LMFDB - Embedded newform 117.2.t.c.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(25,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("117.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.6
Root			$-0.219737 + 1.71806i$ of defining polynomial
Character	$\chi$	$=$	117.25
Dual form			117.2.t.c.103.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.784270 + 0.452798i) q^{2} +(1.66968 + 0.460628i) q^{3} +(-0.589947 - 1.02182i) q^{4} +(-1.94254 + 1.12153i) q^{5} +(1.10091 + 1.11728i) q^{6} +(2.97576 + 1.71806i) q^{7} -2.87970i q^{8} +(2.57564 + 1.53820i) q^{9} -2.03130 q^{10} +(-3.20133 - 1.84829i) q^{11} +(-0.514343 - 1.97785i) q^{12} +(-3.28340 - 1.48972i) q^{13} +(1.55587 + 2.69484i) q^{14} +(-3.76003 + 0.977800i) q^{15} +(0.124029 - 0.214825i) q^{16} -4.21120 q^{17} +(1.32350 + 2.37261i) q^{18} -4.25298i q^{19} +(2.29200 + 1.32329i) q^{20} +(4.17717 + 4.23932i) q^{21} +(-1.67380 - 2.89911i) q^{22} +(1.89162 + 3.27639i) q^{23} +(1.32647 - 4.80817i) q^{24} +(0.0156524 - 0.0271108i) q^{25} +(-1.90053 - 2.65506i) q^{26} +(3.59195 + 3.75471i) q^{27} -4.05425i q^{28} +(-1.18945 + 2.06020i) q^{29} +(-3.39162 - 0.935677i) q^{30} +(6.37163 - 3.67866i) q^{31} +(-4.79325 + 2.76738i) q^{32} +(-4.49381 - 4.56066i) q^{33} +(-3.30272 - 1.90682i) q^{34} -7.70739 q^{35} +(0.0522689 - 3.53930i) q^{36} +5.49928i q^{37} +(1.92574 - 3.33549i) q^{38} +(-4.79602 - 3.99978i) q^{39} +(3.22967 + 5.59395i) q^{40} +(6.86085 - 3.96111i) q^{41} +(1.35647 + 5.21619i) q^{42} +(-0.450266 + 0.779883i) q^{43} +4.36157i q^{44} +(-6.72844 - 0.0993666i) q^{45} +3.42609i q^{46} +(4.80060 + 2.77163i) q^{47} +(0.306043 - 0.301557i) q^{48} +(2.40343 + 4.16287i) q^{49} +(0.0245514 - 0.0141748i) q^{50} +(-7.03134 - 1.93980i) q^{51} +(0.414812 + 4.23390i) q^{52} +7.59566 q^{53} +(1.11693 + 4.57114i) q^{54} +8.29163 q^{55} +(4.94749 - 8.56930i) q^{56} +(1.95904 - 7.10111i) q^{57} +(-1.86571 + 1.07717i) q^{58} +(-4.44379 + 2.56562i) q^{59} +(3.21735 + 3.26522i) q^{60} +(6.50907 - 11.2740i) q^{61} +6.66277 q^{62} +(5.02178 + 9.00242i) q^{63} -5.50838 q^{64} +(8.04892 - 0.788585i) q^{65} +(-1.45930 - 5.61158i) q^{66} +(-11.7002 + 6.75511i) q^{67} +(2.48439 + 4.30308i) q^{68} +(1.64920 + 6.34184i) q^{69} +(-6.04468 - 3.48989i) q^{70} -2.65506i q^{71} +(4.42956 - 7.41708i) q^{72} +5.45741i q^{73} +(-2.49006 + 4.31292i) q^{74} +(0.0386224 - 0.0380563i) q^{75} +(-4.34578 + 2.50904i) q^{76} +(-6.35092 - 11.0001i) q^{77} +(-1.95028 - 5.30853i) q^{78} +(-5.46886 + 9.47234i) q^{79} +0.556410i q^{80} +(4.26787 + 7.92371i) q^{81} +7.17434 q^{82} +(-0.465547 - 0.268784i) q^{83} +(1.86750 - 6.76929i) q^{84} +(8.18044 - 4.72298i) q^{85} +(-0.706259 + 0.407759i) q^{86} +(-2.93499 + 2.89197i) q^{87} +(-5.32252 + 9.21887i) q^{88} -5.75227i q^{89} +(-5.23192 - 3.12456i) q^{90} +(-7.21120 - 10.0741i) q^{91} +(2.23192 - 3.86579i) q^{92} +(12.3331 - 3.20723i) q^{93} +(2.50998 + 4.34740i) q^{94} +(4.76984 + 8.26161i) q^{95} +(-9.27791 + 2.41273i) q^{96} +(5.87585 + 3.39243i) q^{97} +4.35308i q^{98} +(-5.40244 - 9.68481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) $ 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.784270	+	0.452798i	0.554562	+	0.320177i	0.750960	−	0.660348i	$-0.229591\pi$
$2$	0.784270	+	0.452798i	0.554562	+	0.320177i	−0.196398	+	0.980524i	$0.562924\pi$
$3$	1.66968	+	0.460628i	0.963989	+	0.265944i
$3$	1.66968	+	0.460628i	0.963989	+	0.265944i
$4$	−0.589947	−	1.02182i	−0.294974	−	0.510909i
$5$	−1.94254	+	1.12153i	−0.868732	+	0.501563i	−0.866927	−	0.498436i	$-0.833908\pi$
$5$	−1.94254	+	1.12153i	−0.868732	+	0.501563i	−0.00180550	+	0.999998i	$0.500575\pi$
$6$	1.10091	+	1.11728i	0.449443	+	0.456129i
$7$	2.97576	+	1.71806i	1.12473	+	0.649364i	0.942605	−	0.333911i	$-0.108368\pi$
$7$	2.97576	+	1.71806i	1.12473	+	0.649364i	0.182127	+	0.983275i	$0.441702\pi$
$8$		−	2.87970i		−	1.01813i
$9$	2.57564	+	1.53820i	0.858548	+	0.512734i
$10$	−2.03130			−0.642355
$11$	−3.20133	−	1.84829i	−0.965236	−	0.557279i	−0.0674557	−	0.997722i	$-0.521488\pi$
$11$	−3.20133	−	1.84829i	−0.965236	−	0.557279i	−0.897781	+	0.440443i	$0.854821\pi$
$12$	−0.514343	−	1.97785i	−0.148478	−	0.570957i
$13$	−3.28340	−	1.48972i	−0.910652	−	0.413174i
$13$	−3.28340	−	1.48972i	−0.910652	−	0.413174i
$14$	1.55587	+	2.69484i	0.415823	+	0.720226i
$15$	−3.76003	+	0.977800i	−0.970835	+	0.252467i
$16$	0.124029	−	0.214825i	0.0310073	−	0.0537063i
$17$	−4.21120			−1.02137			−0.510683	−	0.859769i	$-0.670607\pi$
$17$	−4.21120			−1.02137			−0.510683	+	0.859769i	$0.670607\pi$
$18$	1.32350	+	2.37261i	0.311953	+	0.559230i
$19$		−	4.25298i		−	0.975701i	−0.872927	−	0.487851i	$-0.837781\pi$
$19$		−	4.25298i		−	0.975701i	0.872927	−	0.487851i	$-0.162219\pi$
$20$	2.29200	+	1.32329i	0.512506	+	0.295896i
$21$	4.17717	+	4.23932i	0.911534	+	0.925095i
$22$	−1.67380	−	2.89911i	−0.356856	−	0.618092i
$23$	1.89162	+	3.27639i	0.394431	+	0.683174i	0.993028	−	0.117876i	$-0.0376085\pi$
$23$	1.89162	+	3.27639i	0.394431	+	0.683174i	−0.598598	+	0.801050i	$0.704275\pi$
$24$	1.32647	−	4.80817i	0.270765	−	0.981464i
$25$	0.0156524	−	0.0271108i	0.00313048	−	0.00542215i
$26$	−1.90053	−	2.65506i	−0.372725	−	0.520700i
$27$	3.59195	+	3.75471i	0.691272	+	0.722595i
$28$		−	4.05425i		−	0.766181i
$29$	−1.18945	+	2.06020i	−0.220876	+	0.382569i	−0.955074	−	0.296367i	$-0.904225\pi$
$29$	−1.18945	+	2.06020i	−0.220876	+	0.382569i	0.734198	+	0.678935i	$0.237558\pi$
$30$	−3.39162	−	0.935677i	−0.619223	−	0.170830i
$31$	6.37163	−	3.67866i	1.14438	−	0.660707i	0.196868	−	0.980430i	$-0.436923\pi$
$31$	6.37163	−	3.67866i	1.14438	−	0.660707i	0.947511	+	0.319723i	$0.103590\pi$
$32$	−4.79325	+	2.76738i	−0.847334	+	0.489209i
$33$	−4.49381	−	4.56066i	−0.782272	−	0.793910i
$34$	−3.30272	−	1.90682i	−0.566411	−	0.327018i
$35$	−7.70739			−1.30279
$36$	0.0522689	−	3.53930i	0.00871149	−	0.589883i
$37$			5.49928i			0.904076i	0.891999	+	0.452038i	$0.149303\pi$
$37$			5.49928i			0.904076i	−0.891999	+	0.452038i	$0.850697\pi$
$38$	1.92574	−	3.33549i	0.312397	−	0.541087i
$39$	−4.79602	−	3.99978i	−0.767977	−	0.640477i
$40$	3.22967	+	5.59395i	0.510655	+	0.884481i
$41$	6.86085	−	3.96111i	1.07148	−	0.618622i	0.142898	−	0.989737i	$-0.454358\pi$
$41$	6.86085	−	3.96111i	1.07148	−	0.618622i	0.928587	+	0.371116i	$0.121025\pi$
$42$	1.35647	+	5.21619i	0.209309	+	0.804875i
$43$	−0.450266	+	0.779883i	−0.0686649	+	0.118931i	−0.898314	−	0.439354i	$-0.855207\pi$
$43$	−0.450266	+	0.779883i	−0.0686649	+	0.118931i	0.829649	+	0.558285i	$0.188541\pi$
$44$			4.36157i			0.657531i
$45$	−6.72844	−	0.0993666i	−1.00302	−	0.0148127i
$46$			3.42609i			0.505150i
$47$	4.80060	+	2.77163i	0.700239	+	0.404283i	0.807436	−	0.589955i	$-0.200854\pi$
$47$	4.80060	+	2.77163i	0.700239	+	0.404283i	−0.107197	+	0.994238i	$0.534188\pi$
$48$	0.306043	−	0.301557i	0.0441736	−	0.0435260i
$49$	2.40343	+	4.16287i	0.343347	+	0.594695i
$50$	0.0245514	−	0.0141748i	0.00347209	−	0.00200461i
$51$	−7.03134	−	1.93980i	−0.984585	−	0.271626i
$52$	0.414812	+	4.23390i	0.0575241	+	0.587136i
$53$	7.59566			1.04334			0.521672	−	0.853146i	$-0.325308\pi$
$53$	7.59566			1.04334			0.521672	+	0.853146i	$0.325308\pi$
$54$	1.11693	+	4.57114i	0.151995	+	0.622053i
$55$	8.29163			1.11804
$56$	4.94749	−	8.56930i	0.661136	−	1.14512i
$57$	1.95904	−	7.10111i	0.259482	−	0.940565i
$58$	−1.86571	+	1.07717i	−0.244979	+	0.141439i
$59$	−4.44379	+	2.56562i	−0.578532	+	0.334016i	−0.760550	−	0.649279i	$-0.775071\pi$
$59$	−4.44379	+	2.56562i	−0.578532	+	0.334016i	0.182018	+	0.983295i	$0.441737\pi$
$60$	3.21735	+	3.26522i	0.415359	+	0.421538i
$61$	6.50907	−	11.2740i	0.833401	−	1.44349i	−0.0619247	−	0.998081i	$-0.519724\pi$
$61$	6.50907	−	11.2740i	0.833401	−	1.44349i	0.895326	−	0.445412i	$-0.146943\pi$
$62$	6.66277			0.846173
$63$	5.02178	+	9.00242i	0.632685	+	1.13420i
$64$	−5.50838			−0.688547
$65$	8.04892	−	0.788585i	0.998346	−	0.0978120i
$66$	−1.45930	−	5.61158i	−0.179627	−	0.690738i
$67$	−11.7002	+	6.75511i	−1.42941	+	0.825269i	−0.997074	−	0.0764454i	$-0.975643\pi$
$67$	−11.7002	+	6.75511i	−1.42941	+	0.825269i	−0.432333	+	0.901714i	$0.642310\pi$
$68$	2.48439	+	4.30308i	0.301276	+	0.521825i
$69$	1.64920	+	6.34184i	0.198541	+	0.763468i
$70$	−6.04468	−	3.48989i	−0.722477	−	0.417122i
$71$		−	2.65506i		−	0.315098i	−0.987511	−	0.157549i	$-0.949641\pi$
$71$		−	2.65506i		−	0.315098i	0.987511	−	0.157549i	$-0.0503592\pi$
$72$	4.42956	−	7.41708i	0.522029	−	0.874112i
$73$			5.45741i			0.638741i	0.947630	+	0.319371i	$0.103472\pi$
$73$			5.45741i			0.638741i	−0.947630	+	0.319371i	$0.896528\pi$
$74$	−2.49006	+	4.31292i	−0.289464	+	0.501366i
$75$	0.0386224	−	0.0380563i	0.00445974	−	0.00439436i
$76$	−4.34578	+	2.50904i	−0.498495	+	0.287806i
$77$	−6.35092	−	11.0001i	−0.723755	−	1.25358i
$78$	−1.95028	−	5.30853i	−0.220825	−	0.601073i
$79$	−5.46886	+	9.47234i	−0.615294	+	1.06572i	0.375038	+	0.927009i	$0.377630\pi$
$79$	−5.46886	+	9.47234i	−0.615294	+	1.06572i	−0.990333	+	0.138712i	$0.955704\pi$
$80$			0.556410i			0.0622085i
$81$	4.26787	+	7.92371i	0.474208	+	0.880413i
$82$	7.17434			0.792273
$83$	−0.465547	−	0.268784i	−0.0511004	−	0.0295029i	0.474232	−	0.880400i	$-0.342726\pi$
$83$	−0.465547	−	0.268784i	−0.0511004	−	0.0295029i	−0.525333	+	0.850897i	$0.676059\pi$
$84$	1.86750	−	6.76929i	0.203761	−	0.738590i
$85$	8.18044	−	4.72298i	0.887294	−	0.512279i
$86$	−0.706259	+	0.407759i	−0.0761579	+	0.0439698i
$87$	−2.93499	+	2.89197i	−0.314664	+	0.310051i
$88$	−5.32252	+	9.21887i	−0.567382	+	0.982735i
$89$		−	5.75227i		−	0.609739i	−0.952394	−	0.304870i	$-0.901387\pi$
$89$		−	5.75227i		−	0.609739i	0.952394	−	0.304870i	$-0.0986129\pi$
$90$	−5.23192	−	3.12456i	−0.551492	−	0.329357i
$91$	−7.21120	−	10.0741i	−0.755939	−	1.05605i
$92$	2.23192	−	3.86579i	0.232693	−	0.403037i
$93$	12.3331	−	3.20723i	1.27888	−	0.332574i
$94$	2.50998	+	4.34740i	0.258884	+	0.448401i
$95$	4.76984	+	8.26161i	0.489375	+	0.847623i
$96$	−9.27791	+	2.41273i	−0.946922	+	0.246248i
$97$	5.87585	+	3.39243i	0.596603	+	0.344449i	0.767704	−	0.640805i	$-0.221399\pi$
$97$	5.87585	+	3.39243i	0.596603	+	0.344449i	−0.171101	+	0.985253i	$0.554733\pi$
$98$			4.35308i			0.439727i
$99$	−5.40244	−	9.68481i	−0.542965	−	0.973360i
$100$	−0.0369364			−0.00369364
$101$	2.48116	−	4.29749i	0.246884	−	0.427616i	−0.715776	−	0.698330i	$-0.753927\pi$
$101$	2.48116	−	4.29749i	0.246884	−	0.427616i	0.962660	+	0.270715i	$0.0872599\pi$
$102$	−4.63613	−	4.70510i	−0.459045	−	0.465875i
$103$	−1.05587	−	1.82881i	−0.104038	−	0.180198i	0.809307	−	0.587386i	$-0.199843\pi$
$103$	−1.05587	−	1.82881i	−0.104038	−	0.180198i	−0.913345	+	0.407188i	$0.866510\pi$
$104$	−4.28995	+	9.45522i	−0.420664	+	0.927161i
$105$	−12.8689	−	3.55024i	−1.25587	−	0.346468i
$106$	5.95705	+	3.43930i	0.578600	+	0.334055i
$107$	−8.07404			−0.780547			−0.390274	−	0.920699i	$-0.627620\pi$
$107$	−8.07404			−0.780547			−0.390274	+	0.920699i	$0.627620\pi$
$108$	1.71757	−	5.88541i	0.165274	−	0.566324i
$109$			10.0020i			0.958021i	0.877809	+	0.479011i	$0.159004\pi$
$109$			10.0020i			0.958021i	−0.877809	+	0.479011i	$0.840996\pi$
$110$	6.50287	+	3.75443i	0.620024	+	0.357971i
$111$	−2.53312	+	9.18202i	−0.240433	+	0.871519i
$112$	0.738163	−	0.426179i	0.0697498	−	0.0402701i
$113$	−9.71733	−	16.8309i	−0.914130	−	1.58332i	−0.808171	−	0.588948i	$-0.799542\pi$
$113$	−9.71733	−	16.8309i	−0.914130	−	1.58332i	−0.105959	−	0.994371i	$-0.533791\pi$
$114$	4.75179	−	4.68213i	0.445046	−	0.438522i
$115$	−7.34912	−	4.24302i	−0.685309	−	0.395664i
$116$	2.80686			0.260611
$117$	−6.16539	−	8.88752i	−0.569990	−	0.821651i
$118$	−4.64684			−0.427776
$119$	−12.5315	−	7.23508i	−1.14876	−	0.663238i
$120$	2.81577	+	10.8278i	0.257044	+	0.988435i
$121$	1.33233	+	2.30766i	0.121121	+	0.209787i
$122$	10.2097	−	5.89459i	0.924346	−	0.533671i
$123$	13.2800	−	3.45348i	1.19742	−	0.311390i
$124$	−7.51786	−	4.34044i	−0.675123	−	0.389783i
$125$		−	11.1451i		−	0.996845i
$126$	−0.137849	+	9.33418i	−0.0122805	+	0.831554i
$127$	−1.76413			−0.156541			−0.0782704	−	0.996932i	$-0.524940\pi$
$127$	−1.76413			−0.156541			−0.0782704	+	0.996932i	$0.524940\pi$
$128$	5.26644	+	3.04058i	0.465492	+	0.268752i
$129$	−1.11103	+	1.09475i	−0.0978211	+	0.0963872i
$130$	6.66959	+	3.02607i	0.584962	+	0.265404i
$131$	3.56490	+	6.17458i	0.311466	+	0.539476i	0.978680	−	0.205391i	$-0.0658465\pi$
$131$	3.56490	+	6.17458i	0.311466	+	0.539476i	−0.667214	+	0.744866i	$0.732513\pi$
$132$	−2.00906	+	7.28241i	−0.174866	+	0.633852i
$133$	7.30686	−	12.6559i	0.633585	−	1.09740i
$134$	−12.2348			−1.05693
$135$	−11.1885	−	3.26522i	−0.962957	−	0.281025i
$136$			12.1270i			1.03988i
$137$	−3.91494	−	2.26029i	−0.334476	−	0.193110i	0.323351	−	0.946279i	$-0.395191\pi$
$137$	−3.91494	−	2.26029i	−0.334476	−	0.193110i	−0.657826	+	0.753170i	$0.728524\pi$
$138$	−1.57816	+	5.72047i	−0.134342	+	0.486959i
$139$	−7.05496	−	12.2195i	−0.598394	−	1.03645i	−0.993058	−	0.117623i	$-0.962472\pi$
$139$	−7.05496	−	12.2195i	−0.598394	−	1.03645i	0.394664	−	0.918825i	$-0.370861\pi$
$140$	4.54696	+	7.87556i	0.384288	+	0.665606i
$141$	6.73876	+	6.83901i	0.567506	+	0.575949i
$142$	1.20221	−	2.08228i	0.100887	−	0.174741i
$143$	7.75782	+	10.8377i	0.648741	+	0.906298i
$144$	0.649899	−	0.362531i	0.0541583	−	0.0302109i
$145$		−	5.33603i		−	0.443133i
$146$	−2.47111	+	4.28008i	−0.204510	+	0.354222i
$147$	2.09542	+	8.05773i	0.172827	+	0.664590i
$148$	5.61927	−	3.24428i	0.461901	−	0.266679i
$149$	5.02499	−	2.90118i	0.411663	−	0.237674i	−0.279841	−	0.960046i	$-0.590282\pi$
$149$	5.02499	−	2.90118i	0.411663	−	0.237674i	0.691504	+	0.722372i	$0.256948\pi$
$150$	0.0475222	−	0.0123582i	0.00388017	−	0.00100904i
$151$	−8.44018	−	4.87294i	−0.686852	−	0.396554i	0.115580	−	0.993298i	$-0.463127\pi$
$151$	−8.44018	−	4.87294i	−0.686852	−	0.396554i	−0.802432	+	0.596744i	$0.796461\pi$
$152$	−12.2473			−0.993389
$153$	−10.8465	−	6.47767i	−0.876891	−	0.523689i
$154$		−	11.5027i		−	0.926917i
$155$	−8.25145	+	14.2919i	−0.662773	+	1.14796i
$156$	−1.25765	+	7.26032i	−0.100693	+	0.581291i
$157$	0.539798	+	0.934957i	0.0430806	+	0.0746177i	0.886762	−	0.462227i	$-0.152949\pi$
$157$	0.539798	+	0.934957i	0.0430806	+	0.0746177i	−0.843681	+	0.536845i	$0.819616\pi$
$158$	−8.57812	+	4.95258i	−0.682438	+	0.394006i
$159$	12.6823	+	3.49878i	1.00577	+	0.277471i
$160$	6.20739	−	10.7515i	0.490738	−	0.849982i
$161$			12.9997i			1.02452i
$162$	−0.240679	+	8.14681i	−0.0189096	+	0.640074i
$163$		−	5.54857i		−	0.434598i	−0.976105	−	0.217299i	$-0.930275\pi$
$163$		−	5.54857i		−	0.434598i	0.976105	−	0.217299i	$-0.0697247\pi$
$164$	−8.09508	−	4.67370i	−0.632120	−	0.364954i
$165$	13.8443	+	3.81936i	1.07778	+	0.297337i
$166$	−0.243410	−	0.421598i	−0.0188923	−	0.0327223i
$167$	11.5515	−	6.66925i	0.893880	−	0.516082i	0.0186702	−	0.999826i	$-0.494057\pi$
$167$	11.5515	−	6.66925i	0.893880	−	0.516082i	0.875210	+	0.483744i	$0.160723\pi$
$168$	12.2080	−	12.0290i	0.941865	−	0.928059i
$169$	8.56147	+	9.78270i	0.658575	+	0.752515i
$170$	8.55423			0.656079
$171$	6.54194	−	10.9542i	0.500275	−	0.837686i
$172$	1.06253			0.0810173
$173$	−3.72080	+	6.44461i	−0.282887	+	0.489975i	−0.972095	−	0.234589i	$-0.924625\pi$
$173$	−3.72080	+	6.44461i	−0.282887	+	0.489975i	0.689208	+	0.724564i	$0.257959\pi$
$174$	−3.61130	+	0.939122i	−0.273772	+	0.0711947i
$175$	0.0931556	−	0.0537834i	0.00704190	−	0.00406564i
$176$	−0.794117	+	0.458484i	−0.0598588	+	0.0345595i
$177$	−8.60150	+	2.23683i	−0.646528	+	0.168130i
$178$	2.60462	−	4.51133i	0.195224	−	0.338138i
$179$	23.2047			1.73440			0.867202	−	0.497957i	$-0.165916\pi$
$179$	23.2047			1.73440			0.867202	+	0.497957i	$0.165916\pi$
$180$	3.86789	+	6.93387i	0.288295	+	0.516820i
$181$	5.18439			0.385353			0.192676	−	0.981262i	$-0.438283\pi$
$181$	5.18439			0.385353			0.192676	+	0.981262i	$0.438283\pi$
$182$	−1.09398	−	11.1660i	−0.0810914	−	0.827682i
$183$	16.0612	−	15.8257i	1.18728	−	1.16987i
$184$	9.43502	−	5.44731i	0.695559	−	0.401581i
$185$	−6.16760	−	10.6826i	−0.453451	−	0.785400i
$186$	11.1247	+	3.06906i	0.815701	+	0.225034i
$187$	13.4814	+	7.78351i	0.985860	+	0.569186i
$188$		−	6.54045i		−	0.477012i
$189$	4.23798	+	17.3443i	0.308268	+	1.26161i
$190$			8.63911i			0.626747i
$191$	−8.07057	+	13.9786i	−0.583966	+	1.01146i	0.411037	+	0.911619i	$0.365167\pi$
$191$	−8.07057	+	13.9786i	−0.583966	+	1.01146i	−0.995003	+	0.0998406i	$0.968167\pi$
$192$	−9.19722	−	2.53732i	−0.663752	−	0.183115i
$193$	2.83991	−	1.63962i	0.204421	−	0.118023i	−0.394295	−	0.918984i	$-0.629011\pi$
$193$	2.83991	−	1.63962i	0.204421	−	0.118023i	0.598716	+	0.800961i	$0.295678\pi$
$194$	3.07217	+	5.32115i	0.220569	+	0.382037i
$195$	13.8023	+	2.39088i	0.988406	+	0.171214i
$196$	2.83580	−	4.91174i	0.202557	−	0.350839i
$197$			7.11249i			0.506744i	0.967369	+	0.253372i	$0.0815396\pi$
$197$			7.11249i			0.506744i	−0.967369	+	0.253372i	$0.918460\pi$
$198$	0.148298	−	10.0417i	0.0105391	−	0.713634i
$199$	−13.8449			−0.981437			−0.490719	−	0.871318i	$-0.663266\pi$
$199$	−13.8449			−0.981437			−0.490719	+	0.871318i	$0.663266\pi$
$200$	−0.0780709	−	0.0450743i	−0.00552045	−	0.00318723i
$201$	−22.6472	+	5.88942i	−1.59741	+	0.415407i
$202$	3.89179	−	2.24693i	0.273825	−	0.158093i
$203$	−7.07906	+	4.08710i	−0.496853	+	0.286858i
$204$	2.16600	+	8.32914i	0.151650	+	0.583156i
$205$	−8.88500	+	15.3893i	−0.620555	+	1.07483i
$206$		−	1.91238i		−	0.133242i
$207$	−0.167596	+	11.3485i	−0.0116488	+	0.788775i
$208$	−0.727267	+	0.520589i	−0.0504269	+	0.0360963i
$209$	−7.86073	+	13.6152i	−0.543738	+	0.941782i
$210$	−8.48511	−	8.61135i	−0.585528	−	0.594239i
$211$	−7.21695	−	12.5001i	−0.496836	−	0.860545i	0.503158	−	0.864195i	$-0.332171\pi$
$211$	−7.21695	−	12.5001i	−0.496836	−	0.860545i	−0.999993	+	0.00365007i	$0.998838\pi$
$212$	−4.48104	−	7.76139i	−0.307759	−	0.533055i
$213$	1.22300	−	4.43309i	0.0837983	−	0.303751i
$214$	−6.33223	−	3.65591i	−0.432862	−	0.249913i
$215$		−	2.01994i		−	0.137759i
$216$	10.8125	−	10.3438i	0.735694	−	0.703803i
$217$	25.2806			1.71616
$218$	−4.52890	+	7.84429i	−0.306736	+	0.531283i
$219$	−2.51384	+	9.11211i	−0.169869	+	0.615739i
$220$	−4.89162	−	8.47254i	−0.329793	−	0.571219i
$221$	13.8271	+	6.27350i	0.930109	+	0.422002i
$222$	−6.14425	+	6.05418i	−0.412375	+	0.406330i
$223$	9.52959	+	5.50191i	0.638149	+	0.368435i	0.783901	−	0.620886i	$-0.213227\pi$
$223$	9.52959	+	5.50191i	0.638149	+	0.368435i	−0.145752	+	0.989321i	$0.546560\pi$
$224$	−19.0181			−1.27070
$225$	0.0820168	−	0.0457511i	0.00546779	−	0.00305007i
$226$		−	17.6000i		−	1.17073i
$227$	−7.03055	−	4.05909i	−0.466634	−	0.269411i	0.248196	−	0.968710i	$-0.420162\pi$
$227$	−7.03055	−	4.05909i	−0.466634	−	0.269411i	−0.714830	+	0.699299i	$0.753496\pi$
$228$	−8.41178	+	2.18749i	−0.557084	+	0.144870i
$229$	−4.65740	+	2.68895i	−0.307769	+	0.177691i	−0.645928	−	0.763398i	$-0.723529\pi$
$229$	−4.65740	+	2.68895i	−0.307769	+	0.177691i	0.338158	+	0.941089i	$0.390196\pi$
$230$	−3.84246	−	6.65534i	−0.253365	−	0.438840i
$231$	−5.53702	−	21.2921i	−0.364309	−	1.40091i
$232$	5.93275	+	3.42528i	0.389504	+	0.224880i
$233$	20.0992			1.31675			0.658373	−	0.752692i	$-0.271245\pi$
$233$	20.0992			1.31675			0.658373	+	0.752692i	$0.271245\pi$
$234$	−0.811073	−	9.76189i	−0.0530215	−	0.638155i
$235$	−12.4338			−0.811094
$236$	5.24321	+	3.02717i	0.341304	+	0.197052i
$237$	−13.4945	+	13.2966i	−0.876559	+	0.863709i
$238$	−6.55206	−	11.3485i	−0.424707	−	0.735614i
$239$	−12.2635	+	7.08034i	−0.793261	+	0.457989i	−0.841109	−	0.540865i	$-0.818097\pi$
$239$	−12.2635	+	7.08034i	−0.793261	+	0.457989i	0.0478485	+	0.998855i	$0.484764\pi$
$240$	−0.256298	+	0.929024i	−0.0165440	+	0.0599683i
$241$	−26.2041	−	15.1289i	−1.68795	−	0.974539i	−0.956084	−	0.293092i	$-0.905316\pi$
$241$	−26.2041	−	15.1289i	−1.68795	−	0.974539i	−0.731867	−	0.681447i	$-0.761351\pi$
$242$			2.41310i			0.155120i
$243$	3.47609	+	15.1959i	0.222991	+	0.974820i
$244$	−15.3600			−0.983326
$245$	−9.33754	−	5.39103i	−0.596554	−	0.344421i
$246$	11.9788	+	3.30470i	0.763742	+	0.210700i
$247$	−6.33575	+	13.9643i	−0.403134	+	0.888525i
$248$	−10.5935	−	18.3484i	−0.672685	−	1.16512i
$249$	−0.653504	−	0.663226i	−0.0414141	−	0.0420303i
$250$	5.04647	−	8.74074i	0.319167	−	0.552813i
$251$	−17.5085			−1.10512			−0.552562	−	0.833472i	$-0.686350\pi$
$251$	−17.5085			−1.10512			−0.552562	+	0.833472i	$0.686350\pi$
$252$	6.23625	−	10.4423i	0.392847	−	0.657803i
$253$		−	13.9850i		−	0.879232i
$254$	−1.38355	−	0.798793i	−0.0868117	−	0.0501208i
$255$	15.8342	−	4.11771i	0.991578	−	0.257861i
$256$	8.26192	+	14.3101i	0.516370	+	0.894379i
$257$	−9.15211	−	15.8519i	−0.570893	−	0.988815i	−0.996475	−	0.0838952i	$-0.973264\pi$
$257$	−9.15211	−	15.8519i	−0.570893	−	0.988815i	0.425582	−	0.904920i	$-0.360069\pi$
$258$	−1.36705	+	0.355503i	−0.0851088	+	0.0221326i
$259$	−9.44807	+	16.3645i	−0.587074	+	1.01684i
$260$	−5.55423	−	7.75931i	−0.344459	−	0.481212i
$261$	−6.23261	+	3.47671i	−0.385789	+	0.215203i
$262$			6.45672i			0.398897i
$263$	4.19661	−	7.26875i	0.258774	−	0.448210i	−0.707140	−	0.707074i	$-0.750015\pi$
$263$	4.19661	−	7.26875i	0.258774	−	0.448210i	0.965914	+	0.258864i	$0.0833481\pi$
$264$	−13.1334	+	12.9408i	−0.808302	+	0.796453i
$265$	−14.7549	+	8.51875i	−0.906387	+	0.523303i
$266$	11.4611	−	6.61707i	0.702725	−	0.405719i
$267$	2.64966	−	9.60443i	0.162156	−	0.587782i
$268$	13.8050	+	7.97032i	0.843275	+	0.486865i
$269$	21.3238			1.30014			0.650069	−	0.759875i	$-0.274740\pi$
$269$	21.3238			1.30014			0.650069	+	0.759875i	$0.274740\pi$
$270$	−7.29635	−	7.62697i	−0.444042	−	0.464162i
$271$			18.4587i			1.12129i	0.828057	+	0.560643i	$0.189446\pi$
$271$			18.4587i			1.12129i	−0.828057	+	0.560643i	$0.810554\pi$
$272$	−0.522312	+	0.904671i	−0.0316698	+	0.0548538i
$273$	−7.39995	−	20.1422i	−0.447865	−	1.21906i
$274$	−2.04691	−	3.54535i	−0.123658	−	0.214183i
$275$	−0.100217	+	0.0578603i	−0.00604331	+	0.00348911i
$276$	5.50727	−	5.42654i	0.331499	−	0.326639i
$277$	4.31390	−	7.47189i	0.259197	−	0.448943i	−0.706830	−	0.707383i	$-0.749875\pi$
$277$	4.31390	−	7.47189i	0.259197	−	0.448943i	0.966027	+	0.258441i	$0.0832087\pi$
$278$		−	12.7779i		−	0.766367i
$279$	22.0696	+	0.325927i	1.32127	+	0.0195127i
$280$			22.1950i			1.32640i
$281$	3.00928	+	1.73741i	0.179518	+	0.103645i	0.587066	−	0.809539i	$-0.300283\pi$
$281$	3.00928	+	1.73741i	0.179518	+	0.103645i	−0.407548	+	0.913184i	$0.633616\pi$
$282$	2.18831	+	8.41493i	0.130312	+	0.501102i
$283$	6.89178	+	11.9369i	0.409674	+	0.709576i	0.994853	−	0.101328i	$-0.0323091\pi$
$283$	6.89178	+	11.9369i	0.409674	+	0.709576i	−0.585179	+	0.810904i	$0.698976\pi$
$284$	−2.71299	+	1.56635i	−0.160986	+	0.0929456i
$285$	4.15857	+	15.9913i	0.246332	+	0.947245i
$286$	1.17691	+	12.0124i	0.0695920	+	0.710311i
$287$	27.2217			1.60684
$288$	−16.6025	−	0.245188i	−0.978310	−	0.0144478i
$289$	0.734202			0.0431884
$290$	2.41615	−	4.18489i	0.141881	−	0.245745i
$291$	8.24813	+	8.37084i	0.483514	+	0.490707i
$292$	5.57648	−	3.21958i	0.326339	−	0.188412i
$293$	24.6911	−	14.2554i	1.44247	−	0.832810i	0.444455	−	0.895801i	$-0.353397\pi$
$293$	24.6911	−	14.2554i	1.44247	−	0.832810i	0.998014	+	0.0629917i	$0.0200642\pi$
$294$	−2.00515	+	7.26824i	−0.116943	+	0.423892i
$295$	5.75484	−	9.96768i	0.335060	−	0.580341i
$296$	15.8363			0.920465
$297$	−4.55923	−	18.6590i	−0.264553	−	1.08271i
$298$	5.25460			0.304391
$299$	−1.33007	−	13.5757i	−0.0769196	−	0.785102i
$300$	−0.0616718	−	0.0170139i	−0.00356062	−	0.000982300i
$301$	−2.67977	+	1.54716i	−0.154459	+	0.0891770i
$302$	−4.41292	−	7.64340i	−0.253935	−	0.439828i
$303$	6.12227	−	6.03252i	0.351715	−	0.346560i
$304$	−0.913648	−	0.527495i	−0.0524013	−	0.0302539i
$305$			29.2004i			1.67201i
$306$	−5.57354	−	9.99154i	−0.318618	−	0.571178i
$307$		−	21.8137i		−	1.24497i	−0.782631	−	0.622486i	$-0.786123\pi$
$307$		−	21.8137i		−	1.24497i	0.782631	−	0.622486i	$-0.213877\pi$
$308$	−7.49342	+	12.9790i	−0.426977	+	0.739546i
$309$	−0.920552	−	3.53989i	−0.0523683	−	0.201377i
$310$	−12.9427	+	7.47249i	−0.735097	+	0.424409i
$311$	3.48161	+	6.03032i	0.197424	+	0.341948i	0.947692	−	0.319185i	$-0.103409\pi$
$311$	3.48161	+	6.03032i	0.197424	+	0.341948i	−0.750268	+	0.661133i	$0.770076\pi$
$312$	−11.5182	+	13.8111i	−0.652088	+	0.781899i
$313$	−11.2253	+	19.4428i	−0.634491	+	1.09897i	0.352131	+	0.935951i	$0.385457\pi$
$313$	−11.2253	+	19.4428i	−0.634491	+	1.09897i	−0.986623	+	0.163020i	$0.947876\pi$
$314$			0.977678i			0.0551736i
$315$	−19.8515	−	11.8555i	−1.11851	−	0.667983i
$316$	12.9054			0.725983
$317$	−8.84739	−	5.10804i	−0.496919	−	0.286896i	0.230522	−	0.973067i	$-0.425957\pi$
$317$	−8.84739	−	5.10804i	−0.496919	−	0.286896i	−0.727440	+	0.686171i	$0.759290\pi$
$318$	8.36211	+	8.48651i	0.468924	+	0.475900i
$319$	7.61567	−	4.39691i	0.426395	−	0.246180i
$320$	10.7003	−	6.17780i	0.598163	−	0.345350i
$321$	−13.4810	−	3.71913i	−0.752438	−	0.207582i
$322$	−5.88622	+	10.1952i	−0.328026	+	0.568158i
$323$			17.9102i			0.996548i
$324$	5.57878	−	9.03557i	0.309932	−	0.501976i
$325$	−0.0917806	+	0.0656979i	−0.00509107	+	0.00364426i
$326$	2.51239	−	4.35158i	0.139148	−	0.241012i
$327$	−4.60722	+	16.7002i	−0.254780	+	0.923521i
$328$	−11.4068	−	19.7572i	−0.629836	−	1.09091i
$329$	9.52362	+	16.4954i	0.525054	+	0.909420i
$330$	9.12830	+	9.26410i	0.502496	+	0.509972i
$331$	−4.67794	−	2.70081i	−0.257123	−	0.148450i	0.365898	−	0.930655i	$-0.380762\pi$
$331$	−4.67794	−	2.70081i	−0.257123	−	0.148450i	−0.623021	+	0.782205i	$0.714095\pi$
$332$			0.634273i			0.0348103i
$333$	−8.45899	+	14.1642i	−0.463550	+	0.776192i
$334$	12.0793			0.660949
$335$	15.1521	−	26.2442i	0.827848	−	1.43387i
$336$	1.42880	−	0.371562i	0.0779476	−	0.0202704i
$337$	16.4621	+	28.5132i	0.896749	+	1.55321i	0.831625	+	0.555338i	$0.187411\pi$
$337$	16.4621	+	28.5132i	0.896749	+	1.55321i	0.0651239	+	0.997877i	$0.479256\pi$
$338$	2.28492	+	11.5489i	0.124283	+	0.628177i
$339$	−8.47201	−	32.5783i	−0.460136	−	1.76941i
$340$	−9.65206	−	5.57262i	−0.523457	−	0.302218i
$341$	−27.1969			−1.47279
$342$	10.0907	−	5.62884i	0.545641	−	0.304373i
$343$		−	7.53586i		−	0.406898i
$344$	2.24583	+	1.29663i	0.121087	+	0.0699097i
$345$	−10.3162	−	10.4697i	−0.555406	−	0.563669i
$346$	−5.83622	+	3.36954i	−0.313757	+	0.181148i
$347$	−6.81390	−	11.8020i	−0.365789	−	0.633566i	0.623113	−	0.782132i	$-0.285868\pi$
$347$	−6.81390	−	11.8020i	−0.365789	−	0.633566i	−0.988902	+	0.148566i	$0.952534\pi$
$348$	4.68655	+	1.29292i	0.251226	+	0.0693078i
$349$	−9.76413	−	5.63732i	−0.522662	−	0.301759i	0.215361	−	0.976534i	$-0.430907\pi$
$349$	−9.76413	−	5.63732i	−0.522662	−	0.301759i	−0.738023	+	0.674776i	$0.764240\pi$
$350$	0.0974121			0.00520690
$351$	−6.20036	−	17.6792i	−0.330951	−	0.943648i
$352$	20.4597			1.09050
$353$	23.0629	+	13.3154i	1.22751	+	0.708706i	0.966509	−	0.256631i	$-0.0826126\pi$
$353$	23.0629	+	13.3154i	1.22751	+	0.708706i	0.261005	+	0.965337i	$0.415946\pi$
$354$	−7.75872	−	2.14047i	−0.412372	−	0.113765i
$355$	2.97773	+	5.15757i	0.158041	+	0.273736i
$356$	−5.87778	+	3.39354i	−0.311522	+	0.179857i
$357$	−17.5909	−	17.8526i	−0.931010	−	0.944860i
$358$	18.1988	+	10.5071i	0.961835	+	0.555316i
$359$			34.9036i			1.84214i	0.389396	+	0.921071i	$0.372684\pi$
$359$			34.9036i			1.84214i	−0.389396	+	0.921071i	$0.627316\pi$
$360$	−0.286146	+	19.3759i	−0.0150812	+	1.02120i
$361$	0.912132			0.0480069
$362$	4.06596	+	2.34748i	0.213702	+	0.123381i
$363$	1.16158	+	4.46676i	0.0609674	+	0.234444i
$364$	−6.03969	+	13.3117i	−0.316566	+	0.697725i
$365$	−6.12064	−	10.6013i	−0.320369	−	0.554895i
$366$	19.7622	−	5.13917i	1.03299	−	0.268629i
$367$	1.35716	−	2.35068i	0.0708434	−	0.122704i	−0.828428	−	0.560096i	$-0.810764\pi$
$367$	1.35716	−	2.35068i	0.0708434	−	0.122704i	0.899271	+	0.437392i	$0.144098\pi$
$368$	0.938467			0.0489210
$369$	23.7641	+	0.350952i	1.23711	+	0.0182698i
$370$		−	11.1707i		−	0.580737i
$371$	22.6029	+	13.0498i	1.17348	+	0.677510i
$372$	−10.5531	−	10.7101i	−0.547151	−	0.555291i
$373$	0.875481	+	1.51638i	0.0453307	+	0.0785150i	0.887800	−	0.460229i	$-0.152233\pi$
$373$	0.875481	+	1.51638i	0.0453307	+	0.0785150i	−0.842470	+	0.538744i	$0.818899\pi$
$374$	7.04872	+	12.2087i	0.364480	+	0.631299i
$375$	5.13373	−	18.6087i	0.265105	−	0.960947i
$376$	7.98146	−	13.8243i	0.411612	−	0.712933i
$377$	6.97457	−	4.99250i	0.359209	−	0.257127i
$378$	−4.52975	+	15.5216i	−0.232985	+	0.798343i
$379$		−	2.90941i		−	0.149446i	−0.997204	−	0.0747231i	$-0.976193\pi$
$379$		−	2.90941i		−	0.149446i	0.997204	−	0.0747231i	$-0.0238073\pi$
$380$	5.62791	−	9.74783i	0.288706	−	0.500053i
$381$	−2.94552	−	0.812607i	−0.150904	−	0.0416311i
$382$	−12.6590	+	7.30868i	−0.647691	+	0.373945i
$383$	−17.7065	+	10.2229i	−0.904760	+	0.522363i	−0.878741	−	0.477298i	$-0.841616\pi$
$383$	−17.7065	+	10.2229i	−0.904760	+	0.522363i	−0.0260185	+	0.999661i	$0.508283\pi$
$384$	7.39267	+	7.50265i	0.377256	+	0.382868i
$385$	24.6739	+	14.2455i	1.25750	+	0.726017i
$386$	2.96968			0.151152
$387$	−2.35934	+	1.31610i	−0.119932	+	0.0669012i
$388$		−	8.00541i		−	0.406413i
$389$	−6.48161	+	11.2265i	−0.328631	+	0.569205i	−0.982240	−	0.187627i	$-0.939920\pi$
$389$	−6.48161	+	11.2265i	−0.328631	+	0.569205i	0.653610	+	0.756832i	$0.273254\pi$
$390$	9.74217	+	8.12477i	0.493314	+	0.411414i
$391$	−7.96600	−	13.7975i	−0.402858	−	0.697771i
$392$	11.9878	−	6.92117i	0.605476	−	0.349572i
$393$	3.10804	+	11.9517i	0.156780	+	0.602881i
$394$	−3.22052	+	5.57811i	−0.162248	+	0.281021i
$395$		−	24.5339i		−	1.23444i
$396$	−6.70897	+	11.2338i	−0.337138	+	0.564522i
$397$			29.1809i			1.46455i	0.681010	+	0.732274i	$0.261541\pi$
$397$			29.1809i			1.46455i	−0.681010	+	0.732274i	$0.738459\pi$
$398$	−10.8581	−	6.26894i	−0.544268	−	0.314233i
$399$	18.0297	−	17.7654i	0.902616	−	0.889385i
$400$	−0.00388271	−	0.00672506i	−0.000194136	−	0.000336253i
$401$	−19.2018	+	11.0862i	−0.958894	+	0.553617i	−0.895832	−	0.444392i	$-0.853420\pi$
$401$	−19.2018	+	11.0862i	−0.958894	+	0.553617i	−0.0630612	+	0.998010i	$0.520086\pi$
$402$	−20.4282	−	5.63570i	−1.01887	−	0.281083i
$403$	−26.4008	+	2.58659i	−1.31512	+	0.128847i
$404$	−5.85500			−0.291297
$405$	−17.1772	−	10.6056i	−0.853542	−	0.526998i
$406$	−7.40253			−0.367381
$407$	10.1642	−	17.6050i	0.503823	−	0.872647i
$408$	−5.58604	+	20.2482i	−0.276550	+	1.00243i
$409$	1.81749	−	1.04933i	0.0898689	−	0.0518858i	−0.454392	−	0.890802i	$-0.650143\pi$
$409$	1.81749	−	1.04933i	0.0898689	−	0.0518858i	0.544261	+	0.838916i	$0.316810\pi$
$410$	−13.9365	+	8.04623i	−0.688273	+	0.397375i
$411$	−5.49553	−	5.57729i	−0.271074	−	0.275107i
$412$	−1.24581	+	2.15781i	−0.0613767	+	0.106307i
$413$	−17.6315			−0.867591
$414$	−5.27002	+	8.82440i	−0.259007	+	0.433695i
$415$	1.20579			0.0591901
$416$	19.8608	−	1.94584i	0.973755	−	0.0954027i
$417$	−6.15083	−	23.6524i	−0.301208	−	1.15826i
$418$	−12.3299	+	7.11865i	−0.603074	+	0.348185i
$419$	−0.195699	−	0.338961i	−0.00956053	−	0.0165593i	0.861206	−	0.508257i	$-0.169710\pi$
$419$	−0.195699	−	0.338961i	−0.00956053	−	0.0165593i	−0.870766	+	0.491697i	$0.836377\pi$
$420$	3.96424	+	15.2441i	0.193435	+	0.743836i
$421$	−9.59987	−	5.54249i	−0.467869	−	0.270124i	0.247478	−	0.968893i	$-0.420398\pi$
$421$	−9.59987	−	5.54249i	−0.467869	−	0.270124i	−0.715347	+	0.698769i	$0.753731\pi$
$422$		−	13.0713i		−	0.636301i
$423$	8.10131	+	14.5230i	0.393899	+	0.706133i
$424$		−	21.8732i		−	1.06226i
$425$	−0.0659154	+	0.114169i	−0.00319737	+	0.00553800i
$426$	2.96646	−	2.92297i	0.143725	−	0.141618i
$427$	38.7389	−	22.3659i	1.87470	−	1.08236i
$428$	4.76326	+	8.25021i	0.230241	+	0.398789i
$429$	7.96088	+	21.6690i	0.384355	+	1.04619i
$430$	0.914627	−	1.58418i	0.0441072	−	0.0763960i
$431$		−	36.4573i		−	1.75609i	−0.478580	−	0.878044i	$-0.658848\pi$
$431$		−	36.4573i		−	1.75609i	0.478580	−	0.878044i	$-0.341152\pi$
$432$	1.25211	−	0.305947i	0.0602424	−	0.0147199i
$433$	8.82757			0.424226			0.212113	−	0.977245i	$-0.431966\pi$
$433$	8.82757			0.424226			0.212113	+	0.977245i	$0.431966\pi$
$434$	19.8268	+	11.4470i	0.951717	+	0.549474i
$435$	2.45793	−	8.90945i	0.117849	−	0.427175i
$436$	10.2203	−	5.90067i	0.489462	−	0.282591i
$437$	13.9344	−	8.04504i	0.666574	−	0.384847i
$438$	−6.09747	+	6.00809i	−0.291349	+	0.287078i
$439$	17.5672	−	30.4273i	0.838438	−	1.45222i	−0.0527626	−	0.998607i	$-0.516803\pi$
$439$	17.5672	−	30.4273i	0.838438	−	1.45222i	0.891200	−	0.453610i	$-0.149864\pi$
$440$		−	23.8774i		−	1.13831i
$441$	−0.212942	+	14.4190i	−0.0101401	+	0.686620i
$442$	8.00352	+	11.1810i	0.380688	+	0.531826i
$443$	−11.9526	+	20.7025i	−0.567885	+	0.983606i	0.428890	+	0.903357i	$0.358905\pi$
$443$	−11.9526	+	20.7025i	−0.567885	+	0.983606i	−0.996775	+	0.0802490i	$0.974428\pi$
$444$	10.8768	−	2.82851i	0.516189	−	0.134235i
$445$	6.45133	+	11.1740i	0.305822	+	0.529700i
$446$	4.98251	+	8.62997i	0.235929	+	0.408641i
$447$	9.72648	−	2.52938i	0.460047	−	0.119636i
$448$	−16.3916	−	9.46370i	−0.774431	−	0.447118i
$449$		−	13.9683i		−	0.659206i	−0.944120	−	0.329603i	$-0.893085\pi$
$449$		−	13.9683i		−	0.659206i	0.944120	−	0.329603i	$-0.106915\pi$
$450$	0.0850393	+	0.00125587i	0.00400879	+	5.92025e-5i
$451$	−29.2851			−1.37898
$452$	−11.4654	+	19.8587i	−0.539288	+	0.934075i
$453$	−11.8478	−	12.0240i	−0.556656	−	0.564938i
$454$	−3.67590	−	6.36684i	−0.172518	−	0.298811i
$455$	25.3065	+	11.4819i	1.18639	+	0.538278i
$456$	−20.4491	−	5.64146i	−0.957616	−	0.264186i
$457$	−15.0872	−	8.71058i	−0.705748	−	0.407464i	0.103737	−	0.994605i	$-0.466920\pi$
$457$	−15.0872	−	8.71058i	−0.705748	−	0.407464i	−0.809485	+	0.587141i	$0.800253\pi$
$458$	−4.87021			−0.227570
$459$	−15.1264	−	15.8118i	−0.706041	−	0.738034i
$460$			10.0126i			0.466841i
$461$	−20.6691	−	11.9333i	−0.962658	−	0.555791i	−0.0656678	−	0.997842i	$-0.520918\pi$
$461$	−20.6691	−	11.9333i	−0.962658	−	0.555791i	−0.896990	+	0.442051i	$0.854251\pi$
$462$	5.29849	−	19.2059i	0.246508	−	0.893538i
$463$	9.12555	−	5.26864i	0.424100	−	0.244854i	−0.272730	−	0.962091i	$-0.587926\pi$
$463$	9.12555	−	5.26864i	0.424100	−	0.244854i	0.696830	+	0.717236i	$0.254593\pi$
$464$	0.295055	+	0.511049i	0.0136976	+	0.0237249i
$465$	−20.3605	+	20.0621i	−0.944197	+	0.930356i
$466$	15.7632	+	9.10090i	0.730217	+	0.421591i
$467$	−8.40923			−0.389133			−0.194566	−	0.980889i	$-0.562330\pi$
$467$	−8.40923			−0.389133			−0.194566	+	0.980889i	$0.562330\pi$
$468$	−5.44418	+	11.5431i	−0.251657	+	0.533579i
$469$	−46.4227			−2.14360
$470$	−9.75148	−	5.63002i	−0.449802	−	0.259693i
$471$	0.470620	+	1.80972i	0.0216850	+	0.0833876i
$472$	7.38823	+	12.7968i	0.340071	+	0.589020i
$473$	2.88290	−	1.66444i	0.132556	−	0.0765310i
$474$	−16.6040	+	4.31788i	−0.762646	+	0.198327i
$475$	−0.115302	−	0.0665694i	−0.00529040	−	0.00305441i
$476$			17.0733i			0.782551i
$477$	19.5637	+	11.6837i	0.895761	+	0.534958i
$478$	−12.8239			−0.586550
$479$	13.6025	+	7.85338i	0.621512	+	0.358830i	0.777457	−	0.628935i	$-0.216509\pi$
$479$	13.6025	+	7.85338i	0.621512	+	0.358830i	−0.155945	+	0.987766i	$0.549842\pi$
$480$	15.3168	−	15.0923i	0.699113	−	0.688865i
$481$	8.19238	−	18.0563i	0.373540	−	0.823298i
$482$	−13.7007	−	23.7303i	−0.624050	−	1.08089i
$483$	−5.98801	+	21.7052i	−0.272464	+	0.987622i
$484$	1.57201	−	2.72280i	0.0714549	−	0.123764i
$485$	−15.2188			−0.691051
$486$	−4.15451	+	13.4917i	−0.188452	+	0.611995i
$487$			37.8948i			1.71718i	0.512666	+	0.858588i	$0.328658\pi$
$487$			37.8948i			1.71718i	−0.512666	+	0.858588i	$0.671342\pi$
$488$	−32.4659	−	18.7442i	−1.46966	−	0.848509i
$489$	2.55583	−	9.26433i	0.115579	−	0.418947i
$490$	−4.88210	−	8.45605i	−0.220551	−	0.382005i
$491$	1.88027	+	3.25672i	0.0848553	+	0.146974i	0.905330	−	0.424710i	$-0.139624\pi$
$491$	1.88027	+	3.25672i	0.0848553	+	0.146974i	−0.820474	+	0.571684i	$0.806291\pi$
$492$	−11.3633	−	11.5324i	−0.512299	−	0.519920i
$493$	5.00903	−	8.67590i	0.225595	−	0.390743i
$494$	−11.2919	+	8.08293i	−0.508048	+	0.363668i
$495$	21.3563	+	12.7542i	0.959893	+	0.573258i
$496$		−	1.82505i		−	0.0819471i
$497$	4.56154	−	7.90082i	0.204613	−	0.354400i
$498$	−0.212216	−	0.816054i	−0.00950961	−	0.0365682i
$499$	7.15464	−	4.13073i	0.320286	−	0.184917i	−0.331234	−	0.943549i	$-0.607465\pi$
$499$	7.15464	−	4.13073i	0.320286	−	0.184917i	0.651520	+	0.758632i	$0.274132\pi$
$500$	−11.3882	+	6.57500i	−0.509298	+	0.294043i
$501$	22.3593	−	5.81455i	0.998939	−	0.259775i
$502$	−13.7314	−	7.92780i	−0.612860	−	0.353835i
$503$	−12.9954			−0.579434			−0.289717	−	0.957112i	$-0.593561\pi$
$503$	−12.9954			−0.579434			−0.289717	+	0.957112i	$0.593561\pi$
$504$	25.9243	−	14.4612i	1.15476	−	0.644154i
$505$			11.1307i			0.495312i
$506$	6.33241	−	10.9680i	0.281510	−	0.487589i
$507$	9.78871	+	20.2776i	0.434732	+	0.900560i
$508$	1.04074	+	1.80262i	0.0461754	+	0.0799782i
$509$	−23.2712	+	13.4356i	−1.03148	+	0.595524i	−0.917408	−	0.397949i	$-0.869722\pi$
$509$	−23.2712	+	13.4356i	−1.03148	+	0.595524i	−0.114070	+	0.993473i	$0.536389\pi$
$510$	14.2828	+	3.94032i	0.632453	+	0.174480i
$511$	−9.37613	+	16.2399i	−0.414776	+	0.718413i
$512$			2.80162i			0.123815i
$513$	15.9687	−	15.2765i	0.705037	−	0.674475i
$514$		−	16.5762i		−	0.731146i
$515$	4.10213	+	2.36837i	0.180761	+	0.104363i
$516$	1.77409	+	0.489432i	0.0780998	+	0.0215461i
$517$	−10.2455	−	17.7458i	−0.450597	−	0.780458i
$518$	−14.8197	+	8.55614i	−0.651139	+	0.375935i
$519$	−9.18110	+	9.04652i	−0.403006	+	0.397098i
$520$	−2.27089	−	23.1785i	−0.0995851	−	1.01644i
$521$	14.2080			0.622464			0.311232	−	0.950334i	$-0.399258\pi$
$521$	14.2080			0.622464			0.311232	+	0.950334i	$0.399258\pi$
$522$	−6.46229	−	0.0954361i	−0.282847	−	0.00417713i
$523$	7.07846			0.309519			0.154760	−	0.987952i	$-0.450540\pi$
$523$	7.07846			0.309519			0.154760	+	0.987952i	$0.450540\pi$
$524$	4.20620	−	7.28536i	0.183749	−	0.318262i
$525$	0.180314	−	0.0468908i	0.00786954	−	0.00204648i
$526$	6.58255	−	3.80044i	0.287013	−	0.165707i
$527$	−26.8322	+	15.4916i	−1.16883	+	0.674824i
$528$	−1.53711	+	0.399727i	−0.0668941	+	0.0173959i
$529$	4.34352	−	7.52320i	0.188849	−	0.327096i
$530$	−15.4291			−0.670198
$531$	−15.3921	−	0.227312i	−0.667959	−	0.00986452i
$532$	−17.2427			−0.747564
$533$	−28.4279	+	2.78519i	−1.23135	+	0.120640i
$534$	6.42692	−	6.33270i	0.278120	−	0.274043i
$535$	15.6842	−	9.05527i	0.678086	−	0.391493i
$536$	19.4527	+	33.6931i	0.840229	+	1.45532i
$537$	38.7444	+	10.6888i	1.67195	+	0.461254i
$538$	16.7236	+	9.65540i	0.721007	+	0.416274i
$539$		−	17.7689i		−	0.765362i
$540$	3.26419	+	13.3590i	0.140468	+	0.574879i
$541$		−	7.18897i		−	0.309078i	−0.987987	−	0.154539i	$-0.950611\pi$
$541$		−	7.18897i		−	0.309078i	0.987987	−	0.154539i	$-0.0493892\pi$
$542$	−8.35807	+	14.4766i	−0.359010	+	0.621823i
$543$	8.65626	+	2.38808i	0.371476	+	0.102482i
$544$	20.1853	−	11.6540i	0.865438	−	0.499661i
$545$	−11.2176	−	19.4294i	−0.480508	−	0.832264i
$546$	3.31680	−	19.1476i	0.141946	−	0.819442i
$547$	15.8887	−	27.5201i	0.679353	−	1.17667i	−0.295823	−	0.955243i	$-0.595594\pi$
$547$	15.8887	−	27.5201i	0.679353	−	1.17667i	0.975176	−	0.221431i	$-0.0710729\pi$
$548$			5.33381i			0.227849i
$549$	34.1068	−	19.0256i	1.45564	−	0.811995i
$550$	−0.104796			−0.00446852
$551$	8.76198	+	5.05873i	0.373273	+	0.215509i
$552$	18.2626	−	4.74921i	0.777309	−	0.202140i
$553$	−32.5480	+	18.7916i	−1.38408	+	0.799100i
$554$	6.76652	−	3.90665i	0.287482	−	0.165978i
$555$	−5.37719	−	20.6774i	−0.228249	−	0.877709i
$556$	−8.32411	+	14.4178i	−0.353021	+	0.611450i
$557$			32.2223i			1.36530i	0.730745	+	0.682650i	$0.239173\pi$
$557$			32.2223i			1.36530i	−0.730745	+	0.682650i	$0.760827\pi$
$558$	17.1609	+	10.2487i	0.726480	+	0.433861i
$559$	2.64021	−	1.88990i	0.111669	−	0.0799343i
$560$	−0.955943	+	1.65574i	−0.0403960	+	0.0699679i
$561$	18.9243	+	19.2059i	0.798986	+	0.810872i
$562$	1.57339	+	2.72519i	0.0663694	+	0.114955i
$563$	16.8257	+	29.1430i	0.709119	+	1.22823i	0.965184	+	0.261571i	$0.0842405\pi$
$563$	16.8257	+	29.1430i	0.709119	+	1.22823i	−0.256065	+	0.966659i	$0.582426\pi$
$564$	3.01272	−	10.9204i	0.126858	−	0.459834i
$565$	37.7527	+	21.7965i	1.58827	+	0.916987i
$566$			12.4824i			0.524672i
$567$	−0.913211	+	30.9115i	−0.0383513	+	1.29816i
$568$	−7.64578			−0.320810
$569$	5.66793	−	9.81715i	0.237612	−	0.411556i	−0.722416	−	0.691458i	$-0.756969\pi$
$569$	5.66793	−	9.81715i	0.237612	−	0.411556i	0.960029	+	0.279902i	$0.0903019\pi$
$570$	−3.97942	+	14.4245i	−0.166679	+	0.604177i
$571$	0.127260	+	0.220421i	0.00532568	+	0.00922435i	0.868676	−	0.495381i	$-0.164971\pi$
$571$	0.127260	+	0.220421i	0.00532568	+	0.00922435i	−0.863350	+	0.504605i	$0.831638\pi$
$572$	6.49751	−	14.3208i	0.271675	−	0.598782i
$573$	−19.9142	+	19.6223i	−0.831928	+	0.819733i
$574$	21.3491	+	12.3259i	0.891095	+	0.514474i
$575$	0.118434			0.00493903
$576$	−14.1876	−	8.47300i	−0.591151	−	0.353041i
$577$			1.91400i			0.0796807i	0.999206	+	0.0398403i	$0.0126849\pi$
$577$			1.91400i			0.0796807i	−0.999206	+	0.0398403i	$0.987315\pi$
$578$	0.575812	+	0.332445i	0.0239506	+	0.0138279i
$579$	5.49699	−	1.42950i	0.228447	−	0.0594079i
$580$	−5.45246	+	3.14798i	−0.226401	+	0.130713i
$581$	−0.923571	−	1.59967i	−0.0383162	−	0.0663656i
$582$	2.67846	+	10.2997i	0.111026	+	0.426938i
$583$	−24.3162	−	14.0390i	−1.00707	−	0.581435i
$584$	15.7157			0.650321
$585$	21.9441	+	10.3497i	0.907279	+	0.427909i
$586$	25.8193			1.06659
$587$	7.69412	+	4.44220i	0.317570	+	0.183349i	0.650309	−	0.759670i	$-0.274639\pi$
$587$	7.69412	+	4.44220i	0.317570	+	0.183349i	−0.332739	+	0.943019i	$0.607973\pi$
$588$	6.99735	−	6.89478i	0.288566	−	0.284336i
$589$	−15.6453	−	27.0984i	−0.644653	−	1.11657i
$590$	9.02670	−	5.21156i	0.371623	−	0.214557i
$591$	−3.27621	+	11.8756i	−0.134765	+	0.488495i
$592$	1.18138	+	0.682072i	0.0485545	+	0.0280330i
$593$		−	43.1136i		−	1.77046i	−0.465152	−	0.885231i	$-0.654000\pi$
$593$		−	43.1136i		−	1.77046i	0.465152	−	0.885231i	$-0.346000\pi$
$594$	4.87311	−	16.6981i	0.199946	−	0.685132i
$595$	32.4574			1.33062
$596$	−5.92896	−	3.42309i	−0.242860	−	0.140215i
$597$	−23.1165	−	6.37734i	−0.946094	−	0.261007i
$598$	5.10392	−	11.2493i	0.208715	−	0.460016i
$599$	5.59868	+	9.69720i	0.228756	+	0.396217i	0.957440	−	0.288634i	$-0.0932009\pi$
$599$	5.59868	+	9.69720i	0.228756	+	0.396217i	−0.728684	+	0.684850i	$0.759868\pi$
$600$	−0.109591	−	0.111221i	−0.00447402	−	0.00454058i
$601$	−2.96273	+	5.13159i	−0.120852	+	0.209322i	−0.920104	−	0.391674i	$-0.871896\pi$
$601$	−2.96273	+	5.13159i	−0.120852	+	0.209322i	0.799252	+	0.600996i	$0.205229\pi$
$602$	−2.80221			−0.114210
$603$	−40.5263	−	0.598498i	−1.65036	−	0.0243727i
$604$			11.4991i			0.467892i
$605$	−5.17622	−	2.98849i	−0.210443	−	0.121499i
$606$	7.53303	−	1.95897i	0.306008	−	0.0795778i
$607$	−2.53470	−	4.39022i	−0.102880	−	0.178194i	0.809990	−	0.586444i	$-0.199472\pi$
$607$	−2.53470	−	4.39022i	−0.102880	−	0.178194i	−0.912870	+	0.408250i	$0.866139\pi$
$608$	11.7696	+	20.3856i	0.477321	+	0.826745i
$609$	−13.7024	+	3.56332i	−0.555249	+	0.144393i
$610$	−13.2219	+	22.9010i	−0.535339	+	0.927235i
$611$	−11.6334	−	16.2519i	−0.470635	−	0.657482i
$612$	−0.220115	+	14.9047i	−0.00889762	+	0.602486i
$613$		−	24.6393i		−	0.995173i	−0.867414	−	0.497587i	$-0.834220\pi$
$613$		−	24.6393i		−	0.995173i	0.867414	−	0.497587i	$-0.165780\pi$
$614$	9.87719	−	17.1078i	0.398611	−	0.690414i
$615$	−21.9238	+	21.6024i	−0.884054	+	0.871094i
$616$	−31.6771	+	18.2888i	−1.27630	+	0.736875i
$617$	38.0933	−	21.9932i	1.53358	−	0.885413i	0.534387	−	0.845240i	$-0.320543\pi$
$617$	38.0933	−	21.9932i	1.53358	−	0.885413i	0.999193	−	0.0401727i	$-0.0127908\pi$
$618$	0.880895	−	3.19305i	0.0354348	−	0.128443i
$619$	17.7979	+	10.2756i	0.715358	+	0.413012i	0.813042	−	0.582206i	$-0.197810\pi$
$619$	17.7979	+	10.2756i	0.715358	+	0.413012i	−0.0976839	+	0.995217i	$0.531143\pi$
$620$	19.4717			0.782002
$621$	−5.50727	+	18.8711i	−0.220999	+	0.757272i
$622$			6.30587i			0.252842i
$623$	9.88272	−	17.1174i	0.395943	−	0.685793i
$624$	−1.45410	+	0.534215i	−0.0582106	+	0.0213857i
$625$	12.5778	+	21.7853i	0.503111	+	0.871414i
$626$	−17.6073	+	10.1656i	−0.703730	+	0.406299i
$627$	−19.3964	+	19.1121i	−0.774619	+	0.763264i
$628$	0.636905	−	1.10315i	0.0254153	−	0.0440205i
$629$		−	23.1586i		−	0.923392i
$630$	−10.2008	−	18.2867i	−0.406408	−	0.728558i
$631$		−	25.1460i		−	1.00105i	−0.865723	−	0.500523i	$-0.833141\pi$
$631$		−	25.1460i		−	1.00105i	0.865723	−	0.500523i	$-0.166859\pi$
$632$	27.2775	+	15.7487i	1.08504	+	0.626449i
$633$	−6.29207	−	24.1955i	−0.250087	−	0.961685i
$634$	−4.62582	−	8.01216i	−0.183715	−	0.318204i
$635$	3.42689	−	1.97852i	0.135992	−	0.0785151i
$636$	−3.90678	−	15.0231i	−0.154914	−	0.595705i
$637$	−1.68994	−	17.2488i	−0.0669577	−	0.683422i
$638$	7.96365			0.315284
$639$	4.08402	−	6.83849i	0.161561	−	0.270526i
$640$	−13.6404			−0.539183
$641$	16.6711	−	28.8751i	0.658467	−	1.14050i	−0.322545	−	0.946554i	$-0.604538\pi$
$641$	16.6711	−	28.8751i	0.658467	−	1.14050i	0.981012	−	0.193945i	$-0.0621283\pi$
$642$	−8.88876	−	9.02100i	−0.350811	−	0.356030i
$643$	−27.1759	+	15.6900i	−1.07171	+	0.618754i	−0.928649	−	0.370959i	$-0.879029\pi$
$643$	−27.1759	+	15.6900i	−1.07171	+	0.618754i	−0.143065	+	0.989713i	$0.545696\pi$
$644$	13.2833	−	7.66911i	0.523435	−	0.302205i
$645$	0.930443	−	3.37265i	0.0366362	−	0.132798i
$646$	−8.10969	+	14.0464i	−0.319072	+	0.552648i
$647$	−47.5495			−1.86936			−0.934681	−	0.355486i	$-0.884315\pi$
$647$	−47.5495			−1.86936			−0.934681	+	0.355486i	$0.884315\pi$
$648$	22.8179	−	12.2902i	0.896373	−	0.482805i
$649$	18.9680			0.744561
$650$	−0.101729	+	0.00996676i	−0.00399012	+	0.000390929i
$651$	42.2104	+	11.6450i	1.65436	+	0.456402i
$652$	−5.66964	+	3.27337i	−0.222040	+	0.128195i
$653$	13.8728	+	24.0284i	0.542884	+	0.940302i	0.998737	+	0.0502473i	$0.0160010\pi$
$653$	13.8728	+	24.0284i	0.542884	+	0.940302i	−0.455853	+	0.890055i	$0.650666\pi$
$654$	−11.1751	+	11.0113i	−0.436981	+	0.430576i
$655$	−13.8499	−	7.99627i	−0.541162	−	0.312440i
$656$		−	1.96518i		−	0.0767273i
$657$	−8.39459	+	14.0563i	−0.327504	+	0.548390i
$658$			17.2491i			0.672440i
$659$	−7.80940	+	13.5263i	−0.304211	+	0.526909i	−0.977085	−	0.212848i	$-0.931726\pi$
$659$	−7.80940	+	13.5263i	−0.304211	+	0.526909i	0.672874	+	0.739757i	$0.265060\pi$
$660$	−4.26474	−	16.3996i	−0.166005	−	0.638355i
$661$	15.5161	−	8.95822i	0.603506	−	0.348434i	−0.166914	−	0.985972i	$-0.553380\pi$
$661$	15.5161	−	8.95822i	0.603506	−	0.348434i	0.770420	+	0.637537i	$0.220047\pi$
$662$	−2.44585	−	4.23633i	−0.0950605	−	0.164650i
$663$	20.1970	+	16.8439i	0.784386	+	0.654161i
$664$	−0.774017	+	1.34064i	−0.0300377	+	0.0520268i
$665$			32.7794i			1.27113i
$666$	−13.0476	+	7.27832i	−0.505586	+	0.282029i
$667$	−9.00000			−0.348481
$668$	−13.6295	−	7.86901i	−0.527342	−	0.304461i
$669$	13.3770	+	13.5760i	0.517185	+	0.524879i
$670$	23.7667	−	13.7217i	0.918187	−	0.530115i
$671$	−41.6753	+	24.0613i	−1.60886	+	0.928875i
$672$	−31.7540	−	8.76026i	−1.22494	−	0.337934i
$673$	2.94960	−	5.10885i	0.113699	−	0.196932i	−0.803560	−	0.595224i	$-0.797064\pi$
$673$	2.94960	−	5.10885i	0.113699	−	0.196932i	0.917259	+	0.398292i	$0.130397\pi$
$674$			29.8161i			1.14847i
$675$	0.158016	−	0.0386103i	0.00608203	−	0.00148611i
$676$	4.94532	−	14.5196i	0.190205	−	0.558444i
$677$	−13.7045	+	23.7369i	−0.526707	+	0.912283i	0.472809	+	0.881165i	$0.343240\pi$
$677$	−13.7045	+	23.7369i	−0.526707	+	0.912283i	−0.999516	+	0.0311180i	$0.990093\pi$
$678$	8.10704	−	29.3863i	0.311349	−	1.12857i
$679$	11.6568	+	20.1901i	0.447345	+	0.774825i
$680$	−13.6008	−	23.5572i	−0.521566	−	0.903379i
$681$	−9.86902	−	10.0158i	−0.378182	−	0.383808i
$682$	−21.3297	−	12.3147i	−0.816757	−	0.471555i
$683$		−	16.0989i		−	0.616006i	−0.951385	−	0.308003i	$-0.900339\pi$
$683$		−	16.0989i		−	0.616006i	0.951385	−	0.308003i	$-0.0996607\pi$
$684$	−15.0526	−	0.222299i	−0.575550	−	0.00849981i
$685$	10.1399			0.387427
$686$	3.41223	−	5.91015i	0.130279	−	0.225651i
$687$	−9.01495	+	2.34435i	−0.343942	+	0.0894425i
$688$	0.111692	+	0.193457i	0.00425823	+	0.00737547i
$689$	−24.9396	−	11.3154i	−0.950124	−	0.431083i
$690$	−3.35003	−	12.8822i	−0.127534	−	0.490418i
$691$	23.9736	+	13.8412i	0.912000	+	0.526543i	0.881074	−	0.472979i	$-0.156821\pi$
$691$	23.9736	+	13.8412i	0.912000	+	0.526543i	0.0309256	+	0.999522i	$0.490155\pi$
$692$	8.78030			0.333777
$693$	0.562687	−	38.1014i	0.0213747	−	1.44735i
$694$		−	12.3413i		−	0.468469i
$695$	27.4091	+	15.8247i	1.03969	+	0.600264i
$696$	8.32800	+	8.45190i	0.315672	+	0.320368i
$697$	−28.8924	+	16.6810i	−1.09438	+	0.631839i
$698$	−5.10514	−	8.84236i	−0.193232	−	0.334688i
$699$	33.5592	+	9.25828i	1.26933	+	0.350180i
$700$	−0.109914	−	0.0634588i	−0.00415435	−	0.00239852i
$701$	−10.0776			−0.380624			−0.190312	−	0.981724i	$-0.560950\pi$
$701$	−10.0776			−0.380624			−0.190312	+	0.981724i	$0.560950\pi$
$702$	3.14237	−	16.6728i	0.118601	−	0.629274i
$703$	23.3883			0.882108
$704$	17.6341	+	10.1811i	0.664611	+	0.383713i
$705$	−20.7605	−	5.72737i	−0.781885	−	0.215705i
$706$	12.0584	+	20.8857i	0.453822	+	0.786043i
$707$	14.7666	−	8.52553i	0.555357	−	0.320635i
$708$	7.36006	+	7.46956i	0.276608	+	0.280723i
$709$	2.79484	+	1.61360i	0.104962	+	0.0606000i	0.551562	−	0.834134i	$-0.314032\pi$
$709$	2.79484	+	1.61360i	0.104962	+	0.0606000i	−0.446600	+	0.894734i	$0.647365\pi$
$710$			5.39324i			0.202405i
$711$	−28.6562	+	15.9852i	−1.07469	+	0.599490i
$712$	−16.5648			−0.620793
$713$	24.1055	+	13.9173i	0.902756	+	0.521207i
$714$	−5.71238	−	21.9664i	−0.213781	−	0.822072i
$715$	−27.2248	−	12.3522i	−1.01815	−	0.461946i
$716$	−13.6896	−	23.7110i	−0.511604	−	0.886123i
$717$	−23.7375	+	6.17296i	−0.886494	+	0.230534i
$718$	−15.8043	+	27.3738i	−0.589811	+	1.02158i
$719$	−30.0712			−1.12147			−0.560733	−	0.827996i	$-0.689481\pi$
$719$	−30.0712			−1.12147			−0.560733	+	0.827996i	$0.689481\pi$
$720$	−0.855870	+	1.43311i	−0.0318964	+	0.0534090i
$721$		−	7.25614i		−	0.270233i
$722$	0.715357	+	0.413012i	0.0266228	+	0.0153707i
$723$	−36.7835	−	37.3307i	−1.36799	−	1.38834i
$724$	−3.05852	−	5.29751i	−0.113669	−	0.196880i
$725$	0.0372356	+	0.0644940i	0.00138290	+	0.00239525i
$726$	−1.11154	+	4.02911i	−0.0412533	+	0.149534i
$727$	9.68860	−	16.7811i	0.359330	−	0.622378i	−0.628519	−	0.777794i	$-0.716339\pi$
$727$	9.68860	−	16.7811i	0.359330	−	0.622378i	0.987849	+	0.155416i	$0.0496719\pi$
$728$	−29.0105	+	20.7661i	−1.07520	+	0.769643i
$729$	−1.19574	+	26.9735i	−0.0442868	+	0.999019i
$730$		−	11.0857i		−	0.410299i
$731$	1.89616	−	3.28424i	0.0701320	−	0.121472i
$732$	−25.6463	−	7.07527i	−0.947915	−	0.261509i
$733$	21.1938	−	12.2362i	0.782810	−	0.451955i	−0.0546155	−	0.998507i	$-0.517393\pi$
$733$	21.1938	−	12.2362i	0.782810	−	0.451955i	0.837425	+	0.546552i	$0.184060\pi$
$734$	2.12877	−	1.22904i	0.0785742	−	0.0453648i
$735$	−13.1074	−	13.3024i	−0.483475	−	0.490667i
$736$	−18.1340	−	10.4697i	−0.668429	−	0.385918i
$737$	49.9416			1.83962
$738$	18.4785	+	11.0356i	0.680204	+	0.406225i
$739$			3.30687i			0.121645i	0.998149	+	0.0608226i	$0.0193724\pi$
$739$			3.30687i			0.121645i	−0.998149	+	0.0608226i	$0.980628\pi$
$740$	−7.27712	+	12.6043i	−0.267512	+	0.463344i
$741$	−17.0110	+	20.3974i	−0.624914	+	0.749316i
$742$	11.8178	+	20.4691i	0.433846	+	0.751444i
$743$	15.1394	−	8.74076i	0.555412	−	0.320667i	−0.195890	−	0.980626i	$-0.562760\pi$
$743$	15.1394	−	8.74076i	0.555412	−	0.320667i	0.751302	+	0.659959i	$0.229426\pi$
$744$	−9.23585	−	35.5155i	−0.338603	−	1.30206i
$745$	−6.50751	+	11.2713i	−0.238417	+	0.412950i
$746$			1.58566i			0.0580553i
$747$	−0.785640	−	1.40840i	−0.0287451	−	0.0515305i
$748$		−	18.3674i		−	0.671580i
$749$	−24.0264	−	13.8717i	−0.877906	−	0.506859i
$750$	12.4522	−	12.2697i	0.454690	−	0.448025i
$751$	14.2922	+	24.7548i	0.521528	+	0.903314i	0.999686	+	0.0250400i	$0.00797130\pi$
$751$	14.2922	+	24.7548i	0.521528	+	0.903314i	−0.478158	+	0.878274i	$0.658695\pi$
$752$	1.19083	−	0.687526i	0.0434251	−	0.0250715i
$753$	−29.2335	−	8.06489i	−1.06533	−	0.293901i
$754$	7.73054	−	0.757392i	0.281530	−	0.0275826i
$755$	21.8606			0.795587
$756$	15.2225	−	14.5627i	0.553639	−	0.529639i
$757$	11.9611			0.434733			0.217367	−	0.976090i	$-0.430253\pi$
$757$	11.9611			0.434733			0.217367	+	0.976090i	$0.430253\pi$
$758$	1.31737	−	2.28176i	0.0478492	−	0.0828772i
$759$	6.44191	−	23.3505i	0.233826	−	0.847570i
$760$	23.7910	−	13.7357i	0.862989	−	0.498247i
$761$	1.84327	−	1.06421i	0.0668185	−	0.0385777i	−0.466219	−	0.884670i	$-0.654384\pi$
$761$	1.84327	−	1.06421i	0.0668185	−	0.0385777i	0.533037	+	0.846092i	$0.321051\pi$
$762$	−1.94214	−	1.97103i	−0.0703562	−	0.0714029i
$763$	−17.1841	+	29.7637i	−0.622105	+	1.07752i
$764$	19.0449			0.689019
$765$	28.3348	+	0.418453i	1.02445	+	0.0151292i
$766$	−18.5156			−0.668994
$767$	18.4128	−	1.80398i	0.664848	−	0.0651379i
$768$	7.20311	+	27.6989i	0.259920	+	0.999496i
$769$	−6.62584	+	3.82543i	−0.238934	+	0.137949i	−0.614687	−	0.788771i	$-0.710718\pi$
$769$	−6.62584	+	3.82543i	−0.238934	+	0.137949i	0.375753	+	0.926720i	$0.377384\pi$
$770$	12.9007	+	22.3446i	0.464907	+	0.805243i
$771$	−7.97922	−	30.6833i	−0.287365	−	1.10503i
$772$	−3.35080	−	1.93458i	−0.120598	−	0.0696272i
$773$			24.6440i			0.886383i	0.896427	+	0.443191i	$0.146154\pi$
$773$			24.6440i			0.886383i	−0.896427	+	0.443191i	$0.853846\pi$
$774$	−2.44629	−	0.0361272i	−0.0879300	−	0.00129856i
$775$		−	0.230320i		−	0.00827333i
$776$	9.76918	−	16.9207i	0.350693	−	0.607418i
$777$	−23.3132	+	22.9714i	−0.836356	+	0.824096i
$778$	−10.1667	+	5.86972i	−0.364492	+	0.210440i
$779$	−16.8465	−	29.1791i	−0.603590	−	1.04545i
$780$	−5.69961	−	15.5140i	−0.204079	−	0.555490i
$781$	−4.90731	+	8.49972i	−0.175598	+	0.304144i
$782$		−	14.4280i		−	0.515943i
$783$	−12.0079	+	2.93407i	−0.429128	+	0.104855i
$784$	1.19238			0.0425851
$785$	−2.09716	−	1.21080i	−0.0748509	−	0.0432152i
$786$	−2.97415	+	10.7806i	−0.106084	+	0.384532i
$787$	−36.2586	+	20.9339i	−1.29248	+	0.746214i	−0.979093	−	0.203411i	$-0.934797\pi$
$787$	−36.2586	+	20.9339i	−1.29248	+	0.746214i	−0.313388	+	0.949625i	$0.601464\pi$
$788$	7.26768	−	4.19599i	0.258900	−	0.149476i
$789$	10.3552	−	10.2034i	0.368654	−	0.363250i
$790$	11.1089	−	19.2412i	0.395237	−	0.684571i
$791$		−	66.7797i		−	2.37441i
$792$	−27.8894	+	15.5574i	−0.991006	+	0.552809i
$793$	−38.1671	+	27.3205i	−1.35535	+	0.970181i
$794$	−13.2131	+	22.8857i	−0.468914	+	0.812183i
$795$	−28.5599	+	7.42704i	−1.01292	+	0.263410i
$796$	8.16775	+	14.1470i	0.289498	+	0.501426i
$797$	20.8781	+	36.1620i	0.739541	+	1.28092i	0.952702	+	0.303906i	$0.0982908\pi$
$797$	20.8781	+	36.1620i	0.739541	+	1.28092i	−0.213161	+	0.977017i	$0.568376\pi$
$798$	22.1843	−	5.76906i	0.785317	−	0.204223i
$799$	−20.2163	−	11.6719i	−0.715200	−	0.412921i
$800$			0.173265i			0.00612583i
$801$	8.84814	−	14.8158i	0.312634	−	0.523490i
$802$	−20.0792			−0.709022
$803$	10.0869	−	17.4709i	0.355957	−	0.616536i
$804$	19.3785	+	19.6668i	0.683429	+	0.693596i
$805$	−14.5795	−	25.2524i	−0.513859	−	0.890030i
$806$	−21.8766	−	9.92565i	−0.770569	−	0.349616i
$807$	35.6039	+	9.82236i	1.25332	+	0.345764i
$808$	−12.3755	−	7.14499i	−0.435368	−	0.251360i
$809$	45.2476			1.59082			0.795410	−	0.606072i	$-0.207256\pi$
$809$	45.2476			1.59082			0.795410	+	0.606072i	$0.207256\pi$
$810$	−8.66935	−	16.0955i	−0.304610	−	0.565537i
$811$			52.8820i			1.85694i	0.371410	+	0.928469i	$0.378874\pi$
$811$			52.8820i			1.85694i	−0.371410	+	0.928469i	$0.621126\pi$
$812$	8.35255	+	4.82235i	0.293117	+	0.169231i
$813$	−8.50260	+	30.8201i	−0.298199	+	1.08091i
$814$	15.9430	−	9.20470i	0.558802	−	0.322625i
$815$	6.22288	+	10.7784i	0.217978	+	0.377549i
$816$	−1.28881	+	1.26992i	−0.0451174	+	0.0444560i
$817$	3.31683	+	1.91497i	0.116041	+	0.0669964i
$818$	1.90053			0.0664505
$819$	−3.07746	−	37.0396i	−0.107535	−	1.29427i
$820$	20.9667			0.732190
$821$	−29.8105	−	17.2111i	−1.04039	−	0.600671i	−0.120449	−	0.992720i	$-0.538433\pi$
$821$	−29.8105	−	17.2111i	−1.04039	−	0.600671i	−0.919945	+	0.392048i	$0.871767\pi$
$822$	−1.78459	−	6.86246i	−0.0622447	−	0.239356i
$823$	5.99853	+	10.3898i	0.209096	+	0.362164i	0.951430	−	0.307866i	$-0.0996147\pi$
$823$	5.99853	+	10.3898i	0.209096	+	0.362164i	−0.742334	+	0.670030i	$0.766281\pi$
$824$	−5.26644	+	3.04058i	−0.183465	+	0.105924i
$825$	−0.193982	+	0.0504452i	−0.00675358	+	0.00175628i
$826$	−13.8279	−	7.98353i	−0.481134	−	0.277783i
$827$			4.35092i			0.151296i	0.997135	+	0.0756482i	$0.0241026\pi$
$827$			4.35092i			0.151296i	−0.997135	+	0.0756482i	$0.975897\pi$
$828$	11.6950	−	6.52377i	0.406429	−	0.226717i
$829$	45.6204			1.58446			0.792230	−	0.610222i	$-0.208920\pi$
$829$	45.6204			1.58446			0.792230	+	0.610222i	$0.208920\pi$
$830$	0.945668	+	0.545982i	0.0328246	+	0.0189513i
$831$	10.6446	−	10.4885i	0.369257	−	0.363844i
$832$	18.0862	+	8.20594i	0.627027	+	0.284490i
$833$	−10.1213	−	17.5307i	−0.350683	−	0.607401i
$834$	5.88586	−	21.3350i	0.203811	−	0.738769i
$835$	−14.9595	+	25.9106i	−0.517695	+	0.896674i
$836$	18.5497			0.641554
$837$	36.6989	+	10.7101i	1.26850	+	0.370194i
$838$		−	0.354449i		−	0.0122442i
$839$	21.3626	+	12.3337i	0.737520	+	0.425808i	0.821167	−	0.570688i	$-0.193323\pi$
$839$	21.3626	+	12.3337i	0.737520	+	0.425808i	−0.0836466	+	0.996495i	$0.526657\pi$
$840$	−10.2236	+	37.0585i	−0.352749	+	1.27864i
$841$	11.6704	+	20.2137i	0.402427	+	0.697025i
$842$	−5.01926	−	8.69361i	−0.172975	−	0.299602i
$843$	4.22422	+	4.28707i	0.145490	+	0.147654i
$844$	−8.51525	+	14.7488i	−0.293107	+	0.507676i
$845$	−27.6026	−	9.40138i	−0.949559	−	0.323417i
$846$	−0.222382	+	15.0582i	−0.00764565	+	0.517712i
$847$			9.15606i			0.314606i
$848$	0.942085	−	1.63174i	0.0323513	−	0.0560341i
$849$	6.00857	+	23.1054i	0.206214	+	0.792974i
$850$	−0.103391	+	0.0596928i	−0.00354628	+	0.00204744i
$851$	−18.0178	+	10.4026i	−0.617641	+	0.356595i
$852$	−5.25132	+	1.36561i	−0.179907	+	0.0467851i
$853$	22.9668	+	13.2599i	0.786369	+	0.454010i	0.838683	−	0.544620i	$-0.183326\pi$
$853$	22.9668	+	13.2599i	0.786369	+	0.454010i	−0.0523138	+	0.998631i	$0.516660\pi$
$854$	40.5089			1.38619
$855$	−0.422605	+	28.6159i	−0.0144528	+	0.978644i
$856$			23.2508i			0.794697i
$857$	3.20474	−	5.55077i	0.109472	−	0.189611i	−0.806085	−	0.591800i	$-0.798417\pi$
$857$	3.20474	−	5.55077i	0.109472	−	0.189611i	0.915556	+	0.402190i	$0.131751\pi$
$858$	−3.56822	+	20.5990i	−0.121817	+	0.703239i
$859$	−12.7998	−	22.1699i	−0.436723	−	0.756427i	0.560711	−	0.828011i	$-0.310528\pi$
$859$	−12.7998	−	22.1699i	−0.436723	−	0.756427i	−0.997435	+	0.0715846i	$0.977194\pi$
$860$	−2.06402	+	1.19166i	−0.0703824	+	0.0406353i
$861$	45.4514	+	12.5391i	1.54898	+	0.427330i
$862$	16.5078	−	28.5924i	0.562258	−	0.973860i
$863$			48.4823i			1.65036i	0.564873	+	0.825178i	$0.308925\pi$
$863$			48.4823i			1.65036i	−0.564873	+	0.825178i	$0.691075\pi$
$864$	−27.6078	−	8.05696i	−0.939238	−	0.274103i
$865$		−	16.6919i		−	0.567542i
$866$	6.92319	+	3.99711i	0.235260	+	0.135827i
$867$	1.22588	+	0.338194i	0.0416331	+	0.0114857i
$868$	−14.9142	−	25.8322i	−0.506222	−	0.876802i
$869$	35.0152	−	20.2160i	1.18781	−	0.685782i
$870$	5.96186	−	5.87446i	0.202126	−	0.199163i
$871$	48.4797	−	4.74975i	1.64267	−	0.160939i
$872$	28.8029			0.975389
$873$	9.91587	+	17.7759i	0.335601	+	0.601624i
$874$	14.5711			0.492876
$875$	19.1478	−	33.1650i	0.647315	−	1.12118i
$876$	10.7940	−	2.80698i	0.364694	−	0.0948391i
$877$	27.0023	−	15.5898i	0.911801	−	0.526429i	0.0307911	−	0.999526i	$-0.490197\pi$
$877$	27.0023	−	15.5898i	0.911801	−	0.526429i	0.881010	+	0.473097i	$0.156864\pi$
$878$	27.5549	−	15.9088i	0.929932	−	0.536897i
$879$	47.7926	−	12.4285i	1.61200	−	0.419203i
$880$	1.02840	−	1.78125i	0.0346675	−	0.0600459i
$881$	−49.6614			−1.67314			−0.836568	−	0.547863i	$-0.815442\pi$
$881$	−49.6614			−1.67314			−0.836568	+	0.547863i	$0.815442\pi$
$882$	−6.69591	+	11.2120i	−0.225463	+	0.377527i
$883$	30.3523			1.02144			0.510718	−	0.859748i	$-0.329380\pi$
$883$	30.3523			1.02144			0.510718	+	0.859748i	$0.329380\pi$
$884$	−1.74686	−	17.8298i	−0.0587532	−	0.599681i
$885$	14.2001	−	13.9920i	0.477332	−	0.470335i
$886$	−18.7481	+	10.8242i	−0.629855	+	0.363647i
$887$	−6.42161	−	11.1226i	−0.215616	−	0.373459i	0.737847	−	0.674968i	$-0.235843\pi$
$887$	−6.42161	−	11.1226i	−0.215616	−	0.373459i	−0.953463	+	0.301510i	$0.902509\pi$
$888$	26.4415	+	7.29464i	0.887318	+	0.244792i
$889$	−5.24962	−	3.03087i	−0.176066	−	0.101652i
$890$			11.6846i			0.391669i
$891$	0.982434	−	33.2547i	0.0329128	−	1.11407i
$892$		−	12.9834i		−	0.434715i
$893$	11.7877	−	20.4169i	0.394460	−	0.683224i
$894$	8.77348	+	2.42042i	0.293429	+	0.0809508i
$895$	−45.0762	+	26.0248i	−1.50673	+	0.869912i
$896$	10.4478	+	18.0961i	0.349035	+	0.604547i
$897$	4.03257	−	23.2797i	0.134643	−	0.777286i
$898$	6.32484	−	10.9549i	0.211063	−	0.365571i
$899$			17.5024i			0.583738i
$900$	−0.0951349	−	0.0568156i	−0.00317116	−	0.00189385i
$901$	−31.9869			−1.06564
$902$	−22.9674	−	13.2602i	−0.764731	−	0.441518i
$903$	−5.18701	+	1.34889i	−0.172613	+	0.0448882i
$904$	−48.4680	+	27.9830i	−1.61202	+	0.930701i
$905$	−10.0709	+	5.81444i	−0.334768	+	0.193279i
$906$	−3.84738	−	14.7947i	−0.127821	−	0.491522i
$907$	10.2993	−	17.8389i	0.341983	−	0.592331i	−0.642818	−	0.766019i	$-0.722235\pi$
$907$	10.2993	−	17.8389i	0.341983	−	0.592331i	0.984801	+	0.173688i	$0.0555683\pi$
$908$			9.57860i			0.317877i
$909$	13.0010	−	7.25228i	0.431215	−	0.240543i
$910$	14.6481	+	20.4636i	0.485581	+	0.678362i
$911$	−21.1949	+	36.7107i	−0.702219	+	1.21628i	0.265466	+	0.964120i	$0.414474\pi$
$911$	−21.1949	+	36.7107i	−0.702219	+	1.21628i	−0.967686	+	0.252159i	$0.918859\pi$
$912$	−1.28252	−	1.30160i	−0.0424684	−	0.0431002i
$913$	0.993579	+	1.72093i	0.0328827	+	0.0569545i
$914$	−7.88827	−	13.6629i	−0.260921	−	0.451928i
$915$	−13.4505	+	48.7553i	−0.444661	+	1.61180i
$916$	5.49524	+	3.17268i	0.181568	+	0.104828i
$917$			24.4988i			0.809021i
$918$	−4.70362	−	19.2500i	−0.155243	−	0.635344i
$919$	−42.7987			−1.41180			−0.705899	−	0.708313i	$-0.749457\pi$
$919$	−42.7987			−1.41180			−0.705899	+	0.708313i	$0.749457\pi$
$920$	−12.2186	+	21.1633i	−0.402836	+	0.697733i
$921$	10.0480	−	36.4218i	0.331093	−	1.20014i
$922$	−10.8068	−	18.7179i	−0.355903	−	0.616441i
$923$	−3.95529	+	8.71764i	−0.130190	+	0.286944i
$924$	−18.4901	+	18.2190i	−0.608279	+	0.599362i
$925$	0.149090	+	0.0860769i	0.00490203	+	0.00283019i
$926$	9.54253			0.313587
$927$	0.0935489	−	6.33450i	0.00307255	−	0.208052i
$928$		−	13.1667i		−	0.432218i
$929$	−10.2242	−	5.90296i	−0.335446	−	0.193670i	0.322810	−	0.946464i	$-0.395372\pi$
$929$	−10.2242	−	5.90296i	−0.335446	−	0.193670i	−0.658257	+	0.752794i	$0.728706\pi$
$930$	−25.0522	+	6.51485i	−0.821494	+	0.213630i
$931$	17.7046	−	10.2218i	0.580245	−	0.335004i
$932$	−11.8575	−	20.5378i	−0.388405	−	0.672738i
$933$	3.03543	+	11.6724i	0.0993754	+	0.382138i
$934$	−6.59511	−	3.80769i	−0.215799	−	0.124591i
$935$	−34.9177			−1.14193
$936$	−25.5934	+	17.7545i	−0.836547	+	0.580323i
$937$	24.7925			0.809935			0.404967	−	0.914331i	$-0.367283\pi$
$937$	24.7925			0.809935			0.404967	+	0.914331i	$0.367283\pi$
$938$	−36.4079	−	21.0201i	−1.18876	−	0.686331i
$939$	−27.6985	+	27.2925i	−0.903907	+	0.890656i
$940$	7.33531	+	12.7051i	0.239251	+	0.414395i
$941$	−20.6367	+	11.9146i	−0.672737	+	0.388405i	−0.797113	−	0.603830i	$-0.793640\pi$
$941$	−20.6367	+	11.9146i	−0.672737	+	0.388405i	0.124376	+	0.992235i	$0.460307\pi$
$942$	−0.450346	+	1.63241i	−0.0146731	+	0.0531867i
$943$	25.9563	+	14.9859i	0.845253	+	0.488007i
$944$			1.27285i			0.0414278i
$945$	−27.6846	−	28.9391i	−0.900580	−	0.941388i
$946$	3.01462			0.0980138
$947$	−42.4532	−	24.5104i	−1.37954	−	0.796480i	−0.387440	−	0.921895i	$-0.626641\pi$
$947$	−42.4532	−	24.5104i	−1.37954	−	0.796480i	−0.992104	+	0.125415i	$0.959974\pi$
$948$	21.5478	+	5.94457i	0.699839	+	0.193071i
$949$	8.13001	−	17.9189i	0.263911	−	0.581671i
$950$	−0.0602850	−	0.104417i	−0.00195590	−	0.00338773i
$951$	−12.4194	−	12.6041i	−0.402726	−	0.408717i
$952$	−20.8349	+	36.0870i	−0.675262	+	1.16959i
$953$	7.78372			0.252140			0.126070	−	0.992021i	$-0.459764\pi$
$953$	7.78372			0.252140			0.126070	+	0.992021i	$0.459764\pi$
$954$	10.0529	+	18.0216i	0.325474	+	0.583469i
$955$		−	36.2055i		−	1.17158i
$956$	14.4697	+	8.35406i	0.467982	+	0.270190i
$957$	14.7410	−	3.83342i	0.476510	−	0.123917i
$958$	7.11200	+	12.3183i	0.229778	+	0.397987i
$959$	−7.76661	−	13.4522i	−0.250797	−	0.434393i
$960$	20.7117	−	5.38609i	0.668466	−	0.173835i
$961$	11.5651	−	20.0314i	0.373069	−	0.646174i
$962$	14.6009	−	10.4515i	0.470752	−	0.336971i
$963$	−20.7958	−	12.4195i	−0.670137	−	0.400213i
$964$			35.7011i			1.14985i
$965$	−3.67777	+	6.37008i	−0.118392	+	0.205060i
$966$	−14.5243	+	14.3114i	−0.467312	+	0.460461i
$967$	32.5591	−	18.7980i	1.04703	−	0.604502i	0.125213	−	0.992130i	$-0.460039\pi$
$967$	32.5591	−	18.7980i	1.04703	−	0.604502i	0.921816	+	0.387627i	$0.126705\pi$
$968$	6.64538	−	3.83671i	0.213590	−	0.123317i
$969$	−8.24993	+	29.9042i	−0.265026	+	0.960661i
$970$	−11.9357	−	6.89105i	−0.383231	−	0.221258i
$971$	−9.16512			−0.294123			−0.147061	−	0.989127i	$-0.546981\pi$
$971$	−9.16512			−0.294123			−0.147061	+	0.989127i	$0.546981\pi$
$972$	13.4768	−	12.5167i	0.432269	−	0.401475i
$973$		−	48.4833i		−	1.55430i
$974$	−17.1587	+	29.7197i	−0.549800	+	0.952281i
$975$	−0.183506	+	0.0674175i	−0.00587690	+	0.00215909i
$976$	−1.61463	−	2.79662i	−0.0516831	−	0.0895177i
$977$	41.0043	−	23.6739i	1.31184	−	0.757394i	0.329443	−	0.944176i	$-0.393139\pi$
$977$	41.0043	−	23.6739i	1.31184	−	0.757394i	0.982401	+	0.186782i	$0.0598058\pi$
$978$	6.19933	−	6.10846i	0.198233	−	0.195327i
$979$	−10.6318	+	18.4149i	−0.339795	+	0.588542i
$980$			12.7217i			0.406380i
$981$	−15.3851	+	25.7617i	−0.491210	+	0.822507i
$982$			3.40553i			0.108675i
$983$	−14.0634	−	8.11949i	−0.448552	−	0.258972i	0.258666	−	0.965967i	$-0.416717\pi$
$983$	−14.0634	−	8.11949i	−0.448552	−	0.258972i	−0.707219	+	0.706995i	$0.750050\pi$
$984$	−9.94499	−	38.2424i	−0.317035	−	1.21912i
$985$	−7.97686	−	13.8163i	−0.254164	−	0.440225i
$986$	7.85686	−	4.53616i	0.250213	−	0.144461i
$987$	8.30312	+	31.9288i	0.264291	+	1.01631i
$988$	18.0067	−	1.76419i	0.572870	−	0.0561263i
$989$	−3.40693			−0.108334
$990$	10.9740	+	19.6728i	0.348777	+	0.625243i
$991$	−37.7634			−1.19959			−0.599797	−	0.800152i	$-0.704752\pi$
$991$	−37.7634			−1.19959			−0.599797	+	0.800152i	$0.704752\pi$
$992$	−20.3605	+	35.2655i	−0.646447	+	1.11968i
$993$	−6.56658	−	6.66428i	−0.208384	−	0.211484i
$994$	7.15496	−	4.13092i	0.226942	−	0.131025i
$995$	26.8943	−	15.5274i	0.852606	−	0.492252i
$996$	−0.292164	+	1.05903i	−0.00925758	+	0.0335567i
$997$	−23.8283	+	41.2718i	−0.754649	+	1.30709i	0.190899	+	0.981610i	$0.438860\pi$
$997$	−23.8283	+	41.2718i	−0.754649	+	1.30709i	−0.945549	+	0.325481i	$0.894474\pi$
$998$	7.48156			0.236824
$999$	−20.6482	+	19.7531i	−0.653280	+	0.624962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.t.c.25.6	yes	20
3.2	odd	2		351.2.t.c.181.5		20
9.2	odd	6		1053.2.b.i.649.6		10
9.4	even	3	inner	117.2.t.c.103.5	yes	20
9.5	odd	6		351.2.t.c.64.6		20
9.7	even	3		1053.2.b.j.649.5		10
13.12	even	2	inner	117.2.t.c.25.5	✓	20
39.38	odd	2		351.2.t.c.181.6		20
117.25	even	6		1053.2.b.j.649.6		10
117.38	odd	6		1053.2.b.i.649.5		10
117.77	odd	6		351.2.t.c.64.5		20
117.103	even	6	inner	117.2.t.c.103.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.5	✓	20	13.12	even	2	inner
117.2.t.c.25.6	yes	20	1.1	even	1	trivial
117.2.t.c.103.5	yes	20	9.4	even	3	inner
117.2.t.c.103.6	yes	20	117.103	even	6	inner
351.2.t.c.64.5		20	117.77	odd	6
351.2.t.c.64.6		20	9.5	odd	6
351.2.t.c.181.5		20	3.2	odd	2
351.2.t.c.181.6		20	39.38	odd	2
1053.2.b.i.649.5		10	117.38	odd	6
1053.2.b.i.649.6		10	9.2	odd	6
1053.2.b.j.649.5		10	9.7	even	3
1053.2.b.j.649.6		10	117.25	even	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.784270 + 0.452798i) q^{2} +(1.66968 + 0.460628i) q^{3} +(-0.589947 - 1.02182i) q^{4} +(-1.94254 + 1.12153i) q^{5} +(1.10091 + 1.11728i) q^{6} +(2.97576 + 1.71806i) q^{7} -2.87970i q^{8} +(2.57564 + 1.53820i) q^{9} -2.03130 q^{10} +(-3.20133 - 1.84829i) q^{11} +(-0.514343 - 1.97785i) q^{12} +(-3.28340 - 1.48972i) q^{13} +(1.55587 + 2.69484i) q^{14} +(-3.76003 + 0.977800i) q^{15} +(0.124029 - 0.214825i) q^{16} -4.21120 q^{17} +(1.32350 + 2.37261i) q^{18} -4.25298i q^{19} +(2.29200 + 1.32329i) q^{20} +(4.17717 + 4.23932i) q^{21} +(-1.67380 - 2.89911i) q^{22} +(1.89162 + 3.27639i) q^{23} +(1.32647 - 4.80817i) q^{24} +(0.0156524 - 0.0271108i) q^{25} +(-1.90053 - 2.65506i) q^{26} +(3.59195 + 3.75471i) q^{27} -4.05425i q^{28} +(-1.18945 + 2.06020i) q^{29} +(-3.39162 - 0.935677i) q^{30} +(6.37163 - 3.67866i) q^{31} +(-4.79325 + 2.76738i) q^{32} +(-4.49381 - 4.56066i) q^{33} +(-3.30272 - 1.90682i) q^{34} -7.70739 q^{35} +(0.0522689 - 3.53930i) q^{36} +5.49928i q^{37} +(1.92574 - 3.33549i) q^{38} +(-4.79602 - 3.99978i) q^{39} +(3.22967 + 5.59395i) q^{40} +(6.86085 - 3.96111i) q^{41} +(1.35647 + 5.21619i) q^{42} +(-0.450266 + 0.779883i) q^{43} +4.36157i q^{44} +(-6.72844 - 0.0993666i) q^{45} +3.42609i q^{46} +(4.80060 + 2.77163i) q^{47} +(0.306043 - 0.301557i) q^{48} +(2.40343 + 4.16287i) q^{49} +(0.0245514 - 0.0141748i) q^{50} +(-7.03134 - 1.93980i) q^{51} +(0.414812 + 4.23390i) q^{52} +7.59566 q^{53} +(1.11693 + 4.57114i) q^{54} +8.29163 q^{55} +(4.94749 - 8.56930i) q^{56} +(1.95904 - 7.10111i) q^{57} +(-1.86571 + 1.07717i) q^{58} +(-4.44379 + 2.56562i) q^{59} +(3.21735 + 3.26522i) q^{60} +(6.50907 - 11.2740i) q^{61} +6.66277 q^{62} +(5.02178 + 9.00242i) q^{63} -5.50838 q^{64} +(8.04892 - 0.788585i) q^{65} +(-1.45930 - 5.61158i) q^{66} +(-11.7002 + 6.75511i) q^{67} +(2.48439 + 4.30308i) q^{68} +(1.64920 + 6.34184i) q^{69} +(-6.04468 - 3.48989i) q^{70} -2.65506i q^{71} +(4.42956 - 7.41708i) q^{72} +5.45741i q^{73} +(-2.49006 + 4.31292i) q^{74} +(0.0386224 - 0.0380563i) q^{75} +(-4.34578 + 2.50904i) q^{76} +(-6.35092 - 11.0001i) q^{77} +(-1.95028 - 5.30853i) q^{78} +(-5.46886 + 9.47234i) q^{79} +0.556410i q^{80} +(4.26787 + 7.92371i) q^{81} +7.17434 q^{82} +(-0.465547 - 0.268784i) q^{83} +(1.86750 - 6.76929i) q^{84} +(8.18044 - 4.72298i) q^{85} +(-0.706259 + 0.407759i) q^{86} +(-2.93499 + 2.89197i) q^{87} +(-5.32252 + 9.21887i) q^{88} -5.75227i q^{89} +(-5.23192 - 3.12456i) q^{90} +(-7.21120 - 10.0741i) q^{91} +(2.23192 - 3.86579i) q^{92} +(12.3331 - 3.20723i) q^{93} +(2.50998 + 4.34740i) q^{94} +(4.76984 + 8.26161i) q^{95} +(-9.27791 + 2.41273i) q^{96} +(5.87585 + 3.39243i) q^{97} +4.35308i q^{98} +(-5.40244 - 9.68481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) \) 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Introduction

L-functions

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