LMFDB - Embedded newform 210.3.o.b.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$-2.63284 - 4.56021i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.b.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(1.94434 - 6.72455i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(1.94434 - 6.72455i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(0.263223 - 0.455915i) q^{11} +(3.00000 - 1.73205i) q^{12} -4.22307i q^{13} +(-9.61071 + 2.37366i) q^{14} -3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-28.8825 - 16.6753i) q^{17} +(2.12132 - 3.67423i) q^{18} +(2.75133 - 1.58848i) q^{19} +4.47214i q^{20} +(-8.74014 + 8.40298i) q^{21} -0.744507 q^{22} +(-5.52954 - 9.57744i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-5.17218 + 2.98616i) q^{26} -5.19615i q^{27} +(9.70292 + 10.0922i) q^{28} -56.1302 q^{29} +(2.73861 + 4.74342i) q^{30} +(-1.63817 - 0.945800i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-0.789668 + 0.455915i) q^{33} +47.1649i q^{34} +(-3.75308 - 15.1959i) q^{35} -6.00000 q^{36} +(4.87682 + 8.44690i) q^{37} +(-3.89097 - 2.24645i) q^{38} +(-3.65729 + 6.33460i) q^{39} +(5.47723 - 3.16228i) q^{40} +4.07377i q^{41} +(16.4717 + 4.76263i) q^{42} +46.3519 q^{43} +(0.526446 + 0.911831i) q^{44} +(5.80948 + 3.35410i) q^{45} +(-7.81995 + 13.5445i) q^{46} +(54.7969 - 31.6370i) q^{47} +6.92820i q^{48} +(-41.4391 - 26.1496i) q^{49} -7.07107 q^{50} +(28.8825 + 50.0259i) q^{51} +(7.31457 + 4.22307i) q^{52} +(23.2606 - 40.2885i) q^{53} +(-6.36396 + 3.67423i) q^{54} -1.17717i q^{55} +(5.49942 - 19.0199i) q^{56} -5.50267 q^{57} +(39.6900 + 68.7452i) q^{58} +(-43.7614 - 25.2657i) q^{59} +(3.87298 - 6.70820i) q^{60} +(89.4583 - 51.6488i) q^{61} +2.67513i q^{62} +(20.3874 - 5.03529i) q^{63} +8.00000 q^{64} +(-4.72153 - 8.17794i) q^{65} +(1.11676 + 0.644762i) q^{66} +(-4.36948 + 7.56816i) q^{67} +(57.7649 - 33.3506i) q^{68} +19.1549i q^{69} +(-15.9572 + 15.3417i) q^{70} +29.0608 q^{71} +(4.24264 + 7.34847i) q^{72} +(14.4912 + 8.36647i) q^{73} +(6.89686 - 11.9457i) q^{74} +(-7.50000 + 4.33013i) q^{75} +6.35393i q^{76} +(-2.55403 - 2.65651i) q^{77} +10.3444 q^{78} +(66.1473 + 114.571i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.98933 - 2.88059i) q^{82} +12.4838i q^{83} +(-5.81425 - 23.5413i) q^{84} -74.5742 q^{85} +(-32.7757 - 56.7692i) q^{86} +(84.1953 + 48.6102i) q^{87} +(0.744507 - 1.28952i) q^{88} +(-59.1101 + 34.1272i) q^{89} -9.48683i q^{90} +(-28.3982 - 8.21107i) q^{91} +22.1182 q^{92} +(1.63817 + 2.83740i) q^{93} +(-77.4945 - 44.7415i) q^{94} +(3.55196 - 6.15217i) q^{95} +(8.48528 - 4.89898i) q^{96} -149.281i q^{97} +(-2.72468 + 69.2429i) q^{98} +1.57934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$			2.44949i			0.408248i
$7$	1.94434	−	6.72455i	0.277762	−	0.960650i
$7$	1.94434	−	6.72455i	0.277762	−	0.960650i
$8$	2.82843			0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	0.263223	−	0.455915i	0.0239293	−	0.0414468i	−0.853813	−	0.520580i	$-0.825716\pi$
$11$	0.263223	−	0.455915i	0.0239293	−	0.0414468i	0.877742	+	0.479133i	$0.159049\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	4.22307i		−	0.324851i	−0.986721	−	0.162426i	$-0.948068\pi$
$13$		−	4.22307i		−	0.324851i	0.986721	−	0.162426i	$-0.0519318\pi$
$14$	−9.61071	+	2.37366i	−0.686479	+	0.169547i
$15$	−3.87298			−0.258199
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−28.8825	−	16.6753i	−1.69897	−	0.980900i	−0.946741	−	0.321997i	$-0.895646\pi$
$17$	−28.8825	−	16.6753i	−1.69897	−	0.980900i	−0.752228	−	0.658903i	$-0.771021\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	2.75133	−	1.58848i	0.144807	−	0.0836044i	−0.425846	−	0.904796i	$-0.640023\pi$
$19$	2.75133	−	1.58848i	0.144807	−	0.0836044i	0.570653	+	0.821191i	$0.306690\pi$
$20$			4.47214i			0.223607i
$21$	−8.74014	+	8.40298i	−0.416197	+	0.400142i
$22$	−0.744507			−0.0338412
$23$	−5.52954	−	9.57744i	−0.240415	−	0.416410i	0.720418	−	0.693540i	$-0.243950\pi$
$23$	−5.52954	−	9.57744i	−0.240415	−	0.416410i	−0.960832	+	0.277130i	$0.910617\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−5.17218	+	2.98616i	−0.198930	+	0.114852i
$27$		−	5.19615i		−	0.192450i
$28$	9.70292	+	10.0922i	0.346533	+	0.360437i
$29$	−56.1302			−1.93552			−0.967762	−	0.251866i	$-0.918956\pi$
$29$	−56.1302			−1.93552			−0.967762	+	0.251866i	$0.918956\pi$
$30$	2.73861	+	4.74342i	0.0912871	+	0.158114i
$31$	−1.63817	−	0.945800i	−0.0528443	−	0.0305097i	0.473345	−	0.880877i	$-0.343046\pi$
$31$	−1.63817	−	0.945800i	−0.0528443	−	0.0305097i	−0.526189	+	0.850367i	$0.676380\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	−0.789668	+	0.455915i	−0.0239293	+	0.0138156i
$34$			47.1649i			1.38720i
$35$	−3.75308	−	15.1959i	−0.107231	−	0.434168i
$36$	−6.00000			−0.166667
$37$	4.87682	+	8.44690i	0.131806	+	0.228294i	0.924373	−	0.381491i	$-0.124589\pi$
$37$	4.87682	+	8.44690i	0.131806	+	0.228294i	−0.792567	+	0.609785i	$0.791256\pi$
$38$	−3.89097	−	2.24645i	−0.102394	−	0.0591172i
$39$	−3.65729	+	6.33460i	−0.0937765	+	0.162426i
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$			4.07377i			0.0993603i	0.998765	+	0.0496802i	$0.0158202\pi$
$41$			4.07377i			0.0993603i	−0.998765	+	0.0496802i	$0.984180\pi$
$42$	16.4717	+	4.76263i	0.392184	+	0.113396i
$43$	46.3519			1.07795			0.538975	−	0.842322i	$-0.318812\pi$
$43$	46.3519			1.07795			0.538975	+	0.842322i	$0.318812\pi$
$44$	0.526446	+	0.911831i	0.0119647	+	0.0207234i
$45$	5.80948	+	3.35410i	0.129099	+	0.0745356i
$46$	−7.81995	+	13.5445i	−0.169999	+	0.294447i
$47$	54.7969	−	31.6370i	1.16589	−	0.673127i	0.213182	−	0.977012i	$-0.431617\pi$
$47$	54.7969	−	31.6370i	1.16589	−	0.673127i	0.952709	+	0.303885i	$0.0982839\pi$
$48$			6.92820i			0.144338i
$49$	−41.4391	−	26.1496i	−0.845696	−	0.533665i
$50$	−7.07107			−0.141421
$51$	28.8825	+	50.0259i	0.566323	+	0.980900i
$52$	7.31457	+	4.22307i	0.140665	+	0.0812129i
$53$	23.2606	−	40.2885i	0.438878	−	0.760160i	−0.558725	−	0.829353i	$-0.688709\pi$
$53$	23.2606	−	40.2885i	0.438878	−	0.760160i	0.997603	+	0.0691934i	$0.0220426\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		−	1.17717i		−	0.0214031i
$56$	5.49942	−	19.0199i	0.0982038	−	0.339641i
$57$	−5.50267			−0.0965380
$58$	39.6900	+	68.7452i	0.684311	+	1.18526i
$59$	−43.7614	−	25.2657i	−0.741719	−	0.428231i	0.0809752	−	0.996716i	$-0.474197\pi$
$59$	−43.7614	−	25.2657i	−0.741719	−	0.428231i	−0.822694	+	0.568485i	$0.807530\pi$
$60$	3.87298	−	6.70820i	0.0645497	−	0.111803i
$61$	89.4583	−	51.6488i	1.46653	−	0.846702i	0.467231	−	0.884135i	$-0.345252\pi$
$61$	89.4583	−	51.6488i	1.46653	−	0.846702i	0.999299	+	0.0374335i	$0.0119182\pi$
$62$			2.67513i			0.0431472i
$63$	20.3874	−	5.03529i	0.323609	−	0.0799252i
$64$	8.00000			0.125000
$65$	−4.72153	−	8.17794i	−0.0726390	−	0.125814i
$66$	1.11676	+	0.644762i	0.0169206	+	0.00976912i
$67$	−4.36948	+	7.56816i	−0.0652161	+	0.112958i	−0.896790	−	0.442457i	$-0.854107\pi$
$67$	−4.36948	+	7.56816i	−0.0652161	+	0.112958i	0.831574	+	0.555414i	$0.187440\pi$
$68$	57.7649	−	33.3506i	0.849484	−	0.490450i
$69$			19.1549i			0.277607i
$70$	−15.9572	+	15.3417i	−0.227960	+	0.219167i
$71$	29.0608			0.409307			0.204653	−	0.978835i	$-0.434393\pi$
$71$	29.0608			0.409307			0.204653	+	0.978835i	$0.434393\pi$
$72$	4.24264	+	7.34847i	0.0589256	+	0.102062i
$73$	14.4912	+	8.36647i	0.198509	+	0.114609i	0.595960	−	0.803014i	$-0.296772\pi$
$73$	14.4912	+	8.36647i	0.198509	+	0.114609i	−0.397451	+	0.917623i	$0.630105\pi$
$74$	6.89686	−	11.9457i	0.0932008	−	0.161429i
$75$	−7.50000	+	4.33013i	−0.100000	+	0.0577350i
$76$			6.35393i			0.0836044i
$77$	−2.55403	−	2.65651i	−0.0331692	−	0.0345001i
$78$	10.3444			0.132620
$79$	66.1473	+	114.571i	0.837308	+	1.45026i	0.892137	+	0.451764i	$0.149205\pi$
$79$	66.1473	+	114.571i	0.837308	+	1.45026i	−0.0548297	+	0.998496i	$0.517462\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	4.98933	−	2.88059i	0.0608455	−	0.0351292i
$83$			12.4838i			0.150407i	0.997168	+	0.0752033i	$0.0239606\pi$
$83$			12.4838i			0.150407i	−0.997168	+	0.0752033i	$0.976039\pi$
$84$	−5.81425	−	23.5413i	−0.0692173	−	0.280254i
$85$	−74.5742			−0.877344
$86$	−32.7757	−	56.7692i	−0.381113	−	0.660107i
$87$	84.1953	+	48.6102i	0.967762	+	0.558738i
$88$	0.744507	−	1.28952i	0.00846030	−	0.0146537i
$89$	−59.1101	+	34.1272i	−0.664158	+	0.383452i	−0.793860	−	0.608101i	$-0.791931\pi$
$89$	−59.1101	+	34.1272i	−0.664158	+	0.383452i	0.129701	+	0.991553i	$0.458598\pi$
$90$		−	9.48683i		−	0.105409i
$91$	−28.3982	−	8.21107i	−0.312068	−	0.0902315i
$92$	22.1182			0.240415
$93$	1.63817	+	2.83740i	0.0176148	+	0.0305097i
$94$	−77.4945	−	44.7415i	−0.824409	−	0.475973i
$95$	3.55196	−	6.15217i	0.0373890	−	0.0647597i
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$		−	149.281i		−	1.53898i	−0.638659	−	0.769490i	$-0.720510\pi$
$97$		−	149.281i		−	1.53898i	0.638659	−	0.769490i	$-0.279490\pi$
$98$	−2.72468	+	69.2429i	−0.0278029	+	0.706560i
$99$	1.57934			0.0159529
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	83.7839	+	48.3726i	0.829543	+	0.478937i	0.853696	−	0.520771i	$-0.174356\pi$
$101$	83.7839	+	48.3726i	0.829543	+	0.478937i	−0.0241531	+	0.999708i	$0.507689\pi$
$102$	40.8460	−	70.7473i	0.400451	−	0.693601i
$103$	90.7268	−	52.3811i	0.880843	−	0.508555i	0.00990642	−	0.999951i	$-0.496847\pi$
$103$	90.7268	−	52.3811i	0.880843	−	0.508555i	0.870936	+	0.491396i	$0.163513\pi$
$104$		−	11.9446i		−	0.114852i
$105$	−7.53038	+	26.0441i	−0.0717179	+	0.248039i
$106$	−65.7908			−0.620668
$107$	62.3022	+	107.911i	0.582263	+	1.00851i	0.995211	+	0.0977548i	$0.0311661\pi$
$107$	62.3022	+	107.911i	0.582263	+	1.00851i	−0.412947	+	0.910755i	$0.635501\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	−42.3042	+	73.2731i	−0.388112	+	0.672230i	−0.992196	−	0.124691i	$-0.960206\pi$
$109$	−42.3042	+	73.2731i	−0.388112	+	0.672230i	0.604083	+	0.796921i	$0.293539\pi$
$110$	−1.44173	+	0.832384i	−0.0131066	+	0.00756712i
$111$		−	16.8938i		−	0.152196i
$112$	−27.1832	+	6.71372i	−0.242707	+	0.0599439i
$113$	−116.241			−1.02868			−0.514340	−	0.857586i	$-0.671963\pi$
$113$	−116.241			−1.02868			−0.514340	+	0.857586i	$0.671963\pi$
$114$	3.89097	+	6.73936i	0.0341313	+	0.0591172i
$115$	−21.4158	−	12.3644i	−0.186224	−	0.107517i
$116$	56.1302	−	97.2204i	0.483881	−	0.838107i
$117$	10.9719	−	6.33460i	0.0937765	−	0.0541419i
$118$			71.4621i			0.605611i
$119$	−168.291	+	161.799i	−1.41421	+	1.35966i
$120$	−10.9545			−0.0912871
$121$	60.3614	+	104.549i	0.498855	+	0.864042i
$122$	−126.513	−	73.0424i	−1.03699	−	0.598708i
$123$	3.52799	−	6.11066i	0.0286829	−	0.0496802i
$124$	3.27635	−	1.89160i	0.0264222	−	0.0152548i
$125$		−	11.1803i		−	0.0894427i
$126$	−20.5830	−	21.4089i	−0.163357	−	0.169912i
$127$	−81.3744			−0.640743			−0.320372	−	0.947292i	$-0.603808\pi$
$127$	−81.3744			−0.640743			−0.320372	+	0.947292i	$0.603808\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−69.5278	−	40.1419i	−0.538975	−	0.311178i
$130$	−6.67726	+	11.5654i	−0.0513635	+	0.0889642i
$131$	208.389	−	120.313i	1.59075	−	0.918421i	0.597574	−	0.801814i	$-0.296131\pi$
$131$	208.389	−	120.313i	1.59075	−	0.918421i	0.993178	−	0.116608i	$-0.0372020\pi$
$132$		−	1.82366i		−	0.0138156i
$133$	−5.33231	−	21.5900i	−0.0400926	−	0.162331i
$134$	12.3588			0.0922295
$135$	−5.80948	−	10.0623i	−0.0430331	−	0.0745356i
$136$	−81.6919	−	47.1649i	−0.600676	−	0.346800i
$137$	−116.831	+	202.357i	−0.852778	+	1.47706i	0.0259125	+	0.999664i	$0.491751\pi$
$137$	−116.831	+	202.357i	−0.852778	+	1.47706i	−0.878691	+	0.477391i	$0.841582\pi$
$138$	23.4598	−	13.5445i	0.169999	−	0.0981489i
$139$		−	211.491i		−	1.52152i	−0.649033	−	0.760760i	$-0.724826\pi$
$139$		−	211.491i		−	1.52152i	0.649033	−	0.760760i	$-0.275174\pi$
$140$	30.0731	+	8.69534i	0.214808	+	0.0621096i
$141$	−109.594			−0.777261
$142$	−20.5491	−	35.5920i	−0.144712	−	0.250648i
$143$	−1.92536	−	1.11161i	−0.0134641	−	0.00777348i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	−108.696	+	62.7555i	−0.749625	+	0.432796i
$146$		−	23.6640i		−	0.162082i
$147$	39.5125	+	75.1117i	0.268792	+	0.510964i
$148$	−19.5073			−0.131806
$149$	−72.0402	−	124.777i	−0.483491	−	0.837431i	0.516329	−	0.856390i	$-0.327298\pi$
$149$	−72.0402	−	124.777i	−0.483491	−	0.837431i	−0.999820	+	0.0189590i	$0.993965\pi$
$150$	10.6066	+	6.12372i	0.0707107	+	0.0408248i
$151$	−46.7563	+	80.9842i	−0.309644	+	0.536319i	−0.978285	−	0.207267i	$-0.933543\pi$
$151$	−46.7563	+	80.9842i	−0.309644	+	0.536319i	0.668640	+	0.743586i	$0.266877\pi$
$152$	7.78195	−	4.49291i	0.0511970	−	0.0295586i
$153$		−	100.052i		−	0.653933i
$154$	−1.44757	+	5.00647i	−0.00939982	+	0.0325095i
$155$	−4.22975			−0.0272887
$156$	−7.31457	−	12.6692i	−0.0468883	−	0.0812129i
$157$	−148.286	−	85.6127i	−0.944494	−	0.545304i	−0.0531280	−	0.998588i	$-0.516919\pi$
$157$	−148.286	−	85.6127i	−0.944494	−	0.545304i	−0.891366	+	0.453284i	$0.850252\pi$
$158$	93.5464	−	162.027i	0.592066	−	1.02549i
$159$	−69.7817	+	40.2885i	−0.438878	+	0.253387i
$160$			12.6491i			0.0790569i
$161$	−75.1553	+	18.5619i	−0.466803	+	0.115291i
$162$	12.7279			0.0785674
$163$	−46.5064	−	80.5515i	−0.285316	−	0.494181i	0.687370	−	0.726307i	$-0.258765\pi$
$163$	−46.5064	−	80.5515i	−0.285316	−	0.494181i	−0.972686	+	0.232126i	$0.925432\pi$
$164$	−7.05598	−	4.07377i	−0.0430243	−	0.0248401i
$165$	−1.01946	+	1.76575i	−0.00617853	+	0.0107015i
$166$	15.2894	−	8.82735i	0.0921049	−	0.0531768i
$167$			104.991i			0.628688i	0.949309	+	0.314344i	$0.101784\pi$
$167$			104.991i			0.628688i	−0.949309	+	0.314344i	$0.898216\pi$
$168$	−24.7208	+	23.7672i	−0.147148	+	0.141471i
$169$	151.166			0.894472
$170$	52.7319	+	91.3344i	0.310188	+	0.537261i
$171$	8.25400	+	4.76545i	0.0482690	+	0.0278681i
$172$	−46.3519	+	80.2838i	−0.269488	+	0.466766i
$173$	176.805	−	102.079i	1.02200	−	0.590049i	0.107314	−	0.994225i	$-0.465775\pi$
$173$	176.805	−	102.079i	1.02200	−	0.590049i	0.914681	+	0.404176i	$0.132442\pi$
$174$		−	137.490i		−	0.790174i
$175$	−24.2573	−	25.2306i	−0.138613	−	0.144175i
$176$	−2.10578			−0.0119647
$177$	43.7614	+	75.7970i	0.247240	+	0.428231i
$178$	83.5943	+	48.2632i	0.469631	+	0.271141i
$179$	97.9495	−	169.653i	0.547204	−	0.947785i	−0.451261	−	0.892392i	$-0.649026\pi$
$179$	97.9495	−	169.653i	0.547204	−	0.947785i	0.998465	−	0.0553926i	$-0.0176410\pi$
$180$	−11.6190	+	6.70820i	−0.0645497	+	0.0372678i
$181$			119.031i			0.657632i	0.944394	+	0.328816i	$0.106650\pi$
$181$			119.031i			0.657632i	−0.944394	+	0.328816i	$0.893350\pi$
$182$	10.0241	+	40.5867i	0.0550776	+	0.223004i
$183$	−178.917			−0.977687
$184$	−15.6399	−	27.0891i	−0.0849994	−	0.147223i
$185$	18.8878	+	10.9049i	0.102096	+	0.0589454i
$186$	2.31673	−	4.01269i	0.0124555	−	0.0215736i
$187$	−15.2050	+	8.77864i	−0.0813104	+	0.0469446i
$188$			126.548i			0.673127i
$189$	−34.9418	−	10.1031i	−0.184877	−	0.0534554i
$190$	−10.0464			−0.0528760
$191$	32.8657	+	56.9250i	0.172072	+	0.298037i	0.939144	−	0.343524i	$-0.111621\pi$
$191$	32.8657	+	56.9250i	0.172072	+	0.298037i	−0.767072	+	0.641561i	$0.778287\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	48.4350	−	83.8919i	0.250959	−	0.434673i	−0.712831	−	0.701335i	$-0.752588\pi$
$193$	48.4350	−	83.8919i	0.250959	−	0.434673i	0.963790	+	0.266662i	$0.0859209\pi$
$194$	−182.831	+	105.558i	−0.942429	+	0.544112i
$195$			16.3559i			0.0838763i
$196$	86.7315	−	45.6251i	0.442508	−	0.232781i
$197$	186.672			0.947574			0.473787	−	0.880640i	$-0.342887\pi$
$197$	186.672			0.947574			0.473787	+	0.880640i	$0.342887\pi$
$198$	−1.11676	−	1.93428i	−0.00564020	−	0.00976912i
$199$	99.8454	+	57.6458i	0.501736	+	0.289677i	0.729430	−	0.684055i	$-0.239785\pi$
$199$	99.8454	+	57.6458i	0.501736	+	0.289677i	−0.227694	+	0.973733i	$0.573119\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$	13.1084	−	7.56816i	0.0652161	−	0.0376525i
$202$		−	136.818i		−	0.677319i
$203$	−109.136	+	377.450i	−0.537616	+	1.85936i
$204$	−115.530			−0.566323
$205$	4.55462	+	7.88883i	0.0222176	+	0.0384821i
$206$	−128.307	−	74.0781i	−0.622850	−	0.359602i
$207$	16.5886	−	28.7323i	0.0801382	−	0.138803i
$208$	−14.6291	+	8.44614i	−0.0703324	+	0.0406064i
$209$		−	1.67250i		−	0.00800239i
$210$	37.2221	−	9.19314i	0.177248	−	0.0437768i
$211$	139.433			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$211$	139.433			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$212$	46.5211	+	80.5769i	0.219439	+	0.380080i
$213$	−43.5912	−	25.1674i	−0.204653	−	0.118157i
$214$	88.1086	−	152.609i	0.411722	−	0.713124i
$215$	89.7600	−	51.8230i	0.417488	−	0.241037i
$216$		−	14.6969i		−	0.0680414i
$217$	−9.54524	+	9.17703i	−0.0439873	+	0.0422905i
$218$	119.654			0.548874
$219$	−14.4912	−	25.0994i	−0.0661697	−	0.114609i
$220$	2.03892	+	1.17717i	0.00926780	+	0.00535076i
$221$	−70.4209	+	121.973i	−0.318647	+	0.551912i
$222$	−20.6906	+	11.9457i	−0.0932008	+	0.0538095i
$223$		−	258.055i		−	1.15720i	−0.815612	−	0.578599i	$-0.803600\pi$
$223$		−	258.055i		−	1.15720i	0.815612	−	0.578599i	$-0.196400\pi$
$224$	27.4440	+	28.5452i	0.122518	+	0.127434i
$225$	15.0000			0.0666667
$226$	82.1947	+	142.365i	0.363693	+	0.629935i
$227$	286.682	+	165.516i	1.26292	+	0.729146i	0.973638	−	0.228099i	$-0.0732509\pi$
$227$	286.682	+	165.516i	1.26292	+	0.729146i	0.289280	+	0.957245i	$0.406584\pi$
$228$	5.50267	−	9.53090i	0.0241345	−	0.0418022i
$229$	211.516	−	122.119i	0.923653	−	0.533271i	0.0388541	−	0.999245i	$-0.487629\pi$
$229$	211.516	−	122.119i	0.923653	−	0.533271i	0.884799	+	0.465974i	$0.154296\pi$
$230$			34.9719i			0.152052i
$231$	1.53044	+	6.19662i	0.00662529	+	0.0268252i
$232$	−158.760			−0.684311
$233$	−105.745	−	183.155i	−0.453840	−	0.786074i	0.544781	−	0.838579i	$-0.316613\pi$
$233$	−105.745	−	183.155i	−0.453840	−	0.786074i	−0.998621	+	0.0525044i	$0.983280\pi$
$234$	−15.5165	−	8.95848i	−0.0663100	−	0.0382841i
$235$	70.7425	−	122.530i	0.301032	−	0.521402i
$236$	87.5228	−	50.5313i	0.370859	−	0.214116i
$237$		−	229.141i		−	0.966840i
$238$	317.162	+	91.7044i	1.33262	+	0.385313i
$239$	344.134			1.43989			0.719946	−	0.694030i	$-0.244167\pi$
$239$	344.134			1.43989			0.719946	+	0.694030i	$0.244167\pi$
$240$	7.74597	+	13.4164i	0.0322749	+	0.0559017i
$241$	−148.392	−	85.6742i	−0.615735	−	0.355495i	0.159472	−	0.987203i	$-0.449021\pi$
$241$	−148.392	−	85.6742i	−0.615735	−	0.355495i	−0.775207	+	0.631708i	$0.782354\pi$
$242$	85.3639	−	147.855i	0.352744	−	0.610970i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$			206.595i			0.846702i
$245$	−109.483	−	4.30810i	−0.446868	−	0.0175841i
$246$	−9.97867			−0.0405637
$247$	−6.70827	−	11.6191i	−0.0271590	−	0.0470408i
$248$	−4.63346	−	2.67513i	−0.0186833	−	0.0107868i
$249$	10.8112	−	18.7256i	0.0434187	−	0.0752033i
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$			327.538i			1.30493i	0.757818	+	0.652467i	$0.226266\pi$
$251$			327.538i			1.30493i	−0.757818	+	0.652467i	$0.773734\pi$
$252$	−11.6660	+	40.3473i	−0.0462937	+	0.160108i
$253$	−5.82200			−0.0230119
$254$	57.5404	+	99.6629i	0.226537	+	0.392374i
$255$	111.861	+	64.5832i	0.438672	+	0.253267i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−190.836	+	110.179i	−0.742552	+	0.428713i	−0.822997	−	0.568046i	$-0.807699\pi$
$257$	−190.836	+	110.179i	−0.742552	+	0.428713i	0.0804442	+	0.996759i	$0.474366\pi$
$258$			113.538i			0.440072i
$259$	66.2837	−	16.3708i	0.255922	−	0.0632077i
$260$	18.8861			0.0726390
$261$	−84.1953	−	145.831i	−0.322587	−	0.558738i
$262$	−294.706	−	170.149i	−1.12483	−	0.649422i
$263$	−66.5976	+	115.350i	−0.253223	+	0.438594i	−0.964411	−	0.264407i	$-0.914824\pi$
$263$	−66.5976	+	115.350i	−0.253223	+	0.438594i	0.711189	+	0.703001i	$0.248157\pi$
$264$	−2.23352	+	1.28952i	−0.00846030	+	0.00488456i
$265$		−	104.024i		−	0.392545i
$266$	−22.6718	+	21.7972i	−0.0852322	+	0.0819443i
$267$	118.220			0.442772
$268$	−8.73896	−	15.1363i	−0.0326080	−	0.0564788i
$269$	−22.9633	−	13.2578i	−0.0853653	−	0.0492857i	0.456710	−	0.889616i	$-0.349028\pi$
$269$	−22.9633	−	13.2578i	−0.0853653	−	0.0492857i	−0.542075	+	0.840330i	$0.682361\pi$
$270$	−8.21584	+	14.2302i	−0.0304290	+	0.0527046i
$271$	−92.6776	+	53.5074i	−0.341984	+	0.197444i	−0.661149	−	0.750255i	$-0.729931\pi$
$271$	−92.6776	+	53.5074i	−0.341984	+	0.197444i	0.319165	+	0.947699i	$0.396598\pi$
$272$			133.402i			0.490450i
$273$	35.4864	+	36.9102i	0.129987	+	0.135202i
$274$	330.447			1.20601
$275$	−1.31611	−	2.27958i	−0.00478587	−	0.00828937i
$276$	−33.1772	−	19.1549i	−0.120207	−	0.0694017i
$277$	−220.191	+	381.381i	−0.794912	+	1.37683i	0.127983	+	0.991776i	$0.459150\pi$
$277$	−220.191	+	381.381i	−0.794912	+	1.37683i	−0.922895	+	0.385052i	$0.874184\pi$
$278$	−259.023	+	149.547i	−0.931737	+	0.537939i
$279$		−	5.67480i		−	0.0203398i
$280$	−10.6153	−	42.9804i	−0.0379119	−	0.153501i
$281$	322.069			1.14615			0.573076	−	0.819502i	$-0.305750\pi$
$281$	322.069			1.14615			0.573076	+	0.819502i	$0.305750\pi$
$282$	77.4945	+	134.224i	0.274803	+	0.475973i
$283$	−59.3514	−	34.2665i	−0.209722	−	0.121083i	0.391460	−	0.920195i	$-0.371970\pi$
$283$	−59.3514	−	34.2665i	−0.209722	−	0.121083i	−0.601182	+	0.799112i	$0.705303\pi$
$284$	−29.0608	+	50.3347i	−0.102327	+	0.177235i
$285$	−10.6559	+	6.15217i	−0.0373890	+	0.0215866i
$286$			3.14410i			0.0109934i
$287$	27.3943	+	7.92079i	0.0954505	+	0.0275986i
$288$	−16.9706			−0.0589256
$289$	411.631	+	712.966i	1.42433	+	2.46701i
$290$	153.719	+	88.7496i	0.530065	+	0.306033i
$291$	−129.281	+	223.922i	−0.444265	+	0.769490i
$292$	−28.9823	+	16.7329i	−0.0992545	+	0.0573046i
$293$		−	147.510i		−	0.503448i	−0.967799	−	0.251724i	$-0.919003\pi$
$293$		−	147.510i		−	0.503448i	0.967799	−	0.251724i	$-0.0809975\pi$
$294$	64.0531	−	101.505i	0.217868	−	0.345254i
$295$	−112.991			−0.383022
$296$	13.7937	+	23.8914i	0.0466004	+	0.0807143i
$297$	−2.36901	−	1.36775i	−0.00797645	−	0.00460521i
$298$	−101.880	+	176.462i	−0.341880	+	0.592153i
$299$	−40.4462	+	23.3516i	−0.135272	+	0.0780991i
$300$		−	17.3205i		−	0.0577350i
$301$	90.1237	−	311.695i	0.299414	−	1.03553i
$302$	132.247			0.437903
$303$	−83.7839	−	145.118i	−0.276514	−	0.478937i
$304$	−11.0053	−	6.35393i	−0.0362018	−	0.0209011i
$305$	115.490	−	200.035i	0.378657	−	0.655852i
$306$	−122.538	+	70.7473i	−0.400451	+	0.231200i
$307$		−	376.010i		−	1.22479i	−0.790553	−	0.612394i	$-0.790207\pi$
$307$		−	376.010i		−	1.22479i	0.790553	−	0.612394i	$-0.209793\pi$
$308$	7.15524	−	1.76720i	0.0232313	−	0.00573767i
$309$	−181.454			−0.587228
$310$	2.99088	+	5.18036i	0.00964801	+	0.0167108i
$311$	−337.599	−	194.913i	−1.08553	−	0.626730i	−0.153146	−	0.988204i	$-0.548941\pi$
$311$	−337.599	−	194.913i	−1.08553	−	0.626730i	−0.932383	+	0.361473i	$0.882274\pi$
$312$	−10.3444	+	17.9170i	−0.0331550	+	0.0574262i
$313$	−123.890	+	71.5282i	−0.395816	+	0.228524i	−0.684677	−	0.728847i	$-0.740057\pi$
$313$	−123.890	+	71.5282i	−0.395816	+	0.228524i	0.288861	+	0.957371i	$0.406723\pi$
$314$			242.149i			0.771176i
$315$	33.8504	−	32.5446i	0.107462	−	0.103316i
$316$	−264.589			−0.837308
$317$	−192.222	−	332.938i	−0.606378	−	1.05028i	−0.991832	−	0.127551i	$-0.959288\pi$
$317$	−192.222	−	332.938i	−0.606378	−	1.05028i	0.385454	−	0.922727i	$-0.374045\pi$
$318$	98.6862	+	56.9765i	0.310334	+	0.179171i
$319$	−14.7747	+	25.5906i	−0.0463158	+	0.0802214i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		−	215.821i		−	0.672340i
$322$	75.8764	+	78.9208i	0.235641	+	0.245096i
$323$	−105.954			−0.328030
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	−18.2864	−	10.5577i	−0.0562659	−	0.0324851i
$326$	−65.7700	+	113.917i	−0.201749	+	0.349439i
$327$	126.913	−	73.2731i	0.388112	−	0.224077i
$328$			11.5224i			0.0351292i
$329$	−106.201	−	429.997i	−0.322799	−	1.30698i
$330$	2.88346			0.00873776
$331$	−96.9539	−	167.929i	−0.292912	−	0.507338i	0.681585	−	0.731739i	$-0.261291\pi$
$331$	−96.9539	−	167.929i	−0.292912	−	0.507338i	−0.974497	+	0.224400i	$0.927958\pi$
$332$	−21.6225	−	12.4838i	−0.0651280	−	0.0376017i
$333$	−14.6305	+	25.3407i	−0.0439353	+	0.0760982i
$334$	128.587	−	74.2397i	0.384991	−	0.222275i
$335$			19.5409i			0.0583310i
$336$	46.5890	+	13.4708i	0.138658	+	0.0400916i
$337$	125.477			0.372337			0.186168	−	0.982518i	$-0.440393\pi$
$337$	125.477			0.372337			0.186168	+	0.982518i	$0.440393\pi$
$338$	−106.890	−	185.139i	−0.316243	−	0.547750i
$339$	174.361	+	100.668i	0.514340	+	0.296954i
$340$	74.5742	−	129.166i	0.219336	−	0.379901i
$341$	−0.862410	+	0.497912i	−0.00252906	+	0.00146015i
$342$		−	13.4787i		−	0.0394115i
$343$	−256.416	+	227.816i	−0.747568	+	0.664186i
$344$	131.103			0.381113
$345$	21.4158	+	37.0933i	0.0620748	+	0.107517i
$346$	−250.040	−	144.361i	−0.722660	−	0.417228i
$347$	251.798	−	436.128i	0.725644	−	1.25685i	−0.233065	−	0.972461i	$-0.574875\pi$
$347$	251.798	−	436.128i	0.725644	−	1.25685i	0.958708	−	0.284391i	$-0.0917913\pi$
$348$	−168.391	+	97.2204i	−0.483881	+	0.279369i
$349$			47.7682i			0.136872i	0.997656	+	0.0684358i	$0.0218008\pi$
$349$			47.7682i			0.136872i	−0.997656	+	0.0684358i	$0.978199\pi$
$350$	−13.7485	+	47.5497i	−0.0392815	+	0.135856i
$351$	−21.9437			−0.0625177
$352$	1.48901	+	2.57905i	0.00423015	+	0.00732684i
$353$	28.5012	+	16.4552i	0.0807399	+	0.0466152i	0.539826	−	0.841776i	$-0.318490\pi$
$353$	28.5012	+	16.4552i	0.0807399	+	0.0466152i	−0.459087	+	0.888392i	$0.651823\pi$
$354$	61.8880	−	107.193i	0.174825	−	0.302805i
$355$	56.2760	−	32.4909i	0.158524	−	0.0915238i
$356$		−	136.509i		−	0.383452i
$357$	392.559	−	96.9543i	1.09960	−	0.271581i
$358$	−277.043			−0.773863
$359$	−133.898	−	231.919i	−0.372976	−	0.646013i	0.617046	−	0.786927i	$-0.288329\pi$
$359$	−133.898	−	231.919i	−0.372976	−	0.646013i	−0.990022	+	0.140914i	$0.954996\pi$
$360$	16.4317	+	9.48683i	0.0456435	+	0.0263523i
$361$	−175.453	+	303.894i	−0.486021	+	0.841812i
$362$	145.783	−	84.1679i	0.402716	−	0.232508i
$363$		−	209.098i		−	0.576028i
$364$	42.6202	−	40.9761i	0.117089	−	0.112572i
$365$	37.4160			0.102510
$366$	126.513	+	219.127i	0.345665	+	0.598708i
$367$	−137.458	−	79.3613i	−0.374545	−	0.216243i	0.300897	−	0.953657i	$-0.402714\pi$
$367$	−137.458	−	79.3613i	−0.374545	−	0.216243i	−0.675442	+	0.737413i	$0.736047\pi$
$368$	−22.1182	+	38.3098i	−0.0601037	+	0.104103i
$369$	−10.5840	+	6.11066i	−0.0286829	+	0.0165601i
$370$		−	30.8437i		−	0.0833614i
$371$	−225.695	−	234.751i	−0.608343	−	0.632752i
$372$	−6.55270			−0.0176148
$373$	−207.172	−	358.832i	−0.555421	−	0.962017i	−0.997871	−	0.0652235i	$-0.979224\pi$
$373$	−207.172	−	358.832i	−0.555421	−	0.962017i	0.442450	−	0.896793i	$-0.354109\pi$
$374$	21.5032	+	12.4149i	0.0574951	+	0.0331948i
$375$	−9.68246	+	16.7705i	−0.0258199	+	0.0447214i
$376$	154.989	−	89.4829i	0.412205	−	0.237986i
$377$			237.042i			0.628758i
$378$	12.3339	+	49.9387i	0.0326293	+	0.132113i
$379$	−72.8000			−0.192084			−0.0960422	−	0.995377i	$-0.530618\pi$
$379$	−72.8000			−0.192084			−0.0960422	+	0.995377i	$0.530618\pi$
$380$	7.10391	+	12.3043i	0.0186945	+	0.0323798i
$381$	122.062	+	70.4723i	0.320372	+	0.184967i
$382$	46.4791	−	80.5042i	0.121673	−	0.210744i
$383$	−246.830	+	142.507i	−0.644464	+	0.372082i	−0.786332	−	0.617804i	$-0.788023\pi$
$383$	−246.830	+	142.507i	−0.644464	+	0.372082i	0.141868	+	0.989886i	$0.454689\pi$
$384$			19.5959i			0.0510310i
$385$	−7.91593	−	2.28881i	−0.0205608	−	0.00594497i
$386$	−136.995			−0.354909
$387$	69.5278	+	120.426i	0.179658	+	0.311178i
$388$	258.562	+	149.281i	0.666398	+	0.384745i
$389$	48.5692	−	84.1242i	0.124856	−	0.216258i	−0.796820	−	0.604216i	$-0.793486\pi$
$389$	48.5692	−	84.1242i	0.124856	−	0.216258i	0.921677	+	0.387959i	$0.126820\pi$
$390$	20.0318	−	11.5654i	0.0513635	−	0.0296547i
$391$			368.827i			0.943291i
$392$	−117.207	−	73.9622i	−0.298999	−	0.188679i
$393$	−416.777			−1.06050
$394$	−131.997	−	228.626i	−0.335018	−	0.580268i
$395$	256.187	+	147.910i	0.648576	+	0.374455i
$396$	−1.57934	+	2.73549i	−0.00398822	+	0.00690781i
$397$	−685.636	+	395.852i	−1.72704	+	0.997108i	−0.825522	+	0.564371i	$0.809119\pi$
$397$	−685.636	+	395.852i	−1.72704	+	0.997108i	−0.901520	+	0.432737i	$0.857548\pi$
$398$		−	163.047i		−	0.409665i
$399$	−10.6990	+	37.0030i	−0.0268146	+	0.0927392i
$400$	−20.0000			−0.0500000
$401$	−251.613	−	435.807i	−0.627464	−	1.08680i	−0.988059	−	0.154077i	$-0.950759\pi$
$401$	−251.613	−	435.807i	−0.627464	−	1.08680i	0.360594	−	0.932723i	$-0.382574\pi$
$402$	−18.5381	−	10.7030i	−0.0461147	−	0.0266244i
$403$	−3.99418	+	6.91812i	−0.00991112	+	0.0171666i
$404$	−167.568	+	96.7453i	−0.414772	+	0.239468i
$405$			20.1246i			0.0496904i
$406$	539.451	−	133.234i	1.32870	−	0.328162i
$407$	5.13476			0.0126161
$408$	81.6919	+	141.495i	0.200225	+	0.346800i
$409$	649.395	+	374.928i	1.58776	+	0.916696i	0.993675	+	0.112296i	$0.0358204\pi$
$409$	649.395	+	374.928i	1.58776	+	0.916696i	0.594088	+	0.804400i	$0.297513\pi$
$410$	6.44120	−	11.1565i	0.0157102	−	0.0272109i
$411$	350.492	−	202.357i	0.852778	−	0.492352i
$412$			209.525i			0.508555i
$413$	−254.987	+	245.151i	−0.617402	+	0.593585i
$414$	−46.9197			−0.113333
$415$	13.9573	+	24.1747i	0.0336319	+	0.0582522i
$416$	20.6887	+	11.9446i	0.0497325	+	0.0287131i
$417$	−183.157	+	317.237i	−0.439225	+	0.760760i
$418$	−2.04839	+	1.18264i	−0.00490044	+	0.00282927i
$419$		−	465.759i		−	1.11160i	−0.831317	−	0.555799i	$-0.812413\pi$
$419$		−	465.759i		−	1.11160i	0.831317	−	0.555799i	$-0.187587\pi$
$420$	−37.5793	−	39.0871i	−0.0894744	−	0.0930645i
$421$	345.980			0.821805			0.410902	−	0.911679i	$-0.365214\pi$
$421$	345.980			0.821805			0.410902	+	0.911679i	$0.365214\pi$
$422$	−98.5939	−	170.770i	−0.233635	−	0.404667i
$423$	164.391	+	94.9110i	0.388630	+	0.224376i
$424$	65.7908	−	113.953i	0.155167	−	0.268757i
$425$	−144.412	+	83.3765i	−0.339794	+	0.196180i
$426$			71.1841i			0.167099i
$427$	−173.378	−	701.990i	−0.406037	−	1.64400i
$428$	−249.209			−0.582263
$429$	1.92536	+	3.33482i	0.00448802	+	0.00777348i
$430$	−126.940	−	73.2888i	−0.295209	−	0.170439i
$431$	−247.300	+	428.336i	−0.573782	+	0.993819i	0.422391	+	0.906414i	$0.361191\pi$
$431$	−247.300	+	428.336i	−0.573782	+	0.993819i	−0.996173	+	0.0874056i	$0.972142\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			730.022i			1.68596i	0.537943	+	0.842981i	$0.319201\pi$
$433$			730.022i			1.68596i	−0.537943	+	0.842981i	$0.680799\pi$
$434$	17.9890	+	5.20135i	0.0414494	+	0.0119847i
$435$	217.391			0.499750
$436$	−84.6085	−	146.546i	−0.194056	−	0.336115i
$437$	−30.4272	−	17.5672i	−0.0696275	−	0.0401994i
$438$	−20.4936	+	35.4959i	−0.0467890	+	0.0810410i
$439$	−321.631	+	185.694i	−0.732645	+	0.422993i	−0.819389	−	0.573238i	$-0.805687\pi$
$439$	−321.631	+	185.694i	−0.732645	+	0.422993i	0.0867437	+	0.996231i	$0.472354\pi$
$440$		−	3.32953i		−	0.00756712i
$441$	5.77993	−	146.886i	0.0131064	−	0.333076i
$442$	199.180			0.450635
$443$	−204.354	−	353.951i	−0.461295	−	0.798987i	0.537731	−	0.843117i	$-0.319282\pi$
$443$	−204.354	−	353.951i	−0.461295	−	0.798987i	−0.999026	+	0.0441299i	$0.985948\pi$
$444$	29.2609	+	16.8938i	0.0659029	+	0.0380491i
$445$	−76.3108	+	132.174i	−0.171485	+	0.297021i
$446$	−316.052	+	182.473i	−0.708636	+	0.409131i
$447$			249.555i			0.558288i
$448$	15.5547	−	53.7964i	0.0347203	−	0.120081i
$449$	725.469			1.61574			0.807872	−	0.589358i	$-0.200619\pi$
$449$	725.469			1.61574			0.807872	+	0.589358i	$0.200619\pi$
$450$	−10.6066	−	18.3712i	−0.0235702	−	0.0408248i
$451$	1.85730	+	1.07231i	0.00411817	+	0.00237763i
$452$	116.241	−	201.335i	0.257170	−	0.445432i
$453$	140.269	−	80.9842i	0.309644	−	0.178773i
$454$		−	468.150i		−	1.03117i
$455$	−64.1732	+	15.8495i	−0.141040	+	0.0348341i
$456$	−15.5639			−0.0341313
$457$	−200.765	−	347.736i	−0.439311	−	0.760909i	0.558325	−	0.829622i	$-0.311444\pi$
$457$	−200.765	−	347.736i	−0.439311	−	0.760909i	−0.997636	+	0.0687128i	$0.978111\pi$
$458$	−299.129	−	172.702i	−0.653121	−	0.377080i
$459$	−86.6474	+	150.078i	−0.188774	+	0.326967i
$460$	42.8316	−	24.7288i	0.0931122	−	0.0537584i
$461$			653.050i			1.41659i	0.705915	+	0.708297i	$0.250536\pi$
$461$			653.050i			1.41659i	−0.705915	+	0.708297i	$0.749464\pi$
$462$	6.50709	−	6.25607i	0.0140846	−	0.0135413i
$463$	−869.580			−1.87814			−0.939072	−	0.343722i	$-0.888312\pi$
$463$	−869.580			−1.87814			−0.939072	+	0.343722i	$0.888312\pi$
$464$	112.260	+	194.441i	0.241941	+	0.419053i
$465$	6.34462	+	3.66307i	0.0136443	+	0.00787757i
$466$	−149.546	+	259.021i	−0.320913	+	0.555838i
$467$	640.168	−	369.601i	1.37081	−	0.791437i	0.379779	−	0.925077i	$-0.376000\pi$
$467$	640.168	−	369.601i	1.37081	−	0.791437i	0.991030	+	0.133641i	$0.0426668\pi$
$468$			25.3384i			0.0541419i
$469$	42.3967	+	44.0978i	0.0903981	+	0.0940252i
$470$	−200.090			−0.425723
$471$	148.286	+	256.838i	0.314831	+	0.545304i
$472$	−123.776	−	71.4621i	−0.262237	−	0.151403i
$473$	12.2009	−	21.1325i	0.0257947	−	0.0446777i
$474$	−280.639	+	162.027i	−0.592066	+	0.341829i
$475$		−	15.8848i		−	0.0334417i
$476$	−111.953	−	453.288i	−0.235196	−	0.952285i
$477$	139.563			0.292586
$478$	−243.339	−	421.476i	−0.509078	−	0.881750i
$479$	−525.006	−	303.112i	−1.09605	−	0.632802i	−0.160866	−	0.986976i	$-0.551429\pi$
$479$	−525.006	−	303.112i	−1.09605	−	0.632802i	−0.935180	+	0.354174i	$0.884762\pi$
$480$	10.9545	−	18.9737i	0.0228218	−	0.0395285i
$481$	35.6718	−	20.5951i	0.0741618	−	0.0428173i
$482$			242.323i			0.502745i
$483$	128.808	+	37.2435i	0.266683	+	0.0771088i
$484$	−241.446			−0.498855
$485$	−166.901	−	289.082i	−0.344126	−	0.596044i
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−324.788	+	562.549i	−0.666916	+	1.15513i	0.311846	+	0.950133i	$0.399053\pi$
$487$	−324.788	+	562.549i	−0.666916	+	1.15513i	−0.978762	+	0.205000i	$0.934281\pi$
$488$	253.026	−	146.085i	0.518497	−	0.299354i
$489$			161.103i			0.329454i
$490$	72.1396	+	137.135i	0.147224	+	0.279866i
$491$	266.629			0.543033			0.271516	−	0.962434i	$-0.412475\pi$
$491$	266.629			0.543033			0.271516	+	0.962434i	$0.412475\pi$
$492$	7.05598	+	12.2213i	0.0143414	+	0.0248401i
$493$	1621.18	+	935.988i	3.28839	+	1.89856i
$494$	−9.48693	+	16.4318i	−0.0192043	+	0.0332628i
$495$	3.05837	−	1.76575i	0.00617853	−	0.00356718i
$496$			7.56640i			0.0152548i
$497$	56.5039	−	195.421i	0.113690	−	0.393200i
$498$	−30.5788			−0.0614033
$499$	340.553	+	589.855i	0.682471	+	1.18207i	0.974225	+	0.225581i	$0.0724279\pi$
$499$	340.553	+	589.855i	0.682471	+	1.18207i	−0.291754	+	0.956493i	$0.594239\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$	90.9247	−	157.486i	0.181487	−	0.314344i
$502$	401.151	−	231.604i	0.799105	−	0.461364i
$503$			453.326i			0.901245i	0.892715	+	0.450622i	$0.148798\pi$
$503$			453.326i			0.901245i	−0.892715	+	0.450622i	$0.851202\pi$
$504$	57.6643	−	14.2419i	0.114413	−	0.0282578i
$505$	216.329			0.428374
$506$	4.11678	+	7.13047i	0.00813592	+	0.0140918i
$507$	−226.749	−	130.913i	−0.447236	−	0.258212i
$508$	81.3744	−	140.945i	0.160186	−	0.277450i
$509$	−43.5300	+	25.1321i	−0.0855206	+	0.0493754i	−0.542150	−	0.840281i	$-0.682390\pi$
$509$	−43.5300	+	25.1321i	−0.0855206	+	0.0493754i	0.456630	+	0.889657i	$0.349056\pi$
$510$		−	182.669i		−	0.358174i
$511$	84.4364	−	81.1792i	0.165238	−	0.158863i
$512$	22.6274			0.0441942
$513$	−8.25400	−	14.2963i	−0.0160897	−	0.0278681i
$514$	269.883	+	155.817i	0.525064	+	0.303146i
$515$	117.128	−	202.871i	0.227433	−	0.393925i
$516$	139.056	−	80.2838i	0.269488	−	0.155589i
$517$		−	33.3103i		−	0.0644300i
$518$	−66.9197	−	69.6048i	−0.129189	−	0.134372i
$519$	−353.610			−0.681330
$520$	−13.3545	−	23.1307i	−0.0256818	−	0.0444821i
$521$	−89.2971	−	51.5557i	−0.171396	−	0.0989553i	0.411848	−	0.911252i	$-0.364883\pi$
$521$	−89.2971	−	51.5557i	−0.171396	−	0.0989553i	−0.583244	+	0.812297i	$0.698217\pi$
$522$	−119.070	+	206.236i	−0.228104	+	0.395087i
$523$	−317.716	+	183.434i	−0.607488	+	0.350733i	−0.771982	−	0.635645i	$-0.780734\pi$
$523$	−317.716	+	183.434i	−0.607488	+	0.350733i	0.164494	+	0.986378i	$0.447401\pi$
$524$			481.253i			0.918421i
$525$	14.5356	+	58.8533i	0.0276869	+	0.112102i
$526$	188.366			0.358111
$527$	31.5430	+	54.6341i	0.0598539	+	0.103670i
$528$	3.15867	+	1.82366i	0.00598234	+	0.00345390i
$529$	203.348	−	352.210i	0.384402	−	0.665803i
$530$	−127.403	+	73.5563i	−0.240384	+	0.138786i
$531$		−	151.594i		−	0.285488i
$532$	42.7273	+	12.3542i	0.0803145	+	0.0232222i
$533$	17.2038			0.0322773
$534$	−83.5943	−	144.790i	−0.156544	−	0.271141i
$535$	241.295	+	139.312i	0.451019	+	0.260396i
$536$	−12.3588	+	21.4060i	−0.0230574	+	0.0399365i
$537$	−293.848	+	169.653i	−0.547204	+	0.315928i
$538$			37.4988i			0.0697005i
$539$	−22.8297	+	12.0096i	−0.0423557	+	0.0222812i
$540$	23.2379			0.0430331
$541$	266.559	+	461.693i	0.492714	+	0.853407i	0.999965	−	0.00839227i	$-0.00267137\pi$
$541$	266.559	+	461.693i	0.492714	+	0.853407i	−0.507250	+	0.861799i	$0.669338\pi$
$542$	131.066	+	75.6709i	0.241819	+	0.139614i
$543$	103.084	−	178.547i	0.189842	−	0.328816i
$544$	163.384	−	94.3297i	0.300338	−	0.173400i
$545$			189.190i			0.347138i
$546$	20.1129	−	69.5612i	0.0368369	−	0.127401i
$547$	69.6218			0.127279			0.0636396	−	0.997973i	$-0.479729\pi$
$547$	69.6218			0.127279			0.0636396	+	0.997973i	$0.479729\pi$
$548$	−233.661	−	404.713i	−0.426389	−	0.738528i
$549$	268.375	+	154.946i	0.488843	+	0.282234i
$550$	−1.86127	+	3.22381i	−0.00338412	+	0.00586147i
$551$	−154.433	+	89.1619i	−0.280277	+	0.161818i
$552$			54.1782i			0.0981489i
$553$	899.048	−	222.047i	1.62576	−	0.401532i
$554$	622.793			1.12418
$555$	−18.8878	−	32.7147i	−0.0340321	−	0.0589454i
$556$	366.314	+	211.491i	0.658838	+	0.380380i
$557$	−8.43122	+	14.6033i	−0.0151368	+	0.0262178i	−0.873495	−	0.486834i	$-0.838152\pi$
$557$	−8.43122	+	14.6033i	−0.0151368	+	0.0262178i	0.858358	+	0.513052i	$0.171485\pi$
$558$	−6.95018	+	4.01269i	−0.0124555	+	0.00719120i
$559$		−	195.747i		−	0.350174i
$560$	−45.1339	+	43.3928i	−0.0805962	+	0.0774871i
$561$	30.4101			0.0542069
$562$	−227.737	−	394.452i	−0.405226	−	0.701872i
$563$	793.093	+	457.892i	1.40869	+	0.813308i	0.995262	−	0.0972290i	$-0.0309979\pi$
$563$	793.093	+	457.892i	1.40869	+	0.813308i	0.413428	+	0.910537i	$0.364331\pi$
$564$	109.594	−	189.822i	0.194315	−	0.336564i
$565$	−225.099	+	129.961i	−0.398406	+	0.230020i
$566$			96.9204i			0.171237i
$567$	43.6632	+	45.4151i	0.0770073	+	0.0800971i
$568$	82.1963			0.144712
$569$	−203.828	−	353.040i	−0.358221	−	0.620456i	0.629443	−	0.777047i	$-0.283283\pi$
$569$	−203.828	−	353.040i	−0.358221	−	0.620456i	−0.987664	+	0.156590i	$0.949950\pi$
$570$	15.0697	+	8.70048i	0.0264380	+	0.0152640i
$571$	447.910	−	775.803i	0.784431	−	1.35867i	−0.144908	−	0.989445i	$-0.546289\pi$
$571$	447.910	−	775.803i	0.784431	−	1.35867i	0.929339	−	0.369229i	$-0.120378\pi$
$572$	3.85072	−	2.22322i	0.00673203	−	0.00388674i
$573$		−	113.850i		−	0.198691i
$574$	−9.66974	−	39.1519i	−0.0168462	−	0.0682088i
$575$	−55.2954			−0.0961659
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	590.115	+	340.703i	1.02273	+	0.590473i	0.914893	−	0.403695i	$-0.132274\pi$
$577$	590.115	+	340.703i	1.02273	+	0.590473i	0.107836	+	0.994169i	$0.465608\pi$
$578$	582.134	−	1008.29i	1.00715	−	1.74444i
$579$	−145.305	+	83.8919i	−0.250959	+	0.144891i
$580$		−	251.022i		−	0.432796i
$581$	83.9476	+	24.2726i	0.144488	+	0.0417773i
$582$	365.662			0.628286
$583$	−12.2454	−	21.2097i	−0.0210041	−	0.0363802i
$584$	40.9872	+	23.6640i	0.0701835	+	0.0405205i
$585$	14.1646	−	24.5338i	0.0242130	−	0.0419381i
$586$	−180.662	+	104.305i	−0.308297	+	0.177996i
$587$			833.001i			1.41908i	0.704665	+	0.709541i	$0.251097\pi$
$587$			833.001i			1.41908i	−0.704665	+	0.709541i	$0.748903\pi$
$588$	−169.610	−	6.67408i	−0.288452	−	0.0113505i
$589$	−6.00955			−0.0102030
$590$	79.8970	+	138.386i	0.135419	+	0.234552i
$591$	−280.008	−	161.663i	−0.473787	−	0.273541i
$592$	19.5073	−	33.7876i	0.0329515	−	0.0570736i
$593$	270.842	−	156.371i	0.456731	−	0.263694i	−0.253938	−	0.967221i	$-0.581726\pi$
$593$	270.842	−	156.371i	0.456731	−	0.263694i	0.710669	+	0.703527i	$0.248392\pi$
$594$			3.86857i			0.00651274i
$595$	−144.997	+	501.478i	−0.243693	+	0.842820i
$596$	288.161			0.483491
$597$	−99.8454	−	172.937i	−0.167245	−	0.289677i
$598$	57.1996	+	33.0242i	0.0956514	+	0.0552244i
$599$	−107.121	+	185.540i	−0.178834	+	0.309749i	−0.941481	−	0.337065i	$-0.890566\pi$
$599$	−107.121	+	185.540i	−0.178834	+	0.309749i	0.762648	+	0.646814i	$0.223899\pi$
$600$	−21.2132	+	12.2474i	−0.0353553	+	0.0204124i
$601$		−	176.849i		−	0.294257i	−0.989117	−	0.147129i	$-0.952997\pi$
$601$		−	176.849i		−	0.294257i	0.989117	−	0.147129i	$-0.0470031\pi$
$602$	−445.474	+	110.023i	−0.739991	+	0.182763i
$603$	−26.2169			−0.0434774
$604$	−93.5125	−	161.968i	−0.154822	−	0.268160i
$605$	233.779	+	134.972i	0.386411	+	0.223095i
$606$	−118.488	+	205.228i	−0.195525	+	0.338660i
$607$	32.1304	−	18.5505i	0.0529331	−	0.0305609i	−0.473300	−	0.880901i	$-0.656937\pi$
$607$	32.1304	−	18.5505i	0.0529331	−	0.0305609i	0.526233	+	0.850340i	$0.323604\pi$
$608$			17.9716i			0.0295586i
$609$	490.586	−	471.661i	0.805559	−	0.774484i
$610$	−326.656			−0.535501
$611$	−133.605	−	231.411i	−0.218666	−	0.378741i
$612$	173.295	+	100.052i	0.283161	+	0.163483i
$613$	449.860	−	779.180i	0.733866	−	1.27109i	−0.221353	−	0.975194i	$-0.571047\pi$
$613$	449.860	−	779.180i	0.733866	−	1.27109i	0.955219	−	0.295899i	$-0.0956192\pi$
$614$	−460.516	+	265.879i	−0.750027	+	0.433028i
$615$		−	15.7777i		−	0.0256547i
$616$	−7.22389	−	7.51374i	−0.0117271	−	0.0121976i
$617$	−626.244			−1.01498			−0.507491	−	0.861657i	$-0.669427\pi$
$617$	−626.244			−1.01498			−0.507491	+	0.861657i	$0.669427\pi$
$618$	128.307	+	222.234i	0.207617	+	0.359602i
$619$	−776.375	−	448.240i	−1.25424	−	0.724136i	−0.282291	−	0.959329i	$-0.591094\pi$
$619$	−776.375	−	448.240i	−1.25424	−	0.724136i	−0.971949	+	0.235193i	$0.924428\pi$
$620$	4.22975	−	7.32614i	0.00682217	−	0.0118164i
$621$	−49.7658	+	28.7323i	−0.0801382	+	0.0462678i
$622$			551.298i			0.886331i
$623$	114.560	+	463.843i	0.183885	+	0.744532i
$624$	29.2583			0.0468883
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	175.207	+	101.156i	0.279884	+	0.161591i
$627$	−1.44843	+	2.50875i	−0.00231009	+	0.00400120i
$628$	296.571	−	171.225i	0.472247	−	0.272652i
$629$		−	325.290i		−	0.517153i
$630$	−63.7947	−	18.4456i	−0.101261	−	0.0292787i
$631$	−500.730			−0.793550			−0.396775	−	0.917916i	$-0.629871\pi$
$631$	−500.730			−0.793550			−0.396775	+	0.917916i	$0.629871\pi$
$632$	187.093	+	324.054i	0.296033	+	0.512744i
$633$	−209.149	−	120.752i	−0.330409	−	0.190762i
$634$	−271.843	+	470.846i	−0.428774	+	0.742659i
$635$	−157.581	+	90.9793i	−0.248159	+	0.143275i
$636$		−	161.154i		−	0.253387i
$637$	−110.431	+	175.000i	−0.173362	+	0.274726i
$638$	41.7893			0.0655005
$639$	43.5912	+	75.5021i	0.0682178	+	0.118157i
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	−310.289	+	537.436i	−0.484070	+	0.838434i	−0.999833	−	0.0182978i	$-0.994175\pi$
$641$	−310.289	+	537.436i	−0.484070	+	0.838434i	0.515763	+	0.856732i	$0.327509\pi$
$642$	−264.326	+	152.609i	−0.411722	+	0.237708i
$643$		−	1127.93i		−	1.75417i	−0.480334	−	0.877086i	$-0.659484\pi$
$643$		−	1127.93i		−	1.75417i	0.480334	−	0.877086i	$-0.340516\pi$
$644$	43.0051	−	148.735i	0.0667782	−	0.230954i
$645$	−179.520			−0.278326
$646$	74.9206	+	129.766i	0.115976	+	0.200877i
$647$	−117.130	−	67.6248i	−0.181035	−	0.104521i	0.406744	−	0.913542i	$-0.366664\pi$
$647$	−117.130	−	67.6248i	−0.181035	−	0.104521i	−0.587779	+	0.809022i	$0.699997\pi$
$648$	−12.7279	+	22.0454i	−0.0196419	+	0.0340207i
$649$	−23.0380	+	13.3010i	−0.0354977	+	0.0204946i
$650$			29.8616i			0.0459409i
$651$	22.2654	−	5.49912i	0.0342018	−	0.00844719i
$652$	186.026			0.285316
$653$	195.145	+	338.001i	0.298843	+	0.517612i	0.975872	−	0.218345i	$-0.0700658\pi$
$653$	195.145	+	338.001i	0.298843	+	0.517612i	−0.677028	+	0.735957i	$0.736733\pi$
$654$	−179.482	−	103.624i	−0.274437	−	0.158446i
$655$	269.028	−	465.971i	0.410730	−	0.711406i
$656$	14.1120	−	8.14755i	0.0215121	−	0.0124200i
$657$			50.1988i			0.0764061i
$658$	−451.542	+	434.123i	−0.686233	+	0.659761i
$659$	−864.853			−1.31237			−0.656186	−	0.754599i	$-0.727831\pi$
$659$	−864.853			−1.31237			−0.656186	+	0.754599i	$0.727831\pi$
$660$	−2.03892	−	3.53150i	−0.00308927	−	0.00535076i
$661$	−873.134	−	504.104i	−1.32093	−	0.762638i	−0.337052	−	0.941486i	$-0.609430\pi$
$661$	−873.134	−	504.104i	−1.32093	−	0.762638i	−0.983877	+	0.178848i	$0.942763\pi$
$662$	−137.113	+	237.487i	−0.207120	+	0.358742i
$663$	211.263	−	121.973i	0.318647	−	0.183971i
$664$			35.3094i			0.0531768i
$665$	−34.4644	−	35.8472i	−0.0518261	−	0.0539055i
$666$	41.3812			0.0621339
$667$	310.374	+	537.584i	0.465328	+	0.805973i
$668$	−181.849	−	104.991i	−0.272230	−	0.157172i
$669$	−223.482	+	387.083i	−0.334054	+	0.578599i
$670$	23.9326	−	13.8175i	0.0357203	−	0.0206231i
$671$		−	54.3806i		−	0.0810441i
$672$	−16.4452	−	66.5850i	−0.0244720	−	0.0990848i
$673$	−109.959			−0.163386			−0.0816928	−	0.996658i	$-0.526033\pi$
$673$	−109.959			−0.163386			−0.0816928	+	0.996658i	$0.526033\pi$
$674$	−88.7259	−	153.678i	−0.131641	−	0.228009i
$675$	−22.5000	−	12.9904i	−0.0333333	−	0.0192450i
$676$	−151.166	+	261.827i	−0.223618	+	0.387318i
$677$	146.213	−	84.4163i	0.215972	−	0.124692i	−0.388112	−	0.921612i	$-0.626872\pi$
$677$	146.213	−	84.4163i	0.215972	−	0.124692i	0.604084	+	0.796921i	$0.293539\pi$
$678$		−	284.731i		−	0.419957i
$679$	−1003.85	−	290.253i	−1.47842	−	0.427471i
$680$	−210.928			−0.310188
$681$	−286.682	−	496.548i	−0.420973	−	0.729146i
$682$	1.21963	+	0.704155i	0.00178832	+	0.00103248i
$683$	218.065	−	377.700i	0.319276	−	0.553002i	−0.661061	−	0.750332i	$-0.729894\pi$
$683$	218.065	−	377.700i	0.319276	−	0.553002i	0.980337	+	0.197330i	$0.0632271\pi$
$684$	−16.5080	+	9.53090i	−0.0241345	+	0.0139341i
$685$			522.482i			0.762748i
$686$	460.329	+	152.954i	0.671034	+	0.222965i
$687$	−423.033			−0.615768
$688$	−92.7038	−	160.568i	−0.134744	−	0.233383i
$689$	−170.141	−	98.2309i	−0.246939	−	0.142570i
$690$	30.2865	−	52.4578i	0.0438935	−	0.0760258i
$691$	−59.2770	+	34.2236i	−0.0857843	+	0.0495276i	−0.542279	−	0.840199i	$-0.682438\pi$
$691$	−59.2770	+	34.2236i	−0.0857843	+	0.0495276i	0.456494	+	0.889726i	$0.349105\pi$
$692$			408.314i			0.590049i
$693$	3.07076	−	10.6203i	0.00443112	−	0.0153251i
$694$	−712.193			−1.02622
$695$	−236.454	−	409.551i	−0.340222	−	0.589282i
$696$	238.140	+	137.490i	0.342156	+	0.197544i
$697$	67.9314	−	117.661i	0.0974625	−	0.168810i
$698$	58.5039	−	33.7772i	0.0838164	−	0.0483914i
$699$			366.311i			0.524050i
$700$	67.9580	−	16.7843i	0.0970828	−	0.0239776i
$701$	1283.41			1.83083			0.915414	−	0.402514i	$-0.131864\pi$
$701$	1283.41			1.83083			0.915414	+	0.402514i	$0.131864\pi$
$702$	15.5165	+	26.8754i	0.0221033	+	0.0382841i
$703$	26.8355	+	15.4935i	0.0381728	+	0.0220391i
$704$	2.10578	−	3.64732i	0.00299117	−	0.00518086i
$705$	−212.227	+	122.530i	−0.301032	+	0.173801i
$706$		−	46.5422i		−	0.0659238i
$707$	488.188	−	469.356i	0.690507	−	0.663870i
$708$	−175.046			−0.247240
$709$	−86.2000	−	149.303i	−0.121580	−	0.210582i	0.798811	−	0.601582i	$-0.205463\pi$
$709$	−86.2000	−	149.303i	−0.121580	−	0.210582i	−0.920391	+	0.391000i	$0.872129\pi$
$710$	−79.5862	−	45.9491i	−0.112093	−	0.0647171i
$711$	−198.442	+	343.712i	−0.279103	+	0.483420i
$712$	−167.189	+	96.5264i	−0.234815	+	0.135571i
$713$			20.9194i			0.0293399i
$714$	−396.325	−	412.227i	−0.555077	−	0.577349i
$715$	−4.97126			−0.00695282
$716$	195.899	+	339.307i	0.273602	+	0.473892i
$717$	−516.201	−	298.029i	−0.719946	−	0.415661i
$718$	−189.361	+	327.983i	−0.263734	+	0.456801i
$719$	−435.015	+	251.156i	−0.605028	+	0.349313i	−0.771017	−	0.636815i	$-0.780252\pi$
$719$	−435.015	+	251.156i	−0.605028	+	0.349313i	0.165989	+	0.986128i	$0.446918\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	−175.836	−	711.943i	−0.243878	−	0.987439i
$722$	496.257			0.687337
$723$	148.392	+	257.023i	0.205245	+	0.355495i
$724$	−206.168	−	119.031i	−0.284763	−	0.164408i
$725$	−140.326	+	243.051i	−0.193552	+	0.335243i
$726$	−256.092	+	147.855i	−0.352744	+	0.203657i
$727$		−	748.693i		−	1.02984i	−0.857238	−	0.514920i	$-0.827822\pi$
$727$		−	748.693i		−	1.02984i	0.857238	−	0.514920i	$-0.172178\pi$
$728$	−80.3223	−	23.2244i	−0.110333	−	0.0319017i
$729$	−27.0000			−0.0370370
$730$	−26.4571	−	45.8251i	−0.0362426	−	0.0627741i
$731$	−1338.76	−	772.931i	−1.83140	−	1.05736i
$732$	178.917	−	309.893i	0.244422	−	0.423351i
$733$	−812.761	+	469.248i	−1.10881	+	0.640175i	−0.938522	−	0.345219i	$-0.887805\pi$
$733$	−812.761	+	469.248i	−1.10881	+	0.640175i	−0.170293	+	0.985394i	$0.554471\pi$
$734$			224.468i			0.305814i
$735$	160.493	+	101.277i	0.218358	+	0.137792i
$736$	62.5596			0.0849994
$737$	2.30029	+	3.98422i	0.00312116	+	0.00540600i
$738$	14.9680	+	8.64178i	0.0202818	+	0.0117097i
$739$	−106.820	+	185.018i	−0.144547	+	0.250363i	−0.929204	−	0.369567i	$-0.879506\pi$
$739$	−106.820	+	185.018i	−0.144547	+	0.250363i	0.784657	+	0.619931i	$0.212839\pi$
$740$	−37.7757	+	21.8098i	−0.0510482	+	0.0294727i
$741$			23.2381i			0.0313605i
$742$	−127.919	+	442.413i	−0.172398	+	0.596244i
$743$	544.013			0.732184			0.366092	−	0.930579i	$-0.380696\pi$
$743$	544.013			0.732184			0.366092	+	0.930579i	$0.380696\pi$
$744$	4.63346	+	8.02538i	0.00622776	+	0.0107868i
$745$	−279.010	−	161.087i	−0.374511	−	0.216224i
$746$	−292.985	+	507.465i	−0.392742	+	0.680249i
$747$	−32.4337	+	18.7256i	−0.0434187	+	0.0250678i
$748$		−	35.1146i		−	0.0469446i
$749$	846.786	−	209.140i	1.13056	−	0.279225i
$750$	27.3861			0.0365148
$751$	−294.705	−	510.443i	−0.392416	−	0.679685i	0.600351	−	0.799736i	$-0.295027\pi$
$751$	−294.705	−	510.443i	−0.392416	−	0.679685i	−0.992768	+	0.120051i	$0.961694\pi$
$752$	−219.187	−	126.548i	−0.291473	−	0.168282i
$753$	283.656	−	491.307i	0.376702	−	0.652467i
$754$	290.316	−	167.614i	0.385034	−	0.222299i
$755$			209.100i			0.276954i
$756$	52.4408	−	50.4179i	0.0693662	−	0.0666903i
$757$	−448.997			−0.593127			−0.296564	−	0.955013i	$-0.595841\pi$
$757$	−448.997			−0.593127			−0.296564	+	0.955013i	$0.595841\pi$
$758$	51.4774	+	89.1614i	0.0679121	+	0.117627i
$759$	8.73300	+	5.04200i	0.0115059	+	0.00664295i
$760$	10.0464	−	17.4010i	0.0132190	−	0.0228960i
$761$	371.914	−	214.725i	0.488718	−	0.282161i	−0.235325	−	0.971917i	$-0.575615\pi$
$761$	371.914	−	214.725i	0.488718	−	0.282161i	0.724042	+	0.689756i	$0.242282\pi$
$762$		−	199.326i		−	0.261582i
$763$	410.475	+	426.944i	0.537975	+	0.559560i
$764$	−131.463			−0.172072
$765$	−111.861	−	193.749i	−0.146224	−	0.253267i
$766$	349.070	+	201.536i	0.455705	+	0.263101i
$767$	−106.699	+	184.807i	−0.139112	+	0.240948i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			32.5790i			0.0423655i	0.999776	+	0.0211827i	$0.00674318\pi$
$769$			32.5790i			0.0423655i	−0.999776	+	0.0211827i	$0.993257\pi$
$770$	2.79419	+	11.3134i	0.00362882	+	0.0146928i
$771$	381.672			0.495035
$772$	96.8700	+	167.784i	0.125479	+	0.217337i
$773$	1076.93	+	621.768i	1.39319	+	0.804357i	0.993667	−	0.112367i	$-0.0358433\pi$
$773$	1076.93	+	621.768i	1.39319	+	0.804357i	0.399520	+	0.916724i	$0.369177\pi$
$774$	98.3272	−	170.308i	0.127038	−	0.220036i
$775$	−8.19087	+	4.72900i	−0.0105689	+	0.00610194i
$776$		−	422.231i		−	0.544112i
$777$	−113.603	−	32.8472i	−0.146207	−	0.0422744i
$778$	−137.374			−0.176574
$779$	6.47112	+	11.2083i	0.00830696	+	0.0143881i
$780$	−28.3292	−	16.3559i	−0.0363195	−	0.0209691i
$781$	7.64946	−	13.2493i	0.00979444	−	0.0169645i
$782$	451.719	−	260.800i	0.577645	−	0.333504i
$783$			291.661i			0.372492i
$784$	−7.70657	+	195.848i	−0.00982981	+	0.249807i
$785$	−382.872			−0.487735
$786$	294.706	+	510.446i	0.374944	+	0.649422i
$787$	165.088	+	95.3138i	0.209769	+	0.121110i	0.601204	−	0.799096i	$-0.294688\pi$
$787$	165.088	+	95.3138i	0.209769	+	0.121110i	−0.391435	+	0.920206i	$0.628021\pi$
$788$	−186.672	+	323.325i	−0.236893	+	0.410311i
$789$	199.793	−	115.350i	0.253223	−	0.146198i
$790$		−	418.352i		−	0.529560i
$791$	−226.011	+	781.667i	−0.285729	+	0.988202i
$792$	4.46704			0.00564020
$793$	−218.116	−	377.789i	−0.275052	−	0.476405i
$794$	969.635	+	559.819i	1.22120	+	0.705062i
$795$	−90.0877	+	156.037i	−0.113318	+	0.196272i
$796$	−199.691	+	115.292i	−0.250868	+	0.144839i
$797$			387.796i			0.486570i	0.969955	+	0.243285i	$0.0782250\pi$
$797$			387.796i			0.486570i	−0.969955	+	0.243285i	$0.921775\pi$
$798$	52.8845	−	13.0614i	0.0662713	−	0.0163677i
$799$	−2110.23			−2.64108
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$	−177.330	−	102.382i	−0.221386	−	0.127817i
$802$	−355.835	+	616.324i	−0.443684	+	0.768484i
$803$	7.62881	−	4.40449i	0.00950038	−	0.00548505i
$804$			30.2726i			0.0376525i
$805$	−124.785	+	119.971i	−0.155012	+	0.149032i
$806$	11.2972			0.0140164
$807$	22.9633	+	39.7735i	0.0284551	+	0.0492857i
$808$	236.977	+	136.818i	0.293288	+	0.169330i
$809$	−182.613	+	316.295i	−0.225727	+	0.390970i	−0.956537	−	0.291610i	$-0.905809\pi$
$809$	−182.613	+	316.295i	−0.225727	+	0.390970i	0.730811	+	0.682580i	$0.239142\pi$
$810$	24.6475	−	14.2302i	0.0304290	−	0.0175682i
$811$		−	944.189i		−	1.16423i	−0.813107	−	0.582114i	$-0.802226\pi$
$811$		−	944.189i		−	1.16423i	0.813107	−	0.582114i	$-0.197774\pi$
$812$	−544.627	−	566.479i	−0.670723	−	0.697635i
$813$	185.355			0.227989
$814$	−3.63082	−	6.28877i	−0.00446047	−	0.00772576i
$815$	−180.119	−	103.992i	−0.221005	−	0.127597i
$816$	115.530	−	200.104i	0.141581	−	0.245225i
$817$	127.529	−	73.6292i	0.156095	−	0.0901214i
$818$		−	1060.46i		−	1.29640i
$819$	−21.2644	−	86.0974i	−0.0259638	−	0.105125i
$820$	−18.2185			−0.0222176
$821$	342.337	+	592.946i	0.416976	+	0.722224i	0.995634	−	0.0933467i	$-0.0297565\pi$
$821$	342.337	+	592.946i	0.416976	+	0.722224i	−0.578657	+	0.815571i	$0.696423\pi$
$822$	−495.670	−	286.175i	−0.603005	−	0.348145i
$823$	522.835	−	905.578i	0.635280	−	1.10034i	−0.351176	−	0.936310i	$-0.614218\pi$
$823$	522.835	−	905.578i	0.635280	−	1.10034i	0.986456	−	0.164028i	$-0.0524486\pi$
$824$	256.614	−	148.156i	0.311425	−	0.179801i
$825$			4.55915i			0.00552625i
$826$	480.550	+	138.946i	0.581780	+	0.168216i
$827$	830.505			1.00424			0.502119	−	0.864798i	$-0.332554\pi$
$827$	830.505			1.00424			0.502119	+	0.864798i	$0.332554\pi$
$828$	33.1772	+	57.4646i	0.0400691	+	0.0694017i
$829$	−621.983	−	359.102i	−0.750280	−	0.433175i	0.0755148	−	0.997145i	$-0.475940\pi$
$829$	−621.983	−	359.102i	−0.750280	−	0.433175i	−0.825795	+	0.563970i	$0.809273\pi$
$830$	19.7385	−	34.1882i	0.0237814	−	0.0411906i
$831$	660.572	−	381.381i	0.794912	−	0.458943i
$832$		−	33.7846i		−	0.0406064i
$833$	760.812	+	1446.27i	0.913339	+	1.73622i
$834$	518.046			0.621158
$835$	117.383	+	203.314i	0.140579	+	0.243490i
$836$	2.89685	+	1.67250i	0.00346514	+	0.00200060i
$837$	−4.91452	+	8.51220i	−0.00587159	+	0.0101699i
$838$	−570.436	+	329.342i	−0.680712	+	0.393009i
$839$			55.2900i			0.0658999i	0.999457	+	0.0329499i	$0.0104902\pi$
$839$			55.2900i			0.0658999i	−0.999457	+	0.0329499i	$0.989510\pi$
$840$	−21.2991	+	73.6637i	−0.0253561	+	0.0876949i
$841$	2309.60			2.74625
$842$	−244.645	−	423.737i	−0.290552	−	0.503251i
$843$	−483.103	−	278.920i	−0.573076	−	0.330866i
$844$	−139.433	+	241.505i	−0.165205	+	0.286143i
$845$	292.731	−	169.008i	0.346427	−	0.200010i
$846$		−	268.449i		−	0.317315i
$847$	820.408	−	202.625i	0.968605	−	0.239226i
$848$	−186.084			−0.219439
$849$	59.3514	+	102.800i	0.0699074	+	0.121083i
$850$	204.230	+	117.912i	0.240270	+	0.138720i
$851$	53.9331	−	93.4149i	0.0633761	−	0.109771i
$852$	87.1823	−	50.3347i	0.102327	−	0.0590783i
$853$			21.9601i			0.0257445i	0.999917	+	0.0128723i	$0.00409748\pi$
$853$			21.9601i			0.0257445i	−0.999917	+	0.0128723i	$0.995903\pi$
$854$	−737.162	+	708.725i	−0.863187	+	0.829889i
$855$	21.3117			0.0249260
$856$	176.217	+	305.217i	0.205861	+	0.356562i
$857$	−1399.33	−	807.903i	−1.63282	−	0.942711i	−0.983217	−	0.182441i	$-0.941600\pi$
$857$	−1399.33	−	807.903i	−1.63282	−	0.942711i	−0.649607	−	0.760271i	$-0.725066\pi$
$858$	2.72287	−	4.71615i	0.00317351	−	0.00549668i
$859$	772.149	−	445.801i	0.898893	−	0.518976i	0.0220523	−	0.999757i	$-0.492980\pi$
$859$	772.149	−	445.801i	0.898893	−	0.518976i	0.876841	+	0.480781i	$0.159647\pi$
$860$			207.292i			0.241037i
$861$	−34.2318	−	35.6053i	−0.0397582	−	0.0413535i
$862$	699.470			0.811450
$863$	448.173	+	776.259i	0.519320	+	0.899489i	0.999748	+	0.0224544i	$0.00714804\pi$
$863$	448.173	+	776.259i	0.519320	+	0.899489i	−0.480428	+	0.877034i	$0.659519\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	228.255	−	395.349i	0.263878	−	0.457050i
$866$	894.090	−	516.203i	1.03244	−	0.596078i
$867$		−	1425.93i		−	1.64467i
$868$	−6.34984	−	25.7099i	−0.00731548	−	0.0296197i
$869$	69.6459			0.0801449
$870$	−153.719	−	266.249i	−0.176688	−	0.306033i
$871$	31.9609	+	18.4526i	0.0366944	+	0.0211855i
$872$	−119.654	+	207.248i	−0.137218	+	0.237669i
$873$	387.844	−	223.922i	0.444265	−	0.256497i
$874$			49.6874i			0.0568506i
$875$	−75.1827	−	21.7383i	−0.0859231	−	0.0248438i
$876$	57.9646			0.0661697
$877$	168.885	+	292.517i	0.192571	+	0.333543i	0.946102	−	0.323870i	$-0.104984\pi$
$877$	168.885	+	292.517i	0.192571	+	0.333543i	−0.753530	+	0.657413i	$0.771651\pi$
$878$	454.855	+	262.611i	0.518059	+	0.299101i
$879$	−127.748	+	221.265i	−0.145333	+	0.251724i
$880$	−4.07783	+	2.35434i	−0.00463390	+	0.00267538i
$881$		−	301.377i		−	0.342085i	−0.985264	−	0.171042i	$-0.945287\pi$
$881$		−	301.377i		−	0.342085i	0.985264	−	0.171042i	$-0.0547135\pi$
$882$	−183.985	+	96.7854i	−0.208600	+	0.109734i
$883$	38.3679			0.0434518			0.0217259	−	0.999764i	$-0.493084\pi$
$883$	38.3679			0.0434518			0.0217259	+	0.999764i	$0.493084\pi$
$884$	−140.842	−	243.945i	−0.159323	−	0.275956i
$885$	169.487	+	97.8535i	0.191511	+	0.110569i
$886$	−289.000	+	500.563i	−0.326185	+	0.564969i
$887$	572.834	−	330.726i	0.645811	−	0.372859i	−0.141038	−	0.990004i	$-0.545044\pi$
$887$	572.834	−	330.726i	0.645811	−	0.372859i	0.786849	+	0.617145i	$0.211711\pi$
$888$		−	47.7829i		−	0.0538095i
$889$	−158.219	+	547.206i	−0.177974	+	0.615530i
$890$	215.840			0.242516
$891$	2.36901	+	4.10324i	0.00265882	+	0.00460521i
$892$	446.965	+	258.055i	0.501082	+	0.289300i
$893$	100.510	−	174.088i	0.112553	−	0.194947i
$894$	305.641	−	176.462i	0.341880	−	0.197384i
$895$		−	438.043i		−	0.489434i
$896$	−76.8857	+	18.9893i	−0.0858099	+	0.0211934i
$897$	80.8924			0.0901810
$898$	−512.984	−	888.515i	−0.571252	−	0.989437i
$899$	91.9510	+	53.0880i	0.102281	+	0.0590522i
$900$	−15.0000	+	25.9808i	−0.0166667	+	0.0288675i
$901$	−1343.64	+	775.753i	−1.49128	+	0.860991i
$902$		−	3.03295i		−	0.00336247i
$903$	−405.122	+	389.494i	−0.448640	+	0.431333i
$904$	−328.779			−0.363693
$905$	133.081	+	230.503i	0.147051	+	0.254700i
$906$	−198.370	−	114.529i	−0.218951	−	0.126412i
$907$	484.152	−	838.576i	0.533795	−	0.924560i	−0.465426	−	0.885087i	$-0.654099\pi$
$907$	484.152	−	838.576i	0.533795	−	0.924560i	0.999221	−	0.0394729i	$-0.0125679\pi$
$908$	−573.365	+	331.032i	−0.631459	+	0.364573i
$909$			290.236i			0.319291i
$910$	64.7889	+	67.3885i	0.0711966	+	0.0740533i
$911$	220.674			0.242233			0.121116	−	0.992638i	$-0.461353\pi$
$911$	220.674			0.242233			0.121116	+	0.992638i	$0.461353\pi$
$912$	11.0053	+	19.0618i	0.0120673	+	0.0209011i
$913$	5.69153	+	3.28601i	0.00623388	+	0.00359913i
$914$	−283.925	+	491.772i	−0.310640	+	0.538044i
$915$	−346.471	+	200.035i	−0.378657	+	0.218617i
$916$			488.476i			0.533271i
$917$	−403.874	−	1635.25i	−0.440430	−	1.78326i
$918$	245.076			0.266967
$919$	574.019	+	994.231i	0.624613	+	1.08186i	0.988616	+	0.150464i	$0.0480766\pi$
$919$	574.019	+	994.231i	0.624613	+	1.08186i	−0.364002	+	0.931398i	$0.618590\pi$
$920$	−60.5731	−	34.9719i	−0.0658403	−	0.0380129i
$921$	−325.634	+	564.015i	−0.353566	+	0.612394i
$922$	799.819	−	461.776i	0.867483	−	0.500841i
$923$		−	122.726i		−	0.132964i
$924$	−12.2633	−	3.54581i	−0.0132720	−	0.00383746i
$925$	48.7682			0.0527223
$926$	614.886	+	1065.01i	0.664024	+	1.15012i
$927$	272.180	+	157.143i	0.293614	+	0.169518i
$928$	158.760	−	274.981i	0.171078	−	0.296315i
$929$	−264.398	+	152.650i	−0.284605	+	0.164317i	−0.635506	−	0.772096i	$-0.719209\pi$
$929$	−264.398	+	152.650i	−0.284605	+	0.164317i	0.350901	+	0.936412i	$0.385875\pi$
$930$		−	10.3607i		−	0.0111406i
$931$	−155.551	−	6.12088i	−0.167079	−	0.00657452i
$932$	422.979			0.453840
$933$	337.599	+	584.739i	0.361843	+	0.626730i
$934$	−905.334	−	522.695i	−0.969308	−	0.559630i
$935$	−19.6296	+	33.9995i	−0.0209943	+	0.0363631i
$936$	31.0331	−	17.9170i	0.0331550	−	0.0191421i
$937$			12.4049i			0.0132390i	0.999978	+	0.00661948i	$0.00210706\pi$
$937$			12.4049i			0.0132390i	−0.999978	+	0.00661948i	$0.997893\pi$
$938$	24.0296	−	83.1070i	0.0256179	−	0.0886002i
$939$	247.781			0.263877
$940$	141.485	+	245.059i	0.150516	+	0.260701i
$941$	−250.409	−	144.573i	−0.266109	−	0.153638i	0.361009	−	0.932562i	$-0.382432\pi$
$941$	−250.409	−	144.573i	−0.266109	−	0.153638i	−0.627118	+	0.778924i	$0.715766\pi$
$942$	209.708	−	363.224i	0.222619	−	0.385588i
$943$	39.0163	−	22.5261i	0.0413747	−	0.0238877i
$944$			202.125i			0.214116i
$945$	−78.9600	+	19.5016i	−0.0835556	+	0.0206366i
$946$	−34.5093			−0.0364792
$947$	713.478	+	1235.78i	0.753409	+	1.30494i	0.946161	+	0.323695i	$0.104925\pi$
$947$	713.478	+	1235.78i	0.753409	+	1.30494i	−0.192752	+	0.981247i	$0.561741\pi$
$948$	396.884	+	229.141i	0.418654	+	0.241710i
$949$	35.3322	−	61.1972i	0.0372310	−	0.0644859i
$950$	−19.4549	+	11.2323i	−0.0204788	+	0.0118234i
$951$			665.876i			0.700186i
$952$	−475.999	+	457.637i	−0.499999	+	0.480711i
$953$	−668.525			−0.701495			−0.350747	−	0.936470i	$-0.614072\pi$
$953$	−668.525			−0.701495			−0.350747	+	0.936470i	$0.614072\pi$
$954$	−98.6862	−	170.929i	−0.103445	−	0.179171i
$955$	127.288	+	73.4899i	0.133286	+	0.0769528i
$956$	−344.134	+	596.058i	−0.359973	+	0.623491i
$957$	44.3242	−	25.5906i	0.0463158	−	0.0267405i
$958$			857.331i			0.894918i
$959$	1133.60	+	1179.08i	1.18206	+	1.22949i
$960$	−30.9839			−0.0322749
$961$	−478.711	−	829.152i	−0.498138	−	0.862801i
$962$	−50.4476	−	29.1259i	−0.0524403	−	0.0302764i
$963$	−186.907	+	323.732i	−0.194088	+	0.336170i
$964$	296.784	−	171.348i	0.307867	−	0.177747i
$965$		−	216.608i		−	0.224464i
$966$	−45.4671	−	184.092i	−0.0470674	−	0.190571i
$967$	1647.14			1.70335			0.851676	−	0.524069i	$-0.175586\pi$
$967$	1647.14			1.70335			0.851676	+	0.524069i	$0.175586\pi$
$968$	170.728	+	295.709i	0.176372	+	0.305485i
$969$	158.931	+	91.7586i	0.164015	+	0.0946941i
$970$	−236.034	+	408.823i	−0.243334	+	0.421467i
$971$	1138.76	−	657.466i	1.17277	−	0.677102i	0.218443	−	0.975850i	$-0.429902\pi$
$971$	1138.76	−	657.466i	1.17277	−	0.677102i	0.954332	+	0.298748i	$0.0965690\pi$
$972$			31.1769i			0.0320750i
$973$	−1422.18	−	411.210i	−1.46165	−	0.422621i
$974$	918.639			0.943161
$975$	18.2864	+	31.6730i	0.0187553	+	0.0324851i
$976$	−357.833	−	206.595i	−0.366633	−	0.211675i
$977$	−778.021	+	1347.57i	−0.796337	+	1.37930i	0.125650	+	0.992075i	$0.459898\pi$
$977$	−778.021	+	1347.57i	−0.796337	+	1.37930i	−0.921987	+	0.387221i	$0.873435\pi$
$978$	197.310	−	113.917i	0.201749	−	0.116480i
$979$			35.9323i			0.0367030i
$980$	116.944	−	185.321i	0.119331	−	0.189103i
$981$	−253.825			−0.258741
$982$	−188.535	−	326.553i	−0.191991	−	0.332538i
$983$	−1188.87	−	686.397i	−1.20944	−	0.698268i	−0.246799	−	0.969067i	$-0.579379\pi$
$983$	−1188.87	−	686.397i	−1.20944	−	0.698268i	−0.962636	+	0.270799i	$0.912712\pi$
$984$	9.97867	−	17.2836i	0.0101409	−	0.0175646i
$985$	361.489	−	208.706i	0.366994	−	0.211884i
$986$		−	2647.37i		−	2.68496i
$987$	−213.087	+	736.968i	−0.215894	+	0.746675i
$988$	26.8331			0.0271590
$989$	−256.304	−	443.932i	−0.259155	−	0.448870i
$990$	−4.32519	−	2.49715i	−0.00436888	−	0.00252237i
$991$	−321.812	+	557.395i	−0.324735	+	0.562457i	−0.981459	−	0.191674i	$-0.938608\pi$
$991$	−321.812	+	557.395i	−0.324735	+	0.562457i	0.656724	+	0.754131i	$0.271942\pi$
$992$	9.26691	−	5.35025i	0.00934165	−	0.00539340i
$993$			335.858i			0.338226i
$994$	−279.295	+	68.9803i	−0.280981	+	0.0693967i
$995$	257.800			0.259095
$996$	21.6225	+	37.4513i	0.0217093	+	0.0376017i
$997$	610.431	+	352.433i	0.612268	+	0.353493i	0.773853	−	0.633366i	$-0.218327\pi$
$997$	610.431	+	352.433i	0.612268	+	0.353493i	−0.161584	+	0.986859i	$0.551660\pi$
$998$	481.615	−	834.181i	0.482580	−	0.835853i
$999$	43.8914	−	25.3407i	0.0439353	−	0.0253661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.31.4	✓	16
3.2	odd	2		630.3.v.c.451.6		16
5.2	odd	4		1050.3.q.e.199.12		32
5.3	odd	4		1050.3.q.e.199.4		32
5.4	even	2		1050.3.p.i.451.6		16
7.3	odd	6		1470.3.f.d.391.9		16
7.4	even	3		1470.3.f.d.391.15		16
7.5	odd	6	inner	210.3.o.b.61.4	yes	16
21.5	even	6		630.3.v.c.271.6		16
35.12	even	12		1050.3.q.e.649.4		32
35.19	odd	6		1050.3.p.i.901.6		16
35.33	even	12		1050.3.q.e.649.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.4	✓	16	1.1	even	1	trivial
210.3.o.b.61.4	yes	16	7.5	odd	6	inner
630.3.v.c.271.6		16	21.5	even	6
630.3.v.c.451.6		16	3.2	odd	2
1050.3.p.i.451.6		16	5.4	even	2
1050.3.p.i.901.6		16	35.19	odd	6
1050.3.q.e.199.4		32	5.3	odd	4
1050.3.q.e.199.12		32	5.2	odd	4
1050.3.q.e.649.4		32	35.12	even	12
1050.3.q.e.649.12		32	35.33	even	12
1470.3.f.d.391.9		16	7.3	odd	6
1470.3.f.d.391.15		16	7.4	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(1.94434 - 6.72455i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(1.94434 - 6.72455i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(0.263223 - 0.455915i) q^{11} +(3.00000 - 1.73205i) q^{12} -4.22307i q^{13} +(-9.61071 + 2.37366i) q^{14} -3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-28.8825 - 16.6753i) q^{17} +(2.12132 - 3.67423i) q^{18} +(2.75133 - 1.58848i) q^{19} +4.47214i q^{20} +(-8.74014 + 8.40298i) q^{21} -0.744507 q^{22} +(-5.52954 - 9.57744i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-5.17218 + 2.98616i) q^{26} -5.19615i q^{27} +(9.70292 + 10.0922i) q^{28} -56.1302 q^{29} +(2.73861 + 4.74342i) q^{30} +(-1.63817 - 0.945800i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-0.789668 + 0.455915i) q^{33} +47.1649i q^{34} +(-3.75308 - 15.1959i) q^{35} -6.00000 q^{36} +(4.87682 + 8.44690i) q^{37} +(-3.89097 - 2.24645i) q^{38} +(-3.65729 + 6.33460i) q^{39} +(5.47723 - 3.16228i) q^{40} +4.07377i q^{41} +(16.4717 + 4.76263i) q^{42} +46.3519 q^{43} +(0.526446 + 0.911831i) q^{44} +(5.80948 + 3.35410i) q^{45} +(-7.81995 + 13.5445i) q^{46} +(54.7969 - 31.6370i) q^{47} +6.92820i q^{48} +(-41.4391 - 26.1496i) q^{49} -7.07107 q^{50} +(28.8825 + 50.0259i) q^{51} +(7.31457 + 4.22307i) q^{52} +(23.2606 - 40.2885i) q^{53} +(-6.36396 + 3.67423i) q^{54} -1.17717i q^{55} +(5.49942 - 19.0199i) q^{56} -5.50267 q^{57} +(39.6900 + 68.7452i) q^{58} +(-43.7614 - 25.2657i) q^{59} +(3.87298 - 6.70820i) q^{60} +(89.4583 - 51.6488i) q^{61} +2.67513i q^{62} +(20.3874 - 5.03529i) q^{63} +8.00000 q^{64} +(-4.72153 - 8.17794i) q^{65} +(1.11676 + 0.644762i) q^{66} +(-4.36948 + 7.56816i) q^{67} +(57.7649 - 33.3506i) q^{68} +19.1549i q^{69} +(-15.9572 + 15.3417i) q^{70} +29.0608 q^{71} +(4.24264 + 7.34847i) q^{72} +(14.4912 + 8.36647i) q^{73} +(6.89686 - 11.9457i) q^{74} +(-7.50000 + 4.33013i) q^{75} +6.35393i q^{76} +(-2.55403 - 2.65651i) q^{77} +10.3444 q^{78} +(66.1473 + 114.571i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.98933 - 2.88059i) q^{82} +12.4838i q^{83} +(-5.81425 - 23.5413i) q^{84} -74.5742 q^{85} +(-32.7757 - 56.7692i) q^{86} +(84.1953 + 48.6102i) q^{87} +(0.744507 - 1.28952i) q^{88} +(-59.1101 + 34.1272i) q^{89} -9.48683i q^{90} +(-28.3982 - 8.21107i) q^{91} +22.1182 q^{92} +(1.63817 + 2.83740i) q^{93} +(-77.4945 - 44.7415i) q^{94} +(3.55196 - 6.15217i) q^{95} +(8.48528 - 4.89898i) q^{96} -149.281i q^{97} +(-2.72468 + 69.2429i) q^{98} +1.57934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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