i	0.100737	−	0.174482i	−0.811252	−	0.584697i	$-0.801213\pi$
$331$	1.83275	−	3.17441i	0.100737	−	0.174482i	0.911988	+	0.410216i	$0.134547\pi$
$332$		0			0
$333$	−1.38144	+	1.15917i	−0.0757027	+	0.0635221i
$334$		0			0
$335$	−1.84002	−	3.18701i	−0.100531	−	0.174125i
$336$		0			0
$337$	−0.579603	+	3.28709i	−0.0315730	+	0.179059i	−0.996516	−	0.0833994i	$-0.973422\pi$
$337$	−0.579603	+	3.28709i	−0.0315730	+	0.179059i	0.964943	+	0.262459i	$0.0845334\pi$
$338$		0			0
$339$	−0.226682	+	0.0825054i	−0.0123117	+	0.00448108i
$340$		0			0
$341$	−16.0351			−0.868348
$342$		0			0
$343$	−41.1438			−2.22156
$344$		0			0
$345$	3.74510	−	1.36310i	0.201629	−	0.0733871i
$346$		0			0
$347$	1.55825	−	8.83726i	0.0836511	−	0.474409i	−0.913988	−	0.405740i	$-0.867014\pi$
$347$	1.55825	−	8.83726i	0.0836511	−	0.474409i	0.997640	−	0.0686688i	$-0.0218752\pi$
$348$		0			0
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	0.680439	−	0.732805i	$-0.261789\pi$
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	−0.974847	+	0.222875i	$0.928456\pi$
$350$		0			0
$351$	6.67752	−	5.60310i	0.356420	−	0.299072i
$352$		0			0
$353$	11.7763	−	20.3972i	0.626790	−	1.08563i	−0.361402	−	0.932410i	$-0.617702\pi$
$353$	11.7763	−	20.3972i	0.626790	−	1.08563i	0.988192	−	0.153222i	$-0.0489649\pi$
$354$		0			0
$355$	−3.75150	−	1.36543i	−0.199109	−	0.0724697i
$356$		0			0
$357$	−2.37939	−	13.4942i	−0.125930	−	0.714187i
$358$		0			0
$359$	17.7854	+	14.9237i	0.938677	+	0.787644i	0.977355	−	0.211608i	$-0.0678700\pi$
$359$	17.7854	+	14.9237i	0.938677	+	0.787644i	−0.0386773	+	0.999252i	$0.512314\pi$
$360$		0			0
$361$	−18.0351	+	5.97794i	−0.949215	+	0.314629i
$362$		0			0
$363$	16.7665	+	14.0688i	0.880014	+	0.738419i
$364$		0			0
$365$	−0.881607	−	4.99984i	−0.0461454	−	0.261704i
$366$		0			0
$367$	−8.44609	−	3.07413i	−0.440882	−	0.160468i	0.112035	−	0.993704i	$-0.464263\pi$
$367$	−8.44609	−	3.07413i	−0.440882	−	0.160468i	−0.552917	+	0.833236i	$0.686485\pi$
$368$		0			0
$369$	1.19459	−	2.06910i	0.0621880	−	0.107713i
$370$		0			0
$371$	45.7845	−	38.4178i	2.37701	−	1.99455i
$372$		0			0
$373$	−10.3229	−	17.8799i	−0.534502	−	0.925785i	−0.999187	−	0.0403087i	$-0.987166\pi$
$373$	−10.3229	−	17.8799i	−0.534502	−	0.925785i	0.464685	−	0.885476i	$-0.346167\pi$
$374$		0			0
$375$	−1.11974	+	6.35035i	−0.0578230	+	0.327930i
$376$		0			0
$377$	−3.50640	+	1.27622i	−0.180589	+	0.0657289i
$378$		0			0
$379$	0.650015			0.0333890			0.0166945	−	0.999861i	$-0.494686\pi$
$379$	0.650015			0.0333890			0.0166945	+	0.999861i	$0.494686\pi$
$380$		0			0
$381$	36.2422			1.85674
$382$		0			0
$383$	−17.4957	+	6.36792i	−0.893989	+	0.325386i	−0.747842	−	0.663877i	$-0.768910\pi$
$383$	−17.4957	+	6.36792i	−0.893989	+	0.325386i	−0.146148	+	0.989263i	$0.546688\pi$
$384$		0			0
$385$	−1.36571	+	7.74535i	−0.0696033	+	0.394740i
$386$		0			0
$387$	−0.560307	−	0.970481i	−0.0284820	−	0.0493323i
$388$		0			0
$389$	0.479055	−	0.401975i	0.0242891	−	0.0203810i	−0.630562	−	0.776139i	$-0.717176\pi$
$389$	0.479055	−	0.401975i	0.0242891	−	0.0203810i	0.654851	+	0.755758i	$0.272731\pi$
$390$		0			0
$391$	4.67752	−	8.10170i	0.236552	−	0.409721i
$392$		0			0
$393$	31.1377	+	11.3332i	1.57069	+	0.571685i
$394$		0			0
$395$	0.142437	+	0.807798i	0.00716677	+	0.0406447i
$396$		0			0
$397$	−6.01889	−	5.05044i	−0.302079	−	0.253475i	0.479130	−	0.877744i	$-0.340952\pi$
$397$	−6.01889	−	5.05044i	−0.302079	−	0.253475i	−0.781209	+	0.624269i	$0.785397\pi$
$398$		0			0
$399$	−19.9795	+	33.4750i	−1.00023	+	1.67585i
$400$		0			0
$401$	−7.97431	−	6.69124i	−0.398218	−	0.334145i	0.421586	−	0.906788i	$-0.361473\pi$
$401$	−7.97431	−	6.69124i	−0.398218	−	0.334145i	−0.819804	+	0.572644i	$0.805918\pi$
$402$		0			0
$403$	1.09967	+	6.23654i	0.0547785	+	0.310664i
$404$		0			0
$405$	3.36571	+	1.22502i	0.167244	+	0.0608717i
$406$		0			0
$407$	8.06418	−	13.9676i	0.399726	−	0.692347i
$408$		0			0
$409$	11.2574	−	9.44610i	0.556644	−	0.467080i	−0.320540	−	0.947235i	$-0.603864\pi$
$409$	11.2574	−	9.44610i	0.556644	−	0.467080i	0.877183	+	0.480155i	$0.159420\pi$
$410$		0			0
$411$	18.4675	+	31.9866i	0.910935	+	1.57779i
$412$		0			0
$413$	−4.67752	+	26.5275i	−0.230166	+	1.30533i
$414$		0			0
$415$	3.76517	−	1.37041i	0.184825	−	0.0672707i
$416$		0			0
$417$	−19.4739			−0.953641
$418$		0			0
$419$	7.03508			0.343686			0.171843	−	0.985124i	$-0.445028\pi$
$419$	7.03508			0.343686			0.171843	+	0.985124i	$0.445028\pi$
$420$		0			0
$421$	−33.3974	+	12.1557i	−1.62769	+	0.592430i	−0.984825	−	0.173550i	$-0.944476\pi$
$421$	−33.3974	+	12.1557i	−1.62769	+	0.592430i	−0.642864	+	0.765980i	$0.722254\pi$
$422$		0			0
$423$	−0.454707	+	2.57877i	−0.0221086	+	0.125384i
$424$		0			0
$425$	3.73783	+	6.47410i	0.181311	+	0.314040i
$426$		0			0
$427$	−36.4295	+	30.5680i	−1.76295	+	1.47929i
$428$		0			0
$429$	8.40420	−	14.5565i	0.405759	−	0.702795i
$430$		0			0
$431$	−19.2690	−	7.01336i	−0.928157	−	0.337821i	−0.166678	−	0.986011i	$-0.553304\pi$
$431$	−19.2690	−	7.01336i	−0.928157	−	0.337821i	−0.761479	+	0.648190i	$0.775526\pi$
$432$		0			0
$433$	−3.50181	−	19.8598i	−0.168286	−	0.954399i	−0.945611	−	0.325299i	$-0.894535\pi$
$433$	−3.50181	−	19.8598i	−0.168286	−	0.954399i	0.777325	−	0.629100i	$-0.216576\pi$
$434$		0			0
$435$	−0.992726	−	0.832996i	−0.0475976	−	0.0399391i
$436$		0			0
$437$	−25.1400	+	8.73951i	−1.20261	+	0.418068i
$438$		0			0
$439$	2.38073	+	1.99767i	0.113626	+	0.0953435i	0.697830	−	0.716263i	$-0.254149\pi$
$439$	2.38073	+	1.99767i	0.113626	+	0.0953435i	−0.584204	+	0.811607i	$0.698593\pi$
$440$		0			0
$441$	1.44562	+	8.19853i	0.0688392	+	0.390406i
$442$		0			0
$443$	8.21941	+	2.99162i	0.390516	+	0.142136i	0.529813	−	0.848114i	$-0.322262\pi$
$443$	8.21941	+	2.99162i	0.390516	+	0.142136i	−0.139297	+	0.990251i	$0.544484\pi$
$444$		0			0
$445$	−0.979055	+	1.69577i	−0.0464117	+	0.0803874i
$446$		0			0
$447$	−0.0111444	+	0.00935122i	−0.000527110	+	0.000442298i
$448$		0			0
$449$	19.4067	+	33.6134i	0.915860	+	1.58632i	0.805637	+	0.592409i	$0.201823\pi$
$449$	19.4067	+	33.6134i	0.915860	+	1.58632i	0.110223	+	0.993907i	$0.464844\pi$
$450$		0			0
$451$	−3.71048	+	21.0432i	−0.174720	+	0.990886i
$452$		0			0
$453$	28.2567	−	10.2846i	1.32762	−	0.483213i
$454$		0			0
$455$	3.10607			0.145615
$456$		0			0
$457$	13.0933			0.612478			0.306239	−	0.951955i	$-0.400929\pi$
$457$	13.0933			0.612478			0.306239	+	0.951955i	$0.400929\pi$
$458$		0			0
$459$	6.67752	−	2.43042i	0.311680	−	0.113442i
$460$		0			0
$461$	−2.03895	+	11.5635i	−0.0949635	+	0.538565i	0.899795	+	0.436313i	$0.143716\pi$
$461$	−2.03895	+	11.5635i	−0.0949635	+	0.538565i	−0.994759	+	0.102252i	$0.967395\pi$
$462$		0			0
$463$	7.57192	+	13.1149i	0.351897	+	0.609503i	0.986582	−	0.163268i	$-0.0522034\pi$
$463$	7.57192	+	13.1149i	0.351897	+	0.609503i	−0.634685	+	0.772771i	$0.718870\pi$
$464$		0			0
$465$	−1.68479	+	1.41371i	−0.0781304	+	0.0655592i
$466$		0			0
$467$	−15.6848	+	27.1669i	−0.725806	+	1.25713i	0.232836	+	0.972516i	$0.425199\pi$
$467$	−15.6848	+	27.1669i	−0.725806	+	1.25713i	−0.958642	+	0.284616i	$0.908134\pi$
$468$		0			0
$469$	47.3842	+	17.2464i	2.18800	+	0.796366i
$470$		0			0
$471$	1.87211	+	10.6173i	0.0862623	+	0.489218i
$472$		0			0
$473$	7.67752	+	6.44220i	0.353013	+	0.296213i
$474$		0			0
$475$	3.99660	−	20.8899i	0.183376	−	0.958493i
$476$		0			0
$477$	−5.11927	−	4.29558i	−0.234395	−	0.196681i
$478$		0			0
$479$	−2.65152	−	15.0375i	−0.121151	−	0.687082i	−0.983520	−	0.180801i	$-0.942131\pi$
$479$	−2.65152	−	15.0375i	−0.121151	−	0.687082i	0.862369	−	0.506281i	$-0.168980\pi$
$480$		0			0
$481$	−5.98545	−	2.17853i	−0.272913	−	0.0993323i
$482$		0			0
$483$	−27.3050	+	47.2936i	−1.24242	+	2.15194i
$484$		0			0
$485$	2.03802	−	1.71010i	0.0925417	−	0.0776517i
$486$		0			0
$487$	−18.5428	−	32.1171i	−0.840256	−	1.45537i	−0.889679	−	0.456587i	$-0.849072\pi$
$487$	−18.5428	−	32.1171i	−0.840256	−	1.45537i	0.0494231	−	0.998778i	$-0.484262\pi$
$488$		0			0
$489$	−0.845647	+	4.79591i	−0.0382415	+	0.216878i
$490$		0			0
$491$	−26.4761	+	9.63652i	−1.19485	+	0.434890i	−0.861424	−	0.507886i	$-0.830427\pi$
$491$	−26.4761	+	9.63652i	−1.19485	+	0.434890i	−0.333426	+	0.942776i	$0.608205\pi$
$492$		0			0
$493$	−3.04189			−0.137000
$494$		0			0
$495$	0.879385			0.0395254
$496$		0			0
$497$	51.4043	−	18.7096i	2.30580	−	0.839241i
$498$		0			0
$499$	2.25284	−	12.7765i	0.100851	−	0.571954i	−0.891946	−	0.452143i	$-0.850660\pi$
$499$	2.25284	−	12.7765i	0.100851	−	0.571954i	0.992797	−	0.119812i	$-0.0382291\pi$
$500$		0			0
$501$	−17.0560	−	29.5419i	−0.762007	−	1.31983i
$502$		0			0
$503$	−8.33615	+	6.99486i	−0.371691	+	0.311885i	−0.809430	−	0.587216i	$-0.800224\pi$
$503$	−8.33615	+	6.99486i	−0.371691	+	0.311885i	0.437739	+	0.899102i	$0.355779\pi$
$504$		0			0
$505$	0.779715	−	1.35051i	0.0346969	−	0.0600967i
$506$		0			0
$507$	16.7208	+	6.08586i	0.742595	+	0.270282i
$508$		0			0
$509$	−1.99437	−	11.3107i	−0.0883991	−	0.501336i	−0.996571	−	0.0827393i	$-0.973633\pi$
$509$	−1.99437	−	11.3107i	−0.0883991	−	0.501336i	0.908172	−	0.418597i	$-0.137478\pi$
$510$		0			0
$511$	53.2909	+	44.7164i	2.35745	+	1.97814i
$512$		0			0
$513$	−18.8957	−	7.18945i	−0.834267	−	0.317422i
$514$		0			0
$515$	−3.99479	−	3.35202i	−0.176031	−	0.147708i
$516$		0			0
$517$	−4.06670	−	23.0634i	−0.178853	−	1.01433i
$518$		0			0
$519$	16.0334	+	5.83569i	0.703790	+	0.256158i
$520$		0			0
$521$	3.43582	−	5.95102i	0.150526	−	0.260719i	−0.780895	−	0.624662i	$-0.785237\pi$
$521$	3.43582	−	5.95102i	0.150526	−	0.260719i	0.931421	+	0.363944i	$0.118570\pi$
$522$		0			0
$523$	−9.52869	+	7.99552i	−0.416660	+	0.349620i	−0.826891	−	0.562362i	$-0.809893\pi$
$523$	−9.52869	+	7.99552i	−0.416660	+	0.349620i	0.410231	+	0.911982i	$0.365448\pi$
$524$		0			0
$525$	−21.8195	−	37.7926i	−0.952283	−	1.64940i
$526$		0			0
$527$	−0.896459	+	5.08407i	−0.0390504	+	0.221466i
$528$		0			0
$529$	−13.4226	+	4.88543i	−0.583592	+	0.212410i
$530$		0			0
$531$	3.01186			0.130704
$532$		0			0
$533$	8.43882			0.365526
$534$		0			0
$535$	3.55303	−	1.29320i	0.153611	−	0.0559098i
$536$		0			0
$537$	2.16385	−	12.2718i	0.0933769	−	0.529567i
$538$		0			0
$539$	−37.2276	−	64.4801i	−1.60351	−	2.77736i
$540$		0			0
$541$	−9.47637	+	7.95162i	−0.407421	+	0.341867i	−0.823354	−	0.567529i	$-0.807900\pi$
$541$	−9.47637	+	7.95162i	−0.407421	+	0.341867i	0.415933	+	0.909395i	$0.363455\pi$
$542$		0			0
$543$	4.77244	−	8.26611i	0.204805	−	0.354733i
$544$		0			0
$545$	2.49747	+	0.909006i	0.106980	+	0.0389375i
$546$		0			0
$547$	−3.98252	−	22.5860i	−0.170280	−	0.965706i	−0.943452	−	0.331510i	$-0.892442\pi$
$547$	−3.98252	−	22.5860i	−0.170280	−	0.965706i	0.773172	−	0.634197i	$-0.218669\pi$
$548$		0			0
$549$	4.07326	+	3.41787i	0.173843	+	0.145871i
$550$		0			0
$551$	6.54829	+	5.65847i	0.278966	+	0.241059i
$552$		0			0
$553$	−8.60994	−	7.22460i	−0.366132	−	0.307221i
$554$		0			0
$555$	−0.384133	−	2.17853i	−0.0163055	−	0.0924733i
$556$		0			0
$557$	−20.0373	−	7.29298i	−0.849008	−	0.309014i	−0.119372	−	0.992850i	$-0.538088\pi$
$557$	−20.0373	−	7.29298i	−0.849008	−	0.309014i	−0.729636	+	0.683836i	$0.760310\pi$
$558$		0			0
$559$	1.97906	−	3.42782i	0.0837051	−	0.144982i
$560$		0			0
$561$	10.4966	−	8.80769i	0.443167	−	0.371861i
$562$		0			0
$563$	−9.37939	−	16.2456i	−0.395294	−	0.684669i	0.597845	−	0.801612i	$-0.296024\pi$
$563$	−9.37939	−	16.2456i	−0.395294	−	0.684669i	−0.993139	+	0.116943i	$0.962691\pi$
$564$		0			0
$565$	0.00774079	−	0.0439002i	0.000325657	−	0.00184689i
$566$		0			0
$567$	−46.1181	+	16.7856i	−1.93678	+	0.704930i
$568$		0			0
$569$	6.16756			0.258557			0.129279	−	0.991608i	$-0.458734\pi$
$569$	6.16756			0.258557			0.129279	+	0.991608i	$0.458734\pi$
$570$		0			0
$571$	22.2175			0.929774			0.464887	−	0.885370i	$-0.346095\pi$
$571$	22.2175			0.929774			0.464887	+	0.885370i	$0.346095\pi$
$572$		0			0
$573$	−15.7297	+	5.72513i	−0.657117	+	0.239171i
$574$		0			0
$575$	5.17365	−	29.3412i	0.215756	−	1.22361i
$576$		0			0
$577$	18.8851	+	32.7099i	0.786196	+	1.36173i	0.928282	+	0.371877i	$0.121286\pi$
$577$	18.8851	+	32.7099i	0.786196	+	1.36173i	−0.142087	+	0.989854i	$0.545381\pi$
$578$		0			0
$579$	27.7631	−	23.2960i	1.15380	−	0.968149i
$580$		0			0
$581$	−27.4513	+	47.5471i	−1.13887	+	1.97258i
$582$		0			0
$583$	56.1630	+	20.4417i	2.32603	+	0.846607i
$584$		0			0
$585$	−0.0603074	−	0.342020i	−0.00249340	−	0.0141408i
$586$		0			0
$587$	−3.29426	−	2.76421i	−0.135969	−	0.114091i	0.572267	−	0.820067i	$-0.306064\pi$
$587$	−3.29426	−	2.76421i	−0.135969	−	0.114091i	−0.708236	+	0.705976i	$0.750509\pi$
$588$		0			0
$589$	11.3871	−	9.27692i	0.469198	−	0.382249i
$590$		0			0
$591$	−25.7802	−	21.6321i	−1.06045	−	0.889827i
$592$		0			0
$593$	1.29204	+	7.32753i	0.0530578	+	0.300906i	0.999776	−	0.0211569i	$-0.00673496\pi$
$593$	1.29204	+	7.32753i	0.0530578	+	0.300906i	−0.946718	+	0.322063i	$0.895624\pi$
$594$		0			0
$595$	2.37939	+	0.866025i	0.0975453	+	0.0355036i
$596$		0			0
$597$	−8.19846	+	14.2002i	−0.335541	+	0.581174i
$598$		0			0
$599$	0.486796	−	0.408471i	0.0198900	−	0.0166897i	−0.632788	−	0.774325i	$-0.718090\pi$
$599$	0.486796	−	0.408471i	0.0198900	−	0.0166897i	0.652678	+	0.757635i	$0.273645\pi$
$600$		0			0
$601$	1.32295	+	2.29141i	0.0539642	+	0.0934687i	0.891746	−	0.452537i	$-0.149481\pi$
$601$	1.32295	+	2.29141i	0.0539642	+	0.0934687i	−0.837781	+	0.546006i	$0.816148\pi$
$602$		0			0
$603$	0.979055	−	5.55250i	0.0398702	−	0.226115i
$604$		0			0
$605$	−3.80066	+	1.38333i	−0.154519	+	0.0562402i
$606$		0			0
$607$	18.3851			0.746227			0.373113	−	0.927786i	$-0.378290\pi$
$607$	18.3851			0.746227			0.373113	+	0.927786i	$0.378290\pi$
$608$		0			0
$609$	17.7570			0.719551
$610$		0			0
$611$	−8.69119	+	3.16333i	−0.351608	+	0.127975i
$612$		0			0
$613$	3.13997	−	17.8076i	0.126822	−	0.719244i	−0.853387	−	0.521278i	$-0.825455\pi$
$613$	3.13997	−	17.8076i	0.126822	−	0.719244i	0.980209	−	0.197966i	$-0.0634334\pi$
$614$		0			0
$615$	1.46538	+	2.53812i	0.0590900	+	0.102347i
$616$		0			0
$617$	14.2533	−	11.9599i	0.573817	−	0.481489i	−0.309093	−	0.951032i	$-0.600026\pi$
$617$	14.2533	−	11.9599i	0.573817	−	0.481489i	0.882910	+	0.469542i	$0.155581\pi$
$618$		0			0
$619$	5.42396	−	9.39458i	0.218007	−	0.377600i	−0.736191	−	0.676774i	$-0.763378\pi$
$619$	5.42396	−	9.39458i	0.218007	−	0.377600i	0.954199	+	0.299174i	$0.0967110\pi$
$620$		0			0
$621$	−26.6129	−	9.68631i	−1.06794	−	0.388698i
$622$		0			0
$623$	−4.65910	−	26.4231i	−0.186663	−	1.05862i
$624$		0			0
$625$	17.7763	+	14.9161i	0.711052	+	0.596644i
$626$		0			0
$627$	−38.9800	−	0.565258i	−1.55671	−	0.0225742i
$628$		0			0
$629$	−3.97771	−	3.33770i	−0.158602	−	0.133083i
$630$		0			0
$631$	−2.62243	−	14.8725i	−0.104397	−	0.592065i	−0.991459	−	0.130416i	$-0.958369\pi$
$631$	−2.62243	−	14.8725i	−0.104397	−	0.592065i	0.887062	−	0.461650i	$-0.152742\pi$
$632$		0			0
$633$	−1.33110	−	0.484481i	−0.0529065	−	0.0192564i
$634$		0			0
$635$	−3.34864	+	5.80002i	−0.132887	+	0.230167i
$636$		0			0
$637$	−22.5253	+	18.9010i	−0.892484	+	0.748883i
$638$		0			0
$639$	−3.05825	−	5.29704i	−0.120982	−	0.209548i
$640$		0			0
$641$	−8.03895	+	45.5912i	−0.317520	+	1.80074i	0.240211	+	0.970721i	$0.422783\pi$
$641$	−8.03895	+	45.5912i	−0.317520	+	1.80074i	−0.557731	+	0.830022i	$0.688328\pi$
$642$		0			0
$643$	12.7610	−	4.64462i	0.503244	−	0.183166i	−0.0779083	−	0.996961i	$-0.524824\pi$
$643$	12.7610	−	4.64462i	0.503244	−	0.183166i	0.581153	+	0.813795i	$0.302602\pi$
$644$		0			0
$645$	1.37464			0.0541263
$646$		0			0
$647$	33.8135			1.32934			0.664672	−	0.747135i	$-0.268571\pi$
$647$	33.8135			1.32934			0.664672	+	0.747135i	$0.268571\pi$
$648$		0			0
$649$	−25.3123	+	9.21291i	−0.993594	+	0.361638i
$650$		0			0
$651$	5.23308	−	29.6783i	0.205101	−	1.16318i
$652$		0			0
$653$	−3.37164	−	5.83986i	−0.131943	−	0.228531i	0.792483	−	0.609894i	$-0.208788\pi$
$653$	−3.37164	−	5.83986i	−0.131943	−	0.228531i	−0.924425	+	0.381363i	$0.875455\pi$
$654$		0			0
$655$	−4.69072	+	3.93598i	−0.183282	+	0.153792i
$656$		0			0
$657$	3.88919	−	6.73627i	0.151732	−	0.262807i
$658$		0			0
$659$	−0.446089	−	0.162363i	−0.0173772	−	0.00632477i	0.333317	−	0.942815i	$-0.391832\pi$
$659$	−0.446089	−	0.162363i	−0.0173772	−	0.00632477i	−0.350694	+	0.936490i	$0.614054\pi$
$660$		0			0
$661$	0.671122	+	3.80612i	0.0261036	+	0.148041i	0.995074	−	0.0991365i	$-0.0316080\pi$
$661$	0.671122	+	3.80612i	0.0261036	+	0.148041i	−0.968970	+	0.247177i	$0.920497\pi$
$662$		0			0
$663$	−4.14543	−	3.47843i	−0.160995	−	0.135091i
$664$		0			0
$665$	−3.51114	−	6.29039i	−0.136156	−	0.243931i
$666$		0			0
$667$	9.28699	+	7.79271i	0.359594	+	0.301735i
$668$		0			0
$669$	−1.55391	−	8.81267i	−0.0600777	−	0.340717i
$670$		0			0
$671$	−44.6874	−	16.2649i	−1.72514	−	0.627899i
$672$		0			0
$673$	−2.11081	+	3.65604i	−0.0813659	+	0.140930i	−0.903837	−	0.427877i	$-0.859262\pi$
$673$	−2.11081	+	3.65604i	−0.0813659	+	0.140930i	0.822471	+	0.568807i	$0.192595\pi$
$674$		0			0
$675$	17.3366	−	14.5472i	0.667287	−	0.559920i
$676$		0			0
$677$	−9.06212	−	15.6960i	−0.348286	−	0.603248i	0.637660	−	0.770318i	$-0.279903\pi$
$677$	−9.06212	−	15.6960i	−0.348286	−	0.603248i	−0.985945	+	0.167070i	$0.946569\pi$
$678$		0			0
$679$	−6.33022	+	35.9005i	−0.242932	+	1.37773i
$680$		0			0
$681$	−50.1985	+	18.2708i	−1.92361	+	0.700137i
$682$		0			0
$683$	27.2608			1.04311			0.521553	−	0.853219i	$-0.325353\pi$
$683$	27.2608			1.04311			0.521553	+	0.853219i	$0.325353\pi$
$684$		0			0
$685$	−6.82531			−0.260782
$686$		0			0
$687$	27.6313	−	10.0570i	1.05420	−	0.383698i
$688$		0			0
$689$	4.09879	−	23.2454i	0.156152	−	0.885580i
$690$		0			0
$691$	13.1186	+	22.7220i	0.499053	+	0.864386i	0.999999	−	0.00109273i	$-0.000347828\pi$
$691$	13.1186	+	22.7220i	0.499053	+	0.864386i	−0.500946	+	0.865479i	$0.667014\pi$
$692$		0			0
$693$	−9.23055	+	7.74535i	−0.350640	+	0.294222i
$694$		0			0
$695$	1.79932	−	3.11651i	0.0682519	−	0.118216i
$696$		0			0
$697$	6.46451	+	2.35289i	0.244861	+	0.0891220i
$698$		0			0
$699$	0.113341	+	0.642788i	0.00428694	+	0.0243125i
$700$		0			0
$701$	18.8195	+	15.7915i	0.710804	+	0.596436i	0.924825	−	0.380394i	$-0.124211\pi$
$701$	18.8195	+	15.7915i	0.710804	+	0.596436i	−0.214020	+	0.976829i	$0.568656\pi$
$702$		0			0
$703$	2.35410	+	14.5843i	0.0887867	+	0.550059i
$704$		0			0
$705$	−2.46064	−	2.06472i	−0.0926730	−	0.0777618i
$706$		0			0
$707$	3.71048	+	21.0432i	0.139547	+	0.791411i
$708$		0			0
$709$	10.2931	+	3.74638i	0.386565	+	0.140698i	0.527989	−	0.849251i	$-0.322946\pi$
$709$	10.2931	+	3.74638i	0.386565	+	0.140698i	−0.141425	+	0.989949i	$0.545168\pi$
$710$		0			0
$711$	−0.628356	+	1.08834i	−0.0235652	+	0.0408161i
$712$		0			0
$713$	15.7613	−	13.2253i	0.590265	−	0.495291i
$714$		0			0
$715$	1.55303	+	2.68993i	0.0580802	+	0.100598i
$716$		0			0
$717$	2.09017	−	11.8540i	0.0780590	−	0.442695i
$718$		0			0
$719$	39.9791	−	14.5512i	1.49097	−	0.542668i	0.537265	−	0.843414i	$-0.319458\pi$
$719$	39.9791	−	14.5512i	1.49097	−	0.542668i	0.953705	+	0.300745i	$0.0972354\pi$
$720$		0			0
$721$	71.4552			2.66113
$722$		0			0
$723$	30.8530			1.14743
$724$		0			0
$725$	−9.10354	+	3.31342i	−0.338097	+	0.123057i
$726$		0			0
$727$	−6.86602	+	38.9391i	−0.254647	+	1.44417i	0.542332	+	0.840164i	$0.317542\pi$
$727$	−6.86602	+	38.9391i	−0.254647	+	1.44417i	−0.796978	+	0.604008i	$0.793570\pi$
$728$		0			0
$729$	−10.3316	−	17.8948i	−0.382651	−	0.662770i
$730$		0			0
$731$	2.47178	−	2.07407i	0.0914221	−	0.0767123i
$732$		0			0
$733$	22.1459	−	38.3578i	0.817977	−	1.41678i	−0.0891928	−	0.996014i	$-0.528429\pi$
$733$	22.1459	−	38.3578i	0.817977	−	1.41678i	0.907170	−	0.420764i	$-0.138238\pi$
$734$		0			0
$735$	−9.59627	−	3.49276i	−0.353964	−	0.128832i
$736$		0			0
$737$	8.75624	+	49.6591i	0.322540	+	1.82922i
$738$		0			0
$739$	−41.2124	−	34.5813i	−1.51602	−	1.27209i	−0.850860	−	0.525392i	$-0.823919\pi$
$739$	−41.2124	−	34.5813i	−1.51602	−	1.27209i	−0.665161	−	0.746700i	$-0.731637\pi$
$740$		0			0
$741$	2.45336	+	15.1993i	0.0901265	+	0.558360i
$742$		0			0
$743$	−9.05303	−	7.59640i	−0.332124	−	0.278685i	0.461441	−	0.887171i	$-0.347333\pi$
$743$	−9.05303	−	7.59640i	−0.332124	−	0.278685i	−0.793564	+	0.608486i	$0.791777\pi$
$744$		0			0
$745$	−0.000466827	−	0.00264750i	−1.71032e−5	−	9.69971e-5i
$746$		0			0
$747$	5.76857	+	2.09959i	0.211061	+	0.0768199i
$748$		0			0
$749$	−25.9047	+	44.8682i	−0.946536	+	1.63945i
$750$		0			0
$751$	−28.8496	+	24.2077i	−1.05274	+	0.883350i	−0.993379	−	0.114886i	$-0.963350\pi$
$751$	−28.8496	+	24.2077i	−1.05274	+	0.883350i	−0.0593573	+	0.998237i	$0.518905\pi$
$752$		0			0
$753$	−0.631759	−	1.09424i	−0.0230226	−	0.0398763i
$754$		0			0
$755$	−0.964918	+	5.47232i	−0.0351170	+	0.199158i
$756$		0			0
$757$	−7.14068	+	2.59900i	−0.259532	+	0.0944621i	−0.468510	−	0.883458i	$-0.655209\pi$
$757$	−7.14068	+	2.59900i	−0.259532	+	0.0944621i	0.208977	+	0.977921i	$0.432987\pi$
$758$		0			0
$759$	−54.6100			−1.98222
$760$		0			0
$761$	−1.51754			−0.0550108			−0.0275054	−	0.999622i	$-0.508756\pi$
$761$	−1.51754			−0.0550108			−0.0275054	+	0.999622i	$0.508756\pi$
$762$		0			0
$763$	−34.2212	+	12.4555i	−1.23889	+	0.450920i
$764$		0			0
$765$	0.0491630	−	0.278817i	0.00177749	−	0.0100807i
$766$		0			0
$767$	5.31908	+	9.21291i	0.192061	+	0.332659i
$768$		0			0
$769$	−13.0831	+	10.9780i	−0.471787	+	0.395877i	−0.847446	−	0.530881i	$-0.821861\pi$
$769$	−13.0831	+	10.9780i	−0.471787	+	0.395877i	0.375659	+	0.926758i	$0.377416\pi$
$770$		0			0
$771$	8.77244	−	15.1943i	0.315932	−	0.547210i
$772$		0			0
$773$	−0.687319	−	0.250164i	−0.0247211	−	0.00899776i	0.329630	−	0.944110i	$-0.393076\pi$
$773$	−0.687319	−	0.250164i	−0.0247211	−	0.00899776i	−0.354351	+	0.935112i	$0.615298\pi$
$774$		0			0
$775$	2.85504	+	16.1917i	0.102556	+	0.581624i
$776$		0			0
$777$	23.2199	+	19.4838i	0.833008	+	0.698977i
$778$		0			0
$779$	−9.53936	−	17.0902i	−0.341783	−	0.612322i
$780$		0			0
$781$	41.9051	+	35.1626i	1.49948	+	1.25822i
$782$		0			0
$783$	1.59910	+	9.06893i	0.0571471	+	0.324097i
$784$		0			0
$785$	−1.87211	−	0.681393i	−0.0668185	−	0.0243200i
$786$		0			0
$787$	−12.4786	+	21.6136i	−0.444816	+	0.770443i	−0.998039	−	0.0625894i	$-0.980064\pi$
$787$	−12.4786	+	21.6136i	−0.444816	+	0.770443i	0.553224	+	0.833033i	$0.313397\pi$
$788$		0			0
$789$	16.3516	−	13.7206i	0.582134	−	0.488468i
$790$		0			0
$791$	0.305407	+	0.528981i	0.0108590	+	0.0188084i
$792$		0			0
$793$	−3.26130	+	18.4957i	−0.115812	+	0.656803i
$794$		0			0
$795$	7.70321	−	2.80374i	0.273205	−	0.0994384i
$796$		0			0
$797$	−46.2877			−1.63959			−0.819797	−	0.572655i	$-0.805914\pi$
$797$	−46.2877			−1.63959			−0.819797	+	0.572655i	$0.805914\pi$
$798$		0			0
$799$	−7.53983			−0.266740
$800$		0			0
$801$	−2.81908	+	1.02606i	−0.0996072	+	0.0362541i
$802$		0			0
$803$	−12.0801	+	68.5095i	−0.426296	+	2.41765i
$804$		0			0
$805$	−5.04576	−	8.73951i	−0.177840	−	0.308027i
$806$		0			0
$807$	26.6989	−	22.4031i	0.939847	−	0.788625i
$808$		0			0
$809$	26.1905	−	45.3632i	0.920808	−	1.59489i	0.122640	−	0.992451i	$-0.460864\pi$
$809$	26.1905	−	45.3632i	0.920808	−	1.59489i	0.798168	−	0.602435i	$-0.205803\pi$
$810$		0			0
$811$	44.9842	+	16.3729i	1.57961	+	0.574930i	0.975119	−	0.221683i	$-0.0711551\pi$
$811$	44.9842	+	16.3729i	1.57961	+	0.574930i	0.604489	+	0.796614i	$0.293377\pi$
$812$		0			0
$813$	7.00222	+	39.7116i	0.245579	+	1.39275i
$814$		0			0
$815$	−0.689378	−	0.578457i	−0.0241479	−	0.0202625i
$816$		0			0
$817$	−9.17917	−	0.133109i	−0.321138	−	0.00465690i
$818$		0			0
$819$	3.64543	+	3.05888i	0.127382	+	0.106886i
$820$		0			0
$821$	−5.87140	−	33.2983i	−0.204913	−	1.16212i	−0.897576	−	0.440859i	$-0.854674\pi$
$821$	−5.87140	−	33.2983i	−0.204913	−	1.16212i	0.692663	−	0.721261i	$-0.256437\pi$
$822$		0			0
$823$	−5.67782	−	2.06656i	−0.197916	−	0.0720357i	0.241160	−	0.970485i	$-0.422472\pi$
$823$	−5.67782	−	2.06656i	−0.197916	−	0.0720357i	−0.439077	+	0.898450i	$0.644694\pi$
$824$		0			0
$825$	21.8195	−	37.7926i	0.759659	−	1.31577i
$826$		0			0
$827$	−18.6612	+	15.6586i	−0.648912	+	0.544502i	−0.906741	−	0.421689i	$-0.861437\pi$
$827$	−18.6612	+	15.6586i	−0.648912	+	0.544502i	0.257829	+	0.966191i	$0.416993\pi$
$828$		0			0
$829$	−11.9534	−	20.7038i	−0.415157	−	0.719074i	0.580288	−	0.814412i	$-0.302940\pi$
$829$	−11.9534	−	20.7038i	−0.415157	−	0.719074i	−0.995445	+	0.0953379i	$0.969607\pi$
$830$		0			0
$831$	−5.23308	+	29.6783i	−0.181533	+	1.02953i
$832$		0			0
$833$	−22.5253	+	8.19853i	−0.780455	+	0.284062i
$834$		0			0
$835$	6.30365			0.218147
$836$		0			0
$837$	15.6287			0.540206
$838$		0			0
$839$	14.8893	−	5.41928i	0.514037	−	0.187094i	−0.0719596	−	0.997408i	$-0.522925\pi$
$839$	14.8893	−	5.41928i	0.514037	−	0.187094i	0.585997	+	0.810313i	$0.300703\pi$
$840$		0			0
$841$	−4.35127	+	24.6773i	−0.150044	+	0.850941i
$842$		0			0
$843$	−17.6027	−	30.4887i	−0.606268	−	1.05009i
$844$		0			0
$845$	−2.51889	+	2.11360i	−0.0866523	+	0.0727099i
$846$		0			0
$847$	27.7101	−	47.9953i	0.952129	−	1.64914i
$848$		0			0
$849$	−12.4500	−	4.53141i	−0.427282	−	0.155518i
$850$		0			0
$851$	3.59358	+	20.3802i	0.123186	+	0.698624i
$852$		0			0
$853$	0.932419	+	0.782392i	0.0319254	+	0.0267886i	0.658611	−	0.752484i	$-0.271144\pi$
$853$	0.932419	+	0.782392i	0.0319254	+	0.0267886i	−0.626685	+	0.779272i	$0.715589\pi$
$854$		0			0
$855$	−0.624485	+	0.508759i	−0.0213569	+	0.0173992i
$856$		0			0
$857$	35.5296	+	29.8129i	1.21367	+	1.01839i	0.999131	+	0.0416731i	$0.0132688\pi$
$857$	35.5296	+	29.8129i	1.21367	+	1.01839i	0.214537	+	0.976716i	$0.431176\pi$
$858$		0			0
$859$	2.65926	+	15.0814i	0.0907329	+	0.514572i	0.995972	+	0.0896685i	$0.0285807\pi$
$859$	2.65926	+	15.0814i	0.0907329	+	0.514572i	−0.905239	+	0.424903i	$0.860308\pi$
$860$		0			0
$861$	−37.7365	−	13.7350i	−1.28606	−	0.468087i
$862$		0			0
$863$	22.8678	−	39.6082i	0.778430	−	1.34828i	−0.154416	−	0.988006i	$-0.549350\pi$
$863$	22.8678	−	39.6082i	0.778430	−	1.34828i	0.932846	−	0.360274i	$-0.117317\pi$
$864$		0			0
$865$	−2.41534	+	2.02671i	−0.0821242	+	0.0689104i
$866$		0			0
$867$	13.7690	+	23.8487i	0.467621	+	0.809943i
$868$		0			0
$869$	1.95171	−	11.0687i	0.0662074	−	0.375481i
$870$		0			0
$871$	18.7135	−	6.81115i	0.634082	−	0.230787i
$872$		0			0
$873$	4.07604			0.137953
$874$		0			0
$875$	16.3277			0.551977
$876$		0			0
$877$	31.1707	−	11.3452i	1.05256	−	0.383101i	0.242932	−	0.970043i	$-0.421891\pi$
$877$	31.1707	−	11.3452i	1.05256	−	0.383101i	0.809628	+	0.586943i	$0.199669\pi$
$878$		0			0
$879$	−2.69594	+	15.2894i	−0.0909317	+	0.515699i
$880$		0			0
$881$	−21.9243	−	37.9739i	−0.738647	−	1.27937i	−0.953105	−	0.302641i	$-0.902132\pi$
$881$	−21.9243	−	37.9739i	−0.738647	−	1.27937i	0.214457	−	0.976733i	$-0.431202\pi$
$882$		0			0
$883$	−38.1942	+	32.0487i	−1.28534	+	1.07853i	−0.292852	+	0.956158i	$0.594604\pi$
$883$	−38.1942	+	32.0487i	−1.28534	+	1.07853i	−0.992485	+	0.122368i	$0.960951\pi$
$884$		0			0
$885$	−1.84730	+	3.19961i	−0.0620962	+	0.107554i
$886$		0			0
$887$	−32.0373	−	11.6606i	−1.07571	−	0.391525i	−0.257399	−	0.966305i	$-0.582866\pi$
$887$	−32.0373	−	11.6606i	−1.07571	−	0.391525i	−0.818308	+	0.574780i	$0.805088\pi$
$888$		0			0
$889$	−15.9354	−	90.3742i	−0.534457	−	3.03105i
$890$		0			0
$891$	−37.5959	−	31.5467i	−1.25951	−	1.05685i
$892$		0			0
$893$	16.2310	+	14.0255i	0.543150	+	0.469345i
$894$		0			0
$895$	1.76399	+	1.48016i	0.0589635	+	0.0494763i
$896$		0			0
$897$	3.74510	+	21.2395i	0.125045	+	0.709167i
$898$		0			0
$899$	−6.28668	−	2.28817i	−0.209673	−	0.0763146i
$900$		0			0
$901$	9.62108	−	16.6642i	0.320525	−	0.555165i
$902$		0			0
$903$	−14.4290	+	12.1074i	−0.480168	+	0.402908i
$904$		0			0
$905$	0.881911	+	1.52752i	0.0293157	+	0.0507763i
$906$		0			0
$907$	8.06629	−	45.7462i	0.267837	−	1.51898i	−0.492997	−	0.870031i	$-0.664098\pi$
$907$	8.06629	−	45.7462i	0.267837	−	1.51898i	0.760833	−	0.648947i	$-0.224790\pi$
$908$		0			0
$909$	2.24510	−	0.817150i	0.0744653	−	0.0271031i
$910$		0			0
$911$	−19.8527			−0.657748			−0.328874	−	0.944374i	$-0.606669\pi$
$911$	−19.8527			−0.657748			−0.328874	+	0.944374i	$0.606669\pi$
$912$		0			0
$913$	−54.9026			−1.81701
$914$		0			0
$915$	−6.12923	+	2.23086i	−0.202626	+	0.0737499i
$916$		0			0
$917$	14.5697	−	82.6289i	0.481134	−	2.72865i
$918$		0			0
$919$	−12.5564	−	21.7484i	−0.414199	−	0.717413i	0.581145	−	0.813800i	$-0.302605\pi$
$919$	−12.5564	−	21.7484i	−0.414199	−	0.717413i	−0.995344	+	0.0963867i	$0.969271\pi$
$920$		0			0
$921$	−6.81180	+	5.71578i	−0.224457	+	0.188341i
$922$		0			0
$923$	10.8020	−	18.7096i	0.355552	−	0.615835i
$924$		0			0
$925$	−15.5398	−	5.65604i	−0.510946	−	0.185969i
$926$		0			0
$927$	−1.38737	−	7.86819i	−0.0455674	−	0.258425i
$928$		0			0
$929$	−41.3790	−	34.7211i	−1.35760	−	1.13916i	−0.976715	−	0.214539i	$-0.931175\pi$
$929$	−41.3790	−	34.7211i	−1.35760	−	1.13916i	−0.380885	−	0.924623i	$-0.624381\pi$
$930$		0			0
$931$	63.7410	+	24.2522i	2.08903	+	0.794833i
$932$		0			0
$933$	16.1839	+	13.5799i	0.529838	+	0.444587i
$934$		0			0
$935$	0.439693	+	2.49362i	0.0143795	+	0.0815501i
$936$		0			0
$937$	33.2991	+	12.1199i	1.08783	+	0.395939i	0.822818	−	0.568305i	$-0.192401\pi$
$937$	33.2991	+	12.1199i	1.08783	+	0.395939i	0.265015	+	0.964244i	$0.414623\pi$
$938$		0			0
$939$	−6.50387	+	11.2650i	−0.212246	+	0.367620i
$940$		0			0
$941$	21.7554	−	18.2549i	0.709205	−	0.595093i	−0.215171	−	0.976576i	$-0.569031\pi$
$941$	21.7554	−	18.2549i	0.709205	−	0.595093i	0.924376	+	0.381483i	$0.124587\pi$
$942$		0			0
$943$	−13.7087	−	23.7442i	−0.446418	−	0.773218i
$944$		0			0
$945$	1.33110	−	7.54904i	0.0433007	−	0.245570i
$946$		0			0
$947$	−38.7429	+	14.1013i	−1.25898	+	0.458230i	−0.883425	−	0.468572i	$-0.844769\pi$
$947$	−38.7429	+	14.1013i	−1.25898	+	0.458230i	−0.375551	+	0.926802i	$0.622546\pi$
$948$		0			0
$949$	27.4739			0.891840
$950$		0			0
$951$	−27.4739			−0.890902
$952$		0			0
$953$	23.8106	−	8.66636i	0.771302	−	0.280731i	0.0737609	−	0.997276i	$-0.476500\pi$
$953$	23.8106	−	8.66636i	0.771302	−	0.280731i	0.697541	+	0.716545i	$0.254278\pi$
$954$		0			0
$955$	0.537141	−	3.04628i	0.0173815	−	0.0985753i
$956$		0			0
$957$	8.87851	+	15.3780i	0.287001	+	0.497101i
$958$		0			0
$959$	71.6425	−	60.1152i	2.31346	−	1.94122i
$960$		0			0
$961$	9.82295	−	17.0138i	0.316869	−	0.548834i
$962$		0			0
$963$	5.44356	+	1.98129i	0.175416	+	0.0638463i
$964$		0			0
$965$	1.16297	+	6.59553i	0.0374373	+	0.212318i
$966$		0			0
$967$	−2.90096	−	2.43419i	−0.0932885	−	0.0782784i	0.594951	−	0.803762i	$-0.297172\pi$
$967$	−2.90096	−	2.43419i	−0.0932885	−	0.0782784i	−0.688239	+	0.725484i	$0.741616\pi$
$968$		0			0
$969$	−2.35844	+	12.3274i	−0.0757640	+	0.396012i
$970$		0			0
$971$	−7.05303	−	5.91820i	−0.226343	−	0.189924i	0.522563	−	0.852601i	$-0.324976\pi$
$971$	−7.05303	−	5.91820i	−0.226343	−	0.189924i	−0.748906	+	0.662677i	$0.769420\pi$
$972$		0			0
$973$	8.56253	+	48.5605i	0.274502	+	1.55678i
$974$		0			0
$975$	−16.1951	−	5.89452i	−0.518657	−	0.188776i
$976$		0			0
$977$	−25.2297	+	43.6991i	−0.807169	+	1.39806i	0.107648	+	0.994189i	$0.465668\pi$
$977$	−25.2297	+	43.6991i	−0.807169	+	1.39806i	−0.914817	+	0.403868i	$0.867665\pi$
$978$		0			0
$979$	20.5535	−	17.2464i	0.656893	−	0.551198i
$980$		0			0
$981$	2.03596	+	3.52638i	0.0650032	+	0.112589i
$982$		0			0
$983$	−8.44175	+	47.8756i	−0.269250	+	1.52699i	0.487403	+	0.873177i	$0.337944\pi$
$983$	−8.44175	+	47.8756i	−0.269250	+	1.52699i	−0.756653	+	0.653816i	$0.773167\pi$
$984$		0			0
$985$	5.84389	−	2.12700i	0.186202	−	0.0677720i
$986$		0			0
$987$	44.0137			1.40097
$988$		0			0
$989$	−12.8598			−0.408917
$990$		0			0
$991$	−34.8748	+	12.6934i	−1.10783	+	0.403219i	−0.830199	−	0.557468i	$-0.811773\pi$
$991$	−34.8748	+	12.6934i	−1.10783	+	0.403219i	−0.277636	+	0.960686i	$0.589551\pi$
$992$		0			0
$993$	−1.19624	+	6.78422i	−0.0379616	+	0.215291i
$994$		0			0
$995$	−1.51501	−	2.62408i	−0.0480292	−	0.0831890i
$996$		0			0
$997$	−31.6648	+	26.5699i	−1.00283	+	0.841477i	−0.987375	−	0.158403i	$-0.949365\pi$
$997$	−31.6648	+	26.5699i	−1.00283	+	0.841477i	−0.0154592	+	0.999880i	$0.504921\pi$
$998$		0			0
$999$	−7.85978	+	13.6135i	−0.248673	+	0.430714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.a.73.1	yes	6
4.3	odd	2		304.2.u.d.225.1		6
19.5	even	9		2888.2.a.q.1.3		3
19.6	even	9	inner	152.2.q.a.25.1	✓	6
19.14	odd	18		2888.2.a.p.1.1		3
76.43	odd	18		5776.2.a.bl.1.1		3
76.63	odd	18		304.2.u.d.177.1		6
76.71	even	18		5776.2.a.bm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.a.25.1	✓	6	19.6	even	9	inner
152.2.q.a.73.1	yes	6	1.1	even	1	trivial
304.2.u.d.177.1		6	76.63	odd	18
304.2.u.d.225.1		6	4.3	odd	2
2888.2.a.p.1.1		3	19.14	odd	18
2888.2.a.q.1.3		3	19.5	even	9
5776.2.a.bl.1.1		3	76.43	odd	18
5776.2.a.bm.1.3		3	76.71	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76604 + 0.642788i) q^{3} +(0.0603074 - 0.342020i) q^{5} +(2.37939 + 4.12122i) q^{7} +(0.407604 - 0.342020i) q^{9} +(-2.37939 + 4.12122i) q^{11} +(1.76604 + 0.642788i) q^{13} +(0.113341 + 0.642788i) q^{15} +(1.17365 + 0.984808i) q^{17} +(-0.694593 - 4.30320i) q^{19} +(-6.85117 - 5.74881i) q^{21} +(-1.06031 - 6.01330i) q^{23} +(4.58512 + 1.66885i) q^{25} +(2.31908 - 4.01676i) q^{27} +(-1.52094 + 1.27622i) q^{29} +(1.68479 + 2.91815i) q^{31} +(1.55303 - 8.80769i) q^{33} +(1.55303 - 0.565258i) q^{35} -3.38919 q^{37} -3.53209 q^{39} +(4.21941 - 1.53574i) q^{41} +(0.365715 - 2.07407i) q^{43} +(-0.0923963 - 0.160035i) q^{45} +(-3.76991 + 3.16333i) q^{47} +(-7.82295 + 13.5497i) q^{49} +(-2.70574 - 0.984808i) q^{51} +(-2.18092 - 12.3686i) q^{53} +(1.26604 + 1.06234i) q^{55} +(3.99273 + 7.15317i) q^{57} +(4.33615 + 3.63846i) q^{59} +(1.73530 + 9.84137i) q^{61} +(2.37939 + 0.866025i) q^{63} +(0.326352 - 0.565258i) q^{65} +(8.11721 - 6.81115i) q^{67} +(5.73783 + 9.93821i) q^{69} +(1.99613 - 11.3206i) q^{71} +(13.7369 - 4.99984i) q^{73} -9.17024 q^{75} -22.6459 q^{77} +(-2.21941 + 0.807798i) q^{79} +(-1.79086 + 10.1565i) q^{81} +(5.76857 + 9.99146i) q^{83} +(0.407604 - 0.342020i) q^{85} +(1.86571 - 3.23151i) q^{87} +(-5.29813 - 1.92836i) q^{89} +(1.55303 + 8.80769i) q^{91} +(-4.85117 - 4.07061i) q^{93} +(-1.51367 - 0.0219501i) q^{95} +(5.86824 + 4.92404i) q^{97} +(0.439693 + 2.49362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} + 6 q^{5} + 3 q^{7} + 6 q^{9} - 3 q^{11} + 6 q^{13} - 6 q^{15} + 6 q^{17} - 15 q^{21} - 12 q^{23} + 6 q^{25} - 3 q^{27} - 6 q^{29} + 3 q^{31} - 3 q^{33} - 3 q^{35} - 12 q^{37} - 12 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 + 6 * q^5 + 3 * q^7 + 6 * q^9 - 3 * q^11 + 6 * q^13 - 6 * q^15 + 6 * q^17 - 15 * q^21 - 12 * q^23 + 6 * q^25 - 3 * q^27 - 6 * q^29 + 3 * q^31 - 3 * q^33 - 3 * q^35 - 12 * q^37 - 12 * q^39 - 6 * q^41 + 12 * q^43 + 3 * q^45 + 6 * q^47 - 6 * q^49 - 6 * q^51 - 30 * q^53 + 3 * q^55 + 6 * q^57 + 30 * q^59 + 6 * q^61 + 3 * q^63 + 3 * q^65 + 18 * q^67 + 15 * q^69 + 36 * q^71 + 6 * q^73 - 12 * q^75 - 54 * q^77 + 18 * q^79 + 21 * q^81 + 15 * q^83 + 6 * q^85 + 21 * q^87 - 18 * q^89 - 3 * q^91 - 3 * q^93 + 12 * q^95 + 30 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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