LMFDB - Embedded newform 770.2.o.a.439.2

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			439.2
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.2

$q$-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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.742103	−	0.670286i	$-0.766171\pi$
$3$	−1.64811	−	2.85461i	−0.951536	−	1.64811i	−0.209433	−	0.977823i	$-0.567162\pi$
$4$	−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	$-0.849832\pi$
$13$		−	3.27717i		−	0.908923i	0.890766	−	0.454461i	$-0.150168\pi$
$14$	−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	−0.343153	−	0.939280i	$-0.611495\pi$
$17$	1.23162	−	0.711075i	0.298711	−	0.172461i	0.641864	+	0.766819i	$0.278161\pi$
$18$	−3.93253	−	6.81133i	−0.926905	−	1.60545i
$19$	1.91637	−	3.31925i	0.439645	−	0.761487i	−0.558017	−	0.829829i	$-0.688438\pi$
$19$	1.91637	−	3.31925i	0.439645	−	0.761487i	0.997662	+	0.0683422i	$0.0217710\pi$
$20$	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	0.281564	−	0.959542i	$-0.409147\pi$
$23$	−1.95978	−	1.13148i	−0.408641	−	0.235929i	−0.690206	+	0.723613i	$0.742480\pi$
$24$	−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	$-0.938615\pi$
$29$		−	2.06417i		−	0.383307i	0.981463	−	0.191654i	$-0.0613850\pi$
$30$	−0.0538997	+	7.37037i	−0.00984070	+	1.34564i
$31$	−4.72022	+	2.72522i	−0.847776	+	0.489464i	−0.859900	−	0.510463i	$-0.829474\pi$
$31$	−4.72022	+	2.72522i	−0.847776	+	0.489464i	0.0121236	+	0.999927i	$0.496141\pi$
$32$	−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	−0.0214609	−	0.999770i	$-0.506832\pi$
$37$	−5.46243	−	3.15373i	−0.898017	−	0.518471i	−0.876556	+	0.481299i	$0.840165\pi$
$38$	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	0.165137	−	0.986271i	$-0.447193\pi$
$47$	6.42172	−	11.1227i	0.936704	−	1.62242i	0.771567	−	0.636148i	$-0.219473\pi$
$48$	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	−0.816781	−	0.576948i	$-0.804243\pi$
$53$	−5.28186	+	3.04948i	−0.725519	+	0.418878i	0.0912618	+	0.995827i	$0.470910\pi$
$54$	−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	0.312495	−	0.949919i	$-0.398835\pi$
$59$	9.91941	−	5.72697i	1.29140	−	0.745588i	0.978902	+	0.204331i	$0.0655019\pi$
$60$	−6.35598	−	3.73186i	−0.820553	−	0.481782i
$61$	0.842907	−	1.45996i	0.107923	−	0.186928i	−0.807006	−	0.590544i	$-0.798913\pi$
$61$	0.842907	−	1.45996i	0.107923	−	0.186928i	0.914929	+	0.403615i	$0.132247\pi$
$62$		−	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	−0.772946	−	0.634472i	$-0.781218\pi$
$67$	−4.99265	+	2.88251i	−0.609950	+	0.352155i	0.162996	+	0.986627i	$0.447884\pi$
$68$	−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	0.380133	−	0.924932i	$-0.375878\pi$
$73$	11.7157	−	6.76404i	1.37121	−	0.791671i	0.991081	+	0.133261i	$0.0425449\pi$
$74$	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	0.479469	−	0.877559i	$-0.340829\pi$
$79$	−0.362507	−	0.209294i	−0.0407852	−	0.0235474i	−0.520254	+	0.854012i	$0.674163\pi$
$80$	−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	$-0.739616\pi$
$83$		−	13.2975i		−	1.45959i	0.683667	−	0.729794i	$-0.260384\pi$
$84$	−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	0.0483217	−	0.998832i	$-0.484613\pi$
$89$	−7.47672	−	4.31669i	−0.792531	−	0.457568i	−0.840853	+	0.541264i	$0.817946\pi$
$90$	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	−0.999733	−	0.0230962i	$-0.992648\pi$
$101$	−5.22461	−	9.04930i	−0.519868	−	0.900439i	0.479865	−	0.877342i	$-0.340686\pi$
$102$	4.05968	−	2.34386i	0.401968	−	0.232076i
$103$	−1.99232	+	3.45080i	−0.196309	+	0.340018i	−0.947329	−	0.320262i	$-0.896229\pi$
$103$	−1.99232	+	3.45080i	−0.196309	+	0.340018i	0.751020	+	0.660280i	$0.229562\pi$
$104$		−	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	−0.918680	−	0.395002i	$-0.870744\pi$
$107$	−1.21293	+	2.10086i	−0.117259	+	0.203098i	0.801422	+	0.598100i	$0.204077\pi$
$108$	−8.01813	−	13.8878i	−0.771545	−	1.33636i
$109$	−1.99272	+	1.15050i	−0.190868	+	0.110198i	−0.592389	−	0.805652i	$-0.701815\pi$
$109$	−1.99272	+	1.15050i	−0.190868	+	0.110198i	0.401521	+	0.915850i	$0.368482\pi$
$110$	−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	$-0.996282\pi$
$113$		−	0.248341i		−	0.0233619i	0.999932	−	0.0116810i	$-0.00371825\pi$
$114$	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	−0.198051	−	0.980192i	$-0.563461\pi$
$131$	8.58237	−	14.8651i	0.749845	−	1.29877i	0.947896	−	0.318578i	$-0.103205\pi$
$132$	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	−0.470527	−	0.882386i	$-0.655936\pi$
$137$	0.683300	−	0.394503i	0.0583782	−	0.0337047i	0.528905	+	0.848681i	$0.322603\pi$
$138$	−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	0.158434	−	0.987370i	$-0.449355\pi$
$149$	−7.53677	−	4.35135i	−0.617436	−	0.356477i	−0.775870	+	0.630893i	$0.782689\pi$
$150$	−16.4793	−	0.241041i	−1.34553	−	0.0196809i
$151$	9.73317	−	5.61945i	0.792074	−	0.457304i	−0.0486179	−	0.998817i	$-0.515482\pi$
$151$	9.73317	−	5.61945i	0.792074	−	0.457304i	0.840692	+	0.541513i	$0.182148\pi$
$152$	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	0.985641	−	0.168853i	$-0.0540064\pi$
$157$	4.34275	+	7.52187i	0.346589	+	0.600310i	−0.639052	+	0.769164i	$0.720673\pi$
$158$	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	−0.162795	−	0.986660i	$-0.552051\pi$
$163$	−14.0268	−	8.09839i	−1.09867	−	0.634315i	−0.935870	+	0.352345i	$0.885384\pi$
$164$	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	$-0.889088\pi$
$167$		−	8.82456i		−	0.682865i	0.939906	−	0.341433i	$-0.110912\pi$
$168$	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	0.838233	−	0.545312i	$-0.183589\pi$
$173$	10.3263	+	5.96191i	0.785096	+	0.453275i	−0.0531373	+	0.998587i	$0.516922\pi$
$174$		−	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	0.540102	−	0.841600i	$-0.318386\pi$
$179$	−6.13827	−	10.6318i	−0.458796	−	0.794658i	−0.998898	+	0.0469420i	$0.985052\pi$
$180$	−0.128609	+	17.5863i	−0.00958597	+	1.31081i
$181$		−	1.61928i		−	0.120360i	−0.998188	−	0.0601802i	$-0.980832\pi$
$181$		−	1.61928i		−	0.120360i	0.998188	−	0.0601802i	$-0.0191675\pi$
$182$	−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	−0.957730	−	0.287667i	$-0.907120\pi$
$191$	−3.17504	+	5.49934i	−0.229738	+	0.397918i	0.727992	+	0.685585i	$0.240454\pi$
$192$	−1.64811	−	2.85461i	−0.118942	−	0.206014i
$193$	2.33260	+	4.04017i	0.167904	+	0.290818i	0.937683	−	0.347493i	$-0.112967\pi$
$193$	2.33260	+	4.04017i	0.167904	+	0.290818i	−0.769779	+	0.638311i	$0.779633\pi$
$194$	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	−0.773755	−	0.633485i	$-0.781624\pi$
$199$	−8.63358	+	4.98460i	−0.612019	+	0.353349i	0.161737	+	0.986834i	$0.448291\pi$
$200$	−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	$0.331940\pi$
$211$			25.0957i			1.72766i	−0.503787	+	0.863828i	$0.668060\pi$
$212$	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	−0.979272	−	0.202551i	$-0.935077\pi$
$227$	−19.4884	+	11.2517i	−1.29349	+	0.746798i	−0.314221	+	0.949350i	$0.601743\pi$
$228$	6.31677	+	10.9410i	0.418338	+	0.724583i
$229$	20.1082	+	11.6095i	1.32879	+	0.767175i	0.985112	−	0.171914i	$-0.0549952\pi$
$229$	20.1082	+	11.6095i	1.32879	+	0.767175i	0.343674	+	0.939089i	$0.388329\pi$
$230$	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	0.370769	+	0.928725i	$0.379094\pi$
$233$	−9.44733	+	16.3632i	−0.618915	+	1.07199i	−0.989684	+	0.143267i	$0.954239\pi$
$234$	−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	$-0.967098\pi$
$239$		−	3.19029i		−	0.206363i	0.994663	−	0.103181i	$-0.0329022\pi$
$240$	−0.0538997	+	7.37037i	−0.00347921	+	0.475755i
$241$	11.2617	+	19.5059i	0.725433	+	1.25649i	0.958796	+	0.284097i	$0.0916938\pi$
$241$	11.2617	+	19.5059i	0.725433	+	1.25649i	−0.233362	+	0.972390i	$0.574973\pi$
$242$	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	$0.0473993\pi$
$251$			4.70092i			0.296719i	−0.988933	+	0.148360i	$0.952601\pi$
$252$	−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	−0.753824	−	0.657077i	$-0.771793\pi$
$257$	3.08013	−	5.33494i	0.192133	−	0.332784i	0.945957	+	0.324292i	$0.105126\pi$
$258$	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	0.840686	−	0.541523i	$-0.182152\pi$
$263$	−0.788649	−	1.36598i	−0.0486302	−	0.0842299i	−0.889316	+	0.457293i	$0.848819\pi$
$264$	−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	−0.892767	−	0.450518i	$-0.851239\pi$
$269$	−15.5646	+	8.98623i	−0.948990	+	0.547900i	−0.0562232	+	0.998418i	$0.517906\pi$
$270$	−30.9222	−	18.1557i	−1.88186	−	1.10492i
$271$	−14.1633	+	24.5316i	−0.860360	+	1.49019i	0.0112225	+	0.999937i	$0.496428\pi$
$271$	−14.1633	+	24.5316i	−0.860360	+	1.49019i	−0.871582	+	0.490250i	$0.836906\pi$
$272$			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	0.921264	−	0.388939i	$-0.127158\pi$
$277$	2.06046	+	3.56882i	0.123801	+	0.214430i	−0.797463	+	0.603368i	$0.793825\pi$
$278$	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	$-0.689415\pi$
$281$		−	27.7634i		−	1.65622i	0.560563	−	0.828111i	$-0.310585\pi$
$282$	21.1674	−	36.6630i	1.26050	−	2.18325i
$283$	10.1873	−	5.88163i	0.605571	−	0.349627i	−0.165659	−	0.986183i	$-0.552975\pi$
$283$	10.1873	−	5.88163i	0.605571	−	0.349627i	0.771230	+	0.636556i	$0.219642\pi$
$284$	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	$0.295245\pi$
$293$			27.3926i			1.60029i	−0.599804	+	0.800147i	$0.704755\pi$
$294$	−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	$-0.693581\pi$
$307$		−	28.7598i		−	1.64141i	0.571352	−	0.820705i	$-0.306419\pi$
$308$	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	0.303863	−	0.952716i	$-0.401724\pi$
$311$	22.5884	−	13.0414i	1.28087	−	0.739511i	0.977007	+	0.213205i	$0.0683902\pi$
$312$	−9.35503	+	5.40113i	−0.529624	+	0.305779i
$313$	−3.06134	+	5.30240i	−0.173037	+	0.299709i	−0.939480	−	0.342603i	$-0.888691\pi$
$313$	−3.06134	+	5.30240i	−0.173037	+	0.299709i	0.766443	+	0.642312i	$0.222025\pi$
$314$	−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	0.911549	−	0.411192i	$-0.134887\pi$
$317$	18.0043	+	10.3948i	1.01122	+	0.583829i	0.0996720	+	0.995020i	$0.468221\pi$
$318$	−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	−0.554497	−	0.832186i	$-0.687089\pi$
$331$	8.06779	−	13.9738i	0.443446	−	0.768071i	0.997942	+	0.0641153i	$0.0204225\pi$
$332$	−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	−0.949261	−	0.314491i	$-0.898166\pi$
$347$	−13.9148	−	24.1012i	−0.746987	−	1.29382i	0.202273	−	0.979329i	$-0.435167\pi$
$348$	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	0.969450	−	0.245290i	$-0.0788832\pi$
$353$	5.11600	+	8.86118i	0.272297	+	0.471633i	−0.697152	+	0.716923i	$0.745550\pi$
$354$	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	0.935871	−	0.352343i	$-0.114615\pi$
$359$	20.8168	+	12.0186i	1.09867	+	0.634317i	0.162798	+	0.986659i	$0.447948\pi$
$360$	−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	−0.999825	−	0.0187252i	$-0.994039\pi$
$367$	−9.88761	−	17.1258i	−0.516129	−	0.893961i	0.483696	−	0.875236i	$-0.339294\pi$
$368$	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	−0.225945	−	0.974140i	$-0.572547\pi$
$373$	14.1113	−	24.4416i	0.730658	−	1.26554i	0.956602	−	0.291396i	$-0.0941199\pi$
$374$	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	−0.832059	−	0.554687i	$-0.812838\pi$
$383$	1.25922	−	2.18103i	0.0643431	−	0.111446i	0.896402	+	0.443241i	$0.146171\pi$
$384$	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	0.921827	+	0.387603i	$0.126697\pi$
$389$	15.7112	+	27.2125i	0.796587	+	1.37973i	−0.125240	+	0.992127i	$0.539970\pi$
$390$	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	−0.809266	−	0.587443i	$-0.800135\pi$
$397$	2.07433	−	3.59285i	0.104108	−	0.180320i	0.913373	+	0.407123i	$0.133468\pi$
$398$		−	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	−0.627791	−	0.778382i	$-0.716041\pi$
$401$	7.21306	−	12.4934i	0.360203	−	0.623890i	0.987994	+	0.154492i	$0.0493741\pi$
$402$	−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	0.647645	−	0.761942i	$-0.275754\pi$
$409$	−6.79595	−	11.7709i	−0.336038	−	0.582035i	−0.983684	+	0.179907i	$0.942420\pi$
$410$	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	$-0.759755\pi$
$419$		−	28.0477i		−	1.37022i	0.728441	−	0.685109i	$-0.240245\pi$
$420$	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	−0.252749	−	0.967532i	$-0.581335\pi$
$431$	9.52461	−	5.49904i	0.458784	−	0.264879i	0.711533	+	0.702653i	$0.248001\pi$
$432$	−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	−0.196028	+	0.980598i	$0.562804\pi$
$439$	−19.8468	+	34.3757i	−0.947237	+	1.64066i	−0.751209	+	0.660065i	$0.770529\pi$
$440$	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	0.0269281	−	0.999637i	$-0.491427\pi$
$443$	−17.3710	−	10.0291i	−0.825319	−	0.476498i	−0.852247	+	0.523139i	$0.824761\pi$
$444$	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	−0.999424	−	0.0339496i	$-0.989191\pi$
$457$	−10.0541	+	17.4142i	−0.470311	+	0.814602i	0.529113	+	0.848551i	$0.322525\pi$
$458$	−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	$0.312737\pi$
$463$			35.8000i			1.66377i	−0.554952	+	0.831883i	$0.687263\pi$
$464$	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	−0.999888	−	0.0149884i	$-0.995229\pi$
$467$	−10.5234	+	18.2270i	−0.486964	+	0.843446i	0.512924	+	0.858434i	$0.328562\pi$
$468$		−	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	0.999516	+	0.0311174i	$0.00990657\pi$
$479$	11.5275	+	19.9663i	0.526706	+	0.912282i	−0.472809	+	0.881165i	$0.656760\pi$
$480$	−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	0.405463	−	0.914111i	$-0.367110\pi$
$487$	30.8917	−	17.8354i	1.39984	−	0.808197i	0.994375	+	0.105914i	$0.0337769\pi$
$488$	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	$0.0880713\pi$
$491$			12.1060i			0.546335i	−0.961966	+	0.273167i	$0.911929\pi$
$492$	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	−0.983622	−	0.180246i	$-0.942311\pi$
$499$	−7.49926	+	12.9891i	−0.335713	+	0.581472i	0.647909	+	0.761718i	$0.275644\pi$
$500$	−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	$-0.823848\pi$
$503$		−	23.5751i		−	1.05116i	0.850743	−	0.525582i	$-0.176152\pi$
$504$	−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	0.301714	−	0.953399i	$-0.402441\pi$
$509$	−8.41745	−	4.85982i	−0.373097	−	0.215408i	−0.674811	+	0.737991i	$0.735775\pi$
$510$	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	−0.142138	−	0.989847i	$-0.545398\pi$
$521$	14.7001	−	8.48713i	0.644025	−	0.371828i	0.786163	+	0.618019i	$0.212064\pi$
$522$	−14.0598	+	8.11741i	−0.615379	+	0.355289i
$523$	−26.4328	−	15.2610i	−1.15583	−	0.667317i	−0.205527	−	0.978651i	$-0.565891\pi$
$523$	−26.4328	−	15.2610i	−1.15583	−	0.667317i	−0.950301	+	0.311334i	$0.899224\pi$
$524$	−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	0.990007	−	0.141016i	$-0.0450368\pi$
$541$	31.7000	+	18.3020i	1.36289	+	0.786864i	0.372881	+	0.927879i	$0.378370\pi$
$542$	−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	0.874772	−	0.484534i	$-0.161011\pi$
$557$	0.419322	+	0.726287i	0.0177672	+	0.0307738i	−0.857005	+	0.515308i	$0.827678\pi$
$558$	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	−0.271771	−	0.962362i	$-0.587609\pi$
$563$	10.1026	−	5.83272i	0.425773	−	0.245820i	0.697544	+	0.716542i	$0.254276\pi$
$564$	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	0.580099	−	0.814546i	$-0.303014\pi$
$569$	3.92946	+	2.26868i	0.164732	+	0.0951079i	−0.415368	+	0.909654i	$0.636347\pi$
$570$	24.3608	+	14.3032i	1.02036	+	0.599097i
$571$	4.88332	−	2.81939i	0.204361	−	0.117988i	−0.394327	−	0.918970i	$-0.629022\pi$
$571$	4.88332	−	2.81939i	0.204361	−	0.117988i	0.598688	+	0.800982i	$0.295689\pi$
$572$	−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	−0.958192	−	0.286127i	$-0.907632\pi$
$577$	−17.4605	−	30.2424i	−0.726889	−	1.25901i	0.231302	−	0.972882i	$-0.425701\pi$
$578$	−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	0.401338	−	0.915930i	$-0.368545\pi$
$593$	−4.65629	−	2.68831i	−0.191211	−	0.110396i	−0.592549	+	0.805534i	$0.701878\pi$
$594$	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	0.714336	−	0.699803i	$-0.246729\pi$
$599$	−6.09118	−	10.5502i	−0.248879	−	0.431071i	−0.963215	+	0.268732i	$0.913395\pi$
$600$	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	−0.357063	−	0.934080i	$-0.616222\pi$
$607$	−33.1257	−	19.1251i	−1.34453	−	0.776265i	−0.987469	+	0.157815i	$0.949555\pi$
$608$	−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	0.975738	−	0.218940i	$-0.0702599\pi$
$613$	7.38461	+	12.7905i	0.298261	+	0.516604i	−0.677477	+	0.735544i	$0.736927\pi$
$614$	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	$0.103305\pi$
$617$			15.8413i			0.637749i	−0.947797	+	0.318874i	$0.896695\pi$
$618$	−6.56712	+	11.3746i	−0.264168	+	0.457553i
$619$	15.0638	−	8.69709i	0.605466	−	0.349566i	−0.165723	−	0.986172i	$-0.552996\pi$
$619$	15.0638	−	8.69709i	0.605466	−	0.349566i	0.771189	+	0.636607i	$0.219662\pi$
$620$	−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	−0.999985	−	0.00540601i	$-0.998279\pi$
$641$	−12.7773	−	22.1310i	−0.504674	−	0.874122i	0.495311	−	0.868716i	$-0.335054\pi$
$642$	−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	0.619529	−	0.784974i	$-0.287324\pi$
$647$	−9.41249	−	16.3029i	−0.370043	−	0.640933i	−0.989572	+	0.144041i	$0.953990\pi$
$648$	−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	0.594686	−	0.803958i	$-0.297276\pi$
$653$	5.00294	+	2.88845i	0.195780	+	0.113034i	−0.398905	+	0.916992i	$0.630610\pi$
$654$	−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	$-0.900539\pi$
$659$		−	15.7828i		−	0.614812i	0.951578	−	0.307406i	$-0.0994610\pi$
$660$	−24.2629	+	2.98163i	−0.944432	+	0.116060i
$661$	−11.7074	+	6.75925i	−0.455364	+	0.262904i	−0.710093	−	0.704108i	$-0.751347\pi$
$661$	−11.7074	+	6.75925i	−0.455364	+	0.262904i	0.254729	+	0.967012i	$0.418014\pi$
$662$	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	−0.296095	−	0.955159i	$-0.595684\pi$
$677$	−33.0791	−	19.0982i	−1.27133	−	0.734005i	−0.975239	+	0.221154i	$0.929018\pi$
$678$		−	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	−0.215490	−	0.976506i	$-0.569135\pi$
$683$	13.6537	−	7.88296i	0.522444	−	0.301633i	0.737934	+	0.674873i	$0.235802\pi$
$684$	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	0.928889	−	0.370359i	$-0.120765\pi$
$691$	28.1951	+	16.2785i	1.07259	+	0.619262i	0.143704	+	0.989621i	$0.454099\pi$
$692$		−	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	$-0.868578\pi$
$701$		−	21.2469i		−	0.802485i	0.915972	−	0.401243i	$-0.131422\pi$
$702$	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	−0.978715	−	0.205222i	$-0.934208\pi$
$709$	−8.29779	+	14.3722i	−0.311630	+	0.539759i	0.667085	+	0.744981i	$0.267542\pi$
$710$	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	0.566664	−	0.823949i	$-0.308234\pi$
$719$	3.65839	+	2.11217i	0.136435	+	0.0787708i	−0.430229	+	0.902720i	$0.641567\pi$
$720$	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	0.670212	−	0.742170i	$-0.266203\pi$
$733$	9.81646	+	5.66754i	0.362579	+	0.209335i	−0.307632	+	0.951505i	$0.599537\pi$
$734$	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	−0.426878	−	0.904309i	$-0.640387\pi$
$739$	3.88297	−	2.24184i	0.142837	−	0.0824673i	0.569716	+	0.821842i	$0.307053\pi$
$740$	−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	−0.758583	−	0.651577i	$-0.774108\pi$
$751$	5.06956	−	8.78074i	0.184991	−	0.320414i	0.943573	+	0.331163i	$0.107441\pi$
$752$	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	$0.219566\pi$
$757$			35.0178i			1.27274i	−0.771382	+	0.636372i	$0.780434\pi$
$758$	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	−0.672061	−	0.740496i	$-0.734591\pi$
$761$	8.42092	−	14.5855i	0.305258	−	0.528722i	0.977319	+	0.211774i	$0.0679240\pi$
$762$	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	0.866179	−	0.499734i	$-0.166569\pi$
$773$	0.00852631	+	0.0147680i	0.000306670	+	0.000531168i	−0.865872	+	0.500266i	$0.833236\pi$
$774$	−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	−0.282122	−	0.959379i	$-0.591038\pi$
$787$	11.4364	−	6.60281i	0.407664	−	0.235365i	0.689785	+	0.724014i	$0.257705\pi$
$788$	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	−0.680301	−	0.732933i	$-0.738151\pi$
$809$	−10.9708	+	6.33399i	−0.385712	+	0.222691i	0.294588	+	0.955624i	$0.404817\pi$
$810$	−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	0.805469	−	0.592639i	$-0.201914\pi$
$821$	19.9128	+	11.4967i	0.694963	+	0.401237i	−0.110506	+	0.993875i	$0.535247\pi$
$822$	2.25230	−	1.30037i	0.0785582	−	0.0453556i
$823$	−6.02644	+	3.47937i	−0.210068	+	0.121283i	−0.601343	−	0.798991i	$-0.705368\pi$
$823$	−6.02644	+	3.47937i	−0.210068	+	0.121283i	0.391275	+	0.920274i	$0.372034\pi$
$824$	−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	−0.682744	+	0.730658i	$0.739213\pi$
$829$	−47.7056	+	27.5428i	−1.65688	+	0.956602i	−0.974140	+	0.225944i	$0.927453\pi$
$830$	−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	$0.0383825\pi$
$839$			6.96852i			0.240580i	−0.992739	+	0.120290i	$0.961618\pi$
$840$	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	$0.0598482\pi$
$853$			10.9180i			0.373825i	−0.982377	+	0.186913i	$0.940152\pi$
$854$	−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	0.259605	−	0.965715i	$-0.416408\pi$
$857$	35.8830	−	20.7171i	1.22574	−	0.707682i	0.966136	+	0.258033i	$0.0830743\pi$
$858$	−21.7728	−	28.4521i	−0.743312	−	0.971338i
$859$	33.0541	+	19.0838i	1.12779	+	0.651131i	0.943379	−	0.331717i	$-0.107628\pi$
$859$	33.0541	+	19.0838i	1.12779	+	0.651131i	0.184414	+	0.982849i	$0.440961\pi$
$860$	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	0.830240	−	0.557405i	$-0.188203\pi$
$863$	22.4038	+	12.9348i	0.762633	+	0.440307i	−0.0676070	+	0.997712i	$0.521536\pi$
$864$	−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	0.362901	+	0.931828i	$0.381786\pi$
$877$	−18.5247	+	32.0858i	−0.625536	+	1.08346i	−0.988437	+	0.151632i	$0.951547\pi$
$878$	−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	$-0.896716\pi$
$881$		−	18.9257i		−	0.637622i	0.947818	−	0.318811i	$-0.103284\pi$
$882$	−14.3145	+	53.1619i	−0.481993	+	1.79005i
$883$			49.8207i			1.67660i	0.545209	+	0.838300i	$0.316450\pi$
$883$			49.8207i			1.67660i	−0.545209	+	0.838300i	$0.683550\pi$
$884$	−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	0.964871	−	0.262726i	$-0.0846214\pi$
$887$	36.3281	+	20.9741i	1.21978	+	0.704240i	0.254908	+	0.966965i	$0.417955\pi$
$888$			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	−0.463914	−	0.885880i	$-0.653555\pi$
$907$	2.14802	−	1.24016i	0.0713238	−	0.0411788i	0.535238	+	0.844701i	$0.320222\pi$
$908$	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	0.271140	−	0.962540i	$-0.412599\pi$
$919$	−12.9407	−	7.47131i	−0.426874	−	0.246456i	−0.698014	+	0.716084i	$0.745933\pi$
$920$	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	0.693294	−	0.720655i	$-0.256159\pi$
$929$	12.6744	+	7.31759i	0.415835	+	0.240082i	−0.277459	+	0.960738i	$0.589492\pi$
$930$	−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	$-0.852237\pi$
$937$		−	27.4096i		−	0.895433i	0.894176	−	0.447717i	$-0.147763\pi$
$938$	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	−0.879385	−	0.476111i	$-0.842046\pi$
$941$	−26.1362	−	45.2693i	−0.852017	−	1.47574i	0.0273685	−	0.999625i	$-0.491287\pi$
$942$	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	0.960572	−	0.278031i	$-0.0896818\pi$
$947$	36.9304	+	21.3218i	1.20008	+	0.692864i	0.239504	+	0.970895i	$0.423015\pi$
$948$	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	−0.345090	−	0.938569i	$-0.612152\pi$
$971$	−41.4583	−	23.9360i	−1.33046	−	0.768142i	−0.985370	+	0.170428i	$0.945485\pi$
$972$	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	−0.392188	−	0.919885i	$-0.628282\pi$
$977$	6.51275	−	3.76014i	0.208361	−	0.120297i	0.600550	+	0.799588i	$0.294949\pi$
$978$	−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	0.925950	−	0.377646i	$-0.123266\pi$
$983$	4.26160	+	7.38131i	0.135924	+	0.235427i	−0.790026	+	0.613073i	$0.789933\pi$
$984$	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	0.653734	−	0.756724i	$-0.273202\pi$
$991$	−10.3405	−	17.9102i	−0.328476	−	0.568937i	−0.982210	+	0.187788i	$0.939868\pi$
$992$	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	−0.708280	−	0.705932i	$-0.750528\pi$
$997$	−14.2425	+	8.22291i	−0.451064	+	0.260422i	0.257215	+	0.966354i	$0.417195\pi$
$998$	−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.439.2	✓	48
5.4	even	2		770.2.o.b.439.23	yes	48
7.3	odd	6	inner	770.2.o.a.549.23	yes	48
11.10	odd	2		770.2.o.b.439.2	yes	48
35.24	odd	6		770.2.o.b.549.2	yes	48
55.54	odd	2	inner	770.2.o.a.439.23	yes	48
77.10	even	6		770.2.o.b.549.23	yes	48
385.164	even	6	inner	770.2.o.a.549.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.2	✓	48	1.1	even	1	trivial
770.2.o.a.439.23	yes	48	55.54	odd	2	inner
770.2.o.a.549.2	yes	48	385.164	even	6	inner
770.2.o.a.549.23	yes	48	7.3	odd	6	inner
770.2.o.b.439.2	yes	48	11.10	odd	2
770.2.o.b.439.23	yes	48	5.4	even	2
770.2.o.b.549.2	yes	48	35.24	odd	6
770.2.o.b.549.23	yes	48	77.10	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
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

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