LMFDB - Embedded newform 770.2.o.a.549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.2
Character	$\chi$	$=$	770.549
Dual form			770.2.o.a.439.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.64811 + 2.85461i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0163520 - 2.23601i) q^{5} +3.29622 q^{6} +(-1.01398 - 2.44374i) q^{7} +1.00000 q^{8} +(-3.93253 - 6.81133i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.64811 + 2.85461i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0163520 - 2.23601i) q^{5} +3.29622 q^{6} +(-1.01398 - 2.44374i) q^{7} +1.00000 q^{8} +(-3.93253 - 6.81133i) q^{9} +(-1.92826 + 1.13217i) q^{10} +(2.63390 + 2.01558i) q^{11} +(-1.64811 - 2.85461i) q^{12} +3.27717i q^{13} +(-1.60935 + 2.10000i) q^{14} +(6.40988 + 3.63851i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.23162 + 0.711075i) q^{17} +(-3.93253 + 6.81133i) q^{18} +(1.91637 + 3.31925i) q^{19} +(1.94462 + 1.10384i) q^{20} +(8.64706 + 1.13302i) q^{21} +(0.428594 - 3.28882i) q^{22} +(-1.95978 + 1.13148i) q^{23} +(-1.64811 + 2.85461i) q^{24} +(-4.99947 + 0.0731264i) q^{25} +(2.83811 - 1.63858i) q^{26} +16.0363 q^{27} +(2.62333 + 0.343734i) q^{28} +2.06417i q^{29} +(-0.0538997 - 7.37037i) q^{30} +(-4.72022 - 2.72522i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-10.0946 + 4.19686i) q^{33} -1.42215i q^{34} +(-5.44763 + 2.30723i) q^{35} +7.86505 q^{36} +(-5.46243 + 3.15373i) q^{37} +(1.91637 - 3.31925i) q^{38} +(-9.35503 - 5.40113i) q^{39} +(-0.0163520 - 2.23601i) q^{40} -9.52703 q^{41} +(-3.34230 - 8.05508i) q^{42} +3.88214 q^{43} +(-3.06249 + 1.27323i) q^{44} +(-15.1659 + 8.90454i) q^{45} +(1.95978 + 1.13148i) q^{46} +(6.42172 + 11.1227i) q^{47} +3.29622 q^{48} +(-4.94368 + 4.95580i) q^{49} +(2.56306 + 4.29310i) q^{50} +(-4.05968 + 2.34386i) q^{51} +(-2.83811 - 1.63858i) q^{52} +(-5.28186 - 3.04948i) q^{53} +(-8.01813 - 13.8878i) q^{54} +(4.46379 - 5.92238i) q^{55} +(-1.01398 - 2.44374i) q^{56} -12.6335 q^{57} +(1.78763 - 1.03209i) q^{58} +(9.91941 + 5.72697i) q^{59} +(-6.35598 + 3.73186i) q^{60} +(0.842907 + 1.45996i) q^{61} +5.45044i q^{62} +(-12.6576 + 16.5166i) q^{63} +1.00000 q^{64} +(7.32777 - 0.0535882i) q^{65} +(8.68191 + 6.64379i) q^{66} +(-4.99265 - 2.88251i) q^{67} +(-1.23162 + 0.711075i) q^{68} -7.45919i q^{69} +(4.72194 + 3.56417i) q^{70} -9.01579 q^{71} +(-3.93253 - 6.81133i) q^{72} +(11.7157 + 6.76404i) q^{73} +(5.46243 + 3.15373i) q^{74} +(8.03092 - 14.3920i) q^{75} -3.83274 q^{76} +(2.25482 - 8.48032i) q^{77} +10.8023i q^{78} +(-0.362507 + 0.209294i) q^{79} +(-1.92826 + 1.13217i) q^{80} +(-14.6319 + 25.3433i) q^{81} +(4.76352 + 8.25065i) q^{82} +13.2975i q^{83} +(-5.30476 + 6.92206i) q^{84} +(1.56983 - 2.76553i) q^{85} +(-1.94107 - 3.36203i) q^{86} +(-5.89240 - 3.40198i) q^{87} +(2.63390 + 2.01558i) q^{88} +(-7.47672 + 4.31669i) q^{89} +(15.2945 + 8.68178i) q^{90} +(8.00853 - 3.32299i) q^{91} -2.26295i q^{92} +(15.5589 - 8.98292i) q^{93} +(6.42172 - 11.1227i) q^{94} +(7.39053 - 4.33929i) q^{95} +(-1.64811 - 2.85461i) q^{96} -2.51839 q^{97} +(6.76369 + 1.80345i) q^{98} +(3.37091 - 25.8667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.64811	+	2.85461i	−0.951536	+	1.64811i	−0.209433	+	0.977823i	$0.567162\pi$
$3$	−1.64811	+	2.85461i	−0.951536	+	1.64811i	−0.742103	+	0.670286i	$0.766171\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.0163520	−	2.23601i	−0.00731284	−	0.999973i
$5$	−0.0163520	−	2.23601i	−0.00731284	−	0.999973i
$6$	3.29622			1.34568
$7$	−1.01398	−	2.44374i	−0.383249	−	0.923645i
$7$	−1.01398	−	2.44374i	−0.383249	−	0.923645i
$8$	1.00000			0.353553
$9$	−3.93253	−	6.81133i	−1.31084	−	2.27044i
$10$	−1.92826	+	1.13217i	−0.609771	+	0.358022i
$11$	2.63390	+	2.01558i	0.794151	+	0.607720i
$11$	2.63390	+	2.01558i	0.794151	+	0.607720i
$12$	−1.64811	−	2.85461i	−0.475768	−	0.824054i
$13$			3.27717i			0.908923i	0.890766	+	0.454461i	$0.150168\pi$
$13$			3.27717i			0.908923i	−0.890766	+	0.454461i	$0.849832\pi$
$14$	−1.60935	+	2.10000i	−0.430116	+	0.561249i
$15$	6.40988	+	3.63851i	1.65502	+	0.939458i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.23162	+	0.711075i	0.298711	+	0.172461i	0.641864	−	0.766819i	$-0.278161\pi$
$17$	1.23162	+	0.711075i	0.298711	+	0.172461i	−0.343153	+	0.939280i	$0.611495\pi$
$18$	−3.93253	+	6.81133i	−0.926905	+	1.60545i
$19$	1.91637	+	3.31925i	0.439645	+	0.761487i	0.997662	−	0.0683422i	$-0.0217710\pi$
$19$	1.91637	+	3.31925i	0.439645	+	0.761487i	−0.558017	+	0.829829i	$0.688438\pi$
$20$	1.94462	+	1.10384i	0.434829	+	0.246827i
$21$	8.64706	+	1.13302i	1.88694	+	0.247246i
$22$	0.428594	−	3.28882i	0.0913765	−	0.701178i
$23$	−1.95978	+	1.13148i	−0.408641	+	0.235929i	−0.690206	−	0.723613i	$-0.742480\pi$
$23$	−1.95978	+	1.13148i	−0.408641	+	0.235929i	0.281564	+	0.959542i	$0.409147\pi$
$24$	−1.64811	+	2.85461i	−0.336419	+	0.582694i
$25$	−4.99947	+	0.0731264i	−0.999893	+	0.0146253i
$26$	2.83811	−	1.63858i	0.556599	−	0.321353i
$27$	16.0363			3.08618
$28$	2.62333	+	0.343734i	0.495762	+	0.0649597i
$29$			2.06417i			0.383307i	0.981463	+	0.191654i	$0.0613850\pi$
$29$			2.06417i			0.383307i	−0.981463	+	0.191654i	$0.938615\pi$
$30$	−0.0538997	−	7.37037i	−0.00984070	−	1.34564i
$31$	−4.72022	−	2.72522i	−0.847776	−	0.489464i	0.0121236	−	0.999927i	$-0.496141\pi$
$31$	−4.72022	−	2.72522i	−0.847776	−	0.489464i	−0.859900	+	0.510463i	$0.829474\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−10.0946	+	4.19686i	−1.75725	+	0.730579i
$34$		−	1.42215i		−	0.243897i
$35$	−5.44763	+	2.30723i	−0.920818	+	0.389993i
$36$	7.86505			1.31084
$37$	−5.46243	+	3.15373i	−0.898017	+	0.518471i	−0.876556	−	0.481299i	$-0.840165\pi$
$37$	−5.46243	+	3.15373i	−0.898017	+	0.518471i	−0.0214609	+	0.999770i	$0.506832\pi$
$38$	1.91637	−	3.31925i	0.310876	−	0.538453i
$39$	−9.35503	−	5.40113i	−1.49800	−	0.864873i
$40$	−0.0163520	−	2.23601i	−0.00258548	−	0.353544i
$41$	−9.52703			−1.48787			−0.743936	−	0.668251i	$-0.767043\pi$
$41$	−9.52703			−1.48787			−0.743936	+	0.668251i	$0.767043\pi$
$42$	−3.34230	−	8.05508i	−0.515729	−	1.24293i
$43$	3.88214			0.592021			0.296011	−	0.955185i	$-0.404344\pi$
$43$	3.88214			0.592021			0.296011	+	0.955185i	$0.404344\pi$
$44$	−3.06249	+	1.27323i	−0.461688	+	0.191947i
$45$	−15.1659	+	8.90454i	−2.26080	+	1.32741i
$46$	1.95978	+	1.13148i	0.288953	+	0.166827i
$47$	6.42172	+	11.1227i	0.936704	+	1.62242i	0.771567	+	0.636148i	$0.219473\pi$
$47$	6.42172	+	11.1227i	0.936704	+	1.62242i	0.165137	+	0.986271i	$0.447193\pi$
$48$	3.29622			0.475768
$49$	−4.94368	+	4.95580i	−0.706241	+	0.707972i
$50$	2.56306	+	4.29310i	0.362472	+	0.607136i
$51$	−4.05968	+	2.34386i	−0.568469	+	0.328206i
$52$	−2.83811	−	1.63858i	−0.393575	−	0.227231i
$53$	−5.28186	−	3.04948i	−0.725519	−	0.418878i	0.0912618	−	0.995827i	$-0.470910\pi$
$53$	−5.28186	−	3.04948i	−0.725519	−	0.418878i	−0.816781	+	0.576948i	$0.804243\pi$
$54$	−8.01813	−	13.8878i	−1.09113	−	1.88989i
$55$	4.46379	−	5.92238i	0.601897	−	0.798574i
$56$	−1.01398	−	2.44374i	−0.135499	−	0.326558i
$57$	−12.6335			−1.67335
$58$	1.78763	−	1.03209i	0.234727	−	0.135520i
$59$	9.91941	+	5.72697i	1.29140	+	0.745588i	0.978902	−	0.204331i	$-0.0655019\pi$
$59$	9.91941	+	5.72697i	1.29140	+	0.745588i	0.312495	+	0.949919i	$0.398835\pi$
$60$	−6.35598	+	3.73186i	−0.820553	+	0.481782i
$61$	0.842907	+	1.45996i	0.107923	+	0.186928i	0.914929	−	0.403615i	$-0.132247\pi$
$61$	0.842907	+	1.45996i	0.107923	+	0.186928i	−0.807006	+	0.590544i	$0.798913\pi$
$62$			5.45044i			0.692207i
$63$	−12.6576	+	16.5166i	−1.59471	+	2.08090i
$64$	1.00000			0.125000
$65$	7.32777	−	0.0535882i	0.908898	−	0.00664680i
$66$	8.68191	+	6.64379i	1.06867	+	0.817794i
$67$	−4.99265	−	2.88251i	−0.609950	−	0.352155i	0.162996	−	0.986627i	$-0.447884\pi$
$67$	−4.99265	−	2.88251i	−0.609950	−	0.352155i	−0.772946	+	0.634472i	$0.781218\pi$
$68$	−1.23162	+	0.711075i	−0.149356	+	0.0862305i
$69$		−	7.45919i		−	0.897981i
$70$	4.72194	+	3.56417i	0.564379	+	0.426000i
$71$	−9.01579			−1.06998			−0.534989	−	0.844859i	$-0.679684\pi$
$71$	−9.01579			−1.06998			−0.534989	+	0.844859i	$0.679684\pi$
$72$	−3.93253	−	6.81133i	−0.463453	−	0.802723i
$73$	11.7157	+	6.76404i	1.37121	+	0.791671i	0.991081	−	0.133261i	$-0.0425449\pi$
$73$	11.7157	+	6.76404i	1.37121	+	0.791671i	0.380133	+	0.924932i	$0.375878\pi$
$74$	5.46243	+	3.15373i	0.634994	+	0.366614i
$75$	8.03092	−	14.3920i	0.927330	−	1.66185i
$76$	−3.83274			−0.439645
$77$	2.25482	−	8.48032i	0.256961	−	0.966422i
$78$			10.8023i			1.22311i
$79$	−0.362507	+	0.209294i	−0.0407852	+	0.0235474i	−0.520254	−	0.854012i	$-0.674163\pi$
$79$	−0.362507	+	0.209294i	−0.0407852	+	0.0235474i	0.479469	+	0.877559i	$0.340829\pi$
$80$	−1.92826	+	1.13217i	−0.215586	+	0.126580i
$81$	−14.6319	+	25.3433i	−1.62577	+	2.81592i
$82$	4.76352	+	8.25065i	0.526042	+	0.911132i
$83$			13.2975i			1.45959i	0.683667	+	0.729794i	$0.260384\pi$
$83$			13.2975i			1.45959i	−0.683667	+	0.729794i	$0.739616\pi$
$84$	−5.30476	+	6.92206i	−0.578796	+	0.755259i
$85$	1.56983	−	2.76553i	0.170272	−	0.299964i
$86$	−1.94107	−	3.36203i	−0.209311	−	0.362537i
$87$	−5.89240	−	3.40198i	−0.631732	−	0.364731i
$88$	2.63390	+	2.01558i	0.280775	+	0.214862i
$89$	−7.47672	+	4.31669i	−0.792531	+	0.457568i	−0.840853	−	0.541264i	$-0.817946\pi$
$89$	−7.47672	+	4.31669i	−0.792531	+	0.457568i	0.0483217	+	0.998832i	$0.484613\pi$
$90$	15.2945	+	8.68178i	1.61218	+	0.915140i
$91$	8.00853	−	3.32299i	0.839522	−	0.348344i
$92$		−	2.26295i		−	0.235929i
$93$	15.5589	−	8.98292i	1.61338	−	0.931485i
$94$	6.42172	−	11.1227i	0.662350	−	1.14722i
$95$	7.39053	−	4.33929i	0.758252	−	0.445202i
$96$	−1.64811	−	2.85461i	−0.168209	−	0.291347i
$97$	−2.51839			−0.255704			−0.127852	−	0.991793i	$-0.540808\pi$
$97$	−2.51839			−0.255704			−0.127852	+	0.991793i	$0.540808\pi$
$98$	6.76369	+	1.80345i	0.683236	+	0.182176i
$99$	3.37091	−	25.8667i	0.338789	−	2.59970i
$100$	2.43640	−	4.36623i	0.243640	−	0.436623i
$101$	−5.22461	+	9.04930i	−0.519868	+	0.900439i	0.479865	+	0.877342i	$0.340686\pi$
$101$	−5.22461	+	9.04930i	−0.519868	+	0.900439i	−0.999733	+	0.0230962i	$0.992648\pi$
$102$	4.05968	+	2.34386i	0.401968	+	0.232076i
$103$	−1.99232	−	3.45080i	−0.196309	−	0.340018i	0.751020	−	0.660280i	$-0.229562\pi$
$103$	−1.99232	−	3.45080i	−0.196309	−	0.340018i	−0.947329	+	0.320262i	$0.896229\pi$
$104$			3.27717i			0.321353i
$105$	2.39205	−	19.3534i	0.233440	−	1.88870i
$106$			6.09896i			0.592384i
$107$	−1.21293	−	2.10086i	−0.117259	−	0.203098i	0.801422	−	0.598100i	$-0.204077\pi$
$107$	−1.21293	−	2.10086i	−0.117259	−	0.203098i	−0.918680	+	0.395002i	$0.870744\pi$
$108$	−8.01813	+	13.8878i	−0.771545	+	1.33636i
$109$	−1.99272	−	1.15050i	−0.190868	−	0.110198i	0.401521	−	0.915850i	$-0.368482\pi$
$109$	−1.99272	−	1.15050i	−0.190868	−	0.110198i	−0.592389	+	0.805652i	$0.701815\pi$
$110$	−7.36083	−	0.904560i	−0.701827	−	0.0862464i
$111$		−	20.7908i		−	1.97337i
$112$	−1.60935	+	2.10000i	−0.152069	+	0.198431i
$113$			0.248341i			0.0233619i	0.999932	+	0.0116810i	$0.00371825\pi$
$113$			0.248341i			0.0233619i	−0.999932	+	0.0116810i	$0.996282\pi$
$114$	6.31677	+	10.9410i	0.591619	+	1.02471i
$115$	2.56204	+	4.36357i	0.238911	+	0.406905i
$116$	−1.78763	−	1.03209i	−0.165977	−	0.0958268i
$117$	22.3219	−	12.8875i	2.06366	−	1.19145i
$118$		−	11.4539i		−	1.05442i
$119$	0.488841	−	3.73076i	0.0448120	−	0.341999i
$120$	6.40988	+	3.63851i	0.585139	+	0.332149i
$121$	2.87487	+	10.6177i	0.261352	+	0.965244i
$122$	0.842907	−	1.45996i	0.0763132	−	0.132178i
$123$	15.7016	−	27.1959i	1.41576	−	2.45218i
$124$	4.72022	−	2.72522i	0.423888	−	0.244732i
$125$	0.245262	+	11.1776i	0.0219369	+	0.999759i
$126$	20.6326	+	2.70349i	1.83810	+	0.240846i
$127$	19.1683			1.70091			0.850455	−	0.526048i	$-0.176327\pi$
$127$	19.1683			1.70091			0.850455	+	0.526048i	$0.176327\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.39819	+	11.0820i	−0.563329	+	0.975715i
$130$	−3.71029	−	6.31924i	−0.325414	−	0.554234i
$131$	8.58237	+	14.8651i	0.749845	+	1.29877i	0.947896	+	0.318578i	$0.103205\pi$
$131$	8.58237	+	14.8651i	0.749845	+	1.29877i	−0.198051	+	0.980192i	$0.563461\pi$
$132$	1.41274	−	10.8407i	0.122963	−	0.943558i
$133$	6.16820	−	8.04875i	0.534851	−	0.697915i
$134$			5.76502i			0.498022i
$135$	−0.262225	−	35.8572i	−0.0225687	−	3.08610i
$136$	1.23162	+	0.711075i	0.105610	+	0.0609742i
$137$	0.683300	+	0.394503i	0.0583782	+	0.0337047i	0.528905	−	0.848681i	$-0.322603\pi$
$137$	0.683300	+	0.394503i	0.0583782	+	0.0337047i	−0.470527	+	0.882386i	$0.655936\pi$
$138$	−6.45985	+	3.72959i	−0.549899	+	0.317484i
$139$	−1.96370			−0.166559			−0.0832796	−	0.996526i	$-0.526539\pi$
$139$	−1.96370			−0.166559			−0.0832796	+	0.996526i	$0.526539\pi$
$140$	0.725696	−	5.87140i	0.0613325	−	0.496224i
$141$	−42.3348			−3.56523
$142$	4.50790	+	7.80791i	0.378294	+	0.655225i
$143$	−6.60539	+	8.63173i	−0.552371	+	0.721822i
$144$	−3.93253	+	6.81133i	−0.327710	+	0.567611i
$145$	4.61551	−	0.0337533i	0.383297	−	0.00280306i
$146$		−	13.5281i		−	1.11959i
$147$	−5.99915	−	22.2800i	−0.494801	−	1.83762i
$148$		−	6.30747i		−	0.518471i
$149$	−7.53677	+	4.35135i	−0.617436	+	0.356477i	−0.775870	−	0.630893i	$-0.782689\pi$
$149$	−7.53677	+	4.35135i	−0.617436	+	0.356477i	0.158434	+	0.987370i	$0.449355\pi$
$150$	−16.4793	+	0.241041i	−1.34553	+	0.0196809i
$151$	9.73317	+	5.61945i	0.792074	+	0.457304i	0.840692	−	0.541513i	$-0.182148\pi$
$151$	9.73317	+	5.61945i	0.792074	+	0.457304i	−0.0486179	+	0.998817i	$0.515482\pi$
$152$	1.91637	+	3.31925i	0.155438	+	0.269226i
$153$		−	11.1853i		−	0.904276i
$154$	−8.47158	+	2.28743i	−0.682659	+	0.184326i
$155$	−6.01643	+	10.5990i	−0.483251	+	0.851333i
$156$	9.35503	−	5.40113i	0.749002	−	0.432436i
$157$	4.34275	−	7.52187i	0.346589	−	0.600310i	−0.639052	−	0.769164i	$-0.720673\pi$
$157$	4.34275	−	7.52187i	0.346589	−	0.600310i	0.985641	+	0.168853i	$0.0540064\pi$
$158$	0.362507	+	0.209294i	0.0288395	+	0.0166505i
$159$	17.4101	−	10.0518i	1.38071	−	0.797156i
$160$	1.94462	+	1.10384i	0.153735	+	0.0872664i
$161$	4.75220	+	3.64188i	0.374526	+	0.287020i
$162$	29.2639			2.29919
$163$	−14.0268	+	8.09839i	−1.09867	+	0.634315i	−0.935870	−	0.352345i	$-0.885384\pi$
$163$	−14.0268	+	8.09839i	−1.09867	+	0.634315i	−0.162795	+	0.986660i	$0.552051\pi$
$164$	4.76352	−	8.25065i	0.371968	−	0.644268i
$165$	9.54928	+	22.5031i	0.743410	+	1.75186i
$166$	11.5160	−	6.64874i	0.893811	−	0.516042i
$167$			8.82456i			0.682865i	0.939906	+	0.341433i	$0.110912\pi$
$167$			8.82456i			0.682865i	−0.939906	+	0.341433i	$0.889088\pi$
$168$	8.64706	+	1.13302i	0.667135	+	0.0874146i
$169$	2.26018			0.173860
$170$	−3.17994	+	0.0232550i	−0.243890	+	0.00178358i
$171$	15.0723	−	26.1060i	1.15261	−	1.99638i
$172$	−1.94107	+	3.36203i	−0.148005	+	0.256353i
$173$	10.3263	−	5.96191i	0.785096	−	0.453275i	−0.0531373	−	0.998587i	$-0.516922\pi$
$173$	10.3263	−	5.96191i	0.785096	−	0.453275i	0.838233	+	0.545312i	$0.183589\pi$
$174$			6.80396i			0.515807i
$175$	5.24807	+	12.1432i	0.396716	+	0.917941i
$176$	0.428594	−	3.28882i	0.0323065	−	0.247904i
$177$	−32.6965	+	18.8774i	−2.45762	+	1.41891i
$178$	7.47672	+	4.31669i	0.560404	+	0.323549i
$179$	−6.13827	+	10.6318i	−0.458796	+	0.794658i	−0.998898	−	0.0469420i	$-0.985052\pi$
$179$	−6.13827	+	10.6318i	−0.458796	+	0.794658i	0.540102	+	0.841600i	$0.318386\pi$
$180$	−0.128609	−	17.5863i	−0.00958597	−	1.31081i
$181$			1.61928i			0.120360i	0.998188	+	0.0601802i	$0.0191675\pi$
$181$			1.61928i			0.120360i	−0.998188	+	0.0601802i	$0.980832\pi$
$182$	−6.88205	−	5.27410i	−0.510132	−	0.390942i
$183$	−5.55681			−0.410771
$184$	−1.95978	+	1.13148i	−0.144477	+	0.0834136i
$185$	7.14110	+	12.1625i	0.525024	+	0.894202i
$186$	−15.5589	−	8.98292i	−1.14083	−	0.658659i
$187$	1.81073	+	4.35533i	0.132414	+	0.318493i
$188$	−12.8434			−0.936704
$189$	−16.2605	−	39.1884i	−1.18278	−	2.85054i
$190$	−7.45320	−	4.23074i	−0.540712	−	0.306930i
$191$	−3.17504	−	5.49934i	−0.229738	−	0.397918i	0.727992	−	0.685585i	$-0.240454\pi$
$191$	−3.17504	−	5.49934i	−0.229738	−	0.397918i	−0.957730	+	0.287667i	$0.907120\pi$
$192$	−1.64811	+	2.85461i	−0.118942	+	0.206014i
$193$	2.33260	−	4.04017i	0.167904	−	0.290818i	−0.769779	−	0.638311i	$-0.779633\pi$
$193$	2.33260	−	4.04017i	0.167904	−	0.290818i	0.937683	+	0.347493i	$0.112967\pi$
$194$	1.25920	+	2.18099i	0.0904050	+	0.156586i
$195$	−11.9240	+	21.0062i	−0.853895	+	1.50429i
$196$	−1.82001	−	6.75926i	−0.130001	−	0.482804i
$197$	−14.6573			−1.04429			−0.522146	−	0.852856i	$-0.674868\pi$
$197$	−14.6573			−1.04429			−0.522146	+	0.852856i	$0.674868\pi$
$198$	−24.0867	+	10.0141i	−1.71177	+	0.711668i
$199$	−8.63358	−	4.98460i	−0.612019	−	0.353349i	0.161737	−	0.986834i	$-0.448291\pi$
$199$	−8.63358	−	4.98460i	−0.612019	−	0.353349i	−0.773755	+	0.633485i	$0.781624\pi$
$200$	−4.99947	+	0.0731264i	−0.353516	+	0.00517082i
$201$	16.4569	−	9.50138i	1.16078	−	0.670176i
$202$	10.4492			0.735205
$203$	5.04429	−	2.09303i	0.354040	−	0.146902i
$204$		−	4.68771i		−	0.328206i
$205$	0.155786	+	21.3025i	0.0108806	+	1.48783i
$206$	−1.99232	+	3.45080i	−0.138812	+	0.240429i
$207$	15.4137	+	8.89912i	1.07133	+	0.618532i
$208$	2.83811	−	1.63858i	0.196788	−	0.113615i
$209$	−1.64269	+	12.6052i	−0.113627	+	0.871917i
$210$	−17.9566	+	7.60513i	−1.23912	+	0.524804i
$211$		−	25.0957i		−	1.72766i	−0.503787	−	0.863828i	$-0.668060\pi$
$211$		−	25.0957i		−	1.72766i	0.503787	−	0.863828i	$-0.331940\pi$
$212$	5.28186	−	3.04948i	0.362759	−	0.209439i
$213$	14.8590	−	25.7366i	1.01812	−	1.76344i
$214$	−1.21293	+	2.10086i	−0.0829144	+	0.143612i
$215$	−0.0634808	−	8.68050i	−0.00432935	−	0.592005i
$216$	16.0363			1.09113
$217$	−1.87350	+	14.2983i	−0.127182	+	0.970631i
$218$			2.30100i			0.155843i
$219$	−38.6174	+	22.2957i	−2.60952	+	1.50661i
$220$	2.89704	+	6.82694i	0.195318	+	0.460272i
$221$	−2.33031	+	4.03622i	−0.156754	+	0.271505i
$222$	−18.0053	+	10.3954i	−1.20844	+	0.697693i
$223$	0.135830			0.00909587			0.00454793	−	0.999990i	$-0.498552\pi$
$223$	0.135830			0.00909587			0.00454793	+	0.999990i	$0.498552\pi$
$224$	2.62333	+	0.343734i	0.175278	+	0.0229667i
$225$	20.1586	+	33.7655i	1.34391	+	2.25103i
$226$	0.215069	−	0.124170i	0.0143062	−	0.00825969i
$227$	−19.4884	−	11.2517i	−1.29349	−	0.746798i	−0.314221	−	0.949350i	$-0.601743\pi$
$227$	−19.4884	−	11.2517i	−1.29349	−	0.746798i	−0.979272	+	0.202551i	$0.935077\pi$
$228$	6.31677	−	10.9410i	0.418338	−	0.724583i
$229$	20.1082	−	11.6095i	1.32879	−	0.767175i	0.343674	−	0.939089i	$-0.388329\pi$
$229$	20.1082	−	11.6095i	1.32879	−	0.767175i	0.985112	+	0.171914i	$0.0549952\pi$
$230$	2.49794	−	4.40058i	0.164710	−	0.290165i
$231$	20.4918	+	20.4131i	1.34826	+	1.34308i
$232$			2.06417i			0.135520i
$233$	−9.44733	−	16.3632i	−0.618915	−	1.07199i	−0.989684	−	0.143267i	$-0.954239\pi$
$233$	−9.44733	−	16.3632i	−0.618915	−	1.07199i	0.370769	−	0.928725i	$-0.379094\pi$
$234$	−22.3219	−	12.8875i	−1.45923	−	0.842485i
$235$	24.7655	−	14.5409i	1.61553	−	0.948543i
$236$	−9.91941	+	5.72697i	−0.645699	+	0.372794i
$237$		−	1.37975i		−	0.0896247i
$238$	−3.47536	+	1.44203i	−0.225274	+	0.0934731i
$239$			3.19029i			0.206363i	0.994663	+	0.103181i	$0.0329022\pi$
$239$			3.19029i			0.206363i	−0.994663	+	0.103181i	$0.967098\pi$
$240$	−0.0538997	−	7.37037i	−0.00347921	−	0.475755i
$241$	11.2617	−	19.5059i	0.725433	−	1.25649i	−0.233362	−	0.972390i	$-0.574973\pi$
$241$	11.2617	−	19.5059i	0.725433	−	1.25649i	0.958796	−	0.284097i	$-0.0916938\pi$
$242$	7.75775	−	7.79855i	0.498687	−	0.501310i
$243$	−24.1757	−	41.8735i	−1.55087	−	2.68618i
$244$	−1.68581			−0.107923
$245$	11.1621	+	10.9731i	0.713118	+	0.701044i
$246$	−31.4032			−2.00219
$247$	−10.8777	+	6.28026i	−0.692133	+	0.399603i
$248$	−4.72022	−	2.72522i	−0.299734	−	0.173052i
$249$	−37.9591	−	21.9157i	−2.40556	−	1.38885i
$250$	9.55750	−	5.80123i	0.604469	−	0.366902i
$251$		−	4.70092i		−	0.296719i	−0.988933	−	0.148360i	$-0.952601\pi$
$251$		−	4.70092i		−	0.296719i	0.988933	−	0.148360i	$-0.0473993\pi$
$252$	−7.97501	−	19.2201i	−0.502379	−	1.21075i
$253$	−7.44244	−	0.969887i	−0.467902	−	0.0609763i
$254$	−9.58414	−	16.6002i	−0.601362	−	1.04159i
$255$	5.30727	+	9.03915i	0.332354	+	0.566054i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.08013	+	5.33494i	0.192133	+	0.332784i	0.945957	−	0.324292i	$-0.105126\pi$
$257$	3.08013	+	5.33494i	0.192133	+	0.332784i	−0.753824	+	0.657077i	$0.771793\pi$
$258$	12.7964			0.796668
$259$	13.2457	+	10.1509i	0.823047	+	0.630746i
$260$	−3.61748	+	6.37283i	−0.224346	+	0.395226i
$261$	14.0598	−	8.11741i	0.870278	−	0.502455i
$262$	8.58237	−	14.8651i	0.530221	−	0.918369i
$263$	−0.788649	+	1.36598i	−0.0486302	+	0.0842299i	−0.889316	−	0.457293i	$-0.848819\pi$
$263$	−0.788649	+	1.36598i	−0.0486302	+	0.0842299i	0.840686	+	0.541523i	$0.182152\pi$
$264$	−10.0946	+	4.19686i	−0.621283	+	0.258299i
$265$	−6.73230	+	11.8601i	−0.413562	+	0.728563i
$266$	−10.0545	−	1.31744i	−0.616482	−	0.0807776i
$267$		−	28.4575i		−	1.74157i
$268$	4.99265	−	2.88251i	0.304975	−	0.176077i
$269$	−15.5646	−	8.98623i	−0.948990	−	0.547900i	−0.0562232	−	0.998418i	$-0.517906\pi$
$269$	−15.5646	−	8.98623i	−0.948990	−	0.547900i	−0.892767	+	0.450518i	$0.851239\pi$
$270$	−30.9222	+	18.1557i	−1.88186	+	1.10492i
$271$	−14.1633	−	24.5316i	−0.860360	−	1.49019i	−0.871582	−	0.490250i	$-0.836906\pi$
$271$	−14.1633	−	24.5316i	−0.860360	−	1.49019i	0.0112225	−	0.999937i	$-0.496428\pi$
$272$		−	1.42215i		−	0.0862305i
$273$	−3.71310	+	28.3379i	−0.224727	+	1.71508i
$274$		−	0.789007i		−	0.0476656i
$275$	−13.3155	−	9.88422i	−0.802954	−	0.596041i
$276$	6.45985	+	3.72959i	0.388837	+	0.224495i
$277$	2.06046	−	3.56882i	0.123801	−	0.214430i	−0.797463	−	0.603368i	$-0.793825\pi$
$277$	2.06046	−	3.56882i	0.123801	−	0.214430i	0.921264	+	0.388939i	$0.127158\pi$
$278$	0.981852	+	1.70062i	0.0588876	+	0.101996i
$279$			42.8680i			2.56644i
$280$	−5.44763	+	2.30723i	−0.325558	+	0.137883i
$281$			27.7634i			1.65622i	0.560563	+	0.828111i	$0.310585\pi$
$281$			27.7634i			1.65622i	−0.560563	+	0.828111i	$0.689415\pi$
$282$	21.1674	+	36.6630i	1.26050	+	2.18325i
$283$	10.1873	+	5.88163i	0.605571	+	0.349627i	0.771230	−	0.636556i	$-0.219642\pi$
$283$	10.1873	+	5.88163i	0.605571	+	0.349627i	−0.165659	+	0.986183i	$0.552975\pi$
$284$	4.50790	−	7.80791i	0.267494	−	0.463314i
$285$	0.206583	+	28.2487i	0.0122369	+	1.67331i
$286$	10.7780	+	1.40457i	0.637316	+	0.0830541i
$287$	9.66023	+	23.2815i	0.570225	+	1.37427i
$288$	7.86505			0.463453
$289$	−7.48875	−	12.9709i	−0.440514	−	0.762993i
$290$	−2.33698	−	3.98027i	−0.137232	−	0.233729i
$291$	4.15058	−	7.18902i	0.243311	−	0.421428i
$292$	−11.7157	+	6.76404i	−0.685607	+	0.395835i
$293$		−	27.3926i		−	1.60029i	−0.599804	−	0.800147i	$-0.704755\pi$
$293$		−	27.3926i		−	1.60029i	0.599804	−	0.800147i	$-0.295245\pi$
$294$	−16.2955	+	16.3354i	−0.950371	+	0.952700i
$295$	12.6434	−	22.2735i	0.736125	−	1.29681i
$296$	−5.46243	+	3.15373i	−0.317497	+	0.183307i
$297$	42.2379	+	32.3224i	2.45089	+	1.87554i
$298$	7.53677	+	4.35135i	0.436593	+	0.252067i
$299$	−3.70804	−	6.42251i	−0.214441	−	0.371423i
$300$	8.44841	+	14.1510i	0.487769	+	0.817008i
$301$	−3.93642	−	9.48693i	−0.226891	−	0.546817i
$302$		−	11.2389i		−	0.646726i
$303$	−17.2215	−	29.8285i	−0.989347	−	1.71360i
$304$	1.91637	−	3.31925i	0.109911	−	0.190372i
$305$	3.25069	−	1.90862i	0.186134	−	0.109287i
$306$	−9.68674	+	5.59264i	−0.553754	+	0.319710i
$307$			28.7598i			1.64141i	0.571352	+	0.820705i	$0.306419\pi$
$307$			28.7598i			1.64141i	−0.571352	+	0.820705i	$0.693581\pi$
$308$	6.21676	+	6.19289i	0.354233	+	0.352873i
$309$	13.1342			0.747181
$310$	12.1872	−	0.0891256i	0.692188	−	0.00506199i
$311$	22.5884	+	13.0414i	1.28087	+	0.739511i	0.977007	−	0.213205i	$-0.0683902\pi$
$311$	22.5884	+	13.0414i	1.28087	+	0.739511i	0.303863	+	0.952716i	$0.401724\pi$
$312$	−9.35503	−	5.40113i	−0.529624	−	0.305779i
$313$	−3.06134	−	5.30240i	−0.173037	−	0.299709i	0.766443	−	0.642312i	$-0.222025\pi$
$313$	−3.06134	−	5.30240i	−0.173037	−	0.299709i	−0.939480	+	0.342603i	$0.888691\pi$
$314$	−8.68551			−0.490151
$315$	37.1383	+	28.0324i	2.09250	+	1.57945i
$316$		−	0.418587i		−	0.0235474i
$317$	18.0043	−	10.3948i	1.01122	−	0.583829i	0.0996720	−	0.995020i	$-0.468221\pi$
$317$	18.0043	−	10.3948i	1.01122	−	0.583829i	0.911549	+	0.411192i	$0.134887\pi$
$318$	−17.4101	−	10.0518i	−0.976313	−	0.563674i
$319$	−4.16051	+	5.43683i	−0.232944	+	0.304404i
$320$	−0.0163520	−	2.23601i	−0.000914104	−	0.124997i
$321$	7.99618			0.446303
$322$	0.777854	−	5.93647i	0.0433481	−	0.330826i
$323$			5.45072i			0.303286i
$324$	−14.6319	−	25.3433i	−0.812886	−	1.40796i
$325$	−0.239647	−	16.3841i	−0.0132932	−	0.908825i
$326$	14.0268	+	8.09839i	0.776874	+	0.448528i
$327$	6.56845	−	3.79230i	0.363236	−	0.209714i
$328$	−9.52703			−0.526042
$329$	20.6695	−	26.9712i	1.13955	−	1.48697i
$330$	14.7136	−	19.5215i	0.809958	−	1.07462i
$331$	8.06779	+	13.9738i	0.443446	+	0.768071i	0.997942	−	0.0641153i	$-0.0204225\pi$
$331$	8.06779	+	13.9738i	0.443446	+	0.768071i	−0.554497	+	0.832186i	$0.687089\pi$
$332$	−11.5160	−	6.64874i	−0.632020	−	0.364897i
$333$	42.9623	+	24.8043i	2.35432	+	1.35927i
$334$	7.64229	−	4.41228i	0.418168	−	0.241429i
$335$	−6.36368	+	11.2108i	−0.347685	+	0.612509i
$336$	−3.34230	−	8.05508i	−0.182338	−	0.439441i
$337$	−15.9039			−0.866342			−0.433171	−	0.901312i	$-0.642605\pi$
$337$	−15.9039			−0.866342			−0.433171	+	0.901312i	$0.642605\pi$
$338$	−1.13009	−	1.95737i	−0.0614687	−	0.106467i
$339$	−0.708916	−	0.409293i	−0.0385030	−	0.0222297i
$340$	1.61011	+	2.74228i	0.0873204	+	0.148721i
$341$	−6.93969	−	16.6919i	−0.375805	−	0.903919i
$342$	−30.1447			−1.63004
$343$	17.1235	+	7.05596i	0.924581	+	0.380986i
$344$	3.88214			0.209311
$345$	−16.6788	+	0.121973i	−0.897957	+	0.00656678i
$346$	−10.3263	−	5.96191i	−0.555147	−	0.320514i
$347$	−13.9148	+	24.1012i	−0.746987	+	1.29382i	0.202273	+	0.979329i	$0.435167\pi$
$347$	−13.9148	+	24.1012i	−0.746987	+	1.29382i	−0.949261	+	0.314491i	$0.898166\pi$
$348$	5.89240	−	3.40198i	0.315866	−	0.182365i
$349$	9.99667			0.535109			0.267555	−	0.963543i	$-0.413784\pi$
$349$	9.99667			0.535109			0.267555	+	0.963543i	$0.413784\pi$
$350$	7.89231	−	10.6166i	0.421861	−	0.567479i
$351$			52.5535i			2.80510i
$352$	−3.06249	+	1.27323i	−0.163232	+	0.0678636i
$353$	5.11600	−	8.86118i	0.272297	−	0.471633i	−0.697152	−	0.716923i	$-0.745550\pi$
$353$	5.11600	−	8.86118i	0.272297	−	0.471633i	0.969450	+	0.245290i	$0.0788832\pi$
$354$	32.6965	+	18.8774i	1.73780	+	1.00332i
$355$	0.147426	+	20.1594i	0.00782457	+	1.06995i
$356$		−	8.63338i		−	0.457568i
$357$	9.84421	+	7.54416i	0.521011	+	0.399279i
$358$	12.2765			0.648835
$359$	20.8168	−	12.0186i	1.09867	−	0.634317i	0.162798	−	0.986659i	$-0.447948\pi$
$359$	20.8168	−	12.0186i	1.09867	−	0.634317i	0.935871	+	0.352343i	$0.114615\pi$
$360$	−15.1659	+	8.90454i	−0.799313	+	0.469310i
$361$	2.15507	−	3.73269i	0.113425	−	0.196457i
$362$	1.40234	−	0.809642i	0.0737054	−	0.0425538i
$363$	−35.0474	−	9.29247i	−1.83951	−	0.487728i
$364$	−1.12647	+	8.59708i	−0.0590433	+	0.450610i
$365$	14.9329	−	26.3069i	0.781622	−	1.37697i
$366$	2.77841	+	4.81234i	0.145230	+	0.251545i
$367$	−9.88761	+	17.1258i	−0.516129	+	0.893961i	0.483696	+	0.875236i	$0.339294\pi$
$367$	−9.88761	+	17.1258i	−0.516129	+	0.893961i	−0.999825	+	0.0187252i	$0.994039\pi$
$368$	1.95978	+	1.13148i	0.102160	+	0.0589823i
$369$	37.4653	+	64.8918i	1.95037	+	3.37813i
$370$	6.96245	−	12.2656i	0.361961	−	0.637658i
$371$	−2.09642	+	15.9996i	−0.108841	+	0.830657i
$372$			17.9658i			0.931485i
$373$	14.1113	+	24.4416i	0.730658	+	1.26554i	0.956602	+	0.291396i	$0.0941199\pi$
$373$	14.1113	+	24.4416i	0.730658	+	1.26554i	−0.225945	+	0.974140i	$0.572547\pi$
$374$	2.86646	−	3.74580i	0.148221	−	0.193691i
$375$	−32.3120	−	17.7219i	−1.66859	−	0.915153i
$376$	6.42172	+	11.1227i	0.331175	+	0.573612i
$377$	−6.76464			−0.348397
$378$	−25.8079	+	33.6762i	−1.32742	+	1.73212i
$379$	−2.86639			−0.147237			−0.0736184	−	0.997286i	$-0.523455\pi$
$379$	−2.86639			−0.147237			−0.0736184	+	0.997286i	$0.523455\pi$
$380$	0.0626729	+	8.57003i	0.00321505	+	0.439633i
$381$	−31.5914	+	54.7179i	−1.61848	+	2.80328i
$382$	−3.17504	+	5.49934i	−0.162449	+	0.281371i
$383$	1.25922	+	2.18103i	0.0643431	+	0.111446i	0.896402	−	0.443241i	$-0.146171\pi$
$383$	1.25922	+	2.18103i	0.0643431	+	0.111446i	−0.832059	+	0.554687i	$0.812838\pi$
$384$	3.29622			0.168209
$385$	−18.9989	−	4.90313i	−0.968275	−	0.249886i
$386$	−4.66519			−0.237452
$387$	−15.2666	−	26.4426i	−0.776046	−	1.34415i
$388$	1.25920	−	2.18099i	0.0639260	−	0.110723i
$389$	15.7112	−	27.2125i	0.796587	−	1.37973i	−0.125240	−	0.992127i	$-0.539970\pi$
$389$	15.7112	−	27.2125i	0.796587	−	1.37973i	0.921827	−	0.387603i	$-0.126697\pi$
$390$	24.1539	−	0.176638i	1.22308	−	0.00894444i
$391$	−3.21826			−0.162754
$392$	−4.94368	+	4.95580i	−0.249694	+	0.250306i
$393$	−56.5787			−2.85402
$394$	7.32866	+	12.6936i	0.369213	+	0.639495i
$395$	0.473910	+	0.807146i	0.0238450	+	0.0406119i
$396$	20.7158	+	15.8526i	1.04101	+	0.796625i
$397$	2.07433	+	3.59285i	0.104108	+	0.180320i	0.913373	−	0.407123i	$-0.133468\pi$
$397$	2.07433	+	3.59285i	0.104108	+	0.180320i	−0.809266	+	0.587443i	$0.800135\pi$
$398$			9.96920i			0.499711i
$399$	12.8102	+	30.8730i	0.641310	+	1.54558i
$400$	2.56306	+	4.29310i	0.128153	+	0.214655i
$401$	7.21306	+	12.4934i	0.360203	+	0.623890i	0.987994	−	0.154492i	$-0.0493741\pi$
$401$	7.21306	+	12.4934i	0.360203	+	0.623890i	−0.627791	+	0.778382i	$0.716041\pi$
$402$	−16.4569	−	9.50138i	−0.820794	−	0.473886i
$403$	8.93100	−	15.4689i	0.444885	−	0.770563i
$404$	−5.22461	−	9.04930i	−0.259934	−	0.450219i
$405$	56.9070	+	32.3027i	2.82773	+	1.60514i
$406$	−4.33476	−	3.32197i	−0.215131	−	0.164866i
$407$	−20.7441	−	2.70334i	−1.02825	−	0.134000i
$408$	−4.05968	+	2.34386i	−0.200984	+	0.116038i
$409$	−6.79595	+	11.7709i	−0.336038	+	0.582035i	−0.983684	−	0.179907i	$-0.942420\pi$
$409$	−6.79595	+	11.7709i	−0.336038	+	0.582035i	0.647645	+	0.761942i	$0.275754\pi$
$410$	18.3706	−	10.7862i	0.907261	−	0.532691i
$411$	−2.25230	+	1.30037i	−0.111098	+	0.0641425i
$412$	3.98464			0.196309
$413$	3.93711	−	30.0475i	0.193733	−	1.47854i
$414$		−	17.7982i		−	0.874736i
$415$	29.7333	−	0.217440i	1.45955	−	0.0106737i
$416$	−2.83811	−	1.63858i	−0.139150	−	0.0803382i
$417$	3.23640	−	5.60560i	0.158487	−	0.274508i
$418$	11.7377	−	4.87997i	0.574111	−	0.238687i
$419$			28.0477i			1.37022i	0.728441	+	0.685109i	$0.240245\pi$
$419$			28.0477i			1.37022i	−0.728441	+	0.685109i	$0.759755\pi$
$420$	15.5645	+	11.7483i	0.759471	+	0.573258i
$421$	−5.76758			−0.281095			−0.140547	−	0.990074i	$-0.544886\pi$
$421$	−5.76758			−0.281095			−0.140547	+	0.990074i	$0.544886\pi$
$422$	−21.7335	+	12.5478i	−1.05797	+	0.610819i
$423$	50.5071	−	87.4809i	2.45574	−	4.25347i
$424$	−5.28186	−	3.04948i	−0.256510	−	0.148096i
$425$	−6.20943	−	3.46493i	−0.301202	−	0.168074i
$426$	−29.7180			−1.43984
$427$	2.71306	−	3.54021i	0.131294	−	0.171323i
$428$	2.42587			0.117259
$429$	−13.7538	−	33.0819i	−0.664040	−	1.59721i
$430$	−7.48579	+	4.39523i	−0.360997	+	0.211957i
$431$	9.52461	+	5.49904i	0.458784	+	0.264879i	0.711533	−	0.702653i	$-0.248001\pi$
$431$	9.52461	+	5.49904i	0.458784	+	0.264879i	−0.252749	+	0.967532i	$0.581335\pi$
$432$	−8.01813	−	13.8878i	−0.385773	−	0.668178i
$433$	−30.3763			−1.45979			−0.729896	−	0.683558i	$-0.760432\pi$
$433$	−30.3763			−1.45979			−0.729896	+	0.683558i	$0.760432\pi$
$434$	13.3194	−	5.52664i	0.639353	−	0.265287i
$435$	−7.51050	+	13.2311i	−0.360101	+	0.634382i
$436$	1.99272	−	1.15050i	0.0954341	−	0.0550989i
$437$	−7.51130	−	4.33665i	−0.359314	−	0.207450i
$438$	38.6174	+	22.2957i	1.84521	+	1.06533i
$439$	−19.8468	−	34.3757i	−0.947237	−	1.64066i	−0.751209	−	0.660065i	$-0.770529\pi$
$439$	−19.8468	−	34.3757i	−0.947237	−	1.64066i	−0.196028	−	0.980598i	$-0.562804\pi$
$440$	4.46379	−	5.92238i	0.212803	−	0.282339i
$441$	53.1968	+	14.1843i	2.53318	+	0.675441i
$442$	4.66062			0.221683
$443$	−17.3710	+	10.0291i	−0.825319	+	0.476498i	−0.852247	−	0.523139i	$-0.824761\pi$
$443$	−17.3710	+	10.0291i	−0.825319	+	0.476498i	0.0269281	+	0.999637i	$0.491427\pi$
$444$	18.0053	+	10.3954i	0.854496	+	0.493343i
$445$	9.77441	+	16.6474i	0.463351	+	0.789164i
$446$	−0.0679151	−	0.117632i	−0.00321587	−	0.00557006i
$447$		−	28.6860i		−	1.35680i
$448$	−1.01398	−	2.44374i	−0.0479061	−	0.115456i
$449$	−27.1775			−1.28259			−0.641294	−	0.767295i	$-0.721602\pi$
$449$	−27.1775			−1.28259			−0.641294	+	0.767295i	$0.721602\pi$
$450$	19.1624	−	34.3406i	0.903326	−	1.61883i
$451$	−25.0933	−	19.2025i	−1.18160	−	0.904210i
$452$	−0.215069	−	0.124170i	−0.0101160	−	0.00584049i
$453$	−32.0827	+	18.5229i	−1.50737	+	0.870283i
$454$			22.5033i			1.05613i
$455$	−7.56118	−	17.8528i	−0.354474	−	0.836952i
$456$	−12.6335			−0.591619
$457$	−10.0541	−	17.4142i	−0.470311	−	0.814602i	0.529113	−	0.848551i	$-0.322525\pi$
$457$	−10.0541	−	17.4142i	−0.470311	−	0.814602i	−0.999424	+	0.0339496i	$0.989191\pi$
$458$	−20.1082	−	11.6095i	−0.939593	−	0.542475i
$459$	19.7506	+	11.4030i	0.921877	+	0.532246i
$460$	−5.05998	+	0.0370038i	−0.235923	+	0.00172531i
$461$	5.09054			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$461$	5.09054			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$462$	7.43238	−	27.9530i	0.345785	−	1.30049i
$463$		−	35.8000i		−	1.66377i	−0.554952	−	0.831883i	$-0.687263\pi$
$463$		−	35.8000i		−	1.66377i	0.554952	−	0.831883i	$-0.312737\pi$
$464$	1.78763	−	1.03209i	0.0829884	−	0.0479134i
$465$	−20.3403	−	34.6429i	−0.943259	−	1.60652i
$466$	−9.44733	+	16.3632i	−0.437639	+	0.758013i
$467$	−10.5234	−	18.2270i	−0.486964	−	0.843446i	0.512924	−	0.858434i	$-0.328562\pi$
$467$	−10.5234	−	18.2270i	−0.486964	−	0.843446i	−0.999888	+	0.0149884i	$0.995229\pi$
$468$			25.7751i			1.19145i
$469$	−1.98163	+	15.1235i	−0.0915034	+	0.698340i
$470$	−24.9756	−	14.1771i	−1.15204	−	0.653943i
$471$	14.3147	+	24.7937i	0.659585	+	1.14243i
$472$	9.91941	+	5.72697i	0.456578	+	0.263605i
$473$	10.2252	+	7.82477i	0.470154	+	0.359783i
$474$	−1.19490	+	0.689877i	−0.0548837	+	0.0316871i
$475$	−9.82354	−	16.4543i	−0.450735	−	0.754976i
$476$	2.98652	+	2.28873i	0.136887	+	0.104904i
$477$			47.9687i			2.19633i
$478$	2.76287	−	1.59514i	0.126371	−	0.0729602i
$479$	11.5275	−	19.9663i	0.526706	−	0.912282i	−0.472809	−	0.881165i	$-0.656760\pi$
$479$	11.5275	−	19.9663i	0.526706	−	0.912282i	0.999516	−	0.0311174i	$-0.00990657\pi$
$480$	−6.35598	+	3.73186i	−0.290109	+	0.170335i
$481$	−10.3353	−	17.9013i	−0.471250	−	0.816228i
$482$	−22.5235			−1.02592
$483$	−18.2283	+	7.56348i	−0.829415	+	0.344150i
$484$	−10.6326	−	2.81913i	−0.483301	−	0.128142i
$485$	0.0411807	+	5.63114i	0.00186992	+	0.255697i
$486$	−24.1757	+	41.8735i	−1.09663	+	1.89942i
$487$	30.8917	+	17.8354i	1.39984	+	0.808197i	0.994375	−	0.105914i	$-0.0337769\pi$
$487$	30.8917	+	17.8354i	1.39984	+	0.808197i	0.405463	+	0.914111i	$0.367110\pi$
$488$	0.842907	+	1.45996i	0.0381566	+	0.0660892i
$489$		−	53.3881i		−	2.41429i
$490$	3.92194	−	15.1532i	0.177175	−	0.684550i
$491$		−	12.1060i		−	0.546335i	−0.961966	−	0.273167i	$-0.911929\pi$
$491$		−	12.1060i		−	0.546335i	0.961966	−	0.273167i	$-0.0880713\pi$
$492$	15.7016	+	27.1959i	0.707882	+	1.22609i
$493$	−1.46778	+	2.54227i	−0.0661055	+	0.114498i
$494$	10.8777	+	6.28026i	0.489412	+	0.282562i
$495$	−57.8933	−	7.11441i	−2.60211	−	0.319769i
$496$			5.45044i			0.244732i
$497$	9.14184	+	22.0322i	0.410068	+	0.988280i
$498$			43.8314i			1.96413i
$499$	−7.49926	−	12.9891i	−0.335713	−	0.581472i	0.647909	−	0.761718i	$-0.275644\pi$
$499$	−7.49926	−	12.9891i	−0.335713	−	0.581472i	−0.983622	+	0.180246i	$0.942311\pi$
$500$	−9.80276	−	5.37642i	−0.438393	−	0.240441i
$501$	−25.1907	−	14.5438i	−1.12544	−	0.649771i
$502$	−4.07111	+	2.35046i	−0.181703	+	0.104906i
$503$			23.5751i			1.05116i	0.850743	+	0.525582i	$0.176152\pi$
$503$			23.5751i			1.05116i	−0.850743	+	0.525582i	$0.823848\pi$
$504$	−12.6576	+	16.5166i	−0.563814	+	0.735709i
$505$	20.3197	+	11.5343i	0.904216	+	0.513270i
$506$	2.88127	+	6.93028i	0.128088	+	0.308089i
$507$	−3.72502	+	6.45192i	−0.165434	+	0.286540i
$508$	−9.58414	+	16.6002i	−0.425227	+	0.736516i
$509$	−8.41745	+	4.85982i	−0.373097	+	0.215408i	−0.674811	−	0.737991i	$-0.735775\pi$
$509$	−8.41745	+	4.85982i	−0.373097	+	0.215408i	0.301714	+	0.953399i	$0.402441\pi$
$510$	5.17450	−	9.11580i	0.229131	−	0.403655i
$511$	4.65006	−	35.4886i	0.205707	−	1.56992i
$512$	1.00000			0.0441942
$513$	30.7314	+	53.2283i	1.35682	+	2.35009i
$514$	3.08013	−	5.33494i	0.135859	−	0.235314i
$515$	−7.68344	+	4.51127i	−0.338573	+	0.198790i
$516$	−6.39819	−	11.0820i	−0.281665	−	0.487858i
$517$	−5.50461	+	42.2397i	−0.242093	+	1.85770i
$518$	2.16809	−	16.5466i	0.0952605	−	0.727014i
$519$			39.3035i			1.72523i
$520$	7.32777	−	0.0535882i	0.321344	−	0.00235000i
$521$	14.7001	+	8.48713i	0.644025	+	0.371828i	0.786163	−	0.618019i	$-0.212064\pi$
$521$	14.7001	+	8.48713i	0.644025	+	0.371828i	−0.142138	+	0.989847i	$0.545398\pi$
$522$	−14.0598	−	8.11741i	−0.615379	−	0.355289i
$523$	−26.4328	+	15.2610i	−1.15583	+	0.667317i	−0.950301	−	0.311334i	$-0.899224\pi$
$523$	−26.4328	+	15.2610i	−1.15583	+	0.667317i	−0.205527	+	0.978651i	$0.565891\pi$
$524$	−17.1647			−0.749845
$525$	−43.3135	−	5.03218i	−1.89036	−	0.219622i
$526$	1.57730			0.0687734
$527$	−3.87567	−	6.71286i	−0.168827	−	0.292417i
$528$	8.68191	+	6.64379i	0.377832	+	0.289134i
$529$	−8.93952	+	15.4837i	−0.388675	+	0.673205i
$530$	13.6373	−	0.0997302i	0.592368	−	0.00433200i
$531$		−	90.0859i		−	3.90939i
$532$	3.88632	+	9.36619i	0.168493	+	0.406076i
$533$		−	31.2217i		−	1.35236i
$534$	−24.6449	+	14.2287i	−1.06649	+	0.615738i
$535$	−4.67771	+	2.74648i	−0.202235	+	0.118741i
$536$	−4.99265	−	2.88251i	−0.215650	−	0.124505i
$537$	−20.2331	−	35.0447i	−0.873122	−	1.51229i
$538$			17.9725i			0.774847i
$539$	−23.0100	+	3.08870i	−0.991111	+	0.133040i
$540$	31.1844	+	17.7015i	1.34196	+	0.761752i
$541$	31.7000	−	18.3020i	1.36289	−	0.786864i	0.372881	−	0.927879i	$-0.378370\pi$
$541$	31.7000	−	18.3020i	1.36289	−	0.786864i	0.990007	+	0.141016i	$0.0450368\pi$
$542$	−14.1633	+	24.5316i	−0.608366	+	1.05372i
$543$	−4.62242	−	2.66876i	−0.198367	−	0.114527i
$544$	−1.23162	+	0.711075i	−0.0528052	+	0.0304871i
$545$	−2.53994	+	4.47456i	−0.108799	+	0.191669i
$546$	26.3979	−	10.9533i	1.12972	−	0.468757i
$547$	20.1720			0.862493			0.431247	−	0.902234i	$-0.358074\pi$
$547$	20.1720			0.862493			0.431247	+	0.902234i	$0.358074\pi$
$548$	−0.683300	+	0.394503i	−0.0291891	+	0.0168523i
$549$	6.62951	−	11.4826i	0.282941	−	0.490067i
$550$	−1.90224	+	16.4737i	−0.0811118	+	0.702439i
$551$	−6.85150	+	3.95571i	−0.291884	+	0.168519i
$552$		−	7.45919i		−	0.317484i
$553$	0.879033	+	0.673651i	0.0373803	+	0.0286466i
$554$	−4.12092			−0.175081
$555$	−46.4884	+	0.339971i	−1.97332	+	0.0144310i
$556$	0.981852	−	1.70062i	0.0416398	−	0.0721222i
$557$	0.419322	−	0.726287i	0.0177672	−	0.0307738i	−0.857005	−	0.515308i	$-0.827678\pi$
$557$	0.419322	−	0.726287i	0.0177672	−	0.0307738i	0.874772	+	0.484534i	$0.161011\pi$
$558$	37.1248	−	21.4340i	1.57162	−	0.907373i
$559$			12.7224i			0.538101i
$560$	4.72194	+	3.56417i	0.199538	+	0.150614i
$561$	−15.4170	−	2.00912i	−0.650907	−	0.0848253i
$562$	24.0438	−	13.8817i	1.01423	−	0.585563i
$563$	10.1026	+	5.83272i	0.425773	+	0.245820i	0.697544	−	0.716542i	$-0.254276\pi$
$563$	10.1026	+	5.83272i	0.425773	+	0.245820i	−0.271771	+	0.962362i	$0.587609\pi$
$564$	21.1674	−	36.6630i	0.891308	−	1.54379i
$565$	0.555292	−	0.00406087i	0.0233613	−	0.000170842i
$566$		−	11.7633i		−	0.494447i
$567$	76.7687	+	10.0590i	3.22398	+	0.422438i
$568$	−9.01579			−0.378294
$569$	3.92946	−	2.26868i	0.164732	−	0.0951079i	−0.415368	−	0.909654i	$-0.636347\pi$
$569$	3.92946	−	2.26868i	0.164732	−	0.0951079i	0.580099	+	0.814546i	$0.303014\pi$
$570$	24.3608	−	14.3032i	1.02036	−	0.599097i
$571$	4.88332	+	2.81939i	0.204361	+	0.117988i	0.598688	−	0.800982i	$-0.295689\pi$
$571$	4.88332	+	2.81939i	0.204361	+	0.117988i	−0.394327	+	0.918970i	$0.629022\pi$
$572$	−4.17260	−	10.0363i	−0.174465	−	0.419639i
$573$	20.9313			0.874417
$574$	15.3323	−	20.0068i	0.639957	−	0.835067i
$575$	9.71509	−	5.80009i	0.405147	−	0.241880i
$576$	−3.93253	−	6.81133i	−0.163855	−	0.283806i
$577$	−17.4605	+	30.2424i	−0.726889	+	1.25901i	0.231302	+	0.972882i	$0.425701\pi$
$577$	−17.4605	+	30.2424i	−0.726889	+	1.25901i	−0.958192	+	0.286127i	$0.907632\pi$
$578$	−7.48875	+	12.9709i	−0.311491	+	0.539518i
$579$	7.68874	+	13.3173i	0.319533	+	0.553448i
$580$	−2.27852	+	4.01402i	−0.0946105	+	0.166673i
$581$	32.4955	−	13.4834i	1.34814	−	0.559385i
$582$	−8.30117			−0.344094
$583$	−7.76541	−	18.6780i	−0.321610	−	0.773565i
$584$	11.7157	+	6.76404i	0.484797	+	0.279898i
$585$	−29.1817	−	49.7012i	−1.20651	−	2.05489i
$586$	−23.7227	+	13.6963i	−0.979976	+	0.565790i
$587$	−32.8201			−1.35463			−0.677315	−	0.735693i	$-0.736856\pi$
$587$	−32.8201			−1.35463			−0.677315	+	0.735693i	$0.736856\pi$
$588$	22.2946	+	5.94458i	0.919414	+	0.245150i
$589$		−	20.8901i		−	0.860761i
$590$	−25.6111	+	0.187295i	−1.05439	+	0.00771081i
$591$	24.1569	−	41.8409i	0.993681	−	1.72111i
$592$	5.46243	+	3.15373i	0.224504	+	0.129618i
$593$	−4.65629	+	2.68831i	−0.191211	+	0.110396i	−0.592549	−	0.805534i	$-0.701878\pi$
$593$	−4.65629	+	2.68831i	−0.191211	+	0.110396i	0.401338	+	0.915930i	$0.368545\pi$
$594$	6.87304	−	52.7403i	0.282004	−	2.16396i
$595$	−8.35001	−	1.03205i	−0.342317	−	0.0423098i
$596$		−	8.70271i		−	0.356477i
$597$	28.4582	−	16.4303i	1.16472	−	0.672449i
$598$	−3.70804	+	6.42251i	−0.151633	+	0.262636i
$599$	−6.09118	+	10.5502i	−0.248879	+	0.431071i	−0.963215	−	0.268732i	$-0.913395\pi$
$599$	−6.09118	+	10.5502i	−0.248879	+	0.431071i	0.714336	+	0.699803i	$0.246729\pi$
$600$	8.03092	−	14.3920i	0.327861	−	0.587552i
$601$	−9.86957			−0.402588			−0.201294	−	0.979531i	$-0.564515\pi$
$601$	−9.86957			−0.402588			−0.201294	+	0.979531i	$0.564515\pi$
$602$	−6.24771	+	8.15250i	−0.254638	+	0.332271i
$603$			45.3422i			1.84648i
$604$	−9.73317	+	5.61945i	−0.396037	+	0.228652i
$605$	23.6942	−	6.60185i	0.963307	−	0.268403i
$606$	−17.2215	+	29.8285i	−0.699574	+	1.21170i
$607$	−33.1257	+	19.1251i	−1.34453	+	0.776265i	−0.987469	−	0.157815i	$-0.949555\pi$
$607$	−33.1257	+	19.1251i	−1.34453	+	0.776265i	−0.357063	+	0.934080i	$0.616222\pi$
$608$	−3.83274			−0.155438
$609$	−2.33875	+	17.8490i	−0.0947711	+	0.723279i
$610$	−3.27826	−	1.86087i	−0.132733	−	0.0753446i
$611$	−36.4511	+	21.0450i	−1.47465	+	0.851391i
$612$	9.68674	+	5.59264i	0.391563	+	0.226069i
$613$	7.38461	−	12.7905i	0.298261	−	0.516604i	−0.677477	−	0.735544i	$-0.736927\pi$
$613$	7.38461	−	12.7905i	0.298261	−	0.516604i	0.975738	+	0.218940i	$0.0702599\pi$
$614$	24.9068	−	14.3799i	1.00515	−	0.580326i
$615$	−61.0671	−	34.6642i	−2.46246	−	1.39779i
$616$	2.25482	−	8.48032i	0.0908493	−	0.341682i
$617$		−	15.8413i		−	0.637749i	−0.947797	−	0.318874i	$-0.896695\pi$
$617$		−	15.8413i		−	0.637749i	0.947797	−	0.318874i	$-0.103305\pi$
$618$	−6.56712	−	11.3746i	−0.264168	−	0.457553i
$619$	15.0638	+	8.69709i	0.605466	+	0.349566i	0.771189	−	0.636607i	$-0.219662\pi$
$619$	15.0638	+	8.69709i	0.605466	+	0.349566i	−0.165723	+	0.986172i	$0.552996\pi$
$620$	−6.17080	−	10.5099i	−0.247825	−	0.422087i
$621$	−31.4275	+	18.1447i	−1.26114	+	0.728120i
$622$		−	26.0828i		−	1.04583i
$623$	18.1301	+	13.8941i	0.726367	+	0.556655i
$624$			10.8023i			0.432436i
$625$	24.9893	−	0.731186i	0.999572	−	0.0292474i
$626$	−3.06134	+	5.30240i	−0.122356	+	0.211926i
$627$	−33.2755	−	25.4639i	−1.32889	−	1.01693i
$628$	4.34275	+	7.52187i	0.173295	+	0.300155i
$629$	−8.97016			−0.357664
$630$	5.70764	−	46.1789i	0.227398	−	1.83981i
$631$	−11.8810			−0.472977			−0.236488	−	0.971634i	$-0.575996\pi$
$631$	−11.8810			−0.472977			−0.236488	+	0.971634i	$0.575996\pi$
$632$	−0.362507	+	0.209294i	−0.0144198	+	0.00832525i
$633$	71.6383	+	41.3604i	2.84737	+	1.64393i
$634$	−18.0043	−	10.3948i	−0.715041	−	0.412829i
$635$	−0.313440	−	42.8604i	−0.0124385	−	1.70086i
$636$			20.1035i			0.797156i
$637$	−16.2410	−	16.2013i	−0.643492	−	0.641918i
$638$	6.78868	+	0.884691i	0.268766	+	0.0350253i
$639$	35.4548	+	61.4096i	1.40257	+	2.42933i
$640$	−1.92826	+	1.13217i	−0.0762213	+	0.0447528i
$641$	−12.7773	+	22.1310i	−0.504674	+	0.874122i	0.495311	+	0.868716i	$0.335054\pi$
$641$	−12.7773	+	22.1310i	−0.504674	+	0.874122i	−0.999985	+	0.00540601i	$0.998279\pi$
$642$	−3.99809	−	6.92490i	−0.157792	−	0.273304i
$643$	8.81233			0.347524			0.173762	−	0.984788i	$-0.444408\pi$
$643$	8.81233			0.347524			0.173762	+	0.984788i	$0.444408\pi$
$644$	−5.53006	+	2.29459i	−0.217915	+	0.0904196i
$645$	24.8841	+	14.1252i	0.979809	+	0.556179i
$646$	4.72046	−	2.72536i	0.185724	−	0.107228i
$647$	−9.41249	+	16.3029i	−0.370043	+	0.640933i	−0.989572	−	0.144041i	$-0.953990\pi$
$647$	−9.41249	+	16.3029i	−0.370043	+	0.640933i	0.619529	+	0.784974i	$0.287324\pi$
$648$	−14.6319	+	25.3433i	−0.574797	+	0.995577i
$649$	14.5836	+	35.0776i	0.572455	+	1.37692i
$650$	−14.0692	+	8.39958i	−0.551840	+	0.329459i
$651$	−37.7283	−	28.9132i	−1.47869	−	1.13320i
$652$		−	16.1968i		−	0.634315i
$653$	5.00294	−	2.88845i	0.195780	−	0.113034i	−0.398905	−	0.916992i	$-0.630610\pi$
$653$	5.00294	−	2.88845i	0.195780	−	0.113034i	0.594686	+	0.803958i	$0.297276\pi$
$654$	−6.56845	−	3.79230i	−0.256847	−	0.148290i
$655$	33.0982	−	19.4333i	1.29325	−	0.759323i
$656$	4.76352	+	8.25065i	0.185984	+	0.322134i
$657$		−	106.399i		−	4.15102i
$658$	−33.6925	−	4.41473i	−1.31347	−	0.172104i
$659$			15.7828i			0.614812i	0.951578	+	0.307406i	$0.0994610\pi$
$659$			15.7828i			0.614812i	−0.951578	+	0.307406i	$0.900539\pi$
$660$	−24.2629	−	2.98163i	−0.944432	−	0.116060i
$661$	−11.7074	−	6.75925i	−0.455364	−	0.262904i	0.254729	−	0.967012i	$-0.418014\pi$
$661$	−11.7074	−	6.75925i	−0.455364	−	0.262904i	−0.710093	+	0.704108i	$0.751347\pi$
$662$	8.06779	−	13.9738i	0.313564	−	0.543108i
$663$	−7.68121	−	13.3042i	−0.298314	−	0.516694i
$664$			13.2975i			0.516042i
$665$	−18.0979	−	13.6605i	−0.701808	−	0.529733i
$666$		−	49.6086i		−	1.92229i
$667$	−2.33556	−	4.04531i	−0.0904334	−	0.156635i
$668$	−7.64229	−	4.41228i	−0.295689	−	0.170716i
$669$	−0.223863	+	0.387742i	−0.00865504	+	0.0149910i
$670$	12.8906	−	0.0942696i	0.498009	−	0.00364195i
$671$	−0.722529	+	5.54433i	−0.0278929	+	0.214037i
$672$	−5.30476	+	6.92206i	−0.204635	+	0.267024i
$673$	−3.78286			−0.145819			−0.0729093	−	0.997339i	$-0.523228\pi$
$673$	−3.78286			−0.145819			−0.0729093	+	0.997339i	$0.523228\pi$
$674$	7.95196	+	13.7732i	0.306298	+	0.530524i
$675$	−80.1728	+	1.17267i	−3.08585	+	0.0451363i
$676$	−1.13009	+	1.95737i	−0.0434649	+	0.0752835i
$677$	−33.0791	+	19.0982i	−1.27133	+	0.734005i	−0.975239	−	0.221154i	$-0.929018\pi$
$677$	−33.0791	+	19.0982i	−1.27133	+	0.734005i	−0.296095	+	0.955159i	$0.595684\pi$
$678$			0.818585i			0.0314376i
$679$	2.55360	+	6.15428i	0.0979982	+	0.236180i
$680$	1.56983	−	2.76553i	0.0602002	−	0.106053i
$681$	64.2381	−	37.0879i	2.46161	−	1.42121i
$682$	−10.9858	+	14.3559i	−0.420668	+	0.549717i
$683$	13.6537	+	7.88296i	0.522444	+	0.301633i	0.737934	−	0.674873i	$-0.235802\pi$
$683$	13.6537	+	7.88296i	0.522444	+	0.301633i	−0.215490	+	0.976506i	$0.569135\pi$
$684$	15.0723	+	26.1060i	0.576305	+	0.998189i
$685$	0.870939	−	1.53431i	0.0332769	−	0.0586232i
$686$	−2.45109	−	18.3573i	−0.0935831	−	0.700887i
$687$			76.5346i			2.91998i
$688$	−1.94107	−	3.36203i	−0.0740026	−	0.128176i
$689$	9.99366	−	17.3095i	0.380728	−	0.659440i
$690$	8.44503	+	14.3833i	0.321497	+	0.547562i
$691$	28.1951	−	16.2785i	1.07259	−	0.619262i	0.143704	−	0.989621i	$-0.454099\pi$
$691$	28.1951	−	16.2785i	1.07259	−	0.619262i	0.928889	+	0.370359i	$0.120765\pi$
$692$			11.9238i			0.453275i
$693$	−66.6294	+	17.9907i	−2.53104	+	0.683412i
$694$	27.8297			1.05640
$695$	0.0321105	+	4.39086i	0.00121802	+	0.166555i
$696$	−5.89240	−	3.40198i	−0.223351	−	0.128952i
$697$	−11.7337	−	6.77443i	−0.444444	−	0.256600i
$698$	−4.99833	−	8.65737i	−0.189190	−	0.327686i
$699$	62.2809			2.35568
$700$	−13.1404	−	1.52665i	−0.496659	−	0.0577020i
$701$			21.2469i			0.802485i	0.915972	+	0.401243i	$0.131422\pi$
$701$			21.2469i			0.802485i	−0.915972	+	0.401243i	$0.868578\pi$
$702$	45.5127	−	26.2768i	1.71777	−	0.991753i
$703$	−20.9360	−	12.0874i	−0.789617	−	0.455886i
$704$	2.63390	+	2.01558i	0.0992689	+	0.0759651i
$705$	0.692258	+	94.6609i	0.0260719	+	3.56514i
$706$	−10.2320			−0.385087
$707$	27.4117	+	3.59176i	1.03092	+	0.135082i
$708$		−	37.7547i		−	1.41891i
$709$	−8.29779	−	14.3722i	−0.311630	−	0.539759i	0.667085	−	0.744981i	$-0.267542\pi$
$709$	−8.29779	−	14.3722i	−0.311630	−	0.539759i	−0.978715	+	0.205222i	$0.934208\pi$
$710$	17.3848	−	10.2074i	0.652441	−	0.383076i
$711$	2.85114	+	1.64610i	0.106926	+	0.0617337i
$712$	−7.47672	+	4.31669i	−0.280202	+	0.161775i
$713$	12.3341			0.461915
$714$	1.61133	−	12.2974i	0.0603024	−	0.460219i
$715$	19.4086	+	14.6286i	0.725842	+	0.547078i
$716$	−6.13827	−	10.6318i	−0.229398	−	0.397329i
$717$	−9.10702	−	5.25794i	−0.340108	−	0.196361i
$718$	−20.8168	−	12.0186i	−0.776876	−	0.448530i
$719$	3.65839	−	2.11217i	0.136435	−	0.0787708i	−0.430229	−	0.902720i	$-0.641567\pi$
$719$	3.65839	−	2.11217i	0.136435	−	0.0787708i	0.566664	+	0.823949i	$0.308234\pi$
$720$	15.2945	+	8.68178i	0.569993	+	0.323551i
$721$	−6.41267	+	8.36775i	−0.238820	+	0.311631i
$722$	−4.31014			−0.160407
$723$	37.1212	+	64.2958i	1.38055	+	2.39119i
$724$	−1.40234	−	0.809642i	−0.0521176	−	0.0300901i
$725$	−0.150945	−	10.3198i	−0.00560597	−	0.383266i
$726$	9.47619	+	34.9982i	0.351695	+	1.29890i
$727$	3.41464			0.126642			0.0633211	−	0.997993i	$-0.479831\pi$
$727$	3.41464			0.126642			0.0633211	+	0.997993i	$0.479831\pi$
$728$	8.00853	−	3.32299i	0.296816	−	0.123158i
$729$	71.5848			2.65129
$730$	−30.2489	+	0.221211i	−1.11956	+	0.00818739i
$731$	4.78131	+	2.76049i	0.176843	+	0.102101i
$732$	2.77841	−	4.81234i	0.102693	−	0.177869i
$733$	9.81646	−	5.66754i	0.362579	−	0.209335i	−0.307632	−	0.951505i	$-0.599537\pi$
$733$	9.81646	−	5.66754i	0.362579	−	0.209335i	0.670212	+	0.742170i	$0.266203\pi$
$734$	19.7752			0.729916
$735$	−49.7201	+	13.7785i	−1.83395	+	0.508226i
$736$		−	2.26295i		−	0.0834136i
$737$	−7.34023	−	17.6553i	−0.270381	−	0.650343i
$738$	37.4653	−	64.8918i	1.37912	−	2.38870i
$739$	3.88297	+	2.24184i	0.142837	+	0.0824673i	0.569716	−	0.821842i	$-0.307053\pi$
$739$	3.88297	+	2.24184i	0.142837	+	0.0824673i	−0.426878	+	0.904309i	$0.640387\pi$
$740$	−14.1035	+	0.103140i	−0.518457	+	0.00379149i
$741$		−	41.4022i		−	1.52095i
$742$	14.9042	−	6.18423i	0.547152	−	0.227030i
$743$	−7.70671			−0.282732			−0.141366	−	0.989957i	$-0.545149\pi$
$743$	−7.70671			−0.282732			−0.141366	+	0.989957i	$0.545149\pi$
$744$	15.5589	−	8.98292i	0.570416	−	0.329330i
$745$	9.85290	+	16.7811i	0.360982	+	0.614813i
$746$	14.1113	−	24.4416i	0.516653	−	0.894869i
$747$	90.5736	−	52.2927i	3.31391	−	1.91329i
$748$	−4.67719	−	0.609524i	−0.171015	−	0.0222864i
$749$	−3.90406	+	5.09432i	−0.142651	+	0.186142i
$750$	0.808439	+	36.8440i	0.0295200	+	1.34535i
$751$	5.06956	+	8.78074i	0.184991	+	0.320414i	0.943573	−	0.331163i	$-0.107441\pi$
$751$	5.06956	+	8.78074i	0.184991	+	0.320414i	−0.758583	+	0.651577i	$0.774108\pi$
$752$	6.42172	−	11.1227i	0.234176	−	0.405605i
$753$	13.4193	+	7.74762i	0.489026	+	0.282339i
$754$	3.38232	+	5.85835i	0.123177	+	0.213348i
$755$	12.4060	−	21.8553i	0.451500	−	0.795397i
$756$	42.0684	+	5.51221i	1.53001	+	0.200477i
$757$		−	35.0178i		−	1.27274i	−0.771382	−	0.636372i	$-0.780434\pi$
$757$		−	35.0178i		−	1.27274i	0.771382	−	0.636372i	$-0.219566\pi$
$758$	1.43320	+	2.48237i	0.0520561	+	0.0901637i
$759$	15.0346	−	19.6468i	0.545721	−	0.713132i
$760$	7.39053	−	4.33929i	0.268083	−	0.157403i
$761$	8.42092	+	14.5855i	0.305258	+	0.528722i	0.977319	−	0.211774i	$-0.0679240\pi$
$761$	8.42092	+	14.5855i	0.305258	+	0.528722i	−0.672061	+	0.740496i	$0.734591\pi$
$762$	63.1828			2.28887
$763$	−0.790932	+	6.03627i	−0.0286337	+	0.218528i
$764$	6.35009			0.229738
$765$	−25.0104	+	0.182902i	−0.904252	+	0.00661282i
$766$	1.25922	−	2.18103i	0.0454975	−	0.0788039i
$767$	−18.7682	+	32.5076i	−0.677682	+	1.17378i
$768$	−1.64811	−	2.85461i	−0.0594710	−	0.103007i
$769$	1.64550			0.0593383			0.0296692	−	0.999560i	$-0.490555\pi$
$769$	1.64550			0.0593383			0.0296692	+	0.999560i	$0.490555\pi$
$770$	5.25323	+	18.9051i	0.189313	+	0.681293i
$771$	−20.3056			−0.731287
$772$	2.33260	+	4.04017i	0.0839520	+	0.145409i
$773$	0.00852631	−	0.0147680i	0.000306670	−	0.000531168i	−0.865872	−	0.500266i	$-0.833236\pi$
$773$	0.00852631	−	0.0147680i	0.000306670	−	0.000531168i	0.866179	+	0.499734i	$0.166569\pi$
$774$	−15.2666	+	26.4426i	−0.548747	+	0.950458i
$775$	23.7979	+	13.2795i	0.854844	+	0.477013i
$776$	−2.51839			−0.0904050
$777$	−50.8072	+	21.0815i	−1.82270	+	0.756293i
$778$	−31.4223			−1.12654
$779$	−18.2573	−	31.6226i	−0.654135	−	1.13300i
$780$	−12.2299	−	20.8296i	−0.437902	−	0.745819i
$781$	−23.7467	−	18.1721i	−0.849724	−	0.650247i
$782$	1.60913	+	2.78709i	0.0575423	+	0.0996663i
$783$			33.1016i			1.18296i
$784$	6.76369	+	1.80345i	0.241560	+	0.0644091i
$785$	−16.8900	−	9.58743i	−0.602829	−	0.342190i
$786$	28.2894	+	48.9986i	1.00905	+	1.74772i
$787$	11.4364	+	6.60281i	0.407664	+	0.235365i	0.689785	−	0.724014i	$-0.257705\pi$
$787$	11.4364	+	6.60281i	0.407664	+	0.235365i	−0.282122	+	0.959379i	$0.591038\pi$
$788$	7.32866	−	12.6936i	0.261073	−	0.452191i
$789$	−2.59956	−	4.50257i	−0.0925467	−	0.160296i
$790$	0.462054	−	0.813991i	0.0164392	−	0.0289605i
$791$	0.606879	−	0.251813i	0.0215781	−	0.00895344i
$792$	3.37091	−	25.8667i	0.119780	−	0.919133i
$793$	−4.78453	+	2.76235i	−0.169904	+	0.0980938i
$794$	2.07433	−	3.59285i	0.0736153	−	0.127506i
$795$	−22.7605	−	38.7649i	−0.807232	−	1.37485i
$796$	8.63358	−	4.98460i	0.306009	−	0.176675i
$797$	−21.2116			−0.751355			−0.375677	−	0.926751i	$-0.622590\pi$
$797$	−21.2116			−0.751355			−0.375677	+	0.926751i	$0.622590\pi$
$798$	20.3317	−	26.5304i	0.719735	−	0.939167i
$799$			18.2653i			0.646179i
$800$	2.43640	−	4.36623i	0.0861399	−	0.154369i
$801$	58.8048	+	33.9510i	2.07777	+	1.19960i
$802$	7.21306	−	12.4934i	0.254702	−	0.441157i
$803$	17.2244	+	41.4297i	0.607836	+	1.46202i
$804$			19.0028i			0.670176i
$805$	8.06556	−	10.6855i	0.284273	−	0.376615i
$806$	−17.8620			−0.629162
$807$	51.3043	−	29.6206i	1.80600	−	1.04269i
$808$	−5.22461	+	9.04930i	−0.183801	+	0.318353i
$809$	−10.9708	−	6.33399i	−0.385712	−	0.222691i	0.294588	−	0.955624i	$-0.404817\pi$
$809$	−10.9708	−	6.33399i	−0.385712	−	0.222691i	−0.680301	+	0.732933i	$0.738151\pi$
$810$	−0.478523	−	65.4343i	−0.0168136	−	2.29913i
$811$	−2.30453			−0.0809231			−0.0404616	−	0.999181i	$-0.512883\pi$
$811$	−2.30453			−0.0809231			−0.0404616	+	0.999181i	$0.512883\pi$
$812$	−0.709527	+	5.41500i	−0.0248995	+	0.190029i
$813$	93.3707			3.27465
$814$	8.03089	+	19.3166i	0.281482	+	0.677046i
$815$	18.3374	+	31.2317i	0.642332	+	1.09400i
$816$	4.05968	+	2.34386i	0.142117	+	0.0820514i
$817$	7.43961	+	12.8858i	0.260279	+	0.450817i
$818$	13.5919			0.475230
$819$	−54.1277	−	41.4810i	−1.89138	−	1.44946i
$820$	−18.5264	−	10.5163i	−0.646970	−	0.367247i
$821$	19.9128	−	11.4967i	0.694963	−	0.401237i	−0.110506	−	0.993875i	$-0.535247\pi$
$821$	19.9128	−	11.4967i	0.694963	−	0.401237i	0.805469	+	0.592639i	$0.201914\pi$
$822$	2.25230	+	1.30037i	0.0785582	+	0.0453556i
$823$	−6.02644	−	3.47937i	−0.210068	−	0.121283i	0.391275	−	0.920274i	$-0.372034\pi$
$823$	−6.02644	−	3.47937i	−0.210068	−	0.121283i	−0.601343	+	0.798991i	$0.705368\pi$
$824$	−1.99232	−	3.45080i	−0.0694058	−	0.120214i
$825$	50.1609	−	21.7202i	1.74638	−	0.756202i
$826$	−27.9904	+	11.6141i	−0.973911	+	0.404106i
$827$	−10.6118			−0.369010			−0.184505	−	0.982832i	$-0.559068\pi$
$827$	−10.6118			−0.369010			−0.184505	+	0.982832i	$0.559068\pi$
$828$	−15.4137	+	8.89912i	−0.535664	+	0.309266i
$829$	−47.7056	−	27.5428i	−1.65688	−	0.956602i	−0.974140	−	0.225944i	$-0.927453\pi$
$829$	−47.7056	−	27.5428i	−1.65688	−	0.956602i	−0.682744	−	0.730658i	$-0.739213\pi$
$830$	−15.0549	−	25.6410i	−0.522565	−	0.890014i
$831$	6.79173	+	11.7636i	0.235602	+	0.408075i
$832$			3.27717i			0.113615i
$833$	−9.61268	+	2.58833i	−0.333059	+	0.0896802i
$834$	−6.47279			−0.224135
$835$	19.7318	−	0.144299i	0.682847	−	0.00499368i
$836$	−10.0950	−	7.72519i	−0.349144	−	0.267181i
$837$	−75.6947	−	43.7024i	−2.61639	−	1.51057i
$838$	24.2900	−	14.0238i	0.839084	−	0.484445i
$839$		−	6.96852i		−	0.240580i	−0.992739	−	0.120290i	$-0.961618\pi$
$839$		−	6.96852i		−	0.240580i	0.992739	−	0.120290i	$-0.0383825\pi$
$840$	2.39205	−	19.3534i	0.0825336	−	0.667756i
$841$	24.7392			0.853076
$842$	2.88379	+	4.99487i	0.0993820	+	0.172135i
$843$	−79.2535	−	45.7570i	−2.72964	−	1.57596i
$844$	21.7335	+	12.5478i	0.748097	+	0.431914i
$845$	−0.0369584	−	5.05377i	−0.00127141	−	0.173855i
$846$	−101.014			−3.47294
$847$	23.0317	−	17.7915i	0.791380	−	0.611325i
$848$			6.09896i			0.209439i
$849$	−33.5795	+	19.3871i	−1.15245	+	0.665365i
$850$	0.103997	+	7.10999i	0.00356706	+	0.243871i
$851$	7.13675	−	12.3612i	0.244645	−	0.423737i
$852$	14.8590	+	25.7366i	0.509061	+	0.881720i
$853$		−	10.9180i		−	0.373825i	−0.982377	−	0.186913i	$-0.940152\pi$
$853$		−	10.9180i		−	0.373825i	0.982377	−	0.186913i	$-0.0598482\pi$
$854$	−4.42244	−	0.579472i	−0.151333	−	0.0198291i
$855$	−58.6198	−	33.2750i	−2.00475	−	1.13798i
$856$	−1.21293	−	2.10086i	−0.0414572	−	0.0718060i
$857$	35.8830	+	20.7171i	1.22574	+	0.707682i	0.966136	−	0.258033i	$-0.0830743\pi$
$857$	35.8830	+	20.7171i	1.22574	+	0.707682i	0.259605	+	0.965715i	$0.416408\pi$
$858$	−21.7728	+	28.4521i	−0.743312	+	0.971338i
$859$	33.0541	−	19.0838i	1.12779	−	0.651131i	0.184414	−	0.982849i	$-0.440961\pi$
$859$	33.0541	−	19.0838i	1.12779	−	0.651131i	0.943379	+	0.331717i	$0.107628\pi$
$860$	7.54928	+	4.28527i	0.257428	+	0.146127i
$861$	−82.3808	−	10.7943i	−2.80753	−	0.367870i
$862$		−	10.9981i		−	0.374596i
$863$	22.4038	−	12.9348i	0.762633	−	0.440307i	−0.0676070	−	0.997712i	$-0.521536\pi$
$863$	22.4038	−	12.9348i	0.762633	−	0.440307i	0.830240	+	0.557405i	$0.188203\pi$
$864$	−8.01813	+	13.8878i	−0.272782	+	0.472473i
$865$	−13.4997	−	22.9923i	−0.459004	−	0.781760i
$866$	15.1882	+	26.3067i	0.516114	+	0.893937i
$867$	49.3691			1.67666
$868$	−11.4459	−	8.77164i	−0.388500	−	0.297729i
$869$	−1.37666	−	0.179404i	−0.0466998	−	0.00608585i
$870$	15.2137	−	0.111258i	0.515793	−	0.00377201i
$871$	9.44647	−	16.3618i	0.320081	−	0.554397i
$872$	−1.99272	−	1.15050i	−0.0674821	−	0.0389608i
$873$	9.90364	+	17.1536i	0.335187	+	0.580562i
$874$			8.67330i			0.293379i
$875$	27.0665	−	11.9333i	0.915016	−	0.403419i
$876$		−	44.5915i		−	1.50661i
$877$	−18.5247	−	32.0858i	−0.625536	−	1.08346i	−0.988437	−	0.151632i	$-0.951547\pi$
$877$	−18.5247	−	32.0858i	−0.625536	−	1.08346i	0.362901	−	0.931828i	$-0.381786\pi$
$878$	−19.8468	+	34.3757i	−0.669798	+	1.16012i
$879$	78.1952	+	45.1460i	2.63746	+	1.52274i
$880$	−7.36083	−	0.904560i	−0.248133	−	0.0304927i
$881$			18.9257i			0.637622i	0.947818	+	0.318811i	$0.103284\pi$
$881$			18.9257i			0.637622i	−0.947818	+	0.318811i	$0.896716\pi$
$882$	−14.3145	−	53.1619i	−0.481993	−	1.79005i
$883$		−	49.8207i		−	1.67660i	−0.545209	−	0.838300i	$-0.683550\pi$
$883$		−	49.8207i		−	1.67660i	0.545209	−	0.838300i	$-0.316450\pi$
$884$	−2.33031	−	4.03622i	−0.0783768	−	0.135753i
$885$	42.7446	+	72.8010i	1.43684	+	2.44718i
$886$	17.3710	+	10.0291i	0.583589	+	0.336935i
$887$	36.3281	−	20.9741i	1.21978	−	0.704240i	0.254908	−	0.966965i	$-0.417955\pi$
$887$	36.3281	−	20.9741i	1.21978	−	0.704240i	0.964871	+	0.262726i	$0.0846214\pi$
$888$		−	20.7908i		−	0.697693i
$889$	−19.4363	−	46.8422i	−0.651872	−	1.57104i
$890$	9.52989	−	16.7886i	0.319443	−	0.562755i
$891$	−89.6205	+	37.2598i	−3.00240	+	1.24825i
$892$	−0.0679151	+	0.117632i	−0.00227397	+	0.00393863i
$893$	−24.6127	+	42.6305i	−0.823634	+	1.42658i
$894$	−24.8428	+	14.3430i	−0.830868	+	0.479702i
$895$	23.8732	+	13.5514i	0.797992	+	0.452972i
$896$	−1.60935	+	2.10000i	−0.0537645	+	0.0701561i
$897$	24.4450			0.816195
$898$	13.5888	+	23.5364i	0.453463	+	0.785421i
$899$	5.62532	−	9.74335i	0.187615	−	0.324959i
$900$	−39.3211	+	0.575143i	−1.31070	+	0.0191714i
$901$	−4.33682	−	7.51159i	−0.144480	−	0.250247i
$902$	−4.08322	+	31.3326i	−0.135957	+	1.04326i
$903$	33.5691	+	4.39856i	1.11711	+	0.146375i
$904$			0.248341i			0.00825969i
$905$	3.62073	−	0.0264785i	0.120357	−	0.000880176i
$906$	32.0827	+	18.5229i	1.06587	+	0.615383i
$907$	2.14802	+	1.24016i	0.0713238	+	0.0411788i	0.535238	−	0.844701i	$-0.320222\pi$
$907$	2.14802	+	1.24016i	0.0713238	+	0.0411788i	−0.463914	+	0.885880i	$0.653555\pi$
$908$	19.4884	−	11.2517i	0.646746	−	0.373399i
$909$	82.1837			2.72586
$910$	−11.6804	+	15.4746i	−0.387201	+	0.512977i
$911$	38.3067			1.26916			0.634578	−	0.772859i	$-0.281174\pi$
$911$	38.3067			1.26916			0.634578	+	0.772859i	$0.281174\pi$
$912$	6.31677	+	10.9410i	0.209169	+	0.362291i
$913$	−26.8021	+	35.0242i	−0.887021	+	1.15913i
$914$	−10.0541	+	17.4142i	−0.332560	+	0.576010i
$915$	0.0908650	+	12.4251i	0.00300390	+	0.410760i
$916$			23.2189i			0.767175i
$917$	27.6240	−	36.0460i	0.912225	−	1.19034i
$918$		−	22.8060i		−	0.752709i
$919$	−12.9407	+	7.47131i	−0.426874	+	0.246456i	−0.698014	−	0.716084i	$-0.745933\pi$
$919$	−12.9407	+	7.47131i	−0.426874	+	0.246456i	0.271140	+	0.962540i	$0.412599\pi$
$920$	2.56204	+	4.36357i	0.0844679	+	0.143863i
$921$	−82.0981	−	47.3993i	−2.70522	−	1.56186i
$922$	−2.54527	−	4.40854i	−0.0838241	−	0.145188i
$923$		−	29.5463i		−	0.972527i
$924$	−27.9242	+	7.53986i	−0.918638	+	0.248043i
$925$	27.0786	−	16.1664i	0.890339	−	0.531549i
$926$	−31.0037	+	17.9000i	−1.01884	+	0.588230i
$927$	−15.6697	+	27.1407i	−0.514661	+	0.891418i
$928$	−1.78763	−	1.03209i	−0.0586817	−	0.0338799i
$929$	12.6744	−	7.31759i	0.415835	−	0.240082i	−0.277459	−	0.960738i	$-0.589492\pi$
$929$	12.6744	−	7.31759i	0.415835	−	0.240082i	0.693294	+	0.720655i	$0.256159\pi$
$930$	−19.8315	+	34.9366i	−0.650299	+	1.14562i
$931$	−25.9234	−	6.91216i	−0.849607	−	0.226537i
$932$	18.8947			0.618915
$933$	−74.4563	+	42.9873i	−2.43759	+	1.40734i
$934$	−10.5234	+	18.2270i	−0.344335	+	0.596406i
$935$	9.70893	−	4.12003i	0.317516	−	0.134739i
$936$	22.3219	−	12.8875i	0.729613	−	0.421243i
$937$			27.4096i			0.895433i	0.894176	+	0.447717i	$0.147763\pi$
$937$			27.4096i			0.895433i	−0.894176	+	0.447717i	$0.852237\pi$
$938$	14.0882	−	5.84562i	0.459996	−	0.190866i
$939$	20.1817			0.658605
$940$	0.210016	+	28.7180i	0.00684996	+	0.936679i
$941$	−26.1362	+	45.2693i	−0.852017	+	1.47574i	0.0273685	+	0.999625i	$0.491287\pi$
$941$	−26.1362	+	45.2693i	−0.852017	+	1.47574i	−0.879385	+	0.476111i	$0.842046\pi$
$942$	14.3147	−	24.7937i	0.466397	−	0.807823i
$943$	18.6708	−	10.7796i	0.608006	−	0.351033i
$944$		−	11.4539i		−	0.372794i
$945$	−87.3597	+	36.9994i	−2.84181	+	1.20359i
$946$	1.66386	−	12.7676i	0.0540968	−	0.415112i
$947$	36.9304	−	21.3218i	1.20008	−	0.692864i	0.239504	−	0.970895i	$-0.423015\pi$
$947$	36.9304	−	21.3218i	1.20008	−	0.692864i	0.960572	+	0.278031i	$0.0896818\pi$
$948$	1.19490	+	0.689877i	0.0388086	+	0.0224062i
$949$	−22.1669	+	38.3942i	−0.719567	+	1.24633i
$950$	−9.33809	+	16.7346i	−0.302968	+	0.542942i
$951$			68.5269i			2.22214i
$952$	0.488841	−	3.73076i	0.0158434	−	0.120915i
$953$	−18.0493			−0.584674			−0.292337	−	0.956315i	$-0.594433\pi$
$953$	−18.0493			−0.584674			−0.292337	+	0.956315i	$0.594433\pi$
$954$	41.5421	−	23.9843i	1.34497	−	0.776521i
$955$	−12.2446	+	7.18935i	−0.396228	+	0.232642i
$956$	−2.76287	−	1.59514i	−0.0893576	−	0.0515907i
$957$	−8.66304	−	20.8371i	−0.280036	−	0.673568i
$958$	−23.0551			−0.744875
$959$	0.271209	−	2.06982i	0.00875778	−	0.0668381i
$960$	6.40988	+	3.63851i	0.206878	+	0.117432i
$961$	−0.646355	−	1.11952i	−0.0208502	−	0.0361135i
$962$	−10.3353	+	17.9013i	−0.333224	+	0.577161i
$963$	−9.53978	+	16.5234i	−0.307415	+	0.532459i
$964$	11.2617	+	19.5059i	0.362717	+	0.628243i
$965$	−9.07201	−	5.14964i	−0.292038	−	0.165773i
$966$	15.6643	+	12.0044i	0.503991	+	0.386236i
$967$	−30.8524			−0.992148			−0.496074	−	0.868280i	$-0.665226\pi$
$967$	−30.8524			−0.992148			−0.496074	+	0.868280i	$0.665226\pi$
$968$	2.87487	+	10.6177i	0.0924018	+	0.341265i
$969$	−15.5597	−	8.98339i	−0.499849	−	0.288588i
$970$	4.85612	−	2.85124i	0.155921	−	0.0915477i
$971$	−41.4583	+	23.9360i	−1.33046	+	0.768142i	−0.985370	−	0.170428i	$-0.945485\pi$
$971$	−41.4583	+	23.9360i	−1.33046	+	0.768142i	−0.345090	+	0.938569i	$0.612152\pi$
$972$	48.3513			1.55087
$973$	1.99116	+	4.79877i	0.0638336	+	0.153842i
$974$		−	35.6707i		−	1.14296i
$975$	47.1651	+	26.3187i	1.51049	+	0.842871i
$976$	0.842907	−	1.45996i	0.0269808	−	0.0467321i
$977$	6.51275	+	3.76014i	0.208361	+	0.120297i	0.600550	−	0.799588i	$-0.294949\pi$
$977$	6.51275	+	3.76014i	0.208361	+	0.120297i	−0.392188	+	0.919885i	$0.628282\pi$
$978$	−46.2355	+	26.6941i	−1.47845	+	0.853582i
$979$	−28.3936	−	3.70021i	−0.907463	−	0.118259i
$980$	−15.0840	+	4.18008i	−0.481841	+	0.133528i
$981$			18.0975i			0.577808i
$982$	−10.4841	+	6.05299i	−0.334560	+	0.193159i
$983$	4.26160	−	7.38131i	0.135924	−	0.235427i	−0.790026	−	0.613073i	$-0.789933\pi$
$983$	4.26160	−	7.38131i	0.135924	−	0.235427i	0.925950	+	0.377646i	$0.123266\pi$
$984$	15.7016	−	27.1959i	0.500548	−	0.866975i
$985$	0.239677	+	32.7739i	0.00763673	+	1.04426i
$986$	2.93556			0.0934873
$987$	42.9267	+	103.455i	1.36637	+	3.29301i
$988$		−	12.5605i		−	0.399603i
$989$	−7.60813	+	4.39255i	−0.241924	+	0.139675i
$990$	22.7854	+	53.6943i	0.724167	+	1.70652i
$991$	−10.3405	+	17.9102i	−0.328476	+	0.568937i	−0.982210	−	0.187788i	$-0.939868\pi$
$991$	−10.3405	+	17.9102i	−0.328476	+	0.568937i	0.653734	+	0.756724i	$0.273202\pi$
$992$	4.72022	−	2.72522i	0.149867	−	0.0865258i
$993$	−53.1864			−1.68782
$994$	14.5095	−	18.9332i	0.460214	−	0.600524i
$995$	−11.0044	+	19.3863i	−0.348864	+	0.614586i
$996$	37.9591	−	21.9157i	1.20278	−	0.694425i
$997$	−14.2425	−	8.22291i	−0.451064	−	0.260422i	0.257215	−	0.966354i	$-0.417195\pi$
$997$	−14.2425	−	8.22291i	−0.451064	−	0.260422i	−0.708280	+	0.705932i	$0.750528\pi$
$998$	−7.49926	+	12.9891i	−0.237385	+	0.411163i
$999$	−87.5969	+	50.5741i	−2.77144	+	1.60009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.a.549.2	yes	48
5.4	even	2		770.2.o.b.549.23	yes	48
7.5	odd	6	inner	770.2.o.a.439.23	yes	48
11.10	odd	2		770.2.o.b.549.2	yes	48
35.19	odd	6		770.2.o.b.439.2	yes	48
55.54	odd	2	inner	770.2.o.a.549.23	yes	48
77.54	even	6		770.2.o.b.439.23	yes	48
385.54	even	6	inner	770.2.o.a.439.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.2	✓	48	385.54	even	6	inner
770.2.o.a.439.23	yes	48	7.5	odd	6	inner
770.2.o.a.549.2	yes	48	1.1	even	1	trivial
770.2.o.a.549.23	yes	48	55.54	odd	2	inner
770.2.o.b.439.2	yes	48	35.19	odd	6
770.2.o.b.439.23	yes	48	77.54	even	6
770.2.o.b.549.2	yes	48	11.10	odd	2
770.2.o.b.549.23	yes	48	5.4	even	2

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.64811 + 2.85461i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0163520 - 2.23601i) q^{5} +3.29622 q^{6} +(-1.01398 - 2.44374i) q^{7} +1.00000 q^{8} +(-3.93253 - 6.81133i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.64811 + 2.85461i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0163520 - 2.23601i) q^{5} +3.29622 q^{6} +(-1.01398 - 2.44374i) q^{7} +1.00000 q^{8} +(-3.93253 - 6.81133i) q^{9} +(-1.92826 + 1.13217i) q^{10} +(2.63390 + 2.01558i) q^{11} +(-1.64811 - 2.85461i) q^{12} +3.27717i q^{13} +(-1.60935 + 2.10000i) q^{14} +(6.40988 + 3.63851i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.23162 + 0.711075i) q^{17} +(-3.93253 + 6.81133i) q^{18} +(1.91637 + 3.31925i) q^{19} +(1.94462 + 1.10384i) q^{20} +(8.64706 + 1.13302i) q^{21} +(0.428594 - 3.28882i) q^{22} +(-1.95978 + 1.13148i) q^{23} +(-1.64811 + 2.85461i) q^{24} +(-4.99947 + 0.0731264i) q^{25} +(2.83811 - 1.63858i) q^{26} +16.0363 q^{27} +(2.62333 + 0.343734i) q^{28} +2.06417i q^{29} +(-0.0538997 - 7.37037i) q^{30} +(-4.72022 - 2.72522i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-10.0946 + 4.19686i) q^{33} -1.42215i q^{34} +(-5.44763 + 2.30723i) q^{35} +7.86505 q^{36} +(-5.46243 + 3.15373i) q^{37} +(1.91637 - 3.31925i) q^{38} +(-9.35503 - 5.40113i) q^{39} +(-0.0163520 - 2.23601i) q^{40} -9.52703 q^{41} +(-3.34230 - 8.05508i) q^{42} +3.88214 q^{43} +(-3.06249 + 1.27323i) q^{44} +(-15.1659 + 8.90454i) q^{45} +(1.95978 + 1.13148i) q^{46} +(6.42172 + 11.1227i) q^{47} +3.29622 q^{48} +(-4.94368 + 4.95580i) q^{49} +(2.56306 + 4.29310i) q^{50} +(-4.05968 + 2.34386i) q^{51} +(-2.83811 - 1.63858i) q^{52} +(-5.28186 - 3.04948i) q^{53} +(-8.01813 - 13.8878i) q^{54} +(4.46379 - 5.92238i) q^{55} +(-1.01398 - 2.44374i) q^{56} -12.6335 q^{57} +(1.78763 - 1.03209i) q^{58} +(9.91941 + 5.72697i) q^{59} +(-6.35598 + 3.73186i) q^{60} +(0.842907 + 1.45996i) q^{61} +5.45044i q^{62} +(-12.6576 + 16.5166i) q^{63} +1.00000 q^{64} +(7.32777 - 0.0535882i) q^{65} +(8.68191 + 6.64379i) q^{66} +(-4.99265 - 2.88251i) q^{67} +(-1.23162 + 0.711075i) q^{68} -7.45919i q^{69} +(4.72194 + 3.56417i) q^{70} -9.01579 q^{71} +(-3.93253 - 6.81133i) q^{72} +(11.7157 + 6.76404i) q^{73} +(5.46243 + 3.15373i) q^{74} +(8.03092 - 14.3920i) q^{75} -3.83274 q^{76} +(2.25482 - 8.48032i) q^{77} +10.8023i q^{78} +(-0.362507 + 0.209294i) q^{79} +(-1.92826 + 1.13217i) q^{80} +(-14.6319 + 25.3433i) q^{81} +(4.76352 + 8.25065i) q^{82} +13.2975i q^{83} +(-5.30476 + 6.92206i) q^{84} +(1.56983 - 2.76553i) q^{85} +(-1.94107 - 3.36203i) q^{86} +(-5.89240 - 3.40198i) q^{87} +(2.63390 + 2.01558i) q^{88} +(-7.47672 + 4.31669i) q^{89} +(15.2945 + 8.68178i) q^{90} +(8.00853 - 3.32299i) q^{91} -2.26295i q^{92} +(15.5589 - 8.98292i) q^{93} +(6.42172 - 11.1227i) q^{94} +(7.39053 - 4.33929i) q^{95} +(-1.64811 - 2.85461i) q^{96} -2.51839 q^{97} +(6.76369 + 1.80345i) q^{98} +(3.37091 - 25.8667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more